Relationship between spectral reflected irradiance at the sea surface and optical properties of marine phytoplankton

Two models of relative spectral reflectances as a function of chlorophyll-like pigment concentrations in the upper layer of oceanic waters and thus absorption and scattering properties of phytoplankton are described. These models are developed on the basis of statistical relationships between measured spectral diffuse attenuation coefficients and chlorophyll density in various oceanic waters (from oligotrophic to eutrophic). The semi-empirical model includes new spectral irradiance measurements in different waters. The strongly nonlinear regression equation (reflectance v. chlorophyll concentration) is compared with direct measurements, giving a negligible systematic error and a standard deviation of only 15% and of 20%, if applied to other spectra. The theoretical model is based on the principle of invariance of the emergent radiation for a semi-infinite plane-parallel medium, the delta function approximation for the forward scattering peak, the approximate solution of the radiative transfer equation as well as Cox and Munk's statistics of the roughness of the sea surface. It recovers formulas derived by others with more complicated models. Both models convert reflectance or reflected radiances reliably into inherent optical phytoplankton properties for different open ocean waters, indicating no need for a regional algorithm.