Solar radiation and shadow modelling with adaptive triangular meshes

Abstract

In this work, we propose a numerical model for generating solar radiation maps with the use of 2-D adaptive meshes of triangles. These triangulations are constructed by using a refinement/derefinement procedure in accordance with the variations of terrain surface orography and albedo. This discretization has the advantage of defining the terrain characteristics with a minimum number of points, which reduces the computational cost for a given accuracy. Moreover, the model takes into account the effect of shadows for each time step, which are detected by analysing the crossing of the trajectory of the shaft of light with the triangles of the mesh. Thus, the solar radiation is first computed for clear-sky considering the different components of radiation, that is, beam, diffuse and reflected radiations. From the results of clear-sky radiation, the real-sky radiation is computed daily in terms of the clear-sky index. The maps of clear-sky index are obtained from a spatial interpolation of observational data that are available for each day at several points of the zone under consideration. Finally, the solar radiation maps of a month are calculated from the daily results. We illustrate the performance of the model with a numerical experiment related to an episode on the island of Gran Canaria.