Deep Learning to Infer Eddy Heat Fluxes from Sea Surface Height Patterns of Mesoscale Turbulence

Mesoscale eddies are the dominant form of oceanic variability and make a key contribution to oceanic heat transport through correlated fluctuations in velocity and temperature. The distribution and intensity of these eddies are expressed through variations in sea surface height (SSH) that are measured globally through satellite altimetry. Eddy heat fluxes are more challenging to monitor as they require simultaneous observations of ocean currents and interior temperature fields, which currently do not exist at mesoscales. However, surface and subsurface expressions of mesoscale turbulence are dynamically coupled, suggesting that SSH observations may contain at least partial information about the eddy fluxes. Here we use Machine Learning to demonstrate that eddy patterns derived from SSH snapshots can be used to estimate spatially-averaged eddy heat fluxes. Using a large volume of training data from idealized simulations of mesoscale turbulence, we show that deep Convolutional Neural Networks (CNNs) can predict up to about 60\% of instantaneous domain-averaged eddy heat flux variance, significantly outperforming other conventional data-driven techniques. Exploring the convergence of the CNN skill as the volume of training data and network complexity increase, we conjecture that there exists a dynamically-constrained upper bound on the information contained in SSH snapshots for diagnosing the heat fluxes. Nonetheless, this upper-bound is sufficiently high to provide much-needed estimates of eddy heat flux variability. Our results suggest that, with the development of appropriate training datasets, satellite altimetry can provide comprehensive monitoring of mesoscale eddy heat fluxes using deep CNNs.