The quasi-single-scattering approximation in which a δ function replaces the forward portion of the volume scattering function is applied to radiative transfer in the ocean. Immediately beneath the surface, the product of the reflectance R and the downwelling irradiance-attenuation coefficient <i>K</i> (—) is equal to an integral of the volume scattering function in the backward direction weighted by a geometrical factor. Spectral variations of the volume scattering function are revealed in <i>K</i> (—)R; this is used to examine the wavelength dependence of scattering in two very different natural waters. In the clear water of Crater Lake, the backscattering is proportional to λ<sup>-3</sup>(λ=wavelength), whereas the turbid, productive waters of San Vicente Reservoir show a complex dependence of backscattering on wavelength, which is associated with anomalous dispersion due to the 670-nm absorption band of the chlorophyll that is contained in the suspended phytoplankton.
Howard R. Gordon, "Spectral variations in the volume scattering function at large angles in natural waters," J. Opt. Soc. Am. 64, 773-775 (1974)