INTERHEMISPHERIC WATER E X C H A N G E IN THE ATLANTIC OCEAN
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Elsevier Oceanography Series, 68
INTERHEMISPHERIC WATER EXCHANGE IN THE ATLANTIC OCEAN
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6.J. Goni
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MIT 54-1416, Department of Earth, Atmospheric and Planetary Science, Cambridge, MA 02139, USA
2003
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CONTENTS P r e f a c e ....................................................................................................................................................... xiii
C h a p t e r 1. C i r c u l a t i o n , v a r i a b i l i t y a n d n e a r - e q u a t o r i a l m e r i d i o n a l flow in t h e c e n t r a l t r o p i c a l A t l a n t i c L. S t r a m m a , J. Fischer, P. B r a n d t a n d F. S c h o t t ............................................................................ 1 .
2. 3. 4.
.
I n t r o d u c t i o n ...................................................................................................................................1 M e t h o d s a n d d a t a ........................................................................................................................3 T h e w a t e r m a s s e s ........................................................................................................................6 R e s u l t s ............................................................................................................................................8 4.1. M e a n c i r c u l a t i o n ............................................................................................................8 4.2. V a r i a b i l i t y ......................................................................................................................11 4.3. N e a r - e q u a t o r i a l m e r i d i o n a l f l o w .............................................................................11 D i s c u s s i o n ....................................................................................................................................19
C h a p t e r 2. C o m p a r i s o n of h y d r o g r a p h i c a n d a l t i m e t e r b a s e d e s t i m a t e s of s e a l e v e l h e i g h t v a r i a b i l i t y in t h e A t l a n t i c O c e a n D. Mayer, M. B a r i n g e r a n d G. Goni .................................................................................................. 23
.
.
5.
I n t r o d u c t i o n ................................................................................................................................2 4 D a t a a n d m e t h o d s .....................................................................................................................27 2.1. H y d r o g r a p h i c d a t a .......................................................................................................27 2.2. A l t i m e t e r d a t a ...............................................................................................................27 A n a l y s i s ........................................................................................................................................2 8 3.1. B a c k g r o u n d s t a t e s a n d c l i m a t o l o g y ........................................................................28 3.2. R e g r e s s i o n b e t w e e n S H A a n d T A a n d D H A .........................................................33 3.3. C o r r e l a t i o n s ...................................................................................................................33 3.4. V a r i a n c e e x p l a i n e d ......................................................................................................38 3.5. P a n u l i r u s d a t a a n d r e f e r e n c e l e v e l s .......................................................................3 9 3.6. I n f e r r e d s a l i n i t y vs. in situ s a l i n i t y ........................................................................41 3.7. B a r o t r o p i c c o m p o n e n t .................................................................................................42 D i s c u s s i o n ....................................................................................................................................43 S u m m a r y .....................................................................................................................................4 5
C h a p t e r 3. E s t i m a t i o n of t h e t r o p i c a l A t l a n t i c c i r c u l a t i o n f r o m a l t i m e t r y d a t a u s i n g a r e d u c e d - r a n k s t a t i o n a r y K a l m a n filter M. B u e h n e r , P. M a l a n o t t e - R i z z o l i , A. B u s a l a c c h i a n d T. I n u i ................................................... 4 9 I n t r o d u c t i o n ................................................................................................................................50 M o d e l o f t h e t r o p i c a l A t l a n t i c .................................................................................................52 A p p r o a c h f o r a s s i m i l a t i n g S H A .............................................................................................57 3.1. T h e r e d u c e d - r a n k K a l m a n f i l t e r ...............................................................................57 3.2. T O P E X / P o s e i d o n a l t i m e t r y d a t a .............................................................................5 9
vi
3.3. S p e c i f i c a t i o n of Qr a n d R ............................................................................................61 3.4. D i a g n o s t i c s of t h e s t a t i o n a r y f o r e c a s t e r r o r c o v a r i a n c e ....................................63 4. I d e n t i c a l t w i n a s s i m i l a t i o n e x p e r i m e n t ..............................................................................68 4.1. C o n f i g u r a t i o n of t h e e x p e r i m e n t ..............................................................................68 4.2. R e s u l t s f r o m a s s i m i l a t i n g s i m u l a t e d S H A o b s e r v a t i o n s ..................................69 5. A s s i m i l a t i o n of t h e T O P E X / P o s e i d o n S H A ........................................................................72 5.1. C o n f i g u r a t i o n of t h e e x p e r i m e n t .............................................................................74 5.2. R e s u l t s f r o m a s s i m i l a t i n g T O P E X / P o s e i d o n S H A .............................................75 6. S u m m a r y a n d c o n c l u s i o n s ......................................................................................................82 A p p e n d i x : D e r i v a t i o n of r e d u c e d - r a n k K a l m a n f i l t e r ..................................................................87
Chapter 4. A s y n t h e t i c float a n a l y s i s of u p p e r - l i m b m e r i d i o n a l o v e r t u r n i n g c i r c u l a t i o n interior o c e a n p a t h w a y s in the t r o p i c a l / s u b t r o p i c a l Atlantic G. Halliwell, R. Weisberg a n d D. M a y e r ..........................................................................................93 1. 2. 3.
I n t r o d u c t i o n ................................................................................................................................94 B a c k g r o u n d a n d g o a l s ..............................................................................................................96 A n a l y s i s p r o c e d u r e s .................................................................................................................98 3.1. T h e n u m e r i c a l m o d e l ...................................................................................................98 3.2. F l o a t / d r i f t e r a n a l y s i s in H Y C O M ..........................................................................101 3.3. V o r t i c i t y b a l a n c e a n a l y s i s .......................................................................................102 4. E u l e r i a n A n a l y s i s ....................................................................................................................104 4.1. M o d e l fields .................................................................................................................104 4.2. T h e s e a s o n a l i n t e r n a l e n e r g y s t o r a g e a n d r e l e a s e m e c h a n i s m .................... 105 5. L a g r a n g i a n a n a l y s i s ..............................................................................................................106 5.1. D e s i g n of t h e s o u t h e r n h e m i s p h e r e f l o a t r e l e a s e e x p e r i m e n t ...................... 106 5.2. O v e r v i e w of s i m u l a t e d u p p e r - l i m b p a t h w a y s ....................................................108 5.3. C o - e x i s t e n c e of t h e u p p e r - l i m b M O C flow a n d s u b t r o p i c a l cells ................. 111 5.4. I m p o r t a n c e of u s i n g p a r t i c l e - f o l l o w i n g f l o a t s to t r a c k u p p e r - l i m b p a t h w a y s ......................................................................................................................112 5.5. F l o a t c e n s u s .................................................................................................................114 6. C a s e s t u d y a n d m e c h a n i s m s ................................................................................................114 6.1. F l o a t 1 a p p r o a c h e s t h e e q u a t o r a n d r e t r o f l e c t s i n t o t h e E U C ...................... 118 6.2. F l o a t 1 t r a n s i t s a c r o s s t h e b a s i n a l o n g t h e e q u a t o r ......................................... 120 6.3. F l o a t 1 d e p a r t s f r o m t h e e q u a t o r a n d e n t e r s i n t o t h e N E C C ....................... 120 6.4. F l o a t 1 m o v e s n o r t h w a r d in t h e i n t e r i o r N o r t h A t l a n t i c ................................ 123 6.5. Float 1 moves s o u t h w e s t w a r d after s u b d u c t i o n in the s u b t r o p i c a l g y r e .........................................................................................................123 6.6. F l o a t 1 t r a v e l s a l o n g t h e w e s t e r n b o u n d a r y .....................................................126 7. D i s c u s s i o n .........................................................................................................................................127 A p p e n d i x 1: D i a g n o s i s of v e r t i c a l v e l o c i t y ....................................................................................129 A p p e n d i x 2: S p a t i a l i n t e r p o l a t i o n of m o d e l v a r i a b l e s to f l o a t s ............................................... 132 A p p e n d i x 3: F l o a t a d v e c t i o n ..............................................................................................................133
vii C h a p t e r 5. A s e a s o n a l a n d i n t e r a n n u a l s t u d y o f t h e w e s t e r n equatorial Atlantic upper thermocline circulation variability M. V i a n n a a n d V. M e n e z e s ................................................................................................................. 1 3 7
1. 2. 3.
I n t r o d u c t i o n .............................................................................................................................. 138 E s t i m a t e s o f c u r r e n t v e l o c i t y f r o m S S H s l o p e s a n d c u r v a t u r e s ................................ 1 4 0 D a t a ............................................................................................................................................ 143 3.1. A l t i m e t e r d a t a ............................................................................................................ 1 4 3 3.2. I n s i t u d a t a ................................................................................................................... 143 4. D a t a p r o c e s s i n g ........................................................................................................................ 1 4 4 4.1. C i r c u l a t i o n f i e l d s f r o m S S H d a t a .......................................................................... 1 4 4 4.2. C o m p u t a t i o n o f t r a n s p o r t f i e l d s ............................................................................ 1 4 6 4.3. C o m p a r i s o n o f i n s i t u d a t a a n d a l t i m e t e r - d e r i v e d f i e l d s ............................... 1 4 6 5. C o m p a r i s o n o f i n s i t u d a t a a n d a l t i m e t e r - d e r i v e d f i e l d s ............................................. 1 4 6 5.1. S S H A t i m e s e r i e s a n d d y n a m i c h e i g h t s f r o m P I R A T A m o o r i n g s ................ 1 4 6 5.2. S S H a n d d y n a m i c h e i g h t f r o m t h e C T D E t a m b o t c r u i s e s ............................. 147 5.3. Current velocities and measurements of SADCP and CTD-derived v e l o c i t i e s ....................................................................................................................... 1 4 8 6. A n a l y s i s of t h e c i r c u l a t i o n f i e l d s ......................................................................................... 151 6.1. T h e m e a n c u r r e n t s .................................................................................................... 152 6.2. T h e s e a s o n a l c y c l e ..................................................................................................... 155 6.3. S t a n d i n g t r a p p e d a n n u a l e q u a t o r i a l w a v e s a n d m e a n d e r i n g ...................... 158 6.4. I n t e r a n n u a l v a r i a b i l i t y ............................................................................................ 162 7. I n t e r - h e m i s p h e r i c t r a n s p o r t s a n d t r a n s p o r t p a t h w a y s ............................................... 165 8. S u m m a r y a n d c o n c l u s i o n s .................................................................................................... 167 A p p e n d i x : P r e p a r a t i o n o f b a n d - l i m i t e d c i r c u l a t i o n a n d t r a n s p o r t f i e l d s .............................. 1 6 9
C h a p t e r 6. F a t e o f t h e e q u a t o r i a l u n d e r c u r r e n t in t h e A t l a n t i c W. H a z e l e g e r a n d P. de V r i e s ............................................................................................................ 175 .
2. 3. .
I n t r o d u c t i o n .............................................................................................................................. M o d e l a n d d a t a h a n d l i n g ...................................................................................................... R e s u l t s ....................................................................................................................................... 3.1. U p w e l l i n g s i t e s a n d p a t h w a y s ............................................................................... S u m m a r y a n d c o n c l u s i o n s ....................................................................................................
175 176 178 179 189
C h a p t e r 7. T h e f l o w o f AAIW a l o n g t h e e q u a t o r M. J o c h u m a n d P. M a l a n o t t e - R i z z o l i ............................................................................................. 193
I n t r o d u c t i o n .............................................................................................................................. 193 T h e m o d e l c o n f i g u r a t i o n ....................................................................................................... 194 S y n t h e s i s o f t h e o r y a n d o b s e r v a t i o n s ................................................................................ 1 9 9 S u m m a r y ................................................................................................................................... 2 1 0
viii C h a p t e r 8. P l a n e t a r y e q u a t o r i a l t r a p p e d w a v e s in t h e A t l a n t i c O c e a n from TOPEX/Poseidon altimetry C. Franqa, I. Wainer, A. M e s q u i t a a n d G. Goni ........................................................................... 2 1 3 .
2. 3. 4. 5. 6.
I n t r o d u c t i o n .............................................................................................................................. Sea height and sea surface temperature d a t a ............................................................... E q u a t o r i a l l y t r a p p e d m o d e s ................................................................................................ R e s u l t s ....................................................................................................................................... D i s c u s s i o n ................................................................................................................................. S u m m a r y a n d c o n c l u s i o n s ...................................................................................................
213 215 219 221 226 229
C h a p t e r 9. P a t h w a y s a n d v a r i a b i l i t y at i n t e r m e d i a t e d e p t h s in t h e tropical Atlantic C. S c h m i d , Z. Garraffo, E. J o h n s a n d S. Garzoli ........................................................................ 2 3 3 I n t r o d u c t i o n .............................................................................................................................. D a t a a n d m e t h o d s ................................................................................................................... L a r g e s c a l e f l o w p a t t e r n s ..................................................................................................... 3.1. V e r t i c a l a n d h o r i z o n t a l s t r u c t u r e ......................................................................... 3.2. I n t e r i o r p a t h w a y s ...................................................................................................... 3.3. W e s t e r n b o u n d a r y p a t h w a y s ................................................................................. 3.4. S e m i - a n n u a l m e a n s o f t h e v e l o c i t y a t i n t e r m e d i a t e d e p t h ........................... T e m p o r a l a n d s p a t i a l v a r i a b i l i t y b e t w e e n 5~ a n d 7~ ................................................ 4.1. O b s e r v a t i o n s ............................................................................................................... 4.2. C o m p a r i s o n w i t h M I C O M ....................................................................................... 4.3. C h a r a c t e r i s t i c l e n g t h s c a l e s ................................................................................... 4.4. C h a r a c t e r i s t i c t i m e s c a l e s ....................................................................................... 4.5. K i n e m a t i c a n a l y s i s .................................................................................................... D i s c u s s i o n a n d c o n c l u s i o n s ..................................................................................................
233 237 239 239 244 247 249 251 251 252 256 256 259 263
C h a p t e r 10. A c o m p a r i s o n o f k i n e m a t i c e v i d e n c e for t r o p i c a l c e l l s in t h e A t l a n t i c a n d P a c i f i c o c e a n s R. Molinari, S. Bauer, D. S n o w d e n , G. J o h n s o n , B. Bourles, Y. G o u r i o u a n d H. Mercier ...................................................................................................................................... 2 6 9 .
2. 3. 4.
I n t r o d u c t i o n .............................................................................................................................. D a t a a n d a n a l y s e s .................................................................................................................. R e s u l t s ....................................................................................................................................... D i s c u s i o n ....................................................................................................................................
269 271 274 280
C h a p t e r 11. S u b t r o p i c a l cells in t h e A t l a n t i c Ocean: An observational summary D. S n o w d e n a n d R. M o l i n a r i ............................................................................................................ 2 8 7
ix
I n t r o d u c t i o n .............................................................................................................................. 2 8 7 S u b d u c t i o n ................................................................................................................................ 2 9 1 2.1. W a t e r m a s s e s a n d s o u r c e s r e g i o n s ....................................................................... 2 9 1 2.2. F o r m a t i o n r a t e s ......................................................................................................... 2 9 4 P a t h w a y s b e t w e e n t h e s u b d u c t i o n r e g i o n s a n d t h e u p w e l l i n g r e g i o n s ................... 2 9 5 3.1. W e s t e r n b o u n d a r y p a t h w a y s ................................................................................. 2 9 5 3.2. I n t e r i o r p a t h w a y s ...................................................................................................... 2 9 8 3.3. I n t e r i o r e n t r a i n m e n t i n t o t h e E q u a t o r i a l U n d e r c u r r e n t ............................... 2 9 9 U p w e l l i n g in t h e t r o p i c a l A t l a n t i c ...................................................................................... 3 0 0 4.1. E q u a t o r i a l u p w e l l i n g ................................................................................................ 3 0 0 4.2. O f f e q u a t o r i a l u p w e l l i n g ......................................................................................... 3 0 3 N e a r s u r f a c e r e t u r n flow to t h e s u b d u c t i o n a r e a s ......................................................... 3 0 5 S u m m a r y a n d r e m a i n i n g q u e s t i o n s ................................................................................... 3 0 6
.
2.
.
.
.
6.
Chapter 12. Spectral, formal, and n o n l i n e a r stability in a layered q u a s i g e o s t r o p h i c m o d e l w i t h a p p l i c a t i o n to the A t l a n t i c North Equatorial Current F. B e r o n - V e r a a n d J. O l a s c o a g a ....................................................................................................... 3 1 3 1. 2.
I n t r o d u c t i o n .............................................................................................................................. 3 1 3 T h e o r y ........................................................................................................................................ 3 1 5 2.1. M o d e l ............................................................................................................................. 3 1 5 2.2. S t a b i l i t y A n a l y s i s ...................................................................................................... 3 1 7 2.2.1. F o r m a l a n d n o n l i n e a r s t a b i l i t y ................................................................ 3 1 8 2.2.2. S p e c t r a l s t a b i l i t y .......................................................................................... 3 2 0 2.2.3. E l e m e n t a r y m o d e s r e s o n a n c e ................................................................... 3 2 0 3. D a t a ............................................................................................................................................ 3 2 1 3.1. B a s i c flow ..................................................................................................................... 3 2 2 3.2. S t a b i l i t y p r o p e r t i e s ................................................................................................... 3 2 3 3.3. C o m p a r i s o n w i t h in s i t u o b s e r v a t i o n s a n d e a r l i e r w o r k s .............................. 3 2 7 4. S u m m a r y a n d c o n c l u s i o n s .................................................................................................... 3 2 9 A p p e n d i x A: E n e r g y a n d C a s i m i r m a t r i c e s ................................................................................... 3 3 0 A p p e n d i x B: D i s p e r s i o n r e l a t i o n ....................................................................................................... 3 3 1 A p p e n d i x C: E i g e n v a l u e p r o b l e m i n ~f c o o r d i n a t e s .................................................................... 3 3 1
Chapter 13. S y n o p t i c study of w a r m rings in the N o r t h Brazil Current retroflection region u s i n g satellite altimetry G. G o n i a n d W. J o h n s ......................................................................................................................... 3 3 5 .
2. 3.
.
5.
I n t r o d u c t i o n .............................................................................................................................. 3 3 5 R e g i o n o f s t u d y ........................................................................................................................ 3 3 8 D a t a ............................................................................................................................................ 3 3 8 3.1. A l t i m e t e r d a t a ............................................................................................................ 3 3 8 3.2. C l i m a t o l o g i c a l d a t a ................................................................................................... 3 4 1 T w o - l a y e r m o d e l a p p r o x i m a t i o n ......................................................................................... 3 4 3 R e s u l t s a n d d i s c u s s i o n ........................................................................................................... 3 4 5 5.1. U p p e r l a y e r t h i c k n e s s f i e l d s .................................................................................. 3 4 5
5.2. 5.3. 5.4. 5.5. .
R i n g s h e d d i n g .............................................................................................................347 R i n g t r a j e c t o r i e s .........................................................................................................347 R i n g p a r a m e t e r s ........................................................................................................350 I n t e r a n n u a l v a r i a b i l i t y ............................................................................................352
S u m m a r y ...................................................................................................................................354
C h a p t e r 14. N o r t h B r a z i l C u r r e n t r i n g s a n d t h e v a r i a b i l i t y in the latitude of the retroflection S. Garzoli, A. Ffield a n d Q. Yao ....................................................................................................... 357 .
2. 3. 4. 5. 6.
I n t r o d u c t i o n ..............................................................................................................................357 M e t h o d o l o g y .............................................................................................................................360 D y n a m i c h e i g h t field ..............................................................................................................362 L a t i t u d e of p e n e t r a t i o n a n d n u m b e r of r i n g s s h e d .......................................................3 6 6 R i n g s v o l u m e a n d t e m p e r a t u r e t r a n s p o r t .......................................................................367 S u m m a r y ...................................................................................................................................370
C h a p t e r 15. N o r t h B r a z i l C u r r e n t r i n g s a n d t r a n s p o r t of s o u t h e r n w a t e r s in a h i g h r e s o l u t i o n n u m e r i c a l s i m u l a t i o n o f t h e North Atlantic Z. Garraffo, W. J o h n s , E. C h a s s i g n e t a n d G. Goni ..................................................................... 375
.
.
.
I n t r o d u c t i o n ..............................................................................................................................375 M o d e l c o n f i g u r a t i o n ...............................................................................................................378 The North Brazil Current system from the model and observations: T h e s e a s o n a l c i r c u l a t i o n ........................................................................................................379 T h e N o r t h B r a z i l r i n g s , s e a s u r f a c e h e i g h t v a r i a b i l i t y a n d effect on t r a n s p o r t s t h r o u g h t h e L e s s e r A n t i l l e s p a s s a g e s ..........................................................383 4.1. S e a s u r f a c e h e i g h t s p a c e - t i m e d i a g r a m s ............................................................383 4.2. S u r f a c e h e i g h t v a r i a b i l i t y f r o m t h e m o d e l a n d o b s e r v a t i o n s ........................ 385 4.3. R i n g t y p e s , a s s o c i a t e d s e a h e i g h t a n o m a l y , a n d t r a j e c t o r i e s ....................... 387 4.4. Effect of N B C r i n g s in t h e t r a n s p o r t s t h r o u g h t h e L e s s e r A n t i l l e s p a s s a g e s .......................................................................................................................393 T r a n s p o r t of s o u t h e r n A t l a n t i c w a t e r s b y r i n g s .............................................................393 5.1. T r a n s p o r t f r o m c r i t e r i a on r a d i u s a n d v e r t i c a l e x t e n t ....................................395 5.2. T r a n s p o r t f r o m w a t e r m a s s a n a l y s i s ...................................................................395 5.3. C o m p a r i s o n of k i n e m a t i c a n d w a t e r m a s s m e t h o d s .......................................401 D i s c u s s i o n a n d c o n c l u s i o n s ..................................................................................................403
C h a p t e r 16. C r o s s - g y r e t r a n s p o r t by N o r t h B r a z i l C u r r e n t r i n g s W. J o h n s , R. Z a n t o p p a n d G. Goni .................................................................................................. 411 .
2.
I n t r o d u c t i o n .............................................................................................................................412 D a t a a n d M e t h o d s ..................................................................................................................413 2.1. S h i p b o a r d s u r v e y s .....................................................................................................413 2.2. M o o r e d t i m e s e r i e s o b s e r v a t i o n s ...........................................................................413
xi
.
.
2.3. W a t e r m a s s i d e n t i f i c a t i o n ....................................................................................... R e s u l t s ....................................................................................................................................... 3.1. S u r v e y e d r i n g s ........................................................................................................... 3.2. R i n g s i d e n t i f i e d b y m o o r i n g s .................................................................................. 3.3. C r o s s - g y r e t r a n s p o r t b y N B C r i n g s ...................................................................... 3.4. R i n g " w a t e r m a s s " vs. " g e o m e t r i c " v o l u m e s ....................................................... D i s c u s s i o n a n d c o n c l u s i o n s ..................................................................................................
416 420 420 423 432 434 436
C h a p t e r 17. I m p a c t o f N o r t h B r a z i l C u r r e n t r i n g s o n t h e local c i r c u l a t i o n a n d c o r a l r e e f fish r e c r u i t m e n t to B a r b a d o s , West I n d i e s R. Cowen, S. S p o n a u g l e , C. Paris, J. Fortuna, K. L w i z a a n d S. Dorsey ............................... 4 4 3
.
.
I n t r o d u c t i o n ............................................................................................................................. M e t h o d s ..................................................................................................................................... 2.1. B i o - p h y s i c a l s a m p l i n g .............................................................................................. 2.2. F l o w f i e l d c a l c u l a t i o n s .............................................................................................. 2.3. B i o l o g i c a l m e a s u r e m e n t s ........................................................................................ R e s u l t s ....................................................................................................................................... 3.1. S u r f a c e s a l i n i t y a n d t r a n s p o r t .............................................................................. 3.2. C h l o r o p h y l l a a n d l a r v a l f i s h v e r t i c a l d i s t r i b u t i o n .......................................... 3.3. F i s h s e t t l e m e n t i n t e n s i t y ........................................................................................ 3.4. O t o l i t h g r o w t h a n d l a r v a l d u r a t i o n ...................................................................... D i s c u s s i o n .................................................................................................................................
444 445 445 447 448 449 449 451 454 454 455
C h a p t e r 18. W i n d b u r s t s a n d e n h a n c e d e v a p o r a t i o n in t h e t r o p i c a l and subtropical Atlantic Ocean K. Katsaros, A. M e s t a s - N u f t e z , A. B e n t a m y a n d E. Forde ........................................................4 6 3 .
2.
.
I n t r o d u c t i o n a n d b a c k g r o u n d .............................................................................................. R e s u l t s ....................................................................................................................................... 2.1. M e a n v a l u e s a n d s t a n d a r d d e v i a t i o n s ................................................................ 2.2. W i n d b u r s t s a n d a s s o c i a t e d l a t e n t h e a t f l u x ..................................................... C o n c l u d i n g r e m a r k s ...............................................................................................................
464 466 466 468 472
C h a p t e r 19. S p a t i a l - t e m p o r a l e v o l u t i o n o f t h e l o w f r e q u e n c y c l i m a t e v a r i a b i l i t y in t h e t r o p i c a l A t l a n t i c L. A y i n a a n d J. S e r v a i n ......................................................................................................................4 7 5 .
2.
I n t r o d u c t i o n .............................................................................................................................. D a t a a n d p r o c e s s i n g ............................................................................................................... 2.1. D a t a ............................................................................................................................... 2.2. P r o c e s s i n g .................................................................................................................... R e s u l t s .......................................................................................................................................
475 479 479 480 481
xii
.
3.1. T h e 5 - y e a r o s c i l l a t i o n ...............................................................................................4 8 2 3.2 T h e 1 . 5 - y e a r o s c i l l a t i o n ............................................................................................4 8 5 C o n c l u s i o n s ...............................................................................................................................4 9 2
I n d e x .........................................................................................................................................................4 9 7
xiii PREFACE The motivation for this book stems from a series of workshops and conferences focused on the tropical Atlantic held during the last five years. At these meetings the results from modeling and observational studies demonstrated that the tropical Atlantic is a critical region for processes that maintain the meridional overturning circulation, such as cross-equatorial exchanges, and for sea surface temperature variability that impacts on atmospheric climate. Furthermore, the sea surface temperature variability has been shown to be influenced by exchanges from the subtropical to the tropical regions, as opposed to cross-equatorial exchanges. Thus, the subject of interhemispheric and inter-gyre exchanges of heat, salt and fresh water is the theme of this endeavor. The goal of a book on this subject is to improve our knowledge of the tropical Atlantic dynamics, which is a key component of the global meridional overturning circulation. There are several processes that affect the flow of mass and heat from the southern into the northern hemisphere in the upper hundred meters in the tropical Atlantic. A clear understanding on the dynamics of these processes and of those associated to the ocean circulation or to surface signals, including planetary waves (Franca et al.) and signals of annual and mesoscale periods (Schmid et al.), becomes necessary to better evaluate their contribution to the interhemispheric mass exchange. These processes are important, as they are believed to be largely responsible in driving the sea surface temperature (Ayina and Servain), which in turn, is a critical parameter to investigate oceanatmospheric interactions (Katsaros, et al.). As in the Pacific Ocean, the tropical Atlantic presents a system of zonal surface currents as observed from in situ observations (Stramma et al.). Output produced by regional models (Jochum and Malanotte-Rizzoli and Hazeleger and de Vries) is also used to complement these observations and to provide additional information on their spatial and temporal variability. These zonal currents partly contribute to the interhemispheric water exchange as they merge with the northward flowing North Brazil Current (NBC) upon encountering the western boundary. Warm and salty anticyclonic rings are shed by the NBC and are now known to have a much broader impact, not only on interhemispheric water mass transfer, but also on the environment of remote regions (Cowen et al.). The NBC rings have been observed by in-situ observations (Garzoli et al., Johns et al.), monitored from satellite altimetry (Goni and Johns) and also investigated through numerical simulations (Garraffo et al.). Finally, the availability of data from process studies, sustained observations, outputs from numerical simulations and satellite observations has translated into a significant growth of knowledge in the region. Observations from different sources are blended together (Mayer et al.), are used to validate model outputs (Vianna et al.) and are also assimilated into models to obtain a more complete and accurate picture of the oceanic circulation (Buehner et al.; Hazeleger and de Vries; Halliwell et a/.;Beron-Vera and Olascoaga).
xiv The inter-hemispheric water exchange is not limited to boundary currents and their associated rings. In the early 1990's the concept of and evidence for oceanic subtropical forcing of the equatorial thermocline, current system and, of the equatorial climate began to emerge. Strong theoretical foundations were laid in a series of contributions by different authors and observational evidence was sought for subtropical/tropical interactions (Snowden and Molinari). The idea of subtropical cell (STCs) was proposed as the oceanic component of a coupled mode of variability, the so-called oceanic tunnel to the equator versus the atmospheric bridge of inter-oceanic teleconnections. The STCs, by bringing water masses subducted in the subtropics to the equator, determine the structure of the equatorial thermocline and sea surface temperatures (SSTs), hence affecting the Hadley-Walker circulation through air/sea interactions. This mechanism of remote forcing of tropical variability acts on inter-annual to decadal and longer time scales. The STCs, the shallow overturning circulations of the tropical oceans, are just another component of the overall issue of inter-hemispheric exchanges of tracers, mass and momentum determining the climate of the equatorial ocean (Molinari et al. ). Because of this growing interest, a series of CLIVAR workshops, supported by NOAA and NSF, was held between 2000 and 2003, with the first workshop focused on the STCs held in Venice, Italy, October 2000. Successive workshops were held in Paris, France, July 2001; in Kiel, Germany, 2002; and in Miami, March 2003. In particular, at the IAPSO (International Association for the Physical Sciences of the Oceans) held in Mar del Plata, Argentina, October 2001, a Symposium was specifically dedicated to these interactions in the Atlantic ocean. The idea of the present book stemmed from this Symposium and was concretized through negotiations between the editors and Elsevier Publishing Company. This book intends to present a picture as exhaustive as possible of the state of knowledge in 2003 of the inter-hemispheric interactions in the tropical Atlantic, covering in situ and satellite observations and modeling. Of the 19 chapters comprised in the book, 10 were presented as preliminary results at the IAPSO Symposium held in Mar del Plata in 2001. Other chapters constitute the presentations, both oral and poster, at the above mentioned workshops. The many funding agencies mentioned in the acknowledgements of each chapter is an indication of the strong fmancial support being received to investigate the tropical Atlantic. The chapters contained in this book might be used as a summary to formulate recommendations for the type of process studies and sustained observations needed to improve our knowledge of the tropical Atlantic dynamics, including the support and enhancement of current observing systems and the implementation of new process studies. Each chapter of this book underwent anonymous peer review by two referees, rigorously following the review process of international journals. We are truly thankful to the referees who generously gave their time and contributed with their expertise to improve the manuscripts and the book. We
XV
also wish to acknowledge the time and effort that all the authors dedicated to this book. The Editors.
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Interhemispheric Water Exchange in the Atlantic Ocean
edited by G.J. Goni and P. Malanotte-Rizzoli 9 2003 ElsevierB.V. All rights reserved.
Circulation, variability and near-equatorial m e r i d i o n a l flow in the central tropical Atlantic Lothar Stramma*, Jtirgen Fischer, Peter B r a n d t and Friedrich Schott Institut ftir Meereskunde an der Universit~it Kiel, Dtisternbrooker Weg 20, 24105 Kiel, G e r m a n y
Observations in the central tropical Atlantic are used to investigate the circulation, the variability, and the near-equatorial meridional flow in this oceanic region. Meridional sections confirm t h a t the southern band of the South Equatorial C u r r e n t is a broad sluggish flow transporting subtropical w a t e r n o r t h w e s t w a r d toward the western boundary. Variability in the South Equatorial C u r r e n t is weak with an a n n u a l signal of about 2 cm/s. Recent equatorial flow observations agree with the previously proposed m e a n flow field, indicating t h a t a p e r m a n e n t tropical circulation exists t h a t is composed of several zonal current and countercurrent bands of small vertical and meridional extent compared to the subtropical gyres. However, wave phenomena superimpose on the m e a n flow field. On seasonal time scales the variability in the zonal flow field n e a r the equator is dominated by the s e m i a n n u a l cycle in the central and eastern p a r t while the a n n u a l cycle dominates in the western part. This seasonal variability is caused by the propagation of equatorial Rossby and Kelvin waves generated mainly by the zonal wind anomaly at the equator. Despite the observations of instantaneous cross-equatorial velocities and of floats crossing the equator it remains unclear w h e t h e r there is a net cross-equatorial flow in the central tropical Atlantic in addition to cross-equatorial exchanges via thermocline convergence, upwelling and E k m a n divergence. Three floats deployed at 200 m and 400 m depth either leave their deployment region at the equator to join the North Equatorial U n d e r c u r r e n t and progress further n o r t h w a r d or in two cases have been deployed in the southern hemisphere and drift towards the equator. 1. I N T R O D U C T I O N
In the equatorial Atlantic w a t e r is exchanged from the southern to the northern hemisphere in the upper ocean as well as in the bottom w a t e r layer *Corresponding author.Tel.:49431-6004103. Fax:49-431-600-4102. E-mail address:
[email protected] and from the northern hemisphere to the South Atlantic in the deep water layers. The north-south exchange is complicated by the general zonal circulation near the equator leading to interactions between different current bands and water mass transformations. S t r a m m a and Schott (1999) summarized the mean horizontal flow field of the tropical Atlantic Ocean between 20~ and 20~ for three layers of the upper ocean. Compared to the subtropical gyres the tropical circulation shows several zonal current and countercurrent bands (Figure 1) of smaller meridional and vertical extent. Despite the importance for the interhemispheric exchange and the complicated zonal flow field of the tropical Atlantic there have been remarkably few studies of the currents and their interaction in the central tropical Atlantic. The tropical Atlantic is special with regard to upper ocean processes (Lee and Csanady, 1999a,b). In the tropical ocean cold thermocline waters of offequatorial origin of both hemispheres are transformed into warm water masses via entrainment and subsequent surface heat flux, and then escape from this region northward as well as southward. The pecularity of the tropical Atlantic is that the net heat transport is northward. The tropical Atlantic warm water pool stores heat during May-October and lets heat escape in November-April (Lee and Csanady, 1999b). Progress was also made in recent numerical model simulations. Monthly mean velocity fields from a global ocean general circulation model were used by Blanke et al. (1999) to study the main circulation patterns within the upper 1200 m of the equatorial Atlantic. The qualitative description in terms of equatorial pathways was found to be coherent with recent circulation schemes inferred from direct measurements. An eddy-resolving numerical ocean circulation model was used by Fratantoni et al. (2000) to investigate the pathways of low-latitude intergyre mass transports associated with the upper limb of the Atlantic meridional overturning cell (MOC). In a realistically forced model experiment, a 14 Sv upper-ocean MOC return flow is partitioned among three pathways connecting the equatorial and tropical wind-driven gyres. Despite the fact that the South Equatorial Current (SEC) is the major water source for the tropical Atlantic, few investigations were made on the SEC in the central Atlantic. The southern band of the SEC (sSEC) is fed by the Benguela Current, which crosses the Greenwich Meridian south of 20~ The sSEC was found to be a broad sluggish flow between 10~ and 25~ (Stramma, 1991), perhaps accounting for the low interest in the sSEC in the past. Recently the sSEC has received more interest, as investigations of the transport of climate signals indicate that the signals are transported from the tropical-subtropical region towards the tropics by the sSEC (e.g. Malanotte-Rizzoli et al. 2000; Lazar et al. 2001). As the water crosses the equator mainly in the Western Boundary Current by the North Brazil Current, the previous major investigations on interhemispheric water exchange were carried out at the western boundary. Nevertheless, several large observational programs dedicated to the central tropical Atlantic took place in the past three decades. These were e.g. the GARP (Global Atmospheric
Research Program) Atlantic Tropical Experiment (GATE), the First GARP Global Experiment (FGGE), the Seasonal Equatorial Atlantic (SEQUAL) program, the Program Fran~ais Oc6an Climat Atlantique Equatorial (FOCAL) and presently the Pilot Research Moored Array in the Tropical Atlantic (PIRATA) program. Before the use of shipboard ADCP only direct current observations with moored stations could be done to investigate the equatorial flow field as geostrophy failed at and near the equator. Most of the former equatorial programs focused on equatorial processes and during FOCAIJSEQUAL also on circulation investigations. The presently conducted PIRATA project focuses on air-sea interaction processes related to climate change investigations. Here we use recent shipboard, float and altimeter observations of the tropical Atlantic Ocean mainly from the WOCE and beginning CLIVAR field program phases to investigate the circulation, variability and near-equatorial meridional flow of the central part of the tropical Atlantic Ocean. The mean flow field based on Stramma and Schott (1999) is compared with observations from a recent cruise to the equatorial western Atlantic with RV Meteor in March/April 2000 (Figure la) as well as on older WOCE surveys. Comparisons are made further with the pathways of floats deployed at 200 m and 400 m depth and satellitederived sea level anomalies for the period from October 1992 to October 2000.
2. M E T H O D S AND D A T A During the Meteor cruise in March/April 2000 a narrow-band 75 kHz ADCP was used for underway current measurements. Navigation was based on the heading information by an Ashtec 3D-GPS and long range differential GPS. The estimated accuracy of the ADCP velocity observations is about 2 cm/s in the upper 400 m, where a combination of shipboard ADCP and lowered ADCP was used, and 5 cm/s in the depth range 400 to 1000 m where the velocity distribution is based on lowered ADCP measurements alone. Hydrographic profiles were collected with a Seabird SBE 9 system during the beginning of the Meteor cruise. For the second part of the Meteor cruise a NeilBrown Mark III CTD-system was used because of a failure of the Seabird system. The calibration of the CTD data for both instruments resulted in accuracies of 0.002~ for temperature, 0.0025 for salinity, 4.5 dbar for pressure and 0.05 mlfl for dissolved oxygen. The meridional sections across the South Equatorial Current (Figure la) were taken from the WOCE data archive. The sections are by RV Maurice Ewing in February 1994 at about 30~ by RV Melville in March 1989 at about 250W, by RV Knorr in April 1994 at about 190W, by RV L'Atalante in J a n u a r y 1995 at about 9~ and again by L'Atalante in March 1995 at about 90E. The altimeter data, which are corrected for geophysical, tidal, sea state, and instrument effects as well as for orbit errors, are part of the TOPEX/POSEIDON
Figure 1 (previous page). Schematic maps showing the horizontal distribution of the major tropical currents for the Tropical Surface Water layer at about 0-100 m depth (modified after Stramma and Schott, 1999 and Stramma and England, 1999) for a) the northern spring including the cruise track and CTD stations (dots) of Meteor cruise M47/1 (16 March to 18 April, 2000) as well as for sections from the WOCE data set at about 30~ 25~ 19~ 9~ and 9~ as lines and for b) the northern fall including the cruise track and CTD stations (dots) of RV Sonne cruise Sol51 (3 November to 26 November, 2000). Shown are the North Equatorial Current (NEC), the Guinea Dome (GD), the North Equatorial Countercurrent (NECC), the Guinea Current (GC), the South Equatorial Current (SEC) with the northern (nSEC), equatorial (eSEC), central (cSEC) and southern branches (sSEC), the Equatorial Undercurrent (EUC), the North Brazil Current (NBC), the Gabon-Congo Undercurrent (GCUC), the Angola Gyre (AG), the Angola Current (AC), the Angola Dome (AD), the South Equatorial Undercurrent (SEUC), the South Equatorial Countercurrent (SECC) and the Brazil Current (BC). The Angola-Benguela Front (ABF) is included as a dashed line. "Up" marks possible areas of upwelling, but not the exact places. sea level anomaly products provided by CNES/NASA (AVISO, 1998). Here, we use sea surface hight anomalies (SSHA) from along-track data (Fu et al., 1994) for the period October 1992 to October 2000. By applying a 6-month low-pass FFT-filter to the along-track SSHA data and by interpolating using an objective analysis to a 1~ x 1 ~ grid, time series are generated, from which zonal geostrophic velocity anomalies are calculated using a B-plane approximation according to:
BU + f 8UIOy=-g 8~/8y 2
(1)
where U is the zonal geostrophic velocity anomaly (ZVA), g is the acceleration of gravity, ~ is the SSHA and y is the horizontal coordinate, positive in n o r t h w a r d direction. Equation (1) is solved implicitly by a s s u m i n g fU=-ga~/Sy north of 10~ and south of 10~ The SSHA data are used to investigate the broad South Equatorial C u r r e n t and the North Equatorial Countercurrent, where a l ~ ~ grid is appropriate, while it would not be useful to investigate current bands with small horizontal width from SSHA. The low-pass filter ensures t h a t nonstationary and advective terms in the equation of motion are negligible compared to Coriolis acceleration. The amplitude and phase of the annual and semiannual cycle of the ZVA are calculated by fitting the corresponding harmonics to the data. Ten APEX floats were launched in March 2000 and 5 additional ones during a Sonne cruise in November 2000 (Figure lb) in the tropical Atlantic (Schott et al. 2002). The APEX floats were programmed for a 9 day duty cycle with parking depths of 200 m and 400 m. After drifting at the duty depth for 9 days the floats descend to 1500 m, measure a profile of t e m p e r a t u r e and salinity on their way up to the surface and t r a n s m i t their position and the profile data via ARGOS during a surface drift of approximately 14 to 20 hours.
3. THE WATER M A S S E S
Water mass exchange, including net northward meridional heat transport across the equator, is accomplished by warm Tropical Surface Water, Central Water, Antarctic Intermediate Water and upper Circumpolar Deep Water moving northward in the upper 1200 m compensated by cold North Atlantic Deep Water moving southward between 1200 and 4000 m. At the bottom, the northward transport of Antarctic Bottom Water also carries a small amount of cold water into the northern hemisphere. The results presented here will be restricted to the upper ocean layers. A short information on the water masses is given below; for detailed information see Stramma and Schott (1999).
The near-surface layer: The near surface layer of the tropical Atlantic is the Tropical Surface Water (TSW). The TSW at about 27~ forms the mixed layer of the tropical Atlantic. In the underlying sharp thermocline, the temperature drops from 25~ to 15~ over about 50 m and the 20~ isotherm well represents the lower boundary of the TSW. Imbedded in the TSW is the salinity maximum water, also called Subtropical Underwater, which is characterized by a salinity maximum at densities slightly below G0 =25.00 kgm-3 at about 100 m depth (Figure 2a). The salinity maximum water is formed in the transition region between the subtropics and the tropics by subduction. It progresses equatorwards as a subsurface salinity maximum, while the overlying water is salinity poor due to high precipitation in the tropics. The central water layer: Two types of South Atlantic Central Water (SACW) are found, the lighter type originating from the southwestern subtropical South Atlantic and circulating in the subtropical gyre, while the denser type probably originates from the South Atlantic as well as the South Indian Ocean and is carried with the Benguela Current and the South Equatorial Current (SEC) into the equatorial region. The Central Water masses are characterized by a nearly linear T-S relationship. The SACW of the subtropical gyre is formed near the subtropical front in the southwestern South Atlantic. However, the SACW found in the tropical regions is to a large amount Indian Central Water brought into the Atlantic Ocean by the Agulhas Current (Sprintall and Tomczak, 1993). The isopycnal G0 = 27.1 kgm-3 at about 500 m depth marks the transition from the central water to the intermediate water. The intermediate water layer: The Antarctic Intermediate Water (AAIW) originates from the surface region of the circumpolar layer, especially the surface waters in the northern Drake Passage and the Falkland Current loop, and has a southern boundary that is
Figure 2 (previous page). The parameter distribution on a meridional section along 23~ from RV Meteor in March to April 2000 for a) salinity with a contour interval of 0.2 (0.02 for salinities lower than 34.6) and b) oxygen in ml/1 with a contour interval of 0.25 ml/l and gray shading for the low oxygen layer. The water mass boundaries are shown by the isopycnals ~0 = 25.0 and 27.1 kgm -3 (dashed lines). essentially the Subantarctic Front. AAIW follows the subtropical gyre of the South Atlantic to enter the equatorial Atlantic ( S t r a m m a and England, 1999). AAIW can be recognized by a subsurface oxygen m a x i m u m and a salinity minimum south of 20~ In the tropical Atlantic AAIW is found between about 500 m and 1200 m depth. The salinity m i n i m u m weakens, but is still present at the equator (Figure 2a). The AAIW oxygen m a x i m u m becomes weak or absent in most areas north of 20~ in the open ocean, while it spreads along the Brazilian shelf equatorwards (Talley, 1996) and then e a s t w a r d just south of the equator (Figure 2b). Below the AAIW, the n o r t h e r n limits of the upper Circumpolar Deep W a t e r (uCDW) occur with a t e m p e r a t u r e m i n i m u m and an oxygen m i n i m u m at about 1000 m. The vertical extent of this w a t e r mass is small n e a r the equator, therefore the uCDW is included in the AAIW in the following. 4. R E S U L T S 4.1. M e a n C i r c u l a t i o n The mean circulation of the different upper ocean layers was discussed in S t r a m m a and Schott (1999) and the detailed discussion of the currents will not be repeated here. The flow schematic of the TSW for the spring and fall situation modified after S t r a m m a and Schott (1999) and S t r a m m a and England (1999) includes the cruise tracks of the two cruises in 2000 and some other cruises from the WOCE data set (Figure 1). The schematic figures were modified to account for recent results in the eastern basin by modelling efforts of L a z a r et al. (2002) who described large-scale tropical gyres and for ship observations by Mercier et al. (2003) showing t h a t both the South Equatorial C o u n t e r c u r r e n t (SECC) and the South Equatorial U n d e r c u r r e n t (SEUC) progress to at least 9~ with a southward shift in the eastward extension. The wind-driven E k m a n layer in the upper tens of meters of the ocean masks at some places the flow structure of the TSW. The sSEC forms the northern part of the subtropical gyre of the South Atlantic and carries subtropical w a t e r from the Benguela C u r r e n t region toward the Brazilian shelf region south of 10~ Near Brazil the North Brazil U n d e r c u r r e n t was observed to be already strongly developed at l l ~ (Schott et al. 2002). Earlier investigations showed t h a t the isopycnal ~1 = 32.15 kgm-3 describes well the boundary between the upper Circumpolar Deep W a t e r and the upper p a r t of the North Atlantic Deep Water (Rhein et al. 1995). The integrated geostrophic westward transports from the surface to 1000 m depth relative to a reference
level of ~ = 32.15 kgm-3 north of 30~ (Figure 3) for several meridional sections (Figure la) from the WOCE data set confirm the earlier description of a broad and sluggish sSEC. The section at about 9~ (dots) shows a strong transport increase near 30~ as it is located within the Benguela Current. This section only reaches a transport of 25 Sv as a large part of the northwestward flowing SEC crosses 9~ south of 30~ All the other sections reach an intregated SEC/SECC transport of about 32 Sv near 8~ The higher transport near 15~ for the 9~ section is caused by the part of the sSEC which remains in the eastern basin (see Figure la). The southern part of the section might be disturbed by Agulhas Rings which were also observed north of 30~ (Byrne et al. 1995; Garzoli and Goni 2000). However, the largest variability in altimeter data caused by Agulhas Rings was observed south of 30~ (Goni et al. 1997) and the rings should have weakened north of 30~ and should have a weak influence on the total transport as long as a ring is not located at an end-point of a section. North of 8~176 the transport slightly reduces due to the weak eastward flow of the SECC or the Angola Dome for the 9~ section. All sections show strong transport decreases near 5~ caused by the South Equatorial Undercurrent or the Angola Gyre at 9~ (see Figure la) near 3~176 The transport at about 30~ (circles) increases more slowly in the southern part, because on the western side of the South Atlantic the SEC has moved further northward due to the northwestward flow of the SEC. Nevertheless, it reaches a similar transport as the other sections near 10~ without an indication of larger variability. Compared to the deep-reaching subtropical gyres the tropical circulation shows several zonal current and countercurrent bands of smaller meridional and vertical extent. Of course, there are large regions where the schematic Figures l a and lb are highly speculative, where the exchanges and interactions between the current branches are still obscure, other exchange routes between the currents might exist and the behavior of the water in crossing the equator is not known. The zonal current distribution across the equator at 23~ in March/April 2000 (Figure 4a) contains the zonal current bands in the upper ocean as described by Stramma and Schott (1999). For the TSW the comparison with Figure l a shows that the known currents are present, except that the SEUC in Figure l a exists only below 80 m depths. Hence at 23~ the SEUC seems to not reach the nearest surface layer in northern spring as in the western tropical Atlantic, and the situation with regard to the SEUC in the TSW layer is closer to the fall situation shown in Figure lb. Furthermore, the equatorial band of the SEC (eSEC) reaches the near surface layer south of 3~ slightly further south than indicated in Figure la. The meridional component of the ADCP observations (Figure 4b) in March/April 2000 is much weaker than the zonal one and might just be short-term movements induced by equatorial waves (see e.g. Weisberg and Colin, 1986; Weisberg and Weingartner, 1988), which do not transport water particles across the equator in the mean. For the central water layer at 23~ the currents of the schematics of Stramma and Schott (1999), the SEUC, the eSEC, the Equatorial Undercurrrent (EUC), the northern band of the SEC (nSEC) and the North Equatorial Undercurrent
10 (NEUC) were present in March/April 2000. In the central w a t e r layer the equatorial flow of the EUC changes to w e s t w a r d flow of the Equatorial Intermediate C u r r e n t (EIC) as the current bands are not restricted to the different w a t e r mass layers. As at 35~ in March 1994 (Schott et al. 1998) a n d April 2000 a clear and strong EIC exists at 23~ and at 35~ (Figure not shown). Boebel et al. (1999) proposed an a n n u a l cycle of the s t r e n g t h a n d direction of the EIC with e a s t w a r d flow of the EIC in March to May. However, in April 2000 there was a clear EIC and the proposed e a s t w a r d flow based on three floats located at a depth of about 800 m (Boebel et al. 1999) is probably not a seasonal reversal of the entire EIC but only an indication t h a t these floats missed the EIC, which is known to change its vertical and horizontal extent (Schott et al. 1998) or some u n d e t e r m i n e d i n t e r a n n u a l variations. Bourles et al. (2002) proposed t h a t two cores of the EIC should be separated for the tropical Atlantic, similar to the definition in the Pacific. According to Figure 4a two EIC velocity cores were present in the EIC in March/April 2000 at 23~ In the AA/W layer the strongest signals are from the Southern I n t e r m e d i a t e Countercurrent (SICC), the EIC, and the N o r t h e r n Intermediate C o u n t e r c u r r e n t (NICC), currents which for the tropical Atlantic were first described by Schott et al. (1995). S t r a m m a and Schott (1999) indicated a weak presence of the SEUC and the eSEC in the AAIW layer and the weak e a s t w a r d and w e s t w a r d flows at 3~ to 4.5~ in Figure 4a confirms this assumption.In general the flow distibution 50
Sv
w 0
v
v
w
r
w
30"W 2/94
45
+ o o . w 1~5 9 Og'E3,gS +
i 30~
~
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+ +
++
+
++++
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.
+
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I
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:
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Figure 3. Integrated geostrophic zonal transport (positive westward) beginning at 30~ for the layer 0 to 1000 m relative to a reference level of Cl = 32.15 kgm -3 on meridional sections from the WOCE data set (lines in Figure la) at about 30~ in February 1994 (0), at 25~ in March 1989 (x), at 19~ in April 1994 (*), at 90W in January 1995 (+) and at about 9~ in March 1995 (dots). Current ranges are indicated for the southern band of the SEC (sSEC), the South Equatorial Countercurrent (SECC) the central band of the SEC (cSEC) and the South Equatorial Undercurrent (SEUC).
ll at 23~ in April 2000 confirms that the zonal currents near the equator described earlier are permanent features. Despite the intensive literature regarding equatorial waves, there is at present increasing discussion about strong wave influence on these currents, e.g. on the EIC, which seems to be responsible for the observed changes in strength. 4.2. Variability The TOPEX/POSEIDON altimeter records are an ideal data set to investigate seasonal and longer-term variability in the geostrophic surface velocity field of the tropical Atlantic. Figure 5 shows the amplitude and phase of the annual and semiannual cycle of the ZVA in the central tropical Atlantic Ocean. While the annual cycle dominates in the western part, the semiannual cycle dominates in the central and eastern part of the equatorial Atlantic, east of 30~ The strong signal in the annual cycle at 5~ is connected to the seasonal variability of the NECC generated by the movement of the Intertropical Convergence Zone (ITCZ). No similar variability can be found south of the equator. Apart from the strong signal associated with the NECC, the ZVA is amplified equatorward. At the equator, the amplitude of the annual cycle reaches about 15 cnds and the amplitude of the semiannual cycle about 20 ChriS. These signals can be associated with equatorial trapped waves on seasonal time scales. The phase velocity of these waves that can be calculated from the sea level anomaly (SLA) data, suggesting that these waves are of lower baroclinic modes. Thus, although the phase of the velocity anomaly as a function of depth results from the superposition of the different equatorial waves, the variability of the ZVA at the sea surface also suggests a seasonal variability at the depth range of the EUC and EIC. The computations of the geostrophic transports of the sSEC showed low variability but the sections were all taken between J a n u a r y and April. Figure 6 shows an latitude-time plot of the ZVA at 23~ south of the equator. Strong signals in the seasonal variations of the ZVA (6-months low-pass filtered data) as well as in the interannual variations of the ZVA (16-months low-pass filtered data) can only be found north of about 8~ with maximum values near the equator. As mentioned before, these variations in the ZVA can be associated with equatorial trapped waves on seasonal and longer-term time scales. South of 8~ the generally weak variability of the ZVA is caused by off-equatorial Rossby waves (see e.g. D56s 1999). Maximum values of the ZVA in the latitudinal range between 10~ and 25~ are around 2 cm/s. Thus, the weak variations in the sSEC described from hydrographic data are confirmed by the TOPEX/POSEIDON time series. 4.3. N e a r - e q u a t o r i a l M e r i d i o n a l Evidence for near-equatorial movement in the central tropical described below, although, these
Flow meridional flow and cross-equatorial water Atlantic is provided by floats which will be movements might be related to equatorial
12 waves. One float released in 1994 at about 800 m depth at the equator was trapped by an equatorial wave of the order of 500 km wavelength, 100 km amplitude and of 50 days periods (Boebel et al. 1999) and progressed with this wave westward near the equator. This shows that the instant velocity observations from the shipboard ADCP (Figure 4b) do not prove cross-equatorial flow. During the Meteor and Sonne cruises APEX floats were deployed to drift either at 200 m or 400 m depth. Some of the float trajectories do indeed suggest cross-equatorial exchanges. However, profiling floats have two important shortcomings compared to Lagrangian followers: after surfacing they do not necessarily return to the same water mass and they drift at fixed depth rates rather than following isopycnals. Float 115 (Figure 8a) was deployed for a drift depth of 200 m just south of the equator at 35~ on 12 April 2000 in a region where the shipboard ADCP (Figure 7) measured northeastward flow. Float 115 left the equatorial region first northwestward with the northern band of the SEC (nSEC), then entered the NEUC and was transported eastward to 28~ where it left the NEUC and stagnated in a region near 9~ 28~ before it continued northeastward. In May/June 2002 it probably reached the southern reaches of the NEC. This float moved clearly northward from the equator at 35~ Float 114 (Figure 8a) was deployed on 14 April 2000 at 3~ 34~ for a drift depth of 200 m. This float drifted eastward at the northern side of the SEUC to 19~ At this location it location it changed direction, as it came under the influence of the eSEC due to a slight northward shift. On 5 May 2001 the float crossed the equator and it was trapped near the equator without larger zonal movement. In October 2001 it moved southward again and returned to near its starting position in December 2001. In 2001 this trajectory followed two of the major near equatorial current bands of the near equatorial circulation, and shows that strong interaction of the different current bands may occur. In 2002 the float drifted almost directly northward and crossed the equator, reaching 2~ in June 2002. Float 123 (Figure 8b) was deployed during the RV Sonne cruise on 19 November 2000 at 5~ 32~ for a drift depth of 400 m. This float was expected to flow eastward with the SEUC, but it stagnated for some weeks and it then moved mainly northward and reached the equator on 20 June 2001, where it was also trapped near the equator without major zonal or meridional movements until December 2001. In spring 2002 this float got a southeastward component and crossed 2~ in May 2002 before turning northeastward in June 2002. The flow field in the lower layer of the AAIW was investigated by Schmid et al. (2001) from P A I ~ C E floats launched in the summer of 1997. The floats drifted at about 1000 m depth and displayed several well defmed currents between the equator and 4~ which are in good agreement with the Stramma and Schott (1999) schematic. Schmid et al. (2001) state that 1000 m floats showed no significant cross-equatorial flow, although all floats that were deployed at the equator (their figure 11), after following the equator westward for some time, moved into the North Atlantic, either as one float at the western boundary, or as
13
Figure 4. Velocity distribution along 23~ in March/April 2000 calculated from a combination of shipboard and lowered ADCP data in the upper 400 m and from the lowered ADCP below 400 m. The horizontal influence radius is 0.2 ~ with a cutoff radius of 0.4 ~ and vertically 25 m (50 m) influence radius in the upper (lower) 400 m with 50 m (100 m) cutoff radius. The velocity distribution is shown for a) Zonal currents in cm/s, positive is eastward, and b) meridional currents in cm/s, positive is northward. Shown are a) the Equatorial Undercurrent (EUC), the South Equatorial Undercurrent (SEUC), the South Equatorial Current (SEC) the Southern Intermediate Countercurrent (SICC), the Equatorial Intermediate Current (EIC), the Northern Intermediate Countercurrent (NICC) and the Northern Equatorial Undercurrent (NEUC).
14
Figure 4 continued
the other floats in the central Atlantic. All these floats were tracked to locations between 4~ and 8~ The one deployed farthest east at the equator at about l l~ left the equator northward after drifting to 15~ and was shown to make its way to 5~ near the
15 African continent. This observations is in contrast with SOFAR-float observations in 1989/90 at 800 m depth, where Richardson and Schmitz (1993) described a general northwestward velocity trend within 200-300 km of the 800 m contour of the South American continent but southeastward velocity further offshore for two floats deployed at the equator. The observations from the floats deployed in summer 1997 and in 2000 indicate northward float tracks towards or across the equator in the western part of the tropical Atlantic within the upper kilometer. The upper ocean floats are
Geostrophic Zonal Velocity Anomaly Annual Cycle
Semiannual Cycle
Figure 5. Amplitude and phase of the annual and semiannual cycle of the geostrophic zonal velocity anomaly (ZVA) in the central tropical Atlantic from TOPEX/POSEIDON data. The phase of the annual cycle is given in month of the year (1 denotes January) and the phase of the semiannual cycle in month of the half-year (1 denotes January and July).
15
Geostrophic Zonal Velocity Anomaly at 23~ [cm/s] Periods >= 6 M o n t h s
Figure 6. Latitude-time plot of the geostrophic zonal velocity anomaly at 23~ as calculated from TOPEX/POSEIDON sea level anomalies for 6-month low-pass filtered data (upper panel) and 16-month low-pass filtered data (lower panel). Contour levels shown are +/-(0, 2, 10, 30 cm/s) for the upper panel and +/-(0, 1, 2, 5, 10 cm/s) for the lower panel. well away from the western boundary current regime, hence they are not transported with the western boundary current. Our floats deployed in 2000 reached the sea surface every 9 days and might be displaced during this time. However, from the positions during the stay at the surface it was determined that the floats presented here did not receive their meridional displacement at the surface. A meridional movement toward the equator not following the major cross-equatorial flow can be observed as in the case of two SOFAR-floats at 800 m depth in 1989/90 (Richardson and Schmitz 1993). Also our float 123 showed a southward component in early 2002. The main reason for the variability of the cross-equatorial float track directions are equatorial wave motions. Another process which could lead to a crossing of the equator could be a meandering of the
17
Figure 7. Distribution of the velocity-vectors from the shipboard ADCP on RV Meteor in March/April 2000 at 175 m to 225 m. Current names are included for the North Brazil Undercurrent (NBUC), the South Equatorial Undercurrent (SEUC), the central band of the SEC (cSEC), the Equatorial Undercurrent (EUC) and the North Equatorial Undercurrent (NEUC).
NBC retroflection feeding the EUC. The mean profile from seven ADCP sections crossing the equator at 35~ showed a n o r t h w a r d component in the EUC layer. Whether there is a net cross-equatorial flow in the central Atlantic in addition to cross-equatorial exchanges via thermocline convergence, upwelling and E k m a n divergence is still unclear.
18
Figure 8. Trajectories of profiling APEX floats (status 15 June 2002) in the tropical Atlantic for a) float 115 deployed on 12 April 2000 at 0~ 35~ drifting at 200 dbar, and float 114 deployed on 14 April 2000 at 3~ 34~ drifting at 200 dbar and b) float 123 deployed on 19 November 2000 at 5~ 32~ drifting at 400 dbar. The deployment position is marked by a square, the positions of the surface drift every 9 days are shown by a series of dots, and the date of last surfacing is show at the end of the trajectory.
19 5. D I S C U S S I O N The meridional WOCE sections as well as the TOPEX/POSEIDON measurements show that the southern band of the SEC has nearly constant flow with weak variability. As this is the major water source of the upper ocean equatorial current system, only weak remote flow variability is imprinted on the equatorial currents by the sSEC. Nevertheless, climate signals from the subtropical South Atlantic could be contained in the water masses transported by the sSEC. The larger variability observed in the NBUC at 5~ (Schott et al. 1998) and in the zonal equatorial currents (e.g. Molinari 1982; Schott et al. 1998; Bourles et al. 1999) has to be related to equatorial processes but not to sSEC variability. Recent observations from lowered ADCP sections show that the current bands of the mean flow field described earlier for the central tropical Atlantic are permanent features. Molinari et al. (1999) observed westward flow between about 500 m and 1100 m depth on a zonal section along the equator between 10~ and 40~ in July 1997, which reflects the continuous zonal extent of the Equatorial Intermediate Current. However, variability in part caused by wave phenomena exists which make the flow field more difficult to investigate. The largest variability is observed near the equator and at 5~ the latter connected to the seasonal variability of the NECC. APEX float trajectories indicate strong interaction of the different current bands. The floats at 200 m and 400 m move in some instances across the equator in the central part of the tropical Atlantic. Observations exist for cross-equatorial float trajectories northward as well as southward, and might be connected to wave phenomena. The different observations indicate that a large continuous contribution of the northward cross-equatorial flow in the upper ocean will take place at the western boundary (Schott et al. 2002), and it remains unclear whether there is a net cross-equatorial flow in the central Atlantic in addition to cross-equatorial exchanges via thermocline convergence, upwelling and Ekman divergence. The strong salinity gradient across the equator in the AAIW layer (Figure 2a) as well as the oxygen gradient in the central water layer (Figure 2b) further show that cross-equatorial flow can not be a major exchange path in the central Atlantic. From two hydrographic sections across the Atlantic at 7~ and 4~ Arhan et al. (1998) proposed a northward path through the eastern basin for the SACW. It seems that the central equatorial Atlantic is governed by zonal flow with some cross-equatorial float paths biased to a northward direction. As the equator is a potential vorticity barrier there should be no mean crossequatorial flow in the central Atlantic, but whether there are other reasons than equatorial waves for the float paths crossing the equator is unknown. For the western boundary the cross-equatorial exchange within the North Brazil Current is well investigated while the cross-equatorial flow and its seasonal variation at the eastern boundary off Africa still is far from being resolved.
20
Acknowledgements We acknowledge financial support by the Bundesministerium ftir Bildung und Forschung, Bonn, Germany, grants 03F157A, 03F0246A, as part of the German WOCE and CLIVAR programs and 03G0151A for the RV Sonne cruise.
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22 South Atlantic Ocean, Journal of Geophysical Research, 104, 20,863-20,883, 1999. Stramma, L., and F. Schott, The mean flow field of the tropical Atlantic Ocean, Deep-Sea Research II, 46, 279-303, 1999. Talley, L.D., Antarctic intermediate water in the South Atlantic, in Wefer, G., W.H. Berger, G. Siedler and D.J. Webb (editors), The South Atlantic - present and past circulation, Springer Berlin, pp. 219-238, 1996. Weisberg, R.H.,and C. Colin, Upper ocean temperature and current variations along the equator in the Atlantic Ocean during 1983-1984, Nature, 322, 240243, 1986. Weisberg, R.H., and T.J. Weingartner, Instability waves in the equatorial Atlantic Ocean, Journal of Physical Oceanography, 18, 1641-1657, 1988.
Interhemispheric Water Exchange in the Atlantic Ocean edited by G.J. Goni and P. Malanotte-Rizzoli Published by Elsevier B.V.
C o m p a r i s o n of h y d r o g r a p h i c and a l t i m e t e r b a s e d e s t i m a t e s of sea l e v e l h e i g h t v a r i a b i l i t y in the Atlantic O c e a n Dennis A. Mayer, Molly O. Baringer* and Gustavo J. Goni National Oceanic and Atmospheric Administration, Atlantic Oceanographic and Meteorological Laboratory, 4301 Rickenbacker Causeway, Miami, Florida, 33149 Our ability to understand the means by which mass and heat are exchanged between the tropics and subtropics is seriously compromised when using only sea level data because the exchange processes span a wide range of variability across the different dynamical regimes in our domain. Expendable bathythermograph (XBT) profiles and TOPEX/Poseidon (T/P) altimeter data are compared to temperature anomalies (TA) and to dynamic height anomalies (DHA) for the period 1993 through 1997 to determine how much can be inferred about the internal field of mass from sea level changes. Our focus is on the annual cycle along two well-sampled XBT sections on the western and eastern sides of the Atlantic Ocean from 10~ to 40~ XBT profiles were matched (time/location) to Sea height anomalies (SHA) derived from T/P data, converted into DHA using TS relationships and then binned monthly into 2~ of latitude by 4~ of longitude boxes. The vertical mass distribution cannot always be inferred from SHA alone, unless there is a strong relationship between SHA and DHA and an understanding of the details of how temperature variability affects DHA. These relationships can be problematic if SHA are small. This occurs in zones of transition in the vicinity of troughs where small fluctuations in SHA belie the true nature of water column variability. These areas separate the mid-latitudes where surface buoyancy fluxes dominate from those in the equatorial region where ocean dynamics cause thermocline effects that dominate the forcing of sea level. Thus, the variability of SHA in transition regions tends to be small because both surface and thermocline variability may be significant but compensating in nature. This emphasizes how important direct observations (in situ data) can be in interpreting SHA correctly. Strong relationships between SHA and DHA occur at locations where more than half of the SHA variance in the annual cycle is due to DHA variability (approximately 30% of the positions along the two XBT sections). These relationships between SHA a n d D H A for residual v a r i a b i l i t y Corresponding author. Tel 305-361-4345. Fax 305-361-4412. Email: molly.baringerC~oaa.gov.
24 (obtained by removing the annual cycle) are weak. The exceptions are in two areas of large sea height variability in the western basin where there is significant interAnnual variability. The first is in the tropics in the vicinity of the tropical gyre trough near 50~ 8~ The second is in the Gulf Stream near 70~ 38~ An analysis of Panulirus data at (32.2~ 64.5~ suggests that in situ data may be needed down to at least 1000m where interannual variability accounts for about 40% of the SHA variance. 1. I N T R O D U C T I O N
Our objective is to investigate the relationship between the structure of upper ocean water column variability and its associated sea height anomaly (SHA). This is a critical issue when deriving inferences about the water column when only SHA measurements are available. In this paper, we focus on two wellsampled meridional sections in the western and eastern Atlantic Ocean that extend from 10~ to 40~ (Figure 1), where expendable bathythermograph data (XBT) data are most plentiful. The XBT locations are displayed on the mean 500m dynamic height field, which serves as a proxy for the geostrophic circulation field (Figure la). Both sections cross several dynamically distinct regions, e.g. in the tropics the seasonal North Equatorial Counter Current (NECC) and the tropical gyre and to form a basis of comparison, also across the northern subtropical gyre. The relationships between SHA and subsurface temperature variability can thus shed some light on where useful inferences about the subsurface mass field can be made in dynamically distinct regimes. The variability of the upper ocean mass field, which is embedded in altimeter observations on large scales, has been studied using both surface observations and model results. Observationally, Stammer (1997) investigated the underlying causes of sea level variability in TOPEX/POSEIDON (T/P) data using surface observations and linear vorticity arguments applied to theoretical wind induced circulation changes. He found that in mid-latitudes, buoyancy fluxes dominate SHA variability, while in the tropics, vertical movements of the thermocline, caused mostly by changing winds and near-surface currents, dominates. Using numerical models, Fukumori et al. (1998) and Ferry, Reverdin and Oschlies (2000) (hereinafter FRO), found similar results using a combination of surface data and model fields. These f'mdings are consistent with earlier studies of the oceanic thermal structure. For example, Gill and Niiler (1973) described the importance of seasonal variability of surface buoyancy fluxes on the mid-latitude temperature structure of the upper ocean. In contrast, Merle and Arnault (1985) discussed the importance of thermocline variability in forcing temperature changes in the tropics by virtue of wind-driven ocean dynamics. Carnes et al. (1990) and Blaha and Lunde (1992) compared inferred temperature profiles and sea height derived from Geosat observations to air deployed XBT data. The largest discrepancies between the two are found in regions of large
25
Figure 1. Two well-sampled western and eastern sections for expendable bathythermograph, (XBT) data denoted by large red dots and yellow boxes. These are positioned at the center of 2~ latitude by 4~ of longitude boxes in which the data were binned. (a) Dark shading indicates areas of the highest density of profiles near major shipping routes where 30 months or more out of a possible maximum 60 months are available for the five years (1993-1997). The eight yellow boxes selected for detailed analysis have at least 41 months of data. The large dark cross indicates the location of the Panulirus station. The 500m dynamic height field is superimposed. Contour interval is 0.05 dynamic meters. The tropical ridges (heavy dark lines) and troughs (heavy dashed lines) are indicated. (b) Satellite tracks for T/P superimposed on the root mean square (rms) deviation of sea height anomalies (SHA).
26 horizontal gradients (differences occasionally exceeding 1.4 m). Using more reliable T/P data, White and Tai (1995) evaluated the role that T/P data can play in estimating upper ocean internal energy anomalies (note they called this heat content, see Warren (1999)) over large portions of the global oceans. They compared internal energy anomalies derived from interpolated XBT data to T/P SHA data and found good agreement on a global scale for the period 1993 to 1994. Gilson et al. (1998) compared T/P SHA signals to those found in an eddyresolving XBT section across the subtropical North Pacific. They found that the 5.2 cm root mean square (rms) of the differences are scale dependent and dominated by scales longer than 500 km. Differences increase near the western boundary, however the signal to noise ratio also increases. They also found that the differences are smaller when in situ salinity data from expendable conductivity temperature depth probes were used instead of climatological salinity data. Many authors have attempted to infer subsurface information from surface fields either through statistical means (e.g. Hulburt et al, 1990) or through dynamical application of surface conditions within a model (e.g. Cooper and Haines, 1996). The combination of SHA derived from satellite altimeter data and in situ temperature and salinity data directly, should be a first step towards studying the dynamics of the upper ocean. In this paper, we show that in situ data, such as XBT data, used together with remote sensing data sets are essential to aid in modeling studies of ocean dynamics, climate forecasts and global sea level changes. Within this context, altimeter data combined with XBT data aid in the interpretation of the variability of the entire water column. In particular, the pathways of mass and heat between the South Atlantic and the North Atlantic across the complex equatorial region of zonal currents that is central in the exchange processes connecting the tropics and the subtropics, can be difficult to quantify if only altimeter data are used. In situ data are needed to interpret sea level changes in terms of how the structure of the upper ocean (density field) is organized. Disregarding tidal effects, changes in sea level can be caused by a combination of surface buoyancy fluxes and ocean dynamical adjustments, either baroclinically through subsurface density changes or barotropically. In the analysis that follows we emphasize subsurface observations and examine in detail the vertical structure of the relationships between SHA and water column variability. Comparisons have been made between SHA from T/P data, TA profiles from XBT's and estimates of dynamic height anomalies (DHA). Because changes in sea level are a consequence of both surface fluxes and ocean dynamics (thermocline variability), we will show that these effects can act in opposition in certain transition regions of the Atlantic (Mayer et al., 2001) to diminish the magnitude of sea level variability there. This chapter is organized as follows. The data sets are introduced in section 2. In section 3 the extent to which TA and DHA can be estimated from SHA data is investigated by means of a regression analysis. Although this work emphasizes the annual cycle (i.e., the monthly means), the interannual variability is also considered. The inferences drawn from our analy~es are discussed in ~ection 4 and ~ummarized in g~ction 5.
27 2. DATA AND M E T H O D S Historical XBT profiles are not spaced uniformly. The highest density of profiles can be found along major shipping routes and in near-coastal regions. Consequently, for comparing time series of TA and DHA with SHA, XBT positions were chosen in areas (which we will term 'sections', though no single ship proceeds along these lines) with the most data along the western and eastern regions within the Atlantic (Figure la). XBT data was binned into a 2~ of latitude by 4~ of longitude boxes in order to compensate for the non-uniform distribution in space and time (Mayer et al 1998). There are 52 selected positions along both sections where the analysis was made. However, only approximately half of them (31) subjectively qualify for a detailed analysis by virtue of adequate temporal sampling (40 months out of a possible 60 months). Of these, the eight positions indicated by the yellow boxes in Figure 1 were selected as representative of the different regions of variability in the analysis domain. The data sets of SHA, TA and DHA in the analyses and discussions that follow represent only departures (anomalies) from the mean background state. The mean background state is referenced to the five years 1993-1997 (the period in common for XBT and T/P data) and anomalies are computed over this time period. Units of DHA are scaled by 10/g, where g is the acceleration of gravity. 2.1. H y d r o g r a p h i c data Along the two sections, there are 8012 individual XBT profiles, which were binned and then matched with the SHA data as explained below. Quality control procedures for the XBT data are given in Molinari et al. (1997). Of the total number of profiles, only 60% reach a depth of 750m but 73% extend to 500m. Thus, to utilize as much data as possible a reference depth of 500m was chosen and unless otherwise stated, DHA values quoted herein are referenced to 500m. Inferred DHA were derived by combining the XBT profiles with the salinity values determined from the local seasonal T verses S relationship obtain from the 1~ x 1~ Levitus monthly climatology (Levitus, 1982). Issues concerning the effect of varying reference levels and errors induced by using climatological versus actual salinity profiles were estimated by using T,S profiles from the Panulirus station (32.2~ 64.5~ (Talley and R a y m e r , 1982). While the Panulirus data is well outside the tropical Atlantic and will not contain the same sensitivity to salinity variability expected in the tropics, the time series provides the best available data to assess temporal variability without contamination from spatial variability. 2.2. A l t i m e t e r d a t a The spatial coverage by T/P is indicated by the satellite ground tracks (Figure lb), which the satellite repeats approximately every 10 days. The along track resolution is 9 km and the separation between consecutive ground tracks is
28 approximately 300 km on the equator. The altimeter data contain the standard corrections for wet and dry troposphere, earth and ocean tides (Cartwright and Ray, 1991), inverse barometer and sea state bias (Cheney et al., 1994). Altimeter errors, including environmental corrections, are estimated to be at worst only 5 cm for single-pass sea level measurements (Cheney et al., 1994). The SHA data were matched in both time and position to individual XBT profiles. Daily SHA gridded (0.1 degrees) fields were computed using a Gaussian interpolator of 0.5 degrees. The SHA value corresponding to each individual XBT observation was obtained by matching the closest SHA grid point to the XBT location. The SHA is then binned into the 2~ latitude x 4 ~ longitude boxes and averaged by month for the 5 year period (1993-1997) used as a reference for the sea height and dynamic height anomalies. The rationale for 2 ~ x 4 ~ binning is offered in Molinari et al. (1997). For the Panulirus site (32.2~ 64.5~ the altimeter data were averaged within 1~ of this location and were obtained from one descending altimeter ground track. Ascending and descending tracks improve the spatial resolution further (Le Traon et al., 1990), with length scales that can be resolved by altimeter data well within the resolution of the 2~ x 4 ~ boxes. Although there are spatial and temporal limitations imposed by the number of XBT observations, all of the T/P data can be used. With all available T/P data in each of the 2~ 4~ boxes, monthly means (annual cycle) were computed for comparison with the smaller matched set corresponding to the XBT data. 3. ANALYSIS
3.1. B a c k g r o u n d s t a t e s and c l i m a t o l o g y Although the mean background states of sea level and dynamic height cannot be compared because of uncertainties in the mean sea surface height field derived from T/P altimeter data, a geophysical context can be provided by superimposing the positions of the two western and eastern sections on the mean dynamic height field referenced to 500m (Figure la). This dynamic height field was derived using the TS relationship from the Levitus climatology as described above, together with the temperature climatology (Mayer et a/.,1998). The circulation gyres of the mean geostrophic velocity field in terms of their temperature climatology and Sverdrup stream function have been studied by Mayer and Weisberg (1993). These circulation gyres are consistent with the mean dynamic height field seen in Figure la, which shows the northern hemisphere subtropical gyre and the tropical gyre just north of the equator. The equatorial gyre, which straddles the equator, is not clearly indicated due in part to the failure of geostrophy close to the equator and the complicated vertical structure down to 500m (Mayer et al., 1998). Both sections can be seen to cross tropical and subtropical gyres and hence, are embedded in many different dynamical regimes that span a broad range of variability. The v a r i a b i l i t y of the circulation g y r e s is m a n i f e s t e d as d e p a r t u r e s
29
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30 (anomalies) from the mean background state. Most regions in our domain have a reasonably large annual cycle. However, where the annual cycle is small, interannual variability and/or higher frequencies prevail (periods less than three months). These higher frequency fluctuations may be real or be caused by aliasing due to temporal and spatial sampling of XBT profiles. Recently, Stammer and Wunsch (2000) addressed the aliasing problem and suggested that barotropic aliasing is problematic in high latitudes. Along our sections however, their estimates of barotropic aliasing of SHA amount to no more than an rms of 2 cm. Henceforth, the term "residual" will refer to data from which the mean annual cycle has been removed. Thus, the "residual" contains both interannual variability and the higher frequencies just discussed. Qualitatively, the effects of the annual cycle on the field of mass can be obtained by looking at the seasonal extremes (March and September) of the western and eastern temperature sections (Figure 2). The seasonal extremes from a smoothed annual cycle were determined by reconstructing the temperature using only the annual and semiannual harmonics. A major difference between the winter and summer seasons are that in winter the isotherms slope almost vertically down from the surface south of 35~ in both sections. The seasonal cycle of temperature profiles in the tropics is evident in the thermocline along both sections. Thus, the largest variability is near the surface north of 20~ in the subtropics, while it is in the 50-200m depth range in the tropics from about 5~ to just north of 10~ Using similar meridional sections Mayer et al. (1998) showed that most of the variability is captured in the upper 200-300 m of the water column. For the eight representative locations (yellow boxes in Figure 1), the annual cycle of the TA profiles (Figure 3) and the temperature depth anomalies, the annual cycle and time series of SHA and DHA with respect to 500 m are examined here. In the tropics in the vicinity of and just north of the equator, the range of temperature that characterizes seasonal extremes is larger below the surface (Figures 3b and 3c and Figures 4b and 4c, middle panel). This is caused by the seasonal cycle of the zonal currents (wind-driven ocean dynamics) and their ridge-trough system (Figure la) manifest as changes in the depth of the thermocline. In the subtropics (Figures 3f-3h and Figures 4f-4h, north of 30~ the range is larger near the surface and is a consequence of the annual cycle of surface buoyancy fluxes. Near the equatorial trough (Figures 3a and 4a, near 34~ 4~ and in the vicinity of the North Equatorial Countercurrent (NECC) trough (Figures 3d and 4d, near 50~ 8~ and 3e and 4e near 26~ 14~ as examples), there are competing influences due to a combination of both surface and thermocline variability that act in opposition. Here, surface and thermocline variability are negatively correlated and their contributions to SHA tend to cancel resulting in diminished SHA. Areas that are characterized by competing influences are termed in this work transition regions and exist between where thermocline variability dominates SHA and where surface fluxes dominate. In the immediate vicinity of the equator, complex processes that are related to equatorial upwelling also conspire to produce surface and thermocline variability that are negatively correlated but for reasons t h a t differ from those in
31
Figure 3. Profiles of temperature anomalies (TA) for eight representative positions indicated by the yellow boxes in Figure 1 for the annual cycle. The thick dashed green/solid red curves correspond to the minimum/maximum temperatures achieved for the month indicated in each legend. The thin black curves are the inferred TA profiles discussed in the text. The thin dashed purple curves are all other months.
32
Figure 4. Depth dependence of temperature anomalies (TA) for the eight positions as in Figure 3 for the 5 yr period 1993 through 1995 (left panels), for the annual cycle repeated for 5 yr (middle panels), and time series of SHA and DHA with respect to 500m (right panels). Anomalies are negative (blue) positive (red). Missing data were filled with the annual cycle.
33 transition regions. Rossby and Kelvin waves affect the vertical temperature profile and thermocline depth and sea height (Franca et al, this volume). These waves deepen or raise the thermocline, where the deepening of the thermocline (downwelling) leads to a warming effect. The opposite takes place when the thermocline rises due to an upwelling event, thus leading to compensating effects on surface dynamic height.
3.2. R e g r e s s i o n b e t w e e n SHA and TA and DHA A linear regression scheme provides a description of the relationship between SHA and TA and DHA. For DHA with reference depths from 50-500m, correlation and regression coefficients are plotted in Figure 5. The linear approximation utilizes the SHA as the predictor or input, and the TA or the DHA as the predictand or output, thus relating a scaled delayed SHA to both TA and DHA. For TA, TA(z,t) = r (SHA(t- ~)) + noise, where TAm(z,t) = r(z) (SHA(t - Z)) is the modeled TA (and similarly for DHA). Hence the regression coefficients (r) have units of gain and are ~ cm -1 if TA are the predictands and the time delay or lag (Z) is in months. These inferred TA profiles are also plotted along with the observed TA profiles in Figure 3. If DHA are the predictands, the units of gain are dyn. meters m -1 or dyn. centimeters cm-1. Questions about the spatial resolution of 2~ 4 ~ binning, involve whether or not the results presented here would have changed substantially if better resolution had been available. One region was densely sampled enough so that sensitivity to spatial resolution could be considered. In the western section sufficient data (64% of the total number of observations from the original 2~ 4 ~ box) are available in a 1~ of latitude by 1.5 ~ of longitude area centered at 70.25~ 37.5~ The same binning procedures were used as described above. The results are essentially the same as indicated by the large dot at 37.5~ in Figures 5a and 5c. Other regions however, lack the data density to consider the effects of spatial resolution.
3.3. Correlations In the western section (Figure 5a) the correlations between SHA and DHA (with respect to 500m) south of the equator from 10 to 4~ in the equatorial gyre are low, in that they fall below the 90% confidence limit as determined by the method of Sciremammano (1979), which accounts for serial correlation in the time series. They are also low in the tropical gyre near 6~ and again near 14~ just north of the tropical gyre axis in the region of the NECC trough and at 36~ in the subtropical gyre. The correlations are high within several degrees of the equator (0~176 and in the subtropical gyre from about 16 to 34~ In the eastern section (Figure 5b) correlations are low f r o m a b o u t 10 to 24~ a n d a t
34 SHA and DHA ,. ,. ,.
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F i g u r e 5. C o r r e l a t i o n s b e t w e e n sea h e i g h t a n o m a l i e s (SHA) a n d d y n a m i c h e i g h t a n o m a l i e s (DHA) for (a) t h e w e s t e r n section a n d (b) t h e e a s t e r n section. G a i n s for (c) t h e w e s t e r n section a n d (b) t h e e a s t e r n section. S H A a n d X B T d a t a w e r e m a t c h e d in t i m e a n d space before b i n n i n g by m o n t h in e a c h 2 ~ of l a t i t u d e by 4 ~ of l o n g i t u d e box. C u r v e s for D H A a r e r e f e r e n c e d to d e p t h s f r o m 5 0 m to 500m. U n i t s for g a i n a r e d y n a m i c m e t e r s m "1 or d y n a m i c c e n t i m e t e r s cm "1. In t h e w e s t e r n section a s e p a r a t e a n a l y s i s w a s p e r f o r m e d on a 1~ of l a t i t u d e by 1.5 ~ of l o n g i t u d e box c e n t e r e d at 70.25~ 37.5~ The r e s u l t i n g c o r r e l a t i o n a n d g a i n (a a n d c, r e s p e c t i v e l y ) a r e i n d i c a t e d by t h e l a r g e dot at 37.5~
35
Figure 6. Sea height anomaly (SHA) and dynamic height anomaly (DHA) and their regressions (inset) at (a) 70~ 38~ and (b) 42~ 2~ Time series of SHA and DHA are normalized by their standard deviations (rms values). To rescale the data multiply each of the time series by their corresponding rms values.
38~ and negative n e a r 14~ The correlations are high just north of the equator in the southern p a r t of the tropical gyre from 0 to 8~ and in the subtropical gyre from about 26 to 36~ The reasons t h a t the correlations between SHA and DHA
35
Figure 7. Seasonal range for indices of near surface (upper left panel, 0-30m) and thermocline (upper right panel, 50-200m) temperatures (~ and the regression between them. Lower left (right) panel shows the correlation (gain) field where the blue (red) are negative (positive). Also shown are green x's where DHA with respect to 500m can account for half or more of the SHA variance. Yellow x's denote transition regions. are high or low depend on the details of how temperature variability in the water column relates to SHA. The relationship between the time series of SHA and DHA in some instances may not be straightforward, shown by the depth dependence of temperature and its relationship to SHA (Figure 4). These relationships can be complex and are generally problematic where SHA are small. Of particular interest is the importance of the annual cycle in the thermocline and how it affects the DHA from 4~ to 14~ (Figures 4a-4e, middle panels). Along the NECC ridge just north of the equator (Figures 4b and 4c), the thermocline variability is dominant and contributes the mo~t to the DHA. The
37 amplitude of the annual cycle is of roughly 7 dyn. cm in the vicinity of the NECC ridge (Merle and Arnault, 1985). This is consistent with the results of DHA (Figures 4b and 6b). In the transition region near 14~ (Figure 4e), the competing influences between surface and thermocline processes are offsetting in their contributions to DHA. Neither changes in thermocline depth or surface processes dominate the variability. Because of this, the areas of transition in the vicinity of trough regions have poor correlations that are intuitive after inspection of the TA with depth fields and the time series of SHA and DHA (Figure 4e). Farther north in the subtropics, surface processes are dominant and contribute most to the DHA. Near 32~ there is a phase lag as a function of depth (Figure 4f). This lag is an artifact of temperature anomalies taken around a mean value and is due to the erosion of the seasonal thermocline through penetrative convection. To appreciate how temperature changes of the upper ocean for the annual cycle co-vary with each other throughout the analysis domain, temperature range and unlagged correlations (Figure 7) between indices of near surface temperature over the upper 30m or so and the thermocline (50-200m) were computed from the 12 month climatology derived in Mayer et al. (1998). The range fields provide definitive areas where surface and thermocline variability are important and are consistent with the discussions above, except that the whole domain is considered rather than just the two western and eastern sections. Surface variability is organized around the mean position of the Intertropical Convergence Zone. Thermocline variability is greatest in the tropics because of ocean dynamics in the vicinity of the equator and the NECC ridge and north of 30~ because of late winter convection (Figure 2). For the correlations and gains (lower panels), the negative shadings delineate the transition regions where surface and thermocline temperature indices are out of phase in the vicinity of the equatorial trough and the NECC trough and include the areas where correlations between SHA and DHA are small. The transition regions along both sections are indicated by the yellow x's in Figure 7. Here, small SHA variability does not always mean that in situ variability is low; just that there are competing processes that diminish observed SHA as in Figures 3e and 4e. For instance, we know variability in the North Brazil Current Retroflection region is high (Figure 1), however competing wind stress driven dynamics adjust the thermocline upwards during summer when surface heating is at a maximum. Directly on the equator correlations are negative in the west and positive in the east. However, there is no evidence of a simple relationship between SST and the thermocline (Weingartner and Weisberg, 1991). The physics entail SST and thermocline variations that are most closely controlled by ocean dynamics when the thermocline is adjusting to basin-wide seasonal changes in the wind stress field. Franca et al. (this volume) show that Kelvin and Rossby waves can have substantial amplitude at annual period that in turn effect sea height and thermocline depth.
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3.4. Variance
explained
The a m o u n t of variance explained for TA or DHA by scaled delayed SHA, is obtained by s q u a r i n g the correlations. R e p r e s e n t a t i v e time series of SHA and DHA from two of the eight locations in Figures 1, 3 and 4 along with their regressions are shown in Figure 6, one in the tropics (Figure 6a, 42~ 2~ where m a x i m u m variability is in the seasonal thermocline and a n o t h e r in the Gulf S t r e a m (Figure 6b, 70~ 38~ w h e r e most of the variability is n e a r the surface. For the most part, the correlations are m a r g i n a l l y significant with respect to a 90% significance level for the null hypothesis d e t e r m i n e d by the method of S c i r e m a m m a n o (1979), which accounts for serial correlation in the
39 time series. The correlations will vary according to the integral timescale determined by the effective degrees of freedom (DOF), which is always less than the length of the time series. Finally, there are no significant lags that improve the correlations between SHA and DHA (i.e., T=O). As will emerge below, correlations are best away from transition regions and where the annual cycle is a significant component of the variability. To further explore the issues of inferred upper ocean structure for the annual cycle, there are locations where DHA can account for a large fraction of the SHA variability. Although somewhat arbitrary, these locations have been chosen where the rms of the differences (SHA minus DHA) reduces the variance of SHA by 50% or more (i.e., for a 50% reduction, the ratio [rms of the difference]/[rms of SHA] less than or equal to 0.707). The rms curves and the rms of the differences were computed for both the annual cycle (Figure 8) and then for the residual variance of SHA for the annual cycle is reduced by 50% or more and are also indicated by the green x's in Figure 7. These include four of the eight positions in Figures 3 and 4 (Figures 3b, 3c, 3f, 3g and 4b, 4c, 4f, 4g) and are candidates for deriving inferred TA profiles (Figure 3). The computation entails computing the regression coefficient (gain) and lag (time delay) between the SHA climatology for a particular location and the temperature climatology at that same location as explained above. Thus, the inferred TA profiles are just a scaled delayed SHA. In contrast, once the annual cycle has been removed the rms of the differences between residual SHA and DHA values (not shown) indicate that the variability of SHA generally can not be accounted for by DHA anywhere along the sections. Moreover, the importance of the annual cycle to the correlations is underscored when the correlations are derived from the residuals. With few exceptions they are no longer significant at the 90% SL and generally degrade substantially after removing the annual cycle. The few exceptions are important because these occur where interannual activity of some significance occurs. This occurs in the vicinity of 50~ 8~ (Figure 4d) and near 70~ 38~ (Figure 4h). There are some noteworthy features that these locations have in common. The annual cycle variance is less than the residual variance and the correlations are relatively unaffected by removing the annual cycle. Near 50~ 8~ the residual profiles (not shown) indicate that interannual variability is similar in amplitude and is confined to approximately the same depth range (50-200m) as that for the annual cycle (Figure 3d). Further, there is a warming trend that extends from 2/94 to 12/95 (Figure 4d). Farther north at 70~ 38~ the residual profiles (not shown) are relatively independent of depth and contrast with the maximum variability for the annual cycle, which is near the surface (Figure 3h). Also, the residual temperatures increase from 1/93 to 12/95 (Figure 4h). 3.5. P a n u l i r u s d a t a a n d r e f e r e n c e l e v e l s The Panulirus data provide an opportunity to consider the relationship between SHA and DHA down to depths of 2000m. The Panulirus station in located at 32.2~ 64.5~ (Talley and R a y m e r , 1982). Calculations were carried out down to 2000m to fully exploit the available data in ways that were similar to
40
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Thin c u r v e s are derived using inferred salinity f r o m Levitus 500
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Figure 9. Fraction of SHA variance (fractional variance, FV) accounted for by DHA for the five-year period (two thick curves) including the annual cycle (blue), without the annual cycle (red) and their difference (green). Thin blue (red) lines represent the fractional SHA variance explained by DHA computed using climatological salinity with (without) the annual cycle.
those using only XBT data. The altimeter data were obtained within 1~ from the Panulirus location. Therefore, questions about DHA in the deeper parts of the w a t e r column can now be addressed t h a t could not otherwise, had only XBT d a t a been available. Although the a m o u n t of d a t a available at the Panulirus station does not exist elsewhere, it does provide some perspective in allowing a more detailed examination of the relationship between SHA and DHA throughout the w a t e r column. The salient points here relate to the depths of a n n u a l cycle variability and residual variability. The latter is effectively the i n t e r a n n u a l component of variance and higher frequency fluctuations discussed earlier.
41 Using the hydrographic data, the two thick curves in Figure 9 are the fraction of SHA variance (fractional variance, FV) accounted for by DHA for the five-year period: Fv = 1 - variance (SHA-DHA) / variance (SHA). One of the curves includes the annual cycle and the other is for the residual alone. Also plotted is their difference that is essentially independent of depth below 100m. The difference curve shows, that in the vicinity of Panulirus, the annual cycle is effectively limited to the upper 100m (see also Figures 3f and 4f) and accounts for a little less than 30% of the SHA variance. The annual cycle is also limited to the upper 100m across the whole basin at this latitude (32~ as indicated by an analysis (not shown) of the temperature climatology from Mayer et al. (1998). For the residual variability, the DHA below 100m continue to account for a larger and larger fraction of SHA variance down to about 1000m. The implication here is that near this location, residual variability (i.e. with the annual cycle removed), which includes interannual variability, is a factor that accounts for a little more than 40% of the total variance at 1000m. Together with the annual cycle, the total variance accounted for is about 70% near 1000m. If the DHA were to perfectly match SHA at some reference depth, then the thick solid curve would approach unity at that depth. Although interannual variability at Panulirus is not well characterized by such a short record of only 5 yr, it is significant that essentially all of the SHA variance that can be accounted for by DHA is accounted for as a depth of 1000m is reached. Similar results were found by Roemmich (1990), who used an EOF analysis on Panulirus data alone. He found that the first EOF associated with the annual cycle, contains a surface maximum in the upper 100m. For yearly anomalies a secondary maximum is near 800m that decreases to negligible values below 1300m. Further, the results concerning correlations and gains (not shown) are consistent with those in Figure 9 in that values level off when nearing 1000m. The correlations with and without the annual cycle are both significant at the 9O% SL. 3.6. I n f e r r e d s a l i n i t y vs. in s i t u s a l i n i t y One of the shortcomings of our analyses relates to the lack of in situ salinity data. Questions arise over how estimates of DHA are compromised by using seasonal TS from the Levitus climatology (Levitus, 1982). This issue was addressed by performing calculations using the Panulirus data described above in ways that were similar to those using only XBT data. The goal was to evaluate the effects of including in situ salinity against those obtained using inferred salinity as if the in situ data were not available. As described in section 2, inferred salinity was derived from the 1~ x 1~ Levitus climatology. The most telling results from our inquiry into the effects of salinity is provided by the fractional variance curves in Figure 9. The fractional variance using inferred salinity (the two thin curves) is approximately the same magnitude as that using in situ salinity (the two thick curves). Although not
42 shown, the rms of the difference (SHA-DHA) using in situ salinity versus using inferred salinity is less than 0.5 cm at 2000m. However, the Panulirus station is in a benign region of ocean variability, e.g. away from strong gradients, fronts, etc. unlike some others in our analysis domain. As pointed out by Gilson et al. (1998), errors on scales of 1000 km and more increase from 0.5 to 2.4 dyn. cm when salinity sampling is absent. Moreover, there are locations in our domain where DHA using inferred salinity from the Levitus climatology would be impacted by high variability of Amazon water in the vicinity of 6~ in the western section. Thus, whether or not the results from Panulirus data apply elsewhere in the analysis domain is an open question and one that cannot be addressed with the available data. Despite this, these findings are encouraging and suggest that using seasonal TS in deriving inferred salinity is a reasonable approach.
3.7. Barotropic component Our ability to assign the fraction of SHA that is barotropic depends on obtaining accurate estimates of the baroclinic component and may be compromised by the uncertainties that relate to the computation of the regression coefficient (gain). The unlagged baroclinic component of SHA is: DHAm(t) = r (SHA(t)), where r is the gain. The calculation that provides the 90% significance level for the correlations also provides the number of DOF. The DOF are in a range from about 5 to 20 DOF and so a 90% confidence interval can be computed. For a gain of unity and DOF--10, the true value (r) is very roughly 0.3r' < r < 1.3r', where r' is the estimated gain. Thus, with such large error bars the ability to assign the fraction of SHA that is barotropic is problematic. In an ideal baroclinic ocean, if the internal pressure field completely compensates for the external field, the regression coefficient (gain) would be unity, the barotropic component of SHA would be zero and the DHA would match the SHA exactly. However, XBT analysis only allows DHA computations to 500m, thus leaving an unknown baroclinic component of the SHA below 500 m. By a rather wide margin in some places, gains computed herein are substantially less than one (Figures 5c and 5d), with values typically ranging from about 0.5 to 0.9 dyn m m -~. In the Gulf Stream region, these gains compare favorably with the 0.8 dyn m m -1 value obtained by Blaha and Lunde (1992) using Geosat data. These gains imply that barotropic variability is between 10-50% of the baroclinic variability. The gains are also consistent with the results of Hallock et al (1989) who found the average magnitude of barotropic fluctuations to be 30-50% of the baroclinic variability. Although we should be able to assign the fraction of SHA that is barotropic by virtue of knowing that the baroclinic fraction of SHA is equal to the modeled DHA (DHAm), the errors discussed above that relate to the computation of the gain may seriously compromise this estimate. Observational studies, such as the Meinen (2001) study of the North Atlantic Current, have
43 showed that the baroclinic and barotropic components of the transport are often only weakly correlated. Hurlburt et al (1990) also showed from a model and altimetry that the subthermocline pressure field can have significant impacts on SHA. 4. DISCUSSION We investigate here the water column variability in terms of SHA and the relationships between SHA, TA and DHA fields. The central issue relates to the question of how much information can be inferred about the upper water column temperature field given only satellite altimeter data. These relationships can be complex and are generally problematic where surface and thermocline variability in transition regions are compensating in nature causing diminished SHA. Several earlier studies have used numerical models and observations to address the relationships between SHA obtained from satellite altimetry and subsurface variability. For example, Stammer (1997) used three years of global T/P data to relate SHA to surface wind and buoyancy flux anomalies. Later, Fukumori et al. (1998) used a numerical model forced by daily winds and monthly surface fluxes over a period from J a n u a r y 1992-January 1994. Both studies concluded that in mid-latitudes, short time scale sea level changes are driven primarily by surface buoyancy fluxes. The results presented herein provide more detail on the vertical structure of the relationships between SHA and water column variability than provided in these earlier studies. North of 20~ these newer results are consistent with those of Stammer (1997) and Fukumori et al. (1998). More recently, FRO, using a combination of numerical model results and observations, studied the processes responsible for the observed annual cycle in a 5-yr T/P record in the Atlantic Ocean north of 10~ (Figure 8). Generally, the rms of the FRO model are akin to those from the observations suggesting that the model is simulating the processes that cause SHA. However, the model underestimates the rms of the observations because only the annual harmonic is considered. The contributions to the annual cycle by the simulated (modeled) buoyancy flux and wind forcing are given separately in Figures 8c and 8d. FRO considered air-sea fluxes, advection, salt content variability, water column variability at depths greater than 150 m and bottom pressure variability as potential candidates for possible forcing mechanisms of SHA. Similar to the results described above for SHA, FRO found that for the annual cycle, there is "an approximate balance between the air-sea heat flux induced changes in TA and DHA and SHA variability" in most regions north of 20~ Our results are consistent with the FRO fmdings north of 20~ where surface buoyancy fluxes dominate the annual cycle of SHA but south of about 10~ wind forcing dominates. Here, FRO found that near surface variability plays a much smaller role in the forcing of the annual cycle of SHA in the tropics where advective water column variability at depths greater than 50m become important. These findings
44 are expected based on the recent analyses of Franca et al (this volume) and the analysis of the equatorial thermocline response to wind forcing during the SEQUAL Program by Weisberg and Tang (1990). This chapter identifies the heretofore undescribed transition regions that tend to occur in the vicinity of trough regions and cautions about such simple characterizations of DHA and SHA variability near the tropics. In the tropics the range of temperature is largest below the surface and is caused by wind-driven ocean dynamics that lead to changes in the depth of the thermocline. In the subtropics the range of temperature is largest near the surface and is caused by surface buoyancy fluxes. Between these regions, the results in Figures 3, 4 and 7 indicate the presence of a transition between the subtropics and the tropics that are generally found in trough regions (NECC and equatorial troughs). Here, surface and thermocline variability are offsetting in their contributions to DHA resulting in diminished SHA and the thermocline is essentially out of phase (negatively correlated) with the annual cycle at the surface (as an example see Figures 3e and 4e at 26~ 14~ In these areas the small changes in SHA are not particularly well suited for drawing inferences about changes in the subsurface temperature structure. Here, correlations are generally poor between SHA and TA and DHA and although the changes in SHA are small, in situ variability can be large. Compensation is caused by a deep (shallow) trough and shallow (deep) thermocline and warm (cold) water near the surface in concert with diminished (enhanced) surface fluxes due to seasonal relaxation (excitation) of winds. Negative correlations are also found along the equator in the western part of the domain, where equatorial upwelling induced by Kelvin and Rossby waves create a complicated picture for interpreting SHA and thermocline correlations. Our ability to consider interannual variability met with marginal success because of the limited time span of our data (5 yr) and because of the number of missing data. The residual signals, which were obtained by removing the annual cycle, contain both interannual variability and higher frequencies. The largest interannual variability occurs in two areas along the western section. The first is in the tropics in a latitude band from 6 to 14~ The second is in the Gulf Stream near 70~ 38~ In the tropics along both sections, residual variability is confmed to a depth range of 50-200m in the thermocline and is approximately the same as that for the annual cycle. J u s t northwest of the retroflection region between 5 and 10~ and west of 46~ intermittent currents occur along with the passage of rings shed by the North Brazil Current (Didden and Schott, 1993). Recent fieldwork (Garzoli et al, this volume) revealed a much smaller SHA signature than the related DHA in observations of a specific ring. These recent observations are consistent with our results in this area for which larger rms of DHA were observed. Some of these rings have been reported to have a very deep velocity structure (>500 m) (Richardson and Schmitz, 1993) and therefore, for comparing DHA with SHA, reference depths of 500m or more would be needed. In the Gulf Stream region near 70~ 38~ ocean variability is characterized by meanders
45 and rings (Hansen, 1970). Specifically, residual variability is important throughout the upper 500m and is largest at levels below the seasonal thermocline unlike the surface intensified annual signal. This depth structure of variability indicates that subsurface anomalies as well as anomalous surface fluxes are responsible for SHA and DHA signals at interannual time scales. Further, an analysis of Panulirus data, only about 5~ of the Gulf Stream, also showed how important residual variability can be in causing SHA down to depths of 1000m or so, well below the seasonal thermocline. Recently Rossby and Benway (2000), related surface salinity residuals to meridional movement of the Gulf Stream along a track between New Jersey and Bermuda (adjacent to the Panulirus station). This track crosses the western section near 70~ 38~ where the residuals are salty and TA are warm during mid-yr in 1995 and residuals are fresh and TA are cold in the beginning of 1997. This coincides with decreasing DHA over this time period (Figures 4h and 6a) and is consistent with southward movement of the Gulf Stream. Hence, the observed TA are directly related to ocean dynamics. 5. SUMMARY The results presented herein support those from earlier studies which indicate that SHA must be used together with in situ data to interpret altimetric observations. It has been shown that the vertical mass distribution cannot always be inferred from SHA alone, unless there is a strong relationship between SHA and TA and DHA and an understanding of the details of how temperature variability affects DHA. These relationships can be problematic if the variability of SHA is small even though water column variability may be large. This can occur in areas of transition that are commonly found in trough regions (NECC and equatorial troughs) between the tropics and the subtropics where surface and thermocline variability of the annual cycle are offsetting (out of phase) in their contributions to DHA. To draw inferences about the upper water column given only satellite altimeter data (SHA) from T/P, an attempt was made to derive inferred TA profiles based on the linear correlation between SHA and the annual cycle of TA over the range of depths available. The calculations are only applicable to the annual cycle because correlations are generally poor for the residuals. Candidates for this calculation are suggested where the variance (rms squared) of the difference between SHA and DHA is less than half that of the variance of SHA (Figures 7 and 8). At these locations (a little more than 30% of the available positions) more than half of the SHA variance in the annual cycle can be accounted for by DHA. However, computing inferred profiles becomes difficult in locations where the SHA have small values in transition regions for reasons stated above, for example near 26~ 14~ (Figures 3e and 4e). For the annual cycle the most important contributions to SHA in the tropics are TA in the 50-200m depth range, and in the subtropics TA in the upper 100m. Using data down to 2000m from the Panulirus station (32.2~ 64.5~ it
46 was found that residual water column variability can be important in contributing to the observed SHA below depths of 500m and that in situ data are needed down to at least 1000m. The inference may be drawn here that this situation may apply elsewhere as well. From Figure 9 it is evident that the annual cycle at Panulirus is effectively limited to the upper 100m or so and accounts for almost 30% of the SHA variance. For the residual a little more than 40% of the SHA variance is accounted for by the DHA as a depth of 1000m is reached and is likely due mostly to interannual variability.
Acknowledgments This research has been funded by NOAA's Office of Atmospheric Research and the Office of Global Programs. The authors are indebted to Yeun-Ho Daneshzadeh for her efforts in quality control of the XBT data, and to Chunzai Wang, Don Hansen, and Sonia Bauer for their thoughtful comments on this manuscript. The authors would also like to thank Bob Cheney (NOAA/NESDIS) for providing the altimeter data and Dr. Ichiro Fukumori for providing data from his model results. References Blaha, J., and B. Lunde, Calibrating altimetry to geopotential anomaly and isotherm depths in the western North Atlantic, J. Geophys. Res., 97, 74657477, 1992: Carnes, M., J. Mitchell, and P. de Witt, Synthetic temperature profiles derived from Geosat altimetry: Comparison with air-dropped expendable bathythermograph profiles, J. Geophys. Res., 95, 17979-17992, 1990. Cartwright, D. E. and R.D. Ray, Energetics of global ocean tides from Geosat altimetry, J. Geophys. Res., 96, 16897-16912, 1991. Cheney, R. L. Miller, R. Argreen, N. Doyle, and J. Lillibridge, TOPEX/POSEIDON: The 2-cm solution, J. Geophys. Res., 99, 24555-24564, 1994. Cooper, M. and IC Haines, Altimetric assimilation with water property conservation. J. Geophys. Res., 101,1059-1077, 1996. Didden, N., and F. Schott, Eddies in the North Brazil Current by Geosat altimetry, J. Geophys. Res., 98, 20121-20131, 1993. Ferry, N., G. Reverdin, and A. Oschlies, Seasonal sea surface height variability in the North Atlantic Ocean, J. Geophys. Res., 105, 6307-6326, 2000. Fukumori, I., R. Raghunath, and L. Fu, Nature of global large-scale sea level variability in relation to atmospheric forcing: A modeling study, J. Geophys. Res., 103, 5493-5512, 1998. Gill, A. E. and P. P. Niiler, The theory of the seasonal variability in the ocean, Deep-Sea Res., 20, 141-177, 1973. Gilson, J., D. Roemmich, B. Cornuelle, and L-L Fu, Relationship of TOPEX/POSEIDON altimetric height to steric height and circulation in the North Pacific, J. Geophys. Res., 103, 27947-27965, 1998.
47 Goni, G., S. Kamholz, S. Garzoli, and D. Olson, Dynamics of the Brazil-Malvinas Confluence based on inverted echo sounders and altimetry, J. Geophys. Res., 101, 16273-16289, 1998. Hallock, Z. R., J. L. Mitchell and J. D. Thompson, Sea surface topographic variability near the New England seamounts: An intercomparison among insitu observations, numerical simulations and Geosat altimetry from the regional energetics experiment. J. Geophys. Res., 94, 8021-8028, 1989. Hansen, D. V., Gulf Stream meanders between Cape Hatteras and the Grand Banks, Deep-Sea Res., 17, 495-511, 1970. Hurlburt, H. E., D. N. Fox and E. J. Metzger, Statistical inference of weaklycorrelated subthermocline fields from satellite altimeter data. J. Geophys. Res., 95, 11375-11409, 1990. Le Traon, P. Y., M. C. Rouquet, and C. Bossier, Spatial scales of mesoscale variability in the North Atlantic as deduced from Geosat data, J. Geophys. Res., 95, 20267-20285, 1990. Levitus, S., Climatological atlas of the world ocean, Noaa Technical Paper 13, 173 pp., U.S. Government Printing Office, Washington, D.C., 1982. Mayer, D. A., R. L. Molinari, M. O. Baringer, and G. J. Goni, Transition regions and their role in the relationship between sea surface height and subsurface temperature structure in the Atlantic Ocean, Geophys. Res. Lett., 28, 39433946, 2001. Mayer, D. A., R. L. Molinari, and J. F. Festa, The mean and annual cycle of upper layer temperature fields in relation to Sverdrup dynamics within the gyres of the Atlantic Ocean, J. Geophys. Res., 103, 18545-18,566, 1998. Mayer, D. A., and R. H. Weisberg, A description of COADS surface meteorological fields and the implied Sverdrup transports for the Atlantic Ocean from 30 ~S to 60 ~N, J. Phys. Oceanogr., 23, 2201-2221, 1993. Meinen, C. S., Structure of the North Atlantic current in stream-coordinates and the circulation in the Newfoundland basin. Deep Sea Res., 48, 1553-1580, 2001. Merle, J., and S. Arnault, Seasonal variability of the surface dynamic topography in the tropical Atlantic Ocean, J. Mar. Res., 43, 267-288, 1985. Molinari, R. L., D. A. Mayer, J. F. Festa, and H. Bezdek, Multi-year variability in the near surface temperature structure of the midlatitude western North Atlantic Ocean. J. Geophys. Res., 102, (C2), 3267-3278, 1997. Richardson., P. L., and W. J. Schmitz Jr., Deep cross-equatorial flow in the Atlantic measured with SOFAR floats, J. Geophys. Res., 98 8371-8387, 1993. Roemmich, D., Sea level change, Geophysics Sudy Committee, Commission on Physical Sciences, Mathematics, and Resources, National Research Council. Sea level and the thermal variability of the ocean, Chapter 13, National Academy Press, Wash., D.C., 208-217, 1990. Rossby, T., and R. L. Benway, Slow variations in mean path of the Gulf Stream east of Cape Hatteras, Geophys. Res. Lett., 27, 117-120, 2000. Sciremammano, F. Jr., A suggestion for the presentation of correlations and their significance levels. J. Phys. Oceanogr., 9, 1273-1276, 1979.
48 Stammer, D., Steric and wind-induced changes in TOPEX/POSEIDON large scale sea surface topography observations, J. Geophys. Res., 102, 20987-21009, 1997. Stammer, D., and C. Wunsch, De-aliasing of global high frequency barotropic motions in altimeter observations, Geophys. Res. Lett., 27, 1175-1178, 2000. Talley, L. D., and M. E. Raymer, Eighteen degree water variability, J. Mar. Res., 40 (Suppl.), 757-775, 1982. Warren, B., Approximating the energy transport across oceanic sections, J. Geophys. Res., 104, 7915-7919, 1999. Weingartner, T. J., and R.H. Weisberg, A description of the annual cycle in sea surface temperature and upper ocean heat in the equatorial Atlantic, J. Phys. Oceanogr., 21, 83-96, 1991.
Interhemispheric Water Exchange in the Atlantic Ocean edited by G.J. Goni and P. Malanotte-Rizzoli 9 2003 Elsevier B.V. All rights reserved.
Estimation of the tropical Atlantic circulation from altimetry data u s i n g a r e d u c e d - r a n k stationary Kalman filter Mark Buehner a*, Paola Malanotte-Rizzoli a, Antonio Busalacchi b and Tomoko Inui a aDepartment of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA bEarth System Science Interdisciplinary Center, University of Maryland, College Park, MD, USA In this study, a reduced-rank stationary Kalman filter is used to assimilate TOPEX/Poseidon sea-surface height anomaly (SHA) data into a realistic model of the tropical Atlantic Ocean. The goal is to assess how the interhemispheric transports between the Atlantic subtropics and tropics are affected by the assimilation of TOPEX/Poseidon altimetry and how the subsurface thermocline structure is dynamically constrained by SHA. The model is a reduced-gravity primitive equation GCM of the upper Atlantic ocean between 30~ and 30~ It is forced by momentum and heat fluxes at the surface and constrained by climatological fields at the northern and southern boundaries. The assimilation scheme is an approximation to the extended Kalman filter in which the error covariances of the state estimates are only calculated in a reduced-dimension subspace. We use O(102) of the leading empirical orthogonal functions calculated from an unconstrained model run to define the subspace. The error covariances are assumed to be stationary, resulting in an assimilation procedure that requires just slightly more computational effort than a simple model integration. The model error covariances are assumed to be proportional to the model's temporal variability with the seasonal cycle removed. The filtering of the seasonal cycle results in a more horizontally localized covariance structure in the forecast error statistics and therefore a more localized impact from the observations. Both an identical twin experiment using simulated SHA observations and an assimilation experiment with TOPEX/Poseidon altimetry data were performed. Results from using simulated SHA data demonstrate the ability of the method to constrain the ocean circulation and subsurface temperature structure (with a 50% reduction in the subsurface error). Assimilation of TOPEX/Poseidon SHA data re*Current Affiliation: Data Assimilation and Satellite MeteorologyDivision, MeteorologicalService of Canada, Dorval, QC, Canada, email: mark.buehnerCCec.gc.ca.
50 duces the root-mean-square misfit with observed SHA by 23.6% relative to the control model run. The variability at timescales less than one year is also increased, resulting in an improved agreement between the power spectra of the observed and estimated SHA. The impact on the subsurface temperature field from assimilating SHA was assessed using data from expendable bathythermographs (XBT). This showed a substantial improvement in the estimated temperature variability only within ~13 ~ latitude of the equator, with no improvements beyond this equatorial band. The impact of SHA altimetry assimilation on the zonally integrated meridional transport across three latitudes in the equatorial band was also examined. Both the mean amplitude and interannual variability of the surface and subsurface transports were significantly enhanced. The meridional transports were only sensitive to SHA assimilation between 10 ~north and south of the equator. The conclusion is that SHA is a powerful constraint for the subsurface thermal structure and interhemispheric transport exchange only in a narrow equatorial band. 1. I N T R O D U C T I O N Due to the possible influence on climate variability, dynamical connections between the tropical and subtropical regions of the Atlantic Ocean have recently attracted considerable interest [e.g. Malanotte-Rizzoli et al., 2000]. The shallow meridional overturning circulation, i.e. the subtropical cells connecting the tropics to the subtropics [McCreary and Lu, 1994; Liu, 1994], can impact the climate by affecting SST through lateral advection or/and propagation of anomalies within the mixed layer or the thermocline. There are three types of mechanisms through which this can be achieved: 1) The transport of temperature and/or salinity (the active tracers) anomalies by the mean circulation, the so-called v-T' mechanism [Gu and Philander, 1997; Schneider et al., 1998]; 2) the transport of the mean temperature gradient by circulation anomalies, specifically the wind-induced changes in the strength of the subtropical cells, the so-called v~T mechanism [Kleeman et al., 1999]; 3) the coupling of circulation and active tracer anomalies, the v~T~ mechanism [Liu, 1999; Huang and Pedlosky, 1999; Lazar et al., 2001]. In a numerical study, Inui et al. [2002] showed that the winds over the boundary between the subtropical and tropical Atlantic gyres (at about 10~ play a critical role in governing the transport of North Atlantic subtropical water to the equator. Observational studies have shown the core of the Atlantic Equatorial Undercurrent (EUC) to consist of water in the range of 14-25~ [Duing et al., 1980], indicating that these waters originate in the subtropics. Therefore, to better predict equatorial SST and its variability, estimates of the transport between the subtropics and tropics must be improved. In this study we use a state-of-the-art, primitiveequation reduced-gravity model [Inui et al., 2002] to evaluate the interhemispheric transport between the northern and southern Atlantic subtropics/tropics and the equator. The major goal of this research is to assess how these transports are affected by the assimilation of TOPEX/Poseidon altimetry data and how the subsurface thermocline structure is dynamically constrained by sea-surface height
51 anomalies (SHA). At present, the ocean is significantly undersampled [Ghil and Malanotte-Rizzoli, 1991]. This limits our ability to estimate the current ocean state and to predict its future evolution. TOPEX/Poseidon altimetry data provided global coverage of the sea-surface topography between October 1992 and April 2000. However, this instrument shares the limitation of all satellite-based instruments in that only surface information is provided. The future deployment of a global network of autonomous drifting floats will eventually provide a consistent source of information on the subsurface hydrography [Argo Science Team, 1999]. Presently, expendable bathythermographs (XBT) provide a reasonably good source of subsurface temperature data over a sufficiently long period for studies of interannual variability. Data assimilation can also provide an effective way of constraining the subsurface fields from surface observations. Information from the observations is spread both horizontally and vertically and to the other variable types when producing the correction fields. However, deriving the required surface-subsurface and horizontal relationships is a difficult task requiring an accurate description of the errors statistics for the model and the observations. Some studies have used a relatively simple blend of statistical and dynamical relationships to explicitly construct the vertical extrapolation functions required to make effective use of surface observations [Mellor and Ezer, 1991; Ezer and Mellor, 1994; Oschlies and Willebrand, 1996; Cooper and Haines, 1996]. Others have used approaches based on the Kalman filter (KF). For linear dynamics, the KF provides the optimal estimate of the ocean state conditioned on all previous observations. However, the computational expense of the KF algorithm requires that some type of simplification be made for applications with realistic ocean models. The most severe limitation results from the need to compute the complete error covariances of the state estimates. Consequently, most simplified versions of the KF involve a reduction in the rank of the required covariance matrices by restricting their calculation to a reduced-dimension subspace. Cane et al. [1996] used a fixed set of the leading empirical orthogonal functions (EOFs) calculated from the output of an ocean model to define the subspace. Using a coarser resolution grid to define the subspace, Fukumori and Malanotte-Rizzoli [1995] increased the efficiency of the EKF further by calculating the asymptotically stationary error covariances and assuming these covariances were valid over the entire period of the assimilation experiment. The SEEK filter described by Verron et al. [1999] uses a small set of dynamically evolved eigenvectors of the analysis error covariances as the basis functions for the forecast error covariances at the subsequent analysis time. For a mid-latitude application of the SEEK filter, Ballabrera-Poy et al. [2001] found that evolving the basis functions improved the long-term filter performance, as compared with using a fixed subspace, only when the basis functions were correctly initialized. However, when estimating surface and subsurface fields from altimetry data in the tropical Pacific, Verron et al. [1999] found no significant improvement from evolving the basis functions in the SEEK filter. In this study a reduced-rank stationary KF is used to assimilate altimetry data
52 with a realistic model of the tropical Atlantic. The filter is implemented following the approach developed and applied by Buehner and Malanotte-Rizzoli [2003] (hereafter referred to as BMR) in an idealized study of the mid-latitude winddriven circulation. We use the leading three-dimensional, multivariate EOFs calculated from the output of an unconstrained model run to define the fixed subspace for the error covariances. The effectiveness of using this subspace relies on the assumption that the forecast error has a strong projection on the dominant modes of the model's temporal variability. Contrary to our previous application of this assimilation approach to the idealized mid-latitude ocean [BMR], the tropical dynamics are expected to be dominated by linear processes. Under certain conditions, including linear dynamics, the forecast error statistics will approach stationarity [see the appendix and Anderson and Moore, 1979, for necessary conditions]. This allows the assimilation procedure to be simplified and the total computational cost reduced to a level similar to a simple model integration. Though stationary, the error statistics used in the reduced-rank KF are determined by the interaction of the model dynamics, model error statistics, observation error statistics and the locations and types of observations assimilated. This differentiates the approach from those that use stationary forecast error statistics which must be prescribed directly, such as Optimal Interpolation (OI). The paper is organized as follows. Section 2 provides background information on the ocean model used in this study. In Section 3 the assimilation approach and the data are described and the computed error covariances are examined using a series of diagnostics. The design and results of the identical twin assimilation experiment are described in Section 4. In Section 5 the results of the experiment assimilating real TOPEX/Poseidon altimetry data are given. The results are summarized and conclusions given in Section 6. 2. MODEL OF T H E T R O P I C A L ATLANTIC The model of the tropical Atlantic Ocean used in this study is based on the nonlinear, reduced-gravity, primitive equation, sigma coordinate model developed by Gent and Cane [1989]. The same model was used by Verron et al. [1999] and Gourdeau et al. [2000] to assimilate altimetry data in the tropical Pacific with the SEEK filter. The vertical structure consists of a surface mixed layer and 19 additional layers with the mixed layer depth and the last sigma layer computed prognostically. The remaining layers are computed diagnostically such that the ratio of each sigma layer thickness to the total layer thickness remains fixed to a prescribed value. The mean sigma layer thicknesses in the outcropping region of the North Atlantic subtropical-tropical circulation are: 14.2 m (layers 2 to 5), 28.4 m (layers 6 to 9), 56.7 m (layers 10 to 13), 85.1 m (layers 14 and 15), 142.0 m (layers 16 and 17), 280.0 m (layer 18) and 420.3 m (layers 19 and 20). The model domain is 100~ to 20~ and 30~ to 30~ The horizontal model grid has variable resolution along the meridians with the equatorial region better resolved (1/3 ~grid spacing) than regions near the northern and southern boundaries (1 ~grid spacing). The resolution in the zonal direction is constant throughout the
53 domain (1 ~ grid spacing). The model state vector consists of temperature, two components of velocity, and layer thickness for a total of 473,607 dimensions. Salinity is not included in this version of the model, however the effect of neglecting salinity should have only minor effects and simply contributes slightly to the other sources of model error in the KF formulation. Also, the impact of salinity on the SHA is much less than the impact of temperature and therefore the corrections to the salinity field from the assimilation procedure would be relatively small. The surface mixed layer employs a hybrid vertical mixing scheme, described by Chen et al. [1994], that combines the traditional bulk formula of Kraus and Turner [1967] with the dynamic instability model of Price et al. [1986]. This allows the inclusion of three major processes of oceanic vertical mixing: 1) the bulk mixed layer model which relates the mixed layer entrainment/detrainment to the atmospheric forcing, 2) the gradient Richardson number mixing which accounts for shear flow instability and 3) a convective adjustment which simulates high frequency convection. The surface forcing from wind stress and surface heat fluxes is calculated using wind speed data from the National Centers for Environmental Prediction reanalysis project [Kalnay et al., 1996] and cloud cover data from the International Satellite Cloud Climatology Project [Rossow and Schiffer, 1991]. Within 5 ~latitude of the northern and southern open boundaries, the model fields are relaxed towards the seasonally varying climatology from Levitus [1982]. The ocean model was first integrated starting from a state of rest for a period of 20 years using an averaged annual cycle of wind stress and surface heat flux forcing. From the resulting fully spun-up state the model was further integrated over the period J a n u a r y 1980 to January 2000 using the real forcing data. The assimilation experiments begin on J a n u a r y 1, 1993. The mean state over the three year period following J a n u a r y 1, 1993 is shown in Figure 1. The mean surface circulation (Figure la) clearly shows the strong North Brazil Current extending northward along the Brazilian coast to about 10~ The mean SST is shown in Figure lb and the February and August mean cross-sections of temperature along 10~ are shown in Figures lc and ld, respectively. Although the SST varies with season, the main thermocline is generally positioned above the 18~ isotherm. The base of the thermocline corresponds approximately with the 14~ isotherm which is also close to the bottom of the EUC. A major underlying hypothesis in this study, and all studies that attempt to infer the subsurface circulation from SHA data, is the presence of a strong connection through the ocean dynamics between SHA and the subsurface temperature (density) field. In the tropics the dynamics tend to be dominated by the first baroclinic mode forced by Ekman pumping. This causes anomalies in the thermocline depth and SHA to have opposite signs, that is, a deepening of the thermocline corresponds with an elevation in SHA. From a previous study [Inui et al., 2002], E k m a n pumping velocity fields were calculated from wind stress data as _1V x ( ~ / f )
w, = p
=
1
-:-] ( v x r + Z ~ ' / f ) ,
(1)
where the wind stress is r = (rz, rY), / is the Coriolis parameter, p is the atmo-
54 (a) ~ :~
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Figure 1. Mean model state over the period J a n u a r y 1, 1993 to J a n u a r y 1, 1996: (a) mean surface currents, (b) mean SST, (c) mean February temperature cross-section at 10~ and (d) mean August temperature cross-section at 10~ Temperature is given in degrees Celsius.
55 spheric density and B = 3f/Oy. The second term on the right hand side causes downwelling, even in the equatorial gyre, which allows water communication from the surface to the interior ocean through the subduction process. According to Inui et al. [2002], the region of the subtropical-tropical communication is between 12~ and 20~ and the gyre boundary, where the volume transport is determined by wind stress, is around 10~ We refer the interested reader to this study for a quantitative assessment of the interhemispheric exchanges between the northern/southern subtropics and the equatorial band in an unconstrained simulation. Results from Inui et al. [2002] are consistent with the previous investigations of S t a m m e r [1997], F u k u m o r i et al. [1998] and Ferry et al. [2000] who were however addressing a different issue. In these studies the underlying causes of sea level variability in TOPEX/Poseidon data were investigated using other surface observations and theoretical arguments or numerical models. They found that in the tropics vertical movements of the thermocline caused by changing winds and ocean dynamics dominate the variability of SHA. In contrast, in the subtropics SHA variability is determined by surface buoyancy fluxes. Their results are also generally consistent with the very recent study by Mayer et al. [2003] who however found a transition between the tropics and subtropics associated with trough regions where the contributions from surface and thermocline variability partially compensate each other, thus resulting in diminished SHA. Mayer et al. [2001] had already shown that the influence of surface buoyancy fluxes may partially cancel out the effect of wind forcing on sea-surface height near 15~ thus complicating the relationship between SHA and thermocline depth outside the restricted equatorial band, 10~ to 10~ A simple way of assessing the connection between SHA and the subsurface temperature field is to calculate the correlation between SHA and the thermocline depth from the ocean model. Here we choose the 14~ isotherm as a proxy for the base of the thermocline. Figure 2a shows the correlation coefficient between SHA and the isotherm depth calculated over the same three year period used for the previous figure. The mean depth of this isotherm over the period is shown in Figure 2b, ranging between 150 m and 250 m in the equatorial region. Over most of the model domain the correlation is greater than 0.8 in magnitude. The predominately negative correlation is consistent with the dynamics being dominated by the first baroclinic mode. The strong correlation indicates that the assimilation approach, which uses a vertical projection operator largely governed by modelgenerated covariances between elements of the state vector, should be capable of making significant changes to the subsurface density structure using SHA data alone. However, the accuracy of the estimated subsurface fields will be highly dependent on how well the model reproduces the vertical thermal structure of the real ocean. Figure 2c shows the mean depth of the 14~ isotherm estimated from XBT data over the same three year period used to compute the model results in Figure 2b. Comparison of these two maps shows a significant difference in the mean meridional gradient in isotherm depth. This indicates that the model has a weaker mean meridional temperature gradient around 200m-400m depth most notably between 10~ and 20~
55
Figure 2. The correlation of SHA with the depth of the 14~ isotherm is shown in (a). In (b), the mean depth (in meters) of the 14~ isotherm is shown. Both (a) and (b) were calculated from the same three year model run used for the previous figure. Panel (c) shows the mean depth of the 14~ isotherm estimated from the XBT data.
57 A common problem when assimilating data with a primitive equation model is the introduction of dynamical imbalances in the corrections added to the model forecasts [Malanotte-Rizzoli et al., 1989; Daley, 1991]. The transient response of the model to such imbalances can often degrade the quality of the forecast significantly. For this reason it was necessary to introduce an initialization procedure for the present study. Consequently, any state supplied to the ocean model as initial condition was first processed to remove most of the dynamical imbalances. The procedure involved applying the boundary conditions, horizontally smoothing all fields with a Shapiro filter, smoothing the vertical structure, and ensuring the stability of the vertical structure. For consistency, this procedure was used at each analysis time for all model runs, even when producing the "true" and "false" ocean runs (with no assimilation) for the identical twin experiment. 3. A P P R O A C H F O R ASSIMILATING S H A
3.1. T h e r e d u c e d - r a n k K a l m a n filter The approach for assimilating altimetry data is similar to that developed for a previous study with an idealized one layer quasi-geostrophic model of the midlatitude wind-driven ocean circulation, described in BMR. The basic strategy is also similar to the approaches used by Fukumori and Malanotte-Rizzoli [1995] and Cane et al. [1996]. An outline of the standard EKF and the derivation of the reduced-rank KF is given in the appendix. Here we only summarize the approximations made to obtain an efficient and affordable assimilation scheme. In the EKF, the numerical model is used to produce a forecast of the ocean state, denoted by x f, and the covariance matrix of forecast error, denoted by P. At the next time measurements of the real ocean state are available, the forecast is corrected to produce the analyzed state, denoted by x a, along with its error covariances, pa. The forecast/analysis process is then repeated. Both the statistics for the errors in the observations and in the numerical model must be specified. These are denoted by R and Q, respectively. It is the prohibitive expense of computing P at each analysis time when using a realistic ocean model that provides the main motivation for using a simplified version of the EKF. The first approximation to the EKF requires the definition of a reduced-dimension subspace within the space spanned by the model state vector. The computational expense can then be greatly reduced by only calculating the error covariances of the state within this subspace. As a result, the corrections made to the forecast at each analysis time only span the subspace. However, the full nonlinear model is used to produce the forecasts. Similar to Cane et al. [1996], we use the leading EOFs of the model state vector, including SHA, as the basis of the resolved subspace. The resulting equations of the EKF required to calculate the gain matrix and the analysis and forecast error covariances in the subspace resolved by the EOFs are given in the appendix. The EOFs were calculated from a three year model run sampled every three days over the period January 1, 1993 to January 1, 1996 (the period used for the identical twin experiment described below). The SHA and SST of the first two EOFs are
58
Figure 3. The SHA and SST components of the first two EOFs calculated over the three year period (January 1, 1993 to January 1, 1996) used for the identical twin experiment: (a) SHA of the first EOF, (b) SHA of the second EOF, (c) SST of the first EOF, and (d) SST of the second EOF.
shown in Figure 3. The first EOF exhibits a large scale meridional temperature gradient in the SST that is clearly related to the meridional gradient in the surface heat flux and the constraints at the open boundaries that vary on an annual timescale. The largest amplitude of SST from the second EOF is concentrated near the equator in the eastern part of the basin. The projection of this EOF on the model state is dominated by an annual cycle, suggesting that this EOF is related to seasonal upwelling. The pattern of SHA for the first EOF consists of a large scale dipole concentrated along the western boundary and centered at about 10~ in the region of the North Brazil Current retroflection. For the second EOF, SHA has a similar structure as SST along the equator, but also exhibits a large scale maximum near the western boundary around 15~ The second approximation to the EKF algorithm is to assume the forecast error covariances are stationary within the subspace. Using the linearized dynamics computed in the resolved subspace, the doubling algorithm [Anderson and Moore, 1979] is employed to obtain the stationary forecast error covariances, Pr. (Here and elsewhere, the subscript r is used to denote quantities projected into the resolved subspace.) The conditions under which the stationary assumption are valid are given in the appendix. The use of stationary error covariances means the computationally expensive task of linearizing the model dynamics within the resolved
59 subspace need only be performed once. Consequently, the reduced-rank KF requires just slightly more computational effort than a simple model integration.
3.2. TOPEX/Poseidon altimetry data The TOPEX/Poseidon altimetry data used in this study have undergone significant pre-processing. The original source is Chet Koblinsky's SHA altimetry data set spanning the period of October 1992 to April 2000 (NASA Ocean PATHFINDER Product). Like most remotely sensed data, the altimetry measurements are located along the ground path of the satellite orbit which takes about 10 days to cover all of the oceans. However, for the assimilation method we wish to employ it is necessary that the observation operator be stationary, that is, the observations must occur at the some locations each time they are used. Since this was not the case for the original altimetry data, the data were grouped over each 10 day period and interpolated onto a uniform 1~horizontal grid covering the model domain from 25~ to 25~ This results in a fixed grid for the observations consisting of 4774 locations. This gridding procedure introduces spatial correlations in the observation errors over spatial scales of 1~that are neglected in the KF formulation. The gridded data were then interpolated in time at three day intervals. Consequently, temporal correlations are introduced to the observation errors over timescales of less than 10 days. However, the impact of correlations over such short timescales will be minor and therefore are also ignored in the formulation of the KF. Due to large uncertainties associated with current estimates of the geoid, the altimetry data can only provide information on the anomalies of sea-surface height. Consequently, the necessary assumption was made that the temporal mean seasurface height computed from the unconstrained model run is perfect. This mean field was removed from each of the forecasts when calculating the differences between the observed and predicted values in the analysis step. Because of this limitation, the assimilation of SHA can not be expected to provide improved estimates of the mean sea-surface height or to improve the mean temperature and velocity fields. This may be a significant limitation for studies that use altimetry data alone to estimate the ocean state and points to the necessity of using complementary data sources and improving geoid estimates. Several statistics of the SHA from TOPEX/Poseidon and an unconstrained model run were calculated to evaluate their consistency. Figure 4 shows both the standard deviation (upper panels) and a particular column of the covariance matrix (lower panels) of the temporal variability of SHA from the observations and the model (lei~ and right panels, respectively). Both the standard deviations and the covariances exhibit very similar magnitude and spatial patterns, except for the increased standard deviations in the north-west corner of the domain for the altimetry data. This indicates that the ocean model can successfully produce a SHA field with reasonably correct variability and spatial correlations over most of the domain. However, as opposed to the similarity in the overall variability, the power spectra of the temporal variability for the observed and model predicted SHA in two locations show significant differences (Figure 5). Only at the lowest frequencies (corresponding to periods of about 10 months and longer for the first location
50
Figure 4. Comparison of the TOPEX/Poseidon and ocean model statistics calculated over the period January 1, 1993 to J a n u a r y 1, 2000. The standard deviations of SHA (in meters) calculated from the altimetry data and the model are shown in panels (a) and (b), respectively. The covariance between the SHA at the grid point near 2~ and 35~ (denoted by the .) and all the other grid points is shown in panel (c) using the altimetry data and in panel (d) using the output from the model for the calculation. The covariances are normalized by the variance of SHA at the selected locations.
61 (a)
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Figure 5. The power spectra of SHA from TOPEX/Poseidon data and the unconstrained ocean model over the period January 1, 1993 to January 1, 2000. The two locations are: (a) 20~ 35~ and (b) 5~ 35~ and three months and longer for the second location) do the spectra have comparable power. At higher frequencies the SHA predicted by the model significantly underestimates the power relative to the observations. Possible causes for the lack of high frequency variability in the model include a high level of model dissipation and a lack of high frequency variability in the external forcing. It is important to note that SHA is not a prognostic variable in the model, but is identified with dynamic height and is therefore diagnosed from the vertical temperature profiles and layer thicknesses. For convenience, we have chosen to include the diagnosed SHA directly in the ocean state vector produced by the model. Therefore, SHA is automatically included in the model forecasts and the EOFs and is treated as if it were a prognostic variable for the assimilation. It can be shown that this is equivalent to the more standard approach of including the diagnostic relationship between the prognostic variables and the observations in the observation operator, 7/, when this operator is linear. It is the forecast error covariances between SHA and the prognostic variables that provide the information required for the filter to infer the values of temperature, layer thickness, and even velocity from the SHA observations. Since SHA is included in the state vector, the observation operator must only perform the horizontal interpolation necessary to map the model grid to the locations of the altimetry observations.
3.3. Specification of Qr and R For the identical twin assimilation experiment, the model is assumed to be perfect. However, due to the dynamic coupling of the subspaces, unresolved error in the analyzed state can evolve into forecast error in the resolved subspace. This effect can be accounted for by using the model error covariances, Qr, to represent
62 this source of resolved forecast error variability, as discussed by BMR. For the experiment in which real altimetry data are used, the model error covariances need to account for the errors in the model dynamics and the external forcing in addition to the influence of the unresolved error. Following the approach of BMR, it was assumed that the model error covariances are proportional to the covariances of the temporal variability from the unconstrained model run according to the proportionality constant ~. Consequently, it was assumed that regions in which the model is most active will also be those regions where the model error will be largest. The model error includes all state variables (listed in Section 2) and is additively applied to the evolved covariances at the end of each three day forecast, as shown in (8) in the appendix. In the previous study applying a similar assimilation approach to an idealized quasi-geostrophic model [BMR], all of the temporal variability in the unconstrained model run was due to internal nonlinear mechanisms. By contrast, much of the variability in the tropical Atlantic model is due to variability in the external forcing. This variability is dominated by an annual seasonal cycle which has a strong projection on the first two EOFs. Because the model error is applied at three day intervals, Qr should represent only the incremental effect of the random error introduced to the forecast over each three day period. The covariance structures associated with the seasonal cycle have strong basin-scale correlations due to large basin-scale correlations in the surface and boundary forcing at the seasonal timescale. Though they are likely present in this model, errors varying over such long timescales have high temporal correlations between analysis times and therefore violate the assumptions of the KF. Consequently, this component of the model's temporal variability is removed when computing the model error covariances. Specifically, the annual and semi-annual Fourier components were removed from the time series of the state projected onto the retained EOFs and the covariances recomputed (hereafter referred to as the filtered covariances). The original variances and the variances after filtering as computed for the three year identical twin experiment (see Section 4) are shown in Figure 6. The variances of the first two modes are affected the most, but the variances up to the sixth EOF are also significantly reduced. The overall variance explained by the covariances in the subspace spanned by the first 50 EOFs is reduced from 98.6% to 26.6% by removing the seasonal cycle in this way. Thus, the majority of the temporal variability is related to the average annual cycle. An empirical approach was used to determine the optimal value for the proportionality constant -y for both the identical twin experiment and the assimilation experiment using real altimetry data. Details about the chosen values of ~ are described in Sections 4 and 5. For the identical twin assimilation experiment perfect observations were used. Therefore, the only contribution to R is from the representativeness error due to the use of reduced-rank forecast error covariances. This is needed to avoid forcing the analyzed state to fit to the unresolved component of the true state. The covariances of representativeness error were initially computed following the approach described by BMR. However, in contrast to that study, significantly improved results were obtained by using instead a simple diagonal observation error covari-
63 |
,
|
|
,
Original
10 s -
-
Filtered
04
/
r"~ 1 0 3
10 2
10
20 30 40 EOF mode number
50
Figure 6. Eigenvalue spectra before and after filtering out the annual and semiannual Fourier components from the principal components. Covariances were calculated over the period J a n u a r y 1, 1993 to J a n u a r y 1, 1996.
ance matrix. This may be due to problems in estimating R, which has a r a n k of 4774, from an ensemble of only several hundred samples. In the experiment with real altimetry data the observations also contain m e a s u r e m e n t error and error (and spatial correlations) from the process of interpolating the observations in space and time to a regular grid every three days. For both experiments R was set to a diagonal covariance matrix where the errors are assumed to have a uniform standard deviation of 6 cm, following Verron et al. [1999]. 3.4. D i a g n o s t i c s o f t h e s t a t i o n a r y f o r e c a s t e r r o r c o v a r i a n c e s To gain insight into the resulting stationary forecast error covariances, several diagnostics were calculated. The diagnostics were calculated from the error covariances obtained for the identical twin experiment after projection into the full model state space according to P = DErP~ETD,
(2)
where D is the square root of the norm used in the EOF calculation, as described in the appendix, and the columns of Er are the retained EOFs. It is computationally infeasible to obtain the entire matrix P, but the diagonal elements and selected columns can easily be computed. The diagonal elements correspond to the forecast error variance for each model variable at each grid point. Within the assimilation, variables with relatively large forecast error variance will tend to be more strongly influenced by the data being assimilated. Figure 7 shows the standard deviations from the forecast error covariances. The panels on the left correspond to the standard deviations of SHA and SST (panels (a) and (c), respectively) obtained using the unfiltered model error covariances. The spatial pattern has a strong resemblance with the first EOF shown in the left panels os Figure 3. This is consistent with the large variance for
64
Figure 7. Standard deviations of forecast error from the asymptotically stationary forecast error covariances: (a) SHA using the unfiltered model error covariances, (b) SHA using the filtered model error covariances, (c) SST using the unfiltered model error covariances, and (d) SST using the filtered model error covariances. The unit for SHA is meters and for SST is degrees Celsius.
the first EOF seen in Figure 6. When Qr is instead derived from the filtered covariances the resulting forecast error standard deviations for SHA and SST are those shown in panels (b) and (d), respectively. The error standard deviations for SST are especially affected by removing the variability related to the average annual cycle. The high values near the northern and southern boundaries are greatly reduced with the m a x i m u m variability now occurring just north of the equator. The matrix P contains a column (and row) for each model variable at each grid point. A column of P describes how the forecast error in the variable along the diagonal covaries with all of the variables at all grid points. These covariances govern how information from a point observation is spread both spatially and to the other variable types by the assimilation. This can be illustrated by considering the correction made in the presence of a single point observation occurring at the location of the j t h state variable: yj - xlj
(3)
where pj is the column of P corresponding to the j th state variable and the denominator is the sum of the forecast error and observation error variances for the same
55
Figure 8. A selected column of the asymptotic forecast error covariances between SHA at the location denoted by 9 and all other grid points of SHA in panels (a) and (b) and between SHA at the location denoted by 9 and t e m p e r a t u r e at about 200 m depth in panels (c) and (d). The left panels correspond to using the unfiltered model error covariances. For the right panels the filtered model error covariances were used. The covariances are normalized by the variance of SHA at the selected location.
state variable. This simple form of the analysis equation results from assuming the observed variable, denoted by yj, to be of the same type as the state variable and located at a model grid point. The observation operator is therefore simply a row vector containing only a single nonzero element t h a t is equal to one. Consequently, the correction made to the forecast is proportional to the column of P corresponding with the observation location and variable type. Figure 8 shows a column of the stationary forecast error covariance matrix calculated using both the filtered and unfiltered model error covariances. The covariances of SHA with respect to a grid point near the seaward boundary of the North Brazil current are shown in the upper panels. For this study, it is especially interesting to see how the forecast error of SHA covaries with the subsurface temperature field. The covariances between SHA at the same location and the temperature field at about 200 m depth are also shown (lower panels). All covariances were normalized by the variance of SHA at the selected location. Consequently, the figure shows the corrections t h a t would be made by the reduced-rank KF from a single perfect observation of SHA t h a t is one unit greater t h a n the forecasted value. As expected, the covariances decrease with increasing distance from the
55
Figure 9. The correlations between the 200 m temperature at the position denoted by 9 and the SHA at all locations. The four locations are: (a) 5~ 40~ (b) 15~ 40~ (c) 0~ 5~ and (d) 15~ 5~ For this figure, the asymptotic covariance matrix computed with the filtered model error covariances was used.
horizontal location of the selected SHA variable. The magnitude of the covariances away from the selected location are generally lower when using the filtered model error covariances (panels on the right). This suggests that distant regions may be largely correlated due to the variability in the model state on the annual timescale, possibly due to large scale spatial correlations in the average annual cycle of the external forcing. Therefore, removing the variability at the seasonal timescale from the model error covariances results in a more spatially localized impact from assimilating SHA. However, significant long-range correlations still exist, likely due to the relatively small number of samples used to compute the EOFs and model error covariances and the truncation of the retained set of basis functions. The addition of a localization technique to suppress long-range correlations, similar to that used by Houtekamer and Mitchell [2001] for an ensemble KF, may be beneficial. Figure 9 shows the forecast error correlations between temperature at four chosen locations at about 200 m depth and the SHA at all locations. This shows how the subsurface temperature at a specific location can be affected by the assimilation of SHA observations at any location. Again, significant basin-scale correlations are present, pointing to the possible benefit from applying correlation localization. The SHA correlations with respect to the location in the northern part of the domain (Figure 9b) shows that the variability of the temperature error in this region is
57
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Figure 10. Vertical profiles of the normalized forecast error covariances between SHA and temperature at the four horizontal locations used for the previous figure.
highly correlated with a dipole in SHA error straddling an axis pointing towards the north-east. Consequently a geostrophic current directed towards the north-east is correlated with a positive temperature anomaly at 200 m. The coupling with a geostrophic current is less clear at the location in the southern part of the domain, though a sharp gradient in SHA about 5 ~ south of this location is consistent with a south-eastward geostrophic current. At the two locations near the equator the subsurface temperature is positively correlated with the SHA locally. This variation in the correlation structure as a function of location m u s t be related to regional differences in the dominant dynamical processes as captured by the linearized dynamics operator and the model error covariances. Consequently, such spatial variation would be difficult to capture using empirical approaches such as OI, in which the forecast error correlations are often assumed to be homogeneous and isotropic. Figure 10 shows the vertical structure of the forecast error covariances between SHA and temperature at the same four locations used in the previous figure. The covariances are again normalized by the SHA variance so t h a t the plotted values correspond to the corrections in degrees Celsius t h a t would result from assimilating a single perfect SHA observation one meter greater t h a n the forecasted value. The t e m p e r a t u r e correction is generally positive from below the surface mixed layer down to about 200 m, except for the location in the southern part of the domain where the correction is positive down to at least 500 m. These covariance structures support the assumption t h a t the SHA variability is closely connected with the first baroclinic mode, especially in the equatorial region.
68
(1) 0
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Figure 11. Proportion of the initial error resolved by the EOFs as a function of the n u m b e r of retained modes. Both the resolved (+) and unresolved (o) fractions of the total variance are shown.
4. I D E N T I C A L T W I N A S S I M I L A T I O N E X P E R I M E N T
The assimilation approach was initially evaluated within an identical twin framework. The tropical Atlantic model was first used to produce the "true" ocean from which simulated observations of SHA were extracted. Then, these observations were assimilated to correct a model integration started from a different initial state. By assessing how well the assimilation system can drive the model towards the true ocean run, the effectiveness of the assimilation system can be tested, independent of the quality of the numerical model or the external forcing data. This type of experiment also allows a detailed evaluation of how well the unobserved variables, such as subsurface temperatures, are estimated using only SHA observations. 4.1. C o n f i g u r a t i o n o f t h e e x p e r i m e n t The "true" ocean run was produced by integrating the ocean model over the three year period from J a n u a r y 1, 1993 to J a n u a r y 1, 1996 starting from a fully spun-up state. The "false" ocean run is the result of integrating the model over the same period, but starting from the incorrect initial state (the true ocean state from Janu a r y 1, 1996). The assimilation run uses the same incorrect initial conditions as the false ocean run. The only source of error in the false ocean and assimilation runs comes from this difference in the initial conditions since the dynamics and external forcing are the same as in the true ocean run. The basis functions of the subspace were taken as the leading 50 EOFs calculated from the true ocean run sampled every three days (the first two EOFs are shown in Figure 3). Figure 11 shows the proportion of the initial error variance resolved by the EOFs for various truncations of the EOF spectrum. By retaining 50 EOFs (i.e. only 14% of the full set os 360), 80% os the initial error is resolved. This is significantly less t h a n the
69 98.6% of the temporal variability of the free model r u n explained by the EOFs, but should be sufficient to resolve the large-scale component of the error. The model error covariances, Q~, were set to 10 -1 times the filtered covariances of the temporal variability from the true ocean r u n (~ =10-1). The observation operator for the interpolated TOPEX/Poseidon altimetry d a t a were used to extract the simulated observations from the true ocean run every three days. Diagnostics of the resulting asymptotically stationary forecast error covariances are shown in Figures 7-10.
4.2. Results from a s s i m i l a t i n g s i m u l a t e d SHA o b s e r v a t i o n s The root-mean-square (rms) errors from the assimilation r u n and the false ocean run were calculated separately for each variable both in the surface layer and in the remaining layers. It was a p p a r e n t t h a t even without assimilation the rms error in the false ocean run decreased significantly over the three year period of the experiment. This m u s t be due to the model having relatively high dissipation and a lack of energetic instabilities to m a i n t a i n the error variability. N e a r the n o r t h e r n and southern limits of the model domain the effect of the model fields being relaxed towards the seasonally varying climatology m a y also contribute to the error reduction. Therefore, the states of any two runs s t a r t i n g from different initial conditions but produced with identical dynamics and external forcing would eventually converge. This aspect of the identical twin experiment is clearly not realistic, since errors in the model and the external forcing will play an i m p o r t a n t role in maintaining the errors in both the control and assimilation runs in the experiment with real TOPEX/Poseidon data. However, the relative error reduction in the assimilation run with respect to the false ocean still provides a useful diagnostic of the effectiveness of the assimilation procedure t h a t is independent of the quality of the model or the external forcing data. Figure 12 shows the rms error of the entire model state vector from the assimilation run after normalizing by the rms error from the false ocean: ([xa - xt]2 ) ~/2
(Ex
-
w h e r e x t and x ~ refer to the true and false ocean runs, respectively, and the overbar denotes spatial averaging. For all variables the rms error was dramatically reduced within the first 10 days, similar to the results ofVerron et al. [1999] for the tropical Pacific. The error was reduced most for the observed variable, SHA, for which the error remains around 15% of the false ocean error. For the t e m p e r a t u r e field, the average error below the surface was reduced by more t h a n for the SST. Below the surface the relative error is about 45% and for the SST the error ranges between 40% and 100%. The velocity components have similar levels of relative error at and below the surface layer with values t h a t range between 30% and 60% of the false ocean errors. The higher errors for the t e m p e r a t u r e and thickness of the surface mixed layer can be explained by the strong effect t h a t surface mixing processes have on these variables, but which may not affect SHA or the surface currents significantly and therefore can not be detected with altimetry data alone.
70 (a) 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
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Figure 12. Relative r m s error, normalized by the error from the false ocean run, from the three year identical twin assimilation experiment: (a) error in the est i m a t e d SHA, (b) error in the e s t i m a t e d t e m p e r a t u r e , (c) error in the e s t i m a t e d layer thicknesses, and (d) error in the zonal and meridional components of velocity. Panels (b)-(d) show the relative error for the surface layer and the r e m a i n i n g subsurface layers separately.
71 (b)
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Figure 13. Evolution of the dimensionless rms error from the identical twin assimilation experiment separated into the component t h a t is resolved by the retained EOFs and the unresolved component: (a) E r r o r in E O F subspace and (b) E r r o r in unresolved subspace. The errors from the r u n s with and without assimilation are both shown.
In the identical twin framework the real error for all elements of the state vector is known. Consequently, the error can be decomposed into the components t h a t span the resolved and unresolved subspaces. The rms error (normalized by the spatially averaged temporal s t a n d a r d deviations for each variable type) in each subspace was calculated for both the assimilation and false ocean runs (Figure 13). It is clear t h a t the error in the false ocean run decreases significantly over the three year period. For both runs, the initial rms error in the resolved subspace (Figure 13a) is about twice as large as in the unresolved subspace (Figure 13b). However, the error in the resolved subspace is rapidly reduced to significantly lower values for both the assimilation and false ocean runs. This may be because the error variability in the unresolved subspace contains relatively more energy at small spatial scales t h a t can be more effectively m a i n t a i n e d by nonlinear source terms. The error in the resolved subspace may therefore become less sensitive to errors in the initial conditions, which are the only source of error in this experiment, more quickly over time. Assimilating the simulated SHA data causes the error in both the resolved and unresolved subspaces to decrease more rapidly even though the reduced-rank assimilation scheme only produces corrections in the resolved subspace. The additional decrease in the unresolved error in the assimilation run, relative to the false ocean run, m u s t be due to the coupling between the subspaces in the dynamics of the full nonlinear model used to produce the forecasts. This coupling allows corrections made to the resolved component of the analyzed state to improve the unresolved component of the subsequent forecast. Since the dominant EOFs tend to be large scale, a simple interpretation of this effect is t h a t by correcting the ocean state at the large (resolved) scales the smaller (unresolved) scales are also improved through the transfer of energy to smaller scales during
72
Figure 14. Correlation of the depth of the 14~ isotherm from: (a) the true versus the false ocean runs and (b) the true versus the assimilation run. The correlations were calculated over only the last year of the three year experiment.
each three day forecast. A major reason for first using the identical twin framework was to evaluate how well the information from the SHA observations is projected onto the subsurface fields. Again using the 14~ isotherm as a proxy for the base of the thermocline, the improvement in the estimated isotherm depth was evaluated. The correlations of the 14~ isotherm depth between the true and false ocean runs and between the true ocean and assimilation runs were calculated. To provide sufficient time for the subsurface ocean state to fully adjust to the assimilation procedure, only the final year of the three year experiment was used for the calculation. The results are shown in Figure 14a for the false ocean run and Figure 14b for the assimilation run. For the false ocean run the correlation is significantly less t h a n one mostly in the region between the equator and 20~ Comparing Figures 14a and 14b it is clear t h a t the assimilation of SHA was able to effectively increase the correlation to nearly one over most of the model domain. Figure 15 shows the time series of both SHA (panels (a) and (b)) and the depth of the 14~ isotherm (panels (c) and (d)) from the true, false, and assimilation runs at two selected locations: 20~ 35~ and 5~ 35~ The SHA and isotherm depth at these locations have strong negative correlations (consistent with Figure 2). The improvements due to the assimilation of SHA for both SHA and the depth of the isotherm are clearly seen at both locations, although the values from all three runs tend to converge during the three year period. 5. A S S I M I L A T I O N OF T O P E X / P O S E I D O N S H A The results from the identical twin experiment suggest t h a t it is possible to constrain the subsurface fields by assimilating only SHA information with the reduced-rank stationary KF. However, the approach relies on m a n y conditions which are satisfied in an identical twin framework, but may not be satisfied when using real observations. These conditions mostly relate to limitations of the ocean
73
Figure 15. The temporal evolution of the SHA for the identical twin experiment from the true ocean, false ocean (No-assim) and assimilation runs is shown in (a) and (b) at two selected locations. The depth of the 14~ isotherm from the true, false and assimilation runs is shown in (c) and (d) at the same two locations. The locations are the same as those used for Figure 5. The unit for all panels is meters.
74 model to reproduce the true variability and mean state of the ocean. The effectiveness of the assimilation approach requires t hat the forecast error in the assimilation run has a strong projection onto the leading EOFs calculated from the temporal variability of the unconstrained model run. Whether or not this is satisfied firstly depends on the ability of the model to reproduce the correct spatial distribution and correlation structure of the variability of the real ocean. A second requirement is that the leading EOFs of the real ocean's temporal variability effectively resolve the forecast error. In the case of the identical twin experiment, the EOFs optimally resolve the temporal variability of the "true" ocean. However, because of model error the EOFs will be less efficient for resolving the forecast error when assimilating real altimetry data. Consequently, a greater fraction of the forecast error will be in the unresolved subspace than for the identical twin experiment. Also, since the data consist of only the anomalies of sea-surface height, the ability to estimate the ocean state requires that the unconstrained model accurately reproduces the mean state of the real ocean. Again, this requirement was completely satisfied for the identical twin experiment, but may not be sufficiently satisfied when assimilating real altimetry data. From the comparison of the mean 14~ isotherm depths computed from the control run and estimated from XBT data (Figure 2) it was shown that the model underestimates the mean subsurface meridional temperature gradient. However, since our focus for assimilating SHA data is on estimating the variability of the ocean state, errors in the mean sea-surface height of the model should be of second order importance.
5.1. Configuration of the experiment The TOPEX/Poseidon altimetry data were assimilated over the period of J a n u a r y 1, 1993 to January 1, 2000. The initial state for the assimilation and control (i.e. with no data assimilated) runs was taken as the fully spun-up state on J a n u a r y 1, 1993 from the unconstrained model run. The asymptotically stationary covariances were calculated in the subspace spanned by the leading 75 EOFs (from the full set of 252) calculated from the control run sampled every 10 days. The coarser time sampling for the EOF calculation (10 days as opposed to 3 days for the identical twin experiment) was chosen to correspond with the effective time resolution of the real altimetry data. These EOFs accounted for 97.0% of the total temporal variability of the control run over the seven year period of the experiment. With the average seasonal cycle removed, the fraction of the explained variability decreased to 35.8%. There is no simple criteria for evaluating the number of EOFs that should be retained since the true forecast error is not known. However, due to the importance of errors in the model and the external forcing data, even retaining a very large set of EOFs from a long model run may not enable the resolution of the components of forecast error related to model error. However, from Figure 4 it appears that the variability, at least for the SHA field, is well reproduced by the model when compared with the observed SHA. The model error covariances were set to 10 -2 times the filtered covariances of the model's temporal variability from the control run (~ = 10-2). Several values for this scaling parameter were considered and the chosen value selected on the basis that
75 it produced the best fit of the three day forecast to the observed SHA. Because the same observation error covariances were used as for the identical twin experiment, the relative size of the corrections made to the forecasts were smaller t h a n for the identical twin experiment (in which 7 =10-1). An approximate m e a s u r e of the magnitude of the relative corrections is given by the average ratio of the forecast error variance to the sum of the forecast plus the observation error variances. This value is 2.6x 10 -3 for the experiment with real altimetry data and 7.6• 10 -3 for the identical twin experiment. Because of errors in the model, the external forcing data and the SHA observations, both the model and observation errors are larger for this experiment t h a n for the identical twin experiment (in which the model and observations were perfect). When calculating the K a l m a n gain matrix, shown in (6) in the appendix, a decrease in the forecast error covariances has the same effect as an equivalent increase in the observation error covariances. Therefore, the reduction in ~/for this experiment m u s t actually be caused by a greater increase in the observation error covariances. Increased observation errors can be expected from i n s t r u m e n t error and also error caused by interpolating the observations both in space and time. Also, the representativeness error should be higher t h a n for the identical twin experiment, due to a relatively larger fraction of the forecast error being in the unresolved subspace. There m a y also be a contribution to the representativeness error from a component of the real SHA variability t h a t the ocean model can not reproduce, such as the increased high frequency component seen in Figure 5. Fully fitting the analyzed state to this component would decrease the analysis error, but may also introduce dynamical imbalances resulting in an increase in the subsequent forecast error. The initialization procedure is m e a n t to ameliorate such problems, but can not completely remove the component of the state t h a t is inconsistent with the model dynamics. Finally, the serial correlation of the observation errors caused by the temporal interpolation of the altimetry data requires an additional inflation of the observation error statistics.
5.2. Results from a s s i m i l a t i n g TOPEX/Poseidon SHA Figure 16 shows the effect of assimilating TOPEX/Poseidon SHA data on the temporal evolution of the rms error of SHA from the estimated states (relative to observed values). In panel (a), the rms error of the analyzed states is normalized by the error from the control run. The rms error of SHA from the runs with and without assimilation are also shown individually in panel (b). The assimilation was successful in reducing the error in SHA consistently over the full seven year period. There appears to be a slight upward trend in both timeseries in panel (b) t h a t may indicate a problem with the model reproducing a component of the SHA variability over decadal timescales. On average, the rms error of SHA in the three day forecasts was reduced by 21.5% and in the analyzed states by 23.6% compared to the error from the control run. Figure 17 shows the rms error of SHA from the assimilation r u n normalized by the error from the control r u n and averaged over the last four years of the experiment as a function of location. The largest reduction in the error occurs in
75
Figure 16. The rms difference between the SHA of the estimated states from the TOPEX/Poseidon altimetry assimilation experiment and the observations. The relative rms error after normalizing by the error from the control run is shown in (a) and the non-dimensional rms error (normalized by D) for the control run and for the analyses from the assimilation run are shown in (b).
the region between 10~ and 20~ in the western p a r t of the basin. However, significant error reductions are also seen over the entire equatorial region between about 5~ and 10~ The least error reduction occurs south of 10~ and also n e a r the eastern boundary, north of 10~ Figure 18 shows the temporal evolution of SHA from the observations and from the control and assimilation runs (upper two panels) for two locations. Consistent with the power spectra shown in Figure 5 for two somewhat different locations, it is clear t h a t the SHA from TOPEX/Poseidon contains significantly more power at higher frequencies t h a n the SHA from the control run. At the first location (15~ 37~ the control run SHA is uncorrelated with the observed SHA. The assimilation is able to significantly improve the fit to the observations at this location and increases the correlation with the observed SHA from - 0 . 0 4 to 0.57 (see Table 1). At the second location, near the origin of the North Equatorial Counter current (7~ 37~ the observed SHA exhibits significantly more variability t h a n the SHA from the control run. The assimilation is capable of improving the fit to the observations at this location, especially around month 24 and after month 60. The correlation with the observed SHA is increased from - 0 . 1 8 to 0.32 by the assimilation. Figure 19 shows the power spectra of the observed and analyzed SHA for the two locations used in Figure 5. Comparison with t h a t figure shows t h a t the assimilation increases the power at the higher frequencies and causes the overall shape of the power spectra to more closely resemble t h a t of the observations.
77
Figure 17. The relative rms error of the estimated states from the assimilation experiment with real altimetry data over the period January 1, 1996 to J a n u a r y 1, 2000. The rms error is normalized by the error in the control run.
Figure 18. The temporal evolution of SHA from the observations and from the control (No-assim) and assimilation runs is shown in (a) and (b) at two selected locations from the experiment with real altimetry data. The 14~ isotherm depths estimated from the XBT data is plotted in panels (c) and (d) for the same two locations. Also shown in the lower panels is the depth of the isotherm with the same time-averaged depth from the control and assimilation runs (14.4~ and 17.9~ for panels (c) and (d), respectively).
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Figure 19. The power spectra of SHA from the TOPEX/Poseidon data and the analyzed states from the assimilation run over the period J a n u a r y 1, 1993 to J a n u a r y 1, 2000. The spectra are shown for the same two locations used for Figure 5. Comparison with Figure 5 shows t h a t the assimilation causes the power spectra to more closely match t h a t of the observations at the two selected locations.
Table 1 Correlations between SHA from TOPEX/Poseidon and from the control and assimilation runs (top two rows) and the correlations between the isotherm depths from XBT data and the control and assimilation runs (bottom two rows). The two locations are 15~ 37~ and 5~ 37~ respectively. The 14~ isotherm from the XBT data was correlated with the isotherm from the model with the same time-averaged depth. Location #1 Location #2 SHA Control -0.04 -0.18 SHA Assim 0.57 0.32 Isotherm Control 0.29 0.01 Isotherm Assim 0.02 0.47
79 An XBT data set (provided by D. Snowden at the Physical Oceanography Division of the Atlantic Oceanographic and Meteorological Laboratory, NOAA) was used to validate the impact of the assimilation procedure on the subsurface temperature variability. The 14~ isotherm depth was first computed from each available XBT profile. These depths were then gridded onto a uniform 1~ grid using both spatial and temporal smoothing. A Gaussian smoothing kernel was used with a horizontal length scale of 1.2 ~ and a temporal scale of 2 months. A simple quality control procedure was also applied where any value differing by more t h a n two s t a n d a r d deviations from the temporal m e a n was excluded. Due to differences in the m e a n isotherm depth between XBT data and the control run, the isotherm from the model runs were chosen to be those with the same time-averaged depth as the XBT 14~ isotherm. The resulting isotherm data from the model runs were t h e n mapped to a uniform 1~ grid using the same smoothing procedure used for the XBT data. In the bottom two panels of Figure 18 the 14~ isotherm depth estimated from the XBT data is compared with the depth of the isotherm from the control and assimilation runs with the same mean depth. At the first location the correspondence between the observed and model isotherm depths is quite poor with the variability in the model significantly less t h a n in the XBT data. This suggests t h a t the model does not adequately reproduce the physical processes responsible for subsurface variability at this location. The assimilation of SHA had only a small impact on increasing the overall magnitude of the variability while the correlation was decreased from 0.29 to 0.02. At the second location the a m o u n t of variability in the isotherm depths from the XBT data and the model runs is much more similar. Also the correlation is increased from 0.01 to 0.47 by the assimilation of SHA. This improved fit to the XBT isotherm depths for locations closer to the equator was seen more generally and is summarized in Figure 20 which shows the average change in the correlation coefficient due to the assimilation as a function of distance from the equator. Positive values show the extent by which the average correlation coefficient between the assimilation run and the XBT data is greater t h a n the correlation coefficient between the control run and the XBT data. It is clear from this figure t h a t the benefit from assimilating SHA for the subsurface t e m p e r a t u r e estimates is m a x i m u m at the equator and beyond about 13 ~latitude the assimilation has no positive impact on the variability of the isotherm depth. This result is consistent with the discussion of Section 2 reporting previous investigations t h a t showed the variability of SHA to be dominated by the variability of the thermocline only in the equatorial band, while at 15~ the influence of surface buoyancy fluxes was already very significant, and dominating in the subtropics. An alternative evaluation of the downward projection of the SHA information can also be made. From Figure 2 it was seen t h a t over a large portion of the model domain the SHA and the depth of the 14~ isotherm exhibit significant negative correlation in the unconstrained model run. Therefore, the correlation of the observed SHA with the isotherm depth from the control and assimilation runs can provide an indication of the impact from the assimilation on the subsurface temperature variability. This assumes t h a t the SHA and the depth of the isotherm
80
IE
0.15 0.125
._o
o.1 o.o75 ,.0.05 o o 0.025 {D
c
0
c
-0.025
tO
-0.05 -0.075 -0.1
0
5 10 15 degrees latitude from equator
Figure 20. The average change in the correlation coefficient between the XBT and model isotherm depths due to the assimilation of SHA from TOPEX/Poseidon. Positive values m e a n the correlation between the assimilation r u n and XBT d a t a is greater t h a n the correlation between the control run and XBT data. This value is shown as a function of distance from the equator. The 14~ isotherm from the XBT data was correlated with the isotherm from the model with the same time-averaged depth.
are also negatively correlated in the real ocean. Figure 21 shows the correlation between the TOPEX/Poseidon SHA and the depth of the model 14~ isotherm over the last four years of the experiment as a function of location. In the left panel the isotherm depth from the control run is used and for the right panel the isotherm depth in the analyzed states from the assimilation run is used. A noticeable reduction in the correlation coefficient due to the assimilation occurs over most of the model domain. The m e a n change is - 0 . 1 1 with large changes approaching - 1 . 0 occurring again in the central equatorial region within 5 ~ latitude of the equator. Large negative changes are also seen in the north-west and south-west regions of the model domain. Conversely a substantial increase in the correlation is seen along the western boundary in the North Brazil current region. To determine how well the variability of the state is estimated at timescales greater t h a n one year, the SHA along 10~ was filtered with a 12-month r u n n i n g mean. The filtered SHA from both the control and assimilation runs and from TOPEX/Poseidon are plotted in Figure 22. These results show t h a t the assimilation is able to significantly improve the i n t e r a n n u a l variability of SHA. At 10~ the rms difference with the observations is reduced on average by 31.0% by the assimilation when only the i n t e r a n n u a l variability is considered. Over the region between 10~ and 10~ the mean correlation coefficient between the model and observed SHA increased from 0.26 to 0.55. Figures 23, 24 and 25 show the zonally integrated meridional t r a n s p o r t from the control and assimilation runs across three chosen latitudes. As in the previous figure, a 12-month r u n n i n g mean filter was applied to the transports. The upper
8!
Figure 21. The correlation over the period January 1, 1996 to January 1, 2000 between the TOPEX/Poseidon SHA and depth of the 14~ isotherm from (a) the control run and (b) the assimilation run using real altimetry data.
Figure 22. Timeseries of SHA along 10~ after filtering with a 12-month running mean from (a) the control run, (b) the assimilation run, and (c) TOPEX/Poseidon. Units are centimeters.
82 panels show the vertical structure of the meridional transport as a function of time from both runs. The vertical layers are split into two sets so that a narrower color scale could be used for the deeper layers. The total transport within the southward flowing deep layers (300m to 700m depth at 5~ and the equator and 150m to 600m depth at 5~ is also shown in the bottom panels. Significant zonally integrated meridional transport is already present in the control run at all three latitudes in the deep layers with southward transport. At 5~ the meridional transport has a time-averaged value o f - 7 . 9 Sv, decreasing to -4.0 Sv at the equator and -3.4 Sv at 5~ The transport loss between 5~ and the equator is most probably due to equatorial upwelling. It is clear that the assimilation strengthens these transports and also enhances their interannual variability. The mean deep layer transports at 5~ the equator and 5~ are enhanced by 1.6 Sv, 2.1 Sv, and 1.3 Sv, respectively. Conversely, the change in the surface layer transport is oriented northward with a mean change in magnitude of 0.54 Sv, 1.2 Sv and 0.24 Sv at the same three latitudes. At the equator and the northern latitude this represents an increase in strength of northward transports, but at the southern latitude the assimilation causes a decrease in the magnitude of the southward transport in the surface layer. A detailed dynamical explanation of this important effect of SHA assimilation on the meridional transports is obviously complex. The only qualitative statement we can make is that, as previously discussed, in the equatorial band SHA variability is controlled by the variability of the thermocline. Constraining the SHA will conversely affect the isotherm depths, changing the meridional and zonal temperature gradients and hence the intensity of the deep geostrophic flow. The increase in the mean meridional transports from assimilating SHA, which has a zero mean value, must originate from nonlinear interactions within the model dynamics. The specific mechanism responsible for this increase is impossible to ascertain without carrying out a detailed diagnostic analysis of the current field and its variability which is beyond the scope of the present study. 6. SUMMARY AND C O N C L U S I O N S The major goal of this study was to assess the effectiveness of TOPEX/Poseidon altimetry data assimilation in constraining the tropical Atlantic circulation, its subsurface thermal structure and the mass exchanges between the subtropics and the tropics. An efficient reduced-rank stationary KF was implemented with a reduced-gravity primitive equation ocean model for this purpose. The ocean model has a strong seasonal cycle that represents a significant proportion of the overall variability. Compared to the three day period for assimilating SHA data, model errors associated with this source of variability have a high serial correlation and therefore appear almost as a model error bias. Therefore, when using model-derived statistics to represent the effect of model error we chose to filter out the annual and semi-annual Fourier components, thus removing the variability associated with the model's seasonal cycle. Consequently, a more horizontally localized impact from individual assimilated observations is obtained. For both the
83
Figure 23. The zonally integrated meridional t r a n s p o r t across the equator after filtering with a 12-month running m e a n from (a) the control run and (b) the assimilation run. Note the difference in scale between the upper and lower set of layers. The units are kg s -1 m -1 with positive values indicating northward transport. The total transport in the layer between 300m and 700m depth is also show in (c) for the control and assimilation runs.
84
Figure 24. Same as figure 23, but at 5~ and with the total transport in the layer between 150m and 600m depth shown in (c).
85
Figure 25. Same as figure 23, but at 5~
86 identical twin and TOPEX/Poseidon assimilation experiments the relative rms error in the estimated state was reduced rapidly to the asymptotic value within the first month. Unlike the experiments of Brasseur et al. [1999] using a stationary error subspace, no subsequent error growth occurs. This suggests that the error in the unresolved subspace, which is not directly controlled by the assimilation procedure, does not experience substantial growth. For the identical twin experiment this was confirmed by explicitly calculating the component of the error in the unresolved subspace. This showed that the unresolved component of the error from the assimilation run was substantially reduced relative to the false ocean run. The ability of the assimilation scheme to control the error in the unresolved subspace is likely due to the nature of the dynamics in the tropics as compared with the midlatitude case considered by Brasseur et al. [1999]. However, the relatively smaller error reduction in our experiment with real altimetry data is at least partly due to a smaller fraction of the error being resolved by the EOFs. Therefore, an adaptive approach may be useful to either modify the basis functions of the resolved subspace [e.g. Brasseur et al., 1999] or to estimate a highly parameterized model for the covariances in the unresolved subspace [e.g. Blanchet et al., 1997]. The use of either approach could provide new information on the statistics of the model error while improving the accuracy of the state estimates. By calculating the correlations from the output of the unconstrained model run, a strong connection was found between SHA and the depth of the thermocline base (14~ isotherm). This provided encouraging evidence that the subsurface temperature variability could be constrained by assimilating SHA alone. Results from the identical twin experiment confirmed that the chosen assimilation method can effectively recover the subsurface temperature and velocity fields. However, for the identical twin experiment several assumptions were satisfied which were not guaranteed to hold when using real altimetry data. These included the poor resolution of the forecast error using model-derived EOFs and error in the mean state of the unconstrained model run. Comparing the TOPEX/Poseidon SHA with the output from the unconstrained model run showed that the ocean model already reproduces the overall variability of SHA quite well. However, the higher frequency contributions to the variability are noticeably underestimated with this effect most pronounced away from the equator. After assimilating the TOPEX/Poseidon SHA data, the fit to the observed SHA was improved by 23.6%. In addition, the assimilation caused the power spectra of the estimated states to match that of the observations more closely. Also, over interannual timescales the average correlation coefficient between the model and observed SHA increased from 0.26 to 0.55 within 10 ~latitude of the equator. Validation of the estimated subsurface temperature fields was performed using gridded and temporally smoothed XBT data. This showed a substantial improvement in the estimated temperature variability due to the TOPEX/Poseidon SHA assimilation only within about 13 ~ of the equator. At the equator the correlation coefficient increased from 0.19 to 0.32 by assimilating the SHA observations. This increase in fit is quite significant considering that the rms difference of the analyzed states with the observed SHA was only decreased by 23.6%, on average. The
87 assimilation caused no improvements beyond this equatorial band. However, it is not clear then why the assimilation caused a significant increase in magnitude of the correlations between isotherm depth and SHA observations over the entire domain. Even though the assimilation produces a significant increase in magnitude of the negative correlations between isotherm depth and SHA observations over the entire domain, it is clear that a major proportion of the subsurface thermal variability outside the equatorial band is not linked to SHA variability. A number of recent studies has in fact shown that in the subtropics SHA variability is dominated by surface buoyancy flux and not by the vertical movements of the thermocline (see Section 2). Consistently, the zonally integrated meridional transports in the equatorial region (5~ to 5~ were substantially affected by the SHA assimilation, in both the mean values and variability in the surface and deeper layers. Meridional transport were insensitive to SHA assimilation beyond about 10 ~north and south of the equator. A detailed explanation of this result is complex and beyond the scope of the present study. A clear message however emerges from the present results: SHA is a powerful dynamical constraint for the subsurface thermal structure and system of currents only in the tropical band around the equator. Acknowledgements
The authors thank Dr. Robert Molinari and Derrick Snowden for providing the XBT data. This research was carried out with the support of the Office of Naval Research, under the Department Research Initiative "Predictability of the Ocean and the Atmosphere", grant N00014-98-1-0881 (M. Buehner), of NASA grant NAG511746 (P. Malanotte-Rizzoli and T Inui) and of NSF grant 5-23964 (A. Busalacchi). A P P E N D I X : DERIVATION OF R E D U C E D - R A N K KALMAN F I L T E R In the EKF, the numerical model is used to produce a forecast of the ocean state, denoted by x f. At each time measurements of the real ocean state are available, the forecast is corrected to produce the analyzed state, denoted by x a, according to
x~(t) = xf(t) + K ( t ) [ y ( t ) - 74 (xf(t))],
(4)
where 7/() is the possibly nonlinear model of the measurement process, y is the vector of observations and K is the Kalman gain matrix. The analyzed state is then used as the initial conditions for the model integration up to the next time observations are available, xf(t + 1 ) = .h4 [x~(t)],
(5)
where r is the nonlinear ocean model. The gain matrix is calculated such that the error variance in the resulting analyzed state is minimized [see e.g. Gelb, 1974, for details]. This requires the specification of the statistics for the errors in the observations (instrument error and error of representativeness) and in the numerical model (uncertain model parameters, unresolved physical processes, discretization
88 error, etc.). These errors are assumed to be unbiased Gaussian random variables with specified covariances and no temporal correlation. The accumulated effect of errors in the model over the forecast period is modeled by the addition of an error vector to the state vector at the end of the forecast period, that is, xt(t + 1)= ~
[xt(t)] + q(t + 1),
where x t is the true ocean state and q is the model error vector with covariance matrix Q. Using the prescribed error statistics for the observations and the model together with the linearized model dynamics, the covariances of the error in the forecast, denoted by P, are then computed. However, the prohibitive expense of computing P at each analysis time when using a realistic ocean model provides the main motivation for using a simplified version of the EKF. The first approximation to the EKF requires the definition of a reduced-dimension subspace within the space spanned by the model state vector. The computational expense can then be greatly reduced by only calculating the error covariances of the state within this subspace. As a result, the corrections made to the forecast at each analysis time only span the subspace. However, the full nonlinear model, (5), is used to produce the forecasts. The subspace should be chosen to efficiently resolve the forecast error expected within the assimilation system. Similar to Cane et al. [1996], we use the leading EOFs of the model state vector, including SHA, as the basis of the resolved subspace. The EOFs are calculated from the covariances of the temporal variability of an unconstrained model run. For each variable type (i.e. velocity, temperature, layer thickness and SHA) the model state was first normalized by its spatially averaged standard deviation, denoted by the matrix D. This is a simple approach for rendering each variable type dimensionless, thus allowing the multivariate EOFs to be obtained using the Euclidean norm. The retained EOFs are denoted as the columns of the matrix E,. The dimension of the resolved subspace is typically between O(10) and O(102) compared with the dimension of the full model state that is typically at least O(105) for realistic models (473,607 for the tropical Atlantic model). The equations of the EKF required to calculate the gain matrix and the analysis and forecast error covariances are projected into the resolved subspace, resulting in the following: KrP~ = P,(t + 1) =
( P ~ - I + HT, R - 1 H,) - 1 HTR -1
(6)
(I - K,.H,.) P,. M~(t)P~(t)lYL(t) T + Q,,
(7) (8)
where P~ is the covariance matrix of the resolved error in the analyzed state, M, is the linearized dynamics describing how perturbations in the resolved subspace evolve to the next analysis time, and H, = HDE, is the linearized operator for mapping perturbations in the resolved subspace into the space of the observations. The matrices Q~ and R are the model error covariances in the resolved subspace and the observation error covariances, respectively. The form used to obtain K~ is equivalent to the form presented in BMR but is more suitable when the number
89
of observations is large compared to the number of retained EOFs and R is easily inverted due to being diagonal or block-diagonal. The second approximation to the EKF algorithm is to assume the forecast error covariances are stationary within the subspace. To obtain the stationary forecast error covariances the model is first linearized with respect to the mean state of the unconstrained model run over the period of the experiment. The linearization is performed numerically only within the reduced-dimension subspace as described by BMR. With this linear propagator the doubling algorithm [Anderson and Moore, 1979] is used to obtain the stationary forecast error covariances. The doubling algorithm is equivalent to, though more efficient than simply repeatedly computing (6)-(8) until Pr becomes effectively constant. However, the assumption of stationarity will only be valid when the observing network and the model and observation error covariances are stationary. The validity of this assumption also requires that any neutral or growing dynamical mode have a nonzero projection onto the observations and the model nonlinearities are relatively unimportant for error growth [Anderson and Moore, 1979]. The linearity assumption is probably only reasonable for tropical regions where linear dynamics dominate for the temporal and spatial scales in which we are interested. Consistent with these assumptions, Verron et al. [1999] found little benefit from dynamically evolving the error covariances when applying the SEEK filter to the tropical Pacific. To compute K~ for the reduced-rank stationary KF, the stationary value of P~ obtained with the doubling algorithm is used in (6). Multiplication of the the gain matrix, K~, with the innovation vector, [y - n (xf)], produces a correction in the resolved subspace that is combined with the forecast according to xa(t) = xf(t) + D E r K ~ ( t ) [ y ( t ) - 7/(xf(t))] .
(9)
Therefore, the full gain matrix in (4) is replaced by the reduced-rank stationary approximation DErKr. However, for the forecast step the full nonlinear ocean model (5) is still used. REFERENCES
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90 Buehner, M., and P. Malanotte-Rizzoli, Reduced-rank Kalman filters applied to an idealized model of the wind-driven ocean circulation, (in press, J. Geophys. Res.) 2003. Cane, M., A. Kaplan, R. N. Miller, B. Tang, E. C. Hackert, and A. J. Busalacchi, Mapping tropical Pacific sea level: Data assimilation via a reduced state space Kalman filter, J. Geophys. Res., 101, 22,599-22,617, 1996. Chen, D., A. Busalacchi, and L. Rothstein, The roles of vertical mixing, solar radiation, and wind stress in a model simulation of the sea surface temperature seasonal cycle in the tropical Pacific Ocean, J. Geophys. Res., 99, 20,345-20,359, 1994. Cooper, M., and K. Haines, Altimetric assimilation with water property conservation, J. Geophys. Res., 101, 1059-1077, 1996. Daley, R., Atmospheric Data Analysis, 457 pp., Cambridge University Press, Cambridge, 1991. Duing, W., R. L. Molinari, and J. C. Swallow, Somali current: Evolution of surface flow, Science, 209, 588-590, 1980. Ezer, T., and G. L. Mellor, Continuous assimilation of Geosat altimeter data into a three-dimensional primitive equation Gulf Stream model, J. Phys. Oceanogr., 24, 832-847, 1994. Ferry, N., G. Reverdin, and A. Oschlies, Seasonal sea surface height variability in the North Atlantic Ocean, J. Geophys. Res., 105, 6307-6326, 2000. Fukumori, I., and P. Malanotte-Rizzoli, An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model, J. Geophys. Res., 100, 6777-6793, 1995. Fukumori, I., R. Raghunath, and L. Fu, Nature of global large-scale sea level variability in relationship to atmospheric forcing, J. Geophys. Res., 103, 5493-5512, 1998. Gelb, A., ed., Applied Optimal Estimation, 374 pp., M.I.T. Press, Cambridge, MA, 1974. Gent, P. R., and M. A. Cane, A reduced gravity primitive equation model of the upper equatorial ocean, J. Comput. Phys., 81,444--480, 1989. Ghil, M., and P. Malanotte-Rizzoli, Data assimilation in meteorology and oceanography, Adv. in Geophys., 33, 141-266, 1991. Gourdeau, L., J. Verron, T. Delcroix, A. Busalacchi, and R. Murtugudde, Assimilation of TOPEX/Poseidon altimetric data in a primitive equation model of the tropical Pacific Ocean during the 1992-1996 E1Nino-Southern Oscillation period, J. Geophys. Res., 105, 8473-8488, 2000. Gu, D., and S. G. H. Philander, Interdecadal climate fluctuations that depend on exchanges between the tropics and extratropics, Science, 275, 805-807, 1997. Houtekamer, P. L., and H. L. Mitchell, A sequential ensemble Kalman filter for atmospheric data assimilation, Mon. Wea. Rev., 129, 123-137, 2001. Huang, R. X., and J. Pedlosky, Climate variability inferred from a layered model of the ventilated thermocline, J. Phys. Oceanogr., 29, 779-790, 1999.
91 Inui, T., A. Lazar, P. Malanotte-Rizzoli, and A. Busalacchi, Wind stress effects on subsurface pathways from the subtropical to tropical Atlantic, J. Phys. Oceanogr., 32, 2257-2276, 2002. Kalnay et al., The NCEP/NCAR reanalysis project, Bull. Amer. Meteor. Soc., 77, 437-471, 1996. Kleeman, R., J. P. McCreary, and B. A. Klinger, A mechanism for the decadal variation ofENSO, Geophys. Res. Lett., 26, 1743-1746, 1999. Kraus, E., and J. Turner, A one-dimensional model of the seasonal thermocline, II, TeUus, 19, 98-105, 1967. Lazar, A., R. Murtugudde, and A. J. Busalacchi, A model study of temperature anomaly propagation from the subtropics to the tropics within the south Atlantic thermocline, Geophys. Res. Lett., 28, 1271-1274, 2001. Levitus, S., Climatological Atlas of the World Ocean, NOAA Prof. Paper No. 13, 173 pp., U.S. Government Printing Office, Washington, D.C., 1982. Liu, Z., A simple model of the mass exchange between the subtropical and tropical ocean, J. Phys. Oceanogr., 24, 1153-1165, 1994. Liu, Z., Forced planetary wave response in a thermocline gyre, J. Phys. Oceanogr., 29, 1036-1055, 1999. Malanotte-Rizzoli, P., R. E. Young, and D. B. Haidvogel, Initialization and data assimilation experiments with a primitive equation model, Dyn. Atmos. Oceans, 13, 349-378, 1989. Malanotte-Rizzoli, P., R. E. Young, K. Hedstrom, H. Arango, and D. B. Haidvogel, Water mass pathways between the subtropical and tropical ocean in a climatological simulation of the North Atlantic Ocean circulation, Dyn. of Atm. and Ocean, 32, 331-371, 2000. Mayer, D. A., R. L. Molinari, M. O'Neil-Baringer, and G. J. Goni, Transition regions and their role in the relationship between sea surface height and subsurface temperature structure in the Atlantic Ocean, Geophys. Res. Lett., 28, 3943-3946, 2001. Mayer, D. A., M. O. Baringer, and G. J. Goni, Comparison of Hydrographic and Al-
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92 Schneider, N., A. J. Miller, M. A. Alexander, and C. Deser, Subduction of decadal Pacific temperature anomalies: observations and dynamics, J. Phys. Oceanogr., 29, 1056-1070, 1998. Stammer, D., Steric and wind-induced changes in TOPEX/Poseidon large scale sea surface topography observations, J. Geophys. Res., 102, 20,987-21,009, 1997. Verron, J., L. Gourdeau, D. T. Pham, R. Murtugudde, and A. J. Busalacchi, An extended Kalman filter to assimilate satellite altimeter data into a nonlinear numerical model of the tropical Pacific Ocean: Method and validation, J. Geophys. Res., 104, 5441-5458, 1999.
Interhemispheric Water Exchange in the Atlantic Ocean
edited by G.J.Goniand P. Malanotte-Rizzoli 9 2003 ElsevierB.V.All rightsreserved.
A synthetic float analysis of upper-limb m e r i d i o n a l o v e r t u r n i n g circulation interior ocean p a t h w a y s in the tropical/subtropical Atlantic G. R. Halliwell, Jr. a *, R. H. Weisberg b , and D. A. Mayer c a a Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Causeway, Miami, Florida, 33149, USA b College of Marine Science, University of South Florida, St. Petersburg, Florida, USA c National Oceanic and Atmospheric Administration, Atlantic Oceanographic and Meteorological Laboratory, Miami, Florida, USA Synthetic floats are released in an ocean general circulation model to study fluid pathways followed by the upper limb of the meridional overturning circulation from the subtropical South Atlantic to the subtropical North Atlantic. The floats are designed to track this fundamentally three-dimensional, nonisentropic flow while sampling water properties and all terms of the equation governing the vertical component of relative vorticity. The low-resolution ocean simulations demonstrate how upper-limb flow navigates the complex, timedependent system of wind-driven gyres. Pathways that extend into the interior North Atlantic before entering the Caribbean Sea are emphasized over the more direct western boundary route. A large number of floats are released in the southern hemisphere to verify the importance of such interior pathways in the model and document key events that occur along them. Upper limb water first approaches the equator in a modified inertial western boundary layer. Equatorial processes (visco-inertial boundary layer dynamics, upwelling, heating) are necessary to reset water properties and permit fluid to permanently cross the equator, typically requiring eastward retroflection into the EUC. After upwelling at the equator, fluid that does not advect northward or southward into the interior returns to the western boundary and turns northward in a frictional western boundary layer. The generation of negative relative vorticity by planetary vorticity advection can break the boundary layer constraint and permit retroflection into the NECC near 5 ~ from late spring through fall. Once in the *Corresponding author: Tel. 1+305+361-4621, E-mail:
[email protected] a Present address: College of Marine Science, University of South Florida, 9t. Petersburg, Florida, USA
94 interior, this fluid advects northward into the southern subtropical gyre in a flow governed by Ekman dynamics. There the fluid subducts and advects southwestward to enter the Caribbean Sea under the influence of layered thermocline dynamics. The importance of interior pathways is conf~rmed although we note that fluid parcels generally take complex paths and frequently make multiple attempts to enter the northern hemisphere or multiple treks around gyres. 1. I N T R O D U C T I O N The overturning circulation of the global ocean exerts an important influence on the storage and redistribution of internal energy within the Earth's climate system. The Atlantic Ocean plays a unique role in this by virtue of the deep water formation that occurs at high latitudes. North Atlantic Deep Water formed near Iceland and Greenland flows southward as a Deep Western Boundary Current that eventually feeds the deep flows of the Indian and Pacific Oceans. This necessitates an upper ocean return flow within the Atlantic basin. The resulting overturning system of cold deep water exiting and warmer surface water entering the North Atlantic is referred to as the Meridional Overturning Circulation (MOC), and the return flow is referred to as the upper-limb of the MOC. The understanding of upper-limb pathways and associated water mass modifications that occur en route is important because these will influence the vertical stability of the flow that eventually reaches the subpolar North Atlantic. This could then influence the deep water formation rate and thus the strength of the MOC and associated net northward heat flux. The upper-limb of the MOC cannot follow a simple path from the South Atlantic to the North Atlantic because of the angular momentum constraint imposed by the Earth's rotation and the resulting system of wind-driven gyres. Of particular interest to the present study are the paths taken by fluid parcels as they navigate from the South Atlantic subtropical gyre, across the equatorial and tropical gyres, and then into the North Atlantic subtropical gyre. It is known from previous studies that the circulation connecting these gyres must be fully three-dimensional and seasonally varying. The equator is a location of special concern because of strong upwelling and surface heating. Western boundary processes are also important. Unlike the Gulf Stream that closes the North Atlantic subtropical gyre over a continuous meridional extent of some 15 degrees latitude, the western boundary currents of the equatorial and tropical gyres generally extend along less than 5 degrees latitude and flow in opposite directions. Munk [1950] suggested that these features should not even be called gyres for these reasons. Moreover, these western boundary currents vary seasonally, and the North Brazil Current (NBC) that closes the equatorial gyre is unstable during the time of year when these gyres are most developed (late spring through fall). During this time, the southeastward western boundary flow of the tropical gyre acts to block the NBC, so a large fraction of the NBC retroflects and flows eastward to become the North Equatorial Countercurrent (NECC). The retroflection is unstable and eddies occasionally pinch off and
95 migrate northward carrying a fraction of the upper-limb fluid. In addition to the gyres, upper-ocean flow also includes subtropical overturning cells that return water subducted in the subtropical North and South Atlantic back toward the equator [Malanotte-Rizzoli et al., 2000; Lazar et al., 2002). These and other processes provide a multitude of possible upper-limb pathways. The observational record is presently inadequate to accurately map these pathways, quantify the mass fluxes associated with them, understand the controlling dynamics, and quantify the water mass modifications that occur. Numerical model experiments are needed, and while ocean general circulation models are imperfect, they are sufficiently realistic to begin identifying and understanding the physical processes that govern upper-limb pathways, and to help guide observational strategies. Recent improvements in numerical models, including the development of the HYbrid-Coordinate Ocean Model (HYCOM) [Bleck, 2002; HaUiweU, 2003] with the addition of improved synthetic float/drifter technology, allow us to pursue a new model analysis of upper-limb pathways. We identify upper-limb pathways, along with important dynamical and thermodynamical processes that control them, in a low-resolution HYCOM simulation of the Atlantic Ocean. Because of the low model resolution, the western boundary pathway and the influence of NBC rings are not a focus of the present study. Instead, specific attention is given to fluid parcels that follow interior pathways as governed by processes resolved in the low-resolution model. In particular, upper-limb water that enters the interior via the NECC before joining the North Atlantic subtropical gyre circulation is studied in the most detail. Thermodynamical variables, along with terms of the relative vorticity balance, are interpolated to the floats to aid in our understanding of the governing processes. In doing this, we demonstrate the importance of five key processes that govern interior upper-limb pathways: (1) boundary layer dynamics, including western, surface, and equatorial boundary layers; (2) equatorial upwelling and the associated water mass modifications; (3) seasonal variability of the wind-driven tropical and equatorial gyres; (4) interior Ekman wind-drift; and (5) subtropical subduction. These processes change or reset fluid parcel vorticity in ways that permit upper-limb fluid to cross the equator and transit between gyres. Despite the limitations of low-resolution simulations, the insights gained are scientifically interesting and will aid in the interpretation of observations and in the design of high-resolution simulations. In carrying out these analyses, we validate the use of synthetic threedimensional Lagrangian (particle-following) floats as a tool for numerical circulation model analysis of thermohaline circulation pathways. The feasibility of using model floats to track fluid pathways have been demonstrated in earlier studies. For example, Fratantoni [1996] seeded the Miami Isopycnic-Coordinate Ocean Model (MICOM) with isopycnic floats to study flow pathways in the tropical Atlantic. Malanotte-Rizzoli et al. [2000] and Lazar et al. [2002] used isopycnic floats to track fluid pathways from the subtropics to the equator, seeding the flow after it had subducted. However, there are limitations to using isopycnic floats in models to track flows that are fundamentally non-isentropic. Harper [2000] seeded subduction regions of the global ocean near the surface
96 with three-dimensional particle-following floats and successfully tracked fluid pathways before and after subduction. The present study demonstrates the importance of using three-dimensional particle-following floats to map pathways of upper-limb MOC fluid as it flows from the subtropical South Atlantic across the equator and into the North Atlantic subtropical gyre. 2. BACKGROUND AND GOALS The tropical Atlantic Ocean circulation has been the subject of studies ranging from major multi-national expeditions to individual efforts. A selected few papers provide the essential backdrop for our work. We begin with the analysis of IGY hydrographic sections by Roemmich [1983] in which estimates of the zonally integrated mass and internal energy transports are presented at several latitudes based on geostrophic and Ekman dynamics. These quantify the MOC and show that the upper-limb transports must transition from primarily within the thermocline layer upon approaching the equator from the South Atlantic to the mixed layer upon leaving the equator to the North Atlantic. This can only occur through water mass modification as fluid is upwelled and heated. Philander and Pacanowski [1986a; 1986b] model the seasonally varying circulation along with meridional mass and internal energy fluxes. These analyses demonstrate a dependence upon the gyres' seasonally varying dynamic topography [e.g., Garzoli and Katz, 1983; Katz, 1987] for the storage and release of the internal energy accumulated as a result of the MOC and surface heat flux. On the basis of this information, plus a seasonal Sverdrup streamfunction analysis, Mayer and Weisberg [1993] hypothesize a composite annual cycle to accommodate across-equator and inter-gyre exchange in a manner consistent with a cyclonic tropical gyre negating a continuous western boundary current (NBC). The hypothesis depends on different processes acting at different locations during different times of year to influence the upper-limb transports (e.g. inertial boundary layer dynamics at the equatorial western boundary during late spring/summer and interior Ekman transports near the NECC ridge/trough region during late fall/winter). These processes force a significant fraction of upper limb fluid to flow into the ocean interior within the NECC during late spring through fall when internal energy is stored at that latitude, and to then flow northward in the near-surface wind-drift during the following winter when internal energy is released to higher latitudes. Since key processes governing this interior pathway hypothesis are reproducible in low-resolution ocean simulations, verification of this hypothesis is a particular focus of the present analysis. According to Schott et al. [1998], up to one-quarter of the upper limb flow on annual average follows a pathway that extends into the interior North Atlantic, either flowing eastward in the NECC or flowing directly northward from the equator. Based on water property analysis, Schmitz and Richardson [1991] and Schmitz and McCartney [1993] also find that upper-limb pathways must include an interior route. Eulerian analysis of Atlantic Ocean simulations by the Navy Layered Ocean Model [Fratantoni et al., 2000] has recently been
97 employed to estimate upper-limb fluxes following different pathways. That study also demonstrates the likely importance of interior pathways. Annual mean flux estimates along different pathways consistent with these and other studies are summarized in Figure 1. We follow the observational synthesis by Schott et al. [1998], who subdivide the MOC upper-limb flow approaching the equator from the southern hemisphere into three vertical layers: surface (~o < 24.5 ), thermocline (24.5 < ~e < 26.8), and intermediate ((r o > 26.8 and above 1000 m). The intermediate layer contributes a substantial fraction of the upper-limb flow, but it follows the western boundary and does not contribute significantly to interior North Atlantic pathways. The thermocline layer flow does contribute to interior pathways, but only after upwelling into the surface layer at the equator, consistent with the asymmetry described by Roemmich [1983]. The 4 Sv annual mean northward surface layer flow in the interior, which represents the interior pathway flows of interest to this study, consists of about equal contributions of fluid entering from the western boundary region via the NECC
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Figure 1. Schematic diagram of the upper limb transport contribution of fluid approaching the equator from the south within three vertical layers: surface layer (a015~ Figure 4) to be impacted by surface cooling and downward Ekman pumping. There they begin to subduct, moving slowly downward and towards the southwest. After spending an extended period of time in the interior during and after subduction (typically 2-4 yr as demonstrated later), the floats selected for display in Figure 8 enter the Caribbean at depths of around 100 m.
111
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5.3. Co-existence of the upper-limb MOC flow and subtropical cells Another complexity not considered in Figure 1 is the North Atlantic subtropical cell, a focus of recent studies such as Malanotte-Rizzoli et al. [2001] and Lazar et al. [2002]. To visualize how the upper-limb MOC flow and subtropical cell coexist, two subsets of 25 floats that took interior pathways are selected; one set that entered the Caribbean and another that did not. Paths from each of these two subsets are plotted in both a meridional cross-section and a horizontal map (Figure 10). The subset that does not enter the Caribbean traces a subtropical overturning cell confined to the upper 120 m. The horizontal map shows that the return paths to the equator are convoluted, with many floats taking eastward excursions in the NECC, consistent with the results of Malanotte-Rizzoli et al. [2001] and Lazar et al. [2002]. Comparing horizontal maps of the two subsets, floats that subduct in the western part of the basin are more likely to enter the Caribbean than floats that subduct in the eastern part. Other factors such as wind stress forcing [Inui et al., 2002] and seasonal variability also play a role.
112
There is also the question of the existence of the North Atlantic subtropical cell. This cell clearly exists in this study and in other low-resolution model studies [Malanotte-Rizzoli et al., 2001; Lazar et al., 2002]. In contrast, nearly all of the particle-following floats released in the North Atlantic subtropical subduction zone in the high-resolution model study of Harper [2000] entered the Caribbean versus advecting to the equator. Further analysis of the interaction between the MOC and the North Atlantic subtropical cell will therefore be deferred to future high-resolution simulations.
5.4. Importance of using particle-following floats to track upper-limb pathways Neither isopycnic floats nor surface drifters can reproduce complete upper-limb interior pathways such as those presented in Figure 8. Upper-limb pathways revealed by both isopycnic and three-dimensional Lagrangian floats are compared by releasing isopycnic floats in the southern hemisphere release box at a depth of 175 m during four seasons: February, May, August, and November (Figure 11). The resulting 200 isopycnic floats are compared to the 200 threedimensional Lagrangian floats released at the same depth and times as part of the full southern hemisphere release experiment. A large fraction of the Lagrangian floats enter the northern hemisphere, many following interior paths. 25 MOC Upper Limb Float Paths
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Figure 10. Paths in meridional-depth space (top), and in horizontal maps (bottom), of 25 floats that followed the interior pathway. Floats that entered the Caribbean as part of the MOC are shown in the left panels while floats that returned to the equatorial region as part of the North Atlantic subtropical overturning cell are shown in the right panels.
113 In contrast, the isopycnic floats remain in the same model layer and cannot upwell into the westward flowing SEC at the equator. As a result, these floats remain permanently confined near the equator or along the eastern boundary region off the African coast. Isopycnic floats released in the southern hemisphere thermocline water cannot reproduce the fluid pathways into the northern hemisphere. This result also supports the necessity of equatorial upwelling for thermocline water to eventually follow an interior pathway (Figure 1). Upper-limb pathways revealed by both surface drifters and three-dimensional Lagrangian floats are compared by releasing both types of floats at a depth of 3 m at 2-degree latitude intervals along a meridional line located at 30~ (Figure 11). Over a three-year time interval, the Lagrangian floats are observed to deepen north of about 15 ~ and to begin their southwestward journey toward either the Caribbean Sea or the equator. In contrast to this, all of the surface drifters continue northward in the Ekman layer until they are trapped in the subtropical convergence zone. For floats to properly track fluid pathways in the subtropical North Atlantic, they must deepen in response to Ekman pumping. 3-D Lagrangian Floats Released at 175m
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114 Although the limitations of both isopycnic floats and surface drifters are evident in Figure 11, we do not mean to imply that they cannot be used to study many aspects of flow pathways in the tropical Atlantic Ocean or in other regions. For example, the use of isopycnic model floats to delineate the return flow of subtropical cells to the equator [Malanotte-Rizzoli et al., 2000; Lazar et al., 2002] is reasonable because the flow along these path segments is only weakly nonisentropic. Neutrally buoyant floats have been successfully used in a wide range of observational studies. Surface drifters can provide useful information over time intervals sufficiently short so that subduction is not important, or so that they do not become trapped in convergence zones. However, a holistic picture of pathways taken by a fundamentally non-isentropic flow such as the upper limb of the MOC can only be delineated using three-dimensional Lagrangian floats. 5.5. F l o a t c e n s u s
Of the 7200 floats that were released in the southern hemisphere, only 2823 penetrated north of 8 ~ during the ten-year simulation. A total of 2646 of the floats eventually entered the Caribbean as part of the MOC upper-limb flow. Of the floats entering the Caribbean, a total of 272 (10.3%) take an interior pathway by flowing directly northward from the equator. A total of 361 floats (13.6%) take an interior pathway by flowing eastward within the NECC from the western boundary region. The remaining 2013 floats (76.1%) flow into the Caribbean without taking one of the interior pathways. Of these, 651 flowed directly along the western boundary from the southern hemisphere into the Caribbean without taking an eastward excursion along the equator. To assess the relative importance of the North Atlantic subtropical cell, there are 418 floats that took one of the interior pathways but never entered the Caribbean Sea. All but a small number of these floats returned to the equator after subducting in the subtropical North Atlantic. Although a larger number of subducted floats entered the Caribbean than did not, we point out that some of the floats entering the Caribbean actually returned to the equator at least once as part of the subtropical cell. Consequently, the importance of the subtropical cell in the model is larger than indicated by the numbers given above. Moreover, since subduction releases energy to the atmosphere, subducted floats returning to the equator via the subtropical cell contribute to the upper limb northward heat flux whether or not they end up in the Caribbean or points farther north. With nearly 1/4 of upper limb floats that entered the Caribbean having taken an interior pathway during part of their existence, these pathways are clearly important in the model simulation. This percentage is in close agreement with the 25% estimate of Schott et al. [1998]. While we again caution against using low-resolution results to update quantitative estimates, the present results do provide a qualitative verification on the interior pathway importance. 6. CASE S T U D I E S AND M E C H A N I S M S So far the path compilations show the upper limb pathways to be fully threedimensional and seasonally dependent. Equatorial upwelling, water mass
115 modifications, and eventual subduction are attributes of all model floats that take interior pathways. We now turn our attention to physical mechanisms that permit the floats to navigate across the equator and between the various gyres. We do this through case studies, focusing in on six individual floats whose paths are illustrated in Figure 12. We compare five floats that took interior pathways to one that did not. Floats 1 and 2 correspond to the two cases highlighted in Figure 8; i.e., floats that follow the interior pathway via the NECC and enter the
Figure 12. Paths of six floats color-coded to reveal the depth. Dots are plotted on 1 January of each year reveal the temporal progression along the paths.
116 Caribbean, but with one first transiting along the equator and the other not. Float 3 also transits along the equator across the basin and upwells into the SEC, but it moves northward into the interior long before reaching the western boundary. Float 4 transits eastward within the NECC and completes a circuit around the clockwise equatorial gyre before entering the North Atlantic subtropical gyre via the ocean interior. It does not initially turn northward because it is at a depth of 40-50 m, or below the northward Ekman wind drift. It crosses its original eastward path into the interior at a time of year when the NECC (and hence the cyclonic tropical gyre) is not strongly developed. Float 5 directly follows the western boundary into the Caribbean. Float 6 follows the interior pathway via the NECC. However, this float shows a more convoluted path, including one complete cycle around the equatorial gyre. Floats 1-5 are selected to provide relatively simple examples of float behaviors. Float 6 is representative of the more typical float that requires multiple attempts at entering the North Atlantic subtropical gyre before actually doing so. This complexity must eventually be taken into account in flow diagrams such as Figure 1. Common to the five floats in Figure 12 that take interior pathways is that they spend a long time in the interior, typically 2-4 yr. Along each of these float paths we sample horizontal position, depth, model layer number, temperature, salinity, density (a2), relative vorticity, and the material derivative of relative vorticity. We also sample the eight terms that comprise the water parcel's relative vorticity balance, with terms labeled according to the letters designated in (2). These time series are shown in Figure 13a for the first six years of the Float 1 trajectory. We emphasize Float 1 in the time series analysis since it represents the principal attributes of the interior pathway hypothesis and because the processes acting on similar path segments of other floats are very similar to those acting on Float 1. The time history in Figure 13a includes pivotal segments of the float's trek to the Caribbean. These segments are: (1) retroflection into the EUC, (2) eastward flow within the EUC, (3) retroflection into the NECC, (4) northward flow in the interior Ekman wind drift, and (5) post-subduction southwestward flow into the NEC. Vertical shading bars highlight these five time intervals in Figure 13a, and time series for all segments except (4) are presented in expanded detail in Figures 13b-e because it is difficult to see important aspects of the vorticity balance in Figure 13a. Figure 13f adds further insight by focusing on that part of the history of Float 5 where it flows directly along the western boundary without retroflecting into the NECC. Errors in the estimation of vorticity balance terms would be a significant issue if we were trying to perform a Lagrangian vorticity budget analysis and prognostically forecast vorticity evolution along pathways. In the present study, however, we analyze the Eulerian vorticity budget along relatively short path segments. At the beginning of each path segment, the fluid parcel has undergone such large prior modifications from processes such as equatorial upwelling and subtropical subduction that it can essentially be considered a new parcel with new initial conditions. In these path segments, we are able to clearly identify the dominant terms in the balance that act to control the motion of fluid parcels.
117 Float 1
Figure 13a. Time series of several variables interpolated to the position of float 1 during the first six years of its existence The top seven panels contain position and thermodynamical variables. The bottom ten panels contain the vorticity analysis, specifically relative vorticity (RV), the material derivative of observed RV, and terms (A) through (H) of the relative vorticity equation (2). Shading indicates time intervals emphasized in the text. Vertical dashed lines mark one-year intervals (the model year is 366 days long).
118
6.1. Float I approaches the equator and retroflects into the EUC We begin our discussion of mechanisms with the time interval (days 360-480) when Float 1 approaches the equator from the south and turns east to begin its transit across the basin. The top two panels of Figure 13b (relative to the top left panel of Figure 12) show that the approach, including an overshoot of the equator, occurs through day 420 as the float moves northwestward along the western boundary. During this time, the depth is at first relatively constant, it deepens slightly as the float approaches the equator, and it then shoals steadily after the equator is reached. Temperature and salinity both covary to keep the density relatively constant. The float is located in model layer 8 except for a brief interval near day 400 when it moves into model layer 9. This produces an abrupt change in float thermodynamical properties that may be viewed as a truncation error resulting from the discrete model layers. During the initial stage of the approach when the float is moving to the northwest along the western boundary the relative vorticity is positive and increasing despite the planetary vorticity tendency (C) acting to decrease it. The controlling term is the stretching term (D) as the thermocline slope decreases along the western boundary toward the equator to ensure a continuous slope across the equator. Positive relative vorticity starts to decrease around day 380 assisted by horizontal stress torque (G). At about 2.5~ the stretching term reverses and the vertical stress torque (H) increases to compensate for this. This corresponds to entry into the equatorial visco-inertial boundary layer [Charney and Spiegel, 1971], where the thermocline deepens and increased dissipation (via vertical friction) is necessary to constrain the relative vorticity. Thereafter, relative vorticity decreases primarily by planetary vorticity advection as the float overshoots the equator to about 2 ~ as it retroflects into the EUC. Once heading eastward and eventually back toward the equator the relative vorticity is controlled by planetary vorticity advection plus vortex stretching, the latter partly compensated by relative vorticity advection. The equatorial visco-inertial boundary layer region of the model is located within about 3 degrees of the equator. As in nature, it arises so that meridional derivatives may be continuous across the equator. Since planetary vorticity advection acts to decrease (increase) the relative vorticity of fluid approaching from the south (north) a cusp in zonal velocity would form on the equator were it not for frictional smoothing. For this particular float, vertical friction torque is the primary smoothing agent with horizontal friction of secondary importance. In summary, the dynamical approach of the float to the equator is in the form of a modified inertial jet adhering to the western boundary. When the jet encounters the equatorial boundary layer its dynamics are altered such that vertical friction plays a larger role. Kinematically, we see how the float is steered by the flow field. From day 360-385, the float hugs the western boundary maintaining positive relative vorticity. It is freed from this constraint around day 385 by entering the equatorial visco-inertial boundary layer, which causes relative vorticity to become negative. Upon overshooting the equator, the accumulated negative relative vorticity is sufficiently large for the float to retroflect eastward and equatorward.
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380
400
420
440
460
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, '
----r
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480
Days
Figure 13b. Same as Figure 13a, but for a short segment along the path of float 1 when it advects northward along the western boundary to the Equator and retroflects eastward into the EUC.
120 6.2. Float I transits across the basin a l o n g the e q u a t o r The next segment of the Float 1 journey is provided by Figure 13c, which highlights the eastward movement across the basin within the EUC over days 560-660. During this time, after the float has adjusted to its overshoot of the equator and the balance terms show minimum variability, the float remains slightly north of the equator and steadily rises in depth by about 90 m. Relative vorticity remains positive (the float is in the cyclonic shear region of the EUC), but displays noticeable oscillations. The lead terms in the vorticity balance include non-linear advection (B), vortex stretching (D), planetary advection (C), and local rate of change (A). Terms (C) and (A) tend to covary at about 20-day time scale consistent with tropical instability waves near the equator [e.g., Weisberg and Weingartner, 1988; Weisberg and Qiao, 2000]. Terms (B) and (D) also tend to covary suggesting that vortex stretching is accommodated by an advective rate of change in relative vorticity along the float path. Eventually, the float is close enough to the surface to flow westward within the SEC. This reversal occurs near day 750 in Figure 13a. Prior to and subsequently, the float upwells steadily through the water column undergoing significant changes in T, S, and a~ as the float continues to cross through several model layers. So long as the latitude changes are small, however, there are no major changes in relative vorticity and hence no need for large terms in the balance tendencies. During this stage the float (or simulated water parcel) is increasing its internal energy via surface heat flux and hence increasing its potential for contributing toward the net northward internal energy flux by the MOC. By the latter stages of this westward transit (illustrated in Figure 13d) the water properties associated with Float 1 are entirely different from the properties when it was initially released. 6.3. Float 1 departs from the e q u a t o r and enters the NECC The Float 1 movement westward is relatively uneventful through around day 950 (Figure 13d). It then approaches the western boundary and turns more rapidly northward along this boundary around day 960. This is followed by eastward retroflection into the NECC around day 970. Western boundary effects first become evident after day 945 when relative vorticity begins to decrease. It reaches its largest negative values during retroflection. The relative vorticity decrease around day 945 is initiated by both the vortex stretching term (D) and the horizontal stress term (G), the former because the thermocline slopes up into the western boundary in the northern hemisphere to accommodate a northward flow. As the northward turn takes effect, planetary vorticity advection then becomes the leading term in generating negative relative vorticity. Coincident with this, however, we see an increase in horizontal frictional torque, which tends to offset planetary vorticity advection, thereby limiting the decrease in relative vorticity. The counteraction of these two terms indicates that horizontal frictional boundary layer dynamics [Munk, 1950] play a significant role in the western boundary of the equatorial gyre. This is different from the modified inertial boundary layer behavior described by Fig 13b when the float first approached the western boundary from the ~outhern hemisphere at
121 Float
1 travels
eastward
along
the
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122
Float I t u r n s north, t h e n e a s t into the N E C C -20
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126 terms. Because of the small values of these vorticity tendencies, this balance is almost impossible to see in Figure 13a. The float is heading southwest into a region of convergent isopycnals so the stretching term is accommodating conservation of potential vorticity as prescribed by layered thermocline theory [Luyten et al, 1983].
6.6. Float 5 travels along the western boundary Float 5 crosses the equator on the western side of the basin and then proceeds northwest along the western boundary directly towards the Caribbean without retroflecting into either the EUC or the NECC. We use this float to examine mechanisms associated with this more direct western boundary route, referring to Figure 13f for a segment of its history beginning on day 300. We begin with Float 5 located at about 65 m depth near the western boundary and south of the equator (much shallower than Float 1). The float deepens to 85 m as it approaches the equator, and then upwells to about 20 m while it resides on the equator. Relative vorticity is initially small and positive. It becomes larger and negative when the float reaches the equator (after day 410), largely because of planetary vorticity advection [term (C)], and it remains negative while the float resides on the equator. Different from Float 1, however, is the relative unimportance of the vortex stretching term as the float enters the equatorial region. Being above the EUC and thermocline it does not participate in the stretching associated with the EUC and hence does not generate sufficient relative vorticity to retroflect. While the float is at the equator several terms contribute to its Lagrangian vorticity tendency, but these tend to cancel one another. After day 360, the float leaves the equator and moves northwestward along the western boundary past the NECC retroflection region. Relative vorticity gradually becomes more negative during this time, but it never grows to the large magnitude observed in Fig 13d by the time it passes the NECC retroflection region. Planetary vorticity advection is primarily responsible for the increase in negative vorticity, but both horizontal and vertical friction torques combine to limit the rate of negative vorticity generation and prevent retroflection. After day 390, the increase in negative vorticity is primarily countered by horizontal friction torque as a Munk boundary layer is established. There are two key points associated with keeping this float attached to the western boundary. The first is its position near the surface where vertical friction torque can act (with the horizontal friction torque) to dissipate the generation of relative vorticity by planetary vorticity advection. The second is the float's crossover to the NEC side of the NECC trough prior to sufficient negative relative vorticity generation to facilitate a retroflection into the NECC. In other words, the NECC is not sufficiently developed when this float transits northwest along the western boundary to accommodate retroflection. Had it been present, the negative relative vorticity effect of stretching (compression by movement towards the NECC trough) would have facilitated retroflection by increasing negative relative vorticity and breaking the Munk layer constraint. Thus, floats positioned near the surface during the time of year (winter/spring)
127 when the surface dynamic topography associated with the equatorial and tropical gyres is relatively flat are able to proceed along the western boundary. 7. D I S C U S S I O N The HYCOM model, which uses an open-ocean vertical coordinate system that transitions from level (pressure) coordinates near the surface to isopycnic coordinates with increasing depth, is analyzed to study upper-limb pathways and mechanisms associated with the Atlantic Ocean's meridional overturning mode of circulation. The model domain extends from 30~ to 70~ on a 1.4-degree horizontal resolution grid with 25 vertical layers. Seasonally varying, climatological atmospheric fields are used to drive the model. The simulated Eulerian fields are similar in their overall attributes to those produced by other investigators using a variety of models. Our emphasis is on determining the three-dimensional Lagrangian pathways and the mechanisms by which these pathways are achieved as an analog to how they may occur in nature. Thus, we seed the model with Lagrangian floats, track these floats from their points of origin in the southern hemisphere subtropical gyre across the equator and across the equatorial and tropical gyres into the northern hemisphere subtropical gyre, and log the material property transformations that occur en route. Specific emphasis is on the vertical component of vorticity and how the various terms comprising the vorticity balance sum together locally to enable the floats to negotiate their individual treks. The meridional overturning circulation is well represented, on average, with a zonally integrated strength of about 16 Sv in the subtropical North Atlantic. Approaching the equator from the south, the upper-limb shows northward flow within the thermocline and southward flow in the surface Ekman layer. A transition occurs in the vicinity of the equator where the thermocline waters upwell and are transported farther north in the surface Ekman layer. This is a well-known attribute described, for example, by Roemmich [1983]. What the pathways are, and how the water mass transformations occur, are questions that we begin to answer in the present study. The system of seasonally varying wind-driven gyres are also well represented, as is the basic seasonal storage and release of internal energy associated with the gyres' dynamic topography. For instance, as in the z-coordinate model simulations of the seasonal cycle by Philander and Pacanowski [1986a; 1986b], we find a net northward internal energy flux by ocean currents into the NECC ridge in boreal spring/summer followed by a release of stored internal energy to the north in fall/winter. How this works is one question that we set out to address. More generally, we have addressed how fluid manages to cross the equator and wend its way through the seasonally varying wind-driven gyres, and also through the subtropical overturning cells. From south to north, the wind-driven gyres consist of the anticyclonic southern hemisphere subtropical gyre, the clockwise equatorial gyre that straddles the equator, the cyclonic tropical gyre, and the
128 anticyclonic northern hemisphere subtropical gyre; these gyres being separated from one another by the zonally flowing (westward) SEC, (eastward) NECC, and (westward) NEC, respectively. Thermocline and lower surface layer water that approaches the equator from the south in the western boundary layer retroflects eastward into the EUC. This water warms and upwells into the westwardflowing SEC. The westward equatorial flow that reaches the western boundary then flows northwestward along the coast as the NBC. Two different routes have been proposed for upper-limb flow within the NBC to reach the Caribbean Sea: 1) a western boundary current route, either directly [Philander and Pacanowski, 1986b] or within eddies [Johns et al., 1993; Barnier et al., 2001] and 2) an interior route [Mayer and Weisberg, 1993]. To highlight the Sverdrup streamfunction inconsistency with a direct western boundary current route, Mayer and Weisberg [1993] suggested the equatorial and tropical gyre naming and proffered a conceptual model of how the upper-limb pathways may negotiate these, with the seasonal cycle playing a fundamental role. Upperlimb flow enters the interior within the NECC during late spring through fall when internal energy is stored at that latitude. At this time of year, horizontal friction torque in the frictional western boundary layer (where Munk layer dynamics prevail) is not strong enough to offset negative vorticity generation in the NBC by planetary vorticity advection. This generation breaks the boundary layer constraint, allowing the fluid to retroflect toward the east. The subsequent winter release of the internal energy stored at this latitude is facilitated by a shift in the wind field that opens up the NEC trough, thereby allowing for vortex stretching and northward flow in the surface Ekman layer. This two-staged hypothesis, utilizing different physical mechanisms during different phases of the annual cycle, accommodates the requirements for water mass transformations and internal energy storage and release. It is also kinematically consistent with the cyclonic tropical gyre negating a strong northwestward boundary current as a continuous feature from the equator to the Caribbean. After advecting northward into the North Atlantic subtropical gyre, upper-limb fluid subducts and advects southward and westward, eventually entering the NEC and the Caribbean. After subduction, the flow is governed by layered thermocline theory. This circuitous, upper-limb interior pathway hypothesis is what we set out to investigate by seeding the model with Lagrangian floats. The interior pathway is confirmed as a feature of the model's seasonal cycle. While somewhat more complex than surmised, it does account for a substantial fraction of the upperlimb northward heat flux. The importance of the set of five processes to interior pathways outlined in the Introduction is also confirmed. Rather than a few simple paths, however, most floats follow complicated paths typically involving multiple loops around gyres or in the North Atlantic subtropical overturning cell before proceeding farther north. Many floats also return to the southern hemisphere, either temporarily or permanently. Common to all of the floats that are analyzed in some detail is that water property modifications are necessary for water parcels to negotiate their paths across the equator and between gyres. Equatorial upwelling appears to play a central role in this, as it should, since the northward meridional internal energy
129 flux increases across the equator by a factor of about 1.5 as water is upwelled and heated [e.g., Bryden and Imawaki, 2001]. Complementing the equatorial upwelling is downwelling farther north in the subtropical gyre where most of the floats undergo subduction prior to entering the Caribbean. Thus, the pathways are fully three-dimensional, non-isentropic, and time dependent, relying on seasonal shifts in the wind and surface buoyancy flux fields to set the stage for water parcel movements between gyres. A corollary finding is that neither isopycnic floats nor surface drifters are adequate to track upper-limb pathways from the subtropical South Atlantic to the subtropical North Atlantic in their entirety. Three-dimensional Lagrangian floats must be used, and since constructing such a float presupposes that we know a proper specification for mixing, they are presently not possible in nature. They can only be employed in models and are then subject to the uncertainties in the model's non-isentropic process parameterizations. Depending on depth and location with respect to the phase of the seasonal cycle, floats can take a direct route to the Caribbean along the western boundary. For instance, floats along the western boundary near the surface in winter can flow directly into the Caribbean since the NECC is not developed during that time of year. The dynamic topography, by affecting the vortex stretching term, is instrumental in steering fluid parcels. When attached to the western boundary and with relatively flat dynamic topography in winter these floats are governed by a modified Munk boundary layer. While our findings are sensible, a major shortcoming is that they result from a rather coarse resolution model that only marginally resolves the boundary layers of importance (the frictional and inertial boundary layers along the western boundary and the visco-inertial boundary layer along the equator). Nevertheless, the technique of tracking Lagrangian floats and diagnosing the material property variations en route, including thermodynamic (temperature and salinity) and dynamic (vorticity) properties, provides a useful tool for developing an understanding of the processes that control the meridional overturning mode of circulation
Acknowledgements This work was initiated through support by the Office of Global Programs, National Oceanic and Atmospheric Administration, Grant number NA96GPO462. Informative discussions with Z. Garraffo, E. Chassignet, and A. Mariano of RSMAS; A. Wallcraft of the Naval Research Laboratory, and R. Bleck of Los Alamos National Laboratory are gratefully acknowledged. The authors thank W. Ebisuzaki of NOAA/NCEP for providing the NCEP/DOE reanalysis fields. A P P E N D I X 1. DIAGNOSIS OF VERTICAL VELOCITY The continuity equation in the HYCOM generalized vertical coordinate domain is
130 dw
"5-_ = - V s .v, a'p
(3)
where the subscripts indicate that the generalized vertical coordinate s is held constant during partial differentiation, and where vertical velocity is defined as
@
w = d-"t"
(4)
The model consists of layers k = 1, 2,..., N, with each layer k bounded by vertical coordinate surfaces located at pressure depths pk (x, y,s) above and pk+a (x, y , s ) below. Since the HYCOM generalized coordinate system is not Cartesian, integration of (3) downward from the surface introduces additional terms related to the sloping s interfaces. Integrating (3) downward from the surface where it is assumed t h a t w - 0, and dropping the subscript s, the vertical velocity at the base of model layer k=lis
~(p;) =
fd[ ~
-
Ov}@ = - ( p ; - a )
+N
Oul
Or1
(s)
where the integration is carried out from the surface down to an infinitesimal distance above interface 2. To obtain the vertical velocity at the top of layer 2, the continuity equation is also integrated across interface 2 from p~ to p+, which gives ( p~ ) - - ( ~
Oul Or1 ) Op2 Op2 - p~ ) ~ + ~ + (u~ - ~1--5-~ + (v~ - v, ) o y
(6)
More genei, ally, the vertical velocity at pressure P located within model layer n is w ( P ) = - - E ( Pk +I -- Pk ) "~x + "-~'y + q ( Pn +, -- P,, ) -"~x + "-~y k=~
n
(7)
OPk
Opk ]
q- E ( uk -- Uk-1 ) -~X q- ( vk -- Vk-1 ) --~y ' k=2
where the first term on the right side is zero for n = 1, and where P = Pn + q ( Pn+l - P n )
It is easy to show that
, O < q < l.
(8)
131
(9)
w(P) = w(p +)+ q[w(p~+l ) - w(p +)].
Thus, w varies linearly in the vertical within each model layer while discontinuities can exist at model interfaces. Although w can be estimated directly from (7), a simpler expression can be derived by considering the HYCOM continuity (thickness tendency) equation. If subgrid-scale processes (thickness diffusion) are neglected, the time evolution of the thickness of model layer k is given by Bleck [2002]"
]
( )
(10)
o Ap k) , = - V , 9(vkApk ) -- S~s Op k+l + ~~s k ' --~(
where (k0p/Os)k is the entrainment velocity in pressure per unit time across interface k and s is held constant during partial differentiation. Assuming that the surface interface is stationary, integrating (10) downward from the surface to interface n + 1 located at the base of layer n gives op,,+l = - ~ ("p k + ~ Ot k=~
- p,~) ~Ouk + -bV Ovk +
OPt:
k=2 ~
OPn+l -un Oz
Opk
( Uk -- Uk_I )--~X + ( V k -- Vk_l )--~y
OPn+l (~Op) v, Oy -~s n+l"
(11)
The interface vertical velocity vertically interpolated to pressure depth P within model layer n, with P given by (8), is
OP ot -
Op, o---i- + q
(
Opn+l
Opn
ot
ot
) {() _
=
~ Op
()
Op
-57.
+ q
~-67
- ~ ~s ,,+~
.
.-1 Ouk Ovk Ou,, 0% --Y~(Pk+l -- Pk ) ~ + --~y + q(P.+I -- P. ) ~ + --~y k=l n OPk Opt:
(12)
" ~ - E ( uk -- Uk-1 )--~X "~ ( vk -- Vk-1 ) W k=2
--Un
OPn --~X + q
( OPn+l Ox
Opn ) Ox
OPn -- Vn - ~ y + q
OPn+l Oy
OPn } Oy
From (7), the third and fourth lines of (12) are identified as the fluid vertical velocity w at pressure depth P. As a result, (12) becomes
(
OPn OPn+l w( P) = ~ + q Ot
){()
Op, + Ot
OPn OPn+l +u. ~ + q Ox
~ Op ~
}2 +
OPn + Vn Ox ~
()
Op _ ~ q S-O-ss. + 1 +q Oy
Oy
n
(13)
132
The vertical velocity of model pressure interfaces can be separated as follows:
0~; _ O~k _ ( &OP
- Or'
"~s) k"
(14)
If the entrainment velocity is zero, the interface vertical velocity equals 0~ k / Ot, which can therefore be interpreted as the local vertical velocity of a material surface. Substituting (14) into (13),
w(P) = ~ + q
at
Opn ( Opn+l +u. -~x + q Ox
Ox
OPn+l +v, L oy +q Oy
)
cOPn Oy
(15)
The first term on the right side of (15) is the vertically interpolated material surface vertical velocity. The other two terms on the right side represent the vertical component of layer k flow parallel to sloping interfaces. The vertical velocity at the top and bottom of layer n are obtained by setting q = 0 and q - 1, respectively:
(16) O ]) n § l jr. U n
Jr- V n
The first step in estimating w for float advection is to calculate threedimensional fields of w(p + ) and w( p~+, ). The vertical velocity is then estimated at the location of each float using the procedures described in Appendix 2. A P P E N D I X 2. SPATIAL I N T E R P O L A T I O N OF M O D E L VARIABLES TO FLOATS To interpolate variables stored on the HYCOM generalized coordinate system to float locations, the first step is to identify the model layer that contains the float. It is initially assumed to be in the same model layer that it was in during the previous time step. The sixteen pressure grid points surrounding the float are then selected. Land points are masked from the interpolation, as are points where the layer containing the float has collapsed to zero thickness at the bottom. If a sufficient number of surrounding grid points remain, a twodimensional polynomial surface is fit to the data to perform the interpolation using the same routine that Mariano and Brown [1992] employed for the largescale trend surface fit in their parameter matrix objective analysis algorithm. If too few surrounding grid points remain, a bilinear scheme using the four surrounding grid points is invoked to perform the interpolation. If only one point
133
remains, field values at that point are assigned to the float location. If the situation arises where no grid points remain, the float is assumed to have run aground. If the three-dimensional velocity field is perfectly known at the float location, this situation should never arise. However, the model grid poorly resolves the topography in coastal regions, and model fields must be extrapolated to floats located at the immediate coast. The relatively large interpolation errors at the coast cause some floats to run aground. Despite this problem, the large majority of floats never run aground. Of floats that follow the interior upper-limb pathway, none of them run aground before entering the Caribbean Sea. With the float initially assumed to be in model layer n, the pressure depths of model interfaces n and n + 1 are each horizontally interpolated to the float location. If the pressure depth of the float is no longer located between p, and p,+l, the new layer containing the float is identified. Other model variables are then interpolated to the float location. These variables are interpolated from their native grid (p for thermodynamical variables, u for zonal velocity, v for meridional velocity, or q for vorticity) on the Arakawa C-mesh. As a result, the grid box selection procedure described above is repeated for each of these grids. Horizontal interpolation of interface pressure and of model layer variables to a float is straightforward because it is values at the surrounding grid points that are interpolated. A different procedure is required for vertical velocity, which from (9) varies linearly with depth within the layer. It is first necessary to vertically interpolate w(p + ) and w(p~+~) from (16) at the surrounding grid points as follows: Given a float located at pressure P within model layer n, the quotient q is determined at the float location using (8) after interpolating p, and p,+~ from the surrounding points: q =
P Pn+l
-
Pn
(17)
-- Pn
The vertically interpolated value of w at each surrounding grid point is then estimated using w =
+ (1 -
),
(18)
and it is these w values that are horizontally interpolated to the float location. A P P E N D I X 3. FLOAT ADVECTION The fourth-order Runga-Kutta algorithm used to temporally interpolate velocity for float advection is a well-known procedure that is commonly used for synthetic floats and drifters in other models [e.g. Malanotte-Rizzoli et al., 2000]. The procedure requires estimates of the model velocity at the present time and at two earlier times. If three-dimensional Lagrangian floats are selected, the time interpolation is performed for all three velocity components; otherwise, it is performed only on the horizontal velocity components. Ideally, the time interval
134 separating each of the velocity component fields used in the interpolation should be between one and two hours, a criterion obtained from the MICOM float experience [Garraffo et al., 2001a; 2001b]. The model baroclinic time interval A tb~ is set prior to starting the model run. The velocity sampling time interval is set to an integer number of baroclinic time steps (Atilt = nvetAtb~). The float is then advected every 2nv~tAtb~ time intervals. When HYCOM is run at low horizontal resolution, A tb~ is typically about one hour, so nv~t is typically set to 2. (In the present study, these values are set to 1/20 day and 2, respectively so that floats are advected five times per day.) When HYCOM is run at high horizontal resolution, A tb~ is substantially less than one hour. In this case, nv~t is set to a value that insures that A t,~l is between one and two hours. With this selection made, the float is advected using fields at the present time and at the two earlier times t - n~tAtbc and t - 2n~tAtbc. When the HYCOM float subroutine is called at intermediate times, it only saves the u, v, and w fields required for the next time interpolation. Time series of float location and model variables are output every two days for analysis. Interpolation of water properties to the float location is performed only at these output time steps. For isopycnic and isobaric floats, w is not estimated or interpolated to float locations. If isopycnic floats are selected, the depth of each float is set to the vertically interpolated depth of the reference isopycnic surface after horizontal advection is performed. For isobaric floats, of course, the pressure depth is not changed.
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136 Lazar, A., T. Inui, P. Malanotte-Rizzoli, A. J. Busalacchi, L. Wang, and R. Murtugudde, Seasonality of the ventilation of the tropical Atlantic thermocline in an OGCM, J. Geophys. Res., in press, 2003. Levitus, S. and T. Boyer, World Ocean Atlas 1994 Volume 4: Temperature, NOAA Atlas NESDIS 4, U.S. Department of Commerce, Washington, D.C., 1994. Levitus, S., R. Burgett, and T. Boyer, World Ocean Atlas 1994 Volume 3: Salinity, NOAA Atlas NESDIS 3, U.S. Department of Commerce, Washington, D.C., 1994. Luyten, J.R., J. Pedlosky, and H. Stommel, The ventilated thermocline, J. Phys. Oceanogr., 13, 292-309, 1983. Malanotte-Rizzoli, P., K. Hedstrom, H Arango, and D. B. Haidvogel, Water mass pathways between the subtropical and tropical ocean in a climatological simulation of the North Atlantic ocean circulation, Dyn. Atmos. Oceans, 32, 331-371, 2000. Mariano, A. J. and O. B. Brown, Efficient objective analysis of dynamically heterogeneous and nonstationary fields via the parameter matrix, Deep Sea Res., 39, 1255-1292, 1992. Mayer, D. A. and R. H. Weisberg, A description of COADS surface meteorological fields and the implied Sverdrup transports for the Atlantic Ocean from 30 ~ to 60 ~N, J. Phys. Oceanogr., 23, 2201-2221, 1993. Munk, W.H., On the wind-driven ocean circulation, J. Meteor., 7, 79-93, 1950. Philander, S. G. H. and R. C. Pacanowski, A model of the seasonal cycle in the tropical Atlantic Ocean, J. Geophys. Res., 91, 14,192-14,206, 1986a. Philander, S. G. H. and R. C. Pacanowski, The mass and heat budget in a model of the tropical Atlantic Ocean, J. Geophys. Res., 91, 14,212-14,220, 1986b. Roemmich, D. H., The balance of geostrophic and Ekman transports in the tropical Atlantic Ocean, J. Phys. Oceanogr., 13, 1534-1539, 1983. Schmitz, W.J. and P.L. Richardson, On the sources of the Florida Current, DeepSea Res., 38 (Suppl. 1), $379-$409, 1991. Schmitz, W.J. and M.S. McCartney, On the North Atlantic circulation, Rev. Geophys., 31, 29-49, 1993. Schott, F. A., J. Fischer, and L. Stramma, Transports and pathways of the upperlayer circulation in the western tropical Atlantic, J. Phys. Oceanogr., 28, 19041928, 1998. Sun, S., R. Bleck, C. G. H. Rooth, J. Dukowicz, E. P. Chassignet, and P. Killworth, Inclusion of thermobaricity in isopycnic-coordinate ocean models, J. Phys. Oceanogr., 29, 2719-2729, 1999. Weisberg, R.H. and T.J. Weingartner, Instability waves in the equatorial Atlantic Ocean, J. Phys. Oceanogr., 18, 1641-1657, 1988. Weisberg and Qiao, Equatorial upwelling in the central Pacific estimated from moored velocity profilers, J. Phys. Oceanogr., 30, 105-124, 2000.
lnterhemispheric Water Exchange in the Atlantic Ocean edited by G.J. Goni and P. Malanotte-Rizzoli 9 2003 Elsevier B.V. All rights reserved.
A seasonal and i n t e r a n n u a l study of the w e s t e r n equatorial Atlantic u p p e r t h e r m o c l i n e c i r c u l a t i o n variability M. L. Vianna a * and V. V. de Menezes b aInstituto Nacional de Pesquisas Espaciais, CP515, S~o Josd dos C~mpos, SP, Brazil bVM Oce~nica S/C Ltda, Av. Lisboa 50/51, S~o Josd dos Campos, SP, Brazil We use five years (1995-2000) of blended Topex/Poseidon-ERS2 altimeter-derived upper ocean currents to investigate the observed seasonal and i n t e r a n n u a l variability of the circulation in the western equatorial Atlantic (15~176 70~ 25~ in the upper thermocline level. We produce a sea surface height field by mapping the Pathfinder collinear sea surface height anomaly data into a 0.25 ~ • 0.25 ~ - 10 day resolution grid, adding at each grid point the annual m e a n dynamic topography relative to 1000 m, which is obtained from the high resolution (0.25 ~ x 0.25 ~ 1997 Boyer-Levitus climatology. This climatology is first filtered to conveniently preserve features at a 300 km scale. The circulation field offshore of the 1000 m isobath was obtained using a generalization of the standard geostrophic equation at each 10-day time step, which is shown to be valid also on the Equator. Comparisons of the altimeter-derived fields are made against data from PIRATA moorings, CTD and ADCP WOCE Etambot cruise data spanning the Equator. It is shown that the currents derived from surface data correlate better with the ADCP-measured subsurface r a t h e r than to surface currents. The time evolution of annual and interannual patterns of the circulation field are obtained by separating the velocity component time series into period bands with a combination of EOF and Multichannel Singular Spectrum Analysis. A double-cored North Equatorial Contercurrent (NECC) is seen in August-September, with the southern branch related to the North Brazil Current (NBC) retroflection, while the northern branch is related to northern hemisphere westward flows turning to the southeast. The NECC main core at 5~ presents a meandering pattern west of 30~ which slowly propagates westward at a speed of 1.8 kin/day. The north branch of the South Equatorial Current (SEC) only appears aider July, recirculating water into a meandering EUC. An annual equatorial standing wave pattern confined to 3~176 has been detected possibly being the cause of the Equatorial Undercurrent (EUC) meanders and the appearance of open ocean windows for leakage of south Atlantic *Corresponding author. Email address:
[email protected];
[email protected].
138 waters into the north Atlantic and vice-versa. The variability between 5~176 is mostly in the interannual band with a very weak annual cycle. The estimation of the mean and interannual variability of the geostrophic meridional transports across 3~ and 3~ revealed an absolute maximum northward transport of 20 Sv at 3~ during January-March 1997, and a relative maximum southward transport of 10 Sv at 3~ centered in June of the same year. 1. I N T R O D U C T I O N In the past few years it has become a consensus that the issue of seasonal, interannual and decadal climate predictability is of importance for global economic and social issues. At these time scales, the ocean-atmosphere interactions determine the overall dynamics of the interacting coupled system, and the role of these processes in the upper layers of the ocean must be understood before predictability is achieved with an acceptable degree of accuracy. In the Atlantic, two modes of ocean-atmosphere interactions have been isolated as important in the genesis of climatically important sea surface temperature (SST) anomalies. One is an El Ni~o-like mode, which is mainly wind-driven; and another is a mode that involves subtropical-tropical interactions, explained as being mainly driven by a wind evaporation-SST positive feedback, generating the so-called Atlantic SST Dipole (see Servain et al. 1998 and references therein). This dipole paradigm has been challenged by a number of authors both by use of more advanced methods of analysis of the SST datasets (Mehta, 1998), or by analysis of subsurface data (Vauclair and du Penhoat, 2001), where it is shown that the dipole is not confirmed by data analysis. Despite these results of data analysis, many simple models suggest that a surface dipole mode may be a process driven by the wind evaporation-SST positive feedback mechanism (Chang et al. 1997; Xie, 1999), where the negative feedback necessary to quench an unbounded growth of SST anomalies is accomplished by ocean currents, but in an unspecified manner. The main periods of variability of this surface dipole mode are found in the 12-13 year and in the quasi-biennial bands (Servain, 1991), with its north side having a certain lag relative to the south. Mehta (1998) shows that the decadal band occurs preferentially in the southern hemisphere side of the dipole, and with different main period in the north. Among some of the open questions of interest, we may list the following: 1. What are the circulation processes through which the Atlantic Ocean can accomplish the negative feedback needed to stabilize unstable oscillations in the interhemispheric SST gradients appearing in the simple models ? 2. What is the role of the Subtropical-Tropical Cell (STC) (Liu and Philander, 1994; McCreary and Lu, 1994), if any, in relation to these oscillations? 3. If the STC plays a role, how does the southern STC interact with its northern counterpart, and what are the transport pathways closing an inter-hemispheric shallow exchange cell? 4. Can the circulation and transport variability in the lower branch of the Atlantic STC be studied by altimeter-derived flow field estimates based on sea
139 surface height fields? The STC processes involve, an off-equatorial mixed layer poleward E k m a n flow, and equatorward geostrophic flows just below the mixed layer, but still in the upper 200 m. The Equator and the eastern ocean are characterized by the vertical advection of subsurface water feeding this circulation cell. The western subtropics is the main region where the mixed layer detrains water to feed the geostrophic flow. In the Atlantic, the upper layer flow does not present symmetry between the two hemispheres. In this ocean, the cross-equatorial southeasterly wind field and the slanted Brazilian northeast coast causes a northwestward net transport by the Ekman currents, and a geostrophic flow, below which may be in the same direction north of 5~ This suggests that the simplest ocean STC models with rectangular basins may have limited applicability in the Atlantic. The surface wind stress and Ekman flow fields and transports in the mixed layer may be estimated from scatterometer wind measurements, while the determination of the upper thermocline fields just below the mixed layer can be also estimated from satellite altimetry, and is a matter of current research. The expensive methods of altimeter data assimilation into ocean models have been under study for some time, and have also been applied in a monitoring mode by leading laboratories (e.g., Malanotte-Rizzoli, 1996). However, we should point out that very few studies involving validation of current estimates obtained from these models have been presented in the published literature. The lack of moored measurements of the subsurface salinity field based on sensor data of acceptable quality is one of the present-day problems faced by these models (Segschneider et al., 2000), with a direct impact on the accuracy in the currents obtained. Two illustrative examples of investigations related to the STC with realistic model Atlantic basin geometry are the model works concentrating on the study of the mean (Malanotte-Rizzoli et al., 2000) and seasonal cycle (Lazar et al., 2002) of the STC transfer of subtropical thermocline waters into the Equatorial Undercurrent (EUC). The results of these studies suggest that horizontal transfers in the lower layer just above the thermocline level are made through complex exchange windows, which are influenced by the equatorial upper ocean zonal current distributions. The exchange window in the North Atlantic involves a large longitude interval (open ocean), where it is believed that the equatorward pathway is mostly a zigzag flow due to the strong zonal currents. The South Atlantic model work indicates that the only important exchange window is the western boundary. However, there is a open-ocean convergence of southern waters in the lower branch of the STC into the EUC through a northward veering branch of the North Brazil Current (NBC) flow at 3~ seen in Lazar et al. (2002). We dedicate this chapter to provide preliminary answers to question 4 and evaluate some issues related to question 3, stated above. In order to address these questions in a simple way, we are faced with the traditional difficulty of the singularity of the geostrophic balance equation over the Equator. We had been investigating how to extend the above-mentioned equation into the Equator, and we found two possible formulations that solve this problem based on the shallow water equations on the beta plane. The simplest formulation is described in the
14o present work. This work is organized as follows. Section 2 contains the derivation of the equation for the zonal velocity component valid at all latitudes, and still based only on slopes and curvatures of the sea surface height. Section 3 and 4 present the data sets used and the data processing methods, respectively. Section 5 shows the comparisons of the altimeter-derived fields against in situ measurements. Section 6 describes the mean, the annual cycle and interannual variability of the altimeter-derived circulation fields, and contrasts our results with those obtained from model studies made by other authors. Section 7 presents transport patterns, open ocean windows for interhemispheric transports and interannual variability of total meridional transport. Section 8 discusses the main conclusions of this work. Appendix describes the time filter used to obtain the separation of the zonal and meridional current velocity and transport data sets into annual and interannual period bands. This method was preferred to the more traditional one based on multi-annual averages for each month because it makes feasible an easier account of all of the variances involved. This method also makes possible to keep track of the small phase and amplitude interannual vacillations in the annual cycle during the study period. 2. ESTIMATES OF C U R R E N T VELOCITY F R O M S S H S L O P E S A N D CURVATURES
It is well-known that the lowest-order upper layer time-dependent (time scale larger than a few days) ocean dynamics can be accounted for by the Ekman and the geostrophic balances, which can be obtained independently from wind stress and surface height data (e.g. Gill, 1982). The problem with the geostrophic approximation is its traditional singularity on the Equator. However, several linear and nonlinear theories of both steady- state and time-dependent equatorial circulation indicate that the EUC is in geostrophic balance, although the standard f-plane geostrophic formula is not applicable at the Equator. The use of the meridionally differentiated form of the geostrophic equation has been studied by several authors to estimate the time-varying EUC flow in the Pacific Ocean, together with the standard form for the off-equator zonal currents (Picaut et al., 1989; Picaut et al., 1990; Picaut and Tournier, 1991). The so-called equatorial geostrophy approximation for zonal flows is based on meridional second derivatives of SSH, obtained by a Taylor expansion near the Equator, assuming that the sea surface slope is negligible there, and can be discarded as noise. Many authors (see Lagerloef et al., 1999, and references therein) have suggested methods to fit the off equatorial with the equatorial geostrophy equation. We present here a alternative methodology to extend the geostrophic approximation into the Equator. The working hypothesis is that the zonal scale of order greater than 600 km is much larger than the meridional scale of 300 km for the EUC, the zonal current being of order of 1 m/s, and the upper layer thickness being of the order 100 m. We start with the shallow water equations for a single baroclinic mode, which
141 may be written down in terms of the sea surface height variable, and assume t h a t the flow is divergence-free: (f + ~)~. x v = - V B , V . v = 0.
(la) (lb)
Here, V is the two dimensional operator, B = g r l + ( 1 / 2 ) ( u ~ + v ~ ) , r = ~.V • and v = u~ + vs where u and v are the horizontal velocity components in the eastward and northward direction respectively, g is the acceleration of gravity, and rl the instantaneous sea surface height relative to the geoid, not to be confused with the altimeter-derived sea surface height anomaly, 5, s i are eastward, northward and upward unit vectors and f is the Coriolis parameter. Taking the divergence of (la): f~u + ~ x v . V~ - (I + ~)r = -V2B,
(2)
where ~ is the meridional derivative of f, and expanding (2) in terms of the expressions for B and r f~ = [~ + ( v . v)~]u + v~(g~) + u~ + v,2 + 2vxuz, + v(V. v)~
(3)
where the x and y subscripts denote derivatives. Taking ~ from the meridional component of (la): f +; = -(1/~)(g~ + ~
+
vv~),
(4)
and inserting (4) in (3), we obtain: au + b + ( c / u ) = O,
(5a)
a = Z+ (V.v)~, b = gV2~ + f2 + u~2 + v~2 + v x % + uxv~ + v(V. v)~ and c = gfr]u + g(rl=vu - rluuu).
(5b)
Using (lb) we can express the exact result in (5a) and (5b) with the coefficients: a-~,
b - gV2y + f 2 + u~,2 + vxuy, c = g.f% - gVrl. Vu.
(5c)
Equation (5a) is a quadratic equation for u, and coefficients in (5c) are exact for flows with zero divergence. A simple scale analysis shows how some terms involving u- and v- derivatives may be neglected in the expression for a, band c. The simplifying assumption t h a t sea surface height field changes reflect the pycnocline depth changes is used: grl,~ g'h,
where g' is the reduced gravity, rl is the upward measuring sea surface height, and h is the corresponding downward pycnocline depth changes (see Gill, 1982 p.l19).
142 The m e a n depth of the pycnocline has a scale H = 100 m. If we assume t h a t the Kelvin wave speed has a scale of c = 2 m/s, then ca = g ' H = 4; and we m a y use the distance scales for x as L = 600 km, for y as I = 300 km and the zonal current speed u as U = 1 m/s. The scale for v is derived from (lb), which is then V = ( l / L ) U . We can then obtain the normalized values for (5a) and (5c), so t h a t the coefficients in (5c) beco m e: a-R0, b= c =
+
+
+
By -
where Ro = U//312 is the equatorial Rossby number, eL = l / L , a n d B,, = g ' H / ( B l 2 ) 2 is an equatorial Burger number. It can be seen t h a t B~ ~ 1.3 while Ro < 1. These values for B~ and R0 are sufficient to justify neglecting the u- and v- derivatives and the second x- derivative of u in the expression for b and c. Returning to dimensional variables, we write the solution to the quadratic equation (5a), with the simplified expressions for b and c, taking into account t h a t a
-'- ] ~ :
= (
2~ ) ( -
b+
.... 4 Z c ) ,
(6a)
b - g~y + f~, c = gf~.
(6b)
We made a thorough study of both roots of (6a), and concluded t h a t only the root with the plus sign was a valid approximation for the zonal velocity. The use of (6b) can be justified even on the Equator (c = 0). There, the nondimensional discriminant is b2 - 4 a c = B ~ h 2 y - 4 B u R o u ~ h ~ . This means t h a t second term on the right h a n d side of the latter expression is negligible in relation to the first term, if the values of B~ and Ro are those estimated above. Off the Equator, this expression is more general t h a n the geostrophic balance equation for zonal flows, since if b = f2 and b2 >:> 4/~c, then u ~ - c / b = - g ~ u / f , a result obtained by Taylor expanding (6a). Equation (6a) incorporates some cyclostrophic effects as well. We found t h a t in the vicinity of strong eddies the pressure gradient represented in c is such t h a t the term in the square root may become negative, a situation which we avoided by using only the real root at these grid points. We speculate t h a t in n a t u r e such pressure gradients never become larger, and this situation m u s t occur only due to imperfect mapping. We also found t h a t the solution along the Equator is 1
u = x-z(-b + Ibl). zp
(7)
143 The zonal velocity field on the Equator given by (7), together with the meridional velocity estimate described below, is continuous with the off-equator geostrophic velocity field. One interesting consequence of (7) is the fact that it does not allow a westward current on the Equator. When the current over the Equator tends to zero, we found that the v-field becomes dominant, corresponding to a veering or divergence of the flow. This one-sidedness in (7) is also consistent with the observation that westward flows due to the northern branch of the SEC are always confined to the mixed layer, extending to greater depths only off the Equator (Gill, 1982). This is interpreted as confirming that the SEC over the Equator is better described as a remnant of the Yoshida jet, which is not a geostrophic current, but an Ekman current. A very good description of this subject may be found in chapter 4 of the book by Philander (1990). The finite-difference implementation of (6) is described in the next Section. To calculate the meridional velocity field, we might integrate (lb) using (5) for the u-field. However, we did not find a proper analytical closed form solution without singularities as we did for the zonal current. Moreover, numerical integration also presented problems with the geometry of the western boundary. Therefore, we decided to use the geostrophic approximation instead. Since v is usually small (less than 50 cm/s) near the Equator, we first tested the applicability of a simple regularization of the type 1 I f -~ f / ( f 2 + e2) to compute v from the geostrophic formula, avoiding the calculation of higher (meridional-zonal) derivatives. However, an examination of Ship-mounted Acoustic Doppler Current Profiler (SADCP) data indicates that v is not zero at the Equator. Therefore, an assumption of v - 0 at the Equator is not realistic in the time scale of 10 days. Our conclusion is that v is geostrophic very near the Equator and its value can be well estimated from a spline interpolation scheme to complete the geostrophic v-data near the equator (between I~ and l~ 3. DATA 3.1. A l t i m e t e r d a t a
We use the collinear sea surface height anomalies (SSHA) from Topex~oseidon (T/P) and ERS2 satellites distributed by the NASA Ocean Altimeter Pathfinder Project. Data from each satellite has been processed by the Pathfinder team, with the standard altimetric corrections, including the inverted barometer, interpolation onto reference ground-tracks at 1 s sampling (approximately 7 kin), and referenced to the mean sea surface GSFC98 (Wang, 2000). A more detailed description of this issue can be found in Koblinsky et al. (1999). Since the ERS2 data set is shorter than the T/P (T/P begins in 1992 while ERS2 in 1995), we only use data from 13 May 1995 to 20 November 2000. Therefore, our T/P collinear data set consists of 205 repeat cycles (T/P has a sampling period of 9.92 days) and the ERS2 of 58 cycles (ERS2 has a sampling period of 35 days). 3.2. I n s i t u d a t a The in situ data used here are those obtained from western moorings of the PIRATA Program (Servain et a/.,1998), and from cross-equatorial cruises of World
144 Ocean Circulation Experiment (WOCE) Etambot 1 and 2 (Diggs et al., 2000; WOCE, 2000) (Figure 1). The PIRATA data consists of the daily time series of dynamic height relative to 500 m from 4 moorings located at 0~176 4~176 8~176 and 12~176 These moorings started to collect data in 1998, except for the last one which started in 1999. For the computation of dynamic height, the PIRATA program uses the temperature and salinity measurements taken in situ and the standard temperature-salinity (T-S) relationship from the Levitus climatology of 1994. This T-S relationship is used to complete the gaps in salinity data, since the temperature is taken at 11 depth levels (from surface to 180m at depth intervals of 20m, and at 300m and 500m) and the salinity is taken at only 4 depth levels (lm, 20m, 40m and 120m). The Etambot 1 and 2 cruises are WOCE repetition lines, and were performed in September 1995 and April 1996, respectively. From all the cruise legs we only used those shown in Figure 1, since the rest were was taken very close to the 1000 m isobath, the cutoff depth of our gridded data (see next section). During these cruises conductivity-temperaturedepth (CTD) and SADCP data were collected, and these were analyzed by Arnault et al. (1999) and Bourl6s et al. (1999). In these works, a partial retroflection of the NBC south of the Equator was observed, consistent with observed eastward jets above the EUC described by these authors. 4. DATA P R O C E S S I N G 4.1. C i r c u l a t i o n fields f r o m S S H d a t a The first step in the data processing consists in the mapping of the SSHA collinear data into a 0.25 ~ x 0.25 ~ regular grid (approximately 27 km x 27 kin) covering the tropical Atlantic between 15~176 A smaller area bounded by 15~ 15~ and 70~176 with 205 cycles of 10-day time steps, is selected for the present work. For both collinear data sets, outliers are first eliminated, and gaps are interpolated along track using a cubic spline (Halpern et al., 2000). The ERS2 data are adjusted with T/P data using the offsets between missions (see Koblinsky et al., 1999). Note that the Pathfinder ERS2 data is already corrected for an estimated instrument bias of 40.9 cm. Those not familiar with these procedures should consult the latter reference. The mapping operation is performed using an objective analysis technique following the procedure of Kessler and McCreary (1993). The values of mapping parameters are chosen to retain the meso (length scale of 200 kin) and the largescale (length scale of 1000 kin) features typical of the region, which proves to be coherent with measured in situ data from the PIRATA moorings. The second step is to estimate the actual sea surface height. To accomplish this, we sum the time-varying anomalies with a mean (long-term multi-year average) dynamic height field, obtained from hydrographic data. We use the high resolution (0.25 ~ x 0.25 ~ Boyer-Levitus climatology (BL) (Boyer and Levitus, 1997) to obtain a dynamic height referenced to 1000 m. The choice of BL and the depth reference is dictated by a compromise made between a small reference velocity at depth, and the de~irod proximity to the western boundary. The usual reference depth at
145
Figure 1. Section map of the study area including the WOCE-Etambot cruise legs, which obtained the hydrographic and SADCP data used in this work, and the four PIRATA mooring sites (squares). Track A is along 7.5~ and B along 35~ The 200, 1000 and 2000 m isobaths are superimposed.
equatorial areas to establish the level of no motion has been 500 m. However, 1000 m can be also acceptable, in view of the measurements recently made at this depth by Molinari et al. (1999), which suggest an average velocity of 10 cm]s at this depth. The SSH data is filtered using a special spatial multi-channel singular spectrum (MSSA) filter (Plaut and Vautard, 1994) to eliminate short wavelength noise but keeping mesoscale features. This filter consists of decomposing each derivativedata field in reconstructed components (RC's), and determining the most energetic spectral peak in each of them. The filtered fields are obtained by superposition of the RC's with maximum spectral peaks corresponding to wavelengths larger than 300 kin. In this way, there is no attenuation or spreading of true naturally occurring spatial peaks, but the noise is eliminated. From the filtered SSH maps the circulation fields are derived using the methodology described in section 2. The computations of the first and second derivatives is done using finite-differences. The one-sided differences are used at the boundaries,
146 while the centered-differences at interior points. The filtering after computation of each derivative was done to avoid losing boundary points, spreading and losing amplitude on true mesoscale features.
4.2. Computation of transport fields The transport pathways are estimated in a simple manner by mapping them in units of distance perpendicular to the transport direction. The mericlional (Tv(x)) and zonal (Tx(y)) volume fluxes are easy means of exhibiting the non-integrated transports across latitude circles and meridians, respectively. In a single baroclinic mode model, we first assume that the mean geostrophic layer has a thickness of H = 100 m, the lower motionless layer has a at = 26.5, and the upper layer a at = 22.5, therefore:
Tz,(x ) = (H + h(x, y))v(x, y), Tx(y) = (H + h(x, y))u(x, y).
(8a) (8b)
The transports are obtained by integrating the first expression in x between two longitudes, and the second expression in y, between two latitudes. Here, h = (g/g')rl is the changing depth of the pycnocline as a function of the 7. 4.3. Comparison of in s i t u data and altimeter-derived fields The altimeter-derived fields described in the previous section, have been compared with in situ measurements: a. SSHA time series with dynamic height obtained from PIRATA moorings. As suggested by Rebert et al. (1985), before performing the comparisons, the daily time series from PIRATA moorings were averaged into 10-day interval time grids. The time series of SSHA near each mooring were constructed by extracting the values of SSHA at grid points coinciding with the mooring positions (see table 1), b. SSH with dynamic height derived from CTD casts obtained during the Etambot cruises, both referenced to 1000 m. In order to do so, the CTD track data were interpolated onto a finer 0.25~ and c. Circulation (zonal and meridional components) with measurements of SADCP and CTD-derived velocities from the Etambot cruises. The following statistical parameters were computed from each comparasion above: minimum, maximum, mean, standard deviation (std), signal-to-noise ratio (snr), correlation coefficient (r), the root-mean-square (rms), and rms difference values. The snr and rms terms used here follow the same definitions as those used by the Pathfinder team in their validation efforts (Koblinsky et al., 1999). Results from these comparisons are presented in Section 5. 5. COMPARISON OF I N S I T U DATA AND A L T I M E T E R - D E R I V E D F I E L D S 5.1. SSHA t i m e s e r i e s and dynamic heights f r o m PIRATA moorings Table 1 summarizes the results obtained from a regression analysis for each mooring, showing a good agreement between the SSHA and the surface dynamic height (ref. 500 m). All results listed below are significant at the 95% level. The analysis showed that it is possible to obtain a single regression line for all the
147
western moorings listed above. Therefore it is clear that the SSHA field reflects a first baroclinic mode quite well in the PIRATA sites in the northern hemisphere. We notice that at the mooring located at 8~ the correlation is lower (0.69). We attribute this to the fact that the dynamic height calculation based on the salinity values obtained from the T-S relationship is faulty, especially because the lack of salinity data at the maximum salinity layer at 80 m depth. The studies of Maes (1998) and Vossepoel et al. (1999) support this conclusion. The former author also estimates the influence of the barotropic component as being negligible relative to the baroclinic. This problem was further investigated by Segschneider et al. (2000), who described problems associated with the salinity influence on the dynamic height estimates in a broad region over the tropical north Atlantic in May 1999. They suggested that the salinity maximum would be at 120 m, when it really occurs at 80 m, probably with strong annual cycle. These salinity effects are now known to be important for dynamic height estimates (Mayer et al., this volume), and SSHA assimilation into operational ocean models (Maes, 1998). This problem can be corrected using the data from an internally recording salinity sensor placed at 80 m during the PIRATA-BR II (second Brazilian cruise of the R/V Antares in 1999). The correlations are similar between SSHA and the depth of the 20~ isotherm (Z20) (between 0.61 and 0.86), but improve when the pycnocline depth is used in place of the Z20 (not shown).
5.2. SSH and d y n a m i c h e i g h t from the CTD E t a m b o t c r u i s e s Table 2 shows a statistical comparison between altimeter SSH and dynamic heights derived from Etambot cruises. The correlation coefficients (r) for Etambot I are larger than those of Etambot 2. The plots (not shown) of the dynamic height and SSH data of Etambot 2 permit clear interpretations of these discrepancies. For track A the dynamic height has very high amplitude spikes, one near 40~ (change of 20 dyn cm in 2 ~ of longitude), while the SSH data do not capture this type of feature. We may note in Table 2 that the standard deviation of the CTD data is 2.5 times the standard deviation of the SSH data. Therefore, it is difficult to evaluate if this problem arises from inaccuracies in the CTD data, or due to of
Table 1 Results of the regression of SSHA and dynamic height (500 m reference depth) from the PIRATA moorings, where r is the correlation coefficients and N is the number of observations (10 day-cycles). Units of offset are in cm and slope are in cm/dyn cm. Mooring 0~176 4~176 8~176 12~176
N 86 39 82 37
offset 91.52 93.96 81.81 79.20
slope 0.71 0.96 0.78 0.92
r 0.83 0.92 0.69 0.88
148
Table 2 Altimeter-derived SSH (ALT) and CTD dynamic height comparisons for tracks A, B and C, including the r m s (of differences), r (correlation coefficients). Units are in am.
Track N mnCTD ....mnALT mxCTD mxALT stdCTD stdALT r m s r A1 59 130.34 135.80 152.08 148.49 4.82 3.09 3.36 0.72 B1 47 136.00 138.45 158.03 153.78 6.45 4.87 2.77 0.94 C1 11 125.17 144.15 151.49 155.64 9.03 4.48 10.2 0.90 A2 55 127.37 133.84 151.95 144.43 6.60 2.84 5.87 0.54 B2 49 122.23 129.56 138.46 141.35 3.36 3.59 5.30 0.67 C2 18 134.32 135.90 146.72 149.63 4.12 3.71 3.90 0.53 m n stands for minimum values and m x for maximum values. (A1, B1, C1) refer to Etambot 1 in September 95 and (A2, B2, C2) to Etambot 2 in April 96.
the SSH data. For track B SSH is larger than the dynamic height between 4-8~ by an average of 8 cm, while it is less than 4 cm elsewhere in the track. For track C both SSH and dynamic height show spikes along the track which differ in position by 50 km. 5.3. C u r r e n t v e l o c i t i e s a n d m e a s u r e m e n t s o f S A D C P a n d C T D - d e r i v e d velocities We show here results of the study to validate our methodology of computation of geostrophic currents based on dynamic heights and altimeter derived SSH. The lateral resolution of the vertical profiles used for this validation during the Etambot 1 cruise was around 1 km, while during the Etambot 2 the resolution was about 50 km due to difficulties with the SADCP data acquisition (Bourl4s e t a l . , 1999). Table 3 shows the correlations between the SADCP depth profiles and CTDderived velocities over the ship tracks A and B. The meridional velocity, v, for track A in Etambot 1 (Table 3(a)) has the highest correlations near the surface, while the zonal velocity, u, along track B has the highest correlations between 70 m - 90 m. Table 3(b) shows the results of the Etambot 2, which present higher correlations. In this case, there is no significant depth dependence in the correlations between the surface and 100 m depth. Table 4(a) shows the corresponding correlations between SADCP depth profiles and altimeter-derived velocities during Etambot 1. We see that the best correlations obtained for track A were at the 50 m - 70 m depth ranges for the zonal velocities. However, the correlations are maximum at the surface for the meridional component. Track B shows maximum correlations better defined at 70 m - 80 m. Table 4(b) shows the same results for the Etambot 2. The correlations are approximately 0.8, except for v in track B, and are better at subsurface depths, although these are not significantly different from the surface values. We speculate
149 Table 3 Correlation coefficients of CTD-derived velocity components with SADCP d a t a at various depths for tracks A and B: (a) E t a m b o t 1 (September 1995) and (b) E t a m b o t 2 (April 1996) (a) Av Bu
20
30
40
50
60
70
80
90
100
110
120
130
0.50 0.56
0.46 0.55
0.37 0.57
0.33 0.61
0.25 0.68
0.19 0.76
0.16 0.79
0.12 0.77
0.11 0.74
0.07 0.71
0.04 0.64
0.13 0.63
(b) Av Bu
24
32
40
48
56
64
72
80
88
96
104
112
0.65 0.81
0.66 0.83
0.67 0.82
0.69 0.79
0.70 0.73
0.69 0.73
0.68 0.77
0.67 0.78
0.62 0.77
0.58 0.75
0.59 0.72
0.60 0.69
First row is depth in meters, u is the zonal velocity and v is the meridional velocity.
Table 4 Correlations coefficients of altimeter-derived velocities with SADCP data at various depths for tracks A and B: (a) Etambot 1 (Sep 1995) and (b) Et~,mbot 2 (April 1996) (a) 20 30 40 50 60 70 80 90 100 110 120 130 A u 0.57 0.58 0.62 0.66 0.67 0.63 0.50 0.31 0.26 0.38 0.45 0.42 A v 0.82 0.77 0.69 0.63 0.58 0.53 0.46 0.35 0.26 0.20 0.14 0.15 B u 0.70 0.70 0.73 0.78 0.83 0.85 0.83 0.78 0.75 0.74 0.70 0.68 B v 0.51 0.47 0.49 0.58 0.68 0.75 0.77 0.76 0.74 0.67 0.57 0.52 (b) A A B B
u v u v
24
32
40
48
56
64
72
80
88
96
104
112
0.79 0.86 0.88 0.48
0.79 0.87 0.86 0.53
0.79 0.87 0.82 0.58
0.79 0.88 0.80 0.64
0.79 0.89 0.79 0.67
0.79 0.88 0.83 0.66
0.80 0.87 0.87 0.63
0.81 0.87 0.89 0.60
0.80 0.85 0.89 0.59
0.82 0.81 0.87 0.57
0.83 0.82 0.84 0.55
0.80 0.81 0.82 0.51
First row is depth in meters, u is the zonal velocity and v is the meridional velocity.
that the correlations shuold be the same throughout the whole upper layer, due to the shallower EUC. Figure 2 shows the altimeter-derived zonal and meridional velocities over the Etambot 1 track B calculated from our methodology and the SADCP d a t a for the depth of m a x i m u m correlation at 70 m. We also include the s t a n d a r d geostrophic estimate with the equatorial singularity for the zonal current, calculated from the
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Figure 2. The zonal and meridional velocities estimated from satellite derived SSH using equation (7) (solid line), the f-plane geostrophic estimate (dashed line), and ADCP data at 70 m depth (dotted line), Etambot 1 cruise (Sep 1995). Notice the good agreement of the meridional velocity estimate over the Equator, which is southward (20 cm/s).
same SSH data. Note the convergence between ours and the standard geostrophic estimates one degree away from the Equator in Figure 2a. The eastward flow is quite broad in the southern hemisphere, and seems to be centered at l~ This is consistent with the high resolution circulation model results of Schott and Boning (1991), which shows that the EUC core in August is not over the Equator, but to the south. Between 4~176 the differences seem to be due to ageostrophic components (Garzoli and Molinari, 2001). For the meridional component the agreement is quite good between 2~176 Notice that at the Equator the meridional velocity is 20 cm/s to the south, suggesting a southward transport, which implies that the core of the EUC is not on the Equator and may be dominated by meandering, as seen in the annual cycle of Schott and Boning (1991). For track B of Etambot 2, the correlations shown on table 4(b) are reasonable from the surface to 130 m for u, but only regular (0.67) around 60 m for v. However, we should note that during Et~mbot 2 there was a failure in the SADCP, and only ADCP data at CTD stations were obtained. This lower resolution SADCP transect is, therefore, not very good for comparing with altimeter-derived currents, although the correlations look reasonable. For track A, both geostrophic and our equation underestimate the zonal currents in a region of strong eddy components. This result is well-known (e.g. Arnault et al., 1999) for synoptic data, but is probably averaged out when low-frequency flow patterns are considered. The results presented in this section reinforce the idea that the SSH-derived currents reflect flows in the upper thermocline level, and the fact that the EUC core may be off the Equator in the western Atlantic. However, a possible limitation
151
to the present method should be mentioned. There are transition regions where the compensating steric and dynamic subsurface effects may produce negligible surface expressions. In these regions, the correlation between SSH and the vertical density profiles are different from the simple single baroclinic mode approximation used here to estimate the geostrophic currents. As a consequence, the geostrophic currents obtained from surface dynamic topography may severely underestimate the true currents in these regions.
6. ANALYSIS OF T H E C I R C U L A T I O N F I E L D S A special adaptive filtering method, described in more detail in the Appendix, is used to separate the circulation and transport fields into components in the period bands of interest (intra-seasonal, semi-annual, annual and interannual). This method allows one to record not only the variance explained by each bandlimited data set, but also the spectral peak periods and their energy within each band. There is a strong motivation for using this method, as opposed to using simple climatological averages and anomalies relative to the annual cycle. Analysis of T/P and tide gauge sea level data near Fortaleza (3~ 39~ showed interannual variability in the phase and amplitude of the annual cycle, with 1996-1997 exhibiting a period of 255 days, and the smallest amplitudes in the period 19932000. These phase and amplitude changes in the annual cycle are preserved with such a filter, but do not have any such time-dependent signatures if we use the more traditional methods of analysis. We believe that this method of analysis can, in principle, be interesting for our future studies on prediction of ocean currents. As a result of the analysis of the partition of the data sets, we found the following percent variances in each of the frequency bands of interest: 1. Intra-seasonal plus turbulence noise (less than 150 days): 51%(u) and 78% (v), 2. Semi-annual(between 150 and 240 days): 9% (u) and 4% (v), 3. Annual (between 240 and 400 days): 27%(u) and ll%(v), and 4. Interannual(more than 400 days): 8% (u) and 5% (v). The first two bands cited above are not investigated in the present work. The interannual band is found to be a superposition of a quasi-biennial (QB) mode, and a 6.8 year period mode. The fact that it is possible to estimate periods larger than the length of a time series is one of the great successes of the maximum entropy and autoregressive spectral analysis methods used in our filter for peak period determination. With these methods, it is possible to estimate what might be the harmonic related to a nonlinear trend, that can be confirmed indirectly by analysis of other related but larger time series. Servain (1991) found that the tropical Atlantic SST interannual variability may be expressed as a sum of a QB and a 13 year mode. If we interpret the 6.8 year variability as possibly being a second harmonic of the 13 year component, the above results suggests that SST and geostrophic circulation modes may be related in these period bands.
152 6.1. T h e m e a n c u r r e n t s
In this section three mean current fields obtained from three annual mean dynamic topography maps (reference depth of 1000 m), are described, as shown in Figure 3: a. The mean circulation based on sea surface dynamic topography (0/1000 m) obtained from the Boyer-Levitus 1997 climatology, b. The mean circulation based on the 100 m depth dynamic topography surface (100/1000 m) from the same climatology, c. The 5-year mean of the SSH-derived circulation time series, where the SSH grids are formed by adding the Boyer-Levitus sea surface dynamic topography to the altimeter-derived SSHA at each 10-day time step. The mean surfaces shown in Figure 3 reveal meandering patterns that may be related to noise due to changing circulations, or may be related to true standing circulation modes. To discern between noise and mean modes in the true mesoscale, one should resort to altimetric observations (if these are standing oscillating features), in situ observing systems and eddy-resolving models. One interesting example of this type of situation may be found in the objective mapping of the mean SSH (relative to 750 m) of the South Pacific Ocean, presented by McCarthy et al. (2000). In their map, the warm-core East Cape Eddy off New Zealand is a typical example of a mesoscale feature in a climatological dynamic height map, which is not noise at all. Analysis of these three mean circulation fields does not show a continuous EUC signature between I~ x l~ The EUC signature is zonally inhomogeneous, resulting from meridionally-aligned cyclonic eddy pairs north and south of the Equator, which causes only eastward currents at eddy current convergences. This is better seen in the Boyer-Levitus 100 m circulation field, where the eddy pairs and the EUC signature are connected (Figure 3b). These facts suggest that the EUC flow might be strongly connected to these mean cyclonic eddy pairs. However, the common view of the relation of the EUC with the subsurface dynamic height topography does not include stationary eddies. The common view of the upper layer equatorial current system is based on the wind forced model described in Gill(1982), with a westward mixed layer current on top of a EUC during the early times (20 days) aider switching on the westward zonal wind. The EUC velocity may be related by equatorial geostrophy to the ridge in the dynamic height field which is formed below the mixed layer. A simple stratified model is described in more detail by Philander (1990). In particular, he shows that after the growth of the Yoshida jet is quenched by the arrival of the Kelvin wave, formed by reflection of the jet perturbation at the western meridional boundary, the westward surface jet is eroded by upwelling of eastward momentum from the EUC. The jet itself is also laterally eroded very fast by meridional Ekman divergence, leaving only the eastward current. The EUC in this model is due to the second baroclinic mode current, which acts to cancel the surface jet. It should be noted here that reflection of baroclinic Rossby waves from a slanted model western equatorial boundary has qualitative differences from the straight meridional boundary counterpart. The latter involves only Kelvin and
153
154
Figure 3. Mean circulation based on sea surface dynamic 0/1000 m topography (a), 100 m (100/1000 m) (b) and 5-year average SSH data (c). See text for details.
boundary-trapped eastward propagating Rossby waves. In contrast, the slanted boundary reflection, in a model with vanishing lateral eddy viscosity, results in interference patterns of incident and reflected waves, which are not only Kelvin waves (Holvorcem and Vianna, 1992). It is shown in this latter work that meridionally propagating evanescent waves may not be of negligible importance, and may generate large amplitude standing wave patterns trapped near the Equator. It can therefore be speculated that for time scales longer than 20 days these interference patterns are more important in the mean than u perturbations due to sudden wind changes. Away from the Equator, Figure 3c is generally consistent with the mean flow field at 133 m (Figure 1 in Schott and Boning, 1991). Between 10~ and the Equator, the flow is essentially eastwards at the open ocean, and to the southeast near the western boundary, attaining 50 cm/s near 5~ Northwest of the (Demerara) continental rise at 8ON offshore Guyana, the flow is to the northwest. In Figure 1 of Schott and Boning (1991), it is important to note that there are also regions of maximum/minimum current intensity in the EUC pathway, which is reflected
155 more drom_atically in our Figure 3c. The results of this section reinforce the conclusion that altimeter-derived circulation data relate more to the subsurface than to the surface structure in the western equatorial Atlantic. This fact has also been explicitly cited by many authors (e.g. Larnicol et al., 2002). In the following sections we show the existence of trapped equatorial standing modes in the seasonal circulation, a fact that may explain why the wild mesoscale variability appears in the mean maps, including the maximum/minimum intensity patterns in the mean EUC signature, and the link to the standing cyclonic eddies which appear in the Figures above. 6.2. The s e a s o n a l cycle The seasonal evolution is now illustrated using 10-day grids of the annual band data sets, for certain months of 1997 (February, April, July, September and November), in order to highlight major transitions in circulation patterns. We display pairs of figures representing anomaly and total flow fields, the latter being included to facilitate interpretations as compared to measurements. We start the sequence of illustration with one corresponding to February 15 (1020 Feb), 1997 (Figure 4a). Between 4~176 a band of westward anomaly flow is seen to be perturbed by a anticyclonic eddy confined between 40~176 and 2~176 with intensity of approximately 25 cm/s. Figure 4b shows the influence of this perturbation in forming a cyclonic loop, with its southern limb being the remains of the North Equatorial Countercurrent (NECC) at 6~ with intensity of approximately 40 cm/s, and with its upstream branch resembling the Guyana Undercurrent (GUC). The bifurcation at the Demerara Rise is present, with a northwest flow to the west and a southeast flow to the east. A meandering EUC appears between 2~176 with longitudinal variations in intensity. Between 1~ 4~ a meandering circulation is seen, representing the central branch of the South Equatorial Current (cSEC). The circulation field appears to be more intensified in mid April (Figure 5). The anticyclonic eddy perturbation has its southern limb westward flow intensified (Figure 5a) while the NECC weakens considerably, but does not completely disappear (Figure 5b). The cSEC intensifies and converges into the EUC at 35~ The EUC signature has an intensified structure between l~ and the Equator (Figure 5b). In mid July we notice that a sharp transition takes place in the anomaly field (Figure 6a). The anticyclonic eddy centered near 5~176 observed in April (Figure 5a) changes into a cyclonic eddy. We now notice a broad retroflection signature between the Equator and 6~ although we do not see the NBC pressed against the coast (Figure 6b). A double-core NECC can also be observed, with its northern branch around 8~ and its southern branch around 5~ This doublecored NECC was first suggested in the model work by Schott and Boning (1991), and its existence is therefore confirmed here. These branches coalesce near 35~ At 2~ we notice the presence of a westward current resembling the northern branch of the SEC (nSEC). The EUC appears disrupted between 30~176 due to recirculations.
156
Figure 4. Mid February 10-day anomaly field (a) and 10-day anomaly plus the 1995-2000 mean (b) in the annual band data set. Signatures of the more intense currents (NECC, EUC, NBC, GUC, cSEC and nSEC) are indicated.
157
Figure 5. Same as Figure 4, but for mid April 1997.
158 By mid September (Figure 7a), we notice an intensification of the current anomaly structures observed in July (Figure 6a), and the appearance of a strong large anticyclonic eddy pressed between 0~176 This feature forms a N-S pair with the cyclonic eddy, which appeared in July. The double-cored NECC is still seen, with the north core around 9~ and the south core at 5~ The two cores coalesce at 32~ at 8~ (Figure 7b). The strong south core of the NECC is mostly originated by the NBC retroflection at 8~ near the Demerara Rise. A westward nSEC is also seen meandering around 2~ The EUC, at this time (Figure 7b) has been quite disrupted by the cyclonic eddies. This is consistent with the Etambot SADCP measurements taken in 1995 at 35~ which showed an eastward velocity core at l~ and a southward subsurface velocity of 20 cm/s at the Equator. Moreover, the flow field in September 19, 1995, resembles the one in Figure 7b between 4~176 (not shown here). These results suggest that the circulation near the Equator at 35~ is dominated by an annually recurring eddy, possibly due to equatorial wave dynamics. In mid November, another transition phase seems to be setting in, with a broadening and intensification of the anticyclonic eddy and a shrinking of the cyclonic eddy (Figure 8a). The meandering seen in the NECC core region at 5~ 6~ can be identified as being due to a wave (Figure 8b). The annual cycle of this meandering can be better observed in the time-longitude diagram of the meridional velocity perturbation (Figure 9). The disturbances propagate westwards from 32~ with a phase speed around 1.8 km/day. To the east, only a weak signature of a standing wave is seen. There are three crests in this wave pattern, a picture which is also consistent with the results presented by Schott and Boning (1991) (their Figure 2b). We suggest that this could be due to a Rossby wave interference pattern of the type described in Holvorcem and Vianna (1992) for intra-seasonal waves, although a more detailed model study must be carried out to obtain more definitive conclusions. No clear EUC signature is seen, although the zonal component between 0~176 is eastward almost everywhere over the Equator. It appears that the EUC is disrupted by eddies. The origin of these eddies may be related to instability waves, or to waves driven by weather events, together with wave scattering from the western boundary. One example of the latter wave process in the TOGA-COARE area with a very high resolution model is presented by Dourado and Carniaux (2001).
6.3. Standing trapped annual equatorial waves and m e a n d e r i n g We have shown that during February to April the EUC signature is present, but dominated by meandering and longitudinal variations in the intensity. During the rest of the months, the EUC is disrupted, and the equatorial eastward flow is dominated by a sequence of counterclockwise eddies. Time-longitude diagrams of the meridional velocity at 0~176 (not shown here) suggest a picture of a tightly standing wave mode throughout the year. The meridional velocity anomaly map for the annual cycle in mid January 1997 (Figure 10) exhibit two clear wave signatures: one consisting of three crests at 5~ which are related to the NECC meandering, and another at 2~ and 9.~ with smaller wavelength. We believe
159
Figure 6. Same as Figure 4, but for mid July 1997.
150
Figure 7. S a n e as Figure 4, but for mid September 1997.
161
Figure 8. Same as Figure 4, but for mid November 1997.
162
Figure 9. Time-longitude diagram for the seasonal march of the meridional velocity at the NECC core at 5~ Contour interval for positive (solid lines) and negative anomalies (dotted lines) is 5 cm/s. It clearly shows the slow westward propagation of the three meanders of the NECC west of 35~
Figure 10. Meridional velocity anomaly plot for the annual cycle in mid Jan 1997. Two distinct wave patterns are seen: a trapped equatorial wave with maxima at 2~ and 2~ and another one with maxima near 5~
that the latter might explain some of the high amplitude mesoscale features observed in the Boyer-Levitus climatology near the Equator, the observed EUC meandering, and the open-ocean windows for interhemispheric transport described in the following section. 6.4. I n t e r a n n u a l v a r i a b i l i t y The interannual flow anomalies in the contrasting years of 1995 and 1996 is shown here to illustrate interannual variability in the upper ocean circulation. Since there is a considerable annual modulation, we choose two months (September and November) in 1995 and one month (November) in 1996 as illustrative of this contrast. During August-September in 1995, when the NECC seasonal peak occurs, a weak southern core and a strong northern core are observed (Figure l la). To better illustrate the weak perturbations in the southern hemisphere we also show the condition during November 1995 (Figure llb). The cSEC is weakened by an eastward broad perturbation. An eddy resembling the one described by Silveira et al. (1994), obtained from analysis of hydrographic data, is also detected, together with a westward perturbation at 14~ These signatures are weak and can hardly be observed in the velocity fields of Figure 11, although can be clearly seen in the current intensity/direction maps (not shown here).
163
164
Figure 11. Interannual anomaly circulation fields in September 1995 (a), November 1995 (b), September 1996 (c) and the time-longitude diagram at 5~ for the zonal velocity, in the southern core of the NECC (d); contour interval for positive (solid lines) and negative anomalies (dotted lines) is 5 cm/s. In (a) and (b) the northern core of the NECC and the EUC are more intense, and the cSEC is weaker, with the opposite situation in 1996, as exemplified for the main NECC core in (c).
165
Figure 12. Multi-annual (1995-2000) average meridional volume flux field (T~(x)) (a), and the same for the zonal volume flux field (Tx(y)) (b).
The situation is exactly the opposite in 1996, both for the September and November patterns. In 1996, the main core of the NECC is at 5~ and is more intensified during the whole year, as illustrated in the September 1996 interannual anomaly pattern (Figure l lc). Finally, as a illustration of the possibly decadal modulation of the biennial anomaly in the circulation field, we show the evolution of the zonal current at the core of the NECC at 5~ (Figure lld). We see that while in 1995 the main core of the NECC was weakened, during 1996 it became strongly intensified. We notice that the biennial variability is somewhat damped in the succeeding years. The opposite is observed around 8~ which is consistent with previous results (Arnault et al., 1999, their Figure l l d ) . 7. I N T E R - H E M I S P H E R I C T R A N S P O R T S AND T R A N S P O R T PATHWAYS The multi-year averages for meridional (Ty(x)) and zonal (T~(y)) volume fluxes calculated using equation (8a) are shown in Figures 12a and 12b. We can observe that T~(x) (Figure 12a) presents a meridionally banded structure across the Equator, predominating the transport windows from the South to the North Atlantic at 420W, 340W and 26~ indicating a 850 km zonal wavelength northward mean transport pattern. For T~(y) (Figure 12b), we see the well-known zonally banded structure, with the westward transport of the two branches of the SEC cut by the EUC eastward flow, and the broad NECC eastward transport. Westward flow into the Caribbean Sea is stronger near the South American shelf. Near the North Brazilian shelf, we notice the strong westward transport into the shelf south of 2~ that, due to continuity, accelerates the NBC. Between 2~ and the Equator, we see the strong change into eastward flow, which by following the same argument feeds the EUC.
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The characteristics of these patterns were analyzed in the interannual period band. It was found that variability in the zonal and meridional directions have different spectral characteristics. In the case of the meridional transports, a nonlinear trend appears in the singular spectrum decomposition, suggesting a 6.8 year period, which is an harmonic of the 13 year dominant period in the SST interhemispheric gradient. The QB spectral peak is very broad in the zonal transport, but quite well defined in the meridional. This situation can be seen more clearly in the total transports at 3~ and 3~ that were computed as a measure of the upper-layer geostrophic transports. The interannual variability is shown here added to each mean (Figures 13a and 13b). We can observe the quasi-biennial variability in these meridional transports, and a small phase difference between the interannual variability of the northern and the southern hemispheres. A phase difference has been also observed by Servain (1991) in his study of basinwide tropical Atlantic SST averages. He calculated monthly northern (30~ - 5~ and southern (5~ - 20~ basin SST indices for the period 1964 - 1990 and noted phase differences between the two, which led him to introduce his SST dipole index. Subsequent work has shown that the mean northern hemisphere SST interannual variability spectrum and phase vary independently from the southern hemisphere counterpart, but still presenting large mean interhemispheric gradients, usually resembling a SST interhemispheric dipole (see Servain et al. 1998 for more details, and references therein). Our result suggests that a subsurface connection with the surface processes possibly exists, coupling a S S T dipole type of oscillation with a STC-type vertical circulation cell.
167 8. SUMMARY AND C O N C L U S I O N S This work documents the variability of the western equatorial Atlantic thermocline circulation and volume transports with eddy-resolving grid resolution, aiming at presenting a picture against which future model work can be tested. Novel methods of computation were used to make possible this description which is summarized here for completeness: 1. Although satellite-derived circulation using the geostrophic approximation has been used by many authors, application of this method to the equatorial ocean is less straightforward. We developed a new alternative by deriving a formulation for the computation of currents spanning the Equator. We showed that the zonal geostrophic balance equation can be generalized to include the Equator using the meridional second derivatives of SSH. The derived expression is one solution of a quadratic equation in the zonal velocity, which follows directly from the shallow water equations and the equatorial scalings. 2. Since this method has not yet been fully explored, we presented a comparison with WOCE cruise data (dynamic height and ADCP current data). We also compared the SSHA grid produced for this work with data from the PIRATA moorings. Our results suggest that altimeter-derived currents in the equatorial western Atlantic correlate better with subsurface currents than the surface mixed layer currents. 3. One not very well-known feature of the high resolution Boyer-Levitus climatology is that it includes both average mesoscale features and noise, which are difficult to separate. The fact that ocean climatologies may contain mesoscale features is known in the case of the South Pacific Ocean, but to our knowledge this has not been studied in the Atlantic to this date. Our altimetric study seems to confirm that some important standing mesoscale oscillating features do appear near the Equator, supporting the view that the Boyer-Levitus average mesoscale features do correspond to reality. 4. The methods used to filter out high frequency-wavenumber noise from the SSH, and to separate the satellite-derived flow grids into period bands, have been briefly described. The mean flow field, and the annual evolution of the thermocline circulation was presented in mid-month 10-day average patterns for the year of 1997, with the aid of the data set filtered to keep only the annual cycle. This preference in relation to the more straightforward method of climatological monthly averages has been explained. The patterns thus obtained were compared to those published in other works, especially with the results of Schott and Boning (1991) at their 133 m level, with which most results are consistent. The NECC presents a 3-crest meander pattern which propagates westwards. One of the differences noticed was the slow meander propagation in the NECC main core (1.8 kin/day), which in the latter
168 work was found to be stationary. We further confirm the double-cored NECC suggest by Schott and Boning (1991). 5. Another important result was that the EUC is not continuous on the Equator in the western Atlantic above the thermocline. The ADCP measurements presently available, show either positive or negative meridional velocities, and our altimeter-derived currents further suggests that this variability may be due to almost standing mesoscale eddies spanning the Equator. However, the absence of a continuous core of the EUC in our circulation fields may be due to dynamics, since the EUC flow is more related to a second baroclinic mode rather than to the first (Philander, 1990), whereas our determination of the current was based on a single baroclinic mode. 6. Interannual variability of the NECC was found to be mostly in the biennial band, with a decadal trend which decays in the 1995-2000 period. We did not find a 4-year nonlinear trend in our analysis of the 1995-2000 records, which would confirm the clear 3-4 year spectral result of Katz (1993), obtained from echosounder data. The variability south of 5~ was found to be mostly in the interannual band. The prominent anomaly feature found was a large eddy which seems to change from cyclonic to anti-cyclonic each year, centered around 10~ However, due to the weaker currents in this region, we did not show these results in the plots present in this work for brevity. 7. One interesting finding was the presence of a quasi-standing equatorial wave pattern, which spatially modulates the interhemispheric open ocean transport pathways into three windows, and channels the northward geostrophic transport. Contrary to expectations, the thermocline waters from the South Atlantic leak into the North Atlantic up to at least 4~ through these windows. The same situation was observed in the southward flow, which was also through a number of windows. In this case, the western boundary window injecting Guyana U n d e r c u r r e n t ~ B C retroflected waters into the EUC was also noted. This makes the mean equatorward transports different between hemispheres, with the South Atlantic at 3~ contributing 10 Sv more than the North Atlantic at 3~ into the Equator. Part of this transport goes into the EUC, and part into the Ekman return flow, including the flow over the continental shelf, which is known to be northwestward. 8. Interannual variability of the geostrophic transports was documented. It was found that the meridional transports present an out-of-phase relation, with the South Atlantic leading the changes. As an example, the equatorward transport at 3~ had a broad peak of 20 Sv between November 1996 and February 1997 (annual cycle filtered out), while at 3~ there was a sharp peak of 10 Sv in June 1997. The study of the coupling between zonal and meridional transports is omitted here for brevity. 9. One important transport process is the one effected by NBC rings (Goni and Johns, 2001), which spread southern water masses into the north Atlantic.
169 Although our grids are eddy-resolving, we did not determine if the filtering method used here results in seasonal and interannual circulation fields that account for the net water transport by moving eddies. This work suggests that a study of the inter-hemispheric STC dynamics can be made based on presently available surface data obtained from space-borne instruments. However, one must keep in mind that a problem with this method is its possible underestimation of upper layer geostrophic currents in transition regions. In these regions, strong subsurface currents may appear, in spite of weak surface dynamic height or sea level gradients, which would give rise to weaker currents. Mayer et al. (2001) reported an investigation into this matter based on thermosteric anomalies. The effects of salinity were not included, so further investigations are needed to clarify this issue. Investigations to better determine the nature of the open-ocean transport pathways suggested here demands the use of very high-resolution eddy-resolving ocean modeling studies, which are presently lacking. Our results also suggest that these models should incorporate parameterizations of subgrid-scale horizontal mixing with smaller eddy viscosities than usual. This would allow for less attenuation of the reflected waves with small wavelength and slow propagation velocity from the western boundary. Future work will concentrate on completing the picture given here with the use of satellite scatterometer winds, and better equations to calculate Ekman currents and Ekman pumping velocities valid also along the Equator, to get a more complete picture of the variability of the three dimensional upper ocean circulation fields. APPENDIX: P R E P A R A T I O N OF BAND-LIMITED C I R C U I ~ T I O N AND TRANSPORT FIELDS This Appendix describes the special adaptive filtering method used to isolate the dominant patterns of circulation and transport fields in the period bands of interest. The filtering procedure is based on a combination of empirical orthogonal function (EOF) methods, Multichannel Singular Spectrum Analysis (MSSA) methods for time domain analysis and modal expansion of the principal components, and Maximum Entropy/(Yule-Walker) autorregressive determination of spectral peak periods. These methods allow to record not only the variance explained by each band-limited data set, but also the spectral peak periods and their energy within each band even for short time series. This procedure was applied separately for each of the current velocity and transport components (zonal and meridional), and can be summarized as follows: a. For each grid point the total time average was removed, b. The anomaly fields were expanded into a number of EOF's necessary to account for 99% of the total variance, c. The corresponding Principal Component (PC) time series of each EOF mode were then analyzed by the MSSA method and decomposed into 205 T-EOF's (Reconstructed time series components-RC's), necessary to account for 99% of the explained variance,
170 d. Each of the RC's from (c) were spectrally analyzed with a Yule-Walker AutoRegressive Analysis, where the most energetic spectral peak was determined. These informations allowed us to select those RC's within the period bands ofintraseasonal (less than 150 days), semi-annual (between 150 and 240 days), the annual (between 240 and 400 days), and the interannual (more than 400 days) variations. Therefore, each PC was decomposed into 4 band-limited series, e. Since each RC has associated with it the variance explained, selection of RC's by a criterion based on their spectra, obtained from analysis (c) and (d), permitted the sum of corresponding variances to obtain the total variance per band, and f. The band-limited data were therefore obtained by a reconstruction using the selected PC-EOF pairs, which were then inverted back into image time series. The method proved to be very efficient and straightforward, with the advantage of keeping track of the variance within each frequency band.
Acknowledgements We are indebted to two anonymous reviewers for constructive criticism, and to Gustavo Goni for his comments, corrections, suggestions, unlimited patience, and encouragement. Very useful final corrections by another reviewer is also acknowledged. One of us (V.V.M.) was supported by project PD001/PCO-01 in VM Oce~ica. We are also grateful to FAPESP, for support to M.L.V., during the 2001 Ocean Odyssey IAPSO conference in Mar del Plata, where this EOS book was proposed. We are also grateful to the NASA Ocean Pathfinder and WOCE Projects for making available their global data sets.
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173 18, 1401-1415, 1999. Wang, V.M. The satellite altimeter data derived mean sea surface. Geophys. Res. Left., 27, 701-704, 2000. WOCE data products committee. WOCE global data: ADCP data, version 2.0, WOCE international project office, WOCE report No.171/00, Southampton, UK, 2000. Xie, S.P. A dynamic ocean-Atmosphere model of the tropical Atlantic decadal variability. J. Climate, 12, 64-70, 1999.
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Interhemispheric Water Exchange in the Atlantic Ocean edited by G.J. Goni and P. Malanotte-Rizzoli 9 2003 Elsevier B.V. All rights reserved.
Fate of the Equatorial U n d e r c u r r e n t in the Atlantic W. Hazeleger and P. de Vries Royal Netherlands Meteorological Institute (KNMI), P.O. Box 201, 3730 AE De Bilt, The Netherlands The fate of water masses in the Equatorial Undercurrent (EUC) in the Atlantic is studied using a high-resolution ocean model. Lagrangian trajectory analysis is used to determine sites where water masses from the EUC upwell and later downwell. The use of Lagrangian mean transports to trace particles takes into account high-temporal variability in the tropics. Most EUC water upwells in the equatorial region. The pathways between the EUC core and the upwelling sites indicate that most particles upwell rather directly at the equator. Other upwelling sites are found close to the African ~contintent) and along the Gulf Stream. After upwelling, particles subduct again in the tropical and subtropical Atlantic. The particles that recirculate back to the EUC experience, on average, five upwellings and downwellings. The sites where the particles subduct for the last time before returning to the EUC are found mainly along the South Equatorial Current. Most particles follow the western boundary back to the tropics. Two thirds of EUC transport at 20~ does not recirculate, but leaves the Atlantic basin at the southwestern side to participate in the global meridional overturning circulation. Most of this water has been transformed in the Atlantic to deep water. 1. INTRODUCTION The equatorial region in the Atlantic has a complex current structure. A number of intense zonal currents are observed of which the eastward flowing Equatorial Undercurrent (EUC) is one of the most prominent [Schott et al., 1998; Stramma and Schott, 1999]. The core of the EUC is relatively cold. The sources of these water masses, as defined as the location where they subduct from the mixed layer into the interior, are mainly located in the South Atlantic. The connection between the extratropics and tropics is indicated by hydrographic measurements that show a low salinity tongue in the subsurface layers stretching from the subtropics into the tropics [Metcalfand Stalcup, 1967]. Also, Lagrangian trajectory analysis in numerical ocean models show that the EUC is mainly ventilated by water that subducts along the South Equatorial Current [Malanotte-Rizzoli et al., 2000; Hazeleger et al., 2003]. The presence of the basin-wide meridional overturning circulation in the Atlantic causes this meridional asymmetry in the sources of the EUC [Fratan-
176
toni et al., 2000]. Strong temporal variability is observed in the tropical Atlantic, partly due to the seasonal cycle in the winds and to the internal ocean variability. Clear examples are the seasonal appearance of the North Equatorial Counter Current and the formation of Brazil Current rings [Johns et al., 1990]. The high-frequency variability has a profound impact on the ventilation of the EUC as shown by Hazeleger et al. [2003]. They present a detailed picture of the subduction sites and pathways from the subduction sites to the EUC. Here, we follow up on this work to study the fate of the water masses in the EUC using a high-resolution model. The fate of the water masses in the EUC can be considered as being twofold. First, the water can recirculate in a Subtropical Cell [McCreary and Lu, 1994]. This means that the subsurface EUC water upwells into the mixed layer at the equator and transfers away from the equator due to Ekman divergence. In the subtropics, water parcels subduct and propagate subsurface to the equator again. Second, the water can escape from the subtropical regions and take part in the basin-wide meridional overturning circulation (MOC) and transfer to other ocean basins. The exact routes can be highly complicated, where recirculations and multiple upwellings and downwellings are possible. Current tracer and hydrographic data are insufficient to identify the routes and pathways of the particles away from the core of the EUC. Using model data this is feasible, especially with the use of Lagrangian trajectory analysis. The temporal variability can be properly accounted for using the methodology presented here. Lagrangian mean transports are used because the eddy-induced transports can be large in regions of high temporal variability [D66s and Webb, 1994; Mcintosh and McDougall, 1996]. In what follows, we first discuss the model and the preparation of the data. Then we analyze the fate of the EUC water by studying the sites where it upwells and subducts. A partitioning is made between particles that recirculate in the Atlantic and particles that leave the basin. 2. MODEL AND DATA HANDLING Data from the high-resolution global ocean model OCCAM [Webb et al., 1994] are analyzed. OCCAM is a primitive-equation model with realistic topography, a horizontal resolution of 0.25 degrees and 36 levels with variable thickness. A Laplacian horizontal diffusion and friction is used, where the diffusion coefficient is 100 m2s -1 and the viscosity coefficient is 200 m2s -1. The vertical mixing of tracers is according the Pacanowski and Philander scheme [Pacanowski and Philander, 1981], which results in diffusivities of 0.5 cm2s -1 away from strong shears. A Laplacian vertical mixing is applied to the velocity fields with a diffusion coefficient of 1 cm2s -1. The surface temperature is restored to the monthly mean sea surface temperature [Levitus and Bayer, 1994]. The fresh water flux is derived from the difference between the simulated surface salinity and that of the Levitus data [Levitus et al., 1994]. The model has been initialized with temperature and salinity from the Levitus data and spun up for 9 years with monthly mean winds and wind stresses from the European Centre for Medium-Range Weather Forecasts [Gibson et al., 1997].
177 The last three years, six-hourly ECMWF winds and wind stresses were used. We also used a five-day running mean data from the last 3 years of the model run for our analysis. General characteristics that are relevant to the problem that is studied here, such as the structure of the EUC, the mixed layer depths, and upper layer velocities, are presented in Hazeleger et al. [2003]. Please refer to this paper for a detailed description of the general characteristics of the model solution. In most studies, mean transports defined on constant z-levels are considered: U(z) = U(z)]Xz. Here, z is the Cartesian vertical coordinate and/Xz is the thickness of the gridbox. However, the subsurface ocean circulation is mainly adiabatic and water masses are transported mainly along isopycnals. Therefore, water mass transports should be analyzed along isopycnal surfaces. As the isopycnals themselves are subject to temporal variability, the correlation between the velocity and the thickness between two isopycnals need to be taken into account. The mean transport in a density layer is defined by U(~) = u(~)h(~) = u(~)h(a) -~ u'(~)h'(~), where ~ is the potential density, u - (u, v, w) is the velocity, and h is the layer thickness between two isopycnals. The bars denote the time average, while the primes denote the departure from the time average. U(~) is the appropriate transport variable to analyze water mass transports because it also takes high-frequency eddy motions into account. To distinguish these mean quantities from the Eulerian ones we refer to them as Lagrangian means, since points of isopycnal surfaces may move in the vertical. The Lagrangian mean flow differs from the Eulerian mean flow. The divergence of the latter appropriately describes mean vertical motions, while the divergence of the former adequately represents mean diapycnal flows. Note that not all vertical motion is necessarily due to diapycnal motion since isopycnals may slant. In addition, eddies may induce large diapycnal transports that are neglected in Eulerian mean transports. Here, we compare results derived from both Eulerian mean and Lagrangian mean transports. When we use Eulerian mean transports the time average is taken over an entire annual cycle. The Lagrangian mean transport consists of four seasonal data sets of u(a)h(o) and includes u'(u)h'(a), which evidently only captures the subseasonal variations. These seasonal Lagrangian mean transports are mostly used throughout this paper. We use a five-day running mean data to calculate the Lagrangian transports. The isopycnal mean mass transports, U(u), are calculated at every gridpoint using an interpolation scheme to determine the physical height of potential density surfaces to obtain the layer thickness. In effect, the model data is transformed to isopycnal coordinates. We employed a discretization of A~= 0.01 kg m -3. Horizontal velocities are assumed constant through each gridbox ~z. Ultimately, at every gridpoint, the averaged isopycnal transport is transformed back to z level transport using the averaged layer thickness. The latter also determines the Lagrangian mean density of each gridbox [McDougall, 1998]. Using these Lagrangian transports we calculate the meridional stream functions and perform Lagrangian trajectory analysis to study the fate of the EUC. The Lagrangian trajectory technique is described by D55s [1995] and Blanke and Raynaud [1997]. Particles are seeded in grid boxes proportional to the transports
178 Ot
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Figure 11: Variance conserving spectrum of the zonal velocity at 25~176 at 500m depth (solid line, peak at 50 cm2/s2), and the spectrum of the zonal wind stress at the same position (dashed line,in 10-6 N2/s4).
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Figure 12: Space-time diagram for the zonal velocity along the equator at 500 m depth (cm/s) for years 21 through 25. Contours are every 5cm/s. corresponding Kelvin wave could not be detected in the model solution because its phase speed is more t h a n 1 m/s and the model results are only stored every 10 days. The Rossby waves are excited by the a n n u a l and semiannual wind field variations (Figure 11) and have the following dispersion relation (Philander, 1990): a = -flA2k/3, where k is the zonal wave number, fl = 2.3. 10-11(ms) -1, and ,k = 250 km is the Rossby radius of the second baroclinic mode. From this, a Rossby wave with yearly forcing is expected to have a wavelength of 15000 km and a phase speed of 0.47 m]s. Figure 12 shows t h a t the waves seen in the model have a wavelength of more t h a n twice the basin width (= 6000 km) and phase speed of approximately 0.4 m/s. Thus, below the thermocline the equatorial flow field is dominated by seasonal Rossby waves of the second baroclinic mode. Water properties and floats are not advected by the time m e a n flow but instead by the t u r b u l e n t flow, m a k i n g the interpretation of observations much more complicated, especially in the presence of strong p l a n e t a r y waves. As an example, Figure 13 shows the p a t h of a virtual float at 500 m depth. Although there is almost no m e a n eastward flow (Figure 14), the final position of this float is 1000 km east of the western boundary. After this introduction, we can now turn to the interpretation of the obser-
204
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F i g u r e 13: The p a t h w a y of a virtual float at 500 m depth. The float was launched in the IWBC at 8~ and its final position aRer 4 years is m a r k e d with a circle. The n u m b e r s indicate the months after launch.
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205
Figure 15: Space-time diagram of the zonal velocity at 700 m depth. The eastward velocity is shaded, the contour intervals are 10 cm/s. The crosses indicate the time and position of the Schott et al. (1998) measurements and the circles show the launching time and position of the two Richardson and Schmitz (1993) SOFAR floats that were released away from the western boundary. vations introduced in section two. The initial motivation for this research is the observation of bands of strong zonal velocities at intermediate depths found by Schott et al. (1998). They interpreted these observations as strong zonal currents, although their existence defied any explanation and contradicts the float observations by R i c h a r d s o n a n d S c h m i t z (1993). Strangely, this has not received any attention in the literature. In fact, model studies interpret the lack of strong intermediate currents as a deficiency of the model (Boening a n d Schott, 1993; B l a n k e et al., 1999). The comparison of Figure 15c of S c h o t t et al. (1998) with Figure 4 shows t h a t the present model is able to reproduce the observed spatial structure of the observations (the amplitude, however, is too small). The model also shows t h a t there is no zonal flow in the yearly mean (Figure 14). This suggests t h a t the interpretation of the observations by S c h o t t et al. (1998) can be explained by aliasing of the tropical wave field. Figure 15 shows a space-time diagram of the zonal velocity at intermediate depths, where the time and locations of the available m e a s u r e m e n t s are indicated by crosses and circles. This diagram illustrates t h a t all six observations (4 ADCP sections and 2 float trajectories) can be explained by seasonal Rossby waves. The model predicts eastward flow for the two floats in January, strong westward flow in October, weak westward flow in March and weak eastward flow in June. Given the uncertainties in the wind field, the comparison with the observations is strikingly good. There are, however, differences between the observations and the model results. Figure 16 shows snapshots of zonal velocity from the model output, which
206 can be compared directly with the observations (see Figure 14 of Schott et al., 1998). Ideally, one would project a long time series of zonal velocity on the different possible equatorial modes and compare their amplitude in the model with the ones in the observations. Unfortunately, this is not possible because of the few number of observations. Furthermore, the zonal velocities of the different equatorial modes are not linearly independent. Therefore, one can only qualitatively compare the observations with the model snapshots. The October snapshots and the October observations compare well with the predicted structure of the first
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Figure 8. Comparison of horizontal divergence (10-Ys) at (a) 30 m computed from the average Atlantic v-section (Figure 7), the dashed line and (b) at 15 m from drifting buoy data using only the ~v/ay term, solid line and both terms, dot-dash line, top panel. Comparison of horizontal divergences at 30 m from the Atlantic SADCP section (Ave. dotdash line) of Figure 7 and 30 m (solid line) and 50 m (dashed line) computed by using the maximum equatorial upwelling position as the zero coordinate, (centered) bottom panel. The latter two curves are plotted relative to the average latitude of maximum divergence.
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0, it follows that s162 + A~ I]~q[[2 _ (~27-(~< C[(~r + A2 [[(~ql]2, where II~qll := {~q~)1/2 (which is an L 2 norm), A1 :-- min{C~'}, and A2 := max{C~'}. Since ~27~ is preserved by the dynamics, then [[1~r
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where J]]5r 2 := s162 + A1 ]lSq]]2 whose square root qualifies as a norm. Arnold II stable states can also be proved to be nonlinearly stable. It can be shown that an upper bound on s162 ] is (W2/zr 2) ]]5q]]2; since C~' < 0 in order for ~2~/~ < 0, then ( B 1 - W2/Tr2) [[~q[[ _< _~2~/~ _< B2 [[6ql[~, where B1 "- min{IC~'[} and B2 ' max{ ICY'I}. Consequently, [[ 2 B2 ~ 2 ~qllt>o -< B, - W2/Tr 2 I[ qllt=o 9
(2.27)
See R i p a [1992] for more details. 2.2.2. Spectral stability For an infinitesimal normal-mode perturbation, ~l = r Existence of nontrivial solutions for ~, which satisfies H ~ - 0,
-ikct + O(r
where r ~ 0. (2.28)
requires the fulfillment of condition dct H~ ::- 0. This implies the eigenvalue c(~; s, bT, b, r,, r2) to satisfy P(c) = 0, where P(.) is a cubic characteristic polynomial given in appendix B. Growing perturbations (i.e. those having Im c > 0) are found in the subset of the p a r a m e t e r space defined by 9l sw (cf. eq. 2.20). In order to obtain (2.28) it is not indispensable, of course, to make any reference to the conservation laws of the system. However, the present approach conduces straightforwardly to the result that growing perturbations can only exist in the region of the p a r a m e t e r space where all Hamiltonians are sign indefinite, i.e. where Arnold theorems are violated [Ripa, 2001]. In particular, because failure of fulfilling theorem 2.2 implies spectral instability of the basic flows treated here, Arnold II stability conditions are not only sufficient, but also necessary.
2.2.3. Elementary modes r e s o n a n c e It is customary to characterize the instability as a consequence of the resonant interplay between certain elementary modes, which need not to be physical modes of the system. A possible set of elementary modes, the "q modes" [Ripa, 2001], is defined by (I-I~). ~ - 0, which results in the eigenvalues ~q~- 1 - 1 + (1 + r l ) b (1 + r l ) R 2 1911,
321 ~q : rl (1 - - b T ) - (1 T rl)b (1 + r l ) R ~ E~, ~g _ fir2 (1 + rl) -1 b T - (1 + rl)bE33 _ bT. (1 + r l ) R 2 s
Here, 5 :-- (a - U~)/U~ =_ a/U~ - bT/s for any a with velocity units. Another possible set, the "r modes" [Pichevin, 1998], follows from the use of r coordinates as basic coordinates. These modes are required to satisfy A~r - 0 (cf appendix C) with eigenvalues 1 + (1 + rl)b 1 + (1 -t- rl)/~ 2' 1 + r l 1 (1 -- 51) -- bT ~ar --(1 + rl) r l r 2 b T - (1 + rl)b _ ~_.~_.. srlr2 + (1 T rl)2a 2 s In many conservative mechanical problems the Hamiltonian can be written in the form H = ~ H~ + Hr, where H~ is the Hamiltonian for a linear oscillator with frequency w,, say, and H~ is that part of the Hamiltonian that represents the (nonlinear) coupling between these modes of oscillation. For this general problem it can be shown that instability occurs whenever there is both resonance, i.e. w~ -- ~j for i ~ j, a n d sign H is indefinite. The Hamiltonian of the present problem can also be written in the above form if q coordinates are adopted as coordinates of the phase space. From the previous exposition and the fact that q coordinates are the most natural coordinates in the Hamiltonian formulation of the system, there is certain preference for using q modes over ~ modes in the study of resonance [Ripa, 2001]. Although neither the q modes nor the r modes are physical modes of the problem, the dispersion relation for ~ modes is simpler than that for q modes and has certain similarity with that for Rossby waves. In this sense the use of 0 modes in the study of resonance acquires certain relevance as well. However, both types of modes are useful in the explanation of the production of instability in the present model. This will be exemplified using data from the NEC in the following section. Of course, resonant scenarios involving other types of modes may also be considered depending on the problem at hand. For instance, Olascoaga [2001] found it more convenient to use the 2.5-layer model stable modes and a short Rossby wave in the study of the limiting case r~ ~ 0. In sum, a resonant scenario is characterized here by the matching of the elementary mode phase speeds, i.e. c~q - c)q or c~ - r for s o m e i ~ j. Yet this condition is not enough to explain the production of the instability: it must be complemented with the stability theorems derived using the integrals of motion of the system. 3.
DATA
Temperature and salinity observations from the Tropical Atlantic are available for the analysis of the present section. The temperature data correspond to three
322
Figure 2. (center panel) Geographic locations of the XBT transects considered in the present analysis. Each transect is identified by month and year. Dashed lines indicate the boundaries of the zonal channel model, roughly defining the latitudinal extension of the NEC. (outer panels) Fit of the isotherms of 11 and 20 ~ to a straight line. Solid lines are estimated depths and shaded bands around these lines the corresponding onestandard-deviation uncertainties. The isotherms of 11 and 20 ~ roughly correspond the lower (main or permanent) and upper (seasonal) thermoclines, respectively, and define the layer model interfaces.
temperature sections obtained from the high density XBT line AX08 that crosses the Atlantic Ocean from NW to SE, while the salinity were computed [Goni and Baringer, 2002] with the aid of TS relationships using the Levitus 94 climatologies [Conkright et al., 1998]. The three temperature sections correspond to December 2000, November 2001 and January 2002. 3.1. B a s i c flow Only those temperature and salinity profiles corresponding to the latitudinal band 10-18~ are considered (Figure 2, center panel) to evaluate the stability results of the previous section. This band roughly defines the limits of the NEC [e.g. Stramma and Schott, 1999] and is considered as the horizontal domain for the stability analysis. The number of temperature profiles available for the portions of the 2000, 2001, and 2002 transects in the band mentioned above are 8, 26 and 31, respectively. The vertical resolution of the temperature and salinity profiles is approximately 1 m. The average depth is about 1 km.
323 Table 1 Estimated basic flow parameters for the NEC three-layer model. Parameter Estimated Value s 1.6• b -0.34 • 0.16 bT 2.4+0.3 rl 0.5 5= 0.2 r2 0.09 =t=0.02 Quoted uncertainties are one standard deviation.
According to Reverdin et al. [1991], the isotherms of 11 and 20 ~ roughly correspond to the lower (main or permanent) and upper (seasonal) thermoclines, respectively. These isotherms are chosen here to define the lower and upper interfaces of the layer model of the previous section, respectively. A similar choice was made by Halliwell et al. [1994] in a study of the Sargasso Sea subtropical frontal zone. The density of the top layer is estimated by averaging all the data in the horizontal (regardless of their geographical position) and in the vertical between the surface and the upper thermocline. The same is done for the middle layer, which is delimited by the upper and lower thermoclines. The average density between the lower thermocline and 1 km depth is taken as representative of the average density of the model's bottom layer, whose lower boundary is assumed at 4 km depth. The buoyancy jumps across the interfaces are computed using these average densities. The depths of the isotherms in the assumed steady basic state are estimated by fitting a straight line to the data (Figure 2, outer panels). The corresponding steady geostrophic zonal basic velocities in the top and middle layers are estimated using the slopes of these lines, the computed buoyancies, and a reference Coriolis parameter taken at 14~N. The inferred values of the relevant parameters of the stability problem are given in Table 1. These values are accompanied by one-standard-deviation uncertainties that do not account for measurement or other random errors [e.g. Ripa, 2002b]. The sign of parameters bT and b reflects the westward flow of the NEC. Also notice the relative large value of s and the relative small value of r2.
3.2. Stability properties We evaluate here the stability results presented in section 2 using the estimated values of the parameters. Figure 3 illustrates stability properties in (bT, b)-space. Regions in this space are discriminated according to the sign of a Hamiltonian. In the shaded regions a Hamiltonian can be shown positive definite, thereby implying that the corresponding basic states are Arnold I stable. In the unshaded region a Hamiltonian can be found to be negative definite whenever the zonal channel is sufficiently narrow, thereby making the corresponding basic current Arnold II stable. Hatched regions are the locus of sign indefinite Hamiltonians, independently of the width of the zonal channel. The basic states in these regions
324
Figure 3. Stability properties in the space of the planetary (b :--/3R2/U~) vs. topographic (bT :- sU2/U~) Charney numbers. Here, s is the stratification parameter,/3 is the gradient of the Coriolis parameter, and R2 :-- glH1H2/(Hf2o). In addition, in this figure rl :-- H1/[t2; r2 :=:: ff/[t3; and ~ := v/k2 + 12R, is the nondimensional wavenumber, with components k (northward) and I (eastward) of a normal-mode perturbation. The high wavenumber cutoff of instability is denoted by ~ t (cf. Figure 4). For parameters in the shaded regions a Hamiltonian (pseudo energy-momentum integral) can be shown to be positive definite. For parameters in the unshaded region, a Hamiltonian can be shown to be negative definite if the zonal channel is sufficiently narrow, i.e. if min ~ (-- 7rR/W) > ~+, where W is the width of the channel. All Hamiltonians in the hatched region are sign indefinite and the corresponding basic states can be unstable through explosive resonant interaction. The location in this space of the NEC is indicated with a dot. Uncertainties are indicated with one-standard-deviation error bars.
are potentially ERI unstable. The u n c e r t a i n t y of the size of all these regions is represented by one-standard-deviation error bars. The estimated location of the NEC in this region is represented by a dot and its u n c e r t a i n t y is indicated with one-standard-deviation error bars. The b o u n d a r y between the Arnold I stable and Arnold II possibly stable regions as predicted by the 2.5-layer model [Olascoaga and Ripa, 1999, but with the condition rl -- 1 relaxed] is also shown with a dashed line. The importance of the interior ocean in the baroclinic instability of a surface trapped c u r r e n t for certain p a r a m e t e r values has been already established by Olascoaga [2001]. The NEC p a r a m e t e r s fall precisely in the region where the interior ocean effects are important. It is shown below t h a t the NEC model is
325
Figure 4. Stability properties in the space of allowable nondimensional wavenumber (n) topographic Charney number (bT). Shaded regions are spectrally unstable. Dashdotted curves indicate ~+, the high wavenumber cutoff of instability. Thick and thin solid curves correspond to the matching of vorticity-related and Rossby-like mode phase speeds, respectively. The possible location of the NEC in this space is indicated by a dashed straight line. The hatched band around this line represents a one standard deviation uncertainty. The upper panel shaded regions correspond to the expected parameter values in table 1. The lower panels depict other two data-compatible (extreme) configurations with parameter values ~ + ~ and b - cb, and s + ~s and b + Cb for the plot on the lei~ and right panels, respectively. Here, ~ and c~ mean expected value and one-standard-deviation uncertainty of parameter a, respectively. vs.
in fact unstable as a consequence of the relatively wide latitudinal band t h a t the current occupies. Figure 4 depicts stability regions in (bT, ~)-space. Shaded regions represent the set of parameter values for which a basic flow is unstable under infinitesimal normal-mode perturbations. The shaded regions in the upper panel is constructed with the expected p a r a m e t e r values shown in Table 1. The shaded regions in the lower panels correspond to other two data-compatible (extreme) configurations t h a t have, instead, ~ + ~ and b-~b (lower-lei~ panel) and ~ and b+~b (lower-right panel). Here, a and ca mean expected value and one-standard-deviation uncertainty of parameter a, respectively. The dashed line in this figure indicates the expected value of the topographic Charney n u m b e r associated with the NEC model, and a subset of possible perturbation wavenumbers to develop in this current, starting at
326
2l ~" 0
--" ~ . . . . . . /.
i
i
i
0'.8
i
0.1
0
"
0.4
0.6
'
tg
\ "~" 0
'
r - - i
.
/
,~ 0.1[ 0.05 0 " 0.2
|
|
,
m
0.1
0.4
A
o.6
~0.05 0.8
i
00.2
fi
o.4
G 0.6
0:s
i
t~
Figure 5. Real (dashed curves) and imaginary (solid curves) parts of the eigenvalue (upper plot in each panel) and perturbation growth rate (lower plot in each panel) as a function of the allowable wavenumber. The plots in the upper pannel are constructed with the expected parameter space values in Table 1. The plots in the lower-left panel use, instead, + es, ~ + e~r, and b - eb, whereas those in the lower-right panne1.3 ~ es, ~r ~ ehT, and b t eb.
the expected minimum allowable perturbation wavenumber in the zonal channel (the data give min ~ - 0.17 i 0.05). The hatched band around the line represents an uncertainty of one standard deviation. In all cases shown, there are two bands of wavenumbers with nonvanishing perturbation growth rates (Ira c =~ 0). Therefore, the present data predict instability for the NEC given its relative wideness, namely no Hamiltonian can be proved to be negative definite for the parameters that characterize the NEC model. Eigenvalue and (an upper bound of the) perturbation growth rate are depicted in Figure 5 as a function of the allowable wavenumber. The plots in the upper panels of this figure are constructed with the expected param_eter space values given in Table 1. The plots in the lower-left panel use, instead, ,~ ~- es, ~r + eT, and b - eb, whereas g + e~, DT ~- ~T, and b + eb in the lower-right plots. Notice the presence of the two unstable wavenumber bands mentioned above. Using the same parameter values as in Figure 4, the phase speeds associated with the elementary q and r modes are plotted along with the perturbation growth rates in Figures 6 and 7, respectively, as a function of the allowable wavenumber. These plots show that the matching of C-mode phase speeds (indicated with a circle in Figure 7) coincide in many cases with the onset of instability. The growth rates for the most destabilizing perturbations are seen related to the
327
,
2 .I
0.1
I
I
.
.
.
.
.
.
I
"~ 0.05 0 " 0.2
0.4
0.6
0.8
4
%
2
~ % 9
0
1
.
!
.
0.1 ~9
0.1 t
0.05 0
2
"~"
I
,
0.2
0.4
0.6
0.8
0.05 L
i
00.2
0.4
0.6
0.8
1
Figure 6. Phase speed of the elementary, vorticity-related "q modes" (upper plot in each panel) and perturbation growth rate (lower plot in each panel) as a function of the allowable wavenumber. Parameter values are the same as in Figure 5. The wavenumber for which there is resonance of elementary modes (matching of phase speeds) is indicated in the plots.
occurrence of resonance of both r and q modes (the matching of the q-mode phase speeds is indicated with a circle in Figure 6). Notice, however, that matching of r and q-mode phase speeds can also occur for wavenumbers outside the range corresponding to growing perturbations. Yet this is consistent with the fact that resonance of these modes does not imply instability by itself, rather it must be complemented with the stability conditions inferred from the conservation laws of the system. A more general view of this picture can be see in Figure 4, where the wavenumber for resonance of q and ~b modes as a function of the topographic Charney number are depicted with solid thick and thin curves, respectively. Despite the earlier mentioned theoretical preference for the use of q modes over r modes in the study of resonance, it is clear that both of them contribute to the explanation of the production of instability.
3.3. Comparison with in situ observations and earlier works For the chosen set of basic state parameters, the most destabilizing perturbations predicted by the three-layer model have wavelengths spanning the range of 350 km through 850 km (Figure 5, lower-right panel), with a minimum e-folding time of about 40 d reached for a wavelength of around 550 km and a period of approximately 40 d. Taking into account the whole range of compatible basic state parameters dictated by the data, i.e. expected values and uncertainties,
328
21 N,.
3
0 '~
~0.05
,I
f
0.2
I
0.4
O.6
.
.
o:8
i
t~
~" 2
~" 2 "r
n
....
,
9
~
9
0.1
0.1
!
O.O5 0 012
1 n
o:4
t
:(/ 0.6
0
"5"
O.O5
o 0.8
1
o.2
0.4
0.6
0:8
i
t~
Figure 7. Phase speed of the elementary, Rossby-like "r modes" (upper plot in each panel) and perturbation growth rate (lower plot in each panel) as a function of the allowable wavenumber. Parameter values are the same as in Figure 5. The wavenumber for which there is resonance of elementary modes (matching of phase speeds) is indicated in the plots.
destabilizing perturbations are found to have wavelengths ranging from 300 km through the maximum allowable (roughly 2, 100 km), with e-folding times larger than 25 d and periods between 15 d and 200 d. In particular, for ~ -~ c~, bT + cb~, and b - e~ (Figure 5, lower-let~ panel), the minimum e-folding time for the growing perturbations with the shortest wavelengths is roughly 70 d, which is reached at a wavelength of around 310 km with a period of approximately 120 d. One of the earliest observations of the variability of the NEC was done by the U.S.S.R. POLYGON experiment [Brekhovskikh et al., 1971], which documented the progress of an eddy in the central part of the NEC with associated wavelengths of the order of 360 km and periods of about 120 d. Mesoscale variability observations from the POLYMODE experiment [Fu et al., 1982] indicated, afterwards, that wavelengths between 80 and 200 km with periods of 100 d and e-folding times of the order of 1 y or more were the most common in the area of the experiment cluster C, which was located far downstream of the NEC. More recently, from the analysis of TOPEX/Poseidon altimeter data, S t a m m e r and Wunsch [1999] indicated the presence of enhanced variability in the NEC region. No precise indication of variability scales was given by these authors, who particularly concentrated on the correlation between the eddy energy variability and the wind stress variability. Since this correlation resulted very poor in the NEC region, the authors concluded
329 that baroclinic instability cannot be ignored as a potential source of variability in the area. The present layer model shows a better agreement with U.S.S.R. POLYGON than with POLYMODE observations. This may be attributed to the fact that POLYMODE measurements are probably contaminated by the eddies produced in the North Brazil Current retroflection region [e.g. Goni and Johns, 2001], which cannot be captured with the present model. A similar explanation was given for the lack of agreement between POLYMODE observations and Keffer's [1983] analysis using the linear baroclinic instability model of Gill et al. [1974]. 4. S ~ Y
AND CONCLUSIONS
In this paper we study the stability properties of a baroclinic zonal current using a quite general three-layer quasigeostrophic model. Neglecting dissipation and external forcings make the system Lie-Poisson Hamiltonian, and the associated integrals of motion (energy, zonal momentum, and vorticity-related Casimirs) are consequently employed in Arnold's method to evaluate formal and nonlinear (or Lyapunov) stability conditions. The following six nondimensional numbers completely characterize the solutions of the stability problem: (i) the wavenumber of a normal-mode perturbation, (ii) a measure of the stratification, (iii) a topographic Charney number, (iv) a planetary Charney number, (v) the ratio of the upper two layer reference thicknesses, and (vi) the ratio of the sum of these thicknesses to the bottom layer reference thickness. The stability properties are then evaluated numerically using data from a region of the ocean mainly influenced by the Atlantic North Equatorial Current (NEC). The NEC model is baroclinically unstable under normal-mode perturbations, which reflects that the current is too wide for a negative definite Hamiltonian (pseudo energy-momentum integral) to exist. The resonance interplay of two possible sets of elementary modes, one vorticity-related and the other Rossby-like, is studied to shed some light on the nature of the instability. The Rossby-like modes explain in most cases the instability onset. Double resonance of Rossbylike and vorticity-related modes is found to favor the maximization of growth rates. A comparison of growth rates and wavelengths of the most destabilizing perturbations with observations reported in the literature is found reasonable, yet there is no general agreement on the observed variability scales in the region. Notwithstanding, the inferred significance of baroclinic instability as a source of variability in the NEC is found to agree with a recent study on eddy energy variability derived from altimeter data. That study have found a poor correlation between the latter and the wind stress variability, thereby increasing the potential of baroclinic instability as a source of eddy motion in the area. Finally, a reducedgravity two-layer model is shown to be incapable of accounting for the instability, suggesting--according to the available d a t a - - t h a t ocean interior effects play an important role on the stability properties of the NEC. The scales of variability predicted by linear theory only characterize the initial stages of the nonlinear evolution. A more complete investigation will thus involve
330 the study of weakly and/or fully nonlinear aspects of the finite-amplitude evolution of baroclinic instability in the current. The validation of the scales of equilibrated baroclinic instability will require a detailed knowledge of the scales of variability in the region, which is currently lacking. A subject not treated here is that relating to the rigorous bounds on eddy-amplitude growth that can be derived thanks to the existence of nonlinear stable states [ S h e p h e r d , 1988; P a r e t a n d V a n n e s t e , 1996; O l a s c o a g a et al., 2003]. These bounds, which impose a p r i o r i constraints on the ergodicity of the flow, will provide a theoretical basis to validate the nonlinear models. Also, the baroclinic instability scenario may be modified if the vertical structure associated with upper thermocline is found to experience a significant seasonal modulation [Pedlosky a n d T h o m s o n , 2003]. Clearly, to address this issue the temporal hydrographic sampling will need to be dense enough to resolve at least an annual cycle. The treatment of all these topics, which may find a basis on the present work, is reserved for future research. Acknowledgment
We dedicate this work to the memory of Professor Pedro Ripa, mentor and friend. We thank Gustavo J. Goni for encouraging us to write this article. Our work was supported by the National Science Foundation. ~L ENERGY AND CASIMIR MATRICES The energy matrix is given by [ ~02 -~ C03~0 '[ 3-10002 8 - 1 Q o (~o2 --[-,~o) s - ~Qo~O2
-- m - I
02 + ~;o ~00/'i;1 (02 t ~;o)~l (] -}- /~-2)/~02 ~- ~O()trI t~2~l
]
Here, A .... ~3 + (1 ff 03)~2 { (0o 4- 0102)~, 01 R2 where ~o'-Qln 2, Qo " - st1,
~1"- 1+~o, Q1 " - 1 + S-1QO,
02
"-- r201
10o,
03 ' - (1 + 8-1)0o + Q2.
The Casimir matrix, in turn, reads
C~
--
i
1 ~-b(1trl) a~l 0 0
& 0
r1(bT-l)+b(1+rl)
0
0
1
0
&+s- 1bT b(1~-r1)--rlr2bT/(l~-rl
.
)2
Here, ~ "- (a - U2)/U~ =- a/U~ - bT/s for any a with velocity units.
331
B. D I S P E R S I O N RELATION The characteristic polynomial for the eigenvalue c is given by
63 + a~G + a~6 +
a3
0
--
where (51 -- ~;I) (S -- K;4~;2)-- (1 + b2~l) ~n + b4~;3 al
-~
-t- b3,
8/~1 -~- /~4/~3
(bl
Nl)[(b3s - ~2ba) - (b2 + ~2b3)ga] - (1 + ~;lb2)(b4 + ~ab3) s~l + ~4~a b2 (~1 - bl)(b4 + ~4b3) -
-
a3 "-8 ~ 1 ~- /~4~3
Here, Re "- 1 + s(1 + 0olno), ~3 "- 1 - nl~e, ~4 "- 1 + ~o~1~o, bl "- 1 + pib, be "- sool(b~ - ~ ) + bT, b3 "-- s-lbT, b4 "- Qe-l(b~ - l) - b3.
C. EIGENVALUE P R O B L E M IN r COORDINATES Assuming r - ~(y) + cCe ik(x-ct) sin ly + O(c2), where c ~ 0, it follows t h a t ~b satisfies A r - 0 with
[
b~ + ( ~ - 1 ) ~
A. . . .
~ 0
1 -~
b~ 4 ~ 2 -((:+b3)
0
]
-~s 1 b4+(6 t ba) n4
REFERENCES Arnold, V., Condition for nonlinear stationary plane curvilinear flows of an ideal fluid, Dokl. Akad. Nauk. U S S R , 162, 975-978, 1965. Engl. transl. Soy. Math., 6, 773-777, 1965. Arnold, V., On an apriori estimate in the theory of hydrodynamical stability, Izv. Vyssh. Uchebn. Zaved Mat., 54, 3-5, 1966. Engl. transl. Am. Math. Soc. Transl. Series H, 79, 267-269, 1969. Beron-Vera, F. J., and Ripa, P., Free boundary effects on baroclinic instability, J. Fluid Mech., 352, 245-264, 1997. Brekhovskikh, L. M., Federov, K. N., Fomin, L. M., Koshlyakov, K. N. and Yampolsky, A. D., Large scale muli-buoy experiment in the Tropical Atlantic, Deep-Sea Res., 18, 1,189-1,206, 1971. Conkright, M., Levitus, S., O'Brien, T., Boyer, T. P., Stephens, C., Johnson, D., Stathoplos, L., Baranova, O., Antonov, J., Gelfeld, R., Burney, J., Rochester, J. and Forgy, C., World ocean database, Technical Report 14, Nat. Oceanogr. Data Center, 1998. Fu, L., Keffer, T. and Niller, P. P., Observations of mesoscale variability in the western North Atlantic: A comparative study, J. Mar. Res., 40, 809-848, 1982.
332 Gill, A., Green, J. and Simmons, A., Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies, Deep Sea Res., 21,499-528, 1974. Goni, G. J. and Baringer, M. O., Surface currents in the tropical Atlantic across high density XBT line AX08, Geophys. Res. Lett., 29(24), 10.1029/2002GL015873, 2002. Goni, G. and Johns, W., Census of warm rings and eddies in the north brazil current retroflection region from 1992 through 1998 using TOPEX/Poseidon altimeter data, Geophys. Res. Let., 28, 1-4, 2001. Halliwell, G. R., J., Peng, G. and Olson, D. B., Stability of the Sargasso Sea subtropical frontal zone, J. Phys. Oceanogr., 24, 1,166-1,183, 1994. Holm, D. D., Marsden, J. E., Ratiu, T., and Weinstein, A. Nonlinear stability of fluid and plasma equilibria, Phys. Rep., 123, 1-116, 1985. Keffer, T., The baroclinic stability of the Atlantic North Equatorial Current, J. Phys. Oceanogr., 13,624-631, 1983. McIntyre, M. and Shepherd, T., An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems, J. Fluid Mech., 181, 527-565, 1987. Olascoaga, M. J., F. J. Beron-Vera and J. Sheinbaum, In O. U. Velasco-Fuentes, J. Sheinbaum and J. Ochoa (eds.), Deep ocean influence on upper ocean baroclinic instability saturation, Nonlinear Processes in Geophysical Fluid Dynamics, Kluwer Academic, submitted, 2003. Olascoaga, M. J., Deep ocean influence on upper ocean baroclinic instability, J. Geophys. Res., 106, 26,863-26,877, 2001. Olascoaga, M. J. and Ripa, P., Baroclinic instability in a two-layer model with a free boundary and 3 effect, J. Geophys. Res., 104, 23,357-23,366, 1999. Paret, J. and Vanneste, J., Nonlinear saturation ofbaroclinic instability in a threelayer model, J. Atmos. Sci., 53, 2905-2917, 1996. Pedlosky, J., Geophysical Fluid Dynamics, Second Edition, Springer, 1987. Pedlosky, J. and Thomson, J., Baroclinic instability of time dependent currents, J. Fluid Mech., submitted, 2003. Pichevin, T., Baroclinic instability in a three layer flow: A wave approach, Dyn. Atmos. Oceans, 28, 179-204, 1998. Reverdin, G., Rual, P., du Penhoat, Y. and Gouriou, Y., Vertical structure of the seasonal cycle in the central equatorial Atlantic Ocean: XBT sections from 1980 to 1988, J. Phys. Ocean., 21,277-291, 1991. Ripa, P., Symmetries and conservation laws for internal gravity waves, AIP Proceedings, 76, 281-306, 1981. Ripa, P., Wave energy-momentum and pseudo energy-momentum conservation for the layered quasi-geostrophic instability problem, J. Fluid Mech., 235, 379-398, 1992. Ripa, P., Arnol'd's second stability theorem for the equivalent barotropic model, J. Fluid Mech., 257, 597-605, 1993. Ripa, P., On improving a one-layer ocean model with thermodynamics, J. Fluid
333
Mech., 303, 169-201, 1995. Ripa, P., "Inertial" oscillations and the /~-plane approximation(s), J. Phys. Oceanogr., 27, 633-647, 1997. Ripa, P., A minimal nonlinear model of free boundary baroclinic instability, Proceedings of the 12th Conference on Atmospheric and Oceanic Fluid Dynamics, American Meteorological Society, pp. 249-252, 1999a. Ripa, P., On the validity of layered models of ocean dynamics and thermodynamics with reduced vertical resolution, Dyn. Atmos. Oceans, 29, 1-40, 1999b. Ripa, P., Baroclinic instability in a reduced gravity, three-dimensional, quasigeostrophic model, J. Fluid Mech., 403, 1-22, 2000a. Ripa, P., On the generation of turbulence by baroclinic instability in the upper ocean, in C. Dopazo et al. (ed.), Advances in Turbulence VIII. Proceedings of the 8th European Turbulence Conference, K]uwer Academic, pp. 371-374, 2000b. Ripa, P., Waves and resonance in free-boundary baroclinic instability, J. Fluid Mech., 428, 387-408, 2001. Ripa, P., On upper ocean baroclinic instability, in J. Ramos-Mora and J. Herrera (eds), Escuela de Turbulencia (School of Turbulence), Sociedad Mexicana de Fisica, 2002a. Ripa, P., Least squares data fitting, Cienc. Mar., 28, 75-105, 2002b. Shepherd, T., Nonlinear saturation of baroclinic instability. Part I: The two-layer model, J. Atmos. Sci., 45, 2014-2025, 1988. Shepherd, T., Symmetries, conservation laws, and Hamiltonian structure in geophysical fluid dynamics, Adv. Geophys., 32, 287-338, 1990. Stammer, D. and Wunsch, C., Temporal changes in eddy energy of the oceans, Deep-Sea Res., 46, 77-108, 1999. Stramma, L. and Schott, F., The mean flow field of the tropical Atlantic Ocean, Dee-Sea Res., 46, 279-303, 1999.
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lnterhemispheric Water Exchange in the Atlantic Ocean edited by G.J. Goni and P. Malanotte-Rizzoli 9 2003 Elsevier B.V. All rights reserved.
Synoptic study of warm rings in the North Brazil Current retroflection region using satellite altimetry Gustavo J. Goni a* and William E. Johns b aNational Oceanic and Atmospheric Administration, Atlantic Oceanographic and Atmospheric Laboratory, 4301 Rickenbacker Causeway,Miami, Florida 33149, USA. bUniversity of Miami, Rosenstiel School of Marine and Atmospheric Science, Miami, Florida 33149, U.S.A. Ten years of altimeter data are used in conjunction with temperature and salinity data within a two-layer reduced gravity approximation to investigate the shedding and translation of North Brazil Current rings. Space-time diagrams of sea height anomalies and residues along the altimeter groundtracks show large seasonal and interannual variability. Results presented here confirm previous estimates that indicate a shedding rate of 3 to 7 rings per year with no marked seasonal variability but with very strong year-to-year variability. Additionally, eddies not shed by the retroflection travel through the region as well. Most of the rings pass very near of Barbados, affecting the environment in the region, of which seven rings during the study period are seen to enter into the Caribbean Sea. A link is found in this study between long-term surface temperature changes in the tropical Atlantic and the number of rings shed at the NBC retroflection, where periods of time with warmer surface temperatures are associated to a higher number of rings shed. 1. I N T R O D U C T I O N
The investigation of the upper ocean heat balance in the equatorial Atlantic is concentrated in the cross-equatorial exchange of near surface waters that make up the upper limb of the Meridional Overturning Circulation. Waters from the South Atlantic subtropical gyre cross through the equatorial circulation system to fmally enter into the North Atlantic subtropical gyre. The winddriven patterns in the tropical Atlantic are complex and contribute to the three dimensional circulation, as in the case of the equatorial upwelling and o f f -
*Corresponding author; Tel: 305-361-4339, Email:
[email protected] 336
Figure 1. The region of study indicating the main surface current in the tropical Atlantic, the central South Equatorial Current (cSEC), the Brazil Current (BC), the north South Equatorial Current (nSEC), the North Brazil Current (NBC), the Guyana Current (GC), the North Equatorial Counter Current (NECC), the North Equatorial Current (NEC) and the Caribbean Current (CC). The shaded area indicates the region where the NBC rings are investigated in this study. equatorial downwelling. Southern hemisphere water makes its way into the North Atlantic through two primary pathways: rings shed by the low latitude North Brazil Current (NBC) as it retroflects into the interior, and seasonal rectification of the upper layer currents that allow warm surface waters to be stored in the North Equatorial Counter Current (NECC)/North Equatorial Current (NEC) ridge system and released northward via Ekman transports (Mayer and Weisberg, 1993). The North Brazil Current is a northward flowing western boundary current that carries warm waters across the Equator off the easternmost tip of Brazil and along the coast of South America (Figure 1). The origin of this current is linked to the bifurcation of the SEC, particularly its central branch (cSEC), which contributes to the formation of the north flowing NBC and the south flowing Brazil Current (Schott et al, 1998). The NBC retroflects between 5 and 10~ (Johns et al, 1990) shedding warm anticyclonic rings, among the largest warm rings in the oceans. Early studies showed that this retroflection occurs mostly during the boreal summer and fall months, and that its waters join the NEC (Molinari and Johns, 1994). The warm rings shed by the NBC then become one of the mechanisms that contributes to the transport of South Atlantic upper waters into the northern hemisphere. These rings travel in a NW direction partly carried by the background current (Guyana Current) and partly by their
337 own translation speed. These rings either enter the Caribbean Sea or the North Atlantic subtropical gyre as part of the Atlantic meridional overturning cell (Johns et al, 1998). The countercurrents, rings and meanders found in the region of the NBC retroflection contribute to the regional variability, which is investigated here using satellite altimetry. The vertical thermal structure of this region has been used to identify mesoscale features and the mass transport using hydrographic data. Reverdin et al (1991) used the 11~ and 20~ isotherm to represent thermocline displacements to investigate the variability of the deep thermocline. Molinari and Johns (1994) investigated the variability and annual and semiannual cycles of the 20~ and 10~ isotherms in the region from historical XBT data. They concluded that the annual and semiannual harmonics account for more than 60% of the total variance in the region. Didden and Schott (1993, DS93 hereafter) used Geosat altimeter data during 1986-1989 to carry out a study of these warm rings based on the sea height anomaly data and concluded that 2 to 3 rings were detached from the NBC retroflection from November through January. Fratantoni et al (1995) also carried out a detailed investigation using near subsurface velocity and temperature measurements, model results and the same Geosat-derived sea height anomaly data used by DS93. Their model and altimetry results showed ring formation limited approximately to December to March, while the velocity fields derived from Acoustic Doppler current profilers show rings translating in the region during the whole year. Goni and Johns (2001, GJ01) later used a six year long (1993-1998) TOPEX/Poseidon altimeter data set to create an expanded census of NBC rings, which represented the first long time series of these features. Results from this work indicated that 2 to 6 rings were formed each year without any marked seasonality and that these rings may account for up to 1/3 of the meridional mass transport across the Equator in the Atlantic Ocean. Most recently, Fratantoni and Glickson (2002) identified 18 NBC rings during a three-year period (September 1997 through September 2000) using ocean color imagery, confirming the larger number of rings shed and a the lack of a marked seasonability in their formation. Observations and models indicate that there are at least three types of rings shed by the NBC retroflection: surface, deep and subsurface (Wilson et al, 2002). Other chapters in this book (Garraffo et al and Johns et al) include references and results on these different types of rings. It is important to mention at this point that the existence of subsurface NBC rings was being reproduced in numerical models before they were actually first observed. These subsurface rings have a small or vanishing sea surface height signal and are a relatively new discovery. The reader is referred to these chapters to complement and enhance the information provided here, particularly to compare with model results (Garraffo et al), inverted echo sounder observations (Garzoli et al) and on the effect of the NBC rings on Barbados (Cowen et al). Two altimeter data sets are used here, one corresponding to the TOPEX/Poseidon (T/P) altimeter and another to a blended data set of three altimeters, TOPEX/Poseidon, the ESA Remote Sensing-2 Satellite 2 (ERS-2) and
338 the Geosat Follow-On (GFO). Results presented in this chapter correspond to the period November 1992 through December 2001. The rings in this work are identified and tracked using the same procedure as described in Goni and Johns (2001). A long period signal in the sea surface temperature data in the tropical Atlantic is also used to explore a possible link between this signal and the formation of NBC rings.
2. R E G I O N O F STUDY The region of study extends from 40oW to 70~ and from 0 to 20~ (Figure 1), which is characterized by the presence of a warm and salty current, the North Brazil Current, which retroflects at approximately 45oW 5oN. While this current retroflects it sheds warm anticyclonic rings that propagate in a NW direction off the coast of South America until reaching the Windward Islands, where they disintegrate, cross into the Caribbean or continue with a northward propagation (DS93; GJ01). Waters from the Amazon River are embedded in the retroflection region. The NBC rings are known to carry fresher waters from the Amazon River causing marked influence on the environmental conditions surrounding the Windward Islands, particularly Barbados (Kelly, 2001 and Cowen et al, this volume).
3. DATA The three main data sets used in this study are: 1. Altimeter-derived sea height anomaly. Alongtrack TOPEX/Poseidon data from November 1992 onward is used throughout this work, while blended alongtrack data from TOPEX/Poseidon, ERS2 and GFO since 1998 is used, and only to create maps with improved spatial resolution to better identify NBC rings. 2. l x l degree temperature and salinity data from the Levitus climatology (Conkright et al, 1998) is used to obtain the mean depth of the 20oC isotherm and reduced gravity fields. 3.1. A l t i m e t e r d a t a
The altimeter-derived sea height anomaly, #', is the value of the deviation of the actual sea height, q, referred to the mean sea height, r], which is computed over a period of time of several years: ~7'(x, y , t ) = ~7(x, y , t ) - ~7(x, y). (1) The altimeter measures the sea height anomaly along the altimeter groundtracks (Figure 2), providing data that is distributed irregularly in space
339
Figure 2. T/P, ERS-2 and GFO altimeter groundtracks in the region of study. Four ascending T/P groundtracks (t287, t301, t304 and t312) are indicated for later reference. and time. Adjacent T/P, GFO and ERS-2 groundtracks are separated approximately 3, 2 and 1 degrees longitudinally, respectively, and are repeated approximately every 10, 17 and 35 days. The sea height anomaly alone is not always a good indicator of the presence of warm rings, particularly in frontal regions close to where rings are being shed, or in regions where the steric effect on the sea height is comparable to the sea height variations produced by these rings. In the first case, an alternation of positive and negative sea height anomalies are usually found in frontal regions (Goni et al, 1996), making the distinction of a ring and a front very difficult. A warm frontal area can be either identified from its negative or positive sea height anomaly values, depending on where the front is located with respect to its mean position. The sea height of a moving front and its relationship with its sea height anomaly can be explained using synthetic sea height anomalies. An ensemble of synthetic alongtrack sea height anomalies profiles (Figure 3) shows how a moving warm front causes a variation in the alongtrack sea height anomaly, even when the frontal shape remains unchanged. Assuming that the altimeter groundtrack crosses through the jet of the current, the location of this jet (maximum alongtrack sea height gradient) can usually be set close to the position of the maximum alongtrack sea height anomaly gradient. Similarly, a warm ring can be observed as an alternation of positive and negative anomalies as the ring travel along its path in a region where the sea height variability of the b a c k ~ o u n d flow is comparable to the sea height anomaly of the ring. Consequently, the location of the jet of a current or the maximum flow around a ring is not always coincident with the position of the maximum alongtrack sea height anomaly. The steric effect, with a clear annual cycle, is one important component of the sea height variability in the study region. It is shown later that the amplitude of this annual signal has a very high dependence on location. This is particularly important when a ring is traveling in a region where the mean sea level exhibits
340
Alongtrack Latitude (deg) Figure 3. (a) Synthetic sea height profiles simulating a moving front with five individual fronts highlighted. (b) Synthetic mean sea height. (c) Synthetic sea height anomalies. (d) Alongtrack gradients of the synthetic sea height and sea height anomalies.
large spatial variability; the sea height displacement produced by the ring may not be enough to result into a positive sea height anomaly. Therefore, is more appropriate to investigate the rings analyzing their properties referenced to their surrounding waters or having the annual signal removed. A nine-year altimeter-derived sea height anomaly data set is used in this study to estimate the variability of the sea surface height, with the anomalies referred to the 1993-1998 mean field. The rms of the sea height anomaly (Figure 4) exhibits values ranging from 4 to 11 cm. The regions with higher variability are associated to the North Brazil Current, its rings, to the NECC, and to the variability in the Caribbean Sea. Due to the low latitude setting these rms values are relatively smaller than in other regions where warm anticyclonic rings are also formed. For example, the Brazil-Malvinas Confluence region and
341 the Agulhas Retroflection region exhibit maximum rms values of approximately 30 cm (Goni et al, 1996; Goni et al., 1997). Space-time diagrams represent a useful means to identify and track features in the ocean. They have been successfully used to track warm rings in the region of study using Geosat altimeter data (DS93). The space-time diagram of the sea height anomaly and residues (Figure 5, left and right panels, respectively) for ten selected ascending T/P groundtracks (Figure 2) show very distinctive features. The sea height residual is obtained by subtracting a mean annual and semiannual cycles (Figure 5, middle panel). The steric effects dominated by the annual cycle in the sea height anomaly and the variability of mesoscale features in the sea height residues are the most distinguishable features. The amplitude of the annual cycle ranges from 6 to 12 cm (Figure 6, left panel). The smallest values of annual amplitude, of approximately 3 cm, correspond to the region affected by the passage of the North Brazil Current rings. The annual cycle accounts for approximately 40% of the variability in this area. This value is slightly smaller than the 60% derived from XBT observations (Molinari and Johns, 1994). The semiannual signal accounts for less than 2 cm in most areas in the region of study. These space-time diagrams and the rms values of the sea height show the very different oceanic conditions east and west of approximately 55oW in terms of both the mean conditions and in the mesoscale variability. The mean annual signal and the sea height residuals reveal very interesting features. First, the annual amplitude (Figure 5, center) is smaller to the east of 55oW and mainly linked to the retroflection of the NBC, which has a marked annual period (Johns et al, 1990). The residuals show an interannual signal on which the mesoscale signal is superimposed. This signal is of interest in light of a previous work that used Geosat sea heightdata and reported an increase of the volume of the equatorial upper ocean during 1987-1989, indicative of the effect of the 19861987 ENSO (Arnault and Cheney, 1994). This signal of long period and its relationship to NBC ring shedding will be presented later in this chapter.
3.2. Climatological data Climatological temperature and salinity data (Conkright et al, 1998) is used to compute the mean values of the upper layer thickness, which extends from the surface to the depth of the 20oC isotherm, and the reduced gravity for the region of study. The reduced gravity field, g', is computed using the mean upper and lower layer densities:
g'(x,y)=e(x,y)g(y)= P2(x'Y)-P'(x'Y) g(y) P2(x,Y)
(2)
342
Figure 4. The rms (in cm) of the sea height from TOPEX/Poseidon altimeter data. Rms values for bottom depths shallower than 500 m are masked.
Figure 5. (left) Sea height anomalies for the ascending T/P groundtracks, (center) Annual plus semiannual amplitude of the sea height anomalies, and (right) Sea height residuals for selected ascending T/P groundtracks (see Figure 2). The latitude and longitude of the southern limit of the section of each groundtrack used in these diagrams is indicated on the left, with the sections extending 5 degrees in longitude from west to east.
343
Figure 6. Amplitude of the annual (lei~) and semiannual (center) cycles and the percentage of variability (right) due to these two cycles obtained using T/P data from 1993 until 2001. where g is the acceleration of gravity, and D o , a n d [5[] are the mean densities of the upper and lower layers, respectively. The lower layer is defined as the layer between the depth of the 20oC isotherm and 1500 m or the sea floor. Hence, the reduced gravity provides a measure of the vertical stratification in the region. These climatologically-derived values (Figure 7) are then used in conjunction with the sea height anomalies within a two-layer reduced gravity scheme to obtain the absolute field of the depth of the 20oC isotherm, described next.
4. TWO-LAYER M O D E L A P P R O X I M A T I O N Some difficulties that arise from using sea height anomaly or residue data to identify and track warm rings have already been discussed. Most of these difficulties can be overcome by adding a mean field of sea height to allow for differentiation of fronts and rings. However, since one of the objectives of this study is to also to investigate the volume of the rings from the displacement of the 20oC isotherm, the rings are investigated here in terms of their upper layer thickness signatures and not in terms of their sea surface height signatures. The understanding of the relationship between the sea surface height signal and the upper ocean thermal and dynamic structures is a key to assessing the limitations of altimeter-derived sea height anomaly data. The reader is referred to a previous study (Mayer et al, 2002) and to the chapter by Mayer et al, which address this topic thoughtfully by combining T/P data and XBT observations. Results presented in that chapter indicate that the sea height anomalies can be used as a proxy to investigate the upper ocean dynamics in the NBCR region. The sea height anomaly data together with historical hydrographic data is used here to estimate the upper layer thickness. In a baroclinic ocean, each change in thermocline depth will be compensated by a change in sea level. Using a two layer model approximation, the upper layer thickness, hi , is (Goni et al, 1996):
344 h,(x,y,t)=h,(x,y)+ 1/e(x,y)[rl'(x,y,t)-B'(x,y)],
(3)
where h, is the mean upper layer thickness, and B' is the barotropic contribution to the sea height anomaly. This last parameter can be estimated, for example, when simultaneous observations of sea height anomaly and thermocline depth are available (Goni et al, 1996). In this study, B' is computed using the available XBT data in the region, and is estimated to have an amplitude of 2 cm. We present here a comparison between altimeter-derived and XBT-derived upper layer thickness estimates to show the reliability of this methodology to estimate the upper layer thickness and, hence, to identify, track and estimate properties of warm rings. Approximately 2,000 values of upper layer thickness derived from XBT data during 1993 through 2000 in the region of study were used. The XBT-derived values were extracted within 10 days of the altimeterderived dates. The rms difference between the XBT observations and the altimeter-derived estimates of the upper layer thickness for all the observations is approximately 15 m. This difference becomes smaller when only data for warm rings (excluding subsurface rings) is used. Upper layer thickness deviations due to the passage of a warm ring range from 0 to 50 meters, with the lower value of 0 m generally observed in the subsurface rings, in which case a colder isotherm (15oC or 10oC) better reflects the isotherm deviation caused by this type of ring (Garraffo et al, this volume). These values indicate that the sea height anomaly can provide a fairly reasonable estimate of the upper layer thickness. The XBT observations presented here also correspond to the data used to estimate the barotropic contribution to the sea height anomaly, B'.
Figure 7. (left) Climatologically-derived upper layer thickness, (right) climatologicallyderived reduced gravity.
345 5. R E S U L T S AND D I S C U S S I O N
5.1. Upper layer thickness fields Daily maps of sea height anomalies are constructed from the altimeter data covering a ten-day period centered at each day. These maps are interpolated into a regular 1/4- degree grid using a Gaussian interpolator with a radius of interpolation of 1/4 degree. The sea height anomaly maps are converted into upper layer thickness maps using (3). These maps are then used to identify and study the retroflection and the w a r m rings in the region. This methodology has been extensively validated in different regions such as the Brazil-Malvinas confluence (Goni et al, 1996), the Agulhas retroflection (Goni et al, 1997), the Gulf of Mexico (Shay et al, 2000), and the Kuroshio Extension (Sainz-Trapaga, et al, 2001). These maps show the North Brazil Current retroflection and w a r m rings in the region, distinguishable by their larger values of upper layer thickness than their surrounding waters. The close correspondence observed between the altimeter-derived and hydrographically-derived upper layer thickness maps is evidenced by the mean difference between them, approximately 5 m, with an rms difference of 15 m. Since the XBT provided observations at different times and locations than the closest altimeter observations, the errors estimated here represent an upper limit of what the actual errors actually are. Two examples that include six maps of sea height anomalies and upper-layer thickness each are presented here to how rings are detected and tracked. Blended data from the three altimeters were used (Figure 9), where w a r m rings
Figure 8. Schematics of the two-layer reduced gravity approximation, with an upper layer of mean density pl, thickness hi that extends to the depth of the 20~ isotherm and a lower layer with mean density p2. The ocean surface has a sea height anomaly ~.
346 are identified as closed contours in the upper layer thickness maps. Since the two-layer scheme provides better results where there is at least weak stratification, only the contours that correspond to depths characteristic of NBC rings are presented, some of which may lie within the region north of 15oN that is not of interest in this study. In the first example (Figure 9a), a ring is shed from the retroflection during the beginning of J a n u a r y 1999, with the retroflection represented by a region of larger upper layer thickness values. The trajectory of this ring closely follows the bathymetry contour and is no longer detected by altimetry by late February, where another ring has already been shed by the retroflection. This ring is also identified from current meter observations (ring #2 in Johns et al, this volume). The second ring reaches the southern portion of the Windward Island by mid April. In the second example (Figure 9b), a region with large positive sea height anomaly values is located at 50oW, 7oN, which corresponds to the shedding of a ring approximately during mid J a n u a r y 2000; when the retroflection reaches its northernmost location. The translation of this ring can be followed for four months until May 2000 when it finally reaches the Caribbean Sea. This ring has sea height anomalies of approximately 12 cm and upper layer thickness variations of 50 m, within the range of typical values for most rings identified in the region. This ring is also identified from current meter observations (ring #10 in Johns et al, this volume). A second feature to the south that appears in the mid February map belongs to the retroflection, which later sheds a ring, and becomes more noticeable during mid March. The ring from the second example and its trajectory has been already investigated using its ocean color signature (Fratantoni and Glickson, 2002, their ring K) and is further investigated in a later section and in other chapters (Johns et al and Garzoli et al, this volume). The centers of the rings, or trajectories, are placed at approximately the geometrical center of the closed contours with the best-resolved rings, a fairly good approximation given the uncertainties involved from using the altimeters' along track data. Maps derived from the methodology presented in the previous section and similar to those shown in Figure 9 are used to identify and track all the warm rings in the region between October 1992 and December 2001. Rings translate at different speed and change speed and shape while they translate, as evidenced in the example shown here. Although these changes can be observed to some degree with altimetry, the component of these changes due to actual variations versus uncertainties in the data and the interpolation of the irregularly distributed data remains to be investigated. The recently discovered subsurface rings have a very weak sea height signal, a characteristic also reproduced by numerical models (Garraffo et al, this volume), which makes them very difficult to even detect in altimetry. Several of these subsurface rings were probably not detected in our survey. A previous study (Goni and Johns, 2001) highlighted several rings that were detected during periods when the retroflection could not be identified from altimetry, and were named 'NBC eddies' to differentiate them from those shed when the NBC retroflection was positively identified. These eddies are mostly formed during
347 the spring months (Goni and Johns, 2000), which also corresponds to periods of time when the mean sea surface height has negative values south of the latitude of ring shedding (Figure 5, center panel). Observations (Garzoli et al, this volume) indicate that the retroflection in fact exists during the spring month and this eddies may therefore be a weak surface height expression of the retroflection translated into the methodology used here. These NBC eddies are hereafter included together with the NBC rings. In addition, 12 eddies were also observed traveling in the region, not coming from the NBC retroflection but generated in the shear zone between the NEC and the NECC. These types of eddies were previously reported (DS93) and, although shown in this work, will not be included in the ring analysis or statistics. The methodology used in this work identifies most of the warm rings, except for some catalogued as subsurface. The survey presented here mostly agrees with another study that identified the warm rings using color SeaWiFs data (Fratantoni and Glickson, 2002). The color signature of the warm rings is set by the high gradient of ocean color at their edge, which is given by the large concentration of nutrients rich Amazon River waters surrounding them.
5.2. Ring shedding A total of 52 rings were observed to shed between October 1992 and December 2001 (Figure 10, top). Previously, five additional rings had also been observed during a 2.5-year period, in which observations were available, between 1987 and 1989 (DS93). Due to differences in techniques and data availability the results of the previous two studies (DS93 and GJ01) may not be directly compared, but they are both included here for completeness. North Brazil Current rings were shed every year, from a minimum of three rings (years 1988 and 1995) to a maximum of seven rings (year 1996, 1997, 1998, and 2000). The mean number of rings shed is approximately 5 to 6 per year, with a marked year-to-year variability. Although NBC rings are shed at any time of the year, they seem to have a weak tendency to form during the first half of the year (Figure 10, bottom).
5.3. Ring trajectories Most of the 52 rings are first detected between 6 and 8oN, with trajectories in the NW direction. Figure 11 shows a map with the trajectories of all the rings identified between November 1992 and December 2001. In general, these rings have their trajectories, denoted by the location of their centers, over regions deeper than 3000 m. Once the rings reach 58oW they usually turn suddenly to the North passing east of Barbados. Although this is the most common trajectory of the rings, only one out of the seven rings formed in 1996 actually followed this trajectory. Topography has already been shown to be a very important factor in the translation of warm rings, as in the case of the Agulhas rings, which have been
348
Figure 9. (a) Sea height anomalies (upper panels) and upper layer thickness panels) fields derived from blended altimeter data from (left) January 1999 until April 1999 (b) Sea height anomalies (upper panels) and upper layer thickness panels) fields derived from blended altimeter data from (left) January 2000 until April 2000. The 500 m isobath is superimposed to the maps.
(lower (right) (lower (right)
349 shown to travel trajectories highly dominated by topography, particularly by the Walvis Ridge (Byrne et al, 1995; Goni et al, 1997; Schouten et al, 2000). The topography is included in the figure of the ring trajectories to help visualize the effect of the bathymetry on the ring trajectories. DS93 found that the trajectory of several rings follow the shape of the continental shelf, the 500 m contour of the bottom topography. This result was later confirmed by GJ01 where it was shown that the center of the rings approximately follow the 3000 m isobath, suggesting that most NBC rings may have vertical density signatures that go deeper than the 20oC isotherm used in this work. Almost none of the 52 rings identified in this study was observed to travel in waters shallower than 2000 m before interacting with the topography of the Lesser Antilles. The time the rings remained in the region of study ranges from two to five months, with most of the rings (27) remaining in the region for an average 3.5 months. Rings that cross into the Caribbean Sea were observed to have larger mean translation speed than the rest of the rings. Of special interest are the rings that interact strongly with the islands of the Eastern Caribbean, particularly Barbados, since the properties carried by their waters greatly affect the environment surrounding the island, (Kelly et al, 2000; and Cowen et al, this volume). The discharge of Amazon River waters into the Atlantic Ocean peaks during the months of May and June, and the rings take approximately two to three months to travel from the retroflection to Barbados.
Figure 10. (top) Number of rings shed per year derived using GEOSAT (DS93) and blended altimeter (this study) data (GJ). The white bars indicate partial results because of altimeter data were not available during all the year. The (smoothed) northern tropical Atlantic index is superimposed. (bottom) Number of rings shed every month as observed from altimeter data since November 1992.
350
Figure 11. (left) Altimeter-derived ring trajectories from 1992 through 2001. The yellow trajectory corresponds to the ring of Figure 9b, the trajectories in purple to the eddies identified in this study. (right) Detail of altimeter-derived ring trajectories in the vicinity of the island of Barbados. The trajectory in yellow is the same as of the map on the left, while the ones in green and red correspond to the two rings studied in the chapter by Cowen et al. T h e bathymetry is included, with contours every 1000 m. Therefore, it would be expected that rings traveling in the region of Barbados between May and September would have a larger impact in the environment of the region. This study indicates that the center of most NBC rings travel within 100 km to Barbados (Figure 11, right map). Seven rings clearly cross through the Windward Islands into the Caribbean Sea through waters shallower than 2000 m, a depth where rings are usually not found east of the Windward Islands. Once these rings cross into the Caribbean Sea, they disintegrate or their surface signal become too small to be identified with the methodology used in this study. More information on rings that enter into the Caribbean Sea and investigated using a numerical model can be found in the chapter by Garraffo et al. Our results indicate that none of the eddies originated in the shear zone between the NECC and NEC enter in the Caribbean Sea.
5.4. Ring parameters The translation speed of a ring is a combination of the propagation speed of the ring and the background flow speed. The mean translation speed of the rings as obtained from the upper layer thickness maps range from 9 to 30 cm/s (7.5 to 24 kin/day), with a standard deviation of 6 cm/s, which falls within the ranges of previous altimeter estimates of 15 cm/s (DS93), and 14 cm/s (Goni and Johns, 2001). The investigation of the number of rings and their seasonal variability represent only one aspect in the study of the transfer of south Atlantic waters into the northern hemisphere. A detailed analysis of the vertical structure of these rings is also desirable. The length scale of the rings, L, are estimated here using the alongtrack sea height anomalies following the methodology used by
351 Goni et al (1997) to investigate Agulhas rings. profiles are assumed to have a Gaussian shape: h 1(r) - h.. = hoe-~'-'~a
As an approximation, these
(4)
where r is the alongtrack distance measured from the center of the ring, h l is the alongtrack upper layer thickness, ho is the maximum alongtrack upper layer thickness depth measured from the depth of the 20oC of the surrounding waters, h~, and L is the length scale. Because only two ascending T/P groundtracks, t301 and t304, are used to compute L, these estimates correspond to a region just west of the retroflection and close in time and space to when the rings were shed. This methodology assumes that the rings are crossed by either altimeter groundtracks through their centers. Therefore, the values obtained here may be underestimated. The parameter h~ is computed from the upper layer thickness profiles north of the rings, where altimeter estimates are less likely to have errors related to shallow water effects, such as tides. An example is presented here with a fit along the groundtrack t304 of the altimeter-derived upper layer thickness during February 10, 2000 (Figure 9b), giving values of L--ll0 km, ho=3Om, and h ~ 1 2 0 m (Figure 12). These values can change as the ring translates. The mean value for the 52 rings identified by altimetry is 100 km with a standard deviation of 27 kin. DS93 estimated the radius of the NBC rings using SHA data and defining this parameter as the distance from the ring center to the location of half the maximum SHA. The mean value of L parameter for the 5 surveyed rings by DS93 using this methodology is 127 kin. The length scale, L, investigated here is similar to the one presented in the chapter by Garraffo et al, that corresponds to the distance of the center of the ring to the radius of maximum velocity. Given that these rings may also have a barotropic or a deeper baroclinic component, which cause the dynamic properties to be translated into deeper waters, a water mass analysis is probably one of the best techniques to better estimate the amount of South Atlantic waters carried by each ring (Johns et al, this volume). The volume anomaly of a ring is defined here as the excess of water (referenced to the surrounding waters) warmer than 20oC that the NBC rings carry. For rings with a Gaussian section shape (4), the volume anomaly is that of a cylinder of radius L and depth ho (Goni et al, 1997). The volume anomaly for the ring presented in Figures 9 and 12 is approximately 4.5x1012m 3. The mean volume anomaly of all the rings surveyed in this study is 3x1012 m 3. It is critical to understand that the volume estimates does not reflect the actual volume of South Atlantic waters carried by the rings, but rather the excess of water mass warmer than 20oC. An investigation on the ratio between the total water mass and south Atlantic water mass in rings based on both observations and model results is presented in a different chapter (Johns et al and Garraffo et al, this volume).
352
E 100 r "
ho~
,,
a 15o 5
10
Latitude
15
(~N)
Figure 12. Upper layer thickness section corresponding to the ring of Figure 9b along t304 during mid March 2000. The crosses represent the altimeter-derived upper layer thickness values, while the solid line is the Gaussian fit (4) to these estimates.
5.5 Interannual variability The cause of the interannual variability in ring formation is unknown but may be linked to other larger-scale transport processes in the basin. Largerscale aspects of the variability in the tropical western Atlantic Ocean has been investigated from the upper ocean temperature and altimeter observations. Sea surface temperature variability has been shown to have a seasonal signal caused by surface heat fluxes and an interannual signal believed to be caused by an ocean-atmospheric positive feedback through the long wave radiation (Wang and Enfield, 2001). These warm and cold events in the Atlantic Ocean have been correlated to the intensification and weakening of the surface currents in the equatorial region, including the SEC, through the changes in the wind fields in the tropical Atlantic (Goes and Wainer, 2002). The transport of the SEC has been shown to be larger during warming periods and lower during cooling periods. The mass transport of the SEC will clearly affect the variability of the NBC, whose transport has already been linked to the shedding of NBC rings (Garzoli et al, this volume). Therefore, it is speculated here that at least a weak relationship exist between the warm and cold events and the generation of rings. We use here the northern tropical Atlantic index (Figure 10, Servain, personal communication) to investigate possible links between warm and cool periods with the shedding of rings. This thermal index is obtained by the monthly standardized anomalies referenced to temperature values from 1964 until 2001 in a region of the north Atlantic bounded by 60oW-15oE, 5oN-30oN. The time series of this index shows very distinctive time periods, with amplitudes of up to 4oC. Of particular interest for this study are the warming events during 1985 through mid 1987 and during 1995 through 1999, and the cooling periods from 1988 through 1995.
353
Figure 13. Time series of the northern tropical Atlantic index, given by the anomalies of the sea surface temperature anomalies. The time periods corresponding to the works of Didden and Schott (1993, DS93), Goni and Johns (2002, GJ02), North Brazil Current Experiment (NBCE), Fratantoni and Glickson (FG, 2002), and this study (GJ03) are indicated in the figure. These cooling and warming periods can also be observed in the space-time diagrams of sea height anomalies and residues (Figure 5) as reflected by the alternation of the extreme low and high values of these parameters. Although the altimeter signal represents an integration of the dynamic and thermal effects in the water column while the thermal index is only representative of the surface conditions, their variability are qualitatively similar. The earlier study of ring shedding (DS93) that used a shorter time series identified a smaller number of rings, only 3 rings during 1988, which corresponds to the end of a cooling period (Figure 13). Although the time series presented in this work is rather short, extending only a nine-year period (plus two of DS93), a longer time series is needed to make more definite statement to confirm this result. The shedding of rings in other regions has also been shown to be intermittent and dependent of surface current variability. For example, Agulhas rings have been closely linked to the variation of the Agulhas Current (Goni et al, 1997) and to the Natal Pulses (DeRuijter et al, 2001), creating long periods of time (8 months during 1993) when no ring was shed at all. Results presented here will be used to validate those from numerical modeling. The long time series already being obtained using remote sensing data, hydrographic observations and models will aid in providing a clearer understanding of the role of the NBC rings in the Meridional Overturning Circulation, and on regional variability of climate patterns. As longer time series, new process studies and methodologies are incorporated there will be a more clear understanding of the mechanisms by which the NBC rings are generated and their impact in regional ocean dynamics.
354 6. SUMMARY Ten years of altimeter data were used to investigate the temporal variability of the ring shedding in the North Brazil Current retroflection region. The ring trajectories are identified from upper layer thickness maps. Results presented here indicate a shedding rate of 3 to 7 rings per year with no marked seasonal variability but with very strong year-to-year variability. Additionally, eddies not shed by the retroflection are identified in this region as well. Most of the rings pass very near of Barbados of which seven rings during the study period are seen to enter into the Caribbean Sea. A link is found in this study between longterm surface temperature changes in the tropical Atlantic and the number of rings shed at the NBC retroflection, where periods of time with warmer surface temperatures are associated to a higher number of rings shed.
Acknowledgements This work was partly funded by NOAA/AOML and by NSF. Robert Cheney (NOAA/NESDIS) provided the alongtrack T/P altimetry data. The blended altimeter data was obtained from the Navoceano web site. The northern tropical Atlantic index was provided by Jacques Servain. The authors acknowledge the comments provided by Silvia L. Garzoli during the writing of this manuscript. The authors also want to thank the two reviewers of this manuscript for their very helpful comments.
REFERENCES Arnault, S. and R.E. Cheney, Tropical Atlantic sea level variability from Geosat (1985--1989), J. Geophys. Res., 99, 18207-18223, 1994. Byrne, D.A., A.L Gordon and W.F. Haxby. Agulhas eddies, A Synoptic view using Geosat ERM Data, J. Phys. Oceanogr, 25, 902-917, 1995. Conkright, M. E., S. Levitus, T. O'Brien, T. P. Boyer, C. Stephens, D. Johnson, L. Stathoplos, O.Baranova, J. Antonov, R. Gelfeld, J. Burney, J. Rochester and C. Forgy. World Ocean Database 1998, Nat. Oceanogr. Data Center Internal Rep., 14, pp. 113, 1998. DeRuijter W. PO. M., H. Ridderinkhof, J. R. E. Lutjeharms, M.W. Schouten, and C. Veth. Observations of flow in the Mozambique Channel, Geophys. Res. Let.,YYY, 2002. Didden, N. and F. Schott. Eddies in the North Brazil Current retroflection region observed by GEOSAT altimetry, J. Geophys., Res., 98, 20121-20131, 1993. Fratantoni, D. M, W. E. Johns and T. L. Townsend. Rings of the North Brazil Current: Their structure and behavior inferred from observations and numerical simulations, J. Geophys., Res., 100, 10633-10654, 1995.
355 Fratantoni, D. M. and D. A. Glickson. North Brazil Current Ring Generation and Evolution Observed with SeaWiFs, J. Phys. Oceanogr., 32, 1058-1074, 2002. Goes M. and I. C. Wainer. Equatorial currents transport changes for extreme warm and cold events in the Atlantic Ocean, Geophys. Res. Let., (in press), 2002 Goni, G. J. and W. E. Johns. A Census of North Brazil Current Rings observed from TOPEX/Poseidon Altimetry: 1992-1998, J. Geophys. Res., 28, 1-4, 2001. Goni, G. J., S. L. Garzoli, A. J. Roubicek, D. B. Olson and O. B. Brown. Agulhas Ring Dinamics from TOPEX/Poseidon Satellite Altimeter Data, J. Mar. Res., 55, 861-883, 1997. Goni, G.J., S. Kamholz, S.L. Garzoli, and D.B. Olson. Dynamics of the Brazil/Malvinas Confluence based on inverted echo sounders and altimetry. J. Geophys. Res., 101, 16,273-16,289 1996. Johns, W. E., T. N. Lee, F. A. Schott, R. J. Zantopp and R. H. Evans. The North Brazil Current retroflection: Seasonal structure and eddy variability, J. Geophys. Res., 95, 22103-22120, 1990. Johns, W. E., T. N. Lee, R. C. Beardsley, J. candela, R. Limeburner and B. Castro. Annual Cycle and Variability of the North Brazil Current, J. Phys. Oceanogr., 28, 103-128, 1998. Kelly, P. S., K. M. M. Lwiza, R. K. Cowen and G. J. Goni. Low-salinity pools at Barbados, West Indies: Their origin, frequency and variability, J. Geophys. Res., 105, 19699-19708, 2000. Mayer, D. A., R. L. Molinari, M. O. Baringer, and G. J. Goni, Transition regions and their role in the relationship between sea surface height and subsurface temperature structure in the Atlantic Ocean, Geophys. Res. Lett., 28, 39433946, 2001. Mayer, D. A., and R. H. Weisberg, A description of COADS surface meteorological fields and the implied Sverdrup transports for the Atlantic Ocean from 30 ~ S to 60 ~N, J. Phys. Oceanogr., 23, 2201-2221, 1993. Molinari, R. L., and E. Johns. Upper layer temperature structure of the western tropical Atlantic, J. Geophys. Res., 99, 18225-18233, 1994. Reverdin, G., P. Del6cluse, C. L6vy, P. Andrich, A. Morli~re, and J.M. Verstraete, The near surface tropical Atlantic in 1982-1984. Results from a numerical simulation and a data analysis, Prog. Oceanogr., 27, 273-340, 1991. Sainz-Trapaga, S.M., G. J. Goni, and T. Sugimoto. Identification of the Kuroshio Extension, its bifurcation and northern branch from altimetry and hydrographic data during October 1992-August 1999: Spatial and temporal variability. Geophys. Res. Let., 28, 1759-1762 2001 Schott, F.A., J. Fischer and L. Stramma, 1998. Transports and pathways of the upper-layer circulation in the western tropical Atlantic, J. Phys. Oceanogr., 28, 1904-1928 Schouten,M. W., W.P.M. de Ruijter and P.J. van Leeuwen, J. Geophys. Res., 105, 21,913-21,925, 2000.
356 Shay, L.K., G. J. Goni and P. G. Black: Effects of Warm Oceanic Features on Hurricane Opal, Month. Weath. Rev., 128, 131-148, 2000. Wang, C. and D. B. Enfield. The tropical Western Hemispheric Warm Pool, Geopys. Res. Let., 28, 8, 1635, 1638, 2001. Wilson, D.W., W.E. Johns, and S.L. Garzoli. Velocity structure of North Brazil Current rings. Geophys. Res. Let., 29, 101029/2001GL013869, 2002
lnterhemispheric Water Exchange in the Atlantic Ocean edited by G.J. Goni and P. Malanotte-Rizzoli 9 2003 Elsevier B.V. All rights reserved.
North Brazil Current rings and the variability in the latitude of retroflection Silvia L. Garzoli ~1, Amy Ffield b, and Qi Yao c aNational Oceanic and Atmospheric Administration, Atlantic Oceanographic and Meteorological Laboratory, 4301 Rickenbacker Causeway, Miami, Florida 33149, USA bLamont-Doherty Earth Observatory of Columbia University, Palisades, New York 10964, USA cUniversity of Miami, Cooperative Institute for Marine and Atmospheric Studies, Miami, Florida 33149, USA An array of 14 inverted echo sounders (IES) were deployed as part of the North Brazil Current Rings (NBCR) experiment, to study the dynamics of the ocean in the region. Synoptic maps of dynamic height were produced from the data collected with the IES. After validating these maps with hydrographic data collected during the four NBCR cruises, they were analyzed to determine the variability of the latitude of retroflection of the North Brazil Current (NBC) and the number of rings shed during this process. Results from this analysis indicate that there is no obvious seasonality in the variability of the latitude of penetration of the NBC and, with the exception of one event, each time that the NBC reaches its northward position a ring is shed at the retroflection. A total of 11 rings were shed during the period of the observations November 1998 to June 2000. The mean diameter of the rings was estimated to be approximately 390 km, and the mean speed of propagation 12.4 km/day. The rings transported an average of 8Sv (1Sv = 106 m3s -1) of water and 0.54 PW of heat per year. These estimates are much larger than previous results, both in the number of rings shed per year and in the contribution of the rings to the inter-hemispheric exchange of mass and heat. 1.
INTRODUCTION
In the Atlantic Ocean, the cold, deep, southward export of 15 + 2 Sv net production of far northern hemisphere waters must be balanced by a I Corresponding author. Te1.:305-361-4338. Fax: 305-361-4392. Email address:
[email protected] 358 compensating warm, shallow, northward flow of southern hemisphere waters (Ganachaud and Wunsch, 2000; 1 Sv = 1 x 106 m3s ~ as part of the global meridional overturning circulation (MOC). In the equatorial region, the North Brazil Current (NBC) is thought to be the only substantial pathway that can complete the upper limb of the interhemispheric loop by moving warm, shallow waters of South Atlantic origin across the equatorial region to the North Atlantic. From its origin near the easternmost protrusion of the South American continent (5~ 35~ the NBC flows northwest off the Brazilian coast continually increasing its transport with input of South Equatorial Current (SEC) waters while becoming more surface intensified (Stramma and Schott, 1996). After crossing the equator, a component of the NBC retroflects eastward into the Equatorial Undercurrent (EUC), and then recirculates within the equatorial region. The remainder of the NBC continues northwestward until approximately 7~ 48~ At this point, there is both a direct and an indirect NBC route to the north Atlantic: 1) directly, by flowing northwestward along the coast to the Caribbean; or 2) indirectly, with substantial potential for recirculation, by flowing eastward with the North Equatorial Countercurrent (NECC), then westward with the North Equatorial Current (NEC), and then finally entering the Caribbean at a more northern latitude than the direct route (Stramma and Schott, 1996; Stramma and Schott, 1999). Historically the direct route of the NBC to the North Atlantic was named the Guyana Current. This current was interpreted as an extension of the SEC and defined as a broad northwestward flow from the vicinity of the Amazon River mouth to the Caribbean (Metcalf, 1968). However, with more varied types of measurements, as well as higher spatial and temporal resolution of these observations, the fundamental description of the NBC flow has been greatly modified and enhanced. Guided by the more recent observations, the "Guyana Current" has generally been reclassified as a series of anticyclonic rings translating westward after detaching from the eastward retroflecting NBC as it joins the NECC. Theory supports the presence of these rings, as it is shown that the momentum flux of the approaching and retroflecting NBC can only be balanced by anticyclonic rings forming, shedding, and drifting to the west (Nor, 1996; Nor and Pichevin, 1996). In previous studies (i.e. Didden and Schott, 1993, Richardson et al., 1994, Fratantoni et al 1995) the presence of these rings has been documented. Recently, Goni and Johns (2001) detected the presence of 5.3 rings per year accounting for approximately 1Sv each, or -5.3 Sv/year from altimeter derived sea height anomaly data. Fratantoni and Glickson (2001) observed 6 rings per year (-6 Sv/year) from ocean color derived chlorophyll gradients which are correlated with sudden and large southeastward retractions of the NBC retroflection. Nonetheless, observations still suggest the existence of a component of the NBC flow to the Caribbean by way of a more-or-less steady coastal current. In order to study the precise mechanisms which contribute to NBC ring formation, the structure and dynamics of the rings themselves, and the role that they play in the inter-ocean exchange of heat and salt, a multiinstitutional program, the North Brazil Current Rings Experiment (NBCR), was
359 conducted Fratantoni et al., 1999). The extensive NBCR field program started in November 1998 and ended in J u n e 2000. In what follows, a subset of the data collected during the NBCR Experiment is analyzed to quantify the contribution of the rings to the transfer of southern hemisphere waters to the northern hemisphere. These time series are unique, in that they are the only in situ measurements of the program that integrate the full depth signal of the rings. The relationship of the migration of the NBC retroflection to ring generation will also be investigated in order to characterize the dynamics of the ring shedding. During the NBCR Experiment an array of 14 inverted echo sounders (IES) were deployed and recovered in the region of NBC retroflection and ring formation region (Figure 1, Table 1), to provide a three dimensional (time/space) field of the dynamic height with which the NBC variability and the related eddy field could be studied. In particular, the array was designed 1) to monitor the displacement of the front associated with the retroflection of the NBC (IES 2, 6, 10, 12, and 16); 2) to monitor the passage of rings and study the process of eddy formation and propagation (IES 1 to 13); and 3) to provide an estimate of the strength of the NBC transport (IES 14 to 17), and determine its relation to the number of rings shed. Herein, data collected with the array of IES will be analyzed to study the variability of the latitude of penetration of the NBC, and the number of rings shed at the retroflection.
Figure 1. Map of the study region and location of the inverted echo sounder (IES) deployments (o).~" indicates the location of the pressure gauge deployed by W. E. Johns (RSMAS/UM). The insert is a schematic of IES deployed on the ocean bottom.
360 Table 1. Location, depth and deployment history of the moored instruments.
PG 1 2 3 5 6 7 8 9 10 12 13 14 16 17
Latitude (~ 01~ 10 ~ 54.612 09 ~ 44.572 8~ 09 ~ 45.764 07 ~ 47.947 5 ~ 56.99 09 ~ 09.014 07 ~ 35.589 06 ~ 27.699 05 ~ 29.900 7 ~ 47.05 06 ~ 46.009 04 ~ 24.890 03 ~ 04.703
Longitude Depth (~ (m) 47 ~ 38.223 68 52 ~ 04.802 4137 53 ~ 46.802 4570 54 ~ 02.461 1115 51 ~ 29.081 4843 51 ~ 09.229 4395 51 ~ 00.08 2700 49 ~ 48.530 4653 49 ~ 10.831 4288 49 ~ 42.522 3858 48 ~ 19.210 3442 52 ~ 34.026 2012 45 ~ 44.603 4200 46 ~ 39.185 3273 47 ~ 09.045 1802
Date of deploymer 5-Mar-99 12-Nov-98 13-Nov-98 14-Nov-98 16-Nov-98 17-Nov-98 24-Feb-99 17-Nov-98 18-Nov-98 18-Nov-98 21-Nov-98 25-Feb-99 22-Nov-98 23-Nov-98 23-Nov-98
Date of recovery 9-Jun-00 19-Jun-00 19-Jun-00 18-Jun-00 16-Jun-00 14-Jun-00 13-Jun-00 16-Jun-00 12-Jun-00 12-Jun-00 ll-Jun-00 14-Jun-00 10-Jun-00 10-Jun-00 09-Jun-00
2. M E T H O D O L O G Y Inverted echo sounders (IES) m e a s u r e the r o u n d trip travel time of an acoustic pulse from the sea floor to the surface a n d back. By defmition, travel time, TT, is a function of the sound velocity, c," T r = ~dz / c (T, S, P)
(2.1)
where c is a direct function of the t e m p e r a t u r e (T), salinity (S) and p r e s s u r e (P). Travel time m e a s u r e m e n t s can be empirically correlated to a n u m b e r of different integrated or discrete oceanic p a r a m e t e r s such as thermocline d e p t h or dynamic height. Correlations v a r y over different regions due to the circumstances of local stratification or how T a n d S co-vary in the region. IES m e a s u r e m e n t s have been used successfully in several regions, for example to study the Gulf S t r e a m dynamic h e i g h t variability (Watts and Rossby, 1977), to study the t r a n s p o r t s and f r o n t a l motions at the Brazil-Malvinas Confluence (Garzoli and Garraffo, 1989; Garzoli, 1993) and the Benguela C u r r e n t (Garzoli et al., 1995) a n d to e x a m i n e the generation and propagation of rings in the South E a s t e r n Atlantic (Garzoli and Gordon, 1996; Duncombe-Rae et al., 1996; Goni et al., 1997). IES m e a s u r e m e n t s
361 have also been used in the equatorial Atlantic to study the North Equatorial Counter Current (Garzoli and Richardson, 1989), and in the Pacific to study the ENSO cycle in the Central Equatorial Pacific (Wimbush et al., 1990, Miller et al., 1985). Dynamic height time series derived from IES have also been used in comparison with altimeter data to study ring propagation and transports (see Garzoli and Goni, 2000, for a review). For the purpose of this paper, IES acoustic travel time series were scaled to dynamic height. Using all 220 CTD stations collected during the four NBCR Experiment cruises the relationship between travel time and dynamic height was obtained as follows. Travel time and dynamic height were estimated from T, S and P for each CTD station at different depths and reference levels, and correlations between the two parameters were computed. Results of the analysis indicated that the correlations were different in the area of ring formation (west of 50~ than in the area of the retroflection (east of 50~ probably due to different vertical stratifications. A very good agreement was observed between travel time and the dynamic height at the surface referenced to 300 m. This depth was therefore adopted as the reference level, and it also contains the core of the NBC flow def'med as above the 26.8 isopycnal (e.g. Bourles et al., 1999). Results of the correlation analysis are given in Figures 2a and 2b. The following relations were used to obtain changes in dynamic height from changes in travel time: West of 50~ (rings area): A DH = -0.054 ATT • 0.0367 dyn m East of 50~ (retroflection area) A DH = -0.061 ATT • 0.0270 dyn m
R2 = 0.70 R 2 = 0.89
Where ADH and ATT are relative changes in dynamic height and travel time between two consecutive times respectively. From these relations, time series of relative dynamic height were calculated at the 14 IES locations. In order to obtain absolute values of the dynamic height, hydrographic data collected at the deployment sites during the NBCR cruises for the purpose of calibration were used. Dynamic heights at the surface referenced to 300 m were calculated at each CTD station and used to add a constant to the dynamic height anomaly specific to each site to best fit the observations. Trends observed in the time series were not altered, as they are believed to be a real part of the signal. The 14 time series of dynamic height at the surface referenced to 300 m obtained by this method are given in Figure 3. The difference in the length of the records is due to technical difficulties during the deployment cruise. The IES sites are numbered 1 to 17. IES instruments were not deployed at site 4, 11 and 15 due to malfunction at the time of deployment. IES 7 and 13 were deployed after the instruments were repaired during the second cruise. The series have been passed through a 40-hour lowpass filter to eliminate all frequencies higher than about 0.5 days -1. The longer time series started in November 1998 and ended in June 2000, and the shorter series started in February 1999 and also ended in June 2000. In Figure 3,
362 circles indicate the dynamic height calculated from the CTD stations. These values are shown for the purpose of comparison and to indicate the agreement in dynamic height between the time series obtained with the IES and the CTD data. In addition to the 14 IES, W. E. Johns (RSMAS/UM) deployed a pressure gauge (PG) during the second cruise. The decision to make this deployment was made after the first cruise when it became evident that a large amount of water was flowing north to the west of IES 17. The PG data were made available for this study. A PG measures the total pressure of the overlying water column. At the very shallow 68 m location on the continental shelf, the water column can be assumed to be homogeneous in density, and therefore the PG effectively monitored all the pressure changes at its location. On the other hand, by measuring the integrated temperature of the water column, the IES estimate only the pressure variations within the water column (baroclinic). At these deep locations (all greater than 1000 m), any full-depth barotropic flows are most likely quite small relative to the 20 to 100 cm s -1 NBC near-surface currents. Therefore, both the PG and the IES are assumed to measure the total variability of the flow. A time series of dynamic height was obtained from the pressure record as follows. First the pressure variability (AP = P - P, ]~ = mean pressure) was transformed into dynamic height variability by using the relation between dynamic height (DH) and pressure (P) (ADH = AP / p) when p is the water density. To obtain an absolute value for dynamic height the same method as for the IES was used, except that in this case the CTD cast only reached a depth of 60 m. Data were extrapolated to 300 m using a historic T, S profile from Levitus et al., 1994, located closest to the site at 300 m depth. This method may add an unknown error to the dynamic height series obtained from the PG. Nevertheless, given the location of the PG, the data serve to enhances the maps without affecting array of the key results. The time series of dynamic height obtained with this procedure is also shown in Figure 3. The three near coastal sites (IES 3 and 7 and PG) show more variability at high frequencies than the other time series.
3. D Y N A M I C H E I G H T F I E L D
From the dynamic height time series, synoptic maps were produced every 3 days using an interpolation routine with a weighting factor, WF (i, j, k), for k dynamic height data values at each grid point (i, j), (Figures 4c and f, 5c and f). The WF used is 1 / R where R is the distance between the grid points and the observed values. Two different series of maps were created: one with 12 time series from November 27, 1998 through J u n e 1, 2000, and a second one with 15 time series from February 25, 1999 through J u n e 1, 2000. From the dynamic height time series, it is possible to calculate the geostrophic velocity. The geostrophic velocity between two stations is given by: from February 25, 1999 through J u n e 1, 2000.
363
~~
J
~3~0.
i oo ~o~ <e:~~
n
~
oo
o
~
: 117
2:o.7 .. 0 . 0 3 7
o
~
o
go 0
_
i
_
-8
-7
~g
~. o.~. ~0.,
-6
v
-5
-4
-3
n
20 v~ ~ ~ _
=
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102
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oo
~176 ~
~0.( o .
-I
o ,
,
-8
-
-
~
-7
,
-6
,
i
-5
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Time
..
-4
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-3
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-I
Figure 2. Results of the correlation analysis between dynamic height at the surface (referenced to 300 m) and travel time. Both variables are obtained from CTD cast collected during the NBCR cruises, a) for the region west at 50~ (rings area) and b) for the region east of 50~ (retroflection area).
Figure 3. Time series of the dynamic height at the surface referenced to 300 m, obtained from data collected from the 14 IES and the PG deployed as part of the NBCR experiment. The circles indicate the value of dynamics high obtained with the CTD data.
354
Figure 4. Left panel: Velocity field collected with the hull-mounted ADCP during the first NBCR cruise: (a) at 20 m and (b) integrated velocity from 20 to 250 m. Data is from November 12 to December 10, 1998. Data is compared (c) to the objective map of the dynamic height from the IES array for December 9, 1998. Right panel: Same as Figure 4 (a, b) but for the second NBCR cruise from February 15 to March 6, 1999. Data is compared to (f) the objective map dynamic height field obtained from the IES array for February 28, 1999. Black arrows are geostrophic velocities between station pairs, in m sec -1. The thicker, red lines and arrows highlight the ring and NBC structures revealed by the dynamic height field.
365 From the dynamic height time series, it is possible to calculate the geostrophic velocity. The geostrophic velocity between two stations is given by: Vg = (l/f) (SDH/Ax)
(3.1)
where g is gravity, f the Coriolis parameter, and 8DH the difference of dynamic height between two stations separated by a distance Ax. Assuming no error in the distance between stations, the error incurred by equation (2) is then due solely to errors in dynamic height. The error in the estimate of dynamic height is ~q3.0033 dyn m west of 50~ and + 0.0022 dyn m east of 50~ Therefore, the errors in the geostrophic velocity are on the order of + 3 to • 5 cm]sec. The black arrows superimposed on the dynamic height contours (Figures 4c and 4f, and 5c and 5f) indicate the magnitude of the geostrophic velocities calculated between station pairs using relation (2). The dynamic height maps display structures that can be associated with rings and with the location of the retroflection. To provide a quantitative validation of our results, comparisons will be shown between dynamic height maps and velocities obtained from the hull-mounted Acoustic Doppler Current Profiler (ADCP) data collected during the four NBCR cruises. During the cruises, intensive hydrographic surveys were also performed in four rings (Wilson et al., 2002). Results from these surveys will also be compared with the IES synoptic dynamic height maps. The first cruise, NBCR1 took place from November 7 to December 11, 1998. Figure 4 (left panels) compares the ADCP velocities at 20 m (Figure 4a) and the integrated velocities from 20 to 250 m (Figure 4b) from this cruise with the surface dynamic height referenced to 300 m (Figure 4c), measured on December 9, 1998. The dynamic height field shows that the retroflection reaches 53~ in agreement with the ADCP survey. During NBCR1 a ring was surveyed (Ring 1, Wilson et al., 2002, WEAR1 from now on). WEAR1 was a subsurface ring, with a weak surface signal. The dynamic height map shows a rotational structure west of 54~ that is the expression of WEAR1. The second cruise, NBCR2, took place during February 1999. The top right side panels of Figure 4 (d and e), shows the surface velocity and the integrated velocities from the ADCP data collected along the track. The lower panel (Figure 4f) shows a map of dynamic height created from the IES data for February 28, 1999. The retroflection can be observed reaching 51~ and a ring appears to have shed farther north, west of 53~ The ring observed from the dynamic height field is the same one surveyed during the cruise (WEAR3). WEAR2 was outside of the IES domain, but was observed when it was formed in December 1998. During the third cruise, NBCR 3, J a n u a r y 30 to February 7, 2000, no ring was observed or surveyed. The velocity field shows a series of rotations that are the expression of meandering of the NBC (Figure 5a and b) both for the surface and the integrated value. A ring was starting to form but was not cut off from the main NBC during the time of the cruise. The same situation is observed in the surface dynamic height map for February 5, 2000 (Figure 5c).
366 A final comparison is made between the data collected during the fourth cruise, NBCR 4, June 7 to June 19, 2000, and the surface dynamic height map for June 1, 2000 (Figure 5, right panels). The dynamic height map is for a date six days earlier than the cruise, but it is the latest one available after filtering and truncating the files to the same length. The dynamic height shows the NBC retroflection between 47 ~ and 48~ and a ring farther north (Figure 5f). The location of this ring is southeast of the location of the ring surveyed during NBCR 4 (WEAR4). This difference is due to the time lag. The position of the ring during the cruise (12 days later) is consistent w i t h the location it had on June 1 and a propagation speed of 14 km/day. A second ring is also observed towards the northwest in the dynamic height field. Although the presence of this ring was noted during the recovery cruise, it was not surveyed due to lack of time.
4. LATITUDE OF P E N E T R A T I O N AND N U M B E R OF R I N G S S H E D A careful subjective analysis of all the dynamic height maps was conducted to determine the latitude of the northward penetration of the NBC retroflection and to determine the number of rings shed. The latitude of penetration was measured as the distance between the northernmost point of the retroflection and an arbitrary set of geographical coordinates (0~ 42~ to allow the description of motions occurring at the same latitude. Thus, during the northward motion, the distance between 0~ 42~ and the northern extension of the NBC is measured. Once the flow closes upon itself and a ring is shed, the location of the new position of the NBC, to the southeast of the new ring formed, is measured. Therefore, the northward motion can be considered as the motion of the northward penetration, which according to the record has a mean speed of 30 km day -1. During the southward motion, it represents more of a resetting of the index than a continuous motion. As the ring separates, the retroflection rapidly reforms further south. A ring (of approximately 300 to 400 km in diameter) is located between the previous northward location and the new one. As a result, southward motion cannot be inferred from the figure. Figure 6. shows the result of this analysis. The maximum northward penetration of the NBC and its retroflection varies from 600 km to 1900 km from the 0~ 42~ reference location. In all cases but one (August 1999), after the retroflection reaches its northward extension a ring is shed. During the 18-month period covered by the coincident time series, November 27, 1998 to June 1 2000, 11 rings were shed from the retroflection. Rings are shed at one to four month intervals, with no obvious periodicity observed. Nevertheless, there is a difference in the number of rings shed during the two overlapping periods of observation (December 1998 through May 1999; December 1999 through May 2000), with fire shed in 1998/1999 and three in 1999/2000. This may be an indication of interannual variability.
367 5. R I N G S V O L U M E AND T E M P E R A T U R E T R A N S P O R T A simple calculation can be performed to determine the volume and temperature transport of these rings (e.g. Duncombe Rae et al., 1996; Garzoli et al., 1999). Rings are assumed to have a Gaussian shape in the horizontal and to carry a volume, V = 2 l'I L2 h0, where L is the radius of maximum velocity, assumed to be half of the radius, and h0 = h - h~ (h is the depth of the ring signature and h~ is the depth of the thermocline in a region outside of the ring's influence). If we assume that all of the South Atlantic water carried by the NBC rings at the retroflection is compensated by cold, deep North Atlantic water, then each ring will transport heat in the amount of approximately Q = p C, V AT, with AT = 15~ the difference between the mean temperature of the two water masses and Cp the specific heat of sea water. Using these formulas, the volume and heat transported by each of the rings was calculated. The approximate diameter for the rings was obtained from the dynamic height maps, and the speed of propagation from the dynamic height time series. Results are given in Table 2, listing the number of rings observed, the dates when the rings were shed, and the parameters calculated as described above. During the period of time covered by the observations (18 months) 11 rings were observed which yields an annualized value of 7.3 rings/year. The ring diameters ranged between 300 and 400 km, and the mean speed of propagation was 12.4 cm sec -1, in agreement with previous results (Fratantoni et al., 1995). Results from the IES array indicate that previous calculations underestimated the component of the MOC return transport carried by NBC rings. An estimate of the long-term averaged transport can be obtained by dividing the total volume carried by the total elapsed time. The total volume transported by the 11 rings in the 18 months of observations is of the order of 40 x 1013 m3 (39.4. x 1013 m3). If this number is divided by the number of seconds in 18 months (the length of the observations), then the estimated transport is of the order of 8 Sv (8.3 Sv). The total annual northward mean transport of the MOC is estimated to be between 14 Sv (Schmitz and McCartney, 1993) to 16 Sv (Ganachaud and Wunsch, 2000). If NBC rings transport 8 Sv/year, then they carry more than half of the total volume of upper water entering the North Atlantic through the MOC. It is interesting to compare these results with a similar previous analysis performed to estimate the contribution of Agulhas rings to the interocean exchange of mass and heat. The Agulhas rings are one of the major contributors to the upper limb of the MOC in the South Atlantic. It is estimated that 4 to 7 rings are shed per year at the retroflection of the Agulhas Current (Garzoli and Goni 2000). The volume transport associated with these rings varies from 3.2 Sv to 9.6 Sv annually depending on the year and the volume of the ring. In a five year period (1993 to 1997) it was estimated that the Agulhas rings contributed a mean transport of 6 Sv per year. These numbers are slightly smaller than, and of the same order of magnitude, as results obtained for the NBC rings in the present study.
368
Figure 5. Left panel: Same as Figure 4 (a, b), but for the third NBCR cruise from January 30 to February 7, 2000. Data is compared to (c) the objective map of the dynamic height field obtained from the IES array for February 5, 2000. Right panel: Same as Figure 4 (a, b) but for the fourth NBCR cruise from June 7 to June 19, 2000. Data is compared to (f) the objective map of the dynamic height field obtained from the IES array for June 1, 2000. Black arrows are geostrophic velocities between station pairs, in m sec -1. The thicker red lines and arrows highlight the ring and NBC structures revealed by the dynamic height field.
369 Fv----~--w----r------r--.T---.v--.--v-r..-r-4~-r-.-T----v----T-----r---~~~~ 2000__ 9 9 ~ng 7 9
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ing 12
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Month/Year Figure 6. Time series of the latitude of penetration of the NBC retroflection observed from the dynamic height synoptic maps, defined as the distance (in km) between the n o r t h e r n m o s t point of the retroflection and a reference set of geographical coordinates. (0~ 42~ Diamonds indicate the times when NBC rings sered.
Table 2. Ring parameters* Ring # D Observed Speed Volume Transport TQ (ref ~ km km/day m3 1013 Sv PW 1 2 3 4 5 6 7 8 9 10 11 Mean
300 380 320 300 333 350 300 330 350 333 400 392
11/27/1998 12/24/1998 2/13/1999 4/5/1999 5/11/1999 6/28/1999 9/14/1999 11/7/1999 12/22/1999 2/20/2000 5/17/2000
11.1 14.3 12.5 12.5 10.7 11.3 13.9 7.9 16.7 12.3 13.3 12.4
2.83 4.54 3.22 2.83 3.48 3.85 2.83 3.42 3.85 3.48 5.03 3.6
0.9 1.4 1 0.9 1.1 1.2 0.9 1.1 1.2 1.1 1.6 1.1
0.06 0.09 0.07 0.06 0.07 0.08 0.06 0.07 0.08 0.07 0.1 0.07
Comments Previously observed by: NBCR1
Altimeter SeaWifs Altimeter NBCR2 SeaWifs Altimeter SeaWifs SeaWifs Altimeter Altimeter SeaWifs Altimeter SeaWifs Altimeter SeaWifs Altimeter NBCR4
*The first column is the ring number, D is the diameter in kin, Observed is the date when the ring was first observed in the dynamic height field, Speed is the translation speed of the ring and TQ is the t e m p e r a t u r e transport. The last row, Mean, is the mean value of each parameter. NBCR 1, 2, and 4 are the NBCR cruise numbers. 1 Sv = 106 mS/sec.
370 The mean heat transported per NBC ring is 0.07 PW (Table 2). During the 18 months of observations, a total of 0.81 PW are transported by the rings. This yields a mean annualized value of 0.54 PW, which represents half of the total heat transported across the tropical Atlantic (1 PW, e.g., Ganachaud and Wunsch, 2000). Given the nature of the assumptions made to obtain these numbers, it is not possible to quantify a precise error and therefore the values should be considered only an estimate. In these simple calculations, we do not distinguish how much water transported by the rings is from the South Atlantic and how much is already mixed with other water masses. In a companion paper (Johns et al., 2002, this volume) a detailed analysis of the percentage of the water transported by the rings is given using all of the CTD stations collected during the NBCR cruises. Also, a similar analysis is done using the results of a high resolution model (Garaffo et al., this volume). The last column of Table 2 compares the rings observed with the IES to those observed with other platforms during the NBCR Experiment: intensive ship surveys (Wilson et al., 2002), Ocean Color (SeaWifs) images (Fratantoni and Glickson, 2001), and altimeter data (Goni, personal communication). Previous estimates for the number of rings shed at the retroflection range from 1 to 4 rings per year (for a comprehensive review see Johns et al., this volume). The latest census done from altimeter data before the NBCR experiment (Goni and Johns, 2001) observed an average of 5 rings/year, with the time interval between rings ranging from 1 to 2 months. The number of rings observed with the IES array, 11 rings shed in 18 months (7.3 rings/year), is larger than previous estimates. However, this number is similar to the number of rings observed with a current meter mooring deployed as part of the NBCR Experiment (Johns et al., this volume). The number of rings observed with the IES array is larger than previous estimates, because this is the first time that a coherent array of moored instruments have been deployed in the region. Satellite observations for example can miss rings having subsurface signals (Wilson et al., 2002).
6. SUMMARY The IES array deployed as part of the NBCR experiment enables continuous monitoring of the variability in the latitude of penetration of the NBC retroflection and the number of NBC rings shed. Results indicate that after the NBC reached its maximum latitude of penetration, in almost all cases a ring was shed. The time series of the latitude of penetration did not show an apparent periodicity, nor was there a period of time when the number of rings shed was larger than another. There was, however, an indication of interannual variability observed during the two overlapping periods of observation (December 1998 through May 1999; December 1999 through May 2000), with fire rings shed in 1998/1999 and three in 1999/2000.
371 It was previously assumed that one third of the MOC was transported from the South Atlantic to the North Atlantic via North Brazil Current rings (Johns et al., 1990; Richardson et al., 1994; Fratantoni et al., 1995). The results obtained in this study indicate that a portion of the MOC large than these prior estimates is actually transported by rings shed at the retroflection. During the 18 months of observations, 11 rings were shed, transporting in the mean 8 Sv or 0.54 PW per year. It should be remembered that results from the simple calculations described in this paper do not distinguish how much water transported by the rings is from the South Atlantic and how much is already mixed with other water masses. A comprehensive analysis of the full data set collected during the NBCR experiment will provide further information on the generation and propagation of NBC rings.
Acknowledgments The authors are indebted to the crew of the R/V Seward Johnson for their support during the four cruises and to Dr. W. E. Johns for providing the pressure gauge data. The IES were prepared for deployment, deployed and recovered by David Bitterman. Roberta Lusic prepared the manuscript for publication. Support for this project was provided by NSF Grant OCE-97-32389 and by NOAA/AOML. NOAA/OAR ship time for the cruises was funded by NSF and NOAA/OAR.
REFERENCES Bourles, B., Y. Gouriou, and R. Chuchla. On the circulation in the upper layer of the western equatorial Atlantic, J. Geophys. Res., 104, 21151-21170, 1999. Didden N. and F. Schott. Eddies in the North Brazil Current Retroflection Region Observed by GEOSAT Altimetry, J. Geophys. Res., 98, 20121-20131, 1993. Duncombe Rae, C. M., S. L. Garzoli and A. L. Gordon. The Eddy Field of the South-East Atlantic Ocean: A Statistical Census from the BEST Project, J.Geophys.Res., 101, 11,949-11,964, 1996. Fratantoni, D. M., W. E. Johns and T. L. Townsend. Rings of the North Brazil Current: Their Structure and Behavior Inferred from Observations and Numerical Simulations, J. Geophys. Res., 100, 10633-10654, 1995. Fratantoni, D. M., P. L. Richardson, W. E. Johns, C.I. Fleurant, R. H. Smith, S. L. Garzoli, W.D. Wilson, and G. J. Goni. The North Brazil Current Experiment. EOS, Transactions AGU, 80, (17), 1999. Fratantoni, D. M. and D. A. Glickson. North Brazil Current Ring Generation and Evolution Observed with SeaWiFS, J. Phys. Ocean., Vol 32, No 3, March 2002. Ganachaud, A. and C. Wunsch. Improved estimates of global ocean circulation, heat transport and mixing from hydrographic data. Nature, 408, 453-456, 2000. Garzoli, S. L. and Z. Garraffo. Transports, Frontal Motions and Eddies at the Brazil-Malvinas Currents Confluence. Deep-Sea Res., 36, 681-703, 1989.
372 Garzoli, S. L. and P. L. Richardson. Low Frequency Meandering of the North Equatorial Counter Current. J. Geophys. Res., 94, C2, 2079-2090, 1989. Garzoli, S. L.. Geostrophic Velocities and Transport Variability in the Brazil/Malvinas Confluence. Deep-Sea Research. 40 No.7, pp.1379-1403, 1993. Garzoli, S. L., A. L. Gordon and C. Duncombe Rae. Benguela Current Sources and Transports. U.S. WOCE Report, 1995, 17-19, 1995. Garzoli, S. L. and A. L. Gordon. Origins and variability of the Benguela Current, J. Geophys. Res., 101,897-906, 1996. Garzoli, S. L., P. L. Richardson, C.M. Duncombe Rae, D.M. Fratantoni, G.J. Goni and A.J. Roubicek. Three Agulhas Rings Observed During the Benguela Current Experiment. J. Geophys. Res, 104, 20971-20985, 1999. Garzoli, S. L. and G. J. Goni. Combining altimeter observations and oceanographic data for ocean circulation studies. Satellites, Oceanography and Society, chap, 5, 79-97, 2000. Garraffo, Z. D., W. E. Johns, E. P. Chassignet and G. Goni (2002). North Brazil rings and transports of southern waters in a High Resolution Numerical Simulation of the North Atlantic. This volume. Goni, G., S. L. Garzoli, A. Roubicek, D. Olson and O. Brown. Agulhas Rings Dynamics from TOPEX/POSEIDON Satellite Altimeter Data. J. Mar. Res., 55, 861-883, 1997. Goni, G. J. and W. E. Johns. A Census of North Brazil Current Rings Observed from TOPEX/POSEIDON Altimetry: 1992-1998, Geophys. Res. Lett., 28, 1-4, 2001. Johns, W. E., R. Zantopp, and G. Goni (2002). Cross-gyre watermass transport by North Brazil Current Rings. This volume. Johns, W. E., T. N. Lee, F. Schott, R. J. Zantopp, and R. H. Evans. The North Brazil Current retroflection: Seasonal structure and eddy variability. J. Geophys. Res., 95, 103-221, 120, 1990. Metcalf, W. G. Shallow Currents Along the Northeastern Coast of South America, J. Mar. Res., 26, 232-243, 1968. Levitus, S., R. Burgett, T. Boyer. World Ocean Atlas 1994, Vol. 3: Salinity. NOAA Atlas NESDIS 3, U.S. Gov. Printing Office, Wash., D.C., 99 pp., 1994. Miller, L. L., D. R. Watts, and M. Wimbush. Oscillation of dynamic topography in the Eastern Equatorial Pacific, J. Phys. Oceanogr., 15, 1759-1770, 1985. Nof, D. Why are rings regularly shed in the western equatorial Atlantic but not in the western Pacific?, Prog. Oceanog., 38, 417-451, 1996. Nof, D. and T. Pichevin. The Retroflection Paradox, J. Phys. Ocean., 26, 23442358, 1996. Richardson, P. L., G. E. Hufford, R. Limeburner and W. S. Brown. North Brazil Current retroflection eddies, J. Geophys. Res., 99, 5081-5093, 1994. Schmitz, W. J. Jr. and M. S. McCartney. On the North Atlantic circulation. Rev. Geophys., 31, 29-49, 1993. Stramma, L., and F. Schott. Western Equatorial Circulation and Interhemispheric Exchange. The Warmwatersphere of the North Atlantic Ocean, pub. Gebruder Borntraeger, ed. by W. Krauss, 195-227, 1996.
373 Stramma, L. and F. Schott. The mean flow field of the tropical Atlantic Ocean, Deep-Sea Res. H, '46, 279-303, 1999. Watts, D. R. and H. T. Rossby. Measuring dynamic height with inverted echo sounders: Results from MODE, J. Phys. Oceanogr., 7, 345-358, 1977. Wilson, D. W., W. Johns and S. L. Garzoli. Velocity structure of North Brazil Current rings, Geophys. Res. Lett., 29, 114 (1-3), 2002. Wimbush, M., S. M. Chiswell, R. Lukas, K. A. Donohue. Inverted echo sounder measurement of dynamic height through an ENSO cycle in the central Equatorial Pacific. IEEE J. Ocean. Eng., 15, 380-383, 1990.
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Interhemispheric Water Exchange in the Atlantic Ocean
edited by G.J. Goniand P. Malanotte-Rizzoli 9 2003 ElsevierB.V. All rightsreserved.
North Brazil Current rings and transport of s o u t h e r n w a t e r s in a h i g h r e s o l u t i o n n u m e r i c a l simulation of the North Atlantic Zulema D. Garraffo a*, William E. Johns a, Eric P. Chassigneta,and Gustavo J. Goni b aRosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Cswy., Miami, FL 33149, USA b NOAA/Atlantic Oceanographic and Meteorological Laboratory, Mia_mi, Florida 33149, USA Output from a very high resolution (1/12 deg.) North Atlantic simulation with the Miami Isopycnic Coordinate Ocean Model (MICOM) is analyzed in a region of the Tropical Atlantic characterized by the presence of the North Brazil C u r r e n t (NBC) retroflection and North Brazil Current rings. The model mean and seasonal circulations present a good qualitative agreement with observations. Quantitatively, the modeled NBC in s u m m e r and fall does not completely retroflect into the North Equatorial Counter Current, and the model upper 100 m NBC is more intense than the observed values by 3-4 Sv. The modeled NBC generates a variety of rings, which we classify as 'shallow', 'intermediate', 'deep', and 'subsurface'. An average of 8.3 rings of all types are generated per year, of which 6 are surface intensifted, in good agreement with altimetry (5.7 rings per year, Goni and Johns, 2001). The transport of southern origin water by the the rings was estimated using two methods. First, the transport was computed kinematically from the rings' volume, resulting in an average transport of 6.6 Sv. Second, an estimation of southern water transport based on an explicit calculation of water mass content was done, resulting in an average transport of 7.5 Sv. The rings' contribution represents ~40% of the total meridional transport from the surface to the intermediate water layers. Possible mechanisms operating in the model ring generation are briefly discussed. 1. I N T R O D U C T I O N The circulation in the western equatorial and tropical Atlantic is very complex, in terms of its mean, seasonal cycle, and mesoscale variability (Schott et al., 1998; Johns et al., 1998). The dominant circulation feature near the western boundary is the North Brazil C u r r e n t (NBC), which has sources in the equatorial region *Corresponding author. Tel.: +1-305-361-4882. Fax: +1-305-361-4696. Email address: zgarraffo@ rsmas.miami.edu.
376 and southern hemisphere. West of 35~ and off the northern continental shelf of eastern Brazil, the surface NBC is principally composed of waters from the equatorial Atlantic, via the South Equatorial Current. The subsurface NBC receives waters from the southern hemisphere North Brazil Undercurrent (NBUC) and, to a lesser extent, the South Equatorial Current. Below the thermocline, sources for the NBC are the southern hemisphere NBUC and probably the Equatorial Intermediate Current (Schott et al., 1998). In the upper layers, the North Brazil current seasonally retroflects into the North Equatorial Counter Current (NECC) (Richardson and Walsh, 1986; Garzoli and Katz, 1993; Johns et al., 1998). Large anticyclonic eddies, the NBC rings, detach from the retroflection and travel northwestward, carrying waters of southern hemisphere origin (Johns et al., 1990; Didden and Schott, 1993; Richardson et al., 1994; Fratantoni et al., 1995; Goni and Johns, 2001). Surface Amazon river waters are partly entrained into the rings' periphery (Steve and Brooks, 1972; Borstad, 1982; Kelly et al., 2000; Fratantoni and Glickson, 2002). The subsurface NBC contributes to the Equatorial Undercurrent (EUC) and to the North Equatorial Undercurrent (NEUC), as discussed by Cochrane et al. (1979), Schott et al. (1998), Johns et al. (1998), and Bourles et al. (1999 a). NBC rings are believed to be one of three principal mechanisms for transporting upper ocean equatorial and South Atlantic waters into the North Atlantic as part of the Meridional Overturning Cell (MOC). Other mechanisms include coastal currents along the South American shelf (Csanady, 1985; Candela et al., 1992) and offshore retroflection into the NECC followed by northward Ekman transport in the ocean interior (Mayer and Weisberg, 1993). It is therefore important to quantify the NBC rings' contribution to the MOC. The Atlantic MOC involves the cross equatorial northward flow of approximately 14 Sv of upper ocean waters (Schmitz, 1996), composed of intermediate waters entering through the Drake Passage and thermocline waters entering off the southern tip of Africa (Rintoul, 1991; Gordon 1986; Gordon et al., 1992). This upper branch of the MOC together with the deep northward flow of Antarctic Bottom Water balance the southward flow of approximately 18 Sv of North Atlantic Deep Water (Schmitz, 1996). Several estimates of the northward NBC ring transport have been made from observations. Johns et al. (1990) estimated that for each ring generated in a year, there is a contribution to the upper branch mass transport of about 1 Sv (1 Sv= 16m3/s). Didden and Schott (1993) pointed out that water mass studies are required for a quantitative estimation of water mass anomalies. They identified 5 rings in a 2.5 year period using GEOSAT altimeter data, and estimated the transport by rings to be on the order of 3 Sv. Fratantoni et al. (1995) identified rings of different penetration depths using data from a mooring located in the NBC retroflection region. They found a correspondence between the deeper rings and those identified from GEOSAT altimetry by Didden and Schott (1993), and estimated the transport by rings to be between 3 and 4 Sv. Richardson and Schmitz (1993) and Richardson et al. (1994) showed anticyclonic eddy signatures reaching 800-900 m depth, and suggested a rlng-induced northward transport of
377 approximately 3 Sv. Recent satellite measurements (TOPEX/Poseidon and SeaWIFS) suggest that the number of formed rings is closer to 5-6 per year with an associated 5-6 Sv of northward transport (Goni and Johns, 2001; Fratantoni and Glickson, 2002). According to all of these estimates, the NBC rings can therefore contribute to as much as one-third of the net 14 Sv of the warm limb of the Atlantic overturning cell. Until recently, there has not been sufficient hydrographic data available to permit study of the water mass composition of NBC rings and to provide a quantitative estimate of the water mass anomaly. Such data were finally acquired in the 1998-2000 North Brazil Current Rings Experiment, which was designed to provide an extensive observational data set to examine the ring structures. According to Johns et al. (2003, this volume), the hydrographic measurements suggest that the NBC ring-induced northward transport can reach 9 Sv, a much larger value than that previously assumed. Despite these recent measurements, many uncertainties remain. For example, the ring vertical structure was found to be very complex (Wilson et al., 2002), implying the need to survey rings of various types. In addition, the magnitude and variability of the MOC over the Atlantic is not precisely known. Numerical ocean models can provide a source of knowledge complementary to observations, allowing complete diagnostics for the study of several aspects of the circulation. Numerical ocean simulations have been successful in producing North Brazil Current rings. Fratantoni et al. (1995) found that NBC rings were generated by the U.S. Navy's layered ocean model (.25 deg. resolution) at a rate of 2-3 rings per year. Barnier et al. (2001) present results from three eddy-permitting models over the same Atlantic domain which differ in the vertical coordinate formulation, all with 1/3 deg. resolution at the equator. These models show significantly different NBC ring activity, ranging from almost no ring activity to a generation rate of 6.4 rings per year, the difference being mainly attributable to different horizontal diffusion formulations. The authors find that the eddy fields vary among the models, but the mean transport of the North Brazil Current remains proportional to the model values of the MOC. The NBC rings are also important for their effect on the variability in the Caribbean, which they influence either by entering the region or by affecting the transports through the Lesser Antilles passages. Rings in the Caribbean Sea and their relation to the NBC rings were recently studied by Carton and Chao (1999) and Murphy et al. (1999). Although these model studies provide information on generation mechanisms, generation rate, and seasonality of NBC rings, they have not carefully examined the water mass structure of the rings and their role in the MOC. In this paper, we take advantage of a fine mesh (1112 deg.) North Atlantic numerical simulation performed with the Miami Isopycnic Coordinate Ocean Model (MICOM) to study several aspects of the North Brazil rings, such as formation rates, structures, trajectories, and effect on the Lesser Antilles passage transports, with emphasis on a quantitative estimation of the rings' water mass transport and contribution to the meridional transport. In order to address the issues noted above, the model results are first validated
378 by comparing the simulated circulation with in-situ measurements and with altimeter data. Having gained confidence that the model mean and seasonal circulations are realistic, we estimate the volume and water mass transport of thermocline waters of southern hemisphere and equatorial origin by rings. The results from the water mass analysis are used to obtain the model ring transport during 6 model years and relate this transport to the meridional transport, allowing us to conclude that an average of 7.5 Sv (~40%) of the model North Atlantic upper and intermediate water meridional transport is southern water transported by the model NBC rings. The paper is organized as follows. The main aspects of the numerical simulation are introduced in section 2. In section 3 and 4, the modeled tropical circulation and NBC rings are compared to published hydrographic observations and to altimetry measurements. In these two sections, we also discuss the mean and seasonal circulation in the surface and subsurface layers, analyze the sea surface height (SSH) fields and variability, and study the vertical structure and trajectories of the modeled NBC rings and their effect on the transports through the Eastern Antilles passages. In section 5, a water mass analysis of the rings is performed, including transport estimates by water mass analysis and by volumetric considerations. We conclude with a discussion relating the results to the upper and intermediate meridional transport. 2. M O D E L C O N F I G U R A T I O N The Miami Isopycnic Coordinate Ocean Model (MICOM) is well documented in the literature. For a review, the reader is referred to Bleck et al. (1992) and Bleck and Chassignet (1994). The fundamental reason for modeling ocean flow in density coordinates is that this system suppresses the diapycnal component of numerically caused dispersion of material and thermodynamic properties, such as temperature and salinity. This characteristic allows isopycnic models to prevent the warming of deep water masses, as has been shown to occur in models framed in Cartesian coordinates (Chassignet et al., 1996). Furthermore, the association of vertical shear with isopycnal packing and tilting in the ocean makes isopycnic models appropriate for studies of strong baroclinic currents such as the Gulf Stream. The computational domain is the north and equatorial Atlantic Ocean basin from 28~ to 65~ including the Caribbean Sea and the Gulf of Mexico. The horizontal grid (6 km on average) is defined on a Mercator projection with resolution given by 1/12 ~ x 1/12~162 where r is the latitude. The bottom topography is derived from a digital terrain data set with 5' latitude-longitude resolution (ETOPO5). The vertical density structure is represented by 15 isopycnic layers, topped by an active bulk Kraus-Turner type surface mixed layer, vertically homogeneous, but of density varying in the horizontal, that exchanges mass and properties with the isopycnic layers underneath (Kraus and Turner, 1967; Bleck et al., 1992). The isopycnic layers have potential density values of 24.70, 25.28, 25.77, 26.18, 26.52, 26.80, 27.03, 27.22, 27.38, 27.52, 27.64, 27.74, 27.82, 27.88, and 27.92. The vertical discretization was chosen to provide maximum resolution in the
379 upper part of the ocean. Open ocean boundaries are treated as closed, but are outfitted with 3 ~ buffer zones in which temperature (T) and salinity (S) are linearly relaxed toward their seasonally varying climatological values (Levitus, 1982), with damping/relaxation time from 5 days at the wall to 30 days at the inner edge of the buffer zone. The buffer zones restore the T and S fields to climatology in order to approximately recover the vertical shear of the currents through geostrophic adjustment. The surface boundary conditions are based on the COADS monthly climatological data sets (da Silva et al., 1994). The model was spun up from rest for a total of 21 years and our analysis focuses on the final 6 years. The high horizontal grid resolution drastically improved the model's behavior in comparison to that of previous coarse-resolution simulations. The major improvements are: (a) a correct Gulf Stream separation (Chassignet and Garraffo, 2001), and (b) higher eddy activity. These results support the view that an inertial boundary layer, which results from the fine resolution, is an important factor in the separation process (()zgSkmen et al., 1997), and that resolution of the first Rossby radius of deformation is necessary for a correct representation of baroclinic instabilities. The 6-year mean transport of 27.4 Sv through the Florida Straits is close to the observed value of 30 Sv, with a seasonal cycle of the same magnitude and phase as those seen in cable data (Larsen, 1992). The behavior of numerical Lagrangian drifters and a comparison to that of real drifters is presented in Garraffo et al., (2001a,b), and the probability density functions for the simulated Lagrangian data are discussed in Bracco et al. (2003). 3. THE N O R T H BRAZIL C U R R E N T SYSTEM F R O M THE M O D E L AND OBSERVATIONS: THE SEASONAL C I R C U I ~ T I O N In this section, the modeled surface and subsurface circulations in the NBC region are compared to published observations. These comparisons are important in order to assess the validity of the model results and, therefore, of the model output analysis. The simulation has already been shown to produce good agreement between the surface fields and drifter observations for the North Brazil current region (Garraffo et al., 2001a): the simulated and observed mean velocities were found to agree, and the model eddy kinetic energy was found comparable to but slightly higher than that observed. The Lagrangian velocity time scales computed from the velocity autocovariances were found to be about 1-2 days for in-situ drifters, and 2-3 days for the numerical drifters for the NBC region. The time scales are shorter in the western boundary currents than in the ocean interior, especially in the modeled NBC region. The short time scale is interpreted as being due to the fast decorrelation between particles trapped in NBC rings and particles outside the rings. The circulation in the NBC region as inferred from the model is compared to recent observations as described in Johns et al. (1998), Schott et al. (1998), and Bourles et al. (1999 b). Following Johns et al. (1998, Figure 18), the model surface and subsurface (a0 = 26.18, layer 5, about 200m depth)velocities seasonally averaged over the 6-year period are shown in Figure 1. As in the observations,
380
Figure 1. a),c),e),g): Model surface velocity averaged for 2-month periods during 6 model years; b),d),f),h): same for subsurface velocity (ao = 26.18, layer 5).
the modeled surface retroflection develops in (boreal) s u m m e r and fall and remain present in winter, but is absent during spring. This is further illlustrated in Figure 2 a,b, showing one realization of the model instantaneous surface circulation for spring (no clear retroflection at ~ 5~ and one for fall (retroflection at ~ 5~ However, the seasonal circulation, being a time average, includes the signature of
381
Figure 2. Instantaneous model surface velocity on one day in spring (lei~, year 16, May 10), and one day in fall (right, year 16, Nov 15).
the NBC rings as they propagate northwestward. For example, the band of southeastward flow found offshore of the NBC between 5-10~ during spring (Figure la) is a rectified signature of NBC rings (Figure 2a), even though the retroflection is absent at this time. The western tip of the NBC surface retroflection derived from the model results is located at approximately 50~ in summer, and moves westward in fall and winter, reaching 53~ in winter before disappearing in the spring (Figure 1 c,e,g,a respectively). The modeled subsurface circulation is in good qualitative agreement with observations, as evidenced by: a) a permanent retroflection of the westward subsurface NBC just north of the equator into the eastward Equatorial Undercurrent (EUC) (Schott et al., 1998; also Cochrane et al., 1979, Molinari and Johns, 1994), and b) a seasonally varying retroflection into the North Equatorial Undercurrent (NEUC), in which the subsurface NBC penetrates farther to the west in summer and fall than in spring [in agreement with Johns et al. (1998)]. The model NBC upper 100 m transports are compared to the observed values in Table 1. Since the modeled mixed layer depth in the region is on average approximately 80 m, the upper 100 m circulation is very similar to that in the mixed layer. In spring, when the surface retroflection is absent, the modeled upper 100 m transport is 13 Sv at 44~ and 11 Sv at 52~ (Table 1, corresponding to Figure la), including the coastal current, which is weak in the model (about 0.6 Sv in all seasons). This transport is slightly higher (by about 3 Sv) than the values of 10 Sv and 8 Sv given in Johns et al. (1998) for similar longitudes (44~ and 48~ Recently published observations at 44~ by Bourles et al. (1999 b) give a similar value, an average of 10.6 Sv from two sections in January, while Bourles et al. (1999 a) give 6 Sv at 45~ for one section in April. During the summer (June-August) and fall (Sept-Nov), when the surface retroflection develops, the modeled NBC upper 100 m transport is 18 Sv at 44~ The value given by Johns et al. (1998) is 14 Sv at 44~ (Table 1), which is consistent with the 13.7 average of 4 sections at 44~ and 45~ in August and September given in Bourles et al. (1999 a, b). The modeled circulation for the incoming NBC is therefore ~ 3-4 Sv more intense than that derived
382 Table 1 Transport (Sv) from model and observations spring fall model obs model obs NBC, 44~ 13 6a-10 b 18 14 NBC, 48 to 52 ~ 11 8 8 0 NECC,44~ 15 19 Model and observed (from Johns et al., 1998, Schott et al., 1998, Bourles et al., 1999 a,b) upper 100m transports in Sv, for the NBC at two longitudes and for the NECC, in spring and fall. a: Bourles et al., 1999a, b: Schott et al., 1998.
from in - situ observations in both seasons. The modeled total upper and intermediate water meridional transport across the Atlantic, discussed in section 6, is also 3-5 Sv more intense than observational estimates. During the s u m m e r and fall, the modeled surface NBC, after retroflecting, contributes to the NECC, into which a small branch of the NEC merges (Figure 1 c, 1 e, 52~ 10~ At 44~ (and 5~ the modeled NECC upper 100 m eastward transport during s u m m e r and fall is 15 Sv, while an observational value of 19 Sv is obtained by averaging 4 sections in August and September from Bourles et al. (1999 a,b), and 1 section in October by Schott et al. (1998). The eastward transport of the NECC is therefore about 4 Sv weaker t h a n the observed value, due in part to an incomplete retroflection of the NBC in the model. At 52~ the model shows 8 Sv continuing westward in the NBC in the fall while observations suggest t h a t essentially all of the NBC waters retroflect, leaving no net transport along the western boundary. Therefore, the modeled NBC contributes about 10 Sv to the NECC during fall. The contribution from the modeled NEC from the north, plus other possible recirculations, is 5 Sv (as obtained by balancing the mass transports), in agreement with the 5 Sv suggested by observations (also by transport balance). In summary, there is a good qualitative agreement between the model and the observed seasonal circulation, with the exceptions t h a t the NBC surface layer in s u m m e r and fall does not completely retroflect into the NECC as indicated by observations, and t h a t the modeled upper 100 m NBC transport slightly exceeds the observed seasonal values by 3 to 4 Sv. The incomplete retroflection of the modeled NBC in s u m m e r and fall appears to be linked to the weaker transport of the NECC in the model (15 Sv) than in observations (19 Sv). The weaker value in the model implies t h a t less water from the NBC is required to separate from the coast and flow eastward into the interior. The comparison of the NECC transport to observations is complicated by the zonal variation of the NECC transport in the model, which increases eastward from 15 Sv at 44~ to 19 Sv at 40~ due to local recirculations. Still, at 44~ the model NECC transport is about 4 Sv weaker than the observed value. This discrepancy can in part be due to the COADS wind forcing, since Townsend et al. (2000) find t h a t the North Atlantic Tropical gyre closed
383 by the NECC shows an annual mean Sverdrup transport of 6 Sv for COADS, the lowest value of the 6 Sv - 17 Sv range given by 11 wind climatologies.
4. THE NORTH BRAZIL RINGS, SEA SURFACE HEIGHT VARIABILITY, AND EFFECT ON TRANSPORTS THROUGH THE L E S S E R A N T ~ S PASSAGES The western boundary circulation west of 50~ breaks into North Brazil rings, large anticyclonic eddies that are generated in the retroflection region and travel northwestward. NBC rings have been studied from current meter data (Johns et al., 1990; Fratantoni et al., 1995), from floats (Richardson et a/.,1994), from altimetry (Didden and Schott, 1993; Goni and Johns, 2001), and from ocean color imagery (Fratantoni and Glickson, 2002). NBC rings are important because they transport water masses northward from the region of generation, contributing to the interhemispheric exchange, and because of environmental issues associated with the impact of the rings on the Lesser Antilles. As can be seen in the model instantaneous circulation realizations (Figure 2 a,b) for one day in spring and one in fall, the NBC rings are generated off South America/Brazil near 50~ and travel northwestward. The figures show NBC rings shortly after generation (rings A1, B1), and others (A2, A3, B2, B3) that were generated earlier and have progressed northwestward. The anticyclonic NBC rings have an associated positive SSH anomaly. In this section, we compare results from the model SSH with altimeter data, examine the vertical structure of the modeled rings and their trajectories, and discuss the effect of the rings on the transport through the Lesser Antilles passages.
4.1. Sea surface h e i g h t space-time d i a g r a m s A detailed identification of NBC rings in the model was done from animations of daily maps of SSH and vertical sections of velocity, with results that will be discussed in detail in sections 4.3 and 5. A total of 45 rings were identified from SSH during the 6 analyzed years, corresponding to 7.5 rings per year with a surface signal. For some of the rings the SSH signal is very weak. During that 6 year period, a total of 5 additional rings with no surface signal were identified. Comparable results were obtained from altimetry by Goni and Johns (2001), who identified a total of 34 NBC rings during the 6 years between 1993 and 1999, or 5.7 rings per year. The information on NBC ring generation and propagation can be compactly displayed by SSH space-time diagrams. The model time series of SSH for sections extending from the NBC retroflection region to the Eastern Antilles (Figure 3a) are shown in Figure 3 b. North Brazil rings are characterized by positive SSH differences with respect to the surrounding values, superimposed on the annual cycle, as the rings travel from the eastern to the western sections essentially parallel to the coast (Figure 3b, 10 lower panels, sections 5-14). The anomalies in sections 10-14 correspond either to rings already separated from the NBC retroflection or to the retroflection itself. As the rings approach the Lesser Antilles, they tend to turn and propagate northward along the island arc (3rd and 4th panel from top,
384
Figure 3. a) sections (extending ~ 8 ~ in latitude), covering from 62~ (section 1) to 49~ (section 14); b) SSH time series for the 6 model years, over the sections, from the eastern section (at 49~ section 14, lower panel) to the western section (at 62~ section 1, top panel).
sections 3 and 4). These rings often i n t e r a c t a n d m e r g e w i t h each other in this area, and t e n d to stall a n d coalesce into a large positive sea level a n o m a l y j u s t east of t h e n o r t h e r n Lesser Antilles. Inside the C a r i b b e a n (top panel, section 1), generally s m a l l e r SSH anomalies are seen p r o p a g a t i n g w e s t w a r d . These s m a l l e r anomalies often originate as a splitting from a ring t h a t r e m a i n s for some t i m e to the e a s t of the Lesser Antilles, as seen by e x a m i n i n g a n i m a t i o n s of the daily SSH maps. It is also a p p a r e n t in Figure 3b t h a t the t i m e interval b e t w e e n suc-
385
Figure 4. a) Ring trajectories obtained from modeled SSH (solid lines), and additional trajectories for rings with no SSH signal (dashed-dotted lines); the 500m isobath is shown as a thick line. The circle (58~ 10~ is marked in relation to Figure 9. b) Ring trajectories derived from TOPEX/Poseidon (Goni and Johns, 2001).
cessive rings varies, with ring generation showing an apparent seasonal cycle and significant year-to-year variability. This interannual variability in the model with climatological forcing can be caused by: a)model internal dynamics; b)the model not having reached complete equilibrium. The modeled ring trajectories derived from SSH horizontal maps and animations are shown in Figure 4 a, while trajectories derived from TOPEX/Poseidon data (adapted from Goni and Johns, 2001) are shown in Figure 4 b. The trajectories of modeled rings not presenting a SSH signal were added in dashed-dotted lines in Figure 4a and will be discussed in section 4.3. Similar to the signals of observed rings, the signals of the modeled rings follow the topography, but the dispersion of the modeled trajectories around a mean path is smaller than in the observations. Reasons for the difference could be the lack of high frequency and interannual forcing in the model, or error associated in determining the rings' center from TOPEX/Poseidon due to the sparse groundtracks. Typical model SSH differences between the ring center and the surrounding waters vary between 15 and 30 cm. Altimetry measurements indicate that SSH anomalies at the center of the rings are smaller, of order 5 to 15 cm (Didden and Schott, 1993; Goni and Johns, 2001). Model and observed ring SSH signals are further discussed in the next section.
4.2. Surface h e i g h t variability from the m o d e l and o b s e r v a t i o n s A comparison between the modeled SSH variability (cm) and that obtained from TOPEX/Poseidon is shown in Figure 5. The North Brazil current system is characterized in the model and in the observations by a region of high variability extending from the NBC retroflection location (~ 8~ 50~ to the Antilles. NBC rings identified in Figures 3 and 4, superimposed on the seasonal cycle, are the major
386
Figure 5. a) SSH variability (rms of sea height) for the North Brazil Current and Caribbean region (cm) obtained from the model; b) the same derived from the first five years of TOPEX/Poseidon sea hight anomaly data.
contributors to the SSH variability between 50~ and the Lesser Antilles. Also consistent with observations, high eddy activity is present in the Caribbean Sea and in a band extending North-East of the Antilles. A secondary maximum of variability is present east of the North Eastern Antilles (north of Barbados) both in the model results and in the observations. This secondary maximum is related to the stalling of rings reaching the eastern Antilles, similar to results found by Simmons and Leben (personal communication) from TOPEX/Poseidon altimetry, extending the Simmons and Nof (2002) study on the mechanisms for ring interaction with the Lesser Antilles. The region of high variability that extends off the coast from the retroflection location to the eastern Antilles is narrower and more intense in the model than in the altimeter observations. This difference can in part be attributed
387 to the model climatological forcing and the absence of high frequency and interannual variability. A model SSH ring signal larger than the altimetry signal can also contribute to this difference. High values of altimeter-derived SSH variability that were present near the mouth of the Amazon River have been filtered out because they are mainly due to tidal aliasing. (Arnault and Le Provost, 1997).
4.3. Ring types, associated sea height anomaly, and trajectories The North Brazil rings that occur in the model show different vertical characteristics, which we classify into four different types: 'shallow', 'intermediate', 'deep', and 'subsurface'. The 'shallow', 'intermediate', and 'deep' rings are characterized by velocity signals larger than 10 cm/s extending from the surface to about 200, 500, and 900-1000 m respectively. The 'subsurface' rings show a very small (or even non-existent) surface velocity signal and a maximum velocity at around 200 m (a0 = 26.52) for most rings (but varying between about 100 m (a0 = 25.28) and 300 m (a0 = 26.80)), and signals larger than 10 cm/s extending to about 800 m (a0 = 27.22). Rings of all types are present among the 45 modeled rings identified from SSH during the 6 model years. Another 5 rings with no surface signal were identified from subsurface salinity and velocity fields during the 6 model years, by examining horizontal maps and movies. Therefore, the total number of modeled rings of all types is 50 during the 6 model years, or an average of 8.3 rings per year. Figure 6 shows, for each ring type, a characteristic vertical cross-section at 10~ in which the velocity structure and layer interfaces are displayed together with the corresponding SSH signal. The trajectories for all the rings of each type are also displayed to the right in Figure 6. Trajectories are marked with dashed lines after a ring splits or merges with another ring or feature. Of the 5 subsurface rings not identified from SSH, 3 rings presented no surface signal. For the other 2 rings the subsurface signal and the SSH anomaly, initially co-located, traveled on different paths, the subsurface ring nearer to the South American coast and slightly slower than the surface signal. These features later merged with the next ring generated from the NBC retroflection. The subsurface trajectories for the 5 subsurface rings with no clear SSH signal are marked with a dashed-dotted line in Figure 6. These 5 rings are generated at a location to the east of the other rings. The model ring types and structures are in close correspondence with those that have been observed using shipboard hydrographic and direct velocity measurements by Wilson et al. (2002). Wilson et al. (2002) found a subsurface ring in Dec. 1998 that had a velocity core at 150 m depth and 40 cm/s velocities extending to 500m; they also found rings of'deep' type (40 cm/s velocities down to 1600 m) and 'shallow' type (significant velocities confined above 200 m). The altimeter-derived SSH anomaly difference between ring center and the surrounding waters, associated with the four rings reported by Wilson et al. (2002), range from 2 cm for the 'subsurface' ring to 12 cm for the other types (Johns et al., 2003). In the model, the SSH center-to-periphery differences associated with the rings are typically 15 cm for those subsurface rings that present a surface signal, and 20 to 30 cm for the ring types that have maximum velocities at the surface (the 'shallow', 'intermediate', and 'deep' rings). The corresponding SSH anomaly differences at 10~ obtained by
388
Figure 6. Sea surface height and vertical structure (velocity contours, cmls, and isopycnic interfaces) for one ring of each type, and trajectories for all rings of the type, for: a) 'shallow' rings, b) 'intermediate', c) 'deep', d) 'subsurface'. Dashed lines indicate rings or anomalies aider splitting or interacting with another ring or feature. 'Subsurface' rings not presenting a SSH signal are marked in dashed-dotted lines.
subtracting the time m e a n from the instantaneous SSH are about 12 cm for the subsurface rings and 15 to 25 cm for rings of other types. Thus the SSH signals of the modeled rings are generally stronger t h a n those of the observed rings. Also, while the modeled subsurface rings show smaller SSH anomalies t h a n the other types of rings, about 2/3 of the modeled subsurface rings are still detectable from the surface. This contrasts with the only observed subsurface ring (Wilson et al., 2002), which showed a very small SSH anomaly. W h e t h e r this observed subsurface
389 Table 2 Ring type characteristics N R(km) aR (kin) N/yr % enter Carib shallow 8 114 17 1.3 37 intermediate 21 125 16 3.3 43 deep 7 130 23 1.2 14 subsurface 14 82 8 2.3 28 all 50 8.3 34 x For each type of ring: number of rings during 6 model years, averaged radius of maximum velocity for the upper part of the ring, radius mean square deviation, number of rings per year, and percentage of rings of the type that move entirely into the Caribbean. Totals for rings of all types are also listed. 1: Percentage of rings of all types moving into the Caribbean (weighted average of the percentages for each type).
ring is typical of these types of features is unknown. The n u m b e r of rings of each type generated during the 6 model years is listed in Table 2, along with the upper average radius of m a x i m u m velocity and its standard deviation for each type, and the average n u m b e r of rings per year. (The upper radius of m a x i m u m velocity is the average distance from the ring center to the m a x i m u m swirl velocity surrounding the center, in the upper part of the ring.) The mean ring radii of m a x i m u m velocity range from 115 to 130 km for the 'shallow', 'intermediate', and 'deep' types, with a standard deviation of 16 to 23 kin. The averaged radius is smaller for the subsurface ring type, with a mean of 82 km and standard deviation of 8 km. This difference is consistent with the results of Wilson et al. (2002), who found an average radius of 150 km for the three surface intensified rings t h a t they surveyed, and a smaller radius of 110 km for their subsurface ring. The actual modeled values appear to be somewhat smaller t h a n observed, by 0(20 kin), regardless of ring type. However, Goni and Johns (2001) estimated the length scale of rings from altimeter-derived upper layer thickness maps, and found a smaller mean value of 95 km with a standard deviation of 25 km. For some subsurface rings, the subsurface signal first appears near the equator (Figure 6 d), in the region of the subsurface NBC retroflection into the Equatorial Undercurrent (Figure 1). West of 50~ the trajectories for different ring types are generally similar to each other in the region off the South American coast, but start to differ when the rings reach the Antilles. Some rings appear to enter the Caribbean nearly intact (shown by solid lines in Figure 6); others interact and merge with other rings or westward-propagating wavelike features, or a percentage of the ring separates and enters the Caribbean (dashed lines in Figure 6). Some rings stay to the east of the Antilles and move northward, where they either decay or merge with other features. The rings t h a t enter the Caribbean, having diameters larger t h a n the Lesser Antilles passage widths, generally go through several passages at the same time and recombine in the lee of the islands, a behavior noted in Simmons and Nof (2002). A larger percentage of shallow (37%)
390 a) Model:all rings
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9
Figure 7. a) Number of rings generated as a function of the month of the year during 6 years, for all types of rings in the model; b) same as a) except subsurface rings are not included; c) same as b) obtained from TOPEX/Poseidon data.
and intermediate (43%) rings move into the Caribbean than do the deep (14%) and subsurface (28%) rings. This suggests that the deep and subsurface rings, having the deepest reaching velocity structures, tend to be more influenced by the island arc topography and are less able to penetrate into the Caribbean. In most cases, there is a northward burst in the rings' propagation speed as they approach the Antilles. The majority of the rings, characterized by their positive SSH anomalies with respect to the surroundings, move northward and pass near to or east of Barbados. As mentioned in section 4.2, the rings then stall for a while before entering the Caribbean Sea, the SSH anomaly increasing when rings merge. This in part explains the secondary maximum in SSH variability north of Barbados (Figure 5). Figure 7a shows the number of rings of all types generated during the 6 model years as a function of the month in which they were formed. Rings are formed in all months of the year, but show the largest number formed in May and the minimum number formed in July. Since subsurface rings may not be detectable from the TOPEX/Poseidon SSH anomalies, Figure 7b also shows the distribution of modeled rings of the shallow, intermediate, and deep types only. This distribution can be compared to the similar figure derived from altimetry (Figure 7c). A total of 34 NBC rings were identified from 6 years of TOPEX/Poseidon data by Goni and Johns (2001), counting only the SSH anomalies that were clearly discernible by their amplitude. The number of modeled surface-intensified rings (i.e., of the shallow, intermediate and deep types) generated during 6 years is 36, or 6 rings per year, in good agreement with the TOPEX/Poseidon observations (Table
391 a) Shallow
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Figure 8. Number of modeled rings generated as a function of the month of the year during 6 years, for rings of each type: a) shallow, b) intermediate, c) deep, d) subsurface.
2). In the model, a maximum number of surface intensified rings are generated in spring/summer (May and June, Figure 7b), while in the observations the maximum occurs in winter (January) but with a less pronounced seasonal variation (Figure 7c). The seasonal distribution of formation rate for each ring type is shown in Figure 8. Subsurface rings are generated in fall and early winter, while deep rings are generated in late winter and spring (with maximum generation in April and May). From June to December, the only rings with significant velocities below 700 m are the subsurface rings, which have a small surface signature. The shallow and intermediate rings can be formed throughout the year but have a maximum formation rate in late spring to early summer (May or June). A discussion of these differences will be presented in the last section of the paper. Further analysis of the ring signal can be carried out from velocity time series. The time series of the north-south velocities at 10~ and 58~ are shown in Figure 9 for one model year, at the surface, for layer 6 ( a o = 26.52, average depth 217 m) and for layer 9 ( a o - 27.22, average depth 752 m). The reference point location was selected between the envelopes of the trajectories of rings with a surface signal and those with no surface signal; most of the trajectories pass just east of the reference location (see Figure 4a; the reference point is marked with a solid circle). These velocity time series show, for most cases, that there is a positive (northward) velocity when a ring approaches, and a drop to a negative value as the ring passes through the longitude of the reference point, with each rapid drop in the time series corresponding to the passage of a ring. Independently determined (from SSH maps for the rings with surface signal, and from subsurface maps otherwise) times for ring passage through the longitude of the reference location are marked by vertical lines, and the type of each ring is indicated. As can be seen in Figure 9a, the surface velocity signatures of most of the modeled rings are very similar, but the shallow rings (e.g., August in Figure 9) decay
392
Figure 9. Time series of northward velocity for year 15, at 10~ 58~ for the surface and for layers 6 and 9 (top, center and bottom panels). Given are the value of ao and the timemean depth at which the layer is located. Rings passing through 58~ are marked, as determined from SSH, velocity, and salinity, b: same for model years 15-20.
rapidly with depth when compared to the other types of rings. The deep rings (Feb. and May in Figure 9) predominate in deeper layers. The subsurface rings have generally a smaller surface velocity signal. The subsurface ring present in Dec.-Jan. shows a larger velocity in layer 6 t h a n at the surface. A previous subsurface ring (October in Figure 9) is not apparent in the time series because the ring passes to the south-west of the reference location, not producing a significant signal there. (this is a ring with no SSH signal, indicated with a dashed-dotted trajectory in Figure 6). The velocity time series shows a quiet period around September, with smaller oscillations in the surface and subsurface meridional velocities t h a n in other periods; this is also a period when no rings were independently identified from SSH. This quiet period is consistent with a m i n i m u m n u m b e r of rings generated in July (Figure 7 b,c), since it takes about two months for the rings to arrive from the region of generation to the reference location at 10~ In Figure 9b, the same velocity time series are shown for all 6 model years. Each large oscillation is associated with the passage of a NBC ring. Only a few rings (generally of the subsurface type) do not produce a velocity signal at the selected reference point; these are rings passing at a distance larger t h a n the ring radius. The less active September period is present in all years, and is especially pronounced in some years (e.g,
393 year 17). It is important to note that the interannual variability in the model is independent from the forcing, since monthly climatological data are used to force the model.
4.4. Effect of NBC rings in the transports through the Lesser Antilles passages As the rings reach the Lesser Antilles, observations indicate that they have a strong impact on the local water characteristics and circulation. For example, transport of entrained Amazon River water by North Brazil rings (Kelly et al., 2000, Fratantoni and Glickson, 2002) influences larvae recruitment around Barbados (Cowen and Castro, 1994). Furthermore, North Brazil rings induce large variability in the transport between the passages through the Lesser Antilles (Johns et al., 2003). The modeled mass transports through the Lesser Antilles passages show energetic oscillations. Time series for the transport through three of the Lesser Antilles passages (Grenada Passage at 12~ the southernmost passage; St. Lucia Passage at 14~ and Dominica Passage at 15~ are shown in Figure 10a. The circulation patterns (SSH contours and velocity vectors) corresponding to four days during the time of a particularly large variation in transport (May of year 15) are also shown in the figure. Positive transports correspond to flow entering the Caribbean. The transport through the southernmost passage diminishes from day 126 to 153 (Figure 10a) as a ring approaches the Antilles (Figures 10 b,c,d). This is due to the anticyclonic circulation associated with the ring, which diverts the flow near the passage northward (Figure 10 d,e) from its otherwise westward direction, resulting in a smaller transport. In this example, the ring moves toward the north, staying east of the Lesser Antilles. Farther north at St. Lucia and Dominica Passages, the decrease in transport occurs at successively later times (day 144 for St. Lucia, day 153 for Dominica). The cycle for the Dominica passage transport is particularly intense as this ring moves northward along the east side of the Lesser Antilles. The next large transport variation in Grenada Passage occurs in June (Figure 10a) and corresponds to the next ring moving along the coast (seen in the lower right of Figure 10d), which induces a similar diversion of the flow. This ring partially enters the Caribbean through the southern passages (not shown), and the resulting amplitude variations in the transports through St. Lucia and Dominica passages have smaller amplitudes than those in March. The next transport oscillation in July-August (Figure 10 a) corresponds to a ring that enters the Caribbean between Grenada and St. Lucia passages (not shown), resulting in transport variability through Grenada and St. Lucia comparable to those in June. The transport fluctuations induced in the passages by the rings are of the same order as the mean transports through each of the passages. 5. T R A N S P O R T OF S O U T H E R N ATLANTIC WATER BY R I N G S The contribution of NBC rings to the upper limb of the meridional overturning circulation in the Atlantic is still an open question. In particular, it is important to quantify how much water of southern hemisphere origin is transported north-
394
Figure 10. a) Time series of the transport through Lesser Antilles passages Grenada(l), St. Lucia(2) and Dominica(3); b),c),d),e): SSH (color coded from 0 to 70 cm, at 10 cm interval, blue to red) and velocity vectors at 4 days shown by vertical lines in a).
ward in the rings as compared to other pathways. In this section, we estimate the ring transport in two ways, by determining the volume of water inside the rings from their physical properties (their depth and diameter), and by calculating the proportion of southern water contained in the NBC rings through a detailed water mass analysis.
395 5.1. T r a n s p o r t f r o m c r i t e r i a o n r a d i u s a n d v e r t i c a l e x t e n t We first present here the traditional approach of computing the geometric volume of the rings from the vertical and horizontal extent of the rings' velocity field. Consistent with Johns et al. (2003 - this issue), the volume of South Atlantic water that is trapped and transported within a ring is assumed to correspond to the portion of the ring that is nearly in solid-body rotation, which is from the center of the ring out to the radius of maximum azimuthal (swirl) velocity. For the following analysis, we use vertical sections of the ring meridional velocity at 10~ In order to compute the ring volume, we consider the following criteria for the depth and radius of the rings: (1) the upper (for subsurface rings) and lower depth limits correspond to the locations where the swirl velocity drops below a minimum of 10 cm/s, and additionally the ring vertical extent is limited to layer 9 or above (ao = 27.22, about 800-900 m), thus eliminating contributions from below the main model depth of the South Atlantic intermediate water (salinity minimum in Figure 11 e), and (2) the ring radius is taken as the distance from the center of the ring to the maximum swirl velocity, with this distance (which can vary with depth in about 25% of the rings) being averaged azimuthally and over the total depth of the ring as defined above. We do not include any contribution to ring transport below layer 9 because those layers do not show a clear ring salinity signal arriving at 10~ (not shown). The resulting ring volumes and other ring characteristics at 10~ are listed in Table 3 for all the rings identified during the six model years (year 15-20). The annualized transport associated with each ring is also shown, which is obtained by dividing the corresponding ring volume by the number of seconds in one year. According to this method, the resulting net transport by rings for the 6 year period is 6.6 Sv. It should be noted that in Table 3 there are only 49 rings crossing 10~ (one less than the total of 50 in Table 2), due to a merger of two sequential rings that took place in year 19 shortly after the rings were formed. 5.2. T r a n s p o r t f r o m w a t e r m a s s a n a l y s i s
An alternate way to determine the amount of South Atlantic water transported by the modeled rings is to specifically identify the South Atlantic waters according to their watermass properties. Waters of South Atlantic origin are characterized by lower salinity throughout the thermocline and intermediate layers than is seen in waters in the North tropical Atlantic on the same density surfaces. To illustrate this, we show in Figure 11 a,b maps of horizontal distribution of salinity at the surface and in layer 5 (a0 - 26.18, 19~ 100m) for a time when a ring is just being formed from the NBC retroflection (year 14 day 330). Signatures of the rings are evident in the subsurface layer (layer 5) north of the retrofleetion in Figure 11 b, one at 9~ and one interacting with the Lesser Antilles south of Barbados. We focus on the transport of this low salinity water from the equator northwards, and call it 'southern water', being the mixture of water of South Atlantic or equatorial origins that arrived at locations around the equator and 45~ We call 'ambient water' the water present at the ring formation region that is not of South Atlantic and equatorial origins, i.e., the background water away from the NBC in the region
396 Table 3 Ring characteristics day t~ype 1 15.040 deep 2 15.085 interm 3 15.120 deep 4 15.160 interm 5 15.205 shallow 6 15.2521 subs 7 15.315 interm 8 15.350 subs
9l~'velM 150' 130 150 130 100 80 105" 95
depth. 900 750 900 450 400 700 500 750
V 64 40 64 24 13 16 17 21
9 10 11 12 13 14 15 16
16.030 16.070 16.128 16.165 16.205 16.272 16.300 16.345
interm subs deep interm shallow subs interm subs
120 80 130 150 120 100 130 80
750 800 800 650 400 650 400 750
34 16 42 46 18 20 21 15
17 18 19 20 21 22 23 24 25
17.030 17.055 17.105 17.140 17.155 17.246 17.295 17.325 17.357
ihterm interm interm interm shallow subs subs shallow subs
130 120 130 105 130 75 90 90 80
550 700 850 700 200 700 700 150 850
29 32 45 24 11 12 18 4 17
transp v 2.0 1.3 2.0 .8 .4 .4 .5 .7 8.1 Sv 1.1 .5 1.3 1.5 .6 .6 .7 .5 6.7 Sv
.,
tot ye.ar 15
tot year 16
.9
1.0 1.4 .8 .3 .4 .6 .1 .5 6.1 Sv tot y e a r 17 26 18.045 interm 120 750 34 1.I 27 18.110 deep 105 850 29 .9 28 18.130 deep 120" 900 41 1.3 29 18.180 interm 160" 700 56 1.8 30 18.210 shallow 120 300 14 .4 31 18.267 subs 75 700 12 .4 32 18.300 shallow 120 500 23 .7 33 18.351 subs 80 500 10 .3 6.9 Sv tot year 18 34 19.035 deep 100" 850 27 .8 35 19.070 shallow 105 400 14 .4 36 19.110 deep 80* 850 17 .5 37 19.160 interm 120" 750 34 1.1 38 19.213 interm 100 700 22 .7 39 19.270 subs 90* 550 14 .4 40 19.315 interm 110" 800 30 1.0 4.9 Sv tot year 19 41 20.015 subs 80 800 16 .5 42 20.030 interm 130 350 19 .6 43 20.075 interm 120 750 34 1.1 44 20.120 interm 120 700 32 1 45 20.140 interm 105 750 26 .8 46 20.180 interm 150 300 21 .7 47 20.225 shallow 130 500 26 .8 48 20.300 subs 80 700 14 .4 49 20.315 interm 120 600 27 .9 6.8 Sv tot year 20 Ring number, date in which the ring is at 10~ type of ring, radius Of m a x i m u m velocity (km), depth-averaged radius, ring volume obtained with the ring depth and radius (106m3), and annualized ring volume transport (Sv). * Depth average radius of max vel different from upper radius. 1 Day and transport at 9~
397
Figure 11. a) Surface and b) subsurface (ao = 26.18) salinity for a day on which a ring is being generated (model year 14, day 330). c) map of locations in 4 subdomains, east (green) and west (blue) of 52~ in a region parallel to the coast containing the North Brazil Current and rings; east (pink) and west (red) of 52~ between the previous regions and 15~ (surface salinity contours indicated; year 14 day 330). d) TS diagrams for locations over the regions, each TS value is indicated with a + sign with color according to location as in c). Layer numbers are indicated; data from 3 model dates are included (day 330 of year 14, days 33 and 210 of year 15). e) TS diagrams for points in the southeast region (corresponding to the region of green crosses in c)) and reference profiles for 'southern' and 'northern' water (dashed lines labeled s and n, with low and high salinity respectively, layers 5-9). Same dates as in d). Density values and layer numbers are indicated.
of ring formation. At the surface (Figure 11 a), w a t e r from the south is actually saltier t h a n w a t e r n e a r the e a s t e r n Antilles, the horizontal salinity g r a d i e n t being reversed with respect to the subsurface (layer 5). This is due to excess precipitation along the latitudes of the ITCZ and to i n p u t of fresh Amazon river water. The river w a t e r is partially e n t r a i n e d in the rings p e r i p h e r y and can move offshore between
398 rings. The model T-S diagram for the region is shown in Figure 11 d, with colors indicating 4 regions as shown in Figure 11 c, for the same model date as in Figure 11 a,b. The T-S diagram shows that for the surface to layer 4 (a0=25.77), a distinct characteristic in the salinity signal can not be defined for each of the regions, and therefore it is not possible to identify from the diagram the origin of the modeled water masses. This is mainly due to the inversion of the horizontal salinity gradient with respect to that of the layers below, resulting from precipitation and Amazon river water induced-mixing. For model layers 5 through 9 (a0 between 26.18 and 27.22), which correspond to waters below the subsurface salinity maximum and above the intermediate water salinity minimum, it is apparent in the T-S diagram that the green region (hereafter referred to as the 'incoming region') has fresher salinity than the rest of the domain (Figure 11 d). We define 'southern water' ('ambient water') as the waters with lowest (highest) salinities for each layer in the incoming region. Reference T-S profiles (Figure 11 e) for 'southern water' and for 'ambient water' for layers 5 to 9 are then constructed by averaging the 10% lowest and highest salinities for each isopycnic layer in the incoming region for data from 3 different model dates (day 330 of year 14, days 33 and 210 of year 15) and obtaining the corresponding temperature from the layer density. The percentage of southern water inside a ring is then calculated by linearly interpolating in distance to the southern and ambient water profiles in T-S space: v / ( T - T,) 2 + ( S - S,) 2 + (S-
+
' Ti
+
-
where T, S, Ts, Tn, Ss, Sn are the temperature (salinity) of the point and those of the southern and ambient water reference profiles at the selected density, and the percentage of southern water is a • 100. Percentages 0 and 100% were assigned to points with S < Sn and S > Ss, respectively. Since the density isolines are close to linear, as seen in Figures 11 d,e, we found no significant difference in the results if the interpolation was instead done in either T or S alone. The volume of southern water carried by the ring between layers 5 and 9 was computed by integrating a over the volume of the ring. The volume of the ring is defined slightly differently than in section 5.1 and can include waters outside the radius of maximum velocity. The contributing layers were selected from horizontal maps and animations of salinity and southern water percentage. The horizontal areas of integration were chosen for each layer from the animations as the area trapped and advected by the ring. The total volume of southern water for layers 5-9 was then obtained by adding the grid volume multiplied by ~ (percentage of southern water divided by 100) over the contributing grid points. For the surface intensified rings, the volume for layers 1-4 (~ upper 150 meters) enclosed by the radius of maximum velocity was added to the water mass derived volume to give the total southern water volume. We illustrate this process by looking in more detail at rings in year 15. The percentage of southern water in layer 5 and below is shown in Figure 12 a for a
399
Figure 12. a)Percentage of southern water in ring 1 of the deep type, layers 5-9 (left; panels), and the same quantity in the region contributing to ring transport (right panels), together with velocity magnitude contours (contour interval 10 cm/s). Model date is year 15 day 33. Ring 1, two features that merge into ring 2, and ring 3, are indicated at layer 8 (R1, R2, R3). b) Same for ring 2 of the intermediate type, layers 5-8, model year 15 day 84. c) Same for ring 6 of the subsurface type, at year 15 day 252.
large ring centered at 10~ 57~ at year 15, day 33, which was generated just after the state shown in Figure 11 a,b. This ring (Figure 12 a, ring 1) is of the deep type and is the result of the merging of two smaller rings at previous times (it was counted as one ring in Table 2). It follows the trajectory in Figure 6c reaching 20~ east of the Lesser Antilles. For this ring, the southern water percentage has
400 Table 4 Water mass characteristics of the rings during day type layer 1 15.040 deep 9 2 15.085 interm 8 3 15.120 deep 9 4 15.160 interm 7 5 15.205 shallow+subs 6,8 6 15.2521 subs 3-8 7 15.315 interm 8 8 15.350 subs 3-9
year 15 vol transp transp kin 66 2.1 2.0 44 1.4 1.3 60 1.9 2.0 25 .8 .8 16 .5 .4 22 .7 .4 19 .6 .5 32 1.0 .7 9.0 Sv tot year 15 8.1 Sv Ring number; date in which the ring is at 10~ (except 1 at 9~ ring type; deeper ring layer (surface intensified rings) or upper and deeper ring layers (subsurface rings); volume of southern water (106m3); annualized ring transport of southern water (Sv); for comparison, ring volume from kinematic considerations as in Table 3.
relatively high values in regions extending beyond the radius of maximum velocity. Southern water percentage maps at later times (not shown) indicate t hat some areas with relatively high southern water content on the perimeter of the ring in layer 8 do not move with the ring (these areas were not included in the volume estimate). The percentage of southern water for a ring of intermediate type is shown in Figure 12 b, for year 15, day 84 (ring 2). This ring clearly has higher southern water percentage in the lower thermocline and upper intermediate layers (layers 7 and 8). Layers above (5 and 6) show a strong mixing of southern and ambient waters in the ring core, indicating a vigorous interleaving process in the rings that can lead to a complex vertical distribution of southern water transported by the rings. In the deeper layers, the ring resulted from the merging of two features that at day 33 were at 53~ (showing no surface signal) and 49~ (see Figure 12 b, layers 7 and 8). At later times, ring 2 follows a trajectory entering into the Caribbean through the mid Lesser Antilles passages. Also seen in Figure 12 b are two rings of the deep type: ring 1 (already discussed) at 14~ just to the east of the Lesser Antilles, and ring 3 at 52~ Ring 3 shows a core with very high southern water percentage in layers 5,6 and 8,9 (layer 9 not shown), but in layer 7 the core had a lower value, showing the complexity of the vertical coupling between the thermocline and the upper intermediate layers. Due to this low core in layer 7, the transport determined by the water mass method is slightly smaller than the value estimated by the kinematic method. A ring of the subsurface type is shown in Figure 12 c, at year 15, day 252 (ring 6). For this ring, the maximum velocity occurs in layer 6 (at about 200m), the southern water percentage is a maximum in layers 6-8, and the velocity isolines
401 Table 5 Estimation of water mass transport for all rings n transp avg T per ring
fact
transp wm
shallow 8 .6 .48 1. .6 interm 21 3.4 .98 1.1 3.7 deep 7 1.5 1.28 1.0 1.5 subs 13 1.1 .49 1.5 1.7 6 years tot 49 avg 6.6 Sv avg 7.5 Sv Estimation of water mass transport by renormalization of the kinematic transport according to the one year water mass results. The table lists type of ring; number of rings during the 6 model years; average annualized transport over the 6 years; average annualized transport per ring; factor to convert to water mass transport; total estimated water mass transport by all rings of the type, renormalized to one year (transp• Last row: totals 6 or averages for the 6 model years.
follow closely the sharply defined core of southern water. Due to mixing and diffusion, regions with anticyclonic motion in the periphery of the rings can have a relatively high southern water percentage, but do not necessarily move with the ring. The water mass calculation is laborious and, consequently, was done for only one model year (year 15). This year was chosen because it has the m a x i m u m number of rings and because at least one ring of each class was represented. The results are shown in Table 4. A total t r a n s p o r t of 9 Sv of southern water was thus obtained for year 15. 5.3. C o m p a r i s o n
of kinematic
and water mass methods
The ring transports for year 15 obtained from both methods are listed for comparison purposes in Table 4. The total of 9 Sv obtained for t h a t year with the water mass method is about 11% higher than the 8.1 Sv obtained with the kinematic method. Averaging the transports for each ring type, the differences between the water mass and kinematic method transports are about 12% for the intermediate rings, 0% for the deep rings, and 50% for the subsurface rings. The t r a n s p o r t s of the shallow rings are identical, by definition, for both methods. The results are listed in Table 5 (5th column), showing for each ring type the ratio between the average ring transports by the water mass and kinematic methods, as obtained from all rings of year 15. The subsurface rings show a larger difference between the two methods, attributable to the fact t h a t they tend to have a high southern water percentage extending farther from the radius of m a x i m u m velocity. For the other ring types, the southern water percentage has generally already decreased substantially from its core value at the radius of m a x i m u m velocity. Assuming that this comparison is representative, we now use the results of year 15 to estimate the southern water transport by rings in the remaining 5 years (years 16-20). The estimated water mass t r a n s p o r t for each ring is obtained by scaling the kinematic method t r a n s p o r t with the factor (ratio) corresponding to
402
Table 6 Transport of southern water by rings and mean meridional transport year Transp SW MT 15 9.2 17.0 16 7.9 16.7 17 7.2 17.9 18 7.7 17.4 19 5.6 17.0 20 7.8 17.5 avg 7.5 Sv 17.3 Sv For each year, estimated transport of southern water by rings, and annual mean meridional transport over the whole Atlantic from the surface to a0=27.22 (layer 9), at 5~
transport 20-, ,
,
,
,
,
,
1
,
,
'
9
i
15 r 5
o
"
"
1
L
2
3
1
4
6
7 month
8
9
10
11
12
Figure 13. Monthly distribution of the transport of southern water by rings at 10~ The transport average is the 7.5 Sv obtained for the ring transport. (The annualized ring transport for each month was multiplied by 12.)
each ring type described above. This results in an estimation of 7.5 Sv of southern water carried by the rings at 10~ for years 15-20 (Table 6). The difference between the two methods is on the order of 15%. Of these 7.5 Sv, we estimate that the upper 300 m transported by rings is 2.6 Sv. The same scaling is applied to obtain the monthly transport of southern water at 10~ averaged over the 6 years. Results are shown in Figure 13. The transport peaks during May due to deep and intermediate rings arriving at 10~ (see Figure 8), is small during August, September, October (during the period of low ring activity at that latitude), and is large in February due to intermediate and deep rings. The monthly distribution of southern water transport has a more pronounced variation than the monthly distribution of the number of generated rings of Figure 7a, due to the predominance of intermediate and deep ring generation during the first half of the year, which transport a larger volume of southern water than rings of shallow and subsurface type (see Figure 8).
403 6. D I S C U S S I O N AND C O N C L U S I O N S Results from a very high resolution North Atlantic simulation with the Miami Isopycnic Coordinate Ocean Model are analyzed and compared with published observations for the North Brazil Current and rings. The modeled mean and seasonal surface circulations show a good qualitative agreement with observations. The largest difference occurs for the NBC retroflection into the NECC in summer and fall: in the model 8 Sv continue westward of 48~ while observations suggest a complete retroflection, and the modeled NECC eastward flow is 15 Sv, 4 Sv weaker than observed. The excess NBC transport can be related to the model's relatively high meridional transport (about 3-5 Sv more intense than observed), while the weakness of the NECC could in part be attributable to the COADS climatological wind forcing. The model generates a variety of rings (which we classify as shallow, intermediate, deep, and subsurface), in an average of 8.3 rings of all types per year, of which 6 are surface-intensified, in good agreement with the altimetry-derived 5.7 rings per year (Goni and Johns, 2001). The modeled rings are generated in all seasons, with maximum ring activity in May and minimum activity in July. Surface intensified rings, with maximum velocity at the surface and depths between 200 and 900 m, are generated with a maximum in May and June and a minimum in the rest of the summer and fall. Rings of the subsurface type, with maximum velocity signal in the subsurface layers, are generated at an average rate of about 2 per year. They are smaller in size and have a larger percentage of southern water associated with them than rings of other types. Deep and subsurface rings are generated in non-overlapping seasons. Deep rings occur in winter and spring. Subsurface rings are generated in summer and fall, when the number of surface intensified rings is smaller, alternating with rings of the intermediate type. In winter, when the deep rings start to be generated, the incoming NBC at 44~ has a slightly greater intensity and larger vertical velocity gradient surface-500 m than in other seasons; the deep rings are also generated in the spring near the location of the subsurface retroflection into the NECC, at a time when the subsurface retroflections into the EU and the NECC are closer. Some subsurface rings result from the detachment of the deep part of a ring of the intermediate or deep type; the subsurface ring then moves more slowly and can merge with a successive ring, showing the complexity in the vertical coupling between the upper and lower layers. Surface intensified rings are mostly generated in the NBC surface retroflection region at latitude ~ 7~ Subsurface rings originate in two regions: the first one near or to the south of the subsurface retroflection of the NBC into the EUC, at 3~ and the second one near the surface NBC retroflection, at ~ 7~ The two regions of ring generation are similar to those found by Barnier et al. (2001). About 40% of the subsurface rings did not show any surface signal, some of them traveling at slower speed and nearer to the South American coast than rings of other types. Several dynamic studies seem to be relevant to the ring generation mechanisms operating in the model. Da Silveira et al. (1999) produced a meandering NBC retroflection, with their equivalent barotropic piecewise constant vorticity formula-
404 tion for the convergence of the northward flowing NBC with the weaker soutward flowing NEC in the presence of a westward tilted coast. Ma (1996) showed that NBC rings can be generated either as a consequence of the reflection of westward propagating equatorial Rossby wave packets deepening the thermocline, or during the spin up by wind forcing. Jochum and Malanotte-Rizzoli (2003) proposed independent formation mechanisms for shallow and subsurface rings. In their model, surface rings are produced by reflection of Rossby waves generated by an unstable NECC on the North Brazil coast. Subthermocline and intermediate water rings are generated by a different process, in which an intermediate western boundary current crossing the equator breaks down into vortices due to the presence of a thin boundary layer unable to provide, by friction, the necessary change in potential vorticity. Deep rings are interpreted as the merger of a surface ring with one of the intermediate rings. In our model, this type of generation for deep rings is indeed observed. At the intermediate water layers (a0 = 27.03 or 27.22), the flow breaks into rings with smaller radius than that of the surface rings, at latitudes ranging from the equator to 5~ Some of the modeled deep rings originate with a ring in the intermediate water layers, which later merges with a surface ring. The interaction between upper and lower flow in ring formation is reminiscent of the mechanisms proposed by Cherubin (2000). As in their study, nonlinear destabilization of the upper layer retroflection front by a lower layer vortex allows subsurface rings generated near the equator to acquire a surface signal when reaching latitudes of the surface retroflection. The model results show that ring formation processes in the NBC region are very complex, involving several processes and interactions between layers from the surface to the intermediate water. The formation of ring 1 of the deep type (formation stage shown in Figure 11 a,b, at 10~ in Figure 12a) involves a subsurface ring that acquired a surface signal at the surface retroflection, shortly followed by the detachment of a surface ring, advancing faster than the subsurface ring, merging, and forming the deep ring. The vertical dependence in the southern water content for this ring further indicates that the ring was formed by the merging of vertically separated ring signatures. For ring 3 of the deep type, the surface and subsurface fronts and an intermediate layer ring are initially aligned vertically. The subsurface front first follows the surface front, then couples with the intermediate ring and detaches, with all layers moving together but the surface detaching last. Ring 11 of the deep type is generated at the end of the winter before the surface retroflection disappears. Its formation starts with two surface signals formed at the retroflection, which merge on top of the next subsurface ring signature to form the deep ring. The results also suggest that further dynamic studies are needed to fully understand the mechanisms for the formation of the variety of rings present in the region. A major focus of this paper was on the determination of the amount of southern water that modeled rings trap and transport in their cores. The transport of water of southern origin by rings was estimated by integrating the southern water present in a region around the rings core that extends farther than the radius of maximum velocity. This resulted in an average value of 7.5 Sv of southern water
405 transported by rings of all types, or ~40% of the 17.3 Sv total meridional transport from the surface to the intermediate water layers (a0 = 27.22, layer 9, mean depth ~ 800 m). The southern water transported by the rings shows a complex vertical distribution, sometimes being contained in different percentages in the rings' subsurface and deep layers. The ring transport for individual years varied from 5.5 Sv to 9 Sv, even though the model was forced with seasonal climatological fields with no interannual variability. The annual mean zonally integrated meridional transport in the model also varies from year to year (Table 6). The transport of southern water by rings varies between 30% and 55% of the total meridional transport for a0 _< 27.22 for the 6 model years. Since most of the annual mean modeled meridional transport occurs in the western boundary, this is also the approximate relation between the transport by rings and the total western boundary transport. There is no obvious correlation between ring transport and total MOC transport in the 6 years analyzed at time scales of 1-2 years. However, results from a similar simulation that had a 40% higher overturning gave about 1.5 more rings per year of the surface intensified types (about 25% increase), suggesting that the number of rings is in part influenced by the MOC. According to Schmitz (1996), the upper branch of the MOC consists of 14 Sv of upper ocean water, with the return flow of 18 Sv of North Atlantic Deep Water balanced by the upper branch plus the deep flow of Antarctic Bottom Water. The model upper and intermediate meridional transport is more intense (3 and 5 Sv) than the observed upper branch and NADW values. It is therefore possible that the model slightly overestimates the ring transport of southern water, the extra ring activity being related to the higher MOC. The results confirm the complexity and importance of the North Brazil rings for the Atlantic interhemispheric transport of water. The agreement of these results with recent experimental ones presented by Johns et al. (2003) makes the present model suitable for further studies on ring generation processes and transport characteristics that cannot be accomplished by the use of observational data alone.
Acknowledgments The authors want to thank F. Schott and C. Rooth for discussions, R. Zantopp for comments and help in technical aspects, L. Smith for her careful reading of the manuscript, and two anonymous reviewers for their comments. This research was supported by NSF grants OCE-9531852 and ATM-9905210, and by NOAA/AOML. Computations were performed on the Department of Defense (DoD) computers at the Stennis Space Center under a challenge grant from the DoD High Performance Computer Modernization Office.
REFERENCES Arnault, S. and C.Le Provost. Regional identification in the tropical Atlantic Ocean of residual tide errors from an empirical orthogonal function analysis of TOPEX/POSEIDON altimetric data. J. Geophys. Res., 102, 21011-21036, 1997.
406 Barnier, B., T. Reynaud, A. Beckmann, C. Boning, J-M Molines, S. Barnard, and Y. Jia. On the seasonal variability and eddies in the North Brazil current: insight from model intercomparison experiments. J. Progress in Oceanogr., 44, 195-230, 2001. Bleck, R., C. Rooth, D. Hu, and L.T. Smith. Salinity-driven thermocline transients in a wind- and thermohaline-forced isopycnic coordinate model of the North Atlantic. J. Phys. Oceanogr., 22, 1486-1505, 1992. Bleck, R. and E. Chassignet. Simulating the oceanic circulation with isopycniccoordinate models. In: Majundar, S.K. (Ed.), The Oceans: Physical-Chemical Dynamics and Human Impact, 17-39, 1994. Borstad, G.A.. The influence of the meandering of the Guiana Current and Amazon River discharge on surface salinity near Barbados. J. Mar. Res., 40, 421434, 1982 Bourles, B., Y. Goriou and R. Chuchla. On the circulation in the upper layer of the western equatorial Atlantic. J. Geophys. Res., 104, C9, 21151-21170, 1999 a. Bourles, B., R.L. Molinari, E. Johns, W.D. Wilson and K.D. Leaman. Upper layer currents in the western tropical North Atlantic (1989-1991). J. Geophys. Res., 104, C1, 1361-1375, 1999 b. Bracco, A., E.P. Chassignet, Z.D. Garraffo, and A. Provenzale. Lagrangian velocity distributions in a high-resolution numerical simulation of the North Atlantic. J. Atmos. Ocean Tech., in press, 2003. Candela, J., R.C. Beardsley and R. Limeburner, 1992. Separation of tidal and subtidal currents in ship mounted acoustic Doppler current profiler (ADCP) observations. J. Geophys. Res., 97 (C1), 769-788, 1992. Carton, J.A. and Y. Chao. Caribbean Sea eddies from TOPEX/POSEIDON altimetry and a 1/6 ~ Atlantic Ocean model simulation. J. Geophys. Res., 104 (C4), 7743-7752, 1999. Chassignet, E.P., L.T. Smith, R. Bleck, and F.O. Bryan. A model comparison: Numerical simulations of the North and Equatorial Atlantic oceanic circulation in depth and isopycnic coordinates. J. Phys. Oceanogr., 26, 1849-1867, 1996. Chassignet, E.P., and Z.D. Garraffo. Viscosity parameterization and the Gulf Stream separation. In "From Stirring to Mixing in a Stratified Ocean ~. Proceedings 'Aha Huliko'a Hawaiian Winter Workshop. U. of Hawaii. January 15-19, 2001. P. Muller and D. Henderson, Eds., 37-41, 2001. Cherubin, L. Descriptive analysis of the hydrology and mixing of the Mediterranean outflow and effects of topography on the stability of the Mediterranean undercurrents. Ph.D thesis, Universite de la Mediterranee, Centre d'Oceanologie de Marseille, 343pp, 2000. Csanady, G.T.. A zero potential vorticity model of the North Brazilian Coastal Current. J. Mar. Res., 43, 553-579, 1985. Cowen, R. K., and L.R. Castro. Relation of coral reef fish larval distributions to island scale circulation around Barbados, West Indies. Bull. Mar. Sci., 54, 228-244, 1994.
407 da Silva, A.M, C.C. Young, and S. Levitus. Atlas of surface marine data 1994. Technical Report. National Oceanic and Atmospheric Administration, 1994. da Silveira, I.C.A., G.R. Flierl, and W.S. Brown. Dynamics of separating western boundary currents. J. Phys. Oceanogr., 29, 119-144, 1999. Didden, N. and F. Schott. Eddies in the North Brazil Current retroflection region observed by Geosat altimetry. J. Geophys. Res., 98, 20,121-20,131, 1993. Fratantoni, D.M., W.E. Johns and T.L. Townsend. Rings of the North Brazil Current: their structure and behavior inferred from observations and a numerical simulation. J. Geophys. Res., C6, 10,633-10,654, 1995. Fratantoni, D.M. and D. Glickson. North Brazil Current ring generation and evolution observed with SeaWiFS, J. Phys. Oceanogr., 32, 1058-1074, 2002. Garraffo, Z.D., A.J. Mariano, A. Griffa, C. Veneziani and E.P. Chassignet. Lagrangian data in a high-resolution numerical simulation of the North Atlantic. I. Comparison with in-situ drifter data. J. Mar. Syst., 29, 157-176, 2001 a. Garraffo, Z.D., A. Griffa, A.J. Mariano and E.P. Chassignet. Lagrangian data in a high-resolution numerical simulation of the North Atlantic. II. On the pseudo-Eulerian averaging of Lagrangian data. J. Mar. Syst., 29, 177-200, 2001 b. Garzoli, S.L. and E.J. Katz. The forced annual reversal of the North Atlantic Equatorial Countercurrent. J. Phys. Oceanogr. 13, 2082-2090, 1993. Goni, G.J., and W.E. Johns. A census of North Brazil current rings observed from TOPEX/Poseidon altimetry: 1992-1998. Geophys. Res. Lett., 28, 1-4, 2001. Gordon, A.. Interocean exchange of thermocline water. J. Geophys. Res., 91, 50375046, 1986. Gordon, A., R.F. Weiss, W.M. Smethie Jr, and M.J. Warner. Thermocline and intermediate water communication between the South Atlantic and Indian Oceans. J. Geophys. Res., 97, 7223-7240, 1992. Johns, W.E, S.L. Garzoli and G.J. Goni. Cross-gyre watermass transport by North Brazil Current Rings. In Interhermispheric Water Exchange in the Atlantic Ocean, Elsevier Oceanographic series, this volume, 2003. Johns, W.E., T.N. Lee, F.A. Schott, R.J. Zantopp and R.H. Evans. The North Brazil Current retroflection: seasonal structure and eddy variability. J. Geophys. Res., 95 (C12), 22,103-22,120, 1990. Johns, W.E., T.N. Lee, R.C. Beardsley, J. Candela, R. Limeburner and B. Castro. Annual cycle and variability of the North Brazil Current, J. Phys. Oceanogr. 28, 103-128, 1998. Johns, W.E, T.L. Townsend, D.M. Fratantoni, W.D. Wilson. On the Atlantic inflow to the Caribbean Sea. Deep Sea Research, 1 49, 211-243, 2002. Jochum, M. and P. Malanotte-Rizzoli. On the generation and importance of North Brazil Current rings, J. Mar. Res., 61,147-162, 2003. Katz, E.J.. An interannual study of the Atlantic North Equatorial Countercurrent. J. Phys. Oceanogr., 23, 116-123, 1993.
408 Kelly, P., Lwiza, R. Cowen and G. Goni. Low-salinity Lenses at Barbados, West Indies: Their Origin, Frequency and Variability. J. Geophys. Res., 105, 1969919708, 2000. Kraus, E.B. and J.S. Turner. A one-dimensional model of the seasonal thermocline: II. The general theory and its consequences. Tellus, 19, 98-106, 1967. Larsen, J.C.. Transport and heat flux of the Florida Current at 27~ derived from cross-stream voltages and profiling data: Theory and observations. Phil. Trans. of the Royal Society of London, 338, 169-236, 1992. Levitus, S.. Climatological Atlas of the World Ocean. NOAA Professional Paper 13, US Dept of Commerce, NOAA, 1982. Ma, H.. The dynam_ics of North Brazil Current retroflection eddies. J. Mar. Res., 54, 35-53, 1996. Mayer, D.A. and R.H. Weisberg. A description of COADS surface meteorological fields and the implied Sverdrup transports for the Atlantic Ocean from 30~ to 60~ J. Phys. Oceanogr., 23, 2201-2221, 1993. Murphy, S.J., H.E. Hurlburt and J.J. O'Brien. The connectivity of eddy variability in the Caribbean Sea, the Gulf of Mexico, and the Atlantic Ocean. J. Geophys. Res., 104 (C1), 1431-1453, 1999. OzgSkmen, T., E.P. Chassignet, and A. Paiva. Impact of wind forcing, bottom topography, and inertia on mid-latitude jet separation in a quasi-geostrophic model. J. Phys. Oceanogr., 27, 2460-2476, 1997. Richardson, P.L., and D. Walsh. Mapping climatological seasonal variations of surface currents in the tropical Atlantic using ship drifts. J. Geophys. Res., 91, 10537-10550, 1986. Richardson, P.L., and W.J. Schmitz. Deep cross-equatorial flow in the Atlantic measured with SOFAR floats, J. Geophys. Res., 98, 8371-8387, 1993. Richardson, P.L., G.E. Hufford, R. Limeburner, and W.S. Brown. North Brazil Current retroflection eddies. J. Geophys. Res., 99(C3) 5081-5093, 1994. Rintoul, S.. South Atlantic interbasin exchange. J. Geophys. Res., 96, 2675-2692, 1991. Simmons, H.L. and D. Nof. The squeezing of eddies through gaps. J. Phys. Oceanogr., 32, 314-335, 2002. Schott, F.A., J. Fischer and L. Stramma. Transports and pathways of the upperlayer circulation in the western tropical Atlantic, J. Phys. Oceanogr., 28, 19041928, 1998. Schmitz, W.J.. On the World Ocean circulation: Volume 1. Some Global features North Atlantic Circulation. Woods Hole Oceanographic Institution Technical Report, WHOI-96-03, June, 1996. Steve, D. M. and A. L. Brooks. Identification of Amazone River Water at Barbados, W. Indies, by Salinity and Silicate Measurements. Mar. Biol, 14, 343-348, 1972. Townsend, T., H.E. Hurlburt and P.J.Hogan. Modeled Sverdrup flow in the North Atlantic from 11 different wind stress climatologies. Dyn. Atmosph. Oc., 32, 373-417, 2000.
409 Wilson, D.W., W.E. Johns and S.L. Garzoli. Velocity structure of North Brazil Current rings, Geophys. Res. Lett., 29, doi=10.1029, 2002.
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Interhemispheric Water Exchange in the Atlantic Ocean edited by G.J. Goniand P. Malanotte-Rizzoli
9 2003 ElsevierB.V. All rightsreserved.
Cross-gyre transport by North Brazil Current rings William E. Johns a*, Rainer J. Zantopp a, and Gustavo. J. Goni b a Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Causeway, Miami, Florida 33149, USA. b National Oceanic and Atmospheric Administration, Atlantic Oceanographic and Meteorological Laboratory, Miami, Florida, USA. Recent observations collected as part of the North Brazil Current Rings Experiment are used to assess the role played by NBC rings in tropical to subtropical cross-gyre transport in the Atlantic Ocean. During the course of the 20 month experiment, four different NBC Rings were surveyed by ships and twelve additional rings were identified by moored current meters and temperature/salinity recorders. Of the total of 16 rings observed, four were subsurface-intensified rings with little or no surface signal. Except for these subsurface rings, generally good agreement was found in the identification of NBC rings during the experiment by various techniques including satellite altimetry, ocean color, and inverted echo sounders. The observations of water properties in the ring cores provided by the i n - s i t u temperature and salinity measurements are used to estimate the trapped core volumes of South Atlantic water in the rings. Based on these new measurements we estimate a ring formation rate of 8-9 rings per year, with no apparent seasonal variation in the formation rate. However, the surface rings show a seasonal cycle in their vertical penetration and associated trapped core volumes. Deeper rings tend to occur in fall and early winter, while shallower rings occur in spring and summer. The subsurface rings are usually smaller in diameter than the surface rings (average radius of maximum velocity 100 km versus 130 km), but have a thicker layer of trapped South Atlantic water and consequently a larger transport per ring. The average ring-induced transport including all ring types is about 1.1 Sv per ring, leading to an estimate of 9.3 Sv for the total annualized ring transport. This value is nearly twice that of most previous estimates, and suggests that NBC rings could account for more than half of the northward transport in the warm limb of the Atlantic meridional overturning cell.
*Corresponding author: Tel.: +1-305-361-4054, Email:
[email protected] 412 1. I N T R O D U C T I O N
The circulation in the western tropical Atlantic Ocean has a number of remarkable features, one of the most prominent being the seasonal retroflection of the North Brazil Current into the North Equatorial Countercurrent near 6 ~ N. It was discovered in the late 1980's that the North Brazil Current retroflection oscillated about its mean location along the western boundary in a semi-periodic manner, and that in association with this variability it shed large anticyclonic rings that moved northwestward along the boundary (Johns et al., 1990; Didden and Schott, 1993; Richardson et al., 1994). Since this discovery it has been suggested by many authors that NBC rings could play an important role in the net meridional transport of warm waters in the upper layers of the Atlantic Ocean as part of the meridional overturning circulation (MOC). A key issue in resolving the importance of the rings within the MOC is to quantify the amount of water of South Atlantic origin that they trap in their cores and carry with them into the North Atlantic. Early studies of NBC rings all suggested a similar amount of South Atlantic water transported by NBC rings, amounting to about 3 Sv on an annualized basis (Johns et al., 1990; Didden and Schott; 1993, Richardson et al, 1994; Fratantoni et al., 1995). However, these estimates were based on different assumptions about the number of rings shed in each year as well as the sizes and vertical structures of the rings. More recent studies have shown that a larger number of rings are shed each year than previously thought (Goni and Johns, 2001) and that NBC rings exhibit a surprising degree of variability in their vertical structures (Wilson et al., 2002). These fmdings have reopened the issue of the interhemispheric mass transport by the rings and cast into doubt some of the earlier estimates that had been based on very limited data. Foremost among the limitations of the earlier studies was a lack of in-situ sampling in NBC rings, which prevented a detailed assessment of the watermass properties of the rings and the volumes of South Atlantic water they trap and transport northward. The purpose of this work is to provide a first assessment of the amount of South Atlantic water contained in NBC rings that were observed by both ships and moored time series data as part of the 1998-2000 North Brazil Current Rings (NBCR) Experiment. The NBCR Experiment utilized a variety of observational techniques including shipboard hydrographic and ADCP surveys, moored current meters and IESs, floats and drifters, and remote sensing observations, to study the variability of the retroflection and the NBC ring generation process. A total of 16 different NBC rings were identified during the experiment, of which four were surveyed in detail by ship. The watermass properties observed in the rings are used herein to make the first quantitative estimates of the trapped core volumes of NBC rings, and are combined with new estimates of the ring formation rate to generate an updated estimate of the annualized South Atlantic water transport by NBC rings.
413 2. DATA AND M E T H O D S 2.1 S h i p b o a r d s u r v e y s Four cruises were conducted as part of the NBCR Experiment, which took place in (i) November-December 1998, (ii) February-March 1999, (iii)JanuaryFebruary 2000, and (iv) June 2000. Shipboard Acoustic Doppler Current Profiler (ADCP) surveys of the NBC retroflection and translating rings were made on each cruise, using a hull-mounted R.D. Instruments narrow-band 150 kHz ADCP. Conductivity-Temperature-Depth-Dissolved Oxygen (CTDO2) stations were occupied at selected locations along the cruise tracks using a dual Seabird 911+ pumped seawater system, and simultaneous lowered-ADCP (LADCP) direct velocity profiles were acquired at all stations from either a 150 or 300 kHz downward-looking ADCP mounted on the CTD package. The C T D O ~ C P profiles were collected to a maximum depth of 2000 m, or to within 10 m of the bottom in water depths less than 2000 m. Water samples were collected from a 24 bottle rosette sampler and analyzed for salinity and dissolved oxygen concentration, which were subsequently used to calibrate the CTDO2 profiles. Details of the data processing and calibrations are given in Fleurant et al. (2000a,b). During the cruises, four NBC rings were found in the region between 6 ~ 10 ~ N that had clearly detached from the retroflection. Each of these rings was surveyed with multiple shipboard ADCP transects and a closely spaced (20 kin) CTDO~CP section taken through the center of each ring (Figure 1). Initial results from these ring surveys have been described in Wilson et al. (2002). Of the four rings surveyed, two were strongly surface trapped (Rings 3 and 4, in February 1999 and June 2000, respectively; Figure. 1), with their identifiable velocity structure confined above 200 m. Another ring (Ring 1, December 1998) showed an unusual (and previously unobserved) vertical structure; its velocity core was located in the thermocline, at about 150 m, and the magnitude of the ring swirl velocity decreased both upward and downward from that level. The fourth ring (Ring 2, February 1999) presented a strong barotropic structure, with 2000 m velocities larger than 20 cm/s. All of the rings showed a relatively weak thermocline depression of only about 50-75 rn at their center, except for the subsurface ring, which had a reversed sense of displacement (a doming of the upper thermocline) due to its subsurface intensified nature, and a larger compensating depression of the deeper isopycnals (-10 ~ C) of nearly 200 m. 2.2 M o o r e d t i m e s e r i e s o b s e r v a t i o n s An array of 16 moored inverted echo sounders (IES) was deployed in retroflection region to monitor the zonal displacement of the NBC and formation of NBC rings (Figure 2). Initial results from the IES/PG array presented in Garzoli et al. (2002; this volume) and Garzoli et al. (2003).
the the are In
414
415 addition, two subsurface moorings with current meters and temperature-salinity recorders were deployed directly in the path of translating rings near 9 ~ N, 53 ~ W (Figure 2). The location for these moorings was chosen based on previous analysis of altimetric data and other available results to lie along the center of the mean translation track of NBC rings just after their separation from the retroflection. These time series provided vertical profiles of azimuthal velocity and watermass properties as rings translated past the location of the moorings. The two moorings were deployed side by side within 3 km of each other (Figure 3). One mooring provided current m e a s u r e m e n t s from 8 conventional current meters (Vector Averaging C u r r e n t Meters; VACMs) topped by an u p w a r d looking 150 kHz ADCP mounted at 250 m; the other mooring provided temperature and salinity time series in the upper ocean between depths of 50 to 1000 m from an array of 10 Seabird Seacat and Microcat recorders. Pressure values were recorded by each of the Seacat/Microcats and a pressure gauge at the top of the current meter mooring to keep track of mooring motion and the m e a s u r e m e n t depths of the sensors. Maximum vertical excursions of the moorings were 160 m during two short-term events with smaller r.m.s, values of about 30 m. The entire moored array was deployed for a 20-month period from November 1998 to J u n e 2000 (except for the PG t h a t was deployed in February 1999). The overall data return from the moored array was excellent. Full d a t a records were obtained from all of the IESs and all of the current meters including the upward looking ADCP at the top of the CM mooring. On the adjacent CTD mooring, one sensor failed (at 100 m nominal depth), and two others had short records that ended about mid-way through the deployment. The remaining sensors returned full records and the CTD sensors showed no obvious salinity drift due to biofouling (a t e s t a m e n t to the effectiveness of the anti-biofouling tubing used on the conductivity cells). As a result, the current meter and CTD moorings provide a unique record of the velocity and watermass structure of more than a dozen NBC rings that passed over the mooring site. Figure 4 shows the time series of the vector velocity ("stick" plots) from the upper levels of the current meter mooring, in which the signatures of NBC rings are shown by the reversals in flow from an offshore to onshore direction as the rings pass over the mooring location. In Figure 2 the tracks of NBC rings identified from satellite
Figure 1. Top panels: Velocity vectors along the cruise track at 150 m (Ring 1) and at 12 m (Rings 2-4) derived from 150 kHz hull-mounted ADCP on the R/V Seward Johnson during cruises in December 1998 (Ring 1), February 1999 (Rings 2 and 3), and June 2000 (Ring 4). The locations of the rings are shown by shaded circles. Lower Panels: Tangential velocity and temperature along cross-ring sections (Rings 1-4 ,from left to right) shown by the bold lines in the upper panels. The velocities are based on LADCP data below 30m and shipboard ADCP data from 8-30 m. Velocity contour level is 20 cm/s; temperature contour level is 5oC and inverted triangles on top of each section denote the location of CTD stations (after Wilson et al., 2002).
416
Figure 2. Tracks of NBC rings identified by altimetry during the period of the NBCR Experiment. The numbers on the tracks correspond to the rings listed in Table 2. The symbols indicate the locations of the CM/CTD mooring pair (circle), the array of inverted echo sounders (triangles), and bottom pressure gauge deployed on the Brazilan shelf (square).
altimetry during the experiment are superimposed on the moored a r r a y sites, showing t h a t most of the rings passed very close to the CM/CTD mooring site. 2.3 W a t e r m a s s i d e n t i f i c a t i o n
In the remainder of this paper we will use w a t e r m a s s characteristics to distinguish between thermocline waters in the study region t h a t are of South Atlantic and North Atlantic origin. Waters of South Atlantic origin crossing the equator in the NBC carry a distinctive T/S/O2 signature, being relatively fresher and higher in dissolved oxygen compared to waters from the North Atlantic on the same density surfaces (Wrist, 1964; Emery and Dewar, 1982; Schmitz and Richardson, 1991; Wilson et al, 1994; Bourles et al., 1998). Rings t h a t pinch off from the NBC retroflection are expected to carry waters with this South Atlantic signature into the North Atlantic and therefore have anomalous properties with respect to the surrounding waters. Traditionally, temperature-salinity (T-S) diagrams are a common tool used for water mass identification. An equivalent approach t h a t contains the same information is to plot salinity versus sigma-theta (S-ce), which is more convenient for the purposes of this paper. Figure 5 shows a scatter pl0t of S-ce from the more t h a n 200 CTD casts collected in the study region during the four
417 cruises. All the curves have the same general characteristics: a salinity m a x i m u m in the u p p e r thermocline located between a0 = 24.5 to 25.5 (-100-150 m), corresponding to Subtropical U n d e r w a t e r s (SUW) t h a t are formed in both hemispheres, a n d an i n t e r m e d i a t e salinity m i n i m u m at ao - 27.25 ( - 8 0 0 m) t h a t corresponds to Antarctic I n t e r m e d i a t e W a t e r s (AAIW), or S u b a n t a r c t i c Mode Waters, t h a t are formed in the s o u t h e r n hemisphere. Deeper in the w a t e r column the salinity increases again to a m a x i m u m corresponding to N o r t h Atlantic Deep W a t e r (NADW), a n d t h e n toward the fresher Antarctic Bottom Waters (AABW). Superimposed on the plot are S- (~0 curves from Levitus (1982) t h a t show the climatological w a t e r m a s s properties at a point on the e q u a t o r n e a r the w e s t e r n b o u n d a r y (0 o, 40oW), and at a point in the w e s t e r n N o r t h Atlantic n o r t h of the NBC retroflection (13 ~ N, 50 ~ W). These curves show t h a t the w a t e r s originating from the S o u t h Atlantic are fresher on all density surfaces from the AAIW up to n e a r the sea surface (a~ - 24.0). In the surface
Figure 3. Instrument configuration on the pair of subsurface moorings deployed along the NBC ring translation path. The current meter mooring (CMM1) had conventional current meters at 8 levels through the water column and an upward-looking ADCP profiling to the surface. The CTD mooring (CMM2) had Seabird Microcat and Seacat temperature-salinity-pressure recorders at 10 levels through the upper 1000 m.
418
layer above ~0 = 24.0 this distinction breaks down, owing to the freshwater input to the surface layers north of the equator by precipitation u n d e r the ITCZ a n d additional large freshwater inputs from the Amazon River. To obtain w a t e r m a s s "endpoints" t h a t are representative of South and North Atlantic source waters, we use our own CTD data and construct m e a n S-~e curves from the data t h a t are given by the m e a n of the highest 10% and lowest 10% of the salinity values observed on each density surface. T h a t is, for a n y given density surface, a "southern" endpoint is constructed by averaging the 10% lowest salinity values observed from all CTD casts, and a "northern" endpoint is constructed from an average of the 10% highest salinities t h a t are observed on t h a t density surface. The CTD casts collected during the program extend from the equator to 13 ~ N and provide a representative sampling of the w a t e r
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Figure 4. Current vectors from five levels (50 to ,tO0 m) on the CM moonng located in
the ring translation corridor. The vectors are rotated 25 degrees from east so that "up" is 025 ~ T, which is normal to the average direction of ring translation. The surface rings that formed during the experiment and passed over the mooring site are labeled chronologically at the top.
419 masses in the region from different seasons. The resulting "endpoint" S-ae curves are shown in Figure 5 along with their • s t a n d a r d deviation envelopes. The southern endpoint closely follows the southern Levitus curve, while the n o r t h e r n endpoint is saltier t h a n the northern Levitus curve. This probably indicates t h a t the Levitus curve from 13oN already includes a mixture of n o r t h e r n and southern source waters. These endpoint S-ae curves are then used to determine the percentage of South Atlantic Water (SAW) contained in any particular CTD cast. Denoting the northern and southern endpoint curves by SN and Ss, respectively, the percentage of SAW on any density surface with a
Figure 5. Watermass S-oe "endpoints" representative of South Atlantic and North Atlantic water properties (green curves) derived from the ensemble of CTD profiles collected during the NBC Rings Experiment (shown by scatter). The shaded envelopes show the one-standard deviation envelopes of the endpoint watermass curves. The red lines are taken from the to Levitus climatology at 0~ 40~ ("South") and 13~ 50oW ("North").
420 salinity value S is simply proportional to the inverse linear distance from the endpoint curves: SAW% = (SN-S) / (SN-SS).100
(1)
This procedure is assumed to be valid for all density surfaces between the AAIW level (a0 =27.2) and the top of the main thermocline (a0 =24.5), but is not applied above a0 =24.5 due to the ambiguity in defming the water mass source above that level. If the observed salinity value is higher or lower than the endpoint curves within the a0 =24.5 to 27.2 range, we assign it to be "pure" (i.e., 100%) northern or southern source water, respectively. In general, any particular CTD cast in the region will have a variable percentage of SAW through the water column as the two water masses interleave and mix. A similar approach can be developed using dissolved oxygen data, where the South Atlantic waters exhibit high dissolved oxygen content compared to North Atlantic waters. Qualitatively this yields similar results, however, since the dissolved oxygen concentration is non-conservative this approach is less quantitative. Also, we wish to apply this same approach to the moored CTD time series observations, where only T-S data is available, therefore for consistency we use the above approach based on the S-~0 relationship.
3. R E S U L T S 3.1 Surveyed rings During the four research cruises conducted as part of the NBC Rings Experiment, four NBC rings were found and surveyed (Table 1). During the first cruise (November 7 - December 11, 1998) one ring was found (Ring 1); during the second cruise (February 6 - March 9, 1999) two rings were found (Rings 2 and 3), and during the fourth cruise (June 7-23, 2000) one additional ring was found (Ring 4). A fifth ring was observed to nearly pinch off from the retroflection on the third cruise (January 29 - February 24, 2000), but it failed to pinch off in time to be considered a fully separated ring. Examples of the C T D O 2 ~ C P sections taken across two of the rings (Rings 1 and 2) are shown in Figure 6, which is used to determine the deep flow structure and watermass characteristics in the rings. For Ring 1, 11 stations were taken in a SE-NW direction across the diameter of the ring, extending from both edges of the ring where the swirl velocities decreased below about 15 cm/s. This ring was the only subsurface ring to be surveyed by ship, and due to its unusual vertical structure it was only confirmed as an NBC ring after its watermass signatures were examined. The S-a0 curves for these stations (Figure 6, bottom right panel) show water properties predominantly of North Atlantic origin near the periphery of the ring and South Atlantic origin near the ring core. Stations 62-64 near the ring core all have a very strong SAW signature
421 from aA = 24.5 to 27.0 (approximately 50-500 m). Stations farther out from the center but inside the radius of maximum velocity of the ring (indicated by the inner circle drawn in Figure 6, top left panel) also show strong SAW characteristics but over a smaller depth or density range than the core stations. Ring 2 (Figure. 6, right panel), which was a more typical surface-intensified ring but with a deep-reaching velocity structure, was sampled by 14 stations across the diameter of the ring. The stations near the center of this ring also show strong SAW characteristics, but in contrast to Ring 1 these strong characteristics are more confined to the surface layers, above ~e-26.0. Deeper in the water column, below a~= 26.5, SAW characteristics again become evident at the core stations with considerable interleaving of North Atlantic waters. To quantify the amount of SAW contained in the rings, the percentage of SAW at each station as determined by the procedure outlined above was integrated over the total volume of each ring. The limits of the integration are
Figure 6. Near-surface (20 m) current vectors from shipboard ADCP for Rings 1 (left panels) and 2 (right panels), showing locations of CTD/LADCP stations across the ring (top), and S-o~ u~profiles for the ring CTD stations (bottom), superimposed on the South Atlantic and North Atlantic watermass curves from Figure. 5.
422 set by the physical characteristics of the ring, which were defined as follows. The edge radius of the ring is defined as the location where the swirl velocity at the core depth of the ring drops below a value of 15 ChriS, averaged around the perimeter of the ring. (The core depth of the ring is the depth where the swirl velocity of the ring is a m a x i m u m - usually at the surface except for subsurface rings.) The radius of maximum velocity (hereafter rmax) is the average distance from center of the ring to the maximum swirl velocity, again averaged around the ring at the core depth. The vertical penetration, or depth limit, of the ring is defined as the depth below which the swirl velocity drops to less than 10 cm/s. An upper limit may also exist for subsurface rings. The choices of the velocity cutoffs for the outer edge (15 cm/s) and vertical penetration (10 cm/s) of the rings are made to ensure that only waters that are circulating with the ring are included in the ring volume calculations. Integration of the SAW volume of each ring is then carried out over limits set by the vertical scale and the edge radius of the ring. For depths in the rings shallower than the a0=24.5 surface (~50-100 m), the percentage of SAW determined at the c0=24.5 surface for each station is assumed to remain constant to the surface. Since the South and North Atlantic waters are indistinguishable above this level from their T-S properties, we are thus assuming that the near surface waters circulating in the cores of surface-intensified rings have SAW percentages at least as high as those in the layers immediately below. For rings that penetrate deeper than 1000 m (of which we observed only one), the integration is stopped at 1000 m, since we are concerned only with the transport of upper ocean waters (at the AAIW level and above) by the rings. Usually only one full section was taken through each ring, and therefore an assumption about the geometry of the rings is needed. In the following calculations we assumed a semicircular symmetry for the rings, such that the section taken across a diameter of each ring samples two "halves" of the ring. Each station at a particular radial distance from the center of the ring is therefore assumed to be representative of the water properties on that side of the ring. Most of the rings observed appeared to be nearly circular in shape, which supports this assumption. However, not all of the rings show a symmetric distribution of SAW percentage across the ring, and the above method allows a better estimate of the volume of SAW in a ring to be obtained than could be made from a single radial section. Examples of the SAW distribution across Rings 1 and 2 and the associated ring velocity structures are shown in Figure 7 . In Ring 1 the ring swirl velocity is a maximum at 150 m and it extends to almost 600 m before dropping to insignificant values. Waters with SAW percentage in excess of 90% are found throughout the core of the ring from depths of 150 m to greater than 500 m. Near the surface the SAW percentage is smaller which is consistent with the subsurface intensified structure of the ring. A close correspondence can be seen between the horizontal limits of the SAW distribution and the location of the swirl velocity maximum (rm~), which is typical of most of the rings observed.
423 Significant amounts of SAW are also found below the ring, but since these waters are not clearly rotating with the ring they are excluded from the SAW volume calculation. Ring 2 has a very different distribution of SAW but one that also closely follows the velocity distribution of the ring. In the surface layers the SAW percentage is relatively high, between 60-90% (which is mostly extrapolated upward from the ~0 =24.5 level), and the edges of the SAW distribution coincide with the swirl velocity maxima. Deeper in the water column the ring has a smaller diameter than at the surface and the SAW distribution similarly contracts to occupy mostly the core region between the deep swirl velocity maxima. Relatively high amounts of SAW are found in the ring core to depths including the AAIW layer. Just below the surface layer, at about 200 m, there is a thin layer of lower SAW percentage across the whole ring that appears to separate the upper and lower cores. This layer occurs at the base of the strongest vertical shear in the upper part of the ring and suggests that enhanced mixing of North Atlantic waters into the core of the ring may be occurring there. Rings 3 and 4 (not shown) were surface-intensified rings like Ring 2 but penetrated less deeply than Ring 2, to depths of approximately 400 m and 200 m, respectively (Table 1). The parameters for all four of the ship-surveyed rings are listed in Table 1, along with the volume of SAW they contain according to the integration procedure described above. The volume of SAW contained in each ring can also be expressed in terms of an equivalent "annualized" volume transport associated with each ring (the last column of Table 1), which is simply the volume of SAW in the ring divided by the number of seconds in one year. Of the four rings, Ring 2 had the largest volume of SAW (4.6 x 1013 m 3, or an annualized transport of 1.5 Sv) and Ring 4 had the smallest volume (2.1 x 1013 m 3, or 0.7 Sv; Table 1). Ring 3 contained nearly as much SAW volume as Ring 2, even though it penetrated much less deeply and had a slightly smaller r~ax (150 km vs. 160 kin). This was due to a larger amount of SAW in the outer parts of Ring 3 beyond rmax, which could be related to the fact that Ring 3 was "younger" when surveyed and may have had less mixing of North Atlantic waters occur on its periphery than for Ring 2. This points up one of the issues with quantification of the SAW volumes carried in these rings; that the surveys can be completed at different stages in the rings' lifetimes. Rings that are older may have already lost considerable amounts of SAW to mixing compared to the time they were formed. Ring 1 also contained a SAW volume similar to that of Ring 2 (and Ring 3), owing to the thick layer of nearly pure SAW in its core, even though its rm~ was substantially smaller (100 kin) than that of the other rings.
3.2 Rings identified by moorings From the moored CM/CTD data we were able to identify 14 anticyclonic features that passed over the mooring site during the period of the observations Figure 8; see also Figure 4). Based on comparisons with the IES and altimetric
424 observations and the in-situ water mass properties we interpret all of these features to be NBC rings. (Note that the rings observed by the moorings are labeled chronologically, and independently, of the ship-surveyed rings, and are denoted by the prefLx "R" hereafter to avoid confusion.) Of the 14 rings observed by the moorings, 11 had a strong surface signature and could also be identified in the IES and/or altimetry data (Garzoli et al., 2002; Goni and Johns, 2002), while 3 were subsurface rings (labeled with an "a" in Figure 8) that had no clear surface signature. These features appear to be variants of the single subsurfaceintensified ring we found and surveyed on the first project cruise (Ring 1 above), which had pinched off before the moored array was first deployed. (The signature of that ring can be seen at the very beginning of the CM record, where only the onshore flow associated with the trailing edge of the ring was observed.). A similar approach to that used in the surveyed rings is applied here to the moored CM/CTD data to estimate the SAW volumes carried in these rings. We use the IES data to determine the average translation speeds of the rings as they pass by the mooring location, which allows the mooring data to be cast in terms of virtual "sections" through each ring. Although this method is more approximate than the estimates derived for the ship-surveyed rings, it greatly increases the sample ring population and helps us to arrive at better statistics and more reliable estimates of the average SAW transport carried by the rings. The steps in the procedure are as follows: 1. Synoptic maps of thermocline depth derived from the IES array (Garzoli et al., 2002) are used to determine the average translation speed of each ring during the time period it passes over the mooring (Table 2). The time series data from the CM and 2. CTD moorings are then mapped into a spatial coordinate relative to the "center" of each feature (which is defined by the reversal in cross-shore velocity component). 3. The SAW percentage at each moored CTD sensor is determined in the same manner as for the shipboard CTD profiles, although this calculation can now only be performed at the discrete depths where the sensors were located. A vertical profile of SAW percentage is then created by linear interpolation (in density coordinate) of the SAW percentage observed at the various sensors. This profile is then mapped into a depth coordinate using the known depths of the sensors. 4. The SAW volume is integrated over the volume of each feature, using the same definitions and procedures defined for the ship-surveyed rings. For the subsurface rings we do not have an independent estimate of their translation speeds, and so we assign a translation speed to them equal to the average translation speed of the surface rings (12.5 kin/d). This is really only a guess but it yields rm~ values for these features in the range of 90-105 km, consistent with the observed rm~ of the one subsurface ring surveyed by ship
425
Figure 7. Cross-sections of tangential velocity (top) and South Atlantic Water percentage (bottom) of ship-surveyed Ring 1 (left) and Ring 2 (right). The dashed lines show oo surfaces across the ring. The dashed lines show oo surfaces across the ring.
426 Table 1. Ring parameters for the NBC rings surveyed during the cruises. The last two columns refer to the volume and associated transport of South Atlantic waters in each ring.
Ring
Date surveyed
Vertical penetration (m)
1 2 3 4
09-Dec-98 12-Feb-99 18-Feb-99 12-Jun-00
50-580 0-2000 0-350 0-200
Radius of max velocity (kin) 100 160 150 150
Volume (1013m3 )
Annualized transport (Sv)
4.1 4.6 4.4 2.1
1.3 1.5 1.4 0.7
(100 km). The one additional difficulty associated with this method is the uncertainty in the track of each ring and how closely the ring centers pass to the mooring site. Some information can be gained from the altimetry and IES data on how close the center of the rings pass to the mooring site, but the absolute accuracy of the ring center location and its track derived from either method is probably not better than 50 km. The tracks derived from altimetry (see Figure. 2) as well as IES nevertheless suggest that all but three of the rings passed within 50 km of the CM/CTD mooring site. The proximity of the rings to the mooring site can also be inferred from the moored current meter data itself by the sense of rotation of the current vectors as the rings pass by it. A rotation of the current vectors in a clockwise direction indicates a passage of the ring center shoreward of the mooring location; likewise a counterclockwise rotation of the vectors indicates a passage of the ring center to the seaward side of the mooring site (Figure 9). The distance by which the ring center misses the mooring site can also be inferred to some extent from the current vectors. For example, a circularly symmetric ring passing to the shoreward side of the mooring site at a distance equal to the rmax of the ring will produce current vectors that increase to a maximum strength in the SE direction (i.e., in the direction of the swirl velocity on the "right" side of the ring) as the ring center passes, and during the entire passage of the ring the vectors will always exhibit this SE component superimposed on the reversing onshore/offshore flow (see Figure 9). The opposite occurs for a passage of the ring center a distance of rmax to the seaward side of the mooring location. In Figure 4 it can be observed that most of the ring passage events show a clockwise rotation of the current vectors, indicating that most of the rings passed slightly shoreward of the mooring location. An exception is moored ring 2 (R2 in Figure. 4), which displays an anticlockwise rotation as the ring passes. Certain
427
Figure 8. Offshore velocity (25~ T) component at the CM mooring, contoured as a function of depth to 1400 m. The 14 rings identified from the record are labeled by consecutive numbers (1 11) for the surface rings, and 3a, 6a, and 10a for the subsurface rings. The approximate depth limits of the rings are indicated by the boxes drawn around each feature. Note the depth scale change at 200 m.
of the rings (e.g., R5, R8) appear to have passed considerably inshore of the mooring site, at a distance of order rma~ according to their velocity signatures. However, most of the rings passed very close to the mooring site according to their velocity signatures, and all but R5 and R8 passed well within a distance of rma~ from their centers. Examples of the velocity structure and SAW percentage in three of the rings observed by the mooring are shown in Figure 10. Moored ring 1 (R1), shown in Figure 10 (left panel), is the same ring that was surveyed by ship on 12 February 1999 (ship Ring 2, see Figure 7, right panel). The ring center passed over the mooring site on 11 J a n u a r y 1999, which was about a month before it was surveyed by the ship. A direct comparison of the two figures shows that there are some significant differences between the two realizations. While the velocity distribution in the upper 150 m is similar in both pictures, the signature of the ring in the moored data lacks the deeply penetrating velocity structure found in the shipboard survey. Another difference is that the shoreward flow on the trailing side of the ring at depths of 200-500 m is shifted forward in the ring so that it nearly underlies the surface center of the ring. This suggests that near
428 Table 2. Ring parameters for the NBC rings observed by the current meter and CTD moorings. The last two columns refer to the volume and transport of South Atlantic waters in each ring.
Ring
Date
Vertical penetration (m)
1 2 3 3a 4 5 6 6a 7 8 9 10 10a 11
11-Jan-99 21-Feb-99 08-Apr-99 31-Mar-99 14-May-99 05-Jul-99 05-Sep-99 19-Sep-99 07-Nov-99 30-Dec-99 02-Feb-00 01-Apr-00 14-Apr-00 IS-May-00
0-500 0-600 0-200 200-1000 0-200 0-180 0-120 120-800 0-800 50-500 0-250 0-130 250-1000 0-180
Radius of max velocity (kin) 150 160 100 90 95 120 150 105 145 150 85 100 105 140
Volume (1013m 3)
Annualized Transport (Sv)
3.9 5.4 1.3 5.7 0.7 0.6 1.6 5.3 7.2 5.0 0.9 0.8 6.6 1.9
1.2 1.7 0.4 1.8 0.2 0.2 0.5 1.7 2.3 1.6 0.3 0.3 2.1 0.6
the time of its formation the vertical axis of the ring may have been tilted forward with depth in the direction of motion of the ring. According to our criteria for the penetration depth of the rings, the penetration depth of R1 is only 500 m, compared to 2000 m (or more) for the ship-surveyed ring. The only reasonable explanation we can give for this difference is t h a t the ring must have evolved to a more barotropic structure after it pinched off from the retroflection; t h a t is, a deep component of anticyclonic circulation was somehow spun up under the ring. The SAW distribution is also different in the two realizations, showing a large mass of high SAW percentage on the forward side of R1 at subsurface levels t h a t is mostly outside of the circulation of the ring. Other features of the SAW distribution are similar, including the high SAW percentages in the upper core, the suggestion of interleaving of North Atlantic waters just below this level, and the waters with high SAW percentage found at depth under the ring core. It is interesting t h a t there is a significant a m o u n t of SAW in the deeper layers below the main circulation of the ring at the time it was formed, but it is not clear why this occurs. It appears likely t h a t this water was entrained into the deep circulation of the ring as it spun up and was carried northward with the ring. The SAW volume estimate we derive for R1 is 3.9 x 1013 m 3 (or 1.2 Sv; Table 2), which is, surprisingly, only about 15% smaller t h a n the estimate derived from
429 the shipboard survey. This agreement results from the relatively higher percentages of SAW in the subsurface layers on the n o r t h e r n side of R1, t h a t compensate partly for the smaller vertical penetration of R1. This level of agreement m a y be fortuitous given the differences in the two observed structures and it illustrates some of the u n c e r t a i n t y t h a t is involved in estimating the trapped core volumes of the rings. The other ring sampled by both moorings and ship was moored ring 2 (R2), which is ship-surveyed Ring 3. In contrast to the above case, this ring was sampled at very nearly the same time by both methods (the ship survey occurred within 3 days of when the ring center passed the mooring site), and the results of the two realizations are in much closer agreement. The structure and SAW distribution of R2 are shown in Figure 10 (center panels). The strong circulation in the ring is mostly trapped to the upper 200 m, with an overall vertical penetration to 600 m according to our velocity criteria. The w a t e r m a s s distribution shows a high percentage of SAW in the ring core extending from the surface layers to depths of about 800 m. Again there are significant amounts of SAW in the core of the ring below our strict cutoff definition of the penetration depth of the ring, which may in fact be weakly circulating as part of the ring. It is possible t h a t our criterion for ~significant" mean swirl velocity at the base of the ring (10 cm/s) is too restrictive and may be excluding some of the
Figure 9. Schematic illustration of a circularly symmetric, anticyclonic ring with a radius of maximum velocity (Rmax) of 100 km. The dark arrows indicate the patterns of current variation that would be observed at a fixed measurement site if the ring passed directly over the site (central line), or if it passed shoreward (top line; +Rmax) or seaward (bottom line; -Rmax) of the site a distance of Rmax from the ring center.
430 SAW t h a t is transported in some rings. However, we prefer to be conservative in this choice so t h a t only waters t h a t are clearly circulating in the ring are included in the volume integration. The shipboard survey of this ring (not shown) is very similar to t h a t shown in Figure 10 (center panels) except t h a t the deeper tails of the velocity structure are somewhat weaker, which results in an official penetration depth of 350 m for this ring based on our criteria. This illustrates again some of the difficulty in defming an unambiguous penetration depth of the rings based on their velocity structures. Accordingly, the calculated SAW volume of R2 derived from the moored data is higher t h a n t h a t estimated from the shipboard survey (5.4 x 1013 m3 versus 4.4 x 1013 m3; Tables 1 and 2). Finally, we show in Figure 10 (right panels) the structure and SAW distribution of one of the subsurface rings observed by the moorings (R3a; Figure 8). This feature occurred in close proximity to a surface-intensified ring (R3), and it is not completely clear w h e t h e r these are separate features or if they are physically coupled. However, there is a clear m i n i m u m in velocity at about 200 m depth and a lateral offset of about 100 km between the surface and deep velocity cores, which leads us to believe they are distinct features. The other subsurface features t h a t occurred in the record (R6a and R10a) also seemed to be paired with nearby shallow, surface-intensified rings but again appear to be distinct features. The SAW distribution for ring R3a shows a definite core of SAW t h a t is enclosed within the subsurface swirl velocity maxima centered at about 800 m and t h a t fills the water column between 200-1000 m. In the overlying ring (R3) the SAW distribution is actually less well defined t h a n in the subsurface ring and it appears to separated from the subsurface ring by an intruding layer of North Atlantic water. The volume of SAW in the subsurface ring (R3a) is calculated to be 5.7 x 10 is m s (or 1.7 Sv; Table 2) whereas the surface ring (R3) has a much smaller SAW volume of 1.3 x 10 is mS (or 0.4 Sv). The weaker and more disorganized SAW signature of the surface ring R3 is characteristic of the other shallow and relatively small diameter rings t h a t occur later in the record (i.e., rings R4, R5, R9, and R10), which, interestingly, are all formed in the F e b r u a r y to July time frame. The ring parameters and SAW volume estimates for all of the rings observed by the moorings are summarized in Table 2. The values of rm~ estimated for the surface rings vary from 85 to 160 km, while those for the three subsurface rings are from 90 to 105 kin. The observed rmax values of the surface rings suggests a bimodal size distribution of the surface rings with a tendency
Figure 10 (next page). Cross-sections of tangential velocity (top) and South Atlantic Water percentage (bottom) of rings R1 (left panels), R2 (center panels) and R3a (right panels) observed by moorings. The dashed lines show oo surfaces across the ring. The SAW percentage in the lower figure is shown only below the level of the uppermost CTD instrument on the mooring, and it is assumed to be constant from that level to the surface. The dashed lines show o0 surfaces across the ring.
431
432 for formation of either "large" rings (with typical rmax of 150 kin) or "small" rings (with a typical rmax of 100 km). As noted above, this distribution also tends to be seasonal, with the large (and more deeply penetrating) rings forming during the fall and early winter months. It is difficult to place precise error bounds on our SAW volume estimates for the rings, as a variety of uncertainties come into play, including the def'mitions of the "endpoint" watermass curves, the ambiguity in defining the cutoff depths for the SAW volume calculation, possible ring asymmetries, the m a n n e r in which the moorings slice the rings, and the differences found between rings that were sampled by both methods. We estimate an overall uncertainty of -+30% for the SAW volume of the individual rings surveyed by ship, and up to -+50 % for rings sampled by the moorings. The large population of rings observed by the two methods however helps to compensate for errors in estimating the SAW volume carried by the individual rings.
3.3 Cross-gyre transport by NBC rings A summary of the rings observed by the moorings is given in Table 3, and a summary of all rings observed by ship and moorings during the experiment is given in Table 4. If we consider first the moored observations only and sum the individual ring SAW transports for the 14 rings observed, the total SAW transport over the 20 months of the moored record is 14.9 Sv. This gives an average SAW transport per ring of 1.1 Sv (including all ring types), and an annual SAW transport of SAW by the rings of 8.9 Sv/yr. Incorporating the shipsurveys, which add two additional rings not sampled by the moorings (for a total of 16 rings over a period of 22 months - see Table 4) the respective estimate is 9.3 Sv for the annual SAW transport by rings. These estimates assume that the ring population we observed is representative of the frequency of occurrence of different ring types and that the seasonal bias resulting from incomplete sampling of two full annual cycles is small. The latter estimate derived from the combined shipboard and moored observations is probably better in this regard. The above estimates also assume that the number of rings shed, and the occurrence of different ring types during this -2 year period, is representative of the climatological behavior of NBC ring shedding, which may not be true (see further discussion below). The rate of NBC ring formation suggested by these observations is about 8.5 rings per year, or one ring every 1.4 months, including all ring types. For the surface-intensified rings, which are most common, this rate is about 6.5 rings per year, or one ring every 1.8 months. For the subsurface rings it is 2 per year. If we subdivide the total SAW transports into the portions corresponding to surface rings and subsurface rings, the annual SAW transport by the surface rings is 5.4 Sv/yr, and for the subsurface rings 3.8 Sv/yr. Thus, even though they occur much less frequently, the subsurface rings appear to carry more than a third of the total ring-induced SAW transport. The average transport per subsurface ring is about double that of the surface rings (-1.7 Sv vs. 0.8 Sv). The
433 Table 3. Summary of NBC Rings observed by the CM]CTD moorings. Total number of rings: 14 Total volume transport by 14.9 Sv rings: 1.1 Sv Average transport per ring: 20 months Time period of observations: Annualized ring transport: 8.9 Sv/year Total "surface" rings: Total volume transport: Average transport per ring: Annualized ring transport:
11 9.3 Sv 0.8 Sv 5.6 Sv/year
Total "subsurface" rings: Total volume transport: Average transport per ring: Annua!i_zed ring transport:
3 5.6 Sv 1.9 Sv 3.3 Sv/u
Table 4. Summary of NBC Rings observed by ship and moorings. Total number of rings: 16 Total volume transport by 16.9 rings: Average transport per ring: 1.1 Sv Time period of observations: 22 months* Annualized ring transport: 9.2 Sv/year Total "surface" rings: Total volume transport: Average Transport per ring: Annualized ring transport:
12 10.0 Sv 0.8 Sv 5.4 Sv/year
Total "subsurface" rings: Total volume transport Average transport per ring Annualized ring transport
4 6.9 Sv 1.7 Sv 3.8 Sv/yea_r
* Assumes first ring shed (ship-surveyed Ring 1) passed the CM location in October 1998, and last ring shed in June 2000 (ship surveyed Ring 4) passed the CM location in July 2000.
434 seasonality of the SAW transport by the surface rings is investigated in Figure 11, where the SAW volume of each ring is plotted by the month in which it was formed. While there is no apparent seasonality in the formation rate of the rings, there is a distinct seasonality in the ring transport with larger SAW volumes occurring in rings that form in the late fall and early winter months. As noted previously these tend to be larger, more deeply penetrating rings, in contrast to the shallow and typically smaller rings that form in the spring and summer months. These larger rings dominate the SAW transport associated with the surface rings and account for about half of the total SAW transport by all rings. In terms of an overall classification for the rings we propose that there are three main ring types: (i) the large surface intensified rings that penetrate to depths typically greater than 400 m, (ii) the smaller surface rings that penetrate to depths less than 200 m, and (iii) the subsurface intensified rings. The corresponding percentages of the total SAW transport that these ring types account for is approximately 45%, 25%, and 30%, respectively. 3.4 R i n g "watermass" vs. "geometric" v o l u m e s It is useful to consider whether the SAW volumes contained in the rings can be approximated by the physical properties of the rings themselves without requiring a detailed watermass assessment of each ring, as we have done here. Oceanic rings are normally viewed as being made up of three regions, a ring interior (or core), an exterior region of mostly ambient waters, and a ring "front" that separates these two regions (Olson, 1986). In the case of rings that are formed from a mid-ocean front, such as the Gulf Stream, the ring core will contain nearly pure waters from one side of the front while the ring front will contain a mixture of waters from both sides of the front. The maximum swirl velocity will occur in this ring front region, which should be approximately aligned with the main watermass boundary. Thus the r~a~ of the ring is a logical choice for delimiting the edge of the ring's watermass core. In many of the observed NBC rings there is a near correspondence between the radius of maximum velocity of the ring and the lateral boundary between the North and South Atlantic water masses. If we were to assume that the waters inside rma~ are made up of "pure" South Atlantic waters, and those outside of pure North Atlantic waters, then we can define a "geometric" volume for each ring which is given by the cylindrical volume ~rm~2"Az, where Az is the vertical penetration (or thickness between upper and lower limits) of the ring. In reality there is mixing of North Atlantic waters into the core of the rings in some cases and also mixing of South Atlantic waters into the periphery of the rings so that this is an over-idealization of the true watermass structure of the rings. However, these effects might be expected to be largely compensatory. The "geometric" volumes of the rings are plotted in Figure 12 against the estimated SAW volumes determined from the watermass analysis. In general,
435
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Figure 11. Annual distribution of rings formed during the experiment plotted with respect to their enclosed South Atlantic Water (SAW) volumes. The rings that form in the late fall and early winter tend to penetrate more deeply and have larger SAW volumes.
there is a good correspondence between the two estimates for the surface rings, but the watermass volumes are higher than the geometric volumes by about 15% on average. For the subsurface rings, the w a t e r m a s s volumes are much higher than the geometric volumes, by about a factor of two. This occurs for two resons; first, the cores of the subsurface rings tend to have very undiluted SAW; and second, the region of relatively high SAW percentage in these features typically extends some distance beyond rma,. The latter effect can be particularly significant since South Atlantic waters t h a t occur on the periphery of the rings have a much larger associated cylindrical volumes. The reason why the geometric volume seems to underestimate the SAW volume of the rings in general may be related to the fact t h a t these rings are formed from a retroflecting current r a t h e r t h a n a mid-ocean front. In the case of the NBC the waters forming the ring "front" are derived from a boundary current that is pressed up against the coast and that can only entrain ambient waters on its edges after the current separates from the coast. Therefore it should be expected t h a t the SAW core of the rings would initially extend beyond rma, before mixing effects across the ring front take effect. The actual volume of water that remains trapped within the ring circulation and is transported northward with the ring is expected to be substantially greater t h a n the above
436
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Figure 12. Comparison of calculated SAW volume for each ring and the "geometric" volume of each ring. The geometric volume is the cylindrical volume inside the radius of maximum velocity over the vertical limits of the ring.
above watermass or geometric volumes. According to Flierl (1981), the trapped volume of a ring coincides with the region where the swirl velocity magnitude exceeds the forward propagation speed of the ring, which for NBC rings is about 10-15 cm/s. Therefore, much of the ring volume, out to near the edge radius of the rings as we have defmed it (swirl velocity > 15 cm/s), should be physically transported with the rings once they have pinched off. For the case of NBC rings, which are anticyclonic, this region would correspond to a volume that is shifted slightly shoreward relative to the center of the ring.
4. D I S C U S S I O N A N D C O N C L U S I O N S
The purpose of this work is to assess the role played by NBC rings in the net cross-gyre transport of South Atlantic waters into the subtropical North Atlantic. It is clear from the observations that a variety of NBC ring types can occur, and that the rings can carry varying amounts of South Atlantic water. An accurate assessment of the net transport carried by the rings on a climatological basis must therefore take into account the probability of occurrence of different ring types and the representativeness of any particular observation period relative to climatology.
437 For the surface rings, we can assess the representativeness of our observation period against estimates of ring formation rates derived from satellite altimetry (Goni and Johns, this volume), which cover a ten year period from 1992 to 2002. The period of our observations corresponds to a relatively active period of NBC ring generation in the context of the available historical record. The ring formation rate derived from altimetry shows interannual variability ranging from a rate of 3 to 7 rings per year (Goni and Johns, their Figure 11), with our -2 years of observations falling among the highest formation rate found in the record. The average rate of surface ring formation derived from the altimetry record is 5 rings per year, which is less than the rate of 6.5 surface rings per year during our measurement period. This suggests that our estimate of SAW transport by the rings may be higher than the climatological value by order 30%. However, it must also be borne in mind that some rings may escape detection by altimetry. A case in point was ring R8 during the period of our experiment which was detected by the moorings and by IES but not clearly identified by altimetry. Thus it is also possible that the climatological ring formation rate derived from altimetry is low. Another complicating factor is the large range of SAW volumes carried by the surface rings, which makes it highly nontrivial to scale the results from this experiment to a climatological ring formation rate, even if such a rate was well determined. Ideally it would be possible to distinguish between the rings that carry large volumes of SAW according to their altimetric signatures, either by their size (e.g., rm~., though this is not infallible) or by other measures such as their longevity (e.g., if more deeply penetrating rings decay more slowly), but such an understanding is not yet available. In most rings the surface swirl velocities are similar, of order 1 m/s, so that the amplitude of the SSH signal associated with a ring is not necessarily a reliable indicator. It is possible to infer (approximately) the SSH anomaly associated with the observed rings by application of a gradient momentum balance to the observed surface velocity structure across the rings; the result we obtain is that the rings have typical SSH anomalies relative to the surrounding waters of 0.15 to 0.25 m, with only marginally greater values for the larger, deep rings. Finally, since the subsurface rings are mostly undetectable by altimetry, there is virtually no way to know how representative our observations are of the typical formation rate of these features. From our observations it appears that about two of these features are formed per year, with the times of formation occurring in the fall (September-October) and spring (March-April), although this pattern could be coincidental. At the present time we can only assume that this formation rate is representative, and that the SAW volumes we determine to be carried in these rings are also representative, despite having a sample size of only four. An important question that arises from the discovery of these subsurface NBC rings is the dynamics that lead to their formation. One possibility is that they may form upstream of the surface NBC retroflection at the location where
438 the thermocline portion of the NBC (the North Brazil Undercurrent, NBUC; Schott et al., 1998) retroflects into the Equatorial Undercurrent (EUC). This could explain the subsurface-intensified nature of these features, but cannot explain why they usually have a thick layer of SAW extending down to intermediate water levels, nor why some of these features have swirl velocity maxima at depths of 600-800 m, which is far below the core level of the EUC (-150 m). Another hypothesis for their generation is that they are the result of an instability process of an intermediate depth current (the Intermediate Western Boundary Current; IWBC) that breaks up into eddies as it crosses the equator (Jochum and Malanotte-Rizzoli, 2003). This could lead to the observed structure of some of these features, but as yet there is not any observational evidence to confmn that such a process is taking place. An equally important question is: Why are two distinct classes of surfaceintensified rings formed, and why do the deep-reaching rings with large SAW volumes preferentially form in the late fall to early winter? The answer likely has to do with the seasonal cycle of the NBC and its retroflection into the NECC. The NBC reaches its maximum strength during August-September, and decreases to minimum strength in April-May (Johns et al., 1998). The NBC retroflection is present from about J u n e to March and is either weak or absent during the period of minimum NBC transport in April-May. The large, deepreaching rings seem to be formed during the period when the NBC is in its declining phase from the summer transport maximum, but while the NBC retroflection is still clearly established. At this time of year the NBC also has a deep reaching flow structure that extends to depths of 800 m, which could explain the formation of deep-reaching rings at this time. In contrast, during spring and early summer the NBC flow is mostly confined to the surface layers above 150 m (Johns et al., 1998), which is consistent with the shallow rings that form at this time of year. A remaining puzzle is the manner in which these shallow rings are formed, since at least some of them form when the retroflection is not clearly established. This suggests a different formation mechanism than the canonical retroflection pinch-off process that occurs during the time when the retroflection is established. The mechanism of the formation of these shallow features requires further investigation. An encouraging development in the study of NBC rings is the emergence of several new basin scale numerical simulations and idealized regional models that exhibit vigorous NBC ring shedding behavior, and that appear to have many similarities to the observed phenomenology of NBC rings (Barnier et al., 2001; Garraffo et al., this volume; Jochum and Malanotte-Rizzoli, 2003). The results described in Garraffo et al. (this volume) in particular, based on a highresolution Atlantic MICOM (Miami Isopycnal coordinate model) simulation, bear a remarkable resemblance to the observations in terms of the number of rings shed, the generation of different ring types (including subsurface-intensified rings), and the volumes of South Atlantic waters transported by the rings. Using a watermass analysis similar to that performed here, Garraffo et al.
439 obtain a mean ring-induced transport of 7.5 Sv over 6 years of their model simulation, with a range from 5.5 to 9.0 Sv in individual model years. Interestingly, the Garraffo et al. results are obtained from a climatologically forced model, which suggests that there may be natural variability in the ring formation rate and its associated cross-gyre transport regardless of variability caused by interannual forcing. In summary, we fred from these new observations that NBC rings form an important part of the net meridional transport of South Atlantic waters from the equatorial to subtropical North Atlantic ocean, and that their contribution to this transport has probably been underestimated by previous studies. The annualized rate of South Atlantic water transport by the rings during the period of our experiment, from October 1998 to J u n e 2000, was approximately 9 Sv, which amounts to more than half of the estimated rate of upper ocean transport in the MOC of 13-17 Sv (Schmitz and Richardson, 1991; Roemmich and Wunsch, 1985). Other important pathways may include seasonal interior transport associated with the storage of southern hemisphere waters in the NECC and subsequent northward transport in the Ekman layer (Mayer and Weisberg, 1993), and residual coastal flow near the western boundary that is not associated with rings. In contrast to previous conclusions, however, the results of our analysis suggest that NBC rings may in fact be the dominant pathway. The results of this experiment also serve to illustrate the point that remote sensing of NBC rings by satellite altimetry or ocean color will not be sufficient to adequately determine the cross-gyre transport carried by NBC rings, due to the great variability in vertical structures of the rings. A combination of remote sensing observations and in-situ time series that can observe the vertical structures of the rings, such as provided here by the moorings, is proposed as a possible strategy for longer term monitoring of the NBC rings and their crossgyre transport.
Acknowledgements This research was supported by the U.S. National Science Foundation under grant number OCE-9730322, and in part by NOAA/AOML (G.G.). We express our gratitude to the captain and crew of the R/V Seward Johnson for their able assistance in the deployment and recovery of the moored instruments and the shipboard survey work during the four project cruises. S. Garzoli kindly provided estimates of the NBC ring translation speeds from the IES array. The authors would like to thank D. Olson, Z. Garraffo, and E. Johns for helpful scientific discussions.
440
REFERENCES Barnier, B., T. Reynaud, A. Beckmann, C. Boning, J-M Molines, S. Barnard, Y. Jia, On the seasonal variability and eddies in the North Brazil Current: Insight from model intercomparison experiments. Prog. Oceanogr., 44, 195230, 2001. Bourles, B., R.L. Molinari, E. Johns, W.D. Wilson, and K.D. Leaman, Upper layer currents in the western tropical North Atlantic (1989-1991). J. Geophys. Res., 104, 8555-8560, 1998. Didden, N. and F. Schott, Eddies in the North Brazil Current retroflection region observed by Geosat altimetry. J. Geophys. Res., 98, 20121-20131, 1993. Emery, W.J., and J.S. Dewar, Mean Temperature-Salinity, Salinity-Depth, and Temperature-Depth curves for the North Atlantic and North Pacific. Prog. Oceanogr., 11219-11305, 1982. Fleurant, C., D. Wilson, W. Johns, S. Garzoli, R. Smith, D. Fratantoni, P. Richardson and G. Goni. CTD02, LADCP and XBT measurements collected aboard the R]V Seward Johnson, February-March 1999 North Brazil Current Rings Experiment Cruise 2 (NBC02). NOAA Data Report OAR AOML-37, 2000. Fleurant, C., D. Wilson, W. Johns, S. Garzoli, R. Smith, D. Fratantoni, P. Richardson and G. Goni. CTD02, LADCP and XBT measurements collected aboard the R/V Seward Johnson, December 1998 North Brazil Current Rings Experiment Cruise 3 (NBC3). NOAA Data Report OAR AOML-38, 2000. Flierl, G.R., Particle motions in large amplitude wave fields. Geophys. Astro. Dyn., 18, 39-74, 1981. Fratantoni, D.M., W.E. Johns, T.L. Townsend, Rings of the North Brazil Current: their structure and behavior inferred from observations and a numerical simulation. J. Geophys. Res., C6, 10,633-10,654, 1995. Fratantoni, D.M. and D. Glickson, North Brazil Current ring generation and evolution observed with SeaWiFS, J. Phys. Oceanogr., 2002. Garzoli, S.L., A. Ffield, W.E. Johns, and Q. Yao. North Brazil Current retroflection and transports. J. Mar. Res, 2003. Goni, G.J., and W.E. Johns, A census of North Brazil Current rings observed from TOPEX/Poseidon altimetry: 1992-1998. Geophys. Res. Lett., 28, 1-4, 2001 Johns, W.E., T.N. Lee, F.A. Schott, R.J. Zantopp, R.H. Evans, The North Brazil Current retroflection: Seasonal structure and eddy variability. J. Geophys. Res., 95 (C12), 22,103-22,120, 1990. Johns, W.E., T.N. Lee, R.C. Beardsley, J. Candela, R. Limeburner and B. Castro, Annual cycle and variability of the North Brazil Current. J. Phys. Oceanogr., 28, 103-128, 1998. Jochum, M. and P. Malanotte-Rizzoli, On the generation and importance of North Brazil Current rings. J.Mar. Res.., 61,147-162, 2003. Levitus, S., Climatological Atlas of the World Ocean,. NOAA Professional Paper 13, US Dept of Commerce, NOAA, 1982.
441 Mayer, D.A and R.H. Weisberg, A description of COADS surface meteorological fields and the implied Sverdrup transports for the Atlantic Ocean from 300S to 60oN. J. Phys. Oceanogr., 23, 2201-2221, 1993. Olson, D.B., Lateral exchange within Gulf stream warm-core ring surface layers. Deep- Sea Res., 33, Nos.11/12, 1691-1704. 1986. Richardson, P.L., G.E. Hufford, R. Limeburner, and W.S. Brown, North Brazil Current retroflection eddies. J. Geophys. Res., 99(C3), 5081-5093, 1994. Roemmich, D., and C. Wunsch, Two transatlantic sections: Meridional circulation and heat flux in the subtropical North Atlantic Ocean. Deep-Sea Res., 32, 609-664, 1985. Schmitz, W. Jr., and P. Richardson, On the sources of the Florida Current. Deep-Sea Res., 38, Suppl., $379-$409, 1991. Schott, F.A., J. Fischer, L. Stramma, Transports and pathways of the Upperlayer circulation in the western tropical Atlantic. J. Phys. Oceanogr., 28. 1904-1928, 1998. Wilson, W.D., E. Johns, and R. L. Molinari, Upper layer circulation in the western tropical North Atlantic during August 1989. J. Geophys. Res., 99, 22,513-22,523, 1994. Wilson, D. W., W. Johns and S. L. Garzoli. Velocity structure of North Brazil Current rings. Geophys. Res. Lets., 29, 10.1029/2001GL013869, 2001. Wrist, G., Stratification and Circulation in the Antillean-Caribbean Basin. Columbia University Press, New York, 201 pp., 1964.
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lnterhemispheric Water Exchange in the Atlantic Ocean
edited by G.J. Goniand P. Malanotte-Rizzoli 9 2003 ElsevierB.V. All rightsreserved.
I m p a c t o f N o r t h B r a z i l C u r r e n t r i n g s on l o c a l c i r c u l a t i o n a n d c o r a l r e e f fish r e c r u i t m e n t to B a r b a d o s , West I n d i e s R.K. Cowen *a, S. Sponaugle a, C.B. Paris a, J.L. Fortuna a, K.M.M. Lwiza b, and S. Dorsey c a Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Cswy., Miami, FL 33149, USA b Marine Sciences Research Center, State University of New York, Stony Brook, NY 11794-5000, USA r Biology Department, Salem College, Winston-Salem, NC 27108-0548, USA Early observations of the flow environment around the island of Barbados indicated frequent occurrence of strong current reversals associated with surface salinity fronts. Higher resolution spatial and temporal measurements of the flow regime in 1996 and 1997 provided a comprehensive view of the local surface circulation (0-100 m), revealing that external forcing by North Brazil Current (NBC) rings plays a dominant role in the near-field flow variability surrounding the island. NBC ring forcing had comparable effects on the velocity field during both years, indicating that the ring structure was retained while interacting with topography. In the present study, the interaction of NBC rings with coastal flow dynamics and the biological response of the system as measured by recruitment of coral reef fishes is examined. Our observations show that NBC rings can remain quite coherent as they pass the Tobago-Barbados ridge. Further, the flow direction and associated residence time in the vicinity of the island appear to vary depending on the orientation of the rings as they collide with the island. Concurrent biological samples revealed complex responses to the presence of rings in that during some of the events, larval fishes appeared to be rapidly advected away, resulting in a failure of larval settlement, whereas under other conditions larval retention was enhanced and was followed by a settlement pulse. Impingement by a ring did not alter the concentration of water column chlorophyll a (Chl a), but it did influence the depth of the Chl a maximum. Simultaneous changes were observed in the vertical distribution of fish larvae. Larval fish encountering ring waters exhibited reduced growth rates and longer ' Corresponding author. Tel.: +1-305-361-4023. Fax: +1-305-361-4600. Email:
[email protected] 444 larval periods, both potentially reducing survival and, ultimately, recruitment success. Overall, results demonstrate that NBC rings interfere with the islandscale flow dynamics around Barbados and interject considerable variability in the local recruitment signal of coral reef fishes.
1. I N T R O D U C T I O N
The upper layer circulation in the northern tropical Atlantic off the coast of South America is characterized by a mean circulation in the NW direction, often referred to as the Guyana Current and fed by the North Brazil Current (NBC). This region is dominated by large anticyclonic rings shed at the retroflection of the North Equatorial Counter Current (NECC) and the NBC, which then move northwestward along the South American coast [Johns et al., 1990; Didden and Schott, 1993; Richardson et al., 1994; Fratantoni et al., 1995]. These rings entrain water masses from the southern hemisphere and often, in their peripheral waters, water from the Amazon River [Fratantoni and Glickson, 2002]. As the NBC rings translate toward the Lesser Antilles, the major shallow topographic feature they encounter is the Tobago-Barbados Ridge and the island of Barbados, which lies along the eastern flank of the Lesser Antilles (Figure 1). Due to this downstream location of Barbados relative to NBC rings [Goni and Johns, 2001], the surrounding pelagic environment of the island is directly impacted by ring passage. Consequently, examination of the impact of NBC rings and their associated water masses on coral reef fish larvae recruiting to Barbados is critical to understanding the ecology of fish populations of the eastern Caribbean. Rising from depths greater than 2000 m, the island of Barbados is a feature of approximately 50 x 145 km (measured at the 1000 m isobath), which may present a real obstacle to a passing ring. Analysis of satellite-derived sea height anomaly fields from Topex/Poseidon data indicate that most NBC rings tend to veer from their generally northwestward trajectories to the north as they approach the Tobago-Barbados Ridge [Kelly et al., 2000; Goni and Johns, 2001], causing the rings to pass directly by or around Barbados. Both structure of the ring [Fratantoni et al., 1995; Goni and Johns, 2001] and its orientation to the island may influence the nature of the flow interaction with the island topography. Theoretical treatments of eddy-island interactions suggest that a ring potentially can pass around an island, trapping anticyclonic motion in a Taylor column around the island [McWilliams, 1986; Simmons and Nor, 2000]. Alternatively, or as a direct result of the initial impingement of a ring with a topographic feature, some outer portion of the ring circulation may peel off the ring and flow around the island as vorticity is maintained, with the added potential of splitting into a separate ring [Simmons and Nof, 2000]. Previous observations of the flow around Barbados demonstrated the variable nature of the incident flow interacting with the local topography [Bowman et al., 1994; Cowen and Castro, 1994; Stansfield et al., 1995]. In these studies, strong
445 current reversals were observed during two years in association with significant low salinity features consistent with the passage of NBC rings in the vicinity of Barbados. However, in one year the resulting flow was anticyclonic, with low salinity passing to the west of the island [Bowman et al., 1994; Cowen and Castro, 1994], whereas in the other year a cyclonic circulation around the island ensued, trapping low salinity water around the south, east and north coastal portions of the island [Stansfield et al., 1995]. Coherent signals of low salinity and strong current reversals were similarly observed in a more recent study [Paris et al., 2002], raising the question regarding the ubiquity of these energetic features and their role in the local coastal dynamics of islands such as Barbados. Analysis of satellite altimeter data and of temperature-salinity recorders moored off of the west coast of Barbados [Goni and Johns, 2001] revealed that NBC rings may pass Barbados up to 4-5 times per year, more frequently than previously thought [Richardson et al., 1994; Fratantoni et al., 1995]. It has been suggested that as many as 6-7 rings per year may develop in the Western Atlantic, all with the potential to collide with the island environment of the Lesser Antilles [Goni and Johns, 2001, Fratantoni and Glickson, 2002]. This suggests that local coral reef species that spawn year-round and have a mean larval duration of 30 to 50 days have a high likelihood of being exposed to a ring event for at least a portion of their pelagic phase. Recurring translations of NBC rings from the retroflection region toward the eastern Caribbean, and collision of rings with the Ridge bathymetry introduce southern hemisphere water masses, including low salinity waters from the Amazon River, into the coastal island environment. These events may have a complex and cumulative effect on the recruitment of coral reef fishes to Barbados. Here we examine the physical and biological interactions among NBC rings, the coastal environment around Barbados, and reef fish larvae. We describe the typical signature of the upper 100 m of the water column prior to and during the passage of a ring in terms of the currents and salinity fields along the coast of Barbados. We also examine how these coastal flow properties may interact strongly with the distribution and survival of larval fishes, ultimately affecting the recruitment of these fishes to coral reef habitats. Specifically, we examine how the larval fish community potentially is impacted by ring passage both in terms of their physical (i.e. vertical) distribution and their daily growth rates. These biological variables directly impact the potential for recruitment by influencing larval retention and survival.
2. METHODS 2.1. Bio-physical Sampling The bio-physical field experiment consisted of two 30-day cruises on the R/V Seward Johnson during May-June of two consecutive years, 1996-1997, in the vicinity of Barbados (13o10'N, 59o30'W), West Indies. The study area extended 15 km from the west coast of Barbados and 20 km parallel to shore (Figure 1). Hydrographic and biological survey measurements, each conducted over a 24-hr
445
Figure 1. Study area - (a) Topography of the Lesser Antilles in the vicinity of the island of Barbados. The biophysical survey area (15 x 20 km) is indicated by the white rectangle. Inserts indicated by the white frame in (a) illustrate (b) the biological sampling consisting of larval fish MOCNESS hauls during day (circle) and night (cross) stations and juvenile fish census and collection sites (star), and (c) the physical sampling consisting of CTD stations (letters) along ADCP tracks (dashed line).
447 period, were repeated every 3 days. During day 1 of each sampling period, a conductivity-temperature-depth (CTD) survey was conducted with a Sea-Bird SBE9 in a grid pattern covering the domain to provide a quasi-synoptic temperature/salinity field. CTD transects ran parallel to shore and on average 21 CTD casts (ca. 2-4 km apart) were made to a maximum depth of 500 m or to within 25 m from the bottom. To maximize sampling resolution, Acoustic Doppler Current Profiler (ADCP) data were continuously recorded along the ship track with short-term maximum error estimates on bottom-tracked velocity of 6 cm s -1 at 400 m. The ADCP data were acquired at a vertical resolution of 4 m and 300 s sampling ensembles. During CTD casts, total chlorophyll a concentration (mg Chl a m "3) was recorded via calibrated fluorometry profiles [Choi et al., 2001]. During day 2 of each survey, 24 vertically discrete ichthyoplankton samples at 20-m intervals from the sea surface to 100 m were taken in a 12-h day/12-h night paired sampling and fixed in 95% Ethanol. Ichthyoplankton samples were collected using a 1 m 2 MOCNESS (Multiple Opening-Closing Net and Environmental Sampling System) fitted with 333 ~un mesh nets. Fish larvae later were sorted and identified to species or the lowest taxonomic level possible. This sampling sequence was repeated a total of 8 times (surveys) during the cruise. The entire experiment was repeated during the following year. 2.2. F l o w F i e l d C a l c u l a t i o n s To understand the dynamic of coastal currents during the impingement of a NBC ring at Barbados, we generated a series of horizontal flow fields for each survey using independent observations of velocities (e.g., dynamic height and currents) via a multivariate spatial objective analysis [Gomis et al., 2001]. Dynamic heights were computed in reference to 200 m for each CTD survey and the ADCP data were filtered using standard statistical analyses. The ADCP and CTD data were analyzed from the surface to 100 m on 5 horizontal planes (every 20 m) and returned velocities in a 12 x 12 mesh (2 km x 1 kin) determined by the density of observed data.The maximum depth for the flow field output matched the depth limit of ichthyoplankton sampling, which also approximated the depth of the inshore CTD line. Since the ADCP measures the total current, it includes ageostrophic flows such as wind-driven current, near-inertial motion, and tides. Tides in Barbados are semidiurnal, with ca. 10 cm s -1 amplitude [estimated from the ADCP mooring; Kelly et al., 2000], and were not explicitly removed from the total current. The objective analysis procedure reduced measurement errors by removing noise from scattered sampling and predicted homogeneous maps of the total horizontal current in the coastal waters of Barbados [Paris et al., 2002]. In order to investigate the potential ring effect on the transport of locally spawned fish larvae, we used the horizontal current maps and measured water residence time in the sampling box as well as before and during ring impact for each year. This procedure allowed us to evaluate the role of the rings in limiting or enhancing larval dispersal. Water residence times were calculated using a Lagrangian particletracking scheme in which sub-grid scale turbulence was added to the deterministic
448 current [Dutkiewicz et al., 1993]. A total of 15,000 tracers was released on a regular mesh of 30 locations across the 12 x12 km grid in each of the five 20-m horizontal layers. Releases at those fixed depths were initiated during survey 1 and repeated daffy until the end of the sampling experiment. Note that residence times may have been underestimated since tracers cannot be tracked for more than the length of the experiment. The horizontal distribution of water residence time was calculated for each layer and for a selected time period (before and during ring impact).
2.3. B i o l o g i c a l M e a s u r e m e n t s For the biological component of this study, we focused our efforts on a single species of coral reef fish, the bluehead wrasse (Thalassoma bifasciatum), due to its common occurrence within our ichthyoplankton samples and previous experience with the recruitment dynamics of the species [e.g., Sponaugle and Cowen, 1997; Searcy and Sponaugle, 2000, 2001; Victor, 1982]. The vertical distribution of the larvae was examined with respect to the vertical structure of the flow field and chlorophyll a (Chl a) profiles, to provide a measure of both potential impacts on retention within the vicinity of the island and a possible food related response of the larvae to a changing physical environment. To examine how NBC rings might influence settlement dynamics, we measured the timing and strength of T. bifasciatum recruitment. Newly settled T. bifasciatum were regularly surveyed every two weeks and collected by two divers from 30 randomly placed 1 x 5 m transects at three sites along the west coast of Barbados (Figure lb), providing an estimate of the relative size of recruitment events (i.e. density of recruits). A portion of each bi-weekly sample was aged to determine the specific timing of settlement. Age was determined using the daily increment analysis of otoliths (ear bones). The otoliths of most reef fishes consist of a series of increments deposited on a daily basis, resulting in a continuous record of age and day-specific relative growth rates [e.g., Searcy and Sponaugle, 2001]. The daffy nature of increment deposition has been validated previously for T. bifasciatum [Victor, 1982]. The combination of the density estimates obtained from the transect data and the sample-specific age data from the fish otoliths provided a daffy recruitment record for T. bifasciatum from March 1996-October 1997. A changing food (prey) environment may directly impact the growth and ultimately survival of fish larvae. Slow-growing larvae may experience longer development times that can translate into greater mortality risks (i.e. longer time exposed to high mortality rates associated with planktonic existence, as well as due to smaller size). Therefore, to examine the potential influence of NBC rings on the growth and pelagic duration of fish larvae present in the water column before and during the passage of the rings, the otoliths of newly settled T. bifasciatum were examined for relative growth. Fish otoliths not only provide an estimate of age and larval duration, but the width between consecutive increments provides a measure of relative larval growth rates. To examine the influence of rings on larval growth, the mean otolith increment widths (or relative growth trajectories) were compared during the larval period for fishes
449 Table 1. Schedule of bio-physical surveys for the 1996 and 1997 Barbados cruises and of observations of low salinity intrusions. CT, conductivity-temperature; ADCP, acoustic Doppler current profiler; MOCNESS, multiple opening-closing net and environmental sensing system. . . . Survey No.-
.
.
.
.
.
.
.
.
.
CT/ADCP
MOCNESS
May 8 May 11 May 14 May 19 May 22 May 27 May 30 June 2 April 30 May 4 May 7 May 12 May 15 May 19 May 22 May 25
May 9 May 12 May 15 May 20 May 23 May 28 May 31 June 3 May 1 May 5 May 8 May 13 May 16 May 20 May 23 May 26
.
.
. . Minimum Salinity at(psu) 10 m
Year 1 96 2 - 96 3 - 96 4 - 96 5 - 96 6 - 96 7 - 96 8 - 96 1 - 97 2 - 97 3 - 97 4 - 97 5 - 97 6 - 97 7 - 97 8 - 97 i
i
i
,
34'.6 . . . . . . 34.7 34.6 34.8 33.5 33.6 33.8 33.9 35.2 35.3 35.8 35.0 32.5 33.7 32.7 33.3 i|
Verticai Extent (m) of water < 34.5
20 32 34 27
ii
i
23 29 35 33
t h a t had encountered a ring for at least 7 days during the first half of their larval period (i.e. during day 1-20), and those t h a t encountered a ring during days 21-40, to those t h a t encountered no ring at any time during their larval period. Presence or absence of a ring was determined from the CT sensor timeseries of Kelly et al. [2000]. A ring was considered to be present when salinities were less t h a n 34.5 psu.
3. R E S U L T S
3.1. S u r f a c e S a l i n i t y a n d T r a n s p o r t During the experiments of both years, near-surface salinity was higher during the first four surveys t h a n the latter four, and surface salinity was initially higher in 1997 compared to 1996 (Table 1). During both years, a strong salinity front appeared in survey 5, separating salty coastal w a t e r from fresher and slightly w a r m e r oceanic waters. This offshore front moved rapidly onshore over
450
Figure 2. Salinity and current fields in the upper 100 m along the western shore of Barbados during (a) May-June 1996 and (b) April-May 1997. Low salinity water (< 34.5 psu) penetrates the domain at the southern boundary and persists throughout the entire domain for the rest of the surveys. Maximum velocity = 50 cm s -1.
451 the entire domain, resulting in waters of lower salinity for the remaining 3 surveys (Figure 2). In 1996, the low salinity front was coupled to warmer sea surface temperatures. However, in 1997, while the change in salinity from survey 4 to survey 5 was larger (surface salinity decreased by 2 psu), warm waters near the surface lagged by 2 surveys [Choi et al., 2001]. The vertical extent of the low salinity (< 34.5 psu) water was similar between years, reaching to as deep as 35 m (Table 1). Horizontal currents in the upper 100 m indicated complex and contrasting flow patterns during 1996 (Figure 2a) and 1997 (Figure 2b) in response to the observed intrusion of low salinity water. Although in 1997 the flow during surveys 1 to 4 had a stronger eastward component, overall the pre-intrusion flow in both years was initially northward then, preceding the low salinity intrusion, reversing southward. During both years, as the low salinity lens penetrated the sampling domain, the flow reversed again (northward). In 1996, the flow associated with the low-salinity intrusion remained northward or northeastward (Figure 2a), whereas in 1997, the low-salinity flow was initially northward then eventually turned southward (Figure 2b). Differences in the residence time of water before and during the low salinity events were associated with the changing salinity and flow field. During 1996, residence time prior to ring passage (May 8-18, 1996) ranged from 0-13 days at 50 m (Figure 3a). Once the NBC ring was present in the vicinity of Barbados, residence time increased over most of the domain to approximately 6-13 days (Figure 3b). An increase in larval abundance coincided with the increase in residence time (Figure 4a). In comparison, during 1997, residence time at 50 m was always higher than in 1996 (Figure 3a), but decreased in the southern part of the sampling domain with ring collision (i.e. May 13-22, 1997; Figure 3b). This decrease coincided with a decrease in larval densities in 1997 (Figure 4b). Change of water residence time with the ring events and associated incident flow, combined with changes in larval fish vertical distributions, results in differences in larval transport (flux). 3.2. C h l o r o p h y l l a a n d l a r v a l fish v e r t i c a l d i s t r i b u t i o n Chlorophyll a (Chl a) content varied within and between years. Chl a concentration was typically higher in 1996 than in 1997 during all surveys, with a maximum of 2 mg m -3 and 0.5 rag m -3, respectively (Figure 5). In 1996, the intrusion of low salinity water brought no appreciable change in the depth of the Chl a maximum, which varied between 40-80 m (Figure 5a). However, in 1997, where the change in salinity between pre- and post- intrusion was greater, there was a concomitant shallowing (and broadening) of the Chl a maximum layer from approximately 100 m to 40-60 m (Figure 5b). The shallower nature of the Chl a maximum in 1997 may be explained in part by the presence of a second (and shallower) peak in concentration just below the low salinity water (see Figure 5b). The vertical distribution of larval T. bifasciatum was generally coincident, though slightly shallower, with the depth of the Chl a maximum. In 1996, T.
452
Figure 3. Maximum residence time (RT) on the western shore of Barbados during the 1996 and 1997 experiments at the mean depth of center of mass for Thalassoma bifasciatum (40-60 m) (a) before and (b) after low salinity intrusions.
Figure
4. Temporal
distribution
of standard
catch
of larval bluehead
Thalassoma bifasciatum, during the (a) 1996 and (b) 1997 experiments.
wrasse,
453
Figure 5. Vertical profile of Chl a (-), salinity (-) and m e a n depth of center of mass for larval T. bifasciatum (circle) for each 3-d survey d u r i n g (a) 1996 and (b) 1997. A total of 17-24 CTD casts and MOCNESS hauls was made d u r i n g each survey; thin lines and vertical bars r e p r e s e n t 1 s t a n d a r d deviation around the m e a n Chl a or mean salinity, and mean depth of center of mass, respectively.
454
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T
V
cn 4 0 ~E Wl,,,=
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r(D
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