Estimating dilation rate fields from sparse drifter data using Gaussian Process Regression

Dilation rate, the time average of divergence over a particle trajectory, reveals convergent and divergent features that persist over a finite time interval. Direct measurements of dilation rate in the ocean are difficult due to the lack of accurate high-resolution velocity fields. Drifter swarms can be used to estimate dilation rates. However, these estimates are sparse and subject to errors as a result of the relative position of drifters within a swarm, limiting the ability to locate regions of strongest convergence and divergence. Adding more drifters to densely cover the space could address these issues, but this is rarely possible. Alternatively, we can synthetically generate drifter trajectories if a velocity field can be estimated. In our study, we use Gaussian Process Regression to obtain velocity fields from sparse drifter data to generate synthetic trajectories and subsequently, estimate dilation rates. A detailed error analysis is performed for various flow features on an analytic system before testing the method on a realistic data-assimilative model of the Western Mediterranean Sea. A parametric study of the effect of spatial and temporal resolution of drifter data on the dilation rate estimates is also performed.