Articles | Volume 32, issue 2
https://doi.org/10.5194/npg-32-189-2025
© 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/npg-32-189-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Rate-induced transitions and noise-driven resilience in vegetation pattern dynamics
Lilian Vanderveken
CORRESPONDING AUTHOR
Earth and Life Institute, UCLouvain, Louvain-la-Neuve, Belgium
Michel Crucifix
Earth and Life Institute, UCLouvain, Louvain-la-Neuve, Belgium
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Lilian Vanderveken, Marina Martínez Montero, and Michel Crucifix
Nonlin. Processes Geophys., 30, 585–599, https://doi.org/10.5194/npg-30-585-2023, https://doi.org/10.5194/npg-30-585-2023, 2023
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In semi-arid regions, hydric stress affects plant growth. In these conditions, vegetation patterns develop and effectively allow for vegetation to persist under low water input. The formation of patterns and the transition between patterns can be studied with small models taking the form of dynamical systems. Our study produces a full map of stable and unstable solutions in a canonical vegetation model and shows how they determine the transitions between different patterns.
Justin Gérard, Alexandre Pohl, Loïc Sablon, Jarno Huygh, Anne-Christine Da Silva, and Michel Crucifix
EGUsphere, https://doi.org/10.5194/egusphere-2025-4238, https://doi.org/10.5194/egusphere-2025-4238, 2025
This preprint is open for discussion and under review for Climate of the Past (CP).
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We studied how changes in Earth’s orbit affected ocean oxygen during the Devonian, a time of repeated environmental crises and extinctions. Using computer simulations, we show that certain orbital cycles, especially eccentricity maxima, exacerbate oxygen loss in the oceans, while obliquity also played a key role at high latitudes. The results also help explain why records from different places show contrasting signals and provide new insight into how natural climate cycles can affect ocean life.
Loïc Sablon, Pierre Maffre, Yves Goddéris, Paul J. Valdes, Justin Gérard, Jarno J. C. Huygh, Anne-Christine Da Silva, and Michel Crucifix
EGUsphere, https://doi.org/10.5194/egusphere-2025-1696, https://doi.org/10.5194/egusphere-2025-1696, 2025
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We propose an innovative climate modelling framework that combines statistical methods with climate simulations to study Earth's environmental systems. The model captures how orbital changes and carbon dioxide levels influence climate atmospheric dynamics, offering a detailed and efficient way to explore long-term processes. This tool provides new opportunities to investigate Earth's climate history and its implications for future changes.
Victor Couplet, Marina Martínez Montero, and Michel Crucifix
Geosci. Model Dev., 18, 3081–3129, https://doi.org/10.5194/gmd-18-3081-2025, https://doi.org/10.5194/gmd-18-3081-2025, 2025
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We present SURFER v3.0, a simple climate model designed to estimate the impact of CO2 and CH4 emissions on global temperatures, sea levels, and ocean pH. We added new carbon cycle processes and calibrated the model to observations and results from more complex models, enabling use over timescales ranging from decades to millions of years. SURFER v3.0 is fast, transparent, and easy to use, making it an ideal tool for policy assessments and suitable for educational purposes.
Justin Gérard, Loïc Sablon, Jarno J. C. Huygh, Anne-Christine Da Silva, Alexandre Pohl, Christian Vérard, and Michel Crucifix
Clim. Past, 21, 239–260, https://doi.org/10.5194/cp-21-239-2025, https://doi.org/10.5194/cp-21-239-2025, 2025
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We used cGENIE, a climate model, to explore how changes in continental configuration, CO2 levels, and orbital configuration affected ocean oxygen levels during the Devonian period (419–359 million years ago). Key factors contributing to ocean anoxia were identified, highlighting the influence of continental configurations, atmospheric conditions, and orbital changes. Our findings offer new insights into the causes and prolonged durations of Devonian ocean anoxic events.
Takahito Mitsui, Peter Ditlevsen, Niklas Boers, and Michel Crucifix
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2024-39, https://doi.org/10.5194/esd-2024-39, 2024
Revised manuscript accepted for ESD
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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 time-scale 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.
Justin Gérard and Michel Crucifix
Earth Syst. Dynam., 15, 293–306, https://doi.org/10.5194/esd-15-293-2024, https://doi.org/10.5194/esd-15-293-2024, 2024
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We used cGENIE, a climate model, to investigate the Atlantic Meridional Overturning Circulation (AMOC) slowdown under a warming scenario. We apply a diagnostic that was used in a previous study (Levang and Schmitt, 2020) to separate the temperature from salinity contribution to this slowdown. We find that, in our model, the initial slowdown of the AMOC was driven by temperature and that salinity takes the lead for the termination of the circulation.
Jonas Van Breedam, Philippe Huybrechts, and Michel Crucifix
Clim. Past, 19, 2551–2568, https://doi.org/10.5194/cp-19-2551-2023, https://doi.org/10.5194/cp-19-2551-2023, 2023
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We investigated the different boundary conditions to allow ice sheet growth and ice sheet decline of the Antarctic ice sheet when it appeared ∼38–34 Myr ago. The thresholds for ice sheet growth and decline differ because of the different climatological conditions above an ice sheet (higher elevation and higher albedo) compared to a bare topography. We found that the ice–albedo feedback and the isostasy feedback respectively ease and delay the transition from a deglacial to glacial state.
Lilian Vanderveken, Marina Martínez Montero, and Michel Crucifix
Nonlin. Processes Geophys., 30, 585–599, https://doi.org/10.5194/npg-30-585-2023, https://doi.org/10.5194/npg-30-585-2023, 2023
Short summary
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In semi-arid regions, hydric stress affects plant growth. In these conditions, vegetation patterns develop and effectively allow for vegetation to persist under low water input. The formation of patterns and the transition between patterns can be studied with small models taking the form of dynamical systems. Our study produces a full map of stable and unstable solutions in a canonical vegetation model and shows how they determine the transitions between different patterns.
Mikhail Y. Verbitsky and Michel Crucifix
Clim. Past, 19, 1793–1803, https://doi.org/10.5194/cp-19-1793-2023, https://doi.org/10.5194/cp-19-1793-2023, 2023
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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.
Marina Martínez Montero, Michel Crucifix, Victor Couplet, Nuria Brede, and Nicola Botta
Geosci. Model Dev., 15, 8059–8084, https://doi.org/10.5194/gmd-15-8059-2022, https://doi.org/10.5194/gmd-15-8059-2022, 2022
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We present SURFER, a lightweight model that links CO2 emissions and geoengineering to ocean acidification and sea level rise from glaciers, ocean thermal expansion and Greenland and Antarctic ice sheets. The ice sheet module adequately describes the tipping points of both Greenland and Antarctica. SURFER is understandable, fast, accurate up to several thousands of years, capable of emulating results obtained by state of the art models and well suited for policy analyses.
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
Ashwin, P., Wieczorek, S., Vitolo, R., and Cox, P.: Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system, Philos. T. Roy. Soc. A, 370, 1166–1184, https://doi.org/10.1098/rsta.2011.0306, 2012. a
Bastiaansen, R. and Doelman, A.: The dynamics of disappearing pulses in a singularly perturbed reaction–diffusion system with parameters that vary in time and space, Physica D, 388, 45–72, https://doi.org/10.1016/j.physd.2018.09.003, 2019. a
Bastiaansen, R., Doelman, A., Eppinga, M. B., and Rietkerk, M.: The effect of climate change on the resilience of ecosystems with adaptive spatial pattern formation, Ecol. Lett., 23, 414–429, https://doi.org/10.1111/ele.13449, 2020. a, b, c
Chen, Y., Kolokolnikov, T., Tzou, J., and Gai, C.: Patterned vegetation, tipping points, and the rate of climate change, Eur. J. Appl. Math., 26, 945–958, https://doi.org/10.1017/S0956792515000261, 2015. a, b
Deblauwe, V., Barbier, N., Couteron, P., Lejeune, O., and Bogaert, J.: The global biogeography of semi-arid periodic vegetation patterns, Global Ecol. Biogeogr., 17, 715–723, https://doi.org/10.1111/j.1466-8238.2008.00413.x, 2008. a
Dijkstra, H. A.: Vegetation pattern formation in a semi-arid climate, Int. J. Bifurcat. Chaos., 21, 3497–3509, https://doi.org/10.1142/S0218127411030696, 2011. a
Gilad, E., von Hardenberg, J., Provenzale, A., Shachak, M., and Meron, E.: A mathematical model of plants as ecosystem engineers, J. Theor. Biol., 244, 680–691, https://doi.org/10.1016/j.jtbi.2006.08.006, 2007. a
Hastings, A., Abbott, K. C., Cuddington, K., Francis, T., Gellner, G., Lai, Y. C., Morozov, A., Petrovskii, S., Scranton, K., and Zeeman, M. L.: Transient phenomena in ecology, Science, 361, eaat6412, https://doi.org/10.1126/science.aat6412, 2018. a
Kéfi, S., Domínguez-García, V., Donohue, I., Fontaine, C., Thébault, E., and Dakos, V.: Advancing our understanding of ecological stability, Ecol. Lett., 22, 1349–1356, https://doi.org/10.1111/ele.13340, 2019. a, b
Klausmeier, C. A.: Regular and irregular patterns in semiarid vegetation, Science, 284, 1826–1828, https://doi.org/10.1126/science.284.5421.1826, 1999. a, b
Lefever, R. and Lejeune, O.: On the origin of tiger bush, B. Math. Biol., 59, 263–294, https://doi.org/10.1007/BF02462004, 1997. a
Meron, E.: Nonlinear Physics of Ecosystems, CRC Press, https://doi.org/10.1201/b18360, 2015. a
Morozov, A., Abbott, K., Cuddington, K., Francis, T., Gellner, G., Hastings, A., Lai, Y. C., Petrovskii, S., Scranton, K., and Zeeman, M. L.: Long transients in ecology: theory and applications, Phys. Life Rev., 32, 1–40, https://doi.org/10.1016/j.plrev.2019.09.004, 2020. a
Murray, J. D.: Mathematical Biology II: Spatial Models and Biomedical Applications, in: 3rd Edn., Springer, New York, NY, ISBN 978-1-4757-7870-0, https://doi.org/10.1007/b98869, 2003. a
Rietkerk, M. and van de Koppel, J.: Regular pattern formation in real ecosystems, Trends Ecol. Evol., 23, 169–175, https://doi.org/10.1016/j.tree.2007.10.013, 2008. a
Sherratt, J. A.: History-dependent patterns of whole ecosystems, Ecol. Complex., 14, 8–20, https://doi.org/10.1016/j.ecocom.2012.12.002, 2013. a
Siteur, K., Siero, E., Eppinga, M. B., Rademacher, J. D., Doelman, A., and Rietkerk, M.: Beyond turing: the response of patterned ecosystems to environmental change, Ecol. Complex., 20, 81–96, https://doi.org/10.1016/j.ecocom.2014.09.002, 2014. a, b
Siteur, K., Liu, Q.-X., Rottschäfer, V., van der Heide, T., Rietkerk, M., Doelman, A., Boström, C., and van de Koppel, J.: Phase-separation physics underlies new theory for the resilience of patchy ecosystems, P. Natl. Acad. Sci. USA, 120, 2017, https://doi.org/10.1073/pnas.2202683120, 2023. a
van de Koppel, J., Rietkerk, M., Dankers, N., and Herman, P. M.: Scale-dependent feedback and regular spatial patterns in young mussel beds, Am. Nat., 165, https://doi.org/10.1086/428362, 2005. a
Vanderveken, L.: Slvanderveken/Riet_Stoch: v1.0.0 (v1.0.0), Zenodo [code], https://doi.org/10.5281/zenodo.13739304, 2024. a
Vanderveken, L., Martínez Montero, M., and Crucifix, M.: Existence and influence of mixed states in a model of vegetation patterns, Nonlin. Processes Geophys., 30, 585–599, https://doi.org/10.5194/npg-30-585-2023, 2023. a, b, c
von Hardenberg, J., Meron, E., Shachak, M., and Zarmi, Y.: Diversity of vegetation patterns and desertification, Phys. Rev. Lett., 87, 198101-1–198101-4, https://doi.org/10.1103/PhysRevLett.87.198101, 2001. a
Zelnik, Y. R., Kinast, S., Yizhaq, H., Bel, G., and Meron, E.: Regime shifts in models of dryland vegetation, Philos. T. Roy. Soc. A, 371, 20120358, https://doi.org/10.1098/rsta.2012.0358, 2013. a, b
Short summary
Vegetation patterns in semi-arid regions arise from interactions between plants and environmental factors. This study uses a numerical model to explore how vegetation responds to changes in rainfall and random disturbances. We identify key timescales that influence resilience, showing that ecosystems rely on both stable and unstable states to adapt. These findings offer insights into the resilience mechanisms that help ecosystems maintain stability under environmental stress.
Vegetation patterns in semi-arid regions arise from interactions between plants and...