Bidirectional reflectance function for oceanic waters with varying chlorophyll concentrations: Measurements versus predictions

The bidirectional reflectance of the ocean is an important parameter in ocean color remote sensing. Model predictions for case-1 waters were compared with measurements over a large range of chlorophyll concentrations (0.1–10 mg m23 Chl, where Chl represents the sum of chlorophyll a and phaeophytin a), but with restricted solar zenith angles. We used the measured chlorophyll concentration and a model to predict the shape of the upwelling spectral radiance distribution. We found that the model predicted the radiance in the view direction, normalized by the nadir radiance, to within 7%. We also found that Q(Eu/Lu) was predicted within 7%. The upward radiance field within oceanic waters is not isotropic, especially near the surface, where it depends strongly on the sun’s position. The radiances in near-horizontal directions always exceed the nadir radiance, and the horizontal radiances toward the sun (dominated by forward scattering) are always greater than in the antisolar direction (back scattering). Notwithstanding that multiple scattering occurs within the medium and thus tends to homogenize the radiant field, the polar and azimuthal asymmetries persist throughout the upper layers of the ocean. The experimental evidence of this phenomenon dates back to the end of the 1950s and 1960s (Jerlov and Fukuda 1960; Tyler 1960; Sasaki et al. 1962); yet, the theoretical analysis and modeling of the upwelling light field has been undertaken more recently (Morel and Gentili 1991, 1993, 1996). The quantitative study of this anisotropy, essentially based on theory and computations, has been prompted by the implication of this phenomenon in the ocean color remote sensing problem, in so far as the radiance emerging from the ocean depends on the bidirectional structure of the upward radiance field just beneath the interface. With the development of new instrumentation (Voss 1989a; Voss and Chapin 1992), measurements of the radiance distribution at sea have been resumed after a long interruption (Voss 1989b; Voss et al. 2003). The anisotropic character of the upward radiance field is conveniently expressed by the bidirectional function, or Qfunction (Austin 1974), by which any upward radiance Lu is related to the planar upward irradiance Eu through E (u , l) u s L (u , u9, w, l) 5 (1) u s Q(u , u9, w, l) s where us is the zenith-sun angle (in air), u9 is the angle be-