Grid-Averaged Surface Fluxes

Abstract

This study examines the inadequacies of formulations for surface fluxes for use in numerical models of atmospheric flow. The difficulty is that numerical models imply spatial averaging over each grid area. Existing formulations am based on the relationship between local fluxes and local gradients and appear to describe the relationship between the grid-averaged flux and the grid-averaged gradient poorly. For example, area-averaging the bulk aerodynamic relationship reveals additional spatial correlation terms and a complex relationship between the grid-averaged exchange coefficient and the stability based on ?model? available? grid-averaged variables. This problem is studied by assuming idealized spatial distributions of the Richardson number over a grid area. Some perspective is provided by consulting observed spatial distributions of the layer Richardson number at the surface. Various contributions to the area-averaged surface flux are studied by employing a small-scale numerical model as a grid box or a larger-scale numerical model. Based on these analyses, a new formulation is proposed for relating the area-averaged flux to the area-averaged gradient. However, this expression cannot be seriously tested with existing observations.