Zhu, X., 1989: Radiative cooling calculated by random band model with S^-1-B tailed distribution. Journal of the Atmospheric Sciences, 46(4), 511-520.

Abstract: Random band models with S^-1-B tailed distribution for line intensity are proposed for both the Lorentz line profile and an approximate Voigt line profile suggested by Zhu. Such a distribution for the weak line intensity is more realistic than a Goody or Malkmus distribution. The transmission functions for the Goody and Malkmus random models can be derived as two special cases (B = -1 and B = 0) of the present formulation, which is expressed in the form of the hypergeometric function. It is shown that if B is greater than or equal to 0.2, the improvement to the calculations using S^-1-B tailed distribution is as great as using the Malkmus rather than the Goody model. The transmission function for the Voigt line profile is applied to the calculations of CO₂ 15 µm band cooling rate in the middle atmospehre. The results show that by choosing more appropriate distribution in random band models, the accuracy in cooling rate can be significantly improved, while the computation effort required is comparable in magnitude to the corresponding models with Goody or Malkmus distribution.