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The Greenland Ice Sheet (GIS) and Atlantic Meridional Overturning Circulation (AMOC) are considered tipping elements in the climate system, where global warming exceeding critical threshold levels in forcing can lead to large-scale and nonlinear reductions in ice volume and overturning strength, respectively. The positive–negative feedback loop governing their interaction with a destabilizing effect on the AMOC due to ice loss and subsequent freshwater flux into the North Atlantic as well as a stabilizing effect of a net cooling around Greenland with an AMOC weakening may determine the long-term stability of both tipping elements. Here we explore the potential dynamic regimes arising from this positive–negative tipping feedback loop in a physically motivated conceptual model. Under idealized forcing scenarios we identify conditions under which different kinds of tipping cascades can occur: herein, we distinguish between overshoot/bifurcation tipping cascades, leading to tipping of both GIS and AMOC, and rate-induced tipping cascades, where the AMOC, despite not having crossed its own intrinsic tipping point, tips nonetheless due to the fast rate of ice loss from Greenland. The occurrence of these different cascades is affected by the ice sheet disintegration time and thus eventually by the imposed forcing and its timescales. Our results suggest that it is necessary not only to avoid surpassing the respective critical levels of the environmental drivers for the Greenland Ice Sheet and Atlantic Meridional Overturning Circulation, but also to respect safe rates of environmental change to mitigate potential domino effects. [ABSTRACT FROM AUTHOR]

The Greenland Ice Sheet and Atlantic Meridional Overturning Circulation are considered tipping elements in the climate system, where global warming exceeding critical threshold levels in forcing can lead to large-scale and nonlinear reductions in ice volume and overturning strength, respectively. The positive-negative feedback loop governing their interaction (with a destabilizing effect on the AMOC due to ice loss and subsequent freshwater flux into the North Atlantic as well as a stabilizing effect of a net-cooling around Greenland with an AMOC weakening) may determine the long-term stability of both tipping elements. Here we explore the potential dynamic regimes arising from this positive-negative tipping feedback loop in a process-based conceptual model. Under idealized forcing scenarios we identify conditions under which different kinds of tipping cascades can occur: Herein, we distinguish between overshoot tipping cascades (leading to tipping of both GIS and AMOC) and rate-induced tipping cascades (where the AMOC despite not having crossed its own intrinsic tipping point tips nonetheless due to the fast rate of ice loss from Greenland). These different cascades occur within corridors of distinct tipping pathways that are affected by the GIS melting patterns and thus eventually by the imposed forcing and its time scales. Our results suggest that it is not only necessary to avoid breaching the respective critical levels of the environmental drivers for the Greenland Ice Sheet and Atlantic Meridional Overturning Circulation, but also to respect safe rates of environmental change to mitigate potential domino effects. [ABSTRACT FROM AUTHOR]

Although spatial polarization of attitudes is extremely common around the world, we understand little about the mechanisms through which polarization on divisive issues rises and falls over time. We develop a theory that explains how political shocks can have different effects in different regions of a country depending upon local dynamics generated by the preexisting spatial distribution of attitudes and discussion networks. Where opinions were previously divided, attitudinal diversity is likely to persist after the shock. Meanwhile, where a clear precrisis majority exists on key issues, opinions should change in the direction of the predominant view. These dynamics result in greater local homogeneity in attitudes but at the same time exacerbate geographic polarization across regions and sometimes even within regions. We illustrate our theory by developing a modified version of the adaptive voter model, an adaptive network model of opinion dynamics, to study changes in attitudes toward the European Union (EU) in Ukraine in the context of the Euromaidan Revolution of 2013 to 2014. Using individual-level panel data from surveys fielded before and after the Euromaidan Revolution, we show that EU support increased in areas with high prior public support for EU integration but declined further where initial public attitudes were opposed to the EU, thereby increasing the spatial polarization of EU attitudes in Ukraine. Our tests suggest that the predictive power of both network and regression models increases significantly when we incorporate information about the geographic location of network participants, which highlights the importance of spatially rooted social networks. [ABSTRACT FROM AUTHOR]

Spreading dynamics and complex contagion processes on networks are important mechanisms underlying the emergence of critical transitions, tipping points and other non-linear phenomena in complex human and natural systems. Increasing amounts of temporal network data are now becoming available to study such spreading processes of behaviours, opinions, ideas, diseases and innovations to test hypotheses regarding their specific properties. To this end, we here present a methodology based on dose–response functions and hypothesis testing using surrogate data models that randomise most aspects of the empirical data while conserving certain structures relevant to contagion, group or homophily dynamics. We demonstrate this methodology for synthetic temporal network data of spreading processes generated by the adaptive voter model. Furthermore, we apply it to empirical temporal network data from the Copenhagen Networks Study. This data set provides a physically-close-contact network between several hundreds of university students participating in the study over the course of 3 months. We study the potential spreading dynamics of the health-related behaviour "regularly going to the fitness studio" on this network. Based on a hierarchy of surrogate data models, we find that our method neither provides significant evidence for an influence of a dose–response-type network spreading process in this data set, nor significant evidence for homophily. The empirical dynamics in exercise behaviour are likely better described by individual features such as the disposition towards the behaviour, and the persistence to maintain it, as well as external influences affecting the whole group, and the non-trivial network structure. The proposed methodology is generic and promising also for applications to other temporal network data sets and traits of interest. [ABSTRACT FROM AUTHOR]

In the Anthropocene, the social dynamics of human societies have become critical to understanding planetary-scale Earth system dynamics. The conceptual foundations of Earth system modelling have externalised social processes in ways that now hinder progress in understanding Earth resilience and informing governance of global environmental change. New approaches to global modelling of the human World are needed to address these challenges. The current modelling landscape is highly diverse and heterogeneous, ranging from purely biophysical Earth system models, to hybrid macro-economic integrated assessments models, to a plethora of models of socio-cultural dynamics. World–Earth models capable of simulating complex and entangled human–Earth system processes of the Anthropocene are currently not available. They will need to draw on and selectively integrate elements from the diverse range of fields and approaches; thus, future World–Earth modellers require a structured approach to identify, classify, select, combine and critique model components from multiple modelling traditions. Here, we develop taxonomies for ordering the multitude of societal and biophysical subsystems and their interactions. We suggest three taxa for modelled subsystems: (i) biophysical, where dynamics is usually represented by "natural laws" of physics, chemistry or ecology (i.e. the usual components of Earth system models); (ii) socio-cultural, dominated by processes of human behaviour, decision-making and collective social dynamics (e.g. politics, institutions, social networks and even science itself); and (iii) socio-metabolic, dealing with the material interactions of social and biophysical subsystems (e.g. human bodies, natural resources and agriculture). We show how higher-order taxonomies can be derived for classifying and describing the interactions between two or more subsystems. This then allows us to highlight the kinds of social–ecological feedback loops where new modelling efforts need to be directed. As an example, we apply the taxonomy to a stylised World–Earth system model that endogenises the socially transmitted choice of discount rates in a greenhouse gas emissions game to illustrate the effects of social–ecological feedback loops that are usually not considered in current modelling efforts. The proposed taxonomy can contribute to guiding the design and operational development of more comprehensive World–Earth models for understanding Earth resilience and charting sustainability transitions within planetary boundaries and other future trajectories in the Anthropocene. [ABSTRACT FROM AUTHOR]

With progressing global warming, there is an increased risk that one or several tipping elements in the climate system might cross a critical threshold, resulting in severe consequences for the global climate, ecosystems and human societies. While the underlying processes are fairly well-understood, it is unclear how their interactions might impact the overall stability of the Earth's climate system. As of yet, this cannot be fully analysed with state-of-the-art Earth system models due to computational constraints as well as some missing and uncertain process representations of certain tipping elements. Here, we explicitly study the effects of known physical interactions among the Greenland and West Antarctic ice sheets, the Atlantic Meridional Overturning Circulation (AMOC) 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. In these experiments, we propagate the uncertainties in critical temperature thresholds, interaction strengths and interaction structure via large ensembles of simulations in a Monte Carlo approach. Overall, we find that the interactions tend to destabilise the network of tipping elements. Furthermore, our analysis reveals the qualitative role of each of the four tipping elements within the network, 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 indicates 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. [ABSTRACT FROM AUTHOR]

We will need collective action to avoid catastrophic climate change, and this will require valuing the long term as well as the short term. Shortsightedness and uncertainty have hindered progress in resolving this collective action problem and have been recognized as important barriers to cooperation among humans. Here, we propose a coupled social-ecological dilemma to investigate the interdependence of three well-identified components of this cooperation problem: 1) timescales of collapse and recovery in relation to time preferences regarding future outcomes, 2) the magnitude of the impact of collapse, and 3) the number of actors in the collective. We find that, under a sufficiently severe and time-distant collapse, how much the actors care for the future can transform the game from a tragedy of the commons into one of coordination, and even into a comedy of the commons in which cooperation dominates. Conversely, we also find conditions under which even strong concern for the future still does not transform the problem from tragedy to comedy. For a large number of participating actors, we find that the critical collapse impact, at which these game regime changes happen, converges to a fixed value of collapse impact per actor that is independent of the enhancement factor of the public good, which is usually regarded as the driver of the dilemma. Our results not only call for experimental testing but also help explain why polarization in beliefs about human-caused climate change can threaten global cooperation agreements. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Analysis of Earth system dynamics in the Anthropocene requires explicitly taking into account the increasing magnitude of processes operating in human societies, their cultures, economies and technosphere and their growing feedback entanglement with those in the physical, chemical and biological systems of the planet. However, current state-of-the-art Earth system models do not represent dynamic human societies and their feedback interactions with the biogeophysical Earth system and macroeconomic integrated assessment models typically do so only with limited scope. This paper (i) proposes design principles for constructing world–Earth models (WEMs) for Earth system analysis of the Anthropocene, i.e., models of social (world)–ecological (Earth) coevolution on up to planetary scales, and (ii) presents the copan:CORE open simulation modeling framework for developing, composing and analyzing such WEMs based on the proposed principles. The framework provides a modular structure to flexibly construct and study WEMs. These can contain biophysical (e.g., carbon cycle dynamics), socio-metabolic or economic (e.g., economic growth or energy system changes), and sociocultural processes (e.g., voting on climate policies or changing social norms) and their feedback interactions, and they are based on elementary entity types, e.g., grid cells and social systems. Thereby, copan:CORE enables the epistemic flexibility needed for contributions towards Earth system analysis of the Anthropocene given the large diversity of competing theories and methodologies used for describing socio-metabolic or economic and sociocultural processes in the Earth system by various fields and schools of thought. To illustrate the capabilities of the framework, we present an exemplary and highly stylized WEM implemented in copan:CORE that illustrates how endogenizing sociocultural processes and feedbacks such as voting on climate policies based on socially learned environmental awareness could fundamentally change macroscopic model outcomes. [ABSTRACT FROM AUTHOR]

Safely achieving the goals of the Paris Climate Agreement requires a worldwide transformation to carbon-neutral societies within the next 30 y. Accelerated technological progress and policy implementations are required to deliver emissions reductions at rates sufficiently fast to avoid crossing dangerous tipping points in the Earth's climate system. Here, we discuss and evaluate the potential of social tipping interventions (STIs) that can activate contagious processes of rapidly spreading technologies, behaviors, social norms, and structural reorganization within their functional domains that we refer to as social tipping elements (STEs). STEs are subdomains of the planetary socioeconomic system where the required disruptive change may take place and lead to a sufficiently fast reduction in anthropogenic greenhouse gas emissions. The results are based on online expert elicitation, a subsequent expert workshop, and a literature review. The STIs that could trigger the tipping of STE subsystems include 1) removing fossil-fuel subsidies and incentivizing decentralized energy generation (STE1, energy production and storage systems), 2) building carbon-neutral cities (STE2, human settlements), 3) divesting from assets linked to fossil fuels (STE3, financialmarkets), 4) revealing the moral implications of fossil fuels (STE4, norms and value systems), 5) strengthening climate education and engagement (STE5, education system), and 6) disclosing information on greenhouse gas emissions (STE6, information feedbacks). Our research reveals important areas of focus for larger-scale empirical and modeling efforts to better understand the potentials of harnessing social tipping dynamics for climate change mitigation. [ABSTRACT FROM AUTHOR]

Changes to climate-carbon cycle feedbacks may significantly affect the Earth system's response to greenhouse gas emissions. These feedbacks are usually analysed from numerical output of complex and arguably opaque Earth system models. Here, we construct a stylised global climate-carbon cycle model, test its output against comprehensive Earth system models, and investigate the strengths of its climate-carbon cycle feedbacks analytically. The analytical expressions we obtain aid understanding of carbon cycle feedbacks and the operation of the carbon cycle. Specific results include that different feedback formalisms measure fundamentally the same climate-carbon cycle processes; temperature dependence of the solubility pump, biological pump, and CO2 solubility all contribute approximately equally to the ocean climate-carbon feedback; and concentration-carbon feedbacks may be more sensitive to future climate change than climate-carbon feedbacks. Simple models such as that developed here also provide "workbenches" for simple but mechanistically based explorations of Earth system processes, such as interactions and feedbacks between the planetary boundaries, that are currently too uncertain to be included in comprehensive Earth system models. [ABSTRACT FROM AUTHOR]

In the Anthropocene, social processes have become critical to understanding planetary-scale Earth system dynamics. The conceptual foundations of Earth system modelling have externalised social processes in ways that now hinder progress in understanding Earth resilience and informing governance of global environmental change. New approaches to global modelling are needed to address these challenges, but the current modelling landscape is highly diverse and heterogeneous, ranging from purely biophysical Earth System Models, to hybrid macro-economic Integrated Assessments Models, to a plethora of models of socio-cultural dynamics. World-Earth models, currently not yet available, will need to integrate all these elements, so future World-Earth modellers require a structured approach to identify, classify, select, and combine model components. Here, we develop taxonomies for ordering the multitude of societal and biophysical subsystems and their interactions. We suggest three taxa for modelled subsystems: (i) biophysical, where dynamics is usually represented by "natural laws" of physics, chemistry or ecology (i.e., the usual components of Earth system models), (ii) socio-cultural, dominated by processes of human behaviour, decision making and collective social dynamics (e.g., politics, institutions, social networks), and (iii) socio-metabolic, dealing with the material interactions of social and biophysical subsystems (e.g., human bodies, natural resource and agriculture). We show how higher-order taxonomies for interactions between two or more subsystems can be derived, highlighting the kinds of social-ecological feedback loops where new modelling efforts need to be directed. As an example, we apply the taxonomy to a stylised World-Earth system model of socially transmitted discount rates in a greenhouse gas emissions game to illustrate the effects of social-ecological feedback loops that are usually not considered in current modelling efforts. The proposed taxonomy can contribute to guiding the design and operational development of more comprehensive World-Earth models for understanding Earth resilience and charting sustainability transitions within planetary boundaries and other future trajectories in the Anthropocene. [ABSTRACT FROM AUTHOR]

Possible future trajectories of the Earth system in the Anthropocene are determined by the increasing entanglement of processes operating in the physical, chemical and biological systems of the planet, as well as in human societies, their cultures and economies. Here, we introduce the copan:CORE open source software library that provides a framework for developing, composing and running World-Earth models, i.e., models of social-ecological co-evolution up to planetary scales. It is an object-oriented software package written in Python designed for different user roles. It allows model end users to run parallel simulations with already available and tested models. Furthermore, model composers are enabled to easily implement new models by plugging together a broad range of model components, such as opinion formation on social networks, generic carbon cycle dynamics, or simple vegetation growth. For the sake of a modular structure, each provided component specifies a meaningful yet minimal collection of closely related processes. These processes can be formulated in terms of various process types, such as ordinary differential equations, explicit or implicit functions, as well as steps or events of deterministic or stochastic fashion. In addition to the already included variety of different components in copan:CORE, model developers can extend the framework with additional components that are based on elementary entity types, i.e., grid cells, individuals and social systems, or the fundamental process taxa environment, social metabolism, and culture. To showcase possible usage we present an exemplary World-Earth model that combines a variety of model components and interactions thereof. As the framework allows a simple activation and deactivation of certain components and related processes, users can test for their specific effects on modeling results and evaluate model robustness in a controlled way. Hence, copan:CORE allows developing process-based models of global change and sustainable development in planetary social-ecological systems and thus fosters a better understanding of crucial mechanisms governing the co-evolutionary dynamics between societies and the natural environment. Due to its modular structure, the framework enhances the development and application of stylized models in Earth system science but also climatology, economics, ecology, or sociology, and allows combining them for interdisciplinary studies at the interface between different areas of expertise. [ABSTRACT FROM AUTHOR]

ABSTRACT In recent years extensive studies on the Earth's climate system have been carried out by means of advanced complex network statistics. The great majority of these studies, however, have been focusing on investigating correlation structures within single climatic fields directly on or parallel to the Earth's surface. Here, we develop a novel approach of node weighted coupled network measures to study correlations between ocean and atmosphere in the Northern Hemisphere extratropics and construct 18 coupled climate networks, each consisting of two subnetworks. In all cases, one subnetwork represents monthly sea-surface temperature ( SST) anomalies, while the other is based on the monthly geopotential height ( HGT) of isobaric surfaces at different pressure levels covering the troposphere as well as the lower stratosphere. The weighted cross-degree density proves to be consistent with the leading coupled pattern obtained from maximum covariance analysis. Network measures of higher order allow for a further analysis of the correlation structure between the two fields and consistently indicate that in the Northern Hemisphere extratropics the ocean is correlated with the atmosphere in a hierarchical fashion such that large areas of the ocean surface correlate with multiple statistically dissimilar regions in the atmosphere. Ultimately we show that this observed hierarchy is linked to large-scale atmospheric variability patterns, such as the Pacific North American pattern, forcing the ocean on monthly time scales. [ABSTRACT FROM AUTHOR]

Changes to climate-carbon cycle feedbacks may significantly affect the Earth System's response to greenhouse gas emissions. These feedbacks are usually analysed from numerical output of complex and arguably opaque Earth System Models (ESMs). Here, we construct a stylized global climate-carbon cycle model, test its output against complex ESMs, and investigate the strengths of its climate-carbon cycle feedbacks analytically. The analytical expressions we obtain aid understanding of carbon-cycle feedbacks and the operation of the carbon cycle. We use our results to analytically study the relative strengths of different climate-carbon cycle feedbacks and how they may change in the future, as well as to compare different feedback formalisms. Simple models such as that developed here also provide "workbenches" for simple but mechanistically based explorations of Earth system processes, such as interactions and feedbacks between the Planetary Boundaries, that are currently too uncertain to be included in complex ESMs. [ABSTRACT FROM AUTHOR]

Human societies depend on the resources ecosystems provide. Particularly since the last century, human activities have transformed the relationship between nature and society at a global scale. We study this coevolutionary relationship by utilizing a stylized model of private resource use and social learning on an adaptive network. The latter process is based on two social key dynamics beyond economic paradigms: boundedly rational imitation of resource use strategies and homophily in the formation of social network ties. The private and logistically growing resources are harvested with either a sustainable (small) or non-sustainable (large) effort. We show that these social processes can have a profound influence on the environmental state, such as determining whether the private renewable resources collapse from overuse or not. Additionally, we demonstrate that heterogeneously distributed regional resource capacities shift the critical social parameters where this resource extraction system collapses. We make these points to argue that, in more advanced coevolutionary models of the planetary social-ecological system, such socio-cultural phenomena as well as regional resource heterogeneities should receive attention in addition to the processes represented in established Earth system and integrated assessment models. [ABSTRACT FROM AUTHOR]

The planetary boundaries framework provides guidelines for defining thresholds in environmental variables. Their transgression is likely to result in a shift in Earth system functioning away from the relatively stable Holocene state. As the climate system is approaching critical thresholds of atmospheric carbon, several climate engineering methods are discussed, aiming at a reduction of atmospheric carbon concentrations to control the Earth's energy balance. Terrestrial carbon dioxide removal (tCDR) via afforestation or bioenergy production with carbon capture and storage are part of most climate change mitigation scenarios that limit global warming to less than 2 °C. We analyse the co-evolutionary interaction of societal interventions via tCDR and the natural dynamics of the Earth's carbon cycle. Applying a conceptual modelling framework, we analyse how the degree of anticipation of the climate problem and the intensity of tCDR efforts with the aim of staying within a "safe" level of global warming might influence the state of the Earth system with respect to other carbon-related planetary boundaries. Within the scope of our approach, we show that societal management of atmospheric carbon via tCDR can lead to a collateral transgression of the planetary boundary of land system change. Our analysis indicates that the opportunities to remain in a desirable region within carbon-related planetary boundaries only exist for a small range of anticipation levels and depend critically on the underlying emission pathway. While tCDR has the potential to ensure the Earth system's persistence within a carbon-safe operating space under low-emission pathways, it is unlikely to succeed in a business-as-usual scenario. [ABSTRACT FROM AUTHOR]

Social and political tensions keep on fueling armed conflicts around the world. Although each conflict is the result of an individual context-specific mixture of interconnected factors, ethnicity appears to play a prominent and almost ubiquitous role in many of them. This overall state of affairs is likely to be exacerbated by anthropogenic climate change and in particular climate-related natural disasters. Ethnic divides might serve as predetermined conflict lines in case of rapidly emerging societal tensions arising from disruptive events like natural disasters. Here, we hypothesize that climate-related disaster occurrence enhances armed-conflict outbreak risk in ethnically fractionalized countries. Using event coincidence analysis, we test this hypothesis based on data on armed-conflict outbreaks and climate-related natural disasters for the period 1980-2010. Globally, we find a coincidence rate of 9% regarding armed-conflict outbreak and disaster occurrence such as heat waves or droughts. Our analysis also reveals that, during the period in question, about 23% of conflict outbreaks in ethnically highly fractionalized countries robustly coincide with climatic calamities. Although we do not report evidence that climate-related disasters act as direct triggers of armed conflicts, the disruptive nature of these events seems to play out in ethnically fractionalized societies in a particularly tragic way. This observation has important implications for future security policies as several of the world'smost conflict-prone regions, including North and Central Africa as well as Central Asia, are both exceptionally vulnerable to anthropogenic climate change and characterized by deep ethnic divides. [ABSTRACT FROM AUTHOR]

We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology. [ABSTRACT FROM AUTHOR]

Effective climate change mitigation necessitates swift societal transformations. Social tipping processes, where small triggers initiate qualitative systemic shifts, are potential key mechanisms instigating societal change. A necessary foundation for societal tipping processes is the creation of enabling conditions. Here we assess future sea-level rise estimates and social survey data within the framework of a social activation model to exemplify the enabling conditions for tipping processes. We find that in many countries, climate change concern is sufficient, the enabling conditions and opportunities for social activation already exist. Further, drawing upon the interrelation between climate change concern and anticipation of future sea level rise, we report three qualitative classes of tipping potential that are regionally clustered, with greatest potential for tipping in Western Pacific rim and East Asian countries. These findings propose a transformative pathway where climate change concern increases the social tipping potential, while extended anticipation time horizons can trigger the system towards an alternative trajectory of larger social activation for climate change mitigation. [ABSTRACT FROM AUTHOR]

In many real-world complex systems, the time evolution of the network's structure and the dynamic state of its nodes are closely entangled. Here we study opinion formation and imitation on an adaptive complex network which is dependent on the individual dynamic state of each node and vice versa to model the coevolution of renewable resources with the dynamics of harvesting agents on a social network. The adaptive voter model is coupled to a set of identical logistic growth models and we mainly find that, in such systems, the rate of interactions between nodes as well as the adaptive rewiring probability are crucial parameters for controlling the sustainability of the system's equilibrium state. We derive a macroscopic description of the system in terms of ordinary differential equations which provides a general framework to model and quantify the influence of single node dynamics on the macroscopic state of the network. The thus obtained framework is applicable to many fields of study, such as epidemic spreading, opinion formation, or socioecological modeling. [ABSTRACT FROM AUTHOR]

A faithful modeling of real-world dynamical systems necessitates model evaluation. A recent promising methodological approach to this problem has been based on complex networks, which in turn have proven useful for the characterization of dynamical systems. In this context, we introduce three local network difference measures and demonstrate their capabilities in the field of climate modeling, where these measures facilitate a spatially explicit model evaluation. Building on a recent study by Feldhoff et al. [1] we comparatively analyze statistical and dynamical regional climate simulations of the South American monsoon system. Three types of climate networks representing different aspects of rainfall dynamics are constructed from the modeled precipitation space-time series. Specifically, we define simple graphs based on positive as well as negative rank correlations between rainfall anomaly time series at different locations, and such based on spatial synchronizations of extreme rain events. An evaluation against respective networks built from daily satellite data provided by the Tropical Rainfall Measuring Mission 3B42 V7 reveals far greater differences in model performance between network types for a fixed but arbitrary climate model than between climate models for a fixed but arbitrary network type. We identify two sources of uncertainty in this respect. Firstly, climate variability limits fidelity, particularly in the case of the extreme event network; and secondly, larger geographical link lengths render link misplacements more likely, most notably in the case of the anticorrelation network; both contributions are quantified using suitable ensembles of surrogate networks. Our model evaluation approach is applicable to any multidimensional dynamical system and especially our simple graph difference measures are highly versatile as the graphs to be compared may be constructed in whatever way required. Generalizations to directed as well as edge- and node-weighted graphs are discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the method has still been missing so far. Here, we interpret an &egr;-recurrence network as a discrete subnetwork of a "continuous" graph with uncountably many vertices and edges corresponding to the system's attractor. This step allows us to show that various statistical measures commonly used in complex network analysis can be seen as discrete estimators of newly defined continuous measures of certain complex geometric properties of the attractor on the scale given by &egr;. In particular, we introduce local measures such as the &egr;-clustering coefficient, mesoscopic measures such as &egr;-motif density, path-based measures such as &egr;-betweennesses, and global measures such as &egr;-efficiency. This new analytical basis for the so far heuristically motivated network measures also provides an objective criterion for the choice of &egr; via a percolation threshold, and it shows that estimation can be improved by so-called node splitting invariant versions of the measures. We finally illustrate the framework for a number of archetypical chaotic attractors such as those of the Bernoulli and logistic maps, periodic and two-dimensional quasiperiodic motions, and for hyperballs and hypercubes by deriving analytical expressions for the novel measures and comparing them with data from numerical experiments. More generally, the theoretical framework put forward in this work describes random geometric graphs and other networks with spatial constraints, which appear frequently in disciplines ranging from biology to climate science. [ABSTRACT FROM AUTHOR]

Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35-3.15 Ma B.P.), (ii) Early Pleistocene (2.25-1.6 Ma B.P.), and (iii) Middle Pleistocene (1.1-0.7 Ma B.P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa. [ABSTRACT FROM AUTHOR]

Abstract: We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potential of these complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime. [Copyright &y& Elsevier]

Identifying and characterising dynamical regime shifts, critical transitions or potential tipping points in palaeoclimate time series is relevant for improving the understanding of often highly nonlinear Earth system dynamics. Beyond linear changes in time series properties such as mean, variance, or trend, these nonlinear regime shifts can manifest as changes in signal predictability, regularity, complexity, or higher-order stochastic properties such as multi-stability. In recent years, several classes of methods have been put forward to study these critical transitions in time series data that are based on concepts from nonlinear dynamics, complex systems science, information theory, and stochastic analysis. These include approaches such as phase space-based recurrence plots and recurrence networks, visibility graphs, order pattern-based entropies, and stochastic modelling. Here, we review and compare in detail several prominent methods from these fields by applying them to the same set of marine palaeoclimate proxy records of African climate variations during the past 5 million years. Applying these methods, we observe notable nonlinear transitions in palaeoclimate dynamics in these marine proxy records and discuss them in the context of important climate events and regimes such as phases of intensified Walker circulation, marine isotope stage M2, the onset of northern hemisphere glaciation and the mid-Pleistocene transition. We find that the studied approaches complement each other by allowing us to point out distinct aspects of dynamical regime shifts in palaeoclimate time series. We also detect significant correlations of these nonlinear regime shift indicators with variations of Earth's orbit, suggesting the latter as potential triggers of nonlinear transitions in palaeoclimate. Overall, the presented study underlines the potentials of nonlinear time series analysis approaches to provide complementary information on dynamical regime shifts in palaeoclimate and their driving processes that cannot be revealed by linear statistics or eyeball inspection of the data alone. [ABSTRACT FROM AUTHOR]

The stability of the Greenland Ice Sheet under global warming is governed by a number of dynamic processes and interacting feedback mechanisms in the ice sheet, atmosphere and solid Earth. Here we study the long-term effects due to the interplay of the competing melt–elevation and glacial isostatic adjustment (GIA) feedbacks for different temperature step forcing experiments with a coupled ice-sheet and solid-Earth model. Our model results show that for warming levels above 2 ∘ C, Greenland could become essentially ice-free within several millennia, mainly as a result of surface melting and acceleration of ice flow. These ice losses are mitigated, however, in some cases with strong GIA feedback even promoting an incomplete recovery of the Greenland ice volume. We further explore the full-factorial parameter space determining the relative strengths of the two feedbacks: our findings suggest distinct dynamic regimes of the Greenland Ice Sheets on the route to destabilization under global warming – from incomplete recovery, via quasi-periodic oscillations in ice volume to ice-sheet collapse. In the incomplete recovery regime, the initial ice loss due to warming is essentially reversed within 50 000 years, and the ice volume stabilizes at 61 %–93 % of the present-day volume. For certain combinations of temperature increase, atmospheric lapse rate and mantle viscosity, the interaction of the GIA feedback and the melt–elevation feedback leads to self-sustained, long-term oscillations in ice-sheet volume with oscillation periods between 74 000 and over 300 000 years and oscillation amplitudes between 15 %–70 % of present-day ice volume. This oscillatory regime reveals a possible mode of internal climatic variability in the Earth system on timescales on the order of 100 000 years that may be excited by or synchronized with orbital forcing or interact with glacial cycles and other slow modes of variability. Our findings are not meant as scenario-based near-term projections of ice losses but rather providing insight into of the feedback loops governing the "deep future" and, thus, long-term resilience of the Greenland Ice Sheet. [ABSTRACT FROM AUTHOR]

The stability of the Greenland Ice Sheet under global warming is governed by a number of dynamic processes and interacting feedback mechanisms in the ice sheet, atmosphere and solid Earth. Here we study the long-term effects due to the interplay of the competing melt-elevation and glacial isostatic adjustment (GIA) feedbacks for different temperature step forcing experiments with a coupled ice-sheet and solid-Earth model. Our model results show that for warming levels above 2 °C, Greenland could become essentially ice-free on the long-term, mainly as a result of surface melting and acceleration of ice flow. These ice losses can be mitigated, however, in some cases with strong GIA feedback even promoting the partial recovery of the Greenland ice volume. We further explore the full-factorial parameter space determining the relative strengths of the two feedbacks: Our findings suggest distinct dynamic regimes of the Greenland Ice Sheets on the route to destabilization under global warming - from recovery, via quasi-periodic oscillations in ice volume to ice-sheet collapse. In the recovery regime, the initial ice loss due to warming is essentially reversed within 50,000 years and the ice volume stabilizes at 61-93 % of the present-day volume. For certain combinations of temperature increase, atmospheric lapse rate and mantle viscosity, the interaction of the GIA feedback and the melt-elevation feedback leads to self-sustained, long-term oscillations in ice-sheet volume with oscillation periods of tens to hundreds of thousands of years and oscillation amplitudes between 15-70 % of present-day ice volume. This oscillatory regime reveals a possible mode of internal climatic variability in the Earth system on time scales on the order of 100,000 years that may be excited by or synchronized with orbital forcing or interact with glacial cycles and other slow modes of variability. Our findings are not meant as scenario-based near-term projections of ice losses but rather providing insight into of the feedback loops governing the "deep future" and, thus, long-term resilience of the Greenland Ice Sheet. [ABSTRACT FROM AUTHOR]

Reinforcement learning in multiagent systems has been studied in the fields of economic game theory, artificial intelligence, and statistical physics by developing an analytical understanding of the learning dynamics (often in relation to the replicator dynamics of evolutionary game theory). However, the majority of these analytical studies focuses on repeated normal form games, which only have a single environmental state. Environmental dynamics, i.e., changes in the state of an environment affecting the agents' payoffs has received less attention, lacking a universal method to obtain deterministic equations from established multistate reinforcement learning algorithms. In this work we present a methodological extension, separating the interaction from the adaptation timescale, to derive the deterministic limit of a general class of reinforcement learning algorithms, called temporal difference learning. This form of learning is equipped to function in more realistic multistate environments by using the estimated value of future environmental states to adapt the agent's behavior. We demonstrate the potential of our method with the three well-established learning algorithms Q learning, SARSA learning, and actor-critic learning. Illustrations of their dynamics on two multiagent, multistate environments reveal a wide range of different dynamical regimes, such as convergence to fixed points, limit cycles, and even deterministic chaos. [ABSTRACT FROM AUTHOR]

Safely achieving the goals of the Paris Climate Agreement requires a world-wide transformation to carbon-neutral societies within the next 30 years. Despite decades-long efforts in international negotiations, not much progress has been achieved and few are convinced that business-as-usual technological progress and gradual policy implementations will deliver emissions reductions at rates sufficiently fast to avoid crossing dangerous tipping points in the Earth's climate system. Here, we present historical, recent empirical and theoretical evidence supporting the potential of social tipping elements (STEs) as drivers of the required disruptive change. STEs are subdomains of the planetary socio-economic system where targeted policy interventions can activate contagious processes of rapid spreading of technologies, behaviors and social norms that can ultimately propel a sufficiently fast reduction in anthropogenic greenhouse gas emissions. We identify six outstanding candidates for STEs and their associated critical intervention points based on online expert elicitation, a subsequent expert workshop, and a literature review. These critical social tipping interventions include (i) removing fossil fuel subsidies and incentivizing distributed energy generation (STE1: energy production and storage systems), (ii) building carbon-neutral cities (STE2: human settlements), (iii) divestments from assets linked to fossil fuels (STE3: financial markets), (iv) revealing the moral implications of fossil fuels (STE4: norms and value systems), (v) strengthened climate education and engagement (STE5: education system) and (vi) greenhouse gas emissions information disclosure (STE6: information feedbacks). Larger-scale empirical and modelling efforts are needed to understand the potentials of STE dynamics and their role in climate change mitigation pathways in more detail. [ABSTRACT FROM AUTHOR]

Analysis of Earth system dynamics in the Anthropocene requires to explicitly take into account the increasing magnitude of processes operating in human societies, their cultures, economies and technosphere and their growing entanglement with those in the physical, chemical and biological systems of the planet. This work (i) introduces design principles for constructing World-Earth models (WEM), i.e., models of social-ecological co-evolution on up to planetary scales, and (ii) presents the copan:CORE open source software library that provides a simulation modeling framework for developing, composing and running such WEMs based on the proposed principles. copan:CORE is an object-oriented software package currently implemented in Python. It provides components of meaningful yet minimal collections of closely related processes in the Earth System that can be plugged together in order to compose and run WEMs. Developers can supplement the already existing model components with additional components that are based on elementary entity types, e.g., grid cells, or fundamental process taxa, e.g., environment or culture. To illustrate the capabilities of the framework, this paper presents a WEM example implemented in copan:CORE that combines a variety of model components and interactions thereof. Due to its modular structure, the simulation modeling framework enhances the development and application of integrated models in Earth system science but also climatology, economics, ecology, or sociology, and allows combining them for interdisciplinary studies such as risk assessment including explicitly the dynamics of human behavior and decision making. [ABSTRACT FROM AUTHOR]

In recent years, several global events have severely disrupted economies and social structures, undermining confidence in the resilience of modern societies. Examples include the COVID-19 pandemic, which brought unprecedented health challenges and economic disruptions, and the emergence of geopolitical tensions and conflicts that have further strained international relations and economic stability. While empirical evidence on the dynamics and drivers of past societal collapse is mounting, a process-based understanding of these dynamics is still in its infancy. Here, we aim to identify and illustrate the underlying drivers of such societal instability or even collapse. The inspiration for this work is Joseph Tainter's theory of the "collapse of complex societies", which postulates that the complexity of societies increases as they solve problems, leading to diminishing returns on complexity investments and ultimately to collapse. In this work, we abstract this theory into a low-dimensional and stylized model of two classes of networked agents, hereafter referred to as "laborers" and "administrators". We numerically model the dynamics of societal complexity, measured as the fraction of "administrators", which was assumed to affect the productivity of connected energy-producing "laborers". We show that collapse becomes increasingly likely as the complexity of the model society continuously increases in response to external stresses that emulate Tainter's abstract notion of problems that societies must solve. We also provide an analytical approximation of the system's dominant dynamics, which matches well with the numerical experiments, and use it to study the influence on network link density, social mobility and productivity. Our work advances the understanding of social-ecological collapse and illustrates its potentially direct link to an ever-increasing societal complexity in response to external shocks or stresses via a self-reinforcing feedback. [ABSTRACT FROM AUTHOR]

The Anthropocene is characterized by accelerating change and global challenges of increasing complexity. Inspired by what some have called a polycrisis, we explore whether the human trajectory of increasing complexity and influence on the Earth system could become a form of trap for humanity. Based on an adaptation of the evolutionary traps concept to a global human context, we present results from a participatory mapping. We identify 14 traps and categorize them as either global, technology or structural traps. An assessment reveals that 12 traps (86%) could be in an advanced phase of trapping with high risk of hard-to-reverse lock-ins and growing risks of negative impacts on human well-being. Ten traps (71%) currently see growing trends in their indicators. Revealing the systemic nature of the polycrisis, we assess that Anthropocene traps often interact reinforcingly (45% of pairwise interactions), and rarely in a dampening fashion (3%). We end by discussing capacities that will be important for navigating these systemic challenges in pursuit of global sustainability. Doing so, we introduce evolvability as a unifying concept for such research between the sustainability and evolutionary sciences. This article is part of the theme issue 'Evolution and sustainability: gathering the strands for an Anthropocene synthesis'. [ABSTRACT FROM AUTHOR]

Mass loss from the Antarctic Ice Sheet is the main source of uncertainty in projections of future sea-level rise, with important implications for coastal regions worldwide. Central to ongoing and future changes is the marine ice sheet instability: once a critical threshold, or tipping point, is crossed, ice internal dynamics can drive a self-sustaining retreat committing a glacier to irreversible, rapid and substantial ice loss. This process might have already been triggered in the Amundsen Sea region, where Pine Island and Thwaites glaciers dominate the current mass loss from Antarctica, but modelling and observational techniques have not been able to establish this rigorously, leading to divergent views on the future mass loss of the West Antarctic Ice Sheet. Here, we aim at closing this knowledge gap by conducting a systematic investigation of the stability regime of Pine Island Glacier. To this end we show that early warning indicators in model simulations robustly detect the onset of the marine ice sheet instability. We are thereby able to identify three distinct tipping points in response to increases in ocean-induced melt. The third and final event, triggered by an ocean warming of approximately 1.2 ∘ C from the steady-state model configuration, leads to a retreat of the entire glacier that could initiate a collapse of the West Antarctic Ice Sheet. [ABSTRACT FROM AUTHOR]

Complex networks are usually characterized in terms of their topological, spatial, or information-theoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories. However, even with the present variety of characteristics at hand it still remains a subject of current research to appropriately quantify a network's complexity and correspondingly discriminate between different types of complex networks, like infrastructure or social networks, on such a basis. Here we explore the possibility to classify complex networks by means of a statistical complexity measure that has formerly been successfully applied to distinguish different types of chaotic and stochastic time series. It is composed of a network's averaged per-node entropic measure characterizing the network's information content and the associated Jenson-Shannon divergence as a measure of disequilibrium. We study 29 real-world networks and show that networks of the same category tend to cluster in distinct areas of the resulting complexity-entropy plane. We demonstrate that within our framework, connectome networks exhibit among the highest complexity while, e.g., transportation and infrastructure networks display significantly lower values. Furthermore, we demonstrate the utility of our framework by applying it to families of random scale-free and Watts-Strogatz model networks. We then show in a second application that the proposed framework is useful to objectively construct threshold-based networks, such as functional climate networks or recurrence networks, by choosing the threshold such that the statistical network complexity is maximized. [ABSTRACT FROM AUTHOR]

Increasingly complex nonlinear World-Earth system models are used for describing the dynamics of the biophysical Earth system and the socioeconomic and sociocultural World of human societies and their interactions. Identifying pathways toward a sustainable future in these models for informing policymakers and the wider public, e.g., pathways leading to robust mitigation of dangerous anthropogenic climate change, is a challenging and widely investigated task in the field of climate research and broader Earth system science. This problem is particularly difficult when constraints on avoiding transgressions of planetary boundaries and social foundations need to be taken into account. In this work, we propose to combine recently developed machine learning techniques, namely, deep reinforcement learning (DRL), with classical analysis of trajectories in the World-Earth system. Based on the concept of the agent-environment interface, we develop an agent that is generally able to act and learn in variable manageable environment models of the Earth system. We demonstrate the potential of our framework by applying DRL algorithms to two stylized World-Earth system models. Conceptually, we explore thereby the feasibility of finding novel global governance policies leading into a safe and just operating space constrained by certain planetary and socioeconomic boundaries. The artificially intelligent agent learns that the timing of a specific mix of taxing carbon emissions and subsidies on renewables is of crucial relevance for finding World-Earth system trajectories that are sustainable in the long term. [ABSTRACT FROM AUTHOR]

Abstract Deforestation in the Amazon with its vast consequences for the ecosystem and climate is largely related to subsequent land use for cattle ranching. In addition to conservation policies, proposals to reduce deforestation include measures to intensify cattle ranching. However, the effects of land-use intensification on deforestation are debated in the literature. This paper introduces the abacra model, a stylized agent-based model to study the interplay of deforestation and the intensification of cattle ranching in the Brazilian Amazon. The model combines social learning and ecological processes with market dynamics. In the model, agents adopt either an extensive or semi-intensive strategy of cattle ranching based on the success of their neighbors. They earn their income by selling cattle on a stylized market. We present a comprehensive analysis of the model with statistical methods and find that it produces highly non-linear transient outcomes in dependence on key parameters like the rate of social interaction and elasticity of the cattle price. We show that under many environmental and economic conditions, intensification does not reduce deforestation rates and sometimes even has a detrimental effect on deforestation. Anti-deforestation policies incentivizing fast intensification can only lower deforestation rates under conditions in which the local cattle market saturates. [ABSTRACT FROM AUTHOR]

Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their macroscopic properties. Here, we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve certain global and local statistics associated with the nodes' embedding in a metric space. Comparing the original network's and the resulting surrogates' global characteristics allows one to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links. We apply our framework to various real-world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes' spatial embedding. Depending on the actual performance of the proposed null models, the networks are categorized into different classes. Since many real-world complex networks are in fact spatial networks, the proposed approach is relevant for disentangling the underlying complex system structure from spatial embedding of nodes in many fields, ranging from social systems over infrastructure and neurophysiology to climatology. [ABSTRACT FROM AUTHOR]

The article discusses the planetary boundaries framework, which identifies nine critical Earth system processes heavily impacted by human activities. The framework aims to establish limits on anthropogenic perturbations to maintain a "Holocene-like" interglacial state, similar to the stable and warm conditions of the past 10,000 years.

Comparable to the traditional notion of stability in system dynamics, resilience is typically measured in a way that assesses the quality of a system's response, for example, the speed of its recovery. We present a broadly applicable complementary measurement framework that quantifies resilience similarly to basin stability by estimating a resilience basin, which reflects the extent of adverse influences that the system can recover from in a sufficient manner. In contrast to basin stability, the adverse influences considered here are not necessarily displacements in state space, but arbitrarily complex impacts to the system, quantified by adequate parameters. As a proof of concept, we present two applications: (i) the well-studied single-node power system as an easy-to-follow example and (ii) a stochastic model of a low-voltage DC power grid undergoing an unregulated energy transition consisting in the random appearance of prosumers. These act as decentral suppliers of photovoltaic power and alter the flow patterns while the grid topology remains unchanged. The resilience measurement framework is applied to evaluate the effect and efficiency of two response options: (i) upgrading the capacity of existing power lines and (ii) installing batteries in the prosumer households. The framework demonstrates that line upgrades can provide potentially unlimited resilience against energy decentralization, while household batteries are inherently limited (achieving ≤ 70 % of the resilience of line upgrades). Further, the framework aids in optimizing budget efficiency by pointing toward threshold budget values as well as budget-dependent ideal strategies for the allocation of line upgrades and for the battery charging algorithm. [ABSTRACT FROM AUTHOR]

Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway, or airline infrastructures over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (as arising if the background flow is perturbed itself). Our results demonstrate that in all three cases, changes to the steady state solution can be analytically expressed in terms of the eigensystem of the unperturbed flow and the perturbation itself. These results are potentially relevant for developing more efficient strategies for coping with contaminations of fluid or gaseous media such as ocean and atmosphere by oil spills, radioactive substances, non-reactive chemicals, or volcanic aerosols. [ABSTRACT FROM AUTHOR]

In recent years, the Northern Hemisphere midlatitudes have suffered from severe winters like the extreme 2012/13 winter in the eastern United States. These cold spells were linked to a meandering upper-tropospheric jet stream pattern and a negative Arctic Oscillation index (AO). However, the nature of the drivers behind these circulation patterns remains controversial. Various studies have proposed different mechanisms related to changes in the Arctic, most of them related to a reduction in sea ice concentrations or increasing Eurasian snow cover. Here, a novel type of time series analysis, called causal effect networks (CEN), based on graphical models is introduced to assess causal relationships and their time delays between different processes. The effect of different Arctic actors on winter circulation on weekly to monthly time scales is studied, and robust network patterns are found. Barents and Kara sea ice concentrations are detected to be important external drivers of the midlatitude circulation, influencing winter AO via tropospheric mechanisms and through processes involving the stratosphere. Eurasia snow cover is also detected to have a causal effect on sea level pressure in Asia, but its exact role on AO remains unclear. The CEN approach presented in this study overcomes some difficulties in interpreting correlation analyses, complements model experiments for testing hypotheses involving teleconnections, and can be used to assess their validity. The findings confirm that sea ice concentrations in autumn in the Barents and Kara Seas are an important driver of winter circulation in the midlatitudes. [ABSTRACT FROM AUTHOR]

Tipping elements are nonlinear subsystems of the Earth system that have the potential to abruptly shift to another state if environmental change occurs close to a critical threshold with large consequences for human societies and ecosystems. Among these tipping elements may be the Amazon rainforest, which has been undergoing intensive anthropogenic activities and increasingly frequent droughts. Here, we assess how extreme deviations fromclimatological rainfall regimes may cause local forest collapse that cascades through the coupled forest-climate system. We develop a conceptual dynamic network model to isolate and uncover the role of atmospheric moisture recycling in such tipping cascades. We account for heterogeneity in critical thresholds of the forest caused by adaptation to local climatic conditions. Our results reveal that, despite this adaptation, a future climate characterized by permanent drought conditions could trigger a transition to an open canopy state particularly in the southern Amazon. Theloss of atmospheric moisture recycling contributes to one-third of the tipping events. Thus, by exceeding local thresholds in forest adaptive capacity, local climate change impacts may propagate to other regions of the Amazon basin, causing a risk of forest shifts even in regions where critical thresholds have not been crossed locally. [ABSTRACT FROM AUTHOR]

Only a fast and global transformation towards decarbonization and sustainability can keep the Earth in a civilization-friendly state. As hotspots for (green) innovation and experimentation, cities could play an important role in this transition. They are also known to profit from each other's ideas, with policy and technology innovations spreading to other cities. In this way, cities can be conceptualized as nodes in a globe-spanning learning network. The dynamics of this process are important for society's response to climate change and other challenges, but remain poorly understood on a macroscopic level. In this contribution, we develop an approach to identify whether network-based complex contagion effects are a feature of sustainability policy adoption by cities, based on dose-response contagion and surrogate data models. We apply this methodology to an exemplary data set, comprising empirical data on the spreading of a public transport innovation (Bus Rapid Transit Systems) and a global inter-city connection network based on scheduled flight routes. Although our approach is not able to identify detailed mechanisms, our results point towards a contagious spreading process, and cannot be explained by either the network structure or the increase in global adoption rate alone. Further research on the role of a city's abstract "global neighborhood" regarding its policy and innovation decisions is thus both needed and promising, and may connect with research on social tipping processes. The methodology is generic, and can be used to compare the predictive power for innovation spreading of different kinds of inter-city network connections, e.g. via transport links, trade, or co-membership in political networks. [ABSTRACT FROM AUTHOR]

Abstract: We introduce a geometric method for identifying the coupling direction between two dynamical systems based on a bivariate extension of recurrence network analysis. Global characteristics of the resulting inter-system recurrence networks provide a correct discrimination for weakly coupled Rössler oscillators not yet displaying generalised synchronisation. Investigating two real-world palaeoclimate time series representing the variability of the Asian monsoon over the last 10,000 years, we observe indications for a considerable influence of the Indian summer monsoon on climate in Eastern China rather than vice versa. The proposed approach can be directly extended to studying coupled subsystems. [Copyright &y& Elsevier]

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related to the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches. [ABSTRACT FROM AUTHOR]