Uncertainties of optical parameters and their propagations in an analytical ocean color inversion algorithm

Following the theory of error propagation, we developed analytical functions to illustrate and evaluate the uncertainties of inherent optical properties (IOPs) derived by the quasi-analytical algorithm (QAA). In particular, we evaluated the effects of uncertainties of these optical parameters on the inverted IOPs: the absorption coefficient at the reference wavelength, the extrapolation of particle backscattering coefficient, and the spectral ratios of absorption coefficients of phytoplankton and detritus/gelbstoff, respectively. With a systematically simulated data set (46,200 points), we found that the relative uncertainty of QAA-derived total absorption coefficients in the blue-green wavelengths is generally within +/-10% for oceanic waters. The results of this study not only establish theoretical bases to evaluate and understand the effects of the various variables on IOPs derived from remote-sensing reflectance, but also lay the groundwork to analytically estimate uncertainties of these IOPs for each pixel. These are required and important steps for the generation of quality maps of IOP products derived from satellite ocean color remote sensing.