2.2.1 Climatological Lagrangian Coherent Structures
In recent decades, the theory of nonlinear dynamics has been applied to vector fields with arbitrary time dependence, such as geophysical datasets. Thorough reviews can be found in Samelson (2013) and Haller (2015). The result of this research—often termed Lagrangian Coherent Structures (LCS)—has been shown in many studies to accurately identify, and even predict, ocean kinematics (e.g., Beron-Vera et al., 2008, 2019; Duran et al., 2021; Filippi et al., 2021; Olascoaga et al., 2006, 2008, 2013; Olascoaga & Haller, 2012). LCS have proven an ideal tool to search for persistent and recurrent pathways in the ocean, enabling the detection of low-frequency structures that tend to modulate parcel’s movements, and that cannot be reliably found using Eulerian methods (Duran et al., 2018). Termed climatological LCS (cLCS), these structures provide a generic yet accurate and detailed Lagrangian climatology without the need to know trajectories’ initial location, initial time, or when the trajectory ends. Of particular interest to our study, cLCS have been shown to be effective in identifying transport barriers and dominant pathways. Comparisons with a variety of observed and synthetic drifter data have shown that strongly attracting cLCS can act as efficient transport barriers, considerably reducing cross-cLCS transport, other strongly attracting cLCS indicate recurrent pathways, including possibly when cLCS are deformed as chevrons (Duran et al., 2018; Gough et al., 2019; Gouveia et al., 2021). In regions where currents are less energetic, cLCS are less attracting and are more often deformed as chevrons, thus indicating recurrent pathways as well (Kurczyn et al., 2021). These Lagrangian transport patterns can be efficiently and accurately extracted from large time series of Eulerian velocity data with the proper tools from nonlinear dynamics (Duran et al., 2018), but cannot be identified with commonly used Eulerian methods, such as streamlines of a time-averaged velocity (e.g., supplemental information of Duran et al., 2018). While cLCS have proven very efficient in identifying predominant and recurrent Lagrangian patterns, we note that they cannot always explain instantaneous patterns, similar to how the climate is useful but cannot always explain the weather. Additional evidence of the adequacy of the climatological velocity for our study is provided in Text S1, where we show that the climatological currents have very similar patterns to the instantaneous 1994–2018 time series using Self-Organizing Maps.
cLCS are based on the concept of hyperbolic LCS, material lines that maximize the normal attraction of nearby trajectories; thus, LCS delineate and shape Lagrangian transport. cLCS differ from LCS in two crucial ways. Firstly, cLCS are computed from a climatological velocity instead of an instantaneous one. Secondly, the Cauchy-Green tensor, needed to solve the normal-attraction maximization problem, is averaged over different initial times while LCS are computed from the Cauchy-Green tensor of one initial time. In Duran et al. (2018), these two averaging steps are shown to efficiently preserve and extract the main Lagrangian transport patterns from large time series of instantaneous velocities. Because of the latter averaging step, cLCS are not material lines but rather result in an Eulerian field representing recurring or persistent trajectory patterns. Interested readers can refer to Duran et al. (2018) for further details and mathematical explanation, while detailed information regarding the numerical implementation is found in Duran et al. (2019).
We obtained cLCS from the daily HYCOM climatology described above, which allows us to characterize the Lagrangian kinematics of the currents in the study area, identifying transport routes and barriers. The code to compute cLCS is freely available (Duran et al., 2019).