Hidden surface dynamical modes and SSH retrievals from a joint analysis of altimetry and microwave SST

The availability of daily satellite Sea Surface Temperature (SST) data and theoretical results (see e.g., [1]) advocate for new methods to retrieve the Sea Surface Height (SSH) and the surface geostrophic currents from SST observations. The underlying hypothesis comes to assume that the local variations of the SST relate to the surface currents. Ocean turbulence models, such as the Surface Quasi Geostrophic (SQG) theory (cf. [2], [3]) or statistical methods like neural networks (cf. [4]) or latent class regressions (cf. [5]) provide different means to state the SST-SSH relationships. This later approach has the advantage to be completely parametric and to account for different transfer functions between SST and SSH. It relies on a conditional setting with respect to a hidden variable related to different dynamical modes at the surface of the ocean. In this paper, we aim at further developing such latent models with an emphasis on two aspects: (i) the modeling and learning of the spatio-temporal dynamics of the hidden dynamical modes using Markovian priors, (ii) the reconstruction of daily SSH fields from a joint analysis of microwave SST and altimetry observation series. We evaluate the proposed model both qualitatively and quantitatively with respect to the reference altimetry product.