Radiative Cooling Calculated by Random Band Models with S-1-β Tailed Distribution

Abstract

Random band models with S-l-u tailed distribution for line intensity are proposed for both the Lorentz lineprofile and an approximate Voigt line profile suggested by Zhu. Such a distribution for the weak line intensityis more realistic than a Goody or Malkmus distribution. The transmission functions for the Goody and Malkmusrandom models can be derived as two special cases (j3 = -I and j3 = 0) of the present formulation, which isexpressed in the form of the hypergeometric function. It is shown that if j3 0.2, the improvement to thecalculations using the 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 Cot 15 pm band coolingrate in the middle atmosphere. The results show that by choosing more appropriate distribution in randomband models, the accuracy in cooling rate can be significantly improved, while the computation effort requiredis comparable in magnitude to the corresponding models with Goody or Malkmus distribution.