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The primitive equations of motion in spherical coordinates are integrated with respect to time on global grids with mean horizontal resolutions of 500 and 250 km. There are nine levels in the models from 80 m to 28 km above the ground. The models have realistic continents with smoothed topography and an ocean surface with February water temperatures prescribed. The insolation is for a Northern Hemisphere winter. In addition to wind, temperature, pressure, and water vapor, the models simulate precipitation, evaporation, soil moisture, snow depth, and runoff. The models were run long enough beyond a state of quasi-equilibrium for meaningful statistics to be obtained. Time means of meteorological and hydrological quantities computed by the models compare favorably with observed climatic means. For example, the thermal structure of the model atmosphere is very similar to that of the actual atmosphere except in the Northern Hemisphere stratosphere; and the simulated distributions of the major arid regions over continents and the distributions of the rain belts, both in the Tropics and in middle latitudes, are successfully simulated by the models described in this paper. The increase in the horizontal computational resolution improved the distributions of mean surface pressure and precipitation rate in particular.

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Based on the box method, finite-difference versions of a system of primitive equations in spherical coordinates are formulated for a spherical grid. Non-linear computational instability cannot occur in time integrations of these equations. Conservation of total mass is guaranteed by the finite-difference form of the continuity equation. The proposed scheme yields no fictitious sources of energy in the derivation of the difference formula for the budget of the total energy over the entire domain. The finite-difference equations for the budget of the relative and absolute angular momentum are not exact analogs of the continuous forms but nevertheless are very accurate.

This system of primitive equations for a nine-level general circulation model of the atmosphere has been numerically integrated for 50 forecast days. The network of grid points covers the entire globe with nearly uniform spacing and has no artificial horizontal boundaries. The initial data were latitude-height-dependent zonal mean winds and pressures and zonal mean temperatures perturbed slightly by random numbers. The time integration was carried out without any finite-difference computational problems and baroclinic waves developed and propagated.

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A simple, free-surface, barotropic model and a nine-level, baroclinic model are numerically time integrated on both latitude-longitude grids and on Kurihara-type grids to compare the results obtained from the two grid systems. The prognostic variables are Fourier space-filtered in the longitudinal direction on the latitude-longitude grids to permit the use of the same time-step length on both grids.

With respect to geopotential height and zonal wind distributions and to the phase speed of wave propagation, the results from the barotropic model, time-integrated on a sector latitude-longitude grid, agree better with a high-resolution control run than those computed on a modified Kurihara grid, particularly at high latitudes. The barotropic model is also time-integrated on a hemispheric, latitude-longitude grid, and the results compare well with a high-resolution control. The latter comparison is performed on initial data having strong cross-polar flow.

The mean sea-level pressure distribution obtained from a 64-day time integration of the baroclinic model on a global, latitude-longitude grid is better than that derived from a similar model using a Kurihara grid of comparable resolution. For example, the tendency for the Kurihara grid model to predict excessive pressures in the north polar region is for the most part corrected by use of the latitude-longitude grid.

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The “primitive equations of motion” are adopted for this study. The nine levels of the model are distributed so as to resolve surface boundary layer fluxes as well as radiative transfer by ozone, carbon dioxide, and water vapor. The lower boundary is a kinematically uniform land surface without any heat capacity. The stabilizing effect of moist convection is implicitly incorporated into the model by requiring an adjustment of the lapse rate whenever it exceeds the moist adiabatic value. The numerical integrations are performed for the mean annual conditions over a hemisphere starting with an isothermal atmosphere at rest. The spatial distribution of gaseous absorbers is assumed to have the annual mean value of the actual atmosphere and to be constant with time.

A quasi-equilibrium is attained about which a cyclic energy variation occurs with an irregular period of about 2 weeks. The dominant wave number of the meridional component of the wind is 5 to 6 in the troposphere but is reduced to about 3 in the stratosphere. The gross structure and behavior of the tropopause and stratosphere below 30 km. agree reasonably well with observation. The meridional circulation obtained from the computation has a 3-cell structure in the troposphere and tends toward a 2-cell structure with increasing altitude in the stratosphere. Although the level of the jet stream as well as that of the maximum northward transport of momentum coincides with observation, the intensity of the jet stream turns out to be much stronger than the observed annual mean. In the stratosphere the temperature increases with increasing latitude because of the effect of large-scale motion. The magnitude of the increase, however, is smaller than that observed.

A detailed study of the vertical distribution of the budget of kinetic energy, of available potential energy, of heat, and of angular momentum is made. The mechanism for maintaining the kinetic energy of the jet stream and of the stratosphere is discussed. It is concluded that in the model the kinetic energy in the stratosphere is maintained against its conversion into potential energy and dissipation through interaction with the troposphere, which is in qualitative agreement with the results derived from an analysis of the actual atmosphere. In the troposphere, the conversion of potential energy reaches a maximum at about the 500-mb. level. This energy is then transferred to the level of the jet stream and to the surface boundary layer by the so-called pressure interaction term, thus providing the source of kinetic energy for these two levels at which dissipation is predominant. As with the results of Phillips [27] and Smagorinsky [37], the ratio of eddy kinetic energy to zonal kinetic energy and that of eddy to zonal available potential energy are computed to be much smaller than those of the actual atmosphere.

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Syukuro Manabe, J. Leith Holloway Jr., and Hugh M. Stone


An analysis is made of the structure and energetics of the tropical circulation which emerged from a numerical time integration of a global circulation model with realistic orography.

Near the earth's surface, the general features of the time mean flow field and the location of the inter-tropical convergence zone of the model compare favorably with those of the actual atmosphere. Along the convergence zone or shear line, disturbances with a characteristic scale of 2000–3000 km develop and cause heavy precipitation. They tend to develop in the geographical areas where the formation of actual tropical storms is most probable. In the upper troposphere of the model tropics, disturbances with planetary scale develop and are responsible for the maximum of eddy kinetic energy there.

In general, both the kinetic energy of the tropical cyclones and that of the planetary-scale disturbances in the model tropics are chiefly maintained by the conversion of available potential energy generated by the heat of condensation. However, the planetary-scale disturbances in the upper troposphere of the tropics seem to be also affected by various factors such as the interaction with higher latitudes and land–sea contrast. It is noteworthy that these disturbances transport angular momentum across the equator in the upper troposphere and strongly affect the budget of angular momentum in the model tropics.

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Syukuro Manabe, Douglas G. Hahn, and J. Leith Holloway Jr.


A mathematical model of the atmosphere with a seasonal variation of insulation and sea surface temperatures is integrated numerically with respect to time over three model years. The model has a global computational domain and a realistic distribution of mountains. It contains a highly idealized parameterization of convection, i.e., dry and moist convective adjustment.

It is found that the model accurately simulates the seasonal variation of the location of the tropical rainbelt as well as that of the flow field associated with it. Over the continental regions of the model, the tropical rainbelt tends to form very close to the equator, whereas, in certain oceanic regions, it has a tendency to form away from the equator. Based upon a comparison of these results with those of another numerical experiment, it is concluded that this tendency is not due to an inherent characteristic of the rainbelt of the model to avoid the equator in oceanic regions, but rather it is due to the equatorial belt of low sea surface temperatures which is not favorable for the formation of a rainbelt. Over the sea, the surface temperature distribution seems to be the primary factor in determining the location of the rainbelt and accompanying tropical disturbances.

The primary source of kinetic energy of the disturbances in the model tropics is the conversion of eddy available potential energy which is generated by the effects of moist convection. A secondary source is the energy supplied from middle latitudes through pressure interaction. This effect has a significant magnitude in the subtropics of the model. The belt of maximum eddy conversion moves from one summer hemisphere to the other with respect to season in a manner similar to the tropical rainbelt. On the other hand, the contribution of pressure interaction to the production of eddy kinetic energy is significant in the winter hemisphere and thus supplements the contribution of eddy conversion. In general, the rate of eddy conversion due to transient eddies is particularly large in areas of relatively warm sea surface temperatures, where the tropical rainbelt and its accompanying disturbances predominate.

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III. Effects of Increased Horizontal Computational Resolution



The results of a numerical time integration of a hemispheric general circulation model of the atmosphere with moist processes and a uniform earth's surface has already been published by Manabe, Smagorinsky, and Strickler. In this study, the integration is repeated after halving the midlatitude grid size from approximately 500 to 250 km.

This increase in the resolution of the horizontal finite differences markedly improves the features of the model atmosphere. For example, the system of fronts and the associated cyclone families in the high resolution atmosphere is much more realistic than that in the low resolution atmosphere. Furthermore, the general magnitude and the spectral distribution of eddy kinetic energy are in better agreement with the actual atmosphere as a result of the improvement in resolution.

In order to explain these improvements, an extensive analysis of the energetics of both the low and high resolution atmospheric models is carried out. It is shown that these improvements are due not only to the increase of the accuracy of the finite differences but also to the shift in the scale of dissipation by the nonlinear lateral viscosity toward a smaller scale resulting from the decrease in grid size. In the low resolution atmospheric model, the transfer of energy from eddy to zonal kinetic energy is missing because of excessive subgrid scale dissipation at medium wave numbers, whereas it has significant magnitude in the high resolution atmospheric model. It is speculated that further increase of resolution should improve the results because it tends to separate the characteristic scale of dissipation from that of the source of eddy kinetic energy.

The analysis of the energetics in wave number space clearly demonstrates the differences between the energetics of the different parts of the atmosphere. In middle latitudes there are essential differences between the energetics of the model troposphere and that of the model stratosphere. In the model troposphere, the eddy kinetic energy is produced by the conversion of eddy potential energy in the range of wave numbers from 2 to 8. Part of the energy thus produced is dissipated by the subgrid scale dissipation, and most of the remainder is decascaded to zonal kinetic energy. In the model stratosphere, where very long waves predominate, the eddy kinetic energy is generated in the range of wave numbers from 2 to 3 by the energy supplied from the troposphere. Most of this energy is then decascaded barotropically to zonal kinetic energy.

In the Tropics, eddy kinetic energy is mainly produced by the release of eddy available potential energy generated by the heat of condensation. Although the rate of conversion is maximum at very low wave numbers, the conversion spectrum extends to very high wave numbers.

A box diagram of the energetics of the high resolution moist model shows that the eddy available potential energy is generated by the heat of condensation as well as by energy transfer from the zonal available potential energy. Furthermore, it is noteworthy that the zonal kinetic energy is maintained not only by the barotropic exchange from the eddy kinetic energy but also from the conversions of zonal potential energy. The intensification of the direct tropical cell and the weakening of the indirect Ferrel cell in middle latitudes caused by the moist processes are responsible for this positive zonal conversion.

One of the highlights of the results from the integration of the high resolution moist model is the successful simulation of the evolution of fronts and the associated cyclone families. The influence of moist processes upon frontal structure as well as other synoptic features is investigated by comparing the moist model atmosphere with the dry model atmosphere without the effect of the selective heating of condensation. It is found that the heat of condensation significantly reduces the width of fronts and the characteristic scale of cyclones in the lower troposphere.

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