Abdou, W.A., J.V. Martonchik, R.A. Kahn, R.A. West, and D. J. Diner
(1997). A modified linear-mixing method for calculating atmospheric
path radiances of aerosol mixtures. *J. Geophys. Res.*, **102**, 16,883-16,888.

The top-of-atmosphere (TOA) path radiance generated by an aerosol
mixture can be synthesized by linearly adding the contributions of the
individual aerosol components, weighted by their fractional optical
depths. The method, known as linear mixing, is exact in the
single-scattering limit. When multiple scattering is significant, the
method reproduces the atmospheric path radiance of the mixture with <3% errors for weakly absorbing aerosols up to optical thickness of 0.5. However, when strongly absorbing aerosols are included in the mixture, the errors are much larger. This is due to neglecting the effect of multiple interactions between the aerosol components, especially when the values of the single-scattering albedos of these components are so different that the parameter ɛ=Σf_{i}|ϖ_{i}−ϖ_{mix}|/ϖ_{i} is larger than ∼0.1, where ϖ_{i} and f_{i} are the single-scattering albedo and the fractional abundance of the ith component, and ϖ_{mix} is the effective single-scattering albedo of the mixture. We describe an empirical, modified linear-mixing method which effectively accounts for the multiple interactions between aerosol components. The modified and standard methods are identical when ɛ=0.0 and give similar results when ɛ≤0.05. For optical depths larger than ∼0.5, or when ɛ>0.05, only the modified method can reproduce the radiances within 5% error for common aerosol types up to optical thickness of 2.0. Because this method facilitates efficient and accurate atmospheric path radiance calculations for mixtures of a wide variety of aerosol types, it will be used as part of the aerosol retrieval methodology for the Earth Observing System (EOS) multiangle imaging spectroradiometer (MISR), scheduled for launch into polar orbit in 1998