An efficient ray-tracing based algorithm to compute terrain horizon and sky view factor to consider topographic effects on surface radiation in spatially distributed land surface models

In mountainous regions, incoming surface radiation is strongly influenced by surrounding and local terrain. The direct beam part of incoming shortwave radiation depends both on local slope angle and azimuth as well as on neighbouring terrain, which can induce topographic shading. Shortwave radiation can be reflected (multiple times) by terrain, which leads to enhanced incoming diffuse shortwave radiation for locations with a reduced sky view factor (SVF) – particularly under snow-covered conditions when surface reflectivity is high. Finally, incoming longwave radiation can also be modulated by neighbouring terrain due to radiation exchange between facing slopes.

Considering these effects in spatially distributed land surface models – either stand-alone or embedded in weather and climate models – typically requires the following topographic quantities: slope angle, slope aspect, terrain horizon and SVF. The first two quantities can be computed rapidly because they only depend on local terrain. The computation of the latter two quantities is however expensive, particularly for high-resolution (~30 m) digital elevation models (DEMs), because a large quantity of non-local DEM information has to be processed. We developed a new efficient algorithm for terrain horizon computation, which is based on a high-performance ray-tracing library. A benchmark against conventional algorithms confirmed its high performance – particularly for DEMs with very high resolution and for large terrain horizon search distances. Furthermore, due to the smooth representation of terrain by a triangle mesh, the new algorithm does not reveal artefacts in the computed horizon line in cases where the horizon is formed by proximal terrain. Finally, we demonstrate that the new algorithm is also eligible to compute sub-grid SVF for large spatial domains in a very efficient way. Sub-grid SVF is a useful quantity to parameterise above-mentioned topographic effects on surface radiation in weather and climate models applied on regional or even global scales.