Nonlinear Balance in Terrain-Following Coordinates

Abstract

Potential vorticity (PV) is a powerful concept in geophysical fluid dynamics. One property of PV that makes it so powerful is that it may be inverted under certain conditions, one of which is the imposition of a balance constraint. Previous studies have made use of a particular nonlinear balance constraint suited to isobaric coordinates as part of their inversion procedures. The present study constructs and tests a new nonlinear balance constraint that may be applied directly to the output of the Weather Research and Forecasting (WRF) model on its native terrain-following vertical coordinate. Output from the nonlinear balance operator is examined in the context of idealized and real-data WRF forecasts, and the results indicate that the simplifications necessary to derive the nonlinear balance operator are justified on the synoptic and meso-α scales. On the other hand, once the scales resolved by the model are small enough, neglected terms reach magnitudes on the order of the retained terms, even over flat terrain. This suggests that the use of this operator within a PV inversion scheme that also uses the WRF vertical coordinate would not capture a divergent portion of the flow that may be significant.