Simple Approximation for Infrared Emissivity of Water Clouds

We have derived a simple approximation for the emissivity and flux emissivity of water clouds inside the atmospheric window between 8 and 14 m. In our approximation the emissivity in the 8–11.5 m band is a function only of the cloud's liquid water content and cloud thickness. When compared with the exact radiative transfer calculations the broad-band flux emissivities (in the 8–11.5 m region) differ by less than 10%. At wavelengths > 11.5 m the emissivity is a function of the droplet size distribution as well. By considering a typical droplet size distribution for stratus, altostratus and cumulus clouds, we have shown that the effect of the size distribution on the broad-band flux emissivity in the 8–14 m band is about 35%. Our approximation should be useful for treatment of cloud infrared properties in climate models.