A simplified physical model of cirrus cloud 8–13-µ radiance is derived, in an attempt to explain measured cloud radiance characteristics. Thermal emission and scattering of irradiance from the earth are considered separately. The scattering diagram for a 50-µ radius ice sphere, which is opaque at these wavelengths, is computed from diffraction theory and specular surface reflection. Thermal emission is found to exceed scattered radiance significantly for all zenith angles, and computed radiance values are found to match measured cloud radiance closely.
Freeman F. Hall, Jr., "A Physical Model of Cirrus 8–13-µ Infrared Radiance," Appl. Opt. 7, 2264-2269 (1968)