Data-Informed Inversion Model (DIIM): a framework to retrieve marine optical constituents in the BOUSSOLE site using a three-stream irradiance model

Abstract. Within the New Copernicus Capability for Trophic Ocean Networks (NECCTON) project, we aim to improve the current data assimilation system by developing a method for accurately estimating marine optical constituents from satellite-derived Remote Sensing Reflectance. We developed and compared two frameworks by implicitly inverting a semi-analytical expression derived from the classical Radiative Transfer Equation. First, we used a Bayesian estimation, which provided retrievals of the optical constituents along with their uncertainties. Moreover, using historical in-situ measurements together with a Markov Chain Monte Carlo (MCMC) algorithm to adjust the model parameters, we were able to reduce the root mean square Error (RMSE) between the retrieved data and in-situ observations. Second, we employed the Stochastic Gradient Variational Bayes (SGVB) framework to efficiently approximate the Maximum Posterior (MAP) estimates of the optical constituents while simultaneously finding the Maximum Likelihood Estimate (MLE) of the model parameters. This approach resulted in faster computations of the optical constituents compared to Bayesian estimations, with equivalent RMSE values between the retrieved data and in-situ observations. We showed that both, the MCMC and SGVB based algorithms, were able to find sets of optimal parameters, which, due to correlations between them, are not unique. We conclude that both methods are consistent with the Radiative Transfer Equation. The first method provides reliable uncertainty estimations, while the second offers a faster alternative to standard inversion techniques, making it suitable for inversion and model optimization problems where MCMC algorithms are intractable.