The term ‘tipping event’ is used to describe a certain class of phenomena as observed in many different fields of science. It refers to an event where a gradual change of external forcing causes a sudden, large, often unwanted, transition to the state of the system. Some examples of known tipping events in science include: Arctic sea ice melting (climate), epileptic seizures (biology), collapse of ecosystems and populations (ecology) and market crashes (finance). Three mathematical mechanisms for tipping events have been proposed in the literature: bifurcation-, noise- or rate-induced tipping. Recent research has focused on developing early-warning indicators to potentially offer forewarning, which can extract from output time series whether the external forcing approaches a critical level at which tipping occurs. Two commonly used early-warning indicators are an increase of autocorrelation and variance in the time series data for the system’s output. The theory behind the presence of these indicators is the loss of stability of the system’s current state known as ‘critical slowing down’ for the approach of a bifurcation-induced tipping. Rate-induced tipping occurs when the external forcing reaches a critical rate instead of level. For rate-induced tipping there is no loss of stability of the system’s current state and therefore it is not clear if the early-warning indicators should exist. In this thesis we investigate the presence of early-warning indicators for models that show rate-induced tipping with additive noise. We also explore a technique for determining the most likely time of tipping using optimal paths for escape. Research has mainly focussed on testing the early-warning indicators for examples of known tipping events in the past. The ultimate aim of early-warning indicators would be to have the ability to predict future tipping events. Using the early-warning indicators in isolation is susceptible to incurring false alarms and missed alarms. We present a method for approximating the probability of experiencing rate-induced tipping with noise for slow to moderate drift speeds.

This thesis examines how early warning signals perform when tested on climate systems thought to exhibit future tipping point behaviour. A tipping point in a dynamical system is a large and sudden change to the state of the system, usually caused by changes in external forcing. This is due to the state the system occupies becoming unstable, causing the system to settle to a new stable state. In many cases, there is a degree of irreversibility once the tipping point has been passed, preventing the system from reverting back to its original state without a large reversal in forcing. Passing tipping points in climate systems, such as the Amazon rainforest or the Atlantic Meridional Overturning Circulation, is particularly dangerous as the effects of this will be globally felt. Fortunately there is potential for early warning signals, designed to warn that the system is approaching a tipping point. Generally, these early warning signals are based on analysis of the time series of the system, such as searching for ‘critical slowing down’, usually estimated by an increasing lag-1 autocorrelation (AR(1)). The idea here is that as a system’s state becomes less stable, it will start to react more sluggishly to short term perturbations. While early warning signals have been tested extensively in simple models and on palaeoclimate data, there has been very little research into how these behave in complex models and observed data. Here, early warning signals are tested on climate systems that show tipping point behaviour in general circulation models. Furthermore, it examines why early warning signals might fail in certain cases and provides prospect for more ‘system specific indicators’ based on properties of individual tipping elements. The thesis also examines how slowing down in a system might affect ecosystems that are being driven by it.

A wide range of ecological communities ranging from polar terrestrial to tropical marine environments are affectedby global climate change. Over the last century, atmospheric temperature has increased by an average of 0. 60 C andis expected to rise by 1.1- 6.40C over the next 100 years. This rising temperature has increased the intensity andfrequency of weather extremes due to which a large number of species are facing risk of extinction. Studies haveshown that species existing on lower latitude are more sensitive to temperature variability compared to speciesexisting on higher latitude but temperature is increasing rapidly in higher latitude compare to lower latitude. Thisuneven distribution of temperature sensitive species and warming rate has highlighted the need for combined studiesof temperature variability and sensitiveness of species to predict how the ecosystems will respond to increasinglyvariable climate. Using a generalized Rosenzweig-MacArthur model, I explored how temperature variability andsensitivity of species will affect the extinction risks of species and how the connectance and species-richness ofecological communities will govern this response. This study showed that the risk of extinction of species mostlydepends on their sensitivity to temperature deviation from the optimum value and level of temperature variability.Among these two, sensitivity of species to temperature deviation was most prominent factor affecting extinction risk.In this study, connectance did not show any effect on mean extinction risk and time taken by a certain proportion ofspecies to reach pre-defined extinction thresholds. But, species-richness showed some effect on mean extinction riskof species. It was found that risk of extinction of species in species-rich communities was higher compared tospecies-poor communities. Species-rich communities also took shorter time before they lost 1/6 of the species. Thepresent study also suggests a possible tipping point due to increasing temperature variability in near future. In furtherstudies, different sensitivity of species at different trophic levels and the possible evolution of sensitivity of speciesshould also be consider while predicting how ecological communities will respond to changing climate in the longrun.

In the era of intense pressures on water resources, the loss of groundwater by increased seawater intrusion (SWI), driven by climate, sea level and landscape changes, may be critical for many people living in commonly populous coastal regions. Analytical solutions have been derived here for interface flow in coastal aquifers, which allow for simple quantification of SWI under extended conditions from previously available such solutions and are suitable for first-order regional vulnerability assessment and mapping of the implications of climate- and landscape-driven change scenarios and related comparisons across various coastal world regions. Specifically, the derived solutions can account for the hydraulically significant aquifer bed slope in quantifying the toe location of a fresh-seawater sharp interface in the present assessments of vulnerability and safe exploitation of regional coastal groundwater.  Results show high nonlinearity of SWI responses to hydro-climatic and groundwater pumping changes on the landside and sea level rise on the marine side, implying thresholds, or tipping points, which, if crossed, may lead abruptly to major SWI of the aquifer. Critical limits of coastal groundwater change and exploitation have been identified and quantified in direct relation to prevailing local-regional conditions and stresses, defining a safe operating space for the human use of coastal groundwater. Generally, to control SWI, coastal aquifer management should focus on adequate fresh groundwater discharge to the sea, rather than on maintaining a certain hydraulic head at some aquifer location. First-order vulnerability assessments for regional Mediterranean aquifers of the Nile Delta Aquifer, the Israel Coastal Aquifer  and the Cyprus Akrotiri Aquifer show that in particular the first is seriously threatened by advancing seawater. Safe operating spaces determined for the latter two show that the current pumping schemes are not sustainable under declining recharge. / <p>The thesis was founded by two research programmes: NEO private-academic sector partnership and Ekoklim, a strategic governmental funding through Stockholm University</p><p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 3: Manuscript.</p><p> </p>

No description available.

Climate change is increasing the frequency and extent of high-severity disturbance, with potential to alter vegetation community composition and structure in environments sensitive to tipping points between alternative states. Shrub species display a range of characteristics that promote resistance and resilience to disturbance, and which yield differential post-disturbance outcomes. We investigated differences in shrub patch size and stem density in response to variations in fire severity, vegetation community, and post-disturbance reproductive strategies in Sky Island forested ecosystems in the southwestern United States. Patterns in shrub structure reflect the effects of fire severity as well as differences among species with alternate post-fire reproductive strategies. Increased fire severity correlates with larger patch sizes and greater stem densities; these patterns are observed across multiple fire events, indicating that disturbance legacies can persist for decades. High severity fire produces the largest shrub patches, and variance in shrub patch size increases with severity. High severity fire is likely to promote expansion of shrub species on the landscape, with implications for future community structure. Resprouting species have the greatest variability in patch structure, while seeding species show a strong response to disturbance: resprouting species dominateatlowdisturbanceseverities,andobligateseedersdominatehighseverityareas. Differential post-fire reproductive strategies are likely to generate distinct patterns of vegetation distribution following disturbance, with implications for community composition at various scales. Shrub species demonstrate flexible responses to wildfire disturbance severity that are reflected in shrub patch dynamics at small and intermediate scales.

The notion of climate tipping points (CTP:s) has gained traction in academia. Unravelling the intricate weave of views in the discourses surrounding CTP:s can be helpful to structure the views in the discursive fabric of climate tipping points and in turn get a better understanding of the views surrounding the phenomenon. This study aims to clarify the different views on climate tipping points by creating a set of distinct ideal types based on the scientific literature surrounding CTP:s. Furthermore, we analyse these views and reflect on their relationship and functions through textual analysis. The analysis yielded four reoccurring, interconnected themes: Knowledge, View on (Ir)reversibility, Risk and Action. Using these themes, we created four ideal types to help intellectually structure the weave of differing views. Furthermore, we found that the relationship between the views on these themes and the acceptance of climate tipping points often is convertibly indicative. The analysis of the literature also revealed that CTP:s have much in common with climate change in large and reifies the urgency, risk implications, uncertainties, and suggested actions expressed in broader climate change literature. A key insight is that accepting CTP:s is not pivotal for voicing strong concerns about climate change but rather they may serve as a metaphoric tool for scientists in communicating climate change issues. / Begreppet climate tipping points (CTP:s) har fått ökande utrymme inom akademin. Att nysta upp den invecklade väven av synsätt inom diskurserna kring CTP:s kan vara till hjälp för att strukturera synsätten på fenomenet och i sin tur få en bättre förståelse för dem. Denna studie syftar till att göra detta genom att skapa en uppsättning distinkta idealtyper baserade på karaktärsdrag från ett urval av den vetenskapliga litteraturen kring CTP:s. Dessutom analyserar vi dessa åsikter och reflekterar över deras relation och funktioner genom att tillämpa en tematisk textanalys. Analysen resulterade i fyra återkommande och sammankopplade teman: Kunskap, Synen på (ir)reversibilitet, Risk och Åtgärder. Med hjälp av dessa teman skapade vi fyra idealtyper ämnade att bidra till att intellektuellt strukturera väven av olika synsätt. Vi fann även att förhållandet mellan synen på dessa teman och accepterandet av CTP:s ofta är indikativt omvändbart. Analysen av litteraturen visade också att CTP:s har mycket gemensamt med klimatförändringar i stort och understryker dess brådskande karaktär, risker, osäkerheter och föreslagna åtgärder som uttrycks i litteraturen rörande klimatförändringar. En nyckelinsikt är att acceptansen för CTP:s inte är avgörande för att uttrycka stark angelägenhet för klimatfrågor, utan snarare att de kan fungera som ett metaforiskt verktyg för forskare att kommunicera klimatfrågor med.

Der technologische Fortschritt hat in jüngster Zeit zu einer großen Zahl von Zeitreihenmessdaten über komplexe dynamische Systeme wie das Klimasystem, das Gehirn oder das globale ökonomische System geführt. Beispielsweise treten im Klimasystem Prozesse wie El Nino-Southern Oscillation (ENSO) mit dem indischen Monsun auf komplexe Art und Weise durch Telekonnektionen und Rückkopplungen in Wechselwirkung miteinander. Die Analyse der Messdaten zur Rekonstruktion der diesen Wechselwirkungen zugrunde liegenden kausalen Mechanismen ist eine Möglichkeit komplexe Systeme zu verstehen, insbesondere angesichts der unendlich-dimensionalen Komplexität der physikalischen Prozesse. Diese Dissertation verfolgt zwei Hauptfragen: (i) Wie können, ausgehend von multivariaten Zeitreihen, kausale Wechselwirkungen praktisch detektiert werden? (ii) Wie kann die Stärke kausaler Wechselwirkungen zwischen mehreren Prozessen in klar interpretierbarer Weise quantifiziert werden? Im ersten Teil der Arbeit werden die Theorie zur Detektion und Quantifikation nichtlinearer kausaler Wechselwirkungen (weiter-)entwickelt und wichtige Aspekte der Schätztheorie untersucht. Zur Quantifikation kausaler Wechselwirkungen wird ein physikalisch motivierter, informationstheoretischer Ansatz vorgeschlagen, umfangreich numerisch untersucht und durch analytische Resultate untermauert. Im zweiten Teil der Arbeit werden die entwickelten Methoden angewandt, um Hypothesen über kausale Wechselwirkungen in Klimadaten der vergangenen hundert Jahre zu testen und zu generieren. In einem zweiten, eher explorativen Schritt wird ein globaler Luftdruck-Datensatz analysiert, um wichtige treibende Prozesse in der Atmosphäre zu identifizieren. Abschließend wird aufgezeigt, wie die Quantifizierung von Wechselwirkungen Aufschluss über mögliche qualitative Veränderungen in der Klimadynamik (Kipppunkte) geben kann und wie kausal treibende Prozesse zur optimalen Vorhersage von Zeitreihen genutzt werden können. / Today''s scientific world produces a vastly growing and technology-driven abundance of time series data of such complex dynamical systems as the Earth''s climate, the brain, or the global economy. In the climate system multiple processes (e.g., El Nino-Southern Oscillation (ENSO) or the Indian Monsoon) interact in a complex, intertwined way involving teleconnections and feedback loops. Using the data to reconstruct the causal mechanisms underlying these interactions is one way to better understand such complex systems, especially given the infinite-dimensional complexity of the underlying physical equations. In this thesis, two main research questions are addressed: (i) How can general causal interactions be practically detected from multivariate time series? (ii) How can the strength of causal interactions between multiple processes be quantified in a well-interpretable way? In the first part of this thesis, the theory of detecting and quantifying general (linear and nonlinear) causal interactions is developed alongside with the important practical issues of estimation. To quantify causal interactions, a physically motivated, information-theoretic formalism is introduced. The formalism is extensively tested numerically and substantiated by rigorous mathematical results. In the second part of this thesis, the novel methods are applied to test and generate hypotheses on causal interactions in climate time series covering the 20th century up to the present. The results yield insights on an understanding of the Walker circulation and teleconnections of the ENSO system, for example with the Indian Monsoon. Further, in an exploratory way, a global surface pressure dataset is analyzed to identify key processes that drive and govern interactions in the global atmosphere. Finally, it is shown how quantifying interactions can be used to determine possible structural changes, termed tipping points, and as optimal predictors, here applied to the prediction of ENSO.

Vom Standpunkt des Physikers aus gesehen, ist die Erde ein dynamisches System von großer Komplexität. Funktionale Netzwerke werden aus Beobachtungs-, und Modelldaten abgeleitet oder aufgrund theoretischer Überlegungen konstruiert. Indem sie statistische Zusammenhänge oder kausale Wirkbeziehungen zwischen der Dynamik gewisser Objekte, z.B. verschiedenen Sphären des Erdsystems, Prozessen oder lokalen Feldvariablen darstellen, bieten funktionale Netzwerke einen natürlichen Ansatz zur Bearbeitung fundamentaler Probleme der Erdsystemanalyse. Dazu gehören Fragen nach dominanten, dynamischen Mustern, Telekonnektionen und Rückkopplungsschleifen in der planetaren Maschinerie, sowie nach kritischen Elementen wie Schwellwerten, sogn. Flaschenhälsen und Schaltern im Erdsystem. Der erste Teil dieser Dissertation behandelt die Theorie komplexer Netzwerke und die netzwerkbasierte Zeitreihenanalyse. Die Beiträge zur Theorie komplexer Netzwerke beinhalten Maße und Modelle zur Analyse der Topologie (i) von Netzwerken wechselwirkender Netzwerke und (ii) Netzwerken mit ungleichen Knotengewichten, sowie (iii) eine analytische Theorie zur Beschreibung von räumlichen Netzwerken. Zur Zeitreihenanalyse werden (i) Rekurrenznetzwerke als eine theoretisch gut begründete, nichtlineare Methode zum Studium multivariater Zeitreihen vorgestellt. (ii) Gekoppelte Klimanetzwerke werden als ein exploratives Werkzeug der Datenanalyse zur quantitativen Charakterisierung der komplexen statistischen Interdependenzstruktur innerhalb und zwischen distinkten Feldern von Zeitreihen eingeführt. Im zweiten Teil der Arbeit werden Anwendungen zur Detektion von dynamischen Übergängen (Kipppunkten) in Zeitreihen, sowie zum Studium von Flaschenhälsen in der atmosphärischen Zirkulationsstruktur vorgestellt. Die Analyse von Paläoklimadaten deutet auf mögliche Zusammenhänge zwischen großskaligen Veränderungen der afrikanischen Klimadynamik während des Plio-Pleistozäns und Ereignissen in der Menschheitsevolution hin. / The Earth, as viewed from a physicist''s perspective, is a dynamical system of great complexity. Functional complex networks are inferred from observational data and model runs or constructed on the basis of theoretical considerations. Representing statistical interdependencies or causal interactions between objects (e.g., Earth system subdomains, processes, or local field variables), functional complex networks are conceptually well-suited for naturally addressing some of the fundamental questions of Earth system analysis concerning, among others, major dynamical patterns, teleconnections, and feedback loops in the planetary machinery, as well as critical elements such as thresholds, bottlenecks, and switches. The first part of this thesis concerns complex network theory and network-based time series analysis. Regarding complex network theory, the novel contributions include consistent frameworks for analyzing the topology of (i) general networks of interacting networks and (ii) networks with vertices of heterogeneously distributed weights, as well as (iii) an analytical theory for describing spatial networks. In the realm of time series analysis, (i) recurrence network analysis is put forward as a theoretically founded, nonlinear technique for the study of single, but possibly multivariate time series. (ii) Coupled climate networks are introduced as an exploratory tool of data analysis for quantitatively characterizing the intricate statistical interdependency structure within and between several fields of time series. The second part presents applications for detecting dynamical transitions (tipping points) in time series and studying bottlenecks in the atmosphere''s general circulation structure. The analysis of paleoclimate data reveals a possible influence of large-scale shifts in Plio-Pleistocene African climate variability on events in human evolution.

In order to study how to reach different climate targets, scientists and policymakers rely on results from computer models known as Integrated Assessment Models (IAMs). These models are used to quantitatively study different ways of achieving warming targets such as the Paris goal of limiting warming to 1.5-2.0 °C, deriving climate mitigation pathways that are optimal in some sense. However, when applied to the Paris goal many IAMs derive pathways that overshoot the temperature target: global temperature temporarily exceeds the warming target for a period of time, before decreasing and stabilizing at the target. Although little is known with certainty about the impacts of overshooting, recent studies indicate that there may be major risks entailed. This thesis explores two different ways of including overshoot risk in a simple IAM by introducing stochastic elements to it. Then, algorithms from Reinforcement Learning (RL) are applied to the model in order to find pathways that take overshoot risk into consideration. In one experiment we apply standard risk-neutral RL to the DICE model extended with a probabilistic damage function and carbon dioxide removal technologies. In the other experiment, the model is further augmented with a probabilistic tipping element model. Using risk-constrained RL we then train an algorithm to optimally control this model, whilst controlling the conditional-value-at-risk of triggering tipping elements below a user-specified threshold. Although some instability and convergence issues are present during training, in both experiments the agents are able to achieve policies that outperform a simple baseline. Furthermore, the risk-constrained agent is also able to (approximately) control the tipping risk metric below a desired threshold in the second experiment. The final policies are analysed for domain insights, indicating that carbon removal via temporal carbon storage solutions could be a sizeable contributor to negative emissions on a time-horizon relevant for overshooting. In the end, recommended next steps for future work are discussed. / För att studera hur globala klimatmål kan nås använder forskare och beslutsfattare resultat från integrerade bedömningsmodeller (IAM:er). Dessa modeller används för att kvantitativt förstå olika vägar till temperaturmål, så som Parisavtalets mål om att begränsa den globala uppvärmningen till 1.5-2.0 °C. Resultaten från dessa modeller är så kallade ”mitigation pathways” som är optimala utifrån något uppsatt kriterium. När sådana modellkörningar görs med Parismålet erhålls dock ofta optimala pathways som överskjuter temperaturmålet tillfälligt: den globala temperaturen överstiger målet i en period innan den sjunker och till slut stabiliseras vid det satta målet. Kunskapen om vilken påverkan en överskjutning har är idag begränsad, men flertalet nyligen gjorda studier indikerar att stora risker potentiellt kan medföras. I denna uppsats utforskas två olika sätt att inkludera överskjutningsrisk i en enkel IAM genom användandet av stokastiska element. Därefter används Förstärkande Inlärning på modellen för att erhålla modellösningar som tar hänsyn till överkjutningsrisk. I ett av experimenten utökas IAM:en med en stokastisk skadefunktion och tekniker för koldioxidinfångning varpå vanlig Förstärkande Inlärning appliceras. I det andra experimentet utökas modellen ytterligare med en stokastisk modell för tröskelpunkter. Med hjälp av risk-begränsad Förstärkande Inlärning tränas därefter en modell för att optimalt kontrollera denna IAM samtidigt som risken att utlösa tröskelpunkter kontrolleras till en nivå satt av användaren. Även om en viss grad av instabilitet och problem med konvergens observeras under inlärningsprocessen så lyckas agenterna i båda experimenten hitta beslutsregler som överträffar en enkel baslinje. Vidare lyckas beslutsregeln som erhålls i det andra experimentet, med den risk-begränsade inlärningen, approximativt kontrollera risken att utlösa tröskelpunkter till det specificerade värdet. Efter träning analyseras de bästa beslutsreglerna i syfte att finna domänmässiga insikter, varav en av dessa insikter är att temporära kollager kan ge betydande bidrag för koldioxidinfångning i en tidshorisont relevant vid överskjutning. Slutligen diskuteras möjliga nästa steg för framtida arbeten inom området.