Effective Longwave Cloud Fraction and Maximum-Random Overlap of Clouds:A Problem and a Solution

Abstract

In emissivity-type (i.e., nonscattering) longwave radiation schemes, the cloud fraction N and emissivity ε are often merged into an effective cloud fraction, N_e = Nε. It is shown that if this approximation is combined with the maximum–random cloud overlap assumption (or with pure maximum overlap), the results can be strongly sensitive to vertical resolution. This problem occurs at least in the European Centre for Medium-Range Weather Forecasts longwave scheme. It is further shown that the maximum–random overlap assumption can be implemented so that this problem is avoided, provided that the effects of N and ε are considered separately. The proposed method is applicable to emissivity-type longwave schemes in general.