High-resolution simulations for Davos, April 20, 2007

Monte Carlo simulations for highly structured terrain can very expensive. For many applications, radiation data are required only for a small area (e.g. around a measurement site). On the other hand we know that the irradiance at a certain location is affected by surface albedo and topography far away, see e.g. Mayer and Deguenther, 2000, for which reason we need a large model domain (10km in diameter or larger) which means many pixels. In a standard forward Monte Carlo calculation the radiation is always calculated for all pixels, irrespectively if they are needed or not, for which reason many many photons are required, even if the irradiance is only required at a specific location. Here the backward Monte Carlo technique can yield much faster results, in particular since only these pixels are calculated which are actually required (for an application see also Emde and Mayer, 2007).

The following images show a high-resolution (700x700 pixels with 25m x 25m) forward calculation. Integrated solar irradiance was calculated for 12:00 (solar zenith angle 36°; surface albedo 0.9). Even after 12 hours computational time (500,000,000 photons), the results are quite noisy and comprise many spikes which are an artifact of the conversion from slope-parallel to horizontal irradiance. In contrast, the 100x100 pixel area (denoted by the black rectangle) was calculated in backward mode. Noise is reduced considerably and the spikes are gone. The result is most striking in the direct component, but equally important for diffuse downward and upward irradiance. Computational time was about 10s per pixel for integrated solar irradiance. Thus, the backward technique makes high-resolution Monte Carlo simulations feasible.
whole domain zoom
google Earth
Diffuse downward
Diffuse upward