An Investigation of Resonant Waves in a Numerical Model of an Observed Sudden Stratospheric Warming

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  • 1 Space Physics Research Laboratory, Department of Atmospheric, Oceanic, and Space Science, University of Michigan, Ann Arbor, Michigan
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Abstract

The major stratospheric sudden warming of February 1979 was characterized by the interaction of the zonal flow with a wavenumber 2 perturbation that was eastward traveling in the early stages of the warming, and slowed to stationary around the time of the wind reversal. Steady state calculations by Smith and Avery 1987 of wave 2 structure for the observed wind fields during this prewarming period indicate a sharp resonance of eastward traveling wave 2. The frequency range for which wave 2 is resonant shifts towards lower (stationary) values with increasing time. This suggests that resonant self-tuning may have played a role in the 1979 sudden warming. In self-tuning, a resonant, or near resonant wave, grows and interacts with the basic state; the change in the basic state modifies the conditions for resonance and the wave frequency then shifts in such a way that it continues to stay near the resonant frequency and to grow.

A quasi-linear time-dependent model is used to investigate several questions about the role of resonance in the 1979 warming. The model is global and has boundaries at the earth's surface and at 100 km to minimize the impact of artificial boundaries on resonance. The basic state is initialized with observations based on the LIMS data for February 1979. A vorticity perturbation with a constant phase speed is applied in the upper troposphere.

Model sensitivity studies are performed to separate those conditions that lead to a sudden warming from those that do not. These tests indicate that the warming simulation has a weak dependence on the frequency of the wave forcing and on the day used for initializing the basic state. Eastward phase progression of the wave 2 forcing is necessary to simulate the warming (for a realistic amplitude of wave forcing), although the model results are not sensitive to the exact frequency. The forcing frequencies for which warmings develop in these tests are close to the resonant frequencies found in steady state calculations using the observed winds. The range of wave frequencies that lead to a sudden warming shifts toward lower frequencies with progressive initialization days.

The zonal wind fields computed by the model during the simulation differ in some ways from the observed wind changes, particularly in the extreme suddenness of the model warming, but overall the winds have a similar structure to those observed. Some of the model-generated zonal wind fields permit very strong resonance for a steady-state traveling wave, thus indicating that an artificial boundary at the tropopause is not necessary for resonance in this simple model. Zonal wind fields generated by the model begin to exhibit resonances one or two days after the beginning of the model integration. The resonance frequency then shifts with increasing time toward the frequency of the prescribed forcing for several days, and then shifts back towards low frequency. The instantaneous frequency of the evolving wave in the model integration follows the same pattern, but remains consistently to one side of the steady-state resonant frequency until the warming has begun. This behavior is a clear signal that self-tuning is occurring in the model warming simulation. The mean flow and wave frequency evolve rapidly during this self-tuning process, and therefore the question remains of how far the analogy to resonance, which is essentially a steady-state phenomenon, can be pushed.

Abstract

The major stratospheric sudden warming of February 1979 was characterized by the interaction of the zonal flow with a wavenumber 2 perturbation that was eastward traveling in the early stages of the warming, and slowed to stationary around the time of the wind reversal. Steady state calculations by Smith and Avery 1987 of wave 2 structure for the observed wind fields during this prewarming period indicate a sharp resonance of eastward traveling wave 2. The frequency range for which wave 2 is resonant shifts towards lower (stationary) values with increasing time. This suggests that resonant self-tuning may have played a role in the 1979 sudden warming. In self-tuning, a resonant, or near resonant wave, grows and interacts with the basic state; the change in the basic state modifies the conditions for resonance and the wave frequency then shifts in such a way that it continues to stay near the resonant frequency and to grow.

A quasi-linear time-dependent model is used to investigate several questions about the role of resonance in the 1979 warming. The model is global and has boundaries at the earth's surface and at 100 km to minimize the impact of artificial boundaries on resonance. The basic state is initialized with observations based on the LIMS data for February 1979. A vorticity perturbation with a constant phase speed is applied in the upper troposphere.

Model sensitivity studies are performed to separate those conditions that lead to a sudden warming from those that do not. These tests indicate that the warming simulation has a weak dependence on the frequency of the wave forcing and on the day used for initializing the basic state. Eastward phase progression of the wave 2 forcing is necessary to simulate the warming (for a realistic amplitude of wave forcing), although the model results are not sensitive to the exact frequency. The forcing frequencies for which warmings develop in these tests are close to the resonant frequencies found in steady state calculations using the observed winds. The range of wave frequencies that lead to a sudden warming shifts toward lower frequencies with progressive initialization days.

The zonal wind fields computed by the model during the simulation differ in some ways from the observed wind changes, particularly in the extreme suddenness of the model warming, but overall the winds have a similar structure to those observed. Some of the model-generated zonal wind fields permit very strong resonance for a steady-state traveling wave, thus indicating that an artificial boundary at the tropopause is not necessary for resonance in this simple model. Zonal wind fields generated by the model begin to exhibit resonances one or two days after the beginning of the model integration. The resonance frequency then shifts with increasing time toward the frequency of the prescribed forcing for several days, and then shifts back towards low frequency. The instantaneous frequency of the evolving wave in the model integration follows the same pattern, but remains consistently to one side of the steady-state resonant frequency until the warming has begun. This behavior is a clear signal that self-tuning is occurring in the model warming simulation. The mean flow and wave frequency evolve rapidly during this self-tuning process, and therefore the question remains of how far the analogy to resonance, which is essentially a steady-state phenomenon, can be pushed.

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