Articles | Volume 16, issue 11
https://doi.org/10.5194/gmd-16-3123-2023
© 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/gmd-16-3123-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Review and perspective paper
| 
02 Jun 2023
Review and perspective paper |
| 02 Jun 2023
| 02 Jun 2023
Differentiable programming for Earth system modeling
Maximilian Gelbrecht
CORRESPONDING AUTHOR
Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany
Potsdam Institute for Climate Impact Research, Potsdam, Germany
Alistair White
Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany
Potsdam Institute for Climate Impact Research, Potsdam, Germany
Sebastian Bathiany
Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany
Potsdam Institute for Climate Impact Research, Potsdam, Germany
Niklas Boers
Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany
Potsdam Institute for Climate Impact Research, Potsdam, Germany
Department of Mathematics and Global Systems Institute, University of Exeter, Exeter, UK
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Lucas Ferreira Correa, Sebastian Bathiany, Yiannis Moustakis, and Julia Pongratz
EGUsphere, https://doi.org/10.5194/egusphere-2026-4899, https://doi.org/10.5194/egusphere-2026-4899, 2026
This preprint is open for discussion and under review for Earth System Dynamics (ESD).
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Moisture recycling in the Amazon provides water essential for forest survival, but external pressures threaten this self-sustaining system. Using Earth System Model simulations, we analyzed hydroclimatic stress from deforestation and global warming. We found that 25 % deforestation can significantly stress over 70 % of the forest, increasing to 89 % when combined with 2 °C warming. Our findings show that forest loss and climate change can reinforce each other, raising the risk of forest dieback.
This article is included in the Encyclopedia of Geosciences
Colin Jones, Isaline Bossert, Donovan P. Dennis, Hazel A. Jeffery, Chris D. Jones, Torben Koenigk, Sina Loriani, Benjamin Sanderson, Roland Séférian, Klaus Wyser, Shuting Yang, Manabu Abe, Sebastian Bathiany, Pascale Braconnot, Victor Brovkin, Friedrich A. Burger, Patrica Cadule, Frederic S. Castruccio, Gokhan Danabasoglu, Andrea Dittus, Jonathan F. Donges, Friederike Fröb, Thomas L. Frölicher, Goran Georgievski, Chuncheng Guo, Aixue Hu, Peter Lawrence, Paul Lerner, José Licón-Saláiz, Bette Otto-Bliesner, Anastasia Romanou, Elena Shevliakova, Yona Silvy, Didier Swingedouw, Jerry Tjiputra, Jeremy Walton, Andy Wiltshire, Ricarda Winkelmann, Richard Wood, Tokuta Yokohata, and Tilo Ziehn
Geosci. Model Dev., 19, 6941–6966, https://doi.org/10.5194/gmd-19-6941-2026, https://doi.org/10.5194/gmd-19-6941-2026, 2026
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We introduce a new Earth system model experiment protocol to help researchers understand how Earth might respond to positive, zero, and negative carbon emissions. This protocol enables different models to be compared following similar warming and cooling rates. Researchers use the models to explore how the Earth reacts to different climate futures, including the risk of tipping points being exceeded and whether changes can be reversed. The results will support improved long-term climate policy.
This article is included in the Encyclopedia of Geosciences
Michael Aich, Philipp Hess, Baoxiang Pan, Sebastian Bathiany, Yu Huang, and Niklas Boers
Geosci. Model Dev., 19, 1791–1808, https://doi.org/10.5194/gmd-19-1791-2026, https://doi.org/10.5194/gmd-19-1791-2026, 2026
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Accurately simulating rainfall is essential to understand the impacts of climate change, especially extreme events such as floods and droughts. Climate models simulate the atmosphere at a coarse resolution and often misrepresent precipitation, leading to biased and overly smooth fields. We improve the precipitation using a machine learning model that is data-efficient, preserves key climate signals such as trends and variability, and significantly improves the representation of extreme events.
This article is included in the Encyclopedia of Geosciences
Clara Hummel, Niklas Boers, and Martin Rypdal
Earth Syst. Dynam., 16, 2035–2062, https://doi.org/10.5194/esd-16-2035-2025, https://doi.org/10.5194/esd-16-2035-2025, 2025
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We revisit early warning signals (EWS) for past abrupt climate changes known as Dansgaard-Oeschger (DO) events. Using advanced statistical methods, we find fewer significant EWS than previously reported. While some signals appear consistent across Greenland ice core records, they are not enough to identify the still unknown mechanisms behind DO events. This study highlights the complexity of predicting climate changes and urges caution in interpreting (paleo-)climate data.
This article is included in the Encyclopedia of Geosciences
Takahito Mitsui, Peter Ditlevsen, Niklas Boers, and Michel Crucifix
Earth Syst. Dynam., 16, 1569–1584, https://doi.org/10.5194/esd-16-1569-2025, https://doi.org/10.5194/esd-16-1569-2025, 2025
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The late Pleistocene glacial cycles are dominated by a 100-kyr periodicity, rather than other major astronomical periods like 19, 23, 41, or 400 kyr. Various models propose distinct mechanisms to explain this, but their diversity may obscure the key factor behind the 100-kyr periodicity. We propose a timescale-matching hypothesis, suggesting that the ice-sheet climate system responds to astronomical forcing at ∼100 kyr because its intrinsic timescale is closer to 100 kyr than to other periods.
This article is included in the Encyclopedia of Geosciences
Ricarda Winkelmann, Donovan P. Dennis, Jonathan F. Donges, Sina Loriani, Ann Kristin Klose, Jesse F. Abrams, Jorge Alvarez-Solas, Torsten Albrecht, David Armstrong McKay, Sebastian Bathiany, Javier Blasco Navarro, Victor Brovkin, Eleanor Burke, Gokhan Danabasoglu, Reik V. Donner, Markus Drüke, Goran Georgievski, Heiko Goelzer, Anna B. Harper, Gabriele Hegerl, Marina Hirota, Aixue Hu, Laura C. Jackson, Colin Jones, Hyungjun Kim, Torben Koenigk, Peter Lawrence, Timothy M. Lenton, Hannah Liddy, José Licón-Saláiz, Maxence Menthon, Marisa Montoya, Jan Nitzbon, Sophie Nowicki, Bette Otto-Bliesner, Francesco Pausata, Stefan Rahmstorf, Karoline Ramin, Alexander Robinson, Johan Rockström, Anastasia Romanou, Boris Sakschewski, Christina Schädel, Steven Sherwood, Robin S. Smith, Norman J. Steinert, Didier Swingedouw, Matteo Willeit, Wilbert Weijer, Richard Wood, Klaus Wyser, and Shuting Yang
EGUsphere, https://doi.org/10.5194/egusphere-2025-1899, https://doi.org/10.5194/egusphere-2025-1899, 2025
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The Tipping Points Modelling Intercomparison Project (TIPMIP) is an international collaborative effort to systematically assess tipping point risks in the Earth system using state-of-the-art coupled and stand-alone domain models. TIPMIP will provide a first global atlas of potential tipping dynamics, respective critical thresholds and key uncertainties, generating an important building block towards a comprehensive scientific basis for policy- and decision-making.
This article is included in the Encyclopedia of Geosciences
Nils Bochow, Anna Poltronieri, and Niklas Boers
The Cryosphere, 18, 5825–5863, https://doi.org/10.5194/tc-18-5825-2024, https://doi.org/10.5194/tc-18-5825-2024, 2024
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Using the latest climate models, we update the understanding of how the Greenland ice sheet responds to climate changes. We found that precipitation and temperature changes in Greenland vary across different regions. Our findings suggest that using uniform estimates for temperature and precipitation for modelling the response of the ice sheet can overestimate ice loss in Greenland. Therefore, this study highlights the need for spatially resolved data in predicting the ice sheet's future.
This article is included in the Encyclopedia of Geosciences
Vasilis Dakos, Chris A. Boulton, Joshua E. Buxton, Jesse F. Abrams, Beatriz Arellano-Nava, David I. Armstrong McKay, Sebastian Bathiany, Lana Blaschke, Niklas Boers, Daniel Dylewsky, Carlos López-Martínez, Isobel Parry, Paul Ritchie, Bregje van der Bolt, Larissa van der Laan, Els Weinans, and Sonia Kéfi
Earth Syst. Dynam., 15, 1117–1135, https://doi.org/10.5194/esd-15-1117-2024, https://doi.org/10.5194/esd-15-1117-2024, 2024
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Tipping points are abrupt, rapid, and sometimes irreversible changes, and numerous approaches have been proposed to detect them in advance. Such approaches have been termed early warning signals and represent a set of methods for identifying changes in the underlying behaviour of a system across time or space that might indicate an approaching tipping point. Here, we review the literature to explore where, how, and which early warnings have been used in real-world case studies so far.
This article is included in the Encyclopedia of Geosciences
Maya Ben-Yami, Lana Blaschke, Sebastian Bathiany, and Niklas Boers
EGUsphere, https://doi.org/10.5194/egusphere-2024-1106, https://doi.org/10.5194/egusphere-2024-1106, 2024
Preprint archived
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Recent work has used observations to find statistical signs that the Atlantic Meridional Overturning Circulation (AMOC) may be approaching a collapse. We find that in complex climate models in which the AMOC does not collapse before 2100, the statistical signs that are present in the observations are not found in the 1850–2014 equivalent model time series. This indicates that the observed statistical signs are not prone to false positives.
This article is included in the Encyclopedia of Geosciences
Takahito Mitsui and Niklas Boers
Clim. Past, 20, 683–699, https://doi.org/10.5194/cp-20-683-2024, https://doi.org/10.5194/cp-20-683-2024, 2024
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In general, the variance and short-lag autocorrelations of the fluctuations increase in a system approaching a critical transition. Using these indicators, we identify statistical precursor signals for the Dansgaard–Oeschger cooling events recorded in two climatic proxies of three Greenland ice core records. We then provide a dynamical systems theory that bridges the gap between observing statistical precursor signals and the physical precursor signs empirically known in paleoclimate research.
This article is included in the Encyclopedia of Geosciences
Nico Wunderling, Anna S. von der Heydt, Yevgeny Aksenov, Stephen Barker, Robbin Bastiaansen, Victor Brovkin, Maura Brunetti, Victor Couplet, Thomas Kleinen, Caroline H. Lear, Johannes Lohmann, Rosa Maria Roman-Cuesta, Sacha Sinet, Didier Swingedouw, Ricarda Winkelmann, Pallavi Anand, Jonathan Barichivich, Sebastian Bathiany, Mara Baudena, John T. Bruun, Cristiano M. Chiessi, Helen K. Coxall, David Docquier, Jonathan F. Donges, Swinda K. J. Falkena, Ann Kristin Klose, David Obura, Juan Rocha, Stefanie Rynders, Norman Julius Steinert, and Matteo Willeit
Earth Syst. Dynam., 15, 41–74, https://doi.org/10.5194/esd-15-41-2024, https://doi.org/10.5194/esd-15-41-2024, 2024
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This paper maps out the state-of-the-art literature on interactions between tipping elements relevant for current global warming pathways. We find indications that many of the interactions between tipping elements are destabilizing. This means that tipping cascades cannot be ruled out on centennial to millennial timescales at global warming levels between 1.5 and 2.0 °C or on shorter timescales if global warming surpasses 2.0 °C.
This article is included in the Encyclopedia of Geosciences
Takahito Mitsui, Matteo Willeit, and Niklas Boers
Earth Syst. Dynam., 14, 1277–1294, https://doi.org/10.5194/esd-14-1277-2023, https://doi.org/10.5194/esd-14-1277-2023, 2023
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The glacial–interglacial cycles of the Quaternary exhibit 41 kyr periodicity before the Mid-Pleistocene Transition (MPT) around 1.2–0.8 Myr ago and ~100 kyr periodicity after that. The mechanism generating these periodicities remains elusive. Through an analysis of an Earth system model of intermediate complexity, CLIMBER-2, we show that the dominant periodicities of glacial cycles can be explained from the viewpoint of synchronization theory.
This article is included in the Encyclopedia of Geosciences
Sara M. Vallejo-Bernal, Frederik Wolf, Niklas Boers, Dominik Traxl, Norbert Marwan, and Jürgen Kurths
Hydrol. Earth Syst. Sci., 27, 2645–2660, https://doi.org/10.5194/hess-27-2645-2023, https://doi.org/10.5194/hess-27-2645-2023, 2023
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Employing event synchronization and complex networks analysis, we reveal a cascade of heavy rainfall events, related to intense atmospheric rivers (ARs): heavy precipitation events (HPEs) in western North America (NA) that occur in the aftermath of land-falling ARs are synchronized with HPEs in central and eastern Canada with a delay of up to 12 d. Understanding the effects of ARs in the rainfall over NA will lead to better anticipating the evolution of the climate dynamics in the region.
This article is included in the Encyclopedia of Geosciences
Keno Riechers, Leonardo Rydin Gorjão, Forough Hassanibesheli, Pedro G. Lind, Dirk Witthaut, and Niklas Boers
Earth Syst. Dynam., 14, 593–607, https://doi.org/10.5194/esd-14-593-2023, https://doi.org/10.5194/esd-14-593-2023, 2023
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Paleoclimate proxy records show that the North Atlantic climate repeatedly transitioned between two regimes during the last glacial interval. This study investigates a bivariate proxy record from a Greenland ice core which reflects past Greenland temperatures and large-scale atmospheric conditions. We reconstruct the underlying deterministic drift by estimating first-order Kramers–Moyal coefficients and identify two separate stable states in agreement with the aforementioned climatic regimes.
This article is included in the Encyclopedia of Geosciences
Taylor Smith, Ruxandra-Maria Zotta, Chris A. Boulton, Timothy M. Lenton, Wouter Dorigo, and Niklas Boers
Earth Syst. Dynam., 14, 173–183, https://doi.org/10.5194/esd-14-173-2023, https://doi.org/10.5194/esd-14-173-2023, 2023
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Multi-instrument records with varying signal-to-noise ratios are becoming increasingly common as legacy sensors are upgraded, and data sets are modernized. Induced changes in higher-order statistics such as the autocorrelation and variance are not always well captured by cross-calibration schemes. Here we investigate using synthetic examples how strong resulting biases can be and how they can be avoided in order to make reliable statements about changes in the resilience of a system.
This article is included in the Encyclopedia of Geosciences
Eirik Myrvoll-Nilsen, Keno Riechers, Martin Wibe Rypdal, and Niklas Boers
Clim. Past, 18, 1275–1294, https://doi.org/10.5194/cp-18-1275-2022, https://doi.org/10.5194/cp-18-1275-2022, 2022
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In layer counted proxy records each measurement is accompanied by a timestamp typically measured by counting periodic layers. Knowledge of the uncertainty of this timestamp is important for a rigorous propagation to further analyses. By assuming a Bayesian regression model to the layer increments we express the dating uncertainty by the posterior distribution, from which chronologies can be sampled efficiently. We apply our framework to dating abrupt warming transitions during the last glacial.
This article is included in the Encyclopedia of Geosciences
Keno Riechers, Takahito Mitsui, Niklas Boers, and Michael Ghil
Clim. Past, 18, 863–893, https://doi.org/10.5194/cp-18-863-2022, https://doi.org/10.5194/cp-18-863-2022, 2022
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Building upon Milancovic's theory of orbital forcing, this paper reviews the interplay between intrinsic variability and external forcing in the emergence of glacial interglacial cycles. It provides the reader with historical background information and with basic theoretical concepts used in recent paleoclimate research. Moreover, it presents new results which confirm the reduced stability of glacial-cycle dynamics after the mid-Pleistocene transition.
This article is included in the Encyclopedia of Geosciences
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Editorial statement
This paper reviews the technique of differentiable programming in Earth System Modeling.
This paper reviews the technique of differentiable programming in Earth System Modeling.
Short summary
Differential programming is a technique that enables the automatic computation of derivatives of the output of models with respect to model parameters. Applying these techniques to Earth system modeling leverages the increasing availability of high-quality data to improve the models themselves. This can be done by either using calibration techniques that use gradient-based optimization or incorporating machine learning methods that can learn previously unresolved influences directly from data.
Differential programming is a technique that enables the automatic computation of derivatives of...
