Parameterizing Grid-Averaged Longwave Fluxes for Inhomogeneous Marine Boundary Layer Clouds

This paper examines the relative impacts on grid-averaged longwave flux transmittance (emittance) for marine boundary layer (MBL) cloud fields arising from horizontal variability of optical depth τ and cloud sides. First, using fields of Landsat-inferred τ and a Monte Carlo photon transport algorithm, it is demonstrated that mean all-sky transmittances for 3D variable MBL clouds can be computed accurately by the conventional method of linearly weighting clear and cloudy transmittances by their respective sky fractions. Then, the approximations of decoupling cloud and radiative properties and assuming independent columns are shown to be adequate for computation of mean flux transmittance. Since real clouds have nonzero geometric thicknesses, cloud fractions Âc presented to isotropic beams usually exceed the more familiar vertically projected cloud fractions Ac. It is shown, however, that when Ac ≲ 0.9, biases for all-sky transmittance stemming from use of Ac as opposed to Âc are roughly 2–5 times smaller than, and opposite in sign to, biases due to neglect of horizontal variability of τ. By neglecting variable τ, all-sky transmittances are underestimated often by more than 0.1 for Ac near 0.75 and this translates into relative errors that can exceed 40% (corresponding errors for all-sky emittance are about 20% for most values of Ac). Thus, priority should be given to development of general circulation model (GCM) parameterizations that account for the effects of horizontal variations in unresolved τ; effects of cloud sides are of secondary importance. On this note, an efficient stochastic model for computing grid-averaged cloudy-sky flux transmittances is furnished that assumes that distributions of τ, for regions comparable in size to GCM grid cells, can be described adequately by gamma distribution functions. While the plane-parallel, homogeneous model underestimates cloud transmittance by about an order of magnitude when 3D variable cloud transmittances are ≲ 0.2 and by ∼20% to 100% otherwise, the stochastic model reduces these biases often by more than 80%.