Analytic Jacobians for ocean color retrieval: Linearization of the coupled atmosphere-ocean discrete ordinate model

Recent work has shown the need for accurate treatment of radiative transfer in ocean color retrieval. The plane-parallel coupled atmosphere-ocean discrete ordinate model CAO-DISORT has been used to investigate the validity of current approximative inverse methods and to study new techniques for improved ocean color retrieval. In this paper we show that CAO-DISORT is fully differentiable with respect to its input optical properties, so that we can define analytic Jacobians with respect to any profile element in the atmosphere and ocean. A single call to the linearized model will produce radiances and Jacobians at arbitrary optical depth and viewing geometry in either medium. The model also has a pseudo-spherical treatment for solar beam attenuation in a curved atmosphere. The linearized model can be used directly in iterative least-squares retrievals requiring forward model simulations of backscatter measurements and their parameter derivatives; there is no need for approximations involving an atmospheric correction. We demonstrate the model's new capability by performing closed-loop least squares fitting to simultaneously retrieve the aerosol optical thickness and marine chlorophyll concentration from a set of 6 synthetic measurements at SeaWifs wavelengths.