# Super-Resolving Ocean Dynamics from Space with Computer Vision Algorithms
In practice, learning first from primitive equation simulations and known observing-system geometry and successively testing over true observation-based products can also be interpreted as a means to assimilate model physics in our data-driven reconstruction. Presently, core estimates of ocean surface currents are obtained by measuring absolute dynamic topography (i.e., the surface height referenced to an empirical geoid) through radar altimeters installed on a constellation of polar-orbiting satellite platforms. Sea level observations are acquired by altimeters along a discrete number of tracks, and surface geostrophic currents are obtained by first interpolating the ADT onto a regular 2D grid [32] and then computing ADT gradients (geostrophy implies velocities are perpendicular to the pressure gradients associated with sea surface level differences, with an inverse dependence on the Coriolis parameter). ADT-interpolated products reach an effective resolution of \(O\)(100 km) at mid-latitudes [33], but recent studies [34; 35] also revealed that many unresolved structures are aliased into larger structures and that the gridded altimetry products contain an unrealistic number of large mesoscale eddies. Hence, even for large scale eddies, having a typical wavelength larger than 100 km, the standard altimetry may be biased, with such large-scale bias mainly occurring in cyclonic eddies. Altimeter-derived ADT maps can thus be thought of as a deformed view of true surface elevation, obtained through a transformation that combines the satellite observation geometry and the space-time surface elevation evolution effectively captured by the interpolation algorithm. Our objective is to set up a neural network that is able to learn the inverse mapping from our limited input ADT to the true sea surface elevation. To do that, we explicitly include as tentative predictors the low-resolution ADT field, the SST field and its temporal derivative, \(\partial\)SST/\(\partial\)t, as well as the formal interpolation error (\(\Delta\)ADT) that is associated with the input ADT product (retrieved as part of the optimal interpolation algorithm), and we set the high-resolution ADT as our target. In fact, at the large scale, SST responds to air-sea fluxes and related upper layer mixing with the deeper oceanic layers, but when getting close to the mesoscale and sub-mesoscale dynamical range (namely at scales between a few kms and a few tens of km, over day-to-weeks timescales), a significant contribution to the local SST variations is given by horizontal advection (though vertical advection is also expected to play a significant role, especially at the sub-mesoscale, e.g., [36]). SST products obtained from thermal images provide synoptic high-resolution data up to (nominal) 1 km spatial resolution over wide portions of the ocean surface [37; 38]. Even if their effective spatial resolution rarely exceeds a few kilometres to tens of kilometres, they allow an almost continuous monitoring of SST changes at daily intervals and longer timescales. As such, several past attempts to improve surface current retrieval have been based on the use of the sequential information provided by SST products, either through maximum cross-correlation techniques [39] or by directly considering tracers' advection equation [40; 41; 42; 43]. Our work exploits the data prepared for an OSSE that was originally designed for different objectives in the framework of the European Space Agency ocean CIRculation from ocean COLour observations (CIRCOL) project [44]. They consist of one year of synthetic, daily ADT and surface geostrophic currents data over the Mediterranean Basin. Full details explaining how we simulate the observing system geometry are reported in Section 2, where all pre-processing steps to prepare our training and test datasets are described.