Some Aspects of Potential Vorticity Inversion

Abstract

Tests of a balance model based on potential vorticity inversion are performed for shallow water flow over mountains. Idealized flows are assumed with Rossby numbers in the range 0.1?0.4. Flow evolutions with forecast times about equal to the advective time scale as obtained from a primitive equation model are compared to the results of parallel runs with long time steps based on the inversion of potential vorticity or on the barotropic vorticity equation. It is found that the inversion method clearly yields better results, in particular so in the presence of mountains. This advantage is greatly reduced if numerical methods are used that are not geared to the conservation of potential vorticity. It is shown that potential temperature and potential vorticity are the only material invariants of hydrostatic flow. This suggests that the ?invertibility principle? should work well when applied to observed large-scale flow.