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

Abstract

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...

Seasonal evolution and interannual variability of the local solar energy absorbed by the Arctic sea ice–ocean system

“…Radiative transfer is parameterized according to Shine [1984]. This parameterization is highly accurate when compared to radiative transfer calculations over arctic surfaces [Key et al, 1996] and requires as inputs cloud fraction, cloud optical depth, and broad-band surface albedo.…”

Assessing the retrieval of cloud properties from radiation measurements over snow and ice

“…First of all, clouds reduce the incoming radiation flux by reflection and absorption. Secondly, the radiation that passes through the cloud will be subject to multiple reflections between the surface and the cloud base (Ångström and Tryselius, 1934;Schneider and Dickinson, 1976;Shine, 1984). Since the spectral albedo of snow (and ice) and the absorption of radiation by clouds are both strongly dependent on wavelength (Liljequist, 1956;Wiscombe and Warren, 1980), the magnitude of cloud effects is also very much wavelength-dependent-clouds not only alter the intensity, but also the spectral composition of the solar radiation arriving at the surface.…”

Role of diurnal processes in the seasonal evolution of sea ice and its snow cover

“…The Shine [1984] When the sea ice model was forced directly with SIMMS 1992 field data (K $, L $, air temperature, wind speed, and albedo), it produced better representations of the modeled snow-ice ablation evolution as well as Q* and surface temperature over the 1992 spring period. This case reproduced observed diurnal melt periods faithfully, whereas the control run produced many more and earlier melt events.…”

“…Since more detailed investigations involving the parameterized and observed downwelling shortwave (K $ ) and longwave (L $ ) fluxes and surface albedo are conducted (sections 3.2 and 3.3), brief descriptions of how the model parameterizes these variables are given here. L $ is computed using the parameterization of Maykut and Church [1973], and K $ is computed using the parameterization of Shine [1984]. Both the L $ and K $ parameterizations use a single total cloud fraction for computing all-sky fluxes.…”

“…Key et al [1996] compared downwelling shortwave and longwave Arctic observations with model parameterizations used in sea ice models. They found the most accurate parameterizations were the shortwave scheme of Shine [1984] and the longwave scheme of Maykut and Church [1973], both of which are used in the Flato and Brown [1996] thermodynamic model used in this study.…”