Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere
Abstract
The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical smallangle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosolladen model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few percent.The analytical solution to the problem which considers an aerosolladen atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.
 Publication:

Journal of Atmospheric Sciences
 Pub Date:
 March 1975
 DOI:
 10.1175/15200469(1975)032<0577:DOPFFM>2.0.CO;2
 Bibcode:
 1975JAtS...32..577W
 Keywords:

 Aerosols;
 Atmospheric Scattering;
 Light Scattering;
 Radiative Transfer;
 Scattering Functions;
 Sunlight;
 Atmospheric Models;
 Elevation Angle;
 Gauss Equation;
 Haze;
 Noise Intensity;
 Phase Shift;
 Rayleigh Scattering;
 Geophysics