Conditions for Reliable Divergence Estimates from Drifter Triplets

Abstract

Abstract Horizontal velocity gradients of a flow field and the related kinematic properties (KPs) of divergence, vorticity, and strain rate can be estimated from dense drifter deployments, e.g., the spatiotemporal average divergence (and other KPs) over a triangular area defined by three drifters and over a given time interval can be computed from the initial and final areas of said triangle. Unfortunately, this computation can be subject to large errors, especially when the triangle shape is far from equilateral. Therefore, samples with small aspect ratios are generally discarded. Here we derive the thresholds on two shape metrics that optimize the balance between retention of good and removal of bad divergence estimates. The primary tool is a high-resolution regional ocean model simulation, where a baseline for the average divergence can be established, so that actual errors are available. A value of 0.2 for the scaled aspect ratio Λ and a value of 0.86π for the largest interior angle θ are found to be equally effective thresholds, especially at scales of 5 km and below. While discarding samples with low Λ or high θ values necessarily biases the distribution of divergence estimates slightly toward positive values, this bias is small compared to (and in the opposite direction of) the Lagrangian sampling bias due to drifters preferably sampling convergence regions. Errors due to position uncertainty are suppressed by the shape-based subsampling. The subsampling also improves the identification of the areas of extreme divergence or convergence. An application to an observational dataset demonstrates that these model-derived thresholds can be effectively used on actual drifter data. Significance Statement Divergence in the ocean indicates how fast floating objects in the ocean spread apart, while convergence (negative divergence) captures how fast they accumulate. Measuring divergence in the ocean, however, remains challenging. One method is to estimate divergence from the trajectories of drifting buoys. This study provides guidance under what circumstances these estimates should be discarded because they are too likely to have large errors. The criteria proposed here are less stringent than some of the ad hoc criteria previously used. This will allow users to retain more of their estimates. We consider how position uncertainty affects the reliability of the divergence estimates. An observational dataset collected in the Mediterranean is used to illustrate an application of these reliability criteria.