Articles | Volume 26, issue 4
Review article
08 Oct 2019
Review article |  | 08 Oct 2019

Numerical bifurcation methods applied to climate models: analysis beyond simulation

Henk A. Dijkstra

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AMOC stability amid tipping ice sheets: the crucial role of rate and noise
Sacha Sinet, Peter Ashwin, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 15, 859–873,,, 2024
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Highly stratified mid-Pliocene Southern Ocean in PlioMIP2
Julia E. Weiffenbach, Henk A. Dijkstra, Anna S. von der Heydt, Ayako Abe-Ouchi, Wing-Le Chan, Deepak Chandan, Ran Feng, Alan M. Haywood, Stephen J. Hunter, Xiangyu Li, Bette L. Otto-Bliesner, W. Richard Peltier, Christian Stepanek, Ning Tan, Julia C. Tindall, and Zhongshi Zhang
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Persistent climate model biases in the Atlantic Ocean's freshwater transport
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Similar North Pacific variability despite suppressed El Niño variability in the warm mid-Pliocene climate
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Mid-Pliocene not analogous to high-CO2 climate when considering Northern Hemisphere winter variability
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Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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Cited articles

Abraham, R. and Shaw, C.: Dynamics: The Geometry of Behavior, Addison-Wesley, Redwood City, California, USA, 1992. a
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, 2012. a
Baars, S., Viebahn, J. P., Mulder, T. E., Kuehn, C., Wubs, F. W., and Dijkstra, H. A.: Continuation of probability density functions using a generalized Lyapunov approach, J. Comput. Phys., 336, 627–643, 2017. a, b, c
Berloff, P. S., Hogg, A. M., and Dewar, W. K.: The turbulent oscillator: a mechanism of low-frequency variability of the wind-driven ocean gyres, J. Phys. Oceanogr., 37, 2362–2386, 2007. a
Castellana, D., Wubs, F., and Dijkstra, H.: A statistical significance test for sea-level variability, Dynamics and Statistics of the Climate System, 3, dzy008,, 2018. a
Short summary
I provide a personal view on the role of bifurcation analysis of climate models in the development of a theory of variability in the climate system. By outlining the state of the art of the methodology and by discussing what has been done and what has been learned from a hierarchy of models, I will argue that there are low-order phenomena of climate variability, such as El Niño and the Atlantic Multidecadal Oscillation.