BAKTRAK: Backtracking drifting objects using an iterative algorithm with a forward trajectory model

Abstract

The task of determining the origin of a drifting object after it has been located is highly complex due to the uncertainties in drift properties and environmental forcing (wind, waves and surface currents). Usually the origin is inferred by running a trajectory model (stochastic or deterministic) in reverse. However, this approach has some severe drawbacks, most notably the fact that many drifting objects go through nonlinear state changes underway (e.g., evaporating oil or a capsizing lifeboat). This makes it difficult to naively construct a reverse-time trajectory model which realistically predicts the earliest possible time the object may have started drifting. We propose instead a different approach where the original (forward) trajectory model is kept unaltered while an iterative seeding and selection process allows us to retain only those particles that end up within a certain time-space radius of the observation. An iterative refinement process named BAKTRAK is employed where those trajectories that do not make it to the goal are rejected and new trajectories are spawned from successful trajectories. This allows the model to be run in the forward direction to determine the point of origin of a drifting object. The method is demonstrated using the Leeway stochastic trajectory model for drifting objects due to its relative simplicity and the practical importance of being able to identify the origin of drifting objects. However, the methodology is general and even more applicable to oil drift trajectories, drifting ships and hazardous material that exhibit non-linear state changes such as evaporation, chemical weathering, capsizing or swamping. The backtracking method is tested against the drift trajectory of a life raft and is shown to predict closely the initial release position of the raft and its subsequent trajectory.