Radiative transfer in the ocean: computations relating to the asymptotic and near-asymptotic daylight field

The asymptotic daylight field in a homogeneous ocean is, like the absorption (a), scattering (b), and attenuation (c) coefficients and the volume scattering function (VSF), an inherent optical property (IOP) of the medium. A simple relationship in the spirit of the van de Hulst similarity relationships is developed from which the diffuse attenuation coefficient K(infinity) of the asymptotic light field can be obtained from a, b, and the VSF with an error of < 2%. In this relationship, the shape of the VSF is characterized by its asymmetry parameter g, whereas omega(0) = b/c characterizes the other IOP's. The relationship applies approximately to other quantities as well, particularly tau(x), which is the optical depth at which the downwelling irradiance attenuation coefficient K(d) can be replaced by K(infinity) with an error no greater than x%. Computations of tau(5) and tau(10) are presented as a function of g, omega(0) and the incident light field, and it is shown that for overcast conditions K(d) can be within 5% of K(infinity) at depths at which the downwelling irradiance is greater than 50% of its value at the surface. Simulations of radiative transfer in verticall inhomogeneous waters reveal that for sufficiently large depth (z), the value of K(infinity)(z) determined from the asymptotic theory that uses the values of the IOP's at z is a good approximation to K(d)(z). Thus our results suggest that in addition to being a pedagogically interesting concept, the asymptotic theory may actually be useful in ocean optics research. The influence of inelastic processes (fluorescence and Raman scattering) on K(infinity) are briefly examined, and it is shown that for an ocean of pure sea water, i.e., no particles or fluorescent compounds, K(infinity)(lambda) approximately 0.02 m(-1) for lambda >/= 430 nm with little spectral variation.