Radiative Transfer in Water Clouds in the 10-Micron Window Region

Abstract

The equation of radiative transfer as applied to water clouds in the window region near 10 microns is solved numerically by using values of the phase function and albedo for single scattering estimated by Deirmendjian (1964). It is found that for monochromatic radiation of 10 microns the upward intensity at the cloud top shows limb darkening and the downward intensity at the cloud base, limb brightening. For the whole window region from 8 to 12 microns, the upward flux at the cloud top and the downward flux at the cloud base, as well as the emissivity of the cloud, transmissivity at the cloud top and reflectivity at the cloud base are evaluated. When the cloud is thin, the upward flux is mostly dependent on the incident flux corresponding to the earth surface temperature, and when the cloud becomes thick, it approaches the black-body flux at the cloud temperature. The downward flux at the cloud base is very small for a thin cloud, increases with cloud thickness and approaches a constant value which is somewhat larger than the upward flux at the cloud top when the cloud becomes very thick. It is also found that the emissivity, transmissivity and reflectivity change with cloud thickness but are practically independent of both the cloud and earth surface temperatures. Therefore, by using the values of these quantities obtained in this study, one can evaluate the upward and downward fluxes for any combination of cloud and earth surface temperatures and cloud thicknesses.