Origins of ambiguity in the inversion of remote sensing reflectance signals by spectral matching in optically complex shelf seas

The reported occurrence of multiple solutions in the inversion of remote sensing reflectance (Rrs) signals is of considerable significance for attempts to recover the concentrations of optically significant materials (OSMs) in shelf seas. The severity of this problem was assessed by quantifying the number of matches between individual multi wavelength remote sensing 'observations' and the entries in a pre-computed look-up table (LUT) spanning the range of possible observations. As a simplifying step, radiative transfer modeling was used to confirm the existence of a linear relationship between Rrs in the visible wavebands and the ratio of the backscattering to absorption coefficients (bb/a) over the full range of OSM concentrations likely to be found in shelf seas. This meant that an LUT of appropriate size and resolution could be constructed from bb/a vectors rather than Rrs spectra, with a considerable saving of computational effort. The number of matches in the LUT was then determined as a function of the degree of noise present in the observation and the strictness of the matching criterion (a simple least-squares fitting routine). Perfect matching for the six visible wavebands of the SeaWiFs satellite radiometer was achieved only when the 'observed' bb/a vector was represented exactly in the library. The introduction of noise representing observational errors rapidly led to multiple matches, as did relaxation of the matching criterion. As an example of the sensitivity of OSM recovery to errors of observation, it was found that an average error of 0.1%, statistically distributed across all wavebands, led to an average recovery error of 6.4% in CHL for 3000 randomly selected observations