An estimate of the eddy diffusivity tensor from observed and simulated Lagrangian trajectories in the Benguela Upwelling System

Abstract. Lateral mixing of unresolved processes in ocean models is usually parameterized with a scalar diffusivity, although the mixing can be highly anisotropic. Estimating the full diffusivity tensor from Lagrangian dispersion observations is challenging because shear dispersion from background currents can prevent the diffusive limit from being reached. This study investigates the diffusivity tensor with Lagrangian single  and pair particle statistics in the Benguela upwelling region, using one set of Lagrangian trajectories derived from a recent drifter data set with hourly resolution and background currents from the OSCAR surface current product, and another set from simulations using the 1/10 ° Parallel Ocean Program (POP) simulation. Theory predicts that pair particle diffusivities, expected to be independent of background mean flows, are twice the single particle diffusivities if the pair velocities are uncorrelated. In this study it is found that although pair particle diffusivities are much less influenced by mean flow they are generally significantly smaller than twice the single particle diffusivities. Subtracting the mean flow reduces this discrepancy and improves convergence in both methods, although single particle diffusivities remain higher. Velocity autocorrelations decay faster than pair correlations, with mean flow subtraction accelerating decorrelation, especially in the zonal direction. The pair correlation term in the diffusivity equation contributes significantly to the differences between single particle and pair particle diffusivities, explaining why pair particle diffusivities are generally smaller making them a less accurate estimate in diffusive parameterizations. In both the POP simulation and the observations, convergence properties improve significantly after mean flow subtraction.  Mean flow removal plays a critical role in achieving convergence in the xx and xy tensor components as well as in the major axis component after diagonalization. The significant anisotropy in the diffusivity tensor is mainly explained by the anisotropy in the Lagrangian integral time scales, while the major axis component of the velocity variance tensor is only about 1.2 times the minor axis component. The motions that are not resolved by the OSCAR surface currents product, but captured by the surface drifters, contribute significantly to the diffusivities, accounting for 8 % and 42 % of the xx and yy components, respectively, after mean flow subtraction. This study highlights the importance of including the full diffusivity tensor in the Benguela upwelling region in lateral mixing parameterizations.