A New Interpretation of Vortex-Split Sudden Stratospheric Warmings in Terms of Equilibrium Statistical Mechanics

Vortex-split sudden stratospheric warmings (S-SSWs) are investigated by using the Japanese 55-year Reanalysis, a spherical barotropic quasigeostrophic (QG) model, and equilibrium statistical mechanics. The statistical mechanics theory predicts a large-scale steady state as the most probable outcome of turbulent stirring, and such a state can be computed without describing all the details of the dynamics. The theory is applied to a disk domain that is modeled on the polar cap north of 45°N in the stratosphere. The equilibrium state is obtained by computing the maximum of an entropy functional. In the range of parameters relevant to the winter stratosphere, this state is anticyclonic. By contrast, cyclonic states are quasi-stationary states corresponding to saddle points of the entropy functional. These results indicate that the mean state of the stratosphere associated with the polar vortex is not close to an equilibrium state but to a quasi-stationary state. The theoretical calculations are compared with the results of a quasi-static experiment in which a wavenumber-2 topographic amplitude is increased linearly and slowly with time. The results suggest that the S-SSW can be qualitatively interpreted as the transition from the cyclonic quasi-stationary state toward the anticyclonic equilibrium state. The polar vortex splits during the transition toward the equilibrium state.