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We present a novel generalization of the two-stream method of radiativetransfer, which allows for the accurate treatment of radiative transfer in thepresence of strong infrared scattering by aerosols. We prove that thisgeneralization involves only a simple modification of the coupling coefficientsand transmission functions in the hemispheric two-stream method. Thismodification originates from allowing the ratio of the first Eddingtoncoefficients to depart from unity. At the heart of the method is the fact thatthis ratio may be computed once and for all over the entire range of values ofthe single-scattering albedo and scattering asymmetry factor. We benchmark ourimproved two-stream method by calculating the fraction of flux reflected by asingle atmospheric layer (the reflectivity) and comparing these calculations tothose performed using a 32-stream discrete-ordinates method. We further compareour improved two-stream method to the two-stream source function (16 streams)and delta-Eddington methods, demonstrating that it is often more accurate atthe order-of-magnitude level. Finally, we illustrate its accuracy using a toymodel of the early Martian atmosphere hosting a cloud layer composed ofcarbon-dioxide ice particles. The simplicity of implementation and accuracy ofour improved two-stream method renders it suitable for implementation inthree-dimensional general circulation models. In other words, our improvedtwo-stream method has the ease of implementation of a standard two-streammethod, but the accuracy of a 32-stream method.

Analytical Models of Exoplanetary Atmospheres. IV. Improved Two-stream Radiative Transfer for the Treatment of Aerosols