Siren Rühs

The Greater Agulhas Current System (GACS) is a dynamically complex western boundary current system that plays a central role in inter-ocean exchange between the Indian and Atlantic Oceans, regional weather and climate over southern Africa, and marine ecosystem variability along the southeast African margin. Since the publication of The Agulhas Current Book nearly two decades ago, major advances in ocean observing systems, satellite remote sensing, numerical modelling, and interdisciplinary research have substantially expanded understanding of the system. Here we provide an integrated review of progress over the period 2006–2025, synthesising recent advances across all components of the GACS, from its upstream source regions to its downstream outflows and global climate connections. We first summarise key technological and methodological developments that have transformed observation and simulation of the Agulhas system, including sustained moored arrays, autonomous platforms, multi-sensor satellite products, and high-resolution numerical models capable of resolving mesoscale and submesoscale dynamics. We then reassess the state of knowledge for each sub-region of the system: the East Madagascar Current, the Mozambique Channel, the Northern and Southern Agulhas Current, the Agulhas Retroflection and leakage, and the Agulhas Return Current, highlighting how recent studies have addressed uncertainties in circulation pathways, variability, and connectivity. Knowledge developments include improved quantification of transport variability and eddy dynamics in upstream source regions, new observational evidence for eddy dissipation and momentum transfer within the Agulhas Current, refined understanding of the processes governing retroflection and leakage, and growing insight into the role of mesoscale and submesoscale dynamics in air–sea interaction, biogeochemical fluxes, and ecosystem responses. We also review emerging evidence linking Agulhas system variability to Southern Hemisphere wind forcing and to downstream impacts on the Atlantic Meridional Overturning Circulation. We conclude by identifying remaining knowledge gaps and outlining priority directions for future research, emphasising the importance of sustained observations, improved representation of fine-scale processes in models, and stronger integration across physical, biogeochemical, and ecosystem perspectives.

Forward‐ and backward‐in‐time Lagrangian advection, used to determine fate and origin of material in the ocean, are mathematically consistent. However, their numerical computations are hampered by round‐off and truncation errors. Trajectory calculations are stable to errors (i.e., errors are dampened) in zones of velocity convergence and unstable (errors are amplified) in regions of divergence. The stability to errors thus flips when time integration is reversed, which, depending on the numerical configuration, can lead to significant discrepancies between forward‐ and backward‐in‐time trajectories. As divergence statistics can be asymmetrical and may be inhomogeneously distributed in space, this can lead to what we call the “stability bias.” Using representative numerical set‐ups, we show that already for timescales of less than half a year, there can be systematic basin‐scale biases in which regions are identified as particle origins or sinks. While the stability bias is linked to divergence, it is not only limited to 2D trajectories in 3D flows, as we discuss how inappropriate treatment of surface boundary conditions in 3D Lagrangian studies can also introduce an effective non‐zero divergence. Backtracking is typically applied to material that has accumulated in convergent zones, for which the stability bias especially impedes source attribution studies. Furthermore, we show how discrepancies between forward and backward trajectories can make a Bayesian approach to backtracking unsuitable. We advise modelers to routinely compare forward‐ and backward trajectories and assess the bias in different numerical set‐ups to increase study robustness. Analytical integration methods are less error‐prone and may be preferred over RK4.

In Lagrangian oceanography, numerical methods for Ordinary Differential Equations (ODEs) are used to model particle transport. In many common applications, the velocity field driving the particle transport is provided as output from ocean models, on a discrete grid of points. Hence, the velocity field must be interpolated. Depending on the choice of interpolation, the velocity field or its derivatives may have discontinuities. These discontinuities have implications for the accuracy of the numerical ODE methods employed. We demonstrate that by using information about the location of the discontinuities, we can take these into account, and improve numerical accuracy over standard integration methods that do not take discontinuities into account. The commonly used combination of the fourth-order Runge-Kutta method and linear interpolation of the velocity field, in fact, only yields second-order accuracy with the standard method. By accounting for discontinuities, we can achieve several orders of magnitude better accuracy with the same timestep. The implementation makes use of a combination of known methods from the field of numerical integration of ODEs. The implementation is quite flexible, agnostic to grid layout and order of interpolation, and contributes only modestly to the code complexity. Hence, the proposed technique for handling discontinuities in interpolated velocity fields could easily be adopted to a range of applications where numerical accuracy or efficiency is of importance. As an example where numerical accuracy is important, we run a backtracking case for particles with known initial conditions, and show that the method with discontinuity handling is to a larger degree able to recover the correct initial positions of the particles, compared to standard fourth-order Runge-Kutta.

Ensemble Lagrangian simulations aim to capture the full range of possible outcomes for particle dispersal. However, single-member Lagrangian simulations are most commonly available and only provide a subset of the possible particle dispersal outcomes. This study explores how to generate the variability inherent in Lagrangian ensemble simulations by creating variability in a single-member simulation. To obtain a reference for comparison, we performed ensemble Lagrangian simulations by advecting the particles from the surface of the Gulf Stream, around 35.61° N, 73.61° W, in each member to obtain trajectories capturing the variability of the full 50-member ensemble. Subsequently, we performed single-member simulations with spatially and temporally varying release strategies to generate comparable trajectory variability and dispersal and also with adding Brownian motion diffusion to the advection. We studied how these strategies affected the number of surface particles connecting the Gulf Stream with the eastern side of the subtropical gyre. We used an information theory approach to define and compare the variability in the ensemble with the single-member strategies. We defined the variability as the marginal entropy or average information content of the probability distributions of the position of the particles. We calculated the relative entropy to quantify the uncertainty of representing the full-ensemble variability with single-member simulations. We found that release periods of 12 to 20 weeks most effectively captured the full ensemble variability, while spatial releases with a 2.0° radius resulted in the closest match at timescales shorter than 10 d. We found that adding relatively high amounts of Brownian motion diffusion (K_h=1000 m² s⁻¹) captures the entropy aspects of the full ensemble variability well but leads to an overestimation of connectivity. Our findings provide insights to improve the representation of variability in particle trajectories and define a framework for uncertainty quantification in Lagrangian ocean analysis.

In Lagrangian oceanography, numerical methods for Ordinary Differential Equations (ODEs) are used to model particle transport. In many common applications, the velocity field driving the particle transport is provided as output from ocean models, on a discrete grid of points. Hence, the velocity field must be interpolated. Depending on the choice of interpolation, the velocity field or its derivatives may have discontinuities. These discontinuities have implications for the accuracy of the numerical ODE methods employed. We demonstrate that by using information about the location of the discontinuities, we can take these into account, and improve numerical accuracy over standard integration methods that do not take discontinuities into account. The commonly used combination of the fourth-order Runge-Kutta method and linear interpolation of the velocity field, in fact, only yields second-order accuracy with the standard method. By accounting for discontinuities, we can achieve several orders of magnitude better accuracy with the same timestep. The implementation makes use of a combination of known methods from the field of numerical integration of ODEs. The implementation is quite flexible, agnostic to grid layout and order of interpolation, and contributes only modestly to the code complexity. Hence, the proposed technique for handling discontinuities in interpolated velocity fields could easily be adopted to a range of applications where numerical accuracy or efficiency is of importance. As an example where numerical accuracy is important, we run a back-tracking case for particles with known initial conditions, and show that the method with discontinuity handling is to a larger degree able to recover the correct initial positions of the particles, compared to standard fourth-order Runge-Kutta.

Ensemble Lagrangian simulations aim to capture the full range of possible outcomes for particle dispersal. However, single-member Lagrangian simulations are most commonly available and only provide a subset of the possible particle dispersal outcomes. This study explores how to generate the variability inherent in Lagrangian ensemble simulations by creating variability in a single-member simulation. To obtain a reference for comparison, we performed ensemble lagrangian simulations by advecting the particles from the surface of the Gulf Stream, around 35.61° N, 73.61° W, in each member of the NATL025-CJMCYC3 ensemble to obtain trajectories capturing the full ensemble variability. Subsequently, we performed single-member simulations with spatially and temporally varying release strategies to generate comparable trajectory variability and dispersal. We studied how these strategies affected the number of surface particles connecting the Gulf Stream with the eastern side of the subtropical gyre. We used an information theory approach to define and compare the variability in the ensemble with the single-member strategies. We defined the variability as the marginal entropy or average information content of the probability distributions of the position of the particles. We calculated the relative entropy to quantify the uncertainty of representing the full-ensemble variability with single-member simulations. We found that release periods of 12 to 30 weeks most effectively captured the full ensemble variability, while spatial releases with a 2.0° radius resulted in the closest match at timescales shorter than 10 days. Our findings provide insights to improve the representation of variability in particle trajectories and define a framework for uncertainty quantification in Lagrangian ocean analysis.

Ensemble Lagrangian simulations aim to capture the full range of possible outcomes for particle dispersal. However, single-member Lagrangian simulations are most commonly available and only provide a subset of the possible particle dispersal outcomes. This study explores how to generate the variability inherent in Lagrangian ensemble simulations by creating variability in a single-member simulation. To obtain a reference for comparison, we performed ensemble lagrangian simulations by advecting the particles from the surface of the Gulf Stream, around 35.61° N, 73.61° W, in each member of the NATL025-CJMCYC3 ensemble to obtain trajectories capturing the full ensemble variability. Subsequently, we performed single-member simulations with spatially and temporally varying release strategies to generate comparable trajectory variability and dispersal. We studied how these strategies affected the number of surface particles connecting the Gulf Stream with the eastern side of the subtropical gyre. We used an information theory approach to define and compare the variability in the ensemble with the single-member strategies. We defined the variability as the marginal entropy or average information content of the probability distributions of the position of the particles. We calculated the relative entropy to quantify the uncertainty of representing the full-ensemble variability with single-member simulations. We found that release periods of 12 to 30 weeks most effectively captured the full ensemble variability, while spatial releases with a 2.0° radius resulted in the closest match at timescales shorter than 10 days. Our findings provide insights to improve the representation of variability in particle trajectories and define a framework for uncertainty quantification in Lagrangian ocean analysis.

Ensemble Lagrangian simulations aim to capture the full range of possible outcomes for particle dispersal. However, single-member Lagrangian simulations are most commonly available and only provide a subset of the possible particle dispersal outcomes. This study explores how to generate the variability inherent in Lagrangian ensemble simulations by creating variability in a single-member simulation. To obtain a reference for comparison, we performed ensemble lagrangian simulations by advecting the particles from the surface of the Gulf Stream, around 35.61° N, 73.61° W, in each member of the NATL025-CJMCYC3 ensemble to obtain trajectories capturing the full ensemble variability. Subsequently, we performed single-member simulations with spatially and temporally varying release strategies to generate comparable trajectory variability and dispersal. We studied how these strategies affected the number of surface particles connecting the Gulf Stream with the eastern side of the subtropical gyre. We used an information theory approach to define and compare the variability in the ensemble with the single-member strategies. We defined the variability as the marginal entropy or average information content of the probability distributions of the position of the particles. We calculated the relative entropy to quantify the uncertainty of representing the full-ensemble variability with single-member simulations. We found that release periods of 12 to 30 weeks most effectively captured the full ensemble variability, while spatial releases with a 2.0° radius resulted in the closest match at timescales shorter than 10 days. Our findings provide insights to improve the representation of variability in particle trajectories and define a framework for uncertainty quantification in Lagrangian ocean analysis.

Numerical simulations of marine surface particle dispersal are a crucial tool for addressing many outstanding issues in physical oceanography of societal relevance, such as marine plastic pollution. However, the quality of these Lagrangian simulations depends on the ability of the underlying numerical model to represent prevailing ocean circulation features. Here, we investigate how simulated marine surface particle dispersal changes if the – often omitted or only approximated – impact of wind-generated surface waves on upper-ocean circulation is considered. We use velocity fields from a high-resolution coupled ocean–wave model simulation and a complementary stand-alone ocean model simulation for the Mediterranean Sea to answer the following questions: (1) how does the explicit representation of waves impact simulated surface particle dispersal, and what is the relative impact of Stokes drift and wave-driven Eulerian currents? (2) How accurately can the wave impact be approximated by the commonly applied approach of advecting particles with non-wave-driven Eulerian currents and Stokes drift from stand-alone ocean and wave models? We find that the representation of surface waves tends to increase the simulated mean Lagrangian surface drift speed in winter through the dominant impact of Stokes drift and tends to decrease the mean Lagrangian surface drift speed in summer through the dominant impact of wave-driven Eulerian currents. Furthermore, simulations that approximate the surface wave impact by including Stokes drift (but ignoring wave-driven Eulerian currents) do not necessarily yield better estimates of surface particle dispersal patterns with explicit wave impact representation than simulations that do not include any surface wave impact. Our results imply that – whenever possible – velocity fields from a coupled ocean–wave model should be used for surface particle dispersal simulations.

Ensemble Lagrangian simulations aim to capture the full range of possible outcomes for particle dispersal. However, single-member Lagrangian simulations are most commonly available and only provide a subset of the possible particle dispersal outcomes. This study explores how to generate the variability inherent in Lagrangian ensemble simulations by creating variability in a single-member simulation. To obtain a reference for comparison, we performed ensemble lagrangian simulations by advecting the particles from the surface of the Gulf Stream, around 35.61° N, 73.61° W, in each member of the NATL025-CJMCYC3 ensemble to obtain trajectories capturing the full ensemble variability. Subsequently, we performed single-member simulations with spatially and temporally varying release strategies to generate comparable trajectory variability and dispersal. We studied how these strategies affected the number of surface particles connecting the Gulf Stream with the eastern side of the subtropical gyre. We used an information theory approach to define and compare the variability in the ensemble with the single-member strategies. We defined the variability as the marginal entropy or average information content of the probability distributions of the position of the particles. We calculated the relative entropy to quantify the uncertainty of representing the full-ensemble variability with single-member simulations. We found that release periods of 12 to 30 weeks most effectively captured the full ensemble variability, while spatial releases with a 2.0° radius resulted in the closest match at timescales shorter than 10 days. Our findings provide insights to improve the representation of variability in particle trajectories and define a framework for uncertainty quantification in Lagrangian ocean analysis.