Time-dependent 2-stream approximation Hogan and Battaglia (JAS 2008): wide-angle scattering Describe diffuse flux in terms of outgoing stream I + and incoming stream I –, and numerically integrate the following coupled PDEs: I + and I – are used to calculate total (unpolarized) backscatter tot = || + T Time derivative Remove this and we have the time- independent two- stream approximation used in weather models Spatial derivative A bit like an advection term, representing how much radiation is upstream Loss by absorption or scattering Some of lost radiation will enter the other stream Gain by scattering Radiation scattered from the other stream Source Scattering from the quasi-direct beam into each of the streams
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