Download a PDF version of the white paper Lagrangian Coherent Structures ? Have you ever noticed swirling, billowing, or circular patterns in the ocean, rivers, or sky, like these shown images below (Figure 1) ? At first glance, these features may seem chaotic, ephemeral and unpredictable and they are indeed difficult to study with traditional modelling and observation approaches. The main reason is that trajectories of fluid parcels can be very sensitive to their initial conditions (e.g. starting on either side of an eddy), and studying individual tracers may provide unreliable estimates of the overall transport. However, behind the complexity of individual tracer patterns, there are robust skeletons of fluid flows, termed “Lagrangian Coherent Structures" (LCS) which shape these patterns. The LCS are free from the uncertainties of single trajectories and provide a valuable framework to identify, quantify, and forecast the key transport features, in the ocean, atmosphere or any fluid. More specifically, LCS identifies regions within a fluid that exhibit the strongest attraction, repulsion, or shearing behavior over a given location and time interval. These structures act as invisible barriers and fronts, organizing the flow into distinct regions and influencing how material, such as pollutants (plastic, oil, debris), marine organisms, or geophysical quantities (heat, salt, nutrient) move through the ocean. LCS provides a powerful new way of looking at ocean circulation, transport and connectivity. A useful analogy is they inform on the “weather” of the oceans; identifying independent transport regions, locating dynamical fronts between them, and how they interact. The concept The LCS concept was initially introduced by Georges Haller’s and his group who applied robust mathematical frameworks drawn from the nonlinear dynamical systems and chaos theories to transport in geophysical flows. These frameworks provided the mathematical foundation for understanding how seemingly random fluid flows (e.g. chaotic mixing in turbulent flows) can exhibit underlying order, allowing identification of attracting and repelling material surfaces, as well as transport barriers (see Haller (2015) for a comprehensive review). A robust tool for the identification of LCS is the derivation of so-called Finite-Time Lyapunov exponent (FTLE), which characterizes the rate of separation of neighboring trajectories over a finite-time interval. The underlying principle is to compute and quantify the degree of flow deformation throughout a region of interest. This is achieved by seeding a grid of virtual particles within a velocity flow field (from hydrodynamic models or observations) and tracking their evolution over a given time interval (see Figure 2). This is typically undertaken both in forward and backward time to identify repelling and attracting fronts respectively. The tracking time interval is chosen according to the processes of interest and should be consistent with their dispersion time scale (e.g. 1 to 7 days for typical weather systems, oil spills or Search and Rescue operations, or equal to pelagic larval duration for marine connectivity assessment). The LCS features are derived from the analysis of the produced diagnostic FTLE field. LCS coincide with maximum ridges in the FTLE field, corresponding to structures responsible for the greatest stretching of particle trajectories and formation of attracting and repelling fronts. A key advantage of LCS is their robustness to errors in flow field measurements or predictions. This property makes LCS particularly valuable in real-world applications where available data is imperfect. In Figure 3 below, we show an animation of daily attracting LCS computed over an entire year for the West coast of New Zealand. Particles were tracked in hydrodynamic flows from our high-resolution NZ-scale ocean datacube. Here, we used an integration period of 7 days for each daily computation (e.g. time between initial and final positions). The approach allows synthesizing large amounts of hydrodynamic data into meaningful circulation features and transport pathways and is generally more insightful than traditional climatologies on ocean currents (e.g. mean annual flows). The application to NZ West Coast reveals many interesting features including :
These daily fields can be averaged over different time periods (weeks, months, seasons, years) to further frame and explore variability over time. Applications in physical oceanography The LCS framework offers a powerful new approach for understanding, quantifying, and predicting ocean transport dynamics, making it a growing area of research with numerous potential applications in the maritime industry. Some examples are outlined below :
How we can help Despite a wide range of potential applications in which LCS could bring valuable new insights, applications in the marine space, beyond academic research, has been hindered by the large computational requirements as well as the need for high-quality hydrodynamic flows to derive meaningful outcomes for applications from ocean to coastal/estuary scale. Building upon our hydrodynamic downscaling and particle-tracking modelling capabilities, integrated within an agile cloud-computing infrastructure, we have developed a suite of tools to robustly derive LCS for any location on the planet, bridging the gap from open-ocean to coastal scale. Like our ocean datacubes, they can be produced for both hindcast periods over several decades to evaluate seasonal and interannual variability, and forecast horizons to anticipate changes in LCS configurations and support operational decision-making. The application of LCS to real-world problems is an exciting field in physical oceanography (and beyond), and we would love to hear how these methods could be useful for your projects. Contact us Comments are closed.
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