Climate response and sensitivity: time scales and late tipping points

Bastiaansen, Robbin; Ashwin, Peter; Heydt, Anna S. von der

doi:10.1098/rspa.2022.0483

Cited by 3 publications

(2 citation statements)

References 73 publications

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“…BDs can also be applied to estimate the climate sensitivity [57,72,73], in particular, to analyze how this metric depends on the attractor, on the nonlinear feedback mechanisms included in the simulations within a given integration time, on the phase space region explored by the considered initial conditions, and on the perturbation amplitude, all aspects recently discussed in Ref. [74].…”

Section: Discussionmentioning

confidence: 99%

Attractors and bifurcation diagrams in complex climate models

Brunetti

Ragon

2023

Phys. Rev. E

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The climate is a complex nonequilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the possible steady states under different forcing is the bifurcation diagram, which reveals the regions of multistability, the position of tipping points, and the range of stability of each steady state. However, its construction is highly time consuming in climate models with a dynamical deep ocean, whose relaxation time is of the order of thousand years, or other feedback mechanisms that act on even longer time scales, like continental ice or carbon cycle. Using a coupled setup of the MIT general circulation model, we test two techniques for the construction of bifurcation diagrams with complementary advantages and reduced execution time. The first is based on the introduction of random fluctuations in the forcing and permits to explore a wide part of phase space. The second reconstructs the stable branches using estimates of the internal variability and of the surface energy imbalance on each attractor, and is more precise in finding the position of tipping points.

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Section: Discussionmentioning

confidence: 99%

Attractors and bifurcation diagrams in complex climate models

Brunetti

Ragon

2023

Phys. Rev. E

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“…Their analysis in asymptotically autonomous systems has been carried out with several mathematical techniques including compactification arguments [35,46,47], statistical early-warning signals [42,43], and the tipping probability of physical measures [5]. Numerous are also the instances of real models which have been studied, for example in climate [9], ecology [41,45], and population dynamics [44].…”

Section: Introductionmentioning

confidence: 99%

Critical transitions for scalar nonautonomous systems with concave nonlinearities: some rigorous estimates

Longo,

Núñez,

Obaya

2024

Nonlinearity

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The global dynamics of a nonautonomous Carathéodory scalar ordinary differential equation x ′ = f ( t , x ) , given by a function f which is concave in x, is determined by the existence or absence of an attractor-repeller pair of hyperbolic solutions. This property, here extended to a very general setting, is the key point to classify the dynamics of an equation which is a transition between two nonautonomous asymptotic limiting equations, both with an attractor-repeller pair. The main focus of the paper is to get rigorous criteria guaranteeing tracking (i.e. connection between the attractors of the past and the future) or tipping (absence of connection) for the particular case of equations x ′ = f ( t , x − Γ ( t ) ) , where Γ is asymptotically constant. Some computer simulations show the accuracy of the obtained estimates, which provide a powerful way to determine the occurrence of critical transitions without relying on a numerical approximation of the (always existing) locally pullback attractor.

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On the predictability of possible storylines for forced complex systems

Lohmann,

Wuyts,

Ditlevsen

et al. 2024

J. Phys. Complex.

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It is well-known that even for fairly simple deterministic nonlinear systems, exact prediction of future state is, on average, impossible beyond some small multiple of the Lyapunov time that quantifies the rate of separation of trajectories within an attractor. Nonetheless, it may be possible to find a physical measure that is the distribution of a trajectory within the attractor. In that sense, there can be a still weaker form of predictability. In this paper, we show that this can also fail but an even weaker form of predictability can appear for non-autonomous (i.e. forced) systems in the presence of tipping points. The {\em predictability of possible storylines} appears when one can interpret the frequencies of runs within an ensemble arriving at one of several possible future attractors (storylines) in a probabilistic manner.As predictability is a major concern and a challenge in climate science, we illustrate this notion of predictability with two climate-related examples: a chaotic energy balance model and a global ocean model featuring a tipping point of the Atlantic Meridional Overturning Circulation.

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Climate response and sensitivity: time scales and late tipping points

Abstract: Climate response metrics are used to quantify the Earth’s climate response to anthropogenic changes of atmospheric CO 2 . Equilibrium climate sensitivity (ECS) is one such metric that measures the equilibrium response to CO … Show more

Cited by 3 publications

References 73 publications

Attractors and bifurcation diagrams in complex climate models

Attractors and bifurcation diagrams in complex climate models

Critical transitions for scalar nonautonomous systems with concave nonlinearities: some rigorous estimates

On the predictability of possible storylines for forced complex systems

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