Radiative upper‐boundary conditions for a non‐hydrostatic atmosphere

A non‐hydrostatic compressible model supports vertically propagating acoustic modes in addition to the modes of meteorological significance, such as the quasi‐geostrophically balanced, and gravity modes. The acoustic modes are stimulated inadvertently, either by initial conditions incompatibly balanced for the model discretization, or by physical processes injecting abrupt impulses of heat or motion into the model during the integration. A standard method for removing unwanted acoustic energy is through the inclusion in the model of three‐dimensional divergence damping. However, an alternative approach is to employ an upper‐boundary condition designed to radiate acoustic waves, at least partially, as they impinge on the model top. This note explores this latter option through the use of an upper‐boundary condition that incorporates a time filter to facilitate the selective absorption of both gravity and acoustic waves at the top. Copyright © 2002 Royal Meteorological Society