Articles | Volume 26, issue 4
https://doi.org/10.5194/npg-26-359-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/npg-26-359-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Review article
| 
08 Oct 2019
Review article |
| 08 Oct 2019
| 08 Oct 2019
Numerical bifurcation methods applied to climate models: analysis beyond simulation
Henk A. Dijkstra
CORRESPONDING AUTHOR
Institute for Marine and Atmospheric research Utrecht, Department of Physics, Utrecht University, Utrecht, the Netherlands
Centre for Complex Systems Studies, Utrecht University, Utrecht, the Netherlands
Invited contribution by Henk A. Dijkstra, recipient of the EGU Lewis Fry Richardson Medal 2005.
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Amber A. Boot and Henk A. Dijkstra
EGUsphere, https://doi.org/10.5194/egusphere-2025-758, https://doi.org/10.5194/egusphere-2025-758, 2025
This preprint is open for discussion and under review for Earth System Dynamics (ESD).
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The Atlantic Meridional Overturning Circulation (AMOC) is a tipping element in the Earth System that affects the global climate. We often use models to understand how the AMOC tips. However, these models are flawed. Here we study the effect of these flaws on the AMOC multistable regime in a climate model. We artificially add additional flaws to the model. We find that AMOC stability can be affected by such flaws and a reductionof such flaws in climate models is therefore thought to be essential.
Woosok Moon, Seung Pyo Lee, Elian Vanderborght, Georgy Manucharyan, and Henk Dijkstra
EGUsphere, https://doi.org/10.5194/egusphere-2025-1004, https://doi.org/10.5194/egusphere-2025-1004, 2025
This preprint is open for discussion and under review for Weather and Climate Dynamics (WCD).
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As the climate warms, extreme weather is becoming more frequent in mid-latitudes. A key factor is the jet stream, shaped by atmospheric waves that influence wind and storm patterns. This study presents a simplified model showing how swirling air currents (eddies) maintain the jet stream and impact weather. As global warming alters these patterns, this research helps improve predictions of future weather changes.
Bouke Biemond, Wouter M. Kranenburg, Ymkje Huismans, Huib E. de Swart, and Henk A. Dijkstra
Ocean Sci., 21, 261–281, https://doi.org/10.5194/os-21-261-2025, https://doi.org/10.5194/os-21-261-2025, 2025
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We study salinity in estuaries consisting of a network of channels. To this end, we develop a model that computes the flow and salinity in such systems. We use the model to quantify the mechanisms by which salt is transported into estuarine networks, the response to changes in river discharge, and the impact of depth changes. Results show that when changing the depth of channels, the effects on salt intrusion into other channels in the network can be larger than the effect on the channel itself.
René M. van Westen, Elian Vanderborght, and Henk A. Dijkstra
EGUsphere, https://doi.org/10.5194/egusphere-2025-14, https://doi.org/10.5194/egusphere-2025-14, 2025
This preprint is open for discussion and under review for Earth System Dynamics (ESD).
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The Atlantic Meridional Overturning Circulation (AMOC) is a tipping element in the fully-coupled Community Earth System Model (CESM). Under varying freshwater flux forcing parameters or climate change, the AMOC may collapse from a relatively strong state to a substantially weaker state. It is important to understand the dynamics of the AMOC collapse in the CESM. We show that the stability of the AMOC in the CESM is controlled by only a few feedback processes.
Aurora Faure Ragani and Henk A. Dijkstra
EGUsphere, https://doi.org/10.5194/egusphere-2025-45, https://doi.org/10.5194/egusphere-2025-45, 2025
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The Atlantic Meridional Overturning Circulation (AMOC) is sensitive to changing surface forcing conditions. Under future greenhouse gas emission reductions, it was shown in a conceptual model that it may be possible to avoid a collapse of the AMOC. Using a detailed global ocean model, we clarify the physics of the collapse and recovery behaviour of the AMOC. The potential to avoid an AMOC collapse is tightly linked to a delicate balance of salt fluxes in the northern North Atlantic.
Amber A. Boot and Henk A. Dijkstra
Earth Syst. Dynam., 16, 115–150, https://doi.org/10.5194/esd-16-115-2025, https://doi.org/10.5194/esd-16-115-2025, 2025
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The ocean is forced at the surface by a heat flux and a freshwater flux. This noise can influence long-term ocean variability and large-scale circulation. Here we study noise characteristics in reanalysis data for these fluxes. We try to capture the noise characteristics by using several noise models and compare these to state-of-the-art climate models. A pointwise noise model performs better than the climate models and can be used as forcing in ocean-only models.
Amber A. Boot, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 15, 1567–1590, https://doi.org/10.5194/esd-15-1567-2024, https://doi.org/10.5194/esd-15-1567-2024, 2024
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We investigate the multiple equilibria window (MEW) of the Atlantic Meridional Overturning Circulation (AMOC) within a box model. We find that increasing the total carbon content of the system widens the MEW of the AMOC. The important mechanisms at play are the balance between the source and sink of carbon and the sensitivity of the AMOC to freshwater forcing over the Atlantic Ocean. Our results suggest that changes in the marine carbon cycle can influence AMOC stability in future climates.
Francesco Guardamagna, Claudia Wieners, and Henk Dijkstra
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-24, https://doi.org/10.5194/npg-2024-24, 2024
Revised manuscript under review for NPG
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Artificial intelligence (AI) has recently shown promising results in ENSO (El Niño Southern Oscillation) forecasting, outperforming traditional models. Yet, AI models deliver accurate predictions without showing the underlying mechanisms. Our study examines a specific AI model, the Reservoir Computer (RC). Our results show that the RC is less sensitive to initial perturbations than the traditional Zebiak and Cane (ZC) model. This reduced sensitivity can explain the RC's superior skills.
Arthur Merlijn Oldeman, Michiel L. J. Baatsen, Anna S. von der Heydt, Frank M. Selten, and Henk A. Dijkstra
Earth Syst. Dynam., 15, 1037–1054, https://doi.org/10.5194/esd-15-1037-2024, https://doi.org/10.5194/esd-15-1037-2024, 2024
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We might be able to constrain uncertainty in future climate projections by investigating variations in the climate of the past. In this study, we investigate the interactions of climate variability between the tropical Pacific (El Niño) and the North Pacific in a warm past climate – the mid-Pliocene, a period roughly 3 million years ago. Using model simulations, we find that, although the variability in El Niño was reduced, the variability in the North Pacific atmosphere was not.
Sacha Sinet, Peter Ashwin, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 15, 859–873, https://doi.org/10.5194/esd-15-859-2024, https://doi.org/10.5194/esd-15-859-2024, 2024
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Some components of the Earth system may irreversibly collapse under global warming. Among them, the Atlantic Meridional Overturning Circulation (AMOC), the Greenland Ice Sheet, and West Antarctica Ice Sheet are of utmost importance for maintaining the present-day climate. In a simplified model, we show that both the rate of ice melting and the natural variability linked to freshwater fluxes over the Atlantic Ocean drastically affect how an ice sheet collapse impacts the AMOC stability.
Julia E. Weiffenbach, Henk A. Dijkstra, Anna S. von der Heydt, Ayako Abe-Ouchi, Wing-Le Chan, Deepak Chandan, Ran Feng, Alan M. Haywood, Stephen J. Hunter, Xiangyu Li, Bette L. Otto-Bliesner, W. Richard Peltier, Christian Stepanek, Ning Tan, Julia C. Tindall, and Zhongshi Zhang
Clim. Past, 20, 1067–1086, https://doi.org/10.5194/cp-20-1067-2024, https://doi.org/10.5194/cp-20-1067-2024, 2024
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Elevated atmospheric CO2 concentrations and a smaller Antarctic Ice Sheet during the mid-Pliocene (~ 3 million years ago) cause the Southern Ocean surface to become fresher and warmer, which affects the global ocean circulation. The CO2 concentration and the smaller Antarctic Ice Sheet both have a similar and approximately equal impact on the Southern Ocean. The conditions of the Southern Ocean in the mid-Pliocene could therefore be analogous to those in a future climate with smaller ice sheets.
René M. van Westen and Henk A. Dijkstra
Ocean Sci., 20, 549–567, https://doi.org/10.5194/os-20-549-2024, https://doi.org/10.5194/os-20-549-2024, 2024
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The Atlantic Meridional Overturning Circulation (AMOC) is an important component in the global climate system. Observations of the present-day AMOC indicate that it may weaken or collapse under global warming, with profound disruptive effects on future climate. However, AMOC weakening is not correctly represented because an important feedback is underestimated due to biases in the Atlantic's freshwater budget. Here we address these biases in several state-of-the-art climate model simulations.
Arthur Merlijn Oldeman, Michiel L. J. Baatsen, Anna S. von der Heydt, Aarnout J. van Delden, and Henk A. Dijkstra
Weather Clim. Dynam., 5, 395–417, https://doi.org/10.5194/wcd-5-395-2024, https://doi.org/10.5194/wcd-5-395-2024, 2024
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The mid-Pliocene, a geological period around 3 million years ago, is sometimes considered the best analogue for near-future climate. It saw similar CO2 concentrations to the present-day but also a slightly different geography. In this study, we use climate model simulations and find that the Northern Hemisphere winter responds very differently to increased CO2 or to the mid-Pliocene geography. Our results weaken the potential of the mid-Pliocene as a future climate analogue.
Michiel Baatsen, Peter Bijl, Anna von der Heydt, Appy Sluijs, and Henk Dijkstra
Clim. Past, 20, 77–90, https://doi.org/10.5194/cp-20-77-2024, https://doi.org/10.5194/cp-20-77-2024, 2024
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This work introduces the possibility and consequences of monsoons on Antarctica in the warm Eocene climate. We suggest that such a monsoonal climate can be important to understand conditions in Antarctica prior to large-scale glaciation. We can explain seemingly contradictory indications of ice and vegetation on the continent through regional variability. In addition, we provide a new mechanism through which most of Antarctica remained ice-free through a wide range of global climatic changes.
Sina Loriani, Yevgeny Aksenov, David Armstrong McKay, Govindasamy Bala, Andreas Born, Cristiano M. Chiessi, Henk Dijkstra, Jonathan F. Donges, Sybren Drijfhout, Matthew H. England, Alexey V. Fedorov, Laura Jackson, Kai Kornhuber, Gabriele Messori, Francesco Pausata, Stefanie Rynders, Jean-Baptiste Salée, Bablu Sinha, Steven Sherwood, Didier Swingedouw, and Thejna Tharammal
EGUsphere, https://doi.org/10.5194/egusphere-2023-2589, https://doi.org/10.5194/egusphere-2023-2589, 2023
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In this work, we draw on paleoreords, observations and modelling studies to review tipping points in the ocean overturning circulations, monsoon systems and global atmospheric circulations. We find indications for tipping in the ocean overturning circulations and the West African monsoon, with potentially severe impacts on the Earth system and humans. Tipping in the other considered systems is considered conceivable but currently not sufficiently supported by evidence.
Valérian Jacques-Dumas, René M. van Westen, Freddy Bouchet, and Henk A. Dijkstra
Nonlin. Processes Geophys., 30, 195–216, https://doi.org/10.5194/npg-30-195-2023, https://doi.org/10.5194/npg-30-195-2023, 2023
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Computing the probability of occurrence of rare events is relevant because of their high impact but also difficult due to the lack of data. Rare event algorithms are designed for that task, but their efficiency relies on a score function that is hard to compute. We compare four methods that compute this function from data and measure their performance to assess which one would be best suited to be applied to a climate model. We find neural networks to be most robust and flexible for this task.
Julia E. Weiffenbach, Michiel L. J. Baatsen, Henk A. Dijkstra, Anna S. von der Heydt, Ayako Abe-Ouchi, Esther C. Brady, Wing-Le Chan, Deepak Chandan, Mark A. Chandler, Camille Contoux, Ran Feng, Chuncheng Guo, Zixuan Han, Alan M. Haywood, Qiang Li, Xiangyu Li, Gerrit Lohmann, Daniel J. Lunt, Kerim H. Nisancioglu, Bette L. Otto-Bliesner, W. Richard Peltier, Gilles Ramstein, Linda E. Sohl, Christian Stepanek, Ning Tan, Julia C. Tindall, Charles J. R. Williams, Qiong Zhang, and Zhongshi Zhang
Clim. Past, 19, 61–85, https://doi.org/10.5194/cp-19-61-2023, https://doi.org/10.5194/cp-19-61-2023, 2023
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We study the behavior of the Atlantic Meridional Overturning Circulation (AMOC) in the mid-Pliocene. The mid-Pliocene was about 3 million years ago and had a similar CO2 concentration to today. We show that the stronger AMOC during this period relates to changes in geography and that this has a significant influence on ocean temperatures and heat transported northwards by the Atlantic Ocean. Understanding the behavior of the mid-Pliocene AMOC can help us to learn more about our future climate.
Amber Boot, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 13, 1041–1058, https://doi.org/10.5194/esd-13-1041-2022, https://doi.org/10.5194/esd-13-1041-2022, 2022
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Atmospheric pCO2 of the past shows large variability on different timescales. We focus on the effect of the strength of Atlantic Meridional Overturning Circulation (AMOC) on this variability and on the AMOC–pCO2 relationship. We find that climatic boundary conditions and the representation of biology in our model are most important for this relationship. Under certain conditions, we find internal oscillations, which can be relevant for atmospheric pCO2 variability during glacial cycles.
Mikael L. A. Kaandorp, Stefanie L. Ypma, Marijke Boonstra, Henk A. Dijkstra, and Erik van Sebille
Ocean Sci., 18, 269–293, https://doi.org/10.5194/os-18-269-2022, https://doi.org/10.5194/os-18-269-2022, 2022
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A large amount of marine litter, such as plastics, is located on or around beaches. Both the total amount of this litter and its transport are poorly understood. We investigate this by training a machine learning model with data of cleanup efforts on Dutch beaches between 2014 and 2019, obtained by about 14 000 volunteers. We find that Dutch beaches contain up to 30 000 kg of litter, largely depending on tides, oceanic transport, and how exposed the beaches are.
Peter D. Nooteboom, Peter K. Bijl, Christian Kehl, Erik van Sebille, Martin Ziegler, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 13, 357–371, https://doi.org/10.5194/esd-13-357-2022, https://doi.org/10.5194/esd-13-357-2022, 2022
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Having descended through the water column, microplankton in ocean sediments represents the ocean surface environment and is used as an archive of past and present surface oceanographic conditions. However, this microplankton is advected by turbulent ocean currents during its sinking journey. We use simulations of sinking particles to define ocean bottom provinces and detect these provinces in datasets of sedimentary microplankton, which has implications for palaeoclimate reconstructions.
Arthur M. Oldeman, Michiel L. J. Baatsen, Anna S. von der Heydt, Henk A. Dijkstra, Julia C. Tindall, Ayako Abe-Ouchi, Alice R. Booth, Esther C. Brady, Wing-Le Chan, Deepak Chandan, Mark A. Chandler, Camille Contoux, Ran Feng, Chuncheng Guo, Alan M. Haywood, Stephen J. Hunter, Youichi Kamae, Qiang Li, Xiangyu Li, Gerrit Lohmann, Daniel J. Lunt, Kerim H. Nisancioglu, Bette L. Otto-Bliesner, W. Richard Peltier, Gabriel M. Pontes, Gilles Ramstein, Linda E. Sohl, Christian Stepanek, Ning Tan, Qiong Zhang, Zhongshi Zhang, Ilana Wainer, and Charles J. R. Williams
Clim. Past, 17, 2427–2450, https://doi.org/10.5194/cp-17-2427-2021, https://doi.org/10.5194/cp-17-2427-2021, 2021
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In this work, we have studied the behaviour of El Niño events in the mid-Pliocene, a period of around 3 million years ago, using a collection of 17 climate models. It is an interesting period to study, as it saw similar atmospheric carbon dioxide levels to the present day. We find that the El Niño events were less strong in the mid-Pliocene simulations, when compared to pre-industrial climate. Our results could help to interpret El Niño behaviour in future climate projections.
André Jüling, Anna von der Heydt, and Henk A. Dijkstra
Ocean Sci., 17, 1251–1271, https://doi.org/10.5194/os-17-1251-2021, https://doi.org/10.5194/os-17-1251-2021, 2021
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On top of forced changes such as human-caused global warming, unforced climate variability exists. Most multidecadal variability (MV) involves the oceans, but current climate models use non-turbulent, coarse-resolution oceans. We investigate the effect of resolving important turbulent ocean features on MV. We find that ocean heat content, ocean–atmosphere heat flux, and global mean surface temperature MV is more pronounced in the higher-resolution model relative to higher-frequency variability.
Johannes Lohmann, Daniele Castellana, Peter D. Ditlevsen, and Henk A. Dijkstra
Earth Syst. Dynam., 12, 819–835, https://doi.org/10.5194/esd-12-819-2021, https://doi.org/10.5194/esd-12-819-2021, 2021
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Tipping of one climate subsystem could trigger a cascade of subsequent tipping points and even global-scale climate tipping. Sequential shifts of atmosphere, sea ice and ocean have been recorded in proxy archives of past climate change. Based on this we propose a conceptual model for abrupt climate changes of the last glacial. Here, rate-induced tipping enables tipping cascades in systems with relatively weak coupling. An early warning signal is proposed that may detect such a tipping.
André Jüling, Xun Zhang, Daniele Castellana, Anna S. von der Heydt, and Henk A. Dijkstra
Ocean Sci., 17, 729–754, https://doi.org/10.5194/os-17-729-2021, https://doi.org/10.5194/os-17-729-2021, 2021
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We investigate how the freshwater budget of the Atlantic changes under climate change, which has implications for the stability of the Atlantic Meridional Overturning Circulation. We compare the effect of ocean model resolution in a climate model and find many similarities between the simulations, enhancing trust in the current generation of climate models. However, ocean biases are reduced in the strongly eddying simulation, and significant local freshwater budget differences exist.
Pascal Wang, Daniele Castellana, and Henk A. Dijkstra
Nonlin. Processes Geophys., 28, 135–151, https://doi.org/10.5194/npg-28-135-2021, https://doi.org/10.5194/npg-28-135-2021, 2021
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This paper proposes two improvements to the use of Trajectory-Adaptive Multilevel Sampling, a rare-event algorithm which computes noise-induced transition probabilities. The first improvement uses locally linearised dynamics in order to reduce the arbitrariness associated with defining what constitutes a transition. The second improvement uses empirical transition paths accumulated at high noise in order to formulate the score function which determines the performance of the algorithm.
Amber Boot, René M. van Westen, and Henk A. Dijkstra
Ocean Sci., 17, 335–350, https://doi.org/10.5194/os-17-335-2021, https://doi.org/10.5194/os-17-335-2021, 2021
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The Maud Rise polynya is a hole in the sea ice surrounding Antarctica that occurs during winter. It appeared in 2016 and 2017. Our study concludes that heat and salt accumulation around 1000 m depth are likely to be important for polynya formation. The heat is mixed upward to the surface where it is able to melt the sea ice and, thus, create a polynya. How often the polynya forms depends largely on the variation in the time of the heat and salt accumulation.
David Wichmann, Christian Kehl, Henk A. Dijkstra, and Erik van Sebille
Nonlin. Processes Geophys., 28, 43–59, https://doi.org/10.5194/npg-28-43-2021, https://doi.org/10.5194/npg-28-43-2021, 2021
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Fluid parcels transported in complicated flows often contain subsets of particles that stay close over finite time intervals. We propose a new method for detecting finite-time coherent sets based on the density-based clustering technique of ordering points to identify the clustering structure (OPTICS). Unlike previous methods, our method has an intrinsic notion of coherent sets at different spatial scales. OPTICS is readily implemented in the SciPy sklearn package, making it easy to use.
Carine G. van der Boog, J. Otto Koetsier, Henk A. Dijkstra, Julie D. Pietrzak, and Caroline A. Katsman
Earth Syst. Sci. Data, 13, 43–61, https://doi.org/10.5194/essd-13-43-2021, https://doi.org/10.5194/essd-13-43-2021, 2021
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Thermohaline staircases are stepped structures in the ocean that contain enhanced diapycnal salt and heat transport. In this study, we present a global dataset of thermohaline staircases derived from 487 493 observations of Argo profiling floats and Ice-Tethered Profilers using a novel detection algorithm.
Michiel Baatsen, Anna S. von der Heydt, Matthew Huber, Michael A. Kliphuis, Peter K. Bijl, Appy Sluijs, and Henk A. Dijkstra
Clim. Past, 16, 2573–2597, https://doi.org/10.5194/cp-16-2573-2020, https://doi.org/10.5194/cp-16-2573-2020, 2020
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Warm climates of the deep past have proven to be challenging to reconstruct with the same numerical models used for future predictions. We present results of CESM simulations for the middle to late Eocene (∼ 38 Ma), in which we managed to match the available indications of temperature well. With these results we can now look into regional features and the response to external changes to ultimately better understand the climate when it is in such a warm state.
René M. van Westen and Henk A. Dijkstra
Ocean Sci., 16, 1443–1457, https://doi.org/10.5194/os-16-1443-2020, https://doi.org/10.5194/os-16-1443-2020, 2020
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During the mid-1970s and quite recently in 2017, a large open-water area appeared in the Antarctic sea-ice pack, the so-called Maud Rise polynya. From several model studies, the reoccurrence time of this polynya seems arbitrary. In this study, we address the reoccurrence time of the polynya using a high-resolution climate model. We find a preferred multidecadal return time in polynya formation. The return time of the polynya is associated with a large-scale ocean mode in the Southern Ocean.
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
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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.
René M. van Westen and Henk A. Dijkstra
Ocean Sci. Discuss., https://doi.org/10.5194/os-2020-33, https://doi.org/10.5194/os-2020-33, 2020
Revised manuscript not accepted
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In 2016 and 2017, an open-water area emerged within the Antarctic sea-ice pack, the so-called Maud Rise polynya. The opening of the sea ice has been linked to intense winter storms. In this study, we investigate another important contributor to polynya formation by analysing subsurface static instabilities. These static instabilities initiate subsurface convection near Maud Rise. We conclude that apart from winter storms, subsurface convection plays an important role in polynya formation.
Ann Kristin Klose, René M. van Westen, and Henk A. Dijkstra
Ocean Sci., 16, 435–449, https://doi.org/10.5194/os-16-435-2020, https://doi.org/10.5194/os-16-435-2020, 2020
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We give an explanation of the decadal timescale path variations in the Kuroshio Current in the North Pacific based on highly detailed climate
model simulations.
Carine G. van der Boog, Julie D. Pietrzak, Henk A. Dijkstra, Nils Brüggemann, René M. van Westen, Rebecca K. James, Tjeerd J. Bouma, Riccardo E. M. Riva, D. Cornelis Slobbe, Roland Klees, Marcel Zijlema, and Caroline A. Katsman
Ocean Sci., 15, 1419–1437, https://doi.org/10.5194/os-15-1419-2019, https://doi.org/10.5194/os-15-1419-2019, 2019
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We use a model of the Caribbean Sea to study how coastal upwelling along Venezuela impacts the evolution of energetic anticyclonic eddies. We show that the anticyclones grow by the advection of the cold upwelling filaments. These filaments increase the density gradient and vertical shear of the anticyclones. Furthermore, we show that stronger upwelling results in stronger eddies, while model simulations with weaker upwelling contain weaker eddies.
Juan-Manuel Sayol, Henk Dijkstra, and Caroline Katsman
Ocean Sci., 15, 1033–1053, https://doi.org/10.5194/os-15-1033-2019, https://doi.org/10.5194/os-15-1033-2019, 2019
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This work uses high-resolution ocean model data to quantify the sinking of waters in the subpolar North Atlantic. The largest amount of sinking is found at the depth of maximum AMOC at 45° N below the mixed layer depth, and 90 % of the sinking occurs near the boundaries in the first 250 km off the shelf. The characteristics of the sinking (total amount, seasonal variability, and vertical structure) vary largely according to the region considered, revealing a complex picture for the sinking.
Koen G. Helwegen, Claudia E. Wieners, Jason E. Frank, and Henk A. Dijkstra
Earth Syst. Dynam., 10, 453–472, https://doi.org/10.5194/esd-10-453-2019, https://doi.org/10.5194/esd-10-453-2019, 2019
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We use the climate-economy model DICE to perform a cost–benefit analysis of sulfate geoengineering, i.e. producing a thin artificial sulfate haze in the higher atmosphere to reflect some sunlight and cool the Earth.
We find that geoengineering can increase future welfare by reducing global warming, and should be taken seriously as a policy option, but it can only complement, not replace, carbon emission reduction. The best policy is to combine CO2 emission reduction with modest geoengineering.
Martijn Westhoff, Axel Kleidon, Stan Schymanski, Benjamin Dewals, Femke Nijsse, Maik Renner, Henk Dijkstra, Hisashi Ozawa, Hubert Savenije, Han Dolman, Antoon Meesters, and Erwin Zehe
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2019-6, https://doi.org/10.5194/esd-2019-6, 2019
Publication in ESD not foreseen
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Even models relying on physical laws have parameters that need to be measured or estimated. Thermodynamic optimality principles potentially offer a way to reduce the number of estimated parameters by stating that a system evolves to an optimum state. These principles have been applied successfully within the Earth system, but it is often unclear what to optimize and how. In this review paper we identify commonalities between different successful applications as well as some doubtful applications.
Mark M. Dekker, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 9, 1243–1260, https://doi.org/10.5194/esd-9-1243-2018, https://doi.org/10.5194/esd-9-1243-2018, 2018
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We introduce a framework of cascading tipping, i.e. a sequence of abrupt transitions occurring because a transition in one system affects the background conditions of another system. Using bifurcation theory, various types of these events are considered and early warning indicators are suggested. An illustration of such an event is found in a conceptual model, coupling the North Atlantic Ocean with the equatorial Pacific. This demonstrates the possibility of events such as this in nature.
Matthias Aengenheyster, Qing Yi Feng, Frederick van der Ploeg, and Henk A. Dijkstra
Earth Syst. Dynam., 9, 1085–1095, https://doi.org/10.5194/esd-9-1085-2018, https://doi.org/10.5194/esd-9-1085-2018, 2018
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We determine the point of no return (PNR) for climate change, which is the latest year to take action to reduce greenhouse gases to stay, with a certain probability, within thresholds set by the Paris Agreement. For a 67 % probability and a 2 K threshold, the PNR is the year 2035 when the share of renewable energy rises by 2 % per year. We show the impact on the PNR of the speed by which emissions are cut, the risk tolerance, climate uncertainties and the potential for negative emissions.
Femke J. M. M. Nijsse and Henk A. Dijkstra
Earth Syst. Dynam., 9, 999–1012, https://doi.org/10.5194/esd-9-999-2018, https://doi.org/10.5194/esd-9-999-2018, 2018
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State-of-the-art climate models sometimes differ in their prediction of key aspects of climate change. The technique of
emergent constraintsuses observations of current climate to improve those predictions, using relationships between different climate models. Our paper first classifies the different uses of the technique, and continues with proposing a mathematical justification for their use. We also highlight when the application of emergent constraints might give biased predictions.
Peter D. Nooteboom, Qing Yi Feng, Cristóbal López, Emilio Hernández-García, and Henk A. Dijkstra
Earth Syst. Dynam., 9, 969–983, https://doi.org/10.5194/esd-9-969-2018, https://doi.org/10.5194/esd-9-969-2018, 2018
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The prediction of the El Niño phenomenon, an increased sea surface temperature in the eastern Pacific, fascinates people for a long time. El Niño is associated with natural disasters, such as droughts and floods. Current methods can make a reliable prediction of this phenomenon up to 6 months ahead. However, this article presents a method which combines network theory and machine learning which predicts El Niño up to 1 year ahead.
Michiel Baatsen, Anna S. von der Heydt, Matthew Huber, Michael A. Kliphuis, Peter K. Bijl, Appy Sluijs, and Henk A. Dijkstra
Clim. Past Discuss., https://doi.org/10.5194/cp-2018-43, https://doi.org/10.5194/cp-2018-43, 2018
Revised manuscript not accepted
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The Eocene marks a period where the climate was in a hothouse state, without any continental-scale ice sheets. Such climates have proven difficult to reproduce in models, especially their low temperature difference between equator and poles. Here, we present high resolution CESM simulations using a new geographic reconstruction of the middle-to-late Eocene. The results provide new insights into a period for which knowledge is limited, leading up to a transition into the present icehouse state.
Inti Pelupessy, Ben van Werkhoven, Arjen van Elteren, Jan Viebahn, Adam Candy, Simon Portegies Zwart, and Henk Dijkstra
Geosci. Model Dev., 10, 3167–3187, https://doi.org/10.5194/gmd-10-3167-2017, https://doi.org/10.5194/gmd-10-3167-2017, 2017
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Researchers from the Netherlands present OMUSE, a software package
developed from core technology originating in the astrophysical
community. Using OMUSE, oceanographic and climate researchers can
develop numerical models of the ocean and the interactions between
different parts of the ocean and the atmosphere. This provides a novel
way to investigate, for example, the local effects of climate change on
the ocean. OMUSE is freely available as open-source software.
Brenda C. van Zalinge, Qing Yi Feng, Matthias Aengenheyster, and Henk A. Dijkstra
Earth Syst. Dynam., 8, 707–717, https://doi.org/10.5194/esd-8-707-2017, https://doi.org/10.5194/esd-8-707-2017, 2017
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The increase in atmospheric greenhouse gases (GHGs) is one of the main causes for the increase in global mean surface temperature. There is no good quantitative measure to determine when it is
too lateto start reducing GHGs in order to avoid dangerous anthropogenic interference. We develop a method for determining a so-called point of no return (PNR) for several GHG emission scenarios. The innovative element in this approach is the applicability to high-dimensional climate models.
Daniel J. Lunt, Matthew Huber, Eleni Anagnostou, Michiel L. J. Baatsen, Rodrigo Caballero, Rob DeConto, Henk A. Dijkstra, Yannick Donnadieu, David Evans, Ran Feng, Gavin L. Foster, Ed Gasson, Anna S. von der Heydt, Chris J. Hollis, Gordon N. Inglis, Stephen M. Jones, Jeff Kiehl, Sandy Kirtland Turner, Robert L. Korty, Reinhardt Kozdon, Srinath Krishnan, Jean-Baptiste Ladant, Petra Langebroek, Caroline H. Lear, Allegra N. LeGrande, Kate Littler, Paul Markwick, Bette Otto-Bliesner, Paul Pearson, Christopher J. Poulsen, Ulrich Salzmann, Christine Shields, Kathryn Snell, Michael Stärz, James Super, Clay Tabor, Jessica E. Tierney, Gregory J. L. Tourte, Aradhna Tripati, Garland R. Upchurch, Bridget S. Wade, Scott L. Wing, Arne M. E. Winguth, Nicky M. Wright, James C. Zachos, and Richard E. Zeebe
Geosci. Model Dev., 10, 889–901, https://doi.org/10.5194/gmd-10-889-2017, https://doi.org/10.5194/gmd-10-889-2017, 2017
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In this paper we describe the experimental design for a set of simulations which will be carried out by a range of climate models, all investigating the climate of the Eocene, about 50 million years ago. The intercomparison of model results is called 'DeepMIP', and we anticipate that we will contribute to the next IPCC report through an analysis of these simulations and the geological data to which we will compare them.
S.-E. Brunnabend, H. A. Dijkstra, M. A. Kliphuis, H. E. Bal, F. Seinstra, B. van Werkhoven, J. Maassen, and M. van Meersbergen
Ocean Sci., 13, 47–60, https://doi.org/10.5194/os-13-47-2017, https://doi.org/10.5194/os-13-47-2017, 2017
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An important contribution to future changes in regional sea level extremes is due to the changes in intrinsic ocean variability, in particular ocean eddies. Here, we study a scenario of future dynamic sea level (DSL) extremes using a strongly eddying version of the Parallel Ocean Program. Changes in 10-year return time DSL extremes are very inhomogeneous over the globe and are related to changes in ocean currents and corresponding regional shifts in ocean eddy pathways.
Michiel Baatsen, Douwe J. J. van Hinsbergen, Anna S. von der Heydt, Henk A. Dijkstra, Appy Sluijs, Hemmo A. Abels, and Peter K. Bijl
Clim. Past, 12, 1635–1644, https://doi.org/10.5194/cp-12-1635-2016, https://doi.org/10.5194/cp-12-1635-2016, 2016
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One of the major difficulties in modelling palaeoclimate is constricting the boundary conditions, causing significant discrepancies between different studies. Here, a new method is presented to automate much of the process of generating the necessary geographical reconstructions. The latter can be made using various rotational frameworks and topography/bathymetry input, allowing for easy inter-comparisons and the incorporation of the latest insights from geoscientific research.
Zun Yin, Stefan C. Dekker, Bart J. J. M. van den Hurk, and Henk A. Dijkstra
Biogeosciences, 13, 3343–3357, https://doi.org/10.5194/bg-13-3343-2016, https://doi.org/10.5194/bg-13-3343-2016, 2016
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Bimodality is found in aboveground biomass and mean annual shortwave radiation in West Africa, which is a strong evidence of alternative stable states. The condition with low biomass and low radiation is demonstrated under which ecosystem state can shift between savanna and forest states. Moreover, climatic indicators have different prediction confidences to different land cover types. A new method is proposed to predict potential land cover change with a combination of climatic indicators.
Qing Yi Feng, Ruggero Vasile, Marc Segond, Avi Gozolchiani, Yang Wang, Markus Abel, Shilomo Havlin, Armin Bunde, and Henk A. Dijkstra
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2015-273, https://doi.org/10.5194/gmd-2015-273, 2016
Revised manuscript not accepted
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We present the toolbox ClimateLearn to tackle problems in climate prediction using machine learning techniques and climate network analysis. Because spatial temporal information on climate variability can be efficiently represented by complex network measures, such data are considered here as input to the machine-learning algorithms. As an example, the toolbox is applied to the prediction of the occurrence and the development of El Niño in the equatorial Pacific.
H. Ihshaish, A. Tantet, J. C. M. Dijkzeul, and H. A. Dijkstra
Geosci. Model Dev., 8, 3321–3331, https://doi.org/10.5194/gmd-8-3321-2015, https://doi.org/10.5194/gmd-8-3321-2015, 2015
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Par@Graph, a software toolbox to reconstruct and analyze large-scale complex climate networks. It exposes parallelism on distributed-memory computing platforms to enable the construction of massive networks from large number of time series based on the calculation of common statistical similarity measures between them. Providing additionally parallel graph algorithms to enable fast calculation of important and common properties of the generated networks on SMP machines.
L. Hahn-Woernle, H. A. Dijkstra, and H. J. Van der Woerd
Ocean Sci., 10, 993–1011, https://doi.org/10.5194/os-10-993-2014, https://doi.org/10.5194/os-10-993-2014, 2014
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Measured vertical mixing profiles are applied to a 1-D phytoplankton model. Results show that shifts in vertical mixing are able to induce a transition from an upper chlorophyll maximum to a deep one and vice versa. Furthermore, a clear correlation between the surface phytoplankton concentration and mixing-induced nutrient flux is found for nutrient-limited cases. This result suggests that characteristics of the vertical mixing could be determined from the surface phytoplankton concentration.
S.-E. Brunnabend, H. A. Dijkstra, M. A. Kliphuis, B. van Werkhoven, H. E. Bal, F. Seinstra, J. Maassen, and M. van Meersbergen
Ocean Sci., 10, 881–891, https://doi.org/10.5194/os-10-881-2014, https://doi.org/10.5194/os-10-881-2014, 2014
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Regional sea surface height (SSH) changes due to an abrupt weakening of the Atlantic meridional overturning circulation (AMOC) are simulated with a high- and low-resolution model. A rapid decrease of the AMOC in the high-resolution version induces shorter return times of several specific regional and coastal extremes in North Atlantic SSH than in the low-resolution version. This effect is caused by a change in main eddy pathways associated with a change in separation latitude of the Gulf Stream.
Z. Yin, S. C. Dekker, B. J. J. M. van den Hurk, and H. A. Dijkstra
Earth Syst. Dynam., 5, 257–270, https://doi.org/10.5194/esd-5-257-2014, https://doi.org/10.5194/esd-5-257-2014, 2014
D. Le Bars, J. V. Durgadoo, H. A. Dijkstra, A. Biastoch, and W. P. M. De Ruijter
Ocean Sci., 10, 601–609, https://doi.org/10.5194/os-10-601-2014, https://doi.org/10.5194/os-10-601-2014, 2014
Z. Yin, S. C. Dekker, B. J. J. M. van den Hurk, and H. A. Dijkstra
Geosci. Model Dev., 7, 821–845, https://doi.org/10.5194/gmd-7-821-2014, https://doi.org/10.5194/gmd-7-821-2014, 2014
G. Sgubin, S. Pierini, and H. A. Dijkstra
Ocean Sci., 10, 201–213, https://doi.org/10.5194/os-10-201-2014, https://doi.org/10.5194/os-10-201-2014, 2014
A. Tantet and H. A. Dijkstra
Earth Syst. Dynam., 5, 1–14, https://doi.org/10.5194/esd-5-1-2014, https://doi.org/10.5194/esd-5-1-2014, 2014
A. A. Cimatoribus, S. Drijfhout, and H. A. Dijkstra
Ocean Sci. Discuss., https://doi.org/10.5194/osd-10-2461-2013, https://doi.org/10.5194/osd-10-2461-2013, 2013
Preprint withdrawn
A. S. von der Heydt, A. Nnafie, and H. A. Dijkstra
Clim. Past, 7, 903–915, https://doi.org/10.5194/cp-7-903-2011, https://doi.org/10.5194/cp-7-903-2011, 2011
M. Tigchelaar, A. S. von der Heydt, and H. A. Dijkstra
Clim. Past, 7, 235–247, https://doi.org/10.5194/cp-7-235-2011, https://doi.org/10.5194/cp-7-235-2011, 2011
J. O. Sewall, R. S. W. van de Wal, K. van der Zwan, C. van Oosterhout, H. A. Dijkstra, and C. R. Scotese
Clim. Past, 3, 647–657, https://doi.org/10.5194/cp-3-647-2007, https://doi.org/10.5194/cp-3-647-2007, 2007
Amber A. Boot and Henk A. Dijkstra
EGUsphere, https://doi.org/10.5194/egusphere-2025-758, https://doi.org/10.5194/egusphere-2025-758, 2025
This preprint is open for discussion and under review for Earth System Dynamics (ESD).
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The Atlantic Meridional Overturning Circulation (AMOC) is a tipping element in the Earth System that affects the global climate. We often use models to understand how the AMOC tips. However, these models are flawed. Here we study the effect of these flaws on the AMOC multistable regime in a climate model. We artificially add additional flaws to the model. We find that AMOC stability can be affected by such flaws and a reductionof such flaws in climate models is therefore thought to be essential.
Woosok Moon, Seung Pyo Lee, Elian Vanderborght, Georgy Manucharyan, and Henk Dijkstra
EGUsphere, https://doi.org/10.5194/egusphere-2025-1004, https://doi.org/10.5194/egusphere-2025-1004, 2025
This preprint is open for discussion and under review for Weather and Climate Dynamics (WCD).
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As the climate warms, extreme weather is becoming more frequent in mid-latitudes. A key factor is the jet stream, shaped by atmospheric waves that influence wind and storm patterns. This study presents a simplified model showing how swirling air currents (eddies) maintain the jet stream and impact weather. As global warming alters these patterns, this research helps improve predictions of future weather changes.
Bouke Biemond, Wouter M. Kranenburg, Ymkje Huismans, Huib E. de Swart, and Henk A. Dijkstra
Ocean Sci., 21, 261–281, https://doi.org/10.5194/os-21-261-2025, https://doi.org/10.5194/os-21-261-2025, 2025
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We study salinity in estuaries consisting of a network of channels. To this end, we develop a model that computes the flow and salinity in such systems. We use the model to quantify the mechanisms by which salt is transported into estuarine networks, the response to changes in river discharge, and the impact of depth changes. Results show that when changing the depth of channels, the effects on salt intrusion into other channels in the network can be larger than the effect on the channel itself.
René M. van Westen, Elian Vanderborght, and Henk A. Dijkstra
EGUsphere, https://doi.org/10.5194/egusphere-2025-14, https://doi.org/10.5194/egusphere-2025-14, 2025
This preprint is open for discussion and under review for Earth System Dynamics (ESD).
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The Atlantic Meridional Overturning Circulation (AMOC) is a tipping element in the fully-coupled Community Earth System Model (CESM). Under varying freshwater flux forcing parameters or climate change, the AMOC may collapse from a relatively strong state to a substantially weaker state. It is important to understand the dynamics of the AMOC collapse in the CESM. We show that the stability of the AMOC in the CESM is controlled by only a few feedback processes.
Aurora Faure Ragani and Henk A. Dijkstra
EGUsphere, https://doi.org/10.5194/egusphere-2025-45, https://doi.org/10.5194/egusphere-2025-45, 2025
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The Atlantic Meridional Overturning Circulation (AMOC) is sensitive to changing surface forcing conditions. Under future greenhouse gas emission reductions, it was shown in a conceptual model that it may be possible to avoid a collapse of the AMOC. Using a detailed global ocean model, we clarify the physics of the collapse and recovery behaviour of the AMOC. The potential to avoid an AMOC collapse is tightly linked to a delicate balance of salt fluxes in the northern North Atlantic.
Amber A. Boot and Henk A. Dijkstra
Earth Syst. Dynam., 16, 115–150, https://doi.org/10.5194/esd-16-115-2025, https://doi.org/10.5194/esd-16-115-2025, 2025
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The ocean is forced at the surface by a heat flux and a freshwater flux. This noise can influence long-term ocean variability and large-scale circulation. Here we study noise characteristics in reanalysis data for these fluxes. We try to capture the noise characteristics by using several noise models and compare these to state-of-the-art climate models. A pointwise noise model performs better than the climate models and can be used as forcing in ocean-only models.
Amber A. Boot, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 15, 1567–1590, https://doi.org/10.5194/esd-15-1567-2024, https://doi.org/10.5194/esd-15-1567-2024, 2024
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We investigate the multiple equilibria window (MEW) of the Atlantic Meridional Overturning Circulation (AMOC) within a box model. We find that increasing the total carbon content of the system widens the MEW of the AMOC. The important mechanisms at play are the balance between the source and sink of carbon and the sensitivity of the AMOC to freshwater forcing over the Atlantic Ocean. Our results suggest that changes in the marine carbon cycle can influence AMOC stability in future climates.
Francesco Guardamagna, Claudia Wieners, and Henk Dijkstra
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-24, https://doi.org/10.5194/npg-2024-24, 2024
Revised manuscript under review for NPG
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Artificial intelligence (AI) has recently shown promising results in ENSO (El Niño Southern Oscillation) forecasting, outperforming traditional models. Yet, AI models deliver accurate predictions without showing the underlying mechanisms. Our study examines a specific AI model, the Reservoir Computer (RC). Our results show that the RC is less sensitive to initial perturbations than the traditional Zebiak and Cane (ZC) model. This reduced sensitivity can explain the RC's superior skills.
Arthur Merlijn Oldeman, Michiel L. J. Baatsen, Anna S. von der Heydt, Frank M. Selten, and Henk A. Dijkstra
Earth Syst. Dynam., 15, 1037–1054, https://doi.org/10.5194/esd-15-1037-2024, https://doi.org/10.5194/esd-15-1037-2024, 2024
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We might be able to constrain uncertainty in future climate projections by investigating variations in the climate of the past. In this study, we investigate the interactions of climate variability between the tropical Pacific (El Niño) and the North Pacific in a warm past climate – the mid-Pliocene, a period roughly 3 million years ago. Using model simulations, we find that, although the variability in El Niño was reduced, the variability in the North Pacific atmosphere was not.
Sacha Sinet, Peter Ashwin, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 15, 859–873, https://doi.org/10.5194/esd-15-859-2024, https://doi.org/10.5194/esd-15-859-2024, 2024
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Some components of the Earth system may irreversibly collapse under global warming. Among them, the Atlantic Meridional Overturning Circulation (AMOC), the Greenland Ice Sheet, and West Antarctica Ice Sheet are of utmost importance for maintaining the present-day climate. In a simplified model, we show that both the rate of ice melting and the natural variability linked to freshwater fluxes over the Atlantic Ocean drastically affect how an ice sheet collapse impacts the AMOC stability.
Julia E. Weiffenbach, Henk A. Dijkstra, Anna S. von der Heydt, Ayako Abe-Ouchi, Wing-Le Chan, Deepak Chandan, Ran Feng, Alan M. Haywood, Stephen J. Hunter, Xiangyu Li, Bette L. Otto-Bliesner, W. Richard Peltier, Christian Stepanek, Ning Tan, Julia C. Tindall, and Zhongshi Zhang
Clim. Past, 20, 1067–1086, https://doi.org/10.5194/cp-20-1067-2024, https://doi.org/10.5194/cp-20-1067-2024, 2024
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Elevated atmospheric CO2 concentrations and a smaller Antarctic Ice Sheet during the mid-Pliocene (~ 3 million years ago) cause the Southern Ocean surface to become fresher and warmer, which affects the global ocean circulation. The CO2 concentration and the smaller Antarctic Ice Sheet both have a similar and approximately equal impact on the Southern Ocean. The conditions of the Southern Ocean in the mid-Pliocene could therefore be analogous to those in a future climate with smaller ice sheets.
René M. van Westen and Henk A. Dijkstra
Ocean Sci., 20, 549–567, https://doi.org/10.5194/os-20-549-2024, https://doi.org/10.5194/os-20-549-2024, 2024
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The Atlantic Meridional Overturning Circulation (AMOC) is an important component in the global climate system. Observations of the present-day AMOC indicate that it may weaken or collapse under global warming, with profound disruptive effects on future climate. However, AMOC weakening is not correctly represented because an important feedback is underestimated due to biases in the Atlantic's freshwater budget. Here we address these biases in several state-of-the-art climate model simulations.
Arthur Merlijn Oldeman, Michiel L. J. Baatsen, Anna S. von der Heydt, Aarnout J. van Delden, and Henk A. Dijkstra
Weather Clim. Dynam., 5, 395–417, https://doi.org/10.5194/wcd-5-395-2024, https://doi.org/10.5194/wcd-5-395-2024, 2024
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The mid-Pliocene, a geological period around 3 million years ago, is sometimes considered the best analogue for near-future climate. It saw similar CO2 concentrations to the present-day but also a slightly different geography. In this study, we use climate model simulations and find that the Northern Hemisphere winter responds very differently to increased CO2 or to the mid-Pliocene geography. Our results weaken the potential of the mid-Pliocene as a future climate analogue.
Michiel Baatsen, Peter Bijl, Anna von der Heydt, Appy Sluijs, and Henk Dijkstra
Clim. Past, 20, 77–90, https://doi.org/10.5194/cp-20-77-2024, https://doi.org/10.5194/cp-20-77-2024, 2024
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This work introduces the possibility and consequences of monsoons on Antarctica in the warm Eocene climate. We suggest that such a monsoonal climate can be important to understand conditions in Antarctica prior to large-scale glaciation. We can explain seemingly contradictory indications of ice and vegetation on the continent through regional variability. In addition, we provide a new mechanism through which most of Antarctica remained ice-free through a wide range of global climatic changes.
Sina Loriani, Yevgeny Aksenov, David Armstrong McKay, Govindasamy Bala, Andreas Born, Cristiano M. Chiessi, Henk Dijkstra, Jonathan F. Donges, Sybren Drijfhout, Matthew H. England, Alexey V. Fedorov, Laura Jackson, Kai Kornhuber, Gabriele Messori, Francesco Pausata, Stefanie Rynders, Jean-Baptiste Salée, Bablu Sinha, Steven Sherwood, Didier Swingedouw, and Thejna Tharammal
EGUsphere, https://doi.org/10.5194/egusphere-2023-2589, https://doi.org/10.5194/egusphere-2023-2589, 2023
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In this work, we draw on paleoreords, observations and modelling studies to review tipping points in the ocean overturning circulations, monsoon systems and global atmospheric circulations. We find indications for tipping in the ocean overturning circulations and the West African monsoon, with potentially severe impacts on the Earth system and humans. Tipping in the other considered systems is considered conceivable but currently not sufficiently supported by evidence.
Valérian Jacques-Dumas, René M. van Westen, Freddy Bouchet, and Henk A. Dijkstra
Nonlin. Processes Geophys., 30, 195–216, https://doi.org/10.5194/npg-30-195-2023, https://doi.org/10.5194/npg-30-195-2023, 2023
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Computing the probability of occurrence of rare events is relevant because of their high impact but also difficult due to the lack of data. Rare event algorithms are designed for that task, but their efficiency relies on a score function that is hard to compute. We compare four methods that compute this function from data and measure their performance to assess which one would be best suited to be applied to a climate model. We find neural networks to be most robust and flexible for this task.
Julia E. Weiffenbach, Michiel L. J. Baatsen, Henk A. Dijkstra, Anna S. von der Heydt, Ayako Abe-Ouchi, Esther C. Brady, Wing-Le Chan, Deepak Chandan, Mark A. Chandler, Camille Contoux, Ran Feng, Chuncheng Guo, Zixuan Han, Alan M. Haywood, Qiang Li, Xiangyu Li, Gerrit Lohmann, Daniel J. Lunt, Kerim H. Nisancioglu, Bette L. Otto-Bliesner, W. Richard Peltier, Gilles Ramstein, Linda E. Sohl, Christian Stepanek, Ning Tan, Julia C. Tindall, Charles J. R. Williams, Qiong Zhang, and Zhongshi Zhang
Clim. Past, 19, 61–85, https://doi.org/10.5194/cp-19-61-2023, https://doi.org/10.5194/cp-19-61-2023, 2023
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We study the behavior of the Atlantic Meridional Overturning Circulation (AMOC) in the mid-Pliocene. The mid-Pliocene was about 3 million years ago and had a similar CO2 concentration to today. We show that the stronger AMOC during this period relates to changes in geography and that this has a significant influence on ocean temperatures and heat transported northwards by the Atlantic Ocean. Understanding the behavior of the mid-Pliocene AMOC can help us to learn more about our future climate.
Amber Boot, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 13, 1041–1058, https://doi.org/10.5194/esd-13-1041-2022, https://doi.org/10.5194/esd-13-1041-2022, 2022
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Atmospheric pCO2 of the past shows large variability on different timescales. We focus on the effect of the strength of Atlantic Meridional Overturning Circulation (AMOC) on this variability and on the AMOC–pCO2 relationship. We find that climatic boundary conditions and the representation of biology in our model are most important for this relationship. Under certain conditions, we find internal oscillations, which can be relevant for atmospheric pCO2 variability during glacial cycles.
Mikael L. A. Kaandorp, Stefanie L. Ypma, Marijke Boonstra, Henk A. Dijkstra, and Erik van Sebille
Ocean Sci., 18, 269–293, https://doi.org/10.5194/os-18-269-2022, https://doi.org/10.5194/os-18-269-2022, 2022
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A large amount of marine litter, such as plastics, is located on or around beaches. Both the total amount of this litter and its transport are poorly understood. We investigate this by training a machine learning model with data of cleanup efforts on Dutch beaches between 2014 and 2019, obtained by about 14 000 volunteers. We find that Dutch beaches contain up to 30 000 kg of litter, largely depending on tides, oceanic transport, and how exposed the beaches are.
Peter D. Nooteboom, Peter K. Bijl, Christian Kehl, Erik van Sebille, Martin Ziegler, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 13, 357–371, https://doi.org/10.5194/esd-13-357-2022, https://doi.org/10.5194/esd-13-357-2022, 2022
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Having descended through the water column, microplankton in ocean sediments represents the ocean surface environment and is used as an archive of past and present surface oceanographic conditions. However, this microplankton is advected by turbulent ocean currents during its sinking journey. We use simulations of sinking particles to define ocean bottom provinces and detect these provinces in datasets of sedimentary microplankton, which has implications for palaeoclimate reconstructions.
Arthur M. Oldeman, Michiel L. J. Baatsen, Anna S. von der Heydt, Henk A. Dijkstra, Julia C. Tindall, Ayako Abe-Ouchi, Alice R. Booth, Esther C. Brady, Wing-Le Chan, Deepak Chandan, Mark A. Chandler, Camille Contoux, Ran Feng, Chuncheng Guo, Alan M. Haywood, Stephen J. Hunter, Youichi Kamae, Qiang Li, Xiangyu Li, Gerrit Lohmann, Daniel J. Lunt, Kerim H. Nisancioglu, Bette L. Otto-Bliesner, W. Richard Peltier, Gabriel M. Pontes, Gilles Ramstein, Linda E. Sohl, Christian Stepanek, Ning Tan, Qiong Zhang, Zhongshi Zhang, Ilana Wainer, and Charles J. R. Williams
Clim. Past, 17, 2427–2450, https://doi.org/10.5194/cp-17-2427-2021, https://doi.org/10.5194/cp-17-2427-2021, 2021
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In this work, we have studied the behaviour of El Niño events in the mid-Pliocene, a period of around 3 million years ago, using a collection of 17 climate models. It is an interesting period to study, as it saw similar atmospheric carbon dioxide levels to the present day. We find that the El Niño events were less strong in the mid-Pliocene simulations, when compared to pre-industrial climate. Our results could help to interpret El Niño behaviour in future climate projections.
André Jüling, Anna von der Heydt, and Henk A. Dijkstra
Ocean Sci., 17, 1251–1271, https://doi.org/10.5194/os-17-1251-2021, https://doi.org/10.5194/os-17-1251-2021, 2021
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On top of forced changes such as human-caused global warming, unforced climate variability exists. Most multidecadal variability (MV) involves the oceans, but current climate models use non-turbulent, coarse-resolution oceans. We investigate the effect of resolving important turbulent ocean features on MV. We find that ocean heat content, ocean–atmosphere heat flux, and global mean surface temperature MV is more pronounced in the higher-resolution model relative to higher-frequency variability.
Johannes Lohmann, Daniele Castellana, Peter D. Ditlevsen, and Henk A. Dijkstra
Earth Syst. Dynam., 12, 819–835, https://doi.org/10.5194/esd-12-819-2021, https://doi.org/10.5194/esd-12-819-2021, 2021
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Tipping of one climate subsystem could trigger a cascade of subsequent tipping points and even global-scale climate tipping. Sequential shifts of atmosphere, sea ice and ocean have been recorded in proxy archives of past climate change. Based on this we propose a conceptual model for abrupt climate changes of the last glacial. Here, rate-induced tipping enables tipping cascades in systems with relatively weak coupling. An early warning signal is proposed that may detect such a tipping.
André Jüling, Xun Zhang, Daniele Castellana, Anna S. von der Heydt, and Henk A. Dijkstra
Ocean Sci., 17, 729–754, https://doi.org/10.5194/os-17-729-2021, https://doi.org/10.5194/os-17-729-2021, 2021
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We investigate how the freshwater budget of the Atlantic changes under climate change, which has implications for the stability of the Atlantic Meridional Overturning Circulation. We compare the effect of ocean model resolution in a climate model and find many similarities between the simulations, enhancing trust in the current generation of climate models. However, ocean biases are reduced in the strongly eddying simulation, and significant local freshwater budget differences exist.
Pascal Wang, Daniele Castellana, and Henk A. Dijkstra
Nonlin. Processes Geophys., 28, 135–151, https://doi.org/10.5194/npg-28-135-2021, https://doi.org/10.5194/npg-28-135-2021, 2021
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This paper proposes two improvements to the use of Trajectory-Adaptive Multilevel Sampling, a rare-event algorithm which computes noise-induced transition probabilities. The first improvement uses locally linearised dynamics in order to reduce the arbitrariness associated with defining what constitutes a transition. The second improvement uses empirical transition paths accumulated at high noise in order to formulate the score function which determines the performance of the algorithm.
Amber Boot, René M. van Westen, and Henk A. Dijkstra
Ocean Sci., 17, 335–350, https://doi.org/10.5194/os-17-335-2021, https://doi.org/10.5194/os-17-335-2021, 2021
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The Maud Rise polynya is a hole in the sea ice surrounding Antarctica that occurs during winter. It appeared in 2016 and 2017. Our study concludes that heat and salt accumulation around 1000 m depth are likely to be important for polynya formation. The heat is mixed upward to the surface where it is able to melt the sea ice and, thus, create a polynya. How often the polynya forms depends largely on the variation in the time of the heat and salt accumulation.
David Wichmann, Christian Kehl, Henk A. Dijkstra, and Erik van Sebille
Nonlin. Processes Geophys., 28, 43–59, https://doi.org/10.5194/npg-28-43-2021, https://doi.org/10.5194/npg-28-43-2021, 2021
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Fluid parcels transported in complicated flows often contain subsets of particles that stay close over finite time intervals. We propose a new method for detecting finite-time coherent sets based on the density-based clustering technique of ordering points to identify the clustering structure (OPTICS). Unlike previous methods, our method has an intrinsic notion of coherent sets at different spatial scales. OPTICS is readily implemented in the SciPy sklearn package, making it easy to use.
Carine G. van der Boog, J. Otto Koetsier, Henk A. Dijkstra, Julie D. Pietrzak, and Caroline A. Katsman
Earth Syst. Sci. Data, 13, 43–61, https://doi.org/10.5194/essd-13-43-2021, https://doi.org/10.5194/essd-13-43-2021, 2021
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Thermohaline staircases are stepped structures in the ocean that contain enhanced diapycnal salt and heat transport. In this study, we present a global dataset of thermohaline staircases derived from 487 493 observations of Argo profiling floats and Ice-Tethered Profilers using a novel detection algorithm.
Michiel Baatsen, Anna S. von der Heydt, Matthew Huber, Michael A. Kliphuis, Peter K. Bijl, Appy Sluijs, and Henk A. Dijkstra
Clim. Past, 16, 2573–2597, https://doi.org/10.5194/cp-16-2573-2020, https://doi.org/10.5194/cp-16-2573-2020, 2020
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Warm climates of the deep past have proven to be challenging to reconstruct with the same numerical models used for future predictions. We present results of CESM simulations for the middle to late Eocene (∼ 38 Ma), in which we managed to match the available indications of temperature well. With these results we can now look into regional features and the response to external changes to ultimately better understand the climate when it is in such a warm state.
René M. van Westen and Henk A. Dijkstra
Ocean Sci., 16, 1443–1457, https://doi.org/10.5194/os-16-1443-2020, https://doi.org/10.5194/os-16-1443-2020, 2020
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During the mid-1970s and quite recently in 2017, a large open-water area appeared in the Antarctic sea-ice pack, the so-called Maud Rise polynya. From several model studies, the reoccurrence time of this polynya seems arbitrary. In this study, we address the reoccurrence time of the polynya using a high-resolution climate model. We find a preferred multidecadal return time in polynya formation. The return time of the polynya is associated with a large-scale ocean mode in the Southern Ocean.
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
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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.
René M. van Westen and Henk A. Dijkstra
Ocean Sci. Discuss., https://doi.org/10.5194/os-2020-33, https://doi.org/10.5194/os-2020-33, 2020
Revised manuscript not accepted
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In 2016 and 2017, an open-water area emerged within the Antarctic sea-ice pack, the so-called Maud Rise polynya. The opening of the sea ice has been linked to intense winter storms. In this study, we investigate another important contributor to polynya formation by analysing subsurface static instabilities. These static instabilities initiate subsurface convection near Maud Rise. We conclude that apart from winter storms, subsurface convection plays an important role in polynya formation.
Ann Kristin Klose, René M. van Westen, and Henk A. Dijkstra
Ocean Sci., 16, 435–449, https://doi.org/10.5194/os-16-435-2020, https://doi.org/10.5194/os-16-435-2020, 2020
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We give an explanation of the decadal timescale path variations in the Kuroshio Current in the North Pacific based on highly detailed climate
model simulations.
Carine G. van der Boog, Julie D. Pietrzak, Henk A. Dijkstra, Nils Brüggemann, René M. van Westen, Rebecca K. James, Tjeerd J. Bouma, Riccardo E. M. Riva, D. Cornelis Slobbe, Roland Klees, Marcel Zijlema, and Caroline A. Katsman
Ocean Sci., 15, 1419–1437, https://doi.org/10.5194/os-15-1419-2019, https://doi.org/10.5194/os-15-1419-2019, 2019
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We use a model of the Caribbean Sea to study how coastal upwelling along Venezuela impacts the evolution of energetic anticyclonic eddies. We show that the anticyclones grow by the advection of the cold upwelling filaments. These filaments increase the density gradient and vertical shear of the anticyclones. Furthermore, we show that stronger upwelling results in stronger eddies, while model simulations with weaker upwelling contain weaker eddies.
Juan-Manuel Sayol, Henk Dijkstra, and Caroline Katsman
Ocean Sci., 15, 1033–1053, https://doi.org/10.5194/os-15-1033-2019, https://doi.org/10.5194/os-15-1033-2019, 2019
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This work uses high-resolution ocean model data to quantify the sinking of waters in the subpolar North Atlantic. The largest amount of sinking is found at the depth of maximum AMOC at 45° N below the mixed layer depth, and 90 % of the sinking occurs near the boundaries in the first 250 km off the shelf. The characteristics of the sinking (total amount, seasonal variability, and vertical structure) vary largely according to the region considered, revealing a complex picture for the sinking.
Koen G. Helwegen, Claudia E. Wieners, Jason E. Frank, and Henk A. Dijkstra
Earth Syst. Dynam., 10, 453–472, https://doi.org/10.5194/esd-10-453-2019, https://doi.org/10.5194/esd-10-453-2019, 2019
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We use the climate-economy model DICE to perform a cost–benefit analysis of sulfate geoengineering, i.e. producing a thin artificial sulfate haze in the higher atmosphere to reflect some sunlight and cool the Earth.
We find that geoengineering can increase future welfare by reducing global warming, and should be taken seriously as a policy option, but it can only complement, not replace, carbon emission reduction. The best policy is to combine CO2 emission reduction with modest geoengineering.
Martijn Westhoff, Axel Kleidon, Stan Schymanski, Benjamin Dewals, Femke Nijsse, Maik Renner, Henk Dijkstra, Hisashi Ozawa, Hubert Savenije, Han Dolman, Antoon Meesters, and Erwin Zehe
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2019-6, https://doi.org/10.5194/esd-2019-6, 2019
Publication in ESD not foreseen
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Even models relying on physical laws have parameters that need to be measured or estimated. Thermodynamic optimality principles potentially offer a way to reduce the number of estimated parameters by stating that a system evolves to an optimum state. These principles have been applied successfully within the Earth system, but it is often unclear what to optimize and how. In this review paper we identify commonalities between different successful applications as well as some doubtful applications.
Mark M. Dekker, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 9, 1243–1260, https://doi.org/10.5194/esd-9-1243-2018, https://doi.org/10.5194/esd-9-1243-2018, 2018
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We introduce a framework of cascading tipping, i.e. a sequence of abrupt transitions occurring because a transition in one system affects the background conditions of another system. Using bifurcation theory, various types of these events are considered and early warning indicators are suggested. An illustration of such an event is found in a conceptual model, coupling the North Atlantic Ocean with the equatorial Pacific. This demonstrates the possibility of events such as this in nature.
Matthias Aengenheyster, Qing Yi Feng, Frederick van der Ploeg, and Henk A. Dijkstra
Earth Syst. Dynam., 9, 1085–1095, https://doi.org/10.5194/esd-9-1085-2018, https://doi.org/10.5194/esd-9-1085-2018, 2018
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We determine the point of no return (PNR) for climate change, which is the latest year to take action to reduce greenhouse gases to stay, with a certain probability, within thresholds set by the Paris Agreement. For a 67 % probability and a 2 K threshold, the PNR is the year 2035 when the share of renewable energy rises by 2 % per year. We show the impact on the PNR of the speed by which emissions are cut, the risk tolerance, climate uncertainties and the potential for negative emissions.
Femke J. M. M. Nijsse and Henk A. Dijkstra
Earth Syst. Dynam., 9, 999–1012, https://doi.org/10.5194/esd-9-999-2018, https://doi.org/10.5194/esd-9-999-2018, 2018
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State-of-the-art climate models sometimes differ in their prediction of key aspects of climate change. The technique of
emergent constraintsuses observations of current climate to improve those predictions, using relationships between different climate models. Our paper first classifies the different uses of the technique, and continues with proposing a mathematical justification for their use. We also highlight when the application of emergent constraints might give biased predictions.
Peter D. Nooteboom, Qing Yi Feng, Cristóbal López, Emilio Hernández-García, and Henk A. Dijkstra
Earth Syst. Dynam., 9, 969–983, https://doi.org/10.5194/esd-9-969-2018, https://doi.org/10.5194/esd-9-969-2018, 2018
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The prediction of the El Niño phenomenon, an increased sea surface temperature in the eastern Pacific, fascinates people for a long time. El Niño is associated with natural disasters, such as droughts and floods. Current methods can make a reliable prediction of this phenomenon up to 6 months ahead. However, this article presents a method which combines network theory and machine learning which predicts El Niño up to 1 year ahead.
Michiel Baatsen, Anna S. von der Heydt, Matthew Huber, Michael A. Kliphuis, Peter K. Bijl, Appy Sluijs, and Henk A. Dijkstra
Clim. Past Discuss., https://doi.org/10.5194/cp-2018-43, https://doi.org/10.5194/cp-2018-43, 2018
Revised manuscript not accepted
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The Eocene marks a period where the climate was in a hothouse state, without any continental-scale ice sheets. Such climates have proven difficult to reproduce in models, especially their low temperature difference between equator and poles. Here, we present high resolution CESM simulations using a new geographic reconstruction of the middle-to-late Eocene. The results provide new insights into a period for which knowledge is limited, leading up to a transition into the present icehouse state.
Inti Pelupessy, Ben van Werkhoven, Arjen van Elteren, Jan Viebahn, Adam Candy, Simon Portegies Zwart, and Henk Dijkstra
Geosci. Model Dev., 10, 3167–3187, https://doi.org/10.5194/gmd-10-3167-2017, https://doi.org/10.5194/gmd-10-3167-2017, 2017
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Researchers from the Netherlands present OMUSE, a software package
developed from core technology originating in the astrophysical
community. Using OMUSE, oceanographic and climate researchers can
develop numerical models of the ocean and the interactions between
different parts of the ocean and the atmosphere. This provides a novel
way to investigate, for example, the local effects of climate change on
the ocean. OMUSE is freely available as open-source software.
Brenda C. van Zalinge, Qing Yi Feng, Matthias Aengenheyster, and Henk A. Dijkstra
Earth Syst. Dynam., 8, 707–717, https://doi.org/10.5194/esd-8-707-2017, https://doi.org/10.5194/esd-8-707-2017, 2017
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The increase in atmospheric greenhouse gases (GHGs) is one of the main causes for the increase in global mean surface temperature. There is no good quantitative measure to determine when it is
too lateto start reducing GHGs in order to avoid dangerous anthropogenic interference. We develop a method for determining a so-called point of no return (PNR) for several GHG emission scenarios. The innovative element in this approach is the applicability to high-dimensional climate models.
Daniel J. Lunt, Matthew Huber, Eleni Anagnostou, Michiel L. J. Baatsen, Rodrigo Caballero, Rob DeConto, Henk A. Dijkstra, Yannick Donnadieu, David Evans, Ran Feng, Gavin L. Foster, Ed Gasson, Anna S. von der Heydt, Chris J. Hollis, Gordon N. Inglis, Stephen M. Jones, Jeff Kiehl, Sandy Kirtland Turner, Robert L. Korty, Reinhardt Kozdon, Srinath Krishnan, Jean-Baptiste Ladant, Petra Langebroek, Caroline H. Lear, Allegra N. LeGrande, Kate Littler, Paul Markwick, Bette Otto-Bliesner, Paul Pearson, Christopher J. Poulsen, Ulrich Salzmann, Christine Shields, Kathryn Snell, Michael Stärz, James Super, Clay Tabor, Jessica E. Tierney, Gregory J. L. Tourte, Aradhna Tripati, Garland R. Upchurch, Bridget S. Wade, Scott L. Wing, Arne M. E. Winguth, Nicky M. Wright, James C. Zachos, and Richard E. Zeebe
Geosci. Model Dev., 10, 889–901, https://doi.org/10.5194/gmd-10-889-2017, https://doi.org/10.5194/gmd-10-889-2017, 2017
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In this paper we describe the experimental design for a set of simulations which will be carried out by a range of climate models, all investigating the climate of the Eocene, about 50 million years ago. The intercomparison of model results is called 'DeepMIP', and we anticipate that we will contribute to the next IPCC report through an analysis of these simulations and the geological data to which we will compare them.
S.-E. Brunnabend, H. A. Dijkstra, M. A. Kliphuis, H. E. Bal, F. Seinstra, B. van Werkhoven, J. Maassen, and M. van Meersbergen
Ocean Sci., 13, 47–60, https://doi.org/10.5194/os-13-47-2017, https://doi.org/10.5194/os-13-47-2017, 2017
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An important contribution to future changes in regional sea level extremes is due to the changes in intrinsic ocean variability, in particular ocean eddies. Here, we study a scenario of future dynamic sea level (DSL) extremes using a strongly eddying version of the Parallel Ocean Program. Changes in 10-year return time DSL extremes are very inhomogeneous over the globe and are related to changes in ocean currents and corresponding regional shifts in ocean eddy pathways.
Michiel Baatsen, Douwe J. J. van Hinsbergen, Anna S. von der Heydt, Henk A. Dijkstra, Appy Sluijs, Hemmo A. Abels, and Peter K. Bijl
Clim. Past, 12, 1635–1644, https://doi.org/10.5194/cp-12-1635-2016, https://doi.org/10.5194/cp-12-1635-2016, 2016
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One of the major difficulties in modelling palaeoclimate is constricting the boundary conditions, causing significant discrepancies between different studies. Here, a new method is presented to automate much of the process of generating the necessary geographical reconstructions. The latter can be made using various rotational frameworks and topography/bathymetry input, allowing for easy inter-comparisons and the incorporation of the latest insights from geoscientific research.
Zun Yin, Stefan C. Dekker, Bart J. J. M. van den Hurk, and Henk A. Dijkstra
Biogeosciences, 13, 3343–3357, https://doi.org/10.5194/bg-13-3343-2016, https://doi.org/10.5194/bg-13-3343-2016, 2016
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Bimodality is found in aboveground biomass and mean annual shortwave radiation in West Africa, which is a strong evidence of alternative stable states. The condition with low biomass and low radiation is demonstrated under which ecosystem state can shift between savanna and forest states. Moreover, climatic indicators have different prediction confidences to different land cover types. A new method is proposed to predict potential land cover change with a combination of climatic indicators.
Qing Yi Feng, Ruggero Vasile, Marc Segond, Avi Gozolchiani, Yang Wang, Markus Abel, Shilomo Havlin, Armin Bunde, and Henk A. Dijkstra
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2015-273, https://doi.org/10.5194/gmd-2015-273, 2016
Revised manuscript not accepted
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We present the toolbox ClimateLearn to tackle problems in climate prediction using machine learning techniques and climate network analysis. Because spatial temporal information on climate variability can be efficiently represented by complex network measures, such data are considered here as input to the machine-learning algorithms. As an example, the toolbox is applied to the prediction of the occurrence and the development of El Niño in the equatorial Pacific.
H. Ihshaish, A. Tantet, J. C. M. Dijkzeul, and H. A. Dijkstra
Geosci. Model Dev., 8, 3321–3331, https://doi.org/10.5194/gmd-8-3321-2015, https://doi.org/10.5194/gmd-8-3321-2015, 2015
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Par@Graph, a software toolbox to reconstruct and analyze large-scale complex climate networks. It exposes parallelism on distributed-memory computing platforms to enable the construction of massive networks from large number of time series based on the calculation of common statistical similarity measures between them. Providing additionally parallel graph algorithms to enable fast calculation of important and common properties of the generated networks on SMP machines.
L. Hahn-Woernle, H. A. Dijkstra, and H. J. Van der Woerd
Ocean Sci., 10, 993–1011, https://doi.org/10.5194/os-10-993-2014, https://doi.org/10.5194/os-10-993-2014, 2014
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Measured vertical mixing profiles are applied to a 1-D phytoplankton model. Results show that shifts in vertical mixing are able to induce a transition from an upper chlorophyll maximum to a deep one and vice versa. Furthermore, a clear correlation between the surface phytoplankton concentration and mixing-induced nutrient flux is found for nutrient-limited cases. This result suggests that characteristics of the vertical mixing could be determined from the surface phytoplankton concentration.
S.-E. Brunnabend, H. A. Dijkstra, M. A. Kliphuis, B. van Werkhoven, H. E. Bal, F. Seinstra, J. Maassen, and M. van Meersbergen
Ocean Sci., 10, 881–891, https://doi.org/10.5194/os-10-881-2014, https://doi.org/10.5194/os-10-881-2014, 2014
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Regional sea surface height (SSH) changes due to an abrupt weakening of the Atlantic meridional overturning circulation (AMOC) are simulated with a high- and low-resolution model. A rapid decrease of the AMOC in the high-resolution version induces shorter return times of several specific regional and coastal extremes in North Atlantic SSH than in the low-resolution version. This effect is caused by a change in main eddy pathways associated with a change in separation latitude of the Gulf Stream.
Z. Yin, S. C. Dekker, B. J. J. M. van den Hurk, and H. A. Dijkstra
Earth Syst. Dynam., 5, 257–270, https://doi.org/10.5194/esd-5-257-2014, https://doi.org/10.5194/esd-5-257-2014, 2014
D. Le Bars, J. V. Durgadoo, H. A. Dijkstra, A. Biastoch, and W. P. M. De Ruijter
Ocean Sci., 10, 601–609, https://doi.org/10.5194/os-10-601-2014, https://doi.org/10.5194/os-10-601-2014, 2014
Z. Yin, S. C. Dekker, B. J. J. M. van den Hurk, and H. A. Dijkstra
Geosci. Model Dev., 7, 821–845, https://doi.org/10.5194/gmd-7-821-2014, https://doi.org/10.5194/gmd-7-821-2014, 2014
G. Sgubin, S. Pierini, and H. A. Dijkstra
Ocean Sci., 10, 201–213, https://doi.org/10.5194/os-10-201-2014, https://doi.org/10.5194/os-10-201-2014, 2014
A. Tantet and H. A. Dijkstra
Earth Syst. Dynam., 5, 1–14, https://doi.org/10.5194/esd-5-1-2014, https://doi.org/10.5194/esd-5-1-2014, 2014
A. A. Cimatoribus, S. Drijfhout, and H. A. Dijkstra
Ocean Sci. Discuss., https://doi.org/10.5194/osd-10-2461-2013, https://doi.org/10.5194/osd-10-2461-2013, 2013
Preprint withdrawn
A. S. von der Heydt, A. Nnafie, and H. A. Dijkstra
Clim. Past, 7, 903–915, https://doi.org/10.5194/cp-7-903-2011, https://doi.org/10.5194/cp-7-903-2011, 2011
M. Tigchelaar, A. S. von der Heydt, and H. A. Dijkstra
Clim. Past, 7, 235–247, https://doi.org/10.5194/cp-7-235-2011, https://doi.org/10.5194/cp-7-235-2011, 2011
J. O. Sewall, R. S. W. van de Wal, K. van der Zwan, C. van Oosterhout, H. A. Dijkstra, and C. R. Scotese
Clim. Past, 3, 647–657, https://doi.org/10.5194/cp-3-647-2007, https://doi.org/10.5194/cp-3-647-2007, 2007
Related subject area
Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
Solving a North-type energy balance model using boundary integral methods
Finite-size local dimension as a tool for extracting geometrical properties of attractors of dynamical systems
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
Rate-Induced Transitions and Noise-Driven Resilience in Vegetation Pattern Dynamics
The role of time-varying external factors in the intensification of tropical cyclones
Negative Differential Resistance, Instability, and Critical Transition in Lightning Leader
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
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
Detecting and tracking eddies in oceanic flow fields: a Lagrangian descriptor based on the modulus of vorticity
Oscillations in a simple climate–vegetation model
A novel method for analyzing the process of abrupt climate change
Aksel Samuelsberg and Per Kristen Jakobsen
Nonlin. Processes Geophys., 32, 23–33, https://doi.org/10.5194/npg-32-23-2025, https://doi.org/10.5194/npg-32-23-2025, 2025
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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 present 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.
Martin Bonte and Stéphane Vannitsem
EGUsphere, https://doi.org/10.5194/egusphere-2024-3915, https://doi.org/10.5194/egusphere-2024-3915, 2024
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In recent years, there has been more and more floods due to intense precipitation, such as the July 2021 event in Belgium. Predicting precipitation is a difficult task, even for the next hours. This study focuses on a tool to assess whether a given situation is stable or not (i.e. is likely to stay as it is or could evolve in an unpredictable manner).
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
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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
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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
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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.
Lilian Vanderveken and Michel Crucifix
EGUsphere, https://doi.org/10.5194/egusphere-2024-2830, https://doi.org/10.5194/egusphere-2024-2830, 2024
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Vegetation patterns in semi-arid regions arise from interactions between plants and environmental factors. This study uses a numerical model to explore how vegetation responds to changes in rainfall and random disturbances. We identify key timescales that influence resilience, showing that ecosystems rely on both stable and transitional states to adapt. These findings offer insights into the resilience mechanisms that help ecosystems maintain stability under environmental stress.
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
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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.
Xueqiang Gou, Chao Xin, Liwen Xu, Ping Yuan, Yijun Zhang, and Mingli Cheng
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-15, https://doi.org/10.5194/npg-2024-15, 2024
Revised manuscript accepted for NPG
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Our research examines lightning's complex behavior by studying changes in its electrical pathways under different conditions. We found that lightning channels switch between stable and unstable states based on their length and surrounding electric fields. This helps explain why lightning often reactivates after a brief pause and offers new insights into these processes. Our findings could improve lightning prediction and protection, benefiting scientific understanding and public safety.
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
Rahel Vortmeyer-Kley, Ulf Gräwe, and Ulrike Feudel
Nonlin. Processes Geophys., 23, 159–173, https://doi.org/10.5194/npg-23-159-2016, https://doi.org/10.5194/npg-23-159-2016, 2016
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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.
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
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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
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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.
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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.
I provide a personal view on the role of bifurcation analysis of climate models in the...
