Siinulation uf ille Iiydrulugic cycle uf the gluhal atmo.sp/ieric circulation

Simulation of the hydrologic cycle of the global atmospheric circulation by a mathematical model

Syukuro Manabe’ and J. Leith Holloway Jr., Geophysical Fluid Dynamics Laboratory/ESSA Princeton University, Princeton, N. J.

SUMMARY: A mathematical model of the global atmospheric circulation is constructed. The model is capable of simulating some of the fundamental features of the climate and the hydrologic cyclc in the earth’s atmosphere. The potential usefulness of such a model for the study of hydrol- ogy and climatology on a global scale is discussed.

SIMULATION DU CYCLE HYDROLOGIQUE DE LA CIRCULATION ATMOSPHÉRIQUE GLOBALE PAR UN MODELE MATHÉMA TIQUE R ~ U M E : U n modèle mathématiquc dc la circulation atmosphérique du globe est constitué. Le modèle peut simuler certaines lignes fondamentales du climat et du cycle hydrologique dans l’at- mosphère terrestre. L’utilité possible d’un tel modele pour l’étude de I’hydrologic et de la climato- logie a l’échelle du globe est discutée.

SIMULACIÓN DEL CICLO HIDROLÓGICO D E LA CIRCULACIÓN GLOBAL ATMOSFERICA MEDIANTE UN MODELO MATEMA.TIC0 RESUMEN: En este documento se clabora un modelo matemático de la circulación global de la atmósfera. Mediante este modclo sc pueden simular alcunas de las características fundamentales dei clima y del ciclo hidrológico en la atmósfera terrestre. Se examina la eventual utilidad de dicho modclo para el estudio de la hidrología y de la climatología a escala mundial.

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1. INTRODUCTION

As is known, the latitudinal gradient of the solar radiation drives the seneral circulation of the atmosphere, which in turn maintains the hydrologic cycle of the atmosphere. On the other hand, the heat of condensation strongly affects the atmospheric circulation. The removal of heat energy from lhe earth’s surface by means of evaporation controls the climate and the heat balance of the earth’s surface. The polar ice cap also has a very important effect on climate by reflecting a large amount of solar radiation. Therefore, it is clear that one cannot comprehend the mechanisms of the general circulation unless one understands the inechanisms of the hydrologic cycle and vice versa. Since the coupling between these processes is highly non-linear, a theoretical discussion of the hydrologic cycle is extremely dificult. Under these circumstances, an effective way of studying global

i. Speaker

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Syukuro Mrincibe und J. Leiíh Hollowuy Jr.

hydrology is to construct a numerical model of the atmospheric circulation with hydrolo- gic processes incorporatcd. If one can create a model climate which is sufficiently similar to the actual climate then one can perform various numerical experiments on a computer to improve our understanding of climatology and global hydrology. For cxample, one can identify the role of mountains in maintaining climate by comparing the results of two experiments with and without mountains. Following the pioneering attempts to simulate the general circulatioii of the atmosphere

by Phillips (1956) and Smagorinsky (1963), intensive efforts have been devoted to the simulation of climate by the mathematical models of the atmosphere at various institutions particularly in the United States, i.e., Department of Meteorology at U.C.L.A. (Mink (1965)), Lawrence Radiation Laboratory (Leith (1965)), National Center for Atmospheric Research (Kasahara and Washington (1967)) and Geophysical Fluid Dynamics Labora- tory of ESSA (Smagorinsky et ul. (1965), Manabe et ul. (1965)). The remarkable improve- ment of electronic computers in recent years has been one of the major factors responsible for the rapid advance in the field of the numerical simulation of climate. In this talk, we would like to describe the mathematical models of the atmosphere developed at GFDL of ESSA, show the similitude of the model climate to the actual climate and to demon- strate the potential usefulness of such a model for the study of hydrology and climatology on a global scale.

2. THE GLOBAL MODEL OF ATMOSPHERIC CIRCULATION

The details of the structure of the global model of the atmosphere can be found in the paper by Holloway and Manabe (1970). Therefore, a very brief description of the model is given here. According to the box diagram shown in figure 1, the global model consists of five major components, i.e., the equations of motion, the thermodynamical equation, the equations of radiative transfer, prognostic equation for water vapor distribution, and the equations of water and heat balance at the earth’s surface. W e shall describe some of these components below.

a) EQUATIONS OF MOTION The equations of motion are written in the spherical coordinate system. Since the hori- zontal scale of atmospheric motion with which we arc concerned is larger than the scale- height of the atmosphere, the hydrostatic approximation is used. The effects of mountains are incorporated by use of the so-called sigma coordinate system, which identifies the earth’s surface as a coordinate surface (Phillips (1957)). The finite difference forms of the dynamical equations and the global grid system are similar to those proposed by Kurihara and Halloway (1967). Figure 2 shows the grid system. The average grid size is approxi- mately 500 km. In the vertical direction, the nine finite difference levels are chosen between earth’s surface and the I6 mb level so as to resolve the structure of the planetary boundary layer as well as that of the stratosphere.

b) RADIATIVE TRANSFER The scheme of computing radiative heating and cooling is identical with that described by Manahe and Strickler (1964) and Manabc and Wetherald (1967). The scheme consists of two parts, i.e., t!ic solar radiation and the long-wave radiation. For this study, the solar insolation of January is assumed at the top of the model atmosphere. For the cake of simplicity the diurnal variation of solar radiation is not taken into account. The climatological distributions of water vapor, carbon dioxidc, ozone, and cloud cover in January are used for this computation. They arc specified as a function of latilude and height.

388

Siniiilation of the hydralogic cycle of the global atmospheric circulation

THERMODYNAMICAL

RADIATIVE TRANSFER PROGNOSTIC EQ. OF WATER VAPOR

HYDROLOGY HEAT BALANCE OF EARTHS SURFACE

PROGNC”“

FIGURE 1. Box diagrani indicating the major coniponents of ihe globrrl model. The links among the components are indicated by solid lines

c) THERMAL BOUNDARY CONDITION AT THE EARTH’S SURFACE Temperatures of continental surfaces are determined by the requirement of heat balance among the turbulent fluxes of sensible and latent heat and the net fluxes of solar and terrestrial radiation. For the sake of simplicity the ground surface is assumed to have no heat capacity. On the other hand, it is assumed that the sea surface has an infinite heat capacity. The normal distribution of sea surface temperature in February, which is compiled by the Hydrographic Office (1944), is used as a lower boundary condition for the thermodynamic equation.

d) HYDROLOGIC CYCLE The prognostic system of water vapor consists of contributions by the three dimensional advection of water vapor, the moist convective adjustment, evaporation from the earth’s surface and by condensation. This prognostic system is described in detail by Manabe et ul. (1965). The hydrology of the ground surface is highly idealized in the model for the sake of

simplicity. A similar scheme of computation was incorporated into the joint ocean- atmosphere model of Manate and Bryan (1969) which successfully simulated some of the fundamental features of the hydrologic cycle (see section 4). The fundamental principles of this scheme are not very different from what Budyko (1956) used for his study of the heat and water balance of the earth’s surface. W e shall describe it very briefly here for the convenience of later discussion. The time change of soil moisture is computed based upon a consideration of the water

budget. In order to siinulate the moisture holding capacity of soil, we assumed that the ground surface is covered Gy boxes 15 c m deep everywhere. The water in the box can increase either by rainfall or snowmelt and decrease by evaporation. The water, vhich overflows the soil moisture box, is regarded ac runcff. It is assumed that the rate of evaporation is the product of the potential evaporation and a simple function of the water depth in the box. (Here, “potential evaporation” means the hypothetical rate of evapora- tion from a complctely wet surface.) The rate of the change of snow depth is determined as the difference between the rate

of snowfall and the sum of the rates of sublimation and snowmelt.

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FIGURE 2. Diagram of one octcint ojthe computatiuncilgrid. Dots indicirie the grid points located ut the centers oftlie boxes. There Lire 24 grid points hetiueeii lhe equator and the pole

e) COUPLING AMONG MAJOR COMPONENTS In concluding this section, we shall briefly describe how the major components of the model shown in figure I are coupled with each other. The equations of motion are related to the thermo dynamical equation through the

equation of state. The distribution.of the wind field obtained from the time integration of the equations of motion is used for the computation of the advection terms in the thermodynamical equation and the prognostic equation of water vapor. The heat of condensation computed in the prognostic system of water vapor constitutes a heat source term in the thermodynamical equation. The computation of radiative transfer yields the rate of radiative heating (or cooling) which also constitutes the source (or sink) term of the thermodynamical equation. (In this study, the climatic distribution of water vapor is used for the computation of radiative flux. In the future, it would be desirable to use the distribution of water vapor obtained from the prognostic system of water vapor.) In order to determine the temperature of the ground surface based upon the requirement

of heat balance, it is necessary to know the net downward radiative fluxes evaluated in the radiative transfer box. The computation of ground hydrology requires information on the rates of precipitation and evaporation. The former is obtained from the prognostic system of water vapor and the latter is computed from the heat balance computation for the ground surface.

3. SIMULATION OF CLIMATE

Starting from a simple, unbiased initial condition, the numerical time integration of the model is continued for a period of approximately 300 days. Towards the end of the time integration, the modcl atmosphere rcached a state of quasi-equilibrium in which the global integrals of kinetic and potential energy fluctuate around certain values without any long-term trend. W e shall briefly describe the atmosphcre in the state of quasi- equilibrium. The distri butions of various quantities to be shown are obtained by time- averaging over a 70-day period of the numerical tinie integration.

390

Simulatiori of tlie hyclrologic cycle of' the glohal atmosplieric circulation

In the upper part of figure 3, the time mean distribution of the daily rate of precipitation of the model is shown. For the sake of comparison, the distribution of the rate of actual daily precipitation during winter (Möller (1951)) is added to the lower half of the figure. This figure shows that the distribution of the tropical rainbell and the locations of the subtropical dry zones are simulated successfully by the inodel. The general features of the distribution of precipitation rate in middle latitudes of the model also compare favorably with those of the observed distribution except in Europe where the computed rate of precipitation is much larger than observed. The distribution of the precipitation rate described above influences the distribution

of the soil moisture of the model shown in figure 4. This figure shows that soil moisture

MEAN PRECIPITATION RAlE

0 Icm/doy 0 .ln .5 cm/dov IConi~uiv 01 .? <m/day)

5 VD IS u4d.r IConiwi% DI Io Im/d.rl

> I5 <-/dor

FIGURE 3. Upper half; the distributioii of 70-day meaii daily precipitation of the model. Loiuer half; the distribiitioti cf actual dai1.v precipitation for tlie three months December, January aizd February (eslimared hy Möller (1951)

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Syiikuro Munube und J. Leith Hollowiiy fr.

is very small iii the Western part of Australia and in the Sahara desert indicating the successful simulation of major arid zones by the model. Soil moisture is also very Small in India because of the assumption of perpetual January insolation. (Note that winter is a dry season in India). On the other hand, the soil moisture is large in the Amazon river basin, the Indonesian islands, and in tropical Africa of the model. As we know, these areas are covered by rainforest in the actual tropics.

MEAN COMPUTED SOIL MOISTURE

._____ h r l v u

c] < 5111 1Conb"ii O, .I and .1 m-1

@j j I cm ,comain o* IO 1-1

0 I I- 5 s (comiowi -I I ond 2 cm1

FIGUKE 4. Computed soil moisture un the model continents. Dotted .slinding delineutes areus ha Uing less than 0.5 cm of soil moisture; slashed slinding, more thun 5 em. Thich dushed lines indicate the bolindury of snow cover

The distribution of the rate of runoff is shown in figure 5. The areas of large runoff correspond well with some of the earth's major rivers. For example, the Amazon in South America; the Congo and the Zamberzi in Africa; the Yangtze in China; the Colorado and Columbia in Western United States; and the Mississippi and Ohio in the Eastern United States. The results described above indicate that it is possible to simulate some of the funda-

mental features of climate and hydrology by the time integration of a global model. Next, we shall demonstrate that this global model enables us to attempt various modifications of the model climate on an electronic computer. Such a numerical experiment is very useful for identifying the role of various factors in maintaining the climate. As an example, we modify the model climate by eliminating all mountains in order to investigate how the hydrology at the earth's surface is affected as a result of the removal of the mountains. In figure 6, the global distribution of daily precipitation of the mountainless model is

compared with that of the model with mountains, This comparison indicates that in middle latitudes, the distribution of the daily precipitation of the mountainless model is more zonal than that of the model with mountains particularily in the Northern Hemisphere. For example, the mountain model has a region of meager precipitation in the central planes of the United States in agreement with observation, whereas the mountainless model lacks such an arid region and, accordingly, has a smaller longitudinal variation of precipitation rate than the mountain model. Differences of similar nature between the distributions of the two models is evident in the Eurasian continent. In the

392

Simrilation of the hydrologic cycle of the globo1 atmospheric circulation

MEAN COMPUTED RUNOFF RATE

FIGURE 5. Distribution of time menn daily run-off

oceanic region, the mountain model has areas of large precipitation rate off the east coasts of the Eurasian and North American continents. Such areas elongate in the zonal direction as a result of the removal of mountains. In the Southern Hemisphere, the distributions of the daily precipitation of the two

models has interesting differences. For example, the rate of daily precipitation in the southern half of the South American continent is extremely small in the mountainless model, whereas it is significant in the mountain model. According to the horizontal distribution of surface pressure of the model, an anticyclone is located off the coast of Chile in agreement with the features of the actual atmosphere. The detailed analysis of low-levei wind indicates that the Andes mountain range has the effect of blocking very dry air flowing out of this oceanic anticyclone. Therefore, the removal of mountains results in a very arid climate in the southern part of South America’. Since an oceanic anticyclone is also located to the west of the Australian continent, it may be possible to eliminate the Australian desert in the model by electing a mountain range along the west coast of that continent. In summary, the results of the comparison described here are convincing evidence of

the usefulness of controlled experiments for clarifying how climate and the hydrologic cycle are maintained. Therefore, we are planning to perform various controlled experi- ments of similar kinds in the near future.

4. THE JOINT OCEAN ATMOSPHERE MODEL One of the major objectives of constructing the mathematical model of the atmosphere is to investigate the climatic changes of past, present, and future. Unfortunately, the

I . Note that the topography of the model is smoothed such that it can be be resolved by a finite difference mesh of about 500 km. Accordingly, the Andes of tlic model are m u c h lower and have m u c h less blocking effect than the actual Andes. Therefore, tlie actual Andes could have a m u c h larger effect upon the distribution of precipitation than this comparison indicates.

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,S.viikiiru Maiicibe nrid f. Leilli lfo//uiufi.v Jr.

MEAN PRECIPITATION RATE

0 < .I cnildar

0 I *& 5 rmldv IConiours 01 .I rm/dirl @ .I Is I I cm/dos (Confoun a# l.U-/davl

z I5 <m/d-y

FIGURE 6. Distribution of time trieun daily precipitatiun. Upper half; the nioitntuin niudel. Lower heiv; the moiintainless model

model, which has been described so far, has an observed distribution of sea-surface temperature as the lower boundary condition. As is konwn, a climatic change is often accompanied by a change in the sea-surface temperature, which in turn controls the climate. In order to discuss the possibility of climatic change, it is therefore desirable to use a joint ocean-atmosphere model in which the sea-surfacc temperature is determined as a result of the interaction between the oceanic and the atmospheric parts of the inodel. Recently, Manabe and Bryan (i 969) have constructed such a joint ocean-atmosphere

394

ATM OS PH E RE

H20 EQ. EQ. MOTION THERMAL EQ.

-1k- RADIATION

OCEAN

FIGURE 7. Box dingrcim shoioiiig the connection hetlueen the mujor components of the atntospfieric part of the model ond those of the ocenriic purt of the model

model at the Geophysical Fluid Dynamics Laboratory. W e shall describe it very briefly here. Figure 7 shows how the various components of the atmospheric part of the model interact with those of the oceanic part of the model, and figure 8 shows the hydrologic cycle of the model in the form of a box diagram. The annual mean distribution of solar radiation is assumed at the top of the model atmosphere. The ocean-continent configura- tion of the model, which is highly idealized for the sake of simplicity, is shown in figure 9. (Cyclic continuity is assumed at the meridional boundaries.) For further details of the structure of the model see Bryan (1969) and Manabe (1969).

FIGURE 8. Box diagram of the hydrulugic system Of’t/ie .joint model

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Syirkirro Mrriiabe crnd f. Leith Holloway fr.

The distribution of the zonal mean temperature of the joint system, which is obtained from the time integration of the joint model is shown in the left-hand side of figure 10. This distribution can be compared with the observed temperatures shown in the right- hand side of the figure. This figure indicates that the general features of the joint tropos- phere-stratosphere system and the oceanic thermocline are successfully simulated. There are, however, some differences between the two distributions. For example, the tempera- ture of both the troposphere and the stratosphere of the model is too low in higher iati- tudes. The depth of the thermocline in the tropics of the model ocean is too great. The distribution of the time mean rate of precipitation, which is obtained from the

time integration of the joint model, is shown in figure 11. One can compare this with the observed distribution shown in figure 12. Again there are many similarities between these two distributions. For example, the rainbelt is maintained in the tropics and middle latitudes. A typical desert is formed in the subtropical region of the continent, and the subtropical belt of meagre rainfall is interrupted by the relatively rainy region along the east coast of the continent. ' Since this is a preliminary study, the joint model is highly simplified. For example,

the effects of seasonal and diurnal variations of solar insolation are neglected. As we pointed out already, the land-sea configuration of the model is idealized, and the earth's surface is assumed to be flat. Since the effect of mountains and realistic geography have

W -81.7'5. FIGURE 9. Ocean-continent configirration of the model

2. See Manabe (1969) for a detailed discussion of the dependence of the modcl climate upon hydrologic paramctcrs such as soil moisture and snow cover.

396

Simrilatioii of the hydrologic cycle of ///e global atmospheric circirltrtion

COMPUTED OBSERVED

-, "

90" 80' 70" 60' 50' 40" 30" 20" IO" O"

-60" <7d m ,' a /"

- --2 5 I

90' 80" 70" 60' 50" 40" 30' 20" IOD O"-4

FIGURE 10. ZOIIUI menn temperature of the joint ocean-atn7osphere .system; left hand side. The disiributions of the two lieniisplieres cire riveraged. Tlie right-hund side shows the observed dfstribu- tioii in the Northern Hemisphere. The titniosplieric port represents the ronully riveraged aniiirnl mean teniperatirre. Tlie oceunic part is hnsed on u cross-section for the western North Atlnntic from Sverdrirp er al. (1942)

been incorporated successfully in the global model already described, it should be possible to build a joint ocean-atmosphere model with realistic topography. Once completed, such a joint model would be useful for investigating the paleoclimate

by performing the numerical time integration of the model with the orography and the land-sea distribution of the geologic past. It may also be useful for evaluating the pos- sibility of inadvertent modification of climate caused by various human activities. For example, the climatic change resulting from the increase of carbon dioxide due to fossil fuel combustion may be evaluated by perforining a long term integration of the joint model for various carbon dioxide amounts in the atmosphere. The results of Manabe and Bryan (1969) indicate that the time constant of the thermal adjustment of the joint ocean-atmosphere system is more than 100 years. Therefore, in order to predict the future evolution of climate for such a long period of time, it seems to be essential to use an extremely high speed computer. W e understand that such a computer will be available in the very near future thanks to the remarkable advance of computer technology. Another possible application of the joint model may be the prediction of the spread

of pollution in the ocean and the atmosphere. As is known, the hydrologic process such as precipitation and runoff play an important roll in transporting various pollutants. In summary, we believe that a realistic model of the joint ocean-atmosphere system with hydrologic cycle is indispensable for investigating future changes in our environment.

It must be emphasized, however, that various improvements of the model are required before the model is good enough for the applications described above. As the report of

397

Siirlri/oriuii of rlre lijclrologic cycle u f ilie global uirtiosplieric circulaiion

-_ - ___ i -- ____- P i T H OCEANIC CIRCULATION

FIGURE I I. Area-distributioil uf /lie /itne meari ra/e ofprecipitation of the joiiit IiiOd~l (ciii/daji) on the Mercator iiiap projection. The arec[ uf the oceciii is indicated hy the box in the lower riglit side. The distribrrtioris o/ /lie flon lieiiiisplieres are nuereigeel. (Note /licit the conurritioil of slicrdir7g iii this figure differs from /licri in figiire 3)

the NAS committee on weather and climate modification pointed out, further improve- ments of the parameterization of the moist convection and of the horizontal subgrid scale diffusion are urgently needed and the further increase of the resolution of the horizontal finite difference grid is essential for the construction of a realistic model. As you may know, intensive efforts towards these improvements have been made under the Global Atmospheric Research Program (GARP). Unfortunately, improvements in the schemes for computing the hydrology at the earth’s surface are not usually included in GARP despite its paramount importance for the study of climatic change and for the development of better methods of long-range forecasting. Therefore, it is clear that the necessity of collaboration between hydrologist and meteorologist in constructing a joint atmosphere-hydrosphere model cannot be overemphasized.

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S.vukirro Munube und J. Leilh Hullowiry fr.

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