Irradiance inversion theory to retrieve volume scattering function of seawater

An attempt to retrieve the volume scattering function (VSF) of source-free and no-inelastic-scattering ocean water is made from the upwelling irradiance Eu and downwelling irradiance Ed. It will be shown, from the radiative transfer equation, that the VSF of seawater can be calculated by the planar irradiances when the scattering phase function of the suspended particles in the backward direction and the molecular VSF are known. On the derivation of the hydrosol VSF, several optical properties such as the absorption coefficient a; the scattering coefficients of hydrosol, b, b(f), b(b) and those of the suspended particles, b(p), b(fp), b(bp); the beam attenuation coefficient c; the average cosines mu, mu(d), and mu(u); and the backscattering shape factor for the downwelling light stream, r(du), will also be obtained. On the derivation of those optical parameters, classical knowledge related to interrelationships between inherent optical properties and apparent optical properties and obtained with Monte Carlo numerical simulations is analytically verified. The present theory can be applied to surface waters and any wavelengths, except for waters and wavelengths with an extremely low b(b)/a ratio.