Early warning signals of tipping points in periodically forced systems

This is the final version of the article. Available from the European Geosciences Union via the DOI in this record.The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much interest recently. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we use alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose timescale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. For these systems, phase lag and amplification of the system response can provide early warning signals, based on a linear dynamics approximation. Furthermore, the Fourier spectrum of the system's time series reveals harmonics of the forcing period in the system response whose amplitude is related to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators as well as a return map analysis to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation.The research leading to these results has received funding from the European Union Seventh Framework Programme FP7/2007-2013 under grant agreement no. 603864 (HELIX). We are grateful to Peter Ashwin, Peter Cox, Michel Crucifix, Vasilis Dakos, Henk Dijkstra, Jan Sieber, Marten Scheffer and Appy Sluijs for the fruitful discussions over beers and balls

Differentiable Programming for Earth System Modeling

Earth System Models (ESMs) are the primary tools for investigating future Earth system states at time scales from decades to centuries, especially in response to anthropogenic greenhouse gas release. State-of-the-art ESMs can reproduce the observational global mean temperature anomalies of the last 150 years. Nevertheless, ESMs need further improvements, most importantly regarding (i) the large spread in their estimates of climate sensitivity, i.e., the temperature response to increases in atmospheric greenhouse gases, (ii) the modeled spatial patterns of key variables such as temperature and precipitation, (iii) their representation of extreme weather events, and (iv) their representation of multistable Earth system components and their ability to predict associated abrupt transitions. Here, we argue that making ESMs automatically differentiable has huge potential to advance ESMs, especially with respect to these key shortcomings. First, automatic differentiability would allow objective calibration of ESMs, i.e., the selection of optimal values with respect to a cost function for a large number of free parameters, which are currently tuned mostly manually. Second, recent advances in Machine Learning (ML) and in the amount, accuracy, and resolution of observational data promise to be helpful with at least some of the above aspects because ML may be used to incorporate additional information from observations into ESMs. Automatic differentiability is an essential ingredient in the construction of such hybrid models, combining process-based ESMs with ML components. We document recent work showcasing the potential of automatic differentiation for a new generation of substantially improved, data-informed ESMs.Comment: 17 pages, 2 figure

Inferring causation from time series in Earth system sciences

The heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In large-scale complex dynamical systems such as the Earth system, real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated data opens up the use of novel data-driven causal methods beyond the commonly adopted correlation techniques. Here, we give an overview of causal inference frameworks and identify promising generic application cases common in Earth system sciences and beyond. We discuss challenges and initiate the benchmark platform causeme.net to close the gap between method users and developers. © 2019, The Author(s)

Global Tipping Points Report 2023: Ch1.2: Cryosphere tipping points.

Drastic changes in our planet’s frozen landscapes have occurred over recent decades, from Arctic sea ice decline and thawing of permafrost soils to polar amplification, the retreat of glaciers and ice loss from the ice sheets. In this chapter, we assess multiple lines of evidence for tipping points in the cryosphere – encompassing the ice sheets on Greenland and Antarctica, sea ice, mountain glaciers and permafrost – based on recent observations, palaeorecords, numerical modelling and theoretical understanding. With about 1.2°C of global warming compared to pre-industrial levels, we are getting dangerously close to the temperature thresholds of some major tipping points for the ice sheets of Greenland and West Antarctica. Crossing these would lock in unavoidable long-term global sea level rise of up to 10 metres. There is evidence for localised and regional tipping points for glaciers and permafrost and, while evidence for global-scale tipping dynamics in sea ice, glaciers and permafrost is limited, their decline will continue with unabated global warming. Because of the long response times of these systems, some impacts of crossing potential tipping points will unfold over centuries to millennia. However, with the current trajectory of greenhouse gas (GHG) emissions and subsequent anthropogenic climate change, such largely irreversible changes might already have been triggered. These will cause far-reaching impacts for ecosystems and humans alike, threatening the livelihoods of millions of people, and will become more severe the further global warming progresses

Global Tipping Points Report 2023: Ch1.5: Climate tipping point interactions and cascades.

This chapter reviews interactions between climate tipping systems and assesses the potential risk of cascading effects. After a definition of tipping system interactions, we map out the current state of the literature on specific interactions between climate tipping systems that may be important for the overall stability of the climate system. For this, we gather evidence from model simulations, observations and conceptual understanding, as well as archetypal examples of palaeoclimate reconstructions where propagating transitions were potentially at play. This chapter concludes by identifying crucial knowledge gaps in tipping system interactions that should be resolved in order to improve risk assessments of cascading transitions under future climate change scenarios

Climate tipping point interactions and cascades: A review

Climate tipping elements are large-scale subsystems of the Earth that may transgress critical thresholds (tipping points) under ongoing global warming, with substantial impacts on the biosphere and human societies. Frequently studied examples of such tipping elements include the Greenland Ice Sheet, the Atlantic Meridional Overturning Circulation (AMOC), permafrost, monsoon systems, and the Amazon rainforest. While recent scientific efforts have improved our knowledge about individual tipping elements, the interactions between them are less well understood. Also, the potential of individual tipping events to induce additional tipping elsewhere or stabilize other tipping elements is largely unknown. Here, we map out the current state of the literature on the interactions between climate tipping elements and review the influences between them. To do so, we gathered evidence from model simulations, observations, and conceptual understanding, as well as examples of paleoclimate reconstructions where multi-component or spatially propagating transitions were potentially at play. While uncertainties are large, we find indications that many of the interactions between tipping elements are destabilizing. Therefore, we conclude that tipping elements should not only be studied in isolation, but also more emphasis has to be put on potential interactions. This means that tipping cascades cannot be ruled out on centennial to millennial timescales at global warming levels between 1.5 and 2.0 ◦C or on shorter timescales if global warming surpassed 2.0 ◦C. At these higher levels of global warming, tipping cascades may then include fast tipping elements such as the AMOC or the Amazon rainforest. To address crucial knowledge gaps in tipping element interactions, we propose four strategies combining observation-based approaches, Earth system modeling expertise, computational advances, and expert knowledge