Ocean Hydrodynamics: Hydrodynamics of Estuaries and Fjords 9th: International Colloquium Proceedings (Elsevier oceanography series ; 23)

Hydrodynamics of Estuaries and Fjords

FURTHER TITLES IN THIS SERIES

1 J.L. MERO THE MINERAL RESOURCES O F THE SEA

2 L.M. FOMIN THE DYNAMIC METHOD IN OCEANOGRAPHY

3 E.J.F. WOOD MICROBIOLOGY O F OCEANS AND ESTUARIES

4 G.NEUMANN OCEAN CURRENTS

5 N.G. JERLOV OPTICAL OCEANOGRAPHY

6 V.VACQUIER GEOMAGNETISM IN MARINE GEOLOGY

7 W.J. WALLACE THE DEVELOPMENT O F THE CHLORINITY/SALINITY CONCEPT IN OCEANOGRAPHY

8 E. LISITZIN SEA-LEVEL CHANGES

9 R.H.PARKER THE STUDY O F BENTHIC COMMUNITIES

1 0 J.C.J. NIHOUL MODELLING O F MARINE SYSTEMS

11 0.1. MAMAYEV TEMPERATURE-SALINITY

ANALYSIS O F WORLD OCEAN WATERS

1 2 E.J. FERGUSON WOOD and R.E. JOHANNES TROPICAL MARINE POLLUTION

1 3 E. STEEMANN NIELSEN MARINE PHOTOSYNTHESIS

14 N.G. JERLOV MARINE OPTICS

15 G.P. GLASBY MARINE MANGANESE DEPOSITS

16 V.M. KAMENKOVICH FUNDAMENTALS O F OCEAN DYNAMICS

1 7 R.A. GEYER SUBMERSIBLES AND THEIR USE IN OCEANOGRAPHY AND OCEAN ENGINEERING

18 J.W. CARUTHERS FUNDAMENTALS O F MARINE ACOUSTICS

19 J.C.J. NIHOUL BOTTOMTURBULENCE

20 P.H. LEBLOND and L.A. MYSAK WAVES IN THE OCEAN

2 1 C.C. VON DER BORCH (Editor) SYNTHESIS O F DEEP-SEA DRILLING RESULTS IN THE INDIAN OCEAN

2 2 P. DEHLINGER MARINE GRAVITY

Elsevier Oceanography Series, 23

Hydrodynamics of Estuaries and Fjords PROCEEDINGS OF THE 9th INTERNATIONAL LIEGE COLLOQUIUM ON OCEAN HYDRODYNAMICS

Edited by JACQUES C.J. NIHOUL Professor of Ocean Hydrodynamics, University o f Liege, LiBge, Belgium

ELSEVTER SCIENTIFIC PUBLISHING COMPANY Amsterdam - Oxford - New York 1978

ELSEVIER SCIENTIFIC PUBLISHING COh5PANY 335 Jan van Galenstraat P.O. Box 211, Amsterdam, The Netherlands

Distributors for the United States and Canada: ELSEVIER NORTH-HOLLAND INC. 52, Vanderbilt Avenue New York, N.Y. 10017

l . i l i r a r , o l ('iingrv\\

(

a i a l o g ~ n gin I'uhlirat,,,,,

~

)

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Colloquium on Ocean Hydrodynamics, 4th, 1977 FIydrodynamics of e s t u a r i e s and f j o r d s .

Li&e

( i : l s e v i e r o c e a n o g r a p h y s e r i e s ; 23) B i b l i o g r a p h y : p. Includes index. 1. C s t u a r i ne o c e a n o g r a p h y - - C o n g r e s s e s . ?. rj ords - - C o n g r e s s e s . 3. Hydrodynamics-Conqresses. I. N i h o u l , J a c q u e s C. J. 11. T i t l e . G C ~ G . ' ~ . L > 1377 ~ 551.h1609 78-1405

ISBN 0-444-4168: -X

ISBN 0-444-41682-x (Vol. 23) ISBN 0-444-41623-4 (Series)

o Elsevier Scientific Publishing Company, 1978 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Scientific Publishing Company, P.O. Box 330,Amsterdam, The Netherlands Printed in The Netherlands

V

Foreword

The I n t e r n a t ional L i P g e Colloquia o n Ocean Hydrodynamics are o r ganized annually.

T h e i r topics d i f f e r from one y e a r t o another and

try to a d d r e s s , a s much a s possible, r e c e n t problems and incentive new s u b j e c t s in physical oceanography. Assembling a group o f active and eminent scientists from d i f f e rent c o u n t r i e s and often different disciplines, they provide a forum for d i s c u s s i o n and foster a mutually beneficial exchange o f informa-

tion o p e n i n g o n to a survey of major recent discoveries, essential mechanisms, i m p elling question-marks and valuable suggestions for future r e s e a r c h . Es t u a r i e s and F j o r d s have been extens ively studied in the past and t h e c h o i c e o f t h i s subject for t h e 1977 Colloquium may appear a little o u t o f line with the tradition. Es t u a r i e s a n d F j o r d s however play an essential r o l e in m a n ' s activities.

C o n n ecting the o c e a n s and the inland r i v e r s , they are

natural t r a n s p o rtation channels.

They provide rational sites for

harbors and i n d ustrial developments and simultaneously natural n u r sing g r o u n d s , r i c h in n u t r i e n t s , for mar ine plants and animals. Es t u a r i e s and F j o r d s , o n the o t h e r hand, have become increasingly vulnerable, receiving the impact o f modern expansion

:

continu-

ously growing p o pulation, production and u s e o f p o w e r , manufacture o f n e w and m o r e diversified materials, intensification of transpor-

tation and f i s h ing effort. Di v e r s i o n s o f r i v e r s , land reclamatio n, excessive siltation, dredging, d u m p i n g of chemical and biolog ical w a s t e s , while c r e a ting severe t h r e ats o n the estuarine env ironment

,

have produced

continuous, o f t e n d r a s t i c , modifications calling for further, more extensive, m o r e elaborate and more interdisciplinary research. The p e r f e c t i n g of n e w equipment, t h e constitution o f more exhaustive d a t a b a n k s , coinciding w i t h the dev elopment o f mathematical modelling t e c h n i ques and the intensive u s e o f modern computers, have p r o v i d e d t h e m e a n s o f a better unde rstanding o f estuarine' d y namics.

V I The Scientific Organizing C o m m i t t e e of the N i n t h I n t e r n a t i o n a l L i G g e Colloquium on O c e a n H y d r o d y n a m i c s s a w the d e s i r a b i l i t y o f

bringing together, on the i m p o r t a n t and p r e s s i n g s u b j e c t of E s t u a r i e s and F j o r d s , specialists f r o m d i f f e r e n t f i e l d s , e x p e r i m e n t a l i s t s and m o d e l l e r s , h y d r o d y n a m i c i s t s , c h e m i s t s and biologists. The present book w h i c h m a y be r e g a r d e d a s the o u t c o m e of t h e colloquium c o m p r i s e s the p r o c e e d i n g s of t h e meeting and s p e c i a l l y commissioned c o n t r i b u t i o n s o n o b s e r v a t i o n s , p a r a m e t e r i z a t i o n and modelling o f e s t u a r i n e d y n a m i c s .

J a c q u e s C.J.

NIHOUL.

V I 1

T h e Scientific Organizing Committee

of the

LiPge Colloquiu m

Ninth on

International

Ocean Hydrodynamics

and all the participants wish to express their gratitude to the

Belgian Minister

of E d u c a t i o n , t he National Science Foundation

of

LiS?ge and

Belgium,

the University

the Office of

of

Naval Research

for their most valuable support.

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I X

LIST O F P A R T I C I P A N T S

Ir.

Y. A D A M , S e c r e t a r i a t d ' E t a t d l ' E n v i r o n n e m e n t , Belgium.

Dr.

G. A L L E N , C e n t r e O c e a n o l o g i q u e d e B r e t a g n e , B r e s t , F r a n c e .

M.

A. H A H , U n i v e r s i t e d e L i e g e , Belgium.

Dr.

W. B A Y E N S , S e c r e t a r i a t d ' E t a t d l ' E n v i r o n n e m e n t , Belgium.

Ir.

G. B E L H O M M E , U n i v e r s i t e d e L i e g e , Belgium.

M.

A. B E R Q U I N , Mission d ' A m e n a g e m e n t Basse N o r m a n d i e , C a e n , France.

M.

G. B I L L E N , V r i j e U n i v e r s i t e i t B r u s s e l , Belgium.

Dr.

R. B O N N E F I L L E , E l e c t r i c i t e d e F r a n c e , C h a t o u , France.

Pr0f.M.J. Dr.

B O W M A N , S t a t e U n i v e r s i t y of N e w Y o r k a t S t o n y B r o o k , U.S.A.

G.A. C A N N O N , P M E L / N O A A , S e a t t l e , U.S.A.

Pr0f.G. C H A B E R T D ' H I E R E S , I n s t i t u t d e M e c a n i q u e , G r e n o b l e , France. Dr.

P.C.

C H A T W I N , U n i v e r s i t y o f L i v e r p o o l , U.K.

Dr.

P . B . C R E A N , U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r , Canada.

M.

D.K.

D E M P S T E R , W a t e r R e s e a r c h C e n t e r , H e r t s , U.K.

Pr0f.A. D I S T E C H E , U n i v e r s i t e d e L i e g e , Belgium. Dr.

J. D R O N K E R S , R i j k s w a t e r s t a a t , R i j s w i j k , T h e Netherlands.

Dr.

K.R. D Y E R , I n s t i t u t e of O c e a n o g r a p h i c S c i e n c e s , T a u n t o n , U.K.

Dr.

A.J.

Dr.

D . M . F A R M E R , I n s t i t u t e of O c e a n S c i e n c e s , V i c t o r i a , Canada.

E L L I O T T , N A T O A S W R e s e a r c h C e n t r e , L a S p e z i a , Italy.

Pr0f.H.G. G A D E , G e o p h y s i c a l I n s t i t u t e , B e r g e n , Norway. M.

Y. G A L L A R D O , Ant. O R S T O M C e n t r e O c e a n o l o g i q u e d e B r e t a g n e , B r e s t , France.

Dr.

R.F. G R A M E N D E , E L S E V I E R S c i e n t i f i c P u b l i s h i n g C o m p a n y , Amsterdam, The Netherlands.

M.

P. H E C Q , u n i v e r s i t e d e L i e g e , Belgium.

M.

H.B.

H E L L E , U n i v e r s i t y of B e r g e n , N o r w a y .

Dr.

D.O.

H O D G I N S , R i v e r and H a r b o u r Lab., T r o n d h e i m , Norway.

X

Dr.

J.L. H Y A C I N T H E , C N E X O , P a r i s , France.

Pr0f.R.G.

I N G R A M , Mc G i l l U n i v e r s i t y , M o n t r e a l , C a n a d a .

Ir.

B. J A M A R T , University of W a s h i n g t o n , S e a t t l e , U.S.A.

Dr.

M. K A R E L S E , D e l f t H y d r a u l i c s L a b o r a t o r y , T h e Netherlands.

Ir.

A. L A N G E R A K , D e l f t H y d r a u l i c s L a b o r a t o r y , T h e N e t h e r l a n d s

Dr.

G. L E B O N , U n i v e r s i t e d e L i e g e , Belgium.

Dr.

J.J. L E E N D E R T S E , R A N D Corp., S a n t a M o n i c a , U.S.A.

Dr.

C. L E P R O V O S T , I n s t i t u t d e M P c a n i q u e , G r e n o b l e , F r a n c e .

Dr.

D. LIU, R A N D Corp.,

IT.

A. L O F F E T , U n i v e r s i t e d e L i e g e , Belgium.

M.

J.P. M A T H I S E N , River and H a r b o u r L a b . , T r o n d h e i m , Norway.

M.

D. M I C H E L , U n i v e r s i t e L i b r e d e B r u x e l l e s , Belgium.

M.

L.R. M U I R , O c e a n

Pr0f.J.C.J. Dr.

&

S a n t a M o n i c a , U.S.A.

Aquatic S c i e n c e s , B u r l i n g t o n , Canada.

N I H O U L , U n i v e r s i t e d e L i e g e , Belgium.

J.P. O ' K A N E , U n i v e r s i t y C o l l e g e , D u b l i n , Ireland.

Pr0f.F.B.

P E D E R S E N , T e c h n i c a l U n i v e r s i t y of D e n m a r k , L y n g b y -

C o p e n h a g e n , D.K. Dr.

P.A. P E R R E L S , D e l f t H y d r a u l i c s Lab., ?he Netherlands.

Dr.

J.J. P E T E R S , W a t e r b o u w k u n d i g L a b o r a t o r i u m , B o r g e r h o u t , Belgium.

Ir.

G. P I C H O T , S e c r e t a r i a t d ' E t a t 21 l ' E n v i r o n n e m e n t , Belgium.

or.

D. P R A N D L E , I n s t i t u t e o f O c e a n o g r a p h i c S c i e n c e s , B i r k e n h e a d , U.K.

Dr.

H.G. R A M M I N G , U n i v e r s i t y of H a m b u r g , Germany.

M.

R.P. R E I C H A R D , U n i v e r s i t y of N e w H a m p s h i r e , D u r h a m , U.S.A.

Dr.

F.C. R O N D A Y , U n i v e r s i t e d e L i e g e , Belgium.

M.

Y . RUNFOLA, Universite d e Liege, Belgium.

Dr.

J.C.

Dr.

H.M. van S C H I E V E E N , R i j k s w a t e r s t a a t , R i j s w i j k , T h e Netherlands.

S A L O M O N , Lab. d ' O c 6 a n o g r a p h i e P h y s i q u e , B r e s t , F r a n c e .

P r 0 f . J . D . S M I T H , U n i v e r s i t y of W a s h i n g t o n , S e a t t l e , U.S.A. P r 0 f . N . P . S M I T H , U n i v e r s i t y o f T e x a s , P o r t A r a n s a s , U.S.A. Dr.

R. S M I T H , U n i v e r s i t y of C a m b r i d g e , D A M P T , U.K.

Ir.

J. S N I T Z , U n i v e r s i t e d e L i S g e , Belgium.

X I M.

J. S T R O N A C H , U n i v e r s i t y of B r i t i s h C o l u m b i a , V a n c o u v e r , Canada.

Dr.

P.J.

M.

H. S V E N D S E N , U n i v e r s i t y o f B e r g e n , Norway.

M.

M.J. T U C K E R , I n s t i t u t e of O c e a n o g r a p h i c S c i e n c e s , T a u n t o n , U.K.

Pr0f.R.E. Dr.

S U L L I V A N , U n i v e r s i t y o f W e s t e r n O n t a r i o , Canada.

U L A N O W I C Z , U n i v e r s i t y o f M a r y l a n d , S o l o m o n s , U.S.A.

R.J. U N C L E S , Inst. f o r Marine E n v i r o n m e n t a l R e s e a r c h , P l y m o u t h , U.K.

M.

J . V O O G T , R i j k s w a t e r s t a a t , R i j s w i j k , T h e Netherlands.

Pr0f.D.F. Dr.

W I N T E R , U n i v e r s i t y o f W a s h i n g t o n , S e a t t l e , U.S.A.

J.T.F. Z I M M E R M A N , N I O Z , T e x e l , T h e Netherlands.

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XI11

CONTENTS

. . . . . . . . . . . . . . . . . . . . . . . . . . . ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . LIST OF P A R T I C I PANTS . . . . . . . . . . . . . . . . . . . . . FOREWORD

R.E. U L A N O W I C K Z and D.A. p l a i n e s t u ary J.C.J.

FLEMER

RONDAY, J.J.

P E T E R S and A. STERLING

H y d r o d y n a m i cs o f the Scheldt Estuary G. BILLEN and J. SMITZ

:

G.B. G A R D N E R and J . D .

. . . . . . . . . . . . . . .

SMITH

. . . . . . . . . . . . . . . . . . :

P.A.J. P E R R E L S and M. KARELSE

:

E L L I O T T a n d Dong-Ping WANG

:

f o r c i n g o n the Chesapeake Bay

D. PR A N D L E and J. WOLF S o u t h e r n N o r t h Sea R. BO N N E F I L L E

:

:

. . . . . . . . . .

:

T h e coupling between an

. . . . .

:

. . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . .

127

147

161

Residual phenomena in es tuaries, application

. . . . . . . . . . . . . . . . . .

187

A s ymmetry and anomalies o f circulation and

v e r t i c a l m i x ing in the branching of a lagoon-estuary ZIMMERMAN

:

. . .

197

Dispersion by tide-induced residual

c u r r e n t v o r t ices :

107

Surge-tide inte raction in the

to t h e G i r o nde Estuary

R. SM I T H

I9

The ef fect o f meteorological

re s p o n s e t o meteorological forcing

J.T.F.

63

L o ng-period, estuarine-shel f exchanges in

:

GA L L A R D O

55

A two-dimensional numerical

e s t u a r i n e system and i t s adjacent co astal waters

Y.

27

Turbulent mixing in a salt

model f o r s alt intrusion i n estuaries

SMITH

:

. . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . .

wedge e s t u a ry

N.P.

1

Modelling o f biological and chemical processes

:

in t h e S c h e ldt Estuary

A.J.

IX

Mathematical model of water quality

in a h i g h l y polluted estuary R. WO L L A S T

VII

A synoptic v i e w o f a coastal

:

. . . . . . . . . . . . . . . . . . . . . .

N I H O U L , F.C.

V

. . . . . . . . . . . . . . . . . . . . .

207

C o r i o l i s , curvature and buoyancy effects upon

d i s p e r s i o n in a n a r r o w channel

. . . . . . . . . . . . . .

217

XIV P.C. CHATWIN and P.J. SULLIVAN

:

H o w some n e w fundamental

results on relative turbulent diffusion c a n be relevant in estuaries and other natural flows L.R. MUIR

233

A o ne-dimensional t i d a l mode l for estuarine

:

. . . . . . . . . . . . . . . . . . . . . . . .

networks

B.M. J A M A R T and D.F.

WINTER

243

A n e w approach to the

:

computation o f tidal m o t i o n s in estu aries P.B. CREAN

. . . . . .

. . . . . . . .

261

A numerical model o f baratropic mixed tides

:

between V a n couver Island and the Mainland and i t s r e l a t i o n t o studies o f the estuarine circulation H.G. RAMMING

:

. . . .

283

Numerical investigations o f the influence of

c o a s t a l s t r uctures upon the dynamic off-shore process by a p p l i c a t i o n o f a nested t i d a l model R.P. REICHARD and B. CELIKKOL

:

. . . . . . . . . . .

315

Application o f a finite

element hydrodynamic model to the Gr eat Bay estuary s y s t e m , N e w Hampshire, U.S.A. M.J. BOWMAN

:

. . . . . . . . . . . . . .

349

S preading and mixing of the Hudson River

e f f l u e n t i n to the N e w York Bight J.J. L E E N D E R T S E and S.K.

LIU

:

. . . . . . . . . . . .

373

A three-d imensional turbulent

energy m o d e l for nonhomogeneous estuaries and coastal sea s y s t e m s

. . . . . . . . . . . . . . . . . . . . . . .

387

F1. Bo. P E D E R S E N : A brief review o f pres ent theories o f

. . . . . . . . . . . . . . . . . . . . .

Fjord d y n a m ics

H.G. G A D E and E. SVENDSEN

P r o p e r t i e s of the Robert R. Long

:

m o d e l o f estuarine circulation i n fj ords H. SVENDSEN and R.O.R.Y. in a fjord H.B. H E L L E

THOMPSON

:

423

Wind-driven circulation 439

S u mmer replacement o f d e e p water in Byfjord,

:

:

Mass exchange a c r o s s the sill induced

. . . . . . . . . . . . . . . . . .

by c o a s t a l upwelling D. FA R M E R and J.D.

SMITH

:

:

LAIRD

:

465

Two-layer analysis o f steady

c i r c u l a t i o n in stratified fjords C A N N O N a n d N.P.

441

Nonlinear int ernal waves in a

. . . . . . . . . . . . . . . . . . . . . . . . .

C.E. P E A R S O N and D.F. WINTER

G.A.

. . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

Western N o r w ay

fjord.

407

. . . . . . . . . . . .

495

Variability o f currents and

water p r o p e r ties from year-long observations i n a fjord estuary

. . . . . . . . . . . . . . . . . . . . . . . . .

Subje c t I n d e x

........................

515 537

1

A SYNOPTIC VIEW OF A COASTAL PLAIN ESTUARY* ROBERT E. ULANOWICZ AND DAVID A.

FLEMERS

University of Maryland, Center for Environmental and Estuarine Studies, Chesapeake Biological Laboratory, Solomons, Maryland 20688 James T. Allison James P. Brown Michael A. Champ Robert Cory

Donald R. Heinle John Klepper Donald W. Lear Charles E. Lewis

Curtis D. Mobley Kent Mountford John W. Pierce James L. Raper Susan K. Smith

ABSTRACT During October, 1972 the Patuxent River Estuary was monitored intensively and synoptically over two tidal cycles to determine the spatial and temporal patterns of various hydrodynamic, chemical and biological features. Forty-one depths at eleven stations along nine transects were sampled simultaneously at hourly intervals for salinity, temperature, dissolved oxygen, chlorohyll 5 , particulate nitrogen, nitrate, nitrite, total kjeldahl nitrogen, ammonia, particulate carbohydrate, dissolved organic carbon, total hydrolizablc phosphorous, dissolved inorganic phosphorous, suspended sediment, particle size distribution, and zooplankton. Tidal velocity was continuously monitored at each depth by recording current meters. Riverine input and meteorological conditions were relatively stable for two weeks preceeding the deployment. This communication describes the calculation of the intrinsic rates of change of the observed variables from their measured distributions in the Estuary. The steady-state, one-dimensional equation of species continuity is employed to separate the advection and tidal dispersion of a hydrodynamically passive substance from its intrinsic rate of change at point. A new spatial transform is introduced for the purpose of interpolation and extrapolation of data *Contribution No. 766 , University of Maryland, Center for Environmental and Estuarine Studies. $Present Address : Division of Biological Services, U. S . Fish and Wildlife Service, Washington, DC 20240.

2

The intrinsic rate of change profiles reveal a region of heavy bloom activity in the upper estuary and a secondary bloom near the point in the River that most of the suspended material settles out. The changes in Ammonia and nitrates are highly correlated to the productivity patterns. productivity.

Phosphorous rates are less closely correlated to

The perturbations that the Chalk Point steam electric

power plant have on the heat and oxygen balances are easily discernible. INTRODUCTION Practically every ecologist who has planned a field study has had to grapple with the limitations finite manpower and equipment impose upon his ability to adequately sample his system over its spatial and temporal domains. Marine and estuarine ecologists are particularly limited by the size and accessibility of their study areas from viewing the manifold physical, chemical and biological processes synoptically. While the developing technology of remote sensing is beginning to alleviate this difficulty, there is still no substitute for in situ sampling through the water column and over its areal extent. In the study described below the investigators have amassed a set of data on key physical, chemical and biological variables taken simultaneously over a net of stations along the Patuxent River Estuary, a tributary estuary of the Chesapeake Bay. The objectives behind such a data acquisition are threefold: 1. To serve as a data set for the purpose of calibrating a combined physical - chemical - biological model yet to be developed. 2. To enable the authors to estimate the magnitude of the rates

of various processes as they occur along the Estuary. 3.

To provide a reference set of data that investigators without

recourse to synoptic data collection may use to evaluate their own hypothesis about estuarine ecosystem dynamics. An opportunity to embark upon such an ambitious task occurred in the fall of 1972 during the acquisition of prototype data for the The Chesapeake

U.S. Army Corps of Engineer's Chesapeake Bay Study.

Biological Laboratory and the Chesapeake Bay Institute of the Johns Hopkins University were under contract to the Corps to deploy current meters and research vessels to measure tidal velocities and salinities in the mid-portion of the Bay.

3

TO monitor the stations prescribed by the Corps in the Bay stem and major tributaries usually required several deployments of the

available manpower.

The Patuxent Estuary, however, was small enough

to cover in a single deployment, yet large enough t'o serve as a replica of most estuarine processes. The study called for the deployment of thirty-four meters at eight stations on six "transects" along the axis of theEstuary. The current meters (Braincon #1301 Histogram Recording Current Meters) recorded tidal speed and direction automatically every ten minutes. The salinity beside each meter was to be measured with an induction salinometer lowered from a shipboard at hourly intervals for thirteen hours of three consecutive daylight periods. With all of the vessels and men deployed for this study it appeared to the authors that, for relatively little extra effort, a host of

chemical and biological variables could be measured simultaneously with the currents and salinities. The result would be a "snapshot" of the Estuary giving detailed information about a complex of phenomena for a short period of time. As extra manpower and equipment would be needed for such a survey beyond that of the two participating organizations, assistance was solicited from neighboring research groups in the Bay. The response was overwhelming.

Nine research institutions volunteered boats,

equipment and manpower to the effort. With the consent of the Corps the program was expanded to cover forty depths of eleven stations on nine transects along the Estuary. Some of the details concerning the study area, sampling location, variables measured and data reduction are given in the following

sections.

Later, the authors present the analysis of the process

rate profiles and attempt to relate these magnitudes to mechanisms occurring at various reaches of the Estuary. STUDY AREA

The Patuxent River is a significant tributary of the Chesapeake Bay some 160 km in length and draining some 2494 km 2 , all within the State of Maryland. The River rises some 48 km west: of the city of Baltimore and flows southeast and south through the Piedmont Plateau to the fall line 90 km above the mouth.

While the upper

32 km of this river is protected as a source of drinking water for

the Washington Metropolitan Area, approximately 200 million liters per day of treated sewage enter the next 56 km.

The region from

4

90 km to 48 km above the mouth is tidal, fresh-brackish water and is characterized by a narrow channel meandering through broad, marshy flats.

The lower 40 km of the Estuary is a drowned river

valley characterized by partially-mixed, two-layer flow, except near the mouth where occasional three-layer phenomena have been reported. The study area is confined to the lower 72 km of the Estuary ending at a point where the Western Branch sub-tributary joins with the main stream. Eleven stations were established at nine distances along the river as shown on Fig. I.

The coordinates of each station

are listed in Table I. along with the depth in meters at which each current meter was suspended. The vertical spacing between the sensors was nominally 3 meters. The lower four stations were sampled only for tidal current, salinity and temperature, whereas stations P-03-01 through P-07-01 were sampled for the full set of physical, chemical and biological data as described below. The study period was from 0600 on 17 October through 0700 on 18 October, 1972 with samples taken at hourly intervals over the two tidal cycles and one diurnal period.

Jug Boy

Nottingham

Fig. I.

Stations on the patuxent River Estuary

5

TABLE 1

Station location and depths

I Station Designation1

;yo

P-01-01 P-01-02

0.0

i I

I Longitude 76O 2 5 '

17"

76

17

25

Depths (M) 38O 1 8 ' 4 3 " 38

18

55

0.6, 3.7, 12.2

6.7,

9.8,

0.6,

6.7,

9.8,

12.8,

3.7, 15.9

P-02-01

10.0

76

29

33

38

20

50

0.6,

3.7,

6.7

P-02-02

10.0

76

29

08

38

21

00

0.6,

3.7,

6.7,

12.8,

15.9,

P-03-01

22.6

76

35

07

38

24

42

1.2,

3.7,

6.7

P-04-01

33.4

76

39

55

38

29

38

1.2,

3.7,

6.7,

P-04-02

39.3

76

40

32

38

32

30

1.2,

3.7

P-05-01

43.6

76

40

44

38

34

46

1.2, 3 . 7

P-05-02

53.3

76

41

03

38

39

23

1.2, 3 . 7 ,

6.7 6.7

P-06-01

61.3

76

42

02

38

42

33

1.2,

P-07-01

71.8

76

42

53

38

46

40

1.2

3.7,

9.8,

18.9,

21.5

9.8

SAMPLING PROCEDURE

At each hour beginning on the hour the following sequence of sampling procedures was carried out at each of the seven stations for every depth at which a current meter was moored: 1. Conductivity and temperature were measured in situ by lowering an induction coil and thermocouple apparatus (Inter-Ocean 503A CST or Beckman RS-5 salinometer). 2.

Dissolved oxygen was measured in situ at three stations equipped with the Inter-Ocean CST-DO units and from the remaining stations by immersing a YSI dissolved oxygen cell into freshly pumped water from the proper depth. 3. Approximately eight liters of water was pumped from the required depth and immediately processed as described below. 4. Zooplankton were filtered from 3 0 liters of water pumped from the prescribed depth through a 7 2 micron plankton net. 5. During the daylight hours Secchi disc extinction depths were

read. Aliquots of the water collected in step 3 above were immediately filtered and processed as follows: Chlorophyll - Mg C o g was added t o a 1 0 0 - 2 0 0 m l (exact amount recorded) aliquot and filtered through a GF/C glass fiber filter. The filtered material was immediately frozen for subsequent analysis in the laboratory.

6

Particulate Nitrogen - 100-200 ml of water was filtered on a different Millipore system and the GF/C filter and material were dehydrated for later analysis. Particulate Carbohydrate - 100-200 ml was filtered through a GF/C filter which had been fired to remove any carbon. The residual material was frozen for later analysis. Dissolved Nitrogen and Phosphorous - Two Whirl-Pax bags were filled with 75-100 ml of filtrate from the two preceeding filtrations and frozen for later chemical analysis. Total Phosphorous and Organic Carbon ~

-

Unfiltered samples of

50-75 ml volume were frozen to be analyzed later. Suspended Sediment - About 50-100 ml was filtered on a "tared" 47 mm Millipore filter to be dehydrated and weighed in the laboratory. ANCILLARY COOPERATIVE STUDIES In addition to the baseline measurements outlined above the schedules of three other Patuxent studies being conducted by cooperating institutions were altered to be cotemporaneous with the Patuxent synoptic survey. Heinle and Flemer (1976) were directing monthly observations of mass transfer between a section of marsh and the Patuxent River channel. The subject marsh was within the synoptic survey area and the sampling protocol was very similar to that described above. Therefore, the 24-hour marsh study took place simultaneous with the synoptic survey. The Philadelphia Academy of Natural Sciences, likewise, was conducting monthly cruises to measure the gross and net photosynthesis along the River by the oxygen-bottle method. Relative numbers of phytoplankton and bacterial taxa were also determined alongside the various stations of the synoptic survey while the study was underway (Mountford et. al. 1972). The National Aeronautics and Space Administration facilities at Wallops Island and Lanqley, Virginia realized an opportunity to acquire ground-truth data from the synoptic operations and arranged to fly two C-147 and one C-130 missions to take black and white, color IR photographs and multi-spectral scans of the Patuxent during the daylight hours of the deployment (Ohlhorst, 1976). The U.S. Coast and Geodetic Survey was also maintaining four automatic recording (six-minute interval) tidal height gauges along the Patuxent as part of the Corps' Chesapeake Bay Study.

7

CHEMICAL ANALYSIS OF SAMPLES Immediately upon the termination of the deployment the samples were sorted and sent to the laboratories of five of the cooperating institutions.

The Chesapeake Biological Laboratory performed the

analysis for chlorophyll a, particulate carbohydrate and particulate nitrogen; the Department of Biology of the American-University analyzed the samples for particulate and dissolved carbon; the Maryland State Water Resources Administration determined the values of total and dissolved phosphorous; and the Annapolis Field Office of the U.S. Environmental Protection Agency effected the measurement of ammonia, kjeldahl nitrogen, nitrate and nitrite. The sedimentology division of the Smithsonian Institution's Museum of Natural History weighed the sediment samples. Active chlorophyll g was determined fluorometrically with a Turner Model 111 fluorometer (Yentsch and Menzel, 1963 and Holm-Hansen et. al., 1965). A specific absorption coefficient of 12.8 was used in the primary spectrophotometric calibration. The Dumas method of high temperature oxidation was used to determine particulate nitrogen. Analysis were carried out on a Coleman Model 29A Nitrogen Analyzer equipped with a Model 29 combustion tube and syringe. Particulate carbohydrate was determined by the anthrone reaction as described in Strickland and Parsons (1972). Particulate and dissolved fractions of organic carbon were measured according to the methods described by Menzel and Vacarro (1964). The remaining fractions of phosphorous and nitrogen were measured on Technicon Auto Analyzers according to Methods for Chemical Analysis of Water and Wastes published by the U.S. Environmental Protection Agency (1974). The single reagent ascorbic acid reduction method (pp. 249-255) was used to obtain dissolved orthophosphorous, while the total hydrolyzable phosphorous values were the results of the colorometric ascorbic acid reduction method (pp. 256-263). Total kjeldahl nitrogen Values resulted from the automated phenate method (pp. 182-186); ammonia from the automated colorometric phenate method (pp. 168-172); and both nitrite and nitrate from the automated cadmium reduction method (pp. 207-212). In summary, the tidal speed and direction were recorded at each depth at ten-minute intervals. Other variables measured each hour at the forty depths include salinity, temperature, dissolved oxygen,

8

suspended sediment, chlorophyll

a,particulate

nitrogen, particulate

carbohydrate, nitrate, nitrite, ammonia, total kjeldahl nitrogen, total hydrolyzable phosphorous, dissolved orthophosphorous, particulate organic carbon, dissolved organic carbon and zooplankton density. Other variables observed on an opportunistic basis include gross and net photosynthesis, phytoplankton taxa and relative numbers, insolation, coliform counts, river flow and tidal height. Meteorological data from the Patuxent River Naval Air Station near the mouth of the Estuary are probably available, but have not been assembled to date. All processed data is available to the public through the National Oceanographic Data Center*. ESTIMATION OF PROCESS RATES The primary objective of the Patuxent Synoptic Study as cited in the introduction is to enable the development of a combined physical chemical - biological model of a coastal plain estuary. Ideally, if one is to set about modeling a system of such complexity, it is useful to develop a preliminary model based on fragmentary empirical data and other a_ priori _ _ estimates. Such an initial model is often a substantial aid in prescribing a data acquisition scheme. Unfortunately, the opportunistic and @ hot nature of this study did not allow for such preliminaries, and the authors must begin the modeling process after the data collection. The model structure (especially the chemical and biological sub-models) will thus be guided by the results of the initial data manipulations. The entire modeling procedure will then take on much of the nature of a posteriori modeling as described elsewhere (Ulanowicz et. al., 1975 and 1978). Under this approach the structure of the reaction kinetics results from comparing the rates at which species (inorganic, organic, and living) are appearing and disappearing with the amounts present. The data acquisition scheme described above will result in information on the stocks of the species. The rates at which they are intrinsically changing, however, is confounded by the association advection and dispersion in the Estuary. The remainder of this presentation will be devoted to the estimation of the process rates and the qualitative behavior evinced by the results.

*NOAA Master Reel #9008, Environmental Data Services, National Oceanographic Data Center, Washington, D.C. 20235, U.S.A.

9

The separation of the intrinsic rates from the hydrological transport requires a statement of mass balance. Since data was acquired from a string of single stations along the estuary, it is natural to begin with a one-dimensional mass balance, i.e., all variables are averaged over a cross-section of the estuary. Since concentrations and velocities are available at frequent intervals, it is possible to state the equation of species conservation at various times during the tidal cycle.

To do so,

however, would yield results with little statistical significance. Therefore, a one-dimensional, tidally-averaged equation of species continuity is chosen to begin with: A

(CQ) -

=

at where

ax

a (KA -)ac

+

R

ax

ax

C is the tidally-averaged concentration Q is the cumulative freshwater input up to point x A is the local cross-sectional area K is the longitudinal dispersion coefficient

R is the rate of appearance or disappearance of C

x is the t is the Mow the middle of the synoptic study,

distance upstream time October, 1972 was a propitious time to perform since the U . S . Geological Survey records indicate

that riverine input to the lower estuary was virtually constant for the two weeks preceeding the observations. Hence, the River was, most likely, as close to tidally-averaged steady-state conditions as one could hope to achieve.

During the measurement period a

meteorological high pressure front did pass through the area causing a net loss of water from the Estuary, but the effect of this short-term phenomenon upon the steady-state gradients was probably small. Henceforth, the Estuary will be assumed at steady-state, and equation (1) can thus be solved for the "reactions term" as: d dC R = K d x (A=)

dC d K + A -dx dx

-

3 dx

dC

Qdx

Each term on the right-hand-side of e q u a t i m (2) can be reasonably estimated - the concentration profiles are known from the measurements, the freshwater input profile can be evaluated with minor assumptions from USGS data, the areas are available from bathymetric charts, and the dispersion coefficient profile can be calculated from the observed salinities.

There are, however, a number of numerical

details associated with these estimates which should be discussed.

10

To begin with the values for the concentrations at a station are averaged over the station depths. In this averaging each point reading is weighted according to the fraction of the cross-sectional area associated with the particular depth. The resultant station values are subsequently averaged over the two tidal cycles (and one diurnal period) of the study. Each variable then has one "steadystate" value associated with each station at which measurements were taken. The calculated steady-state values are listed in Table I1 The longitudinal distances between stations are greater than is desirable, with distances of over 10 km separating the biological stations.

Furthermore, the lower 22 kilometers were not covered by

the chemical and biological sampling program. A rational method of interpolation and extrapolation of the variables and their derivatives is therefore, in order. Reasoning heuristically that longitudinal mixing becomes greater (in the absolute sense) as the Estuary crosssection increases, it would follow that longitudinal gradients are dampened as the Estuary widens. The cross-sectional area thus becomes a weighting factor for the existing gradients, and it is convenient to define a new independent variable, A , characterizing longitudinal distance as: dh

=-

dx A (x)

(3)

or equivalently:

This transformation of the independent variable has the advantage that the transformed descriptions of advection and dispersion become independent of estuary qeometry, i.e., equation (2) becomes:

Straightforward linear extrapolation of C ( A ) and its derivatives into the downstream range gave more plausible results than similar efforts using several different non-linear regression schemes an C (x). The areas used in this transform are graphed in Figure 2. Encouraged by the utility of this transform, the author proceeded to estimate C ( X ) and its two derivatives by the simplest means possible. Concentrations at any longitudinal distance were

TABLE I1

Averaged c o n c e n t r a t i o n s Species (Units)

33.4

39.3

11810

10430

10.25

7.464

0.081

0.166

K j e l d a h l N i t r o g e n (MGA/L)

0.567

D i s s o l v e d O r t h o P h o s p h a t e (MG/L)

0.026

T o t a l P h o s p h o r o u s (MG/L)

22.6

43.6

53.3

61.3

71.8

7640

6340

1410

300

203

16.85

22.46

40.20

68.50

8.715

0.130

0.100

0.153

0.114

0.075

0.759

0.174

0.101

0.118

0.224

0.717

2.150

0.502

0.629

0.507

0.416

0.609

1.387

0.052

0.055

0.019

0.058

0.071

0.767

0.052

0.134

0.114

0.100

0.070

0.262

1.187

D i s s o l v e d O r g a n i c Carbon (MG/L)

3.192

3.483

3.196

3.190

4.278

4.962

3.562

P a r t i c u l a t e Carbon (MG/L)

2.210

2.088

1.881

2.438

3.527

4.015

2.290

Suspended M a t e r i a l

S a l i n i t y (MG/L) C h l o r o p h y l l -A

( G/L)

Ammonia Nitrate-Nitrite

(MGA/L)

(KM)

18.651

-----

35.507

68.486

52.380

44.034

30.00

D i s s o l v e d Oxygen (MG/L)

9.42

9.34

8.98

8.62

10.80

12.11

7.13

H e a t C o n t e n t (KCAL/LITER)

16.83

16.38

15.69

16.02

15.12

14.62

13.59

(MG/L)

12

approximated by linear interpolation of the two nearest stations. The derivatives at the mid-point between two stations were estimated by the difference quotient of the concentration change and the interval of A . Derivatives at other points were acquired by linear inter polation and extrapolation. Second derivatives were calculated by a repeat application of the derivative scheme.

0.025 Potuxent Estuary

Cross -Sectional Areas

0.020

0.015

-0 0 ._ c

j

0.010-

n v)

?

U

0.005 10

OO

20

,

L

30 1

1 L ---

40

50

60

- L L - - . L

70

-

River Kilometer

Fig. 2.

Patuxent estuary cross-sectional areas.

Over 40% of the area of the Patuxent watershed lies adjacent to the study area, making it impractical to consider that all of the freshwater input occurs at the head of the model. By pro-rating the input according to area, one estimates that Q increases from about 4.75 M3/sec at the head of the Estuary to around 8.10 M3/sec at the mouth. Now observation of the watershed reveals that most of the feeder streams run perpendicular to the longitudinal axis of the Estuary and their mouths are evenly dispersed along both banks. An appropriate assumption, therefore, is that the rate of accumulation of freshwater input, dQ/dx, is nearly c3ntinuous along the main River axis and proportional to the width of the watershed at that point. Figure 3a shows the schematic representation of the watershed adjacent to the study area. Figure 3b below it illustrates the cumulative riverine input at any point in the Estuary. Under the above assumptions Q varies almost linearly along the region of interest.

13

1

Drainage Basin Schematic

, 0

20

1

,

I

40

60

I

River Kilometer

Fig. 3 . (a) Drainage basin schematic showing width as a function of distance upstream (b) Cumulative freshwater input as calculated along the estuary The only remaining terms from equation (4) to be estimated are K and dK/dh.

They may be calculated from the observed salinity profile. Salt, being a conservative substance, should have a zero intrinsic rate of change. There is a source term for salt, however, associated which arises from the input of residual salinity (C,) with the freshwater input. Equation (4) is then written as:

%(K

dC dX -

d or -[K dX

dQ CQ) = -C r dh

dC dh - (C-Cr ) Q ] = 0

14 Assuming that advection balances dispersion at steady-state allows one to estimate K as:

and subsequently calculate:

TO avoid the possibility of a negative value of K resulting from noise

in the derivatives of the salinity, the salinity was approximated by the implicit function: (S

-

.17)1.04776

[A

+

814.04(S-.17)

-

107941 = 3255.7

where S is the salt content in parts per thousand and in reciprocal kilometers. mated salinities.

A

is measured

Figure 4 shows the measured and approxi-

151

lo-

\

0

8 > 4

(S-0.171"'"[A

+ Sl4.04(S-O.I7)-lO794.0] ;3255.7

A

OO

10

20

30

Fig. 4 . Salinity as a function of reduced longitudinal coordinate (river month = 0.0).

15

The longitudinal variation of the dispersion coefficient is depicted in Figure 5. Qualitatively, the variation is similar to that obtained from the Escaut Estuary by Wollast (1973) and discussed by Ronday (1975). The dispersion coefficient declines upstream to a minimum near the point at which theEstuary narrows and rises thereafter to values higher than those found in the lower estuary

.

'20i

7-

COEFFICIENT OF L O N G I T U D I N A L DISPERSION

I

10

20

30 RIVER

Fig. 5.

40

50

60

70

KILOMETER

Calculated coefficient of longitudinal dispersion.

Now Q , K and their derivatives have been estimated independently of the outlined interpolation scheme. A useful test of how compatible the interpolation estimates are with the assumptions used on Q and K would be to calculate the reaction rates of the salt as if it were

a reactive substance.

Performing such a balance yields a total

gain of 0.41 metric tons of salt per day for the entire Estuary. This is an inconsequential fraction of the 5.7 million metric tons of salt present in the Estuary.

16

DISCUSSION OF THE INTRINSIC RATES OF CHANGE The calculated profiles for the rates of change are depicted in Figure 6. A positive value for the rate of change indicates a source of the given material and a negative value denotes a sink. The reader will notice that the term "reaction" has been avoided where possible so as not to infer .a priori the mechanism contributing to a given source or sink. Other mechanisms besides chemical or ___.

biological reactions which might contribute to the intrinsic rates of change include inputs associated with freshwater inflows and adsorption onto sedimenting material. Chlorophyll2 is often used as an indicator of primary productivity of an aquatic ecosystem. The appearance of chlorophyll 2 is then, indicative of an algal "bloom". A very significant bloom is observed in the upper estuary (60-72 km), and a secondary bloom is observed along the range from 39 to 45 km (Figure 6a). A sewage treatment plant introduces nutrients into the Western Branch which enters the mainstream of the River about two kilometers above the study area. It is reasonable to assume that the observed bloom is in response to this nutrient addition. The secondary bloom is coincident with the initial disappearance of suspended material and is possibly the result of light no longer being limiting to productivity.

Chlorophyll

a

is lost in the remainder of the Estuary presumably due to herbivorous uptake. On balance the Estuary as a whole is a source of approximately 0.04 metric tons of chlorophyll per day. It is of primary interest to follow the behavior of the nutrient species to see how they relate to the observed patterns of phytoplankton growth and death. The most striking correlation to the productivity is exhibited by ammonia, Figure 6b. Its rate of change is practically inversely proportional to that of chlorophyll a. With the exception of a small reach of the Estuary (53-57 km), the appearance of one microgram of chlorophyll g is accompanied by the disappearance of approximately ten microgram atoms of ammonia (and vice-versa)

.

Nitrate and nitrite also exhibit close correlation to the primary production patterns (Figure 6c). The loss of these species is slightly heavier than that of ammonia in the upper estuary (>45 km) and the inverse correlation with primary production breaks down more drastically in the stretch from 47-57 km. In the lower estuary nitrates appear on almost a mole-for-mole basis with ammonia.

17

I Chlorophyl

E

I

1

.-U c n ._

-c

t

I

I

c

I

- 0.02 0

10

20

30

40

50

,

__--

60

70

River Kilometer

0)

:

. E

Y

>.

1 U

-d

o-2i

Ammonia

I

0.11

I-

a

F

L

V c

0

a

L

0

DI

.-U C n ._ c L

-C _.

0

10

20

.

30

40

50

60

70

River Kilometer

Fig. 6. Daily rates of appearance ( + ) or disappearance ( - ) of vdrious substances for kilometer sequents of the Patuxent River Estuary.

0.2 -

Nitrates

6

Nitrita

0.1 -

0

-0.1

-0.2I

0

10

20

30

40

50

60

70

River Kilometer

0.l6

Total Kjeldohl Nitrogen (dissolved)

0.08

I

0

10

20

I

30

40

River Kilometer

50

60

70

19

0.2

Dissolved O r t h o p k q h t e

0.1

0

-0.1

-0.21 10

0

20

30

40

50

60

70

River Kilometer

Total Hydrolyzable Phosphorus

-0.08

-0.161

, L

0

,

10

'

,

20

'

'

-.A__ '

30

40

River Kilometer

50

60

70

Dissolved Organic Carbon

-0.4 40 River Kilometer

0.4

-0.2 -

-0A-

Porticubte C

h

50

60

70

21

0

10

20

30-

50

40

River Kilometer

1

.

0

6

7

-10

20

1

30

40

River Kilometer

1

,

50

,

-L

60

70

60

70

23

Total (kjeldahl) nitrogen is lost throughout the entire length of the Estuary (see Figure 6d) with the exception of the reach from 38-45 km.

The gain in total nitrogen coincides with the secondary bloom of phytoplankton just below the sediment trap. There is loss of all species of nitrogen from the Estuary as a whole. Cumulative loss of total nitrogen amounts to about 4.7 metric ton atoms per day with 1.9 metric ton atoms of nitrate-nitrite and about 0.5 metric ton atoms of ammonia disappearing from the study area each day. Phosphorous appears to be less correlated to productivity than was the case with the nitrogen species. Dissolved orthophosphate (see Figure 6e) was lost from the upper Estuary ('45 km) with heavy disappearance above G O km. The lower Estuary hosted a small gain in the same species. Apparently, the dissolved phosphorous does not remain long in the water column after its addition from the Western Branch. Total phosphorous (Figure 6f) behaves similarly, except that there is significantly more phosphorous gained in the lower Estuary (presumably in the particulate form). Total phosphorous is almost conserved over the whole range with a l o s s of only 0.4 metric ton atoms occurring per day. Dissolved phosphorous, in apposition, is lost at the rate of 1.7 metric ton atoms per day. There are several hypotheses which might explain the observed patterns of phosphorous behavior.

The phosphorous lost in the

upper ~ s t u a r yis likely due to adsorption to the suspended sediments. There does not appear to be any uptake of dissolved phosphorous in the region of the secondary bloom. The source of phosphorous in the lower Estuary is in question. It could originate in the main stem of the Bay, or it could conceivably be regenerated from the sediments. Dissolved and particulate carbon (see Figures Gg, h) follow similar patterns. Both are accreted in the upper regions ( > 5 5 km) and the lower Estuary ( < 3 5 km), but the forms are lost in the transitional region. The bloom and detrital contributions from the marsh are likely sources of carbon in the upper reach. Metabolic products could possibly explain the source of carbon in the lower Estuary. The disappearance of chlorophyll 5 in the lower Estuary does not imply the absence of carbon fixation in these regions. It simply states that losses (e.g. consumption by grazers) exceeds production by growth.

The productivity of the lower Estuary is

24

revealed by the carbon figures. Over 20 metric ton atoms of carbon are produced each day by the study area with 13.5 ton atoms appearing in the dissolved phase and 6 - 7 ton atoms in the particulate form. The calculations reveal (Figure 6i) that 150 metric tons of suspended material are lost to the system each day with most of that figure probably going to the sediments. The upper region where suspended material is accreted is well demarcated from the lower region (J

tron flux H ( s , t ) d u e t o t h e b a c t e r i a l a c t i v i t y

C . i s the t o t a l e l e c i i ; the s u m o f the p r o -

d u c t i o n t e r m s C v , P i r e d u c e s t o t h e r e a e r a t i o n , c a l c u l a t e d by a r e lation

where K i s a k n o w n c o n s t a n t . The e q u a t i o n ( 9 ) budget

-

VA F ( s , t )

-

which represents a global oxido-reduction

can be w r i t t e n =

Vl

sat K(X1 - XI)

-

T h e set of e q u a t i o n s ( 2 ) -

H(s,t)

(11)

( l l ) , with the corresponding boundary

c o n d i t i o n s , a l l o w s a c o m p l e t e d e t e r m i n a t i o n o f t h e X . ' s ( s , t ) and 1

t h e Y i ' s (s,t). T h e n u m e r i c a l d i s c r e t i z a t i o n of the e q u a t i o n s p r o v i d e s t r i d i a g o nal m a t r i c i a l e q u a t i o n s , w h i c h a r e c a l c u l a t e d b y r e c u r r e n t a l g o r i t h m s (Adam and Runfola 1 9 7 1 , Adam 1975).

A s the e q u a t i o n ( 1 1 ) c o n t a i n s

the o x y g e n c o n c e n t r a t i o n X I e x p l i c i t l y , the term

i s c a l c u l a t e d w i t h the v a l u e o f XI a t t h e p r e c e e d i n g t i m e s t e p ( i f X1

v a r i e s s l o w l y ) , o r w i t h a n i t e r a t i v e c o m p u t a t i o n scheme. During t h i s n u m e r i c a l i t e r a t i v e p r o c e s s , a k i n e t i c l i m i t a t i o n o f

the local n i t r a t e p r o d u c t i o n term is i n t r o d u c e d , to r e n r o d u c e t h e a c t i v i t y r a t e of n i t r i f y i n g b a c t e r i a in the d o w n s t r e a m p a r t of the estuary. T h e r e s u l t s of the c a l c u l a t i o n s are shown a t f i g . 2.a.b. situation

:

february

I

summer situation

:

(winter

july).

ACKNOWLEDGEMENT T h i s work w a s c o n d u c t e d in the s c o p e o f

the Belgian National

E n v i r o n m e n t P r o g r a m , s p o n s o r e d by the S c i e n c e P o l i l c y a d m i n i s t r a t i o n , Office

of the P r i m e Minister.

REF 3 ' REN C E S

A d a m , Y. and Runfola Y., '1971. N u m e r l c a l R e s o l u t l o n o f d i f f u s i o n e q u a t i o n , R a p p o r t N.9, P r o g r . Nat. E n v i r o n n e m e n t p h y s i q u e e t B i o l o q i q u e , P r o l e t Mer.

A d a m , Y., 1975. A H e r m i t l a n f i n i t e d l f f e r e n c e m e t h o d f o r the s o l u tion of p a r a b o l ~ c e q u a t i o n s , to be p u b l i s h e d .

62 B i l l e n , G., 1975. N i t r i f i c a t i o n in the S c h e l d t E s t u a r y ( B e l g i u m and the Netherlands). E s t u a r i n e a n d Coastal M a r i n e S c i e n c e , 3, 79-89. A m a t h e m a t i c a l m o d e l of oxido-reduction Billen G . and S m i t z J., 1975. p r o c e s s e s in the S c h e l d t E s t u a r y , M a t h M o d e l s e a - I C E S Hydrography Committee C.M. 1 9 7 5 , C : 2 1 .

B i l l e n , G., S m i t z , J., S o m v i l l e , M. and W o l l a s t , R., 1976. Degradation d e la m a t i e r e o r g a n i q u e e t p r o c e s s u s d ' o x i d o - r e d u c t i o n d a n s 1 ' E s t u a i r e d e 1'Escaut. P r o g . Nat. R-D E n v i r o n n e m e n t - P r o j e t Mer - R a p p o r t F i n a l - v o l X , p. 102 - 152. Redox p o t e n t i a l s , in T h e S e a , G o l d b e r g ed., vol B r e c k , W.G., 1974. 5 , W i l e y , N e w York. N i h o u l , J.C.J., Amsterdam.

1975. Modelling o f M a r i n e S y s t e m s , E l s e v i e r P u b l . ,

N i h o u l , J.C.,T., R o n d a y , F.C., S m i t z , J. and B i l l e n , G., 1977. H y d r o d y n a m i c and water q u a l i t y m o d e l o f t h e S c h e l d t E s t u a r y . Marsh-Estuarine S i m u l a t i o n Symposia. Georgetown, South Carolina, J a n v i e r 6-8, 1 9 7 7 , in press. O v e r b e c k , J. and D a l e y , R.J., 1973. S o m e p r e c a u t i o n a r y c o m m e n t s o n the Romanenko techniqu'e for estimating h e t e r o t r o p h i c b a c t e r i a l B u l l . E c o l . R e s . C o m m . ( S t o c k h o l m ) , 1 7 , 342-344. production. 1964. Heterotrophic CO a s s i m i l a t i o n by bacterial Romanenko, V . I . , f l o r a o f water. M i k r o b i o l . , 3 3 , 7 7 9 - 6 6 3 . R o n d a y , F.C., 1975. Ecude de l'envasement e t de la variation longitudinale d u coefficient d e dispersion dans les estuaires partiell e m e n t stratifies. A n n a l e s d e s T r a v a u n : Publics, 4 , 1975. T h o r s t e n s o n , D.C., 1970. E q u i l i b r i u m d i s t r i b u t i o n o f s m a l l o r g a n i c Geochim. Cosmochim. A c t a , 34, m o l e c u l e s in n a t u r a l waters. 745-770. Wollast, R . , 1973. C i r c u l a t i o n , a c c u m u l a t i o n e t bilan d e m a s s e d a n s l'estuaire d e l ' E s c a u t , R a p p o r t d e s y n t h e s e 1 9 7 2 , C o m m i s s i o n Interministerielle de la Politique Scientifique (Belgium).

63

MODELLING OF BIOLOGICAL AND CHEMICAL PROCESSES IN THE SCHELDT ESTUARY.

R. WOLLAST Laboratory of Oceanography, University of Brussels (Belgium). INTRODUCTION Research chemists and biologists involved in a dynamical description of the behaviour of chemical species or living organisms in estuarine systems are faced with the difficult problem of evaluating the in situ rates of transformation of the species considered, and distinguishing concentration changes due to the mixing of water masses from changes related to biological or chemical processes. Generally, they do not have the opportunity to use elaborated hydrodynamica1 models, for two reasons, either because these models are inexistant, or too complicated in order to include in a tractable manner, the kinetic terms describing the evolution of the chemical and biological parameters. Hereafter, we intend to show by means of a few examples, that the use of simplified unidimensional and stationnary models of the estuarine system constitute a first approach allowing a better understanding of the chemical and the biological processes occuring in the system, when considering long term evolutions of the parameters. The basic principle of these models is to use the distribution of salinity, which i s a conservative parameter, in order to evaluate the mixing processes of fresh water and sea-water. The longitudinal distribution is then simply reduced to : d (u-S) dx

=

Id - (A A dx

dS dx

K -)

The longitudinal mixing coefficient K deduced from the salinity profile then includes effects related to the complicated hydrodynamical circulation of estuarine system and, to a certain extent, non-stationnary effects due to changes of the fresh water discharge and the tidal amplitude. For a non-conservative substance, the longitudinal profile will be described by :

! !-(uC) dx

=

Id dC - (A K -)dx A dx

+

P

-

C

if P and C are respectively the production and the consumption terms affecting the considered constituant.

64

The principal aim of the model is however for the biologist or the chemist to evaluate their importance and their dependence on other environmental parameters. The utilisation of the same longitudinal mixing coefficient in order to describe the hydrodynamical behaviour of such substances, and particularly those introduced in the estuary by the fresh water flow, must be considered with great care.

It is for example easy to understand that such a simplifica-

tion is out of the question when the estuary is vertically stratified or when the residence

time of the fresh water is short in relation to the fluctuations

of the water discharge.

Thus, the model must be tested with other conservative

parameters, ideally characteristic of the fresh water flow. It will be shown in the following paragraphs that the simplified unidimensional model may be applied in the case of the vertically well mixed Scheldt estuary, and that it resulted in the identification of several important mechanisms and rate constants about the behaviour of various chemical species in the estuarine system. THE BEHAVIOUR OF DISSOLVED SILICA The estuaries constitute an important source of dissolved silica for the marine environment since river water has a mean content of 15 mgr SiO /l 2 compared to that of 6 mgr Si02/l for the mean ocean and values as low as 0 , l mgr SiO /l for surface sea-water. It is an essential nutrient for diatoms, 2 which are the dominant phytoplancton species in many areas. The behaviour of dissolved silica in the estuarine systems is at the present time a subject of controversy. The consumption of dissolved silica which varies from l O , 2 0 % in many estuaries (Burton and Liss, 1973) to 80, 90 i

in estuaries like the Scheldt (Wollast and De Broeu, 1971) and the Rhine (Van Bennekom, 1974) is explained either by chemical reactions with the suspended matter or by an intense activity of brackish diatoms. The conservative or non conservative character of chemical species is well illustrated by plotting the evolution of its concentration in the estuary as a function of the salinity (Fig. I ) .

In the case of dissolved silica, for the

month of February, one obtains a fairly good linear relation, corresponding to simple mixing law and a strong deviation from the mixing line for September indicating an intense consumption of dissolved silica in the estuarine zone. We will use the particular behaviour of this compound for testing the possibility of using the simplified unidimensional model to describe the longitudinal profile of a conservative substance, such as dissolved Si during the winter, as well as to evaluate the rate and consumption mechanism of the same compound during the period from spring to fall.

a

mg S i 0 2 aq

c

65

mg S i 0 2

l5

February 1973 10

5

September 1973

\ -

I 10

5

1s g c1-/1

)

g c1-/1

Fig. 1 . Evolution of dissolved silica as a function of salinity during February 1973 and September 1973 compared to the mixing line. The points A correspond to the composition of the coastal sea-water. Distribution of silica for conservative conditions The evolution of the longitudinal mixing coefficient K along the estuary calculated from the salinity profile during the month of February is given in figure 2.

It should be noted that the longitudinal concentration profiles are

always measured by following the low water slag starting from the mouth of the river. The calculated distribution of dissolved silica, considered as conservative and submitted to the same mixing processes as salinity (same K) is compared to the measured distribution in figure 3. The agreement is very satisfactory and justifies the use of the simplified model in the case of the Scheldt. Distribution of silica for non-conservative conditions The montly evolution of the longitudinal profile of dissolved silica over one year shows that, if this compound behaves as a fairly conservative substance during the winter, it undergoes an uptake in the estuary beginning in May, increasing during the summer and decreasing rapidly after September. This already suggests that the removal is related to biological processes. In order to estimate more quantitatively the rate of removal and to localize the area of silica uptake, the net consumption term (P

-

C)

of equation 2

was estimated €or successive 5 km long sections along sections along the estuary, using again the salinity profile as a tracer of the mixing properties of the water masses.

66

2

n Isec

K

200

100

1

I

50

100

bn

Fig. 2. Longitudinal mixing coefficient calculated from the salinity profile for the river Scheldt in February 1973.

1s

-

5 -

I

1 1 10 10

1 1

1

20 20

30 30

I 40 40

I I

II

w

m

I I

m

I I 00

I 8

I

im

b

Fig. 3. Calculated and measured profile of dissolved silica for the river Scheldt in February 1973 assuming a conservative behaviour for silica.

67

r

*In0

Production

PS'O2

0

50

Consumption

-IW *1W

-

75

March 1973

kT

1no

Production

gSi02

L

0

-100

-zoo

- 3oo +loo

+

0

1no

Sea

-loo

July 1973 -Jon

Consumption

Fig. 4 . Calculated production and consumption terms for dissolved silica as a function of the distance to the sea. The results of these computations for three typical months are represented in figure 4 .

These profiles indicate that the uptake of silica is restricted in

well defined zones of the lower part of the estuary.

This conclusion corres-

ponds to well known facts about the biological activity in the Scheldt estuary. The high turbidity (Fig. 5.) of the upper part of the estuary (above km 60) strongly inhibits the activity of the phytoplancton and explains the conservative behaviour of dissolved silica in that region.

On the other hand, the activity

of the diatoms is characterized by successive blooms of restricted expance usual-

ly starting early in the year near the mouth and progressing upwards during summer and fall. This is well demontrated in figure 6 which shows the evolution of the number of diatom cells recorded by De Pauw (1975) at two stations of the Scheldt during three successive years. Another direct proof of the role of the phytoplancton in the silica uptake observed in the Scheldt, as well as the validity of the consumption rate evaluated with the help of the model, was obtained by comparing the calculated uptake 14

of silica to the primary productivity measured in the zone of uptake by H incorporation.

68

Fig. 5. Longitudinal turbidity profile in the Scheldt estuary

I (10.

ono

I(1

.oon

I

.nnc

.

/--

196:

I

1968

1969

Fig. 6. Seasonnal evolution of the diatoms at Vlissingen (km 5) and Bath (km 4 0 ) (after De Pauw, 1975)

69

During the month of September 1973 the zone of highest primary producti2 vity was situated between k m 35 and km 65 from the mouth and reached 50 mg C/m .day. The mean rate of uptake of silica deduced from the model for the same region was 2 estimated at 138 mg S i O 2/m .day. The weight ratio of silica to C uptake is thus 2.76 in agreement with a weight ratio of Si02/C equal to 2.3 based on the mean composition of marine diatoms (Lizitsine, 1972). Taking these facts into account, we have used the unidimensional model in order to predict the longitudinal distribution of silica in the estuary, where the biological uptake of Si02 is simply proportionnal to the concentration of diatom cells (C),

as measured by De Pauw (1975).

The equation is then simply :

-

d2C + 1 dC K - (-K dX2

A dX

d dX

V)

dV + -1 (C - C') +

k C

(3)

A dX

where V is the fresh water discharge and C' the silica concentration in the various small tributaries. The results of the calculation are summarized in figure 7.

The upper curve

corresponds to a very low activity of the diatoms achieved during the winter and the lower curve to a maximum of the activity with a pronounced bloom of diatoms between km 50 and km 40 reached during the summer. As we can see, this model is very useful in order to evaluate the activity of the diatoms and allows one to relate this activity with various environmental

factors. The model was also used in order to evaluate the amount of dissolved silica discharge by the estuary into the North sea (figure 8). In fact, the amount of dissolved silica delivered to the North sea is considerably reduced from May until September. The same situation occurs in the river Rhine (Van Rennekom, 1974).

These unusual situations must b e related to

the eutrophication of these rivers due to their high concentration levels of dissolved nitrogen and phosphorus. This low input of dissolved silica has a considerable effect on the phytoplancton composition of the North sea where silica may become limitant

(Van Rennekom et al., 1975). NITRIFICATION IN THE SCHELDT ESTUARY Nitrification means the oxydation of ammonia into nitrite and nitrate caused by the activity of autotrophic bacteria.

This process is very important because

it modifies the speciation of the inorganic nitrogen and effects its assimilation

rate by the phytoplancton. Nitrification also consumes large quantities of dissolved oxygen and may affect the quality of the estuarine water.

Sea

150

100

50

)on

Fig. 7. Computed longitudinal profils of dissolved silica for winter (upper curve), summer (lower curve) and a medium situation. The vertical dashes correspond to the observed evolution of dissolved silica over one year (from De Pauw, 1975) g SiOz /sec

900

800

?on p.bny 1973 600

May 1973

son

400

300

200

1 no

SU

10

M

3 0 4 0 o s o

6

0

x

1

n

w

wa-

Fig. 8. Evolution o f the flux of dissolved silica in the Scheldt.

71 It is generally admitted that the nitrification process occurs only when

the heterotrophic degradation of organic matter is completed, but there is no physiological argument to support this hypothesis. We have thus tried to develop a model of the nitrification in the Scheldt estuary which occurs intensively in the lower part of the estuary where the organic load has severely decreased and oxydative conditions are restored. However, this model takes into account known physiological properties of bacteria and is based furthermore, on several in-situ or laboratory experiments (Billen, 1975, Somville, 1975). First of all it is important to underline that the oxydation of ammonia into nitrite and nitrate constitutes the sole source of energy in the metabolism of the nitrifying bacteria.

Thus nitrification can only occur in the area of

the estuary where this oxydation process is exoenergetic.

This condition may

be expressed thermodynamically by introducing the value of the oxydo-reduction potential Eh, above which nitrate and nitrite become more stable than ammonia. In the case of the Scheldt the zone where this condition is fulfilled is restricted to the lower part of the estuary and its extent depends upon the fresh water discharge, the pollution load, the temperature, etc... Even when the thermodynamical conditions are favourable in the estuary, the nitrification takes place rather slowly and nitrification is rarely complete. Some in-situ observations clarify this particular behaviour. Comparative counts of nitrifying bacteria grown on fresh water or sea-water mediums show that the nitrifying bacterial populations of the Scheldt estuary are essentially of continental origin.

Even in the coastal zone near the estua-

ry no halophile population is developing. The nitrifying organisms show no activity in the upper zone of the estuary because of the unfavourable redox conditions and nitrate appears only when the critical value of Eh is reached (figure 9).

On the other hand, the growth of

the fresh water populations is rapidly inhibed with the increase of salinity and the bacterial populations are more rapidely diluted by sea-water than they can expand by reproduction (figure 10a). The in-situ measured activity of the nitrifying bacteria (figure l o b ) reflects both the inhibition due to unfavourable redox condition in the upper part of the estuary and the rapid dilution of the fresh water population by the sea-water in the lower part of the estuary. Modelling of the nitrification A bacteriological model of nitrification must necessarily first of all

define the evolution of the biomass B of the nitrifying organisms, which may be decomposed into a growth term and a mortality term.

Fig. 9. Relation between nitrification and the oxydoreduction conditions in the Scheldt nitrification n n o nitrification

A A A

1 .o

0.5

Fig. 10a. Activity index of nitrifying bacteria as a function of salinity. Curves a, b,c correspond to the activity of cultures adapted progressively to higher salinities.

73 1.0

L wles/l.h

0.5

-

Fig. lob. In-situ measurements of the nitrification activity during October 1975.

If BA represents the "hydrodynamic" operator : BA

=

a + -

a - -l a (A ax A ax

u

at

a

K -)

(4)

ax

the evolution of the bacterial biomass may be written : VA B

=

KB - MB

where K and M are respectively the growth and mortality coeffecients. The growth coefficient is a function of temperature, salinity, concentration of ammonia and Eh. If k is defined as the optimal growth coefficient, the influence of these various parameters may be conveniently described by the following relation : K

= k

. fl

(T)

. f2

(S)

. f3

(NH4)

. ( Eh)

(5)

f l , f2 and f3 being equal to 1 for the optimal values of temperature, salinity and ammonia concentration. The function (Eh) expresses simply that nitrification is only possible above a given redox potential where the oxydation of ammonia becomes exoenergetic :

(Eh)

0

Eh
JUN

I

"

"

"

I

6 JUL

"

'

"

'

I

"

13

'

"

'

1

"

'

"

'

1

20

27

3AUG

Fig. 7. Half-hourly, long-channel current components from Site B , in cm/sec, 29 June to 3 August, 1976. along the ship channel.

The same basic pattern appears, with a

well-defined transition from tropic to equatorial tidal conditions. Current speed ranges are somewhat diminished, reflecting the frictional and constrictional effects of the shallow waters and channels. The numerically filtered, non-tidal estuarine-shelf exchanges are shown in Figure 8. A markedly different pattern is apparent, however, contrasting with that recorded during May and June of the previous year.

The approximately 31 days of data from the mid sum-

mer, 1976, study shows a net inflow past Site B.

During the first

155

Fig. 8. Filtered long-channel current components from Site B, in cm/sec, 30 June to 3 August, 1976. two weeks of the study there was a net flood into Corpus Christi Bay. This resumed for the final two weeks, following a period of about a week during which there was a net outflow. Intermediate time scale non-tidal variations are apparent superimposed onto the very long period exchanges. Non-tidal currents during this time interval varied between approximately i-10 cm/sec. The average flow was a flood of just under 5 cm/sec. Figure 9 shows the cumulative net displacement past Site B during the 31-day study period. Again, the tidal motions appear as relatively small perturbations, with the most important exchanges occurring over much longer time scales. The dominant inflow during this time interval may be explained largely in terms of the very long period, semi-annual variations in coastal water levels. This study was conducted during the time of, and just following the July minimum, and as water levels began rising toward the October maximum. The net inflow thus reflects a slow flooding of the bays in response to rising coastal water levels. The brief period of net outflow may reflect the fact that the time period of the study fell so close to the time of lowest water that a quasi-steady rise had not yet begun. DISCUSSION In a recent paper, Weisberg (1976) discussed the need for sufficiently long current meter records, in view of non-tidal forcing occurring over time scales well in excess of the semi-diurnal

156

E

r:

v

0-

NET EBB ___-

NET FLOOO

30 -

GO I-

W z

2 90 W

120-

Fig 9. Cumulative net displacement, in km, past Site B, 30 June to 3 August, 1976. and diurnal tidal periodicities.

The results presented here sup-

port this suggestion, but indicate that in some areas at least seasonal variations in coastal water levels may result in correspondingly long period variations in the mean flow of water between estuaries and the inner continental shelf. In the northwestern Gulf of Mexico, with relatively small freshwater inflow into coastal bays from rivers draining South Texas, the semi-annual variations in coastal water levels appear to reverse the net estuarine-shelf transport over the same time scales. In other areas, the very long period variations may just alter the rate at which estuarine waters are exported onto the shelf. Superimposed onto the semi-annual variations in estuarineshelf exchanges, but occurring over time scales well in excess of tidal periodicities, are the quasi-periodic, meteorologically-forced exchanges, characteristically at time scales on the order of three to six days. Many other investigators have noted similar variations in current meter and water level records. Weisberg (1976) filtered out the tidal contribution to a 51-day current record from the Providence River, Rhode Island, and found quasi-periodic variations occurring over time scales on the order of four to seven days.

157

Beardsley, et a l . (1977) have reported coastal water level variations and sub-surface pressure fluctuations over time scales on the order of several days. Groves (1957) documented non-tidal water level variations over intermediate time scales at many coastal and island stations in the Atlantic and Pacific, and discussed some of the most probable meteorological forcing mechanisms. Two additional studies have recently been carried out in the northwestern Gulf of Mexico to investigate variations in coastal water levels and thus estuarine-shelf exchanges. In the first (Smith, 1977), regional pressure gradients were used to infer surface windstress over shelf waters. Statistically significant coherence-squared values were computed between variations in the volume of Corpus Christi Bay and variations in both the longshore and cross-shelf windstress components. Results indicated that the cross-shelf component of the windstress produces a set-up or setdown of coastal water levels over time scales on the order of two to four days, and thus forces a slow filling or draining of the bay. One may tentatively assign at least a part of the intermediate time scale variability noted in Figures 4 and 8 to the cross-shelf component of the surface windstress. Over longer time scales, the volume of the bay is more coherent with variations in the longshore component of the windstress, suggesting coastal water levels rise and fall in response to a cross-shelf Ekman transport of shelf waters. In a second study, just being completed, as yet unpublished data suggest that significant variations in coastal water levels may be forced by spatial variations in the surface pressure field. This inverse barometer effect seems to be particularly important over time scales on the order of two to six days, and water level variations estimated to be approximately ? 5 cm are exceeded by only three astronomical tidal constituents in the northwestern Gulf of Mexico. Analysis of non-tidal current or water level data and locally measured meteorological variables suggests that the estuarineshelf exchanges occurring over time scales on the order of a few days do not occur as a local response to meteorological forcing. Coherence spectra (not shown) computed from the long-channel current components at Site B and both the longshore and cross-shelf windstress components computed from coastal wind data indicated statistically insignificant values over time scales associated with meteorological forcing.

On the other hand, estuarine-shelf

158

exchanges were found to be statistically significant when windstress values were computed from regional pressure gradients (Smith 1977). Similarly, the theoretical inverse barometer relationship of -1 cm/mb was very nearly matched when cross-Gulf atmospheric pressure differences were compared with cross-Gulf water level differences. Yet a comparison of local atmospheric pressure and water level variations measured at Port Aransas, Texas, resulted in a relationship of -0.82 cm/mb. This suggests that the estuarine-shelf exchanges observed at some point along a coast may be more a response to meso-scale meteorological forcing than a purely locally driven process. CONCLUSIONS One may conclude that where tidal processes are small, such as in the Gulf of Mexico, or in many estuarine areas sufficiently removed from the coast, meteorological forcing over time scales on the order of several days may play a significant role in estuarineshelf exchanges. This is especially true in estuaries having little inflow of fresh water. Meteorological forcing may occur in several forms, with windstress and perhaps inverse barometric effects dominating. Studies repeated at various times of the year indicate that regions having substantial seasonal water level variations and small inflow of fresh water may undergo long-period reversals in the net transport between the estuary and the adjacent inner continental shelf lasting over periods of many weeks. The higher coherences between estuarine-shelf exchanges and regional meteorological forcing suggest that these exchanges do not occur at a response to purely local conditions. ACKNOWLEDGMENTS Mr. James C. Evans provided valuable help in the computer analysis of the current and water level data; Dr. J. S. Holland assisted in the installation and recovery of the recording current meters. Water level data used in the study were provided by Mr. D. T. Graham of the Army Corps of Engineers in Galveston, Texas. Harbor Branch Foundation, Inc., Contribution Number 75. REFERENCES Beardsley, R., H. Mofjeld, M. Wimbush, C. Flagg and J. Vermersch, Jr. 1977. Ocean tides and weather-induced bottom pressure fluctuations in the Middle Atlantic Bight. Journ. of Geophysical Res. 82 (21): 3175-3182.

159

Fee, E.

1969. Digital computer programs for spectral analysis of time series. Univ. of Wisconsin, Milwaukee, Center for Great Lakes Research, Special Report No. 6, 17 pages. Groves, G. 1957. Day to day variation of sea level. Meteorological Monographs 2(10):32-45. Marmer, H. 1954. Tides and sea level in the Gulf of Mexico. In: Gulf of Mexico, its origin, waters and marine life. Fishery Bulletin, Fish and Wildl. Serv. U. S. 55(89):101-118. Smith, N. 1977. Meteorological and tidal exchanges between Corpus Christi Bay, Texas, and the northwestern Gulf of Mexico. Estuarine and Coastal Marine Science 5(4):511-520. Sturges, W. and J. Blaha. 1976. A western boundary current in the Gulf of Mexico. Science 192:367-369. Weisberg, R. 1976. A note on estuarine mean flow estimation. Journ. of Marine Res. 34(3) :387-394. Whitaker, R. 1971. Seasonal variations of steric and recorded sea level of the Gulf of Mexico. Texas A & M University, Ref. 71-14T, 110 pages. Zetler, B. and D. Hansen. 1970. Tides in the Gulf of Mexico--a review and proposed program. Bulletin of Marine Sci. 20(1): 57-69.

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161

SURGE-TIDE INTERACTION I N THE SOUTHERN NORTH SEA

D.

PRANDLE and J. WOLF

I n s t i t u t e of Oceanographic S c i e n c e s , B i d s t o n O b s e r v a t o r y , M e r s e y s i d e , ENGLAND.

ABSTRACT O b s e r v a t i o n s o f s t o r m s u r g e s i n t h e R i v e r Thames show t h a t s u r g e p e a k s t c n d t o o c c u r on t h e r i s i n g t i d e and seldom, i f e v e r , o c c u r on h i g h t i d e .

This

t e n d e n c y h a s been a t t r i b u t e d t o t h e i n t e r a c t i o n between t i d e and s u r g e p r o p a g a t i o n

as d e s c r i b e d by t h e n o n - l i n e a r t e r m s i n t h e a s s o c i a t e d hydrodynamic e q u a t i o n s . A r e c e n t s t u d y by P r a n d l e and Wolf

( 4 ) examined t h e mechanics o f i n t e r a c t i o n

w i t h i n t h e R i v e r Thames and showed t h a t a n i m p o r t a n t component o f i t o r i g i n a t e s o u t s i d e o f t h e r i v e r ; t h i s component i s i n v e s t i g a t e d i n t h e p r e s e n t p a p e r . A method o f i d e n t i f y i n g i n t e r a c t i o n i n t h e s o u t h e r n N o r t h Sea i s d e v e l o p e d

i n v o l v i n g t h e u s e o f two hydrodynamic n u m e r i c a l m o d e l s , one s i m u l a t i n g t i d a l p r o p a g a t i o n and t h e o t h e r s u r g e p r o p a g a t i o n .

O p e r a t i n g t h e s e models c o n c u r r e n t l y ,

t h e c o u p l i n g between t i d e and s u r g e i s i n t r o d u c e d by p e r t u r b a t i o n terms which r e p r e s e n t t h e i n f l u e n c e i n e i t h e r model o f sea l e v e l s and v e l o c i t i e s computed by the other.

T h i s approach h a s been used t o s i m u l a t e t h e p a t t e r n o f i n t e r a c t i o n

which o c c u r r e d d u r i n g t h e d i s a s t r o u s s t o r m s u r g e o f 3 0 J a n u a r y t o 2 F e b r u a r y

1953.

I t i s shown t h a t i n t e r a c t i o n i n t h e s o u t h e r n N o r t h S e a r e s u l t s p r i m a r i l y

from the q u a d r a t i c f r i c t i o n term, d e v e l o p i n g s i g n i f i c a n t l y i n t h e c o a s t a l r e g i o n o f f LowestoEt as f a r s o u t h as t h e Thames e s t u a r y due t o t h e h i g h v e l o c i t i e s a s s o c i a t e d w i t h b o t h t i d e and s u r g e p r o p a g a t i o n i n t h a t area.

Changes i n t h e

s u r f a c e e l e v a t i o n o f t i d e and s u r g e due t o t h e e f f e c t s o f i n t e r a c t i o n may d e v e l o p r a p i d l y i n c e r t a i n l o c a l i s e d r e g i o n s s u c h a s t h e Thames e s t u a r y .

There

may a l s o b e l o n g e r p e r i o d c h a n g e s o f t h e o r d e r o f t h e d u r a t i o n o f t h e storm due t o a s y s t e m a t i c d i s p l a c e m e n t o f t h e M2 t i d a l regime.

1.

INTRODUCTION The o b s e r v e d t e n d e n c y o f s u r g e p e a k s t o o c c u r on t h e r i s i n g t i d e i n t h e

Thames h a s long i n t r i g u e d r e s e a r c h e r s i n t e r e s t e d i n t i d e and s u r g e phenomena.

I t i s a l s o o f m a j o r p r a c t i c a l i m p o r t a n c e s i n c e t h e e m p i r i c a l f o r m u l a e t h a t have been d e r i v e d t o p r e d i c t c o a s t a l f l o o d l e v e l s a r i s i n g from s t o r m s u r g e s must t a k e account o f t h i s t e n d e n c y .

Hence s u c h q u e s t i o n s a r i s e as t o w h e t h e r it i s

p o s s i b l e f o r s u r g e p e a k s t o o c c u r a t h i g h t i d e a n d , i f s o , u n d e r what c o n d i t i o n s . P r a n d l e and Wolf

( 4 ) have i n v e s t i g a t e d t h e dynamics o f t i d e - s u r g e i n t e r a c t i o n

162

OoE

1cig.1

I"E

3%

4'E

S c h e m a t i c representation o f the s o u t h e r n N o r t h Sea.

5OE

~n t h e R i v e r Thames and have t h e r e b y a t t e m p t e d t o p r o v i d e some e x p l a n a t i o n f o r t h e obsprved d i s t r i b u t i o n o f s u r g e s .

By a n a l y s i n g s t a t i s t i c a l l y t h e s o u t h w a r d

p r o p a g a t i o n o f a number o*f d i s c r e t e s u r g e p e a k s a l o n g t h e e a s t c o a s t o f B r i t a i n t h r y showed t h a t t h e p e a k s t e n d t o o c c u r on t h e r i s i n g t i d e i n t h e Thames

irrespective o f t h e p h a s e r e l a t i o n s h i p between t i d e and s u r g e i n t h e n o r t h e r n North Sea.

Using n u m e r i c a l models t o s i m u l a t e t i d e and s u r g e p r o p a g a t i o n a l o n g

t h e r i v e r from a s e a w a r d boundary a t Walton t h e o b s e r v e d i n c r e a s e i n i n t e r a c t i o n e f f e c t s alonq t h e r i v e r w a s reproduced.

However t h e predominance o f s u r g e p e a k s

o c c u r r i n c j on t h e r i s i n g t i d e w a s shown t o b e d u e , i n p a r t , t o i n t e r a c t i o n e f f f c t s which modify s u r g e p r o f i l e s p r i o r t o t h e i r a r r i v a l a t t h e mouth o f t h e Thames.

I n t h e i r s t a t i s t i c a l a n a l y s i s o f o b s e r v e d s u r g e s , P r a n d l e and Wolf

showed t h a t t h i s i n t e r a c t i o n , o c c u r r i n g o u t s i d e o f t h e r i v e r , s i g n i € i c a n t l y between L o w e s t o f t and Walton;

developed

it i s t h i s f e a t u r e o f i n t e r a c t i o n

t h a t i s of primary i n t e r e s t i n t h e present paper. The p a p e r c o n s i d e r s t h e p r o p a g a t i o n o f t i d e and s u r g e i n t h e s o u t h e r n North Sra w i t h t h e o b j e c t i v e o f e x a m i n i n g t h e m e c h a n i c s o f t h e i r i n t e r r e l a t i o n ship i n t h a t region.

The s t u d y i s l i m i t e d t o t h e s i m u l a t i o n o f a p a r t i c u l a r

s u r g e e v e n t , namely t h e m a j o r s u r g e o f 3 1 J a n u a r y t o 2 F e b r u a r y

(3)

1977;

Prandle

madr a c o m p r e h e n s i v e s t u d y o f t h i s s u r g e w i t h t h e a i d o f a n u m e r i c a l model.

The p r e s e n t a p p r o a c h employs two v e r s i o n s of t h i s same model o p e r a t e d c o n c u r r e n t l y and r e f e r r e d t o s u b s e q u e n t l y a s p a r a l l e l models. p r o p a g a t i o n and t h e o t h e r s u r g e p r o p a g a t i o n .

One model s i m u l a t e s t i d a l

N o n - l i n e a r i n t e r a c t i o n between

t i d e and s u r g e i s i n t r o d u c e d by p e r t u r b a t i o n terms which r e p r e s e n t t h e i n f l u e n c e o f t h e s u r g e on t h e t i d a l p r o p a g a t i o n a n d , l i k e w i s e , t h e i n f l u e n c e o f t h e t i d e on t h e s u r g c p r o p a g a t i o n .

I n t h i s way, it i s p o s s i b l e t o a c c o u n t f o r t h e

i n t e r a c t i o n between t i d e and s u r g e w h i l e r e t a i n i n g t h e s e p a r a t e i d e n t i t i e s o f

th? two plienornena.

It i s t h e n p o s s i b l e , f o r i n s t a n c e , t o d e t e r m i n e t h e way i n

which t h e M 2 t i d a l amphidromic s y s t e m i n t h e s o u t h e r n N o r t h S e a c h a n g e s d u r i n g t h i , c o u r s e of t h e s t o r m .

It i s a l s o p o s s i b l e t o v a r i o u s l y i n c l u d e o r omit

c e r t a i n o f t h e p e r t u r b a t i o n t e r m s so t h a t t h e i n t e r a c t i o n due t o a p a r t i c u l a r tcrm c a n be e x p l i c i t l y i d e n t i f i e d . The a p p l i c a t i o n o f t h e s e p a r a l l e l m o d e l s h a s d e m o n s t r a t e d t h a t t h e m a j o r s o u r c e o f i n t e r a c t i o n a r i s e s from t h e q u a d r a t i c f r i c t i o n t e r m .

I n consequence,

t h c a r c a s where t h i s i n t e r a c t i o n i s most e f f e c t i v e were i d e n t i f i e d by e x a m i n i n g t h r s p a t i a l d i s t r i b u t i o n of t h e v e l o c i t y f i e l d f o r b o t h t i d e and s u r g e p r o p a g a t i o n .

Throughout t h i s t e x t t h c word i n t e r a c t i o n i s u s e d t o d e n o t e b o t h a n a c t u a l p h y s i c a l p r o c e s s and i t s r e s u l t a n t e f f e c t o n s u r f a c e e l e v a t i o n ,

’

whcre t h e l a t t e r i s d e f i n e d as t h e d i f f e r e n c e i n s u r f a c e e l e v a t i o n between t h e v a l u e computcd from a s i m u l a t i o n o f t i d e p l u s s u r g e combined,

zc ,

of t h e s e p a r a t e components computed from s i m u l a t i o n s of t i d e a l o n e ,

surge a l o n e ,

Zs

;

i.e.

ZI = Z c

-

ZT - Z s

and t h e sum

ZT

,

and

SURGE HEIGHT (CMS)

140

-

120

-

100

-

80

-

I

4

--

20(/ 0

-100

Lerwick

-

Wlck

-

Aberdeen

N. Shlelds

1

-

Recorded s u r g e s t a t i s t i c s ;

I

ILowestoft I

0

-0

Walton

5% 20vo

Southend Tllbury Tower Pier

I

I

I

1

I

I

0.25%

I

-120-

Fig.2

0.25%

l i n e s c o n n e c t v a l u e s of

Z p as computed a t e a c h l o c a t i o n f o r P 2

= 0.25,

1,

5 a n d 20%.

165 2.

STATISTICS OF OBSERVED SURGES An analysis was made of observed surges at tlie following ports:

Lerwick,

Wick, Aberdeen, North Shields, Lowestoft, Walton, Southend, Tilbury and Tower Pier.

The locations of these ports are shown in figure 1 and extend from the

northern North Sea southwards along the east coast of Britain and thence into the Thames as far as Tower Pier. The observed data comprised 5 years of hourly recordings at each location for the years

1969 to 1973.

At each port, hourly residual heights were

calculated as follows:

Rt = Ot where R t

and

-

Pt - M

(1)

is the residual elevation, or surge (at time t 1;

Ot

the recorded elevation;

Pt

the predicted astronomical tide;

M

the annual mean of O t , calculated for each year separately. At each location, the surge data were analysed to compute probability

distributions expressed in terms of percentage exceedances of a particular surge The percentage of surges exceeding a value Z p

level. by

pz= n / N x 100, where

n is the number of surge values exceeding Z

a total number of hourly surge values period).

was denoted by PZ given

N

out of P (approximately 44,000 for the 5 year

The analysis was performed for positive and negative surges separately.

The results are shown in figure 2 in the form of the values of Zp corresponding to p z

=

0.25,

1,

5 and 2096 respectively for the various ports along the path of

propagation of the surge.

The horizontal scale in figure 2 represents the

distance between the ports.

The values of Zp for

pz = 0.25% and Pz

=

1%are

representative of peak surge levels at each location as might be observed during the propagation of a moderate to large storm surge. these two values of

pz,

The variations in Zp

,

for

show a steady and regular increase in amplitude between

Lerwick and Lowestoft and thereafter remain reasonably constant between Lowestoft and Tower Pier. The above analysis was then repeated but, rather than analyse the complete data set as a whole, the data was first separated into distinct subsets according to the timing of any particular observation relative to tidal high water. subset was then analysed separately as before.

Each

Figure 3 shows the mean surge

level for each port at four tidal phases namely; (a) rising tide, 3Q to 24 hours before high tide (HT); (b) high tide, HT -8h to HT +Qh; (c) falling tide, HT +2$n to HT +39h and (d) low tide, HT -6ih to HT -54h.

The divergence of the four

curves is a measure of the degree of interaction at each location.

The larger

values indicated by the curves for surges on the rising tide clearly illustrate the increase in interaction as surges propagate southwards.

The figure

166 MEAN SURGE HEIGHT

30-

I

(CYS)

28-

I

I

24

-

I

RISING T I D E

I I I

22 -

10

P , , , ",

I I I

26 -

/'

\,/' /---d

I I

-

I

8-

I I

6-

I

4-

I I I

I

I

2Lerrlck

Wlck

Aberdem

N. Shlelds

~LOl..l0fl

WO!IO"

-2 -4 -

-6

-

-8

-

-10

-

I I

I I

I I I

I I I

I

I I I I

-

0 t i o t i ~ o n l o l scale

Fig.3

'

100 200x)o

km

I I

I

I

Recorded mean s u r g e levels at f o u r tidal phases.

Southend

Tllbry

Tower Pler

i n d i c a t e s t h a t i n t e r a c t i o n can be d e t e c t e d as f a r northwards as Wick and it t h e n i n c r e a s e s c o n t i n u o u s l y as f a r as Tower P i e r .

An e x c e p t i o n t o t h i s c o n t i n u o u s

i n c r e a s e i s t h e s m a l l d e c r e a s e between North S h i e l d s and Lowestoft;

t h i s may

p o s s i b l y be a t t r i b u t e d t o d i s c o n t i n u i t i e s i n t h e t i d a l regimes between t h e c e n t r a l and s o u t h e r n North Sea and a l s o t h e d i s c o n t i n u i t y i n t h e c o a s t l i n e i n However, t h e p r e s e n t f e a t u r e of i n t e r e s t i s t h e

t h e r e g i o n of t h e Wash.

s i g n i f i c a n t i n c r e a s e i n i n t e r a c t i o n which o c c u r s between Lowestoft and Walton. The pronounced e f f e c t o f i n t e r a c t i o n clearly illustrated i n figure

4

a t p o r t s s o u t h of Lowestoft i s

which shows t i m e - s e r i e s o f observed surge and

p r e d i c t e d t i d e ( t h e l a t t e r t o one q u a r t e r of t h e v e r t i c a l s c a l e used f o r t h e s u r g e ) a t Lowestoft and Southend d u r i n g 1970.

The t i m e - s e r i e s shown were

considered t o be r e p r e s e n t a t i v e of c o n d i t i o n s a t t h e s e two p o r t s . of i n t e r e s t a r e :

The f e a t u r e s

( a ) a t Lowestoft, t h e r e i s an a p p a r e n t l y random d i s t r i b u t i o n

o f t h e timing of s u r g e peaks r e l a t i v e t o t h e phase of t h e t i d e , whereas ( b ) a t Southend, t h e surge peaks almost always o c c u r on t h e r i s i n g t i d e and never on high t i d e .

Hence f i g u r e

4

emphasises t h e e f f e c t s of i n t e r a c t i o n i n t h i s r e g i o n

a s p r e v i o u s l y e n u n c i a t e d from t h e s t a t i s t i c a l a n a l y s i s of recorded s u r g e s . Prandle and Wolf

(41

examined i n t e r a c t i o n i n t h e Thames using t h e

p a r a l l e l model approach ( $ 3 ) study.

;

figure

5

shows some of t h e r e s u l t s from t h i s

S t a r t i n g from a p r e s c r i b e d t i d e and s u r g e i n p u t a t t h e mouth of t h e

model ( W a l t o n - M a r g a t e ) t h e e f f e c t s of i n t e r a c t i o n a t Tower P i e r a r e i l l u s t r a t e d by t h e m o d i f i c a t i o n of t h e t i d e due t o t h e i n f l u e n c e of t h e s u r g e and, l i k e w i s e , t h e m o d i f i c a t i o n of t h e s u r g e by t h e i n f l u e n c e of t h e t i d e .

The f i g u r e

i l l u s t r a t e s t h a t t h e most s i g n i f i c a n t e f f e c t of i n t e r a c t i o n i s t h e r e d u c t i o n of t h e surge peaks through t h e i n f l u e n c e of t h e t i d e , i t was a l s o shown t h a t t h i s r e d u c t i o n of t h e s u r g e peaks w a s due t o t h e q u a d r a t i c f r i c t i o n term. examination of f i g u r e

5

shows t h a t t h e i n t e r a c t i o n s

s'- s

and

TI-T

r i v e r , a r e n o t r e s p o n s i b l e f o r t h e peak of t h e n e t r e s i d u a l , S'+T'-T on t h e r i s i n g t i d e .

within t h e

,

occurring

T h i s phenomenon must t h e r e f o r e be a f u n c t i o n of t h e s u r g e -

t i d e phase r e l a t i o n s h i p a t t h e mouth. e v i d e n t l y non-random

,

An

S i n c e t h i s phase r e l a t i o n s h i p i s

it may t h e n be concluded t h a t t h e timing of s u r g e peaks i n

t h e Thames i s dependent on i n t e r a c t i o n o c c u r r i n g seawards o f t h e l i n e between Walton and Margate.

3.

PARALLEL MODELS The b a s i s of t h e p r e s e n t modelling approach c o n s i s t s o f a combined model

of t h e s o u t h e r n North Sea and R i v e r Thames developed by P r a n d l e ( 2 ) m o d r l comprises two p a r t s dynamically i n t e r f a c e d ,

.

This

a one dimensional r e p r e s e n -

t a t i o n o f t h e River Thames t o g e t h e r w i t h a two dimensional r e p r e s e n t a t i o n of t h a t p a r t of t h e North Sea s o u t h of l a t i t u d e 53O20' extending westwards i n t o t h e E n g l i s h Channel a s f a r as t h e Greenwich meridian.

The model u s e s a n

168 SURGE lrn HEIGHT LOWESTOFT

I m TIDAL HElGHl

SOUTHEND

LOWESTOFT

SOUTHENO

LOWESTOFT

SOUTHENO

t

I

LOWESTOFT

SOUTHENO

291

1

292

1

293

I

294

I

295

I

296

1

297

,

298

1

299

I

3W

LOWESTOF T

SOUTHEND

Fig.4

T i m e - s e r i e s of p r e d i c t e d t i d e and r e c o r d e d s u r g e a t Lowestoft and Southend d u r i n g 1970.

metres.

(a) Mouth of the model : Walton-Margate. Fig.5

(b) Tower Pier.

P r o p a g a t i o n of t i d e a n d s u r q e i n t h e ‘l’hames computed hy parallel models (F’randle a n d WolI surge alone S t i d r m o d i f i r d by i n t e r a c t i o n T‘ , s u r g e modified by i n t e r a c t i n n S ’

.

.

{ 4 ) );

tide alone

T

I

170 explicit finite difference scheme for solving, by means of a forward timestepping procedure, the relevant equations of motion.

The schematic represen-

tation of the southern North Sea is shown in figure 1. Prandle (3) showed that this numerical model was able to accurately simulate the propagation of tide and surge throughout this region.

The present

objective is to gain an understanding of the properties of interaction by simulating tide and surge separately while introducing interaction between the two phenomena in the form of perturbations as already mentioned.

The applica-

tion of the parallel model approach to a one dimensional representation of the

,

Thames has been described by Prandle and Wolf ( 4 )

hence only the application

to the two dimensional representation of the southern North Sea will be described here. The relevant hydrodynamic equations may be expressed for space coordinates along lines of latitude and longitude :

% at

where

+

ax H

7 +

a

-

u v + H g - az + K U ( U * + V ~ ) ' / ~ - RV

ay H

ax

x , y are orthogonal axes positive to the east and to the north, t

time,

g

qravitational constant,

Z

elevation of the water surface above a horizontal datum,

D

depth of the bed below the same datum

u,v velocities (depth-averaged) in the respectively ,

and

= 0 ,

K

friction coefficient,

R

Coriolis parameter,

H = D+Z

, U

=

uH

,

V

=

X

and

y directions

vH.

Numerical simulation of tide and surge propagation in the southern North Sea (Prandle (3))

has indicated that interaction is largely insensitive to the

inclusion or omission of the convective terms (second and third terms in cquations ( 2 ) and ( 3 ) ) and hence, on this basis, it is justifiable, and also convenient, to omit these terms from further consideration. T h e concept of the parallel model approach requires that, for all

171 locations and at all times, the elevation and transports in the tidal model, Z

us

,

UT

and

andVT

vs

respectively, together with the corresponding values

zs ,

in the surge model must satisfy the relationships :

zC

= z T + z

uc

= UT

+

us

(6)

vc

= VT

+

vs

(7)

S

(5)

where the subscript C denotes values computed in a combined simulation of tide and surge.

Inserting ( 5 ) , ( 6 ) and

(7)into equations

(Z),

( 3 ) and ( 4 ) produces

the following equations for the combined propagation of tide and surge -a( U T + U S ) + ( D + Z S + Z T ) g - ( Z S + Za

at

a

at("+ZS)+-(U

a ax

T

+ u s )+-(Vaa y

)')'I2

) + K ( u s + u T ) ( ( u S + u T ) 2 +(vs+v

ax

~

T

T

:

T

+v ) = 0

s

I n the friction term in ( 8 ) and ( 9 ) it is assumed that the relationships

( 6 ) and (7)for transports in the

X

and

Y directions respectively also apply

for the associated depth-averaged velocities.

It may be shown that this

approximation is justifiable for small values o f

z/n .

The open-sea boundary conditions employed in the simulation of the propagation of tide, surge and tide plus surge involve the specification of the sea surface elevation

Z B ( t ) at every boundary grid square

B

.

Hence the boundary conditions to be satisfied in the parallel models are:

Z

B,C

= zB , T + zB , S

(11)

The assumption made in the use of parallel models is that equations ( 8 ) ,

( 9 ) and (10) may be separated into two parts as f o l l o w s :

aa t V T + ( D + Z + Z T S -

172

with boundary conditions

,?j'

=

'B,S

In operating the tidal model with ( 1 2 1 , (13) and (14), the surge parameters

zs,

Us

and

Vs

wliich appear in equations ( 1 2 ) and (13) are

cxvaluatcd from the simultaneous operation of the surge model, while in operating the surge model with (151, (16) and (17) the tidal parameters

ZT, U T and vT which appear in (15) and ( 1 6 ) are obtained from the concurrently-running tidal modcl.

Usinq this parallel model technique to simulate various surge events,

it was shown that the results from the separate simulations of tide and surge could be combined to give values in close agreement with results obtained from the simulation of tide and surge combined, thus satisfying conditions (51, ( 6 ) and ( 7 ) as required.

Hence, the additional terms underlined in equations

12) 1

(13), ( 1 5 ) an? ( 1 6 ) may be considered to represent the interaction between tide arid surge.

The magnitude of the shallow water interaction terms are

proportional to a product of surge amplitude and tidal amplitude.

However

the

magnitude of the interaction associated with the frictional terms is a more complex function involving products of the surge amplitude and the tidal amplitude with the respective powers of these amplitudes varying according to both the, instantaneous ratio of the tide and surge velocities and also their diffr,rence in direction. The interaction terms in ( 1 2 ) and (13) involving the value of

zs

are

subsequently referred to as the shallow water terms while the other interaction terms in (12) and (13) involving U s friction terms;

and

vs

are referred to as the quadratic

similar descriptions are used to refer t o the corresponding

terms in (15) and (16).

173

4.

STORM SURGE OF 3 l JANUARY

-

2 FEBRUARY 1953

The l o s s of l i f e and damage caused by t h e storm surge of 3 1 January

-

2

February 1953 r e p r e s e n t s one of t h e worst n a t u r a l d i s a s t e r s experienced i n r e c e n t h i s t o r y along t h e s h o r e s of B r i t a i n and t h e North Sea c o a s t of C o n t i n e n t a l Europe. The propagation of t h i s s u r g e i n t h e s o u t h e r n North Sea was s i m u l a t e d using t h e p a r a l l e l model t e c h n i q u e o u t l i n e d i n

3.

T i d e and s u r g e e l e v a t i o n s along t h e

o p e n - s e a boundaries of t h e models were p r e s c r i b e d from t h e d a t a used by Prandle

(3)

i n an e a r l i e r comprehensive examination of t h i s surge event.

In a d d i t i o n ,

t h e e f f e c t of l o c a l wind f o r c i n g w a s i n c o r p o r a t e d by adding f u r t h e r terms t o e q u a t i o n s (15) and ( 1 6 ) ; t h e form of t h e s e wind f o r c i n g t e r m s and t h e corresponding wind speed d a t a were a l s o e x t r a c t e d from t h e e a r l i e r s t u d y of Prandle. One l i m i t i n g f a c t o r p r e s e n t throughout t h e following d i s c u s s i o n of t h e r e s u l t s of t h i s s i m u l a t i o n i s t h e i m p l i c i t assumption t h a t t h e r e i s no i n t e r a c t i o n between t h e t i d e and s u r g e a t t h e open-sea b o u n d a r i e s of t h e model. While t h e a n a l y s i s o f recorded s u r g e d a t a d e s c r i b e d i n

5

2 showed t h a t some

i n t e r a c t i o n does o c c u r o u t s i d e of t h e model r e g i o n , i t i s c o n s i d e r e d t h a t t h e e s s e n t i a l f e a t u r e s of t h e r e s u l t s o b t a i n e d w i l l remain v a l i d . Computer r u n s were c a r r i e d o u t f o r ( 1 ) model of t i d e a l o n e ( T ) , (2)

model of s u r g e a l o n e ( S ) ,

(3)

model o f t i d e w i t h i n t e r a c t i o n from model ( 4 ) , below, due t o shallow w a t e r and q u a d r a t i c f r i c t i o n (TI),

( 4 ) model o f s u r g e w i t h i n t e r a c t i o n from model ( 3 ) , above, due t o shallow w a t e r and q u a d r a t i c f r i c t i o n ( S T ) ,

( 5 ) model o f t i d e p l u s surge combined (T+S 1. The purpose o f o p e r a t i n g model models ( 3 ) and

( 5 ) w a s t o confirm t h a t t h e v a l u e s from

( 4 ) s a t i s f i e d t h e r e q u i r e m e n t s o f ( 5 ) , ( 6 ) and ( 7 ) and hence

t h e r e s u l t s from t h i s model w i l l n o t be d i s c u s s e d f u r t h e r . ( a ) I n t e r a c t i o n a t Lowestoft and Southend

E l e v a t i o n s a t Lowestoft and Southend computed from t h e s e f o u r models a r e shown i n f i g u r e s 6 and

7

r e s p e c t i v e l y , v e r t i c a l l i n e s drawn on t h e s e

f i g u r e s i n d i c a t e t h e t i m e of h i g h t i d e a t t h e p a r t i c u l a r l o c a t i o n a s computed by model ( 1 ) .

The m o d i f i c a t i o n of t h e s u r g e through t h e i n f l u e n c e of t h e t i d e

i s shown b o t h by t h e divergence of t h e c u r v e s f o r S separate curve f o r

ST-s

,

and

s'

and a l s o by t h e

s i m i l a r l y t h e m o d i f i c a t i o n of t h e t i d e through t h e

i n f l u e n c e of t h e s u r g e i s shown by t h e d i v e r g e n c e of t h e c u r v e s f o r T and by t h e curve o f T'-T

.

and T'

The average magnitude of t h e i n t e r a c t i o n a t

Lowestoft i s about h a l f t h a t a t Southend, i . e .

approximately i n t h e r a t i o of

t h e magnitude of t h e r e s p e c t i v e t i d a l r a n g e s as suggested by t h e form of t h e i n t e r a c t i o n terms

( 5 3).

The t i m e - s e r i e s f o r

S'-Sat

Lowestoft shows l i t t l e

c o r r e l a t i o n w i t h t h e t i d a l phase whereas t h e corresponding t i m e - s e r i e s a t

174

J

O F 1 &i

'\

g ',I

'

-Im.

0.5m.

s'- S

& - _..-,--T'-T

G

w

an 1953

953

r

Fig.6

Computed values of tide, surge and interaction at Lowestoft.

175

3m. 2m.

I m. 0 -I m.

t

Im. 0 -1m.

0.5m.

&

0

-0.5m. 0.5m 0 -0-5m. -Im

Fig.7

$4 + s\- s +T-'

T

1953

-4 I

1st. Feb 1.953

.

2nd. Feb 953

Computed v a l u e s o f t i d e , s u r g e a n d i n t e r a c t i o n a t Southend.

176 Southend i s c l e a r l y i n f l u e n c e d by t h e t i d a l s t a g e .

The c u r v e s f o r T '

and T

at

both Lowestoft and Southend show t h a t t h e i n f l u e n c e of t h e s u r g e t e n d s t o reduce mean water l e v e l s f o r about

24 hours from 12.00 31 January t o 12.00 1 February.

This i s followed over t h e n e s t 24 hours by an a p p r e c i a b l e i n c r e a s e i n t h e t i d a l range a t Southend and a s i g n i f i c a n t phase d e l a y a t Lowestoft; an examination of t h e m o d i f i c a t i o n of t h e t i d a l regime throughout t h e a r e a of t h e model i s described i n

5 4(e).

The r e d u c t i o n i n mean t i d a l l e v e l a t b o t h l o c a t i o n s may be

a t t r i b u t e d t o t h e n e g a t i v e s u r g e l e v e l s preceding t h i s e f f e c t , t h e long d u r a t i o n of t h e s e changes t o t h e t i d a l regime a c c o r d s w i t h t h e s u g g e s t i o n made l a t e r (

§ k ( e ) ) t h a t a time c o n s t a n t of t h e o r d e r of a day o r more may be involved i n

t h e response of t h e t i d a l regime t o t h e i n f l u e n c e of t h e surge.

S'-S

andT'-T

The c u r v e s f o r

show, a t b o t h Lowestoft and Southend, a tendency t o c o u n t e r a c t

The n e t i n t e r a c t i o n c u r v e a t Southend, S ' - S + T ' - T , s h o w s

each o t h e r .

some

c o r r e l a t i o n with t i d a l phase, i n p a r t i c u l a r i t i l l u s t r a t e s t h e tendency f o r i n t e r a c t i o n t o i n c r e a s e s u r g e l e v e l s on t h e r i s i n g t i d e .

However, t h e n e t

i n t e r a c t i o n curve a t Lowestoft shows no obvious c o r r e l a t i o n w i t h t i d a l phase. ( b ) Components of i n t e r a c t i o n The model r u n s d e s c r i b e d i n t h e p r e v i o u s s u b s e c t i o n were r e p e a t e d but with t h e i n t e r a c t i o n between models

(3) and (4)l i m i t e d

f r i c t i o n only and (B) shallow w a t e r only.

t o ( A ) quadratic

The r e s u l t i n g i n t e r a c t i o n f o r t h e

( A ) and (B) and a l s o f o r t h e complete i n t e r a c t i o n examined i n t h e

c a s e s of

p r e v i o u s s u b s e c t i o n a r e shown i n f i g u r e 8 f o r f o u r l o c a t i o n s .

These r e s u l t s

show t h a t , a t a l l f o u r l o c a t i o n s , t h e m o d i f i c a t i o n of t h e s u r g e through t h e i n f l u e n c e o f t h e t i d e i n d i c a t e d by t h e c u r v e s f o r

s'-s

i s of t h e same o r d e r

a s t h e m o d i f i c a t i o n of t h e t i d e by t h e s u r g e as i n d i c a t e d by t h e c u r v e s f o r

TI-T

.

The tendency f o r t h e s e two i n t e r a c t i o n s t o oppose one a n o t h e r i s a l s o

e v i d e n t again.

The s e p a r a t e c u r v e s f o r i n t e r a c t i o n e f f e c t s of q u a d r a t i c

f r i c t i o n and shallow w a t e r r e s p e c t i v e l y show t h a t t h e q u a d r a t i c f r i c t i o n term

i s dominant throughout t h e a r e a and a c c o u n t s f o r almost a l l of t h e t o t a l interaction.

The i n t e r a c t i o n e f f e c t due t o shallow w a t e r of t h e t i d e on t h e

propagation of t h e s u r g e i s almost n e g l i g i b l e whereas t h e corresponding e f f e c t of t h e surge on t h e t i d a l p r o p a g a t i o n i s of some consequence p a r t i c u l a r l y a t Southend.

The t i m e - s e r i e s

f o r t h i s l a t t e r e f f e c t a t Southend i s h i g h l y

c o r r e l a t e d w i t h t h e t i d a l phase and c o n t r i b u t e s towards t h e c h a r a c t e r i s t i c i n c r e a s e i n surge l e v e l s on t h e r i s i n g t i d e .

The l a c k of any obvious s p a t i a l

coherence between t h e r e s u l t s a t d i f f e r e n t l o c a t i o n s i s d i s c u s s e d f u r t h e r i n t h e following s u b s e c t i o n . ( c ) S p a t i a l d i s t r i b u t i o n of i n t e r a c t i o n The s p a t i a l d i s t r i b u t i o n , a t 06.00

s' ,

t h e modified t i d e ,

T'

,

1 February 1953, of t h e modified s u r g e ,

t i d e p l u s s u r g e combined, ( T + S ) ( o r

(TI) +

(s'))

0.25rn.

s'-s

s'- s

T'-T

T\-T

s;s'

s'-s

T ~ T

T ~ T

LOWESTOFT

DOVER

HT.

s'- s

s'- s

T\-T

T\-T

s-' s

-

-

T ~ T 12,oo

24105

12,oo

24 00

HT.

s-' s T ~ T OSTEND 12100 24100

1st. Feb 1953.

Fig.8

HT.

Components o f i n t e r a c t i o n a t L o w e s t o f t , S o u t h e n d , Dover and O s t e n d . f r i c t i o n o n l y , --------- s h a l l o w w a t e r o n l y .

-

12100 1st. Feb 1953.

complete i n t e r a c t i o n ,

24 00

-q u a d r a t i c

178 t o g e t h e r with a l l o f t h e v a r i o u s components of i n t e r a c t i o n a r e shown i n f i g u r e s

9 and 10.

The v a l u e s shown f o r t h i s s p e c i f i c time may be regarded as

r e p r e s e n t a t i v e of v a l u e s o c c u r r i n g during a l a r g e s u r g e e v e n t .

The v a l u e s o f

i n t e r a c t i o n due t o q u a d r a t i c f r i c t i o n a r e shown t o be everywhere i n c l o s e aqreement with t h e v a l u e s f o r complete i n t e r a c t i o n .

The v a l u e s of i n t e r a c t i o n

due t o shallow water a r e shown t o be much s m a l l e r i n r e l a t i o n t o t h e i n t e r a c t i o n due t o q u a d r a t i c f r i c t i o n .

However, t h e shallow w a t e r i n t e r a c t i o n of t h e s u r g e

on t i d a l propagation i s s i g n i f i c a n t i n t h e r e g i o n of t h e Thames e s t u a r y and eastwards along a s e c t i o n from Ostend t o t h e mouth of t h e Rhine. a l s o c o i n c i d e s w i t h t h e maximum t o t a l i n t e r a c t i o n ;

This region

t h i s may be a t t r i b u t e d t o

13).

t h e l a r g e magnitude o f both t i d e and s u r g e e l e v a t i o n s i n t h i s r e g i o n (

The s p a t i a l d i s t r i b u t i o n of t h e v a r i o u s components of i n t e r a c t i o n appear An a t t e m p t w a s made t o f o l l o w t h e development through

t o be r a t h e r complex.

time of t h e s e s p a t i a l d i s t r i b u t i o n s , however an examination of s u c c e s s i v e d i s t r i b u t i o n s of t h e type shown i n f i g u r e 9 and 10 f o r v a l u e s a t h o u r l y i n t e r v a l s d i d not r e v e a l any c l e a r t r e n d s i n t h e changing d i s t r i b u t i o n s of interaction.

I t was concluded t h a t i n t e r a c t i o n i n t h i s r e g i o n does not develop

i n a slow and g r a d u a l f a s h i o n i n e i t h e r space o r time b u t , on t h e c o n t r a r y , develops r a p i d l y and o f t e n i n a l o c a l i s e d sense. ( d ) S p a t i a l d i s t r i b u t i o n of v e l o c i t y

S i n c e i t h a s been shown t h a t q u a d r a t i c f r i c t i o n i s t h e major cause of i n t e r a c t i o n i n t h e s o u t h e r n North S e a , it f o l l o w s t h a t t h e a r e a s where i n t e r a c t i o n develops most s t r o n g l y w i l l be t h o s e where b o t h t i d e and s u r g e velocities are largest.

F i g u r e 11 shows t h e s p a t i a l d i s t r i b u t i o n of mean

absolute v e l o c i t i e s f o r ( A ) t i d e alone, plus surge, ( T + s )

,

T

,

( B ) surge alone, S

,

and ( C ) t i d e

where t h e s e mean v a l u e s were o b t a i n e d by averaging v a l u e s

over a semi-diurnal p e r i o d from 14.30 1 February t o 03.00 2 February.

The

d i s t r i b u t i o n of t i d a l v e l o c i t i e s i n t h i s region i s f a i r l y well e s t a b l i s h e d and t h e r e s u l t s f o r f i g u r e l l ( a ) a r e i n good agreement w i t h t h e d i s t r i b u t i o n of maximum v a l u e s shown i n t h e a t l a s p u b l i s h e d by Seehydrographischer D i e n s t ,

1975 ( 5 )

Rostock

.

The d i s t r i b u t i o n f o r s u r g e a l o n e shows high v e l o c i t i e s

along t h e e a s t c o a s t of B r i t a i n extending i n t o t h e Dover S t r a i t and E n g l i s h Channel.

S i m i l a r l y t h e d i s t r i b u t i o n f o r t i d e p l u s s u r g e confirms t h i s

c o n c e n t r a t i o n of high v e l o c i t i e s .

Hence,

s i n c e almost a l l l a r g e s u r g e s which

occur i n t h e Thames e s t u a r y c o n t a i n a s i g n i f i c a n t component o r i g i n a t i n g i n t h e n o r t h e r n North Sea, t h i s component w i l l e x p e r i e n c e c o n s i d e r a b l e i n t e r a c t i o n as

i t p r o p a g a t e s i n t h e c o a s t a l r e g i o n o f f Lowestoft as f a r s o u t h as t h e Thames estuary

.

179

f S'

I50 100 5 0

. ..

> ..... "

Fig.9

T\-T

Computed t i d e , s u r g e , t i d e p l u s s u r g e a n d c o m p o n e n t s o f i n t e r a c t i o n ; i n s t a n t a n e o u s v a l u e s a t 06.00 1 F e b r u a r y 1953 in c m .

80

I-

i

........ 0 .....

PIO

s-s

........

s-s

r

T-T

I ( a ) Quadratic Friction Only

Fig.10

(b) Shallow Water Only

Computed components o f i n t e r a c t i o n due t o ( a ) q u a d r a t i c f r i c t i o n o n l y and ( b ) s h a l l o w w a t e r o n l y ; i n s t a n t a n e o u s v a l u e s a t 06.00 1 F e b r u a r y 1953 i n c m .

181

60

I

1

TIDE ALONE ( T I

SURGE ALONE ( S ) 2

TIDE PLUS SURGE (T+S)

Fig.11

D i s t r i b u t i o n o f mean v e l o c i t i e s computed f o r t i d e a l o n e , s u r g e a l o n e and t i d e p l u s s u r g e ; v a l u e s s h o w n a r e i n cms-1 averaged o v e r t h e p e r i o d 14.30 1 F e b r u a r y t o 03.00 2 F e b r u a r y 1953.

182 (el V a r i a t i o n i n t h e M2 d i s t r i b u t i o n o v e r t h e p e r i o d o f t h e s t o r m The s i m u l a t i o n s d e s c r i b e d i n

$ & ( a )w e r e r e p e a t e d w i t h t h e d i f f e r e n c e

t h a t t h e t i d a l d i s t r i b u t i o n s p e c i f i e d a t t h e open b o u n d a r i e s i n ( A ) model (1)

of t i d e a l o n e ; model

(5)

(C) in

o f t i d e p l u s s u r g e combined, w a s r e s t r i c t e d t o t h e s i n g l e M

2 I n t h e o r i g i n a l case t h e t i d e w a s composed o f t h e c o n s t i t u e n t s

constituent. f o r M2,

( 3 ) o f t i d e w i t h t h e i n f l u e n c e o f s u r g e and

( B ) model

S,,

K2, N2,

simulation of t h e

01,

K

1

and M k ( P r a n d l e

(2)

).

The r e s u l t s from t h i s

'53 s u r g e and t h e M2 t i d e showed t h a t t h e v a l u e s f o r

i n t e r a c t i o n o f ( A ) t i d e on s u r g e p r o p a g a t i o n ,

( B ) s u r g e o n t i d e p r o p a g a t i o n and

( C ) t h e c o m b i n a t i o n o f ( A ) and ( B ) w e r e , i n a l l c a s e s , a l m o s t i d e n t i c a l t o t h e v a l u e s o b t a i n e d f o r t h e s i m u l a t i o n o f t h e same s u r g e w i t h t h e more c o m p l e t e T h i s i n d i c a t e s t h a t t h e major surge t i d e i n t e r a c t i o n i n t h i s

t i d a l regime.

r e g i o n i s between t h e s u r g e and t h e M2 by Banks ( 1 )

t i d e , c o n f i r m i n g a s i m i l a r r e s u l t found

.

A p a r t i c u l a r advantage of r e s t r i c t i n g t h e simulation t o surge p l u s t h e t i d e o n l y i s t h a t it a l l o w s t h e d i s t r i b u t i o n o f t h e c o - p h a s e and c o - r a n g e 2 l i n e s a s s o c i a t e d w i t h t h e M2 t i d e t o b e e a s i l y d e t e r m i n e d a t a n y s t a g e d u r i n g

M

t h e surge event.

F i g u r e 1 2 shows s u c c e s s i v e d i s t r i b u t i o n s o f t h e M2 t i d e ,

e a c h r l ~ t e r m i n e dfrom a F o u r i e r a n a l y s i s o v e r o n e t i d a l c y c l e w i t h t h e t i m e o f t h e m i d - c y c l e as i n d i c a t e d , t h e i n t e r v a l between e a c h d i s t r i b u t i o n shown i s e q u a l t o t h e p e r i o d o f M2.

I n e a c h case, t h e l a t e s t d i s t r i b u t i o n i s s u p e r -

imposed o v e r t h e p r e v i o u s d i s t r i b u t i o n i n o r d e r t o i l l u s t r a t e r e l a t i v e d i s p l a c e m e n t s between s u c c e s s i v e t i d a l d i s t r i b u t i o n s .

The amphidromic s y s t e m

i s shown t o b e i n i t i a l l y d i s p l a c e d w e s t w a r d s and t h e n t o r o t a t e i n a n a n t i c l o c k w i s e s e n s e u n t i l it r e t u r n s t o t h e o r i g i n a l d i s t r i b u t i o n a f t e r approximately

3 days corresponding t o t h e d u r a t i o n o f t h e storm.

T h i s evidence

of a r e l a t i v e l y l o n g e r p e r i o d displacement of t h e t i d a l r e g i m e i s p a r t i c u l a r l y i n t e r e s t i n g s i n c e it o f f e r s t h e p o s s i b i l i t y of i n c l u d i n g a s y s t e m a t i c c o r r e c t i o n t o t h e predicted t i d e i n t h e course of a l a r g e surge event.

However, t h e

d i s p l a c e m e n t s shown by t h e p r e s e n t model a r e s e v e r e l y r e s t r i c t e d by t h e assumption o f f i x e d boundary c o n d i t i o n s .

An e q u i v a l e n t s i m u l a t i o n u s i n g a model

o f t h e whole o f t h e N o r t h S e a s h o u l d p r o v e e x t r e m e l y i n t e r e s t i n g .

5.

CONCLUSIONS

1.

An e x a m i n a t i o n o f s t o r m s u r g e s r e c o r d e d i n t h e R i v e r Thames h a s shown t h a t

s u r g e p e a k s t e n d t o o c c u r on t h e r i s i n g t i d e .

This effect is attributed t o

i n t e r a c t i o n between t i d e and s u r g e a s d e s c r i b e d by t h e n o n - l i n e a r terms i n t h e r e l e v a n t hydrodynamic e q u a t i o n s .

,

Fig.12

Variation in the M2 tidal regime over the period of the '53 s t o r m ; continuous lines show the distribution at the times stated, dashed lines show distribution one (MZ) period earlier. Co-range lines show amplitude in cm.

183

184 2.

A method of i d e n t i f y i n g t h e mechanics of i n t e r a c t i o n i n t h e s o u t h e r n North

Sea has been developed i n v o l v i n g t h e use of two numerical models, one s i m u l a t i n g t i d a l propagation and t h e o t h e r s u r g e propagation.

The two models a r e o p e r a t e d

c o n c u r r e n t l y w i t h c r o s s l i n k a g e from p e r t u r b a t i o n t e r m s which i n t r o d u c e t h e i n f l u e n c e of t h e s u r g e i n t o t h e model of t i d a l propagation.and t h e i n f l u e n c e of t h e t i d e i n t o t h e s u r g e model.

The magnitude of t h e s e i n t e r a c t i o n terms

were shown t o be a f u n c t i o n of s u r g e amplitude and t i d a l amplitude with t h e r e s p e c t i v e powers of t h e s e a m p l i t u d e s , i n p a r t , dependent on i n s t a n t a n e o u s flow conditions.

3.

T h i s modelling approach w a s used t o s i m u l a t e t h e i n t e r a c t i o n o c c u r r i n g

during t h e d i s a s t r o u s storm of

30 January t o 2 February 1953.

I t w a s shown t h a t

i n t e r a c t i o n i n t h e s o u t h e r n North Sea r e s u l t s p r i m a r i l y from t h e q u a d r a t i c f r i c t i o n term and t h a t t h e m o d i f i c a t i o n of t h e s u r g e p r o p a g a t i o n by t h e t i d e i s of a s i m i l a r o r d e r of magnitude a s t h e m o d i f i c a t i o n of t h e t i d a l propagation by t h e surge.

The i n t e r a c t i o n from shallow w a t e r terms i s g e n e r a l l y r e s t r i c t e d t o

t h e m o d i f i c a t i o n of t i d a l propagation by t h e surge and is only of s i g n i f i c a n c e i n t h e Thames e s t u a r y and t h e r e g i o n e a s t of t h e e s t u a r y between Ostend and t h e mouth of t h e Rhine.

However, t h e t i m e - s e r i e s f o r t h e shallow water i n t e r a c t i o n

i n t h e Thames shows t h a t t h i s term c o n t r i b u t e s t o t h e i n c r e a s e i n s u r g e h e i g h t s

on t h e r i s i n g t i d e i n t h e r i v e r .

k.

A n examination of t h e s p a t i a l and temporal developments o f t h e v a r i o u s

components of i n t e r a c t i o n s u g g e s t s t h a t changes i n w a t e r l e v e l due t o i n t e r a c t i o n can develop r a p i d l y i n time and may be l o c a l i s e d i n space.

5.

A s t u d y of t h e s p a t i a l d i s t r i b u t i o n s o f v e l o c i t y f o r both t i d e and s u r g e w a s

made s i n c e t h e importance of t h e q u a d r a t i c f r i c t i o n term s u g g e s t s t h a t i n t e r a c t i o n w i l l develop most e f f e c t i v e l y i n t h o s e r e g i o n s where t h e v e l o c i t i e s a s s o c i a t e d w i t h b o t h t i d e and s u r g e p r o p a g a t i o n a r e g r e a t e s t .

These s p a t i a l

d i s t r i b u t i o n s showed t h a t t h e c o a s t a l r e g i o n around Lowestoft as f a r s o u t h a s t h e Thames e s t u a r y i s an a r e a of h i g h v e l o c i t i e s f o r both t i d e and s u r g e and hence t h i s a c c o r d s w i t h t h e important o b s e r v a t i o n t h a t i n t e r a c t i o n develops r a p i d l y between Lowestoft and t h e Thames.

6.

A s i m u l a t i o n of t h e

'53 s u r g e w i t h t h e M2 t i d e only,showed t h a t almost

of t h e s u r g e - t i d e i n t e r a c t i o n may be accounted f o r by t h i s c o n s t i t u e n t .

all

This

s i m u l a t i o n a l s o enabled t h e displacement o f t h e M2 t i d a l regime by t h e surge event t o be t r a c e d .

The displacement w a s found t o c o n s i s t of an o r d e r l y a n t i -

clockwise r o t a t i o n of t h e amphidromic system w i t h an a s s o c i a t e d t i m e - c o n s t a n t of about

3 days o r , e f f e c t i v e l y , t h e t o t a l d u r a t i o n of t h e storm.

185 ACKNOWLEDGEMENTS The work described in this paper was funded by a Consortium consisting of the Natural Environment

Research Council, the Ministry of Agriculture

Fisheries and Food, and the Departments of Energy, Environment, and Industry.

REFERENCES

J. E. Banks, Phil. Trans. R. SOC. Lond., A , 275 (1974) 567-609. Prandle, Institute of Oceanographic Sciences, Bidston, Merseyside, England, 4 (1974). 3 D. Prandle, Proc. R. SOC. Lond., A, 344 (1975) 509-539. 4 D. Prandle and J. Wolf, "The Interaction of Surge and Tide in the North Sea and River Thames" (in press). 5 "Atlas der Gezeitenstrome fur die Nordsee, den Kana1 und die Irische See" Uritte, verbesserte Auflage Seehydrographischer Dienst, der Deutschen Demokratischen Republik, Rostock 1975. 1 2

D.

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187

RESIDUAL PHENOMENA IN ESTUARIES, APPLICATION TO THE GIRONDE ESTUARY R. BONNEFILLE Electricit6 de France, Chatou (France)

ABSTRACT Integration of equation of residual phenomena (velocity and salinity) in the case of an estuary with constant width and depth, shows the possibility to have some closed residual streamlines near the bottom. In the general case, integration is more complicated, but the conclusion is the same. Numerous data about the Gironde estuary are used to estimate the value of the three more important new coefficients introduced by the theory of residual

phenomena : the longitudinal and vertical mixing coefficients of salinity and the vertical mixing coefficient of momentum. BRIEF REVIEW OF RESIDUAL PHENOMENA The theory of residual phenomena (Pritchard, 1956) is based on the division of physical events in two elements. The first one i s independant of the time, there is the residual part ; it is the time-averaged value of the considered evenLs during a given period, at the minimum a tide-period. The second element depends on the time ; it represents the fluctuation of the physical event, induced by the tide,relatively their mean values. For example let us considering the velocity vector

6; and

the salinity s

-f

and V, and sm are the fluctuante components, the time-averaged values of those are n u l l . If, we introduce these fonctions in the momentum and diffusion equations ; then, i f this equations are time-averaged, as in the conventional theory of the turbulence, new terms are appearing ; they are introduced bv the products of -f

fluctuantes components Vm and .,s

This terms are modelised by using mixing

188 coefficients. The horizontal components of these coefficients represent the dispersion by tide currents-on areas the dimensions of whose are from 100 m to I0 km. Of course, the mixing coefficients are greather than the turbulent

coefficients, about 100 times more, for example from 100 to 1000 m2/s. Nevertheless the vertical mixing coefficients have about the same value of vertical coefficients of turbulence ( I to 10 cm2/s). The same method is used to define the width-averaged residual quantities + from the time-averaged residual events ; for example V and defined by the

s

relationships. + vo = 3(x,z) + +V’(x,y,z) so = s ( x , z ) + s’(x,y,z) with

on which b(x,z) i s the width of the estuary and Ox, Oy, Oz the longitudinal,

lateral and vertical axes of coordinates. Their averaging operation over the width of the estuary introduces new terms due to the fluctuations of the velocity and salinity from a side to the other side of the estuary. These new terms are also modelised by new mixing coefficients (Ronday, 1975). But by the effects of the sides of the estuary the equation transformations are more complicated, and it is necessary to do some assumptions about the values of residual quantities on the sides. A preliminary study showed that it is usefull to assume that the residual velocity is null on the side : Vo(x,*b/2,z)

=

0

It is now possible to modelise the side effects as the mixing effects, and

define the general mixing coefficients : Kdx, Kdz for the momentum, from the momentum equation, Ksx,

Ksz

for the salinity from the diffusion equation.

After elimination of negligeable terms, the equation are reduced at the following forms (Chatwin, 1976) :

- momentum equation :

-

continuity equation :

a (bw) axa (bu) +x

=

0

- diffusion equation :

189 where x

is longitudinal seawards, z vertical upwards,

g

is the gravity acceleration,

p

is the specific mass of water,

+ u a n d w are the horizontal and vertical components of the residual velocity V. The continuity equation suggests to search a stream function Y o , that is obtained easily if we do the following assumptions :

-

the depth of the estuary is constant : ho doesn't depend of x or z , the width b is constant in a cross-section : b(x,z) becomes b(x), the residual discharge

QR =

dz

is constant along the estuary,

-

the mixing coefficient of momemtum Kdz is independant of z, the residual velocity is null on the bottom, as on sides,

u(x,-ho)

-

=

w(x,-ho)

=

0

the water specific mass p depends linearly on the residual salinity :

p = p0(l+aS)

a is a constant, its value is approximatly 0,76 if the salinity is expressed in gr/liters,

-

-

the residual salinity is assumed to be constant on the vertical ; we put

s = S,(X)

where S s is the superficial width and time-averaged salinity ; this assumption consists on the first order solution of the diffusion equation. Let we us define the non-dimensional stream-function Yo(x,Z) by :

we obtain :

Yo

=

1 (22-1) (2+1)2Z 2A

1

+ - (Z2-1)2 2

with

and for u and w

w(x,Z)

=

h d - (bus) (22-1) (1+2)'2 b dx

where there are introduced :

- the vertical-averaged horizontal residual velocity

190 - the horizontal residual velocity due to the salinity gradient us(x)

aghd dSs -48Kdz dx This solution shows that the horizontal residual velocity u contains two

=

proportional parts to um and us. The first one flows seawards ;which is more important near the mouth and near the end of the estuary in the zone where the variation of salinity is small. The second part is seaward near the free surface and upward near the bottom ; it is important on the central zone of the estuary near the inflexion point of the longitudinal distribution of salinity. This opposition between the two parts of the velocity u gives to the vertical distribution of the residual velocity its specifical aspect, particularly the change of direction near the bottom in the zone called the "neutral point" (Hansen and Rattray, 1965). As Yo is function of x by the parameter A, it is easy to trace the stream lines, defined for the constant values of Y o , by the equation : 24

3+A + -z3

2

1 +3A - -z2 2

- ~y~

= 0

The figure 1 shows that the neutral point doesn't exist if A

I 1

only ; that is

happening on the mouth and the end of the estuary. On the contrary for A < 1 the direction of the residual velocitycbanges near the bottom. In this case we could have closed residual trajectories as it is shown in the figure 2, for which the stream lines are computed for a possible distribution of A ( x ) along the estuary. Using this results it is easy to integrate the diffusion equation at the second order approximation ; it appears a small variation of the salinity along the verticale

s(x,Z)

=

usho dSs [ (SZ3+15Z2-10)z2 SS(X) - __20Ksz dx

-3(2-Z2) Z2] 2%

EXTENSION TO THE ESTUARIES WITH VARIABLE DEPTH Taking in account that the depth h is function of x and y , brings a set of complications in the equations. But it is possible to use the same method : let we us define the functions q(x,y),

5(x) and the mean depth ho(x),

by the

relationship :

It is also possible to obtain results like with a constant depth ; if we introduce

the function G(x) :

191 which is used in the expression of us :

In the case of an estuary with a flat bottom, we have f3

=

0, and we find

again the same expression for u(x,Z) except that h, depends on x. The expression of the vert cal component w is more complicated by the fact of the slope of the bottom : W(X,Z)

=

4

1

is the mean elevation of the free surface and hl(x)

where h2(x)

the elevation of

the flat bottom, or ho

h2 - hi

=

APPLICATION TO THE GIRONDE ESTUARY The numerous measurements of velocities and salinities made in Gironde (Bonnefille, 1971) (17 surveys from 1965 to 1975, with sometimes simultaneous explorations on 5 verticales) allowed us trying to confirm the theories of residual phenomena and to estimate the new mixing coefficients Kdz, Ksx and Ksz. The figures3 and 4 show the mean characteristics of the estuary S,, b and ho. The figure 5 gives an example of comparisons of theoritical and measured distributions of residual velocity u(Z) and salinity s ( Z ) for differents sections of the estuary. It has been also possible to compute for each set of measurements, respectively um, us, Kdz, K,,

and finally QR.

The analysis of data shows an interesting first result. The residual depth ho(x) and the horizontal gradient of salinity dSs have about always the dx same value ; this fact increases the interest of residual phenomena, because

-

the determination of A(x) becomes very easy. The analysis of results carrier on the following conclusions. Residual discharge QR (figure 6) Theoretically, if f3 is null, QR is constant ; this assumption is not well confirmed by the results. Nevertheless a more interesting hypothese would be that the rapport QR/h is nearly non-dependant on x. In this case we have UmSs

=

Ksx

dSx

dx

expression giving easily Ksx Longitudinal mixing coefficient of salinity Ksx (figure 7) K,,

-

This coefficient could be considered as constant 4000 m2/s

192

Vertical mixing coefficient of salinity Ksz (figure 8) The distribution of Ksz along the estuary is not simple ; but this coefficient is not important because it appears only on the vertical distribution of salinity. That is a second order phenomena. We can admit K,, Ks,

-

-

3-6 cm2/s for ho 17 cm2/s for ho

-

7 m 11 m

Vertical mixing coefficient of momentum Kdz (figure 9) This coefficient increases with the size o f the flow, and mainly wi h the size of the aera of the cross-section. Kdz is very important because it is a main parameter on A(x) which determines the general form of the residual circulation. The mean value of Kd, is Kdz

-

1

to 20 cm2/s

for the cross-section areas 30000 to I00000 m2. REFERENCES Bonnefille, R., 1971. Remarques sur les gcoulements moyens 1 l'aval de la Gironde. AIRH, Paris, 4 : 229-233. Chatwin, D.C., 1976. Some Remarks on the Maintenance of the Salinity Distribution in Estuaries. Estuarine and Coastal Marine Science, 4 : 555-566. Hansen, D.V. and Rattray, M., 1965. Gravitational circulation in straits and estuaries. Journal of Marine Research, 23 : 104-122. Ronday, F.C., 1975. Etude de l'envasement et de la variation longitudinale du coefficient de dispersion dans les estuaires partiellement stratifigs. Annales des Travaux Publics de Belgique, 4 : 1-18. Pritchard, D.W., 1956. The dynamic structure of a coastal plains estuary. Journal of Marine Research, 1 5 ( 1 ) : 33-42.

193 2 0

-

a6

-1

0

F i g . 1 - Residual streamlines of a partially stratified estuary.

Z 0

- 0.5

-1

Pig.2

7 w

Example of residual streamlines in an estuary

-

0

20

Mkm


>u1, we get:

Averaging (6) over the tidal cycle gives:

where w o stands for the residual vorticity. As is shown in Fig. 1, the left hand side of (7) is of opposite sign on both sides of the shoal, but does not reverse sign during the tidal cycle. Hence, a cyclonic and an anticyclonic vortex are produced near the shoal (Fig. lb). Now, in the real situation of many shallow tidal areas, the perturbations in water depth have a quasi random character, thereby randomizing the residual current velocity field. The latter, therefore, can be thought of as to exist of a random distribution of eddies of different strenght and size. Assuming now an ensemble of such random residual current fields, we may construct the spatial covariance , from which a 2 %

representative velocity scale < u g > = O

7 0

and length scale:

dr



are derived.

LONGITUDINAL DISPERSION By definition the Eulerian residual current velocity field is a random function of space but time-independent. In a qualitative way it may now be shown that the Lagrangian residual velocity of a single waterparcel is a random function of time, if an oscillatory tidal current is added to the Eulerian residual current velocity field. The random structure in space of the residual current velocity field is shown in Fig. 2, together with the path of a particular waterparcel.

211 Starting at position 0 at the beginning of the flood tide, the parcel arrives at A' at slack water. If only the tide were acting it should arrive at A at that

time. Hence the displacement A A' is due to the residual current velocity field. The same way of reasoning applies during its backward (ebb) motion from A' to B'. Here BB' is the displacement due to the residual current velocity field. Thus, during one tidal cycle the particle experiences a residual displacement OB'. The procedure may be repeated for all tidal cycles here after. Because of the random

Fig. 2. Path of a particle during a tidal cycle shown by a solid line. The residual current velocity field is represented by dashed streamlines. The tidal motion proper, during the flood and ebb stages of the tide each, is shown by the thick straight dashed lines.

212

character of the residual current velocity it will be obvious that successive displacements AA', BB',

._....form

a random vector series, i.e. the particle

experiences a "tidal random walk". Of course, neighbour vectors may be correlated, the magnitude of the correlation depending on the ratio of the r.m.s. step length of the tidal random walk and the integral length scale (lo) of the residual current velocity field. Considering now the problem of longitudinal particle dispersion as a random walk problem, we may use Taylor's (1921) classical theory of turbulent diffusion to express the effective longitudinal diffusion coefficient in the r.m.s. 2

longitudinal step length, , and the correlation coefficient of neighbour steps, c, provided that the successive displacements constitute a first-order Markov process. If now y(") denotes the displacement due to the residual current velocity field during the n'th step and

E

is the time-interval of each step, assumed to

be half a tidal period here, then the mean-square Lagrangian residual velocity 2

during each step is defined by 2

< v > = 7 2

(9)

E

whereas the correlation coefficient between the n'th and the m'th step is given by (n) (m+m)> >T, K attains the well-known form: 2

K =

T

2

up to here K is expressed in Lagrangian quantities and T. Since, in

general, our information about the residual current velocity field is of Eulerian character we have to express the former quantities in the characteristics of the Eulerian velocity field. The latter is now supposed to consist of a homogeneous and normal random distribution in space of characteristic eddies represented by a stream function of Gaussian form (Zimmerman, 1976) upon which is superimposed an oscillatory tidal current. The Eulerian velocity field is then represented by the following set of parameters: tidal m.s. velocity length scale

residual

ratio tidal/res.

"1

2 QO>

U

.l1

10

A

2

213 2 %

By using the assumption U1>> in a perturbation procedure for the EulerLagrange transformation (Zimmerman, 1976) it can be shown that the effective longitudinal diffusion coefficient may ultimately be expressed by : K = b

(U,X)

(14)

Ulll

where b ( u , X ) is a complicated function of the energy density spectrum of the residbal current velocity field, weighted by functions which depend on U and A. Note that (15) resembles ( 1 ) . However, here b

(U,X)

is not an empirical factor Of

proportionality but is theoretically related to the characteristics of the components of the Eulerian current velocity field. An equivalent expression, similar to (21, for K is: 2 4

K

=

c (U,h)



(15)

10

Here again c (u,A) is a complicated function of u and A. Formulas ( 1 5 ) and (16) show that K can neither be described by either only the tidal parameters (U1, 11) or only the parameters (u0,lo) of the residual current velocity field. Although

dimensionally the products of both sets of parameters produce a diffusion coefficient, it is shown by the dependence of the factors b and c on u and A, that it is the interaction of both field which does give rise to a dispersion process.

AN APPLICATION OF THE TELEGRAPH-EQUATION The equation (11) for the second moment of the particle position corresponds to a transport equation of the form (Monin and Yaglom, 1971; Corrsin, 1974):

where c is the cross-sectional mean concentration of the transported dissolvent This equation is the Telegraph equation which has a "wavelike" character for t