Lagrangian methods for flow climatologies and trajectory error assessment

A non-eddy-resolving primitive equation model was used to simulate the climatological annual cycle of the North Atlantic Ocean circulation. A series of Lagrangian sensitivity experiments using an offline trajectory model were run over a 10-year period to determine the sensitivity of three-dimensional (3D) trajectories to changes in the temporal resolution of the input velocity field. The reference experiment, against which all test experiments were compared, involved trajectories computed with model velocity data averaged every 15 hours (nine model time steps) but with the same spatial resolution as the model simulation (roughly 200 km). The trajectories of the test experiments were calculated with model velocity data averaged over several periods ranging from 2.5 to 360 days. tory errors, as determined by the ensemble-averaged position deviations from the reference case, increased approximately linearly with travel time and revealed the expected degradation of trajectory accuracy for a decreasing temporal resolution of the input velocity field. Upper bounds for trajectory errors were found to be typically 2.5–8% of the travel distance, when a 30-day averaging interval or less was used to compute trajectories, and of the order of 11–12% for time averages greater than 30 days. As a general rule, 3D trajectories limit trajectory errors: neglecting the vertical velocity component yielded results with unacceptably large errors, of the order of 40% or more of the travel distance. In this case, the vertical shear of the horizontal velocity was the dominant cause of horizontal trajectory deviations.