Stochastic Lagrangian trajectory model for drifting objects in the ocean

The prediction of drifting object trajectories in the ocean is a complex problem plagued with uncertainties. This problem is usually solved simulating the possible trajectories based on wind and advective numerical and/or instrumental data in real time, which are incorporated into Lagrangian trajectory models. However, both data and Lagrangian models are approximations of reality and when comparing trajectory data collected from drifter exercises with respect to Lagrangian models results, they differ considerably. This paper introduces a stochastic Lagrangian trajectory model that allows quantifying the uncertainties related to: (i) the wind and currents numerical and/or instrumental data, and (ii) the Lagrangian trajectory model. These uncertainties are accounted for within the model through random model parameters. The quantification of these uncertainties consists in an estimation problem, where the parameters of the probability distribution functions of the random variables are estimated based on drifter exercise data. Particularly, it is assumed that estimated parameters maximize the likelihood of our model to reproduce the trajectories from the exercise. Once the probability distribution parameters are estimated, they can be used to simulate different trajectories, obtaining location probability density functions at different times. The advantage of this method is that it allows: (i) site specific calibration, and (ii) comparing uncertainties related to different wind and currents predictive tools. The proposed method is applied to data collected during the DRIFTER Project (eranet AMPERA, VI Programa Marco), showing very good predictive skills.