A Particle Filter for Inverse Lagrangian Prediction Problems

The authors present a numerical method for the inverse Lagrangian prediction problem, which addresses retrospective estimation of drifter trajectories through a turbulent flow, given their final positions and some knowledge of the flow field. Of particular interest is probabilistic estimation of the origin (or launch site) of drifters for practical applications in search and rescue operations, drifting sensor array design, and biochemical source location. A typical solution involves a Monte Carlo simulation of an ensemble of Lagrangian trajectories backward in time using the known final locations, a set of velocity estimates, and a stochastic model for the unresolved flow components. Because of the exponential dispersion of the trajectories, however, the distribution of the drifter locations tends to be too diffuse to be able to reliably locate the launch site. A particle filter that constrains the drifter ensemble according to the empirical dispersion characteristics of the flow field is examined. Using the filtering method, launch-site prediction cases with and without a dispersion constraint are compared in idealized as well as realistic scenarios. It is shown that the ensemble with the dispersion constraint can locate the launch site more specifically and accurately than the unconstrained ensemble.