Stochastic Lagrangian Trajectory Modeling of Surface Drifters Deployed during the Deepwater Horizon Oil Spill

Lagrangian trajectory models have been demonstrated to be a useful tool in oil spill response. Despite the improvements in this kind of models, surface drift prediction remains a difficult task plagued with uncertainties. This work presents a Stochastic Lagrangian Trajectory Model (SLTM) that quantifies the uncertainties in trajectory simulations and defines the most likely search area of possible trajectories. The methodology includes the following steps: 1) Numerical scheme based on the transport equation in Lagrangian form; (2) Parameter estimation process, which includes: (i) time independent parameter estimation based on the maximum likelihood method and (ii) time dependent parameter estimation through autoregressive moving average; (3) Monte Carlo simulation of multiple trajectories based on the joint probability distribution function and the temporal dependency model. The model is used to simulate the trajectories of surface drifters deployed in the Gulf of Mexico during the Deepwater Horizon oil spill incident using surface currents provided by the Global model HYCOM. A set of drifters was selected to estimate the model parameters and another one for simulation and validation. Observed drifter trajectories were compared with the modeled trajectories obtained with the deterministic and the SLTM approaches. After 5 days of simulation the root mean squared error of Lagrangian separation distance was found to be 115 km and 37 km for the deterministic approach and the best simulation of the SLTM, respectively. Moreover, actual trajectories were in the areas where the model predicted that the drifter was likely to go through, showing the capabilities of the SLTM for oil spill trajectory modelling and search and rescue applications.