Simultaneous dynamical reconstructions of Sea Surface Height and Temperature from multi-sensor satellite observations.

For many years, satellite observations of sea surface height (SSH) and sea surface temperature (SST) have provided invaluable information on the dynamics of the upper ocean at many scales. SSH and SST variables are dynamically linked, and are very often used together for many scientific studies (e.g. estimating heat transport in the upper layer by SSH-derived geostrophic currents). As observations are unevenly distributed in space and time (SSH is measured along one-dimensional trajectories and SST measurements are affected by clouds), many scientific and operational applications rely on gridded SSH and SST products. However, these products suffer from two main limitations. Firstly, conventional mapping techniques rely on static optimal interpolation schemes, which limits the estimation of nonlinear dynamics at scales poorly sampled by altimetry or, for SST, in regions densely affected by clouds (e.g. near western boundary currents). Secondly, SSH and SST reconstructions are performed separately, without relying on synergies between the two variables, which has an impact on the consistency of the two reconstructed fields. We introduce an original dynamical mapping algorithm to simultaneously reconstruct SSH and SST from multi-sensor satellite observations. This innovative method combines a weakly constrained, reduced-order, 4-dimensional variational scheme with simple physical models quasi-geostrophic for SSH and advection-diffusion for SST. The weak constraint of the models on the inversion procedure ensures that the reconstructed SSH and SST fields closely match the observations while preserving the space-time continuity of the dynamical structures. The work focuses on the North Atlantic Ocean over the year 2023 and considers the available along-track altimetric SSH, microwave and infrared SST data. The performances of the method are evaluated through Observing System Experiments, utilizing independent altimetric (from conventional and SWOT satellites) and drifter data. Results show a significant improvement of the reconstruction of short energetic structures, both in terms of SSH and SST, compared to operational products. The benefit of using SST observations for reconstructing SSH fields increases as the number of altimeters is reduced. This opens new opportunity to use the method for sea-level related climate applications that rely on a stable two altimeters constellation.