Articles | Volume 23, issue 4
https://doi.org/10.5194/npg-23-159-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/npg-23-159-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
05 Jul 2016
Research article |
| 05 Jul 2016
Detecting and tracking eddies in oceanic flow fields: a Lagrangian descriptor based on the modulus of vorticity
Rahel Vortmeyer-Kley
CORRESPONDING AUTHOR
Institute for Chemistry and Biology of the Marine Environment, Theoretical Physics/Complex Systems, Carl von Ossietzky University Oldenburg, Oldenburg, Germany
Ulf Gräwe
Leibniz Institute for Baltic Sea Research, Rostock-Warnemünde, Germany
Institute of Meteorology and Climatology, Leibniz Universität Hannover, Hanover, Germany
Ulrike Feudel
Institute for Chemistry and Biology of the Marine Environment, Theoretical Physics/Complex Systems, Carl von Ossietzky University Oldenburg, Oldenburg, Germany
Related authors
No articles found.
Marvin Lorenz, Katri Viigand, and Ulf Gräwe
Nat. Hazards Earth Syst. Sci. Discuss., https://doi.org/10.5194/nhess-2024-198, https://doi.org/10.5194/nhess-2024-198, 2024
Preprint under review for NHESS
Short summary
Short summary
This study divides the sea level components that contribute to extreme sea levels in the Baltic Sea into three parts: the filling state of the Baltic Sea, seiches and storm surges. In the western part of the Baltic Sea, storm surges are the main factor, while in the central and northern parts, the filling state plays a larger role. Using a numerical model, we show that wind and air pressure are the main drivers of these events, with Atlantic sea level also playing a small role.
Florian Börgel, Sven Karsten, Karoline Rummel, and Ulf Gräwe
EGUsphere, https://doi.org/10.5194/egusphere-2024-2685, https://doi.org/10.5194/egusphere-2024-2685, 2024
Short summary
Short summary
Forecasting river runoff, crucial for managing water resources and understanding climate impacts, can be challenging. This study introduces a new method using Convolutional Long Short-Term Memory (ConvLSTM) networks, a machine learning model that processes spatial and temporal data. Focusing on the Baltic Sea region, our model uses weather data as input to predict daily river runoff for 97 rivers.
Ann Kristin Klose, Jonathan F. Donges, Ulrike Feudel, and Ricarda Winkelmann
Earth Syst. Dynam., 15, 635–652, https://doi.org/10.5194/esd-15-635-2024, https://doi.org/10.5194/esd-15-635-2024, 2024
Short summary
Short summary
We qualitatively study the long-term stability of the Greenland Ice Sheet and AMOC as tipping elements in the Earth system, which is largely unknown given their interaction in a positive–negative feedback loop. Depending on the timescales of ice loss and the position of the AMOC’s state relative to its critical threshold, we find distinct dynamic regimes of cascading tipping. These suggest that respecting safe rates of environmental change is necessary to mitigate potential domino effects.
Marvin Lorenz and Ulf Gräwe
Ocean Sci., 19, 1753–1771, https://doi.org/10.5194/os-19-1753-2023, https://doi.org/10.5194/os-19-1753-2023, 2023
Short summary
Short summary
We study the variability of extreme sea levels in a 13 member hindcast ensemble for the Baltic Sea. The ensemble mean shows good agreement with observations regarding return levels and trends. However, we find great variability and uncertainty within the ensemble. We argue that the variability of storms in the atmospheric data directly translates into the variability of the return levels. These results highlight the need for large regional ensembles to minimise uncertainties.
Ulrike Feudel
Nonlin. Processes Geophys., 30, 481–502, https://doi.org/10.5194/npg-30-481-2023, https://doi.org/10.5194/npg-30-481-2023, 2023
Short summary
Short summary
Many systems in nature are characterized by the coexistence of different stable states for given environmental parameters and external forcing. Examples can be found in different fields of science, ranging from ecosystems to climate dynamics. Perturbations can lead to critical transitions (tipping) from one stable state to another. The study of these transitions requires the development of new methodological approaches that allow for modeling, analyzing and predicting them.
Joshua Kiesel, Marvin Lorenz, Marcel König, Ulf Gräwe, and Athanasios T. Vafeidis
Nat. Hazards Earth Syst. Sci., 23, 2961–2985, https://doi.org/10.5194/nhess-23-2961-2023, https://doi.org/10.5194/nhess-23-2961-2023, 2023
Short summary
Short summary
Among the Baltic Sea littoral states, Germany is anticipated to experience considerable damage as a result of increased coastal flooding due to sea-level rise (SLR). Here we apply a new modelling framework to simulate how flooding along the German Baltic Sea coast may change until 2100 if dikes are not upgraded. We find that the study region is highly exposed to flooding, and we emphasise the importance of current plans to update coastal protection in the future.
Bronwyn E. Cahill, Piotr Kowalczuk, Lena Kritten, Ulf Gräwe, John Wilkin, and Jürgen Fischer
Biogeosciences, 20, 2743–2768, https://doi.org/10.5194/bg-20-2743-2023, https://doi.org/10.5194/bg-20-2743-2023, 2023
Short summary
Short summary
We quantify the impact of optically significant water constituents on surface heating rates and thermal energy fluxes in the western Baltic Sea. During productive months in 2018 (April to September) we found that the combined effect of coloured
dissolved organic matter and particulate absorption contributes to sea surface heating of between 0.4 and 0.9 K m−1 d−1 and a mean loss of heat (ca. 5 W m−2) from the sea to the atmosphere. This may be important for regional heat balance budgets.
Pia Kolb, Anna Zorndt, Hans Burchard, Ulf Gräwe, and Frank Kösters
Ocean Sci., 18, 1725–1739, https://doi.org/10.5194/os-18-1725-2022, https://doi.org/10.5194/os-18-1725-2022, 2022
Short summary
Short summary
River engineering measures greatly changed tidal dynamics in the Weser estuary. We studied the effect on saltwater intrusion with numerical models. Our analysis shows that a deepening of the navigation channel causes saltwater to intrude further into the Weser estuary. This effect is mostly masked by the natural variability of river discharge. In our study, it proved essential to recalibrate individual hindcast models due to differences in sediments, bed forms, and underlying bathymetric data.
Matthias Gröger, Manja Placke, H. E. Markus Meier, Florian Börgel, Sandra-Esther Brunnabend, Cyril Dutheil, Ulf Gräwe, Magnus Hieronymus, Thomas Neumann, Hagen Radtke, Semjon Schimanke, Jian Su, and Germo Väli
Geosci. Model Dev., 15, 8613–8638, https://doi.org/10.5194/gmd-15-8613-2022, https://doi.org/10.5194/gmd-15-8613-2022, 2022
Short summary
Short summary
Comparisons of oceanographic climate data from different models often suffer from different model setups, forcing fields, and output of variables. This paper provides a protocol to harmonize these elements to set up multidecadal simulations for the Baltic Sea, a marginal sea in Europe. First results are shown from six different model simulations from four different model platforms. Topical studies for upwelling, marine heat waves, and stratification are also assessed.
Jens Daniel Müller, Bernd Schneider, Ulf Gräwe, Peer Fietzek, Marcus Bo Wallin, Anna Rutgersson, Norbert Wasmund, Siegfried Krüger, and Gregor Rehder
Biogeosciences, 18, 4889–4917, https://doi.org/10.5194/bg-18-4889-2021, https://doi.org/10.5194/bg-18-4889-2021, 2021
Short summary
Short summary
Based on profiling pCO2 measurements from a field campaign, we quantify the biomass production of a cyanobacteria bloom in the Baltic Sea, the export of which would foster deep water deoxygenation. We further demonstrate how this biomass production can be accurately reconstructed from long-term surface measurements made on cargo vessels in combination with modelled temperature profiles. This approach enables a better understanding of a severe concern for the Baltic’s good environmental status.
Erik Jacobs, Henry C. Bittig, Ulf Gräwe, Carolyn A. Graves, Michael Glockzin, Jens D. Müller, Bernd Schneider, and Gregor Rehder
Biogeosciences, 18, 2679–2709, https://doi.org/10.5194/bg-18-2679-2021, https://doi.org/10.5194/bg-18-2679-2021, 2021
Short summary
Short summary
We use a unique data set of 8 years of continuous carbon dioxide (CO2) and methane (CH4) surface water measurements from a commercial ferry to study upwelling in the Baltic Sea. Its seasonality and regional and interannual variability are examined. Strong upwelling events drastically increase local surface CO2 and CH4 levels and are mostly detected in late summer after long periods of impaired mixing. We introduce an extrapolation method to estimate regional upwelling-induced trace gas fluxes.
Robert Daniel Osinski, Kristina Enders, Ulf Gräwe, Knut Klingbeil, and Hagen Radtke
Ocean Sci., 16, 1491–1507, https://doi.org/10.5194/os-16-1491-2020, https://doi.org/10.5194/os-16-1491-2020, 2020
Short summary
Short summary
This study investigates the impact of the uncertainty in atmospheric data of a storm event on the transport of microplastics and sediments. The model chain includes the WRF atmospheric model, the WAVEWATCH III® wave model, and the GETM regional ocean model as well as a sediment transport model based on the FABM framework. An ensemble approach based on stochastic perturbations of the WRF model is used. We found a strong impact of atmospheric uncertainty on the amount of transported material.
Hagen Radtke, Sandra-Esther Brunnabend, Ulf Gräwe, and H. E. Markus Meier
Clim. Past, 16, 1617–1642, https://doi.org/10.5194/cp-16-1617-2020, https://doi.org/10.5194/cp-16-1617-2020, 2020
Short summary
Short summary
During the last century, salinity in the Baltic Sea showed a multidecadal oscillation with a period of 30 years. Using a numerical circulation model and wavelet coherence analysis, we demonstrate that this variation has at least two possible causes. One driver is river runoff which shows a 30-year variation. The second one is a variation in the frequency of strong inflows of saline water across Darss Sill which also contains a pronounced 30-year period.
Beate Stawiarski, Stefan Otto, Volker Thiel, Ulf Gräwe, Natalie Loick-Wilde, Anna K. Wittenborn, Stefan Schloemer, Janine Wäge, Gregor Rehder, Matthias Labrenz, Norbert Wasmund, and Oliver Schmale
Biogeosciences, 16, 1–16, https://doi.org/10.5194/bg-16-1-2019, https://doi.org/10.5194/bg-16-1-2019, 2019
Short summary
Short summary
The understanding of surface water methane production in the world oceans is still poor. By combining field studies and incubation experiments, our investigations suggest that zooplankton contributes to subthermocline methane enrichments in the central Baltic Sea by methane production within the digestive tract of copepods and/or by methane production through release of methane precursor substances into the surrounding water, followed by microbial degradation to methane.
Joeran Maerz, Richard Hofmeister, Eefke M. van der Lee, Ulf Gräwe, Rolf Riethmüller, and Kai W. Wirtz
Biogeosciences, 13, 4863–4876, https://doi.org/10.5194/bg-13-4863-2016, https://doi.org/10.5194/bg-13-4863-2016, 2016
Short summary
Short summary
We investigated sinking velocity (ws) of suspended particulate matter (SPM) in the German Bight. By inferring ws indirectly from an extensive turbidity data set and hydrodynamic model results, we found enhanced ws in a coastal transition zone. Combined with known residual circulation patterns, this led to a new conceptual understanding of the retention of fine minerals and nutrients in shallow coastal areas. The retention is likely modulated by algal excretions enhancing flocculation of SPM.
M. Duran-Matute, T. Gerkema, G. J. de Boer, J. J. Nauw, and U. Gräwe
Ocean Sci., 10, 611–632, https://doi.org/10.5194/os-10-611-2014, https://doi.org/10.5194/os-10-611-2014, 2014
Related subject area
Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
Dynamically optimal models of atmospheric motion
A robust numerical method for the generation and propagation of periodic finite-amplitude internal waves in natural waters using high-accuracy simulations
Energy transfer from internal solitary waves to turbulence via high-frequency internal waves: seismic observations in the northern South China Sea
The role of time-varying external factors in the intensification of tropical cyclones
Solving a North-type energy balance model using boundary integral methods
Transformation of internal solitary waves at the edge of ice cover
Review article: Interdisciplinary perspectives on climate sciences – highlighting past and current scientific achievements
Variational techniques for a one-dimensional energy balance model
A new approach to understanding fluid mixing in process-study models of stratified fluids
Sensitivity of the polar boundary layer to transient phenomena
Aggregation of slightly buoyant microplastics in 3D vortex flows
Existence and influence of mixed states in a model of vegetation patterns
Rate-induced tipping in ecosystems and climate: the role of unstable states, basin boundaries and transient dynamics
Review article: Dynamical systems, algebraic topology and the climate sciences
An approach for projecting the timing of abrupt winter Arctic sea ice loss
An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling
Review article: Large fluctuations in non-equilibrium physics
On the interaction of stochastic forcing and regime dynamics
Applying dynamical systems techniques to real ocean drifters
Observations of shoaling internal wave transformation over a gentle slope in the South China Sea
Climate bifurcations in a Schwarzschild equation model of the Arctic atmosphere
Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation
Estimate of energy loss from internal solitary waves breaking on slopes
Regional study of mode-2 internal solitary waves at the Pacific coast of Central America using marine seismic survey data
The effect of strong shear on internal solitary-like waves
Enhanced diapycnal mixing with polarity-reversing internal solitary waves revealed by seismic reflection data
Enhanced internal tidal mixing in the Philippine Sea mesoscale environment
Detecting flow features in scarce trajectory data using networks derived from symbolic itineraries: an application to surface drifters in the North Atlantic
Review article: Hilbert problems for the climate sciences in the 21st century – 20 years later
Anthropocene climate bifurcation
Effects of upwelling duration and phytoplankton growth regime on dissolved-oxygen levels in an idealized Iberian Peninsula upwelling system
Baroclinic and barotropic instabilities in planetary atmospheres: energetics, equilibration and adjustment
Numerical bifurcation methods applied to climate models: analysis beyond simulation
Lyapunov analysis of multiscale dynamics: the slow bundle of the two-scale Lorenz 96 model
Competition between chaotic advection and diffusion: stirring and mixing in a 3-D eddy model
Climatic responses to systematic time variations of parameters: a dynamical approach
Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance
Wave propagation in the Lorenz-96 model
Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years
On the CCN (de)activation nonlinearities
Detecting changes in forced climate attractors with Wasserstein distance
Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex
Subvisible cirrus clouds – a dynamical system approach
Influence of finite-time Lyapunov exponents on winter precipitation over the Iberian Peninsula
Dynamics of the Hadley circulation in an axisymmetric model undergoing stratification periodic forcing
Oscillations in a simple climate–vegetation model
A novel method for analyzing the process of abrupt climate change
Equilibrium temperature distribution and Hadley circulation in an axisymmetric model
Alexander G. Voronovich
Nonlin. Processes Geophys., 31, 559–569, https://doi.org/10.5194/npg-31-559-2024, https://doi.org/10.5194/npg-31-559-2024, 2024
Short summary
Short summary
A derivation of discrete dynamical equations for the dry atmosphere without dissipative processes based on the least action principle is presented. For a given set of generally irregularly spaced grid points and a given mode of interpolation, through the minimization of action, the algorithm ensures maximal closeness of the evolution of the discrete system to the motion of the continuous atmosphere. The spatial resolution can be adjusted while executing calculations.
Pierre Lloret, Peter J. Diamessis, Marek Stastna, and Greg N. Thomsen
Nonlin. Processes Geophys., 31, 515–533, https://doi.org/10.5194/npg-31-515-2024, https://doi.org/10.5194/npg-31-515-2024, 2024
Short summary
Short summary
This study presents a new approach to simulating large ocean density waves that travel long distances without breaking down. This new approach ensures that these waves are depicted more accurately and realistically in our models. This is particularly useful for understanding wave behavior in lakes with distinct water layers, which can help predict natural phenomena and their effects on environments like swash zones, where waves meet the shore.
Linghan Meng, Haibin Song, Yongxian Guan, Shun Yang, Kun Zhang, and Mengli Liu
Nonlin. Processes Geophys., 31, 477–495, https://doi.org/10.5194/npg-31-477-2024, https://doi.org/10.5194/npg-31-477-2024, 2024
Short summary
Short summary
With seismic data, we observed high-frequency internal waves (HIWs) with amplitudes of around 10 m. A shoaling thermocline and gentle slope suggest that HIWs result from fission. Remote sensing data support this. Strong shear caused Ri below 0.25 over 20–30 km, indicating instability. HIWs enhance mixing, averaging 10-4 m2s-1, revealing a new energy cascade from shoaling waves to turbulence, and enhancing our understanding of energy dissipation and mixing in the northern South China Sea.
Samuel Watson and Courtney Quinn
Nonlin. Processes Geophys., 31, 381–394, https://doi.org/10.5194/npg-31-381-2024, https://doi.org/10.5194/npg-31-381-2024, 2024
Short summary
Short summary
The intensification of tropical cyclones (TCs) is explored through a conceptual model derived from geophysical principals. Focus is put on the behaviour of the model with parameters which change in time. The rates of change cause the model to either tip to an alternative stable state or recover the original state. This represents intensification, dissipation, or eyewall replacement cycles (ERCs). A case study which emulates the rapid intensification events of Hurricane Irma (2017) is explored.
Aksel Samuelsberg and Per Kristen Jakobsen
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-11, https://doi.org/10.5194/npg-2024-11, 2024
Revised manuscript accepted for NPG
Short summary
Short summary
We explored a simplified climate model based on Earth's energy budget. One advantage of such models is that they are easier to study mathematically. Using a mathematical technique known as boundary integral methods, we have found a new way to solve these climate models. This method is particularly useful for modeling climates very different from Earth's current state, such as those on other planets or during past ice ages.
Kateryna Terletska, Vladimir Maderich, and Elena Tobisch
Nonlin. Processes Geophys., 31, 207–217, https://doi.org/10.5194/npg-31-207-2024, https://doi.org/10.5194/npg-31-207-2024, 2024
Short summary
Short summary
The transformation of internal waves at the edge of ice cover can enhance the turbulent mixing and melting of ice in the Arctic Ocean and Antarctica. We studied numerically the transformation of internal solitary waves of depression under smooth ice surfaces compared with the processes beneath the ridged underside of the ice. For large keels, more than 40% of wave energy is lost on the first keel, while for relatively small keels energy losses on the first keel are less than 6%.
Vera Melinda Galfi, Tommaso Alberti, Lesley De Cruz, Christian L. E. Franzke, and Valerio Lembo
Nonlin. Processes Geophys., 31, 185–193, https://doi.org/10.5194/npg-31-185-2024, https://doi.org/10.5194/npg-31-185-2024, 2024
Short summary
Short summary
In the online seminar series "Perspectives on climate sciences: from historical developments to future frontiers" (2020–2021), well-known and established scientists from several fields – including mathematics, physics, climate science and ecology – presented their perspectives on the evolution of climate science and on relevant scientific concepts. In this paper, we first give an overview of the content of the seminar series, and then we introduce the written contributions to this special issue.
Gianmarco Del Sarto, Jochen Bröcker, Franco Flandoli, and Tobias Kuna
Nonlin. Processes Geophys., 31, 137–150, https://doi.org/10.5194/npg-31-137-2024, https://doi.org/10.5194/npg-31-137-2024, 2024
Short summary
Short summary
We consider a one-dimensional model for the Earth's temperature. We give sufficient conditions to admit three asymptotic solutions. We connect the value function (minimum value of an objective function depending on the greenhouse gas (GHG) concentration) to the global mean temperature. Then, we show that the global mean temperature is the derivative of the value function and that it is non-decreasing with respect to GHG concentration.
Samuel George Hartharn-Evans, Marek Stastna, and Magda Carr
Nonlin. Processes Geophys., 31, 61–74, https://doi.org/10.5194/npg-31-61-2024, https://doi.org/10.5194/npg-31-61-2024, 2024
Short summary
Short summary
Across much of the ocean, and the world's lakes, less dense water (either because it is warm or fresh) overlays denser water, forming stratification. The mixing of these layers affects the distribution of heat, nutrients, plankton, sediment, and buoyancy, so it is crucial to understand. We use small-scale numerical experiments to better understand these processes, and here we propose a new analysis tool for understanding mixing within those models, looking at where two variables intersect.
Amandine Kaiser, Nikki Vercauteren, and Sebastian Krumscheid
Nonlin. Processes Geophys., 31, 45–60, https://doi.org/10.5194/npg-31-45-2024, https://doi.org/10.5194/npg-31-45-2024, 2024
Short summary
Short summary
Current numerical weather prediction models encounter challenges in accurately representing regimes in the stably stratified atmospheric boundary layer (SBL) and the transitions between them. Stochastic modeling approaches are a promising framework to analyze when transient small-scale phenomena can trigger regime transitions. Therefore, we conducted a sensitivity analysis of the SBL to transient phenomena by augmenting a surface energy balance model with meaningful randomizations.
Irina I. Rypina, Lawrence J. Pratt, and Michael Dotzel
Nonlin. Processes Geophys., 31, 25–44, https://doi.org/10.5194/npg-31-25-2024, https://doi.org/10.5194/npg-31-25-2024, 2024
Short summary
Short summary
This paper investigates the aggregation of small, spherical, slightly buoyant, rigid particles in a simple 3D vortex flow. Our goal was to gain insights into the behaviour of slightly buoyant marine microplastics in a flow that qualitatively resembles ocean eddies. Attractors are mapped out for the steady, axisymmetric; steady, asymmetric; and nonsteady, asymmetric vortices over a range of flow and particle parameters. Simple theoretical arguments are used to interpret the results.
Lilian Vanderveken, Marina Martínez Montero, and Michel Crucifix
Nonlin. Processes Geophys., 30, 585–599, https://doi.org/10.5194/npg-30-585-2023, https://doi.org/10.5194/npg-30-585-2023, 2023
Short summary
Short summary
In semi-arid regions, hydric stress affects plant growth. In these conditions, vegetation patterns develop and effectively allow for vegetation to persist under low water input. The formation of patterns and the transition between patterns can be studied with small models taking the form of dynamical systems. Our study produces a full map of stable and unstable solutions in a canonical vegetation model and shows how they determine the transitions between different patterns.
Ulrike Feudel
Nonlin. Processes Geophys., 30, 481–502, https://doi.org/10.5194/npg-30-481-2023, https://doi.org/10.5194/npg-30-481-2023, 2023
Short summary
Short summary
Many systems in nature are characterized by the coexistence of different stable states for given environmental parameters and external forcing. Examples can be found in different fields of science, ranging from ecosystems to climate dynamics. Perturbations can lead to critical transitions (tipping) from one stable state to another. The study of these transitions requires the development of new methodological approaches that allow for modeling, analyzing and predicting them.
Michael Ghil and Denisse Sciamarella
Nonlin. Processes Geophys., 30, 399–434, https://doi.org/10.5194/npg-30-399-2023, https://doi.org/10.5194/npg-30-399-2023, 2023
Short summary
Short summary
The problem of climate change is that of a chaotic system subject to time-dependent forcing, such as anthropogenic greenhouse gases and natural volcanism. To solve this problem, we describe the mathematics of dynamical systems with explicit time dependence and those of studying their behavior through topological methods. Here, we show how they are being applied to climate change and its predictability.
Camille Hankel and Eli Tziperman
Nonlin. Processes Geophys., 30, 299–309, https://doi.org/10.5194/npg-30-299-2023, https://doi.org/10.5194/npg-30-299-2023, 2023
Short summary
Short summary
We present a novel, efficient method for identifying climate
tipping pointthreshold values of CO2 beyond which rapid and irreversible changes occur. We use a simple model of Arctic sea ice to demonstrate the method’s efficacy and its potential for use in state-of-the-art global climate models that are too expensive to run for this purpose using current methods. The ability to detect tipping points will improve our preparedness for rapid changes that may occur under future climate change.
Bin Shi and Guodong Sun
Nonlin. Processes Geophys., 30, 263–276, https://doi.org/10.5194/npg-30-263-2023, https://doi.org/10.5194/npg-30-263-2023, 2023
Short summary
Short summary
We introduce a sample-based algorithm to obtain the conditional nonlinear optimal perturbations. Compared with the classical adjoint-based method, it is easier to implement and reduces the required storage for the basic state. When we reduce the number of samples to some extent, it reduces the computation markedly more when using the sample-based method, which can guarantee that the CNOP obtained is nearly consistent with some minor fluctuating errors oscillating in spatial distribution.
Giovanni Jona-Lasinio
Nonlin. Processes Geophys., 30, 253–262, https://doi.org/10.5194/npg-30-253-2023, https://doi.org/10.5194/npg-30-253-2023, 2023
Short summary
Short summary
Non-equilibrium is dominant in geophysical and climate phenomena. Most of the processes that characterize energy flow occur far from equilibrium. These range from very large systems, such as weather patterns or ocean currents that remain far from equilibrium, owing to an influx of energy, to biological structures. In the last decades, progress in non-equilibrium physics has come from the study of very rare fluctuations, and this paper provides an introduction to these theoretical developments.
Joshua Dorrington and Tim Palmer
Nonlin. Processes Geophys., 30, 49–62, https://doi.org/10.5194/npg-30-49-2023, https://doi.org/10.5194/npg-30-49-2023, 2023
Short summary
Short summary
Atmospheric models often include random forcings, which aim to replicate the impact of processes too small to be resolved. Recent results in simple atmospheric models suggest that this random forcing can actually stabilise certain slow-varying aspects of the system, which could provide a path for resolving known errors in our models. We use randomly forced simulations of a
toychaotic system and theoretical arguments to explain why this strange effect occurs – at least in simple models.
Irina I. Rypina, Timothy Getscher, Lawrence J. Pratt, and Tamay Ozgokmen
Nonlin. Processes Geophys., 29, 345–361, https://doi.org/10.5194/npg-29-345-2022, https://doi.org/10.5194/npg-29-345-2022, 2022
Short summary
Short summary
Techniques from dynamical systems theory have been widely used to study transport in ocean flows. However, they have been typically applied to numerically simulated trajectories of water parcels. This paper applies different dynamical systems techniques to real ocean drifter trajectories from the massive release in the Gulf of Mexico. To our knowledge, this is the first comprehensive comparison of the performance of different dynamical systems techniques with application to real drifters.
Steven R. Ramp, Yiing Jang Yang, Ching-Sang Chiu, D. Benjamin Reeder, and Frederick L. Bahr
Nonlin. Processes Geophys., 29, 279–299, https://doi.org/10.5194/npg-29-279-2022, https://doi.org/10.5194/npg-29-279-2022, 2022
Short summary
Short summary
Earlier work in the vicinity of the shelf and slope in the northeastern South China Sea serendipitously revealed the presence of large, stunning bed forms (sand dunes) whose height (>15 m) and length (>350 m) are quite unique and unusual. We hypothesize that the dunes formed due to shoaling very large-amplitude nonlinear internal waves that scour the bottom and resuspend and redistribute the sediments. As a first step, the wave characteristics are observed and described in detail.
Kolja L. Kypke, William F. Langford, Gregory M. Lewis, and Allan R. Willms
Nonlin. Processes Geophys., 29, 219–239, https://doi.org/10.5194/npg-29-219-2022, https://doi.org/10.5194/npg-29-219-2022, 2022
Short summary
Short summary
Climate change is causing rapid temperature increases in the polar regions. A fundamental question is whether these temperature increases are reversible. If we control carbon dioxide emissions, will the temperatures revert or will we have passed a tipping point beyond which return to the present state is impossible? Our mathematical model of the Arctic climate indicates that under present emissions the Arctic climate will change irreversibly to a warm climate before the end of the century.
Karl R. Helfrich and Lev Ostrovsky
Nonlin. Processes Geophys., 29, 207–218, https://doi.org/10.5194/npg-29-207-2022, https://doi.org/10.5194/npg-29-207-2022, 2022
Short summary
Short summary
Internal solitons are an important class of nonlinear waves commonly observed in coastal oceans. Their propagation is affected by the Earth's rotation and the variation in the water depth. We consider an interplay of these factors using the corresponding extension of the Gardner equation. This model allows a limiting soliton amplitude and the corresponding increase in wavelength, making the effects of rotation and topography on a shoaling wave especially significant.
Kateryna Terletska and Vladimir Maderich
Nonlin. Processes Geophys., 29, 161–170, https://doi.org/10.5194/npg-29-161-2022, https://doi.org/10.5194/npg-29-161-2022, 2022
Short summary
Short summary
Internal solitary waves (ISWs) emerge in the ocean and seas in various forms and break on the shelf zones in a variety of ways. This results in intensive mixing that affects processes such as biological productivity and sediment transport. Mechanisms of wave interaction with slopes are related to breaking and changing polarity. Our study focuses on wave transformation over idealized shelf-slope topography using a two-layer stratification. Four types of ISW transformation over slopes are shown.
Wenhao Fan, Haibin Song, Yi Gong, Shun Yang, and Kun Zhang
Nonlin. Processes Geophys., 29, 141–160, https://doi.org/10.5194/npg-29-141-2022, https://doi.org/10.5194/npg-29-141-2022, 2022
Short summary
Short summary
Compared with mode-1 internal solitary waves (ISWs), mode-2 ISWs in the ocean require further study. A mass of mode-2 ISWs developing at the Pacific coast of Central America have been imaged using seismic reflection data. We find that the relationship between the mode-2 ISW propagation speed and amplitude is diverse. It is affected by seawater depth, pycnocline depth, and pycnocline thickness. The ISW vertical amplitude structure is affected by the ISW nonlinearity and the pycnocline deviation.
Marek Stastna, Aaron Coutino, and Ryan K. Walter
Nonlin. Processes Geophys., 28, 585–598, https://doi.org/10.5194/npg-28-585-2021, https://doi.org/10.5194/npg-28-585-2021, 2021
Short summary
Short summary
Large-amplitude waves in the interior of the ocean-internal waves in the ocean propagate in a dynamic, highly variable environment with changes in background current, local depth, and stratification. These waves have a well-known mathematical theory that, despite considerable progress, has some gaps. In particular, waves have been observed in situations that preclude an application of the mathematical theory. We present numerical simulations of the spontaneous generation of such waves.
Yi Gong, Haibin Song, Zhongxiang Zhao, Yongxian Guan, Kun Zhang, Yunyan Kuang, and Wenhao Fan
Nonlin. Processes Geophys., 28, 445–465, https://doi.org/10.5194/npg-28-445-2021, https://doi.org/10.5194/npg-28-445-2021, 2021
Short summary
Short summary
When the internal solitary wave propagates to the continental shelf and slope, the polarity reverses due to the shallower water depth. In this process, the internal solitary wave dissipates energy and enhances diapycnal mixing, thus affecting the local oceanic environment. In this study, we used reflection seismic data to evaluate the spatial distribution of the diapycnal mixing around the polarity-reversing internal solitary waves.
Jia You, Zhenhua Xu, Qun Li, Robin Robertson, Peiwen Zhang, and Baoshu Yin
Nonlin. Processes Geophys., 28, 271–284, https://doi.org/10.5194/npg-28-271-2021, https://doi.org/10.5194/npg-28-271-2021, 2021
Short summary
Short summary
Turbulent mixing in the ocean is mainly attributed to internal wave breaking, but the modulation of the mesoscale environment is unclear. The spatially inhomogeneous and seasonally variable diapycnal diffusivities in the upper Philippine Sea were estimated from Argo float data using a strain-based, fine-scale parameterization. Internal tides contributed significant diapycnal mixing here, with the mesoscale environment greatly regulating the intensity and spatial inhomogeneity of tidal mixing.
David Wichmann, Christian Kehl, Henk A. Dijkstra, and Erik van Sebille
Nonlin. Processes Geophys., 27, 501–518, https://doi.org/10.5194/npg-27-501-2020, https://doi.org/10.5194/npg-27-501-2020, 2020
Short summary
Short summary
The surface transport of heat, nutrients and plastic in the North Atlantic Ocean is organized into large-scale flow structures. We propose a new and simple method to detect such features in ocean drifter data sets by identifying groups of trajectories with similar dynamical behaviour using network theory. We successfully detect well-known regions such as the Subpolar and Subtropical gyres, the Western Boundary Current region and the Caribbean Sea.
Michael Ghil
Nonlin. Processes Geophys., 27, 429–451, https://doi.org/10.5194/npg-27-429-2020, https://doi.org/10.5194/npg-27-429-2020, 2020
Short summary
Short summary
The scientific questions posed by the climate sciences are central to socioeconomic concerns today. This paper revisits several crucial questions, starting with
What can we predict beyond 1 week, for how long, and by what methods?, and ending with
Can we achieve enlightened climate control of our planet by the end of the century?We review the progress in dealing with the nonlinearity and stochasticity of the Earth system and emphasize major strides in coupled climate–economy modeling.
Kolja Leon Kypke, William Finlay Langford, and Allan Richard Willms
Nonlin. Processes Geophys., 27, 391–409, https://doi.org/10.5194/npg-27-391-2020, https://doi.org/10.5194/npg-27-391-2020, 2020
Short summary
Short summary
The climate of Earth is governed by nonlinear processes of geophysics. This paper presents energy balance models (EBMs) embracing these nonlinear processes which lead to positive feedback, amplifying the effects of anthropogenic forcing and leading to bifurcations. We define bifurcation as a change in the topological equivalence class of the system. We initiate a bifurcation analysis of EBMs of Anthropocene climate, which shows that a catastrophic climate change may occur in the next century.
João H. Bettencourt, Vincent Rossi, Lionel Renault, Peter Haynes, Yves Morel, and Véronique Garçon
Nonlin. Processes Geophys., 27, 277–294, https://doi.org/10.5194/npg-27-277-2020, https://doi.org/10.5194/npg-27-277-2020, 2020
Short summary
Short summary
The oceans are losing oxygen, and future changes may worsen this problem. We performed computer simulations of an idealized Iberian Peninsula upwelling system to identify the main fine-scale processes driving dissolved oxygen variability as well as study the response of oxygen levels to changes in wind patterns and phytoplankton species. Our results suggest that oxygen levels would decrease if the wind blows for long periods of time or if phytoplankton is dominated by species that grow slowly.
Peter Read, Daniel Kennedy, Neil Lewis, Hélène Scolan, Fachreddin Tabataba-Vakili, Yixiong Wang, Susie Wright, and Roland Young
Nonlin. Processes Geophys., 27, 147–173, https://doi.org/10.5194/npg-27-147-2020, https://doi.org/10.5194/npg-27-147-2020, 2020
Short summary
Short summary
Baroclinic and barotropic instabilities are well known as the processes responsible for the production of the most important energy-containing eddies in the atmospheres and oceans of Earth and other planets. Linear and nonlinear instability theories provide insights into when such instabilities may occur, grow to a large amplitude and saturate, with examples from the laboratory, simplified numerical models and planetary atmospheres. We conclude with a number of open issues for future research.
Henk A. Dijkstra
Nonlin. Processes Geophys., 26, 359–369, https://doi.org/10.5194/npg-26-359-2019, https://doi.org/10.5194/npg-26-359-2019, 2019
Short summary
Short summary
I provide a personal view on the role of bifurcation analysis of climate models in the development of a theory of variability in the climate system. By outlining the state of the art of the methodology and by discussing what has been done and what has been learned from a hierarchy of models, I will argue that there are low-order phenomena of climate variability, such as El Niño and the Atlantic Multidecadal Oscillation.
Mallory Carlu, Francesco Ginelli, Valerio Lucarini, and Antonio Politi
Nonlin. Processes Geophys., 26, 73–89, https://doi.org/10.5194/npg-26-73-2019, https://doi.org/10.5194/npg-26-73-2019, 2019
Short summary
Short summary
We explore the nature of instabilities in a well-known meteorological toy model, the Lorenz 96, to unravel key mechanisms of interaction between scales of different resolutions and time scales. To do so, we use a mathematical machinery known as Lyapunov analysis, allowing us to capture the degrees of chaoticity associated with fundamental directions of instability. We find a non-trivial group of such directions projecting significantly on slow variables, associated with long term dynamics.
Genevieve Jay Brett, Larry Pratt, Irina Rypina, and Peng Wang
Nonlin. Processes Geophys., 26, 37–60, https://doi.org/10.5194/npg-26-37-2019, https://doi.org/10.5194/npg-26-37-2019, 2019
Short summary
Short summary
The relative importance of chaotic stirring and smaller-scale turbulent mixing for the distribution of dye in an idealized ocean flow feature is quantified using three different methods. We find that stirring is the dominant process in large areas with fast stirring, while mixing dominates in small fast-stirring regions and all slow-stirring regions. This quantification of process dominance can help oceanographers think about when to model stirring accurately, which can be costly.
Catherine Nicolis
Nonlin. Processes Geophys., 25, 649–658, https://doi.org/10.5194/npg-25-649-2018, https://doi.org/10.5194/npg-25-649-2018, 2018
Short summary
Short summary
Ordinarily the climatic impact of systematic variations of parameters arising from anthropogenic effects is addressed on the basis of large numerical models, where parameters are set to a prescribed level and the system is subsequently left to relax. We have revisited the problem from a nonlinear dynamics perspective in which the time variation of parameters is fully incorporated into the evolution laws. Some universal trends of the response have been identified.
Gabriele Vissio and Valerio Lucarini
Nonlin. Processes Geophys., 25, 413–427, https://doi.org/10.5194/npg-25-413-2018, https://doi.org/10.5194/npg-25-413-2018, 2018
Short summary
Short summary
Constructing good parametrizations is key when studying multi-scale systems. We consider a low-order model and derive a parametrization via a recently developed statistical mechanical approach. We show how the method allows for seamlessly treating the case when the unresolved dynamics is both faster and slower than the resolved one. We test the skill of the parametrization by using the formalism of the Wasserstein distance, which allows for measuring how different two probability measures are.
Dirk L. van Kekem and Alef E. Sterk
Nonlin. Processes Geophys., 25, 301–314, https://doi.org/10.5194/npg-25-301-2018, https://doi.org/10.5194/npg-25-301-2018, 2018
Short summary
Short summary
In this paper we investigate the spatiotemporal properties of waves in the Lorenz-96 model. In particular, we explain how these properties are related to the presence of Hopf and pitchfork bifurcations. We also explain bifurcation scenarios by which multiple stable waves can coexist for the same parameter values.
Davide Faranda, Gabriele Messori, M. Carmen Alvarez-Castro, and Pascal Yiou
Nonlin. Processes Geophys., 24, 713–725, https://doi.org/10.5194/npg-24-713-2017, https://doi.org/10.5194/npg-24-713-2017, 2017
Short summary
Short summary
We study the dynamical properties of the Northern Hemisphere atmospheric circulation by analysing the sea-level pressure, 2 m temperature, and precipitation frequency field over the period 1948–2013. The metrics are linked to the predictability and the persistence of the atmospheric flows. We study the dependence on the seasonal cycle and the fields corresponding to maxima and minima of the dynamical indicators.
Sylwester Arabas and Shin-ichiro Shima
Nonlin. Processes Geophys., 24, 535–542, https://doi.org/10.5194/npg-24-535-2017, https://doi.org/10.5194/npg-24-535-2017, 2017
Short summary
Short summary
The paper bridges cloud/aerosol modelling with bifurcation analysis. It identifies two nonlinear peculiarities in the differential equations describing formation of atmospheric clouds through vapour condensation on a population of aerosol particles. A key finding of the paper is an analytic estimate for the timescale of the process. The study emerged from discussions on the causes of hysteretic behaviour of the system that we observed in the results of numerical simulations.
Yoann Robin, Pascal Yiou, and Philippe Naveau
Nonlin. Processes Geophys., 24, 393–405, https://doi.org/10.5194/npg-24-393-2017, https://doi.org/10.5194/npg-24-393-2017, 2017
Short summary
Short summary
If climate is viewed as a chaotic dynamical system, its trajectories yield on an object called an attractor. Being perturbed by an external forcing, this attractor could be modified. With Wasserstein distance, we estimate on a derived Lorenz model the impact of a forcing similar to climate change. Our approach appears to work with small data sizes. We have obtained a methodology quantifying the deformation of well-known attractors, coherent with the size of data available.
Jezabel Curbelo, Víctor José García-Garrido, Carlos Roberto Mechoso, Ana Maria Mancho, Stephen Wiggins, and Coumba Niang
Nonlin. Processes Geophys., 24, 379–392, https://doi.org/10.5194/npg-24-379-2017, https://doi.org/10.5194/npg-24-379-2017, 2017
Short summary
Short summary
Lagrangian coherent structures have supported the description of transport processes in fluid dynamics. In this work we use the M function to provide new insights into the 3-D Lagrangian structure of the southern stratosphere. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied to describe the vertical extension of the stratospheric polar vortex and its evolution.
Elisa Johanna Spreitzer, Manuel Patrik Marschalik, and Peter Spichtinger
Nonlin. Processes Geophys., 24, 307–328, https://doi.org/10.5194/npg-24-307-2017, https://doi.org/10.5194/npg-24-307-2017, 2017
Short summary
Short summary
We developed a simple analytical model for describing subvisible cirrus clouds qualitatively. Using theory of dynamical systems we found two different states for the long-term behaviour of subvisible cirrus clouds, i.e. an attractor case (stable equilibrium point) and a limit cycle scenario. The transition between the states constitutes a Hopf bifurcation and is determined by environmental conditions such as vertical updraughts and temperature.
Daniel Garaboa-Paz, Nieves Lorenzo, and Vicente Pérez-Muñuzuri
Nonlin. Processes Geophys., 24, 227–235, https://doi.org/10.5194/npg-24-227-2017, https://doi.org/10.5194/npg-24-227-2017, 2017
Short summary
Short summary
This paper evaluates the connection between winter precipitation over the Iberian Peninsula and the large-scale tropospheric mixing over the eastern Atlantic Ocean. Finite-time Lyapunov exponents (FTLEs) have been calculated from 1979 to 2008 to evaluate this mixing. Our study suggests that significant negative correlations exist between summer FTLE anomalies and winter precipitation over Portugal and Spain.
Nazario Tartaglione
Nonlin. Processes Geophys., 24, 167–178, https://doi.org/10.5194/npg-24-167-2017, https://doi.org/10.5194/npg-24-167-2017, 2017
Short summary
Short summary
This paper aims to show how the tropical circulation responds to changes of the vertical stratification of the imposed temperature that drives the model. These changes mimic the presence of water vapor cycles. Thus, for simplicity's sake we impose a periodic change of this stratification with variable periods of 10–90 days. The model responds with quasi-periodic oscillations having two or more dominant frequencies. After a long forcing time period, chaotic behavior starts to appear cyclically.
J. Rombouts and M. Ghil
Nonlin. Processes Geophys., 22, 275–288, https://doi.org/10.5194/npg-22-275-2015, https://doi.org/10.5194/npg-22-275-2015, 2015
Short summary
Short summary
Our conceptual model describes global temperature and vegetation extent. We use elements from Daisyworld and classical energy balance models and add an ocean with sea ice. The model exhibits oscillatory behavior within a plausible range of parameter values.
Its periodic solutions have sawtooth behavior that is characteristic of relaxation oscillations, as well as suggestive of Quaternary glaciation cycles. The model is one of the simplest of its kind to produce such oscillatory behavior.
P. C. Yan, G. L. Feng, and W. Hou
Nonlin. Processes Geophys., 22, 249–258, https://doi.org/10.5194/npg-22-249-2015, https://doi.org/10.5194/npg-22-249-2015, 2015
Short summary
Short summary
A novel method is created to detect the process of the abrupt change, which has not been mentioned yet in traditional research. By building an ideal time series with a transition process, the results show that the process could be detected clearly. When applied to a climate index, this method detects five processes, and all of them have reappeared via the “start-end states” phase diagram. Additionally, it is detectable that the persist time of the process is related to global warming.
N. Tartaglione
Nonlin. Processes Geophys., 22, 173–185, https://doi.org/10.5194/npg-22-173-2015, https://doi.org/10.5194/npg-22-173-2015, 2015
Short summary
Short summary
At the Equator, where the heating is larger than that at other latitudes, air rises and diverges poleward in the upper troposphere, descending more or less at 30° latitude; this circulation is the Hadley cell.
We studied the impact of different meridional and vertical temperature distributions on a few features of the Hadley cell. Some parameters show a regular dependence on these distributions; others remain rather stable with distributions, but when they change, they do it in an abrupt way.
Cited articles
Abraham, E. R.: The generation of plankton patchiness by turbulent stirring, Nature, 391, 577–580, 1998.
Artale, V., Boffetta, G., Celani, M., Cencini, M., and Vulpiani, A.: Dispersion of passive tracers in closed basins: Beyond the diffusion coeffcient, Phys. Fluids, 9, 3162–3171, 1997.
Bastine, D. and Feudel, U.: Inhomogeneous dominance patterns of competing phytoplankton groups in the wake of an island, Nonlin. Processes Geophys., 17, 715–731, https://doi.org/10.5194/npg-17-715-2010, 2010.
Bettencourt, J. H., López, C., and Hernández-García, E.: Oceanic three-dimensional Lagrangian coherent structures: A study of a mesoscale eddy in the Benguela upwelling region, Ocean Model., 51, 73–83, 2012.
Boffetta, G., Lacorata, G., Redaelli, G., and Vulpiani, A.: Detecting barriers to transport: a review of different techniques, Physica D, 159, 58–70, 2001.
Bracco, A., Provenzale, A., and Scheuring, I.: Mesoscale vortices and the paradox of the plankton, P. Roy. Soc. Lond. B, 267, 1795–1800, 2000.
Branicki, M. and Wiggins, S.: Finite-time Lagrangian transport analysis: stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents, Nonlin. Processes Geophys., 17, 1–36, https://doi.org/10.5194/npg-17-1-2010, 2010.
Branicki, M., Mancho, A., and Wiggins, S.: A Lagrangian description of transport associated with a front-eddy interaction: Application to data from the North-Western Mediterranean Sea, Physica D, 240, 282–304, 2011.
Chaigneau, A., Gizolme, A., and Grados, C.: Mesoscale eddies off Peru in altimeter records: Identification algorithms and eddy spatio-temporal patterns, Prog. Oceanogr., 79, 106–119, 2008.
Chelton, D. B., Schlax, M. G., and Samelson, R. M.: Global observations of nonlinear mesoscale eddies, Prog. Oceanogr., 91, 167–216, 2011.
de la Cámara, A., Mancho, A. M., Ide, K., Serrano, E., and Mechoso, C. R.: Routes of Transport across the Antarctic Polar Vortex in the Southern Spring, J. Atmos. Sci., 69, 741–752, 2012.
Dong, C., Idica, E. Y., and McWilliams, J. C.: Circulation and multiple-scale variability in the Southern California Bight, Prog. Oceanogr., 82, 168–190, 2009.
Dong, C., Lin, X., Liu, Y., Nencioli, F., Chao, Y., Guan, Y., Chen, D., Dickey, T., and McWilliams, J. C.: Three-dimensional oceanic eddy analysis in the Southern California Bight from a numerical product, J. Geophys. Res., 117, C00H14, https://doi.org/10.1029/2011JC007354, 2012.
Dong, C., McWilliams, J. C., Liu, Y., and Chen, D.: Global heat and salt transports by eddy movement, Nat. Commun., 5, 1–6, 2014.
Donlon, C. J., Martin, M., Stark, J., Roberts-Jones, J., Fiedler, E., and Wimmer, W.: The Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) system, Remote Sens. Environ., 116, 140–158, 2012.
Douglass, E. M. and Richman, J. G.: Analysis of ageostrophy in strong surface eddies in the Atlantic Ocean, J. Geophys. Res.-Oceans, 120, 1490–1507, 2015.
d'Ovidio, F., Fernández, V., Hernández-García, E., and López, C.: Mixing structures in the Mediterranean Sea from Finite-Size Lyapunov Exponents, Geophys. Res. Lett., 31, L17203, https://doi.org/10.1029/2004GL020328, 2004.
Eugenio, F. and Marqués, F.: Automatic Satellite Image Georeferencing Using a Contour-Matching Approach, IEEE T. Geosci. Remote, 41, 2869–2880, 2003.
Fennel, K.: The generation of phytoplankton patchiness by mesoscale current patterns, Ocean Dynam., 52, 58–70, 2001.
Fernandes, M. A., Nascimento, S., and Boutov, D.: Automatic identification of oceanic eddies in infrared satellite images, Comput. Geosci., 37, 1783–1792, 2011.
Froyland, G. and Padberg, K.: Almost-invariant sets and invariant manifolds – Connecting probabilistic and geometric descriptions of coherent structures in flows, Physica D, 238, 1507–1523, 2009.
García-Garrido, V. J., Mancho, A. M., Wiggins, S., and Mendoza, C.: A dynamical systems approach to the surface search for debris associated with the disappearance of flight MH370, Nonlin. Processes Geophys., 22, 701–712, https://doi.org/10.5194/npg-22-701-2015, 2015.
Gawlik, E. S., Marsden, J. E., Du Toit, P. C., and Campagnola, S.: Lagrangian coherent structures in the planar elliptic restricted three-body problem, Celest. Mech. Dyn. Astr., 103, 227–249, 2009.
Gräwe, U., Holtermann, P., Klingbeil, K., and Burchard, H.: Advantages of vertically adaptive coordinates in numerical models of stratified shelf seas, Ocean Model., 92, 56–68, 2015a.
Gräwe, U., Naumann, M., Mohrholz, V., and Burchard, H.: Anatomizing one of the largest saltwater inflows into the Baltic Sea in December 2014, J. Geophys. Res.-Oceans., 120, 7676–7697, 2015b.
Haller, G.: Lagrangian Coherent Structures, Annu. Rev. Fluid Mech., 47, 137–162, 2015.
Haller, G. and Beron-Vera, F.: Coherent Lagrangian vortices: the black holes of turbulence, J. Fluid Mech., 731, R4, https://doi.org/10.1017/jfm.2013.391, 2013.
Haller, G. and Yuan, G.: Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D, 147, 352–370, 2000.
Haller, G., Hadjighasem, A., Farazmand, M., and Huhn, F.: Defining coherent vortices objectively from the vorticity, J. Fluid Mech., 795, 136–173, 2016.
Hernández-Carrasco, I., Rossi, V., Hernández-García, E., Garçon, V., and López, C.: The reduction of plankton biomass induced by mesoscale stirring: A modeling study in the Benguela upwelling, Deep-Sea Res. Pt. I, 83, 65–80, 2014.
Huhn, F., Kameke, A., Pérez-Muñuzuri, V., Olascoaga, M., and Beron-Vera, F.: The impact of advective transport by the South Indian Ocean Countercurrent on the Madagaskar plankton bloom, Geophys. Res. Lett., 39, L06602, https://doi.org/10.1029/2012GL051246, 2012.
Ide, K., Small, D., and Wiggins, S.: Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets, Nonlin. Processes Geophys., 9, 237–263, https://doi.org/10.5194/npg-9-237-2002, 2002.
Isern-Fontanet, J., García-Ladona, E., and Font, J.: Vortices of the Mediterranean Sea: An Altimetric Perspective, J. Phys. Oceanogr., 36, 87–103, 2006.
Jacobs, G. A., Huntley, H. S., Kirwan, A., Lipphardt, B. L., Campbell, T., Smith, T., Edwards, K., and Bartels, B.: Ocean processes underlying surface clustering, J. Geophys. Res.-Oceans, 121, 180–197, 2016.
Jung, C., Tél, T., and Ziemniak, E.: Application of scattering chaos to particle transport in a hydrodynamical flow, Chaos, 3, 555–568, 1993.
Karrasch, D., Huhn, F., and Haller, G.: Automated detection of coherent Lagrangian vortices in two-dimensional unsteady flows, P. Roy. Soc. A, 471, 20140639, https://doi.org/10.1098/rspa.2014.0639, 2015.
Klingbeil, K., Mohammadi-Aragh, M., Gräwe, U., and Burchard, H.: Quantification of spurious dissipation and mixing – Discrete variance decay in a Finite-Volume framework, Ocean Model., 81, 49–64, 2014.
Koh, T. Y. and Legras, B.: Hyperbolic lines and the stratospheric polar vortex, Chaos, 12, 382–394, 2002.
Leprince, S., Barbot, S., Ayoub, F., and Avouac, J. P.: Automatic and precise orthorectification, coregistration, and subpixel correlation of satellite images, application to ground deformation measurements, IEEE T. Geosci. Remote, 45, 1529–1558, 2007.
Madrid, J. A. J. and Mancho, A. M.: Distinguished trajectories in time dependent vector fields, Chaos, 19, 013111, https://doi.org/10.1063/1.3056050, 2009.
Mahoney, J., Bargteil, D., Kingsbury, M., Mitchell, K., and Solomon, T.: Invariant barriers to reactive front propagation in fluid flows, Europhys. Lett., 98, 44005, https://doi.org/10.1209/0295-5075/98/44005, 2012.
Mahoney, J. R. and Mitchell, K. A.: Finite-time barriers to front propagation in two-dimensional fluid flows, Chaos, 25, 087404, https://doi.org/10.1063/1.4922026, 2015.
Mancho, A., Small, D., and Wiggins, S.: A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues, Phys. Rep., 437, 55–124, 2006.
Mancho, A., Wiggins, S., Curbelo, J., and Mendoza, C.: Lagrangian Descriptors: A method of revealing phase space structures of general time dependent dynamical systems, Commun. Nonlin. Sci., 18, 3530–3557, 2013.
Martin, A.: Phytoplakton patchiness: the role of lateral stirring and mixing, Prog. Oceanogr., 57, 125–174, 2003.
Martin, A., Richards, K., Bracco, A., and Provenzale, A.: Patchy productivity in the open ocean, Global Biogeochem. Cy., 16, 9-1–9-9, https://doi.org/10.1029/2001GB001449, 2002.
McIlhany, K. and Wiggins, S.: Eulerian indicators under continuously varying conditions, Phys. Fluids, 24, 073601, https://doi.org/10.1063/1.4732152, 2012.
McIlhany, K., Mott, D., Oran, E., and Wiggins, S.: Optimizing mixing in lid-driven flow designs through predictions from Eulerian indicators, Phys. Fluids, 23, 082005, https://doi.org/10.1063/1.3626022, 2011.
McIlhany, K., Guth, S., and Wiggins, S.: Lagrangian and Eulerian analysis of transport and mixing in the three dimensional, time dependent Hill's spherical vortex, Phys. Fluids, 27, 063603, https://doi.org/10.1063/1.4922539, 2015.
Mendoza, C. and Mancho, A.: Hidden geometry of ocean flows, Phys. Rev. Lett., 105, 038501, https://doi.org/10.1103/PhysRevLett.105.038501, 2010.
Mendoza, C. and Mancho, A. M.: Review Article: "The Lagrangian description of aperiodic flows: a case study of the Kuroshio Current", Nonlin. Processes Geophys., 19, 449–472, https://doi.org/10.5194/npg-19-449-2012, 2012.
Mendoza, C., Mancho, A. M., and Rio, M.-H.: The turnstile mechanism across the Kuroshio current: analysis of dynamics in altimeter velocity fields, Nonlin. Processes Geophys., 17, 103–111, https://doi.org/10.5194/npg-17-103-2010, 2010.
Mezić, I., Loire, S., Fonoberov, V. A., and Hogan, P.: A New Mixing Diagnostic and Gulf Oil Spill Movement, Science, 330, 486–489, 2010.
Mitchell, K. A. and Mahoney, J. R.: Invariant manifolds and the geometry of front propagation in fluid flows, Chaos, 22, 037104, https://doi.org/10.1063/1.4746039, 2012.
Morrow, R. and Le Traon, P.-Y.: Recent advances in observing mesoscale ocean dynamics with satellite altimetry, Adv. Space Res., 50, 1062–1076, 2012.
Nencioli, F., Dong, C., Dickey, T., Washburn, L., and McWilliams, J. C.: A Vector Geometry-Based Eddy Detection Algorithm and Its Application to a High-Resolution Numerical Model Product and High-Frequency Radar Surface Velocities in the Southern California Bight, J. Atmos. Ocean. Tech., 27, 564–579, 2010.
Okubo, A.: Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences, Deep-Sea Res. Oceanogr. Abstr., 17, 445–454, 1970.
Olascoaga, M. J. and Haller, G.: Forecasting sudden changes in environmental pollution patterns, P. Natl. Acad. Sci. USA, 109, 4738–4743, 2012.
Onu, K., Huhn, F., and Haller, G.: LCS Tool: A Computational Platform for Lagrangian Coherent Structures, J. Comput. Sci., 7, 26–36, 2015.
Oschlies, A. and Garçon, V.: An eddy-permitting coupled physical-biological model of the North-Atlantic, sensitivity to advection numerics and mixed layer physics, Global Biogeochem. Cy., 13, 135–160, 1999.
Petersen, M. R., Williams, S. J., Maltrud, M. E., Hecht, M. W., and Hamann, B.: A three-dimensional eddy census of a high-resolution global ocean simulation, J. Geophys. Res.-Oceans, 118, 1759–1774, 2013.
Rossi, V., López, C., Sudre, J., Hernández-García, E., and Garçon, V.: Comparative study of mixing and biological activity of the Benguela and Canary upwelling systems, Geophys. Res. Lett., 35, L11602, https://doi.org/10.1029/2008GL033610, 2008.
Sadarjoen, I. A. and Post, F. H.: Detection, quantification, and tracking of vortices using streamline geometry, Comput. Graph., 24, 333–341, 2000.
Sandulescu, M., Hernández-García, E., López, C., and Feudel, U.: Kinematic studies of transport across an island wake, with application to Canary islands, Tellus A, 58, 605–615, 2006.
Sandulescu, M., López, C., Hernández-García, E., and Feudel, U.: Plankton blooms in vortices: the role of biological and hydrodynamic timescales, Nonlin. Processes Geophys., 14, 443–454, https://doi.org/10.5194/npg-14-443-2007, 2007.
Sturman, R. and Wiggins, S.: Eulerian indiators for predicting and optimazing mmixing quality, New J. Phys., 11, 075031, https://doi.org/10.1088/1367-2630/11/7/075031, 2009.
Tang, W. and Luna, C.: Dependence of advection-diffusion-reaction on flow coherent structures, Phys. Fluids, 25, 106602, https://doi.org/10.1063/1.4823991, 2013.
Thacker, W. C., Lee, S.-K., and Halliwell, G. R.: Assimilating 20 years of Atlantic XBT data into HYCOM: a first look, Ocean Model., 7, 183–210, 2004.
Weiss, J.: The dynamics of enstrophy transfer in two-dimensional hydrodynamics, Physica D, 48, 273–294, 1991.
Wiggins, S.: The dynamical systems approach to Lagrangian transprt in oceanic flows, Annu. Rev. Fluid Mech., 37, 295–328, 2005.
Wiggins, S. and Mancho, A. M.: Barriers to transport in aperiodically time-dependent two-dimensional velocity fields: Nekhoroshev's theorem and "Nearly Invariant" tori, Nonlin. Processes Geophys., 21, 165–185, https://doi.org/10.5194/npg-21-165-2014, 2014.
Wilson, M. M., Peng, J., Dabiri, J. O., and Eldredge, J. D.: Lagrangian coherent structures in low Reynolds number swimming, J. Phys.-Condens Mat., 21, 204105, https://doi.org/10.1088/0953-8984/21/20/204105, 2009.
Wischgoll, T. and Scheuermann, G.: Detection and visualization of closed streamlines in planar flows, IEEE T. Vis. Comput. Gr., 7, 165–172, 2001.
Yang, Q., Parvin, B., and Mariano, A.: Detection of vortices and saddle points in SST data, Geophys. Res. Lett., 28, 331–334, 2001.
Short summary
Since eddies play a major role in the dynamics of oceanic flows, it is of great interest to gain information about their tracks, lifetimes and shapes. We develop an eddy tracking tool based on structures in the flow with collecting (attracting) or separating (repelling) properties. In test cases mimicking oceanic flows it yields eddy lifetimes close to the analytical ones. It even provides a detailed view of the dynamics that can be useful to gain more insight into eddy dynamics in oceanic flows.
Since eddies play a major role in the dynamics of oceanic flows, it is of great interest to gain...
