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 u sing Lagrangian data are studied, considering the classical "binning" appro ach 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 trajector ies are computed, simulating the motion of surface drifters initially launc hed on a regular 1 degrees x 1 degrees array, transmitting positions every Deltat = 12 h, and analyzed over approximately 2 years of the simulation. T he drifter distribution in time is influenced by the Ekman flow, resulting in maximum data concentration in the subtropical convergence regions and mi nimum concentration in the upwelling regions. Pseudo-Eulerian averages U-pE, computed from Langrangian data, are compared to "true" Eulerian averages U-E, computed from grid point velocities insid e 1 degrees X 1 degrees bins for approximately 2 years. For the full Lagran gian data set (which is substantially larger than the WOCE requirement), U- pE - U-E 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 fe w regions. Patterns of the magnitude of the differences between U-pE and U- E in these regions show that U-pE tends to underestimate (overestimate) the velocity in the eastern equatorial upwelling regime/South Equatorial curre nt (western boundary currents). This study suggests that these under/overes timates by pseudo-Eulerian averaging of Lagrangian data are related to a bi as due to mesoscale divergences, and result in nonzero correlations between instantaneous drifter concentration and velocity, (U) over cap (B) = (u 'c ')/C (Davis. 1998; Gent and McWilliams, 1990). In this framework,, the ove restimates (underestimates) are interpreted as due to preferential (reduced ) sampling of high velocity regions by Lagrangian particles, due to converg ent (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 rime. For Delt at = 3 days, we actually find underestimates, probably because instantaneou s high velocities are smoothed and energetic drifters are not appropriately accounted for in the bins. Direct implications of the results for the anal ysis of real data, and directions for future work (in particular investigat ion of the bias) are discussed. (C) 2001 Elsevier Science B.V. All rights r eserved.