ALBERT

Description: Tropical rainforests are recognized as one of the terrestrialtipping elements which could have profound impacts on the global cli-mate, once their vegetation has transitioned into savanna or grasslandstates. While several studies investigated the savannization of, e.g., theAmazon rainforest, few studies considered the influence of fire. Fire isexpected to potentially shift the savanna-forest boundary and henceimpact the dynamical equilibrium between these two possible vegeta-tion states under changing climate. To investigate the climate-inducedhysteresis in pan-tropical forests and the impact of fire under future cli-mate conditions, we employed the Earth system model CM2Mc, whichis biophysically coupled to the fire-enabled state-of-the-art dynamicglobal vegetation model LPJmL. We conducted several simulation ex-periments where atmospheric CO2concentrations increased (impactphase) and decreased from the new state (recovery phase), each withand without enabling wildfires. We find a hysteresis of the biomassand vegetation cover in tropical forest systems, with a strong regionalheterogeneity. After biomass loss along increasing atmospheric CO2concentrations and accompanied mean surface temperature increase ofabout 4°C (impact phase), the system does not recover completely intoits original state on its return path, even though atmospheric CO2concentrations return to their original state. While not detecting large-scale tipping points, our results show a climate-induced hysteresis intropical forest and lagged responses in forest recovery after the climatehas returned to its original state. Wildfires slightly widen the climate-induced hysteresis in tropical forests and lead to a lagged response inforest recovery by ca. 30 years.

Description: pycascades - a software package to simulate dynamics of tipping cascades on complex networks. This first release of pycascades goes along with the submission of the model description paper.

Description: There exists a range of subsystems in the climate system exhibiting threshold behaviour which could be triggered under global warming within this century resulting in severe consequences for biosphere and human societies. While their individual tipping thresholds are fairly well understood, it is of yet unclear how their interactions might impact the overall stability of the Earth's climate system. This cannot be studied yet with state-of-the-art Earth system models due to computational constraints as well as missing and uncertain process representations of some tipping elements. Here, we explicitly study the effects of known physical interactions between the Greenland and West Antarctic Ice Sheet, the Atlantic Meridional Overturning Circulation, the El-Nino Southern Oscillation and the Amazon rainforest using a conceptual network approach. We analyse the risk of domino effects being triggered by each of the individual tipping elements under global warming in equilibrium experiments, propagating uncertainties in critical temperature thresholds and interaction strengths via a Monte-Carlo approach. Overall, we find that the interactions tend to destabilise the network. Furthermore, our analysis reveals the qualitative role of each of the five tipping elements showing that the polar ice sheets on Greenland and West Antarctica are oftentimes the initiators of tipping cascades, while the AMOC acts as a mediator, transmitting cascades. This implies that the ice sheets, which are already at risk of transgressing their temperature thresholds within the Paris range of 1.5 to 2 °C, are of particular importance for the stability of the climate system as a whole.

Description: 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.

Description: The growth of cell colonies is determined by the migration and proliferation of the individual cells. This is often modeled with the Fisher–Kolmogorov (FK) equation, which assumes that cells diffuse independently from each other, but stop to proliferate when their density reaches a critial limit. However, when using measured, cell-line specific parameters, we find that the FK equation drastically underestimates the experimentally observed increase of colony radius with time. Moreover, cells in real colonies migrate radially outward with superdiffusive trajectories, in contrast to the assumption of random diffusion. We demonstrate that both dicrepancies can be resolved by assuming that cells in dense colonies are driven apart by repulsive, pressure-like forces. Using this model of proliferating repelling particles, we find that colony growth exhibits different dynamical regimes, depending on the ratio between a pressure-related equilibrium cell density and the critial density of proliferation arrest.

Description: Tipping elements in the Earth System receive increased scientific attention over the recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element undergoes a drastic shift in its state upon an additional small parameter change when close to its tipping point. Recently, the focus of research broadened towards emergent behavior in networks of tipping elements, like global tipping cascades triggered by local perturbations. Here, we analyze the response to the perturbation of a single node in a system that initially resides in an unstable equilibrium. The evolution is described in terms of coupled nonlinear equations for the cumulants of the distribution of the elements. We show that drift terms acting on individual elements and offsets in the coupling strength are sub-dominant in the limit of large networks, and we derive an analytical prediction for the evolution of the expectation (i.e., the first cumulant). It behaves like a single aggregated tipping element characterized by a dimensionless parameter that accounts for the network size, its overall connectivity, and the average coupling strength. The resulting predictions are in excellent agreement with numerical data for Erd\"os-R\'enyi, Barab\'asi-Albert and Watts-Strogatz networks of different size and with different coupling parameters.

Description: Societal transformations are necessary to address critical global challenges, such as mitigation of anthropogenic climate change and reaching UN sustainable development goals. Recently, social tipping processes have received increased attention, as they present a form of social change whereby a small change can shift a sensitive social system into a qualitatively different state due to strongly self-amplifying (mathematically positive) feedback mechanisms. Social tipping processes with respect to technological and energy systems, political mobilization, financial markets and sociocultural norms and behaviors have been suggested as potential key drivers towards climate action. Drawing from expert insights and comprehensive literature review, we develop a framework to identify and characterize social tipping processes critical to facilitating rapid social transformations. We find that social tipping processes are distinguishable from those of already more widely studied climate and ecological tipping dynamics. In particular, we identify human agency, social-institutional network structures, different spatial and temporal scales and increased complexity as key distinctive features underlying social tipping processes. Building on these characteristics, we propose a formal definition for social tipping processes and filtering criteria for those processes that could be decisive for future trajectories towards climate action. We illustrate this definition with the European political system as an example of potential social tipping processes, highlighting the prospective role of the FridaysForFuture movement. Accordingly, this conceptual framework for social tipping processes can be utilized to illuminate mechanisms for necessary transformative climate change mitigation policies and actions.

Description: Tipping points occur in diverse systems in various disciplines such as ecology, climate science, economy, and engineering. Tipping points are critical thresholds in system parameters or state variables at which a tiny perturbation can lead to a qualitative change of the system. Many systems with tipping points can be modeled as networks of coupled multistable subsystems, e.g., coupled patches of vegetation, connected lakes, interacting climate tipping elements, and multiscale infrastructure systems. In such networks, tipping events in one subsystem are able to induce tipping cascades via domino effects. Here, we investigate the effects of network topology on the occurrence of such cascades. Numerical cascade simulations with a conceptual dynamical model for tipping points are conducted on Erdős-Rényi, Watts-Strogatz, and Barabási-Albert networks. Additionally, we generate more realistic networks using data from moisture-recycling simulations of the Amazon rainforest and compare the results to those obtained for the model networks. We furthermore use a directed configuration model and a stochastic block model which preserve certain topological properties of the Amazon network to understand which of these properties are responsible for its increased vulnerability. We find that clustering and spatial organization increase the vulnerability of networks and can lead to tipping of the whole network. These results could be useful to evaluate which systems are vulnerable or robust due to their network topology and might help us to design or manage systems accordingly.

Description: In this study, we investigate how specific micro-interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erdős–Rényi networks and an exemplary moisture recycling network of the Amazon rainforest. Within these networks, decisive small-scale motifs are the feed forward loop, the secondary feed forward loop, the zero loop, and the neighboring loop. Of all motifs, the feed forward loop motif stands out in tipping cascades since it decreases the critical coupling strength necessary to initiate a cascade more than the other motifs. We find that for this motif, the reduction of critical coupling strength is 11% less than the critical coupling of a pair of tipping elements. For highly connected networks, our analysis reveals that coupled feed forward loops coincide with a strong 90% decrease in the critical coupling strength. For the highly clustered moisture recycling network in the Amazon, we observe regions of a very high motif occurrence for each of the four investigated motifs, suggesting that these regions are more vulnerable. The occurrence of motifs is found to be one order of magnitude higher than in a random Erdős–Rényi network. This emphasizes the importance of local interaction structures for the emergence of global cascades and the stability of the network as a whole. Tipping elements are nonlinear systems, where a small perturbation can be sufficient to induce a qualitative change in the whole system as soon as a critical threshold (tipping point) is crossed. Coupled tipping elements exist, for instance, in connected lake systems, in the Earth’s climate system, or in social systems. Here, we investigate networks of interacting tipping elements, where each node consists of a stylized tipping element and explore important interaction structures on the microscale of the network, the so-called motifs. Such motifs in complex networks have been found in multiple systems such as cell metabolism, food webs, or neural networks and are known to be significantly overexpressed in real-world compared to random networks. However, motifs have not yet been studied extensively in complex networks, where nodes have their own dynamics. In our study, we find that tipping cascades occur more often at locations with a high motif frequency revealing locations (nodes) of decreased robustness.