Abstract
The cloud‐matrix method for describing the mutual cloud‐coverage relationship between any two levels is systematically discussed. A general method is devised for calculating the effective cloud emissivity for maximum‐random overlap clouds. For several cloud configurations with extreme variation in fractional cloud amounts, the errors are generally very small (<5%). The radiative‐transfer process that corresponds to the random‐overlap cloud scheme is discussed. Compared with the purely random clouds scheme, the maximum‐random overlap scheme always produces a smaller cooling rate in the lower layers of a cloud block and a smaller downward flux. The difference in cooling rate can be about 3 K d^−1^ and the difference in the downward flux near the surface can be as large as 20 W m^−2^. The calculations show that the scheme of effective cloud emissivity commonly used in general‐circulation models could cause underestimation of cloud cooling rate. The clear‐sky and the cloudy‐sky radiation field can be obtained through a single calculation process but with different water‐vapour profiles. The results show that for the all‐sky case the separate treatment of the water‐vapour profile for clear and cloudy portions makes only a very small difference in the cooling rate and upward flux at the top of the atmosphere in comparison with the results of an averaged water‐vapour profile.