Nature of optical products inverted semianalytically from remote sensing reflectance of stratified waters

Analytical expressions between inherent optical properties (IOPs) retrieved using semi-analytical algorithms (SAAs) and the vertical distributions of IOPs are derived based on an analytical model for subsurface remote sensing reflectance (r(rs)). These expressions provide a theoretical and comprehensive understanding of the inverted IOPs for stratified waters and lay the foundation to obtain equivalent products from profiling measurements for apple-to-apple comparison of the remotely sensed properties. It is found that the backscattering coefficient (b(b)) derived from an r(rs) spectrum via an SAA is governed by r(rs) in the longer wavelengths, consequently the inverted b(b) has less (or negligible) contributions from deeper depths, such as the subsurface chlorophyll maximum. In addition, the inverted b(b) spectrum does not have the spectral feature of the vertically weighted average b(b). The SAA-derived absorption coefficients, on the other hand, are found related to both the weighting profile at the wavelength of interest and the weighting profile in the longer wavelength(s). As a result, the absorption coefficients in the shorter wavelengths inverted from a perfect SAA are generally lower (can be 40% or more) than its vertically weighted average unless the surface layer dominates the diffuse attenuation of light. Furthermore, unlike the historical perception of remotely sensed chlorophyll concentration (Chl) for stratified waters, SAA-derived Chl is also sensitive to the vertical profile of b(b) and tends to be lower than its vertically weighted average assuming perfect bio-optical relationships, unless surface properties dominate the water column.