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Climate tipping points occur when change in a part of the climate system becomes self-perpetuating beyond a warming threshold, leading to substantial Earth system impacts. Synthesizing paleoclimate, observational, and model-based studies, we provide a revised shortlist of global “core” tipping elements and regional “impact” tipping elements and their temperature thresholds. Current global warming of ~1.1°C above preindustrial temperatures already lies within the lower end of some tipping point uncertainty ranges. Several tipping points may be triggered in the Paris Agreement range of 1.5 to

Chapter 18 deals with statistical methods, which are mathematical tools that can help aggregate, present and explore complex datasets from various sources. These methods can be very useful for understanding interactions, dependencies and relationships between social and ecological variables. The chapter discusses descriptive statistics, regression models, multivariate regression analysis, group comparison, clustering and non-metric dimensional scaling, principal component analysis, redundancy analysis, canonical correspondence analysis, factor analysis, multiple correspondence analysis, and time series analysis. It goes on to discuss the types of social-ecological systems (SES) problems and research questions commonly addressed by this set of methods, as well as their limitations, resource implications and new emerging research directions. The chapter also includes an in-depth case study showcasing the application of statistical analyses, and suggested further readings on these methods.

Climate change and deforestation have increased the risk of drought-induced forest-to-savanna transitions across the tropics and subtropics. However, the present understanding of forest-savanna transitions is generally focused on the influence of rainfall and fire regime changes, but does not take into account the adaptability of vegetation to droughts by utilizing subsoil moisture in a quantifiable metric. Using rootzone storage capacity (S r), which is a novel metric to represent the vegetation's ability to utilize subsoil moisture storage and tree cover (TC), we analyze and quantify the occurrence of these forest-savanna transitions along transects in South America and Africa. We found forest-savanna transition thresholds to occur around a S r of 550-750 mm for South America and 400-600 mm for Africa in the range of 30%-40% TC. Analysis of empirical and statistical patterns allowed us to classify the ecosystem's adaptability to droughts into four classes of drought coping strategies: lowly water-stressed forest (shallow roots, high TC), moderately water-stressed forest (investing in S r, high TC), highly water-stressed forest (trade-off between investments in S r and TC) and savanna-grassland regime (competitive rooting strategy, low TC). The insights from this study are useful for improved understanding of tropical eco-hydrological adaptation, drought coping strategies, and forest ecosystem regime shifts under future climate change.

The planetary boundaries framework defines the “safe operating space for humanity” represented by nine global processes that can destabilize the Earth System if perturbed. The water planetary boundary attempts to provide a global limit to anthropogenic water cycle modifications, but it has been challenging to translate and apply it to the regional and local scales at which water problems and management typically occur. We develop a cross‐scale approach by which the water planetary boundary could guide sustainable water management and governance at subglobal contexts defined by physical features (e.g., watershed or aquifer), political borders (e.g., city, nation, or group of nations), or commercial entities (e.g., corporation, trade group, or financial institution). The application of the water planetary boundary at these subglobal contexts occurs via two approaches: (i) calculating fair shares, in which local water cycle modifications are compared to that context's allocation of the global safe operating space, taking into account biophysical, socioeconomic, and ethical considerations; and (ii) defining a local safe operating space, in which interactions between water stores and Earth System components are used to define local boundaries required for sustaining the local water system in stable conditions, which we demonstrate with a case study of the Cienaga Grande de Santa Marta wetlands in Colombia. By harmonizing these two approaches, the water planetary boundary can ensure that water cycle modifications remain within both local and global boundaries and complement existing water management and governance approaches., Key Points Local and regional water management responds to and is influenced by global water cycle processesThe planetary boundaries framework is useful for reconciling local and global water sustainability goalsThe framework can be applied at scales including nations, watersheds, aquifers, or commercial entities

Water harvesting has been widely applied in different social-ecological contexts, proving to be a valuable approach to sustainable intensification of agriculture. Global estimates of the potential of water harvesting are generally based on purely biophysical assessments and mostly neglect the socioeconomic dimension of agriculture. This neglect becomes a critical factor for the feasibility and effectiveness of policy and funding efforts to mainstream this practice. This study uses archetype analysis to systematically identify social-ecological regions worldwide based on > 160 successful cases of local water harvesting implementation. We delineate six archetypal regions which capture the specific social-ecological conditions of the case studies. The archetypes cover 19% of current global croplands with hotspots in large portions of East Africa and Southeast Asia. We estimate that the adoption of water harvesting in these cropland areas can increase crop production up to 60-100% in Uganda, Burundi, Tanzania and India. The results of this study can complement conventional biophysical analysis on the potential of these practices and guide policy development at global and regional scales. The methodological approach can be also replicated at finer scales to guide the improvement of rainfed agricultural.

Extended exposure to change in rainfall patterns and permanent land-use change (LUC) have reduced the capability of the forests to withstand any external stresses, also defined as forest resilience loss. Major parts of the Amazon forest is under threat of tipping towards a treeless savanna state due to these changes in rainfall patterns and LUC. This loss in forest resilience thus also prevents the forest to return to its pre-disturbed state of the natural cycle and makes the forest more prone to tipping. Yet, this change in natural cycle is not sudden and involves a certain time lag for the forest system to respond. Previous studies determined the forest resilience, but have only considered precipitation or climatological drought to be the key influencing factor. However, neither are a direct measure of the water stress of the forest and thus do not fully reflect the hydrological dynamics underlying forest resilience loss. This study addresses the research questions: (i) do change in climatic patterns have a significant effect on forest resilience?, (ii) how does the change in rainfall patterns orLUC affect the environmental dynamics of the forest over time?, (iii) whether the quantification of rainfall, rootzone storage capacity and LUC patterns at a temporal scale better for understanding the resilience loss of the forest? The present study aims at understanding the complex dynamics of the resilience of the forest system using a time-series approach. Advanced remote sensing resources allow us to determine and understand patterns in the tipping behaviour at a temporal scale as well as to understand the hydrological dynamics and environmental triggers. For this, we combined precipitation data, root zone storage capacity and satellite-based forest cover and LUC data analyzed along a time-series. This is to better represent the resilience loss of the forest towards hydrological interactions and also provide a better understanding of the hydrological process for the forest tipping rather than a statistical relation. Landsat-7 data is ideal for determining the forest change, due to its regional time-series availability from early 2000’s until today. This study provides a better understanding of the hydrological dynamics of the rainforest by utilizing a time-series approach. Root zone storage capacity represents the water stored in the roots of the forest (a.k.a., water available to the forest) and it is a much better representation for assessing water stress of the Amazonian rainforest than precipitation. Thus, also a better parameter for evaluating forest resilience loss over time.