# Earth system resilience and tipping behavior

Chuixiang Yi, Vasilis Dakos, Paul D L Ritchie, Jana Sillmann, Juan C Rocha, Manjana Milkoreit, Courtney Quinn

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Chuixiang Yi, Vasilis Dakos, Paul D L Ritchie, Jana Sillmann, Juan C Rocha, et al. Earth system resilience and tipping behavior. Environmental Research Letters, 2024, 19 (7), pp.070201. 10.1088/1748-9326/ad5741. hal-04794206

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ENVIRONMENTAL RESEARCH
LETTERS

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EDITORIAL

Earth system resilience and tipping behavior

Chuixiang Yi<fnref n="1" />,<fnref n="2" />,* , Vasilis Dakos<fnref n="3" />, Paul D L Ritchie<fnref n="4" />,<fnref n="5" /> <fnref n="1" />⁾, Jana Sillmann<fnref n="6" />,<fnref n="7" /> <fnref n="1" />⁾, Juan C Rocha<fnref n="8" /> <fnref n="1" />⁾,
Manjana Milkoreit<fnref n="9" /> <fnref n="1" />⁾ and Courtney Quinn<fnref n="10" />,<fnref n="11" />

E-mail: cyi@qc.cuny.edu

**Keywords:** earth system resilience, tipping point, climate change, instability

Abstract

Anthropogenic climate change, marked by unprecedented extremes, is an immediate concern. The Earth's limited ability to adapt to abrupt changes within our societal timeframe has raised global alarm. Resilience, the capacity to withstand and recover from disturbances, diminishes as disturbances intensify. For avoiding potential catastrophic changes, it is crucial to identify tipping points, where a change in part of a system becomes self-perpetuating beyond some threshold, leading to substantial, widespread, often abrupt and irreversible, impacts. This ERL focus collection has published 27 papers, which contribute novel research findings into the scientific literature in: (1) formulating theories of resilience and tipping points, (2) determining ecological resistance, resilience, and recovery, (3) examining tipping behavior of the Earth system, and (4) identifying social-ecological resilience and tipping points. Some of these results also are useful for policymakers and resource managers in addressing catastrophic disasters as a result of increasingly anthropogenic heating.

1. Introduction

Global warming is not only happening but also accel-
erating, leading to an increase in extreme events such
as wildfires and floods occurring more frequently
worldwide. Climate data (ERA5) shows that in the
past 85 years (back to 1940), the global temperat-
ure measured for September and November of 2023
were the most anomalous warm months of any year
(figure 1). The average sea surface temperature for
September over 60 °S–60 °N reached 20.92 °C.
Due to the specific heat of water being higher, sea
surface temperature change is much slower than air

temperature change. Warm oceans can therefore lead
to prolonged warm weather conditions.

Global warming is a source of extreme weather
and climate because hot air can hold more moist-
ure (Yi *et al* 2015). Thus, global warming repres-
ents a double-edged sword, as it not only contrib-
utes to flooding but also exacerbates the occurrence
of widespread wildfires due to enhancing fire weather
conditions. On one hand, warming temperatures lead
to an atmosphere capable of holding more moisture,
increasing the likelihood of extreme precipitation
events and flooding. On the other hand, elevated tem-
peratures drive the evaporation of moisture from soils

<footnote n="1">¹ School of Earth and Environmental Sciences, Queens College, City University of New York, New York, NY 11367, United States of America</footnote>

<footnote n="2">² Earth and Environmental Sciences Department, Graduate Center, City University of New York, New York, NY 10016, United States of America</footnote>

<footnote n="3">³ Institut des Sciences de l'Evolution de Montpellier (ISEM), Université de Montpellier, IRD, EPHE, Montpellier, France</footnote>

<footnote n="4">⁴ Department of Mathematics and Statistics, Faculty of Environment, Science and Economy, University of Exeter, North Park Road, Exeter EX4 4QE, United Kingdom</footnote>

<footnote n="5">5 Global Systems Institute, Faculty of Environment, Science and Economy, University of Exeter, North Park Road, Exeter EX4 4QE, United Kingdom</footnote>

<footnote n="6">⁶ University of Hamburg, Research Unit for Sustainability and Climate Risks, Grindelberg 5, 20144 Hamburg, Germany</footnote>

<footnote n="7">7 CICERO, Center for International Climate Research, Oslo, Norway</footnote>

<footnote n="8">⁸ Stockholm Resilience Centre and Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden</footnote>

<footnote n="9">⁹ Department of Sociology and Human Geography, University of Oslo, Moltke Moes vei 31, 0851 Oslo, Norway</footnote>

<footnote n="10">¹⁰ School of Natural Sciences, University of Tasmania, Churchill Avenue, Sandy Bay, 7001 Tasmania, Australia</footnote>

<footnote n="11">¹¹ CSIRO Environment, Hobart, Tasmania 7000, Australia</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Global daily surface air temperature (°C) from 1 January 1940 to 17 November 2023, plotted as time series for each year. 2023 and 2016 are shown with thick lines shaded in bright red and dark red, respectively. Other years are shown with thin lines and shaded according to the decade, from blue (1940s) to brick red (2020s). The dotted line and grey envelope represent the 1.5 °C threshold above preindustrial level (1850–1900) and its uncertainty. Data source: ERA5. Credit: European Union, Copernicus Sentinel-3/ECMWF imagery (Hersbach *et al* 2018).</figcaption></figure>

and vegetation, making these areas more susceptible to wildfires by reducing soil moisture, increasing surface air temperature and drying out vegetation. Global warming also fosters the conditions for wildfires by promoting droughts, heatwaves, and extreme weather events that further desiccate vegetation and elevate the risk of ignition (Yi *et al* 2022). Wildfires impact ecosystems by releasing substantial amounts of carbon dioxide into the atmosphere, exacerbating global warming in an amplifying feedback loop (Yi *et al* 2015).

One might ask, what are the effects of global warming on the overall stability and resilience of Earth's system? To conceptualise Earth's stability, Rockstrom *et al* (2009) introduced the planetary boundaries framework, which identifies nine critical processes significantly impacted by human activities. The framework aims to establish boundaries that limit human-induced disturbances, aiming to maintain Earth's state akin to the Holocene interglacial period, characterized by stable and warm planetary conditions. Human activities act as additional drivers influencing Earth's system, making the anthroposphere an integral component capable of altering the planet's state. These nine boundaries proposed by Rockstrom *et al* (2009) represent safe operating limits designed to prevent catastrophic environmental changes and to identify thresholds for environmental risks. In a recent study, Richardson *et al* (2023) quantified all nine boundaries for the first time, revealing that six of them have been surpassed (www.stockholmresilience.org/research/planetary-boundaries.html). In the face of catastrophic changes induced by anthropogenic heating, it is vitally important for policy makers and

others to know the conditions at which a tipping point could be reached and exceeded. The earth system is highly nonlinear with many positive and negative feedback interactions such that the tipping behavior is complicated. The science of resilience and tipping points have made significant progress in theories (e.g. Dakos and Kéfi 2022) and applications (e.g. Yi and Jackson 2021).

The Focus Issue on 'Earth System Resilience and Tipping Behavior' presents a collection of recent advances in addressing the following questions: (1) How can we identify tipping elements? (2) What are the early-warning signals for system transitions? (3) What are the potential domino effects in tipping cascades leading to abrupt transitions? (4) Does a warming climate increase the risk of triggering tipping points?

This editorial offers a comprehensive overview of the key insights presented in each article within this Focus Issue. The focus is on research questions covering four main aspects: (1) theoretical foundations, (2) ecological resistance, resilience, and recovery, (3) Earth system tipping behavior, and (4) social-ecological resilience and tipping points. The note concludes with a summary and a glimpse into future research challenges.

## 2. Theory

Despite theoretical advances and a long-history of definitions in the quest of capturing resilience and tipping points, differences still remain. Dakos and Kéfi (2022) revisit the concept of resilience—a concept that has been used across multiple scientific disciplines, each with a different understanding of
what resilience means—focusing on the mathem-
atical description of resilience based on the meta-
phor of a stability landscape. Their review paper
synthesizes what is known about resilience metrics
and summarizes current approaches for measuring
resilience in models and data. In particular, they cla-
rify connections between ecological and engineering
resilience metrics in simple but widely used ecolo-
gical models in an attempt to identify correlations
between the metrics in the two areas. Their work does
not provide definitive answers but highlights a way
of bridging the gap between the metaphors of sta-
bility landscapes and the quantification of ecological
resilience. Meanwhile, Boers et al (2022) reviews the
study of tipping elements in the past and the poten-
tial of tipping events in the future with a special focus
on the Earth system. The authors summarize empir-
ical evidence of abrupt climate transitions in past cli-
mates focusing on the glacial-interglacial cycles of
the Pleistocene, the Dansgaard-Oeschger events of
previous glacial intervals, and the Bond events of
the Holocene. They also describe several compom-
ents of the Earth system that have been proposed
as likely candidates of tipping elements in response
to ongoing anthropogenic global warming, namely
the Greenland and Antarctic ice sheets, the Atlantic
Ocean component of the global thermohaline circu-
lation, the Amazon rainforest, and tropical monsoon
systems. Despite recent successes in modeling abrupt
climate transitions, the authors discuss the lack of a
broad consensus in the climate community regarding
tipping points and related instabilities, particularly
under anthropogenic forcing. They conclude that the
next steps should work towards a better exploration
of the suspected—or even new—tipping elements in
the climate system.

One major concern over present Earth system tip-
ping elements is the risk of tipping cascades lead-
ing to domino effects. The study of Klose et al
(2021) conceptualizes such a risk of cascading tip-
ping events with a simple model. Tipping cascades,
possibly exhibited by interacting (sub-)systems, are
defined as the sequential occurrence of similar events,
but their nature has been described rather roughly in
the literature. Using a stylized model of two inter-
acting tipping elements, Klose et al systematically
identify, characterize and name patterns of cascades
into a domino cascade, a two-phase cascade, and a
joint cascade. They show that the potential for inter-
vention and anticipation by common early warning
indicators based on critical slowing down depends on
the type of cascade, and discuss these implications for
the resilience of the Earth system, as well as the need
for future research. Along similar lines, Bastiaansen
et al (2022) analyzes the dynamics of tipping in spa-
tially extended systems, which are spatially heterogen-
eous. Using conceptual models, the authors illustrate
the presence of additional coexistence stable equilib-
rium states, where part of the domain may be in one

state and the other part of the domain in another
state. Therefore, changing some external forcing past
a critical threshold may not cause the full system to
undergo tipping, but instead fragmented tipping may
occur where only part of the domain experiences tip-
ping. The spatial interfaces between tropical forests
and savannah, different types of clouds, sea ice and
water, and algae blooms are some examples of where
these coexistence states can be observed in the real
world.

A considerable effort is still dedicated to refin-
ing and developing resilience indicators. Prettyman
et al (2022) develop the theoretical support for the
use of the power spectrum (PS) scaling exponent
as an indicator of critical slowing down and proxy
for loss of resilience and an approach to a tipping
point. The authors justify the use of the PS indic-
ator analytically, assess the usefulness of estimating
the PS scaling exponent in a tipping point context,
and show that the method is robust against trends
and oscillations in the time series. Thus, making it a
good candidate for studying resilience of systems with
periodic oscillations which are observed in ecology
and geophysics. Similarly, Clarke et al (2023) propose
an indicator utilizing the PS to detect critical slow-
ing down, which is specifically applicable for systems
not subject to additive white noise. Commonly used
indicators for critical slowing down, such as increas-
ing autocorrelation and variance, implicitly assume
a stationary white noise forcing and a clear separa-
tion between forced trends and variability. However,
in many applications this is not the case, such as
the climate, which for example is typically forced
by time-correlated processes. The authors propose
ROSA, the method of considering the ratio of spec-
tra of a state variable relative to its forcing. A con-
ceptual model with different types of noise is used to
demonstrate the applicability of ROSA compared to
using the autocorrelation and variance. Furthermore,
ROSA is shown to successfully identify a higher pro-
portion, than the conventional early-warning signals,
of abrupt Amazon dieback events seen in multiple
state-of-the-art Earth System Models. On the other
hand, more specific indicators can also prove useful
in the quest of quantifying resilience. Zampieri et al
(2021) introduce an Annual Production Resilience
Indicator derived from the gross primary productiv-
ity to analyze the impact on vegetation under global
warming. Using the latest generation of climate mod-
els, the authors explore if vegetation gains or loses
resilience under different emission scenarios. For the
lower emission scenarios, the size of regions where
vegetation gains resilience far outweighs the size of
regions that are predicted to lose resilience in the
future. However, in the high emissions scenario the
results are dramatically reversed. In particular, Brazil
and consequently the Amazon rainforest is expected
to be at high risk of suffering multiple years of anom-
ally low gross primary production.
### 3. Ecological resistance, resilience, and recovery

Complementing the theoretical approaches with applications to Earth system science, a number of contributions applied resilience indicators to ecological problems. Rocha (2022) studies the resilience of primary productivity in terrestrial and marine ecosystems globally by using state-of-the-art Earth system observations. He shows that ~30% of the terrestrial biosphere and ~25% of the marine ecosystems are showing symptoms of resilience loss. Besides the common critical slowing down indicators, he also applied indicators for critical speeding up and the fractal dimension to account for the possibility of stochastically induced transitions. An innovation of his analysis is the use of machine learning approaches and feature engineering to investigate the role of drivers in the early warnings and the time scale at which they are relevant. Similarly, Luo et al (2022) investigate the effect of droughts in forest recovery in China. They depart from the assumption that old forests can be more resilient to extreme events, and wonder which forests are more at risk given that the intensity and frequency of droughts is expected to increase. They find a legacy effect that lasts up to 3 years, and confirm that -as expected- forest conditions such as stock volume and forest type influence the path to recovery after droughts. For China, natural coniferous forests with high stock volumes are particularly vulnerable to droughts, which identifies opportunities for management. On a similar vein, Oddi et al (2022) investigate the forest transition from carbon sink to source in the Alps. Using a variety of observational datasets, the authors studied the role of the 2015 and 2017 dry spells in the region. They do not find significant evidence on the gas exchange data. However, they do report reductions of plant growth during the 2017 period. Their results suggest that dynamics of carbon sink and source can be independent.

Several contributions to the special issue developed new methods for particular problems or applications, either for particular geographies or for engaging with specific actors. For example, Lade et al (2022) develop an impact metric that captures the interaction between climate, the water cycle, and land use change. Their metric builds upon modeling work on the interaction of these three systems and explores how it can be used in the context of setting targets for companies and cities. They find, for example, that accounting for climate-water-land use interactions duplicate the impacts of deforestation in tropical forests. The metric development is an important step in involving companies or cities with concrete actions that they can take responsibility to avoid local to regional tipping points. Another contribution with a practical lessons for managing tipping point risks is Xu et al (2022) who investigate the role

of canopy size on the resilience of forest to droughts in Southwestern China. They apply linear regressions and random forest to vegetation index datasets before and after the 2010 drought. They find that taller forest drought resistance has declined, and recommend taking into consideration forest structure when managing these ecosystems. Similarly, Ribeiro et al (2022) quantify the relationship between climate and fire propensity in two regions of the Brazilian Amazon. With intensifying climate change fire intensity is likely to increase, but the effect is relatively unknown. The work of Ribeiro et al contributes to answering this question by studying the features that are predictive of fires (e.g. air dryness, low precipitation). They find that fire risk has already increased 5%-10% and will continue to increase under future climate change scenarios. If warming is limited to a 1.5 C scenario, the risk will be constrained to 14%, but can go higher if climate change is unchecked.

### 4. Tipping behavior of the Earth system

The concept of tipping points, critical thresholds beyond which a system undergoes rapid and irreversible changes, has gained considerable attention in the study of the Earth system. In a recent study by Lux et al (2022), the impact of parametric uncertainty on tipping points of the Atlantic meridional overturning circulation (AMOC) was examined using a Bayesian inversion technique. This novel approach significantly reduces the uncertainty in model parameters compared to previous literature, providing a more constrained understanding of AMOC tipping points. One of the key contributions of this study is the extension of classical tipping diagrams to include probabilistic bifurcation curves. By inferring the distribution of model parameters, Lux et al showcase the uncertain locations of tipping points along these curves. This probabilistic framework allows for a more nuanced exploration of tipping behavior and facilitates the identification of regions with higher probabilities of tipping. Looking ahead, future research directions in the field of Earth system resilience and tipping behavior involve applying similar methodologies to other tipping elements. Lux et al suggest that if suitable paleo-proxy time series are available, the Bayesian inversion technique can be applied to other components of the Earth system. This expands the scope of understanding tipping points beyond the AMOC, offering insights into the likelihoods and positions of tipping points even in cases where historical data does not capture tipping events. However, several open questions remain. First, the availability of long enough paleo-proxy or observed time series (>1400 years) is crucial to apply the framework effectively. Furthermore, there is a need to assess the representativeness of the simple framework in capturing the complexities of the real world. Additionally,
while modeling a larger number of uncertain para-
meters is desirable, the efficiency of computational
cost requires further exploration.

The dynamics of sea ice and its interaction with
Antarctic ice shelves is considered as another import-
ant tipping point in the Earth system. In a pion-
eering study, Teder et al (2022) employ innovative
algorithms applied to daily satellite sea ice concentra-
tion data to analyze sea ice-free corridors connected
to Antarctic ice shelves and the potential impact of
large swell on these corridors. The key contribution
of this study lies in providing the first comprehens-
ive analysis of sea ice-free corridors and the availab-
ility of large swell that can influence the ice shelves.
By tracking trends in corridor properties and sea ice
extent, Teder et al establish a relationship and high-
light the potential pathways through which large swell
can reach and affect Antarctic ice shelves. To further
advance our knowledge in this field, future research
should focus on testing the corridor properties and
available swell by utilizing different sea ice concen-
tration and spectral wave data. By exploring altern-
ative datasets, researchers could validate and refine
the algorithms used in this study. Furthermore, the
potential application of these algorithms in climate
model studies can provide valuable projections of
corridors and available swell, offering insights into
future scenarios.

The Green Sahara during the early to mid-
Holocene represents a fascinating case of an abrupt
climate change event that has already happened in the
past. Hopcroft and Valdes (2022) employ a coupled
global climate model (HadCM3) to investigate the
tipping points associated with the ‘Greening’ and sub-
sequent desertification of the Sahara. A key contri-
bution of this research is the demonstration that the
climate model can reproduce abrupt climate changes
comparable to real paleo-climate events. By focus-
ing on the processes related to the Green Sahara,
Hopcroft and Valdes shed light on the dynamics
behind this significant climatic transition. Future
research efforts should aim to refine the under-
standing of the response in the eastern regions
of Africa and evaluate the vegetation feedback in
more comprehensive models. High-resolution paleo-
climate records are crucial for constraining the sea-
sonality and decadal-to-centennial variability over
several centuries, thereby improving the evaluation
of climate models. However, a major challenge lies
in evaluating the realism of the simulated tipping
thresholds due to the lack of sufficient paleo-climate
data. Acquiring more robust and extensive paleo-
climate data will be vital for validating the simulated
system thresholds and enhancing our understanding
of tipping points in the Green Sahara.

Understanding the relationship between global
warming and extreme events is crucial for assessing
the impacts of climate change and potential envir-
onmental and social tipping points. Diffenbaugh

and Davenport (2021) investigate whether certain
extreme events would have been impossible in the
absence of global warming. Using a large single-
model ensemble of climate simulations, the study
sheds light on the influence of historical greenhouse
gas emissions and other non-greenhouse gas anthro-
pogenic forcings on the emergence of extreme events.
One of the key contributions is the demonstration
that the hottest possible events in the current climate
may have been nearly impossible without historical
greenhouse gas emissions. However, the study also
highlights that other non-greenhouse gas anthropo-
genic forcings (like aerosols and anthropogenic land-
use changes) have muted the emergence of previ-
ously impossible events, emphasizing the complex-
ity of the climate system. To expand on these find-
ings, future research should explore additional large
single-model ensemble experiments to enhance our
understanding of the role of different climate mod-
els. Investigating the role of ocean variability in shap-
ing the emergence of previously impossible temper-
ature thresholds is an important area for further
investigation, which could involve analyzing atmo-
spheric initial-condition large ensembles and bench-
mark simulations with prescribed ocean conditions.
While this study primarily focuses on temperature-
related extremes, future research efforts can extend
the methodology to other types of extreme events.
However, the emergence of previously impossible
thresholds and the underlying physical ingredients
would require in-depth analysis specific to each event
type. Several open questions remain, such as the
influence of climate model biases related to internal
climate variability and external climate forcing on the
calculation of impossible event thresholds. Robustly
isolating the influence of individual human forcings
on the most extreme hot events in different regions
necessitates large single-model ensembles.

Lucarini et al (2023) focus on a particular heat-
wave event, the 2021 Western North America summer
heatwave (WNAHW), that captured global atten-
tion due to its unprecedented severity. They employ
a methodological framework based on large devi-
ation theory and simulations from a state-of-the-art
Earth system model to investigate the typicality of
this extreme event. Their findings reveal that while
the event is rare and unusual in the overall statist-
ics of weather variability, it becomes typical when
considering specific constraints, such as the occur-
rence of a large and persistent summer temperat-
ure anomaly at a specific location. A significant con-
tribution of this research is the demonstration that
the 2021 WNAHW can be seen as an unlikely mani-
festation of climate variability, yet its probability of
occurrence is greatly amplified by ongoing climate
change. This understanding provides insights into the
complex interplay between natural climate variab-
ility and anthropogenic influences. Future research
directions should explore whether similar results
can be obtained using other climate models within the CMIP6 framework. It is important to note that Earth system models tend to globally underestim- ate the duration, intensity, and frequency of heat- waves. Additionally, further investigations are needed to characterize the features of the studied event, such as the separate contributions of dynamical and ther- modynamical factors, preconditioning effects, and the role of teleconnections. Complementing the cur- rent study, an approach that examines atmospheric circulation compounds, as described in Faranda et al (2021), could provide a deeper understanding of the dynamical properties responsible for exacerbat- ing dry conditions in the region. By combining mul- tiple approaches, researchers can unravel the complex mechanisms driving extreme events and their interac- tions with the broader climate system.

The sea surface temperature (SST)—atmospheric convection relationship in the Indo-Pacific warm pool (IPWP) is non-monotonic, with studies indic- ating intensified convection up to a certain SST threshold, beyond which the relationship breaks down. Kim et al (2023) investigate shifts in the SST-precipitation relationship and the SST threshold for deep convection under a warming climate in the IPWP, addressing the gaps in understanding the non-continuous increase in precipitation with SST warming.

## 5. Social-ecological resilience and tipping points

Special issue contributions focusing on resilience and tipping points in social-ecological systems addressed a number of different themes, especially current modeling challenges and ways to advance modeling efforts, the value of a long-time perspective, includ- ing the use of palaeoenvironmental data, adaptation to climate change risks, and the concept of social metabolism.

In their paper, Franzke et al (2022) emphasize the urgent need for modeling the multiple interactions between human societies and Earth systems that cre- ate tipping dynamics and cascades. This is an inter- and transdisciplinary challenge of knowledge devel- opment that can support decision making and gov- ernance in response to tipping threats. The authors review different disciplinary perspectives of tipping dynamics (e.g. bifurcations, phase transitions, social change processes), and discuss cascading effects and telecoupling. Based on these discussions, Franzke et al argue that new integrated climate economy models are needed that are capable of reflecting the inter- actions between social and Earth systems to better understand and assess tipping risks. They discuss a range of challenges to advance such modeling efforts, both regarding biophysical and social system dynam- ics. Summarizing critiques of the damage functions in existing Integrated Assessment Models (IAMs),

the authors caution that modeling efforts of future impacts of tipping points in the Earth system will be challenging due to lack of observations. They make the case that urgent efforts are needed to tackle these obstacles in the development of Human-Earth system models.

In response to the urgent need highlighted by Franzke et al (2022) for integrated modeling of tip- ping dynamics and cascades within social-ecological systems, further contributions by researchers like Tamberg et al (2022) have also delved into modeling challenges pertinent to resilience, particularly focus- ing on climate tipping points. Reflecting the argu- ments made by Dakos and Kéfi (2022), the authors are concerned with the persistence of multiple definitions and understandings of resilience, which can under- mine modeling efforts and impede communication across research programs. To alleviate these problems, Tamberg et al (2022) provide guidelines for resili- ence modelers that can work in very diverse model- ing contexts. Their guideline consists of four ques- tions: (1) Resilience of what?, (2) Resilience regarding what?, (3) Resilience against what?, and (4) Resilience how? The answers to these questions (the system, the ‘sustainant’, the adverse influence, and the response options) enable the ‘translation’ of models and model results across domains, potentially advancing system- atic knowledge development through comparability and synthesis. The authors illustrate the power of their guidelines with an application to modeling the resilience of the Amazon rainforest to dieback.

Adding to the discourse on modeling resilience within complex systems, Anderies et al (2023) con- tribute a third paper focusing on the long-term resi- lience of the World-Earth System (WES). Bringing together resilience theory and world systems theory, they develop a simplified two-region model with link- ages between the natural and social system compon- ents. The objective of this model is to provide an extensible framework that balances complexity and accessibility to enable deeper understanding of resi- lience dynamics at large scales, especially the risk of tipping points. Based on the assumption that the world is currently in a transitional (i.e, unstable) state, Anderies et al focus on the availability of transition pathways towards future sustainable states (safe and just operating space) of the WES. Their multi-century model demonstrates the importance of social vari- ables for pathway resilience, especially perceptions of fairness and inequality between the modeled regions.

Expanding upon the examination of long-term global land-use dynamics, Taylor and Rising (2021) undertake a comprehensive analysis spanning from 1780 to 2010. They found evidence for a tipping point in land-use intensification tied to income levels (eco- nomic development). Treating land-use and the eco- nomy as a coupled social-environmental system, the analysis reveals income levels as a key driver of com- plex change dynamics, strengthening arguments that
economic development will be key driver of land-use
change in the future.

In alignment with the call for a long-term per-
spective on resilience analysis, Allen et al (2022)
underscore the significance of considering historical
and paleo-environmental data. They discuss the util-
ity of paleo-environmental and historical data not
only for research on resilience and sustainability, but
decision making related to the sustainable develop-
ment goals (SDGs) and climate change policy. They
argue that archival records emphasize themes that are
relevant to the SDGs, including diversity, inclusion,
innovation and connectivity. Hence, Allen et al make
the case that a long-term historical perspective is valu-
able when considering what social-ecological resili-
ence means and how it can be achieved, i.e. draw-
ing on the ‘long-term memory encoded in historical,
archaeological and related “paleo-data”’. The authors
also point out issues with SDG baselines and indic-
ators that are rooted in too short time perspectives
and corresponding misunderstandings of ecosystems
variability.

In their study, Raymond *et al* (2022) underscore the critical importance of considering the compound- ing effects of heat and precipitation extremes when examining tipping points in socio-environmental sys- tems. By utilizing a large single model ensemble, they quantitatively demonstrate the increasing spa- tiotemporal proximity of such compound events in a warming world. A key contribution of this research is the revelation that concurrent heat and drought conditions leading to simultaneous crop fail- ures become more prevalent across multiple bread- basket regions. The study also indicates an increased likelihood of interannual wet-dry oscillations in sub- tropical regions. These compound events, with their potential high-end impacts, underscore the potential for crossing tipping points in socio-environmental systems, thus amplifying the social, political, and eco- nomic crises at the regional scale. Future research endeavors should aim to incorporate compounding interactions, both from physical and societal per- spectives, in extreme event analysis and projections. While the thermodynamic effects of global-mean warming dominate the changes in extreme heat and precipitation, regionally varying nonlinear contribu- tions may vary substantially across different mod- els and regional aggregations. It is essential to con- sider these regional nuances and explore their model dependencies. Future research should also consider other multivariate events, such as storms or humid heat, to develop comprehensive risk assessments. Furthermore, predicting periods with an increased likelihood of compound events at sub-seasonal and longer timescales, particularly for heat and precipit- ation/drought, could be possible through the use of multi-member ensemble prediction systems. While using a large single model ensemble, such as the

Max Planck Institute Grand Ensemble (MPI-GE),
uncertainties related to internal climate variability
can be estimated, but it relies on the timing of
extremes in a single model. A comprehensive uncer-
tainty analysis should encompass multiple models,
parameterizations, and sensitivity tests to capture a
broader range of possibilities and provide a more
comprehensive understanding of compound climate
extremes.

In their comprehensive review, Hagen *et al* (2022) meticulously analyze climate change risks and the corresponding adaptation potential in Central and South America. They differentiate eight topical risk clusters, including food and water insecurity, and tipping point risks in the Amazon, arguing that climate risks in all of these eight could become severe during this century. Risks are heterogenous throughout the region, which is characterized by low adaptive capacity. The insights provided by Hagen *et al* (2022) can help guide future adaptation policies for Central and South America, especially efforts at strengthening adaptive capacity.

Considering the specific context of small island
developing states, Singh *et al* (2022) analyze the
potential for tipping points on small islands using
the framework of socio-metabolic risk (SMR)—a
subset of systemic risk. The social-metabolic risk
framework applied to social-ecological systems refers
to the availability of critical resources, the integ-
rity of material circulation, and the distribution of
products and services, making SMR a type of social-
ecological coupling. The sectoral focus of the ana-
lysis (water, waste, infrastructure) allows the authors
to identify strategies for fostering adaptation and
resilience, e.g. resource localization and increases in
resource circularity rates. Like other papers in this cat-
egory, it makes a conceptual contribution and uses an
illustrative case study in the absence of data for all rel-
evant variables.

6. Concluding remarks and outlook

Here, we highlight the reliance on extensive numerical
simulation models to understand the cascading
tipping dynamics of the climate system or the stability
of social-ecological systems. Within these systems,
the stability of one element is often intertwined with
another through complex multiple feedback inter-
actions. The nature of feedback is crucial for sys-
tem stability: positive feedbacks act as driving forces
for perturbation growth, while negative feedbacks act
as driving forces for perturbation decay. The resili-
ence and tipping behavior of a system are determ-
ined by the competition and cooperation between
positive and negative feedback loops included in the
models (Yi and Jackson 2021). However, the cur-
rent generation of climate-economy models gen-
erally do not take these feedbacks into account
(Franzke et al 2022). Anderies et al (2023) pointed out that existing Earth system models are typically too complex, lack transparency, and are difficult to access. Meanwhile, more accessible dynamic models used for resilience analysis are too simple to capture the key feedback interactions of social-ecological systems. Anderies et al (2023) proposed a modeling framework for World-Earth System resilience. The idea is to use the ball-in-cup heuristic model as a principle to merge ideas from Earth system models and social-economic theory and capture feedbacks between global biophysical and global social and economic processes that co-determine development pathways, World Earth Resilience, and tipping points. While we may be able to describe physical and ecosystem tipping points with Earth System models and mathematical equations as derived in the previous section, the complexity of cascading physical and social tipping precludes a ‘one-fits-all’ modeling approach and ask for novel research approaches embracing qualitative and quantitative information within a systemic risk framing (Sillmann et al 2021).

## Acknowledgments

We thank all the authors for their contributions to this focus collection. C Y acknowledges support from the US-Austria Fulbright Program. P D L R acknowledges support from the European Research Council ‘Emergent Constraints on Climate-Land feedbacks in the Earth System (ECCLES)’ Project, Grant Agreement Number 742472. P D L R was also supported by the Optimal High Resolution Earth System Models for Exploring Future Climate Changes (OptimESM) Project, Grant Agreement Number 101081193.

## ORCID iDs

Chuixiang Yi https://orcid.org/0000-0001-8546-6157

Paul D L Ritchie https://orcid.org/0000-0002-7649-2991

Jana Sillmann https://orcid.org/0000-0002-0219-5345

Juan C Rocha https://orcid.org/0000-0003-2322-5459

Manjana Milkoreit https://orcid.org/0000-0002-7862-3561

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