A model of the optical properties of the ocean, providing the absorption and scattering coefficients of the medium as nonlinear functions of the concentration of pigments associated with phytoplankton and their immediate detrital material, is presented. Monte Carlo computations of the attenuation coefficient of downwelling irradiance Kd for an ocean–atmosphere system illuminated by the sun at zenith, agree well with experimental data and demonstrate the validity of such a model for studying the influence of phytoplankton biomass on the propagation to the surface of light generated through bioluminescence. The radiative transfer equation for the irradiance at the sea surface resulting from illumination by a point source embedded in the water is solved by Monte Carlo techniques. The solution technique is validated through comparison with an asymptotic analytic solution for isotropic scattering. The computations show that the irradiance distribution just beneath the surface as a function of R, the distance measured along the surface from a point vertically above the source, is described by two regimes: (1) a regime in which the irradiance is governed mostly by absorption and geometry with scattering playing a negligible role—the near field; (2) a regime in which the light field at the surface is very diffuse and the irradiance decays approximately exponentially in R and is a very weak function of the source depth—the diffusion regime. The near field is of primary interest because it contains most of the power reaching the sea surface. An analytical model of the irradiance distribution just beneath the surface as a function of R, the source depth, and the pigment concentration for the near field is presented. This model is based on the observation that at most scattering events the change in the photon's direction is slight, and therefore, scattering is rather ineffective in attenuating the irradiance. An analytic solution for the irradiance from the point source, then, is first carried out ignoring scattering altogether; however, recognizing that backscattering will attenuate the irradiance, the absorption coefficient is replaced by an effective attenuation coefficient k. This effective attenuation coefficient is determined by fitting the total power just beneath the surface determined from the Monte Carlo computations to the analytical model. The resulting k is closely related to Kd, and the Monte Carlo irradiance as a function of R and source depth in the near-field regime can be approximated with high accuracy using the model. These results indicate Kd can be estimated at night by releasing a point source in the water, measuring the irradiance at the surface as it sinks, and fitting the measurements to the relationships developed here to determine k. The analytic model also enables estimation of the source depth and power from the irradiance distribution just beneath the surface.
© 1987 Optical Society of America
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