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Radiative transfer two-stream shape factors for ocean optics.

The mean upward-scattering coefficient of the downward-traveling photons and the mean downward-scattering coefficient of the upward-traveling photons are two factors needed for the two-stream approximation to the radiative-transfer equation. Numerical values of each shape factor just beneath the surface and at asymptotic depths give an indication of the range of values at intermediate depths in spatially uniform waters with no sources and are used to obtain an approximate depth-dependent model for each shape factor. The shape factors are computed for different surface-illumination conditions, wavelengths, and chlorophyll concentrations.