Learning Sea Surface Height Interpolation From Multi‐Variate Simulated Satellite Observations

Satellite‐based remote sensing missions have revolutionized our understanding of the Ocean state and dynamics. Among them, space‐borne altimetry provides valuable Sea Surface Height (SSH) measurements, used to estimate surface geostrophic currents. Due to the sensor technology employed, important gaps occur in SSH observations. Complete SSH maps are produced using linear Optimal Interpolations (OI) such as the widely used Data Unification and Altimeter Combination System (duacs). 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 propose a new multi‐variate Observing System Simulation Experiment (OSSE) emulating 20 years of SSH and SST satellite observations. We train an Attention‐Based Encoder‐Decoder deep learning network (abed) on this data, comparing two settings: one with access to ground truth during training and one without. On our OSSE, we compare abed reconstructions when trained using either supervised or unsupervised loss functions, with or without SST information. We evaluate the SSH interpolations in terms of eddy detection. We also introduce a new way to transfer the learning from simulation to observations: supervised pre‐training on our OSSE followed by unsupervised fine‐tuning on satellite data. Based on real SSH observations from the Ocean Data Challenge 2021, we find that this learning strategy, combined with the use of SST, decreases the root mean squared error by 24% compared to OI. Plain Language Summary The surface of the ocean is observed through various sensors embedded in satellites. Specifically, the height of the sea surface is a crucial variable as it can be used to estimate surface currents. It is currently measured through satellite altimeters, but the data acquisition process leaves gaps in their observations. Providing fully gridded maps of the sea surface height is thus an important interpolation problem. The widely used interpolated product has some troubles, especially when dealing with small and rapidly evolving eddies. To enhance its quality, we propose an artificial neural network, a trainable method able to estimate complete sea surface height images. The flexibility of these methods allows us to use different satellite information, such as the sea surface temperature, which has a better resolution. Usually, neural networks are trained on a data set upon which they learn the link between input and output d