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- ItemModelling nonlinear dynamics of interacting tipping elements on complex networks: the PyCascades package(Berlin ; Heidelberg : Springer, 2021) Wunderling, Nico; Krönke, Jonathan; Wohlfarth, Valentin; Kohler, Jan; Heitzig, Jobst; Staal, Arie; Willner, Sven; Winkelmann, Ricarda; Donges, Jonathan F.Tipping elements occur in various systems such as in socio-economics, ecology and the climate system. In many cases, the individual tipping elements are not independent of each other, but they interact across scales in time and space. To model systems of interacting tipping elements, we here introduce the PyCascades open source software package for studying interacting tipping elements (https://doi.org/10.5281/zenodo.4153102). PyCascades is an object-oriented and easily extendable package written in the programming language Python. It allows for investigating under which conditions potentially dangerous cascades can emerge between interacting dynamical systems, with a focus on tipping elements. With PyCascades it is possible to use different types of tipping elements such as double-fold and Hopf types and interactions between them. PyCascades can be applied to arbitrary complex network structures and has recently been extended to stochastic dynamical systems. This paper provides an overview of the functionality of PyCascades by introducing the basic concepts and the methodology behind it. In the end, three examples are discussed, showing three different applications of the software package. First, the moisture recycling network of the Amazon rainforest is investigated. Second, a model of interacting Earth system tipping elements is discussed. And third, the PyCascades modelling framework is applied to a global trade network.
- ItemImpact of an AMOC weakening on the stability of the southern Amazon rainforest(Berlin ; Heidelberg : Springer, 2021) Ciemer, Catrin; Winkelmann, Ricarda; Kurths, Jürgen; Boers, NiklasThe Atlantic Meridional Overturning Circulation (AMOC) and the Amazon rainforest are potential tipping elements of the Earth system, i.e., they may respond with abrupt and potentially irreversible state transitions to a gradual change in forcing once a critical forcing threshold is crossed. With progressing global warming, it becomes more likely that the Amazon will reach such a critical threshold, due to projected reductions of precipitation in tropical South America, which would in turn trigger vegetation transitions from tropical forest to savanna. At the same time, global warming has likely already contributed to a weakening of the AMOC, which induces changes in tropical Atlantic sea-surface temperature (SST) patterns that in turn affect rainfall patterns in the Amazon. A large-scale decline or even dieback of the Amazon rainforest would imply the loss of the largest terrestrial carbon sink, and thereby have drastic consequences for the global climate. Here, we assess the direct impact of greenhouse gas-driven warming of the tropical Atlantic ocean on Amazon rainfall. In addition, we estimate the effect of an AMOC slowdown or collapse, e. g. induced by freshwater flux into the North Atlantic due to melting of the Greenland Ice Sheet, on Amazon rainfall. In order to provide a clear explanation of the underlying dynamics, we use a simple, but robust mathematical approach (based on the classical Stommel two-box model), ensuring consistency with a comprehensive general circulation model (HadGEM3). We find that these two processes, both caused by global warming, are likely to have competing impacts on the rainfall sum in the Amazon, and hence on the stability of the Amazon rainforest. A future AMOC decline may thus counteract direct global-warming-induced rainfall reductions. Tipping of the AMOC from the strong to the weak mode may therefore have a stabilizing effect on the Amazon rainforest.
- ItemBasin stability and limit cycles in a conceptual model for climate tipping cascades([London] : IOP, 2020) Wunderling, Nico; Gelbrecht, Maximilian; Winkelmann, Ricarda; Kurths, Jürgen; Donges, Jonathan F.Tipping elements in the climate system are large-scale subregions of the Earth that might possess threshold behavior under global warming with large potential impacts on human societies. Here, we study a subset of five tipping elements and their interactions in a conceptual and easily extendable framework: the Greenland Ice Sheets (GIS) and West Antarctic Ice Sheets, the Atlantic meridional overturning circulation (AMOC), the El–Niño Southern Oscillation and the Amazon rainforest. In this nonlinear and multistable system, we perform a basin stability analysis to detect its stable states and their associated Earth system resilience. By combining these two methodologies with a large-scale Monte Carlo approach, we are able to propagate the many uncertainties associated with the critical temperature thresholds and the interaction strengths of the tipping elements. Using this approach, we perform a system-wide and comprehensive robustness analysis with more than 3.5 billion ensemble members. Further, we investigate dynamic regimes where some of the states lose stability and oscillations appear using a newly developed basin bifurcation analysis methodology. Our results reveal that the state of four or five tipped elements has the largest basin volume for large levels of global warming beyond 4 °C above pre-industrial climate conditions, representing a highly undesired state where a majority of the tipping elements reside in the transitioned regime. For lower levels of warming, states including disintegrated ice sheets on west Antarctica and Greenland have higher basin volume than other state configurations. Therefore in our model, we find that the large ice sheets are of particular importance for Earth system resilience. We also detect the emergence of limit cycles for 0.6% of all ensemble members at rare parameter combinations. Such limit cycle oscillations mainly occur between the GIS and AMOC (86%), due to their negative feedback coupling. These limit cycles point to possibly dangerous internal modes of variability in the climate system that could have played a role in paleoclimatic dynamics such as those unfolding during the Pleistocene ice age cycles.