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APPENDIX A 195 stratigraphy of equatorial Pacific core V28-238: oxygen isotope temperatures and ice volumes on a 10° and 10° year scale, Quaternary Res., 3:39-55. Starr, V. P., and A. H. Oort, 1973: Five-year climatic trend for the Northern Hemisphere, Nature, 242:310-313. Steiner, J., and E. Grillmair, 1973: Possible galactic causes for periodic and epi- sodic glaciation, Geol. Soc. Am. Bull., 84:1003-1018. Suess, H. E., 1970: The three causes of secular C⢠fluctuations, their amplitudes and time constants, in Radiocarbon Variations and Absolute Chronology, Nobel Symposium 12, I. U. Olsson, ed., Wiley, New York, pp. 595-604. Sverdrup, H. U., M. W. Johnson, and R. H. Fleming, 1942: The Oceans, Prentice- Hall, Englewood Cliffs, N.J., 1087 pp. Taljaard, J. J.. H. Van Loon, H. L. Crutcher, and R. L. Jenne, 1969: Climate of the Upper Air: Southern Hemisphere, 1. Temperatures, dew points and heights at selected pressure levels, NAVAIR 50-1Câ55, Naval Weather Service, Washing- ton, D.C. Van der Hammen, T., T. A. Wijmstra, and W. H. Zagwijn, 1971: The floral record of the late Cenozoic of Europe, in The Late Cenozoic Glacial Ages, K. Turekian, ed., Yale U.P., New Haven, Conn., pp. 391-424. Veeh, H. H., and J. Chappell, 1970: Astronomical theory of climatic change: sup- port from New Guinea, Science, 167:862â865. Vonder Haar, T. H., and A. H. Oort, 1973: New estimates of annual poleward energy transport by Northern Hemisphere oceans, J. Phys. Oceanog., 3:169-â172. Vonder Haar, T. H., and V. E. Suomi, 1971: Measurements of the earthâs radia- tion budget from satellites during a five-year period, Part I: Extended time and space means, J. Atmos. Sci., 28:305â3 14. Wagner, A. J., 1971: Long-period variations in seasonal sea-level pressure over the Northern Hemisphere, Mon. Wea. Rev., 99:49-69. Wahl, E. W., 1972: Climatological studies of the large-scale circulation in the Northern Hemisphere, Mon. Wea. Rev., 100:553â564. Walcott, R. I., 1972: Past sea levels, eustasy and deformation of the earth, Quaternary Res., 2:1-14. Washburn, A. L., 1973: Periglacial Processes and Environments, Arnold Press, London, 320 pp. Webb, T., and R. A. Bryson, 1972: Late- and post-glacial climatic change in the northern midwest, USA: quantitative estimates derived from fossil pollen spectra by multivariate statistical analysis, Quaternary Res., 2:70-111. Weyl, P. K., 1968: The role of he oceans in climatic change: a theory of the ice ages, Meteorol. Monogr., 8:37-62. Willett, H. C., 1967: Maps of standard deviation of monthly mean sea level pres- sure for January, April, July and October, 1899-1960, Massachusetts Inst. of Tech., Cambridge, Mass. (unpublished ). Wilson, C. L. (Chairman), 1971: Study of Manâs Impact on Climate (smIc) Report, Inadvertent Climate Modification, W. H. Matthews, W. W. Kellogg, and G. D. Robinson, eds., MIT Press, Cambridge, Mass., 308 pp. Winstanley, D., 1973: Rainfall patterns and general atmospheric circulation, Nature, 245:190-194. Winston, J. S., 1969: Temporal and meridional variations in zonal mean radiative heating measured by satellites and related variations in atmospheric energetics, PhD dissertation, Dept. of Meteorol. and Oceanog., NYU, New York, 152 pp.
APPENDIX B SURVEY OF THE CLIMATE SIMULATION CAPABILITY OF GLOBAL CIRCULATION MODELS INTRODUCTION Much of the present effort within GARP, as well as other research pro- grams in the atmospheric and oceanic sciences, is aimed toward the development of a quantitative understanding of the behavior of the atmosphere, with the immediate objective of improving the accuracy of weather forecasts. Other research efforts and plans, and the research program proposed in this report in particular, are directed to the longer-range objective of understanding the physical basis of climate and climatic change. Essential to both of these objectives are the dy- namical models of the global atmospheric and oceanic circulation. These general circulation models (or GCMâs) have been developed over a number of years, in parallel with the growth of computing capability and the increase of atmospheric data coverage. The several atmospheric and oceanic GCMâs have now reached the point where reasonably accurate simulations of the global distribution of many im- portant climatic elements are possible and where their coupling into a single dynamical system is now feasible. This therefore seems to be a useful time to survey briefly these modelsâ climate simulation capabilities. Here we have not attempted to present a detailed discussion of the various GCMâs, as such descriptions are readily available both in the literature and in documents describing special models. Model reviews have recently been prepared by Robinson (1971), Willson (1973). Smagorinsky (1974), and Schneider and Dickinson (1974), and general 196
APPENDIX B 197 discussions of the use of such models for weather prediction and for studies of the general circulation are available [see, for example, the review by Smagorinsky (1970) and also Haltiner (1971) and Lorenz (1967)]. A survey of the physical and mathematical structure of both regional and global atmospheric models is also in preparation for GARP (1974). What has not been assembled heretofore is the comparative climatic performance of the various models, and this Appendix is an initial effort to fill this need for both the atmospheric and oceanic global GCMâs. In general, any formulation that relates variables of the climatic system to the external or boundary conditions may be considered a climatic model. We can thus identify basically empirical and statistical climatic models, as well as those that rest on the systemâs dynamical equations. Within the dynamical climate models, a wide variety of the type and degree of parameterization may be seen. At one extreme are the vertically and zonally averaged atmospheric models that address the mean heat balance at the earthâs surface, such as those of Budyko (1969) and Sellers (1973). In such models, the transport of heat is parameterized in terms of mean zonal variables, which are in turn re- lated to the surface temperature. At the other extreme are the high- resolution global general circulation models or GcMâs. In these models, the details of the transient cyclone-scale motions are resolved, along with the global distribution of the elements of the heat and hydrologic balances. Even these models, however, parameterize certain physical processes, in that they employ empirical or statistical representations of some of the subgrid scale processes in the surface boundary layer and in the free atmosphere and open ocean, such as the effects of diffusion and convection. Dynamical climate models also display a wide variety of parameter- ization with respect to time. This ranges from equilibrium or steady- state models, such as that of Saltzman and Vernekar (1971), to the GCMâs that explicitly calculate the time dependence of the circulation in steps of a few minutes. With respect to their treatment of both space and time, therefore, a wide range of models exists, and each is suited to the investigation of particular aspects of the climatic problem. The GCMâs (of both the atmosphere and ocean) provide the most detailed representation of the physical processes involved but require large amounts of computation. These models have therefore been used up to the present time to study only the climatic variations on time scales of the order of years (for the atmosphere) to centuries (for the oceans). The more highly parameterized models, on the other hand, provide
198 UNDERSTANDING CLIMATIC CHANGE less detail but are capable of treating the longer-period climatic varia- tions with much less computation. Once they are adequately calibrated with respect to observations, an important use of the GcMâs will be to generate detailed climatic statistics, from which parameterizations ap- propriate to the various statistical-dynamical models may be prepared. In the remainder of this Appendix we give our attention to the princi- pal atmospheric and oceanic general circulation models, for the pur- pose of indicating their present capability to simulate climate. Before presenting these results, however, it is useful to review briefly the historical development of numerical modeling in general. DEVELOPMENT AND USES OF NUMERICAL MODELING The basis for the mathematical modeling of the behavior of the at- mosphere was first unambiguously stated by V. Bjerknes in 1904. It is only in the last 20 years or so, however, that the means for carrying out such modeling on a practical basis have become available. These include adequate observations for model calibration and verification, a knowledge of the important physical processes and their parameteriza- tion, and the computers and numerical methods necessary to perform the calculations. The observational base for numerical modeling of the atmosphere has grown steadily since the 1940âs and early 1950âs, when the global radiosonde network began to take shape. The icy provided further ex- pansion, but the observational coverage still needs augmentation, espe- cially over the oceanic regions. The real breakthrough toward the global measurements necessary for numerical modeling has come from the remote-sensing capabilities of meteorological satellites; with the aid of suitable surface (ground-truth) observations, these are capable of providing the first truly worldwide observations of the air and ocean surface temperature, moisture and cloudiness, and elements of the heat and hydrologic balance. By using the numerical models diagnostically, there is then the prospect of deducing the accompanying global distribu- tions of other variables, such as the wind velocity. Such a scheme is the observational basis of the proposed First GARP Global Experiment (FGGE) in 1978. The physical and theoretical basis for numerical modeling has grown significantly with the development of the theory of baroclinic instability, the parameterization of moist convection, and advances in our knowledge of the behavior of the stratosphere and the planetary boundary layer. Our growing understanding of these processes has increased the pros- pects for improved weather forecasts. These hopes are bounded, how-
APPENDIX B 199 ever, by the realization that the atmosphere possesses limited predict- ability, i.c., that there is a time range beyond which the local variations of weather appear as random fluctuations as far as their explicit pre- diction by numerical models is concerned. Present indications are that this limit lies at about two weeksâ time. The key physical processes that control the longer-period variations of the atmosphereâthose that are properly associated with climateâ are largely unknown, although we are beginning to recognize the im- portance of a number of feedback relationships, such as the air-sea coupling and cloudinessâtemperature feedback. Numerical models that incorporate such effects are our best tool to develop a quantitative understanding of their role in climate and climatic variation. The computational base for numerical modeling has grown during the last 20 years in parallel with the development of successive genera- tions of high-speed computers, as shown in Figure B.1. This overview makes clear the interrelated development of numerical models, theory, and computer speed. Numerical weather prediction may be considered to have begun with the first successful numerical integration of the application modeling -~ 4 Computer speed = Atmospheric model Oceanic model 2 (relative to z deve lopments developments £3 tne IBM 360-91) ee 1950 | j First numerical forecasts Wind-driven barotropic Barotropic (vorticity) models J mode 1s & : Baroclinic atmospheric models 8 IBM 701 (0003) Primitive equation models First baroclinic models | 1955 First numerical GCM IBM 704 (.001) ' (idealized geometry) ââââââ» | First hemispheric GCli prediction 3 IBM 709 (.01) 1960 = a : a . n \ 1a 7094 (.05) weather circulation First global GCM 1965 âââââ> Â¥ First annual GCM simulations CDC 6600 (.5) dumerical UNIVAC 1108 (.4) General IBM 360-91 (1) 1970 First coupled air/sea model GLOBAL Climate (idealized zeometry) CDC 7600 (2) Climatic â First world ocean GCM variation IBM 360-195 (3) â 1974 â First global coupled atmosphere-ocean model TI-ASC (8) â ILLIAC-4 (15) â : FIGURE B.1 Highlights in the development of numerical modeling of the atmosphere and ocean.
200 UNDERSTANDING CLIMATIC CHANGE vorticity equation (Charney et al., 1950), with the demonstration of the ability of baroclinic models to forecast cyclonic development (Charney and Phillips, 1953), or with the commencement of operational numerical weather prediction in 1955. Numerical general circulation studies may be considered to have begun with the simulation of the atmospheric energy cycle in an idealized model with sources and sinks of energy and momentum (Phillips, 1956), with the first successful hemispheric circulation experiments (Smagorinsky, 1963), or with the first extended global integration (Mintz, 1965). Numerical climate models for the atmosphere may be considered to have begun with the global simulation of the seasonal and interannual variation of the primary climatic elements (Mintz et al., 1972), although the modeling of climate by other methods has a much longer history. The numerical modeling of climatic variation, on the other hand, which addresses the coupled oceanâatmosphere climatic system, has only just begun (Bryan et al., 1974; Manabe et al., 1974a, 1974b). The development during the past decade of numerical methods whose Stability and accuracy can be suitably controlled has made it possible to carry out such calculations for extended periods of time. Even with todayâs fastest computers, however, the solution of the more detailed global numerical models proceeds only at a rate between one and two orders of magnitude faster than nature itself, and our ability to per- form the large number of numerical integrations required for the system- atic exploration of climate and climatic change requires the continued development and dedication of new computer resources. A similar pattern of development has occurred in the numerical modeling of the oceans, except that the rate of progress has been slower due principally to a lack of suitable oceanic observations. The data base for the oceans is fragmentary in comparison with that for the atmosphere, and there is no oceanic counterpart of the radiosonde or weather station network. The bathythermograph has been widely used to measure the thermal structure of the oceanâs surface layer for the past few decades, but even this has not been done on a synoptic basis. The bulk of the data for oceanic temperature, salinity, and currents has been obtained in the course of occasional oceanographic expeditions or special observational programs. Even so, the number of direct velocity measurements is quite small, and our knowledge of the oceanic circulation is largely based on geostrophic estimates from conventional hydrographic observations. Our knowledge of the dynamics of the ocean circulation is also less complete than is that for the atmosphere. While the character of the vorticity balance of the ocean was first established by Sverdrup (1947)
APPENDIX B 201 and Stommel (1948), the role of the thermohaline circulation was demonstrated with a numerical model only a few years ago (Bryan and Cox, 1968), and the effects of bottom topography have been established even more recently (see, for example, Holland and Hirschman, 1972). Numerical models are proving of great value in the study of time- dependent behavior of the oceanic general circulation and in the analysis of oceanic mesoscale motions such as those now being revealed by the MODE observations. The structure of these eddies and the role that they play in the oceanic heat balance is one of the principal unsolved prob- lems in physical oceanography. Other important questions concern the nature of vertical mixing in the ocean, especially in the surface layer, and the mechanics of the formation of deep and bottom water. Each of these can perhaps be most fruitfully studied with appropriate regional numerical models, in order to lay the foundation for their parameteriza- tion in three-dimensional models of the world ocean. But perhaps the most important problem of all from the viewpoint of climate is the interaction between the ocean and the atmosphere; the numerical modeling of this coupled system offers our best hope of achieving a quantitative understanding of the dynamics of climatic variation. Numerical models thus lie at the heart of the modern study of climate and climatic change: they complement (and may even be regarded as a part of) the observing system, they serve as tools for climatic analysis and diagnosis, and they offer the most rational way of assessing the course of future climatic events. Whether or not climate forecasting in the time-dependent sense ever becomes feasible, the use of numerical models to simulate the average or equilibrium climates of the past and the likely climatic consequences of various natural or anthropogenic effects in the future will justify their development. ATMOSPHERIC GENERAL CIRCULATION MODELS Formulation All general circulation models are based on the fundamental dynamical equations that govern the large-scale behavior of the atmosphere. This system consists of the equation of motion (expressing the conserva- tion of momentum), the thermodynamic energy equation (expressing the conservation of heat energy), the equations of mass and water vapor continuity, and the equation of state. When geometric height (z) is the vertical coordinate, these equations can be written in vector form as follows:
202 UNDERSTANDING CLIMATIC CHANGE v7. VP wh 42 P44 | vp=F, (1) oP + pg=0, (2) 06 Or Fe. Vo+wer =Q, = (3) P+ V-pV+S (pw) =0, (4) S147. Vv q+w ot = S, (5) p=pRT. (6) Here V is the horizontal velocity, w is the vertical velocity, © is the rotation vector of the earth, p is the density, p is the pressure, g is the gravitational acceleration, 6 is potential temperature [which is related to the ordinary temperature TJ by the relation 6=T(p./p)*, where Po=1000 mbar and «=0.286 is the ratio of the specific heats], q is the water vapor mixing ratio, R is the gas constant for (moist) air, and V is the horizontal gradient operator. The terms F, Q, and S on the right-hand sides of Eqs. (1), (3), and (5) represent the sources and sinks of momentum, heat, and water vapor due to a variety of physical processes in the atmosphere and must be either prescribed or parameterized in terms of the primary dependent variables 1 in order to close the system (1)â(6). The net frictional force F consists of the frictional drag at the earthâs surface and the internal friction in the free atmosphere, as well as the changes of large-scale momentum due to smaller-scale processes. The net (diabatic) heating rate Q consists of the latent heat released during condensation, the heating due to the exchange of both long-wave and shortwave radia- tion, and the sensible heating of the atmosphere by turbulent heat fluxes from the underlying surface. The net moisture addition rate S consists of the difference between the evaporation rate (from both the surface and from cloud and precipitation) and the condensation rate. An important contribution to each of these source terms is the vertical flux of momentum, heat, and moisture, which accompanies cumulus- scale convection in the atmosphere. We may note that such convective- scale processes are not governed by the system (1)â(6) and must be represented in terms of the larger-scale variables. This parameterization is particularly critical for the net heating, because most of the latent heating in the atmosphere is accomplished by convective motions, which are also responsible for much of the cloudiness (see Figure 3.2).
APPENDIX B 203 The various atmospheric GCMâs are each formulated in slightly dif- ferent ways and employ different treatments of the source terms. There is at present insufficient evidence to decide which particular formulation is the most satisfactory, and there is even more uncertainty regarding the most correct parameterization of the unresolved physical processes contained within F, Q, and S. A summary of some of the features of the better-known atmospheric general circulation models is given in Table B.1. Each of the models shown here uses generally similar pro- cedures to determine the ground-surface temperature (from an assumed heat balance over land and ice), the surface hydrology (with runoff permitted after saturation of the surface soil), and the occurrence of convection (from vertical stability criteria depending on the moist static energy). Each of the models also incorporates the observed large- scale distributions of terrain height, surface albedo, and sea-surface temperature. Solution Methods All the atmospheric GcMâs considered here employ finite-difference methods of second-order accuracy, with the dependent variables gen- erally determined on a spatially staggered grid with a resolution of several hundred kilometers (see Table B.1). Time differencing is also generally of second-order accuracy, with time steps between 5 and 10 min used to maintain (linear) computational stability. Long-term (nonlinear) computational stability is inherent in some of the modelsâ space differencing schemes, while others employ eddy diffusion processes to achieve this end. Various degrees of smoothing are also employed in the modelsâ solution, in addition to that inherent in the finite-difference approximations themselves. Depending on the computer used, the number of model levels, and the frequency with which the radiative heating calculations are performed, global atmospheric GCMâs gen- erally run between 10 and 100 times faster than real time. Selected Climatic Simulations In order to display the level of accuracy characteristic of present-day atmospheric GCMâs in the simulation of climate, we have here assembled the results of model integrations drawn from recently published (and in some cases as yet unpublished) sources. To facilitate comparison, these are presented in a common format, along with the corresponding ob- served distributions.
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APPENDIX B 205 Sea-Level Pressure Although the various GCMâs differ greatly in their resolution of the vertical structure of the atmosphere, each simulates the distribution of a number of climatic variables at the earthâs surface. Of these, perhaps the distribution of sea-level pressure is the most familiar; it is shown here as simulated by four different models for the month of January. In Figure B.2 the average sea-level pressure simulated by the 11-level GFDL atmospheric model is shown for the months of December, January, and February (Manabe et al., 1974b). Figures B.3, B.4, and B.5 show the corresponding average January sea-level pressure simulated by the six-level NCAR model (Kasahara and Washington, 1971), by the two- level Rand model (Gates, 1972), and by the nine-level Giss model (Somerville et al., 1974). In each case the observed average January sea-level pressure distribution is also shown. While the modelsâ results differ in a number of details, these results generally show a useful level of accuracy. As might be anticipated, the largest errors (and the greatest differences among the models) occur in the middle and higher latitudes of the northern hemisphere where cyclonic activity is the most frequent. It should be recalled, however, that sea-level pressure alone is by no means a complete indicator of climate. Tropospheric Temperature and Pressure In Figure B.6 the average January 800-mbar temperature simulated by the two-level Rand model (Gates, 1972) is shown, along with the ob- served distribution. Although systematic errors may be noted over the continents, the simulated large-scale temperature distribution clearly reflects the positions of the major thermal perturbations in the lower troposphere. The average January 500-mbar height simulated by the nine-level Giss model (Somerville et al., 1974) is shown in Figure B.7, along with the observed distribution. These results also clearly show that the mean position and intensity of the long waves in the westerlies are portrayed reasonably well in the simulation. Cloudiness and Precipitation Among the more difficult climatic elements to simulate accurately in a GCM are the cloudiness and precipitation. This is doubtless due to the fact that a substantial portion of the total cloudiness and precipitation observed occurs in connection with convective-scale motions, especially
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218 UNDERSTANDING CLIMATIC CHANGE in the lower latitudes. As noted earlier, these processes must be parame- terized in the Gcmâs, and their accurate calibration is relatively difficult. In Figure B.8, the average January total cloudiness simulated by the six-level NCAR model (Kasahara and Washington, 1971) is shown, along with a composite observed distribution for January and for De- cember, January, and February. With the exception of the equatorial region and the low latitudes of the northern hemisphere, the large-scale areas of maximum and minimum cloudiness are reasonably well simulated. In Figure B.9, the annual average precipitation simulated by the 11-level GFDL model (Manabe et al., 1974b) is shown, along with the corresponding observed distribution. In addition to the large-scale precipitation pattern in middle latitudes, this simulation also portrays a number of the smaller-scale features, including the zone of heavy precipitation near the equator. Although this comparison is for a some- what longer time period than the others shown here, the difficulty of correctly parameterizing the precipitation process makes the skill of this simulation impressive. OCEANIC AND COUPLED ATMOSPHERE-OCEAN GENERAL CIRCULATION MODELS Estimates based on observed data show that the heat transported by ocean currents plays a major role in the global heat balance (Vonder Haar and Oort, 1973). A model that is to be useful for the study of climatic variation must therefore include the ocean as well as the atmosphere. As suggested by the simulations just reviewed, the speci- fication of a fixed ocean surface temperature in atmospheric GCMâs is a strong boundary condition and may mask weaknesses in the modelsâ simulation of the heat balance. The problem of climatic variation there- fore furnishes a major motivation for the accelerated development of numerical models of the oceanic general circulation. Relative to numerical models of the atmosphere, numerical modeling of the ocean is still in a primitive state. As previously noted, this is primarily due to the lack of sufficient data to perform a careful verifica- tion of the models and to parameterize properly the effects of the smaller-scale motions. The only large body of data presently available for verifying ocean circulation models is the collection of measurements of density structure. While these data were sufficient to calibrate the earlier analytic theories of the ocean thermocline, global numerical models require a much more extensive data base for adequate verifica- tion.
APPENDIX B 219 It is now recognized that many of the earlier studies, such as those by Bryan and Cox (1967) and Haney (1974) for idealized basins, as well as the higher-resolution simulations of Cox (1970) for the Indian Ocean and of Friedrich (1970) for the North Atlantic, represent transient rather than equilibrium solutions for the boundary conditions imposed. The extended integration of even more detailed numerical models will be necessary in the future, in order to design and calibrate adequately other simpler models. Such models will require less calcula- tion and thereby allow more freedom to carry out the large number of numerical experiments required. General reviews of numerical model- ing of the ocean circulation are given in the proceedings of a recent symposium (Ocean Affairs Board, 1974) and by Gilbert (1974). Formulation The principal dynamical components of an oceanic general circulation model are similar to those of its atmospheric counterpart, namely, the equations of motion, conservation equations for potential temperature and salinity, the continuity equation, and an equation of state. In addi- tion, an oceanic model should contain equations for the growth and movement of pack ice. In some problems of oceanic circulation, it is not necessary to treat the temperature and salinity separately, and these variables can be combined into a single density variable. In climatic studies, however, we are interested in the heat transported by ocean currents explicitly; and in many regions of the world ocean, particularly the polar seas, the density and temperature are not proportional. In these regions at least, it is therefore necessary to predict salinity as a separate inde- pendent variable. A changing salinity structure in the ocean may pro- vide the basis of climatic change mechanisms that have not yet received sufficient attention. In an ocean model, the equation of motion (1) may be simplified by treating the density p as a constant p, (Boussinesq approximation), while the hydrostatic equation (2) remains unchanged. The thermo- dynamic energy equation (3) and the water vapor continuity equation (5) are represented in the ocean by conservation equations for po- tential temperature 6 and salinity s of the form 2 (0,8) +0-V (0s) +w 5 (8) =(Q.0), (7) where Q and o denote source functions. The continuity equation (4)
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224 UNDERSTANDING CLIMATIC CHANGE may be simplified by considering the ocean to be incompressible, in which case we may write Ow â Bz +V-V=0. (8) The oceanic equation of state may be written symbolically as p=p(6,s,D), (9) where the actual expression is a polynomial of high order, whose co- efficients have been determined by laboratory experiments. To close the system, expressions must be chosen for F [in the simplified form of Eq. (1)] and for Q and a in terms of the dependent variables. As in the case of atmospheric models, this closure is an important problem in the formulation of oceanic models and includes the parameterization of the mesoscale oceanic eddies. Solution Methods The predictive equations for momentum, temperature, and salinity given in the previous section are generally approximated by centered differences of second-order accuracy, with care taken to conserve both linear and quadratic quantities. The numerical methods that have been used successfully for large-scale models of the atmosphere are usually further modified by the exclusion of external gravity waves from the system. This permits the use of a time step 50 to 100 times larger than is possible for the atmosphere. This is accomplished by requiring the total, vertically integrated flow to be divergence-free, in which case it is possible to specify the total transport by a stream function. The numerical time integration of an oceanic GCM formulated in this manner proceeds by a combination marching and jury process, in- volving the explicit prediction of 0,5 and V, and the iterative solution for the total transport stream function. Takano (1974) has recently introduced the implicit treatment of Rossby waves, which allows a con- siderably longer time step with little loss in accuracy for problems in which the emphasis is on low-frequency oceanic phenomena. Selected Climatic Simulations To illustrate the characteristic climatic performance of global oceanic GCMâs, we here present comparative solutions from the recent models of Takano et al. (1974), Cox (1974), and Alexander (1974). A number of characteristics of these models are given in Table B.2. These
APPENDIX B 225 TABLE B.2 Characteristics of Recent Global Ocean Circulation Models Feature UCLA * GFDL â Rand ° Number of levels 5 9 2 Horizontal spacing Ag=4° Ag=2° A¢gâ4° A\=2.5° Ax=2° A\= 5° Salinity No Yes No Depth 4km Actual 300 m Horizontal mixing¢ Ayu =10° Ayu=2x 10° Ay=7x 10° (cm? secâ) An=2.5x 10° An=10° An=5 X10" Initial condition Isothermal Observed T,s Observed T Time span of experiment 30 yr 2.5 yr 1.5 yr Upper boundary condi- Momentum flux, Momentum flux, Momentum flux, tion thermal forcing T,s specified heat flux @ Takano et al. (1974); see also Mintz and Arakawa (1974) and Takano (1974). >â Cox (1974); see also Bryan et al. (1974). ¢ Alexander (1974). ¢ Here A,, and A,, denote the eddy coefficients for momentum and heat, respectively. models are currently undergoing further development, and similar oceanic models are under construction at NCAR and at Giss. It is a general characteristic of all such oceanic models that the circulation is dominated by the large values of viscosity, and further efforts are re- quired to extend the solutions into the less viscous and more nonlinear range. Surface Current The annual surface current simulated by the nine-level GFDL model (Cox, 1974) is shown in Figure B.10, along with the observed currents for February and March. The February surface currents simulated by the five-level UCLA model (Takano et al., 1974) and the March 1 sur- face currents simulated by the two-level Rand model (Alexander, 1974) are similarly shown in Figures B.11 and B.12. In each case the overall pattern of the large-scale circulation is simulated successfully, although in general the strength of the equatorial and major western boundary currents is underpredicted. We may note, however, that the UCLA modelâs solution represents a 30-year integration, the GFDL solu- tion is for 2.5 years, and the Rand solution is for 1.5 years. Closer examination reveals that the simulated surface currents diverge from the equator somewhat more than do those observed, due to the modelsâ effective averaging over the depth of the surface Ekman layer.
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FIGURE B.10 The an nual average ocean surface current: (a) simulated by the nine-levei GFDL oceanic model (Cox, 1974); (b) observed (sche- matic) for FebruaryâMarch from Bryan et al. (1974), based on data of Sverdrup et al. (1942).
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236 UNDERSTANDING CLIMATIC CHANGE Sea-Surface Temperature The February sea-surface temperature simulated by the five-level UCLA model (Takano et al., 1974) is shown in Figure B.13, along with the observed distribution. To some extent the agreement of the simulation with observation is due to the use of observed components in the sur- face heat balance condition. The prediction of low surface temperatures at the equator, however, is a feature entirely due to the modelâs internal dynamics. Coupled OceanâAtmosphere Models As has been previously noted, a dynamical model adequate for the study of climatic variation should include the coupling of the ocean and atmosphere. The first attempt at such coupling was made by Manabe and Bryan (1969) for an idealized ocean basin and later extended by Wetherald and Manabe (1972). In such a joint model, the net fluxes of heat, moisture, and momentum at the air-sea interface are determined by the atmospheric model, while the ocean model in turn provides the sea-surface temperature as a lower boundary condition for the at- mosphere. These studies at GFDL have recently been extended to the entire world ocean, and the results of a coupled numerical integration are now available (Manabe et al., 1974a; Bryan et al., 1974). In this study, the nine-level GFDL atmospheric model was integrated for 0.85 of a year simulated time, while a twelve-layer*ocean model was integrated for 256 yearsâ time. The annual sea-surface temperatures simulated in this joint model are shown in Figure B.14, along with the observed distribu- tion. The general level of accuracy may be considered satisfactory, especially in view of the absence of any specification of observed quanti- ties at the air-sea interface. Much further development and testing of such coupled models is required so that their potential for the study of global climatic variations may be realized. REFERENCES Alexander, R. C., 1974: Ocean circulation and temperature prediction model, The Rand Corporation, Santa Monica, Calif. (in preparation). Alexander, R. C., and R. L. Mobley, 1974: Updated global monthly mean ocean surface temperatures, R-1310-ARPA, The Rand Corporation, Santa Monica, Calif. (in preparation). Arakawa, A., and Y. Mintz, 1974: The ucLa atmospheric general circulation model, Dept. of Meteorol., U. of Calif., Los Angeles, 403 pp.
APPENDIX B 237 Bryan, K., and M. D. Cox, 1967: A numerical investigation of the oceanic general circulation, Tellus, 19:54â-80. Bryan, K., and M. D. Cox, 1968: A nonlinear model of an ocean driven by wind and differential heating. Parts I and II, J. Atmos. Sci., 25:945-978. Bryan, K., S. Manabe, and R. C. Paconowski, 1974: Global oceanâatmosphere climate model. Part II. The oceanic circulation, Geophysical Fluid Dynamics Laboratory/NOAA, Princeton U., Princeton, N.J., 55 pp. J. Phys. Oceanog. (to be published). Budyko, M. I., 1956: Heat Balance of the Earthâs Surface, U.S. Weather Bureau, Washington, D.C., 259 pp. Budyko, M. I., 1969: The effect of solar radiation variations on the climate of the earth, Tellus, 21:611-619. Charney, J. G., and N. A. Phillips, 1953: Numerical integration of the quasigeo- strophic equations for barotropic and simple baroclinic flows, J. Meteorol., 10: 71-99. Charney, J. G., R. Fjortoft, and J. von Neumann, 1950: Numerical integration of the barotropic vorticity equation, Tellus, 2:237-â254. Clapp, P. F., 1964: Global cloud cover for seasons using TIROS nephanalysis, Mon. Wea. Rev., 92:495â507. Cox, M. D., 1970: A mathematical model of the Indian Ocean, Deep-Sea Res., 17:47-75. Cox, M. D., 1974: A baroclinic numerical model of the world ocean: preliminary results, in Numerical Models of the Ocean Circulation, Proceedings of Sym- posium Held at Durham, New Hampshire, October 17-20, 1972, National Acad- emy of Sciences, Washington, D.C. (in press). Crutcher, H. L., and J. M. Meserve, 1970: Selected level heights, temperatures and dew points for the Northern Hemisphere, NAVAIR 50â1C-52, Naval Weather Service, Washington, D.C., 370 pp. Environmental Technical Applications Center, U.S. Air Force, 1971: Northern Hemisphere Cloud Cover, Project 6168, Washington, D.C. (unpublished data). Friedrich, H. J., 1970: Preliminary results from a numerical multilayer model for the circulation of the North Atlantic, Dtsch. Hydrogr. Z., 23:145â-164. GARP, Joint Organizing Committee, 1974: Modelling for the first GARP global ex- periment, GARP Publications Series, No. 14, World Meteorological Organiza- tion, Geneva, 261 pp. Gates, W. L., 1972: The January global climate simulated by the two-level Mintz- Arakawa model: a comparison with observation, Râ1005-âarpa, The Rand Corporation, Santa Monica, Calif., 107 pp. (to be published). Gilbert, K. D., 1974: A review of numerical models of oceanic general circulation, The Rand Corporation, Santa Monica, Calif. (in preparation). Haltiner, G. J., 1971: Numerical Weather Prediction, Wiley, New York, 317 pp. Haney, R. L., 1974: A numerical study of the large-scale response of an ocean circulation to surface-heat and momentum flux, J. Phys. Oceanog. (to be pub- lished ). Heastie, H., and P. M. Stephenson, 1960: Upper winds over the world, Part I, H.M.S.O., London, Geophys. Mem. No. 103, 13(3). Holland, W. R., and A. D. Hirschman, 1972: A numerical calculation of the cir- culation in the North Atlantic ocean, J. Phys. Oceanog., 2:336-354. Kasahara, A., and W. M. Washington, 1971: General circulation experiments with
238 UNDERSTANDING CLIMATIC CHANGE a six-layer NCAR model, including orography, cloudiness and surface temperature calculation, J. Atmos Sci., 28:657-701. Lorenz, E. N., 1967: The Nature and Theory of the General Circulation of the Atmosphere, World Meteorological Organization, Geneva, 161 pp. Manabe, S., and K. Bryan, 1969: Climate calculations with a combined ocean- atmosphere model, J. Atmos. Sci., 26:786â789. Manabe, S., K. Bryan, and M. J. Spelman, 1974a: A global atmosphereâocean climate model. Part 1. The atmospheric circulation, Geophysical Fluid Dynamics Laboratory/Noaa, Princeton U., Princeton, N.J., 76 pp. (to be published). Manabe, S., D. G. Hahn, and J. L. Holloway, Jr., 1974b: The seasonal variation of the tropical circulation as simulated by a global model of the atmosphere, J. Atmos. Sci., 31:43-83. Mintz, Y., 1965: Very long-term global integration of the primitive equations of atmospheric motion, in WMo-1UGG Symposium on Research and Development Aspects of Long-range Forecasting, WMO Tech. Note No. 66, pp. 141-155. Mintz, Y., and A. Arakawa, 1974: The uCLa oceanic general circulation model, Dept. of Meteorol., U. of Calif., Los Angeles, 138 pp. Mintz, Y., A. Katayama, and A. Arakawa, 1972: Numerical simulation of the seasonally and inter-annually varying tropospheric circulation, in Proc. Survey Conf., CIAP, Department of Transportation, Cambridge, Mass., pp. 194-216. Ocean Affairs Board, 1974: Numerical Models of the Ocean Circulation, Proceed- ings of Symposium Held at Durham, New Hampshire, October 17-20, 1972, National Academy of Sciences, Washington, D.C. (in press). _ Phillips, N. A., 1956: The general circulation of the atmosphere: a numerical ex- periment, Q. J. R. Meteorol. Soc., 82:123-164. Robinson, G. D., 1971: Review of climate models, in Manâs Impact on the Cli- mate, W. H. Matthews, W. W. Kellogg, and G. D. Robinson, eds., MIT Press, Cambridge, Mass., pp. 205-215. Saltzman, B., and A. D. Vernekar, 1971: An equilibrium solution for the axially symmetric component of the earthâs macroclimate, J. Geophys. Res., 76:1498- 1524. Schneider, S. H., and R. E. Dickinson, 1974: Climate modeling, Rev. Geophys. Space Phys., 12:447-493. Schutz, C., and W. L. Gates, 1971: Global climatic data for surface, 800 mb: January, R-915âarpa, The Rand Corporation, Santa Monica, Calif., 173 pp. Sellers, W. D., 1973: A new global climatic model, J. Atmos. Sci., 12:241-â254. Smagorinsky, J., 1963: General circulation experiments with the primitive equa- tions: I. The basic experiment, Mon. Wea. Rev., 91:99-164. Smagorinsky, J., 1970: Numerical simulation of the global atmosphere, in The Global Circulation of the Atmosphere, G. A. Corby, ed., Royal Meteorol. Soc., London, pp. 24-41. Smagorinsky, J., 1974: Global atmospheric modeling and the numerical simulation of climate, in Weather Modification, W. N. Hess, ed., Wiley, New York (to be published ). Somerville, R. C. J., P. H. Stone, M. Halem, J. E. Hansen, J. S. Hogan, L. M. Druyan, G. Russell, A. A. Lacis, W. J. Quirk, and J. Tenenbaum, 1974: The Giss model of the global atmosphere, J. Atmos. Sci., 31:84â-117. Stommel, H., 1948: The westward intensification of wind-driven ocean currents, Trans. Am. Geophys. Union, 29:202-â206. Sverdrup, H. U., 1947: Wind-driven currents in a baroclinic ocean; with applica-
APPENDIX B 239 tion to the equatorial currents of the eastern Pacific, Proc. Nat. Acad. Sci., U.S., 33:318-326. Sverdrup, H. U., M. W. Johnson, and R. H. Fleming, 1942: The Oceans, Prentice- Hall, Englewood Cliffs, N.J., 1087 pp. Takano, K., 1974: A general circulation model for the world ocean, Dept. of Meteorol., U. of Calif., Los Angeles (unpublished report). Takano, K., Y. Mintz, and Y. J. Han, 1974: Numerical simulation of the season- ally varying baroclinic world ocean circulation, Dept. of Meteorol., U. of Calif., Los Angeles (unpublished). Taljaard, J. J.. H. Van Loon, H. L. Crutcher, and R. L. Jenne, 1969: Climate of the upper air: Southern Hemisphere, 1. Temperatures, dew points and heights at selected pressure levels, NAVAIR 50-1Câ55, Naval Weather Service, Washing- ton, D.C. Van Loon, H., 1972: Cloudiness and precipitation in the Southern Hemisphere, in Meteorology of the Southern Hemisphere, Meteorol. Monogr., 13, No. 35, Am. Meteorol. Soc., Boston, Mass., pp. 101-111. Vonder Haar, T. H., and A. H. Oort, 1973: New estimate of annual poleward energy transport by Northern Hemisphere oceans, J. Phys. Oceanog., 3:169-172. Washington, W. M., and L. G. Thiel, 1970: Digitized global monthly mean ocean surface temperatures, Tech. Note 54, National Center for Atmospheric Re- search, Boulder, Colo. Wetherald, R. T., and S. Manabe, 1972: Response of the joint oceanâatmosphere model to the seasonal variation of the solar radiation, Mon. Wea. Rev., 100: 42-59. Willson, M. A. G., 1973: Statistical-dynamical modelling of the atmosphere, Internal Scientific Report No. 17, Commonwealth Meteorol. Res. Centre, Mel- bourne, 53 pp.