Results from Finite Time Lyapunov Exponent calculations using High Frequency Radar observed surface currents around Palmer Deep Canyon from January to March of 2020

Abstract

Several LCS techniques have been applied to ocean systems in the past decade for their ability to quantify areas in ocean currents (or any velocity field) that exert an impact on nearby drifting particles (Haller, 2015). Such areas are known as coherent structures. Coherent structures can identify local extrema of repulsion, attraction, and shearing of flow (Haller, 2015). Attracting coherent structure will quantify the attraction of passive drifters in a flow field, or plankton in ocean currents (Shadden et al., 2005; Haller, 2015). These data contains results from Finite Time Lyapunov Exponent calculations using High Frequency Radar observed surface currents around Palmer Deep Canyon from January - March 2020.

Finite Time Lyapunov Exponents use the horizontal separation distance between two particles relative to a fixed point over a defined time interval to quantify the strength of coherent structure (either repelling or attracting) at each point on a gridded velocity field. To calculate repelling FTLEs, a forward trajectory is used, and to calculate attracting FTLEs, a backward trajectory is used. In this study, attracting FTLEs were calculated. FTLE’s ability to integrate over trajectories sets this technique apart from instantaneous separation rate (Okubo, 1970; Weiss, 1991) by introducing particle position “memory”. Coherent structures are defined by the FTLE metric as ridges in the flow field where neighbouring particles are converged toward, and then diverged along the ridge. The strengths of these ridges are quantified by the integrated separation rate between two particles (Veatch et al., 2024 Figure 2D). This relative motion between two neighbouring particles is the key way in which the FTLE metric differs from the RPD metric. Like RPD, FTLE will vary over space and time when applied to a discrete set of velocity data.

FTLE calculations result in a material surface that then can be projected at a set resolution back onto the study region. FTLE results were projected at the resolution of the HFR (1km) so as to not stretch the observations further than the input data should be able to resolve. FTLE calculations were performed using a MATLAB software toolbox (Haller) that was modified for use on HFR data (Veatch et al., 2024 Figure 2D). To negate artifacts in results caused by the edges of the HFR domain where it may seem that particles suddenly stop or are lost, the domain of FTLE results used was smaller than the domain of the inputted velocity field. The domain was shrunk by three kilometers (Veatch et al., 2024 Figure 3). This about how far the average particle travels over the integration time of 6 hours.

For a complete list of measurements, refer to the full dataset description in the supplemental file 'Dataset_description.pdf'. The most current version of this dataset is available at: https://www.bco-dmo.org/dataset/917914