Articles | Volume 16, issue 3
https://doi.org/10.5194/esd-16-915-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esd-16-915-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A simple physical model for glacial cycles
Department of Sedimentary Geology and Environmental Change, Geosciences Institute (IGEO, CSIC-UCM), Madrid, Spain
Department of Earth Physics and Astrophysics, Complutense University of Madrid (UCM), Madrid, Spain
Jorge Alvarez-Solas
CORRESPONDING AUTHOR
Department of Sedimentary Geology and Environmental Change, Geosciences Institute (IGEO, CSIC-UCM), Madrid, Spain
Department of Earth Physics and Astrophysics, Complutense University of Madrid (UCM), Madrid, Spain
Jan Swierczek-Jereczek
Department of Earth Physics and Astrophysics, Complutense University of Madrid (UCM), Madrid, Spain
Daniel Moreno-Parada
Laboratoire de Glaciologie, Faculty of Sciences, Université Libre de Bruxelles (ULB), Laboratoire de Glaciologie, Brussels, Belgium
Alexander Robinson
Department of Polar Terrestrial Environmental Systems, Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Potsdam, Germany
Marisa Montoya
Department of Sedimentary Geology and Environmental Change, Geosciences Institute (IGEO, CSIC-UCM), Madrid, Spain
Department of Earth Physics and Astrophysics, Complutense University of Madrid (UCM), Madrid, Spain
Related authors
Sergio Pérez-Montero, Jorge Alvarez-Solas, Jan Swierczek-Jereczek, Daniel Moreno-Parada, Alexander Robinson, and Marisa Montoya
EGUsphere, https://doi.org/10.5194/egusphere-2025-2467, https://doi.org/10.5194/egusphere-2025-2467, 2025
This preprint is open for discussion and under review for Climate of the Past (CP).
Short summary
Short summary
Almost 3 million years ago, the planet began to experience a succession of cold and warm periods every 40,000 years. However, about 1 million years ago, they began to occur every 100,000 years. In this paper we explore how the change in the basal velocity of the ice sheets could have produced this change in behavior. On the other hand, we also see that in our model, decreasing in time the sensitivity of snowfall to temperature is also an effective mechanism with which to reproduce the records.
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
This preprint is open for discussion and under review for Earth System Dynamics (ESD).
Short summary
Short summary
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.
Sergio Pérez-Montero, Jorge Alvarez-Solas, Jan Swierczek-Jereczek, Daniel Moreno-Parada, Alexander Robinson, and Marisa Montoya
EGUsphere, https://doi.org/10.5194/egusphere-2025-2467, https://doi.org/10.5194/egusphere-2025-2467, 2025
This preprint is open for discussion and under review for Climate of the Past (CP).
Short summary
Short summary
Almost 3 million years ago, the planet began to experience a succession of cold and warm periods every 40,000 years. However, about 1 million years ago, they began to occur every 100,000 years. In this paper we explore how the change in the basal velocity of the ice sheets could have produced this change in behavior. On the other hand, we also see that in our model, decreasing in time the sensitivity of snowfall to temperature is also an effective mechanism with which to reproduce the records.
Antonio Juarez-Martinez, Javier Blasco, Alexander Robinson, Marisa Montoya, and Jorge Alvarez-Solas
The Cryosphere, 18, 4257–4283, https://doi.org/10.5194/tc-18-4257-2024, https://doi.org/10.5194/tc-18-4257-2024, 2024
Short summary
Short summary
We present sea level projections for Antarctica in the context of ISMIP6-2300 with several forcings but extend the simulations to 2500, showing that more than 3 m of sea level contribution could be reached. We also test the sensitivity on a basal melting parameter and determine the timing of the loss of ice in the west region. All the simulations were carried out with the ice sheet model Yelmo.
Therese Rieckh, Andreas Born, Alexander Robinson, Robert Law, and Gerrit Gülle
Geosci. Model Dev., 17, 6987–7000, https://doi.org/10.5194/gmd-17-6987-2024, https://doi.org/10.5194/gmd-17-6987-2024, 2024
Short summary
Short summary
We present the open-source model ELSA, which simulates the internal age structure of large ice sheets. It creates layers of snow accumulation at fixed times during the simulation, which are used to model the internal stratification of the ice sheet. Together with reconstructed isochrones from radiostratigraphy data, ELSA can be used to assess ice sheet models and to improve their parameterization. ELSA can be used coupled to an ice sheet model or forced with its output.
Daniel Moreno-Parada, Alexander Robinson, Marisa Montoya, and Jorge Alvarez-Solas
The Cryosphere, 18, 4215–4232, https://doi.org/10.5194/tc-18-4215-2024, https://doi.org/10.5194/tc-18-4215-2024, 2024
Short summary
Short summary
Our study tries to understand how the ice temperature evolves in a large mass as in the case of Antarctica. We found a relation that tells us the ice temperature at any point. These results are important because they also determine how the ice moves. In general, ice moves due to slow deformation (as if pouring honey from a jar). Nevertheless, in some regions the ice base warms enough and melts. The liquid water then serves as lubricant and the ice slides and its velocity increases rapidly.
Javier Blasco, Ilaria Tabone, Daniel Moreno-Parada, Alexander Robinson, Jorge Alvarez-Solas, Frank Pattyn, and Marisa Montoya
Clim. Past, 20, 1919–1938, https://doi.org/10.5194/cp-20-1919-2024, https://doi.org/10.5194/cp-20-1919-2024, 2024
Short summary
Short summary
In this study, we assess Antarctic tipping points which may had been crossed during the mid-Pliocene Warm Period. For this, we use data from the PlioMIP2 ensemble. Additionally, we investigate various sources of uncertainty, like ice dynamics and bedrock configuration. Our research significantly enhances our comprehension of Antarctica's response to a warming climate, shedding light on potential future tipping points that may be surpassed.
Jan Swierczek-Jereczek, Marisa Montoya, Konstantin Latychev, Alexander Robinson, Jorge Alvarez-Solas, and Jerry Mitrovica
Geosci. Model Dev., 17, 5263–5290, https://doi.org/10.5194/gmd-17-5263-2024, https://doi.org/10.5194/gmd-17-5263-2024, 2024
Short summary
Short summary
Ice sheets present a thickness of a few kilometres, leading to a vertical deformation of the crust of up to a kilometre. This process depends on properties of the solid Earth, which can be regionally very different. We propose a model that accounts for this often-ignored heterogeneity and run 100 000 simulation years in minutes. Thus, the evolution of ice sheets is modeled with better accuracy, which is critical for a good mitigation of climate change and, in particular, sea-level rise.
Daniel Moreno-Parada, Alexander Robinson, Marisa Montoya, and Jorge Alvarez-Solas
EGUsphere, https://doi.org/10.5194/egusphere-2023-2690, https://doi.org/10.5194/egusphere-2023-2690, 2023
Short summary
Short summary
We introduce Nix, an ice-sheet model designed for understanding how large masses of ice behave. Nix as a computer program that simulates the movement and temperature changes in ice sheets. Nix helps us study how ice sheets respond to changes in the atmosphere and ocean. We found that how fast ice melts under the shelves and how heat is exchanged, play a role in determining the future of ice sheets. Nix is a useful tool for learning more about how climate change affects polar ice sheets.
Daniel Moreno-Parada, Jorge Alvarez-Solas, Javier Blasco, Marisa Montoya, and Alexander Robinson
The Cryosphere, 17, 2139–2156, https://doi.org/10.5194/tc-17-2139-2023, https://doi.org/10.5194/tc-17-2139-2023, 2023
Short summary
Short summary
We have reconstructed the Laurentide Ice Sheet, located in North America during the Last Glacial Maximum (21 000 years ago). The absence of direct measurements raises a number of uncertainties. Here we study the impact of different physical laws that describe the friction as the ice slides over its base. We found that the Laurentide Ice Sheet is closest to prior reconstructions when the basal friction takes into account whether the base is frozen or thawed during its motion.
Matteo Willeit, Andrey Ganopolski, Alexander Robinson, and Neil R. Edwards
Geosci. Model Dev., 15, 5905–5948, https://doi.org/10.5194/gmd-15-5905-2022, https://doi.org/10.5194/gmd-15-5905-2022, 2022
Short summary
Short summary
In this paper we present the climate component of the newly developed fast Earth system model CLIMBER-X. It has a horizontal resolution of 5°x5° and is designed to simulate the evolution of the Earth system on temporal scales ranging from decades to >100 000 years. CLIMBER-X is available as open-source code and is expected to be a useful tool for studying past climate changes and for the investigation of the long-term future evolution of the climate.
Alexander Robinson, Daniel Goldberg, and William H. Lipscomb
The Cryosphere, 16, 689–709, https://doi.org/10.5194/tc-16-689-2022, https://doi.org/10.5194/tc-16-689-2022, 2022
Short summary
Short summary
Here we investigate the numerical stability of several commonly used methods in order to determine which of them are capable of resolving the complex physics of the ice flow and are also computationally efficient. We find that the so-called DIVA solver outperforms the others. Its representation of the physics is consistent with more complex methods, while it remains computationally efficient at high resolution.
Andreas Born and Alexander Robinson
The Cryosphere, 15, 4539–4556, https://doi.org/10.5194/tc-15-4539-2021, https://doi.org/10.5194/tc-15-4539-2021, 2021
Short summary
Short summary
Ice penetrating radar reflections from the Greenland ice sheet are the best available record of past accumulation and how these layers have been deformed over time by the flow of ice. Direct simulations of this archive hold great promise for improving our models and for uncovering details of ice sheet dynamics that neither models nor data could achieve alone. We present the first three-dimensional ice sheet model that explicitly simulates individual layers of accumulation and how they deform.
Javier Blasco, Jorge Alvarez-Solas, Alexander Robinson, and Marisa Montoya
The Cryosphere, 15, 215–231, https://doi.org/10.5194/tc-15-215-2021, https://doi.org/10.5194/tc-15-215-2021, 2021
Short summary
Short summary
During the Last Glacial Maximum the Antarctic Ice Sheet was larger and more extended than at present. However, neither its exact position nor the total ice volume are well constrained. Here we investigate how the different climatic boundary conditions, as well as basal friction configurations, affect the size and extent of the Antarctic Ice Sheet and discuss its potential implications.
Alexander Robinson, Jorge Alvarez-Solas, Marisa Montoya, Heiko Goelzer, Ralf Greve, and Catherine Ritz
Geosci. Model Dev., 13, 2805–2823, https://doi.org/10.5194/gmd-13-2805-2020, https://doi.org/10.5194/gmd-13-2805-2020, 2020
Short summary
Short summary
Here we describe Yelmo v1.0, an intuitive and state-of-the-art hybrid ice sheet model. The model design and physics are described, and benchmark simulations are provided to validate its performance. Yelmo is a versatile ice sheet model that can be applied to a wide variety of problems.
Jorge Alvarez-Solas, Marisa Montoya, and Alexander Robinson
Clim. Past Discuss., https://doi.org/10.5194/cp-2019-96, https://doi.org/10.5194/cp-2019-96, 2019
Publication in CP not foreseen
Short summary
Short summary
Modelling the past abrupt climate changes often resorts to the use of freshwater flux (FWF) in the North Atlantic as an effective method to cause reorganizations of the Atlantic Meridional Overturning Circulation. This procedure has allowed to reproduce the timing of the events. However, the required FWF is inconsistent with reconstructions. Conversely, using a forcing derived from the sea-level record results in a poor fit with the data, highlighting the need of exploring other mechanisms.
Ilaria Tabone, Alexander Robinson, Jorge Alvarez-Solas, and Marisa Montoya
The Cryosphere, 13, 1911–1923, https://doi.org/10.5194/tc-13-1911-2019, https://doi.org/10.5194/tc-13-1911-2019, 2019
Short summary
Short summary
Recent reconstructions show that the North East Greenland Ice Stream (NEGIS) retreated away from its present-day position by 20–40 km during MIS-3. Atmospheric and external forcings were proposed as potential causes of this retreat, but the role of the ocean was not considered. Here, using a 3-D ice-sheet model, we suggest that oceanic warming is sufficient to induce a retreat of the NEGIS margin of many tens of kilometres during MIS-3, helping to explain this conundrum.
Jorge Alvarez-Solas, Rubén Banderas, Alexander Robinson, and Marisa Montoya
Clim. Past, 15, 957–979, https://doi.org/10.5194/cp-15-957-2019, https://doi.org/10.5194/cp-15-957-2019, 2019
Short summary
Short summary
The last glacial period was marked by the existence of of abrupt climatic changes; it is generally accepted that the presence of ice sheets played an important role in their occurrence. While an important effort has been made to investigate the dynamics and evolution of the Laurentide ice sheet during this period, the Eurasian ice sheet (EIS) has not received much attention. Here we investigate the response of the EIS to millennial-scale climate variability using a hybrid 3-D ice-sheet model.
Ilaria Tabone, Alexander Robinson, Jorge Alvarez-Solas, and Marisa Montoya
Clim. Past, 15, 593–609, https://doi.org/10.5194/cp-15-593-2019, https://doi.org/10.5194/cp-15-593-2019, 2019
Short summary
Short summary
By using a 3-D hybrid ice-sheet–shelf model, we investigate the impact of millennial-scale oceanic variability on the Greenland Ice Sheet (GrIS) evolution during the last glacial period (LGP). We show that the GrIS may have strongly reacted to oceanic temperature fluctuations associated with Dansgaard–Oeschger cycles, contributing to sea-level variations of more than 1 m. Our results open the chance for a non-negligible role of the GrIS in millennial-scale oceanic reorganisations during the LGP.
Javier Blasco, Ilaria Tabone, Jorge Alvarez-Solas, Alexander Robinson, and Marisa Montoya
Clim. Past, 15, 121–133, https://doi.org/10.5194/cp-15-121-2019, https://doi.org/10.5194/cp-15-121-2019, 2019
Short summary
Short summary
The LGP is a period punctuated by the presence of several abrupt climate events and sea-level variations of up to 20 m at millennial timescales. The origin of those fluctuations is attributed to NH paleo ice sheets, but a contribution from the AIS cannot be excluded. Here, for the first time, we investigate the response of the AIS to millennial climate variability using an ice sheet–shelf model. We shows that the AIS produces substantial sea-level rises and grounding line migrations.
Rubén Banderas, Jorge Alvarez-Solas, Alexander Robinson, and Marisa Montoya
Geosci. Model Dev., 11, 2299–2314, https://doi.org/10.5194/gmd-11-2299-2018, https://doi.org/10.5194/gmd-11-2299-2018, 2018
Short summary
Short summary
Here we present a new approach to force ice-sheet models offline, which accounts for a more realistic treatment of millennial-scale climate variability as compared to the existing methods. Our results reveal that an incorrect representation of the characteristic pattern of millennial-scale climate variability within the climate forcing not only affects NH ice-volume variations at millennial timescales but has consequences for glacial–interglacial ice-volume changes too.
Ilaria Tabone, Javier Blasco, Alexander Robinson, Jorge Alvarez-Solas, and Marisa Montoya
Clim. Past, 14, 455–472, https://doi.org/10.5194/cp-14-455-2018, https://doi.org/10.5194/cp-14-455-2018, 2018
Short summary
Short summary
The response of the Greenland Ice Sheet (GrIS) to palaeo-oceanic changes on a glacial–interglacial timescale is studied from a modelling perspective. A 3-D hybrid ice-sheet–shelf model which includes a parameterization of the basal melting rate at the GrIS marine margins is used. The results show that the oceanic forcing plays a key role in the GrIS evolution, not only by controlling the ice retreat during the deglaciation but also by driving the ice expansion in glacial periods.
Jorge Alvarez-Solas, Rubén Banderas, Alexander Robinson, and Marisa Montoya
Clim. Past Discuss., https://doi.org/10.5194/cp-2017-143, https://doi.org/10.5194/cp-2017-143, 2017
Revised manuscript not accepted
Short summary
Short summary
The last glacial period was marked by the existence of of abrupt climatic changes. It is generally accepted that the presence of ice sheets played an
important role in their occurrence. While an important effort has been made to investigate the dynamics and evolution of the Laurentide Ice Sheet during this period, the Eurasian Ice Sheet (EIS) has not received much attention. Here we investigate the response of the EIS to millennial-scale climate variability. We use a hybrid 3D ice-sheet model.
Mario Krapp, Alexander Robinson, and Andrey Ganopolski
The Cryosphere, 11, 1519–1535, https://doi.org/10.5194/tc-11-1519-2017, https://doi.org/10.5194/tc-11-1519-2017, 2017
Short summary
Short summary
We present the snowpack model SEMIC. It calculates snow height, surface temperature, surface albedo, and the surface mass balance of snow- and ice-covered surfaces while using meteorological data as input. In this paper we describe how SEMIC works and how well it compares with snowpack data of a more sophisticated regional climate model applied to the Greenland ice sheet. Because of its simplicity and efficiency, SEMIC can be used as a coupling interface between atmospheric and ice sheet models.
A. Robinson and M. Perrette
Geosci. Model Dev., 8, 1877–1883, https://doi.org/10.5194/gmd-8-1877-2015, https://doi.org/10.5194/gmd-8-1877-2015, 2015
Short summary
Short summary
Here we present a concise interface to the NetCDF library designed to simplify reading and writing tasks of up to 6-D arrays in Fortran programs.
R. Calov, A. Robinson, M. Perrette, and A. Ganopolski
The Cryosphere, 9, 179–196, https://doi.org/10.5194/tc-9-179-2015, https://doi.org/10.5194/tc-9-179-2015, 2015
Short summary
Short summary
Ice discharge into the ocean from outlet glaciers is an important
component of mass loss of the Greenland ice sheet. Here, we present a
simple parameterization of ice discharge for coarse resolution ice
sheet models, suitable for large ensembles or long-term palaeo
simulations. This parameterization reproduces in a good approximation
the present-day ice discharge compared with estimates, and the
simulation of the present-day ice sheet elevation is considerably
improved.
A. Robinson and H. Goelzer
The Cryosphere, 8, 1419–1428, https://doi.org/10.5194/tc-8-1419-2014, https://doi.org/10.5194/tc-8-1419-2014, 2014
Cited articles
Abe-Ouchi, A., Saito, F., Kawamura, K., Raymo, M. E., Okuno, J., Takahashi, K., and Blatter, H.: Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume, Nature, 500, 190–193, https://doi.org/10.1038/nature12374, 2013. a, b, c, d
Adhémar, J.: Révolution des mers, Déluges périodiques. Première édition: Carilian-Goeury et V, Dalmont, Paris. Seconde édition: Lacroix-Comon, Hachette et Cie, Dalmont et Dunod, Paris, 1842. a
Agassiz, L.: Études sur les glaciers, Neuchâtel, Aux frais de l'auteur, 368 pp., 1840. a
Barker, S., Knorr, G., Edwards, R. L., Parrenin, F., Putnam, A. E., Skinner, L. C., Wolff, E., and Ziegler, M.: 800,000 years of abrupt climate variability, Science, 334, 347–351, https://doi.org/10.1126/science.1203580, 2011. a
Benn, D. I., Fowler, A. C., Hewitt, I., and Sevestre, H.: A general theory of glacier surges, J. Glaciol., 65, 701–716, https://doi.org/10.1017/jog.2019.62, 2019. a, b, c
Berends, C. J., Köhler, P., Lourens, L. J., and van de Wal, R. S. W.: On the Cause of the Mid-Pleistocene Transition, Rev. Geophys., 59, e2020RG000727, https://doi.org/10.1029/2020RG000727, 2021a. a, b, c, d
Berends, C. J., de Boer, B., and van de Wal, R. S. W.: Reconstructing the evolution of ice sheets, sea level, and atmospheric CO2 during the past 3.6 million years, Clim. Past, 17, 361–377, https://doi.org/10.5194/cp-17-361-2021, 2021b. a
Berger, A.: Milankovitch theory and climate, Rev. Geophys., 26, 624–657, https://doi.org/10.1029/RG026i004p00624, 1988. a, b
Bintanja, R. and Van de Wal, R.: North American ice-sheet dynamics and the onset of 100,000-year glacial cycles, Nature, 454, 869–872, https://doi.org/10.1038/nature07158, 2008. a
Braithwaite, R. J.: Regional modelling of ablation in West Greenland, Rapport Grønlands Geologiske Undersøgelse, 98, 1–20, https://doi.org/10.34194/rapggu.v98.7664, 1980. a
Broecker, W. S. and Van Donk, J.: Insolation changes, ice volumes, and the O18 record in deep-sea cores, Rev. Geophys., 8, 169–198, https://doi.org/10.1029/RG008i001p00169, 1970. a
Charbit, S., Paillard, D., and Ramstein, G.: Amount of CO2 emissions irreversibly leading to the total melting of Greenland, Geophys. Res. Lett., 35, L12503, https://doi.org/10.1029/2008GL033472, 2008. a
Clark, P. U. and Pollard, D.: Origin of the middle Pleistocene transition by ice sheet erosion of regolith, Paleoceanography, 13, 1–9, https://doi.org/10.1029/97PA02660, 1998. a, b
Clark, P. U., Archer, D., Pollard, D., Blum, J. D., Rial, J. A., Brovkin, V., Mix, A. C., Pisias, N. G., and Roy, M.: The middle Pleistocene transition: characteristics, mechanisms, and implications for long-term changes in atmospheric pCO2, Quaternary Sci. Rev., 25, 3150–3184, https://doi.org/10.1016/j.quascirev.2006.07.008, 2006. a
Cogley, J. G.: Area of the ocean, Mar. Geod., 35, 379–388, https://doi.org/10.1080/01490419.2012.709476, 2012. a
Cuffey, K. M. and Marshall, S. J.: Substantial contribution to sea-level rise during the last interglacial from the Greenland ice sheet, Nature, 404, 591–594, https://doi.org/10.1038/35007053, 2000. a
Cuffey, K. M. and Paterson, W. S. B.: The physics of glaciers, Academic Press, https://doi.org/10.3189/002214311796405906, 2010. a, b
Esmark, J.: Bidrag til vor jordklodes historie, Magazin for Naturvidenskaberne, 2, 28–49, 1824. a
Esmark, J.: Remarks tending to explain the geological history of the Earth, The Edinburgh New Philosophical Journal, 2, 107–121, 1826. a
Garbe, J., Albrecht, T., Levermann, A., Donges, J. F., and Winkelmann, R.: The hysteresis of the Antarctic ice sheet, Nature, 585, 538–544, https://doi.org/10.1038/s41586-020-2727-5, 2020. a
Gildor, H. and Tziperman, E.: A sea ice climate switch mechanism for the 100-kyr glacial cycles, J. Geophys. Res.-Ocean., 106, 9117–9133, https://doi.org/10.1029/1999JC000120, 2001. a, b
Glen, J.: The flow law of ice: A discussion of the assumptions made in glacier theory, their experimental foundations and consequences, IASH Publ., 47, e183, 1958. a
Hodell, D. A., Crowhurst, S. J., Lourens, L., Margari, V., Nicolson, J., Rolfe, J. E., Skinner, L. C., Thomas, N. C., Tzedakis, P. C., Mleneck-Vautravers, M. J., and Wolff, E. W.: A 1.5-million-year record of orbital and millennial climate variability in the North Atlantic, Clim. Past, 19, 607–636, https://doi.org/10.5194/cp-19-607-2023, 2023. a
Huybrechts, P., Payne, T., and The EISMINT Intercomparison Group: The EISMINT benchmarks for testing ice-sheet models, Ann. Glaciol., 23, 1–12, https://doi.org/10.3189/S0260305500013197, 1996. a
Huybrechts, P., Gregory, J., Janssens, I., and Wild, M.: Modelling Antarctic and Greenland volume changes during the 20th and 21st centuries forced by GCM time slice integrations, Glob. Planet. Change, 42, 83–105, https://doi.org/10.1016/j.gloplacha.2003.11.011, 2004. a
Imbrie, J. Z., Imbrie-Moore, A., and Lisiecki, L. E.: A phase-space model for Pleistocene ice volume, Earth Planet. Sc. Lett., 307, 94–102, https://doi.org/10.1016/j.epsl.2011.04.018, 2011. a
Jóhannesson, T., Raymond, C., and Waddington, E.: Time–scale for adjustment of glaciers to changes in mass balance, J. Glaciol., 35, 355–369, https://doi.org/10.3189/S002214300000928X, 1989. a
Laskar, J., Robutel, P., Joutel, F., Gastineau, M., Correia, A. C., and Levrard, B.: A long-term numerical solution for the insolation quantities of the Earth, Astron. Astrophys., 428, 261–285, https://doi.org/10.1051/0004-6361:20041335, 2004. a, b, c
Le Meur, E. and Huybrechts, P.: A comparison of different ways of dealing with isostasy: examples from modelling the Antarctic ice sheet during the last glacial cycle, Ann. Glaciol., 23, 309–317, https://doi.org/10.3189/S0260305500013586, 1996. a
Legrain, E., Parrenin, F., and Capron, E.: A gradual change is more likely to have caused the Mid-Pleistocene Transition than an abrupt event, Commun. Earth Environ., 4, 90, https://doi.org/10.1038/s43247-023-00754-0, 2023. a
Lisiecki, L. E. and Raymo, M. E.: A Pliocene-Pleistocene stack of 57 globally distributed benthic δ18O records, Paleoceanography, 20, PA1003, https://doi.org/10.1029/2004PA001071, 2005. a, b
Lüthi, D., Le Floch, M., Bereiter, B., Blunier, T., Barnola, J.-M., Siegenthaler, U., Raynaud, D., Jouzel, J., Fischer, H., Kawamura, K., and Stocker, T. F.: High-resolution carbon dioxide concentration record 650,000–800,000 years before present, Nature, 453, 379–382, https://doi.org/10.1038/nature06949, 2008. a
Margold, M., Stokes, C. R., and Clark, C. D.: Ice streams in the Laurentide Ice Sheet: Identification, characteristics and comparison to modern ice sheets, Earth-Sci. Rev., 143, 117–146, https://doi.org/10.1016/j.earscirev.2015.01.011, 2015. a, b
Milankovitch, M.: Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitenproblem, Royal Serbian Academy Special Publication, 133, 1–633, 1941. a
Mitsui, T., Willeit, M., and Boers, N.: Synchronization phenomena observed in glacial–interglacial cycles simulated in an Earth system model of intermediate complexity, Earth Syst. Dynam., 14, 1277–1294, https://doi.org/10.5194/esd-14-1277-2023, 2023. a
Murphy, J. J.: The glacial climate and the polar ice-cap, Q. J. Geol. Soc., 32, 400–406, 1876. a
Myhre, G., Highwood, E. J., Shine, K. P., and Stordal, F.: New estimates of radiative forcing due to well mixed greenhouse gases, Geophys. Res. Lett., 25, 2715–2718, https://doi.org/10.1029/98GL01908, 1998. a
Nick, F. M., Vieli, A., Howat, I. M., and Joughin, I.: Large-scale changes in Greenland outlet glacier dynamics triggered at the terminus, Nat. Geosci., 2, 110–114, https://doi.org/10.1038/ngeo394, 2009. a, b
Nye, J. F.: The response of a glacier to changes in the rate of nourishment and wastage, Proc. Roy. Soc. Lond. Ser. A, 275, 87–112, 1963. a
Oerlemans, J.: Model experiments on the 100,000-yr glacial cycle, Nature, 287, 430–432, https://doi.org/10.1038/287430a0, 1980. a
Oerlemans, J.: A quasi-analytical ice-sheet model for climate studies, Nonlinear Proc. Geoph., 10, 441–452, https://doi.org/10.5194/npg-10-441-2003, 2003. a
Oerlemans, J.: Minimal glacier models, Igitur, Utrecht Publishing & Archiving Services, ISBN: 978-90-6701-022-1, 2008. a
Paillard, D.: The timing of Pleistocene glaciations from a simple multiple-state climate model, Nature, 391, 378–381, https://doi.org/10.1038/34891, 1998. a, b, c
Paillard, D.: Glacial cycles: toward a new paradigm, Rev. Geophys., 39, 325–346, https://doi.org/10.1029/2000RG000091, 2001. a
Paillard, D.: Quaternary glaciations: from observations to theories, Quaternary Sci. Rev., 107, 11–24, https://doi.org/10.1016/j.quascirev.2014.10.002, 2015. a, b
Paillard, D. and Parrenin, F.: The Antarctic ice sheet and the triggering of deglaciations, Earth Planet. Sc. Lett., 227, 263–271, https://doi.org/10.1016/j.epsl.2004.08.023, 2004. a, b
Pattyn, F.: Antarctic subglacial conditions inferred from a hybrid ice sheet/ice stream model, Earth Planet. Sc. Lett., 295, 451–461, https://doi.org/10.1016/j.epsl.2010.04.025, 2010. a
Payne, A. J., Vieli, A., Shepherd, A. P., Wingham, D. J., and Rignot, E.: Recent dramatic thinning of largest West Antarctic ice stream triggered by oceans, Geophys. Res. Lett., 31, L23401, https://doi.org/10.1029/2004GL021284, 2004. a, b
Pellicciotti, F., Brock, B., Strasser, U., Burlando, P., Funk, M., and Corripio, J.: An enhanced temperature-index glacier melt model including the shortwave radiation balance: development and testing for Haut Glacier d’Arolla, Switzerland, J. Glaciol., 51, 573–587, https://doi.org/10.3189/172756505781829124, 2005. a
Pérez-Montero, S.: sperezmont/Pacco.jl, v1.0.0-rc2.1 (v1.0.0-rc2.1), Zenodo [code], https://doi.org/10.5281/zenodo.14534680, 2024a. a
Pérez-Montero, S.: sperezmont/Perez-Montero-etal_2025_ESD, v1.0.0-rc2 (v1.0.0-rc2), Zenodo [data set and video], https://doi.org/10.5281/zenodo.14524609, 2024b. a, b
Pikovsky, A., Kurths, J., and Rosenblum, M.: Synchronization: a universal concept in nonlinear sciences, Cambridge University Press, ISBN 9780521533522, 2003. a
Pollard, D.: A simple ice sheet model yields realistic 100 kyr glacial cycles, Nature, 296, 334–338, https://doi.org/10.1038/296334a0, 1982. a
Reeh, N.: Parameterization of melt rate and surface temperature in the Greenland ice sheet, Polarforschung, 59, 113–128, 1991. a
Ritz, C., Fabre, A., and Letréguilly, A.: Sensitivity of a Greenland ice sheet model to ice flow and ablation parameters: consequences for the evolution through the last climatic cycle, Clim. Dynam., 13, 11–23, https://doi.org/10.1007/s003820050149, 1996. a
Robinson, A., Calov, R., and Ganopolski, A.: An efficient regional energy-moisture balance model for simulation of the Greenland Ice Sheet response to climate change, The Cryosphere, 4, 129–144, https://doi.org/10.5194/tc-4-129-2010, 2010. a, b
Robinson, A., Calov, R., and Ganopolski, A.: Multistability and critical thresholds of the Greenland ice sheet, Nat. Clim. Change, 2, 429–432, https://doi.org/10.1038/nclimate1449, 2012. a
Saltzman, B.: Dynamical paleoclimatology: generalized theory of global climate change, Chap. 9, Elsevier, ISBN: 0 12 617331 1, 2001. a
Spratt, R. M. and Lisiecki, L. E.: A Late Pleistocene sea level stack, Clim. Past, 12, 1079–1092, https://doi.org/10.5194/cp-12-1079-2016, 2016. a
Van Den Berg, J., van de Wal, R., and Oerlemans, H.: A mass balance model for the Eurasian Ice Sheet for the last 120,000 years, Glob. Planet. Change, 61, 194–208, https://doi.org/10.1016/j.gloplacha.2007.08.015, 2008. a
Verbitsky, M. Y. and Crucifix, M.: Do phenomenological dynamical paleoclimate models have physical similarity with Nature? Seemingly, not all of them do, Clim. Past, 19, 1793–1803, https://doi.org/10.5194/cp-19-1793-2023, 2023. a
Weertman, J.: Equilibrium profile of ice caps, J. Glaciol., 3, 953–964, 1961. a
Willeit, M. and Ganopolski, A.: The importance of snow albedo for ice sheet evolution over the last glacial cycle, Clim. Past, 14, 697–707, https://doi.org/10.5194/cp-14-697-2018, 2018. a, b, c
Willeit, M., Ganopolski, A., Calov, R., and Brovkin, V.: Mid-Pleistocene transition in glacial cycles explained by declining CO2 and regolith removal, Sci. Adv., 5, eaav7337, https://doi.org/10.1126/sciadv.aav7337, 2019. a, b, c, d
Yamamoto, M., Clemens, S. C., Seki, O., Tsuchiya, Y., Huang, Y., O’ishi, R., and Abe-Ouchi, A.: Increased interglacial atmospheric CO2 levels followed the mid-Pleistocene Transition, Nat. Geosci., 15, 307–313, https://doi.org/10.1038/s41561-022-00918-1, 2022. a
Short summary
The climate of the last 3 Myr has varied between cold and warm periods. Numerous independent mechanisms have been proposed to explain this; however, no effort has been made to study their competing effects. Here we present a simple but physically motivated model that includes these mechanisms in a modular way. We identify ice-sheet dynamics and lithosphere displacement as main triggers, but reproducing the climate records additionally requires the natural darkening of ice.
The climate of the last 3 Myr has varied between cold and warm periods. Numerous independent...
Altmetrics
Final-revised paper
Preprint