Increase due to surface albedo

In presence of high surface albedo, the down-welling irradiance is increased due to reflection of photons at the surface and consecutive back-scattering by the atmosphere (for a more detailed and quantitative explanation see e.g. [Kylling et al., 1999]). The upper plot shows the ratio of measured and calculated erythemal irradiance, with a typical snow-free surface albedo of 0.05 as model input. There is considerable difference between snow-free surface (dots) and snow-covered surface (stars). The enhancement of erythemal irradiance by snow cover is thus found to be about 10-15%. The lower plot shows the average enhancement, that is, the ratio of measurement and model during snow-covered conditions normalized to the respective ratio during snow-free conditions, as a function of wavelength. Absolute magnitude as well as spectral dependence are well described by a model calculation using a wavelength-independent albedo of 0.38 (thick curve). This relatively low value is explained by large fractions of the surrounding area which are woodland or city. Neither trees, roads, nor roofs are usually covered with snow, except for short periods directly after snow showers. For completely snow-covered areas, the albedo would be about 0.8 - 0.9 which would result in a considerably higher increase of 40-50% in the surface irradiance. [Schwander et al., 1999] extended these studies by establishing an empirical relationship between snow depth, time elapsed since the last snowfall, and the surface albedo for the dataset shown above.

For a Lambertian (isotropically reflecting) surface, the increase of global irradiance with albedo A can be shown to be 1 / (1 - sA) where s is the downward reflectivity of the atmosphere for isotropic radiation. Knowing the increase for any two different albedos, the increase for any other albedo can thus be calculated using this formula. Note also that the increase is independent of solar zenith angle in the Lambertian case which is also true in the above figure. For more details see e.g. [Kylling et al., 1999]).