Articles | Volume 28, issue 1
https://doi.org/10.5194/npg-28-135-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-28-135-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
24 Feb 2021
Research article |
| 24 Feb 2021
| 24 Feb 2021
Improvements to the use of the Trajectory-Adaptive Multilevel Sampling algorithm for the study of rare events
Univ. Lyon, ENS de Lyon, Univ. Claude Bernard, CNRS, Laboratoire de Physique, Lyon, France
Daniele Castellana
Institute for Marine and Atmospheric research Utrecht, Department of Physics, Utrecht University, Utrecht, the Netherlands
Henk A. Dijkstra
Institute for Marine and Atmospheric research Utrecht, Department of Physics, Utrecht University, Utrecht, the Netherlands
Centre for Complex Systems Studies, Department of Physics, Utrecht University, Utrecht, the Netherlands
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Jelle Soons, Elian Vanderborght, and Henk A. Dijkstra
EGUsphere, https://doi.org/10.5194/egusphere-2025-6565, https://doi.org/10.5194/egusphere-2025-6565, 2026
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 major ocean circulation that regulates the global climate and could potentially collapse under climate change. Previously it has been shown that constructing a closure of the Bering Strait could prevent this collapse. In this study we use a box model to represent the global ocean circulation, and show that closing this Strait can either weaken or protect the AMOC, depending on background conditions and the rate of temperature increase.
Emma J. V. Smolders, René M. van Westen, and Henk A. Dijkstra
EGUsphere, https://doi.org/10.5194/egusphere-2026-209, https://doi.org/10.5194/egusphere-2026-209, 2026
This preprint is open for discussion and under review for Ocean Science (OS).
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The Southern Ocean shows strong natural variability on multi-decadal time scales, known as the Southern Ocean Mode (SOM). Using high-resolution ocean simulations, we show that a collapse of the Atlantic Meridional Overturning Circulation (AMOC) strongly weakens the SOM. This weakening is linked to changes in ocean density, a slowdown of the Antarctic Circumpolar Current, and shifts in deep convection across the Southern Ocean.
René M. van Westen, Elian Vanderborght, and Henk A. Dijkstra
Earth Syst. Dynam., 16, 2063–2085, https://doi.org/10.5194/esd-16-2063-2025, https://doi.org/10.5194/esd-16-2063-2025, 2025
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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.
Swinda K. J. Falkena, Henk A. Dijkstra, and Anna S. von der Heydt
Earth Syst. Dynam., 16, 1833–1844, https://doi.org/10.5194/esd-16-1833-2025, https://doi.org/10.5194/esd-16-1833-2025, 2025
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The subpolar gyre is a wind-driven circulation in the North Atlantic Ocean that enables the mixing of water between the surface and deeper layers. We investigate the interactions between the strength of the gyre circulation, salinity, temperature, and mixing in climate models. We find that most models capture an increase in salinity or a decrease in temperature, leading to mixing. However, the feedback from the density in the gyre centre to the strength of its circulation is poorly represented.
Sina Loriani, Yevgeny Aksenov, David I. Armstrong McKay, Govindasamy Bala, Andreas Born, Cristiano Mazur Chiessi, Henk A. Dijkstra, Jonathan F. Donges, Sybren Drijfhout, Matthew H. England, Alexey V. Fedorov, Laura C. Jackson, Kai Kornhuber, Gabriele Messori, Francesco S. R. Pausata, Stefanie Rynders, Jean-Baptiste Sallée, Bablu Sinha, Steven C. Sherwood, Didier Swingedouw, and Thejna Tharammal
Earth Syst. Dynam., 16, 1611–1653, https://doi.org/10.5194/esd-16-1611-2025, https://doi.org/10.5194/esd-16-1611-2025, 2025
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In this work, we draw on palaeo-records, 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 regarded as conceivable but is currently not sufficiently supported by evidence.
Aurora Faure Ragani and Henk A. Dijkstra
Earth Syst. Dynam., 16, 1287–1301, https://doi.org/10.5194/esd-16-1287-2025, https://doi.org/10.5194/esd-16-1287-2025, 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, 1221–1235, https://doi.org/10.5194/esd-16-1221-2025, https://doi.org/10.5194/esd-16-1221-2025, 2025
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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 reduction in such flaws in climate models is therefore thought to be essential.
Francesco Guardamagna, Claudia Wieners, and Henk A. Dijkstra
Nonlin. Processes Geophys., 32, 201–224, https://doi.org/10.5194/npg-32-201-2025, https://doi.org/10.5194/npg-32-201-2025, 2025
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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–Cane (ZC) model. This reduced sensitivity can explain the RC's superior skills.
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
Preprint archived
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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.
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.
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.
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.
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.
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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.
This paper proposes two improvements to the use of Trajectory-Adaptive Multilevel Sampling, a...
