Effective longwave cloud fraction and maximum-random overlap of clouds: A problem and a solution

In emissivity-type (i.e., nonscattering) longwave radiation schemes, the cl oud fraction N and emissivity epsilon are often merged into an effective cl oud fraction, N-e = N-epsilon. It is shown that if this approximation is co mbined with the maximum-random cloud overlap assumption (or with pure maxim um overlap), the results can be strongly sensitive to vertical resolution. This problem occurs at least in the European Centre for Medium-Range Weathe r Forecasts longwave scheme. It is further shown that the maximum-random ov erlap assumption can be implemented so that this problem is avoided, provid ed that the effects of N and epsilon are considered separately. The propose d method is applicable to emissivity-type longwave schemes in general.