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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.
- ItemClimate-induced hysteresis of the tropical forest in a fire-enabled Earth system model(Berlin ; Heidelberg : Springer, 2021) Drüke, Markus; Bloh, Werner von; Sakschewski, Boris; Wunderling, Nico; Petri, Stefan; Cardoso, Manoel; Barbosa, Henrique M.J.; Thonicke, KirstenTropical rainforests are recognized as one of the terrestrial tipping elements which could have profound impacts on the global climate, once their vegetation has transitioned into savanna or grassland states. While several studies investigated the savannization of, e.g., the Amazon rainforest, few studies considered the influence of fire. Fire is expected to potentially shift the savanna-forest boundary and hence impact the dynamical equilibrium between these two possible vegetation states under changing climate. To investigate the climate-induced hysteresis in pan-tropical forests and the impact of fire under future climate conditions, we employed the Earth system model CM2Mc, which is biophysically coupled to the fire-enabled state-of-the-art dynamic global vegetation model LPJmL. We conducted several simulation experiments where atmospheric CO2 concentrations increased (impact phase) and decreased from the new state (recovery phase), each with and without enabling wildfires. We find a hysteresis of the biomass and vegetation cover in tropical forest systems, with a strong regional heterogeneity. After biomass loss along increasing atmospheric CO2 concentrations and accompanied mean surface temperature increase of about 4 ∘C (impact phase), the system does not recover completely into its original state on its return path, even though atmospheric CO2 concentrations return to their original state. While not detecting large-scale tipping points, our results show a climate-induced hysteresis in tropical forest and lagged responses in forest recovery after the climate has returned to its original state. Wildfires slightly widen the climate-induced hysteresis in tropical forests and lead to a lagged response in forest recovery by ca. 30 years.