Satellite altimeters provide global observations of sea surface height (SSH) and present a unique data set for advancing our theoretical understanding of upper‐ocean dynamics and monitoring its variability. Considering that mesoscale SSH patterns can evolve on timescales comparable to or shorter than satellite return periods, it is challenging to accurately reconstruct the continuous SSH evolution as currently available altimetry observations are still spatially and temporally sparse. Here we explore the possibility of SSH interpolation via Deep Learning by using synthetic observations from an idealized quasigeostrophic model of baroclinic ocean turbulence. We demonstrate that Convolutional Neural Networks with Residual Learning are superior in SSH reconstruction to linear and recently developed dynamical interpolation techniques. Also, the deep neural networks can provide a skillful state estimate of unobserved deep ocean currents at mesoscales. These conspicuous results suggest that SSH patterns of eddies might contain substantial information about the underlying deep ocean currents that are necessary for SSH prediction. Our training data are focused on highly idealized physics and diversification of processes needs to be considered to more accurately represent the real ocean. In addition, methodological improvements such as transfer learning and implementation of dynamically aware loss functions might be necessary to consider before its ultimate use with real satellite observations. Nonetheless, by providing a proof of concept based on synthetic data, our results point to deep learning as a viable alternative to existing interpolation and, more generally, state estimation methods for satellite observations of eddying currents. Plain Language Summary: Satellite observations of sea surface height (SSH) are widely used to derive surface ocean currents on a global scale. However, due to gaps in SSH observations, it remains challenging to retrieve the dynamics of rapidly evolving upper‐ocean currents. To overcome this limitation, we propose a Deep Learning framework that is based on pattern recognition extracted from SSH observations. Using synthetic data generated from a simplified model of ocean turbulence, we demonstrate that deep learning can accurately estimate both surface and subsurface ocean currents, significantly outperforming the most commonly used techniques. By providing a proof of concept, our study highlights the strong potential of deep learning for estimating ocean currents from satellite observations. Key Points: The efficacy of Deep Learning in exploiting sparse sea surface height (SSH) data is demonstrated in a quasigeostrophic modelResidual Neural Networks are superior to linear and dynamical interpolation techniques for SSH reconstructionDeep networks skillfully reconstruct the unobserved deep flows from SSH data to provide a complete state estimate of geostrophic turbulence [ABSTRACT FROM AUTHOR]
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