Safe and just Earth system boundaries.

The stability and resilience of the Earth system and human well-being are inseparably linked1-3, yet their interdependencies are generally under-recognized; consequently, they are often treated independently4,5. Here, we use modelling and literature assessment to quantify safe and just Earth system boundaries (ESBs) for climate, the biosphere, water and nutrient cycles, and aerosols at global and subglobal scales. We propose ESBs for maintaining the resilience and stability of the Earth system (safe ESBs) and minimizing exposure to significant harm to humans from Earth system change (a necessary but not sufficient condition for justice)4. The stricter of the safe or just boundaries sets the integrated safe and just ESB. Our findings show that justice considerations constrain the integrated ESBs more than safety considerations for climate and atmospheric aerosol loading. Seven of eight globally quantified safe and just ESBs and at least two regional safe and just ESBs in over half of global land area are already exceeded. We propose that our assessment provides a quantitative foundation for safeguarding the global commons for all people now and into the future.

The planetary commons: A new paradigm for safeguarding Earth-regulating systems in the Anthropocene.

The Anthropocene signifies the start of a no-analogue trajectory of the Earth system that is fundamentally different from the Holocene. This new trajectory is characterized by rising risks of triggering irreversible and unmanageable shifts in Earth system functioning. We urgently need a new global approach to safeguard critical Earth system regulating functions more effectively and comprehensively. The global commons framework is the closest example of an existing approach with the aim of governing biophysical systems on Earth upon which the world collectively depends. Derived during stable Holocene conditions, the global commons framework must now evolve in the light of new Anthropocene dynamics. This requires a fundamental shift from a focus only on governing shared resources beyond national jurisdiction, to one that secures critical functions of the Earth system irrespective of national boundaries. We propose a new framework-the planetary commons-which differs from the global commons framework by including not only globally shared geographic regions but also critical biophysical systems that regulate the resilience and state, and therefore livability, on Earth. The new planetary commons should articulate and create comprehensive stewardship obligations through Earth system governance aimed at restoring and strengthening planetary resilience and justice.

The hysteresis of the Antarctic Ice Sheet.

More than half of Earth's freshwater resources are held by the Antarctic Ice Sheet, which thus represents by far the largest potential source for global sea-level rise under future warming conditions1. Its long-term stability determines the fate of our coastal cities and cultural heritage. Feedbacks between ice, atmosphere, ocean, and the solid Earth give rise to potential nonlinearities in its response to temperature changes. So far, we are lacking a comprehensive stability analysis of the Antarctic Ice Sheet for different amounts of global warming. Here we show that the Antarctic Ice Sheet exhibits a multitude of temperature thresholds beyond which ice loss is irreversible. Consistent with palaeodata2 we find, using the Parallel Ice Sheet Model3-5, that at global warming levels around 2 degrees Celsius above pre-industrial levels, West Antarctica is committed to long-term partial collapse owing to the marine ice-sheet instability. Between 6 and 9 degrees of warming above pre-industrial levels, the loss of more than 70 per cent of the present-day ice volume is triggered, mainly caused by the surface elevation feedback. At more than 10 degrees of warming above pre-industrial levels, Antarctica is committed to become virtually ice-free. The ice sheet's temperature sensitivity is 1.3 metres of sea-level equivalent per degree of warming up to 2 degrees above pre-industrial levels, almost doubling to 2.4 metres per degree of warming between 2 and 6 degrees and increasing to about 10 metres per degree of warming between 6 and 9 degrees. Each of these thresholds gives rise to hysteresis behaviour: that is, the currently observed ice-sheet configuration is not regained even if temperatures are reversed to present-day levels. In particular, the West Antarctic Ice Sheet does not regrow to its modern extent until temperatures are at least one degree Celsius lower than pre-industrial levels. Our results show that if the Paris Agreement is not met, Antarctica's long-term sea-level contribution will dramatically increase and exceed that of all other sources.

Recurrent droughts increase risk of cascading tipping events by outpacing adaptive capacities in the Amazon rainforest.

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 from climatological 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. The loss 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.

Trajectories of the Earth System in the Anthropocene.

We explore the risk that self-reinforcing feedbacks could push the Earth System toward a planetary threshold that, if crossed, could prevent stabilization of the climate at intermediate temperature rises and cause continued warming on a "Hothouse Earth" pathway even as human emissions are reduced. Crossing the threshold would lead to a much higher global average temperature than any interglacial in the past 1.2 million years and to sea levels significantly higher than at any time in the Holocene. We examine the evidence that such a threshold might exist and where it might be. If the threshold is crossed, the resulting trajectory would likely cause serious disruptions to ecosystems, society, and economies. Collective human action is required to steer the Earth System away from a potential threshold and stabilize it in a habitable interglacial-like state. Such action entails stewardship of the entire Earth System-biosphere, climate, and societies-and could include decarbonization of the global economy, enhancement of biosphere carbon sinks, behavioral changes, technological innovations, new governance arrangements, and transformed social values.

How motifs condition critical thresholds for tipping cascades in complex networks: Linking micro- to macro-scales.

In this study, we investigate how specific micro-interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erdos-Rényi networks and an exemplary moisture recycling network of the Amazon rainforest. Within these networks, decisive small-scale motifs are the feed forward loop, the secondary feed forward loop, the zero loop, and the neighboring loop. Of all motifs, the feed forward loop motif stands out in tipping cascades since it decreases the critical coupling strength necessary to initiate a cascade more than the other motifs. We find that for this motif, the reduction of critical coupling strength is 11% less than the critical coupling of a pair of tipping elements. For highly connected networks, our analysis reveals that coupled feed forward loops coincide with a strong 90% decrease in the critical coupling strength. For the highly clustered moisture recycling network in the Amazon, we observe regions of a very high motif occurrence for each of the four investigated motifs, suggesting that these regions are more vulnerable. The occurrence of motifs is found to be one order of magnitude higher than in a random Erdos-Rényi network. This emphasizes the importance of local interaction structures for the emergence of global cascades and the stability of the network as a whole.

Future sea level rise constrained by observations and long-term commitment.

Sea level has been steadily rising over the past century, predominantly due to anthropogenic climate change. The rate of sea level rise will keep increasing with continued global warming, and, even if temperatures are stabilized through the phasing out of greenhouse gas emissions, sea level is still expected to rise for centuries. This will affect coastal areas worldwide, and robust projections are needed to assess mitigation options and guide adaptation measures. Here we combine the equilibrium response of the main sea level rise contributions with their last century's observed contribution to constrain projections of future sea level rise. Our model is calibrated to a set of observations for each contribution, and the observational and climate uncertainties are combined to produce uncertainty ranges for 21st century sea level rise. We project anthropogenic sea level rise of 28-56 cm, 37-77 cm, and 57-131 cm in 2100 for the greenhouse gas concentration scenarios RCP26, RCP45, and RCP85, respectively. Our uncertainty ranges for total sea level rise overlap with the process-based estimates of the Intergovernmental Panel on Climate Change. The "constrained extrapolation" approach generalizes earlier global semiempirical models and may therefore lead to a better understanding of the discrepancies with process-based projections.

In-ice light measurements during the MOSAiC expedition.

We present light measurements in Arctic sea ice obtained during the year-long MOSAiC drift through the central Arctic Ocean in 2019-2020. Such measurements are important as sea ice plays a fundamental role in the Arctic climate and ecosystem. The partitioning of solar irradiance determines the availability of radiation energy for thermodynamic processes and primary productivity. However, observations of light partitioning along the vertical path through the ice are rare. The data we present were collected by two measurement systems, the lightharp and the lightchain, both measuring autonomously multi-spectral light intensity in different depths within the ice. We present the dataset, retrieval methods for derived optical properties, and the conversion into the final, freely available data product, following standardized conventions. We particularly focus on the specifications of the newly developed lightharp system. Combined with the interdisciplinary and multi-instrument setup of MOSAiC, we expect great potential of the dataset to foster our understanding of light transmission and reflection in the sea-ice cover and interactions with physical sea-ice properties and the polar ecosystem.

Remotely sensing potential climate change tipping points across scales.

Potential climate tipping points pose a growing risk for societies, and policy is calling for improved anticipation of them. Satellite remote sensing can play a unique role in identifying and anticipating tipping phenomena across scales. Where satellite records are too short for temporal early warning of tipping points, complementary spatial indicators can leverage the exceptional spatial-temporal coverage of remotely sensed data to detect changing resilience of vulnerable systems. Combining Earth observation with Earth system models can improve process-based understanding of tipping points, their interactions, and potential tipping cascades. Such fine-resolution sensing can support climate tipping point risk management across scales.

Exceeding 1.5°C global warming could trigger multiple climate tipping points.

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 <2°C global warming, with many more likely at the 2 to 3°C of warming expected on current policy trajectories. This strengthens the evidence base for urgent action to mitigate climate change and to develop improved tipping point risk assessment, early warning capability, and adaptation strategies.

Emergence of cascading dynamics in interacting tipping elements of ecology and climate.

In ecology, climate and other fields, (sub)systems have been identified that can transition into a qualitatively different state when a critical threshold or tipping point in a driving process is crossed. An understanding of those tipping elements is of great interest given the increasing influence of humans on the biophysical Earth system. Complex interactions exist between tipping elements, e.g. physical mechanisms connect subsystems of the climate system. Based on earlier work on such coupled nonlinear systems, we systematically assessed the qualitative long-term behaviour of interacting tipping elements. We developed an understanding of the consequences of interactions on the tipping behaviour allowing for tipping cascades to emerge under certain conditions. The (narrative) application of these qualitative results to real-world examples of interacting tipping elements indicates that tipping cascades with profound consequences may occur: the interacting Greenland ice sheet and thermohaline ocean circulation might tip before the tipping points of the isolated subsystems are crossed. The eutrophication of the first lake in a lake chain might propagate through the following lakes without a crossing of their individual critical nutrient input levels. The possibility of emerging cascading tipping dynamics calls for the development of a unified theory of interacting tipping elements and the quantitative analysis of interacting real-world tipping elements.

Global warming due to loss of large ice masses and Arctic summer sea ice.

Several large-scale cryosphere elements such as the Arctic summer sea ice, the mountain glaciers, the Greenland and West Antarctic Ice Sheet have changed substantially during the last century due to anthropogenic global warming. However, the impacts of their possible future disintegration on global mean temperature (GMT) and climate feedbacks have not yet been comprehensively evaluated. Here, we quantify this response using an Earth system model of intermediate complexity. Overall, we find a median additional global warming of 0.43 °C (interquartile range: 0.39-0.46 °C) at a CO2 concentration of 400 ppm. Most of this response (55%) is caused by albedo changes, but lapse rate together with water vapour (30%) and cloud feedbacks (15%) also contribute significantly. While a decay of the ice sheets would occur on centennial to millennial time scales, the Arctic might become ice-free during summer within the 21st century. Our findings imply an additional increase of the GMT on intermediate to long time scales.

Dynamics of tipping cascades on complex networks.

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

Combustion of available fossil fuel resources sufficient to eliminate the Antarctic Ice Sheet.

The Antarctic Ice Sheet stores water equivalent to 58 m in global sea-level rise. We show in simulations using the Parallel Ice Sheet Model that burning the currently attainable fossil fuel resources is sufficient to eliminate the ice sheet. With cumulative fossil fuel emissions of 10,000 gigatonnes of carbon (GtC), Antarctica is projected to become almost ice-free with an average contribution to sea-level rise exceeding 3 m per century during the first millennium. Consistent with recent observations and simulations, the West Antarctic Ice Sheet becomes unstable with 600 to 800 GtC of additional carbon emissions. Beyond this additional carbon release, the destabilization of ice basins in both West and East Antarctica results in a threshold increase in global sea level. Unabated carbon emissions thus threaten the Antarctic Ice Sheet in its entirety with associated sea-level rise that far exceeds that of all other possible sources.