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For interpretating remotely sensed diffuse reflectance of stratified case 1 waters, Gordon and Clark [ Appl. Opt. 19, 3428 ( 1980)] suggested that the reflectance of a stratified ocean is identical to that of a hypothetical homogeneous ocean with a phytoplankton pigment concentration (〈C〉) that is a depth-weighted average of the actual depth-varying concentration [C(z)]. However, this hypothesis has not been tested experimentally or theoretically. In this paper, the hypothesis is examined with Monte Carlo simulations of radiative transfer in case 1 waters by using a refined bio-optical model of the inherent optical properties of the medium. This bio-optical model, which includes separate plankton and detrital particle absorption and scattering, parameterized by the pigment concentration, is presented and tuned to Morel’s statistical analysis of the average diffuse attenuation coefficient over the euphotic zone. It provides a reasonable fit to diffuse attenuation and reflectance data of individual stations. The stratification model of Morel and Berthon [ Limnol. Oceanogr. 34, 1545 ( 1989)] characteristic of open ocean case 1 waters and a synthetic model of somewhat stronger stratification (maximum stratification of the pigment concentration |dC/dz| ≈ 0.43 mg/m3/m) are tested first. Two scenarios are used to relate the inherent optical properties to the pigment profile. In the first, the particle absorption and the scattering coefficients covary with C(z) and simulations show that the maximum error in the hypothesis is ≲ 2–3% for the pigment profiles considered. In contrast, in the second scenario, the particle absorption coefficient was permitted to covary with C(z), but the scattering coefficient was independent of depth. Here, errors in the hypothesis of as much as 22% were observed for the stronger stratifications. Finally, a synthetic example of strong stratification (|dC/dz|, as large as 8.9 mg/m3/m) is examined, and errors in the hypothesis of the order of 20–25% are found when both the particle absorption and the scattering covary with C; however, for the depth-independent particle scattering case, the hypothesis can lead to large errors in R. Interestingly, for both scenarios, the ratio of reflectances at two wavelengths shows a much smaller deviation from the hypothesis than the reflectance itself.
© 1992 Optical Society of America
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