Radiance—irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters

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Abstract
A full multiple-scattering algorithm for inverting upwelling radiance (L u) or irradiance (E u) and downwelling irradiance (E d) profiles in homogeneous natural waters to obtain the absorption (a) and backscattering (b b) coefficients is described and tested with simulated data. An attractive feature of the algorithm is that it does not require precise knowledge of the scattering phase function of the medium. For the E u – E d algorithm, tests suggest that the error in the retrieved a should usually be ≲1%, and the error in b b ≲10–20%. The performance of the L u –E d algorithm is not as good because it is more sensitive to the scattering phase function employed in the inversions; however, the error in a is usually still small, i.e., ≲3%. When the algorithm is extended to accommodate the presence of a Lambertian-reflecting bottom, the retrievals of a are still excellent, even when the presence of the bottom significantly influences the upwelling light field; however, the error in b b can be large.