Numerical Simulation of Stratospheric Sudden Warmings with a Primitive Equation Spectral Model

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  • 1 Department of Meteorology, The University of Utah, Salt Lake City 84112
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Abstract

A 26-level primitive equation spherical harmonic spectral model allowing for both wave-wave and wave-zonal flow interactions is developed for the study of stratospheric sudden warmings simulated by the forcing of a single planetary wave at the tropopause. Four numerical experiments were performed. The fist two cases, designated N1 and L1, involve both wave-wave and wave-zonal flow interactions and only wave-zonal flow interactions, respectively, with wavenumber 1 forcing. The other two cases, N2 and L2, are the same as N1 and L1, respectively, except for wavenumber 2 forcing.

Nonlinear wave-wave interactions appear to play an important role in the evolution of the flow and temperature fields in the middle to upper stratosphere particularly in case N1 as manifested by the split in the initial polar vortex into a quasi-wavenumber 2 pattern. Also in case N1 the weighted geopotential amplitude of wavenumber 2 is as much as 70% that of wavenumber 1. There is a tendency toward an out-of-phase relationship between the weighted geopotential amplitudes of wavenumbers 1 and 2 in the course of time integration. In fact, just prior to the sudden warming, the weighted geopotential amplitude of wavenumber 2 reaches maximum, while that of wavenumber 1 starts to weaken.

In cases N1 and N2 at 60°N, easterlies develop first in the upper mesosphere and descend gradually. About the same time or a little later, easterlies also develop in the mid-stratosphere. Eventually two separate easterly layers are merged. The linear cases L1 and L2 exhibit warmings which are both more shallow and more intense at 30 km than the nonlinear cases. Wave-wave interactions present in cases N1 and N2 seem to moderate the restoring forces on the zonal flow contributed by Rayleigh friction and Newtonian cooling/heating included in the model. Comparisons of the present results with those of Matsuno (1971), Holton (1976) and Schoeberl and Strobel (1980) are discussed.

Abstract

A 26-level primitive equation spherical harmonic spectral model allowing for both wave-wave and wave-zonal flow interactions is developed for the study of stratospheric sudden warmings simulated by the forcing of a single planetary wave at the tropopause. Four numerical experiments were performed. The fist two cases, designated N1 and L1, involve both wave-wave and wave-zonal flow interactions and only wave-zonal flow interactions, respectively, with wavenumber 1 forcing. The other two cases, N2 and L2, are the same as N1 and L1, respectively, except for wavenumber 2 forcing.

Nonlinear wave-wave interactions appear to play an important role in the evolution of the flow and temperature fields in the middle to upper stratosphere particularly in case N1 as manifested by the split in the initial polar vortex into a quasi-wavenumber 2 pattern. Also in case N1 the weighted geopotential amplitude of wavenumber 2 is as much as 70% that of wavenumber 1. There is a tendency toward an out-of-phase relationship between the weighted geopotential amplitudes of wavenumbers 1 and 2 in the course of time integration. In fact, just prior to the sudden warming, the weighted geopotential amplitude of wavenumber 2 reaches maximum, while that of wavenumber 1 starts to weaken.

In cases N1 and N2 at 60°N, easterlies develop first in the upper mesosphere and descend gradually. About the same time or a little later, easterlies also develop in the mid-stratosphere. Eventually two separate easterly layers are merged. The linear cases L1 and L2 exhibit warmings which are both more shallow and more intense at 30 km than the nonlinear cases. Wave-wave interactions present in cases N1 and N2 seem to moderate the restoring forces on the zonal flow contributed by Rayleigh friction and Newtonian cooling/heating included in the model. Comparisons of the present results with those of Matsuno (1971), Holton (1976) and Schoeberl and Strobel (1980) are discussed.

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