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- Author or Editor: Mao-Sung Yao x

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## Abstract

The maintenance of the quasi-stationary waves obtained through numerically integrating a two-level quasi-geostrophic spectral model on a β-plane is studied. An idealized topography which has only wave-number *n* in the zonal direction and the first mode in the meridional direction is used to force the quasi-stationary waves. However, the model's motion contains wavenumbers 0, *n* and 2*n* in the zonal direction, while the first three modes in the meridional direction are allowed for each wave. The cases *n* = 2 and *n* = 3 are considered.

The mechanism for maintaining the quasi-stationary waves is investigated by varying the imposed thermal equilibrium temperature gradient, Δ*T _{e}*, and the reciprocal of the internal frictional coefficient, 0.5

*k*

_{I}^{−1}. If the flow is not highly irregular, the available potential energy of quasi-stationary waves (

*A*) is maintained by the energy conversion

_{s}*A*→

_{z}*A*, where

_{S}*A*is the available potential energy of the time-averaged zonal mean flow. For

_{z}*n*= 3 and moderately large Δ

*T*and

_{e}*k*

_{I}^{−1}, the kinetic energy of these waves (

*K*) is maintained by the energy conversion

_{s}*A*→

_{s}*K*. If Δ

_{s}*T*, or

_{e}*k*

_{I}^{−1}is smaller while

*n*=3, kinetic energy is supplied to the quasi-stationary waves by the energy conversion

*K*→

_{z}*K*through the topographic forcing, where

_{s}*K*is the kinetic energy of the time-averaged zonal mean flow. The latter mechanism also maintains the kinetic energy of the quasi-stationary waves for

_{z}*n*=2 with relatively small Δ

*T*and

_{e}*k*

_{I}^{−1}is sufficiently large, the flow is highly irregular and a unique regime cannot be defined for either

*n*= 2 or

*n*= 3.

In the case of *n* = 3 and moderately large Δ*T _{e}* and

*k*

_{I}^{−1}, the energy cycle, spectra and form of the quasi-stationary waves suggest that the quasi-stationary waves are largely baroclinic waves which draw their energy from the forced waves.

## Abstract

The maintenance of the quasi-stationary waves obtained through numerically integrating a two-level quasi-geostrophic spectral model on a β-plane is studied. An idealized topography which has only wave-number *n* in the zonal direction and the first mode in the meridional direction is used to force the quasi-stationary waves. However, the model's motion contains wavenumbers 0, *n* and 2*n* in the zonal direction, while the first three modes in the meridional direction are allowed for each wave. The cases *n* = 2 and *n* = 3 are considered.

The mechanism for maintaining the quasi-stationary waves is investigated by varying the imposed thermal equilibrium temperature gradient, Δ*T _{e}*, and the reciprocal of the internal frictional coefficient, 0.5

*k*

_{I}^{−1}. If the flow is not highly irregular, the available potential energy of quasi-stationary waves (

*A*) is maintained by the energy conversion

_{s}*A*→

_{z}*A*, where

_{S}*A*is the available potential energy of the time-averaged zonal mean flow. For

_{z}*n*= 3 and moderately large Δ

*T*and

_{e}*k*

_{I}^{−1}, the kinetic energy of these waves (

*K*) is maintained by the energy conversion

_{s}*A*→

_{s}*K*. If Δ

_{s}*T*, or

_{e}*k*

_{I}^{−1}is smaller while

*n*=3, kinetic energy is supplied to the quasi-stationary waves by the energy conversion

*K*→

_{z}*K*through the topographic forcing, where

_{s}*K*is the kinetic energy of the time-averaged zonal mean flow. The latter mechanism also maintains the kinetic energy of the quasi-stationary waves for

_{z}*n*=2 with relatively small Δ

*T*and

_{e}*k*

_{I}^{−1}is sufficiently large, the flow is highly irregular and a unique regime cannot be defined for either

*n*= 2 or

*n*= 3.

In the case of *n* = 3 and moderately large Δ*T _{e}* and

*k*

_{I}^{−1}, the energy cycle, spectra and form of the quasi-stationary waves suggest that the quasi-stationary waves are largely baroclinic waves which draw their energy from the forced waves.

## Abstract

The effect of eddy momentum fluxes on the general circulation is investigated with the aid of perpetual January simulations with a two-dimensional, zonally averaged model. Sensitivity experiments with this model show that the vertical eddy flux has a negligible effect on the general circulation, while the meridional eddy flux has a substantial effect. The experiments on the effect of the mefidional eddy flux essentially confirm the resultsfound by Schneider in a similar (but not identical) set of sensitivity experiments, and, in addition, show that the vertical structure of the mefidional eddy flux has a relatively small effect on the general circulation.

In order to parameterize the vertically integrated mefidional eddy momentum flux, we take Green's parameterization of this quantity and generalize it to allow for the effects of condensation. In order to do this, it is necessary to use Leovy's approximation for the eddy fluctuations in specific humidity. With this approximation the equivalent potential vorticity defined by Saltzman is conserved even when condensation occurs. Leovy's approximation also allows one to generalize the relation between quasi-geostrophic potential vorticity and theEliassen-Palm flux by replacing the potential vorticity and potential temperature by the corresponding equivalent quantities. Thus, the eddy momentum flux can be related to the eddy fluxes of two conserved quantities even when condensation is present. The eddy fluxes of the two conserved quantities are parametefized by mixing-length expressions, with the mixing coefficient taken to be the sum of Branscome's mixing coefficient, plus a correction which allows for nonlinear effects onthe eddy structure and ensures global momentum conservation.

The parametefization of the mefidional eddy transport is tested in another perpetual January simulation with the two-dimensional averaged model. The results are compared with a parallel three-dimensional simulation which calculates the eddy transport explicitly. The parameterization reproduces the latitudinal and seasonal (interhemisphefic) variations and the magnitude of the eddy transport calculated in the three-dimensional simulation reasonably well.

## Abstract

The effect of eddy momentum fluxes on the general circulation is investigated with the aid of perpetual January simulations with a two-dimensional, zonally averaged model. Sensitivity experiments with this model show that the vertical eddy flux has a negligible effect on the general circulation, while the meridional eddy flux has a substantial effect. The experiments on the effect of the mefidional eddy flux essentially confirm the resultsfound by Schneider in a similar (but not identical) set of sensitivity experiments, and, in addition, show that the vertical structure of the mefidional eddy flux has a relatively small effect on the general circulation.

In order to parameterize the vertically integrated mefidional eddy momentum flux, we take Green's parameterization of this quantity and generalize it to allow for the effects of condensation. In order to do this, it is necessary to use Leovy's approximation for the eddy fluctuations in specific humidity. With this approximation the equivalent potential vorticity defined by Saltzman is conserved even when condensation occurs. Leovy's approximation also allows one to generalize the relation between quasi-geostrophic potential vorticity and theEliassen-Palm flux by replacing the potential vorticity and potential temperature by the corresponding equivalent quantities. Thus, the eddy momentum flux can be related to the eddy fluxes of two conserved quantities even when condensation is present. The eddy fluxes of the two conserved quantities are parametefized by mixing-length expressions, with the mixing coefficient taken to be the sum of Branscome's mixing coefficient, plus a correction which allows for nonlinear effects onthe eddy structure and ensures global momentum conservation.

The parametefization of the mefidional eddy transport is tested in another perpetual January simulation with the two-dimensional averaged model. The results are compared with a parallel three-dimensional simulation which calculates the eddy transport explicitly. The parameterization reproduces the latitudinal and seasonal (interhemisphefic) variations and the magnitude of the eddy transport calculated in the three-dimensional simulation reasonably well.

## Abstract

The moist convection parameterization used in the GISS 3-D GCM is adapted for use in a two-dimensional (2-D) zonally averaged statisticai-dynamical model. Experiments with different versions of the parameterization show that its impact on the general circulation in the 2-D model does not parallel its impact in the 3-D model unless the effect of zonal variations is parameterized in the moist convection calculations. A parameterization of the variations in moist static energy is introduced in which the temperature variations are calculated from baroclinic stability theory, and the relative humidity is assumed to be constant. Inclusion of the zonal variations of moist static energy in the 2-D moist convection parameterization allows just a fraction of a latitude circle to be unstable and enhances the amount of deep convection. This leads to a 2-D simulation of the general circulation very similar to that in the 3-D model.

The experiments show that the general circulation is sensitive to the parameterized amount of deep convection in the subsident branch of the Hadley cell. The more there is, the weaker are the Hadley cell circulations and the westerly jets. The experiments also confirm the effects of momentum mixing associated with moist convection found by earlier investigator and, in addition, show that the momentum mixing weakens the Ferrel cell. An experiment in which the moist convection was removed while the hydrological cycle was retained and the eddy forcing was held fixed shows that moist convection by itself stabilizes the tropics, reduces the Hadley circulation, and reduces the maximum speeds in the westerly jets.

## Abstract

The moist convection parameterization used in the GISS 3-D GCM is adapted for use in a two-dimensional (2-D) zonally averaged statisticai-dynamical model. Experiments with different versions of the parameterization show that its impact on the general circulation in the 2-D model does not parallel its impact in the 3-D model unless the effect of zonal variations is parameterized in the moist convection calculations. A parameterization of the variations in moist static energy is introduced in which the temperature variations are calculated from baroclinic stability theory, and the relative humidity is assumed to be constant. Inclusion of the zonal variations of moist static energy in the 2-D moist convection parameterization allows just a fraction of a latitude circle to be unstable and enhances the amount of deep convection. This leads to a 2-D simulation of the general circulation very similar to that in the 3-D model.

The experiments show that the general circulation is sensitive to the parameterized amount of deep convection in the subsident branch of the Hadley cell. The more there is, the weaker are the Hadley cell circulations and the westerly jets. The experiments also confirm the effects of momentum mixing associated with moist convection found by earlier investigator and, in addition, show that the momentum mixing weakens the Ferrel cell. An experiment in which the moist convection was removed while the hydrological cycle was retained and the eddy forcing was held fixed shows that moist convection by itself stabilizes the tropics, reduces the Hadley circulation, and reduces the maximum speeds in the westerly jets.

## Abstract

We examine the response of the GISS global climate model to different parameterizations of moist convective man flux. A control run with arbitrarily specified updraft mass flux is compared to experiments that predict cumulus mass flux on the basis of low-level convergence, convergence plus surface evaporation, or convergence and evaporation modified by varying boundary layer height. An experiment that includes a simple parameterization of saturated convective-scale downdrafts is also described. Convergence effects on cumulus mass flux significantly improve the model's January climatology by increasing the frequency of occurrence of deep convection in the tropics and decreasing it at high latitudes, shifting the ITCZ from 12°N to 4°5, strengthening convective heating in the western Pacific, and increasing tropical long-wave eddy kinetic energy. Surface evaporation effects generally oppose the effects of convergence but are necessary to produce realistic continental convective heating and well-defined marine shallow cumulus regions. Varying boundary layer height (as prescribed by variations in lifting condensation level) has little effect on the model climatology. Downdrafts, however, reinforce many of the positive effects of convergence while also improving the model's vertical humidity profile and radiation balance. The diurnal cycle of precipitation over the West Pacific is best simulated when convergence determines cumulus mass flux, while surface flux effects are needed to reproduce diurnal variations in the continental ITCZ. In each experiment the model correctly simulates the observed correlation between deep convection strength and tropical sea surface temperature; the parameterization of cumulus mass flux has little effect on this relationship. The experiments have several implications for cloud effects on climate sensitivity. The dependence of cumulus mass flux on vertical motions, and the insensitivity of mean vertical motions to changes in forcing, suggests that the convective response to climate forcing may be weaker than that estimated in previous global climate model simulations that link convection only to moist static instability. This implies that changes in cloud cover and hence positive cloud feedback have been overestimated in these climate change experiments. Downdrafts may affect the feedback in the same sense by replenishing boundary layer moisture relative to cumulus parameterization schemes with only dry compensating subsidence.

## Abstract

We examine the response of the GISS global climate model to different parameterizations of moist convective man flux. A control run with arbitrarily specified updraft mass flux is compared to experiments that predict cumulus mass flux on the basis of low-level convergence, convergence plus surface evaporation, or convergence and evaporation modified by varying boundary layer height. An experiment that includes a simple parameterization of saturated convective-scale downdrafts is also described. Convergence effects on cumulus mass flux significantly improve the model's January climatology by increasing the frequency of occurrence of deep convection in the tropics and decreasing it at high latitudes, shifting the ITCZ from 12°N to 4°5, strengthening convective heating in the western Pacific, and increasing tropical long-wave eddy kinetic energy. Surface evaporation effects generally oppose the effects of convergence but are necessary to produce realistic continental convective heating and well-defined marine shallow cumulus regions. Varying boundary layer height (as prescribed by variations in lifting condensation level) has little effect on the model climatology. Downdrafts, however, reinforce many of the positive effects of convergence while also improving the model's vertical humidity profile and radiation balance. The diurnal cycle of precipitation over the West Pacific is best simulated when convergence determines cumulus mass flux, while surface flux effects are needed to reproduce diurnal variations in the continental ITCZ. In each experiment the model correctly simulates the observed correlation between deep convection strength and tropical sea surface temperature; the parameterization of cumulus mass flux has little effect on this relationship. The experiments have several implications for cloud effects on climate sensitivity. The dependence of cumulus mass flux on vertical motions, and the insensitivity of mean vertical motions to changes in forcing, suggests that the convective response to climate forcing may be weaker than that estimated in previous global climate model simulations that link convection only to moist static instability. This implies that changes in cloud cover and hence positive cloud feedback have been overestimated in these climate change experiments. Downdrafts may affect the feedback in the same sense by replenishing boundary layer moisture relative to cumulus parameterization schemes with only dry compensating subsidence.

## Abstract

We illustrate the potential complexity of the feedback between global mean cloud amount and global mean surface temperature when variations of the vertical cloud distribution are included by studying the behavior of a one-dimensional radiative–convective model with two types of cloud variation: 1) variable cloud cover with constant optical thickness and 2) variable optical thickness with constant cloud cover. The variable parameter is calculated assuming a correlation between cloud amount and precipitation or the vertical flux convergence of latent heat. Since the vertical latent heat flux is taken to be a fraction of the total heat flux, modeled by convective adjustment, we examine the sensitivity of the results to two different critical lapse rates, a constant 6.5 K km^{−1} lapse rate and a temperature-dependent, moist adiabatic lapse rate. The effects of the vertical structure of climate perturbations on the nature of the cloud feedback are examined using two cases: a 2% increase in the solar constant and a doubling of the atmospheric carbon dioxide concentration. The model results show that changes in the vertical cloud distribution and mean cloud optical thickness can be as important to climate variations as are changes in the total cloud cover. Further the variety and complexity of the feedbacks exhibited even by this simple model suggest that proper determination of cloud feedbacks must include the effects of varying vertical distribution.

## Abstract

We illustrate the potential complexity of the feedback between global mean cloud amount and global mean surface temperature when variations of the vertical cloud distribution are included by studying the behavior of a one-dimensional radiative–convective model with two types of cloud variation: 1) variable cloud cover with constant optical thickness and 2) variable optical thickness with constant cloud cover. The variable parameter is calculated assuming a correlation between cloud amount and precipitation or the vertical flux convergence of latent heat. Since the vertical latent heat flux is taken to be a fraction of the total heat flux, modeled by convective adjustment, we examine the sensitivity of the results to two different critical lapse rates, a constant 6.5 K km^{−1} lapse rate and a temperature-dependent, moist adiabatic lapse rate. The effects of the vertical structure of climate perturbations on the nature of the cloud feedback are examined using two cases: a 2% increase in the solar constant and a doubling of the atmospheric carbon dioxide concentration. The model results show that changes in the vertical cloud distribution and mean cloud optical thickness can be as important to climate variations as are changes in the total cloud cover. Further the variety and complexity of the feedbacks exhibited even by this simple model suggest that proper determination of cloud feedbacks must include the effects of varying vertical distribution.