We present a novel generalization of the two-stream method of radiative
transfer, which allows for the accurate treatment of radiative transfer in the
presence of strong infrared scattering by aerosols. We prove that this
generalization involves only a simple modification of the coupling coefficients
and transmission functions in the hemispheric two-stream method. This
modification originates from allowing the ratio of the first Eddington
coefficients to depart from unity. At the heart of the method is the fact that
this ratio may be computed once and for all over the entire range of values of
the single-scattering albedo and scattering asymmetry factor. We benchmark our
improved two-stream method by calculating the fraction of flux reflected by a
single atmospheric layer (the reflectivity) and comparing these calculations to
those performed using a 32-stream discrete-ordinates method. We further compare
our improved two-stream method to the two-stream source function (16 streams)
and delta-Eddington methods, demonstrating that it is often more accurate at
the order-of-magnitude level. Finally, we illustrate its accuracy using a toy
model of the early Martian atmosphere hosting a cloud layer composed of
carbon-dioxide ice particles. The simplicity of implementation and accuracy of
our improved two-stream method renders it suitable for implementation in
three-dimensional general circulation models. In other words, our improved
two-stream method has the ease of implementation of a standard two-stream
method, but the accuracy of a 32-stream method.Comment: Accepted by ApJS. 7 pages, 5 figure
