Computing Hydrostatic Potential Vorticity in Terrain-Following Coordinates

Abstract

The hydrostatic potential vorticity (HPV) formulated in terrain-following coordinates is reviewed and shown to be equivalent to the widely used HPV formulations in the height, pressure, and isentropic coordinates in the sense that they all represent the same HPV substance and retain the same conservation property. The HPV formulation in terrain-following coordinates can be applied directly to model-simulated velocity and thermodynamic fields on the model’s original terrain-following grid to avoid coordinate transformation and eliminate grid interpolation error. This advantage and its significance are demonstrated by a numerical example.