A non‐hydrostatic mesoscale model

Abstract A 3‐dimensional non‐hydrostatic compressible model designed for mesoscale studies is discussed. A semi‐implicit scheme for integrating the equations has been developed where the terms which involve the horizontal and vertical propagation of sound waves are treated implicitly and all other terms are represented explicitly. In an atmosphere with a neutrally stable lapse rate the sound waves are then unconditionally stable while the stability of advection is governed by a criterion similar to the usual Courant‐Freidrichs‐Lewy condition. When the atmosphere is stratified the stability criterion for sound waves, which depends on the Brunt‐Väisalä frequency but is independent of the grid length, is also sufficient for the stability of gravity waves. Tests conducted to simulate a sea‐breeze in Florida agree qualitatively with published results for a hydrostatic model.