Learning deep emulators for the interpolation of satellite altimetry data

Over the last few years, a very active field of research has aimed at exploring new data-driven and learning-based methodologies to propose computationally efficient strategies able to benefit from the large amount of observational remote sensing and numerical simulations for the reconstruction, interpolation and prediction of high-resolution derived products of geophysical fields. These approaches now reach state-of-the performance for the reconstruction of satellite-derived geophysical fields. In this context, deep emulators emerge as new means to bridge model-driven and learning-based frameworks. Here, we focus on deep emulators for reconstruction and data assimilation issues, and more specifically on 4DVarNet schemes. These schemes bridge variational data assimilation formulation and deep learning schemes to learn 4DVar models and solvers from data. Here, we present an application of 4dVarNet schemes to the reconstruction of sea surface dynamics. More specifically, we aim at learning deep emulators for the interpolation from altimetry data. Similarly to a classic optimal interpolation, we leverage a minimization-based strategy but we benefit from the modeling flexibility of deep learning framework to embed non-linear and multi-scale priors and learn jointly a gradient-based solver for the underlying variational cost. Overall, the proposed 4dVarNet scheme defines an end-to-end neural architecture which use irregularly-sampled altimetry data as inputs and outputs a gridded and gap-free fields. We report numerical experiments within a data challenge dedicated to the benchmarking of SSH (Sea Surface Height) mapping algorithms. This data challenge relies on an observation system simulation experiments (OSSE) setting in a Gulf Stream region with nadir and wide-swath SWOT satellite altimetry data.
Our numerical experiments demonstrate that we can train neural interpolation schemes with very large missing data rates (between 90% and 95%) in a supervised manner. The proposed approach outperforms state-of-the-art schemes, including model-driven ones, and significantly improves the resolved space and time scales compared to the operational optimally-interpolated SSH product. We further discuss the extensions of the proposed scheme especially towards the multi-scale reconstruction of sea surface dynamics from multi-source data.