Lagrangian analysis of submesoscale flows from sparse data using Gaussian Process Regression for field reconstruction

Abstract

Lagrangian analyses of oceanic flows provide insight into the various transport pathways in the ocean. This analysis typically relies on a dense set of trajectories that can be computed using high-resolution velocity fields, which are often not available during field experiments. Instruments like drifters and floats are often employed to overcome the limitations imposed by satellite- and radar-based velocity fields, to understand the transport pathways in the ocean. However, the sparsity in available drifter-trajectory data proves prohibitive to obtaining a comprehensive map of the Lagrangian characteristics of the underlying flow. To circumvent these issues, we use Gaussian Process Regression (GPR) to obtain velocity fields from sparse drifter data to generate synthetic trajectories and subsequently estimate two Lagrangian metrics, FTLE and dilation rate. A detailed error analysis is performed for drifter clusters deployed within various dynamical regions in the analytic Bickley jet system. The uncertainties in velocity reconstruction obtained from the GPR method, averaged along particle trajectories, locate Lagrangian confidence regions that are applicable both to synthetic trajectories and the dilation rate field. A sensitivity analysis reveals the role played by factors such as the spatial sampling density and temporal resolution of the drifter data, as well as the effect of position uncertainty as a result of GPS inaccuracy. The method is then applied to the drifter data from the Lagrangian Submesoscale Experiment in 2016 to locate convergent filaments. The results present a marked improvement over direct estimation of area-averaged dilation rates using drifter clusters.