Articles | Volume 30, issue 2
https://doi.org/10.5194/npg-30-195-2023
© Author(s) 2023. 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-30-195-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
28 Jun 2023
Research article |
| 28 Jun 2023
| 28 Jun 2023
Data-driven methods to estimate the committor function in conceptual ocean models
Valérian Jacques-Dumas
CORRESPONDING AUTHOR
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
René M. van Westen
Institute for Marine and Atmospheric research Utrecht, Department of Physics, Utrecht University, Utrecht, the Netherlands
Freddy Bouchet
CNRS, Laboratoire de Physique, Univ. Lyon, ENS de Lyon, Univ. Claude Bernard, Lyon, France
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
Related authors
No articles found.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
René M. van Westen, Karin van der Wiel, Swinda K. J. Falkena, and Frank Selten
EGUsphere, https://doi.org/10.5194/egusphere-2025-1440, https://doi.org/10.5194/egusphere-2025-1440, 2025
Short summary
Short summary
The Atlantic Meridional Overturning Circulation (AMOC) moderates the European climate. The AMOC is a tipping element and may collapse to a substantially weaker state under climate change. Such an event induces global and regional climate shifts. The European hydroclimate becomes drier under an AMOC collapse, this response is not considered in the 'standard' hydroclimate projections. Our results indicate a considerable influence of the AMOC on the European hydroclimate.
Swinda K. J. Falkena, Henk A. Dijkstra, and Anna S. von der Heydt
EGUsphere, https://doi.org/10.48550/arXiv.2408.16541, https://doi.org/10.48550/arXiv.2408.16541, 2025
Short summary
Short summary
The subpolar gyre is a wind-driven circulation in the North Atlantic Ocean, which 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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
The surface transport of heat, nutrients and plastic in the North Atlantic Ocean is organized into large-scale flow structures. We propose a new and simple method to detect such features in ocean drifter data sets by identifying groups of trajectories with similar dynamical behaviour using network theory. We successfully detect well-known regions such as the Subpolar and Subtropical gyres, the Western Boundary Current region and the Caribbean Sea.
Cited articles
Altman, N. S.: An Introduction to Kernel and Nearest-Neighbor Nonparametric
Regression, Am. Stat., 46, 175–185,
https://doi.org/10.1080/00031305.1992.10475879, 1992. a
Armstrong McKay, D. I., Staal, A., Abrams, J. F., Winkelmann, R., Sakschewski,
B., Loriani, S., Fetzer, I., Cornell, S. E., Rockström, J., and Lenton,
T. M.: Exceeding 1.5 ∘C global warming could trigger multiple
climate tipping points, Science, 377, eabn7950, https://doi.org/10.1126/science.abn7950, 2022. a
Baars, S., Castellana, D., Wubs, F., and Dijkstra, H.: Application of adaptive
multilevel splitting to high-dimensional dynamical systems, J.
Comput. Phys., 424, 109876,
https://doi.org/10.1016/j.jcp.2020.109876, 2021. a, b
Benedetti, R.: Scoring Rules for Forecast Verification, Mon. Weather Rev., 138, 203–211, https://doi.org/10.1175/2009MWR2945.1, 2010. a, b
Bentley, J. L.: Multidimensional Binary Search Trees Used for Associative
Searching, Commun. ACM, 18, 509–517, https://doi.org/10.1145/361002.361007, 1975. a
Berry, T. and Harlim, J.: Variable Bandwidth Diffusion Kernels, ArXiv,
https://doi.org/10.48550/ARXIV.1406.5064, 2014. a, b
Berry, T., Giannakis, D., and Harlim, J.: Nonparametric forecasting of
low-dimensional dynamical systems, Physical Review E, 91, 3,
https://doi.org/10.1103/physreve.91.032915, 2015. a
Bouchet, F., Rolland, J., and Simonnet, E.: Rare event algorithm links
transitions in turbulent flows with activated nucleations, Phys. Rev.
Lett., 122, 074502, https://doi.org/10.1103/PhysRevLett.122.074502, 2019. a, b
Bryden, H. L., King, B. A., and McCarthy, G. D.: South Atlantic overturning
circulation at 24∘ S, J. Marine Res., 69, 38–56, 2011. a
Cérou, F. and Guyader, A.: Adaptive Multilevel Splitting for Rare Event
Analysis, Stoch. Anal. Appl., 25, 417–443,
https://doi.org/10.1080/07362990601139628, 2007. a
Cérou, F., Delyon, B., Guyader, A., and Rousset, M.: On the Asymptotic
Normality of Adaptive Multilevel Splitting, SIAM/ASA Journal on Uncertainty
Quantification, 7, 1–30, https://doi.org/10.1137/18M1187477, 2019. a
Chen, Y., Hoskins, J., Khoo, Y., and Lindsey, M.: Committor functions via
tensor networks, J. Comput. Phys., 472, 111646,
https://doi.org/10.1016/j.jcp.2022.111646, 2023. a
Cimatoribus, A. A., Drijfhout, S. S., and Dijkstra, H. A.: Meridional
overturning circulation: stability and ocean feedbacks in a box model,
Clim. Dynam., 42, 311–328, https://doi.org/10.1007/s00382-012-1576-9, 2014. a
den Toom, M., Dijkstra, H. A., and Wubs, F. W.: Spurious multiple equilibria
introduced by convective adjustment, Ocean Model., 38, 126–137,
https://doi.org/10.1016/j.ocemod.2011.02.009, 2011. a
de Vries, P. and Weber, S. L.: The Atlantic freshwater budget as a diagnostic
for the existence of a stable shut down of the meridional overturning
circulation, Geophys. Res. Lett., 32, L09606,
https://doi.org/10.1029/2004GL021450, 2005. a
Dijkstra, H. A.: Characterization of the multiple equilibria regime in a global
ocean model, Tellus, 59A, 695–705, 2007. a
Du, Q.: Sequential Monte Carlo and Applications in Molecular Dynamics,
Theses, Sorbonne Université,
https://tel.archives-ouvertes.fr/tel-02969115 (last access: 2022), 2020. a
Elber, R., Bello-Rivas, J. M., Ma, P., Cardenas, A. E., and Fathizadeh, A.:
Calculating Iso-Committor Surfaces as Optimal Reaction Coordinates with
Milestoning, Entropy (Basel, Switzerland), 19, 219, https://doi.org/10.3390/e19050219,
2017. a
Finkel, J., Webber, R. J., Gerber, E. P., Abbot, D. S., and Weare, J.: Learning
Forecasts of Rare Stratospheric Transitions from Short Simulations, Mon.
Weather Rev., 149, 3647–3669, https://doi.org/10.1175/MWR-D-21-0024.1, 2021. a, b, c, d
Freidlin, M. I. and Wentzell, A. D.: Random Perturbations, pp. 15–43, Springer
New York, New York, NY, https://doi.org/10.1007/978-1-4612-0611-8_2, 1998. a
Garzoli, S., Baringer, M., Dong, S., Perez, R., and Yao, Q.: South Atlantic
meridional fluxes, Deep-Sea Res. Pt. I,
71, 21–32, https://doi.org/10.1016/j.dsr.2012.09.003, 2013. a
Gonon, L. and Ortega, J.-P.: Reservoir Computing Universality With Stochastic
Inputs, IEEE T. Neur. Net. Lear., 31,
100–112, https://doi.org/10.1109/TNNLS.2019.2899649, 2020. a
He, K., Zhang, X., Ren, S., and Sun, J.: Delving Deep into Rectifiers:
Surpassing Human-Level Performance on ImageNet Classification, in: 2015 IEEE
International Conference on Computer Vision (ICCV), 1026–1034,
https://doi.org/10.1109/ICCV.2015.123, 2015. a
Helfmann, L., Borrell, E. R., Schütte, C., and Koltai, P.: Extending
Transition Path Theory: Periodically Driven and Finite-Time Dynamics, J. Nonlin. Sci., 30, 3321–3366, https://doi.org/10.1007/s00332-020-09652-7, 2020. a
Jacques-Dumas, V.: ValerianJD/Committor-Estimation: Methods comparison for data-driven committor estimation (v1.0.0), Zenodo [code], https://doi.org/10.5281/zenodo.7380724, 2022. a
Jacques-Dumas, V., Ragone, F., Borgnat, P., Abry, P., and Bouchet, F.: Deep
Learning-Based Extreme Heatwave Forecast, Front. Climate, 4, 789641,
https://doi.org/10.3389/fclim.2022.789641, 2022. a
Jaeger, H.: The “echo state” approach to analysing and training recurrent
neural networks-with an erratum note, Bonn, Germany: German National
Research Center for Information Technology GMD Technical Report, 148, 2001. a
Jiang, S., Jin, F.-F., and Ghil, M.: Multiple Equilibria, Periodic, and
Aperiodic Solutions in a Wind-Driven, Double-Gyre, Shallow-Water Model,
J. Phys. Oceanogr., 25, 764–786,
https://doi.org/10.1175/1520-0485(1995)025<0764:MEPAAS>2.0.CO;2, 1995. a
Khoo, Y., Lu, J., and Ying, L.: Solving for high dimensional committor
functions using artificial neural networks, ArXiv, https://doi.org/10.48550/ARXIV.1802.10275,
2018. a
Kong, L.-W., Fan, H.-W., Grebogi, C., and Lai, Y.-C.: Machine learning
prediction of critical transition and system collapse, Phys. Rev. Res.,
3, 013090, https://doi.org/10.1103/PhysRevResearch.3.013090, 2021. a
Lakshminarayanan, B., Roy, D. M., and Teh, Y. W.: Mondrian Forests: Efficient
Online Random Forests, ArXiv, https://doi.org/10.48550/ARXIV.1406.2673, 2014. a
Lenton, T. M., Held, H., Kriegler, E., Hall, J. W., Lucht, W., Rahmstorf, S.,
and Schellnhuber, H. J.: Tipping elements in the Earth's climate system,
P. Natl. Acad. Sci. USA, 105, 1786–1793,
https://doi.org/10.1073/pnas.0705414105, 2008. a
Lestang, T., Ragone, F., Bréhier, C.-E., Herbert, C., and Bouchet, F.:
Computing return times or return periods with rare event algorithms, J. Stat. Mech.-Theory E., 2018, 043213,
https://doi.org/10.1088/1742-5468/aab856, 2018. a
Lguensat, R., Tandeo, P., Ailliot, P., Pulido, M., and Fablet, R.: The Analog
Data Assimilation, Mon. Weather Rev., 145, 4093–4107,
https://doi.org/10.1175/MWR-D-16-0441.1, 2017. a, b
Li, Q., Lin, B., and Ren, W.: Computing committor functions for the study of
rare events using deep learning, J. Chem. Phys., 151,
054112, https://doi.org/10.1063/1.5110439, 2019. a
Lorenz, E. N.: Atmospheric Predictability as Revealed by Naturally Occurring
Analogues, J. Atmos. Sci., 26, 636–646,
https://doi.org/10.1175/1520-0469(1969)26<636:APARBN>2.0.CO;2, 1969a. a, b
Lucente, D., Duffner, S., Herbert, C., Rolland, J., and Bouchet, F.: MACHINE
LEARNING OF COMMITTOR FUNCTIONS FOR PREDICTING HIGH IMPACT CLIMATE EVENTS,
in: Climate Informatics, Paris, France,
https://hal.archives-ouvertes.fr/hal-02322370 (last access: 2022), 2019. a
Lucente, D., Rolland, J., Herbert, C., and Bouchet, F.: Coupling rare event
algorithms with data-based learned committor functions using the analogue
Markov chain, J. Stat. Mech.-Theory E., 2022,
083201, https://doi.org/10.1088/1742-5468/ac7aa7, 2022b. a, b, c
Lukoševičius, M. and Jaeger, H.: Reservoir computing approaches to recurrent
neural network training, Comput. Sci. Rev., 3, 127–149,
https://doi.org/10.1016/j.cosrev.2009.03.005, 2009. a
Miloshevich, G., Cozian, B., Abry, P., Borgnat, P., and Bouchet, F.:
Probabilistic forecasts of extreme heatwaves using convolutional neural
networks in a regime of lack of data, ArXiv, https://doi.org/10.48550/ARXIV.2208.00971, 2022. a
Nemoto, T., Bouchet, F., Jack, R. L., and Lecomte, V.: Population-dynamics
method with a multicanonical feedback control, Phys. Rev. E, 93, 062123,
https://doi.org/10.1103/physreve.93.062123, 2016. a
Noé, F. and Rosta, E.: Markov Models of Molecular Kinetics, J.
Chem. Phys., 151, 190401, https://doi.org/10.1063/1.5134029, 2019. a
Platzer, P., Yiou, P., Naveau, P., Filipot, J.-F., Thiébaut, M., and
Tandeo, P.: Probability Distributions for Analog-To-Target Distances, J. Atmos. Sci., 78, 3317–3335, https://doi.org/10.1175/jas-d-20-0382.1,
2021a. a, b
Platzer, P., Yiou, P., Naveau, P., Tandeo, P., Zhen, Y., Ailliot, P., and
Filipot, J.-F.: Using local dynamics to explain analog forecasting of chaotic
systems, J. Atmos. Sci., 78, 2117–2133, https://doi.org/10.1175/jas-d-20-0204.1,
2021b. a, b
Prinz, J.-H., Held, M., Smith, J. C., and Noé, F.: Efficient Computation,
Sensitivity, and Error Analysis of Committor Probabilities for Complex
Dynamical Processes, Multiscale Model. Sim., 9, 545–567,
https://doi.org/10.1137/100789191, 2011. a, b
Ragone, F., Wouters, J., and Bouchet, F.: Computation of extreme heat waves in
climate models using a large deviation algorithm, P. Natl.
Acad. Sci. USA, 115, 24–29, https://doi.org/10.1073/pnas.1712645115, 2018. a, b
Rahmstorf, S.: On the freshwater forcing and transport of the Atlantic
thermohaline circulation, Clim. Dynam., 12, 799–811,
https://doi.org/10.1007/s003820050144, 1996. a
Rolland, J., Bouchet, F., and Simonnet, E.: Computing Transition Rates for the
1-D Stochastic Ginzburg–Landau–Allen–Cahn
Equation for Finite-Amplitude Noise with a Rare Event Algorithm, J.
Stat. Phys., 162, 277–311, https://doi.org/10.1007/s10955-015-1417-4, 2015. a
Schütte, C., Fischer, A., Huisinga, W., and Deuflhard, P.: A Direct Approach
to Conformational Dynamics Based on Hybrid Monte Carlo, J.
Comput. Phys., 151, 146–168,
https://doi.org/10.1006/jcph.1999.6231, 1999. a
Sikorski, A., Weber, M., and Schütte, C.: The Augmented Jump Chain, Adv.
Theory Sim., 4, 2000274,
https://doi.org/10.1002/adts.202000274, 2021. a
Simonnet, E., Ghil, M., and Dijkstra, H.: Homoclinic bifurcations in the
quasi-geostrophic double-gyre circulation, J. Marine Res., 63, 931–956,
https://doi.org/10.1357/002224005774464210, 2005. a
Simonnet, E., Rolland, J., and Bouchet, F.: Multistability and rare spontaneous
transitions in barotropic β-plane turbulence, J. Atmos. Sci., 78, 1889–1911, https://doi.org/10.1175/jas-d-20-0279.1, 2021. a
Stommel, H.: Thermohaline Convection with Two Stable Regimes of Flow, Tellus,
13, 224–230, https://doi.org/10.1111/j.2153-3490.1961.tb00079.x, 1961. a
Strahan, J., Antoszewski, A., Lorpaiboon, C., Vani, B. P., Weare, J., and
Dinner, A. R.: Long-Time-Scale Predictions from Short-Trajectory Data: A
Benchmark Analysis of the Trp-Cage Miniprotein, J. Chem. Theor. Comput., 17, 2948–2963, https://doi.org/10.1021/acs.jctc.0c00933, 2021.
a
Tantet, A., van der Burgt, F. R., and Dijkstra, H. A.: An early warning
indicator for atmospheric blocking events using transfer operators, Chaos, 25, 036406,
https://doi.org/10.1063/1.4908174, 2015. a
Yiou, P.: AnaWEGE: a weather generator based on analogues of atmospheric circulation, Geosci. Model Dev., 7, 531–543, https://doi.org/10.5194/gmd-7-531-2014, 2014. a, b
Yiou, P. and Déandréis, C.: Stochastic ensemble climate forecast with an analogue model, Geosci. Model Dev., 12, 723–734, https://doi.org/10.5194/gmd-12-723-2019, 2019. a, b
Short summary
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.
Computing the probability of occurrence of rare events is relevant because of their high impact...
