Characteristic disruptions of an excitable carbon cycle

Volcanic CO2 degassing postdates thermogenic carbon emission during the end-Permian mass extinction

Massive carbon dioxide (CO₂) emissions are widely assumed to be the driver of the end-Permian mass extinction (EPME). However, the rate of and total CO₂ released, and whether the source changes with time, remain poorly understood, leaving a key question surrounding the trigger for the EPME unanswered. Here, we assimilate reconstructions of atmospheric Pco₂ and carbonate δ¹³C in an Earth system model to unravel the history of carbon emissions and sources across the EPME. We infer a transition from a CO₂ source with a thermogenic carbon isotopic signature associated with a slower emission rate to a heavier, more mantle-dominated volcanic source with an increased rate of emissions. This implies that the CO₂ degassing style changed as the Siberian Traps emplacement evolved, which is consistent with geochemical proxy records. Carbon cycle feedbacks from terrestrial ecosystem disturbances may have further amplified the warming and the severity of marine extinctions.

A data-driven approach for discovering the most probable transition pathway for a stochastic carbon cycle system

Many natural systems exhibit tipping points where changing environmental conditions spark a sudden shift to a new and sometimes quite different state. Global climate change is often associated with the stability of marine carbon stocks. We consider a stochastic carbonate system of the upper ocean to capture such transition phenomena. Based on the Onsager-Machlup action functional theory, we calculate the most probable transition pathway between the metastable and oscillatory states via a neural shooting method. Furthermore, we explore the effects of external random carbon input rates on the most probable transition pathway, which provides a basis to recognize naturally occurring tipping points. Particularly, we investigate the transition pathway's dependence on the transition time and further compute the optimal transition time using a physics-informed neural network, toward the maximum carbonate concentration state in the oscillatory regimes. This work may offer some insights into the effects of noise-affected carbon input rates on transition phenomena in stochastic models.

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.

Climate Endgame: Exploring catastrophic climate change scenarios

Prudent risk management requires consideration of bad-to-worst-case scenarios. Yet, for climate change, such potential futures are poorly understood. Could anthropogenic climate change result in worldwide societal collapse or even eventual human extinction? At present, this is a dangerously underexplored topic. Yet there are ample reasons to suspect that climate change could result in a global catastrophe. Analyzing the mechanisms for these extreme consequences could help galvanize action, improve resilience, and inform policy, including emergency responses. We outline current knowledge about the likelihood of extreme climate change, discuss why understanding bad-to-worst cases is vital, articulate reasons for concern about catastrophic outcomes, define key terms, and put forward a research agenda. The proposed agenda covers four main questions: 1) What is the potential for climate change to drive mass extinction events? 2) What are the mechanisms that could result in human mass mortality and morbidity? 3) What are human societies' vulnerabilities to climate-triggered risk cascades, such as from conflict, political instability, and systemic financial risk? 4) How can these multiple strands of evidence-together with other global dangers-be usefully synthesized into an "integrated catastrophe assessment"? It is time for the scientific community to grapple with the challenge of better understanding catastrophic climate change.

Estimation of drift and diffusion functions from unevenly sampled time-series data

Complex systems can often be modeled as stochastic processes. However, physical observations of such systems are often irregularly spaced in time, leading to difficulties in estimating appropriate models from data. Here we present extensions of two methods for estimating drift and diffusion functions from irregularly sampled time-series data. Our methods are flexible and applicable to a variety of stochastic systems, including non-Markov processes or systems contaminated with measurement noise. To demonstrate applicability, we use this approach to analyze an irregularly sampled paleoclimatological isotope record, giving insights into underlying physical processes.

Rate-induced collapse in evolutionary systems

Recent work has highlighted the possibility of 'rate-induced tipping', in which a system undergoes an abrupt transition when a perturbation exceeds a critical rate of change. Here, we argue that this is widely applicable to evolutionary systems: collapse, or extinction, may occur when external changes occur too fast for evolutionary adaptation to keep up. To bridge existing theoretical frameworks, we develop a minimal evolutionary-ecological model showing that rate-induced extinction and the established notion of 'evolutionary rescue' are fundamentally two sides of the same coin: the failure of one implies the other, and vice versa. We compare the minimal model's behaviour with that of a more complex model in which the large-scale dynamics emerge from the interactions of many individual agents; in both cases, there is a well-defined threshold rate to induce extinction, and a consistent scaling law for that rate as a function of timescale. Due to the fundamental nature of the underlying mechanism, we suggest that a vast range of evolutionary systems should in principle be susceptible to rate-induced collapse. This would include ecosystems on all scales as well as human societies; further research is warranted.

An Onsager-Machlup approach to the most probable transition pathway for a genetic regulatory network

We investigate a quantitative network of gene expression dynamics describing the competence development in Bacillus subtilis. First, we introduce an Onsager-Machlup approach to quantify the most probable transition pathway for both excitable and bistable dynamics. Then, we apply a machine learning method to calculate the most probable transition pathway via the Euler-Lagrangian equation. Finally, we analyze how the noise intensity affects the transition phenomena.

The Balance of Nature: A Global Marine Perspective

The ancient idea of the balance of nature continues to influence modern perspectives on global environmental change. Assumptions of stable biogeochemical steady states and linear responses to perturbation are widely employed in the interpretation of geochemical records. Here, we review the dynamics of the marine carbon cycle and its interactions with climate and life over geologic time, focusing on what the record of past changes can teach us about stability and instability in the Earth system. Emerging themes include the role of amplifying feedbacks in producing past carbon cycle disruptions, the importance of critical rates of change in the context of mass extinctions and potential Earth system tipping points, and the application of these ideas to the modern unbalanced carbon cycle. A comprehensive dynamical understanding of the marine record of global environmental disruption will be of great value in understanding the long-term consequences of anthropogenic change.

Most probable transitions from metastable to oscillatory regimes in a carbon cycle system

Global climate changes are related to the ocean's store of carbon. We study a carbonate system of the upper ocean, which has metastable and oscillatory regimes, under small random fluctuations. We calculate the most probable transition path via a geometric minimum action method in the context of the large deviation theory. By examining the most probable transition paths from metastable to oscillatory regimes for various external carbon input rates, we find two different transition patterns, which gives us an early warning sign for the dramatic change in the carbonate state of the ocean.

Massive and rapid predominantly volcanic CO2 emission during the end-Permian mass extinction

The end-Permian mass extinction event (∼252 Mya) is associated with one of the largest global carbon cycle perturbations in the Phanerozoic and is thought to be triggered by the Siberian Traps volcanism. Sizable carbon isotope excursions (CIEs) have been found at numerous sites around the world, suggesting massive quantities of ¹³C-depleted CO₂ input into the ocean and atmosphere system. The exact magnitude and cause of the CIEs, the pace of CO₂ emission, and the total quantity of CO₂, however, remain poorly known. Here, we quantify the CO₂ emission in an Earth system model based on new compound-specific carbon isotope records from the Finnmark Platform and an astronomically tuned age model. By quantitatively comparing the modeled surface ocean pH and boron isotope pH proxy, a massive (∼36,000 Gt C) and rapid emission (∼5 Gt C yr^-1) of largely volcanic CO₂ source (∼-15%) is necessary to drive the observed pattern of CIE, the abrupt decline in surface ocean pH, and the extreme global temperature increase. This suggests that the massive amount of greenhouse gases may have pushed the Earth system toward a critical tipping point, beyond which extreme changes in ocean pH and temperature led to irreversible mass extinction. The comparatively amplified CIE observed in higher plant leaf waxes suggests that the surface waters of the Finnmark Platform were likely out of equilibrium with the initial massive centennial-scale release of carbon from the massive Siberian Traps volcanism, supporting the rapidity of carbon injection. Our modeling work reveals that carbon emission pulses are accompanied by organic carbon burial, facilitated by widespread ocean anoxia.

Asymmetry of extreme Cenozoic climate-carbon cycle events

The history of Earth's climate and carbon cycle is preserved in deep-sea foraminiferal carbon and oxygen isotope records. Here, we show that the sub-million-year fluctuations in both records have exhibited negatively skewed non-Gaussian tails throughout much of the Cenozoic era (66 Ma to present), suggesting an intrinsic asymmetry that favors "hyperthermal-like" extreme events of abrupt global warming and oxidation of organic carbon. We show that this asymmetry is quantitatively consistent with a general mechanism of self-amplification that can be modeled using stochastic multiplicative noise. A numerical climate-carbon cycle model in which the amplitude of random biogeochemical fluctuations increases at higher temperatures reproduces the data well and can further explain the apparent pacing of past extreme warming events by changes in orbital parameters. Our results also suggest that, as anthropogenic warming continues, Earth's climate may become more susceptible to extreme warming events on time scales of tens of thousands of years.

Evidence of non-stationary relationships between climate and forest responses: Increased sensitivity to climate change in Iberian forests

Climate and forest structure are considered major drivers of forest demography and productivity. However, recent evidence suggests that the relationships between climate and tree growth are generally non-stationary (i.e. non-time stable), and it remains uncertain whether the relationships between climate, forest structure, demography and productivity are stationary or are being altered by recent climatic and structural changes. Here we analysed three surveys from the Spanish Forest Inventory covering c. 30 years of information and we applied mixed and structural equation models to assess temporal trends in forest structure (stand density, basal area, tree size and tree size inequality), forest demography (ingrowth, growth and mortality) and above-ground forest productivity. We also quantified whether the interactive effects of climate and forest structure on forest demography and above-ground forest productivity were stationary over two consecutive time periods. Since the 1980s, density, basal area and tree size increased in Iberian forests, and tree size inequality decreased. In addition, we observed reductions in ingrowth and growth, and increases in mortality. Initial forest structure and water availability mainly modulated the temporal trends in forest structure and demography. The magnitude and direction of the interactive effects of climate and forest structure on forest demography changed over the two time periods analysed indicating non-stationary relationships between climate, forest structure and demography. Above-ground forest productivity increased due to a positive balance between ingrowth, growth and mortality. Despite increasing productivity over time, we observed an aggravation of the negative effects of climate change and increased competition on forest demography, reducing ingrowth and growth, and increasing mortality. Interestingly, our results suggest that the negative effects of climate change on forest demography could be ameliorated through forest management, which has profound implications for forest adaptation to climate change.

Routes to global glaciation

Theory and observation suggest that Earth and Earth-like planets can undergo runaway low-latitude glaciation when changes in solar heating or in the carbon cycle exceed a critical threshold. Here, we use a simple dynamical-system representation of the ice-albedo feedback and the carbonate-silicate cycle to show that glaciation is also triggered when solar heating changes faster than a critical rate. Such 'rate-induced glaciations' remain accessible far from the outer edge of the habitable zone, because the warm climate state retains long-term stability. In contrast, glaciations induced by changes in the carbon cycle require the warm climate state to become unstable, constraining the kinds of perturbations that could have caused global glaciation in Earth's past. We show that glaciations can occur when Earth's climate transitions between two warm stable states; this property of the Earth system could help explain why major events in the development of life have been accompanied by glaciations.