Parametrization of the shortwave flux over high albedo surfaces as a function of cloud thickness and surface albedo



A simple method for the calculation of the net shortwave flux at the surface for overcast situations is presented. Explicit account is taken of the effect of cloud optical thickness and multiple reflections between the surface and cloud base. Using simple two-stream theory, a theoretical form for the flux is proposed, and then results from a detailed radiative transfer scheme are used to determine the values of a number of empirical coefficients. Over a range of cosines of the solar zenith angle from 0.1 to 0.7, of cloud optical thickness from 1.8 to 20 and of surface albedo from 0.0 to 0.9, the empirical equation reproduces results from the radiative transfer scheme to within 2.7%, and is shown to perform well outside the range of fit. The method was derived with high latitudes in mind but is applicable generally. It is shown that the spectral properties of snow and ice surfaces play an important role in surface net flux prediction. For totally overcast skies the influence of cloud height and atmospheric water vapour content are shown to be minor. Finally, for clear skies, an empirical equation due to J. W. Zillman is investigated and by adjustments to his coefficients, is brought into good agreement with the detailed calculations described here.