Paul David Longden Ritchie

A key concern with anthropogenic climate change is that continued warming may trigger transitions in tipping systems. These are Earth system components where small additional climate changes cause large, often irreversible, shifts in state. Such nonlinear transitions could have profound ecological and societal consequences, yet the global warming thresholds at which they occur remain highly uncertain. Current estimates rely mainly on Earth System Models (ESMs), but large inter-model differences undermine confidence in projected thresholds and complicate adaptation and mitigation planning. Alternatively, Early Warning Systems (EWSs) infer proximity to tipping directly from observations, seeking statistical signatures that emerge before transitions. Most existing EWSs rely on generic indicators, such as critical slowing down, making limited use of process understanding. We argue that further progress, or refinement of existing EWSs, will require more process-informed rather than solely generic EWSs, where statistical indicators are guided by the dynamics of the Earth system component under investigation. Earth Observation (EO) offers combining its extensive spatial coverage of, for instance, land ecosystem state with parallel observations of key environmental drivers. EO enables space-for-time approaches that exploit spatial variations and how they may change with proximity to a tipping point. Complementary datasets, such as meteorological records, describe the forcing behind observed EO variability, which may help explain the behaviour of candidate EWSs that incorporate satellite measurements. Combined with reduced dynamical-system representations or ESM process descriptions, these datasets offer a foundation for more targeted and informative EWSs. We review existing approaches to EWS development from climate science and related disciplines, then present theoretical hypotheses and conceptual frameworks for process-informed EWSs. Central to many suggestions is the proposition that the structure of an optimal EWS should reflect the governing dynamics of the underlying climate system component. We further argue that this relationship is bidirectional. Observations can enhance EWSs, which in turn could constrain ESM parameterisation and structure, improving projections by these models of future tipping behaviour. We propose that integrating EO, process understanding, dynamical systems theory, and ESM improvement offers a promising pathway to more robust EWSs and, ultimately, more reliable prediction of climate tipping risks.

Early warning indicators (EWIs) have been developed in an attempt to forewarn of approaching tipping points. In the case of bifurcation-induced tipping (Ashwin et al 2025 Proc. R. Soc. A 481 20250405), the most commonly used EWIs are related to the phenomenon of ‘Critical Slowing Down (CSD)’, which involves an increase in the variance and autocorrelation of a state variable prior to the bifurcation (Scheffer et al 2009 Nature 461 53–59). CSD can provide useful early warning in systems which remain close to a quasi-equilibrium state as they approach the bifurcation (Dakos et al 2008 Technical Report ). Under these circumstances, fluctuations reveal the declining stability of the steady state. However, CSD is far less reliable in a strongly forced system where the control variable is changing quickly compared to the characteristic timescale of the system. In such strongly forced systems, it is possible to temporarily overshoot the bifurcation, without causing tipping (Ritchie et al 2021 Nature 592 517–523). However, currently there is no robust way of determining when a strongly forced system has passed the bifurcation. Here we develop a more reliable EWI for strongly forced systems, by looking instead at the fluctuations about a reconstructed quasi-equilibrium state. The variance of the reconstructed quasi-equilibrium state blows-up as the bifurcation point is approached, such that the inverse of the variance goes to zero at the bifurcation. We show that our new EWI, which we call ‘Increased Variance of Quasi-equilibrium’, is able to forewarn of a critical point being crossed in both weakly and strongly forced systems.

The future behavioural fate of a forced nonlinear system can depend sensitively on how it is forced, and on natural fluctuations within the system. This is especially the case if there is rate-induced tipping, where small changes in the forcing can lead to drastically different eventual behaviours. This sensitivity may be present only for a limited period of time, for example, when the forcing is changing most rapidly. We extend a recently proposed geometric early warning that can measure when a system is in such a sensitive state. We show how to compute the signed distance to an approximate R-tipping threshold, which we refer to as the R-tipping indicator. The R-tipping threshold is a dynamic state that embeds knowledge of the system and future behaviour of the forcing. As an example, we consider early prediction of the final state for a 3-box model of the Atlantic meridional overturning circulation with specified and rapid forcing. For this model, we give a method to approximate the R-tipping indicator and estimate its skill in forecasting the eventual state of the system, even when the forcing is still underway. The skill of the geometric early warning based on the R-tipping indicator compares favourably to thresholds based on state variables or critical slowing down.

The risk that the climate system may contain tipping points remains a concern. Firstly, a level of global warming may be reached at which relatively small additional warming could cause major parts of the Earth system to transition to a new state. Depending on the location and specific Earth system component, this could disproportionately impact large sectors of society. Secondly, the Earth system component may exhibit hysteresis effects, and therefore, if global temperatures are subsequently lowered after triggering a jump in state, a return to earlier conditions may not occur until warming is substantially reduced. Earth System Models (ESMs) are numerical frameworks that operate at fine spatial scales. Such models are designed to estimate how all components of the climate system will evolve in response to changes in atmospheric greenhouse gas concentrations caused by human activity. Many ESM projections suggest that various parts of the climate system are capable of tipping. Yet, these models are computationally demanding and have therefore been operated only over a small range of scenarios. Very few “overshoot” simulations with ESMs exist, where climate change is reversed, resulting in limited understanding of hysteresis effects following a tipping event. Advances in nonlinear mathematics include developing dynamical systems whose equations frequently contain a bifurcation parameter. These equations can accurately replicate tipping points, jumps in state, and hysteresis as the bifurcation parameter changes. Recent progress in ESM development often introduces higher spatial resolution, enhancing process representation and increasing accuracy in predicting local changes. However, mapping the broad behaviour of the components of ESM projections onto simpler dynamical system models may also offer many advantages, including the overall characterisation of climate models and a method to rapidly extrapolate their projections to a wider range of forcing scenarios. The bifurcation parameters in such equations may represent changing forcings, such as an increasing warming level that leads to a tipping event. Progress has already been made in mapping many components of the Earth system onto large-scale variables for representation as dynamical systems. Most advances to date have focused on understanding whether tipping events can be avoided if systems possess substantial inertia, i.e. respond over long timescales, allowing climate change to temporarily exceed thresholds that might otherwise trigger major nonlinear change. However, potential hysteresis effects in the context of climate change are less well represented in equation form. Achieving such a mathematical formulation requires a dynamic system to describe a climate system component not only at the point of tipping but also for substantial periods before and after. This behaviour corresponds to a bifurcation parameter that first increases and then decreases, with the modelled behaviours differing significantly during the return phase. To support such necessary developments, we present a parameter-sparse dynamical system model that can exhibit hysteresis following a tipping occurrence, offering the potential for characterising Earth system components with this feature. We place particular emphasis on presenting in full the algebra needed to map known or modelled key attributes of a system that can tip onto the simplified dynamical system equation. We drive the equation with a time-evolving forcing representing an “overshoot” trajectory of global warming that exceeds a threshold for potential tipping. Calculations are performed over a range of system inertia values, illustrating a threshold inertia above which full tipping and hysteresis can be avoided. We use scale analysis to relate this threshold to those reported in existing climate research on behaviour near potential tipping points. In some instances, a basic equation may be too simple to capture the dominant qualitative behaviour of a large-scale environmental system. In those cases, a more complex model from any hierarchy of suggested simulations of climate components may be appropriate. However, should a system be amenable to representation by a dynamical system, we hope the framework we present offers a simple-to-use equation structure that may quantify tipping points in the climate system. Such a framework may illustrate a more complete description of behaviours both before and after tipping, and depending on the post-tipping forcing scenario, it may involve substantial hysteresis.

Abrupt transitions are a central concern in climate and ecological research and may arise when critical thresholds known as tipping points are crossed. However, previous work has shown that finite-time overshoots of tipping points can be safe, and that such behavior is captured by an inverse-square-law criterion when overshoots are sufficiently small and slow. So far studied in isolated systems with external drivers, (un)safe overshoots may also emerge from interactions between subsystems. Here, we investigate safe-overshoot phenomena in unidirectionally coupled slow–fast systems featuring both nonlinear interactions and coupling through time derivatives. Specifically, we derive a criterion for the occurrence of safe overshoots analogous to the inverse-square law for isolated systems, but adapted to interactive settings, and expressed explicitly in terms of the timescale separation and coupling strength between subsystems. We illustrate these results using two conceptual models in which the Atlantic Meridional Overturning Circulation interacts with either the Amazon rainforest or the Greenland Ice Sheet.

The concept of a “tipping point” is widely used to describe abrupt, potentially irreversible changes in complex systems - from climate subsystems to ecosystems and social dynamics. However, concerns have been raised about definitional ambiguity and conceptual overuse that may obscure rather than highlight potential systemic risk. Here, we offer a cross-disciplinary synthesis of the tipping point literature that identifies three essential properties—self-reinforcing feedbacks, threshold behavior, and persistence—as the defining characteristics of tipping dynamics. While different interpretations reflect genuine system-specific differences and offer complementary insights, these three properties help identify underlying patterns and causal mechanisms across diverse systems. This synthesis promotes conceptual clarity in how tipping point terminology is applied across diverse contexts. In doing so, we identify research priorities: moving beyond single-threshold models, developing cross-system early warning indicators, understanding cascading dynamics between interconnected systems, and advancing integrated models capturing climate-ecological-social feedbacks.

Solar radiation modification (SRM) aims to artificially cool the Earth, counteracting warming from anthropogenic greenhouse gases by increasing the reflection of incoming sunlight. One SRM strategy is stratospheric aerosol injection (SAI), which mimics explosive volcanoes by injecting aerosols into the stratosphere. There are concerns that SAI could suppress vegetation productivity by reducing the amount of sunlight reaching the Earth's surface and by shifting rainfall patterns. Here we examine results from five Earth System Models that use SAI to reduce the global mean temperature from that of a high emissions world (SSP585), to that of a more moderate global warming scenario (SSP245). Compared to SSP245, the SAI simulations project higher global net primary productivity (NPP) values (+15.6 %) and higher land carbon storage (+5.9 %), primarily because of increased CO₂ fertilisation. The effects of SAI are especially clear in Amazonia where land carbon storage increases compared to both SSP245 (+8.6 %) and SSP585 (+10.8 %), even though the latter scenario has the same atmospheric CO₂ scenario as the SAI scenario. Our results therefore suggest that SAI could provide some protection against the risk of climate change induced carbon losses from the Amazon rainforest, though this is not universally observed in all tropical forests. Additionally, we observe decreases in NPP and land carbon storage in some regions, such as eastern Africa, the northern high latitudes, and Indonesia.

As tipping points are extremely difficult to predict using an initial value modelling approach, forewarning of bifurcation tipping points instead often depends on the analysis of observational data, using approaches that aim to detect reducing system resilience. The most commonly used Early Warning Indicators (EWIs) rely on the phenomenon of critical slowing down, which is the tendency for fluctuations of a state variable to get larger (increased variance) and longer lived (increased temporal autocorrelation), as the bifurcation is approached. This is measurable in low dimensional systems that remain close to a quasi-equilibrium state in the run-up to the bifurcation. However, in systems that are subject to rapid changes in external forcing, such as the contemporary Earth system, this condition is unlikely to be met and EWIs become less reliable. In addition, temporal EWIs require long observational time series. For these reasons, it makes sense to consider spatial EWIs that can make use of the spatial detail resolved by present-day observations, especially from remote sensing. In this paper, we explore the conditions under which spatial and temporal EWIs will each be reliable, using a simple spatially coupled model with a fold bifurcation. In the weak coupling limit, we find spatial EWIs give reliable warning of the bifurcation, even if the external forcing is changing rapidly. However, in the limit of strong spatial coupling, spatial early warning disappears. Under these conditions, we find temporal EWIs give reliable warning as long as the external forcing is not changing quickly compared to the characteristic timescale of the system. We conclude that spatial early warnings will be especially useful in systems that have relatively weak spatial coupling, but which are also subject to rapidly changing external forcing (e.g. forests under contemporary climate change).

The future behavioural fate of a forced nonlinear system may at times depend sensitively on the forcing profile as well as natural fluctuations within the system. This is especially the case for rate-induced tipping, where the forcing pushes the system to a basin boundary of a future behaviour and small changes in the forcing can lead to drastically different behaviours. This sensitivity may be present only for a limited time when the forcing is most rapidly changing and so we investigate a geometric early warning to evaluate whether we are in such a sensitive state. This involves computing an approximation of the R-tipping edge state which is a dynamic state that requires knowledge of the future behaviour of the forcing. We contrast this with early warnings of bifurcation-induced tipping, where an assumption of slow variation of forcing is needed. We provide an example of early prediction of future state for a 3-box model of the Atlantic Meridional Overturning Circulation (AMOC) with specified rapid forcing and show that the skill compares favourably with a simple threshold approach.

The climate and carbon cycle interact in multiple ways. An increase in carbon dioxide in the atmosphere warms the climate through the greenhouse effect, but also leads to uptake of CO2 by the land and ocean sink, a negative feedback. However, the warming associated with a CO 2 increase is also expected to suppress carbon uptake, a positive feedback. This study addresses the question: “under what circumstances could the climate–carbon cycle system become unstable?” It uses both a reduced form model of the climate–carbon cycle system as well as the complex land model JULES, combined with linear stability theory, to show that: (i) the key destabilising loop involves the increase in soil respiration with temperature; (ii) the climate–carbon system can become unstable if either the climate sensitivity to CO2 or the sensitivity of soil respiration to temperature is large, and (iii) the climate–carbon system is stabilized by land and ocean carbon sinks that increase with atmospheric CO2 , with CO2-fertilization of plant photosynthesis playing a key role. For central estimates of key parameters, the critical equilibrium climate sensitivity (ECS) that would lead to instability at current atmospheric CO2 lies between about 11K (for large CO2 fertilization) and 6K (for no CO2 fertilization). Given the apparent stability of the climate–carbon cycle, we can view these parameter combinations as implausible. The latter value is close to the highest ECS values amongst the latest Earth Systems Models. We find that the stability of the climate–carbon system increases with atmospheric CO2 , such that the glacial CO2 concentration of 190 ppmv would be unstable even for ECS greater than around 4.5 K in the absence of CO2 fertilization of land photosynthesis.