Extracting submesoscales from drifter observations using adaptive Gaussian Process regression techniques

Objective mapping applications commonly rely on Gaussian Process (GP) regression, also known as optimal interpolation, and on a static and stationary covariance matrices to interpolate scattered observations. This leads to undesirable results, such as excessive smoothness and artifacts, when applied to observations in regions with strongly varying flow regimes. Two machine-learning based techniques are proposed here to overcome these limitations in the context of estimating the Eulerian velocity field from surface drifters over intense submesoscale frontal features. The first approach relies on clustering observations and adjusting the space-time coordinates continuously to follow an evolving large-scale feature; a stationary homogeneous covariance matrix in the moving coordinates is then used in the GP step. The second approach relies on the Deep Gaussian Process (DGP) with non-stationary/non-homogeneous covariances to construct the Eulerian field. DGPs are multi-layer generalizations of GPs and can be shown to be equivalent to neural networks with infinitely wide hidden layers. The observations used here are velocity displacements from hundreds of surface drifters released in the DeSoto Canyon during the Lagrangian Submesoscale Experiment, conducted by the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment. Preliminary results show that both techniques significantly improve the velocity field reconstructions when compared to a standard GP application.