The c's are parameterized in terms of the following cloud categories: thin cirrus and
cirrostratus, thick cirrus and cirrostratus, altostratus and altocumulus, and low clouds.
The value of the coefficients can be found in the code or in Shapiro (1987).
The reflected shortwave flux is calculated from the downwelling shortwave flux and the
surface albedo as follows
I s↑ = α I s↓ .
The surface albedo α has been parameterized in terms of the land cover type.
The net shortwave radiation on a horizontal surface is given as
∆I s = I s↓ - I s↑ .
2.4 Sloping Surface
All fluxes calculated above pertain to a flat surface. If the surface is sloping, correction
factors must be used to get the insolation at the surface. The correction factor differs for
the different components of the solar flux: downwelling direct, diffuse, total, and the
reflected flux. For the direct beam, the corrected downwelling shortwave flux impinging
on a sloping surface is given as
I sc↓ir = I sd↓r [cos ϕ + sin ϕo sin ϕ cosϑr / cos ϕo ] .
φ is the slope of the surface, and ϑr is the relative azimuth and is defined as the
difference (ϑ - ϑo ) between the azimuth of the surface ϑ relative to north and the solar
azimuth ϑo relative to north. The corrected diffuse component for a sloping surface is
I sc↓iff = I sd↓ff ⎡(180 - ϑr ) ( f s + cosϑr ) + ϑr (1 + f s cosϑr )⎤ 180 (1 + f s ) .
fs is given as
fs = 1 + 0.5 sin ϕo + 2 sin(2ϕo ) .
The corrected reflected solar flux for a sloping surface is given as
I sc↑ = I s↑ (1 - cos ϕ ) / 2 .