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

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 compared two frameworks based on the implicit inversion of a semi-analytical model derived from the classical radiative transfer equation. The first approach employed an iterative Bayesian inversion with a Gaussian approximation, which provides maximum a posteriori (MAP) estimates of the optical constituents along with their associated uncertainties. To improve the model performance, we optimized the model parameters using historical in situ measurements from the BOUSSOLE buoy and a Markov chain Monte Carlo (MCMC) algorithm, which reduced the root mean square error (RMSE) between the retrieved and observed values. The second approach employed the stochastic gradient variational Bayes (SGVB) estimator, which is designed to approximate the MAP estimates of the optical constituents while simultaneously optimizing the model parameters through maximum likelihood. This method resulted in faster computations than the iterative Bayesian inversion while maintaining comparable RMSE values. While the iterative Bayesian inversion provided reliable uncertainty estimates, the SGVB estimator offered faster computations of the optical constituents. Moreover, using a dataset of in situ sea surface chlorophyll a concentrations across a broad region of the northwestern Mediterranean Sea, we compared the inversion techniques with a state-of-the-art algorithm used within the Copernicus Marine Service, finding comparable performances across methods. Notably, the SGVB estimator showed the highest correlation between in situ measurements and retrievals throughout the analyzed region. We conclude that both inversion methods achieve a performance comparable to existing state-of-the-art algorithms. The Gaussian approximation offers robust uncertainty quantification, while the SGVB estimator provides a reliable and computationally efficient alternative.