Frequency integration for radiative transfer problems involving homogeneous non-gray gases: The inverse transmission function

It is shown that narrow-band frequency integration for radiative-transfer problems, involving homogeneous non-gray gases, can be accomplished by an integration with respect to the absorption coefficient. The kernel of the absorption-coefficient integral is a property of the gas and can be obtained directly from the absorption coefficient for a simple dependence of the absorption coefficient on frequency. It is shown that the kernel (called the ‘inverse transmission function’) can also be obtained as the inverse Laplace transform of the transmission function, without explicit knowledge of the absorption coefficient. The kernel has been obtained using the inverse transmission-function method for two statistical band models: the Goody model and the Malkmus model. The kernel for the Malkmus model offers a simple, accurate, straightforward method for narrow-band frequency integration.