The deltaEddington approximation for radiative flux transfer.
Abstract
Simple approximations, like the Eddington, are often incapable of coping with the highly asymmetric phase functions typical of particulate scattering. A simple yet accurate method called the deltaEddington approximation is proposed for determining monochromatic radiative fluxes in an absorbingscattering atmosphere. In this method, the governing phase function is approximated by a Dirac delta function forward scatter peak and a twoterm expansion of the phase function. The fraction of scattering into the truncated forward peak is taken proportional to the square of the phase function asymmetry factor, which distinguishes the deltaEddington approximation from others of similar nature. The transmission, reflection, and absorption predicted by the deltaEddington approximation are compared with doubling method calculations for realistic ranges of optical depth, singlescattering albedo, surface albedo, sun angle and asymmetry factor. The approximation is shown to provide an accurate and analytically simple parameterization of radiation to replace the empirism currently encountered in many general circulation and climate models.
 Publication:

Journal of the Atmospheric Sciences
 Pub Date:
 December 1976
 DOI:
 10.1175/15200469(1976)033<2452:TDEAFR>2.0.CO;2
 Bibcode:
 1976JAtS...33.2452J
 Keywords:

 Albedo;
 Atmospheric Optics;
 Atmospheric Scattering;
 Delta Function;
 Eddington Approximation;
 Radiative Transfer;
 Absorptivity;
 Atmospheric Circulation;
 Atmospheric Models;
 Atmospheric Radiation;
 Climatology;
 Monochromatic Radiation;
 Parameterization;
 Reflectance;
 Transmissivity