Articles | Volume 18, issue 3
https://doi.org/10.5194/cp-18-547-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/cp-18-547-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
25 Mar 2022
Research article |
| 25 Mar 2022
| 25 Mar 2022
Influence of the choice of insolation forcing on the results of a conceptual glacial cycle model
Gaëlle Leloup
CORRESPONDING AUTHOR
Agence Nationale pour la gestion des déchets radioactifs (ANDRA), 1 Rue Jean Monnet, 92290 Châtenay-Malabry, France
Laboratoire des Sciences du Climat et de l'Environnement, LSCE/IPSL, CEA-CNRS-UVSQ-Université Paris-Saclay, 91198 Gif-sur-Yvette, France
Didier Paillard
Laboratoire des Sciences du Climat et de l'Environnement, LSCE/IPSL, CEA-CNRS-UVSQ-Université Paris-Saclay, 91198 Gif-sur-Yvette, France
Related authors
Gaëlle Leloup and Didier Paillard
Earth Syst. Dynam., 14, 291–307, https://doi.org/10.5194/esd-14-291-2023, https://doi.org/10.5194/esd-14-291-2023, 2023
Short summary
Short summary
Records of past carbon isotopes exhibit oscillations. It is clear over very different time periods that oscillations of 400 kyr take place. Also, strong oscillations of approximately 8–9 Myr are seen over different time periods. While earlier modelling studies have been able to produce 400 kyr oscillations, none of them produced 8–9 Myr cycles. Here, we propose a simple model for the carbon cycle that is able to produce 8–9 Myr oscillations in the modelled carbon isotopes.
Jean-Baptiste Brenner, Aurélien Quiquet, Didier Roche, Didier Paillard, and Pradeebane Vaittinada Ayar
EGUsphere, https://doi.org/10.5194/egusphere-2025-3617, https://doi.org/10.5194/egusphere-2025-3617, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
Due to the limited spatial and temporal coverage of observations, global models are essential tools to study climate. However, long-term climate data at fine spatial scale are difficult to obtain because of elevated computational costs such algorithms involve. This paper presents a simple model based on the description of climate/topography interactions to generate local precipitation fields at low cost. The objective is to provide a flexible and easy to use method for paleoclimate studies.
Didier Paillard
EGUsphere, https://doi.org/10.5194/egusphere-2025-2885, https://doi.org/10.5194/egusphere-2025-2885, 2025
Short summary
Short summary
This paper presents classical and new mathematical formulas to compute various "flavors" of the insolation forcing used to interpret paleoclimatic series, or to simulate climate at different times. It provides a description of the usual concepts while insisting on the difficulties associated with them, like the definition of a calendar. Then it presents novel formulas to compute extrema of insolation for a given latitude. It thus presents a new open-source software package available online.
Quentin Pikeroen, Didier Paillard, and Karine Watrin
Geosci. Model Dev., 17, 3801–3814, https://doi.org/10.5194/gmd-17-3801-2024, https://doi.org/10.5194/gmd-17-3801-2024, 2024
Short summary
Short summary
All accurate climate models use equations with poorly defined parameters, where knobs for the parameters are turned to fit the observations. This process is called tuning. In this article, we use another paradigm. We use a thermodynamic hypothesis, the maximum entropy production, to compute temperatures, energy fluxes, and precipitation, where tuning is impossible. For now, the 1D vertical model is used for a tropical atmosphere. The correct order of magnitude of precipitation is computed.
Nathaelle Bouttes, Fanny Lhardy, Aurélien Quiquet, Didier Paillard, Hugues Goosse, and Didier M. Roche
Clim. Past, 19, 1027–1042, https://doi.org/10.5194/cp-19-1027-2023, https://doi.org/10.5194/cp-19-1027-2023, 2023
Short summary
Short summary
The last deglaciation is a period of large warming from 21 000 to 9000 years ago, concomitant with ice sheet melting. Here, we evaluate the impact of different ice sheet reconstructions and different processes linked to their changes. Changes in bathymetry and coastlines, although not often accounted for, cannot be neglected. Ice sheet melt results in freshwater into the ocean with large effects on ocean circulation, but the timing cannot explain the observed abrupt climate changes.
Gaëlle Leloup and Didier Paillard
Earth Syst. Dynam., 14, 291–307, https://doi.org/10.5194/esd-14-291-2023, https://doi.org/10.5194/esd-14-291-2023, 2023
Short summary
Short summary
Records of past carbon isotopes exhibit oscillations. It is clear over very different time periods that oscillations of 400 kyr take place. Also, strong oscillations of approximately 8–9 Myr are seen over different time periods. While earlier modelling studies have been able to produce 400 kyr oscillations, none of them produced 8–9 Myr cycles. Here, we propose a simple model for the carbon cycle that is able to produce 8–9 Myr oscillations in the modelled carbon isotopes.
Fanny Lhardy, Nathaëlle Bouttes, Didier M. Roche, Xavier Crosta, Claire Waelbroeck, and Didier Paillard
Clim. Past, 17, 1139–1159, https://doi.org/10.5194/cp-17-1139-2021, https://doi.org/10.5194/cp-17-1139-2021, 2021
Short summary
Short summary
Climate models struggle to simulate a LGM ocean circulation in agreement with paleotracer data. Using a set of simulations, we test the impact of boundary conditions and other modelling choices. Model–data comparisons of sea-surface temperatures and sea-ice cover support an overall cold Southern Ocean, with implications on the AMOC strength. Changes in implemented boundary conditions are not sufficient to simulate a shallower AMOC; other mechanisms to better represent convection are required.
Cited articles
Abe-Ouchi, A., Saito, F., Kawamura, K., Raymo, M., 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
Archer, D. and Ganopolski, A.: A movable trigger: Fossil fuel CO2 and the onset
of the next glaciation, Geochem. Geophy. Geosy., 6, Q05003,
https://doi.org/10.1029/2004GC000891, 2005. a, b
Ashkenazy, Y. and Tziperman, E.: Are the 41 kyr glacial oscillations a linear
response to Milankovitch forcing?, Quaternary Sci. Rev., 23, 1879–1890,
https://doi.org/10.1016/j.quascirev.2004.04.008, 2004. a
Berger, A.: Milankovitch, the father of paleoclimate modeling, Clim. Past, 17, 1727–1733, https://doi.org/10.5194/cp-17-1727-2021, 2021. a
Berger, A. and Loutre, M.-F.: Insolation values for the climate of the last 10
million years, Quaternary Sci. Rev., 10, 297–317,
https://doi.org/10.1016/0277-3791(91)90033-Q, 1991. a
Berger, A. and Loutre, M.-F.: Climate: An Exceptionally Long Interglacial
Ahead?, Science, 297, 1287–1288, https://doi.org/10.1126/science.1076120, 2002. a
Bintanja, R., van de Wal, R., and Oerlemans, J.: Modelled atmospheric
temperatures and global sea levels over the past million years, Nature, 437,
125–128, https://doi.org/10.1038/nature03975, 2005. a
Bouttes, N., Paillard, D., Roche, D. M., Waelbroeck, C., Kageyama, M., Lourantou, A., Michel, E., and Bopp, L.: Impact of oceanic processes on the carbon cycle during the last termination, Clim. Past, 8, 149–170, https://doi.org/10.5194/cp-8-149-2012, 2012. a
Calder, N.: Arithmetic of ice ages, Nature, 252, 216–218,
https://doi.org/10.1038/252216a0, 1974. a
Chappell, J. and Shackleton, N. J.: Oxygen isotopes and sea level, Nature, 324,
137–140, 1986. a
Clark, P. 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
Clark, P., Archer, D., Pollard, D., Blum, J. D., Rial, J., Brovkin, V., Mix,
A., Pisias, N., 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, b
Croll, J.: XIII. On the physical cause of the change of climate during
geological epochs, The London, Edinburgh, and Dublin Philosophical Magazine
and Journal of Science, 28, 121–137, https://doi.org/10.1080/14786446408643733, 1864. a, b
Elderfield, H., Ferretti, P., Greaves, M., Crowhurst, S., Mccave, I. N.,
Hodell, D., and Piotrowski, A. M.: Evolution of Ocean Temperature and Ice
Volume Through the Mid-Pleistocene Climate Transition, Science, 337, 704–709,
https://doi.org/10.1126/science.1221294, 2012. a
Gallée, H., Van Yperselb, J. P., Fichefet, T., Marsiat, I., Tricot, C., and
Berger, A.: Simulation of the last glacial cycle by a coupled, sectorially
averaged climate-ice sheet model: 2. Response to insolation and CO2
variations, J. Geophys. Res.-Atmos., 97, 15713–15740,
https://doi.org/10.1029/92JD01256, 1992. a
Ganopolski, A. and Calov, R.: The role of orbital forcing, carbon dioxide and regolith in 100 kyr glacial cycles, Clim. Past, 7, 1415–1425, https://doi.org/10.5194/cp-7-1415-2011, 2011. a, b
Gildor, H. and Tziperman, E.: Sea ice as the glacial cycles’ Climate switch:
role of seasonal and orbital forcing, Paleoceanography, 15, 605–615,
https://doi.org/10.1029/1999PA000461, 2000. a, b
Hays, J., Imbrie, J., and Shackleton, N. J.: Variations in the Earth's Orbit:
Pacemaker of the Ice Ages, Science, 194, 1121–1132,
https://doi.org/10.1126/science.194.4270.1121, 1976. a, b
Hönisch, B., Hemming, N. G., Archer, D., Siddall, M., and McManus, J. F.:
Atmospheric Carbon Dioxide Concentration Across the Mid-Pleistocene
Transition, Science, 324, 1551–1554, https://doi.org/10.1126/science.1171477, 2009. a
Huybers, P.: Combined obliquity and precession pacing of late Pleistocene
deglaciations, Nature, 480, 229–232, https://doi.org/10.1038/nature10626, 2011. a
Huybers, P. and Wunsch, C.: Obliquity pacing of the late Pleistocene glacial
terminations, Nature, 434, 491–494, https://doi.org/10.1038/nature03401, 2005. a
Imbrie, J. and Imbrie, J. Z.: Modeling the Climatic Response to Orbital
Variations, Science, 207, 943–953, https://doi.org/10.1126/science.207.4434.943, 1980. a, b, c
Jakob, K. A., Wilson, P. A., Pross, J., Ezard, T. H. G., Fiebig, J.,
Repschläger, J., and Friedrich, O.: A new sea-level record for the
Neogene/Quaternary boundary reveals transition to a more stable East
Antarctic Ice Sheet, P. Natl. Acad. Sci. USA, 117, 30980–30987,
https://doi.org/10.1073/pnas.2004209117, 2020. a
Jouzel, J., Masson-Delmotte, V., Cattani, O., Dreyfus, G., Falourd, S.,
Hoffmann, G., Minster, B., Nouet, J., Barnola, J., Chappellaz, J., Fischer,
H., Gallet, J.-C., Johnsen, S., Leuenberger, M., Loulergue, L., Lüthi, D.,
Oerter, H., Parrenin, F., Raisbeck, G., and Wolff, E.: Orbital and Millennial
Antarctic Climate Variability over the Past 800,000 Years, Science, 317,
793–796, https://doi.org/10.1126/science.1141038, 2007. a
Khodri, M., Leclainche, Y., Ramstein, G., Braconnot, P., Marti, O., and
Cortijo, E.: Simulating the amplification of orbital forcing by ocean
feedbacks in the last glaciation, Nature, 410, 570–574, 2001. a
Lambeck, K., Rouby, H., Purcell, A., Sun, Y., and Sambridge, M.: Sea level and
global ice volumes from the Last Glacial Maximum to the Holocene, P. Natl.
Acad. Sci. USA, 111, 15296–15303, https://doi.org/10.1073/pnas.1411762111, 2014. a
Laskar, J., Robutel, P., Joutel, F., Gastineau, M., Correia, A., and Levrard,
B.: A long-term numerical solution for the insolation quantities of the
Earth, Astron. Astrophys., 428, 261–285, 2004. a
Leloup, G.: Data and code for results and figures in Climate of the Past “Influence of the choice of insolation forcing on the results of a conceptual glacial cycle model”, Zenodo [code and data set], https://doi.org/10.5281/zenodo.6045532, 2022 a
Lisiecki, L. E.: Links between eccentricity forcing and the 100,000-year
glacial cycle, Nat. Geosci., 3, 349–352, https://doi.org/10.1038/ngeo828, 2010. a
Liu, Z., Cleaveland, L., and Herbert, T.: Early onset and origin of 100-kyr
cycles in Pleistocene tropical SST records, Earth Planet. Sci. Lett., 265,
703–715, https://doi.org/10.1016/j.epsl.2007.11.016, 2008. a
MacAyeal, D. R.: Irregular oscillations of the West Antarctic ice sheet,
Nature, 359, 29–32, https://doi.org/10.1038/359029a0, 1992. a
Marshall, S. J. and Clark, P. U.: Basal temperature evolution of North American
ice sheets and implications for the 100-kyr cycle, Geophys. Res. Lett.,
29, 67-1–67-4, https://doi.org/10.1029/2002GL015192, 2002. a
Milankovitch, M.: Kanon der Erdbestrahlung und seine Anwendung auf das
Eiszeitenproblem, Royal Serbian Academy Special Publication, 133, 1–633,
1941. a
Oerlemans, J.: Model experiments on the 100,000-yr glacial cycle, Nature, 287,
430–432, https://doi.org/10.1038/287430a0, 1980. a
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
Paillard, D.: The Plio-Pleistocene climatic evolution as a consequence of orbital forcing on the carbon cycle, Clim. Past, 13, 1259–1267, https://doi.org/10.5194/cp-13-1259-2017, 2017. a
Paillard, D. and Parrenin, F.: The Antarctic ice sheet and the triggering of
deglaciations, Earth Planet. Sci. Lett, 227, 263–271,
https://doi.org/10.1016/j.epsl.2004.08.023, 2004. a
Paillard, D., Labeyrie, L., and Yiou, P.: Macintosh Program performs
time-series analysis, Eos Transactions, AGU, 77, 379–379,
https://doi.org/10.1029/96EO00259, 1996. a
Peltier, W. R. and Marshall, S.: Coupled energy-balance/ice-sheet model
simulations of the glacial cycle: A possible connection between terminations
and terrigenous dust, J. Geophys. Res.-Atmos., 100, 14269–14289,
https://doi.org/10.1029/95JD00015, 1995. 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, b
Raymo, M.: The timing of major climate terminations, Paleoceanography, 12,
577–585, https://doi.org/10.1029/97PA01169, 1997. a, b, c
Raymo, M. E. and Nisancioglu, K. H.: The 41 kyr world: Milankovitch's other
unsolved mystery, Paleoceanography, 18, 1011, https://doi.org/10.1029/2002PA000791, 2003. a
Raymo, M. E., Kozdon, R., David, E., Lisiecki, L., and Ford, H. L.: The
accuracy of mid-Pliocene δ18O-based ice volume and sea level
reconstructions, Earth-Sci. Rev., 177, 291–302,
https://doi.org/10.1016/j.earscirev.2017.11.022, 2018. a
Reeh, N.: Parameterization of Melt Rate and Surface Temperature on the
Greenland Ice Sheet, Polarforschung, 59, 113–128, 1991. 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
Saltzman, B. and Sutera, A.: The Mid-Quaternary Climatic Transition as the Free
Response of a Three-Variable Dynamical Model, J. Atmos. Sci., 44, 236–241,
https://doi.org/10.1175/1520-0469(1987)044<0236:TMQCTA>2.0.CO;2,
1987. a
Saltzman, B., Hansen, A., and Maasch, K.: The Late Quaternary Glaciations as
the Response of a Three-Component Feedback System to Earth-Orbital Forcing,
J. Atmos. Sci., 41, 3380–3389,
https://doi.org/10.1175/1520-0469(1984)041<3380:TLQGAT>2.0.CO;2, 1984. a
Shackleton, N.: Oxygen Isotope Analyses and Pleistocene Temperatures
Re-assessed, Nature, 215, 15–17, https://doi.org/10.1038/215015a0, 1967. a, b
Shackleton, N. J. and Opdyke, N. D.: Oxygen isotope and palaeomagnetic
stratigraphy of Equatorial Pacific core V28-238: Oxygen isotope temperatures
and ice volumes on a 105 year and 106 year scale, Quaternary Res., 3, 39–55,
https://doi.org/10.1016/0033-5894(73)90052-5, 1973. a, b
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
Talento, S. and Ganopolski, A.: Reduced-complexity model for the impact of anthropogenic CO2 emissions on future glacial cycles, Earth Syst. Dynam., 12, 1275–1293, https://doi.org/10.5194/esd-12-1275-2021, 2021. a, b
Toggweiler, J. R.: Origin of the 100,000-year timescale in Antarctic
temperatures and atmospheric CO2, Paleoceanography, 23, PA2211,
https://doi.org/10.1029/2006PA001405, 2008. a
Tziperman, E. and Gildor, H.: On the mid-Pleistocene transition to 100-kyr
glacial cycles and the asymmetry between glaciation and deglaciation times,
Paleoceanography, 18, 1-1–1-8, https://doi.org/10.1029/2001pa000627, 2003. a
Tziperman, E., Raymo, M. E., Huybers, P., and Wunsch, C.: Consequences of
pacing the Pleistocene 100 kyr ice ages by nonlinear phase locking to
Milankovitch forcing, Paleoceanography, 21, PA4206, https://doi.org/10.1029/2005PA001241, 2006. 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, Global Planet. Change, 61,
194–208, https://doi.org/10.1016/j.gloplacha.2007.08.015, 2008. a
Verbitsky, M. Y., Crucifix, M., and Volobuev, D. M.: A theory of Pleistocene glacial rhythmicity, Earth Syst. Dynam., 9, 1025–1043, https://doi.org/10.5194/esd-9-1025-2018, 2018. a
Yan, Y., Bender, M. L., Brook, E. J., Clifford, H. M., Kemeny, P. C., Kurbatov,
A. V., Mackay, S., Mayewski, P. A., Ng, J., Severinghaus, J. P., and Higgins,
J. A.: Two-million-year-old snapshots of atmospheric gases from Antarctic
ice, Nature, 574, 663–666, https://doi.org/10.1038/s41586-019-1692-3, 2019. a
Short summary
Over the last 2.6 Myr, the Quaternary period has been marked by the alternation of extended and reduced Northern Hemisphere ice sheets, known as glacial-interglacial cycles. With a simple model, we are able to reproduce the main features of the ice volume evolution, like the switch of periodicity, from 41 kyr cycles to 100 kyr cycles, observed in the data after 1 Ma. The quality of the model-data agreement depending on the input insolation and period considered is discussed.
Over the last 2.6 Myr, the Quaternary period has been marked by the alternation of extended and...
