Effect of Raman scattering on the asymptotic average cosine in the ocean

Using the numerical radiative transfer model we investigate vertical changes in the average cosine of the underwater light field throughout the water column and into the asymptotic regime in the presence of Raman scattering. Results from these simulations show that Raman scattering strongly influences the asymptotic average cosine at wavelengths greater than about 500 nm in clear waters and 600 nm more turbid waters. At these wavelengths both the vertical behavior and the asymptotic value of the average cosine differ drastically in the presence of Raman scattering as compared to source-free waters. In red wavelengths and in clear waters, the effect of Raman scattering on the average cosine is most pronounced and a quasi-asymptotic field may be present. Our radiative transfer simulations confirm that the asymptotic diffuse attenuation coefficients at excitation and emission wavelengths are equivalent in the presence of Raman scattering. Using Gershun's equation with a source, we identify a new parameter P which is the ratio of scalar irradiance due to local inelastic scattering to total scalar irradiance. Similar to the asymptotic average cosine, P(subscript INF, is only dependent on the inherent optical properties of the asymptotic field.