Estimating Lagrangian Travel Times from Satellite Tracked Drifters

A goal of many biological applications is to test for correlation between a genetic dissimilarity matrix and a geographical dissimilarity matrix between a set of locations. Such an application is termed as an isolation by distance (IBD) analysis. A common choice for the geographical dissimilarity matrix is to simply use a geodesic distance between the points of measurement. In oceanographic applications, geodesic distance will often be a poor measure of separation due to ocean currents and pathways. In this work we present data-driven methodology to estimate such a geographical dissimilarity matrix inspired by the travel times of satellite tracked drifters; in particular we use the Global Drifter Program database. We term such travel times as Lagrangian travel times. Lagrangian travel times constitute a powerful and accurate tool to investigate marine planktonic species, the evolution of which are deeply shaped by oceanic currents.

The objective is to estimate the travel time of the most likely path a drifter would take between two points. However, it is unlikely that any single drifter has ever taken such a path, especially as the two points become further apart. Therefore, we use modern methodology from machine learning and statistics to incorporate information from multiple drifters. The method focuses on filling gaps in the data, where sparsely sampled areas would prevent us from taking an estimate from the drifter data directly. The result is a data-driven product which can efficiently compute Lagrangian travel times between arbitrary locations in the ocean, without having to resort to numerical GFD models and the biases they will inevitably induce.