Numerical Bifurcation Methods applied to Climate Models:
Analysis beyond Simulation

Dijkstra, Henk A.

doi:10.5194/npg-2019-29

Cited by 4 publications

(6 citation statements)

References 48 publications

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“…Today, there is widespread agreement that the climate of the Earth is changing, but the precise trajectory of future climate change is still a matter of debate. Recently there has been much interest in the possibility of "tipping points" (or bifurcation points) at which abrupt changes in the Earth climate system occur (see Brovkin et al, 1998;Ghil, 2001;Alley et al, 2003;Seager and Battisti, 2007;Lenton et al, 2008;Ditlevsen and Johnsen, 2010;Lenton, 2012;Ashwin et al, 2012;Barnosky et al, 2012;Drijfhout et al, 2015;Bathiany et al, 2016;North and Kim, 2017;Steffen et al, 2018;Dijkstra, 2019;Wallace-Wells, 2019). Section 12.5.5 in IPCC (2013) gives an overview of such potential abrupt changes.…”

Section: Introductionmentioning

confidence: 99%

Anthropocene climate bifurcation

Kypke

Langford

Willms

2020

Nonlin. Processes Geophys.

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Abstract. This article presents the results of a bifurcation analysis of a simple energy balance model (EBM) for the future climate of the Earth. The main focus is on the following question: can the nonlinear processes intrinsic to atmospheric physics, including natural positive feedback mechanisms, cause a mathematical bifurcation of the climate state, as a consequence of continued anthropogenic forcing by rising greenhouse gas emissions? Our analysis shows that such a bifurcation could cause an abrupt change to a drastically different climate state in the EBM, which is warmer and more equable than any climate existing on Earth since the Pliocene epoch. In previous papers, with this EBM adapted to paleoclimate conditions, it was shown to exhibit saddle-node and cusp bifurcations, as well as hysteresis. The EBM was validated by the agreement of its predicted bifurcations with the abrupt climate changes that are known to have occurred in the paleoclimate record, in the Antarctic at the Eocene–Oligocene transition (EOT) and in the Arctic at the Pliocene–Paleocene transition (PPT). In this paper, the EBM is adapted to fit Anthropocene climate conditions, with emphasis on the Arctic and Antarctic climates. The four Representative Concentration Pathways (RCP) considered by the IPCC (Intergovernmental Panel on Climate Change) are used to model future CO2 concentrations, corresponding to different scenarios of anthropogenic activity. In addition, the EBM investigates four naturally occurring nonlinear feedback processes which magnify the warming that would be caused by anthropogenic CO2 emissions alone. These four feedback mechanisms are ice–albedo feedback, water vapour feedback, ocean heat transport feedback, and atmospheric heat transport feedback. The EBM predicts that a bifurcation resulting in a catastrophic climate change, to a pre-Pliocene-like climate state, will occur in coming centuries for an RCP with unabated anthropogenic forcing, amplified by these positive feedbacks. However, the EBM also predicts that appropriate reductions in carbon emissions may limit climate change to a more tolerable continuation of what is observed today. The globally averaged version of this EBM has an equilibrium climate sensitivity (ECS) of 4.34 K, near the high end of the likely range reported by the IPCC.

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Section: Introductionmentioning

confidence: 99%

Anthropocene climate bifurcation

Kypke

Langford

Willms

2020

Nonlin. Processes Geophys.

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“…In the present study, only 2-D flows are considered, assuming a fluid layer of infinite horizontal extent. The presence of lateral boundaries can develop three dimensional (3-D) flow structures even at the first bifurcation point as observed in thermal convection (Dijkstra et al 2014). In bubbly flow systems, furthermore, the physics at bubble scales, such as the path instability and bubble-bubble interactions (Risso 2018), provides 3-D perturbations to flows and would induce transition to 3-D convections even in laterally non-confined systems.…”

Section: Discussionmentioning

confidence: 99%

“…ijkl , and C ij are coefficients. We solve these equations by the numerical continuation with varying Ra from the critical value (Dijkstra et al 2014). To determine the solution at a given Ra, the Newton-Raphson iterative scheme is invoked with a convergence criterion Δ = max j (Δ j ) < 10 −6 , where Δ j is the relative improvement to (I − 1)th estimate X I−1 j to X j by the Ith iteration (Deguchi & Nagata 2011).…”

Section: Perturbation Analysismentioning

confidence: 99%

Bifurcation analysis of bubble-induced convection in a horizontal liquid layer: role of forces on bubbles

et al. 2021

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“…Dynamical system theory is a powerful framework for studying asymptotic states of the climate system. Thanks to the separation of time scales, like the one presented in the previous section, it is possible to attribute climate variability phenomena to low-order behaviour [Dijkstra, 2019].…”

Section: Dynamical Systems Frameworkmentioning

confidence: 99%

“…[Stocker et al, 2013]. However, a more practical definition includes all time scales of variability (intrinsic and forced) [Dijkstra, 2019].…”

Section: Introduction 11 Climate Variabilitymentioning

confidence: 99%

Noise-induced phenomena in the large-scale ocean circulation

Castellana¹

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Each research question in climate science requires an appropriate climate model to be formulated, where specific approximations are made and a certain number of physical processes is considered. Conceptual climate models occupy the lowest position in the hierarchy of models: they represent only fundamental processes and they are particularly useful when trying to capture the essence of a certain system. Moreover, when two well-separated time scales can be identified in the system, the processes characterised by the smaller time scale are parametrised, often using a stochastic approach. This is the case, for example, when the ocean circulation is forced by high-frequency atmospheric fluctuations. This thesis focuses on the effect of atmospheric noise on the large-scale ocean variability, in particular concerning sea surface height (SSH) variability and the stability of the Atlantic Meridional Overturning Circulation (AMOC). Both problems are addressed by using low-dimensional stochastic dynamical systems. The effect of high-frequency wind-stress variations can be represented as a correlated additive and multiplicative noise (CAM) stochastic model of sea-level variations. The one-dimensional model developed allows to formulate an appropriate null hypothesis for SSH variability: given a time series of sea-level anomalies, specific phenomena in the ocean circulation can be detected by analysing peaks in its power spectrum, and the significance of such peaks can be tested against the null hypothesis. In other words, the model can be used to attribute specific sea-level variability to other effects than wind-stress noise. From the power spectrum analysis of several time series of SSH anomalies in the ocean, we can conclude that the CAM noise process under investigation can explain most of the variability of the sea level. Moreover, we found that some peaks are significant under the traditional red-noise test, but not significant under the CAM noise test. This indicates that using the incorrect test may lead to erroneous attribution of phenomena in the sea-level variability. Atmospheric noise is not only responsible for the existence of a background signal in the ocean time series. In special kind of systems, noise can lead to the occurrence of tipping points. One of these systems is constituted by the AMOC, which is the zonally integrated volume transport generated by a complex system of currents in the Atlantic Ocean. It represents a crucial component of the climate system, as it redistributes heat northward in the Atlantic. Thanks to the presence of the AMOC, vii north-western Europe experiences a relatively mild climate, compared to maritime regions at similar latitudes on the Pacific (up to 6 C warmer). Whether the AMOC is in a multistable regime, i.e. if the system can be in two different states under the same external forcing, is under debate in the climate community. However, if the present-day AMOC were in a multiple equilibria regime, a potential collapse in the near future would cause large and rapid changes ...

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Numerical Bifurcation Methods applied to Climate Models: Analysis beyond Simulation

Cited by 4 publications

References 48 publications

Anthropocene climate bifurcation

Anthropocene climate bifurcation

Bifurcation analysis of bubble-induced convection in a horizontal liquid layer: role of forces on bubbles

Noise-induced phenomena in the large-scale ocean circulation

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