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End-to-End Kalman Filter for the Reconstruction of Sea Surface Dynamics from Satellite Data

The reconstruction of sea surface geophysical variables typically relies either on Optimal Interpolation (OI) or on model-based approaches which explicitly exploit a dynamical model. While the optimal interpolation suffers from smoothing issues making it unreliable in retrieving fine scale variability, the selection and parametrization of a dynamical model, when considering model based data assimilation strategies, remains a complex issue since several trade-offs between the models complexity and its applicability in sea surface data assimilation need to be carefully addressed. In this work, and motivated by the success of artificial intelligence algorithms in various signal processing fields as well as the increasing amounts of observations and simulation datasets, we explore a data driven Koopman model and formulate the reconstruction problem as solution of the classical Kalman filter in a space of observables. The proposed architecture although linear, is shown to outperform state-of-the-art non linear data-driven filtering schemes such as the Analog Data Assimilation (AnDA).