The Onset of Vortex-splitting Sudden Stratospheric Warming in a Global Shallow Water Model

We consider the dynamics of the vortex-splitting Sudden Stratospheric Warmings (SSW) from the point of view of transition between quasi-stable and unstable vortex states, following the recent work of Matthewman and Esler (2011). We examine to what extent the simple f-plane nonlinear model provides a realistic representation of the wintertime stratospheric polar vortex, in particular when the effects of spherical geometry and compressibility are taken into consideration. We focus on the situation where the vortex adjusts adiabatically in response to a stationary wavenumber-2 topographic forcing with amplitude that varies slowly in time, tracing out a family of approximately elliptical quasi-steady states. These states lose stability when their aspect ratios exceed some critical threshold, with the values of the thresholds and the nature of the instabilities related to factors such as the orientation of the vortex. For some critical thresholds the vortex undergoes a sudden split similar to those observed in the stratosphere.

The predominantly barotropic dynamics involved in observed vortex-splitting SSWs suggest that a single-layer shallow water model is an appropriate model to capture the essential dynamics. This enables us to consider at high-resolution the way the transition to sudden warming depends on the physical parameters of the vortex. Specifically, we consider the dependence of the onset of warming on the forcing amplitude and background flow profile (the state of the "surf-zone"), and how this dependence changes with vortex size and stratification of the initial state. We find that the initial vortex size is significantly more important in determining vortex stability than other parameters. In addition to the freely-forced problem, we also consider the more realistic situation in which the vortex is relaxed back to the equilibrium profile corresponding to its initial state, using a simple Newtonian relaxation on the height field.