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Open accessJournal ArticleDOI: 10.1073/PNAS.2017989118

Risk of tipping the overturning circulation due to increasing rates of ice melt

02 Mar 2021-Proceedings of the National Academy of Sciences of the United States of America (Proceedings of the National Academy of Sciences)-Vol. 118, Iss: 9
Abstract: Central elements of the climate system are at risk for crossing critical thresholds (so-called tipping points) due to future greenhouse gas emissions, leading to an abrupt transition to a qualitatively different climate with potentially catastrophic consequences. Tipping points are often associated with bifurcations, where a previously stable system state loses stability when a system parameter is increased above a well-defined critical value. However, in some cases such transitions can occur even before a parameter threshold is crossed, given that the parameter change is fast enough. It is not known whether this is the case in high-dimensional, complex systems like a state-of-the-art climate model or the real climate system. Using a global ocean model subject to freshwater forcing, we show that a collapse of the Atlantic Meridional Overturning Circulation can indeed be induced even by small-amplitude changes in the forcing, if the rate of change is fast enough. Identifying the location of critical thresholds in climate subsystems by slowly changing system parameters has been a core focus in assessing risks of abrupt climate change. This study suggests that such thresholds might not be relevant in practice, if parameter changes are not slow. Furthermore, we show that due to the chaotic dynamics of complex systems there is no well-defined critical rate of parameter change, which severely limits the predictability of the qualitative long-term behavior. The results show that the safe operating space of elements of the Earth system with respect to future emissions might be smaller than previously thought.

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Topics: Abrupt climate change (63%), Climate model (57%)
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10 results found


Open accessJournal ArticleDOI: 10.5194/ESD-12-819-2021
Abstract: . We propose a conceptual model comprising a cascade of tipping points as a mechanism for past abrupt climate changes. In the model, changes in a control parameter, which could for instance be related to changes in the atmospheric circulation, induce sequential tipping of sea ice cover and the ocean's meridional overturning circulation. The ocean component, represented by the well-known Stommel box model, is shown to display so-called rate-induced tipping. Here, an abrupt resurgence of the overturning circulation is induced before a bifurcation point is reached due to the fast rate of change of the sea ice. Because of the multi-scale nature of the climate system, this type of tipping cascade may also be a risk concerning future global warming. The relatively short timescales involved make it challenging to detect these tipping points from observations. However, with our conceptual model we find that there can be a significant delay in the tipping because the system is attracted by the stable manifold of a saddle during the rate-induced transition before escaping towards the undesired state. This opens up the possibility for an early warning of the impending abrupt transition via detection of the changing linear stability in the vicinity of the saddle. To do so, we propose estimating the Jacobian from the noisy time series. This is shown to be a useful generic precursor to detect rate-induced tipping.

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3 Citations


Open accessPosted Content
Abstract: We identify the phase of a cycle as a new critical factor for tipping points (critical transitions) in cyclic systems subject to time-varying external conditions. As an example, we consider how contemporary climate variability induces tipping from a predator-prey cycle to extinction in two paradigmatic predator-prey models with an Allee effect. Our analysis of these examples uncovers a counter-intuitive behaviour, which we call phase-sensitive tipping or P-tipping, where tipping to extinction occurs only from certain phases of the cycle. To explain this behaviour, we combine global dynamics with set theory and introduce the concept of partial basin instability for limit cycles. This concept provides a general framework to analyse and identify sufficient criteria for the occurrence of phase-sensitive tipping in externally forced systems.

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3 Citations


Open accessPosted Content
Abstract: 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. We develop an accessible mathematical framework and give testable criteria for R-tipping in multidimensional nonautonomous dynamical systems with an autonomous future limit. Our focus is on R-tipping via loss of tracking of base attractors that are equilibria in the frozen system, due to crossing what we call regular thresholds. These thresholds are associated with regular edge states: compact hyperbolic invariant sets with one unstable direction and orientable stable manifold that lie on a basin boundary in the frozen system. 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 future limit system that is not an attractor. We then focus on the case when the limit set is a regular edge state of the future limit system, which we call the regular R-tipping edge state that anchors the associated regular R-tipping threshold at infinity. We then introduce the concept of edge tails to rigorously classify R-tipping into reversible, irreversible and degenerate cases. The main idea is to use autonomous dynamics and regular edge states of the future limit system to analyse R-tipping in the nonautonomous system. To that end, we compactify the original nonautonomous system to include the limiting autonomous dynamics. This allows us to give easily verifiable conditions in terms of simple properties of the frozen system and input variation that are sufficient for the occurrence of R-tipping. Additionally, 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 compactified system.

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Topics: Limit set (56%), Stable manifold (55%), Attractor (55%) ... read more

2 Citations


Open accessJournal ArticleDOI: 10.1098/RSPA.2021.0059
Abstract: We identify the phase of a cycle as a new critical factor for tipping points (critical transitions) in cyclic systems subject to time-varying external conditions. As an example, we consider how con...

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2 Citations


Journal ArticleDOI: 10.1126/SCIENCE.ABJ0359
08 Oct 2021-Science
Abstract: The concept of tipping points and critical transitions helps inform our understanding of the catastrophic effects that global change may have on ecosystems, Earth system components, and the whole E...

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Topics: Evasion (ethics) (53%), Earth system science (50%)

1 Citations


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49 results found


Journal ArticleDOI: 10.1256/QJ.04.176
S. Uppala1, Per Kållberg1, Adrian Simmons1, U. Andrae1  +43 moreInstitutions (10)
Abstract: ERA-40 is a re-analysis of meteorological observations from September 1957 to August 2002 produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) in collaboration with many institutions. The observing system changed considerably over this re-analysis period, with assimilable data provided by a succession of satellite-borne instruments from the 1970s onwards, supplemented by increasing numbers of observations from aircraft, ocean-buoys and other surface platforms, but with a declining number of radiosonde ascents since the late 1980s. The observations used in ERA-40 were accumulated from many sources. The first part of this paper describes the data acquisition and the principal changes in data type and coverage over the period. It also describes the data assimilation system used for ERA-40. This benefited from many of the changes introduced into operational forecasting since the mid-1990s, when the systems used for the 15-year ECMWF re-analysis (ERA-15) and the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) re-analysis were implemented. Several of the improvements are discussed. General aspects of the production of the analyses are also summarized. A number of results indicative of the overall performance of the data assimilation system, and implicitly of the observing system, are presented and discussed. The comparison of background (short-range) forecasts and analyses with observations, the consistency of the global mass budget, the magnitude of differences between analysis and background fields and the accuracy of medium-range forecasts run from the ERA-40 analyses are illustrated. Several results demonstrate the marked improvement that was made to the observing system for the southern hemisphere in the 1970s, particularly towards the end of the decade. In contrast, the synoptic quality of the analysis for the northern hemisphere is sufficient to provide forecasts that remain skilful well into the medium range for all years. Two particular problems are also examined: excessive precipitation over tropical oceans and a too strong Brewer-Dobson circulation, both of which are pronounced in later years. Several other aspects of the quality of the re-analyses revealed by monitoring and validation studies are summarized. Expectations that the ‘second-generation’ ERA-40 re-analysis would provide products that are better than those from the firstgeneration ERA-15 and NCEP/NCAR re-analyses are found to have been met in most cases. © Royal Meteorological Society, 2005. The contributions of N. A. Rayner and R. W. Saunders are Crown copyright.

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6,867 Citations


Open accessBook
Sydney Levitus1Institutions (1)
01 Jun 1982-
Abstract: A project to objectively analyze historical ocean temperature, salinity, oxygen, and percent oxygen saturation data for the world ocean has recently been completed at the National Oceanic and Atmospheric Administration's (NOAA) Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey. The results of the project are being made available through distribution of the Climatological Atlas of the World Ocean (NOAA Professional Paper No. 13), and through distribution of magnetic tapes containing the objective analyses. The sources of data used in the project were the Station Data, Mechanical Bathythermograph, and Expendable Bathythermograph files of the National Oceanographic Data Center (NODC) in Washington, D.C., updated through 1977–1978. The raw data were subjected to quality control procedures, averaged by one-degree squares, and then used as input to an objective analysis procedure that fills in one-degree squares containing no data and smooths the results. Due to the lack of synoptic observations for the world ocean, the historical data are composited by annual, seasonal, and (for temperature) monthly periods.

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Topics: World Ocean Atlas (69%), World Ocean Circulation Experiment (59%), Parallel Ocean Program (56%) ... read more

2,892 Citations


Peter R. Gent1, James C. McWilliams1Institutions (1)
Abstract: A subgrid-scale form for mesoscale eddy mixing on isopycnal surfaces is proposed for use in non-eddy-resolving ocean circulation models. The mixing is applied in isopycnal coordinates to isopycnal layer thickness, or inverse density gradient, as well as to passive scalars, temperature and salinity. The transformation of these mixing forms to physical coordinates is also presented.

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Topics: Isopycnal (71%), Mixing (physics) (55%), Ocean general circulation model (55%) ... read more

2,869 Citations



Open accessJournal ArticleDOI: 10.1073/PNAS.0705414105
Timothy M. Lenton1, Hermann Held2, Elmar Kriegler3, Elmar Kriegler2  +5 moreInstitutions (5)
Abstract: The term "tipping point" commonly refers to a critical threshold at which a tiny perturbation can qualitatively alter the state or development of a system. Here we introduce the term "tipping element" to describe large-scale components of the Earth system that may pass a tipping point. We critically evaluate potential policy-relevant tipping elements in the climate system under anthropogenic forcing, drawing on the pertinent literature and a recent international workshop to compile a short list, and we assess where their tipping points lie. An expert elicitation is used to help rank their sensitivity to global warming and the uncertainty about the underlying physical mechanisms. Then we explain how, in principle, early warning systems could be established to detect the proximity of some tipping points.

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2,308 Citations


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