Unveiling the hidden skeleton of oceanic flows with “Lagrangian Coherent Structures”

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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.

Figure 1. Satellite image of an oil slick in the Gulf of Mexico (left) (Image : NASA Wikimedia Commons) and phytoplankton bloom in the Baltic Sea (right) (Image : NASA Earth Observatory).

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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).

Figure 2. Flow deformation illustrated by the trajectories of particles seeded on a rectangular grid within hydrodynamic flows on the West Coast of New Zealand.

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).

Figure 3. Example of daily FTLE field (left). Key LCS features are identified on the right panel.

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 :

• Convergence along the continental shelf.
• Clear identification of the d’Urville Current, flowing SW to NE into the South Taranaki Bight, and its modulation over time.
• Influence of tidal flushing from natural harbours (Kaipara Harbour, Manukau Harbour, Kawhia Harbour) and general mixing length scale.
• Convergence zones and transport barriers south of Cook Strait and around South Island’s headlands.
• Weak convergence westward of the continental shelf.

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 :

• Oceanic Fronts and Eddies: LCS help identify oceanic fronts (sharp gradients between different water masses),  eddies (circular currents), and filaments (elongated shear current). These structures govern transport in the ocean and have a major influence on nutrient distribution and biological productivity in the ocean.

 

• Oceanic pollution modelling and mitigation: LCS can track the movement of pollutants, such as oil, marine plastics, waste water or chemicals, by identifying where the pollutant material will be carried by currents. This is crucial for anticipating and predicting potential environmental damage and can support the development of more efficient pollution mitigation strategies and response efforts.

 

• Fisheries management: LCS are important for understanding the movement of nutrients and biological organisms (e.g. plankton), which directly influences fish populations and behaviors. By quantifying the underlying flow backbone, LCS can provide valuable insights on the locations of rich fishing grounds, areas where marine species aggregate, as well as hot spots of increased by-catch risks.

 

• Marine protected areas and Biosecurity: In marine conservation, LCS provide valuable insights on marine connectivity, and variability over time i.e identify critical habitats and the pathways that connect them. For example, LCS can reveal marine organisms (e.g. fish, larvae, plankton community) migration patterns or how marine protected areas (MPAs) are interconnected through ocean currents. LCS derivation can be tailored to specific marine species using dedicated biophysical modules reproducing species-specific behavior ( e.g. pelagic larvae duration). They can also be used for biosecurity purposes to evaluate underlying marine connectivity and anticipate impacts of invasive species on surrounding ecosystems.

 

• Forecasting currents and hazards for safety at sea: LCS can provide a valuable addition to traditional ocean forecasting methods by identifying most intense and dangerous currents and convergence areas in the oceans (e.g. increased risk for debris collision). In Search and Rescue (SAR) context, knowledge of the underlying LCS can save valuable time in anticipating drift patterns and efficiently guide the first-response efforts.

 

• Influence on ocean mixing in a changing climate: LCS objectively frame and highlight regions where different water masses mix or remain separated. This plays a critical role in understanding how the ocean circulates heat and other properties. Developing an understanding of historical and current LCS patterns can provide robust baseline information for evaluating impacts of climate change.

 

• Carbon cycling: LCS helps identify regions of the ocean where carbon sequestration (the absorption of CO₂ by the ocean) is most effective. This is vital for understanding how the ocean contributes to regulating global carbon levels and may assist engineered ocean carbon sequestration methods.

 

• Guiding observational efforts: By providing insights into the large-scale oceanic patterns, LCS can help guide the placement of instruments such as drifters, floats, or autonomous vehicles in the ocean to maximize the effectiveness of ocean monitoring by better targeting the processes of interest e.g. identify local eddies and strong shear currents, or larger scale El Nino Southern Oscillation (ENSO) or  Atlantic Meridional Overturning Circulation (AMOC) circulation patterns.

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.

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