786 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 26Climate Calculations with a Combined Ocean-Atmosphere Model SYUKUR0 MANABE AND KIRK BRYAN Geophysical Fluid Dynamics Laboratory, E$SA, t~rinceton University, Princeton, N. J. 13 March 1969 and 6 May 1969 Empirical evidence indicates that the poleward heattransport by ocean currents is of the same order ofmagnitude as the poleward transport of energy in theatmosphere (Sverclrup, 1957). A significant contributionto the heat exchange across latitude circles is also associated with polar pack ice. Thus, any serious attemptto calculate climate must take into account the entirefluid envelope of the earth, consisting of the atmosphereand the hydrosphere. Although the cryosphere, consisting of ice packs over the oceans and continental ice,is not a fluid in the usual sense, it must be included in ageneral climatic model because of its large reflectivityto the solar insolation and its ability to store and transport heat. The object of this note is to report the completionof a calculation based on a combined numerical modelof the atmosphere and the ocean carried out at theGeophysical Fluid Dynamics Laboratory, ESSA. Theextended numerical integration of this model is successful in producing many realistic features of climatestarting with quite arbitrary initial conditions. Onlya brief description will be given here. For the fulldetails the reader is referred to Manabe (1969) andBryan (1969). The numerical model of the atmosphere is verysimilar to that described by Manabe -t aL (1965)except that the hydrology of the continental surface isFio. 1. Ocean-continent configuration of the model.taken into consideration. Velodty, temperature, watervapor and surface pressure are calculated at each ofthe grid points which are spaced approximately 500 kmapart. Calculations are carried out at 9 levels which arechosen so that they resolve the structure of the lowerstratosphere and the Eckman boundary layer. Theradiation model is essentially that described by Manabeand Strickler (1964). For the sake of simplicity, theseasonal and diurnal variation of solar insolation arenot taken into consideration; instead, annum meaninsolation is assumed for this study. The depletion ofsolar radiation and the transfer of terrestial radiationis computed taking into consideration cloud and gaseousabsorbers such as water vapor, carbon dioxide andozone. The distribution of these absorbers is specifiedin advance to correspond to zonal averages taken fromclimatological data. The prognostic equation of watervapor involves the three-dimensional advection ofwater vapor, condensation and evaporation. Overcontinental surfaces, the depth of snow cover and theamount of soil moisture are predicted based upon detailed balance computations of snow and soil moisture,respectively. The ocean model is similar to that of Bryan and Cox(1968), except that the fields of temperature andsalinity are calculated explicitly, and density is calculated from a realistic equation of state. Anothernew feature of the ocean model is a simplified methodof calculating the growth and movement of pack icein polar latitudes. Calculations are carried out for 5different levels with respect to the vertical coordinate.The horizontal resolution is similar to the atmosphericmodel in the interior, with extra rows of grid points forgreater resolution near the western boundary. The calculations are carried for a region on a globebounded by two meridians 120- of longitude apart,cyclic symmetry being assumed in the atmosphere atthese meridional boundaries. The regions immediatelyadjacent to the poles are excluded by free slip, insulatedwalls at 81.7N and 81.7S. In the interval between 66.5Nand 66.5S, half of the area is covered by ocean. Fig. 1shows the ocean-continent distribution chosen for thisstudy. In the first stage of the calculation the effect of heattransfer in the ocean model is suppressed. The oceansurface is simply regarded as a wet surface withoutany heat capacity. An equilibrium state is reached bynumerically integrating the atmospheric model startingJULY 1969 NOTES AND CORRESPONDENCE 787from isothermal initial conditions. The final "climate"attained is used to specify fixed boundary conditions forthe ocean model in the second stage of the calculations.These fixed surface boundary conditions consist of thewind stress pattern, the sea surface temperature, andthe rate of supply of water at the ocean surface. Theinitial condition for the ocean model is a resting oceanwith a horizontally uniform distribution of temperatureand salinity. At the end of the numerical integration ofthe ocean model over the equivalent of 60 years withfixed boundary conditions, an equilibrium is attainedin the upper layers with only minor changes takingplace below the main thermocline. An extensive icepack with a thickness of 1-4 m forms in the northernpart of the ocean. In the final part of the calculation interaction between the atmosphere and the ocean is allowed. Sincedifferent types of fluid motion occur in the atmosphericand ocean models, the atmospheric model requiresapproximately 40 times more computation to integrateover a given time period as the ocean model. Accordingto the stage I results of the numerical integration of theatmospheric model, the thermal relaxation time of theatmosphere is of the order of 1 year. On the other hand,an estimate of the ratio of heating to heat capacityof the ocean indicates that the thermal relaxation timeof the ocean is of the order of centuries. Obviously, itwas not feasible to make a synoptic calculation of theinteracting models over a long enough period for theoceanic part of the model to reach adjustment. In orderto optimize the amount of the computation, the couplingbetween the atmospheric part and the oceanic part ofthe model is adjusted such that the evolution of theformer during 1 atmospheric year is coupled with thatof the latter during 100 oceanic years. For example,the atmosphere on 0th, 0.5th and 1st atmosphericyear interacts with the ocean on 0th, 50th and 100thoceanic year of the time integration, respectively. Theaverage temperature of the upper 50 m of the ocean istaken to be representative of the surface mixed layer.The temperature of this surface layer is used as thelower boundary condition of the atmospheric model.The rates of supply of heat, momentum and water tothe ocean surface, which are computed in the atmospheric model, serve as the upper boundary condition forthe ocean model. The running time-mean operator isapplied to vertical fluxes to avoid an overresponse of theocean model to features caused by individual synopticdisturbances in the atmospheric model. The latitude-height distributions of temperature ofthe joint model shown in Fig. 2 are zonal averages atthe end of the numerical integration of the final partof the computation. Since the zonally averaged temperatures over the land surface are much lower thanthose over the sea at higher latitudes, the isotherms donot exactly coincide at the air-sea interface in Fig. 2.This distribution is computed as an average state forthe last two-sevenths of the period of the final stage ofthe time integration. This integration of the joint modelis performed over 1 year of atmospheric time, which isequivalent to 100 years for the ocean model. It requiredabout 1200 hours of computing on a UNIVAC 1108.1Q COMPUTED OBSERVED....I '.,2' '~.7o..,/ ~'~ / _ / ?s'~__~~---~~3O90- 80G 70- 60- 50- 40- 30- 20- 1O-' 0- 90- 80~ 70- 60- 50- 40- 30- 20- 10- O' Fro. 2. Zonal mean temperature of the joint ocean-atmosphere system, left-hand side. This distribution,which is the average of two hemispheres, represents the time mean over two-sevenths of the period of thefinal stage of the time integration. The right-hand side shows the observed distribution in the NorthernHemisphere. The atmospheric part represents the zonally averaged, annual mean temperature. The oceanicpart is based on a cross section for the western North Atlantic from Sverdrup et al. (1942).788JOURNAL OF THE ATMOSPHERIC SCIENCESVOLUME 26 WITHOUT OCEANIC CIRCULATION N I WiTH O~EANiG CIRCULATION 240' 245-----'-~ ~ ~2S0 ~ ' "~ ' 28S Fro. 3. The surface temperature pattern (-K), the distributions of two hemispheres being averaged. The left-handside of the figure represents an average over the final 100-day period of the time integration of the atmospheric model(the first stage integration) while the right-hand side is the final 100 atmospheric days (or 28 oceanic years) of thetime integration of the joint ocean-atmosphere model (the final stage of the integration).Even after this very time-consuming calculation, aclimatic equilibrium is not completely attained. Theatmospheric and ocean surface temperatures are nearlysteady, but the mean temperature of the ocean continues to increase at an average rate of 1.3C percentury toward the end of the integration. The resultis an average net flow of heat into the ocean equal to0.01 ly min-~, which is about 0.5% of the solar constant.This net warming is associated with the cold watermass near the bottom shown in Fig. 2 and is a relic ofthe second stage of the calculation, in which fixedsurface boundary conditions are maintained at theocean surface. In short, this result indicates that thethermal relaxation time of the model ocean is longerthan 100 years. The free interaction of the atmosphericand ocean models stops the formation of deep waterat temperatures ~3C, and eliminates the ice pack atpolar latitudes. Also, it reduces the snow cover over thecontinent significantly. The most interesting result~ of the calculation isthe quantitative demonstration of the effect of oceancurrents on the distribution of temperature, relativehumidity, and precipitation patterns. This is done by 2 In the final stages of the analysis it was discovered that thestress values used as an upper boundary condition over the oceanwere multiplied by an extraneous factor, the cosine of latitude.A new run corresponding to three decades of ocean time was madeto test the effect of this error. The subarctic ocean gyre becamemuch stronger, while the strength of the subtropical gyre and thethermohaline circulation remained the same. Warming by 1-2Cin the upper ocean takes place at both high and equatorial latitudes at the expense of middle latitudes. The level of sensibleheat transfer between the ocean surface and deeper layers hasroughly the same d/stribution as in the main run and the mainfeatures of Figs. 2-4 are unchanged. More details are given inManable (1969) and Bryan (1969).comparing the state, which is obtained from the timeintegration of the atmospheric model (the first stage)with the state, which is obtained from that of the jointocean-atmosphere model (the final stage). For example,Fig. 3 shows the surface temperature patterns averagedover the final periods of the first and final stages of thecalculation. In the final stage, upwelling near theequator forms a weak temperature minimum there,instead of a maximum. The ocean currents also causeisotherms over the northern part of the ocean to have amuch more realistic NE-SW trend. A tight gradientappears along the poleward wall of the ocean in thefinal stage of the calculation. The rates of precipitationcorresponding to the two temperature patterns areshown in Fig. 4. The comparison indicates a drasticreduction of rainfall over the tropical ocean due to theeffect of equatorial upw~lling. The overall ratio ofprecipitation falling over land compared to that fallingover the sea is very much altered by this effect. Also, asignificant increase in the rate of precipitation is evidentalong the east coast of the continent in the subtropicsowing to the effect of the poleward advection of warmwater by the so called "subtropical gyre." Anothermodification of interest caused by the ocean currents isthe general poleward shift of the rainbelt in middlelatitudes. It is hoped that the experience gained in thispreliminary study will be useful in planning and carrying out more extensive climatic calculations in thenear future. Acknowledgments. The authors are grateful to Dr.Joseph Smagorinsky, Director of the GeophysicalFluid Dynamics Laboratory, who originally suggested1969 NOTES AND CORRESPONDENCE~///J////J///l////J///////////////////////////////////////////////~WITHOUT OCEANIC CIRCULATION789FIG,. 4. The distributions of the rate of precipitation (cm day-~) corresponding to the temperature patterns of Fig. 3.this study and is responsible for creating an idealenvironment.!;." They wish to thank Messrs. J. Leith Holloway, Jr.,Michael D. Cox, David Durdall and Richard T.Wetherald, whose assistance was essential to carryingout this study. REFERENCESBryan, K., 1969: Climate and ocean circulation, Part III: The ocean model. Submitted to Mort. Wea. Rev. , and M. D. Cox, 1968: A nonlinear model of an ocean driven by wind and differential heating, Parts I and II. J. Atmos. Sd., 25, 945-978.Manabe, S., 1969: Climate and ocean circulation. Part I: The atmospheric circulation and the hydrology of earth's surface. Part II: The atmospheric circulation and the effect of heat transfer by ocean currents. Submitted to Mon. Wea. Re*. -, J. Smagorinsky and R. Strickler, 1965: Physical climatology of a general circulation model with a hydrologic cycle. Mon. Wea. Rev., 93, 769-798. , and R. Strickler, 1964: On the thermal equilibrium of the atmosphere with a convective adjustment. J. Atmos. Sci., 21, 361-385.Sverdrup, H. U., 1957: Oceanography. Handbuch der lPhysik, Vol. 48, Berlin, Springer-Verlag.--, M. W. Johnson and R. H. Fleming, 1942: The Oceans. New York, Prentice-Hall, 1087 pp.