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Climate change will worsen conditions for people in the Global South, while conditions in large parts of the North will improve. Migration seems an effective adaptation strategy. However, making that a win-win for migrants and receiving communities requires revision of the food system, rules for mobility, and strategies for social integration.

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.

ABSTRACTDespite its well-established negative impacts on society and biodiversity, eutrophication continues to be one of the most pervasive anthropogenic influences along the freshwater to marine continuum. The interaction between eutrophication and climate change, particularly climate warming, was explicitly focused upon a decade ago by Brian Moss and others in “Allied attack: climate change and eutrophication,” which called for an integrated response to both problems, given their apparent synergy. In this review, we summarise advances in the theoretical framework and empirical research on this issue and analyse the current understanding of the major drivers and mechanisms by which climate change can enhance eutrophication, and vice versa, with a particular focus on shallow lakes. Climate change can affect nutrient loading through changes at the catchment and landscape levels by affecting hydrological patterns and fire frequency and through temperature effects on nutrient cycling. Biotic communities and their interactions can also be directly and indirectly affected by climate change, leading to an overall weakening of resilience to eutrophication impacts. Increasing empirical evidence now indicates several mechanisms by which eutrophying aquatic systems can increasingly act as important sources of greenhouse gases to the atmosphere, particularly methane. We also highlight potential feedback among eutrophication, cyanobacterial blooms, and climate change. Facing both challenges simultaneously is more pressing than ever. Meaningful and strong measures at the landscape and waterbody levels are therefore required if we are to ensure ecosystem resilience and safe water supply, conserve biodiversity, and decrease the carbon footprint of freshwaters.

Resilience was compared for alternate states of phytoplankton pigment concentration in two multiyear whole‐lake experiments designed to shift the manipulated ecosystem between alternate states. Mean exit time, the average time between threshold crossings, was calculated from automated measurements every 5 min during summer stratification. Alternate states were clearly identified, and equilibria showed narrow variation in bootstrap analysis of uncertainty. Mean exit times ranged from 13 to 290 h. In the reference ecosystem, Paul Lake, mean exit time of the low‐pigment state was about 100 h longer than mean exit time of the high‐pigment state. In the manipulated ecosystem, Peter Lake, mean exit time of the high‐pigment state exceeded that of the low‐pigment state by 30 h in the cascade experiment. In the enrichment experiment mean exit time of the low‐pigment state was longer than that of the high‐pigment state by about 100 h. Mean exit time is a useful measure of resilience for stochastic ecosystems where high‐frequency measurements are made by consistent methods over the full range of ecosystem states.

Researcher and media alarms have caused plastic debris to be perceived as a major threat to humans and animals. However, although the waste of plastic in the environment is clearly undesirable for aesthetic and economic reasons, the actual environmental risks of different plastics and their associated chemicals remain largely unknown. Here we show how a systematic assessment of adverse outcome pathways based on ecologically relevant metrics for exposure and effect can bring risk assessment within reach. Results of such an assessment will help to respond to the current public worry in a balanced way and allow policy makers to take measures for scientifically sound reasons.

Tree transpiration in the Amazon may enhance rainfall for downwind forests. Until now it has been unclear how this cascading effect plays out across the basin. Here, we calculate local forest transpiration and the subsequent trajectories of transpired water through the atmosphere in high spatial and temporal detail. We estimate that one-third of Amazon rainfall originates within its own basin, of which two-thirds has been transpired. Forests in the southern half of the basin contribute most to the stability of other forests in this way, whereas forests in the south-western Amazon are particularly dependent on transpired-water subsidies. These forest-rainfall cascades buffer the effects of drought and reveal a mechanism by which deforestation can compromise the resilience of the Amazon forest system in the face of future climatic extremes.

Climate change research often focuses on trends in the mean and variance. However, analyses of palaeoclimatic and contemporary dynamics reveal that climate memory — as measured for instance by temporal autocorrelation — may also change substantially over time. Here, we show that elevated temporal autocorrelation in climatic variables should be expected to increase the chance of critical transitions in climate-sensitive systems with tipping points. We demonstrate that this prediction is consistent with evidence from forests, coral reefs, poverty traps, violent conflict and ice sheet instability. In each example, the duration of anomalous dry or warm events elevates chances of invoking a critical transition. Understanding the effects of climate variability thus requires research not only on variance, but also on climate memory.

Coral reefs support immense biodiversity and provide important ecosystem services to many millions of people. Yet reefs are degrading rapidly in response to numerous anthropogenic drivers. In the coming centuries, reefs will run the gauntlet of climate change, and rising temperatures will transform them into new configurations, unlike anything observed previously by humans. Returning reefs to past configurations is no longer an option. Instead, the global challenge is to steer reefs through the Anthropocene era in a way that maintains their biological functions. Successful navigation of this transition will require radical changes in the science, management and governance of coral reefs.

The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modelling techniques is quite difficult. This has led to the development of an alternative suite of methods that seek to identify signatures of critical phenomena in data, which are expected to occur in advance of many classes of dynamical bifurcation. Crucially, the manifestations of these critical phenomena are generic across a variety of systems, meaning that data-intensive deep learning methods can be trained on (abundant) synthetic data and plausibly prove effective when transferred to (more limited) empirical datasets. This paper provides a proof of concept for this approach as applied to lattice phase transitions: a deep neural network trained exclusively on two-dimensional Ising model phase transitions is tested on a number of real and simulated climate systems with considerable success. Its accuracy frequently surpasses that of conventional statistical indicators, with performance shown to be consistently improved by the inclusion of spatial indicators. Tools such as this may offer valuable insight into climate tipping events, as remote sensing measurements provide increasingly abundant data on complex geospatially resolved Earth systems.

Recent work suggests that episodes of drought and heat can bring forests across climate zones to a threshold for massive tree mortality. As complex systems approach a threshold for collapse they tend to exhibit a loss of resilience, as reflected in declining recovery rates from perturbations. Trees may be no exception, as at the verge of drought-induced death, trees are found to be weakened in multiple ways, affecting their ability to recover from stress. Here we use worldwide time series of satellite images to show that temporal autocorrelation, an indicator of slow recovery rates, rises steeply as mean annual precipitation declines to levels known to be critical for tropical forests. This implies independent support for the idea that such forests may have a tipping point for collapse at drying conditions. Moreover, the demonstration that reduced rates of recovery (slowing down) may be detected from satellite data suggests a novel way to monitor resilience of tropical forests, as well as other ecosystems known to be vulnerable to collapse.

The statistical association between temperature and greenhouse gases over glacial cycles is well documented, but causality behind this correlation remains difficult to extract directly from the data. A time lag of CO2behind Antarctic temperature—originally thought to hint at a driving role for temperature—is absent at the last deglaciation, but recently confirmed at the last ice age inception and the end of the earlier termination II (ref. ). We show that such variable time lags are typical for complex nonlinear systems such as the climate, prohibiting straightforward use of correlation lags to infer causation. However, an insight from dynamical systems theory now allows us to circumvent the classical challenges of unravelling causation from multivariate time series. We build on this insight to demonstrate directly from ice-core data that, over glacial–interglacial timescales, climate dynamics are largely driven by internal Earth system mechanisms, including a marked positive feedback effect from temperature variability on greenhouse-gas concentrations.

Climatic warming is substantially intensifying the global water cycle and is projected to increase rainfall variability. Using satellite data, we show that higher climatic variability is associated with reduced tree cover in the wet tropics globally. In contrast, interannual variability in rainfall can have neutral or even positive effects on tree cover in the dry tropics. In South America, tree cover in dry lands is higher in areas with high year-to-year variability in rainfall. This is consistent with evidence from case studies suggesting that in these areas rare wet episodes are essential for opening windows of opportunity where massive tree recruitment can overwhelm disturbance effects, allowing the establishment of extensive woodlands. In Australia, wet extremes have similar effects, but the net effect of rainfall variability is overwhelmed by negative effects of extreme dry years. In Africa, effects of rainfall variability are neutral for dry lands. It is most likely that differences in herbivore communities and fire regimes contribute to regulating tree expansion during wet extremes. Our results illustrate that increasing climatic variability may affect ecosystem services in contrasting, and sometimes surprising, ways. Expansion of dry tropical tree cover during extreme wet events may decrease grassland productivity but enhance carbon sequestration, soil nutrient retention and biodiversity.

AbstractGlobal warming and eutrophication in fresh and coastal waters may mutually reinforce the symptoms they express and thus the problems they cause.

Abstract: Generic early-warning signals such as increased autocorrelation and variance have been demonstrated in time-series of systems with alternative stable states approaching a critical transition. However, lag times for the detection of such leading indicators are typically long. Here, we show that increased spatial correlation may serve as a more powerful early-warning signal in systems consisting of many coupled units. We first show why from the universal phenomenon of critical slowing down, spatial correlation should be expected to increase in the vicinity of bifurcations. Subsequently, we explore the applicability of this idea in spatially explicit ecosystem models that can have alternative attractors. The analysis reveals that as a control parameter slowly pushes the system towards the threshold, spatial correlation between neighboring cells tends to increase well before the transition. We show that such increase in spatial correlation represents a better early-warning signal than indicators derived from time-series provided that there is sufficient spatial heterogeneity and connectivity in the system.

In many aquatic ecosystems, free-floating plants compete with submerged plants for nutrients and light. Being on top of the water surface free-floating plants are superior competitors for light. Submerged plants can take up nutrients from the sediment and the water column, hereby reducing these levels for free-floating plants. Global warming may change chances of successful species invasion and can alter species dominance. We studied the combined effects of nutrient loading and increased temperature on the competition between the potentially invasive free-floating Salvinia natans (L.) All. and the naturalized submerged Elodea nuttallii Planch. St. John by an outdoor mesocosm experiment under temperate climate conditions (The Netherlands) over a period of 71 days. The free-floating S. natans benefited from increased temperature and increased nutrient loading and limited the chances for the submerged E. nuttallii to take advantage of these changed conditions. S. natans substantially increased temperature in the top layer, while limiting the temperature increase below the mat. Our results suggest that with global warming, invasive free-floating plants might become more successful at the expense of submerged plants.

Abstract: The lumpy distribution of species along a continuous one-dimensional niche axis recently found by Scheffer and van Nes (Scheffer and van Ness 2006) is explained mathematically. We show that it emerges simply from the eigenvalue and eigenvectors of the community matrix. Both the transient patterns—lumps and gaps between them—as well as the asymptotic equilibrium are explained. If the species are evenly distributed along the niche axis, the emergence of these patterns can be demonstrated analytically. The more general case, of randomly distributed species, shows only slight deviations and is illustrated by numerical simulation. This is a robust result whenever the finiteness of the niche is taken into account: it can be extended to different analytic dependence of the interaction coefficients with the distance on the niche axis (i.e., different kernel interactions), different boundary conditions, etc. We also found that there is a critical value both for the width of the species distribution σ and the number of species n below which the clusterization disappears.

Key variables in ecosystems tend to operate on widely different time‐scales. These time‐scales become relevant when a disturbance rocks the ecosystem. Here we try to explain the fast dynamics of plankton and nutrients in the water column of floodplain lakes after disturbances (inundations). We take advantage of natural experiments, that is occasional massive overflow of floodplain lakes with river water. We sampled 10 lakes in two floodplains along the Dutch river Waal monthly for 3 years, capturing the impact of three inundation events. The inundations reset the plankton as well as chemical composition of most lakes to largely the same state. While biologically inert macro‐ion data reflected a large and long lasting impact of the river water, dynamics of nutrients, phytoplankton and zooplankton communities between lakes diverged in a few weeks to regimes characteristic for the different lakes. While one spring inundation synchronized plankton dynamics to let the subsequent clear water phase occur at the same moment in different lakes, winter inundations did not have the same effect and apparently dynamics quickly diverged. Our results showed that effects of inundations and other processes that affect the state of the ecosystem should be studied considering the level of the slow components such as the sediment nutrient pool, fish stock and macrophyte communities. Plankton communities and lake water nutrient status give a practically instantaneous reflection of the condition of these slow components. Copyright © 2008 John Wiley & Sons, Ltd.

Duckweed (Lemna gibba) growth was found to be strongly reduced by unicellular green algae (Scenedesmus conspicua, Chlorella sp., Chlamydomonas sp.) in indoor experiments. These algae reduced N, P, Fe and Mn concentrations of the medium drastically, moreover they increased the pH beyond 10. Subsequent additions of nutrients and pH neutralisation removed the growth inhibition of duckweed. This growth inhibition is, therefore, concluded to be due to pH increase and N, P and trace element (Fe, Mn) removal. Of the five factors significantly inhibiting duckweed growth, depletion of N was strongest, increase in pH was second, followed by reduction of P > Fe > Mn.

Sediment erosion by water movement affects turbidity and thus benthic communities in numerous aquatic systems. This aspect has been widely studied in coastal habitats and estuaries, but less studied in freshwater systems such as shallow lakes. Here we present a simple device to study the effects of biota on the resistance of aquatic sediments to erosion by water movement. Circular 75 l tanks are used to incubate selected sediments with microbial communities. The tank size allows addition of organisms such as small fish, invertebrates and aquatic plants. Effects are studied by gradually increasing water movement by means of a rotor and continuously monitoring the increase of suspended solids. The water speed needed for resuspension is a measure of sediment erosion resistance. With this device we found a linear increment of erosion resistance over time if sediments are left undisturbed, and a significant reduction of erosion resistance with small holes punched randomly in the top layer of sediment (to mimic the effect of benthivorous fish foraging behaviour). Fish biotic perturbation was indicated by a reduction of sediment resistance associated with benthivorous fish presence. However, three spined stickleback did not create the same effect. Measurements with this simple device are reasonably precise and suggest that the set-up can be used to study effects of numerous factors that may affect sediment erosion resistance. For example, sediment consolidation associated with light, temperature, and microbial and plant colonization, along with sediment perturbation related to big invertebrates and fish behaviour.

A simple novel method for indoor culture experiments with small floating water plants, such as Lemnaceae, is described. Experiments demonstrate that the method allows for longer lasting culture experiments with Lemna, avoiding algal growth and self-shading of fronds by overcrowding. This is achieved by enclosing the Lemna fronds in tubes, which are replaced during growth by tubes of increasing diameter. The RGR of Lemna reached optimal values (RGR > 0.3 day-1) when not hampered by algal growth. In competition experiments with algae growing outside the tubes and Lemna inside the tubes, the growth of the fronds decreased dramatically; chlorophyll content of the fronds was 91-97% less and RGR 29-55 % less. This method allows for multifactorial experiments, handling up to 100 experimental units per researcher. This paves the road to competition experiments among and between water plants for light, nutrients and space.

Abstract: Most arid ecosystems have suffered from severe overexploitation by excessive wood harvesting, overgrazing, and agriculture, resulting in depletion of vegetation biomass and soil erosion. These changes are often difficult to reverse due to positive feedbacks that tend to stabilize the new situation. In this paper, we briefly review evidence for the idea that different states in these ecosystems might represent alternative equilibria and present a graphic model that summarizes the implications for their response to changing environmental conditions. We show how, in the light of this theoretical framework, climatic oscillations such as El Niño Southern Oscillation (ENSO) could be used in combination with grazer control to restore degraded arid ecosystems. We also present evidence that, depending on grazing pressure, ENSO episodes can trigger structural and long-lasting changes in these ecosystems.

The interaction of fast and slow processes is an integral part of the sudden large shifts that sometimes occur in ecosystems. To study the effects of slow/fast variables on ecosystems, we used a range of examples from natural and exploited aquatic and terrestrial systems. So-called catastrophic bifurcations in the dynamics of the fast components are at the heart of such dramatic shifts. We discuss some of the most important bifurcations and show how they can be analyzed. Subsequently, we show how the interaction with slowly changing variables can be understood from graphs constructed in a simple way using the singular perturbation approach.

Ecosystems provide a wide range of services to society. Some forms of use affect the quality of the ecosystem, reducing its value for other users. This leads to a conflict of interest that is often settled through political processes, resulting in some form of regulation. We link theory on ecosystem response to theories from the socioeconomic branches of science to analyze the mechanisms behind two widespread problems associated with such political solutions. First, they often represent a compromise rather than an integrative solution. We demonstrate that, particularly in sensitive ecosystems, integrative solutions yield a higher average social utility and imply a higher ecosystem quality. Integrative solutions require insight into ecosystems responses to different forms of use and a complete overview of ecosystem services to society. Second, there is a systematic bias away from optimal shared use toward activities that are detrimental to ecosystem quality. This bias arises from the fact that utilities depending on ecosystem quality are often shared by large diffuse groups, whereas pollution and harvesting activities can usually be traced to relatively small and well-organized groups. Theory and data indicate that this type of concentrated group is systematically better at mustering political power than large groups, which find it difficult to realize collective action due to what is known in game theory as "free-rider problems." Our analysis suggests that the following three key ingredients are needed to correct the problems of bias and compromise: (a) clear insight into ecosystem dynamic responses to human use, (b) a broad inventory of credible measurements of ecosystem utilities, (c) avoidance of bias due to differences in the organizational power of groups of stakeholders. We argue that good ecosystem models, institutionalized ecosystem valuation, and innovative tax-setting schedules are essential to achieving a socially fair and sustainable use of ecosystems by societies. In addition, we highlight the fact that many environmental problems remain unresolved for a long time and briefly identify the social mechanisms responsible for this delay.

Abstract: It is shown with the use of minimal models that several ecological relationships in freshwater systems potentially give rise to the existence of alternative equilibria over a certain range of nutrient values. The existence of alternative stable states has some implications for the management of such systems. An important consequence is that signs of eutrophication are only apparent after the occurrence of changes that are very difficult to reverse. Reduction of the nutrient level as a measure to restore such systems gives poor results, but biomanipulation as an additional measure can have significant effects, provided that the nutrient level has been reduced enough to allow the existence of a stable alternative clear water equilibrium.

The question to what extent predators regulate the populations of their food species has a long history of debate, and today top-down control of plankton dynamics still is a major issue in limnology. Over the last decade a fascinating extra dimension of this topic has been revealed. Fish, zooplankton and algae can sense their potential predators through chemical cues and adjust their ‘life style’ in a flexible way to minimize the risk of being eaten. Although much progress has been made in elucidating the mechanisms involved, the implications of such predation avoidance for the potential of predators to reduce the abundance of their food populations are still poorly understood. Model analyses suggest that predation avoidance leads to more stable food webs in which the effects of nutrient enrichment are more evenly distributed over the trophic levels. In this article it is argued that the cost which predation avoidance usually has in terms of food conditions implies a tricky caveat in interpreting observations on predation rates and nutritional status in natural populations. Prey that sense the presence of predators and aggregates at safe sites where food conditions are poor, may appear starved and actual predation losses may be low. Such observations suggest that food limitation is the dominant force limiting their population development, but although starvation may indeed be the proximate cause of poor growth and reproduction, predation is clearly the ultimate factor involved in this situation. Thus when predation avoidance occurs, standard demographic analyses will tend to underestimate the importance of predators in regulating the dynamics of their prey in the field.

AbstractWe applied an individual-based model to an age-0 cohort of smallmouth bass Micropterus dolomieuto simulate the cohort's growth and survivorship through its first growing season. The purpose was to determine whether the stock–recruitment characteristics of the age-0 fish could be predicted. The model smallmouth bass were exposed to size-dependent predation, size-independent mortality, and starvation mortality resulting from depletion of their prey supply. Survivorship curves were produced by model simulations. When survivorship at a given time was plotted against initial egg density during the early growing season, the curve resembled the peaked pattern of a Ricker-type curve. In contrast, curves for survivorship during the late growing season had no noticeable peak or maximum. Other results showed (1) strong density dependence of the mortality rate early in the growing season and density independence late in the growing season; (2) a distinct critical time (CT) during which the slope of the survivorship curve changed from a steep to a shallow decline, and (3) a decrease in CT as a function of the initial egg density. Competition for and overexploitation of prey during the early growing season produced these results. The model simulation results resembled patterns of some empirical data.

We applied an individual-based model to an age-0 cohort of smallmouth bass Micropterus dolomieuto simulate the cohort's growth and survivorship through its first growing season. The purpose was to determine whether the stock–recruitment characteristics of the age-0 fish could be predicted. The model smallmouth bass were exposed to size-dependent predation, size-independent mortality, and starvation mortality resulting from depletion of their prey supply. Survivorship curves were produced by model simulations. When survivorship at a given time was plotted against initial egg density during the early growing season, the curve resembled the peaked pattern of a Ricker-type curve. In contrast, curves for survivorship during the late growing season had no noticeable peak or maximum. Other results showed (1) strong density dependence of the mortality rate early in the growing season and density independence late in the growing season; (2) a distinct critical time (CT) during which the slope of the survivorship curve changed from a steep to a shallow decline, and (3) a decrease in CT as a function of the initial egg density. Competition for and overexploitation of prey during the early growing season produced these results. The model simulation results resembled patterns of some empirical data.

A generic simulation model for the dynamics of submerged macrophytes is presented, called MEGAPLANT (‘Model Evaluating General Aquatic Pland Laws And New Theories’). Although the model is kept relatively simple, it includes many aspects that have an effect on vegetation dynamics during the seasonal cycle, such as grazing, overwintering strategies, wave action and seed dispersal. The characteristics of both the plant and the environment can be adjusted by the user. The model is meant as an aid to enhance insight into the interplay of processes that influence vegetation dynamics. As an example, it is used to analyze mechanisms that determine the survival of vegetation in turbid eutrophic lakes. The following results were found. (1) Hot spots of propagule-producing vegetation can permanently maintain vegetation stands at sites that would otherwise be devoid of macrophytes. (2) Moderate fluctuations in environmental factors that normally have little impact on the vegetation can cause large year-to-year fluctuations in biomass of vegetation growing under suboptimal conditions. (3) Grazing by herbivores such as coots can cause the existence of two alternative stable states: under-exploited and overgrazed. This implies that herbivores may prevent the recovery of submerged macrophytes in lakes that are recovering from eutrophication, but also that temporary exclusion of herbivores can trigger permanent recovery of the vegetation.

A rise in fragility as a system approaches a tipping point may be sometimes estimated using dynamical indicators of resilience (DIORs) that measure the characteristic slowing down of recovery rates before a tipping point. A change in DIORs could be interpreted as an early warning signal for an upcoming critical transition. However, in order to be able to estimate the DIORs, observational records need to be long enough to capture the response rate of the system. As we show here, the required length of the time series depends on the response rates of the system. For instance, the current rate of anthropogenic climate forcing is fast relative to the response rate of some parts of the climate system. Therefore, we may expect difficulties estimating the resilience from modern time series. So far, there have been no systematic studies of the effects of the response rates of the dynamical systems and the rates of forcing on the detectability trends in the DIORs prior to critical transitions. Here, we quantify the performance of the resilience indicators variance and temporal autocorrelation, in systems with different response rates and for different rates of forcing. Our results show that the rapid rise of anthropogenic forcing to the Earth may make it difficult to detect changes in the resilience of ecosystems and climate elements from time series. These findings suggest that in order to determine with models whether the use of the DIORs is appropriate, we need to use realistic models that incorporate the key processes with the appropriate time constants.

Shallow cloud fields over the subtropical ocean exhibit many spatial patterns. The frequency of occurrence of these patterns can change under global warming. Hence, they may influence subtropical marine clouds’ climate feedback. While numerous metrics have been proposed to quantify cloud patterns, a systematic, widely accepted description is still missing. Therefore, this study suggests one. We compute 21 metrics for 5,000 satellite scenes of shallow clouds over the subtropical Atlantic Ocean and translate the resulting data set to its principal components (PCs). This yields a unimodal, continuous distribution without distinct classes, whose first four PCs explain 82% of all 21 metrics’ variance. The PCs correspond to four interpretable dimensions: Characteristic length, void size, directional alignment, and horizontal cloud top height variance. These dimensions span a space in which an effective pattern description can be given, which may be used to better understand the patterns’ underlying physics and feedback on climate. Satellite images show that clouds which develop in the lowest 5 km of the atmosphere organize into many visually distinct patterns. Because different patterns reflect sunlight differently, a change in the relative occurrence of a pattern may influence Earth's response to warming. To study this effect, one typically first encapsulates various aspects of the complex patterns in a few, simple “metrics.” In this paper, we compute 21 commonly used metrics for 5,000 cloud fields observed by satellite over the Atlantic Ocean east of Barbados. We show that these 21 metrics contain a large amount of redundant information: To effectively describe and interpret the cloud patters, one only needs four derived metrics, which capture a cloud field's typical cloud size, the size of connected clear sky patches, the clouds’ degree of directional alignment and spatial variance in cloud top height. Combinations of these four metrics do not identify the existence of multiple, typical cloud patterns, as previously suggested. However, the four metrics form a new, effective and interpretable pattern description, which can be used to better understand how cloud patterns develop and how this impacts the wider climate system. Shallow cloud patterns in satellite observations are quantified by 21 metrics and follow a unimodal, continuous distributionMost existing metrics are redundant; four principal components capture 82% of the variance of 21 metricsCharacteristic length, void size, directional alignment, and cloud top height variance combine to effectively describe the patterns Shallow cloud patterns in satellite observations are quantified by 21 metrics and follow a unimodal, continuous distribution Most existing metrics are redundant; four principal components capture 82% of the variance of 21 metrics Characteristic length, void size, directional alignment, and cloud top height variance combine to effectively describe the patterns

Predicting which marine systems are close to abrupt transitions into oxygen‐deficient conditions (“anoxia”) is notoriously hard but important—as rising temperatures and coastal eutrophication drive many marine systems toward such tipping points. Rapid oxic‐to‐anoxic transitions occurred regularly within the eastern Mediterranean Sea on (multi)centennial time scales, and hence, its sedimentary archive allows exploring statistical methods that can indicate approaching tipping points. The here presented high‐resolution reconstructions of past oxygen dynamics in the Mediterranean Sea reveal that early‐warning signals in these deoxygenation time series occurred long before fast transitions to anoxia. These statistical indicators (i.e., rise in autocorrelation and variance) are hallmarks of so‐called critical slowing down, signaling a steady loss of resilience of the oxygenated state as the system approaches a tipping point. Hence, even without precise knowledge of the mechanisms involved, early‐warning signals for widespread anoxia in marine systems are recognizable using an appropriate statistical approach. As a result of rising temperatures and input of excess nutrients to coastal regions, today's oceans and seas are losing oxygen. In the geological past, large‐scale anoxic events have occasionally triggered mass extinction events, and the current loss of oxygen in the marine realm has increased worries about such events happening again. Predicting these rapid transitions to anoxia has been nearly impossible until now. By studying past large‐scale anoxic events in the Mediterranean Sea, we show, however, that before a fast transition to anoxia, there are early‐warning signals recognizable in deoxygenation time series. These early‐warning signals make it potentially possible to develop an approach to forecast rapid transitions to anoxia in areas sensitive for fast deoxygenation. Deoxygenation events in the eastern Mediterranean Sea show tipping point behavior at which the system abruptly shifted to an anoxic stateRise in variance and autocorrelation (“early‐warning signals”) in deoxygenation proxies generally signal an upcoming transition to anoxiaFirst empirical proof that these statistical indicators are applicable to marine systems sensitive to fast deoxygenation

CRAIG R.ALLEN AND C.S. HOLLING (Eds.) 2008. Discontinuities in Ecosystems and other Complex Systems. Columbia University Press, New York. ISBN 978‐0231144445. 288 p. US$84.50