Abstract
A simple approximation has been developed for the infrared emittance of clouds composed of water spheres based on the absorption approximation for the emittance and on the polynomial approximation to the Mie absorption efficiency. The expression for the IR emittance is obtained in a simple analytical form as a function of the liquid water content and two size distribution parameters, namely, the effective radius and effective variance. The approximation is suitable for numerical weather prediction, climate modeling, and radiative transfer calculations. The accuracy, when compared to the exact Mie calculation and integration over the size distribution, is within a few percent, while the required computer time is reduced by several orders of magnitude. In the limit of small droplet sizes, the derived IR emittance reduces to a term proportional to the liquid water content.
