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Joseph Smagorinsky

The past 20 years have encompassed remarkable scientific and technical advances in the atmospheric and oceanic sciences which herald a new era for deterministically predicting atmospheric behavior. Many of the key innovations were directly influenced, if not originated by Harry Wexler during his very productive career. This paper will deal with a critique of recent progress in modelling the atmosphere-ocean system, some of the newly exposed problems, and the needs and expectations for the future.

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Joseph Smagorinsky
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SYUKURO MANABE
and
JOSEPH SMAGORINSKY

Abstract

The thermal and dynamical structure of the tropical atmosphere which emerged from the numerical integration of our general circulation model with a simple hydrologic cycle is analyzed in detail.

According to the results of our analysis, the lapse rate of zonal mean temperature in the model Tropics is super-moist-adiabatic in the lower troposphere, and is sub-moist-adiabatic above the 400-mb. level in qualitative agreement with the observed features in the actual Tropics. The flow field in the model Tropics also displays interesting features. For example, a zone of strong convergence and a belt of heavy rain develops around the equator. Synoptic-scale disturbances such as weak tropical cyclones and shear lines with strong convergence develop and are reminiscent of disturbances in the actual tropical atmosphere. The humid towers, which result from moist convective adjustment and condensation, develop in the central core of the regions of strong upward motion, sometimes reaching the level of the tropical tropopause and thus heating the upper tropical troposphere. This heating compensates for the cooling due to radiation and the meridional circulation.

According to the analysis of the energy budget of the model Tropics, the release of eddy available potential energy, which is mainly generated by the heat of condensation, constitutes the major source of eddy kinetic energy of disturbances prevailing in the model Tropics.

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JOSEPH SMAGORINSKY
,
SYUKURO MANABE
, and
J. LEITH HOLLOWAY Jr.

Abstract

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
,
JOSEPH SMAGORINSKY
, and
ROBERT F. STRICKLER

Abstract

A numerical experiment with a general circulation model with a simple hydrologic cycle is performed. The basic framework of this model is identical with that adopted for the previous study [35] except for the incorporation of a simplified hydrologic cycle which consists of the advection of water vapor by large-scale motion, evaporation from the surface, precipitation and an artificial adjustment to simulate the process of moist convection. This adjustment is performed only when the relative humidity reaches 100 percent and the lapse rate exceeds the moist adiabatic lapse rate. The radiative flux is computed for the climatological distribution of water vapor instead of using the distribution calculated by the prognostic equation of water vapor. A completely wet surface without any heat capacity is chosen as the lower boundary. The initial conditions consist of a completely dry and isothermal atmosphere. A state of quasi-equilibrium is obtained as a result of the time integration of 187 days. A preliminary analysis of the result is performed for the 40-day period from 148th day to 187th day.

According to this analysis, the hemispheric mean of the rate of precipitation is about 1.06 m./yr. which is close to the estimate of the annual mean rainfall obtained by Budyko [5]. In the Tropics rainfall exceeds evaporation and in the subtropics the latter exceeds the former in qualitative agreement with observation. The difference between them, however, is too exaggerated, and an extremely large export of water vapor from the dry subtropics into the wet, Tropics by the meridional circulation takes place. In the troposphere, relative humidity increases with decreasing altitude. In the stratosphere it is very low except at the tropical tropopause, and the mixing ratio of water vapor is extremely small in qualitative agreement with observation. Although water vapor is transported from the troposphere into the stratosphere, it is then transported toward low latitudes and condenses at the tropical tropopause where the temperature is very low and the relative humidity is high.

Based upon a harmonic analysis of the flow field and the surface pressure field, it, is concluded that the effect of condensation tends to increase the wave number of the tropospheric flow and surface pressure field. Also, the incorporation of the moist process in the model seems to increase the intensity of meridional circulation in the Tropics. As a result of this increase, the transport of momentum and heat by the meridional circulation in the Tropics is much larger than that obtained from the previous study. In middle latitudes, the poleward transport of total energy in the moist-model atmosphere is less than that in the dry-model atmosphere because of the effect of the poleward transport of Intent energy or the heat of condensation.

The latitudinal distributions of radiative fluxes at the top of the atmosphere and at the earth's surface coincide very well with those obtained by London [17] for the actual atmosphere. Bowen's ratio increases with increasing latitude and its magnitude coincides reasonably well with that obtained by Budyko [5] or Jacobs [11] for the ocean surface.

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SIMULATED CLIMATOLOGY OF A GENERAL CIRCULATION MODEL WITH A HYDROLOGIC CYCLE

III. Effects of Increased Horizontal Computational Resolution

SYUKURO MANABE
,
JOSEPH SMAGORINSKY
,
J. LEITH HOLLOWAY JR.
, and
HUGH M. STONE

Abstract

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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