Simulation of the transport of particles in coastal waters using forward and reverse time diffusion

Particle models are often used to simulate the spreading of a pollutant in coastal waters in case of a calamity at sea. Here many different particle tracks starting at the point of release are generated to determine the particle concentration at some critical locations. This Monte Carlo method, however, consumes a large CPU time. Recently, Milstein, et al. [Milstein, GN, Schoenmakers JGM, Spokoiny, V. Transition density estimation for stochastic differential equations via forward-reverse representations. Bernoulli 2004:10(2);281-312] introduced the concept of reverse-time diffusion and derived a reverse particle model from the original forward simulation model. While the original forward model provides results on where the pollutant will go to, the reverse system gives information about where the pollutant came from. The Monte Carlo estimator for the particle concentration can also be based on realizations of this reverse system. In this paper we apply this concept to estimate particle concentrations in coastal waters. The results of the experiments show that the CPU time compared with the classical Monte Carlo method is reduced at least order of magnitude.