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).