Parameterization of the spatially averaged sky view factor in complex topography

Abstract

Large-scale meteorological, land surface or climate models require precise subgrid parameterizations to reproduce unresolved subgrid processes. This is particularly important in mountainous terrain where subgrid surface properties (e.g., glacier area extent) are used to illustrate the impact of global climate change. The sky view factor is one of the most frequently used terrain characteristics to parameterize the influence of topography on the surface radiation balance in complex terrain. A precise subgrid parameterization of sky view factors is therefore essential for accurate parameterizations of radiative fluxes such as shortwave diffuse sky and terrain reflected radiation. While its computation is straightforward for a particular site, a systematic characterization of the spatially averaged sky view factor is still missing. We use Gaussian random fields with a Gaussian covariance as topography model, and based on an analytical approximation, we derive a parameterization for the spatially averaged sky view factor. The sky view factor parameterization is solely based on computationally cheap terrain parameters, namely the correlation length of subgrid topographic features and the mean-squared slope in the grid cell of the large-scale model. For validation we compare parameterized to numerically exact sky view factors computed for real terrain of the Swiss Alps from a 25 m digital elevation model, with subsequent averaging to varying target domain sizes. We obtain a very good agreement when approaching the resolutions of regional climate models. The parameterization also compares well for various real topographies from the U.S.