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## Abstract

A numerical experiment with an atmospheric general model (GCM) indicate that moist convection in the equatorial region is spontaneously organized into a form of “supercluster” which is an area of precipitation with a spatial extent of about 2000 km and an eastward propagation speed of about 1 5 m s^{−1}.

In this article, the existence of superclusters in the real atmosphere is shown through a comparison between satellite observations and the GCM results. It is argued that eastward motion of convective activity occurs not only as the well-known property of the 30–60 day oscillation, but as a property of synoptic-scale disturbances at the equator.

## Abstract

A numerical experiment with an atmospheric general model (GCM) indicate that moist convection in the equatorial region is spontaneously organized into a form of “supercluster” which is an area of precipitation with a spatial extent of about 2000 km and an eastward propagation speed of about 1 5 m s^{−1}.

In this article, the existence of superclusters in the real atmosphere is shown through a comparison between satellite observations and the GCM results. It is argued that eastward motion of convective activity occurs not only as the well-known property of the 30–60 day oscillation, but as a property of synoptic-scale disturbances at the equator.

## Abstract

The cumulus model presented by Lindzen et al. for calculating one-dimensional radiative convective equilibria is examined. When only the balance of moist static energy is considered, the value of the convective mass flux *M _{c}* is required to be externally specified. Dependency of equilibrium solutions on

*M*shows that an upper limit of the value of

_{c}*M*exists above which the temperature in the region of upward motion is lower than that in the region of downward motion; that is, the buoyancy is negative. Lindzen et al. tried to specify the value of

_{c}*M*by introducing the surface heat fluxes. However, it is found that the buoyancy of their solution is negative.

_{c}In order to obtain an appropriate equilibrium solution where the buoyancy is positive, the balance of kinetic energy, especially the dissipative process, should be considered. It is found that the value of *M _{c}*, which gives a realistic value of the dissipation rate, is close to the upper limit. In order to have a solution with a more realistic temperature profile, the model assumption that

*M*is independent of time and height should be released.

_{c}Calculations on the greenhouse effect show that dependency of *M _{c}* on the total optical thickness changes sign within the range of the observed dissipation rate. The water vapor content at the tropopause becomes larger as the total optical thickness increases.

## Abstract

The cumulus model presented by Lindzen et al. for calculating one-dimensional radiative convective equilibria is examined. When only the balance of moist static energy is considered, the value of the convective mass flux *M _{c}* is required to be externally specified. Dependency of equilibrium solutions on

*M*shows that an upper limit of the value of

_{c}*M*exists above which the temperature in the region of upward motion is lower than that in the region of downward motion; that is, the buoyancy is negative. Lindzen et al. tried to specify the value of

_{c}*M*by introducing the surface heat fluxes. However, it is found that the buoyancy of their solution is negative.

_{c}In order to obtain an appropriate equilibrium solution where the buoyancy is positive, the balance of kinetic energy, especially the dissipative process, should be considered. It is found that the value of *M _{c}*, which gives a realistic value of the dissipation rate, is close to the upper limit. In order to have a solution with a more realistic temperature profile, the model assumption that

*M*is independent of time and height should be released.

_{c}Calculations on the greenhouse effect show that dependency of *M _{c}* on the total optical thickness changes sign within the range of the observed dissipation rate. The water vapor content at the tropopause becomes larger as the total optical thickness increases.

## Abstract

A series of numerical experiments on two-dimensional decaying turbulence is performed for a barotropic fluid on a rotating sphere. Numerical calculations have confirmed two important asymptotic features: emergence of the banded structure of zonal flows and their extreme latitudinal inhomogeneities in which kinetic energy is accumulated into the easterly circumpolar jets. The banded structure of zonal flows is established relatively early on in the initial stage. Later, after extended periods of time integration, only the circumpolar jets are intensified gradually, while there is no further evolution in the banded structure in the low and midlatitudes. Wave activity flux analysis illustrates that the initial vortices in the low and midlatitudes propagate poleward as Rossby waves and converge to produce easterly circumpolar flows. In association with this convergence, accumulation of the mean zonal component of kinetic energy proceeds. The tendency for the accumulation becomes strong as the rotation rate is increased, and nearly all of the kinetic energy is concentrated to the circumpolar flows in cases of rapid rotation.

A theoretical model is constructed under the assumption that a circumpolar jet emerges around the latitude where the local Rhines scale is equal to the distance from the Pole, and that initial vortices at the lower latitudes contribute to the generation of the jets. The model describes the mean zonal component of kinetic energy and the averaged speed and width of the circumpolar jets as functions of the rotation rate, which agree satisfactorily with the numerical results.

## Abstract

A series of numerical experiments on two-dimensional decaying turbulence is performed for a barotropic fluid on a rotating sphere. Numerical calculations have confirmed two important asymptotic features: emergence of the banded structure of zonal flows and their extreme latitudinal inhomogeneities in which kinetic energy is accumulated into the easterly circumpolar jets. The banded structure of zonal flows is established relatively early on in the initial stage. Later, after extended periods of time integration, only the circumpolar jets are intensified gradually, while there is no further evolution in the banded structure in the low and midlatitudes. Wave activity flux analysis illustrates that the initial vortices in the low and midlatitudes propagate poleward as Rossby waves and converge to produce easterly circumpolar flows. In association with this convergence, accumulation of the mean zonal component of kinetic energy proceeds. The tendency for the accumulation becomes strong as the rotation rate is increased, and nearly all of the kinetic energy is concentrated to the circumpolar flows in cases of rapid rotation.

A theoretical model is constructed under the assumption that a circumpolar jet emerges around the latitude where the local Rhines scale is equal to the distance from the Pole, and that initial vortices at the lower latitudes contribute to the generation of the jets. The model describes the mean zonal component of kinetic energy and the averaged speed and width of the circumpolar jets as functions of the rotation rate, which agree satisfactorily with the numerical results.

## Abstract

A simple one-dimensional radiative–convective equilibrium model is used to investigate the relationship between the surface temperature and the outgoing infrared radiation at the top of the atmosphere. The model atmosphere has a gray infrared absorption coefficient and is composed of a radiative equilibrium stratosphere and a moist adiabat troposphere.

An upper limit of the outgoing infrared radiation is found to exist. The existence of the upper limit is characterized by the radiation limits that appear when the optical depth of the entire atmosphere becomes sufficiently deep and the temperature structure around the levels where the optical depth is about unity approaches a fixed profile. This appearance of an upper limit differs from that found by Komabayashi and Ingersoll, which is obtained from the constraint of the stratospheric radiation balance.

As one of those radiation limits, the outgoing infrared radiation has an asymptotic limit as the surface temperature increases. This is caused by the tropospheric structure approaching the water vapor saturation curve. It is considered that the asymptotic limits appearing in the radiatively and thermodynamically more complicated models utilized by Abe and Matsui and Kasting are corresponding to this asymptotic limit indicated in our model.

## Abstract

A simple one-dimensional radiative–convective equilibrium model is used to investigate the relationship between the surface temperature and the outgoing infrared radiation at the top of the atmosphere. The model atmosphere has a gray infrared absorption coefficient and is composed of a radiative equilibrium stratosphere and a moist adiabat troposphere.

An upper limit of the outgoing infrared radiation is found to exist. The existence of the upper limit is characterized by the radiation limits that appear when the optical depth of the entire atmosphere becomes sufficiently deep and the temperature structure around the levels where the optical depth is about unity approaches a fixed profile. This appearance of an upper limit differs from that found by Komabayashi and Ingersoll, which is obtained from the constraint of the stratospheric radiation balance.

As one of those radiation limits, the outgoing infrared radiation has an asymptotic limit as the surface temperature increases. This is caused by the tropospheric structure approaching the water vapor saturation curve. It is considered that the asymptotic limits appearing in the radiatively and thermodynamically more complicated models utilized by Abe and Matsui and Kasting are corresponding to this asymptotic limit indicated in our model.

## Abstract

A numerical study on the runaway greenhouse state is performed by using a general circulation model (GCM) with simplified hydrologic and radiative processes. Except for the inclusion of three-dimensional atmospheric motion, the system utilized is basically equivalent to the one-dimensional radiative–convective equilibrium model of Nakajima et al. in which the runaway greenhouse state is defined.

The results of integrations with various values of solar constant show that there exists an upper limit of the solar constant with which the atmosphere can reach a statistical equilibrium state. When the value of solar constant exceeds the limit, 1600 W m^{−2}, the atmosphere sets in a “thermally runaway” state. It is characterized by continuous increase of the amount of water vapor, continuous decrease of the outgoing longwave radiation, and continuous warming of the atmosphere and the ground surface.

The upper-limit value of the solar constant obtained by the GCM experiments corresponds to the upper limit of outgoing longwave radiation determined by the one-dimensional model of Nakajima et al. with a fixed value of relative humidity, 60%, which is a typical value obtained by the GCM. The thermally runaway states realized in the GCM are caused by the radiation structure found by Nakajima et al. that prohibits the existence of thermal equilibrium states. The calculated values of the upper limit of radiation and water vapor content cannot be directly applied to describing real planetary atmospheres, since the model physical processes are quite simple—gray radiation scheme without clouds. However, because of this simplification, the GCM gives deeper insight into the structure of a runaway atmosphere.

## Abstract

A numerical study on the runaway greenhouse state is performed by using a general circulation model (GCM) with simplified hydrologic and radiative processes. Except for the inclusion of three-dimensional atmospheric motion, the system utilized is basically equivalent to the one-dimensional radiative–convective equilibrium model of Nakajima et al. in which the runaway greenhouse state is defined.

The results of integrations with various values of solar constant show that there exists an upper limit of the solar constant with which the atmosphere can reach a statistical equilibrium state. When the value of solar constant exceeds the limit, 1600 W m^{−2}, the atmosphere sets in a “thermally runaway” state. It is characterized by continuous increase of the amount of water vapor, continuous decrease of the outgoing longwave radiation, and continuous warming of the atmosphere and the ground surface.

The upper-limit value of the solar constant obtained by the GCM experiments corresponds to the upper limit of outgoing longwave radiation determined by the one-dimensional model of Nakajima et al. with a fixed value of relative humidity, 60%, which is a typical value obtained by the GCM. The thermally runaway states realized in the GCM are caused by the radiation structure found by Nakajima et al. that prohibits the existence of thermal equilibrium states. The calculated values of the upper limit of radiation and water vapor content cannot be directly applied to describing real planetary atmospheres, since the model physical processes are quite simple—gray radiation scheme without clouds. However, because of this simplification, the GCM gives deeper insight into the structure of a runaway atmosphere.

## Abstract

Jet formation in decaying two-dimensional turbulence on a rotating sphere is reviewed from the viewpoint of Rossby waves. A series of calculations are performed to confirm the behavior of zonal mean flow generation on the parameter space of the rotation rate Ω and Froude number Fr. When the flow is nondivergent and Ω is large, intense easterly circumpolar jets tend to emerge in addition to the appearance of a banded structure of zonal mean flows with alternating flow directions. When the system allows surface elevation, circumpolar jets disappear and an equatorial easterly jet emerges with increasing Fr. The appearance of the intense easterly jets can be understood by the angular-momentum transport associated with the generation, propagation, and absorption of Rossby waves. When the flow is nondivergent, long Rossby waves tend to be absorbed near the poles. In contrast, when Fr is large, Rossby waves can hardly propagate poleward and tend to be absorbed near the equator.

## Abstract

Jet formation in decaying two-dimensional turbulence on a rotating sphere is reviewed from the viewpoint of Rossby waves. A series of calculations are performed to confirm the behavior of zonal mean flow generation on the parameter space of the rotation rate Ω and Froude number Fr. When the flow is nondivergent and Ω is large, intense easterly circumpolar jets tend to emerge in addition to the appearance of a banded structure of zonal mean flows with alternating flow directions. When the system allows surface elevation, circumpolar jets disappear and an equatorial easterly jet emerges with increasing Fr. The appearance of the intense easterly jets can be understood by the angular-momentum transport associated with the generation, propagation, and absorption of Rossby waves. When the flow is nondivergent, long Rossby waves tend to be absorbed near the poles. In contrast, when Fr is large, Rossby waves can hardly propagate poleward and tend to be absorbed near the equator.

## Abstract

Cloud convection of a CO_{2} atmosphere where the major constituent condenses is numerically investigated under a setup idealizing a possible warm atmosphere of early Mars, utilizing a two-dimensional cloud-resolving model forced by a fixed cooling profile as a substitute for a radiative process. The authors compare two cases with different critical saturation ratios as condensation criteria and also examine sensitivity to number mixing ratio of condensed particles given externally.

When supersaturation is not necessary for condensation, the entire horizontal domain above the condensation level is continuously covered by clouds irrespective of number mixing ratio of condensed particles. Horizontal-mean cloud mass density decreases exponentially with height. The circulations below and above the condensation level are dominated by dry cellular convection and buoyancy waves, respectively.

When 1.35 is adopted as the critical saturation ratio, clouds appear exclusively as intense, short-lived, quasi-periodic events. Clouds start just above the condensation level and develop upward, but intense updrafts exist only around the cloud top; they do not extend to the bottom of the condensation layer. The cloud layer is rapidly warmed by latent heat during the cloud events, and then the layer is slowly cooled by the specified thermal forcing, and supersaturation gradually develops leading to the next cloud event. The periodic appearance of cloud events does not occur when number mixing ratio of condensed particles is large.

## Abstract

Cloud convection of a CO_{2} atmosphere where the major constituent condenses is numerically investigated under a setup idealizing a possible warm atmosphere of early Mars, utilizing a two-dimensional cloud-resolving model forced by a fixed cooling profile as a substitute for a radiative process. The authors compare two cases with different critical saturation ratios as condensation criteria and also examine sensitivity to number mixing ratio of condensed particles given externally.

When supersaturation is not necessary for condensation, the entire horizontal domain above the condensation level is continuously covered by clouds irrespective of number mixing ratio of condensed particles. Horizontal-mean cloud mass density decreases exponentially with height. The circulations below and above the condensation level are dominated by dry cellular convection and buoyancy waves, respectively.

When 1.35 is adopted as the critical saturation ratio, clouds appear exclusively as intense, short-lived, quasi-periodic events. Clouds start just above the condensation level and develop upward, but intense updrafts exist only around the cloud top; they do not extend to the bottom of the condensation layer. The cloud layer is rapidly warmed by latent heat during the cloud events, and then the layer is slowly cooled by the specified thermal forcing, and supersaturation gradually develops leading to the next cloud event. The periodic appearance of cloud events does not occur when number mixing ratio of condensed particles is large.