Lagrangian data in a high-resolution numerical simulation of the North Atlantic: II. On the pseudo-Eulerian averaging of Lagrangian data

In this paper, the statistical properties of the mean flow reconstruction using Lagrangian data are studied, considering the classical “binning” approach based on space-time averaging of finite difference velocity estimates. The work is performed numerically, using as the test flow a solution from a high resolution MICOM simulation of the North Atlantic. A set of trajectories are computed, simulating the motion of surface drifters initially launched on a regular 1°×1° array, transmitting positions every Δt=12 h, and analyzed over approximately 2 years of the simulation. The drifter distribution in time is influenced by the Ekman flow, resulting in maximum data concentration in the subtropical convergence regions and minimum concentration in the upwelling regions. Pseudo-Eulerian averages UpE, computed from Langrangian data, are compared to “true” Eulerian averages UE, computed from grid point velocities inside 1°×1° bins for approximately 2 years. For the full Lagrangian data set (which is substantially larger than the WOCE requirement), UpE−UE is on the order of 10–20 cm/s in regions of major ocean currents. These differences are usually not significant with respect to the sampling error, due to subgrid-scale variability and finite sampling, except in a few regions. Patterns of the magnitude of the differences between UpE and UE in these regions show that UpE tends to underestimate (overestimate) the velocity in the eastern equatorial upwelling regime/South Equatorial current (western boundary currents). This study suggests that these under/overestimates by pseudo-Eulerian averaging of Lagrangian data are related to a bias due to mesoscale divergences, and result in nonzero correlations between instantaneous drifter concentration and velocity, ÛB= u′c′ /C (Davis and Gent). In this framework, the overestimates (underestimates) are interpreted as due to preferential (reduced) sampling of high velocity regions by Lagrangian particles, due to convergent (divergent) phenomena. A similar phenomenon has been observed for real drifters and biological organisms. The overestimates are found to increase with sub-sampling in space and decrease with sub-sampling in time. For Δt=3 days, we actually find underestimates, probably because instantaneous high velocities are smoothed and energetic drifters are not appropriately accounted for in the bins. Direct implications of the results for the analysis of real data, and directions for future work (in particular investigation of the bias) are discussed.