SUMMARYA 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.
INTRODUC~IONThe accurate prediction of the shortwave flux at the surface in conditions of snow and ice cover is of considerable importance. The onset of surface melting or freezing is dictated by the surface energy balance and the state of the surface cover in turn feeds back on the energy balance through the albedo. At times of melt, the shortwave component of the energy balance dominates all other terms. Therefore any meteorological investigation, from microclimatological studies to the prediction of snow and ice cover in general circulation climate models, must correctly simulate this flux.There is an acknowledged need for relatively simple methods of flux calculation (see e.g. Maykut 1983) and many recent studies which consider high latitude processes (e.g. Andreas and Ackley 1982; Bennett 1982) adopt highly simplified parametrizations for shortwave flux determination, in situations where errors may be of great significance. The principal problem over high albedo surfaces is that multiple reflections between surface and cloud base contribute a substantial amount of downward radiation. 1982). This paper uses a relatively detailed radiative transfer scheme to derive an empirical equation (with a physically justifiable form) which allows the calculation of the net shortwave flux at the surface for cloudy conditions using the minimum number of input parameters (solar zenith angle, surface albedo and cloud optical thickness). The accuracy of the fit is consistent with the knowledge (or lack of) of input parameters but incorporates the important functional dependences.Finally, an equation for the shortwave flux in clear sky conditions is fitted to the fluxes from the detailed scheme; this equation along with the cloudy sky equation allows the calculation of surfac...