PARAMETERIZING GRID-AVERAGED LONGWAVE FLUXES FOR INHOMOGENEOUS MARINEBOUNDARY-LAYER CLOUDS

This paper examines the relative impacts on grid-averaged longwave flu x transmittance (emittance) for marine boundary layer (MEL) cloud fiel ds arising from horizontal variability of optical depth tau and cloud sides. First, using fields of Landsat-inferred tau and a Monte Carlo p hoton transport algorithm, it is demonstrated that mean all-sky transm ittances for 3D variable MBL clouds can be computed accurately by the conventional method of linearly weighting clear and cloudy transmittan ces by their respective sky fractions. Then, the approximations of dec oupling cloud and radiative properties and assuming independent column s are shown to be adequate for computation of mean flux transmittance. Since real clouds have nonzero geometric thicknesses, cloud fractions (A) over cap(c) presented to isotropic beams usually exceed the more familiar vertically projected cloud fractions A(c). It is shown, howev er, that when A(c) less than or similar to 0.9, biases for all-sky tra nsmittance stemming from use of A(c) as opposed to (A) over cap(c) are roughly 2-5 times smaller than, and opposite in sign to, biases due t o neglect of horizontal variability of tau. By neglecting variable tau , all-sky transmittances are underestimated often by more than 0.1 for A(c) near 0.75 and this translates into relative errors that can exce ed 40% (corresponding errors for all-sky emittance are about 20% for m ost values of A(c)). Thus, priority should be given to development of general circulation model (GCM) parameterizations that account for the effects of horizontal variations in unresolved tau, effects of cloud sides are of secondary importance. On this note, an efficient stochast ic model for computing grid-averaged cloudy-sky flux transmittances is furnished that assumes that distributions of tau, for regions compara ble in size to GCM grid cells, can be described adequately by gamma di stribution functions. While the plane-parallel, homogeneous model unde restimates cloud transmittance by about an order of magnitude when 3D variable cloud transmittances are less than or similar to 0.2 and by s imilar to 20% to 100% otherwise, the stochastic model reduces these bi ases often by more than 80%.