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Lacis, A.A., J. Chowdhary, M.I. Mishchenko, and B. Cairns, 1998: Modeling errors in diffuse-sky radiation: Vector vs. scalar treatment. Geophys. Res. Lett., 25, 135-138, doi:10.1029/97GL03613.
Radiative transfer calculations that utilize the scalar approximation of light produce intensity errors as large as 10% in the case of pure Rayleigh scattering. This modeling error, which arises primarily from second order scattering, is greatly reduced for flux and albedo results because of error cancellation brought about by integration over scattering angle. However, polarized light scattered from an underlying ocean surface, or from atmospheric aerosols, interacts with the pattern of Rayleigh scattered polarization to distort the error cancellation and thus incur larger flux and albedo errors. While addition of scattered radiation from clouds, aerosols or ground surface into the Rayleigh atmosphere tends to reduce the magnitude of scalar approximation intensity errors, the scalar errors in fluxes and albedos are not proportionately reduced, but are actually increased.
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