Scaling of shortwave radiation fluxes for sub grid topography

Shortwave radiation plays an important role in the surface energy balance for understanding mass balances, snow cover distribution as well as snow melt. Incident shortwave radiation is greatly altered by mountainous terrain. While distributed radiation balance models can account for all topographic influences at small scales, for larger scale applications, such as climate and hydrological models, physically based sub grid parameterizations are required. We present a complete shortwave radiation parameterization scheme for sub grid topography accounting for shading, limited sky view and terrain reflections. Each radiative flux is parameterized individually. The parameters required are sun elevation angle, domain-averaged surface albedo and terrain parameters such as slope angle, slope distribution and sky view factor. We show that the domain-averaged sky view factor as an important parameter of the scheme can be theoretically related to the slope distribution. This suggests that the parametrization can solely be computed from slope characteristics and the numerically expensive computation of horizons angles can be abandoned. To validate the parameterization scheme we used domain-averaged values from a detailed radiation balance model for the three-dimensional radiative transfer in complex terrain. In order to minimize influences in the modeled distributed radiation arising from specific geomorphology and climate we compiled a large ensemble of several thousand Gaussian topographies with a broad range of characteristic scales and used fixed sun positions. Overall, modeled radiation from the simulated topographies compared well with parameterized values. We found that depending on sun elevation angles, shading and limited sky view alter direct beam and diffuse sky radiation by up to 40% each. We confirmed that when using domain-averaged values, multiple, anisotropic terrain reflections can be approximated with single, isotropic terrain reflections.