A Resonant Wave in a Numerical Model of the 1979 Sudden Stratospheric Warming

Abstract

A simple numerical model of the stratosphere has been used to examine the possibility that a resonant growth of wave 2 was responsible for the 1979 major sudden warning. The model solves for linear steady state solutions to the quasi-geographic wave equation in the presence of realistic damping. The basic state is taken from observations (NMC and LIMS), and the frequency of the wave forcing is varied over a wide range. The model results show that in the days during the initial observed amplification of wave 2 (14?15 February), a clear resonant mode existed. The maximum response is for a wave moving eastward with a period of 12?16 days. Another peak at very low frequency (period greater than 100 days) occurs on 22 February. Other days during the period 12?24 February show weaker, but nevertheless significant peaks for particular frequencies. The frequency of the maximum is lower for later days and is nearly stationary at the height of the warming around 21 February. This frequency shift found in the model corresponds closely to the observed wave behavior. Although the details of the results vary with changes in the model resolution or lower boundary position, the resonant wave does not disappear. However, when the wave forcing is applied at the earth&'s surface rather than in the tropopause region, no resonance occurs. To test the effect of the lower boundary, the troposphere-stratosphere model was run with an internal vorticity forcing similar to the structure of the observed wave 2 in the troposphere. In this case the frequency dependence of the amplitude within the stratosphere was similar to that of the model with a tropopause boundary, although the magnitude was considerably smaller. This suggests that for resonance to have occurred, a planetary scale disturbance that did not propagate from the surface must have been maintained in the upper troposphere. The two well-developed blocking ridges present in the troposphere during this period may have contributed enough to planetary wave 2 to provide the necessary boundary conditions.