Biases in Structure Functions from Observations of Submesoscale Flows. Issue 6 (12th June 2020) - Pearson, Jenna; Fox‐Kemper, Baylor; Pearson, Brodie; Chang, Henry; Haus, Brian K.; Horstmann, Jochen; Huntley, Helga S.; Kirwan, A. D.; Lund, Björn; Poje, Andrew
Abstract: Surface drifter observations from the LAgrangian Submesoscale ExpeRiment (LASER) campaign in the Gulf of Mexico are paired with Eulerian (ship‐borne X‐band radar) data to demonstrate that velocity structure functions from drifters differ systematically from Eulerian structure functions over scales from 0.4 to 7 km. These differences result from drifters oversampling surface convergences and regions of intense vorticity. The first‐, second‐, and third‐order structure functions are calculated using quasi‐Lagrangian (drifter) and Eulerian data from approximately the same location and time. Differences between quasi‐Lagrangian and Eulerian structure functions are attributed to two forms of bias. The first bias results from the mean divergence or vorticity of the background flow creating nonzero first‐order structure functions. This background bias affects both quasi‐Lagrangian and Eulerian data when insufficiently time‐averaged. It severely biases the drifter third‐order structure functions but is smaller in Eulerian structure functions at both second and third order. This bias can be corrected for using lower‐order structure functions. The second form of bias results from drifters accumulating in regions with flow statistics that differ from undersampled regions. This accumulation bias is diagnosed by identifying the dependence of the Eulerian structure functions on divergence and vorticity as well as scale. Together, both biases suggest that caution is needed when interpreting second‐order drifter statistics and that linking raw third‐order drifter statistics to energy fluxes is often erroneous in ocean data: Even with background correction and sufficient time‐averaging, drifters overestimate the Eulerian estimate of the third‐order structure function by up to a factor of 5 when signs are consistent. Plain Language Summary: Structure functions are a statistic used to measure the spreading of material floating in the ocean, such as plastics or spilled oil, as well as the transfer of properties like energy across scales. Their calculation requires knowledge of velocities of nearby particles. These can be measured either by (nearly) stationary instruments, such as a radar, or by tracking drifters. Offshore drifter tracking is generally easier, but they are known to be attracted to specific flow features, such as fronts, windrows, and vortices, leading to less sampling of other areas. By considering a unique data set of nearly simultaneous velocity measurements from both radar and drifters, this paper investigates how the uneven sampling by drifters, as well as the limited area coverage of radar measurements, impacts the structure function statistics and their interpretation. Key Points: Structure functions calculated from observed drifters are subject to accumulation bias when compared to those from Eulerian observations Structure functions calculated from either drifters or Eulerian data may be subject to a background bias due to mean gradients in the flow These biases preclude inferences about energy cascades or fluxes from structure functions from drifters or localized Eulerian data