Locating convergent filaments from dilation rate fields obtained using Gaussian Process Regression

Lagrangian convergence in the ocean is identified using the metric dilation rate, the time average of divergence over a particle trajectory. Trajectories of drifter triads over a finite time interval can be used to estimate dilation rates in the absence of accurate high-resolution velocity fields. However, this method yields area-averaged estimates that are sparse, limiting the ability to accurately identify features with large aspect ratios like convergent submesoscale filaments. While these filaments can play an outsized role in the surface flow field, measuring its strength and shape directly with drifters requires accurately releasing drifters on and near the filament. To circumvent these issues, we compute point-wise dilation rate fields from velocity fields reconstructed using Gaussian Process Regression (GPR) to analyze sparse drifter trajectories. 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. The method is first tested on an analytic system, before being applied to the drifter data from the Lagrangian Submesoscale Experiment in 2016 to locate convergent filaments.