The oceans plays a pivotal role in the global climate system, and to develop our understanding there is a need to connect physical models of ocean dynamics with vast arrays of data collected from modern sensors. In this talk, I will present a stochastic spatiotemporal model that describes the motion of freely drifting satellite-tracked instruments, commonly known as “drifters”. The trajectories of drifters provide useful measurements about currents, turbulence and dispersion across our oceans. The challenge is that the data moves in both time and space, sometimes referred to a “Lagrangian” perspective, and these types of data require new data science methodology. Our spatiotemporal model captures effects that are oscillatory, spatially anisotropic, and have varying degrees of small-scale roughness or fractal dimension. We use our model to analyse the entire Global Drifter Program database of observations since 1979, constituting over 70 million data points from over 20,000 drifters. Our findings uncover interesting spatial patterns and develop general understanding of ocean circulation and ocean surface dynamics. This is a joint work with Sofia Olhede (UCL) and Jonathan Lilly and Jeffrey Early (NWRA, Seattle).