A MODIFIED LINEAR-MIXING METHOD FOR CALCULATING ATMOSPHERIC PATH RADIANCES OF AEROSOL MIXTURES

The top-of-atmosphere (TOA) path radiance generated by an aerosol mixt ure can be synthesized by linearly adding the contributions of the ind ividual aerosol components, weighted by their fractional optical depth s. The method, known as linear mixing, is exact in the single-scatteri ng limit. When multiple scattering is significant, the method reproduc es the atmospheric path radiance of the mixture with <3% errors for we akly absorbing aerosols up to optical thickness of 0.5. However, when strongly absorbing aerosols are included in the mixture, the errors ar e much larger. This is due to neglecting the effect of multiple intera ctions between the aerosol components, especially when the values of t he single-scattering albedos of these components are so different that the parameter epsilon = Sigma f(i)\pi(i) - pi(mix)\/pi(i) is larger t han similar to 0.1, where pi(i) and f(i) are the single-scattering alb edo and the fractional abundance of the ith component, and pi(mix) is the effective single-scattering albedo of the mixture. We describe an empirical, modified linear-mixing method which effectively accounts fo r the multiple interactions between aerosol components. The modified a nd standard methods are identical when epsilon = 0.0 and give similar results when epsilon less than or equal to 0.05. For optical depths la rger than similar to 0.5, or when epsilon > 0.05, only the modified me thod can reproduce the radiances within 5% error for common aerosol ty pes up to optical thickness of 2.0. Because this method facilitates ef ficient and accurate atmospheric path radiance calculations for mixtur es of a wide variety of aerosol types, it will be used as part of the aerosol retrieval methodology for the Earth Observing System (EOS) mul tiangle imaging spectroradiometer (MISR), scheduled for launch into po lar orbit in 1998.