Stochastic Particle Trajectory Modeling Techniques for Spill and Search and Rescue Models

The majority of oil and chemical spill, search and rescue, and particle transport models employ a random walk procedure to predict the trajectory and dispersal of the relevant variables. The random walk model is the first in a hierarchy of stochastic particle models, where the object's position (random walk), velocity (random flight), and acceleration are progressively represented as Markovian processes. This hierarchy of models has been extensively developed and applied to study the movement of Lagrangian drifters in the ocean and the dispersal of air pollutants in flows over complex terrain. They have not however been incorporated in state of the art spill, research and rescue, and particle transport models. The goal of this paper is to investigate the impact of applying a random flight model to predict the trajectories in the above referenced models. Numerical implementation and testing of the first and second order models (random walk and random flight) against an analytic solution to the diffusion equation show very good agreement, provided that a sufficient number of independent simulations are ensemble averaged. The random flight model is shown to predict smaller dispersal areas than the random walk model, with a long term reduction in the area proportional to the dispersion coefficient times the velocity autocorrelation time scale. This offset ramps in immediately after the release, and is fully developed over multiples of the velocity autocorrelation time scale. In order for a random flight model to provide improved predictions over its random walk counterpart, accurate estimates of the dispersion coefficient and the autocorrelation time scale must be available. Simulation of typical coastal trajectory problems shows that the uncertainty in the value of the dispersion coefficient used as input to the model must be no greater than 1/n, where n (>3) is the number of autocorrelation time scales, if the random flight model is to provide improved predictive performance relative to a random walk model. Application of random walk and flight models to typical search and rescue are provided to illustrate the use of both models.