Radiative transfer in the ocean: the asymptotic daylight field

Abstract

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 of the medium. In contrast, the light field near the surface is an apparent optical property because it depends on the solar zenith angle, the surface roughness, etc., as well as the IOPs. A simple relationship in the spirit of the van de Hulst [Multiple Scattering, (Academic Press, 1980)] similarity relationships is developed from which the diffuse attenuation coefficient K in the asymptotic field can be obtained from a, b, and the VSF with an error <2%. In this relationship, the shape of the VSF is characterized by its asymmetry parameter g, while b/c characterizes the other IOPs. The relationship is shown to apply to other quantities as well, in particular to Dx the depth at which the downwelling irradiance attenuation coefficient can be replaced by K with an error no greater than x%. Computations of D10 are presented as a function of g, b/c, and the incident light field. Simulations of radiative transfer in vertically inhomogeneous waters reveal that for sufficiently large depth (z), the value of K determined from asymptotic theory using the values of the IOPs at z is a good approximation to the downwelling irradiance attenuation coefficient at z.