Articles | Volume 19, issue 9
https://doi.org/10.5194/cp-19-1793-2023
© 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/cp-19-1793-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
13 Sep 2023
Research article |
| 13 Sep 2023
| 13 Sep 2023
Do phenomenological dynamical paleoclimate models have physical similarity with Nature? Seemingly, not all of them do
Mikhail Y. Verbitsky
CORRESPONDING AUTHOR
Gen5 Group, LLC, Newton, MA, USA
UCLouvain, Earth and Life Institute, Louvain-la-Neuve, Belgium
Michel Crucifix
UCLouvain, Earth and Life Institute, Louvain-la-Neuve, Belgium
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Mikhail Verbitsky
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Preprint archived
Short summary
Short summary
Phenomenological models may be impressive in reproducing empirical time series but this is not sufficient to claim physical similarity with nature until comparison of similarity parameters is performed. We illustrated such a process of diagnostics of physical similarity by comparing a phenomenological dynamical paleoclimate model with a more physically explicit dynamical model.
Mikhail Y. Verbitsky
Earth Syst. Dynam., 13, 879–884, https://doi.org/10.5194/esd-13-879-2022, https://doi.org/10.5194/esd-13-879-2022, 2022
Short summary
Short summary
Reconstruction and explanation of past climate evolution using proxy records is the essence of paleoclimatology. In this study, we use dimensional analysis of a dynamical model on orbital timescales to recognize theoretical limits of such forensic inquiries. Specifically, we demonstrate that major past events could have been produced by physically dissimilar processes making the task of paleo-record attribution to a particular phenomenon fundamentally difficult if not impossible.
Mikhail Verbitsky and Michael Mann
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2021-87, https://doi.org/10.5194/esd-2021-87, 2021
Revised manuscript not accepted
Short summary
Short summary
In this study, we highlight a component of global warming variability, a scaling law that is based purely on fundamental physical properties of the climate system.
Jonas Van Breedam, Philippe Huybrechts, and Michel Crucifix
Geosci. Model Dev., 14, 6373–6401, https://doi.org/10.5194/gmd-14-6373-2021, https://doi.org/10.5194/gmd-14-6373-2021, 2021
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Ice sheets are an important component of the climate system and interact with the atmosphere through albedo variations and changes in the surface height. On very long timescales, it is impossible to directly couple ice sheet models with climate models and other techniques have to be used. Here we present a novel coupling method between ice sheets and the atmosphere by making use of an emulator to simulate ice sheet–climate interactions for several million years.
Mikhail Y. Verbitsky and Michel Crucifix
Earth Syst. Dynam., 12, 63–67, https://doi.org/10.5194/esd-12-63-2021, https://doi.org/10.5194/esd-12-63-2021, 2021
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We demonstrate here that a single physical phenomenon, specifically, a naturally changing balance between intensities of temperature advection and diffusion in the viscous ice media, may influence the entire spectrum of the Pleistocene variability from orbital to millennial timescales.
Cited articles
Barenblatt, G. I.: Scaling, Cambridge University Press, Cambridge, ISBN 0521533945, 2003.
Berger, A. and Loutre, M. F.: Insolation values for the climate of the last
10 million years, Quaternary Sci. Rev., 10, 297–317, 1991.
Buckingham, E.: On physically similar systems; illustrations of the use of
dimensional equations, Phys. Rev., 4, 345–376, 1914.
Crucifix, M.: Why could ice ages be unpredictable?, Clim. Past, 9, 2253–2267, https://doi.org/10.5194/cp-9-2253-2013, 2013.
De Saedeleer B., Crucifix, M. and Wieczorek, S.: Is the astronomical forcing
a reliable and unique pacemaker for climate? A conceptual model study, Clim. Dynam., 40, 273–294, https://doi.org/10.1007/s00382-012-1316-1, 2013.
Ganopolski, A.: Toward Generalized Milankovitch Theory (GMT), Clim. Past Discuss. [preprint], https://doi.org/10.5194/cp-2023-57, in review, 2023.
Guckenheimer, J., Hoffman, K., and Weckesser, W.: The Forced van der Pol
Equation I: The Slow Flow and Its Bifurcations, SIAM J. Appl. Dynam. Syst., 2, 1–35, https://doi.org/10.1137/S1111111102404738, 2003.
Haken, H.: Information and self-organization: A macroscopic approach to
complex systems, Springer Science & Business Media, ISBN 3-540-66286-3, 2006.
Kaufmann, R. K., and Pretis, F.: Understanding glacial cycles: A multivariate disequilibrium approach, Quaternary Sci. Rev., 251, 106694, https://doi.org/10.1016/j.quascirev.2020.106694, 2021.
Leloup, G. and Paillard, D.: Influence of the choice of insolation forcing
on the results of a conceptual glacial cycle model, Clim. Past, 18, 547–558, https://doi.org/10.5194/cp-18-547-2022, 2022.
Paillard, D.: The timing of Pleistocene glaciations from a simple multiple-state climate model, Nature, 391, 378–381, 1998.
Saltzman, B.: Dynamical paleoclimatology: generalized theory of global
climate change, in: Vol. 80, Academic Press, San Diego, CA, ISBN 0126173311, 2002.
Saltzman, B. and Maasch, K. A.: A first-order global model of late Cenozoic
climatic change II. Further analysis based on a simplification of CO2
dynamics, Clim. Dynam., 5, 201–210, 1991.
Saltzman, B. and Verbitsky, M. Y.: Asthenospheric ice-load effects in a global dynamical-system model of the Pleistocene climate, Clim. Dynam., 8, 1–11, 1992.
Saltzman, B. and Verbitsky, M. Y.: Multiple instabilities and modes of glacial rhythmicity in the Plio-Pleistocene: a general theory of late Cenozoic climatic change, Clim. Dynam., 9, 1–15, 1993.
Saltzman, B. and Verbitsky, M.: Late Pleistocene climatic trajectory in the
phase space of global ice, ocean state, and CO2: Observations and theory, Paleoceanography, 9, 767–779, 1994.
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.
Tzedakis, P. C., Crucifix, M., Mitsui, T., and Wolff, E. W.: A simple rule to
determine which insolation cycles lead to interglacials, Nature, 542, 427–432, 2017.
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.
van der Pol, B.: On oscillation hysteresis in a triode generator with two
degrees of freedom, Philos. Mag. Ser., 6, 700—719, https://doi.org/10.1080/14786442208633932, 1922.
Verbitsky, M. Y.: Inarticulate past: similarity properties of the ice–climate system and their implications for paleo-record attribution, Earth Syst. Dynam., 13, 879–884, https://doi.org/10.5194/esd-13-879-2022, 2022.
Verbitsky, M. Y.: Supplementary code and data to Climate of the Past paper “Do phenomenological dynamical paleoclimate models have physical similarity with Nature? Seemingly, not all of them do” by Mikhail Y. Verbitsky and Michel Crucifix, Zenodo [code], https://doi.org/10.5281/zenodo.8329443, 2023.
Verbitsky, M. Y. and Chalikov, D. V.: Modelling of the Glaciers-Ocean-Atmosphere System, edited by: Monin, A. S., Gidrometeoizdat, Leningrad, 135 pp., 1986.
Verbitsky, M. Y. and Crucifix, M.: π-theorem generalization of the ice-age theory, Earth Syst. Dynam., 11, 281–289, https://doi.org/10.5194/esd-11-281-2020, 2020.
Verbitsky, M. Y. and Crucifix, M.: ESD Ideas: The Peclet number is a cornerstone of the orbital and millennial Pleistocene variability, Earth
Syst. Dynam., 12, 63–67, https://doi.org/10.5194/esd-12-63-2021, 2021.
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.
Short summary
Are phenomenological dynamical paleoclimate models physically similar to Nature? We demonstrated that though they may be very accurate in reproducing empirical time series, this is not sufficient to claim physical similarity with Nature until similarity parameters are considered. We suggest that the diagnostics of physical similarity should become a standard procedure before a phenomenological model can be utilized for interpretations of historical records or future predictions.
Are phenomenological dynamical paleoclimate models physically similar to Nature? We demonstrated...
