Representing drag on unresolved terrain as a distributed momentum sink

Abstract

In numerical weather prediction models, drag on unresolved terrain is usually represented by augmenting the boundary drag on the model atmosphere, in terms of an effective surface roughness length. But as is shown here, if a terrain-following coordinate is defined relative to smoothed terrain, the residual unresolved terrain component implies a volumetric momentum sink, as recently implemented in the Canadian Climate Centre GCM, and as is implicit in the "orographic-stress profile" method. Thus treating drag on unresolved terrain by way of an internal (rather than enhanced surface) momentum sink is a better method in principle. While the skill of both methods hinges on limited fundamental knowledge of drag on terrain, a distributed momentum sink arguably offers greater flexibility to improve modeling of mountain winds, if necessary by tailoring the sink to achieve success, in specific regions, by trial and error. A consequence of the new method is that unresolved terrain results in a ground-based (stress divergence) layer, that is somewhat analogous to a plant canopy layer, from the point of view of its momentum balance.