Unsupervised Learning of Sea Surface Height Interpolation from
  Multi-variate Simulated Satellite Observations
Theo Archambault Arthur Filoche Anastase Charantonis Dominique Bereziat Sylvie Thiria
Satellite-based remote sensing missions have revolutionized our understanding
of the Ocean state and dynamics. Among them, spaceborne altimetry provides
valuable measurements of Sea Surface Height (SSH), which is used to estimate
surface geostrophic currents. However, due to the sensor technology employed,
important gaps occur in SSH observations. Complete SSH maps are produced by the
altimetry community using linear Optimal Interpolations (OI) such as the
widely-used Data Unification and Altimeter Combination System (DUACS). However,
OI is known for producing overly smooth fields and thus misses some
mesostructures and eddies. On the other hand, Sea Surface Temperature (SST)
products have much higher data coverage and SST is physically linked to
geostrophic currents through advection. We design a realistic twin experiment
to emulate the satellite observations of SSH and SST to evaluate interpolation
methods. We introduce a deep learning network able to use SST information, and
a trainable in two settings: one where we have no access to ground truth during
training and one where it is accessible. Our investigation involves a
comparative analysis of the aforementioned network when trained using either
supervised or unsupervised loss functions. We assess the quality of SSH
reconstructions and further evaluate the network's performance in terms of eddy
detection and physical properties. We find that it is possible, even in an
unsupervised setting to use SST to improve reconstruction performance compared
to SST-agnostic interpolations. We compare our reconstructions to DUACS's and
report a decrease of 41\% in terms of root mean squared error.