Articles | Volume 30, issue 4
https://doi.org/10.5194/npg-30-481-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/npg-30-481-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| Highlight paper
| 
03 Nov 2023
Research article | Highlight paper |
| 03 Nov 2023
| 03 Nov 2023
Rate-induced tipping in ecosystems and climate: the role of unstable states, basin boundaries and transient dynamics
Ulrike Feudel
CORRESPONDING AUTHOR
Institute for Chemistry and Biology for the Marine Environment, Carl von Ossietzky University Oldenburg, Oldenburg, Germany
Related authors
Alessandro Cotronei, Ulrike Feudel, and Angelika Humbert
EGUsphere, https://doi.org/10.5194/egusphere-2025-6334, https://doi.org/10.5194/egusphere-2025-6334, 2026
This preprint is open for discussion and under review for Earth System Dynamics (ESD).
Short summary
Short summary
We construct a mathematical model to describe the formation of lakes on the Greenland Ice Sheet across multiple years. The model represents the dynamics of ice, snow, and surface water, accounting for the influence of air temperature. Our results indicate that lakes can enhance ice melt by absorbing sunlight, thereby accelerating the loss of Greenland ice under realistic scenarios of temperature increase.
Ann Kristin Klose, Jonathan F. Donges, Ulrike Feudel, and Ricarda Winkelmann
Earth Syst. Dynam., 15, 635–652, https://doi.org/10.5194/esd-15-635-2024, https://doi.org/10.5194/esd-15-635-2024, 2024
Short summary
Short summary
We qualitatively study the long-term stability of the Greenland Ice Sheet and AMOC as tipping elements in the Earth system, which is largely unknown given their interaction in a positive–negative feedback loop. Depending on the timescales of ice loss and the position of the AMOC’s state relative to its critical threshold, we find distinct dynamic regimes of cascading tipping. These suggest that respecting safe rates of environmental change is necessary to mitigate potential domino effects.
Alessandro Cotronei, Ulrike Feudel, and Angelika Humbert
EGUsphere, https://doi.org/10.5194/egusphere-2025-6334, https://doi.org/10.5194/egusphere-2025-6334, 2026
This preprint is open for discussion and under review for Earth System Dynamics (ESD).
Short summary
Short summary
We construct a mathematical model to describe the formation of lakes on the Greenland Ice Sheet across multiple years. The model represents the dynamics of ice, snow, and surface water, accounting for the influence of air temperature. Our results indicate that lakes can enhance ice melt by absorbing sunlight, thereby accelerating the loss of Greenland ice under realistic scenarios of temperature increase.
Ann Kristin Klose, Jonathan F. Donges, Ulrike Feudel, and Ricarda Winkelmann
Earth Syst. Dynam., 15, 635–652, https://doi.org/10.5194/esd-15-635-2024, https://doi.org/10.5194/esd-15-635-2024, 2024
Short summary
Short summary
We qualitatively study the long-term stability of the Greenland Ice Sheet and AMOC as tipping elements in the Earth system, which is largely unknown given their interaction in a positive–negative feedback loop. Depending on the timescales of ice loss and the position of the AMOC’s state relative to its critical threshold, we find distinct dynamic regimes of cascading tipping. These suggest that respecting safe rates of environmental change is necessary to mitigate potential domino effects.
Cited articles
Alberti, T., Faranda, D., Lucarini, V., Donner, R., Dubrulle, B., and Daviaud, F.: Scale dependence of fractal dimension in deterministic and stochastic Lorenz-63 systems, Chaos, 33, 023144, https://doi.org/10.1063/5.0106053, 2023. a
Alligood, K. T., Sauer, T. D., and Yorke, J. A.: Chaos: An Introduction to Dynamical Systems, Springer, New York, https://doi.org/10.1007/b97589, 1992. a
Armstrong McKay, D. I., Staal, A., Abrams, J. F., Winkelmann, R., Sakschewski, B., Loriani, S., Fetzner, I., Cornell, S. E., Rockström, J., and Lenton, T. M.: Exceeding 1.5C global warming could trigger multiple climate tipping points, Science, 1171, eabn7950, https://doi.org/10.1126/science.abn7950, 2022. a
Ashwin, P., Perryman, C., and Wieczorek, S.: Parameter shifts for nonautonomous systems in low dimension: bifurcation-and rate-induced tipping, Nonlinearity, 30, 2185, https://doi.org/10.1088/1361-6544/aa675b, 2017. 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
Bastiaansen, R., Dijkstra, H. A., and von der Heyd, A. S.: Fragmented tipping in a spatially heterogeneous world, Environ. Res. Lett., 17, 045006, https://doi.org/10.1088/1748-9326/ac59a8, 2022. a, b
Bel, G., Hagberg, A., and Meron, E.: Gradual regime shifts in spatially extended ecosystems, Theor. Ecol., 5, 591–604, https://doi.org/10.1007/s12080-011-0149-6, 2012. a, b
Binzer, A., Guill, C., Brose, U., and Rall, B. C.: The dynamics of food chains under climate change and nutrient enrichment, Philos. T. Roy. Soc. B, 367, 2935–2944, https://doi.org/10.1098/rstb.2012.0230, 2012. a
Boers, N.: Observation-based early-warning signals for a collapse of the Atlantic Meridional Overturning Circulation, Nat. Clim. Change, 11, 680–688, https://doi.org/10.1038/s41558-021-01097-4, 2021. a
Boers, N. and Rypdal, M.: Critical slowing down suggests that the western Greenland Ice Sheet is close to a tipping point, P. Natl. Acad. Sci. USA, 118, e2024192118, https://doi.org/10.1073/pnas.2024192118, 2021. a
Boettiger, C. and Hastings, A.: Early warning signals and the prosecutor's fallacy, P. Roy. Soc. B, 279, 4734–4739, https://doi.org/10.1098/rspb.2012.2085, 2012. a
Boettiger, C., Ross, N., and Hastings, A.: Early warning signals: the charted and uncharted territories, Theor. Ecol., 6, 255–264, https://doi.org/10.1007/s12080-013-0192-6, 2013. a
Boulton, C., Allison, L., and Lenton, T.: Early warning signals of Atlantic Meridional Overturning Circulation collapse, Nat. Commun., 5, 5752, https://doi.org/10.1038/ncomms6752, 2014. a
Boulton, C. A., Lenton, T. M., and Boers, N.: Pronounced loss of Amazon rainforest resilience since the early 2000s, Nat. Clim. Change, 12, 271–278, https://doi.org/10.1038/s41558-022-01287-8, 2022. a
Cameron, M. K.: Finding he quasipotential for nongradient SDEs, Physica D, 241, 1532–1550, https://doi.org/10.1016/j.physd.2012.06.005, 2012. a
Carpenter, S. and Brock, W. A.: Rising variance: a leading indicator of ecological transition, Ecol. Lett., 9, 311–318, https://doi.org/10.1111/j.1461-0248.2005.00877.x, 2006. a
Charo, G. D., Chekroun, M. D., Sciamarella, D., and Ghil, M.: Noise-driven topological changes in chaotic dynamics, Chaos, 31, 103115, https://doi.org/10.1063/5.0059461, 2021. a
Clarke, J. J., Huntingford, C., Ritchie, P. D. L., and Cox, P. M.: Seeking more robust early warning signals for climate tipping points: the ratio of spectra method (ROSA), Environ. Res. Lett., 18, 035006, https://doi.org/10.1088/1748-9326/acbc8d, 2023. a
Dakos, V., Scheffer, M., van Nes, E., Brovkin, V., Petoukhov, V., and Held, H.: Slowing down as an early warning signal for abrupt climate change, P. Natl. Acad. Sci. USA, 105, 14308–14312, https://doi.org/10.1073/pnas.0802430105, 2008. a
Ditlevsen, P. and Johnsen, S.: Tipping points: early warning and wishful thinking, Geophys. Res. Lett., 37, 2–5, https://doi.org/10.1029/2010GL044486, 2010. a
d'Ovidio, F., Fernandez, V., Hernandez-Garcia, E., and Lopez, C.: Mixing structures in the Mediterranean Sea from finite-size Lyapunov exponents, Geophys. Res. Lett., 31, L17203, https://doi.org/10.1029/2004GL020328, 2004. a
Ebeling, W. and Malchow, H.: Bifurcations in a Bistable Reaction-Diffusion System, Ann. Phys., 36, 121–134, 1979. a
Eisenman, I.: Factors controlling the bifurcation structure of sea ice retreat, J. Geophys. Res.-Atmos., 117, D01111, https://doi.org/10.1029/2011JD016164, 2012. a, b
Eisenman, I. and Wettlaufer, J. S.: Nonlinear threshold behavior during the loss of Arctic sea ice, P. Natl. Acad. Sci. USA, 106, 28–32, https://doi.org/10.1073/pnas.0806887106, 2009. a, b
Fan, J., Meng, J., Ludescher, J., Chen, X., Ashkenazy, Y., Kurths, J., Havlin, S., and Schellnhuber, H. J.: Statistical physics approaches to the complex Earth system, Phys. Rep., 896, 1–84, https://doi.org/10.1016/j.physrep.2020.09.005, 2021. a
Feudel, U., Grebogi, C., Hunt, B. R., and Yorke, J. A.: Map with more than 100 coexisting low-period periodic attractors, Phys. Rev. E, 54, 71–81, https://doi.org/10.1103/PhysRevE.54.71, 1996. a
Ficetola, G. F. and Denoel, M.: Ecological thresholds: an assessment of methods to identify abrupt changes in species-habitat relationships, Ecography, 32, 1075–1084, https://doi.org/10.1111/j.1600-0587.2009.05571.x, 2009. a
Folke, C., Carpenter, S., Walker, B., Scheffer, M., Elmqvist, T., Gunderson, L., and Holling, C.: Regime shifts, resilience, and biodiversity in ecosystem management, Annu. Rev. Ecol. Evol. S., 35, 557–581, https://doi.org/10.1146/annurev.ecolsys.35.021103.105711, 2004. a
Franzke, C. L. E., O'Kane, T. J., Berner, J., Williams, P. D., and Lucarini, V.: Stochastic climate theory and modeling, Wiley Interdisciplinary Reviews-Climate Change, 6, 63–78, https://doi.org/10.1002/wcc.318, 2015. a
Freidlin, M. I. and Wentzell, A. D.: Random perturbations of dynamical systems, Springer, https://doi.org/10.1007/978-3-642-25847-3, 1998. a
Freund, J. A., Mieruch, S., Scholze, B., Wiltshire, K., and Feudel, U.: Bloom dynamics in a seasonally forced phytoplankton-zooplankton model: Trigger mechanisms and timing effects, Ecol. Complex., 3, 126–136, https://doi.org/10.1016/j.ecocom.2005.11.001, 2006. a
Ganapathisubramanian, N. and Showalter, K.: Critical slowing down in the bistable iodate-arsenic(III) reaction, J. Phys. Chem., 87, 1098–1099, https://doi.org/10.1021/j100230a004, 1983. a
Ghil, M. and Lucarini, V.: The physics of climate variability and climate change, Rev. Mod. Phys., 92, 035002, https://doi.org/10.1103/RevModPhys.92.035002, 2020. a
Gossner, M. M., Lewinsohn, T. M., Kahl, T., Grassein, F., Boch, S., Prati, D., Birkhofer, K., Renner, S. C., Sikorski, J., Wubet, T., Arndt, H., Baumgartner, V., Blaser, S., Bluethgen, N., Boerschig, C., Buscot, F., Diekoetter, T., Jorge, L. R., Jung, K., Keyel, A. C., Klein, A.-M., Klemmer, S., Krauss, J., Lange, M., Mueller, J., Overmann, J., Pasalic, E., Penone, C., Perovic, D. J., Purschke, O., Schall, P., Socher, S. A., Sonnemann, I., Tschapka, M., Tscharntke, T., Tuerke, M., Venter, P. C., Weiner, C. N., Werner, M., Wolters, V., Wurst, S., Westphal, C., Fischer, M., Weisser, W. W., and Allan, E.: Land-use intensification causes multitrophic homogenization of grassland communities, Nature, 540, 266–269, https://doi.org/10.1038/nature20575, 2016. a
Goswami, B. N., Venugopal, V., Sengupta, D., Madhusoodanan, M. S., and Xavier, P. K.: Increasing trend of extreme rain events over India in a warming environment, Science, 314, 1442–1445, https://doi.org/10.1126/science.1132027, 2006. a
Graham, R., Hamm, A., and Tel, T.: Nonequilibrium Potentials for Dynamic-Systems with Fractal Attractors or Repellors, Phys. Rev. Lett., 66, 3089–3092, https://doi.org/10.1103/PhysRevLett.66.3089, 1991. a
Grassberger, P.: On Phase-Transitions in Schloegl 2nd Model, Z. Phys. B Con. Mat., 47, 365–374, https://doi.org/10.1007/BF01313803, 1982. a
Guckenheimer, J. and Holmes, P.: Nonlinear Oscillations, Dynamical systems, and Bifurcations of Vector Fields, Springer Verlag, Berlin, Heidelberg, New York, https://doi.org/10.1007/978-1-4612-1140-2, 1986. a, b
Hairer, E., Wanner, G., and Noersett, S. P.: Solving Ordinary Differential Equations I: Nonstiff Problems, Springer, 1993 (code available at: https://doi.org/10.1007/978-3-540-78862-1). a
Halekotte, L. and Feudel, U.: Minimal fatal shocks in multistable complex networks, Sci. Rep., 10, 11783, https://doi.org/10.1038/s41598-020-68805-6, 2020. a, b
Haller, G.: Lagrangian Coherent Structures, in: Annual Review of Fluid Mechanics, edited by: Davis, S. and Moin, P., vol. 47, Annu. Rev. Fluid Mech., 137–162, https://doi.org/10.1146/annurev-fluid-010313-141322, 2015. a
Hasan, C. R., Mac Cárthaigh, R., and Wieczorek, S.: Rate-induced tipping in heterogeneous reacion-diffusion systems: An invariant manifold framework and geographically shifting ecosystems, arXiv [preprint], https://doi.org/10.48550/arXiv.2211.13062, 23 November 2022. a
Heinrichs, M. and Schneider, F.: Relaxation kinetics of steady statea in the continuous flow stirred tank reactor. Response to small and large perturbations: critical slowing down, J. Phys. Chem., 85, 2112–2116, https://doi.org/10.1021/j150614a031, 1981. a
Held, H. and Kleinen, T.: Detection of climate system bifurcations by degenerate fingerprinting, Geophys. Res. Lett., 31, L23207, https://doi.org/10.1029/2004GL020972, 2004. a
Hillebrand, H., Donohue, I., Harpole, W. S., Hodapp, D., Kucera, M., Lewandowska, A. M., Merder, J., Montoya, J. M., and Freund, J. A.: Thresholds for ecological responses to global change do not emerge from empirical data, Nat. Ecol. Evol., 4, 1502–1509, https://doi.org/10.1038/s41559-020-1256-9, 2020. a
Holbrook, S. J., Schmitt, R. J., Adam, T. C., and Brooks, A. J.: Coral Reef Resilience, Tipping Points and the Strength of Herbivory, Sci. Rep., 6, 35817, https://doi.org/10.1038/srep35817, 2016. a
Holling, C. S.: Engineering resilience versus ecological resilience, in: Engineering within ecological constraints, edited by: Schulze, P. C., 31–43, National Academies Press, https://doi.org/10.17226/4919, 1996. a
Horsthemke, W. and Lefever, R.: Noise-induced Transitions, Springer, Berlin, https://doi.org/10.1007/3-540-36852-3, 1984. a
Kai, E. T., Rossi, V., Sudre, J., Weimerskirch, H., Lopez, C., Hernandez-Garcia, E., Marsac, F., and Garcon, V.: Top marine predators track Lagrangian coherent structures, P. Natl. Acad. Sci. USA, 106, 8245–8250, https://doi.org/10.1073/pnas.0811034106, 2009. a
Kaszás, B., Feudel, U., and Tél, T.: Death and revival of chaos, Phys. Rev. E, 94, 062221, https://doi.org/10.1103/PhysRevE.94.062221, 2016. a, b
Kaszás, B., Feudel, U., and Tél, T.: Tipping phenomena in typical dynamical systems subjected to parameter drift, Sci. Rep., 9, 8654, https://doi.org/10.1038/s41598-019-44863-3, 2019. a, b, c, d
Khovanov, I. A., Luchinsky, D. G., McClintock, P. V. E., and Silchenko, A. N.: Fluctuational escape from chaotic attractors in multistable systems, Int. J. Bifurcat. Chaos, 18, 1727–1739, https://doi.org/10.1142/S0218127408021312, 2008. a
Klinshov, V. V., Nekorkin, V. I., and Kurths, J.: Stability threshold approach for complex dynamical systems, New J. Phys., 18, 013004, https://doi.org/10.1088/1367-2630/18/1/013004, 2015. a
Klose, A. K., Karle, V., Winkelmann, R., and Donges, J. F.: Emergence of cascading dynamics in interacting tipping elements of ecology and climate, Roy. Soc. Open Sci., 7, 200599, https://doi.org/10.1098/rsos.200599, 2020. a, b
Klose, A. K., Donges, J. F., Feudel, U., and Winkelmann, R.: Rate-induced tipping cascades arising from interactions between the Greenland Ice Sheet and the Atlantic Meridional Overturning Circulation, Earth Syst. Dynam. Discuss. [preprint], https://doi.org/10.5194/esd-2023-20, in review, 2023. a, b
Kouvaris, N. E., Kori, H., and Mikhailov, A. S.: Travelling and pinned fronts in bistable reaction diffusion systems on networks, Plos ONE, 7, e45029, https://doi.org/10.1371/journal.pone.0045029, 2012. a
Kraut, S. and Feudel, U.: Noise-induced Escape through a Chaotic Saddle: Lowering of the Activation Energy, Physica D, 181, 222–234, https://doi.org/10.1016/S0167-2789(03)00098-8, 2003. a
Kroenke, J., Wunderling, N., Winkelmann, R., Staal, A., Stumpf, B., Tuinenburg, O. A., and Donges, J. F.: Dynamics of tipping cascades on complex networks, Phys. Rev. E, 101, 042311, https://doi.org/10.1103/PhysRevE.101.042311, 2020. a, b, c
Kuehn, C.: A mathematical framework for critical transitions: Bifurcations, fast–slow systems and stochastic dynamics, Physica D, 240, 1020–1035, https://doi.org/10.1016/j.physd.2011.02.012, 2011. a
Kuhlbrodt, T., Titz, S., Feudel, U., and Rahmstorf, S.: A simple model of seasonal open ocean convection. Part II: Labrador Sea stability and stochastic forcing, Ocean Dynam., 52, 36–49, 2002. a
Kuznetsov, Y. A.: Elements of applied bifurcation theory, Springer, New York, https://doi.org/10.1007/978-1-4757-3978-7, 1995. a
Lenderink, G. and Haarsma, R.: Variability and Multiple Equilibria of the Thermohaline Circulation Associated with Deep-Water Formation, J. Phys. Oceanogr., 24, 1480–1493, https://doi.org/10.1175/1520-0485(1994)024<1480:VAMEOT>2.0.CO;2, 1994. a
Lenton, T. M.: Early warning of climate tipping points, Nat. Clim. Change, 1, 201–209, https://doi.org/10.1038/NCLIMATE1143, 2011. a
Lenton, T. M., Held, H., Kriegler, E., Hall, J. W., Lucht, W., Rahmstorf, S., and Schellnhuber, H. J.: Tipping elements in the Earth's climate system, P. Natl. Acad. Sci. USA, 105, 1786–1793, https://doi.org/10.1073/pnas.0705414105, 2008. a
Lenton, T. M., Livina, V. N., Dakos, V., van Nes, E. H., and Scheffer, M.: Early warning of climate tipping points from critical slowing down: comparing methods to improve robustness, Philos. T. Roy. Soc. A, 370, 1185–1204, https://doi.org/10.1098/rsta.2011.0304, 2012. a
Lohmann, J., Castellana, D., Ditlevsen, P. D., and Dijkstra, H. A.: Abrupt climate change as a rate-dependent cascading tipping point, Earth Syst. Dynam., 12, 819–835, https://doi.org/10.5194/esd-12-819-2021, 2021. a, b, c
Lohmann, J., Dijkstra, H. A., Jochum, M., Lucarini, V., and Ditlevsen, P. D.: Multistability and Intermediate Tipping of the Atlantic Ocean Circulation, arXiv [preprint], https://doi.org/10.48550/arXiv.2304.05664, 12 April 2023. a
Lorenz, E. N.: Deterministic Nonperiodic Flow, J. Atmos. Sci., 20, 130–141, https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2, 1963. a
Lovejoy, S. and Schertzer, D.: Stochastic and scaling climate sensitivities: Solar, volcanic and orbital forcings, Geophys. Res. Lett., 39, L11702, https://doi.org/10.1029/2012GL051871, 2012. a
Maier, R. and Stein, D.: Transition-Rate Theory for Nongradient Drift Fields, Phys. Rev. Lett., 69, 3691–3695, https://doi.org/10.1103/PhysRevLett.69.3691, 1992. a
Mancho, A. M., Wiggins, S., Curbelo, J., and Mendoza, C.: Lagrangian descriptors: A method for revealing phase space structures of general time dependent dynamical systems, Communi. Nonlinear Sci., 18, 3530–3557, https://doi.org/10.1016/j.cnsns.2013.05.002, 2013. a
Mehling, O., Bellomo, K., Angeloni, M., Pasquero, C., and von Hardenberg, J.: High-Latitude precipitation as a driver of multicentennial variability of the AMOC in a climate model of intermediate complexity, Clim. Dynam., 61, 1519–1534, https://doi.org/10.1007/s00382-022-06640-3, 2022. a, b
Mitra, C., Kurths, J., and Donner, R. V.: An integrative quantifier of multistability in complex systems based on ecological resilience, Sci. Rep., 5, 16196,https://doi.org/10.1038/srep16196, 2015. a
Mou, C., Luo, J., and Nicolis, G.: Stochastic Thermodynamics of Nonequilibrium Steady-States in Chemical-Reaction Systems, J. Chem. Phys., 84, 7011–7017, https://doi.org/10.1063/1.450623, 1986. a
Mumby, P. J., Hastings, A., and Edwards, H. J.: Thresholds and the resilience of Caribbean coral reefs, Nature, 450, 98–101, https://doi.org/10.1038/nature06252, 2007. a
Notz, D.: The future of ice sheets and sea ice: Between reversible retreat and unstoppable loss, P. Natl. Acad. Sci. USA, 106, 20590–20595, https://doi.org/10.1073/pnas.0902356106, 2009. a, b
O'Keeffe, P. E. and Wieczorek, S.: Tipping Phenomena and Points of No Return in Ecosystems: Beyond Classical Bifurcations, SIAM J. Appl.Dyn. Syst., 19, 2371–2402, https://doi.org/10.1137/19M1242884, 2020. a, b, c
Ott, E.: Chaos in Dynamical Systems, Cambridge University Press, Cambridge, https://doi.org/10.1017/CBO9780511803260, 1992. a
Pierini, S. and Ghil, M.: Tipping points induced by parameter drift in an excitable ocean model, Sci. Rep., 11, 11126, https://doi.org/10.1038/s41598-021-90138-1, 2021. a
Rahmstorf, S.: Multiple convection patterns and thermohaline flow in an idealized OGCM, J. Climate, 8, 3028–3039, https://doi.org/10.1175/1520-0442(1995)008<3028:MCPATF>2.0.CO;2, 1995. a, b
Rahmstorf, S.: On the freshwater forcing and transport of the Atlantic thermohaline circulation, Clim. Dynam., 12, 799–811, https://doi.org/10.1007/s003820050144, 1996. a
Ritchie, P. and Sieber, J.: Probability of noise- and rate-induced tipping, Phys. Rev. E, 95, 052209, https://doi.org/10.1103/PhysRevE.95.052209, 2017. a
Ritchie, P. D. L., Clarke, J. J., Cox, P. M., and Huntingford, C.: Overshooting tipping point thresholds in a changing climate, Nature, 592, 517–523, https://doi.org/10.1038/s41586-021-03263-2, 2021. a
Ritchie, P. D. L., Alkhayuon, H., Cox, P. M., and Wieczorek, S.: Rate-induced tipping in natural and human systems, Earth Syst. Dynam., 14, 669–683, https://doi.org/10.5194/esd-14-669-2023, 2023. a
Rooth, C.: Hydrology and Ocean Circulation, Prog. Oceanogr., 11, 131–149, https://doi.org/10.1016/0079-6611(82)90006-4, 1982. a
Rossi, V., Ser-Giacomi, E., Lopez, C., and Hernandez-Garcia, E.: Hydrodynamic provinces and oceanic connectivity from a transport network help designing marine reserves, Geophys. Res. Lett., 41, 2883–2891, https://doi.org/10.1002/2014GL059540, 2014. a
Sandulescu, M., López, C., Hernández-García, E., and Feudel, U.: Plankton blooms in vortices: the role of biological and hydrodynamic timescales, Nonlin. Processes Geophys., 14, 443–454, https://doi.org/10.5194/npg-14-443-2007, 2007. a
Scheffer, M., Hosper, S., Meijer, M., Moss, B., and Jeppesen, E.: Alternative Equilibria in Shallow Lakes, Trends Ecol. Evol., 8, 275–279, https://doi.org/10.1016/0169-5347(93)90254-M, 1993. a
Scheffer, M., Bascompte, J., Brock, W., Brovkin, V., Carpenter, S., Dakos, V., Held, H., van Nes, E., Rietkerk, M., and Sugihara, G.: Early warning signals for critical transitions, Nature, 461, 53–59, https://doi.org/10.1038/nature08227, 2009. a
Schellnhuber, H. J., Rahmstorf, S., and Winkelmann, R.: Commentary: Why the right climate target was agreed in Paris, Nat. Clim. Change, 6, 649–653, https://doi.org/10.1038/nclimate3013, 2016. a
Schertzer, D. and Lovejoy, S.: Multifractals, Generalized Scale Invaiance and Complexity In Geophysics, Int. J. Bifurcat. Chaos, 21, 3417–3456, https://doi.org/10.1142/S0218127411030647, 2011. a
Schlögl, F.: Chemical reaction models for non-equilibrium phase transitions, Z. Physik, 253, 147–161, 1972. a
Schoenmakers, S. and Feudel, U.: A resilience concept based on system functioning: A dynamical systems perspective, Chaos, 31, 053126, https://doi.org/10.1063/5.0042755, 2021. a
Sharma, Y., Abbott, K. C., Dutta, P. S., and Gupta, A. K.: Stochasticity and bistability in insect outbreak dynamics, Theor. Ecol., 8, 163–174, https://doi.org/10.1007/s12080-014-0241-9, 2015. a
Siteur, K., Siero, E., Eppinga, M. B., Rademacher, J. D. M., 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
Siteur, K., Eppinga, M. B., Doelman, A., Siero, E., and Rietkerk, M.: Ecosystems off track: rate-induced critical transitions in ecological models, Oikos, 125, 1689–1699, https://doi.org/10.1111/oik.03112, 2016. a
Smith, L., Ziehmann, C., and Fraedrich, K.: Uncertainty dynamics and predictability in chaotic systems, Q. J. Roy. Meteor. Soc., 125, 2855–2886, https://doi.org/10.1256/smsqj.56004, 1999. a
Stephens, P., Sutherland, W., and Freckleton, R.: What is the Allee effect?, Oikos, 87, 185–190, https://doi.org/10.2307/3547011, 1999. a
Stommel, H.: Thermohaline Convection with 2 Stable Regimes of Flow, Tellus, 13, 224–230, https://doi.org/10.1111/j.2153-3490.1961.tb00079.x, 1961. a
Surovyatkina, E.: Prebifurcation noise amplification and noise-dependent hysteresis as indicators of bifurcations in nonlinear geophysical systems, Nonlin. Processes Geophys., 12, 25–29, https://doi.org/10.5194/npg-12-25-2005, 2005. a
Tel, T., Bodai, T., Drotos, G., Haszpra, T., Herein, M., Kaszas, B., and Vincze, M.: The Theory of Parallel Climate Realizations A New Framework of Ensemble Methods in a Changing Climate: An Overview, J. Stat. Phys., 179, 1496–1530, https://doi.org/10.1007/s10955-019-02445-7, 2020. a
Tredicce, J., Lippi, G., P.Mandel, Charasse, B., Chevalier, A., and Picque, B.: Critical slowing down at a bifurcation, Am. J. Phys., 72, 799–809, https://doi.org/10.1119/1.1688783, 2004. a
Turing, A. M.: The Chemical Basis of Morphogenesis, Philos. T. R. Soc. Lond. B, 237, 37–72, https://doi.org/10.1098/rstb.1952.0012, 1952. a
Van Nes, E. H., Amaro, T., Scheffer, M., and Duineveld, G. C.: Possible mechanisms for a marine benthic regime shift in the North Sea, Mar. Ecol. Prog. Ser., 330, 39–47, https://doi.org/10.3354/meps330039, 2007. a
Vanselow, A., Wieczorek, S., and Feudel, U.: When very slow is too fast – collapse of a predator-prey system, J. Theor. Biol., 479, 64–72, https://doi.org/10.1016/j.jtbi.2019.07.008, 2019. a, b, c
Vanselow, A., Halekotte, L., Pal, P., Wieczorek, S., and Feudel, U.: Rate-induced tipping can trigger plankton blooms, arXiv [preprint], https://doi.org/10.48550/arXiv.2212.01244, 17 November 2022. a, b, c
Wagner, T. J. W. and Eisenman, I.: False alarms: How early warning signals falsely predict abrupt sea ice loss, Geophys. Res. Lett., 42, 10333–10341, https://doi.org/10.1002/2015GL066297, 2015. a
Weijer, W., Maltrud, M. E., Hecht, M. W., Dijkstra, H. A., and Kliphuis, M. A.: Response of the Atlantic Ocean circulation to Greenland Ice Sheet melting in a strongly-eddying ocean model, Geophys. Res. Lett., 39, L09606, https://doi.org/10.1029/2012GL051611, 2012. a
Weijer, W., Cheng, W., Drijfhout, S. S., Fedorov, A. V., Hu, A., Jackson, L. C., Liu, W., McDonagh, E. L., Mecking, J. V., and Zhang, J.: Stability of the Atlantic Meridional Overturning Circulation: A Review and Synthesis, J. Geophys. Res.-Oceans, 124, 5336–5375, https://doi.org/10.1029/2019JC015083, 2019. a
Wieczorek, S., Ashwin, P., Luke, C. M., and Cox, P. M.: Excitability in ramped systems: the compost-bomb instability, P. Roy. Soc. A, 467, 1243–1269, https://doi.org/10.1098/rspa.2010.0485, 2011. a, b, c
Wiggins, S.: The dynamical systems approach to Lagrangian transport in oceanic flows, Annu. Rev. Fluid Mech., 37, 295–328, https://doi.org/10.1146/annurev.fluid.37.061903.175815, 2005. a
Wood, R. A., Rodriguez, J. M., Smith, R. S., Jackson, L. C., and Hawkins, E.: Observable, low-order dynamical controls on thresholds of the Atlantic meridional overturning circulation, Clim. Dynam., 53, 6815–6834, https://doi.org/10.1007/s00382-019-04956-1, 2019. a
Wunderling, N., Donges, J. F., Kurths, J., and Winkelmann, R.: Interacting tipping elements increase risk of climate domino effects under global warming, Earth Syst. Dynam., 12, 601–619, https://doi.org/10.5194/esd-12-601-2021, 2021. a, b
Zelnik, Y., 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
Zelnik, Y., Gandhi, P., Knobloch, E., and Meron, E.: Implications of tristability in pattern-forming ecosystems, Chaos, 28, 033609, https://doi.org/10.1063/1.5018925, 2018. a
Executive editor
This study suggests a necessary shift in the paradigm of nonlinear dynamical systems analysis in climate science, ecology, and beyond. The author delves into a relatively unexplored facet of critical transitions, which is of great importance in examples within the Earth and environmental sciences. In particular, she explains mechanisms based on these ideas in examples of systems that describe population dynamics and climate transitions.
This study suggests a necessary shift in the paradigm of nonlinear dynamical systems analysis in...
Short summary
Many systems in nature are characterized by the coexistence of different stable states for given environmental parameters and external forcing. Examples can be found in different fields of science, ranging from ecosystems to climate dynamics. Perturbations can lead to critical transitions (tipping) from one stable state to another. The study of these transitions requires the development of new methodological approaches that allow for modeling, analyzing and predicting them.
Many systems in nature are characterized by the coexistence of different stable states for given...
