  The upcoming Surface Water Ocean Topography (SWOT) satellite altimetry
mission is expected to yield two-dimensional high-resolution measurements of
Sea Surface Height (SSH), thus allowing for a better characterization of the
mesoscale and submesoscale eddy field. However, to fulfill the promises of this
mission, filtering the tidal component of the SSH measurements is necessary.
This challenging problem is crucial since the posterior studies done by
physical oceanographers using SWOT data will depend heavily on the selected
filtering schemes. In this paper, we cast this problem into a supervised
learning framework and propose the use of convolutional neural networks
(ConvNets) to estimate fields free of internal tide signals. Numerical
experiments based on an advanced North Atlantic simulation of the ocean
circulation (eNATL60) show that our ConvNet considerably reduces the imprint of
the internal waves in SSH data even in regions unseen by the neural network. We
also investigate the relevance of considering additional data from other sea
surface variables such as sea surface temperature (SST).
