Radiance–irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies

Abstract

A full multiple-scattering algorithm for inverting profiles of the upwelling and downwelling irradiances to yield profiles of the absorption and backscattering coefficients in a vertically stratified water body is described and tested with simulated data. The algorithm does not require knowledge of the scattering phase function of the medium. The results are better the closer the phase function assumed in the retrievals is to the true phase function, although excellent retrievals of the absorption coefficient can still be obtained with an inaccurate phase function. Simulations show that the algorithm is capable of determining the vertical structure of a stratified water body and usually provides the absorption coefficient profile with an error ≲2% and the backscattering coefficient profile with an error ≲10%, as long as the spacing between pseudodata samples is sufficiently small that the necessary derivatives of the irradiances can be accurately computed. The performance is only slightly degraded when the upwelling radiance (nadir viewing) is substituted for the upwelling irradiance.