Solar Radiative Fluxes for Stochastic, Scale-invariant Broken Cloud Fields

Solar radiative fluxes for broken, cumuloform cloud fields are examined from the point of view of subgrid parameterization for general circulation models (GCMs). A simple stochastic scaling model is used to simulate extensive broken cloud fields having horizontal variation of optical depth τ characterized by power-law wave-number spectra and power-law area/perimeter and cloud-size distribution properties. Fluxes are computed with the Monte Carlo method of photon transport. Accurate flux estimates for extensive cloud fields are attainable with as few as 50 000 photons/simulation. Radiative fluxes for individual realizations of the cloud model represent the population well. Also, the effect of anisotropic scaling on azimuthally averaged fluxes may often be minimal. The latter two points are beneficial for flux parameterization purposes. Solar fluxes for various scaling, regular, and plane-parallel broken cloud fields are compared. Scaling cloud fields the size of GCM grid boxes often produce significantly different reflectances from those produced by the extreme cases of plane-parallel and white noise arrays. When calculating fluxes at low sun periods, abundant small clouds should not be neglected. Reflectances for model cloud fields with horizontally variable τ are about 10%–15% smaller than those produced by the same cloud field but with all clouds having τ equal to the mean cloudy value of τ for the variable field. In some conditions, fluxes for extensive cloud fields are approximated well by both regular arrays and when horizontal transfer of photons is neglected.