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

## TL;DR

This paper offers a new interpretation of vortex-split sudden stratospheric warmings using equilibrium statistical mechanics, showing that these events can be viewed as transitions toward an anticyclonic equilibrium state in the polar vortex.

## Contribution

It introduces a novel theoretical framework applying equilibrium statistical mechanics to understand vortex-split S-SSWs, linking vortex dynamics to large-scale steady states.

## Key findings

- Vortex-split S-SSWs can be interpreted as transitions to anticyclonic equilibrium states.
- The QG model reproduces the composite PV evolution observed in reanalysis data.
- The theory predicts vortex splitting during the transition to equilibrium.

## Abstract

Vortex-split sudden stratospheric warmings (S-SSWs) are investigated by using the Japanese 55-year Reanalysis (JRA-55), a spherical barotropic quasi-geostrophic (QG) model, and equilibrium statistical mechanics. The QG model reproduces well the evolution of the composite potential vorticity (PV) field obtained from JRA-55 by considering a time-dependent effective topography given by the composite height field of the 550 K potential temperature surface. The zonal-wavenumber-2 component of the effective topography is the most essential feature required to observe the vortex splitting. 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 solving the QG dynamics. The theory is applied to a disk domain, which is modeled on the north polar cap 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. The theoretical calculations are compared with the results of the quasi-static experiment in which the wavenumber-2 topographic amplitude is increased linearly and slowly with time. The results suggest that S-SSWs 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. Without any forcing such as radiative cooling, the anticyclonic equilibrium state would be realized sufficiently after an S-SSW.