Semibalance Model in Terrain-Following Coordinates

Abstract

y partitioning the hydrostatically balanced flow into a nonlinearly balanced primary-flow part and a remaining secondary-flow part and then truncating the secondary-flow vorticity advection and stretching?tilting terms in the vector vorticity equation, the previous semibalance model (SBM) in pseudoheight coordinates is rederived in terrain-following pressure coordinates, called ? coordinates. The involved truncation is topologically the same as that in pseudoheight coordinates but the truncated terms in ? coordinates are not equivalent to those in pseudoheight coordinates. Because its potential vorticity (PV) is conserved and invertible, the rederived SBM is suitable for studying balanced dynamics via ?PV thinking? in real weather events, such as slowly varying vortices and curved fronts in which the primary-flow velocity and secondary-flow vorticity are nearly parallel in ? coordinates.