Scaling and parametrization of clear-sky solar radiation over complex topography

[1] Solar radiation at the land surface is influenced by slope, aspect, shadows, and obstruction of the sky, all of which vary over a wide range of length scales in regions of complex topography, with important consequences for the surface energy balance. Atmospheric models, however, generally assume the surface to be flat on subgrid scales. For four areas in North America, ranging in latitude from 39N to 69N and in topography from rolling to mountainous, we simulate spatial patterns of clear-sky incoming solar radiation. It is found that distributions of slope components and variations in shaded area with solar elevation can be approximated by simple functions that scale to each of the areas studied. From these results, parametrizations are developed for averages, standard deviations, and distributions of direct-beam and diffuse solar radiation. Results from these parametrizations, and from a modified form of a simpler parametrization presented previously, compare well with statistics from the spatial simulations. The only topographic input required by the parametrizations is the standard deviation of slope components; this parameter is again found to have simple scaling relationships with the resolution and extent of the underlying elevation grid and with the standard deviation of elevation.