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- Author or Editor: Mark R. Schoeberl x
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Abstract
A fully nonlinear model of barotropic instability including dissipation is used to investigate the evolution of the integrated enstrophy and vorticity. The dissipation independent limits on the integrated enstrophy and the long period oscillation in the integrated enstrophy found by Schoeberl and Lindzen are verified. The enstrophy oscillations are similar to those previously noted for two-dimensional Kelvin-Helmholtz instabilities. They are produced by advection of the vorticity back and forth across the region of instability by the largest scale wave. A simple expression that accurately estimates the period of these oscillations is derived using the saturation theory.
Abstract
A fully nonlinear model of barotropic instability including dissipation is used to investigate the evolution of the integrated enstrophy and vorticity. The dissipation independent limits on the integrated enstrophy and the long period oscillation in the integrated enstrophy found by Schoeberl and Lindzen are verified. The enstrophy oscillations are similar to those previously noted for two-dimensional Kelvin-Helmholtz instabilities. They are produced by advection of the vorticity back and forth across the region of instability by the largest scale wave. A simple expression that accurately estimates the period of these oscillations is derived using the saturation theory.
Abstract
The Northern Hemisphere, quasi-geostrophic, integrated enstrophy budget for the 1978/79 winter has been analyzed from 10-0.1 mb using LIMS data. The stratospheric integrated enstrophy builds up during early winter as a result of the diabatic forcing of the polar vortex. Starting in January, an irregular and generally irreversible transfer of enstrophy from the zonal mean reservoir to planetary waves begins to reduce the total. This transfer of enstrophy to the waves produces significant imbalances in the integrated enstrophy budget at 10 mb. The imbalances appear to result from the transfer of enstrophy to smaller scales not resolved by the LIMS instrument. We believe that these imbalances are signature of Rossby wave breaking, as the imbalance episodes correspond well to the appearance of Ertel Vorticity filaments recently shown by McIntyre and Palmer.
In the mesosphere the total enstrophy shows little seasonal trend. Our analysis indicates that the mesophere may be region of continuous wave breaking during water.
Abstract
The Northern Hemisphere, quasi-geostrophic, integrated enstrophy budget for the 1978/79 winter has been analyzed from 10-0.1 mb using LIMS data. The stratospheric integrated enstrophy builds up during early winter as a result of the diabatic forcing of the polar vortex. Starting in January, an irregular and generally irreversible transfer of enstrophy from the zonal mean reservoir to planetary waves begins to reduce the total. This transfer of enstrophy to the waves produces significant imbalances in the integrated enstrophy budget at 10 mb. The imbalances appear to result from the transfer of enstrophy to smaller scales not resolved by the LIMS instrument. We believe that these imbalances are signature of Rossby wave breaking, as the imbalance episodes correspond well to the appearance of Ertel Vorticity filaments recently shown by McIntyre and Palmer.
In the mesosphere the total enstrophy shows little seasonal trend. Our analysis indicates that the mesophere may be region of continuous wave breaking during water.
Abstract
Lincizen's model of gravity wave breaking is shown to be inconsistent with the process of convective adjustment and associated turbulent outbreak. The K-theory turbulent diffusion model used by Lindzen implies a spatially uniform turbulent field which is not in agreement with the fact that gravity wave saturation and the associated convection produce turbulence only in restricted zones. The Lindzen model may be corrected to some extent by taking the turbulent Prandtl number for a diffusion acting on the wave itself to he very large. The eddy diffusion coefficients computed by Lindzen then become a factor of 2 larger and eddy transports of heat and constituents by wave fields vanish to first order.
Abstract
Lincizen's model of gravity wave breaking is shown to be inconsistent with the process of convective adjustment and associated turbulent outbreak. The K-theory turbulent diffusion model used by Lindzen implies a spatially uniform turbulent field which is not in agreement with the fact that gravity wave saturation and the associated convection produce turbulence only in restricted zones. The Lindzen model may be corrected to some extent by taking the turbulent Prandtl number for a diffusion acting on the wave itself to he very large. The eddy diffusion coefficients computed by Lindzen then become a factor of 2 larger and eddy transports of heat and constituents by wave fields vanish to first order.
Abstract
The propagation of orographic gravity waves into an atmosphere with exponentially decreasing density is simulated with a two-dimensional, nonlinear, time-dependent numerical model. After the stationary wave is established over the mountain, the model predicts that wave breaking causes a large reduction of the vertical momentum flux in the flow, not only at levels where wave breaking is present, but also far below the lowest occurrence of overturning. More than half of the decrease in momentum flux is explained by the presence of large amplitude, downward propagating waves, which are generated in regions of wave breaking. The downward propagating waves appear almost simultaneously with overturning, and have nonzero phase speeds, suggesting a strongly nonlinear generation mechanism that depends on local wave properties. The generation of these downward propagating waves is a robust process, insensitive to mountain height, mountain width, or density scale height. These results have important implications for observational studies of orographically generated waves as well as for schemes that seek to parameterize the effects of orography in large-scale models.
Abstract
The propagation of orographic gravity waves into an atmosphere with exponentially decreasing density is simulated with a two-dimensional, nonlinear, time-dependent numerical model. After the stationary wave is established over the mountain, the model predicts that wave breaking causes a large reduction of the vertical momentum flux in the flow, not only at levels where wave breaking is present, but also far below the lowest occurrence of overturning. More than half of the decrease in momentum flux is explained by the presence of large amplitude, downward propagating waves, which are generated in regions of wave breaking. The downward propagating waves appear almost simultaneously with overturning, and have nonzero phase speeds, suggesting a strongly nonlinear generation mechanism that depends on local wave properties. The generation of these downward propagating waves is a robust process, insensitive to mountain height, mountain width, or density scale height. These results have important implications for observational studies of orographically generated waves as well as for schemes that seek to parameterize the effects of orography in large-scale models.
Abstract
The constraints imposed by conservation of potential vorticity and hydrodynamic stability on the amplitude of Rossby waves are investigated.
Abstract
The constraints imposed by conservation of potential vorticity and hydrodynamic stability on the amplitude of Rossby waves are investigated.
Abstract
A propagation equation valid for determining the vertical and latitudinal structure of stationary planetary waves in winter is derived. This equation reduces to that used by Matsuno (1970) for an isothermal atmosphere where Rayleigh friction and Newtonian cooling are taken to be equal and constant. Quasi-analytical solutions to the propagation equation are obtained for the idealized case of an isothermal atmosphere in constant rotation to illustrate some of its important properties. Solutions are obtained numerically for altitudes between the forcing level at 100 mb and the 100 km level, where a radiation boundary condition is assumed. For various realistic models of the mean zonal wind field, radiative damping rates and mean temperatures profiles, we find that the structure of our computed stationary planetary-scale waves is more sensitive to the former two than to the latter.
The structural behavior of the numerical solutions is interpreted using modal decomposition. Two principal modes compose most of the structure of wavenumber 1, while wavenumber 2 is dominated by a single mode. The trapping of these modes at different heights appears to explain the variability of the wave amplitude and phase with change in the mean wind structure. Overall, the numerical results give reasonable agreement with observations.
We also discuss the associated energy fluxes and conversion terms due to vertically propagating planetary waves.
Abstract
A propagation equation valid for determining the vertical and latitudinal structure of stationary planetary waves in winter is derived. This equation reduces to that used by Matsuno (1970) for an isothermal atmosphere where Rayleigh friction and Newtonian cooling are taken to be equal and constant. Quasi-analytical solutions to the propagation equation are obtained for the idealized case of an isothermal atmosphere in constant rotation to illustrate some of its important properties. Solutions are obtained numerically for altitudes between the forcing level at 100 mb and the 100 km level, where a radiation boundary condition is assumed. For various realistic models of the mean zonal wind field, radiative damping rates and mean temperatures profiles, we find that the structure of our computed stationary planetary-scale waves is more sensitive to the former two than to the latter.
The structural behavior of the numerical solutions is interpreted using modal decomposition. Two principal modes compose most of the structure of wavenumber 1, while wavenumber 2 is dominated by a single mode. The trapping of these modes at different heights appears to explain the variability of the wave amplitude and phase with change in the mean wind structure. Overall, the numerical results give reasonable agreement with observations.
We also discuss the associated energy fluxes and conversion terms due to vertically propagating planetary waves.
Abstract
A mechanistic, quasi-geostrophic, semi-spectral model with a self-consistent calculation of the mean zonal flow fields is used to numerically simulate sudden stratospheric warmings generated by a single zonal harmonic (m) planetary wave. The development of a warming depends critically on the two factors which govern the transmission of planetary waves to the upper stratosphere: 1) the strength of the westerly winds in the lower stratosphere and 2) the magnitude of wave damping in the same region. Major warmings can only develop when the prewarming lower stratospheric winds and tropospheric forcing are strong but insufficient to trap the wave at low altitudes. Damping controls the maximum amplitude that a warming can attain and the time constant for its growth rate. The growth rate of a m = 2 warming is accelerated during the westerly zonal wind phase of the quasi-biennial oscillation, but the maximum amplitude of the warming is independent of QBO phase.
The evolution of m = 1 and m = 2 warmings are very different. An m = 1 warming is characterized by pronounced oscillation of wave amplitude and mean flow that result from resonantly trapped, westward propagating planetary waves moving in and out of phase with the tropospherically forced stationary planetary wave. This oscillation can reach sufficient amplitude to decelerate the zonal flow during a cycle to easterlies and create a critical level. Although formation of a mesopheric critical level is not required to initiate a warming, the development and propagation of critical levels in the middle atmosphere is central to the evolution of sudden warmings. During an m = 1 event the critical level forms initially in the polar region and advances equatorward in its development. But a m = 2 critical level first develops in the equatorial region and advances poleward. A m = 2 warming is also characterized by a sudden intensification after an initially slow growth in contrast to slowly developing m = 1 warmings. Both m = 1 and m = 2 warmings are accompanied by polar mesospheric cooling, low-latitude stratospheric cooling and equatorial mesospheric heating as a result of the induced secondary circulation in response to eddy heat transport to the polar stratosphere.
Long-term integrations with a steady forced m = 1 wave show that the mean flow evolves to a steady, asymptotic state with net cooling in the polar mesosphere from planetary waves. But steady m = 2 forcing of greater than approximately 200 m at 300 mb leads to multiple generation of warmings which are similar to stratospheric vacillations.
Abstract
A mechanistic, quasi-geostrophic, semi-spectral model with a self-consistent calculation of the mean zonal flow fields is used to numerically simulate sudden stratospheric warmings generated by a single zonal harmonic (m) planetary wave. The development of a warming depends critically on the two factors which govern the transmission of planetary waves to the upper stratosphere: 1) the strength of the westerly winds in the lower stratosphere and 2) the magnitude of wave damping in the same region. Major warmings can only develop when the prewarming lower stratospheric winds and tropospheric forcing are strong but insufficient to trap the wave at low altitudes. Damping controls the maximum amplitude that a warming can attain and the time constant for its growth rate. The growth rate of a m = 2 warming is accelerated during the westerly zonal wind phase of the quasi-biennial oscillation, but the maximum amplitude of the warming is independent of QBO phase.
The evolution of m = 1 and m = 2 warmings are very different. An m = 1 warming is characterized by pronounced oscillation of wave amplitude and mean flow that result from resonantly trapped, westward propagating planetary waves moving in and out of phase with the tropospherically forced stationary planetary wave. This oscillation can reach sufficient amplitude to decelerate the zonal flow during a cycle to easterlies and create a critical level. Although formation of a mesopheric critical level is not required to initiate a warming, the development and propagation of critical levels in the middle atmosphere is central to the evolution of sudden warmings. During an m = 1 event the critical level forms initially in the polar region and advances equatorward in its development. But a m = 2 critical level first develops in the equatorial region and advances poleward. A m = 2 warming is also characterized by a sudden intensification after an initially slow growth in contrast to slowly developing m = 1 warmings. Both m = 1 and m = 2 warmings are accompanied by polar mesospheric cooling, low-latitude stratospheric cooling and equatorial mesospheric heating as a result of the induced secondary circulation in response to eddy heat transport to the polar stratosphere.
Long-term integrations with a steady forced m = 1 wave show that the mean flow evolves to a steady, asymptotic state with net cooling in the polar mesosphere from planetary waves. But steady m = 2 forcing of greater than approximately 200 m at 300 mb leads to multiple generation of warmings which are similar to stratospheric vacillations.
Abstract
The steady-state, zonally averaged circulation of the middle atmosphere (15–125 km) is studied with a quasigeostrophic, numerical model that explicitly includes a self-consistent calculation of solar radiative heating due to O2 and O3 absorption, Newtonian cooling, Rayleigh friction, tropopause boundary conditions based on climatological averages, and the effects of vertically propagating planetary waves. We find the direct, radiatively driven pole-to-pole circulation at solstice is sufficient to account for the cold summer mesopause and warm isothermal winter mesosphere with associated zonal jets of realistic magnitude. The climatological heat and momentum fluxes associated with planetary wavenumber 2 have a negligible effect on the mean circulation. With planetary wavenumber 1 no steady-state solution could be obtained due to the formation of easterlies and hence critical layers in the winter mesosphere. We also find that the radiative heating associated with secondary peaks in the O3 density at the mesopause could render the polar mesopause region convectively unstable.
Abstract
The steady-state, zonally averaged circulation of the middle atmosphere (15–125 km) is studied with a quasigeostrophic, numerical model that explicitly includes a self-consistent calculation of solar radiative heating due to O2 and O3 absorption, Newtonian cooling, Rayleigh friction, tropopause boundary conditions based on climatological averages, and the effects of vertically propagating planetary waves. We find the direct, radiatively driven pole-to-pole circulation at solstice is sufficient to account for the cold summer mesopause and warm isothermal winter mesosphere with associated zonal jets of realistic magnitude. The climatological heat and momentum fluxes associated with planetary wavenumber 2 have a negligible effect on the mean circulation. With planetary wavenumber 1 no steady-state solution could be obtained due to the formation of easterlies and hence critical layers in the winter mesosphere. We also find that the radiative heating associated with secondary peaks in the O3 density at the mesopause could render the polar mesopause region convectively unstable.
Abstract
The effects of various ozone density reductions on the zonally averaged circulation are evaluated with a numerical quasi-geostrophic model. If the ozone perturbation are confined to the polar regions and are minuscule on a global basis as was characteristic of the August 1972 solar proton event, then our calculation indicate a negligible effect on the mean circulation. For global ozone perturbations by predicted halocarbon pollution, we calculate about a 10% reduction in the zonal jet strength and less than a 5% change in global mean stratosphere temperature. Large, uniform ozone reductions (>50%) produce significant effects on the mean circulation: a substantial collapse of the stratosphere due to cooler temperatures, and a weak polar night jet. The reflection and transmission of quasi-stationary planetary waves in the middle atmosphere are computed to be insensitive to solar activity as extreme as the August 1972 solar proton event. It thus seems improbable that planetary waves are a viable mechanism for solar-weather interactions that involve perturbations of the zonally averaged circulation by ozone density reductions.
Abstract
The effects of various ozone density reductions on the zonally averaged circulation are evaluated with a numerical quasi-geostrophic model. If the ozone perturbation are confined to the polar regions and are minuscule on a global basis as was characteristic of the August 1972 solar proton event, then our calculation indicate a negligible effect on the mean circulation. For global ozone perturbations by predicted halocarbon pollution, we calculate about a 10% reduction in the zonal jet strength and less than a 5% change in global mean stratosphere temperature. Large, uniform ozone reductions (>50%) produce significant effects on the mean circulation: a substantial collapse of the stratosphere due to cooler temperatures, and a weak polar night jet. The reflection and transmission of quasi-stationary planetary waves in the middle atmosphere are computed to be insensitive to solar activity as extreme as the August 1972 solar proton event. It thus seems improbable that planetary waves are a viable mechanism for solar-weather interactions that involve perturbations of the zonally averaged circulation by ozone density reductions.
Distinct medium scale disturbances in Southern Hemisphere total ozone were observed by the Nimbus 7 Total Ozone Mapping Spectrometer during the 1979 FGGE observing period. These disturbances are shown to be a result of advection by the zonal harmonic wave five which is centered near the tropopause (Salby, 1982). The contribution to the total ozone field by vertical advection due to this wave is shown to be nearly equal to that due to horizontal advection.
Distinct medium scale disturbances in Southern Hemisphere total ozone were observed by the Nimbus 7 Total Ozone Mapping Spectrometer during the 1979 FGGE observing period. These disturbances are shown to be a result of advection by the zonal harmonic wave five which is centered near the tropopause (Salby, 1982). The contribution to the total ozone field by vertical advection due to this wave is shown to be nearly equal to that due to horizontal advection.
