High spectral resolution atmospheric radiative transfer: Application of the equivalence theorem

This paper introduces several new variations of the equivalence theorem of Irvine [1964] which may increase the speed and accuracy of spectral radiative transfer models that calculate spectral radiance or flux. Using this theory, spectral gaseous, cloud, and surface absorptions are accommodated by integrating or summing over photon path length and scattering probability density functions (pdfs) after the completion of the multiple-scattering calculation. This procedure can be performed for absorption coefficients at any spectral resolution within a wavelength interval in which scattering properties of the atmosphere can be considered constant. This technique eliminates the need to run the multiple-scattering portion of a model more than once for each interval in lieu of integration and/or summation. If this procedure can be performed efficiently, dramatic increases in model speed may be realized. Also, because absorption coefficient spectral resolution can be extremely fine, the need for approximations or parameterizations is eliminated, increasing model accuracy. Unlike the original derivation, the new version of the gaseous absorption equation allows the use of complex model scattering atmospheres. An approximation is introduced which allows the use of gas profiles which vary in the vertical. Because employment of the complete theory requires a relatively large amount of computer memory, a pdf approximation is introduced to make it tractable. Validation of each relation is presented using a Monte Carlo model simulating shortwave flux. An example of shortwave flux transmitted through a three-dimensional model atmosphere obtained from the Monte Carlo/equivalence theorem (MC/ET) model is shown along with an analysis of the effect of constant scattering property wavelength interval size on the resulting broadband flux.