# 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]).