A comparison of surface-layer implementations over steep terrain

Interactions with the lower boundary are typically modeled in terms of surface-layer parameterizations, whose main job is to predict the fluxes of heat, moisture and momentum across the boundary. Various formulations can be found in the literature, with differences mostly related to the treatment of stability effects. However, one common limitation is that the parameterizations are typically implemented as if the lower boundary were flat---that is, by assuming vertical fluxes across a horizontal surface.

In the present study, we review the available methods for implementing surface fluxes across arbitrary surfaces, taking full account of the underlying terrain geometry. Particular attention is given to fluxes of momentum (i.e., stresses), since the associated boundary conditions depend on terrain shape in subtle ways. The generalized flux methods are applied to a number real-world test cases, including Mount Rainier (in WA), Mount Ngauruhoe (in New Zealand), and the Arizona Meteor Crater. Examples are computed for several upstream flow states, including stably stratified flows and well-mixed boundary layers, as well as several shear profiles.

Preliminary results comparing to the conventional (flat-boundary) implementation show that the sensitivity to the flux condition depends on the flow type, with the largest differences found for well-mixed flows. Strongly stratified flows, on the other hand, show much less sensitivity. The sensitivity to the momentum fluxes in isolation (i.e., without heat fluxes) is found to be relatively modest, with the generalized implementation leading to wind-speed differences on the order of 25 to 30%, as compared to the flat-boundary approach. The effects of the heat-flux condition are somewhat larger, with differences in updraft strength on the order of 50% in some cases.

The sensitivity to the heat-flux condition, in particular, would appear to have implications for the prediction of convective initiation.