How to reverse time in stochastic particle tracking models

Many oceanographic studies perform individual-based simulations of the transport and dispersal of particles such as fish larvae and eggs. An increasing number of these studies take place in reverse time, for example as to locate the origins of a particle observed at a given time and position. This paper demonstrates that when turbulent dispersal is taken into account, such backtracking can be done in different ways, which have different justifications and which may yield quite different results. We discuss three methods for reversing time: First, following the streamlines backwards while letting the eddy diffusivity perturb the trajectory; next, considering the initial position of an unknown parameter and estimating it using the maximum likelihood principle; and finally; assuming the trajectory to be a path in a stationary stochastic process and identifying the reversed-time transition probabilities. We illustrate the conceptual and algorithmic differences between the approaches. © 2011 Elsevier B.V. All rights reserved.