Propagating Particle Tracking Uncertainty Defined by Fuzzy Numbers in Spatially Variable Velocity Fields

Accurate prediction of the trajectories of material drifting on the ocean surface is critical for risk assessment and responses to environmental emergencies. Prediction of these trajectories is subject to uncertainty arising from a number of sources, with a primary source being uncertainty in the modelled ocean surface currents and winds used as input to the trajectory model. This article presents a fuzzy number-based algorithm for propagating uncertainty through a particle tracking scheme in a time- and space-varying velocity field. The performance of the algorithm was tested by applying it to idealized, analytical velocity fields and scoring the results against the analytical solution. Both epistemic and aleatoric uncertainty were considered and combined using a fractional Brownian motion model for temporal autocorrelation of the uncertainty. In the evaluation of the algorithm, sensitivity was quantified with respect to parameters such as timestep size, resolution of the forcing velocity field, spatial and temporal gradients in the forcing, and resolution of the applied uncertainty. Parameter values optimizing uncertainty representation and computational cost were identified. The applied uncertainty was found to evolve in agreement with classical relative dispersion relationships.