On the correlated k-distribution approximation in atmospheric calculations

Water vapor transmission function calculations are performed in the case of nonhomogeneous atmospheric paths based on the exact formulas for the coefficients of expansion into the series of exponents that we obtained earlier. A comparison of the results obtained with the exact formulas and those obtained in the context of the correlated k distribution (CKD) approximation shows that the CKD approximation is successful due to the fact that the optical thicknesses are the real correlating values in the Earth atmosphere, whereas the differences in the absorption coefficient behavior for various thermodynamic conditions are not of great importance in this problem. Situations in which the CKD approximation may break down are pointed out. It is noted that the accuracy of the expansion into a series of exponents depends on the accuracy of the absorption coefficient corresponding to the abscissas of the quadrature formulas more than on the number of points. Cases are mentioned in which the CKD approximation gives results far from the line-by-line results, whereas a calculation that uses exact formulas works well in these cases.