INSIGHT INTO THREE-DIMENSIONAL RADIATION TRANSPORT PROCESSES FROM DIFFUSION THEORY, WITH APPLICATIONS TO THE ATMOSPHERE

DOI: 10.1615/ICHMT.1997.IntSymLiqTwoPhaseFlowTranspPhenCHTRadTransfProc.100
29 pages

Anthony B. Davis
NASA's Goddard Space Flight Center, Climate and Radiation Branch NASA-GSFC (Code 913), Greenbelt, MD 20771, USA

Alexander Marshak
NASA's Goddard Space Flight Center, Climate and Radiation Branch NASA-GSFC (Code 913), Greenbelt, MD 20771, USA

Warren J. Wiscombe
NASA's Goddard Space Flight Center, Climate and Radiation Branch NASA-GSFC (Code 913), Greenbelt, MD 20771, USA

Robert F. Cahalan
NASA's Goddard Space Flight Center, Climate and Radiation Branch NASA-GSFC (Code 913), Greenbelt, MD 20771, USA

Abstract

There are two simple approaches to the manifestly 3D problem of radiative transfer in the cloudy atmosphere in the solar spectrum. First, the “weighted plane-parallel” approximation uses standard (homogeneous) plane-parallel theory to compute reflectance R, or any other property, for clear and cloudy conditions; results are then combined linearly according to cloud fraction. Second, the “independent pixel” approximation generalizes the linear weighting scheme by allowing for continuous (rather than Bernoulli) distributions of optical depth τ. Both approaches generally invoke the popular two-stream approximation that is formally analogous to diffusion through a horizontally homogeneous slab. Both approaches explain, via the nonlinear dependence of R on τ, the well-known negative bias between the variable situation and a homogeneous one with the same mean τ. However, neither approach accounts for the horizontal fluxes excited by the strong horizontal variability of extinction by cloud droplets. This suggests that the next logical step is to use 3D photon diffusion theory, without the homogeneity assumption. In this framework, we propose an essentially hydrodynamical model of photon flow that leads to a new analytical result: δR is proportional to the 1-point covariance of the fluctuations in extinction and the associated perturbation in flux.