Solving the Equation of Radiative Transfer: Propagator Method Improvements

The radiative transfer equation in a planar stratified atmosphere with multiple scattering can be solved using a previously reported method of propagators. This method here is improved in several ways. Cross-polarized scattering is added. A new propagator equation improves the calculation efficiency. The previous use of only down propagation sometimes gave no solution near the Earth surface. The combined use of up and down propagation gives a solution at all altitudes. New details about the error structure and limitations of the method are provided. A previously unreported problem with computer precision is solved using a new technique called bootstrapping. Bootstrapping also extends the analysis capability of the method to atmospheres with higher total attenuation.