Advances in Geophysics, Vol. 26

ADVANCES IN GEOPHYSICS VOLUME 26 Contributors to This Volume CHRISTOPHER R. LLOYD DAVID E. LOPER MIRLES. V. RAO MI...

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ADVANCES IN

GEOPHYSICS

VOLUME 26

Contributors to This Volume

CHRISTOPHER R. LLOYD DAVID E. LOPER MIRLES. V. RAO MICHAEL E. SCHLESINGER

Advances in

GEOPHYSICS VOLUME 26

Edited by

BARRY SALTZMAN Department of Geology and Geophysics Yale University New Haven, Connecticut

1984

ACADEMIC PRESS, INC. (Harcourt Brace Jovanovich, Publishers)

Orlando San Diego New York London Toronto Montreal Sydney Tokyo

COPYRIGHT @ 1984, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM O R BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR A N Y INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER.

ACADEMIC PRESS, INC.

O r l a n d o , F l o r i d a 32887

United Kingdom Edition publislied by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road, London N W l IDX

LIBRARY OF CONGRESS CATALOG CARDNUMBER: 52-12266

ISBN 0-12-018826-0 PRINTED IN THE UNITED STATES OF AMERICA 84 85 86 87

9 8 7 6 5 4 3 2 1

CONTENTS CONTRIBUTORS ................................................... ERRATUM ........................................................

vii ix

Structure of the Core and Lower Mantle

DAVIDE. LOPER 1. Introduction ................................................... 2 . Dynamo Energetics ............................................. 3 . Structure of the Outer Core ...................................... 4 . Structure of the Inner Core ....................................... 5 . Structure of D” ................................................. 6 . Structure of Deep-Mantle Plumes ................................. 7 . Thermal History of the Earth ..................................... 8. Summary...................................................... Appendix. Energy Available from Gravitational Separation ........... References.....................................................

i 4

6 12 15 19 21 24 25 27

Pre-Pleistocene Paleoclimates: The Geological and Paleontological Evidence; Modeling Strategies. Boundary Conditions. and Some Preliminary Results

CHRISTOPHER R . LLOYD 1. Introduction ................................................... 2. Paleoclimatic Indicators ......................................... 3 Pre-Pleistocene Paleoclimates and Paleoceanography................. 4 Forcing Mechanisms in Long-Term Climatic Change ................ 5 . Boundary Conditions for Paleoclimatic Modeling.................... 6. Paleoclimatic Modeling Strategies ................................. 7 . A Survey of Paleoclimatic Modeling Results ........................ 8 . Summary ...................................................... References. ....................................................

. .

36

39 52 74 80 101 108 120 124

Climate Model Simulations of CO. Induced Climatic Change

MICHAEL E. SCHLESINGER

1. Introduction .................................................. 2. Mathematical Climate Models ................................... 3. Comparison of Model Simulations of COJnduced Climatic Change . . 4. Discussion .................................................... 5 . Conclusions and Recommendations .............................. References.................................................... V

141 143 152 216 228 230

vi

CONTENTS

Retrieval of Worldwide Precipitation and Allied Parameters from Satellite Microwave Observations

MIRLES . V. RAO 1. Introduction .................................................. 2. The ESMR System............................................. 3. Conversion of Brightness Temperature to Rain Rate: A Theoretical Approach .................................................... 4 . Verification with Radar Data .................................... 5. Verification by a Specially Designed Experiment ................... 6. Generation of Oceanic Rainfall Maps ............................. 7. Intercomparison ............................................... 8. Analysis of Rainfall Maps ....................................... 9. New Features of Global Climatology Revealed by ESMR Rainfall Studies ....................................................... 10. Periodic Variations of Precipitation in the Tropical Atlantic Ocean .... 11. IceMapping .................................................. 12. Storm Structure Studies ........................................ I3. Qualitative Estimation of Rainfall Over Land Areas ................. 14. Retrieval of Other Geophysical Parameters ........................ 15. Conclusion ................................................... Appendix. Explanatory Notes ................................... References....................................................

INDEX

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

238 241 246 249 252 257 268 276 290 297 304 308 311 317 325 330 331 337

CONTRIBUTORS Numbers in parentheses indicate the pages on which the authors’ contributions begin.

CHRISTOPHER R. LLOYD,*Climatic Research Institute, Oregon State University, Cowallis, Oregon 97331 (35) DAVID E. LOPER,Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, Florida 32306 ( 1 ) MIRLES. V. RAO, 7223 North Olney Street, Indianapolis, Indiana 46240 (237) MICHAEL E. SCHLESINGER, Department of Atmospheric Sciences, and Climatic Research Institute, Oregon State University, Corvallis, Oregon 97331 (141)

* Present address: Geophysical Fluid Dynamics Laboratory, Princeton University, Princeton, New Jersey 08540. vii

This Page Intentionally Left Blank

Erratum Advances in Geophysics Volume 25 The following figures should appear on page 248:

O U T G O I N G LONGWAVE R A D I A T I O N

SUMMER ( 1 9 7 4

(Wrn-')

NOAA SR 0

0

NET R A D I A T I O N

SUMMER ( 1 9 7 4 - 1 9 7 7 )

(Wrn-')

N O A A SR 0

0

(4 FIG.3b and c. ix

-

1977)


STRUCTURE OF THE CORE AND LOWER MANTLE DAVIDE. LOPER Geophysical Fluid Dynamics Institute Florida State University Tallahassee, Florida 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Dynamo Energetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Structure of the Outer Core. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Structure of the Inner Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Structure of D”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Structure of Deep-Mantle Plumes . . . . . . . . . . . . . . . . . . . . . . . . . 7. Thermal History of the Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. S u m m a r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix. Energy Available from Gravitational Separation . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

4 6

12 15 19 21 24 25

27

1. INTRODUCTION

The earth’s deep interior is inaccessible and is likely to remain so. Therefore, our knowledge of it depends to a large degree on the interpretation of data available to us at or near the surface, from observations and measurements of phenomena containinginformation of the interior of the earth such as seismic waves and free oscillations,topography and gravity, magnetic and electric fields, heat flow and hydrothermal circulations, and chemical and isotopic variations in volcanic rocks. Accurate interpretation of these data requires the construction of models based upon the fundamental principles of physics, chemistry, and thermodynamics and tempered by laboratory experimentsat high pressure and temperature. This procedure is akin to the solution of an inverse problem in that the interpretation, and the model it is based upon, are not unique. Thus we are forced to choose between models on a somewhat subjective basis, discarding those that are impossible or appear implausible and retainingthose that are most elegant and in harmony with the data. This article is a review of recent progress in the construction of such models of the earth’s deep interior, particularly the inner and outer core and the lower mantle. The focal point of this review is the energy source for the geodynamo: What is the best explanation for the energy source and what are the implications for the structure and thermal evolution of the earth? The models provide a coherent, plausible picture of the core and lower mantle, although a number of questions remain unanswered. 1 ADVANCES IN GEOPHYSICS, VOLUME 26

Copyright D 1984 by Academic Press, Inc. All rights of reproductionin any form resewed.

.^_., - .^

^.^^^,

-

2

DAVID E. LOPER

For many years, one of the paradigms of geophysics was that the earth’s interior is in a thermal steady state, with the heat flux out at the surface equal to that produced by radioactivity within the interior. This model was based upon two observations. First, the radioactive heating of an earth of chondritic composition is very close to the heat flux observed at the surface (see Stacey, 1977a, pp. 183- 192). Second, the strong temperature dependence of viscosity regulates the speed of convective motion and hence the heat flux from the earth, thereby tending to stabilize the temperature (Tozer, 1972). Several studies (Verhoogen, 1961; Braginsky, 1963)of the power source for the geodynamo suggested that the earth may be cooling, but these were largely ignored. It apparently was not realized until recently that, because the strength ofradioactivitydiminisheswith time, the earth cannot remain at a constant temperature, but must evolve thermally. In the past few years, it has become abundantly clear that the model of an earth in thermal steady state is not correct (Schubert and Young, 1976; Sharpe and Peltier, 1978, 1979;Schubert et al., 1979a,b, 1980;Sleep, 1979;Daly, 1980a;Davies, 1980; McKenzie and Weiss, 1980; Stacey, 1980; Turcotte, 1980; Cook and Turcotte, 1981;McKenzie and Richter, 1981;Sleep and Langan, 1981;Spohn and Schubert, 1982) and that the earth is cooling at a rate of 10- 100 K/ 1O9 yr, with 50 K/ lo9 yr being a reasonable value. The development of a plausible model of the energy source for the geodynamo proceeded in parallel with the studies of thermal evolution; for a review of possible driving mechanisms, see Gubbins and Masters ( 1979). Precessional motion as an energy source (Malkus, 1963, 1968)appears implausible (Rochester et al., 1975;Loper, 1975;Stevenson, 1983). For along time, the most viable model was thermal convection, but there are serious problems concerning the efficiency of a thermally driven dynamo (see Stacey, 1977a, pp. 197-209; Verhoogen, 1980, pp. 75-83). However, in the past few years it has become clear that the best model for the energy source is gravitational energy released by the growth of the solid inner core, as first proposed by Braginsky (1963, 1964; Gubbins, 1976, 1977, 1978; Loper, 1978a,b;Gubbins et al., 1979;Gubbins and Masters, 1979;Loper and Roberts, 1983). It is of interest to note that this mechanism requires the earth to be cooling. The rate of cooling can be related to the growth of the inner core; the cooling rates thus obtained, 10 K/ 1O9 yr by Gubbins et al. ( 1979)and 23 K/ 1O9 yr by Loper and Roberts ( 1983),are compatible with those estimated for the entire earth by parameterized convection models. The existence of a solid inner core appears to play an important role in the magnetism of the terrestrial planets (Stevenson et al., 1983; Stevenson, 1983),and the growth of the solid inner core is caused by the cooling of the core from above. In such a situation, with the core coolest at the top,

STRUCTURE OF THE CORE AND LOWER MANTLE

3

freezing occurs first at the bottom provided the liquidus gradient with pressure, dTL/dP,is steeper than the adiabat, dTA/dP:

dTL/dP > dTA/dP The adiabat is given by

dT,/dP

= yT/K,

where

Y = aKslpC,

(1.3)

is the Griineisen parameter, a is the coefficient of thermal expansion, K, is the adiabatic incompressibility,p is the density, and C, is the specific heat. Assuming Lindemann’s law is valid (Stacey and Irvine, 1977),the liquidus gradient is given by

dTL/dP= 2(y - i)T/K,

(1.4)

It follows from Eqs. (1. l), (1.2),and (1.4)that if y > 3, the earth will grow a solid inner, as opposed to outer, core as it cools. A decade ago Higgins and Kennedy ( 1971) caused a great stir by asserting that Eq. (1.1)does not hold within the core, giving rise to the “core paradox” (Kennedy and Higgins, 1973). Current opinion (Irvine and Stacey, 1975;Jamieson et al., 1978; Stevenson, 1980) is that Eq. (1.1) is well satisfied within the core and that there is no core paradox, although there is some opinion to the contrary (Ullman and Walzer, 1980). In fact, from liquid-state theory, Stevenson (1980)prefers a value of y as high as 1.6 to 1.7. The idea that the power supply for the dynamo arises from the continual gravitationalseparation of the heavier and lighter constituentsof the core has gained rapid acceptance and has been extensively reviewed (Gubbins and Masters, 1979;Jacobs, 1980;Gubbins, 1981; Stevenson, 1981 ; Loper and Roberts, 1983). Therefore, the focus here will primarily be upon the implications of this idea for the structure and thermal evolution of the earth. Also, this article will not attempt to survey the seismologicalliterature; for a recent summary, see Bolt and Uhrhammer (1981) or Bolt (1 982). Following a brief review of dynamo energeticsin Section 2,the convective stability and morphological stability of the core are discussed in Sections 3 and 4. Next, the structure of D”, treated as a thermal boundary layer, is considered in Section 5, and the plumes that carry the core heat upward through the lower mantle are examined in Section 6. The thermal history ofthe earth is discussed briefly in Section 7. The current state of our knowledge of the structure of the core and lower mantle is summarized in Section 8.

4

DAVID E. LOPER

2. DYNAMO ENERGETICS It is very likely that the earth's core is composed principally of iron, with a small but significantpercentage of some light constituent. The nature and amount of this constituent is uncertain, with 5 -2OYo of sulfur or oxygen being quoted most often (Brett, 1976; Ringwood, 1977; Stevenson, 198 1; Brown and McQueen, 1982). However, this uncertainty does not affect the model of gravitational separation provided the light constituent in the core fractionates into the liquid as core material solidifies. Fractionation upon solidification is a universal property of alloys that are not at the eutectic composition (Chalmers, 1964). If the mass fraction of light material in the liquid is less than the eutectic value, the solid that forms contains less of the light material than does the liquid (see Fig. 1.4a of Chalmers, 1964), and a dense inner core grows. This leads to a simple model of the energy source for the geomagnetic field. Recently McCammon et al. (1983) revived the idea, first proposed by Braginsky (1 963), that the mass fraction of light material in the liquid exceeds the eutectic value. In this case, the structure of the inner core is complicated and the rate of growth of the inner core is severely constrained (Fearn and Loper, 1983). This possibility is considered to be implausible and will not be discussed further. The secular cooling of the core causes the growth of the inner core by freezing of iron-rich material from the outer core. This process leaves a residue of iron-poor material in the liquid above the inner-core boundary. This material is less dense than that above and consequently is convectively unstable. The details of this process are reviewed in Section 3, but for a rough estimate of the energy released, a simple calculation suffices. Consider a self-gravitating sphere of radius ro and mass Mo composed of two incompressible materials, one heavy and one light. Suppose the materials are uniformly distributed initially and, after some period of time, the heavy constituent collects into a central sphere of radius ri. In order to form this central sphere, heavy material must move downward and an equal volume of light material must move upward, releasing gravitational potential energy. The amount A E of energy released by this separation process is calculated in the Appendix and simplified for the case $ < po where $ is the density jump at r = ri due to change in composition and po is the mean density. The result is

AE = (2n/5)GM0~(r3r,,)( 1

- r:/r:)

where G = 6.67 X lo-'' N m2 kg-2 is the gravitational constant.

STRUCTURE OF THE CORE AND LOWER MANTLE

5

The power QG released by this process is QG

= d(AE)/dt

Assuming G, M,, r,, and6 constant, Eq. (2.1)may be used to write Eq. (2.2) as QG = 27cGMOj.?(3/5- r:/r2)(r:/r0)ti

where a dot denotes differentiation with respect to time. This may be expressed in terms of the rate of growth of the mass Mi of the inner sphere, noting that

hi= 4npi r: ii

(2.4)

where pi is the mass of the inner sphere. Now Eq. (2.3) is (2.5) QG = (GMo6/2rOpi)(3/5- rf/r2)Aki The parameters appearing in Eq. (2.5) are estimated in Table I. Using the preferred values we estimate the current QG = 2.5 X 10” W, sufficient to drive a geodynamowith a large toroidal field. Of the parametersused in this estimate, the most uncertain is the growth rate of the inner core. The value 6.8 X lo5kg sec-’ is obtained by dividing the current mass of the inner core, 1023kg, by the age of the earth, roughly 1.4 X 1O”sec. This assumes that the inner core has grown from zero size 4.5 X lo9yr ago at a constant mass rate of freezing. This gives an overestimate if the core were not completely molten followingits formation. On the other hand, it is an underestimate if the core remained molten for much of its history and the inner core is a recent feature. The age of the inner core is tied up with the question of the cooliiig of the core and mantle. We will return to this point in Section 7 and give an improved estimate for the power supply. In this simple calculation, the gravitationalenergy released due to compression has been ignored. This is a small fraction (7- 1OYo) of the total (Miiller and Hage, 1979) and goes primarily into adiabatic compression and hence is not available to drive motions in the core. Also, loss of gravitational potential energy due to diffusion of material has been neglected. It is difficult to estimate the size of the toroidal magnetic field sustained by a given power source because a realistic model of the geodynamo is not available. Using the parameterization of Loper and Roberts (1983) Q,= 1015 w T - 2 ( ~ a ) 2 (2.6) where Q, is the ohmic power loss and Ba is the averagetoroidal-fieldstrength in the core, we may equate Q, and QG to obtain an estimate for Ba of 1.58 X T (158 G).

6

DAVID E. LOPER

TABLEI. PREFERRED PARAMETER VALUES FOR THE CORE, INCLUDING SOURCE AND ESTIMATEDERROR ~~

Parameter

Magnitude

G rl(I r0 g,

Source

6.67 X lo-" N m2kg-' 1.22 X 106 m 3.48 X lo6 m 4.4 m s e c 2 10.68 m set+ 1.87 X loL3m2 1.52 X lOI4 m2 0.97 X kg 1.95 X kg 12.76 X lo3 kg m-3 9.9 X lo3 kg m-3 50 8X K-I 15.7 X K-' 670 J kg-I K-I 4168 K 3157 K 31 W m-I K-I 4.2 X m2 sec-l 8 X lo5J kg-' 0.0 12 500 kg m-3 6.8 X lo5kg sec-l 1.2 0.05 3X m2 sec-' 6.2 X lo7 J kg-l 1.2 X 10) kg sec-l 219

go

A, A0 MI M O PI

ps M ff, ff0

CP TI

TO

k K

L

!P.*

MI

f3 5

-D P. MCR

5M

Stacey (1977a) PREMb PREM PREM PREM A = 4nr2 A = 4nr2 Stacey (1977a) Stacey (1977a) PREM PREM Stacey (1977a) Stacey (19778) Stacey (1977b) Stacey (1977b) Stacey (1977b) Stacey (1977b) Stacey (1977b)

klPG Stacey (1977~) Stacey (1 977c) Masters (1 979) Text Loper ( 1978a) Loper and Roberts (1981) Loper and Roberts (1981) Eq. (3.10) Eq. (3.17)

Estimated error (%) 1 1

1 1 1 2 2 5 5

5 5 10 10 10 10 20 20 20 20 20 20 50 50 100 100 100 100 100 100

A subscript i denotes a value at the inner-core boundary; subscript o denotes the top of the core. PREM refers to Dziewonski and Anderson (1981).

3. STRUCTURE OF THE OUTERCORE The convective instability of a layer of fluid is governed by the vertical variation of density. If the fluid is modeled as a binary alloy, the density is a function of pressure, P; temperature, T; and mass fraction of the light constituent? However, the earth's interior is, to a very good approximation, in hydrostatic balance:

IZ-1 can occur by chance with a probability P = 3 1.74 and 0.26%, respectively. The confidence interval for the change in the population means can also be calculated. A [loo( 1 - a)]% confidence interval for p(2XC02) - p( 1XCO, ) is (4.2) where Z,/, is determined such that the probability that Z > Z,,, = a/2. For example, a 95% confidence interval gives a = 0.05 and, using the Gaussian distribution, Z,: = 1.96. For the precipitation rate the statistical significance has been determined by the parametric time-seriesmodeling approach developed by Katz ( 1982a, 1983) for climatic quantities whose occurrence is discontinuous in time. The mean and variance for both the control and the experiment are esti-

223

MODELS OF C02-INDUCED CLIMATIC CHANGE

mated from their individual time seriesby estimatingthe mean and variance of the amount of precipitation only on those days with precipitation (wet days), and the mean and variance of the total number of wet days. Because there are no days with negative precipitation, the probability distribution of precipitation amounts on wet days is not Gaussian. However, the probability distribution of the logarithm of precipitation amounts is approximately Gaussian. Therefore the above estimates are obtained for logarithmically transformed precipitation data rather than for the precipitation data themselves. Then the statistical significance test proceeds as given by Eq. (4.1) and the preceding description. However, the corresponding confidence interval for the transformed data that could be obtained from Eq. (4.2) would correspond to the difference of the medians, not the means, of the control and experiment precipitation rates. For this reason it is not dealt with in the following discussion. The statistical significance parameters obtained by the preceding methods for the changes in global-mean surface air temperature, precipitation rate, and soil moisture are presented in Table X. The 2.00"C change in the global-mean surface air temperature induced by doubled COz (the signal) is 32 times larger than the noise (see Figs. 5 and 39), hence the probability that this difference is due to chance is virtually zero. The corresponding 95% confidence interval is 0.12"C, that is, the probability that the simulated global-mean warming is smaller than 1.88"C or larger than 2.12"C is only 5%. Similarly, the change in the logarithmically transformed global-mean precipitation rate is significant at virtually the 0% level. However, the 0.02-cm decrease in the global-mean soil moisture is less than the noise, consequently this change could occur by chance with a probability of 72%. The 95% confidence interval of 0.09 means that the probability that the TABLEX. STATISTICAL SIGNIFICANCE PARAMETERS OF THE CHANGE IN GLOBAL MEAN QUANTITIES SIMULATED BY THE osu MODELFOR DOUBLED COz4

Surface air temperature ("C)

Experiment Control Difference Signal/noise Significance 95% confidence interval

precipitation [lo&(mm/da~)l

Soil moisture (cm)

19.87 (2.5 X 10-2)b 1.05 (3.5 X 10-3)b 3.41 (3.0 X 10-2)b 17.88 (5.7 X 10-2)b 1.00 (3.6 X 3.43 (3.5 X 10-2)b 2.00 0.05 -0.02 32.1 9.6 -0.4 0.0% 0.0% 7 I .9% 0.12 No estimate 0.09

a From Schlesinger (1983b). The results are for the last 180 days of the 72Oday simulation. The first and second numbers are the mean and estimated standard deviationof the mean.

224

MICHAEL E. SCHLESINGER 20

I6

-

c- I2

Q

L

Z B

N

4

-

0 I00

c

0) c

Y

-g

80

J

W

> 60 W

-I

w

U

z

40

a

u

k

z 2 v)

20

0 90N

70

50

30

ION

IOS

30

50

70

90s

Latitude

FIG.41. Top: the absolute value of the signal-to-noise ratio for the zonal-mean surface air temperaturechanges simulated for doubled C02by the OSU atmosphericGCM/swamp ocean model (Schlesinger, I983b). Bottom: the significance level ofchanges in zonal-mean precipitation rate (transformed}and soil moisture. Results are for averagesover the last 180 days of the 720-day simulation.

change is smaller than -0.1 1 or larger than +0.07 is 5%. Because this interval includes zero, that is, no change, the simulated change in globalmean soil moisture is not statistically significant. We now consider the statistical significance of the changes in the zonalmean surface air temperature, precipitation rate, and soil moisture. The top panel of Fig. 4 1 shows the absolute value of the signal-to-noise ratio for the zonal-mean surface air temperature. Because the values are everywhere greater than three except at the South Pole, the corresponding changes are significant at better than the 0.1% level. The bottom panel of Fig. 4 1 shows directly the significance levels for the changes in zonal-mean precipitation rate and soil moisture. This shows that the precipitation rate changes are not everywhere significant at the 10%level or less, and the soil moisture changes are significant at the 10% level almost nowhere. In other words,


225

there is a degradation in the statistical significance of the changesin the zonal means compared to that of the global means, at least for precipitation rate. The statisticalsignificanceof the simulated changes is further degraded for the geographical distributions, as is evident from Fig. 42. In this figure the regions where the significance level P I 1% are unshaded, the regions where 1Yo IP I10%are lightly shaded, and the regions where P > 10%are heavily shaded. The top panel is the significancelevel of the surface air temperature change shown in Fig. 10. It can be seen that most of the simulated temperature changes are significant at below the 1% level over most of the ocean, while many of the simulated changesover land are above the 109'0 level. It is particularly noteworthy that the cooling over central east Africa is not statistically significant. The data for Tanzania in Fig. 40c show that this is the case because of the large noise in the 180-dayaverage caused by the low-frequency variations in the time series. Returning to Fig. 42, the middle panel shows the significancelevel of the (transformed) precipitation rate change shown in Fig. 23. Here it can be seen that the significancelevel is higher than 10%almost everywhere, indicating that the changes are not statistically significant. It is interesting, however, that the large increase in precipitation rate simulated over central east Africa is significant at below the lYo level. This is also true for the increased soil moisture in this region (Fig. 32), as well as for the drying in north Africa. The changes in soil moisture almost everywhereelse over the continents are not statistically significant. The point that must be taken from Fig. 42 is that it is senselessto compare the climate changes simulated by different models without first establishing the statistical significance of those simulated climate changes. Otherwise, we may simply be comparing the models' noise levels, a not very fruitful exercise. But, having performed the analysis of statistical significance as illustrated in Fig. 42, what should be done about the nonsignificant changes such as for surface air temperature in central east Africa? It may be that although the simulated change is not statistically significant, it is too small based on some other criterion to be of interest even if its statistical significance were established somehow. In this case, we can simply not continue the analysis. On the other hand, if the simulated change is of such a magnitude as to be of interest, then its statistical significance can be established by reducing the noise through extending the averaging period. How long an averaging period is required to reduce the noise, say, by a factor of two? The conventional wisdom would suggest a fourfold increase in the averagingperiod, at least for a reasonably well-behaved quantity such as temperature. To illustrate this noise reduction by increased averaging period, Fig. 43 shows the significancelevel of a 400-day period in compari-

081

30EI

3021

306

309

30E

0

MOE

M09

M06

MOZI MOEL

I

081 SO6

SOL

SOE

s OE .sot NO1

.NO€ N OE a N OL N 06

081

I

30SI

I

3021

306

309

1

1

30E

I

0

I

MOE

I

M09

I

M06

I

MOZl MOE!

I

I

081

I NO6

221

MODELS OF C02-INDUCED CLIMATIC CHANGE I

..

I

I

I

I

I

I

9dW

6dW

3dW

b

36E

I

I

I

1

I

1

I

1

6i)E

96E

12bE

l5bE

1

I

1

I

I

1

70N 50 N 3 0N ION

10s 30 S 50s

70 S 90 s 180 9aNI

156W l26W I

1

180 4

I

4?

50 7 0NN k ,

.:'io..> 30Ni ION

10s 0

30 S

50 S

70s 90s 180

150W 120W

90W

60W

30W

0

30E

60E

90E

120E

150E

180

FIG.43. The significance level (percentage) of the change in surface air temperature simulated by the OSU atmospheric GCM/swamp ocean model for doubled COz. The averaging period is the last 400 days (top) and last 180days (bottom) of the 720-day simulation. Shading as in Fig. 42.

son with that of a 180-dayperiod for surface air temperature. As is evident, there is a reduction in the significancelevel over the oceans and most of the continents. But it is noteworthy that more than doubling the averaging period does little to improve the statistical significanceover several regions, FIG.42. The significance level (percentage) of the change in surface air temperature (top), precipitation rate (transformed) (middle), and soil moisture (bottom) simulated by the OSU atmospheric GCM/swamp Ocean model for doubled C02. The averagingperiod is the last 180 days ofthe 72O-day simulation. Dense stipple indicates a level greater than 10%; sparsestipple, between 1 and 10%;and no stipple, less than 1%.

228


both where the signal is small and large, as, for example, over the United States and central east Africa, respectively. And, while it might be argued that this occurs for surface air temperature because of the absence of thermal inertia for the earth’s surface by the assignment of zero heat capacity everywhere, there is also little improvement for the soil moisture that has hydrologic inertia and for the precipitation rate (not shown). In summary, it may require very long integrationsto establish the statistical significance of the climatic change simulated for increased CO, levels. Even the 8-yr analysis period of the Wetherald and Manabe (1981) simulation may not be sufficientlylong to establish the statistical significanceof the geographical distributionsof many ofthe climaticquantities of interest. For example, if the statistical significanceof the simulated changes for a particular month is desired, then there are at most 248 data points in an 8-yr record. This is less than the 400 data points used to create the top panel of Fig. 43. The number of data points can of course be increased by extending the period from a month to a season or longer. But then the seasonal cycle must be removed lest it increase the variance. The analysis of the statistical significance of multiyear simulations deserves increased attention. 5 . CONCLUSIONS AND RECOMMENDATIONS

As stated in Section 1, the object of this article is to formulate and describe the current issues concerning the study of possible C0,-induced climatic change by the physical method, that is, by the use of mathematical climate models. In this article we have focused on the general circulation models and their simulations of C0,-induced climatic change because it is the geographical distribution of that change that is of importance to humanity, and because only the GCMs simulate that geographical distribution. The equilibrium simulations of eight GCMs for both doubled and quadrupled concentrations of CO, have been considered and the geographical distributions, zonal means, and global means of the C0,-induced changes in surface air temperature, precipitation rate, and soil moisture have been compared. While these comparisons reveal similarities and differences among the models’ simulations, it may be premature to draw firm conclusions at this time. The reasons for this are as follows. First, the differences between the models’ geography/orography (sector with idealized land/sea geography at zero elevation versus realistic land/sea geography and realistic orography), ocean treatment (swamp ocean versus slab mixed-layer ocean), solar forcing (annually averaged insolation versus the annual cycle), and vertical resolution (number of levels in the vertical) reduce the comparisons that can be rigorously made between the models’ simulations. Second, it may be that

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some of the simulations were not run sufficiently long for equilibrium to have been reached by the time at which the averaging of the results was begun. Finally, it is likely that not all of the simulated climatic changes are statistically significant. The following recommendations are made to reduce these problems in comparing the GCM simulations of C0,-induced climate change: 1. The existing simulations should be extended as required to ensure that they reach equilibrium. 2. The statistical significanceof the C0,-induced climate changes should be determined for the existing or extended simulations. 3. The simulations should be extended further as required to obtain statistically significant results or to decide that the nonstatistically significant changes are too small to be of interest, even if they were subsequentlyshown to be statistically significant. 4. The comparison of this article should be expanded to include other climatic quantities, in particular the cryospheric quantities of sea ice and snow. 5. EBMs and RCMs should be used where possible, and GCMs where necessary, to perform studies to understand the causes for the differences among the existing (or extended) simulations. 6. Seasonal model simulationsof C0,-induced climatic change should be performed with models other than the GFDL model, and the comparison of this article and recommendations (1) through ( 5 ) should be repeated as necessary. 7. Seasonal model simulationsof C0,-induced climatic change should be performed with coupled atmosphere/ocean GCMs to incorporate the oceanic horizontal and vertical heat transports, and such simulationsshould be compared with each other and with the simulations made with the simpler ocean models.

ACKNOWLEDGMENTS I would like to thank Syukuro Manabe and Richard T. Wetherald of the Geophysical Fluid Dynamics Laboratory and Warren M. Washington and Gerald A. Meehl of the National Center for Atmospheric Research for making their results available to me, and for their discussions of those results. I especiallywant to thank R. T. Wetherald and G. A. Meehl for providingme with the unpublished results that appear in this article. I also want to thank Michael R. Riches ofthe Carbon Dioxide Research Division, Office of Energy Research, Department of Energy, for inviting me to prepare this article for presentation at the DOE C02 Research Conference “Carbon Dioxide, Science and Consensus,”which was held at the Coolfont Conference Center, Berkeley Springs, West Virginia, September 19-23, 1982.

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I express my gratitude to W. L.Gates for reviewing a preliminary version of the manuscript, to R. L. Mobley, D. S. Christopherson, and C. S. Mitchell for assistingwith the computations and graphics, to C. Beck, L. Riley, and N. Zielinski for typing the manuscript, and to J. Stark for drafting the figures. This research was supported by the National Science Foundation and the U.S. Department of Energy under Grants ATM 80-01702 and ATM 82-05992. REFERENCES

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RETRIEVAL OF WORLDWIDE PRECIPITATION AND ALLIED PARAMETERS FROM SATELLITE MICROWAVE OBSERVATIONS MIRLES. V. RAO 7223 North OIney Street Indianapolis. Indiana

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. The ESMR System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Nimbus-5 ESMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Nimbus6 ESMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. What the Instrument Measures . . . . . . . . . . . . . . . . . . . . . . . 2.4. Factors Contributing to the Observed Brightness Temperature . . . . . . . . . . . 2.5. The Suitability of ESMR for Rainfall Estimation . . . . . . . . . . . . . . . . 3. Conversion of Brightness Temperature to Rain Rate: A Theoretical Approach . . . . . . . 4. Verification with Radar Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Verification by a Specially Designed Experiment . . . . . . . . . . . . . . . . . . . 6. Generation of Oceanic Rainfall Maps . . . . . . . . . . . . . . . . . . . . . . . 6.1. Sources of Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Steps in Writing the Program . . . . . . . . . . . . . . . . . . . . . . . . 7. Intercomparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Analysis of Rainfall Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. New Features of Global Climatology Revealed by ESMR Rainfall Studies . . . . . . . . . 9.1. Characteristicsof the ITCZ in the Pacific . . . . . . . . . . . . . . . . . . . 9.2. Previously Unrecognized Rain Area in the South Atlantic . . . . . . . . . . . . . 9.3. Bimodal Behavior and Other Features of Rainbelts in the Indian Ocean . . . . . . . 9.4. Interannual Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5. Low Southern Hemispheric Rain . . . . . . . . . . . . . . . . . . . . . . 9.6. Periodical Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. Periodic Variations of Precipitation in the Tropical Atlantic Ocean . . . . . . . . . . . 10.1. Mainstudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2. Comparison with Other Results . . . . . . . . . . . . . . . . . . . . . . . 10.3. Models and Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4. Another InterestingOscillation . . . . . . . . . . . . . . . . . . . . . . . 10.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Ice Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2. Bulk-Emitting Media- Effective Physical Temperature. . . . . . . . . . . . . . 11.3. Satellite Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 1.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. Storm Structure Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

238 241 241 241 242 243 245 246 249 252 257 257 262 262 268 276 290 290 293 294 295 296 297 297 297 302 303 303 304 304 304 304 306 307 308 308

237 ADVANCES IN GEOPHYSICS.VOLUME 26

Copyright 0 1984 by Academic Press. Inc. All nghts ofreproduction in any form reSNed . rcnhin-t?-ntQQ?r: n

238

MIRLE S. V. RAO

12.2. Case Studies . . . . . . . . . . . . . . . . . . . . . 12.3. Study of Western Pacific Storms . . . . . . . . . . . . . 13. Qualitative Estimation of Rainfall Over Land Areas . . . . . . . 13.1.General. . . . . . . . . . . . . . . . . . . . . . . 13.2. Intensity and Polarization of Radiation Received at the Satellite 13.3. A Statistical Technique for Detecting Rainfall Over Land . . . 13.4. Error Analysis . . . . . . . . . . . . . . . . . . . . 13.5. Verification . . . . . . . . . . . . . . . . . . . . . 13.6. Summary and Conclusion . . . . . . . . . . . . . . . 14. Retrieval of Other Geophysical Parameters . . . . . . . . . . . 14.1. Ovewiew . . . . . . . . . . . . . . . . . . . . . . 14.2. TheSMMR. . . . . . . . . . . . . . . . . . . . . 14.3. General Principles . . . . . . . . . . . . . . . . . . 14.4. Retrieval Technique. . . . . . . . . . . . . . . . . . IS. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . 15.1. Suggestions for Further Work . . . . . . . . . . . . . . 15.2. Long-Term Goals. . . . . . . . . . . . . . . . . . . 15.3. Summary. . . . . . . . . . . . . . . . . . . . . . Appendix. Explanatory Notes . . . . . . . . . . . . . . . . A. 1. General Notation . . . . . . . . . . . . . . . . . . . A.2. Grid Cell Legend . . . . . . . . . . . . . . . . . . . A.3. Method of Averaging . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . .

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308 3 10 31 1 311 3 12 3 14 315 3 15 316 3 17 317 318 3 I9 322 325 325 329 329 330 330 330 33 I 33 1

1. INTRODUCTION

Two of the major parameters in atmospheric and hydrospheric investigations are rainfall and sea ice. Satellite-borne microwave radiometers provide a unique method of estimating these variables on a global scale. In particular, the Electrically Scanning Microwave Radiometer (ESMR) has proved of value in the quantitative determination of oceanic rainfall from satellite data. The objective of this article is to describe how significant meteorological, hydrological, glaciological,and oceanographic information has been extracted from satellite microwave observations (especially those from ESMR) and to discuss the limitations, as well as the vast capabilities,of such observations in future investigations. Since oceans cover more than two-thirds' of the earth's surface, a better estimation of oceanic precipitationand sea ice will enhance substantially our knowledge of global climatology. Some of the following contributions may be expected: 1. Indications of the annual variability of precipitation and of possible long-term changes in climate.

' According to Rand McNally (1982), the total area of the earth is 196,940,400 square miles, whereas the total land area (includinginland water and Antarctica) is 57,280,000 square miles. The remaining sea area works out to be 139,660,400 square miles, which is 70.9% of the earth's surface.

SATELLITE-DERIVED PRECIPITATION PARAMETERS

239

2. A better understanding of the shorter time scale motion of rainbelts such as the Intertropical Convergence Zone (ITCZ) and the monsoonal type of precipitating systems. 3. An understanding of the large amount of latent heat released over oceans; consequently, an improvement in the description of the energy balance not only over the oceans, but over all areas influenced by the global general circulation. Progress in the field was very slow until the mid 197Os, even with the availability of visible and infrared satellite imagery. In the presatellite era (i.e., before 1960), the dependence was mainly upon island reports and relatively infrequent ship observations. Island reports are not truly representative of surrounding oceans because of the orographic modification of airflow and the radiative heating effect. Additionally, there is a sampling problem, because it is not uncommon to find vast oceanic areasthat have too few islands in them. Precipitation measurements from ships are unsatisfactory due to platform instability and sea-spray problems. Therefore, most ships do not even carry precipitation gauges. Radar did, to a certain degree, provide some insight into the complex nature of rainfall structureand variability. But serious problems with attenuation and calibration limit the accuracy of radar for determination of precipitation, and its fixed location and limited range make it unsuitable for global-scale measurements over the oceans. This position improved to some extent in the early years of satellite observations (the 1960s) due to better coverage. However, improvement was not significant because the derivational methods were indirect and generally qualitative. Many ingenious schemes for indirect estimation of rainfall have been devised in the recent past. They fall generally into two categories: those based on the relationship between rainfall and cloud observations (extent, type, etc.) and those based on indirect statisticalrelationships. A few examples may be cited here. Barrett (1970) worked out a rainfall coefficient based on cloud cover and cloud type. Follansbee (1973) modified Barrett’s aerial statisticstechnique, concentrating upon rain-producing clouds (Cb, Ns, and Cu congestus) to the exclusion of others. Another approach that has been developed relies upon the relationship of reflected solar brightness of satellite pictures and rainfall rates. Martin and Suomi (1972) found that brightness regions correlate well with large radar echoes. Similarly, Woodley et al. (1972) concluded that the relationship of brightness area and precipitation depends upon whether the cloud system is young and vigorous or old and decaying. (It is also worthwhile to remember that the brightness enhancement technique suffersfrom the dependence of sun angle and viewinggeometry as well as from signal saturation and signal degradation.) Griffith et al.

240

MIRLE S. V. RAO

(1976, 1978) adapted this technique to estimate rainfall from geosynchronous visible and infrared imagery. Scherer and Hudlow ( 197 1) utilized cloud height and area derived from High-Resolution Infrared Radiometer (HRIR) data to estimate precipitation,cirrus contamination being ignored. One more noteworthy life history scheme is that of Scofield and Oliver (1977), which attempts to monitor storm rainfall utilizing enhanced infrared satellite pictures. Yet another indirect method adapted by Tucker ( 1 96 1) and followed by Reed and Elliott (1973) to estimate precipitation in the northern Pacific involves developing quantitative relationships between current weather (ww) and rainfall amounts (RR) in the present weather reports from land stations and extending these relations to infer rainfall from ship weather reports. A good review of most of these efforts is contained in Barrett and Martin (1981). The ESMR provides the first direct approach to the problem. The main advantage of the system is its selective response to liquid water in the atmosphere. Furthermore, because the emissivity of water tzW in the vicinity of 19 GHz is low (approximately0.4)and inversely proportional to the thermodynamic temperature (T, ), whereas the brightness temperature as observed by ESMR is proportional to the product E , T,, the oceans provide a convenient uniform background to the satellite-borne radiometer. Although admittedly there are certain limitations, ESMR seems to be a better system than any other available at present for estimation of rainfall over oceans. Over land areas, the problem becomes complicated. The emissivity of land is generally high and greatly variable, depending upon various factors such as soil type, moisture content, vegetation cover, temperature, frost conditions, snow cover, etc. However, upwelling radiation at 37 GHz emerging from hydrometeors is essentially unpolarized, whereas emission from a land surface, when viewed obliquely, is polarized when the dielectric constant is increased (e.g., by adding moisture). Therefore, with the use of two polarizations, it is possible to obtain some qualitative information over dry land. Such limited information would be useful over areas where conventional methods fail to provide adequate data. The microwave radiometer is a useful tool in detecting sea ice through clouds and in the polar night. This capability results from the high emissivity of sea ice. With the use of multiple wavelengths (emissivity being a function of wavelength) and dual polarization, there is a potential for unfolding certain ice surface parameters. Attempts are currently in progress to retrieve other geophysical parameters (such as surface wind over oceans, sea surface temperature, atmospheric water vapor, and liquid water content) from satellite microwave data. The Scanning Multichannel Microwave Radiometer is a major system in this context. The degree of success attained to date using this and other systems is discussed in Section 14.


24 1

2. THEESMR SYSTEM Treatment is given in this section only to those aspects of the ESMR system that are pertinent to understandingand utilizing intelligentlythe data received from spacecraft. The instruments carried on Nimbus-5 and Nimbus-6 satellites are briefly described. An introduction to microwave radiometry follows, stressing aids to the interpretation of ESMR data. A discussion of to what extent ESMR is suitable for estimation of precipitation is also included.

2.1. Nimbus-5 ESMR

The ESMR system aboard Nimbus-5 had a microwave receiver sensitive to radiation from 19.225 to 19.475 GHz (except for a 10-MHz gap in the center of the band). The antenna beam scans perpendicular to the satellite velocity vector beginning 50" to the left of nadir in 78 steps to 50" to the right, every 4 sec. The half-power beam width of the antenna is 1.4" at nadir. At the 50" scan extreme, the beam width remains 1.4"downtrackbut degrades in the crosstrack direction to 2.2". This corresponds (for a nominal orbit of 1 100 km) to a resolution of a 25-km circle near nadir, degrading to an oval 45 km downtrack X 160 km crosstrack at the ends of the scan. The polarization is linear, parallel to the satellite velocity vector. Since the orbit-to-orbitcoverageoverlapsat the equator, completeglobal coveragecan be obtained every 12 hr. (It may, however, be mentioned here that at large scan angles, data are subject to slight error; consequently, if only high-quality data are desired, there would be a small gap between orbits.) Onboard calibration is achieved by using warm (instrument ambient) and cold (cosmic background) inputs to the radiometer.

2.2. Nimbus-4 ESMR The main differences between the ESMR systems on Nimbus-5 and Nimbus-6 are in wavelength, polarization, and scanning geometry. The underlying physical principles are similar. The Nimbus-6 ESMR system operates on a center frequency of 37.0 GHz (bandwidth 250 MHz). The antenna beam scans ahead of the satellite with a constant earth incidence angle of 50" along a conical surface every 5.3 sec. In azimuth, the beam positions are from 35 to the right in 7 1 steps to 35 to the left. The angular resolution in elevation varies from 0.84" at the extremes of scan to 1.Oo at the midscan position 36 (when the beam is viewing O

O

242

MIRLE S. V. RAO

straight ahead). In azimuth, the resolution varies from 1.17 at the scan extremes to 0.95” at beam position 36. Expressed in terms of distance on earth, the resolution is approximately 45 km downtrack and 20 km crosstrack. Two separate radiometer channels are used to receive both the horizontally and vertically polarized components of microwave radiation. At 37 GHz the resolution is good and the sensitivity is high, but there is a saturation problem. Furthermore, due to the small width of the image area (compared to Nimbus-5 ESMR) there are substantial coverage gaps in the tropics. the gaps decreasing farther away from the equator. O

2.3. What the Instrument Measures The ESMR measuresthe intensity of microwave radiation it receives. It is convenient to put forth the data in terms of brightnesstemperatures, because at microwave frequenciesand at temperaturesprevailing in the earth’s atmosphere, the intensity or radiance becomes simply proportional to the equivalent blackbody temperature, as shown in the following relations. Planck‘s function for the intensity of radiation (energy flux per unit wavelength per solid angle) emitted by a blackbody is

W,(T)= (2hc2/A5)/(ek’lclT - 1)

(2.1)

with the usual notation. At wavelengths of the order of a centimeter and at temperatures in the range 200-300 K (hc/kAT -c l), the Rayleigh-Jeans approximation becomes applicable and so the intensity reduces to W J T ) = (2ck/a4)~ which (holding wavelength constant) may be written simply as

(2.2)

(2.3) W ( T )= aT a = 2ck/A4 being constant when A is held constant. When the emitting source (at thermodynamic temperature T) is not black, the radiance diminishes to W’(T ) = a T,

(2.4) where TBis the equivalentblackbody temperature, which in this case may be called the “brightness temperature.” Furthermore, by definition, the emissivity of the nonblackbody at physical temperature T is E=

W’(T ) /W(T )

Therefore

E = T ~ T or T , = E T

243


It must be mentioned that the preceding arguments are not valid when it is not appropriate to apply the Rayleigh- Jeans approximation,in which case, reverting to Planck's formula, we may write

W' = ( 2 h ~ ~ / A ~ ) / (1)e ~ ~ / ~ ~ e

(2.7) where T, is the generalized equivalent blackbody temperature. Solving for T, we obtain T, = For large I

T,

-

hc/kA ln(2hcZ/A5 W'

+ 1)

(A4/2ck)W' = W'/a = TB

(2.9)

where TB is as previously defined.

2.4. Factors Contributing to the Observed Brightness Temperature From simple considerations of microwave radiative transfer it is obvious that the brightness temperature TB(H)recorded by ESMR aboard a satellite at height H above the earth's surface may be expressed as

+ z(1 - ~ , ) ] e -+?

TB(H)= [T,E,

r

ThF(h)dh

(2.10)

where T, is surface thermodynamic temperature and surface emissivity/ absorptivity, so that brightness temperature of the surface is TB( S )= T,E, . q i s the temperaturecharacteristicofthe radiation incident on the surface, of which a fraction Ges is absorbed and the remainder Ti(1 - E,) reradiated. The term within the brackets corresponds to the total radiance at height h = 0. e-? is the transmittance of the atmosphere from surface to satellite altitude. Evidently, 7 = J fy sec 8 dh, where y is the absorption coefficient and 8 the viewing angle measured from vertical. In Eq.(2.lo), the entire term [TSes q(1- ~,)]e-'corresponds to the total radiation from the surface attenuated by the atmosphere up to satellite height H. This the physical temperature of the atmosphere at height h. F(h) is a weighting function such that the product ThF(h)Ah= AT,, the fractional contribution to the brightness temperature registered by ESMR due to the net radiance from the atmospheric layer between heights h and h Ah. F(h)involves ( 1) E h , the emissivity at height h, which in turn is a function of yh, the local absorption coefficient, as well as (2) e-$ (where z'= J f y sec 8 dh), the transmissivity of the portion of the atmosphere above height h up to satellite level, or, in other words, the distribution of y all the

+

+

244

MIRLE S. V. RAO

way between levels h and H . The entire integrable term of Eq. (2.10) is the total contribution to the satellite-observed TB from all the atmosphere intervening between the surface and the radiometer. The main variables affecting TB as measured by ESMR are the surface emissivity and associated temperature, as well as the profile of the atmospheric absorption coefficient (7)and the profile of temperature. Ground emissivity may vary from 0 to 1, but the factor by which the absolutetemperature of the surface vanes is much smaller. Similarly, the fluctuation in atmospheric temperature profile is usually less significant than the fluctuation in the absorption coefficient. At microwave frequencies, the main constituents responsible for absorption are oxygen, water vapor, and liquid water. Ice crystals are essentially transparent. The spectrum of atmospheric oxygen (Meeks and Lilley, 1963; Lenoir, 1968) has no prominent peaks in the vicinity of 19 or 37 GHz. There is certainly a component in this frequency range, due to the pressure broadening of oxygen resonances at other frequencies (principally 50- 70 GHz). However, since the mixing ratio of oxygen is substantially constant, and the absorption coefficient is only weakly dependent on temperature, the effect is no more than a constant offset to the observed values, So, when consideringvariations in TB,oxygen is not a problem. This leaves only water vapor and liquid water. The latter may be subdivided into nonraining clouds and rain. (Although the difference is only in drop size, there is important variation in resultant attenuation.) Thus, for purposes of further discussion, it is possible to express the radiometric brightness temperature in the following form: (2.1 I ) TB = A ( E , ) +.L(V) +h(LS) +h(LL) where E, is surface emissivity, I/ is water vapor in a vertical column of unit cross section, L, is liquid water in small nonraining droplets in a unit vertical column, and LL is liquid water in large drops (or rain) in a unit vertical column. A consideration of the relative magnitude of terms and their variations reveals that the dominant contributors to TB and (more importantly) its fluctuations are surface emissivity and rain. Let us first consider terms involving V,L,, and LL. The attenuation due to water vapor (Staelin, 1966) at 19 GHz is of the order 0.0 1 dB/km. The attenuation due to nonraining cloud droplets (approximately 0.2 g/m3) is of the order of 1.0 dB/km. Obviously, of these three terms, the final one involving LL is the most vital. Turning our attention to E ~ the , value of emissivity over land is large (typically 0.9) and highly variable. This can cause fluctuations in the observed TB of the order of 100 K, virtually masking all the other factors, thereby rendering the simple (single-frequency and polarization) ESMR unsuitable for rain estimation.


245

Over oceans, the situation is totally different. The emissivityew ofwater is low and nearly constant (approximately 0.4)In the vicinity of 19 GHz, E , 0: l/T,,,, where T, is the thermodynamic temperature of water. This is fortunate because the brightness temperature observed by the satellite depends on the product of E, and T,. Therefore, the sea provides a uniform background against which the raining atmosphere can be viewed. Salinity variationshave a negligible effect on the resultant TB. The only factorworth considerationis surface wind, which, when strong, may produce foam coverage (Nordberg et al., 197 1) affecting the radiometric brightness temperature. The brightness temperature observed over oceans may therefore be written TB= A B(FF) C V + DL, E(L,) (2.12) Here, A , a constant, is 125 K (Wilheit, 1972). B(FF) is a function of the surface wind speed FF. This will be discussed later in more detail. C is a constant of normal value 7 K/g per cm2(Wilheit, 1972). D is a constant of normal value 300 K/g per cm2(Wilheit, 1972). E(L,) is a function of liquid water of large drop size or rain. The order of magnitude of B(FF)can be judged from the followingconsideration (Nordberg et al., 1971). The change in sea surface brightness temperature is zero for wind speeds less than 7.5 m/sec, and for higher wind speeds may be expressed approximately as2 B,(FF) = 1.27(FF- 7.5) (2.13)

+

+

+

Thus, a value of FF = 12 m/sec (i.e., 25 mph) elevates the surface (unattenuated) brightness temperature by only about 5 K. The magnitude of the next term of Eq. (2.12)for a typical value of Vof 3 g/cm2is 2 1 K. The succeeding term, for a value of LL= 0.02 g/cm2,attains a magnitude of 6 K. The final term, for a rain rate of 10 mm/hr (0.4 inches/hr), has a magnitudeof 100 K. Thus, the last term is by far the largest of the variable terms. When we consider the range of variations (which really concerns us far more than the absolute magnitude), the differences are even more pronounced. The last, or rain, term becomes at least one order of magnitude higher than the other terms in the expression for brightness temperature.

2.5. The Suitability of ESMR for Rainfall Estimation From the foregoing discussion it is apparent that the use of ESMR for the estimation of rainfall over land is extremely difficult, mainly because of the large and highly variable value of surface emissivity. However, further Foam generation begins at wind speed 7-7.5 m/sec and affects emissivity significantly at higher speeds.

246

MIRLE S. V. RAO

research with dual-polarization and multiple-frequency microwave radiometers may be expected to lead to improved qualitative precipitation estimates. The problem is less complex over oceans. Undoubtedly there are limitations, some of which, such as atmospheric water vapor and nonraining clouds, have already been discussed; others, such as anomalous mode, saturation, field of view, freezing-level height, etc., will be dealt with at appropriate places in the succeeding sections. These problems are not insurmountable, and with good experience and proper interpretive skills valuable quantitative results can be obtained. A critical and comprehensive survey of presently available methods of estimation of oceanic precipitation, many of which were mentioned in Section I, reveals that every method without exception is fraught with problems. It also becomes clear that ESMR remains, as of today, the best method of estimating rainfall over the oceanic areas of the world.

3. CONVERSION OF BRIGHTNESS TEMPERATURE TO RAINRATE:A THEORETICAL APPROACH In order to interpret the ESMR readingsquantitativelyin terms ofrainfall, it is important to obtain a calibration curve. A good first approach would be a theoretical model, the results of which are experimentally verified as far as practicable. But, as any meteorologist of experience knows too well, because of the idealization and parameterization that are involved even in the best of models, in actual complex atmosphericsituations skilled adjustments will be necessary before applying model results. Wilheit et af.(1977) proposed a model for calculating microwave radiative transfer in raining atmospheres, taking into account both absorption and scattering. Their reasoning, in simplified logical terms so that it may be grasped by the average atmospheric scientist, is outlined below. The reader who desires to contend with a more rigorous treatment is referred to the original paper. The model assumes essentially a Marshall - Palmer dropsize distribution with slight modification. The modifications to this distribution and the other main assumptionsinvolved in the model are as follows: 1. An additional 0.5 km of cloud water droplets (with a concentration of 25 mg cm-2) just beneath the freezing level. 2. Considering fall velocity, and modifying the rain rate in accordance with Waldteufel ( 1973)and Foote and du Toit (1969). Ifp represents drop radius, V(p) the fall velocity, and N( p) dp the number density of drops with


radius between p and p

247

+ dp, the computed (modified) rain rate is

R' = /(4n/3)Plv(P)N(P) dP

(3.1)

the value of V(p)at sea level being Vo(p)= 965 - 1030e-*2p(Waldteufel, 1973) and the value at any other level (height h) being given by the Foote and du Toit relationship Atmospheric density at sea level Atmospheric density at height h 3. A lapse rate of 6.5"/km (the surface temperature being adjusted as a parameter of the calculation for five different freezing levels, i.e., 1, 2, 3, 4, and 5 km). 4. A vertical profile of humidity, with the relative humidity value at 80% near surface, increasing linearly to 100% near freezing level. The relative humidity above the freezing level is assumed to be that given by the 1962 United States Standard Atmosphere. 5. The reflectivity at the surface of the ocean according to Fresnel relations (Jackson 1962). For purposes of determiningthe angulardistribution, the ocean surface is assumed to be infinitely rough or Lambertian (Born and Wolf, 1975). The rationale for amving at a relationship between rain intensity and brightness temperature may be expressed succinctly as follows: 1 . For a given rain rate R,the Marshall-Palmer relationship

N( p) dp = Noe-&'p

dp

(3.3)

gives a particular drop-size distribution, i.e., a number density depending on the radius p. 2. The interaction of a plane electromagnetic wave with a dielectric sphere was first treated by Mie (1908) and was discussed in the context of cloud and rain droplets by Gunn and East (1954), yielding the equations m

o,,,

=

-(A2/2n)Re C(2n + l)(a,+

b,)

(3.4)

lb,12)

(3.5)

1

m

oca= (A2/2n)X ( 2 n 1

+ l)(ja,12 +

These enable the extinction and scattering cross sections of a liquid droplet, pCxtand pe, to be evaluated from the magnetic and electric 2" pole coeffi-

248

MIRLE S. V. RAO

cients a,, and b, . The radiation is obtained by summing the radiation from the magnetic and electric 2" poles. 3. Combining these cross-sectional values with the Marshall - Palmer number density N( p), the absorption and scattering coefficients Yabs

= N ( P ) % s ( P dP )

(3.6)

,Y

= N P ) % a ( P ) dP

(3.7)

and and angular distribution can be readily obtained. 4. These coefficients may now be substituted in the general equation of radiative transfer (Chandrasekhar 1960): dTB(e)/ah

= Yabs T(h) - Yext

TB(8) + ?sea

I"

TB(es)F(8,

8s)

sin es

des

(3.8)

Here, the change in radiance in thedirection 8, i.e., aTB(8)/dh,is expressed as the algebraic sum of three terms, viz. (1) the emission of the medium of thermodynamic temperature r h ) , (2) the change due to extinction, i.e., both absorption and scattering away from the specified angle, and (3) the increase in radiance in the 8 direction due to scattering from other angles [F(8,8,) is the angular distribution of scattering integrated azimuthally and normalized such that F(8, 8,) sin 8, dos= I]. 5. The equation of radiative transfer [Eq. (3.8)] is now solved iteratively for TB, first ignoring scattering so that intermediate values of T, could be computed for a number ofangles independently, and then using these values for the scattering term and recomputing the final values of TB iteratively until satisfactory convergence (to better than 0.1 K) is attained. Brightness temperaturescorresponding to any rain rate value are obtained as described above, separately for the five freezing levels 1,2,3,4, and 5 km. The results for 19S GHz are presented in graphical form in Fig. 1. In the graphical representation,the brightness temperature (TB)is plotted on a linear scale, whereas the rain rate (R)is plotted on a logarithmic scale. Notice that the brightness temperature versus rainfall relationship is highly nonlinear. TB increases very slowly from 0 to 1 mm/hr and then rapidly to a maximum (saturation) between 20 and 50 mm/hr depending upon the freezing level. At higher rain rates TB decreases slightly due to strong backscattering. It may also be noticed that for a given brightness temperature, rain rate increases greatly as the freezing level decreases. At a typical value of TB = 225 K, for example, the magnitude of R decreases by 100%from 5 to 4 km, and a further 75% from 4 to 3 km, 40%from 3 to 2 km, and 15% from 2 to 1


249

RAINFALL RATE Imm/hr]

FIG.1. Calculatedbrightness temperature (at 19.5 GHz) as a functionof rain rate for freezing levels of 1 - 5 km.

km (an overall 800%from 5 to 1 km). This dependence on freezing level is unrealistically excessive. The method of parameterization by adjusting the surface temperature (model assumption 3) may be largely responsible. In any event, this is one of the major weaknesses of the model, as will be discussed later. 4. VERIFICATION WITH RADAR DATA

One of the means by which the calibration curve deduced from the model may be checked is radar. Radar measurements of precipitation are subject to a number of uncertainties. 1. The estimation depends upon an empirical 2 and R relationship of the form 2 = uRb, where 2 is the radar reflectivity factor defined by Z N O D , No being the number of hydrometeors of diameter D per unit volume (Rayleigh scatteringbeing assumed). The values of u and b have been found to be within a wide range, from 200 to 600 and 1.5 to 2.0, respectively, depending upon the type of precipitation involved. 2. There are possible differencesin the precipitation sampled by radar and that which reaches the surface. 3. For intercomparison purposes, there are additional drawbacks. Because of the high temporal and spatial variability of rainfall, simultaneous radar observations with satellite overpasses are needed, but these are rare. 4. Most radars are ground based and have a limited range. Thus, over

250

MIRLE S. V. RAO

oceans they are capable only of detecting coastal rainfall. It is precisely in this region, i.e., close to the coast, that satellite-borneESMR observationsare subject to a serious error due to an earth-location problem, as will be discussed later. Nevertheless, a few of the measurements by the WSR-57 meteorological radar at Miami, Florida (a system that has been calibrated by gauge measurements) were found to be within 5 min of certain Nimbus-5 overpasses and could be used for intercomparison. A detailed description of the radar and the interpretation of its readings are given by Wiggert and Ostlund (1975). Briefly, WSR-57 has the followingcharacteristics:operating frequency, 2.96 GHz (10.3 cm); range, 200 km; and resolution (1) in azimuth, 2" and (2) in range, 1.2 km. The return signal in each range-azimuth bin is converted into rain rate (expressed in tenths of millimeters/hour) by means of a statisticallyderived relationship. Four cases were found in which data taken by the Miami meteorological radar observations and Nimbus-5 overpasses were near simultaneous (to within 5 min). The dates and times are given in Table I. In each of these cases, in order to compare the data, the WSR-57data were first plotted on a map base. The ESMR data were then overlaid using the sharp change of brightness temperature in these data at the coastline of Florida as well as at the Lake Okeechobee coast to ensure proper alignment. An example is shown in Fig. 2, in which the crosshatchedregion is a sample ofthe radar data and the crosses indicate the location of the beam centers for the ESMR data. The two ovals surrounding one of these crosses in the figure show the approximate 3-dB (half-power) and 1S-dB antenna gain contours for a typical ESMR beam position. While averaging the radar data around an ESMR beam center (in the effort to match the two types of data), full weightage was given to radar data within the 1S-dB gain contour, whereas half-weightage was given to the data between the 1.5- and 3.0-dB contours. Because ESMR data at high scan angles as well as those close to land are subject to error, only those beam positions with scan angles less than 40" and beam positions with centers more than 50 km from the coast were considered. On all four dates TABLE I. DATESAND TIMES OF RADAR OBSERVATIONS

Date

Time (GMT)

June 20, 1973 July 07, 1973 June 24, 1974 June 25, 1974

1632 1610 1605 1705

25 1


\ 80"W

82"W 27"N

-

+

+ 26"N

+

-+

-26"N

+

+ +

+

+

+ +

+

+

+ 25'N-

+

+ I 82"W

+

i

81"W

r250N

80"W

FIG.2. A portion of the WSR-57 radar data for the June 25,1973, case. The crosshatching shows the range and azimuth resolution of the radar. Isopleths of 0,5, 10, and 50 mm/hr rain rate are indicated. The crosses (+) indicate the locations of the beam centersofthe corresponding Nimbus-5 ESMR data. The 1 S-dB (inner oval) and 3-dB (outer oval) contours are shown for a typical ESMR beam position.

listed in Table I, a tropical maritime atmosphere was assumed over the Florida coast, with the freezing level at 4 km. When all the available data were processed in the above manner and tabulated prior to plotting, it was found that most of the points (more than could be plotted retaining clarity) fell within the rain intensity range of less than 1.5 mm/hr, and very few (all ofwhich were plotted) fell within the range of higher rain rates. The number available in the range 1.5 mm/hr and higher was so few that it is questionable whether the comparison is really meaningful. Figure 3 includes the final results. The solid line in the figure is the theoretical calibration curve for the 4-km freezing level. The solid points are the radar rain rates versus ESMR brightness temperature. The two dashed lines represent departures of a factor of 2 in rain rate, or 1 mm/hr, whichever is greater. It has been argued that the departure of the radar observations from the theoretical curve is mainly to the right of the curve and below it, supposedly because within the ESMR field of view local intense rain would contribute

252

MIRLE S. V. RAO

150

-

I

I

I

0.1

-

I

1

I 10 RAINFALL R A T E (mmlhr)

I

U

100

1000

+,

FIG.3. Intercomparison of brightness temperature curves: 0, radar data; trailer experiment data; solid line, theoretical curve; dashed lines, departures of 1 mm/hr or a factor of 2 in rain rate, whichever is greater.

(because of ESMR saturation) a smaller value of brightness temperature than is due, toward the average brightness temperature of the entire field of view. Although the reasoning is plausible, the quality of the observations is not good enough to prove it. With the same reasoning, the bias (in departures to the right and lower side) should be expected to increase at higher rain intensities, but there is little evidence of this in the figure. In reality, radar has many shortcomings as a tool for rain estimation (as pointed out earlier in this section), and the scatter of radar observations is too large to draw very definite conclusions. The utmost that could be stated with genuine confidence is that there is broad agreement between the radar observations and the theoretically based ESMR calibration curve.

5. VERIFICATION BY A SPECIALLY DESIGNED EXPERIMENT A second method of verification, which helped greatly in making necessary modification to the calibration curve derived from the theoretical model, is described in this section. This was a speciallydesigned experimental arrangement set up at NASA/Goddard Space Flight Center (GSFC) in Greenbelt, Maryland.


253

Two microwave radiometer receivers were installed in a trailer, each being connected to a rectangular pyramid-shaped (standard gain) antenna horn mounted on the top of the trailer. The main parameters ofthe two receivers are listed in Table 11. The axes of the pyramidal horns were pointed upward at an angle of 45 '. The antennas were mounted with the electric-fieldvector horizontal so that the E-plane antenna gain pattern caused a minimum variation in elevation throughout the field of view. The horns were shielded from direct rain by a wooden (dog-kennel-type) housing open on one side. They were protected against wetting from blowing rain or against otherwise reaching saturation with moisture by using a plastic wrapping across their apertures and a blower device that directed a stream of dry air across the plastic wrap. The receivers were connected in turn for a period of 15 sec each ( 1 ) to their antennas, (2) to a reference cold load, and (3) to a reference warm load. The output from this radiometer system was fed to a small computer that worked out both of the mean brightness temperatures for the 15 sec when the radiometerswere sensingthe radiation from outside through the antennas (separately at 19.35 and 37.0 GHz) and printed out the results at intervals of 0.8 min. Two rain gages of different types were used to measure the rainfall intensities simultaneously with the radiometer observations. The first was a conventional tipping-bucket rain gage located on the top of the trailer adjacent to the antenna housing. The number of times the bucket tipped was registered by a counter and recorded on the computer alongside the radiometer readings. The second was the recently developed (Raymond and Wilson, 1974) electronic rain intensity gage with a fast (1-sec) response time, located at a horizontal distance of 77 feet (23.5 m) from the radiometers, in the direction of the antenna beam. In this type of rain gage, measurement is made of the ratio of the resistance of rainwater flowing in a trough between two electrodes spaced along the trough (R,) to the resistance of the same rainwater in a chamber of fixed geometry (Rz). Since R, varies as the resistivity divided by the cross-sectional area of the flowing water, while R, varies only as the resistivity, the ratio RJR, is independent of resistivity and varies directly as the cross-sectional area, i.e., it is proportional only to the TABLE11. RADIOMETER RECEIVER PARAMETERS

Frequency Wavelength Bandwidth E-Plane beam width H-Plane beam width

Radiometer I

Radiometer I1

19.35 GHz 1.55 cm 400 MHz 6.5" 9.0"

37.0 GHz 0.81 cm 400 MHz 6.5"

9.0"

254

MIRLE S. V. RAO

rate of flow. An alternating current is used in the measurement to avoid electrolyticaction. The frequency of the current is varied as the conductivity of the water (by means of a multivibrator) because the frequencyrequired to prevent electrolysis increases with the conductivity of the electrolyte. Furthermore, the capacitative coupling that disturbs the measurements of resistance is significant when the conductivity is low, and so the reduction in frequency at low conductivity becomes an important compensating factor. Prior to the installation of the rain gage, it is essential to calibrate it, and this was done in the laboratory using a varistalic pump (Monostat Corporation), with controlled rates of flow up to 900 ml/min. The flow generated by the motor was increased in steps from 0 to 820 ml/min (i.e., rain rate 0 to 75 mm/hr for a funnel aperture of 36 inches) and then decreased in steps back to 0. The gage voltage was sampled for a minute at each step and was plotted against the flow rate to arrive at the rain gage calibration curve. The rain gage was then placed inside a barrel and a funnel 36 inches (91 cm) in diameter was supported over it. The output terminals were connected to a recorder (Brush Recorder Mark 280) in which two pens with different sensitivities traced records of the output voltages on moving chart paper. The recorder system accuracy was 0.5%. For purposes of synchronization between the temperature records on the computer printout and the rain rate records on the chart, at frequent intervals simultaneous time marks were made on the two charts. With this experimental arrangement, data were coIlected at NASA/GSFC during the period June through September, 1974. On all occasions on which data were collected, the freezing levels, as interpolated from the National Weather Service freezing-level charts, for the trailer location (i.e., 39.0°N,76.8"W, and for the times ofthe experiment)were within 0.5 km of 4 km. With the aid of the laboratory calibration curve, the voltage records on chart paper were translated to rainfall rates. The brightness temperatures of the 19- and 37-GHz radiometer systems were tabulated against rainfall inten~ities.~ For this purpose, only those occasions when rain rate and temperatures were sensibly steady for 2 min or more were considered (in order to avoid excessive scatter in the data). The observations were then grouped under 18 categories according to rainfall rate intervals (10 categories at 1 mm/hr intervals from 0 to 10 mm/hr, 5 categories at 2 mm/hr intervals from 10to 20 mm/hr, 2 categories In actual practice, it was found that the sensitivity of the tipping-bucket rain gage (with a 36-inch funnel) is better at low rainfall rates, but at moderate and high rainfall rates the performance of the electronic rain gage was superior both with respect to sensitivity and to response time. Accordingly, weightage was given more to the tipping-bucket readings in the low-intensity range, and more to the electronic rain gage in the other intensity ranges.


255

RAINFALL RATE (mm/hr)

FIG.4. Trailer experiment results( 19-GHzsensor looking up). At each point, the height and width of the error bars represent two standard deviations in the corresponding dimensions. The line is the theoretically calculated curve.

at 10 mm/hr intervals from 20 to 40 mm/hr, and 1 category greater than 40 mm/hr). In each category, the mean and standard deviations were calculated separately with respect to brightness temperature (TBand oTB) and rainfall (Rand oR). The diagramsin Figs. 4 and 5 show the results for 19and 37 GHz, respectively. In both diagrams, in the error bars, the vertical lines are equal to two standard deviations in brightness temperature (20,)~ and the horizontal lines to two standard deviations in rainfall (20,).

-L

12 14 16

i a 20

A

A _L--L

22 24 30 32 34 36 38 40 42 44 4 48 50 RAINFALL RATE (mrn/hr)

FIG. 5. Trailer experiment results (37-GHz sensor looking up). Explanation same as in Fig. 4.

256

MIRLE S. V. RAO

It is possible to convert the brightness temperature as observed from the trailer (sensor looking up at 45") to the brightness temperature as observed by the satellite (sensor looking down at or near nadir) from theoretical considerations of radiative transfer. A simplified first approach would be as follows. Consider the atmosphere as a rectangular block of transmissivity e-7scceand assume that we are looking at a region of emission at 273 K (freezinglevel) from the ground upward at 45" elevation. Since the absorptivity (= emissivity) = I - crJZ, the brightness temperature as observed on the ground would be

TB= ( 1

- e-'&)273

(5.1)

Therefore t = -(

l/&) In( 1 - Td273)

Looking vertically downward from the satellite, if it is assumed that the thermodynamic temperature of the ocean background is T, = 293 K and that the emissivity of the background water surface for I9 GHz is E, = 0.4, i.e., the product cwTw= 12 1 K, then the brightnesstemperature, as observed by the radiometer in the spacecraft, is

TB= ( 1 - e-')273

+ I2le-'+

[(I - e-7JZ)273(1- 0.4)]e-'

(5.3)

The first term on the right-hand side of Eq. (5.3)represents the emission from the atmosphere (rain level), the second term the ocean surface emission

160 -


257

(attenuated by the atmosphere), and the third term the ocean surface reradiation (also attenuated by the atmosphere). So, from the temperature observed from the trailer, the values of z can be worked out from Eq. (5.2); substituting these in Eq. (5.3) the corresponding values of TBfor Nimbus geometry could be evaluated. A table of equivalent temperatureswas thus constructed for all 19-GHztrailer temperaturesfrom 10 to 272.75 K in steps of 0.25 K. Individually observed trailer temperatures were all then converted to equivalent satellite brightnesstemperatures, and with these the statisticalanalysis previously described was repeated. By this means, another curve for downward-looking brightness temperature versus rainfall rate was obtained (Fig. 6). Here again the error bars are two standard deviations, i.e., 2a, (vertical) and 2aR(horizontal). It will be seen from this curve that the threshold temperature for the detection of rainfall by 19-GHzsatellite-borneESMR seems to be 172 K. It is also apparent that the curve becomes sensibly parallel to the x (rainfall) axis at approximately 22 mm/hr, i.e., saturation is reached at about that intensity.

6. GENERATION OF OCEANIC RAINFALL MAPS Rao et al. (1976) attempted to map oceanic rainfall on aglobal scale, using the calibration curves derived theoretically from the model as a guide, adjusted suitably to fit in with the more dependable experimental curve discussed in the Section 5. In actual practice, several problems4developed and various sources of error became apparent, necessitating many corrections and modifications. Final adjustment had also to be made by generating preliminary global maps and comparing them with available global-scale rainfall data. 6.1. Sources of Error The possible sources of error that came to light are categorized below and their relative importance pointed out. 6.1.I . Problems Associated with the Model. (1) The model assumes a Marshall - Palmer distribution, which works best for rain from stratiform These problems were faced and solved as best as could be done within certain logistic (financial and time) constraints, before the first Global Oceanic Rainfall Atlas was published. The remedial measures that were taken, as well as those that could be adopted with better logistic support, are outlined in this section.

258

MIRLE S. V. RAO

clouds. The deviations of the actual atmospheric conditions from this assumption led to error (though this may not be serious). (2) Above the freezing level, there is supercooled water, which is ignored in the model. This calls for investigation and appropriate modification of the model. (3) Melting snow causes a similar problem not taken care of in the model, calling for parallel action. (4) It was realized in actual practice that the model is grossly oversensitive to 0" isotherm height. When preliminary maps were generated, it was found that if rainfall in the middle latitudes was normalized,the tropics (high freezing-level zone) would go dry; conversely, if tropical rainfall was normalized, the middle and high latitudes (lower freezinglevel zones) would be extensively under deluge. (The degree of dependence of the calibration curves on freezing level was discussed in Section 3.) Part of the reason for this could be supercooled water above the freezing level, apart from model assumption 3 mentioned in Section 3. The error is serious, and a thorough investigation of its causesand of the necessary modifications to the model would be well worth the effort. Empirical correctionshad to be applied prior to the production of the Global Oceanic Rainfall Atlas in order to achieve a realisticdistribution of rainfall. It was found most expedient (instead of again adjusting the calibration curves for this purpose) to make an equivalent change by feeding the computer a modified freezinglevel pattern over the globe, with 0°C isotherm height at 4 km (instead of 5 km) over the equator, sloping to 2 km (instead of 0 or 1 km) at high latitudes. ( 5 ) Water vapor in the atmosphere is ignored in the model. This results in a minor error, which was discussed in Section 3. Simplified correction was effected by lumping it together with similar errors under low-level noises [see (18) in Section 6.1.41. (6) Nonraining clouds not being considered adequately cause again another minor error (treated in Section 3). This was also dealt with for purposes of correction within logistic limits under low-level noises [see (18) in Section 6.1.41. (7) Variation of sea surfacetemperature and sea surfaceemissivity is a nearly negligible source of error (see Section 2), which again is taken care of lumped under low-level noises [see (1 8) in Section 6.1.41. 6.1.2. Problems Inherent in the ESMR System. Mainly because of the characteristic inadequate isolation of a femte switch in the ESMR system and also because of the effects of antenna side lobes, the calibration temperatures depend upon scan number. In the system recording design, corrections for these sources of error have been applied (Wilheit, 1972), but the result is far from perfect. Probably there has been some overcorrection. Preliminary study by Kidder ( 1976), as well as the experience of the author, indicates that when the average of day and night observations is considered, the brightness temperature for a given rain rate increases slightly for beam


259

positions away from nadir. For oblique view close to extremes of scan, the error is not small. Furthermore, there is a day- night variation possibly due to the thermal effect of the solar cycle on the orbiting ESMR system. These problems form a subset, giving rise to minor errors, and they were treated as follows. (8) A small correction was applied to remedy the linkage of brightness temperature to scanning angle by approximatingthe dependence to a linear variation. Satellite brightness temperatureswere decreased to the extent of 7% of the nadir angle in degrees (i.e., 0-2.1 K linearly from nadir to 30"). (9) Owing to the unreliability of data near extremes of scan, beam positions with oblique view greater than 30"were ignored (i.e., only data from scan positions 14-64 were taken into account for rainfall computation). (10) The day- night variation in calibration leads to offsets in brightness temperature in the range 2 - 4 K and may therefore be regarded as a minor-to-average error, which is worth investigation. However, when generatingmaps of precipitation temporally averaged for day and night over several days, the error becomes negligible, and was therefore ignored. There are other problems (some serious) associated with the ESMR system. These are now considered. ( I 1) With the passage of years, there is probably a change in calibration due to deterioration of the ESMR instrument. Periodical recalibration (at least once a year) becomes necessary when the instrument gets old. As the Global Oceanic Rainfall Atlas was produced with data of only the first 2 yr of ESMR, this was not done. (12) The field of view of Nimbus-5 ESMR is relatively large (resolution of 25 X 25 km at nadir, changing to 45 X 160 km at scan extremes). The radiometer registersthe average brightness temperature over the field of view. This can be translated through the calibration curve to the rain rate similarly averaged over the footprint area, without any error as long as the relationship between TBand R is linear. It is only when aZT&3R2 is appreciably different from zero that error arises. (For discussion in this context, Fig. 1 is unsuitable, not only because the rainfall is plotted on a logarithmic scale, but also because of the limitations of the model referred to in Section 6.1.1. Figure 6 is really more satisfactory.) For the 19-GHz ESMR, the curvature of the TB-R curve becomes appreciable only above rain rates of 12 mm/hr, and even here the curvature is too small to cause large error. Furthermore, in areas of synoptic-scaleand mesoscale rainfall, the beam partial-filling problem rarely arises, and it is only in the case of convective rainfall that the footprint problem needs to be considered at all. Everything considered, the problem is so trivial for large-scale study that it was ignored while producing the atlas maps. (1 3) Nimbus-5 ESMR reaches saturation (see Fig. 6) at about 22 mm/hr, causing a problem similar to the preceding one. Even when the beam is fully filled, if there is a heavy

260

MIRLE S. V. RAO

rain (exceeding 22 mm/hr), partially or wholly in the field of view, the registered brightness temperature will be somewhat lower than it should be without the problem. This was remedied by normalizing the calibration with the aid of preliminary maps and corresponding ground truth on a large spatial scale. However, this saturation problem, of average significance, is worth some attention. In this connection, a possible overestimation of rainfall in the low precipitation range due to a curvature in the opposite direction of the calibration curve may also be examined. (14) During certain periods the ESMR system gets into anomalous mode due to an intermittent problem with a few instrumental parts. This gives rise to a very seriouserror in the mapping process. Improvement of the ESMR system to eliminate this defect is advisable. The alternative of removing abnormal brightness temperatures through computer programming is by far less satisfactory. During the production of the atlas, Nimbus-5 ESMR pictorial displays were individually examined, and all data at times when the system was in anomalous mode were carefully removed. (15 ) Uncertainties in the instrumental count and other factors leading to the measurement of TB (brightness temperature) need to be looked into. 6.1.3. Data Collection Errors. (16) The geographical referencing process is imperfect and gives rise to an earth-location error. This error is not systematic and has no directional bias, but is totally random. When a preliminary ESMR rainfall map of a huge island such as Australia was generated, spurious high rainfall was observed uniformly along the entire coast, extending to about 50 miles away from land (due to smearing of the high brightness temprature of land over the adjoining sea). In order to eliminate this problem, all data within 1 (- 110 km) of coastlines and all significant islands were disregarded in preparing maps for the atlas. This is a minor-to-averagesource of error that could be amelioratedby improving the geographical referencing. ( 1 7) Ephemeris errors occur at times, the conespondence between the time registered and the geographical location becoming disrupted. This does not happen often, but is a minor-to-average source of error worth investigationand elimination. One type of ephemeris error that was detected and corrected after the publication of the atlas arose during orbits being executed at midnight (Universal Time). The change of the clock from 2359 to 0000 brought about an offset, which threw out ofgear the readings for the remainder ofthe particular orbit (until the orbit number changed).

6.1.4. MiscellaneousProblems. ( 18) Low-level noises attributable to factors such as surface wind, water vapor, and nonraining clouds give rise to a minor source of error. Surface wind, when strong, produces foam coverage


26 1

over oceans, the effect of which was dealt with in Section 2. Water vapor, nonraining clouds, and sea surface temperature [see (4), (5), and (6) in Section 6.1.11 were also discussed in Section 2. The estimated research effort to eliminate/minimize these errors is of average magnitude. While producing the maps for the atlas, a low-level cutoff was imposed, ranging from 1 mm/hr in the tropics to 2 mm/hr in high latitudes. (The main reason for adopting a greater cutoff at higher latitudes is the higher frequency of storms.) (19) Sampling only twice a day (near local noon and near local midnight) is inadequate and causes error. A second orbiting satellite would enable four observationsto be made per day (at 6-hr intervals). Preliminary statistical study shows that this would reduce the samplingerror a great deal, TABLE111. SOURCES OF ERROR

Category'

Source of error

Problems associated with the model 1 Deviation from Marshall-Palmer distribution Supercooled water above freezing level 2 3 Melting snow Oversensitivity to 0°C isotherm height 4 5 Water vapor 6 Nonraining clouds 7 Variation of surface temperature and emissivity Problems inherent in the ESMR system 8 Scanning angle variation Invalidity at oblique view greater than 30" 9 10 Day-night variation in calibration Change in calibration due to instrument deterioration 11 12 Partial beam filling 13 Saturation 14 Anomalous mode 15 Uncertainties in T, measurement Data collection errors 16 Earth location Ephemeriserrors (includingGMT midnight problem) 17 Miscellaneous 18 Low-level noises 19 Sampling 20 Defects in software 21 Unidentified

Estimated effect on datab

Estimated effort to minimize ero+'

2 2

2 2

2 3 1-5 1-5

3 5 3 1-5

Numbers refer to discussion in Section 6.1. Number scale for estimates ofeffect as well as effort: 1, insignificant;2, minor; 3, average; 4, major; 5, serious. a

262

MIRLE S. V. R A O

bringing it within acceptable limits for most purposes. While generatingthe atlas maps, this deficiency was ignored, relying upon large spatial and temporal averagesto keep the error within limits. (20)In the development ofthe complex computer program to generate precipitation maps, errors creep in from time to time. These defects in software need to be avoided with vigilance, but when they do creep in, require detection, by careful testing at every stage, and removal. (21) It is not presumed here that all possible sources of error have been discovered and discussed. Other as yet unidentified errors may come to light and will have to be dealt with as is appropriate. It is, however, hoped (in view of degree of agreement, on a large spatial and temporal scale, of the results with ground truth) that no seriouserrorsremain other than those discussed above. Table 111 contains a list of the souces of error along with an estimate of the seriousnessof the effect on the data set and also an indication of the degree of effort needed to eliminate/minimize each of the errors. In this table, both effect and effortare gauged on a scale from 1 to 5 , l being least (or minor) and 5 most (or major).

6.2. Error Analysis Estimation of the overall error may be accomplished in different ways. It is conventional to attempt to parameterize a certain number of the souces of error and compute error rates according to well-known formulas. A second approach (which may be combined with the first or adopted by itself) is to make case studies. A fairly good example of error analysis (combined method) is given in Section 13. However, experience indicates that efforts on these lines, although impressive, prove in general of little value. Most often the procedures are seen in the last analysis to be subjective, both with respect to the number of parameters chosen and to the mode of parameterization. Furthermore, in the field of meteorology, case studies that produce striking results in one or two cases fail too often when applied to other cases. A third method of assessing errors by making comparative studies based on large spatial- and temporal-scale data is preferable in many situations. This approach was deemed best in the present instance. The procedure and the results obtained are presented at length in Section 7.

6.3. Steps in Writing the Program The main steps in writing a computer program for rain mapping are briefly as follows:


263

1. Read in TB-R relationships at suitable intervals in appropriate matrices separately for five freezing levels. 2. Read in the freezing levels for grid blocks over the globe, for four different seasons in appropriate matrices. 3. Read in a matrix showing land or water state (say, in a 1 latitude X 1 ’ longitude grid) over the entire globe. 4. Read in the observationtimes for the period to be depicted on the map. 5. Bypass the observations (during the map time) made over land. 6. For each observation during the mapping period, read out TB. 7. Apply scan angle correction to each observation. 8. From the time of observation, check season of the year. 9. Check the freezing level from geographical position and season. 10. Convert TBto rain rate. 11. Cut off at lower limit. Adjust at upper limit. 12. Skip data close to land (say, within 1 of coast or island). 13. Arrange precipitation data in a 1 latitude X 1 longitude grid over the entire seaflake area. 14. Average the data over 4” latitude X 5 ” longitude grid blocks. 15. Print (on world map outline). O

O

O

Proceeding in the manner outlined above, global oceanic rainfall maps were generated for the period December 11, 1972 (ie., the day of Nimbus-5 launch), through the end of February, 1975, on a weekly, monthly, and seasonal basis. Annual averages for 1973 and 1974 were also worked out and ~ h a r t e d .A~ specimen of each of the time period averages (weekly, monthly, seasonal, and annual) appears in Figs. 7,8,9, and 10,respectively. As these maps are intended for the study of oceanicrainfall, care was taken to preserve the major oceans unsplit by choosing the vertical edges of the map to cut the African continent in half. The entire set of maps was published as National Aeronautics and Space Administration Special Publication-410, under the title “Satellite-Derived Global Oceanic Rainfall Atlas (1973 and 1974)” (Rao et al., 1976). The Appendix at the end of this article contains explanatory notes needed to interpret the numbers on the maps reproduced from the atlas. Of the maps presented in the atlas, only the annual and monthly maps and just a few of the weekly maps could be analyzed within the time frame for publication. Some examples of the maps so analyzed appeared in color in the first few pages. However, all the maps generated prior to publication were printed without isopleths or analysis in the appendices to the preliminary edition of the atlas. Data for later years have been collected and partially processed; these will be included in later editions of the atlas.

264

2 Q 0

.c

265

266

3 'R * 0;

d G

268

MlRLE S. V. RAO

7. INTERCOMPARISON There is a scarcity of precipitation data acquired over oceans that can be considered reliable enough to make intercomparison. Two means of intercomparison exist, but each has limitations. First, large-scale precipitation maps may be used, such as those put forth by the Weather Service of the Federal Republic of Germany. These maps, produced on a monthly basis, are available for periods concurrent with ESMR maps. [Under the same category we may consider global climatologicalannual precipitation charts such as the one produced by Dr. Rudolph Geiger, of which an updated version has been published by the German Weather Service in Bericht No. 139( Jaeger, 1976).] Second, localized radar data [of which a good example is Global Atmosphere Research Project (GARP) Atlantic Tropical Experiment (GATE)data] may be used, but are limited both in spatial extent and in times concurrent with ESMR observations. The first means of intercomparison is imperfect because it is based on ship observations (which suffer from platform instability and sea-spray problems) and island reports (which do not correctly represent the surrounding ocean because orographic and radiative heating effects modify air flow). The second means (radar) is unsatisfactory because of its dependence on the Z-R relationship, with its indeterminate coefficients, its limited range, and other shortcomings as discussed in Section 4. Of the two means, the author has a personal preference for the first because it enables large spatial- and temporal-scale comparisons, i.e., the scale on which ESMR data yield valuable results. Figure 1 1 depicts the January, 1973,map produced from ESMR data; Fig. 12 is a map for the same month, produced by the Weather Service of the Federal Republic of Germany. The rain regions are marked by letters A, B, C, and D on the maps. It may be seen that there is a broad agreement between the two maps. Both maps indicate the principal areas of rainfall to be the southwest Indian Ocean (A), the mid-Pacific Ocean (B and C),and the North Atlantic Ocean (D). When the magnitudes are examined, these are also found to be comparable. In the southwestIndian Ocean, the rain rate in the maximum rain area (A) is 0.4 mm/hr in the ESMR map, compared to a monthly total of 450 mm in the German map. When converted to commensurate units, a mean rain rate of 1 mm/hr corresponds to a normal (30 days) monthly total of 720 mm. [The total value changes a little, proportionately with the number of days in months (28, 29, or 31 days); thus, in January, an average intensity of 1 mm/hr would match a monthly total of 744 mm.] In the mid-Pacific, the rain rate figures in the rainy area are (B) 0.8 and (C) 0.6 mm/hr (ESMR); the corresponding German map monthly total values are (B) 700 and (C)470 mm. In the North Atlantic in the region marked (D), ESMR gives a rain rate of 0.5 mm/hr while the German map shows a monthly total of 200 mm.

FIG.1 1. Analyzed satellite-derived rainfall map for January, 1973. Explanation same as in Fig. 7. Rain regions: A, southwest Indian Ocean; Band C, mid-Pacific; D, North Atlantic.

FIG. 12. Monthly precipitation map for January, 1973 (Weather Service of the Federal Republic of Germany). Rain regions denoted as in Fig. 1 1.


27 1

Figures 13and 14show the ESMR July, 1973, and the German July, 1973, monthly maps, respectively. In this case, the comparable areas are Bay of Bengal (A), the China Sea (B), and the South Pacific (C). In these areas, the ESMR rain rates of 0.6,0.5, and 0.4 mm/hr roughly conform to the equivalent German monthly totals of 250,300, and 300 mm. (See Table IV for a little more clarification.) Figure 15 is the annual ESMR map for 1973. No parallel map from conventional data is available for comparison. However, comparison was made with the climatological annual precipitation chart produced by Dr. Rudolph Geiger (Fig. 16). There is a striking similaritybetween the regions of intense rainfall in both maps. The coincidencewith respect to regions of very low rainfall is even better. The regions of maxima are (a) eastern Indian Ocean and Bay of Bengal (magnitudes 0.2-0.3 mm/hr compared6 to an annual total of 2000- 3000 mm), (b) China Sea (0.4 mm/hr compared to a total of 2000 mm), (c) equatorial Pacific and Atlantic (i.e., the Intertropical ConvergenceZone; magnitude 0.2 mm/hr compared to a total of 2000 mm), and (d) Gulf of Alaska (0.2 mm/hr as against a total of 2000 mm). Furthermore, we have the following extraordinarily similar regions of minima: (1) the northwest Arabian Sea and the west coasts of (2) California, (3) north Africa, (4) Australia, ( 5 ) South America, and (6) South Africa. The ESMR rain rates in these regions were < 100 mm, often as low as 50 mm. Table IV summarizes the intercomparison. It must be conceded that the differencesare not small, although there is general agreement. However, it would be precipitatejudgment to conclude that ESMR results are unreliable, based on the comparison. It is not beyond possibility that the fault lies to a greater extent in the conventional observations. The effort to improve the quality of ESMR-derived data should, nevertheless, continue. Prior to the production of the atlas, no reliable radar data to enable largescale comparison could be found. For this reason, and also because of the unsatisfactory nature of radar in general for estimation of rainfall as discussed earlier, no intercomparison with radar data was attempted, apart from the attempt to verify the calibration curves with the aid of Miami, Florida, coastal radar (described in Section 4). Subsequent to the publication of the atlas, however, radar data over a limited region of the Atlantic Ocean became available during the period of the GATE experiment? In a comparative study, Austin and Geotis (1978) concluded that relative to radar, ESMR underestimates rainfall by nearly 40%, and that the variability of the difference between radar and ESMR estimates is large. The merits An average rain rate of 1 mm/hr corresponds to a normal annual total of 8760 mm (8784 mm in a leap year). In the course of GATE, rainfall measurements were made by radar as well as by ships’rain gages; large differences are found among these data.

N

4

N

FIG.13. Analyzed satellite-derivedrainfall map for July, 1973. Explanation same as in Fig. 7. Rain regions;A, Bay of Bengal; B, China Sea;C, South Pacific.

h, -4 W

FIG.14. Monthly precipitation map for July, 1973 (Weather Service of the Federal Republic of Germany). Rain regions denoted as in Fig. 13.

214

N 4

P

FIG.15. Analyzed satellite-derivedrainfall map for 1973. Regions of maxima and minima (letters and numbers, respectively)are discussed in text.

FIG. 16. Mean annual precipitation map (from Prof. Rudolph Geiger). Regions of maxima and minima as in Fig. 15. See text for details.

276

MlRLE S. V. RAO

TABLE IV. INTERCOMPARISONS Total Rain Region

Rain rate ESMR (mm/hr)

ESMR (mm)

Comparison maps (mm)

Month January, 1973

German A

B C D

0.4 0.8 0.6 0.5

298 595 446 372

450 700 470 200

Month July, 1973 A

B

0.6 0.5

C

0.4

446 372 298

250 300 300

Year January - December, 1973

Climatological a b C

1-6

0.2-0.3 0.4 0.2

-

=-

x x

247

'

*

+

-

*

+

a

+ I

I

I

I

I

I

I

I

I

samples than is possible by conventional methods and (2) under cloudy weather conditions when visible or even infrared approaches fail. The disadvantage, however, is that the accuracy of the measurement attained (up to the present time, at any rate) is not good enough to be of any practical use. The foremost among the systems conceived to extract the above-mentioned parameters is the Scanning Multichannel Microwave Radiometer (SMMR). Although systems such as the Nimbus-E Microwave Spectrometer (NEMS) on Nimbus-5 and the Scanning Microwave Spectrometer (SCAMS)on Nimbus-6 made significantatmospheric observations, it is not proposed to discuss them within the limited scope of this article. Also omitted from discussion is the attempt to measure wave height using radar pulses. Interested readers are referred to Chelton et a/. ( I 98 I). 14.2. The SMMR

The Nimbus-7 and Seasat satellites,both of which were launched in 1978, carried SMMR. A detailed description of the instrument is contained in


319

Gloersen and Hardis (1978), and an algorithm for retrieval of geophysical parameters from its observations is outlined in Wilheit and Chang ( 1 979). The radiometer delivers orthogonallypolarized antenna temperaturedata at five microwave frequencies (6.6,10.7,18.0,21.O, and 37.0 GHz). An 80-cm parabolic reflector focuses the received power into a simple feedhorn covering the entire range of operating frequencies. The scan of the radiometer is such that the antenna beam sweeps a conical arc of 50°,with a cone angle of 42 at the satellite (the incidence angle at the earth's surface being approximately 49"). The physics of microwave radiative transfer insofar as it relates to rainfall measurement was dealt with fully in Sections 2 and 3, and the extent of benefit that may be derived from dual polarization observations was explained at length in Section 13. It will suffice to recall now a few aspects relevant to measurements by SMMR and to make additional observations wherever needed as we proceed. In SMMR, all frequencies share a common aperture. Therefore, the spatial resolution at the earth's surface is proportional to the wavelength. At 37 GHz, the resolution is good (30 km), but it will be remembered from earlier discussions that although the sensitivity is high, there is a serious saturation problem. SMMR 37-GHz brightness temperatures are found to saturate at a rain rate as low as 4 mm/hr. Probably the best SMMR frequency for rain measurement is 18 GHz, but the resolution is coarse (60 km as against the 25 km of Nimbus-5 ESMR). At lower frequencies, the problem worsens, the resolution becoming 150 km at 6.6 GHz. Previous discussion has also demonstrated that sensitivity of brightness temperature to rain far outweighs the sensitivity to the parameters now proposed to be measured. Indeed, Wilheit and Chang (1979) concluded that the retrieval errors induced by rain become comparable to the retrieval error due to all other causes (and thus unacceptably large) at rain rates even in a range as low as 0.5 - 1 .O mm/hr. O

14.3. General Principles

The actual retrieval is made through regression equations, bearing in mind certain basic principles; this physical background may first be examined. 14.3.1. Suvface Wind. When wind blows across the surface of the ocean, it generates roughness and foam. As was pointed out in Section 2, Nordberg et al. (197 1) showed that for nadir viewing at 19 GHz there is no effect on brightness temperature for wind speeds less than 7 m/sec, and an increase occurs of about 1.27 K per m/sec for higher wind speeds. Webster et al. (1 976) examined a frequency range from 1.4to 37 GHz (both polarizations)

320

MIRLE S . V. RAO

NADIR

+ VERTICAL (36)

+ HORIZONTAL (38') (0)

-1.01' 2

'

6

10

I

14

I

18

INFERRED

'

22

I

26

I

30

I

34

38

FREQUENCY (GHz)

FIG.36. Spectrum of increase in brightness temperature caused by wind at the ocean surface. [Webster ei a!. (1976).]

and a view angle of 38 Figure 36 represents their results. It may be seen that brightness temperature is only weakly frequency dependent, and in horizontal and vertical polarization TBenhances and diminishes, respectively, relative to nadir viewing. Wilheit (1978a) came up with a model in which the roughness of the surface is partially obscured by foam at wind speeds greater than 7 m/sec. The question may well be asked, "What precisely is near-surface wind?' Wilheit ( 1978b) suggests the following definition, which is as good as any other. First obtain the friction velocity ( U * )using actual air and sea temperatures. following the Cordone (1 969) model. Then, assuming the air/sea temperatures to be equal (neutral stability), compute the wind speed at an altitude of 20 m. O .

14.3.2. Water Vapor. Water vapor has a weak resonance at 22 GHz. It has strong resonances at and above 183 GHz. The wings ofthese contribute significantly to the absorption coefficient at the frequencies SMMR is concerned with (although mainly above 10 GHz). Owing to pressure broadening, the absorption is undoubtedly a function of height. However, it may reasonably be assumed that the bulk of water vapor is to be found in the lowest few kilometers of the atmosphere, where the variation in pressure broadening is not large. This assumption reduces the number of degrees of freedom and enables estimation of this and other parameters.

14.3.3. Liquid Water in Cloud Form. In Section 3 the interaction was alluded to of a plane electromagnetic wave with a dielectric sphere. This interaction was discussed in the context of clouds by Gunn and East (1954) using the Rayleigh approximation and the dielectric data of Lane and Saxton (1 952). Wilheit and Chang (1979) examined the absorption coefficientfor a


32 1

' I

ABSORPTION COEFFICIENT .ol k m-'

1 1

///.;. b

10

40

FREQUENCY (GHzI FIG.37. Microwave absorption coefficient for 1 g/m3 concentration of cloud water droplets. [After Wilheit and Chang (1979).]

cloud with a liquid water content of 1 g/m3, at three different temperatures (- 20,0, and 20°C). Figure 37 shows the results, from which the conclusion is drawn that the absorption coefficientis almost precisely quadratic in frequency and varies by about a factor of three with temperature, over the range considered. This spectral characteristic may be borne in mind in attempts at correcting for clouds or estimating cloud liquid water.

+

14.3.4. Sea Surface Temperature. For most meteorological purposes (long-range weather forecasting, general circulation studies, etc.) the degree of accuracy needed in sea surface temperature values is of the order of 0.1 "C. This degree of accuracy is presently unattainable from satellite microwave observation. The radiometer brightness temperature (see Section 2) is proportional to the thermodynamic temperature (TB= ET),and so it should be possible to estimate sea surface temperature (SST). This advantage is largely offset by the variation of emissivity with SST, however. (Indeed, in the vicinity of 19 GHz, E varies almost inversely with T.) However, Wilheit and Chang (1979) developed a regression equation to retrieve SST, using as input the 10 SMMR temperatures and the earth incidence angle. In the equation, weightage is given principally to the two coarse-resolution channels 6.6 and 10.7 GHz. The nonlinearitiesinherent in the problem are removed by following two techniques in the regression process, as will be described later.

322

MIRLE S. V. RAO

14.4. Retrieval Technique

The brightness temperature observed at the satellite depends upon a multitude of meteorological parameters, some of which (e.g., water vapor, liquid water content) are functions ofaltitude. The problem has infinitedegrees of freedom; a solution from a finite set of brightness temperatures (dual polarization at five frequencies) is possible only by resorting to many gross approximations. Another problem of much smaller magnitude arises from the variation of SMMR spatial resolution inversely with the frequency. In order to use all five frequencies in determining any parameter, some common basis has to be found such that all measurementsapply to the same area. This is strictly possible by accepting the resolution of the lowest frequency, i.e., 150 km. Since this is unsatisfactory, the following scheme is resorted to. SMMR outputs are reduced to four grids (see Njoku, 1979). Grid 1 has a resolution of 150 km and uses all the frequencies. This grid is considered suitable for retrieving sea surface temperature. Grid 2 has a resolution of 90 km and leaves out 6.6 GHz while retaining all the other frequencies and is used for near-surface wind speed estimation. Grid 3 has a resolution of 60 km, leaves out 6.6 and 10.7 GHz, and uses the remaining three frequencies. It is deemed suitable for estimation of cloud liquid water.'' Grid 4 has a resolution of 30 km and only 37-GHz information. Its use is limited merely to add structural detail to rain rate retrieval that depends primarily on the I8-GHz output. Wilheit and Chang (1979) modified a statistical technique originally applied by Waters ef al. (1975) to derive atmospheric temperature from satellite microwave observations. In the modified scheme, an artificial data set covering the approximate expected range of all the concerned geophysical parameters is generated. The database assumes 10 wind speeds, 9 sea surface temperatures, 9 cloud models, and 9 atmospherictemperature profiles. Apart from the above meteorological parameters, another variable is also taken into account. Because of small variations in spacecraft attitude (pitch, roll, and yaw) and scanning geometry, the angle at which the earth's surface is viewed is dependent on time and scan position. Therefore, the angle of incidence (6& is treated as one more observable variable in the process of regression and is included in two steps, 48 and 50 . Each combination of the parameters represents a member of the data set ensemble. Expected correlations are, in general, left out (e.g., even arctic winter atmospheric profile with an SST of 299 K is included). A weak correlation is, however, introduced between water vapor and cloud liquid water. O

It

37-GHz information is not used in the regression equation for water vapor.


323

For each member of the ensemble, 10 brightness temperatures (five frequencies with dual polarization) are computed, as well as the parameters of interest in the final form (e.g., water vapor in g/cm2). An attempt is made to reduce the effect of nonlinearities ignored by the (essentiallylinear) regression technique in the following manner. First, on the basis of arguments that produce results, although difficult to justify physically (Wilheit et al., 1977),use is made of a certain function of brightness temperature in the place of actual brightness temperature. For the channels 18, 2 1, and 37 GHz (which are affected most by the atmospheric constituents) the function employed is F(TB) = ln(280 - TB)

(14.1)

A further step in the direction of compensatingfor nonlinearity is taken in limited cases. The expression of Nordberg et al. (1971) for brightness temperature (see Section 2) is

B,(FF) = 0

for FF 5 7.5

(14.2)

and

B,(FF) = 1.27(FF- 7.5)

for FF> 7.5

(14.3)

The abrupt change in slope at 7 - 7.5 m/sec causes a nonlinearity. Wilheit and Chang ( 1979) attempted to mitigate this problem by resorting to iteration. The general principle is to interpret the data using the retrieval based on the entire ensemble and then utilizing the approximate values of the geophysical parameter(s)to select the matrix derived from the most appropriate restricted ensemble. This principle is applied only to sea surface temperature and wind speed, the solution being iterated (in both cases) once to decide whether the wind speed is above or below 7 m/sec. The regression equations of Wilheit and Chang (1979) for the retrieval of the various parameters are as follows:

Wind Speed Retrieval- Wind Speed Unknown

ws

+

+

(m/SeC) = -465.3 O.62l6TBlO,, 0.28737~10.7~ 168.7 ln(280 - TB18v) - 86.31 ln(280 - TB18H) 15.84 ln(280 - TBzIv) - 37.18 ln(280 - TBZIH) 2.357e,, (14.4)

+ +

+

Wind Speed < 7 m/sec

ws

+

(m/SeC) = -523.9 - O.2229TB10.7v 0.6056T~lo.7~ 130.3 ln(280 - TB18v) - 39.19 ln(280 - TBI8H) 10.24 ln(280 - TB21v) - 32.75 ln(280 - TB21H) 2.999emC (14.5)

+ + +

324

MIRLE S. V. RAO

Wind Speed > 7 m f sec

+

+

WS (m/sec) = - 338.4 0.31 1 5TB10.7v 0.4509TB,0,7H 151.8 ln(280 - TBl8V) - 9 1.12 ln(280 - TB18H) - 26.66 ln(280 - TBzIv) f 12.89 ln(280 - TB2IH) 1.4326mc (14.6)

+ +

Sea Siivface Temperature (Wind Speed > 7 m/sec)

+

SST (K)= 188.9 3.040T~6.6~-1.188T~6.6~ - o.709TB10,7v 0.2405TB10,7H - 6.1 14 ln(280 - TBl8V) 20.37 ln(280 - TB18H) - 4.003 ln(280 - T,,,,) 0.986 ln(280 - TB21H) - 4.735emC (14.8)

+

+

+

Cloud Liquid Water

+

CLW (mg/cm2)= 246.1 - 5 1.72 ln(280 - TB18V) 134.4 ln(280 - TBI8H) 46.14 ln(280 - T B I I V ) 24.95 ln(280 - TB21H) - 155.5 ln(280 - TB37V) - 36.63 ln(280 - TB'37I.3) - 3.39 16,Nc (14.9)

+

+

Wilheit and Chang (1979) claimed the following accuracy. For wind speeds greater than 7 m/sec, the wind speed retrieval precision is about 1 mfsec and SST retrieval precision is about 1.5"C. For lower wind speeds, the accuracy of the wind speed retrieval degrades to 1.6 m/sec, while that of the SST retrieval improves to less than 1"C. Regardless of wind speed, the accuracy in water vapor retrieval is about 0.15 gfcm', and in liquid water content, about 4 mg/cm2.


325

15. CONCLUSION Enough was said earlier to indicate the potentialities as well as the limitations of satellite-bornemicrowave radiometer systems in deriving geophysical parameters on a global scale. The conclusions that may be drawn from the previous discussions are briefly as follows. It is safe to conclude that in spite of various drawbacks, the microwave radiometer is at present indeed the best available means for estimating oceanic rainfall on a worldwide scale. With the use of improved radiometers operating at appropriate frequencies (preferably in the range 1820 GHz) it should be possible to get really accurate quantitative estimates of oceanic precipitation.'* It would then be possible to evaluate the enormous energy released as latent heat over oceans, a parameter vital for a deep insight into the general circulation of the atmosphere. Incidentally, a better understanding of storm structure may be expected from studies of precipitation over oceans. Over land the problem bristles with difficulties. As explained in Section 13, it is barely possible to glean some qualitative information, and even that under certain favorable conditions (e.g., during daytime when the ground is dry and not cold). It is similarly difficult to obtain an idea of soil moisture (based on the inverse relationship between microwave brightness temperature and moisture levels as indicated by antecedent rainfall) in regions where vegetation cover is sparse. The microwave radiometer is capable of sensing sea ice through clouds and in the polar night. Although quantitative evaluation is complicated by size and growth rate of ice crystals, storms in the intervening atmosphere, and other factors outlined in Section 1 1, the current microwave technique is certainly applicable to mapping sea ice. It is difficult to be equally sanguine right at present about evaluatingother geophysical parameters such as sea surface temperature, surface wind over oceans, atmospheric water vapor, and liquid water. The accuracy attained is indeed limited. This is not to say that future developmentscannot change the situation.

15.1. Suggestions for Further Work The satellite-deriveddata of oceanic rainfall could be improved with just a little effort, at a relatively low cost. Used in conjunction with other data l2 The Commission for Marine Meteorology of the World Meteorological Organization agreed at their seventh session (November-December, 1976) that continuous study ofprecipitation over oceans is essential.

326

MIRLE S. V. RAO

(based on radar or other observations, or derived from satellite by means other than microwave), satellitederived data provide a base for investigation that can hardly fail to produce interesting and significant new insights into precipitation climatology. The following lines of research are promising. 15.1.1. Energy Releasedfrom Latent Heat. One important aspect of precipitation is the accompanying energy release from latent heat. Over any area A , the amount of energy released may be evaluated simply from the expression

E=

1

RLdxdy

(15.1)

A

where R is the precipitation and L the latent heat of evaporation. The energy thus released over the oceansof the world is enormous. Just over a 1 latitude X 1 longitude cell, even when it is raining at a modest rate of 3 mm/hr, lo9 kJ are generated every second. In the atmosphere, latent heat amounts to as much as one-third of the net solar input. This is bound to have a serious impact on the energy budget of the earth-atmosphere system. A study of the spatial and temporal distribution of latent heat release, with its far-reaching consequences, is rendered possible by satellite-derived precipitation data. O

O

15.1.2. General Circulation Models. Oceanic precipitation is a good index of vertical motion in the absence of orography. How well general circulation models (GCMs) reproduce this feature is a test of the models. Here we have an opportunity to verify GCMs. The convective and largescale precipitation predicted by modelsL3such as the Smagorinsky - Manabe (GFDL) model, the Arakawa- Mintz (UCLA) model, the Kuo - Schneider (NCAR) model, and other models may be compared with the quantitative seasonal and regional distribution of oceanic precipitation from microwave data. The possibility also arises of defining an initial state of a new dynamical model with vertical motion (obtained through the inversion of the w equation) and latent heat as inputs. 15.1.3. Rainfall Patterns in the Major OceanicAreas and ClimaticAnomalies. Analysis of data in the three major oceanic areas of the world (in continuation of the preliminary work reported in Sections 8 and 9) is of surpassing importance. For the first time ever, a significant amount of data l 3 GFDL, General Fluid Dynamics Laboratory; UCLA, University of California, Los Angeles; NCAR, National Center for Atmospheric Research.


327

on precipitation over the oceanic areas of the world has become available from Nimbus-5 and -6 satellites (which camed ESMR) as well as Nimbus-7 and Seasat satellites (both of which were launched in 1978 and carried SMMR). Preliminary to analysis, it would be profitable to collect all the above data in combination with data from surface sourcesand aircraft. This would greatly aid the investigation of patterns of rainfall in the major oceans of the world (the Pacific, Atlantic and Indian oceans), of characteristicsof the Intertropical Convergence Zone, of the progress of other rainbelts, and of possible interactions with weather phenomena over continental areas. 15.I .4. Histograms. Histograms representing frequency distribution of precipitation intensity regionally and in different months may be prepared. This will assist the studies indicated above and those to be suggested hereafter. 15.1.5. Interannual Variability. The variability of rainfall from year to year is important from an economic point of view. This ought to be studied on a global hemispheric scale as well as on smaller regional scales.

15.I .6. Periodic Variations.Diurnal variation. The preliminary study in the tropical Atlantic reported in Section 10 indicated a large diurnal variation in rain frequency as well as in intensity. Dynamical considerations do not favor such large variation being uniformly valid everywhere over the oceans. The phase difference between the diurnal variation in different regions is worth exploration. Monthly and seasonal variation. The movement of rain patterns in the major oceanic areas of the world can lead to new insights into monsoons of the world. This again is a problem of considerableeconomic consequence. Other periodic variations. Graphical analysis of GATE area ESMR rainfall observations indicates an oscillation of periodicity of 3.3 days, which is consistent with easterly waves traveling from the African continent over the GATE oceanic belt. This deserves further investigation. Oscillations of different time periods are certainly to be expected regionally-a matter that should be looked into. 15.I . 7. Diagnostic Studies. Climatic anomalies may be expected to stand out from the scrutiny of histograms and other studies referred to above. Regional and global diagnostic studies could be conducted, attempting to explain the underlying mechanism wherever possible.

15.1.8. Signijicance of the Southern Hemisphere to the Global General Circulation. Very little is known about the precipitation characteristics of

328

MlRLE S . V. RAO

the Southern Hemisphere, which is largely a water hemisphere. Meteorological phenomena occurring over the vast region affect markedly the global general circulation. Satellite microwave radiometry is a valuable means of filling this serious data gap. 15.1.9. Teleconnections. If the atmosphere is considered as a conservative system, marked deviations from normal over one region are likely to be compensated for elsewhere in the system. The physical linkage usually takes the form of a pressure oscillation. The following three global teleconnections are well recognized: 1. In the Atlantic, an oscillation involving the Icelandic low and the Azores high. 2. In the Pacific, an oscillation involving the Aleutian low and the North Pacific high. 3. The southern oscillation involving the South Pacific Ocean and the equatorial Indian Ocean.

All these teleconnections were discovered by studies such as those of Walker (1923, 1924) in the presatellite era, when observations over oceans were relatively sparse. There must be other linkages and teleconnections over the earth, and there is a good chance that the extensive data from satellites will reveal some new and possibly valuable ones. Two major phenomena that have been discussed before deserve further attention. A detailed investigation of the El Niiio phenomenon in relation to precipitation in the equatorial Pacific would be useful. It would be interesting to correlate the precipitation over the United States and its annual variation to the precipitation in the preceding years over the Pacific and other regions. Possible interrelationshipsthrough mechanisms such as the southern oscillation and Walker circulation may be investigated. Similar investigation may be carried out with respect to the Indian and Southeast Asian monsoons. The data acquired in the Indian Ocean and the China Sea may profitably be scrutinized for intercorrelations that will enable longrange monsoon forecasting. 15.1.10. Extended Forecasts. Two main parameters in extended forecasts are temperature and precipitation. It is recognized that precipitation forecasting is more difficult than temperature forecasting. Working with empirical orthogonal functions, Gilman (1957) found that three such functions could reproduce the pattern of mean monthly temperature anomaly over the United States so that 81% of the variance was accounted for. Twenty functions accounted for practically all the variance. On the other


329

hand, precipitationrequired 20 functionsto account for an 80%reduction in variance. It is hoped that investigation with the aid of satellite-derived oceanic precipitation data will improve the situation.

15.2. Long-Term Goals The ultimate aim of this research is to utilize precipitation as well as sea surface temperature data as inputs into a suitable general circulation model to derive extended-rangeforecasts. But first, primary physical mechanisms must be understood. It may be advisable to start with a spatial and temporal matrix of precipitation data in grid cells covering the globe in weekly periods. At the beginning, time-lag correlations could be worked out and physical reasoning for high cross-correlations sought. From diagnostic studies we may initially be able to explain gross characteristics before detailed answers can be provided. In this connection,Namias (1 968) holds the view that “these details may require even more exact knowledge of such elusive physical processes as release of latent heat, momentum and water vapor exchanges, internal turbulent exchanges, radiation transfers, and in fact the entire gamut of meteorological processes . . . there is no guarantee that a completely physical solution will be found.” This is a view based upon vast experience. Therefore, during the course of this investigation, in addition to the search for physical mechanisms, it is preferable that a semiempirical approach also proceed. 15.3. Summary In summary, the research effort may be three-pronged, in the following manner: 1. All validated data may be put into a three-dimensional grid (say, 2” latitude X 2” longitude X 1 week). Cross-correlations could be worked out. Physical reasons for high correlationsshould be sought and at the same time regression functions established wherever appropriate. 2. Simultaneously, the analysis of oceanic precipitation data might be progressed further with a view to examining seasonalvariations, interannual fluctuations, and movement of rain patterns. Regional diagnostic studies could be conducted, looking for linkages through Hadley-type and Walkertype circulations. 3. Sea surface temperature, latent heat, and other related data may be examined. Every effort should be made to look into energy budget problems, particularly with the objective of sensing new teleconnections or offer-

330

MlRLE S. V. RAO

ing a thermodynamic explanation for those teleconnectionssuspected from the two preceding approaches. Analysis of the substantial amount of new satellite-deriveddata along these lines is very likely to lead to valuable new insights into ocean/land interactions and to improvements in extended forecasts, particularly in midlatitudes. The scheme of research outlined herein intentionally avoids being overspecific in the description both of the method of approach and of the expected findings. Flexibility rather than rigidity ought to be the keynote of the investigation. It is considered prudent to poke and peer among the data within prescribed guidelines, in the best tradition of basic experimental science. The retrieval of parameters such as sea surface temperature, oceanic surface wind, atmosphere water content, etc., is a long-term and high-cost proposition. Nevertheless, it is desirable that research in that direction should continue, although it does not appear likely that in the immediate future the microwave approach would yield quantitative information to the degree of accuracy needed for most purposes. APPENDIX. EXPLANATORY NOTES A . 1. General Notation

Notations on the maps are defined as follows: r Average rain rate in millimeters/hour (the figure inside each 4" latitude X 5" longitude grid cell). N Number of observations (available in printout-not shown in map).

A.2. Grid Cell Legend

r Average rain rate in millimeters/hour (corrected to tenths of a millimeter). (r) Same as above, but observations are few ( N < 100). -- No observations ( N = 0). x Excessive rain, indicative of bad data (probably attributable to ice on surface or anomalous mode); r 2 4 mm/hr in weekly maps; r 2 2 mm/hr in monthly, seasonal, and yearly maps. ( x ) Same as above, but observations are few ( N < 100). (blank) Land predominating (more than 75% land in grid cell).


33 1

A . 3 . Method ofAveraging

The average rain rate in the monthly maps (r)and the average rain rate in the weekly maps (rl,r, ,r, ,etc.) are interrelated in the following manner:

where w is the number of weeks in a month. Note: r is not equal to (rl r, r, r, * * rw)/w. Similarly, the average rain rate in the seasonal and annual maps is

+ + + +- +

or

where n is the number of months and nwis the number of weeks in the season or year, as appropriate. ACKNOWLEDGMENTS My thanks are due to the American Meteorological Society for permission to reproduce Figs. 1- 5 from the Journal of Applied Meteorology and Figs. 8, 10, 17, 19,23,26, and 27 from the Bulletin of the American Meteorological Society. Justus Perthes, Geographische Verlagsanstalt, Darmstadt, Federal Republic of Germany, permitted the reproduction of one oftheir wall maps (Fig. 16). I am indebted to the American Geophysical Union for Fig. 36, which is reproduced from the Journal of Geophysical Research, and to the National Aeronautics and Space Administration for Figs. 7,9, 1 1 - 15,18,20 -22, and 24 from NASA Special Publication410; Figs. 28-31 from NASA Conference Publication-2076; and Figs. 33-35 and 37 from NASA TechnicalMemorandum- 79361.

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INDEX A Advective-diffusiveocean model, ancient anoxic events and, 6 1 Aerosols, in atmosphere, effects on paleoclimate modeling, 97-98 Africa ancient collision with Europe, 73 C0,-induced temperature changes over, 172, 178,228 C0,-related precipitation, changes in, 193 paleoclimate indicators from, 54, 56, 57 simulated soil moisture, changes in, 209 Alaska paleoclimate indicators from, 56 paleocontinental reconstruction of, 82 paleofloras of, 70 Albian epoch, paleoclimate indicators from, 58 Aleutian low, 90 Alexander Island, paleoclimate indicators from, 56 Alloys fractionation upon solidification of, 4 “mushy zone” formation in, 13 Amazon Basin, glacial epoch of, 53 Ammonia, disappearance from early atmosphere, 99 Ammonites, extinction of, 63 Analog method, of climate estimation, 142 Andes, ancient connection to Antarctica, 82 Angiosperms, as paleoclimate indicators, 43 Angola-Brazil Basin ancient anoxic event in, 60 paleocean temperatures of, 63 Animals, as paleoclimate indicators, 44-45 Anoxic events, in oceans, 78-79 of Cretaceous period, 60-6 1 Antarctica C0,-induced temperature changes in, 172, 177 glaciation beginning in, 54, 121 paleocontinental reconstruction of, 82 progressive separation from Australia, 72, 82, 121

Antarctic Circumpolar Current, beginning of, 121 Antarctic glaciation, in Tertiary period, 7074,121 Antarctic ice sheet, formation of, 73,74 Antarctic Sea, sea ice mapping of, by satellite, 308 Aragonite-to-calciteratio, of shell carbonates, temperature effects on, 4 1 Arakawa- Mintz model (GCM), satellite-derived data coupled with, 326 Arctic C0,-induced temperature changes over, 177 paleoclimate of, 1 15 indicators, 56 Arctic glaciation, initiation of, in ancient times, 74, 121 Arctic Ocean, paleotemperature of, 88 Argentina, paleoclimate indicators from, 57 Asia paleoclimate indicators from, 56 paleofloras of,70 simulated soil moisture, changes in, 208 209,210 Atlantic Ocean ancient anoxic events in, 60 - 6 1 C0,-induced temperature changes over, 178 C02-related precipitation, changes in, 193 evaporites from margins of, 54 paleobathymetry of, 85 -86 paleotemperatures of, 68 pressure oscillation in, 328 satellite-derived rainfall data on, 277, 279 variations in tropical part of, 297-304 surface paleotemperature of, 87, 89 Atlantic-Pacific passage, restriction in ancient times, 74 Atmosphere, aerosol content of, effects on paleoclimate modeling, 97-98 Atmosphere/ocean/ice/land/biomassclimatic system, schematic illustration of, 143

337

338

INDEX

Atmosphere/ocean/sea ice, general circulation model coupled to, 152 Australia C0,-induced temperature changes over, 172, 178 progressive separation from Antarctica, 72, 82 simulated soil moisture changes in, 208 Austral Realm, characteristics of, 57 Averaging method, for rainfall, 33 1

B Barodiffusion, effect on earths core, 10 Barrett’saerial statisticstechnique, for rainfall estimation, 239 Basalts, hot-spot type, chemistry of, 19 Batholiths, D”-originated, 16 Bathymetry of Ocean basins, effects on climate, 76 Bauxites, as paleoclimate indicators, 40, 54 Bay of Biscay, paleotemperatures of, 66 Belemnites, 87 extinction of, 63 Belemnite shell, as standard for oxygen-isotope paleotemperature method, 46, 49, 51 Bellingshausen- Amundsen seas, sea ice mapping of, by satellite, 308 Black Sea, C0,-induced temperature changes over, 172 Boreal Realm, characteristics of, 57 Brachiopods, as paleosalinity indicators, 45 Brazil. C0,-induced temperature changes over, 172, 178 C Calcareous phytoplankton, extinction of, 63 Calcite, in shells, nonequilibrium deposition Of. 48-49 Calcite compensation depth (CCD), in determination of isotopic temperatures, 50-51

Calcium carbonate, deposition in environmental water, 46 Calcrete, as paleoclimate indicator, 40 California, paleocontinental reconstruction of, 82 Campanian period, paleocean temperatures of, 62

Cape -Argentine basin, ancient anoxic event in, 60 Carbon dioxide atmospheric, 36 effect on climate, 77, 79, 80, 120 effect on paleoclimate modeling, 98 101

increase in, 14 1 Carbon dioxide-induced climatic change, 141-235 comparison of model simulations of, 152216 doubling and quadrupling of CO, levels in studies of, 160 equilibrium vs nonequilibrium studies, 156 lag time in, 157 model-dependent results, 2 I7 - 2 19 simulated precipitation changes in, 19 1 206 simulated soil moisture changes, 206-2 16 simulated temperature changes, 165- 190 for CO, doubling, 165- 175, 185-206 for CO, quadrupling, 175 - 185 statistical studies on, 222- 228 time required to reach equilibrium in, 219-221

Carbon-isotope analyses, in paleoclimate studies, 45 method, 52 Carbonates in deep ocean, as buffer for high carbon dioxide in atmosphere, 100 in marine sediments, 4 1 Carboniferous period, glaciations in, 53 Carbon monoxide, disappearance from early atmosphere, 99 Caribbean - Gulf Coast region, paleoclimate indicators from, 58 Caribbean Sea ancient anoxic event in, 6 1 Cretaceous island arcs in ancient times of, 86 paleotemperatures of, 68 Caspian Sea, C0,-induced temperature changes over, 172, 178 Cenomanian period, paleoclimate indicators from, 58 Cenozoic era energy balance models of climates in, 1 15 near-coastal upwelling in, 90

339

INDEX

ocean temperatures of, 66-67 paleoclimates of, 38 Central America, paleocontinental reconstruction of, 82 “Chimney,” in deep-mantle plume, 20 Chlorite, as paleoclimate indicator, 69 Circum-Antarctic current, development of, 73,74

Circumequatorial current, disruption of, in Tertiary period, 7 1 Clausius-Clapeyron equation, 205 Clay minerals in marine sediments, 4 1 as paleoclimate indicators, 40, 69 as salinity indicators, 4 1 Climate carbon dioxide-induced changes in, 141235

models of, 36 - 37 Climate estimation by analog method, 142 mathematical models for, 143- 152 by physical method, 142 Climatic change, long-term, forcing mechanisms in, 74- 80 Clouds as diagnostic variables in climate estimation, 146 C0,-induced changesand, 161,164,172, 173, 178, 187 use in rainfall estimation, 239, 293

water in, satellite-derived data on, 320321,324

Coals, as paleoclimate indicators, 39-40, 54, 56

Coastline, changes in, during geologicaltime, 83

Coefficient of material diffusion, for liquids, 8 Computer in studies of mantle convection, 22 use in climate estimation, 146 use in rain mapping, 262 -263 Continent- ocean positions,constant changes in, effects on climate, 76 Continents ancient sites of, 41-42 reconstruction of, 80 - 86 surface elevation of, 148 Cooling of earth, 2

Corals as paleoclimate indicators, 57, 94 as paleosalinity indicators, 45 Coral Sea, paleoceanography of, 7 1 Core (of earth) cooling of, 4,22 - 23 hydrostatic balance of, 6 - 7 inner age of, 5 boundary, see Inner-core boundary glassy transition of, 15 mushiness of, 14 seismic model of, 14 structure of, 12- 15, 24-25 iron in, 4 -mantle boundary, see Core-mantle boundary (CMB) models of, 1 outer stable layer in, 10 structure of, 6 - 12,24 preferred parameter values for, 6 steady state, erroneous concepts of, 2 structure of, 1- 34 ‘summary, 24-25 velocity structure at top of, 10 Core-mantle boundary (CMB) structure of, 15 temperature increment at, 16 thermal gradient at base of, 18 Core paradox, 3 Coriolis parameter, changes in, effect on climate, 75, 94, 296 Cretaceous period atmosphere-ocean system of, 38 atmospheric carbon dioxide levels in, 100101

foraminifera from, 50 fossil family survival from, 43 isotopic composition of ocean water in, 48 marine biogeography of, 67-68 paleoclimate indicators of, 42,43, 46, 121 marine isotopic temperature record, 6 1 67

oxygen-isotope studies, 46 paleotemperature studies on, 52 sea level changes in, 77 sea surface temperature in, 87, 88 Cretaceous-Tertiary boundary event faunal group extinction in, 63

340

INDEX

hypotheses on causes of, 64,65 Crocodiles, as paleoclimate indicators, 44 Cyclones in paleoclimates, I 12 satellite-deriveddata on, 3 I 1 in South Atlantic. 294

D D layer of earth’s mantle deepmantle plumes and, 19-20 structure of, 15- 18 as thermal boundary layer, 15- 16,23, 24 Days per year, in ancient times, 94,95 Deep-sea cores, in paleoclimate studies, 4 1, 45, 50, 58 Deep Sea Drilling Project (DSDP), Ocean floor studies in, 5 I Dendrites, from inner core, 14- 15 Density, as diagnostic variable in climate estimation, 146 Desert dunes, ancient, paleowind direction markers on, 40 Detritus, wind-transported, as temperature indicator, 4 1 Diamictites, as paleoclimate indicators, 4 1 Dinosaurs extinction of, 63,64 temperature tolerances of, 44 Diurnal variation in oceanic rainfall, 297,327 explanations for, 303 Dolomite, as salinity indicator, 41 Downslope slide deposits, 41 Drake Passage, closure of, in ancient times, 73

E Earth cooling of, 2 rate, 2 core of, see Core (of earth) radioactive heating of, 2 in steady state, erroneous notion of, 2 thermal history of, 1 , 2 1 - 27 computer studies, 22 Earth-orbital parameters efftfect on climatic change, 75 in paleoclimate modeling, 96-97 Echinoderms, as paieosalinity indicators, 45 ElectricallyScanning Microwave Radiometer (ESMR), 239-336

brightness temperature from conversion to rain rate, 246-247 factors contributing to, 243 -245 description of system, 24 1 - 246 precipitation parameters derived from, 239-336 advantages, 240,3 17- 3 18 computer use in, 262-263 data collection errors, 260 diagnostic studies, 327 diurnal variation, 297, 303, 327 error analyses, 262 extended forecasts, 328-329 histograms, 327 interannual variation, 295 -296, 327 intercomparison, 268 - 276 oscillations in, 303 problems in, 258-260 radar compared to, 249 -252 suitability, 245 - 246 telecommunications, 328 verification by experiment, 252-257 retrieval of other geophysical parameters by, 317-324 SMMR, 318-319 techniques in, 322-324 storm structure studies by, 308 - 3 1 1 in qualitative estimation of rainfall over land areas, 31 1- 317 sea ice mapping by, 304-308 what it measures, 242-243 Electric fields, in core studies, 1 Ellesmere Island, paleotemperature indicators from, 70 El Niiio phenomenon, satellite-derived data and maps on, 282, 285-287, 295296,328 Energy, from gravitational separation, 25 -27 Energy balance models (EBMs) comparison of, for C0,-induced climate changes, 153- 155, 189- 190,229 of paleoclimates, results of, 1 15 - 1 18 as thermodynamic climate models, 144 Eocene epoch atmospheric carbon dioxide levels in, 101 glaciations in, 53, 121 ocean temperatures in, 7 1, 121 sea surface temperatures in, 87 - 89 Eocene-Oligocene boundary cooling event, 65, 66, 70

INDEX

Equador, C0,-related precipitation changes in, 193 Equation of radiative transfer, 248 Equator, paleoclimate of, 37 Europe C0,-induced temperature changes in, 172, 178 simulated soil moisture changes in, 208209,2 12 Evaporites as paleoclimate indicators, 40,54, 56, 100 F Feldspar in marine sediments, 4 1 as paleoclimate indicator, 69 Ferns, extinction of certain genera of, 64 Ferrous oxide, as proposed light constituent in earth’s core, 8, 1 I Ferrous sulfide, in systems of earth’s core, 8 Fish teeth and bones, paleotemperature determinations using, 5 1 Flemish Cap, paleoclimate indicators from, 57 Foote and du Toit relationship for rain rate, 246,247 Foraminifera extinction of, 64 as paleoclimate indicators, 45, 50-51, 52, 57, 71, 87,90 Forcing mechanisms, in long-term climatic change, 74 - 80 diagram, 78 Forecastsofweather, satelliteuse in, 328 - 329 Fossil faunas, as paleoclimate indicators, 37, 39,40 Fossil floras, as paleoclimate indicators, 37, 39,56 Fossil fuels, atmospheric carbon dioxide increase from, 141 Fossil species, current existence of, 43 Free oscillations, in core studies, 1 Fresnel relations, 247 Fruit, as paleoclimate indicators, 43 G General circulation models (GCMs) ofclimates, 145- 152

34 1

for C0,-induced climate changes characteristics, 162- 163 comparison of, 153- I55 description of, 158- 165 for doubled and quadrupled CO,, 165206 problem reduction in, 229 equations for, 146 grid point models and, 146 oceanic, 151 - 152 ofpaleoclimates, 38, 81, 101, 103-106 comparison with paleoclimaticevidence, 107- 108 modeling strategies, 104- 106 resultsof, 113-115, 119-120, 123 sea surface temperatures from, 86 satellite-derived data use with, 326 slab models coupled with, 150- 15 1 spatial resolution of, 146- 147 subgrid-scale processes serving as parameters for, 149 swamp ocean model coupled with, 105, 150 three-dimensional, 157- 158 two-level atmospheric, 147 variable-depth mixed-layer model coupled with, 151 Geodynamo energy source for, 1 - 3 theory, 4-6,22 Geological time scale, major divisions of, 36, 37 Geophysical Fluid Dynamics Laboratory (GFDL) general circulation model of paleoclimates from, 120 satellite data coupled with GCMs of, 326 studies of C0,-induced climate changes at, 159, 160,218 characteristics, 162- 163 precipitation changes, 193, 194,203 soil moisture changes, 207,2 13-2 15 temperature changes, 165, 168- 175, 181- 185 Geophysics, steady state of core in, 2 Geopotential height, as diagnostic variable in climate estimation, 146 German Weather Service,rainfall maps from, compared with satellite-derived data, 268-276

342

INDEX

Gilda (typhoon), satellite-derived data on, 310 Glacial conditions, diamictites as indicators of, 41 Glacial epochs, paleoclimates of, 53- 54 Glacial moraines, tillites as consolidated, 4 1 Glassy transition, in inner core, 15 Global Atlantic Tropical Experiment (GATE) data on rainfall, 268, 271, 297-302, 327 Global Atmosphere Research Project (CARP), radar rainfall data from, 268 Global Oceanic Rainfall Atlas, from ESMR data, 257-259,263 Global rainfall, satellite-deriveddata on, 277, 28 1 Goddard Space Right Center C0,-induced climate change studies at, 158,228 satellite rainfall experiment at, 252-257 Gondwanaland continents, glacial epochs in, 53 Gravitational constant, 4 Gravitational energy calculations of, 25 - 27 as probable energy source for geodynamo, 2, 3 theory, 4 - 6 Gravitational separation, of core constituents, 4 Gravity, in core studies, 1 Greenhouse effect description of, 14 1 - 142 paleoclimates and, 98 Greenland, paleofloras of, 70 Greenland Sea passage, opening of, 72 sea ice mapping of, by satellite, 307 Grid cell legend, 330 Grid point models, in climate estimation, 146 Griineisen parameter, 3 Gulf of Bothnia, sea ice mapping of, by satellite, 307 Gulf Stream, 297 movement of, in ancient time, 74 proto-, development of, 58 Gymnosperms, extinction of certain genera of, 64 Gypsum-rich horizons, as salinity indicators, 41

H Hadley cell, 296 Hadley circulations, in paleoclimates, 112 Heat flow, in core studies, 1 Heat flux, of inner-core boundary, 9 Heat transport, in earth’s interior, 2 I High-Resolution Infrared Radiometer (HRIR), in rainfall estimation, 240 Himalayas, orogeny of, effect on paleocontinental boundaries, 82 Horizontal velocity, in climate estimation, 146 Hurricanes, satellite-deriveddata on, 308 Hurricane tracks, in paleoclimate records, 110

Hydrodynamic mathematical climate models, 143, 144, 151 Hydrothermal circulations, in core studies, 1 I Ice albedo feedback in C0,-induced temperature changes, 167 Iceland-Faroe Ridge, 72 Ice mapping, by satellite, 304- 308 Illite, 49 in wind-transported detritus, 4 1 India, paleocontinental reconstruction of, 82 Indian Ocean ancient anoxic events in, 40 paleobathymetry of, 86 pressure oscillations in, 328 satellite-derived rainfall data and maps on, 217,280,282,283,284,294-295 sea ice mapping of, by satellite, 308 surface paleotemperature of, 87 Indonesia, precipitation changes in, C0,-related, 193 Inner-core boundary (ICB) convoluted form of, 13 heat flux causes of, 9 inner core growth and, 12 seismic properties of, 14 warming of due to adiabatic compression, 14

Inoceramids, extinction of, 63 Inocerumzcs shells, paleotemperature determinations on. 49, 43 Insects, as paleoclimate indicators, 44

343

INDEX

Intermontane basin deposits, as paleoclimate indicators, 56 Intertropical Convergence Zone (ITCZ) equatorial rain beIt association with, in Africa, 56 satellite-derived data on, 276-282, 290293 Iridium in K-T boundary clays, 64 Irma (typhoon), satellite-deriveddata on, 3 10 Iron alloys, elements in, 8 in earth’s care, 4, 11 - 12 silicon compound of, in systems of earth’s core, 8 J

Jurassic period, paleotemperature indicators of, 51, 52

K Kaolinite as paleoclimate indicator, 40 as salinity indicator, 4 1 Komatiite lavas, mantle rheology and, 24 Kuo- Schneider model (GCM), satellite-derived data coupled with, 326 Kuroshio current. 297 L Lacustrine animals, as paleoclimate indicators, 44 Land areas, qualitative estimation of rainfall over, by satellite, 3 1 1 - 317 Latent heat energy released from, satellitederived data in studies on, 326 release over oceans,239 Laterites, as paleoclimate indicators, 40, 56 Lawrence Livermore National Laboratory (LLNL), CO,-induced climate change studies at, 158, 159 Leaves, as paleoclhate indicators, 43-44,56 Lindemann’s law, 3 Liquids, coefficient of material diffusion for, 8 Liquid-state theory, core cooling and, 3 Liquidus gradient, for earth’s core, derivation of, 3

Lithosphere changes a c t i n g climate, 75 - 76, 8 1 on ocean floor, 85 Lithospheric slabs, lateral heterogeneities of lower mantle and, 2 1,25 Lizards, as paleoclimate indicators, 44 Lower mantle (of earth) discontinuities in, 18 structure of, 1 M Maastrichtian period, paleocean temperatures of, 62, 63, 65 Madagascar paleoclimate indicators from, 57 paleocontinental reconstruction of, 82 Magnesium, of shell cabonate, temperature effects on, 41 Magnetic fields, in core studies, 1 Magnetism, of terrestrial planets, relation to earth’s core, 2- 3 Mantle (of earth) cooling of, 5 -core boundary, see Core - mantle boundary D” layer of, 15 - 18 lower, see Lower mantle Newtonian rheology of, 23 plumes from deep area of, 19-2 1 rheology of, 2 1,24 thermal histories of, 24 viscosity of material in, 17 Mariana Basin, ancient anoxic event in, 60 Marine biogeography, of late Cretaceous period, 67-68 Marine faunas, as paleoclimate indicators, 44-45 Marine sediments as glaciation indicators, 4 1 as paleoclimate indicators, 4 1,46- 52 in studies of paleocean temperatures, 68 69 Marshall -Palmer dropsize distribution, 246, 241,248,257 Mathematical climate models, 143- 152 hydrodynamic type, 143 thermodynamic type, 143 use in climate estimation, 142 Maxwell relation, 8

344

INDEX

Mediterranean Sea, as survivor of “Tethys” ocean, 85, 86 Mesozoic era energy balance models of climates in, I 15 near-coastal upwelling in, 90 paleoclimate indicators from, 58 Messinian salinity event, in Mediterranean, 74 Methane, disappearance from early atmosphere, 99 Miami, rainfall estimation at, radar and satellite data compared, 250-252 Micas, in marine sediments, 41 Microplates, movements of, 82 Mid-Cretaceous period climate of. 38, 54-61 paleocontinental map of, 84 paleogeography of, 110, 1 I8 Mid-Devonian period, glaciations in, 53 Mid-Miocene epoch glaciations in, 53 ocean temperatures of, 67 sea level in, 73 Mid-Permian period, glaciations in, 53 Minerals, in marine sediments, 4 1 Modeling of paleoclimates, 80- 101 boundary conditions, 102 strategies, 101 - 108 survey of results, 108 - 120 Mollusks, fossil species of, 43 Monsoons, 239 forecasting of, 328 in paleoclimates, 1 12 satellite-derivedrainfall maps of, 276, 282 theories of, 295 Montana, plant extinction evidence in, 64 Mountains, pre-Pleistocene, erosion of, 39 Mushy zone formation in alloys, 13 in inner core, 14 seismic properties, 15 N Nannofossil assemblages, as paleoclimate indicators, 57, 58 National Center for Atmospheric Research (NCAR) C0,-induced climate change studiesat 158, 160-162, 218,219 characteristics of, 163

precipitation changes, 195 soil moisture changes, 2 12 temperature changes, 165, 167, 175179, 183-185, 187, 188 satellite rainfall data coupled with GCMs of, 326 NCAR Community Climate Model, results Of, 119-120 Neogene age, fossil species survival from, 43 New Zealand paleocontinental reconstruction of, 82 paleotemperatures of, 68 Nimbus-5 ESMR description of, 241,259 rainfall data derived from, 264,265,312 Nimbus-6 ESMR, description of, 24 1 -242 Nimbus-7 SMMR, description of, 3 18 - 3 19 Nitrogen, as biolimiting nutrient, 42 Nonglacial epochs, paleoclimates of, 53 - 54 Nora (cyclone), satellite-derived data on, 308 - 3 10 North America paleoclimate indicators from, 56 west coast of, paleoclimate indicators from, 68 Northern Hemisphere, paleofloras of, 70 Nusselt number-Rayleigh number relations, in studies of thermal history of earth, 22,23 0 Ocean@) ancient anoxic events in, 60-61 cooling of, 12 1 circulation of, in paleoclimate modeling, 86-92 deep circulation of, importance of, 106 general circulation models of, 15 1- 152 lithosphere changes in, effects on climate, 76 paleotemperatures of, from general circulation models, 1 13 rainfall maps for, from satellite-derived data, 257-267 rainfall over, satellite-derived data on, 238 satellite-derived precipitation data over, 244-245 improvement, 325 - 326

INDEX

345

surface temperature of, in paleoclimate isotopic composition variation in oceans modeling, 86-92 using, 48 map, 91 shell calcite deposition studies using, 48 Ocean/atmosphere/biosphere system, two 50 principal regimes in, 78-79 Ocean floor P changes in, 8 1, 85 - 86 spreading of, from volcanism, 97 - 98 Pacific Ocean Ocean gateways, paleogeography of, 85 ancient anoxic events in, 60 Ocean/sea ice model, for CO,-induced cliC0,-related precipitation changes in, 193 Cretaceous siliceous sediments from, 42 mate changes, 159- 160 Ocean waters paleobathymetry of, 106 ancient paleoceanography indicators from, 58 isotopic composition variation in, 48 pressure oscillation in, 328 mean isotopic composition of, 47-48 satellitederived rainfall data on, 277, 278, paleotemperatures of, 56-61 282 Oligocene epoch, sea level in, 73 ITCZ characteristics, 290-293 Opaline silica, as paleoclimate indicator, 42 storms of, satellite-derived data on, 308Orbitolina, as paleoclimate indicator, 57, 58 311 Ordovician period, glaciations in, 53 surface paleotemperaturesof, 87,89,90,92 Oregon State University (OSU) Pacific plate, survival of, 85, 86 C0,-induced climate change studies at, Paleobathymetry, in reconstruction of ocean 159-160, 161-162, 218, 219, 220, floor changes, 85-86, 102, 106 22 1 Paleobotany, paleoclimate studies using, 43 characteristics of, 163 Paleoceanography, 52 -74 precipitation changes, 193, 195, 203, Paleocene age 204 fossil genera survival from, 43 soil moisture changes, 208,209 sea surface temperatures of, 88-89 temperature changes, 168, 170, 172- Paleoclimates in pre-Pleistocene ages, 35 175, 177-178, 187 140 Orogeny (mountain building) factors external to the earth in, 75, 121 factors internal to ocean/atmosphere/bioeffects on climate, 76 in GCM modeling of paleoclimates, 1 15 sphere system, 77, 121- 122 Orphan Knoll, paleoclimate indicators from, forcing mechanisms in, 39, 74 - 80 diagram, 78 58 indicators of, 39-52 Oxygen mid-Cretaceous period, 54 -6 1 in ancient atmosphere; 99 modeling of, 38, 80- 101 application of to ancient ocean water, 47-48 boundary conditions, 102, 122- 123 results from, 1 13- 1 15 to mid-Cretaceous period, 59-60 strategiesfor, 101 - 108 in paleotemperature modeling, 96, 122123 results from, 1 13- 115 nonglacial, 121 basic theory of, 46-47 pdeobotanical evidence of, 43-44 ecological factors in, 50-51 paleoceanography in studies of, 52 - 74 in earth’s core, 4 paleozoological evidence for, 44-45 in iron alloy, 8 qualitative evidence for, 39-45, 120-121 sea surface temperature by, 87 quantitative evidence for, 45-52, 121 studies on noncalcite materials, 5 1 Oxygen-isotope paleotemperature method, Paleocontinental maps from mid-Cretaceous period, 84 45,46-52

346

INDEX

modifications to, 82-83 Paleocontinental reconstructions, in paleoclimate modeling, 80 - 82, 122 Paleodepths, of oceans, determination of, 50-51 Paleofloras, as climate indicators, 69- 70 Paleogeography, 55 in paleoclimate modeling, 80-86, 122 Paleontology, use in paleoclimate studies, 42-44 Paleosalinity, indicators of, 41,45 Paleosols, as paleoclimate indicators, 40 Palynomorphs, as paleoclimate indicators, 44 “Panama” sill, removal in Santonian era, 6 I Panama Strait, closure of, 74, 121 Parameterization, in atmospheric general circulation models, 149 PDB standard for oxygen-isotope paleotemperature method, 46 Permian period glaciations in, 53 precipitation simulation on continents of, 109 Phanerozoic era atmospheric carbon dioxide levels in, 100 coal deposits of, 40 Phosphorites, as paleoclimate indicators, 42 Phosphorus, as biolimiting nutrient, 42 Photosynthesis,atmospheric oxygen from, 99 Physical method, of climate estimation, 142 PKJIKP phase of inner core, 14 P K I W phase of inner core, 14 PKP precursors, in core- mantle boundary, 9 Planck’s function for the intensity of radiation by a blackbody, 242,243 Planets, terrestrial, magnetism of related to earth’s core, 2 - 3 Plants, as paleoclimate indicators, 43-44 Plate tectonics hypothesis, 75, 80 paleoclimate studies and, 37-38 Pleistocene age, paleowind indicators of, 42 Plumes from inner cure, 15- 17,22 hot-spot volcanoes and, 19 structure of, 19-21 thermal and dynamical model of, 20 Polar regions, warm paleocfimate of, 37 Poles, ice formation on, sensitivity experiments on, 119 Pollen, as paleoclimate indicator, 43,44, 54 Polynya, determination by satellite, 308

Precambrian era, glaciations in, 53 Precessional motion, as possible energy source for geodynamo, 2 Precipitation, see also Rainfall C0,-induced changes in, I9 1- 206 satellite-derivedparameters of, 239-336 Pre-Cretaceous period, global climates of, 53-54 Preliminary reference earth model (PREM), data from, application to studies of core- mantle boundary, 16- 17 Pre-Pleistocene ages, paleoclimates in, 35 140 Psychrosphere, 71

Q Quartz, 69 in marine sediments, 4 1 Quartz grains, wind velocity markers on, 40 Quaternary period glacial climates of, 67 paleoclimates of, 37, 53, 121 Queen Charlotte Island, paleoclimate indicators from, 57

R Radar rainfall estimation by, 239 comparison with satellite data, 249-252 Radiative- convective models (RCMs) comparison of, for C0,-induced climate changes, 153-155,157,189-190,229 as thermodynamic climate models, 144145 Rainfall over land areas, qualitative estimation by satellite, 3 1 1 - 3 17 over oceans, maps of from satellite-derived data, 257-267 satellite-derivedparameters of, 239 -336 Rainfall maps, analysis of, 276-290 Rayleigh-Jeans approximation, 242,243 Rayleigh number, high, of constant-velocity fluid, 16 Rayleigh scattering, 249 Red sediments, as paleoclimate indicators, 40-41 Reptiles, as paleoclimate indicators, 44 Rheology, of earth’s mantle, 2 I

INDEX

Rio Grande Rise, breaching of, 72 Rock fragments, in marine sediments, 4 1 Rocks, in studies of paleoclimates, 37 Rossby’s theorem ofconsemation ofpotential energy, 293 Ross embayment, paleotemperature of seas in, 73 Ross Sea, sea ice mapping of, by satellite, 308 Rotation of earth effect on climatic change, 75 importance in paleoclimate modeling, 94 Rudist bivalves extinction of, 63 as paleoclimate indicators, 57 S

Sahara Desert C0,-induced temperature changes over, 172, 178 glacial epoch in, 53 simulated soil moisture changes in, 2 10 San Andreas Fault, 82 Sandstones,desert-type,as paleoclimate indicators, 40, 56 Santonian period, ancient anoxic events in, 61 Satellite-derived precipitation parameters, 239 - 336 by ESMR, 239-336 information from, 238-239 Saturn-like ring, around earth, as proposed mechanism for Eocene- Oligocene boundary cooling event, 72 Scanning Microwave Spectrometer (SCAMS), atmospheric observations made by, 3 18 Scanning Multichannel Microwave Radiometer, rainfall data from, 240, 3 18 319,327 Sea ice in climate estimation, 149, 150, 164 satellite mapping of, 240, 304-308, 325 Sea level, changes, effects on climate, 76-77, 79 Sea of Okhotsk, sea ice mapping of, by satellite, 307 Seasat satellites, SMMR-derived atmospheric data derived by, 3 18- 3 19 Sea surface, paleotemperatures of, 106

347

Sea surface temperature (SST) as boundary for paleoclimate modeling, 122, 124 reconstruction of, 90-92 satellitederived data on, 32 I, 324 in validation of atmospheric general circulation model, 149, 150 Sedimentaryrocks as paleoclimateindicators, 39 Seeds, as paleoclimate indicators, 43 Seismic analyses of D” layer of mantle, 15 - 16 of lower mantle, 25 Seismic data, of deepmantle plumes, 2 I Seismic waves in core studies, 1, 3 inner core, 14- 15 Sensitivity experiments, in modeling of paleoclimates, 107 energy balance models, 115 - 118 results of, 1 15 - 120 Shallow-water marine sediments, as paleoclimate indicators, 4 1 Shatsky Rise, paleotemperature studies on, 59,62 Shells, of marine organisms, oxygen-isotope paleotemperature method applied to, 46 Siberia paleocontinental reconstruction of, 82 paleofloras of, 70 Silica, 7 1 biogenic, in marine sediments, 41 of deep-ocean cherts, paleotemperature determinations on, 5 1 Silicate dusts, from volcanic interruptions, 97,98 Silicate rocks, weathering in paleoclimates,40 Silicon as biolimiting nutrient, 42 in iron alloy, 8 Silurian period, glaciations in, 53 Slab models, general circulation models COUpled with, 150- 151 Smagorinsky-Manabe model (GCM), satellite-derived data coupled with, 326 Smectite in marine sediments, 68,69 as paleoclimate indicator, 40 volcanic origin of, 4 1

348

INDEX

“Snapshot” simulations of paleoclimates, 96, 97, 106-107, 123 results Of, 109 - 11 5 Snow mass, in climate estimation, 146, 164 Soil moisture, in climate estimation, 146 C0,-induced changes, 206-216 Soil temperature, in climate estimation, 146 Soils, ancient, see Paleosols Solar luminosity effects on climatic change, 75 in paleoclimate modeling, 94-96 South America glacial epoch in, 53 paleoclimate indicators from, 56 simulated soil moisture changes in, 210, 212 South Atlantic, previously unrecognized rain area in, 29 1- 294 Southern Hemisphere satellite-derived data on rainfall in, 296297 global general circulation and, 327 - 328 Southern Ocean evolution of, 85 paleobathymetry of, 86 paleotemperature of, 7 1 sea ice mapping of, by satellite, 308 Southern pressure oscillation, 328 South Pacific Convergence Zone, ITCZ convergence with, 290 South Pacific ocean, pressure oscillation in, 328 South Tasman Rise,ancient sea over, 73 Spores, as paleoclimate indicators, 44,54 Standard mean ocean water (SMOW), 47,48, 59 Statistical-dynamical models (SDMs) of paleoclimates, 38, 101- 103, 123 Storms, satellite-derived data on, 308- 3 11 Strontium/calcium ratios, in calcite, 50 Structure of earth’s core, 1 - 34 Sulfur in earth‘s core, 4 in iron alloy, 8 Sulfur gases, from volcanic eruptions, 97 Superanomaly method, in studies of carbon dioxide-induced climatic change, 157 Surface albedo as diagnostic variable in climate estimation, 146

importance in paleotemperature reconstruction, 92 GCM modeling, 1 14 Surface elevations, changes in, effects on paleocontinental maps, 83 Surface pressure, in climate estimation, 146 Surface weathering, carbon dioxide levels and, 99 Surface wind, satellite-deriveddata on, 319320, 323-324 Swamp ocean model GCM Ocean modeling based on, 105, 150, 216,219-221 spectral general circulation model of, 1 19 120 T Tanzania, paleoclimate indicators from, 57 Tasman Sea, paleoceanography of, 7 1 Teleconnections, in global precipitation, 328 Temperature in climate estimation, 146 simulated changes in, from atmospheric CO,, 165-190 Tertiary period climates of, 37, 38,42,61-74, 121 marine isotopic temperature record, 61 67 oxygen-isotopestudies, 46 foraminifera from, 5 1 glacial climates of, 67 glacial epochs in, 53-54 global cooling and Antarctic glaciation in, 70-74 isotopic composition of ocean water in, 48 paleotemperature studies on, 52 plant taxa of, as paleoclimate indicators, 43 progressive cooling during, 38 - 39 sea level changes in, 77 Tethyan Realm, 85 characteristics of, 57, 58 Tethys ocean, 82, 85 paleobathymetry of, 106 Thermal convection, as possible energy source for geodynamo, 2 Thermal evolution, of earth, 1, 3 Thermal history, of earth, I , 2 I - 27 Thermodynamic mathematical climate models, 143

INDEX

energy balance models (EBMs), 144 radiative-convective models (RCMs), 144-145

Tillites, as paleoclimate indicators, 41, 53 Topography, in core studies, 1 Toroidal magnetic field, 5 Transfer function, in superanomaly method for climate simulation, 157 Triassic period, precipitation simulation on continents of, 109 Tropical organisms, as paleoclimate indicators, 45 Troposphere, aerosolsin, effect on climate, 98 Turonian period, paleocean temperatures of, 63

Turtles, as paleoclimate indicators, 44 Typhoons, satellite-deriveddataon, 308 - 309

U United Kingdom Metereological Office (UKMO) C0,-induced climate change studies at, 159, 186-188

precipitation changes, 204 United States C0,-related climate changes in, 228 paleofloras of, 70 simulated soil moisture changes in, 208, 212

rainfall over, satellite-derived data on, 315-316

USSR C0,-induced climate change studiesin, 159 paleofloras of, 70

Vertical velocity, as diagnostic variable in climate estimation, 146 Volcanic rocks, use in core studies, 1 Volcanism in ancient Pacific Ocean, 86 effect on climate, 77, 97-98 in Tertiary period, 72 Volcanoes hot-spot type deep-mantle plumes and, 19 molten material from D’ layer from, 20 W

Waldteufel relationship, for rain rate, 246, 247

Walker circulations, in paleoclimates, 1 12 Warm saline bottom-water (WSBW) hypothesis, climatic implications of, 88 Water vapor in climate estimation, 145- 146 satellite-derived data on, 320, 324 Weddel Sea, sea ice mapping of, by satellite, 307 - 308

Westerly winds, in paleoclimates, 1 12 West Pacific Atolls, rainfall data for, 302 White Sea, sea ice mapping of, by satellite, 307

Wind($ detritus transported by, as climate indicator, 41 hypothetical, in mid-Cretaceous period, 111 Wisconsin glacial age, general circulation model applied to, 150 Wood, as paleoclimate indicator, 43

V

Variable-depth mixed-layer model, general circulation model coupled with,15 1

Z Zeolites, in marine sediments, 41


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