Linking cumulative carbon emissions to observable climate impacts

Anthropogenic CO2 emissions are causing climate change, and impacts of climate change are already affecting every region on Earth. The purpose of this review is to investigate climate impacts that can be linked quantitatively to cumulative CO2 emissions (CE), with a focus on impacts scaling linearly with CE. The reviewed studies indicate a proportionality between CE and various observable climate impacts such as regional warming, extreme daily temperatures, heavy precipitation events, seasonal changes in temperature and precipitation, global mean precipitation increase over ocean, sea ice decline in September across the Arctic Ocean, surface ocean acidification, global mean sea level rise, different marine heatwave characteristics, changes in habitat viability for non-human primates, as well as labour productivity loss due to extreme heat exposure. From the reviewed literature, we report estimates of these climate impacts resulting from one trillion tonne of CE (1 Tt C). These estimates are highly relevant for climate policy as they provide a way for assessing climate impacts associated with every amount of CO2 emitted by human activities. With the goal of expanding the number of climate impacts that could be linked quantitatively to CE, we propose a framework for estimating additional climate impacts resulting from CE. This framework builds on the transient climate response to cumulative emissions (TCRE), and it is applicable to climate impacts that scale linearly with global warming. We illustrate how the framework can be applied to quantify physical, biological, and societal climate impacts resulting from CE. With this review, we highlight that each tonne of CO2 emissions matters in terms of resulting impacts on natural and human systems.


Introduction
The industrial revolution of the 18th century marked the beginning of intensive exploitation of fossil fuels for energy use by humans, resulting in a steady rise in CO 2 emissions from anthropogenic sources (Callendar 1938).The exploitation of various fossil fuels (e.g.coal, crude oil, and natural gas) has accelerated since the year 1950, leading to unprecedented amounts of anthropogenic CO 2 emissions and subsequent changes in the Earth system (Syvitski et al 2020).In parallel, there has been substantial increase in CO 2 emissions from land use and land cover changes over the last two centuries (Gasser et al 2020).To date, human-made CO 2 emissions are the principal driver of observed global warming (Forster et al 2021).Furthermore, CE are the main driver of long-term warming and subsequent changes in the climate system (Eby et al 2009, Clark et al 2016, Tokarska et al 2016).
Climate change is already affecting physical, biological, and human-managed systems in every region on Earth (O'Neill et al 2022).Observed climate impacts on physical systems (hereafter physical impacts) consist of climate hazards and extremes, including extreme weather events.Observed climate impacts on biological systems (hereafter biological impacts) include habitat shifts for different species as well as biodiversity losses in terrestrial and marine ecosystems.Observed climate impacts on human society (hereafter societal impacts) include heat-related discomfort, labour productivity loss, changes in food production, and the damage of built infrastructures.In particular, weather and climate extreme events are becoming more frequent and intense due to human activities (Seneviratne et al 2021), and so are related biological and societal impacts (O'Neill et al 2022).
To assess future climate impacts, researchers and practitioners commonly rely on simulations by global and regional climate models.While the development of these numerical models has significantly progressed in recent decades, their deployment and use are still limited to trained users.Running these models and analysing their results can be challenging to non-technical experts (e.g.policymakers) and very demanding in terms of computing resources (Alexander and Easterbrook 2015).With ongoing climate change, however, there is a compelling need for novel and simple methods to assess climate impacts, especially in the context of climate change adaptation and mitigation.
Towards the end of the 2000s, climate scientists identified a near-linear relationship between CE from anthropogenic activities and globally-averaged surface temperature increase (Allen et al 2009, Matthews et al 2009), which has been shown to occur independently of the timing, rate, and pathway of emissions (Herrington and Zickfeld 2014).This near-linear proportionality emerges from the diminishing radiative forcing per unit mass of CO 2 added in the atmosphere, being compensated by the weakening efficiency of carbon sinks (both land and ocean) and the resulting increased fraction of airborne carbon (Matthews et al 2009, MacDougall 2016).Such a simple proportionality allows us to directly link the major cause of climate change (i.e.anthropogenic CO 2 emissions) to the most central manifestation of climate change (i.e.global warming), despite the complex processes and feedbacks operating in the climate system (MacDougall 2016).There are three major implications of the near-linear relationship between CE and global warming: (1) every amount of CO 2 emitted contributes to additional warming in the Earth system; (2) there is a finite quota for the amount of CO 2 that can be emitted over time to limit global warming to any specific level; (3) stabilizing the global mean surface air temperature will require achieving a balance between CO 2 emissions and CO 2 removals (i.e.reaching net-zero CO 2 emissions) (Seneviratne et al 2016, Matthews et al 2021).
In recent years, several studies investigated climate impacts associated with every degree of projected change in global mean surface temperature independently of future emission scenarios (e.g.Perkins-Kirkpatrick and Gibson 2017, Frölicher et al 2018, Arnell et al 2019, Seneviratne et al 2021, Tebaldi et al 2021).These studies were primarily motivated by the need to assess climate impacts that could be avoided for every degree of global warming, and particularly for a 1.5 versus a 2 • C warming in the context of the 2015 Paris Agreement (e.g.Chadburn et al 2017, Arnell et al 2018, Warren et al 2018).Furthermore, several physical impacts (e.g.weather and climate extremes), biological impacts (e.g.disruption and loss of biodiversity), as well as societal impacts (e.g.heat-related morbidity and mortality) have been assessed at global warming levels (GWLs) ranging from 1 to 5 • C above pre-industrial levels in the recent Sixth Assessment Report (AR6) by the Intergovernmental Panel on Climate Change (IPCC) (Seneviratne et al 2021, O'Neill et al 2022).While these studies are highly policy-relevant, it is fundamentally important to link climate impacts to the principal cause of global warming: the total amount of CO 2 emissions accumulated over time.
The climate system is complex, and its complexity gets reflected in the effort of linking CE to observable climate impacts on natural and human systems.Figure 1 illustrates physical, biological and societal climate impacts that can be potentially linked to CE based on process understanding combined with multiple evidence from the scientific literature (e.g.O'Neill et al 2022, Seneviratne et al 2021).As an example, there is a potential link between CE and terrestrial heatwaves, which can then be linked to habitat shifts and food chain changes on land, and thus affecting food security and socio-economic well-being.Furthermore, ocean acidification resulting from CE has the potential to induce several impacts on marine life and ecosystems (Steinacher and Joos 2016), suggesting a link between CE and consequences of ocean acidification such as the disruption of marine food chains and its implications for fishing productivity.The latter two marine impacts may also occur in response to global warming induced by CE (figure 1), emphasizing the high level of complexity in the Earth-human system.Despite such a complexity, assessing climate impacts as a function of CE presents a great opportunity for advancing policy-relevant climate research.
Here we conduct a literature review to investigate climate impacts that can be quantified as a function of CE, with a focus on impacts that scale (near-)linearly with CE.The main benefits of identifying such climate impacts are: (1) simplified predictions for impact assessments; (2) policy implications in the context of both impact attributions as well as mitigation targets.This review is guided by the following questions: Which observable climate impacts can be linked quantitatively to CE? What are the climate impacts per unit of CE? Throughout the review, we consider changes in surface air temperature and precipitation patterns to be part of physical climate impacts, under the assumption that these climate changes (or climate-impact drivers) can induce various impacts on natural and human systems contingent to exposure and vulnerability.The A conceptual diagram illustrating observable climate impacts that can be potentially linked to cumulative carbon emissions.This is a non-exhaustive illustration.Climate impacts documented from the published literature to be linked quantitively to cumulative carbon emissions are shown in bold (section 2).We consider changes in surface air temperature and precipitation patterns to be physical climate impacts, under the assumption that these climate changes (or climate-impact drivers) can induce various impacts on natural and human systems contingent to exposure and vulnerability.
remainder of the paper is structured as follows: section 2 presents a comprehensive review of climate impacts linked quantitatively to CE; section 3 summarizes the concept of transient climate response to cumulative emissions (TCRE); section 4 introduces and illustrates a TCRE-based framework that can be used to link CE to climate impacts scaling (near-)linearly with global warming; sections 5 and 6 are for a discussion and a conclusion, respectively.

A review of climate impacts linked quantitatively to cumulative carbon emissions
We review the published literature with a focus on studies that investigated the direct link between CE and observable climate impacts.(Allen et al 2009, Matthews et al 2009) to link CE to regional climate impacts such as regional warming and precipitation changes (Leduc et al 2016, Partanen et al 2017).
For this review, we report on 18 observable climate impacts documented in the peer-reviewed literature (table 1).The identified climate impacts were found to scale near-linearly with CE, depending on the considered spatial and temporal scales as well as the upper limit for CE.In particular, all identified climate impacts show a proportionality with CE of up to 2-3 Tt C (table 1), with the exception of committed sea level rise whose relationship with CE deviates from linearity beyond 1 Tt C of CE (Clark et al 2018).Most of the identified climate impacts are related to temperature changes on land, whereas other climate impacts either occur in the ocean or are associated with precipitation changes.With regards to identified precipitation-related impacts, large uncertainties exist in their linear relationship with CE especially at seasonal scales (Partanen et al 2017) and for extreme events (Moore et al 2023).In addition, more than 80% of the identified climate impacts affect physical systems (i.e.physical impacts).So far, the only biological or societal impacts that have been linked to CE are: (1) labour productivity loss induced by excessive heat exposure at the global and national scales (Chavaillaz et al 2019), and (2) changes in habitat viability for non-human primate species (Stewart et al 2020).
Figure 2 illustrates reviewed climate impacts resulting from 1 Tt C of CE.Ocean acidification is a major impact of rising CO 2 emissions, occurring through increased atmospheric CO 2 concentration and subsequent CO 2 uptake by the ocean.A study shows that there is a proportionality between CE and changes in surface ocean pH-a key indicator of surface ocean acidification-over a wide range of CE (Steinacher and Joos 2016).It is estimated that 1 Tt C of CE results in a decline of 0.19 (0.18-0.22) in surface ocean pH (Steinacher and Joos 2016).Surface warming is another major impact of rising CO 2 emissions.According to the latest IPCC Assessment Report, 1 Tt C of CE results in a global mean surface air temperature increase of 1.65 (1.0-2.3)• C (Canadell et al 2021).Consequences of this global warming include several marine impacts.The globally-averaged sea surface warming resulting from 1 Tt C of CE is 1.4 (1.1-1.7)• C (Leduc et al 2016), slightly lower than the total global warming.Various characteristics of marine heatwaves are expected to increase with CE (Frölicher et al 2018).For instance, the annual cumulative mean intensity of marine heatwaves is estimated to increase by 100 (70-140) • C days for 1 Tt C of CE (figure 2).From the reviewed literature on sea ice decline, observation-based analyses suggest a loss of 3.0 (2.7-3.3)m 2 across the Arctic Ocean in September for CE of 1 tonne CO 2 (Notz and Stroeve 2016).By assuming a continued linear Table 1.Reviewed climate impacts linked quantitatively to cumulative carbon emissions (CE) in the published peer-reviewed literature.For each climate impact (Ic), we provide the literature reference(s), evidence of linear scaling with CE, the upper limit for CE in the linear scaling with Ic, the estimated ratio of Ic to CE (with an uncertainty range when available), and key comments based on reviewed literature and scientific understanding.The symbol ' §' shows reference studies that analysed simulations by multiple models.scaling between CE and sea ice coverage in the Arctic Ocean, we estimate a rate of 0.8 (0.7-0.9) × 10 6 km 2 /Tt C for regional sea ice loss in September (figure 2).This estimate is consistent with analyses based on climate model simulations, which show a near-linear relationship between Arctic sea ice cover in September and CE of more than 1 Tt C (Herrington and Zickfeld 2014).However, as regional sea ice cover declines over time (i.e.towards an ice-free Arctic Ocean), a critical threshold and non-linear transition are expected with regards to the relationship between CE and sea ice decline in the Arctic Ocean (Herrington andZickfeld 2014, Notz andStroeve 2016).Unlike sea surface warming and sea ice melting that respond relatively fast to CE, sea level rise responds very slowly to CE due to inertia in the climate system.When only accounting for thermal ocean expansion, the global sea level rise resulting from 1 Tt C of CE may vary between 0.14 and 1.0 m depending on the time horizon in the future (Williams et al 2012, Steinacher and Joos 2016).For example, the global mean sea level may rise by 0.2 (0.13-0.27) m by the year 2300 (Steinacher and Joos 2016).When accounting for thermal ocean expansion as well as the melting of land ice and ice sheets, the committed sea level rise for 1 Tt C of CE may vary between 0.6 and 13.0 m depending on the time horizon in the future (Clark et al 2018).For instance, the committed sea level rise for 1 Tt C is projected to be approximately 1.0 (0.6-1.4) m, 1.6 (1.1-2.0)m, 2.6 (1.7-3.4)m, 2.6 (1.7-3.4)m, 4.2 (3.1-5.4)m, and 10.3 (7.5-13.0)m when considering a future time horizon of 2300, 2500, 3000, 4000, and 9000, respectively (Clark et al 2018).However, the relationship between CE and committed sea level rise is expected to deviate from linearity beyond CE of 1 Tt C (Clark et al 2016(Clark et al , 2018)).
Surface warming is expected to be significant on land, inducing different climate impacts.At the global scale, land surface warming resulting from 1 Tt C of CE is estimated to be 2.2 (1.7-2.7)• C (Leduc et al 2016), significantly larger than the total global warming.At the regional scale, the surface warming per 1 Tt C in sub-tropical and mid-latitude regions is generally comparable to the global average (figure 2).For the northern high-latitude regions, however, the surface warming resulting from 1 Tt C of CE is consistently higher than the global average (figure 2): Alaska by 3.6 (1.2-5.0)• C, Eastern North America by 2.4 (1.9-2.9)• C, Northern Europe by 2.4 (1.9-2.9)• C, Greenland by 3.1 (2.2-4.0)• C, and Northern Asia by 3.9 (2.2-4.0)• C (Leduc et al 2016).At the seasonal scale, global mean surface warming per 1 Tt C of CE is comparable for all seasons: 1.72 • C, 1.63 • C, 1.64 • C, and 1.73 • C in DJF, MAM, JJA, and SON, respectively (Partanen et al 2017).The most significant seasonal warming is visible during the boreal winter across the Arctic region, with some parts of the region experiencing a temperature increase of 7-9 • C/Tt C in DJF (Partanen et al 2017).Potential future habitat conditions of non-human primates have also been investigated as a function of CE and their implications for regional warming (Stewart et al 2020).For 1 Tt C of CE, it is estimated that 26.09% of the habitat area for non-human primates would experience regional and seasonal temperature increase above suitable conditions (i.e.pre-industrial seasonal maximum temperatures) across the world (figure 2).
There is an established link between CE and temperature extremes at different spatial scales (Seneviratne et al 2016).For instance, per 1 Tt C of CE, Arctic and northern Asia regions experience increases in coldest nighttime temperatures (∆T Nn ) of 6.5 (5.5-8.5)• C and 7.0 (5.1-9.2) • C, respectively (figure 2).These regional extreme temperature changes are approximately the double of the globally-averaged increase in ∆T Nn of 3.5 (3.3-4.2) • C for 1 Tt C of CE (figure 2).Changes in hottest daytime temperatures (∆T Xx ) are generally lower than changes in coldest nighttime temperatures (∆T Nn ) at both the global and regional scales.It is estimated that 1 Tt C of CE results in increased ∆T Xx of 3.9 (3.3-4.3)• C over the Mediterranean Basin, 5.0 (3.0-9.1)• C over Central Asia, 3.9 (3.3-5.3)• C over Brazil and 2.5 (1.4-3.1)• C over Southern Africa (figure 2).
Heat exposure is another observable climate impact that has been linked quantitatively to CE.There is research that demonstrates a direct link between CE and annual total heat exposure over land areas using different thresholds of the Wet-Bulb Globe Temperature (WBGT) index (Chavaillaz et al 2019).At the global scale, it is estimated that heat exposure above the light, extreme, and deadly WGBT thresholds increases by 213.1 (±05.1)Kelvin-days/Tt C, 55.30 (±53.31)Kelvin-days/Tt C, 18.44 (±28.37)Kelvin-days/Tt C, respectively (Chavaillaz et al 2019).At the regional scale, the largest heat exposure is shown for equatorial regions with hotspots in Northern South America, Central Africa, South-East Asia, and Southern India (Chavaillaz et al 2019).A persistent exposure to excessive heat is expected to have multiple consequences on society including labour productivity.CE have been linked quantitatively to labour productivity loss in vulnerable sectors such as agriculture, manufacturing, construction, and mining (Chavaillaz et al 2019).It is estimated that 1 Tt C of CE would result in a global average loss in gross domestic productivity (GDP) of 1.84 (0.90-2.78) % (figure 2), with higher (lower) losses in lower (higher) income countries (Chavaillaz et al 2019).
The direct link between precipitation changes and CE has been investigated in different studies (Liddicoat et al 2016, Partanen et al 2017).The proportionality between CE and precipitation changes highly A geographical distribution of documented climate impacts resulting from one trillion tonne of cumulative carbon emissions (1 Tt C).The climate impacts listed at the left side of the map (below the globe) are evaluated at the global scale.We consider changes in surface air temperature and precipitation patterns to be physical climate impacts, under the assumption that these climate changes (or climate-impact drivers) can induce various impacts on natural and human systems contingent to exposure and vulnerability.
depends on spatial and temporal scales as well as the region of interest (Liddicoat et al 2016, Partanen et al 2017).For instance, while global mean precipitation increase over ocean is shown to be proportional to CE, there is a considerable slowdown in total global mean precipitation increase-due to a global mean precipitation decrease over land-as CE increase (Liddicoat et al 2016).Such a precipitation decline over land is mostly attributed to a rainfall reduction in tropical regions, including the Amazon rainforest where a rapid decline in vegetation (i.e.broadleaf trees) is simulated to occur beyond CE of 1 Tt C (Liddicoat et al 2016).Nevertheless, from the proportionality between CE and global mean precipitation change over ocean (Liddicoat et al 2016), we estimate a rate of 3 (2-3) %/Tt C for the average precipitation increase over global ocean areas.At the seasonal scale, a similar rate (2-3 %/Tt C) is estimated for total global mean precipitation increase in summer and winter months (Partanen et al 2017).At the regional scale, there is a variability in seasonal precipitation change per 1 Tt C of CE in various parts of the world (Partanen et al 2017).For instance, precipitation over the Arctic is simulated to increase by 20-40%/Tt C in DJF and by less than 24%/Tt C in other seasons (Partanen et al 2017).For some regions (parts of Southern Africa, Australia, Northern America, Southern America), 1 Tt C of CE can result in precipitation increase and decrease depending on the season.For example, in Southern Africa, a slight precipitation increase of 0-8%/Tt C is simulated for DJF, whereas the region experiences significant precipitation reduction (up to about −20%/Tt C) for other seasons (Partanen et al 2017).
Apart from changes in mean and seasonal precipitation, changes in the intensity of heavy precipitation events have been quantified as a function of CE although with significant uncertainties depending on the spatial scale and region of interest (Seneviratne et al 2016, Moore et al 2023).At the global scale, the intensity of annual maximum 1 day precipitation (R X1day ) increases by about 7 (0-13)%/Tt C, whereas the intensity of annual maximum consecutive 5 day precipitation (R X5day ) increases by about 4 (−1-10) %/Tt C (Moore et al 2023).At the regional scale, significant increases in the intensity of R X5day occur in monsoon regions of South-East Asia and West Africa (Seneviratne et al 2016), with estimates of about 14 (2-38) %/Tt C and 8 (0-32) %/Tt C, respectively (figure 2).While there is a demonstrated near-linear relationship between CE and changes in extreme precipitation events (both R X1day and R X5day ) across spatial scales, such a proportionality is less distinct at smaller (from local to national) scales than at larger (from sub-continental to global) scales (Moore et al 2023).

The transient climate response to cumulative carbon emissions
The transient climate response to cumulative emissions (TCRE) is a metric defined as the ratio between the increase in globally-averaged surface temperature and the total amount of CO 2 emissions accumulated over time (Canadell et al 2021).The TCRE is a simple, yet very useful metric for estimating the level of global warming associated with a given amount of CE from anthropogenic activities.This metric has been shown to be robust across Earth system models (ESMs), with a recent observationally-constrained estimate of 1.65 (1.0-2.3)• C per 1 Tt C of CE (Canadell et al 2021).
Given its simplicity and robustness, the TCRE has found many policy-relevant applications including the assessment of remaining carbon budgets for limiting global warming levels to 1.5 • C or 2 • C above pre-industrial levels in the context of the Paris Agreement (Matthews et al 2021).In addition, the TCRE is fundamental for the concept of science-based targets (SBTs) in the context of reducing greenhouse gas emissions to achieve the temperature goals of the Paris Agreement (Bjørn et al 2022).Mathematically, the TCRE is given by the following formula (MacDougall 2016, Matthews et al 2021): where ∆T CO2 is the level of global warming due to only CO 2 emissions.Conventionally, the TCRE is defined at the time of doubling of CO 2 concentration in simulations with 1% annual increase in anthropogenic CO 2 emissions (1pctCO 2 ).The quasi-linear relationship between CE and global warming only holds for a certain range of increasing CE, generally up to 2 Tt C or 2000 Gt C (MacDougall 2016).This so-called TCRE window is valid throughout 21st century when considering a total amount of 705 ± 70 Gt C for historical fossil-fuel and land-use CO 2 emissions since the mid-1800s and assuming a future with sustained human-made CO 2 emissions at their current rate of about 11 Gt C yr −1 (Friedlingstein et al 2023).As such, the TCRE remains very relevant in the context of assessing the rise in global mean surface temperature and subsequent climate impacts in the current century.
By definition, the TCRE does not directly relate to global mean temperature change caused by all anthropogenic emissions (i.e.CO 2 and non-CO 2 emissions).Nevertheless, the TCRE can be related to total global mean temperature change by considering an additional term that accounts for the effect of non-CO 2 forcing as described in the following approximation (Matthews et al 2021): where ∆T g is the level of global warming associated with all forcing agents (CO 2 and non-CO 2 forcing), and f nc is the fraction of total anthropogenic forcing (contributing to ∆T g ) associated with non-CO 2 forcing agents.

Using the TCRE concept to estimate climate impacts resulting from cumulative carbon emissions
Apart from the climate impacts directly linked to CE in the reviewed literature (section 2), we assert that additional climate impacts can be indirectly evaluated as a function of CE building on the TCRE concept (section 3).In the published literature, many climate impacts have been directly linked to global warming but not necessarily to CE (e.g.For instance, while the latest IPCC Assessment Report demonstrates the proportionality between global warming and various extreme events, several other climate impacts are only evaluated at specific GWLs of Previous studies highlighted the proportionality between global warming and different observable climate impacts such as extreme daily temperatures (Seneviratne et al 2016), terrestrial heatwaves (Perkins-Kirkpatrick and Gibson 2017), marine heatwaves (Frölicher et al 2018), heavy precipitation events on land (Seneviratne et al 2016), temperature-related diseases and health risks (Lee et al 2019), as well as crop growth duration (Arnell et al 2019).Most of these climate impacts were found to scale near-linearly with global warming, suggesting a potential link between CE and the climate impacts through their proportionality with global warming.Such a link has already been explored for marine heatwave characteristics and extreme weather events at different spatial scales (Seneviratne et al 2016, Frölicher et al 2018).
Therefore, we propose a framework for generalizing how any climate impact (∆I c ) that scales (near-)linearly with global warming (∆T g ) could be quantified as a function of CE.The framework builds on the following two conditions: (1) a demonstrated (near-)linear relationship between the climate impact and global warming, and (2) the proportionality between CE and global warming through the TCRE concept introduced in section 3.This framework builds on the TCRE formulation as follows: which is equivalent to the following formula, when considering equation ( 2): To illustrate how the proposed framework can be applied, we estimate different observable climate impacts resulting from 1 Tt C of CE by using equation ( 4) and climate impacts quantified as a function of global warming in the peer-reviewed literature.For that, we consider a value of 1.65 (1.0-2.3)• C/Tt C for the TCRE (Canadell et al 2021) and a historical estimate of 0.14 (−0.11-0.33)for f nc over the 1900-2019 period (Matthews et al 2021).The value of f nc may be time-dependent and subject to uncertainty in the future, but we are using its median estimate here only for the sake of illustrating an application of equation ( 4).
In the first illustration, we estimate the following three climate impacts resulting from 1 Tt C of CE: (1) changes in terrestrial heatwave duration at the regional scale as an example for physical impacts (Perkins-Kirkpatrick and Gibson 2017), (2) changes in crop growth duration at the global scale as an example for biological impacts (Arnell et al 2019), and (3) changes in heat-attributable mortality in various countries as an example for societal impacts (Lee et al 2019).From the published literature, we consider that 1 • C of global warming results in: (1) a range of 7-38 days for the increase in terrestrial heatwave duration across regions of the world (Perkins-Kirkpatrick and Gibson 2017); (2) a reduction of the growth duration for major crops (such as maize, soybean, wheat, and rice) by 3-5 days (Arnell et al 2019); and (3) a rise in heat-related mortality ranging between 0.4% and 12% across the globe, with larger increase in tropical countries in Asia such as Vietnam and the Philippines (Lee et al 2019).By applying equation ( 4), we estimate that 1 Tt C of CE would result in: (1) an increase of at least 9-44 days in terrestrial heatwave duration in different regions (See calculation details in supplementary table S2); (2) a reduction of 4-15 days for the growth duration of major crops such as maize, soybean, wheat, and rice (See calculation details in supplementary table S3); and (3) an increase of about 10%-30% in heat-related mortality in Vietnam and the Philippines (See calculation details in supplementary table S4).
In the second illustration, we show that equation ( 4) can be used to estimate climate impacts resulting from CE exceeding 1 Tt C. By considering estimates of changes in extreme event intensity at different levels of global warming (up to 4 • C) relative to the 1850-1900 period from the IPCC AR6 (Seneviratne et al 2021), we apply equation ( 4) to link CE to changes in intensity for three extreme events (figure 3): 1-in-10 year extreme temperature on land; 1-in-10 year extreme precipitation on land; 10 year soil moisture drought-an indicator of agricultural/ecological drought-in drying regions.In particular, we show that there is a (near-)linear relationship between changes in intensity for the three extreme events and CE of up to 4 Tt C (figure 3; bottom panels).According to our results, every 1 Tt C of CE results in a sustained increase in the intensity of each of the three extreme events (figure 3).For 1 Tt C of CE, we estimate an increase of 2.2 (0.8-4.1) • C in the intensity of a 1-in-10 year extreme temperature on land as well as an increase of 12.4 (5.6-20.6)% in the intensity of a 1-in-10 year extreme precipitation on land.Both extreme event intensities increase by slightly more than twofold for CE of 2 Tt C, and by considerably more than fourfold (4-5 times) for CE of 4 Tt C. Similarly, we estimate that changes in intensity for a 10 year soil moisture drought event in drying regions resulting from 4 Tt C of CE is twice to thrice the changes in drought intensity resulting from 1 Tt C of CE (figure 3).

Discussion
In recent years, several climate impacts and climate-impact drivers have been assessed at different levels of future global warming and presented in the latest IPCC Assessment Report (e.g.Seneviratne et al 2021, O'Neill et al 2022).Many of these climate impacts and climate-impact drivers were assessed at discrete GWLs ranging from 1 • C to 5 • C above pre-industrial levels, based on time-slicing approaches to determine periods associated with a given future GWL (Seneviratne et al 2021, Tebaldi et al 2021).However, according to the literature reviewed in this study, fewer (less than 20) climate impacts and climate-impact drivers have been directly linked to the primary cause of global warming: anthropogenic CO 2 emissions accumulated over time (table 1).More climate impacts should be assessed as a function of CE to make climate impact assessments relatable to many people.
The direct link between CE and observable climate impacts should be investigated based on either observed data (e.g.Notz and Stroeve 2016) or fully-coupled ESM simulations with a carbon cycle (e.g.Leduc et al 2016, Clark et al 2018, Chavaillaz et al 2019).However, to expand the number of climate impacts that could be linked quantitatively to CE, further studies can consider the framework proposed in section 4 of this study.Building on the TCRE, this framework is suited for quantifying any climate impact as a function of CE as much as the climate impact has a demonstrated proportionality with global warming.Such a framework provides an opportunity for better communicating the human influence on the multitude of climate impacts that have been previously quantified as a function of future global warming (e.g.Seneviratne et al 2016, 2021, Perkins-Kirkpatrick and Gibson 2017, Frölicher et al 2018, Arnell et al 2019, Lee et al 2019).Nonetheless, it should be noted that the proposed framework is only applicable to climate impacts that are caused by changes in temperature (i.e.temperature-dependent impacts).
While the focus here is put on climate impacts that scale (near-)linearly with CE either directly or indirectly via global warming and the TCRE, the proportionality between CE and resulting climate impacts may not hold under certain conditions.For instance, the proportionality between CE and many climate impacts may only hold under increasing CO 2 emissions up to a certain limit for CE (e.g.table 1).Moreover, such a proportionality may no longer hold under net negative CO 2 emissions associated with temperature overshooting (i.e.peak-and-decline temperature changes) (Tachiiri et al 2019, Koven et al 2022).Furthermore, zero emissions commitment (ZEC) scenarios constitute another potential challenge for the proportionality between CE and resulting climate impacts in general and global warming in particular.Despite recent ZEC estimates of nearly 0  ).An extreme temperature event is defined as the daily maximum temperature (TXx) that was exceeded on average once during a 10-year period during the 1850-1900 reference period.An extreme precipitation event is defined as the daily maximum precipitation (R x1day ) that was exceeded on average once during a 10-year period during the 1850-1900 reference period.A soil moisture drought event is defined as a 10-year drought event whose annual mean soil moisture was below its 10th percentile from the 1850-1900 reference period.Climate change is already affecting every region of the world, having more significant impacts on natural and human systems than previously anticipated (Syvitski et al 2020, Capua and Rahmstorf 2023).In particular, there is growing evidence for co-occurrent and consecutive climate hazards in a warming world (Aghakouchak et al 2020, de Ruiter et al 2020, Gruber et al 2021, Vicedo-Cabrera et al 2021, Ribeiro et al 2022, Baumbach et al 2023, Capua and Rahmstorf 2023).This aspect of climate impacts is highly relevant for the environment and society, but it has not yet been investigated in the context of its link to CE.

Conclusion
Climate scientists have known for more than a decade that the level of global warming is proportional to anthropogenic CO 2 emissions accumulated over time (Allen et al 2009, Matthews et al 2009).In addition to global warming, the literature reviewed in this study shows that CE can be directly linked to different climate impacts including regional warming, extreme daily temperatures, heavy precipitation events, changes in seasonal temperature and precipitation, surface ocean acidification, sea ice decline in the Arctic Ocean, changes in primate habitat suitability, and labour productivity loss (table 1 and figure 2).Assessing climate impacts directly from CE provides an intuitive way for linking quantitatively the consequences of climate change to their principal human cause.As much as CO 2 emissions from the burning of fossil fuels are not yet phased out, we recommend that further studies investigate additional physical, biological, and societal climate impacts that could be quantified as function of CE.Determining and quantifying such climate impacts directly from CE should allow a wide community of scientists, policymakers, planners, activists, institutions, and companies to comprehend the consequences of each tonne of emitted CO 2 through human activities.
Ribeiro A F S, Brando P M, Santos L, Rattis L, Hirschi M, Hauser M, Seneviratne S I and Zscheischler J 2022 A compound event-oriented framework to tropical fire risk assessment in a changing climate Environ.Res.Lett.17 065015 Seneviratne S I, Donat M G, Pitman A J, Knutti R and Wilby R L 2016 Allowable CO2 emissions based on regional and impact-related Figure 1.A conceptual diagram illustrating observable climate impacts that can be potentially linked to cumulative carbon emissions.This is a non-exhaustive illustration.Climate impacts documented from the published literature to be linked quantitively to cumulative carbon emissions are shown in bold (section 2).We consider changes in surface air temperature and precipitation patterns to be physical climate impacts, under the assumption that these climate changes (or climate-impact drivers) can induce various impacts on natural and human systems contingent to exposure and vulnerability.
(0.18-0.22)/TtC Ocean pH decline is a key indicator of ocean acidification.acidification inSteinacher and Joos (2016)    Global pH decline.For CE between 0 and 3 Tt C, pH decreases by about 0.2/Tt C. The relationship between CE and sea ice coverage is expected loss in SeptemberHerrington and Zickfeld (2014) inNotz and Stroeve (2016) Only for September.to deviate from linearity as sea ice continues to melt.depends on the season For all seasons, there are large uncertainties for precipitation change in Partanen et al(2017)    and region of interest.change per 1 Tt C at regional scales.Marine heatwave annual Frölicheret al (2018) § For example, see figure 1(a) 2.5 Tt C 32 (27-38) fold increase/Tt C h Lit.reference links the impact to CE indirectly via ∆Tg (TCRE).mean probability ratio in Frölicher et al (2018) Global estimate.Lin.scaling is less evident for CE below 0.5 and above 2.0 Tt C. Marine heatwave annual Frölicher et al (2018) § For example, see figure 1(b) 2.5 Tt C 14 (10-22) fold increase/Tt C h Lit.reference links the impact to CE indirectly via ∆Tg (TCRE).spatial extent change in Frölicher et al (2018) Global estimate.Lin.scaling is less evident for CE below 0.5 and above 2.0 Tt C. (Continued.) Figure 2.A geographical distribution of documented climate impacts resulting from one trillion tonne of cumulative carbon emissions (1 Tt C).The climate impacts listed at the left side of the map (below the globe) are evaluated at the global scale.We consider changes in surface air temperature and precipitation patterns to be physical climate impacts, under the assumption that these climate changes (or climate-impact drivers) can induce various impacts on natural and human systems contingent to exposure and vulnerability.
and 4 • C relative to pre-industrial levels without a clear indication of linear relationship between these impacts and global warming (Seneviratne et al 2021, O'Neill et al 2022).

Figure 3 .
Figure 3.The link between cumulative carbon emissions (CE) and changes in intensity for three extreme events: 1-in-10 year extreme temperature on land (Panels (a) and (d)); 1-in-10 year extreme precipitation on land (Panels (b) and (e)); 10 year soil moisture drought-an indicator of agricultural/ecological drought-in drying regions (Panels (c) and (f)).The quantification of these changes in extreme event intensity as a function of CE is based on the application of equation (4) from this study considering estimates of changes in extreme event intensity at different levels of global warming (up to 4 • C) relative to the 1850-1900 period from the IPCC AR6 report (Seneviratne et al 2021).An extreme temperature event is defined as the daily maximum temperature (TXx) that was exceeded on average once during a 10-year period during the 1850-1900 reference period.An climate targets Nature 529 477-83 Seneviratne S I, Zhang X and Adnan M 2021 Weather and climate extreme events in a changing climate, in Climate Change 2021: the Physical Science Basis Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change ed V Masson-Delmotte, P Zhai, A Pirani, S L Connors, C Péan, S Berger, N Caud, Y Chen, L Goldfarb, M I Gomis, M Huang, K Leitzell, E Lonnoy, J B R Matthews, T K Maycock, T Y O Waterfield, R Yu and B Zhou (Cambridge University Press) pp 1513-766 Steinacher M and Joos F 2016 Transient Earth system responses to cumulative carbon dioxide emissions: linearities, uncertainties, and probabilities in an observation-constrained model ensemble Biogeosciences 13 1071-103 Stewart B M, Turner S E and Matthews H D 2020 Climate change impacts on potential future ranges of non-human primate species Clim.Change 162 2301-18 Syvitski J et al 2020 Extraordinary human energy consumption and resultant geological impacts beginning around 1950 CE initiated the proposed Anthropocene Epoch Commun.Earth Environ. 1 1-13 Tachiiri K, Hajima T and Kawamiya M 2019 Increase of the transient climate response to cumulative carbon emissions with decreasing CO2 concentration scenarios Environ.Res.Lett.14 124067 Tebaldi C and Arblaster J M 2014 Pattern scaling: its strengths and limitations, and an update on the latest model simulations Clim.Change 122 459-71 Tebaldi C, Ranasinghe R, Vousdoukas M, Rasmussen D J, Vega-Westhoff B, Kirezci E, Kopp R E, Sriver R and Mentaschi L 2021 Extreme sea levels at different global warming levels Nat.Clim.Change 11 746-51 Tokarska K B, Gillett N P, Weaver A J, Arora V K and Eby M 2016 The climate response to five trillion tonnes of carbon Nat.Clim.Change 6 851-5 Vicedo-Cabrera A M et al 2021 The burden of heat-related mortality attributable to recent human-induced climate change Nat.Clim.Change 11 492-500 Warren R, Price J, Graham E, Forstenhaeusler N and Vanderwal J 2018 The projected effect on insects, vertebrates, and plants of limiting global warming to 1.5 • C rather than 2 • C Science 360 791-5 Williams R G, Goodwin P, Ridgwell A and Woodworth P L 2012 How warming and steric sea level rise relate to cumulative carbon emissions, Geophys Res.Lett.39 1-6 Zha J, Shen C, Li Z, Wu J, Zhao D, Fan W, Sun M, Azorin-Molina C and Deng K 2021 Projected changes in global terrestrial near-surface wind speed in 1.5 • C-4.0 • C global warming levels Environ.Res.Lett.16 2-12 Zickfeld K et al 2013 Long-term climate change commitment and reversibility: an EMIC intercomparison J. Clim.26 5782-809 Notz and Stroeve 2016), Frölicher et al 2018).While it would be ideal to investigate the link between observable climate impacts and CE based on observed data (e.g.Notz and Stroeve 2016), the causality between these climate impacts and CE is commonly investigated using ensembles of Earth system model (ESM) simulations featuring the carbon cycle.Such ESM simulations are generally driven by idealized scenarios of 1% annual increase in atmospheric CO 2 levels (1pctCO 2 ), although some studies also used conventional emission scenarios such as the Representative Concentration Pathways (RCPs) that include non-CO 2 forcing agents (e.g.Seneviratne et al 2016, Chavaillaz et al 2019).Furthermore, the reviewed studies investigated the link between CE and climate impacts either directly with variables simulated by ESMs (e.g.Clark et al 2018), or indicators computed using model outputs (e.g.Chavaillaz et al 2019).Using linear pattern scaling of global changes (Tebaldi and Arblaster 2014, Herger et al 2015), a few studies extended the concept of proportionality between CE and global warming

Table 1 .
a For each climate impact (Ic), the reported limit represents the upper limit for CE in their linear scaling with Ic as documented in or identified from the reviewed literature.bTheuncertainty range is reported only when provided in the reference(s).cThe reported estimate for the transient climate response to cumulative emissions (TCRE) is from the latest IPCC Assessment Report: Canadell et al (2021).dThe reported ratio is an estimate from this current study, based on figure 9(b) in Liddicoat et al (2016).eThe reported ratio is for 5 day maximum precipitation (R x5day ) as reported in Moore et al (2023).The global estimate for 1 day maximum precipitation (R x1day ) from the same study is 7.11 (0.33-12.50) %/Tt C. f This is the upper limit from Herrington and Zickfeld (2014) in their figure 8(d).The upper limit for observed CE in Notz and Stroeve (2016) is 1.5 Tt CO2, which is approximately 0.4 Tt C. g The study by Notz and Stroeve (2016) reports an observed sea ice loss of 3.0 h The reported ratios are estimates from this current study, based on figure 1 in Frölicher et al (2018).iWBGT stands for Wet-Bulb Global Temperature.Considered WBGT thresholds include light and deadly thresholds whose ratios are 213 (±105) and 18 (±28) Kelvin-days/Tt C, respectively (Chavaillaz et al 2019).jFour key sectors are considered in the study by Chavaillaz et al (2019): agriculture, manufacturing, construction, and mining.kThisnumber represents the percentage of habitat area where the temperature (i.e.pre-industrial seasonal maximum temperature or PSMT) increases above suitable conditions for primate species for 1 Tt C.
Chadburn et al 2017, Kompas et al 2018, Arnell et al 2019, Brown et al 2021, Ebi et al 2021, Seneviratne et al 2021, Tebaldi et al 2021, Zha et al 2021, Ribeiro et al 2022).Assessments of the link between climate impacts and global warming are performed using numerical models and time-slicing approaches to determine periods associated with a given global warming level (GWL) in the future (Seneviratne et al 2021, Tebaldi et al 2021).In most cases, the focus is put on the evaluation of climate impacts at specific global warming levels (GWLs) of 1.5 • C and 2 • C relative to pre-industrial levels in the context of the Paris Agreement (e.g.Chadburn et al 2017, Arnell et al 2018, Tebaldi et al 2021).As such, not all studies explicitly report on a continuous proportionality between global warming and climate impacts.
(Herrington and Zick, Frölicher and Paynter 2015, MacDougall 2016, Palazzo Corner et al 2023)l 2021)s contributing to the Coupled Model Intercomparison Project Phase 6 (CMIP6) under different Shared Socio-economic Pathway (SSP) forcing scenarios.Changes in drought intensity are expressed as standard deviations of the interannual variability in soil moisture over the 1850-1900 period in a given model (Seneviratne et al 2021).Top panels illustrate the distribution of the changes in extreme event intensity as a function of CE,whereas bottom panels show the (near-)linear scaling between changes in extreme event intensity (medians) and CE under the assumption that 0 CE induces no changes in event median intensity.For each box plot in the top panels, the horizontal line and the box represent the median and central 66% uncertainty range, respectively, of the intensity changes across the multi-model ensemble, and the 'whiskers' extend to the 90% uncertainty range.For the bottom panels, each dotted line connects a square point (CE level and median changes in event intensity) with the origin point (0 CE and no changes in event intensity).circulation may not scale linearly with CE over multi-centennial to millennial timescales(Herrington and Zickfeld 2014, Steinacher and Joos 2016, Chadburn et al 2017, Fox-Kemper et al 2021).To link CE to such climate impacts associated with inertia in the Earth system, a generalized framework accounting for the effect of ZEC and long-term temperature stabilization on observable climate impacts and the TCRE would be needed(Zickfeld et al 2013, Frölicher and Paynter 2015, MacDougall 2016, Palazzo Corner et al 2023).