Abstract
We have developed a simple analytical approximation for the infrared attenuation and emissivity of clouds and fogs composed of water spheres, based on a polynomial approximation to the Mie attenuation efficiencies. The attenuation coefficients can be obtained in simple analytic form as a function of the liquid water content and two parameters characterizing the size distribution of the water droplets, such as its effective radius and effective variance. The coefficients representing the approximation can be precalculated and stored in a form suitable for use in the inversion of remotely sensed cloud radiances, climate modeling, and numerical weather prediction. The resulting accuracies are within a few percent when compared with exact Mie calculations and integration over the size distribution, while the computational burden is reduced by several orders of magnitude. The radiances from clouds, as well as the cloud reflectance and emittances, calculated with radiative transfer theory using these approximations for the cloud scattering and absorption properties are compared with calculations using exact Mie scattering results. These comparisons show that the radiances, using the new approximations, generally are calculated with greater accuracy than might be expected on the basis of the accuracy of the approximations for the separate parameters.
