Lagrangian Tracking in Stochastic Fields with Application to an Ensemble of Velocity Fields in the Red Sea

We describe an efficient parallel algorithm for forward and backward tracking of passive particles in stochastic flow fields whose statistics are described are prescribed by an underlying ensemble. The construction is designed to address challenges arising from random resampling procedure applied following each assimilation cycle, which leads to rapid growth in the number of particles. To control this growth, the algorithm incorporates an adaptive binning procedure, which conserves the zeroth, first and second moments of probability (total probability, mean position, and variance). Implementation of the method is illustrated based on results of forward and backward tracking experiments, within a realistic high-resolution ensemble assimilation setting of the Red Sea. In particular, the results were used to analyze the effects of the maximum number of particles, the time step, the variance of the ensemble, the travel time, the source location, and history of transport.