Satellite sensors already supply high-resolution (HR) observations of the ocean and this will become even more true in the future, especially for dynamic topography (altimetry) and for tracers (ocean color for example). In particular, the NASA/CNES SWOT (Surface Water Ocean Topography) mission will provide in 2020, high resolution Sea Surface Height measurements giving unprecedented information on the meso and submeso-scale dynamics.

This study aims at performing a three-dimensional (3D) and multivariate reconstruction of an oceanic state at meso-scale combining information from SSH and HR image structure observations. In this purpose, an inversion method was developed which consists in two steps : (i) first, the analysis step of the SEEK filter is applied to reconstruct a first guess of the ocean state at moderate resolution ; (ii) the second step applies a minimization method as in Gaultier et al., 2013 using HR image structure observations to compute additional corrections at higher resolution. The inversion method in Gaultier et al, 2013, was designed to estimate a surface velocity field at meso-scale. Here, three main extensions are developed : (i) a 3D and multivariate reconstruction of an oceanic state; (ii) a preconditionning (first step of the method); (iii) an implementation of a probabilistic approach. Since HR SWOT observations are still not available, a twin experiment is used to check the validity of the two-step inversion method. This twin experiment is defined using simulations from a HR regional numerical model of the Solomon Sea at 1/36° of spatial resolution [Djath et al., 2014]. The main interest of this region is its large Rossby radius of deformation at low latitudes, creating a significant range of meso- to submesoscale features as well as high energetic dynamics. These simulations are used to create a set of 3D multivariate states. To define the twin experiment, a true ocean among the multivariate states is chosen and a false ocean (background state) is also generated. In addition, synthetic observations of SSH and HR image structure are simulated from the true state. The two-step inversion method is used to correct the background state using these synthetic observations. A probabilistic approach is implemented which provides an update of the probability distribution at each step, and a sample is generated describing the uncertainties in the background state and subsequent estimates. Consequently, three samples are produced and different diagnostics show the ability of the two-step inversion method to significantly reduce the error and the dispersion of the sample. In particular, HR image structures play a key role to compute corrections at smaller scales.

Further research will be carried out to generate synthetic SSH observations by implementing similar experiments using (i) classic nadir along-track altimeter data, (ii) SWOT large swath data, and (iii) SWOT observation errors.