Rate-induced tipping in natural and human systems

Ritchie, Paul; Alkhayuon, Hassan; Cox, Peter M.; Wieczorek, Sebastian

doi:10.5194/egusphere-2022-1176

Cited by 6 publications

(8 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We find that even GHG levels that reflect relatively small increases above current concentrations lead to committed equilibrium temperatures that are higher than the thresholds expected to trigger multiple climate tipping points (with all tipping elements committed to a more than 25% chance of tipping as seen in Figure 4). There are a range of underlying mechanisms (physical, structural, thermal, biophysical, and biogeochemical) driving climate tipping points processes (Armstrong McKay et al., 2022; Wang et al., 2023), some possibly rate‐dependent or operating on long timescales (Ashwin et al., 2012; Ritchie et al., 2021, 2023). Some evidence even suggests that certain tipping points may be closer than previously thought (Boers & Rypdal, 2021).…”

Section: Discussionmentioning

confidence: 99%

Committed Global Warming Risks Triggering Multiple Climate Tipping Points

Abrams,

Huntingford,

Williamson

et al. 2023

Earth's Future

View full text Add to dashboard Cite

Many scenarios for limiting global warming to 1.5°C assume planetary‐scale carbon dioxide removal sufficient to exceed anthropogenic emissions, resulting in radiative forcing falling and temperatures stabilizing. However, such removal technology may prove unfeasible for technical, environmental, political, or economic reasons, resulting in continuing greenhouse gas emissions from hard‐to‐mitigate sectors. This may lead to constant concentration scenarios, where net anthropogenic emissions remain non‐zero but small, and are roughly balanced by natural carbon sinks. Such a situation would keep atmospheric radiative forcing roughly constant. Fixed radiative forcing creates an equilibrium “committed” warming, captured in the concept of “equilibrium climate sensitivity.” This scenario is rarely analyzed as a potential extension to transient climate scenarios. Here, we aim to understand the planetary response to such fixed concentration commitments, with an emphasis on assessing the resulting likelihood of exceeding temperature thresholds that trigger climate tipping points. We explore transients followed by respective equilibrium committed warming initiated under low to high emission scenarios. We find that the likelihood of crossing the 1.5°C threshold and the 2.0°C threshold is 83% and 55%, respectively, if today's radiative forcing is maintained until achieving equilibrium global warming. Under the scenario that best matches current national commitments (RCP4.5), we estimate that in the transient stage, two tipping points will be crossed. If radiative forcing is then held fixed after the year 2100, a further six tipping point thresholds are crossed. Achieving a trajectory similar to RCP2.6 requires reaching net‐zero emissions rapidly, which would greatly reduce the likelihood of tipping events.

show abstract

Section: Discussionmentioning

confidence: 99%

Committed Global Warming Risks Triggering Multiple Climate Tipping Points

Abrams,

Huntingford,

Williamson

et al. 2023

Earth's Future

View full text Add to dashboard Cite

show abstract

“…To define the rate of external forcing we follow Ritchie et al (2023) and define an external forcing parameter σ ≡ σ(λt), where u = λt is dimensionless. The rate parameter λ has units per second/day/year/ect.…”

Section: Rate-induced Dynamicsmentioning

confidence: 99%

“…which has units of σ per second/day/year/ect. and depends on λ and σ(u) itself (Ritchie et al, 2023). So, for a fixed forcing profile σ(u), λ quantifies the rate of change of this profile.…”

Section: Rate-induced Dynamicsmentioning

confidence: 99%

“…A phenomenon closely related to rate-induced tipping is the overshooting of a bifurcation point without tipping, sometimes referred to as return tipping (Ritchie et al, 2023). In this case, the system is externally forced across a bifurcation but may avoid tipping and recover its original state if the reversal in the forcing is faster than some critical rate.…”

Section: Rate-induced Dynamicsmentioning

confidence: 99%

See 1 more Smart Citation

The Role of the Radial Vorticity Gradient in Intensification of Tropical Cyclones

Watson,

Quinn

2024

Preprint

View full text Add to dashboard Cite

Abstract. The role of the radial vorticity gradient in tropical cyclone dynamics is explored through a low-order conceptual box model. Specifically, we look at stable-to-stable state transitions which may be linked to tropical cyclone intensification, dissipation, or eyewall replacement cycles. To this end, we identify two parameters of interest: the exponent of radial decline and sea surface temperature. We examine how variation in these parameters affect the stable states of the model and consider the behaviour of the system under time-dependent parameters. By externally forcing the exponent of radial decline and sea surface temperature we show the existence of rate-dependent behaviour in the model. These findings are brought together in a case study of Hurricane Irma (2017). The results highlight the role of the radial vorticity gradient in behaviour such as rate-induced tipping and overshoot recovery. They also show that a simple model can be used to explore relatively complex tropical cyclone dynamics.

show abstract

“…The focus of this work is on systems that are particularly sensitive to how fast the external input changes [60,101]. Such systems may not even have any critical levels of the external input, but they may have critical rates of change of the external input: they suddenly and unexpectedly move to a different state if the external input changes faster than some critical rate.…”

Section: Motivation: Critical Factors and R-tippingmentioning

confidence: 99%

Rate-induced tipping: thresholds, edge states and connecting orbits

2023

Self Cite

View full text Add to dashboard Cite

Rate-induced tipping (R-tipping) occurs when time-variation of input parameters of a dynamical system interacts with system timescales to give genuine nonautonomous instabilities. Such instabilities appear as the input varies at some critical rates and cannot, in general, be understood in terms of autonomous bifurcations in the frozen system with a fixed-in-time input. This paper develops an accessible mathematical framework for R-tipping in multidimensional nonautonomous dynamical systems with an autonomous future limit. We focus on R-tipping via loss of tracking of base attractors that are equilibria in the frozen system, due to crossing what we call regular R-tipping thresholds. These thresholds are anchored at infinity by regular R-tipping edge states: compact normally hyperbolic invariant sets of the autonomous future limit system that have one unstable direction, orientable stable manifold, and lie on a basin boundary. We define R-tipping and critical rates for the nonautonomous system in terms of special solutions that limit to a compact invariant set of the autonomous future limit system that is not an attractor. We focus on the case when the limit set is a regular edge state, introduce the concept of edge tails, and rigorously classify R-tipping into reversible, irreversible, and degenerate cases. The central idea is to use the autonomous dynamics of the future limit system to analyse R-tipping in the nonautonomous system. We compactify the original nonautonomous system to include the limiting autonomous dynamics. Considering regular R-tipping edge states that are equilibria allows us to prove two results. First, we give sufficient conditions for the occurrence of R-tipping in terms of easily testable properties of the frozen system and input variation. Second, we give necessary and sufficient conditions for the occurrence of reversible and irreversible R-tipping in terms of computationally verifiable (heteroclinic) connections to regular R-tipping edge states in the autonomous compactified system.

show abstract

Rate-induced tipping in natural and human systems

Cited by 6 publications

References 35 publications

Committed Global Warming Risks Triggering Multiple Climate Tipping Points

Committed Global Warming Risks Triggering Multiple Climate Tipping Points

The Role of the Radial Vorticity Gradient in Intensification of Tropical Cyclones

Rate-induced tipping: thresholds, edge states and connecting orbits

Contact Info

Product

Resources

About