Calculating Lagrangian trajectories using time-dependent velocity fields

We report on the development of an efficient and accurate tool for computing Lagrangian trajectories using time-varying velocities. By linearly interpolating the velocities both in space and time one can obtain analytical expressions for the trajectory inside each model grid box. In combination with a numerical determination of the transit times through each grid box these expressions allow for the implementation of expedient algorithms for off-line analyses of large data sets resulting from general circulation models. We demonstrate the efficacy of our approach on a time-varying two-dimensional model gyre.