An upper gravity-wave absorbing layer for NWP applications

Here, a new technique is proposed for nonhydrostatic model equations that are solved using split-explicit time-integration techniques. In this method, an implicit Rayleigh damping term is applied only to the vertical velocity, as a final adjustment at the end of each small (acoustic) time step.

The adjustment is equivalent to including an implicit Rayleigh damping term in the vertical momentum equation together with an implicit vertical diffusion of w, and could be applied in this manner in other time-integration schemes. This implicit damping for the vertical velocity is unconditionally stable and remains effective even for hydrostatic gravity waves. The good absorption characteristics of this layer across a wide range of horizontal scales are confirmed through analysis of the linear wave equation and numerical mountain-wave simulations, and through simulations of an idealized squall line and of mountain waves over the Colorado Rocky Mountains.