Effect of Raman scattering on the average cosine and diffuse attenuation coefficient of irradiance in the ocean

We have investigated the effect of Raman scattering on the average cosine of underwater irradiance, <(mu)over bar>, the diffuse attenuation coefficient of irradiance, K, and the Raman scattering source coefficient, P*, throughout the water column and into the asymptotic field. The Raman scattering source coefficient is the fractional gain in the scaler irradiance from local Raman scattering at a given depth, and it can be found from the Gershun equation with a Raman source term. In particular, by using calculations from a radiative transfer model (Hydrolight 3.0), we compare <(mu)over bar>, K, and P* from simulations that include and that omit Raman scattering. These simulations are performed at wavelengths between 355 and 665 nm in a vertically homogeneous ocean with inherent optical properties (IOPs) determined from case 1 bio-optical models for three different chlorophyll concentrations (0.05, 0.5, and 5 mg m(-3)). We also investigated several two-layered oceans that assumed different inherent optical properties in the surface and deep layers. Our calculations showed that when Raman scattering is present, there may exist strong vertical gradients in the average cosine and the diffuse attenuation coefficient, especially at long wavelengths for low chlorophyll concentrations. In addition, a quasi-asymptotic field may be a feature of the vertical profiles of the average cosine and the diffuse attenuation coefficient. In the asymptotic field, there is no effect of Raman scattering at shorter wavelengths, there is a strong effect of Raman scattering at longer wavelengths and between these two spectral regions, and there is a transition that increases from 500 to 590 nm as the concentration of chlorophyll increases from 0.05 to 5 mg m(-3). Over a broad range of IOPs, the asymptotic parameters <(mu)over bar>(infinity)*, K-infinity*, and P*(infinity) are related by a quadratic relationship. Neither the magnitude or angular distribution of surface light nor changes in the absorption and scattering coefficients in the surface layer of a two-layered ocean have any effect on the values of <(mu)over bar>(infinity)*, K-infinity*, and P*(infinity),; the values of these parameters depend only upon the IOPs in the deepest layer.