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## Abstract

Results are studied from a numerical experiment using a version of the NCAR Community Climate Model with high vertical resolution and extending from the surface to the lower mesosphere. The model was integrated for 370 days using external forcing fixed at values appropriate to 15 January (perpetual January), in order to isolate the effects of variability due purely to wave-mean flow interactions from variations due to other sources.

The model gives a reasonably accurate simulation of the mean atmospheric state from the surface to the stratopause, including the winter stratosphere. Two qualitatively different mean states are found in the winter stratosphere for periods separated in time by a sudden warming. The changes in the atomspheric state between the two periods extend from the surface to the stratopause.

By use of the refractive index and the EP flux, the zonal mean state in the two periods is shown to affect the vertical propagation of waves quite differently. The momentum balance of the two mean states is examined using transformed Eulerian diagnostics. Substantial changes in the Eliassen–Palm (EP) flux divergence are found between the two periods, indicating that the eddies affect the zonal mean state differently. A positive feedback mechanism appears to exist through which a strong lower stratospheric jet tends to favor weak wave forcing of the jet, while a weak jet favors stronger wave forcing.

## Abstract

Results are studied from a numerical experiment using a version of the NCAR Community Climate Model with high vertical resolution and extending from the surface to the lower mesosphere. The model was integrated for 370 days using external forcing fixed at values appropriate to 15 January (perpetual January), in order to isolate the effects of variability due purely to wave-mean flow interactions from variations due to other sources.

The model gives a reasonably accurate simulation of the mean atmospheric state from the surface to the stratopause, including the winter stratosphere. Two qualitatively different mean states are found in the winter stratosphere for periods separated in time by a sudden warming. The changes in the atomspheric state between the two periods extend from the surface to the stratopause.

By use of the refractive index and the EP flux, the zonal mean state in the two periods is shown to affect the vertical propagation of waves quite differently. The momentum balance of the two mean states is examined using transformed Eulerian diagnostics. Substantial changes in the Eliassen–Palm (EP) flux divergence are found between the two periods, indicating that the eddies affect the zonal mean state differently. A positive feedback mechanism appears to exist through which a strong lower stratospheric jet tends to favor weak wave forcing of the jet, while a weak jet favors stronger wave forcing.

## Abstract

The mean circulation of the winter stratosphere depends strongly on the interaction between the planetary waves and the zonally averaged flow. The theory of wave-mean flow interactions is used to determine the acceleration of the mean zonal flow by linear stationary waves as a function of the wave's amplitude, vertical structure and damping rate. The theory can be used to determine the expected response to changes in wave damping processes and mean drag.

Sensitivity experiments in which the above terms are modified in a version of the NCAR Community Climate Model are used to show that the model responds as expected from the theory. Different forms of wave damping are shown to have similar effects on the mean flow as long as their time scales are comparable. Wave damping significantly in excess of the internally determined relative damping of the model is required in order to produce a reasonable simulation of the lower winter stratosphere. In the context of this study it cannot be determined whether this damping is required because of inadequate tropospheric forcing top boundary effects or missing damping or drag terms which are present in the atmosphere.

## Abstract

The mean circulation of the winter stratosphere depends strongly on the interaction between the planetary waves and the zonally averaged flow. The theory of wave-mean flow interactions is used to determine the acceleration of the mean zonal flow by linear stationary waves as a function of the wave's amplitude, vertical structure and damping rate. The theory can be used to determine the expected response to changes in wave damping processes and mean drag.

Sensitivity experiments in which the above terms are modified in a version of the NCAR Community Climate Model are used to show that the model responds as expected from the theory. Different forms of wave damping are shown to have similar effects on the mean flow as long as their time scales are comparable. Wave damping significantly in excess of the internally determined relative damping of the model is required in order to produce a reasonable simulation of the lower winter stratosphere. In the context of this study it cannot be determined whether this damping is required because of inadequate tropospheric forcing top boundary effects or missing damping or drag terms which are present in the atmosphere.

## Abstract

Amplitude vacillation is studied using a spectral version of the two-level quasi-geostrophic model in a β-plane channel. The parameters are chosen so that only a single wave may be unstable to the undisturbed basic state. It is shown that the weakly nonlinear theories which have been proposed do not work well on the β-plane, because nonlinear interactions are not negligible even though only a single wave has any significant amplitude. The energetics and mechanism of amplitude vacillation on a β-plane are discussed for a case with moderate dissipation and contrasted with the mechanism on an *f*-plane.

## Abstract

Amplitude vacillation is studied using a spectral version of the two-level quasi-geostrophic model in a β-plane channel. The parameters are chosen so that only a single wave may be unstable to the undisturbed basic state. It is shown that the weakly nonlinear theories which have been proposed do not work well on the β-plane, because nonlinear interactions are not negligible even though only a single wave has any significant amplitude. The energetics and mechanism of amplitude vacillation on a β-plane are discussed for a case with moderate dissipation and contrasted with the mechanism on an *f*-plane.

## Abstract

Dynamical measures of the climate (e.g., winds, eddy fluxes) simulated by a general circulation model are compared at different horizontal and vertical resolutions for the December, January, and February period. The simulations of the troposphere are found to improve significantly as the horizontal resolution increases in the range of spectral truncations from T21 to T63. Little sensitivity is found to changes in vertical resolution between about 2.8 km and 0.7 km vertical grid spacing.

The improvements in the Southern Hemisphere troposphere are greater than in the Northern Hemisphere as the horizontal resolution increases. The eddy momentum fluxes and kinetic energies in both hemispheres increase monotonically with horizontal resolution. At T63, the Southern Hemisphere winds, eddy fluxes, and eddy kinetic energies agree favorably with observations, while serious discrepancies are present at lower resolutions. In the Northern Hemisphere, the eddy momentum flux at T63 is slightly larger than observed, while the transient eddy kinetic energy is still barely half of the observed.

The gravity wave drag parameterization plays a significant role in the simulations at all resolutions. Eddy momentum fluxes increase when gravity wave drag is removed with a corresponding increase in low-level winds and surface stress.

## Abstract

Dynamical measures of the climate (e.g., winds, eddy fluxes) simulated by a general circulation model are compared at different horizontal and vertical resolutions for the December, January, and February period. The simulations of the troposphere are found to improve significantly as the horizontal resolution increases in the range of spectral truncations from T21 to T63. Little sensitivity is found to changes in vertical resolution between about 2.8 km and 0.7 km vertical grid spacing.

The improvements in the Southern Hemisphere troposphere are greater than in the Northern Hemisphere as the horizontal resolution increases. The eddy momentum fluxes and kinetic energies in both hemispheres increase monotonically with horizontal resolution. At T63, the Southern Hemisphere winds, eddy fluxes, and eddy kinetic energies agree favorably with observations, while serious discrepancies are present at lower resolutions. In the Northern Hemisphere, the eddy momentum flux at T63 is slightly larger than observed, while the transient eddy kinetic energy is still barely half of the observed.

The gravity wave drag parameterization plays a significant role in the simulations at all resolutions. Eddy momentum fluxes increase when gravity wave drag is removed with a corresponding increase in low-level winds and surface stress.

## Abstract

The dynamics of vacillation is examined for the case where several waves are unstable and the wave-mean flow interactions are shown to be the same as in the case where only one wave is unstable, as has been done previously. However, the wave-wave interactions are at least as large as any of the other energy conversions. These vacillations occur for parameter settings similar to those of the atmosphere. Two classes of vacillation (wavenumber and structural) exist for different forcings, and these classes are distinguished not by differences in the wave-mean flow dynamics but only by the number of waves interacting effectively with the mean flow. Amplitude vacillation would be a special case of the wavenumber vacillation found here, for weak wave-wave interactions. It is suggested that only structural vacillation is likely to he found in the atmosphere based on the sensitivity of the amplitude and wavenumber vacillations to weak perturbations.

## Abstract

The dynamics of vacillation is examined for the case where several waves are unstable and the wave-mean flow interactions are shown to be the same as in the case where only one wave is unstable, as has been done previously. However, the wave-wave interactions are at least as large as any of the other energy conversions. These vacillations occur for parameter settings similar to those of the atmosphere. Two classes of vacillation (wavenumber and structural) exist for different forcings, and these classes are distinguished not by differences in the wave-mean flow dynamics but only by the number of waves interacting effectively with the mean flow. Amplitude vacillation would be a special case of the wavenumber vacillation found here, for weak wave-wave interactions. It is suggested that only structural vacillation is likely to he found in the atmosphere based on the sensitivity of the amplitude and wavenumber vacillations to weak perturbations.

## Abstract

Amplitude vacillation is studied using a spectral version of the two-level quasi-geostrophic model in an *f*-plane channel. The numerical results are compared to those of a weakly nonlinear asymptotic theory of amplitude vacillation formulated by Pedlosky (1970, 1971, 1972). Although the two systems give similar results for weak instabilities, they are quite different for larger instabilities. In particular, the transition from steady to vacillating waves requires much greater instability than it does in the asymptotic theory for moderate dissipation levels.

The energetics of the amplitude vacillation cycles are discussed using a nonstandard formulation for the energy, and it is shown that there are significant differences between the energetics for small and large instabilities. Even for large instabilities, however, the amplitude vacillation period is much longer than it appears to be in laboratory experiments or in the atmosphere.

## Abstract

Amplitude vacillation is studied using a spectral version of the two-level quasi-geostrophic model in an *f*-plane channel. The numerical results are compared to those of a weakly nonlinear asymptotic theory of amplitude vacillation formulated by Pedlosky (1970, 1971, 1972). Although the two systems give similar results for weak instabilities, they are quite different for larger instabilities. In particular, the transition from steady to vacillating waves requires much greater instability than it does in the asymptotic theory for moderate dissipation levels.

The energetics of the amplitude vacillation cycles are discussed using a nonstandard formulation for the energy, and it is shown that there are significant differences between the energetics for small and large instabilities. Even for large instabilities, however, the amplitude vacillation period is much longer than it appears to be in laboratory experiments or in the atmosphere.

## Abstract

The thermal balance of the NCAR Community Climate Model is examined using the zonally averaged temperature tendency equation of the model. The perpetual January and perpetual July control simulations are used to determine the relative importance of individual dynamical and diabatic terms as a function of latitude and pressure. Although the terms calculated compare reasonably well with observational results, the principle intent of this paper is to understand the maintenance of the model’s temperature structure. This understanding is required in order to make sense of the changes introduced by various physical parameterizations which are being tested in the model.

Long-term means are used so that the net dynamical and diabatic heating cancel very closely. It is found that the net dynamical and diabatic heating terms in the troposphere are generally much smaller than their individual components. There is a great deal of cancellation between the eddies and the mean meridional circulation as is expected from the theory of wave–mean flow interactions. There is also a great deal of cancellation between convective heating and radiative cooling. The latter cancellation will be sensitive both to the cumulus parameterization used and to the way in which cloud fractions are determined for radiative purposes.

The surface layer is found to be a region of extremely large and nearly compensating diabatic terms. The vertical diffusion, a very important term, has been linearized for computational reasons in the current model. Using a nonlinear diffusion operator is likely to make major changes in the surface layer balances, as will any refinements in boundary layer parameterizations.

## Abstract

The thermal balance of the NCAR Community Climate Model is examined using the zonally averaged temperature tendency equation of the model. The perpetual January and perpetual July control simulations are used to determine the relative importance of individual dynamical and diabatic terms as a function of latitude and pressure. Although the terms calculated compare reasonably well with observational results, the principle intent of this paper is to understand the maintenance of the model’s temperature structure. This understanding is required in order to make sense of the changes introduced by various physical parameterizations which are being tested in the model.

Long-term means are used so that the net dynamical and diabatic heating cancel very closely. It is found that the net dynamical and diabatic heating terms in the troposphere are generally much smaller than their individual components. There is a great deal of cancellation between the eddies and the mean meridional circulation as is expected from the theory of wave–mean flow interactions. There is also a great deal of cancellation between convective heating and radiative cooling. The latter cancellation will be sensitive both to the cumulus parameterization used and to the way in which cloud fractions are determined for radiative purposes.

The surface layer is found to be a region of extremely large and nearly compensating diabatic terms. The vertical diffusion, a very important term, has been linearized for computational reasons in the current model. Using a nonlinear diffusion operator is likely to make major changes in the surface layer balances, as will any refinements in boundary layer parameterizations.

## Abstract

The influence of the polar night jet structure in determining the wave properties in the troposphere is examined using a general circulation model (GCM). It is shown that there are significant differences in the tropospheric simulation when the polar night jet is changed. Planetary wave theory leads us to expect that this will be the case for the stationary planetary waves; however, the changes found here extend to the transient eddies as well and to all scales in the model. The degree of trapping of the planetary waves in the troposphere is determined by the strength and structure of the polar night jet, resulting in the sensitivity of the troposphere to that structure.

The most significant changes in the height field occur at high latitudes, beneath the polar night jet, but significant changes in the heat and momentum fluxes take place at both middle and high latitudes.

The results indicate that inaccuracies in the stratospheric simulations of any general circulation model will produce serious errors in the planetary waves and therefore in the general eddy properties of the model.

## Abstract

The influence of the polar night jet structure in determining the wave properties in the troposphere is examined using a general circulation model (GCM). It is shown that there are significant differences in the tropospheric simulation when the polar night jet is changed. Planetary wave theory leads us to expect that this will be the case for the stationary planetary waves; however, the changes found here extend to the transient eddies as well and to all scales in the model. The degree of trapping of the planetary waves in the troposphere is determined by the strength and structure of the polar night jet, resulting in the sensitivity of the troposphere to that structure.

The most significant changes in the height field occur at high latitudes, beneath the polar night jet, but significant changes in the heat and momentum fluxes take place at both middle and high latitudes.

The results indicate that inaccuracies in the stratospheric simulations of any general circulation model will produce serious errors in the planetary waves and therefore in the general eddy properties of the model.

## Abstract

The validity of the geostrophic approximation is examined for the Northern Hemisphere from the lower troposphere to the stratopause in January, using a general circulation model. Substantial errors are found when the geostrophic winds are compared to the true winds in the stratosphere. The errors in the winter stratosphere are, in fact, much larger than the errors in the troposphere. The relative errors in quantities derived from the wind field, such as eddy momentum and heat fluxes are found to be even larger than the errors in the zonal wind field.

The Eliasen–Palm (EP) flux divergence is now commonly used to diagnose the interactions of the eddies with the mean flow. The errors in the quasi-geostrophic EP flux divergence am found to be as large (or larger) than the true divergence in the winter stratosphere. The true EP flux from the model is convergent almost everywhere in the stratosphere although observational studies have shown a region of divergence at high latitudes, indicating an apparent source of wave activity. A divergent region is also found in the quasi-geostrophic EP flux from the model and is shown to result primarily from the use of geostrophic winds although the terms omitted in the quasi-geostrophic equations are not negligible.

The rotational winds are calculated for the model and the errors associated with their use are shown to be much smaller than the errors associated with the geostrophic winds. Geostrophic winds are extremely easy to calculate from the height field but it is likely that higher order approximations to the rotational winds would produce much more accurate results in diagnostic studies of the stratosphere.

The instantaneous and short-term mean errors associated with a quasi-geostrophic analysis during a minor stratospheric warming are similar in character to the long-term mean errors.

## Abstract

The validity of the geostrophic approximation is examined for the Northern Hemisphere from the lower troposphere to the stratopause in January, using a general circulation model. Substantial errors are found when the geostrophic winds are compared to the true winds in the stratosphere. The errors in the winter stratosphere are, in fact, much larger than the errors in the troposphere. The relative errors in quantities derived from the wind field, such as eddy momentum and heat fluxes are found to be even larger than the errors in the zonal wind field.

The Eliasen–Palm (EP) flux divergence is now commonly used to diagnose the interactions of the eddies with the mean flow. The errors in the quasi-geostrophic EP flux divergence am found to be as large (or larger) than the true divergence in the winter stratosphere. The true EP flux from the model is convergent almost everywhere in the stratosphere although observational studies have shown a region of divergence at high latitudes, indicating an apparent source of wave activity. A divergent region is also found in the quasi-geostrophic EP flux from the model and is shown to result primarily from the use of geostrophic winds although the terms omitted in the quasi-geostrophic equations are not negligible.

The rotational winds are calculated for the model and the errors associated with their use are shown to be much smaller than the errors associated with the geostrophic winds. Geostrophic winds are extremely easy to calculate from the height field but it is likely that higher order approximations to the rotational winds would produce much more accurate results in diagnostic studies of the stratosphere.

The instantaneous and short-term mean errors associated with a quasi-geostrophic analysis during a minor stratospheric warming are similar in character to the long-term mean errors.

## Abstract

The effects of an artificial upper boundary on the climate of a general circulation model are examined using two versions of the model. The complete model has 26 levels extending from the surface to 0.1 mb (∼65 km) and the second version approximates the usual tropospheric general circulation model, having 15 levels extending to 10 mb (∼30 km). The two model versions are identical over the common part of the domain.

Vertically propagating Kelvin waves are found in the tropics of both versions of the model. In the version extending only to 10 mb, the Kelvin waves are reflected by the top boundary, and resemble standing oscillations in the vertical. while retaining (approximately) their original zonal phase speed. Some of these reflected waves develop much larger lower stratospheric amplitudes than when they are able to propagate freely into the mesosphere.

Placing the topmost model level at 10 mb is found to radically alter the winter stratospheric circulation and to produce significant changes in the tropospheric circulation. Stationary planetary waves are reflected off the model's top boundary and become approximately equivalent barotropic in the stratosphere, with no vertical phase tilt and reduced meridional phase tilt. The altered planetary waves have larger geopotential amplitude but produce very small poleward fluxes of heat. The stationary planetary wave amplitudes in the troposphere are not strongly affected by the changed upper boundary, but the phase structures are quite different.

A third experiment was performed in which the zonal mean wind was controlled directly through an additional Rayleigh friction term. The results of this experiment indicate that the tropospheric stationary planetary wave structure responds to the mean flow structure of the lower stratosphere, rather than directly to the presence of a top boundary.

## Abstract

The effects of an artificial upper boundary on the climate of a general circulation model are examined using two versions of the model. The complete model has 26 levels extending from the surface to 0.1 mb (∼65 km) and the second version approximates the usual tropospheric general circulation model, having 15 levels extending to 10 mb (∼30 km). The two model versions are identical over the common part of the domain.

Vertically propagating Kelvin waves are found in the tropics of both versions of the model. In the version extending only to 10 mb, the Kelvin waves are reflected by the top boundary, and resemble standing oscillations in the vertical. while retaining (approximately) their original zonal phase speed. Some of these reflected waves develop much larger lower stratospheric amplitudes than when they are able to propagate freely into the mesosphere.

Placing the topmost model level at 10 mb is found to radically alter the winter stratospheric circulation and to produce significant changes in the tropospheric circulation. Stationary planetary waves are reflected off the model's top boundary and become approximately equivalent barotropic in the stratosphere, with no vertical phase tilt and reduced meridional phase tilt. The altered planetary waves have larger geopotential amplitude but produce very small poleward fluxes of heat. The stationary planetary wave amplitudes in the troposphere are not strongly affected by the changed upper boundary, but the phase structures are quite different.

A third experiment was performed in which the zonal mean wind was controlled directly through an additional Rayleigh friction term. The results of this experiment indicate that the tropospheric stationary planetary wave structure responds to the mean flow structure of the lower stratosphere, rather than directly to the presence of a top boundary.