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Global warming in the pipeline [1]

['Hansen', 'James E', 'Climate Science', 'Awareness', 'Solutions', 'Columbia University Earth Institute', 'New York', 'Ny', 'Sato', 'Simons']

Date: 2023-02-14

Abstract

Improved knowledge of glacial-to-interglacial global temperature change yields Charney (fast-feedback) equilibrium climate sensitivity 1.2 ± 0.3°C (2σ) per W/m2, which is 4.8°C ± 1.2°C for doubled CO 2 . Consistent analysis of temperature over the full Cenozoic era—including ‘slow’ feedbacks by ice sheets and trace gases—supports this sensitivity and implies that CO 2 was 300–350 ppm in the Pliocene and about 450 ppm at transition to a nearly ice-free planet, exposing unrealistic lethargy of ice sheet models. Equilibrium global warming for today’s GHG amount is 10°C, which is reduced to 8°C by today’s human-made aerosols. Equilibrium warming is not ‘committed’ warming; rapid phaseout of GHG emissions would prevent most equilibrium warming from occurring. However, decline of aerosol emissions since 2010 should increase the 1970–2010 global warming rate of 0.18°C per decade to a post-2010 rate of at least 0.27°C per decade. Thus, under the present geopolitical approach to GHG emissions, global warming will exceed 1.5°C in the 2020s and 2°C before 2050. Impacts on people and nature will accelerate as global warming increases hydrologic (weather) extremes. The enormity of consequences demands a return to Holocene-level global temperature. Required actions include: (1) a global increasing price on GHG emissions accompanied by development of abundant, affordable, dispatchable clean energy, (2) East-West cooperation in a way that accommodates developing world needs, and (3) intervention with Earth’s radiation imbalance to phase down today’s massive human-made ‘geo-transformation’ of Earth’s climate. Current political crises present an opportunity for reset, especially if young people can grasp their situation.

Background information and structure of paper

It has been known since the 1800s that infrared-absorbing (greenhouse) gases (GHGs) warm Earth’s surface and that the abundance of GHGs changes naturally as well as from human actions [1, 2].1 Roger Revelle wrote in 1965 that we are conducting a ‘vast geophysical experiment’ by burning fossil fuels that accumulated in Earth’s crust over hundreds of millions of years [3] Carbon dioxide (CO 2 ) in the air is now increasing and already has reached levels that have not existed for millions of years, with consequences that have yet to be determined. Jule Charney led a study in 1979 by the United States National Academy of Sciences that concluded that doubling of atmospheric CO 2 was likely to cause global warming of 3 ± 1.5°C [4]. Charney added: ‘However, we believe it is quite possible that the capacity of the intermediate waters of the ocean to absorb heat could delay the estimated warming by several decades.’

After U.S. President Jimmy Carter signed the 1980 Energy Security Act, which included a focus on unconventional fossil fuels such as coal gasification and rock fracturing (‘fracking’) to extract shale oil and tight gas, the U.S. Congress asked the National Academy of Sciences again to assess potential climate effects. Their massive Changing Climate report had a measured tone on energy policy—amounting to a call for research [5]. Was not enough known to caution lawmakers against taxpayer subsidy of the most carbon-intensive fossil fuels? Perhaps the equanimity was due in part to a major error: the report assumed that the delay of global warming caused by the ocean’s thermal inertia is 15 years, independent of climate sensitivity. With that assumption, they concluded that climate sensitivity for 2 × CO 2 is near or below the low end of Charney’s 1.5–4.5°C range. If climate sensitivity was low and the lag between emissions and climate response was only 15 years, climate change would not be nearly the threat that it is.

Simultaneous with preparation of Changing Climate, climate sensitivity was addressed at the 1982 Ewing Symposium at the Lamont Doherty Geophysical Observatory of Columbia University on 25–27 October, with papers published in January 1984 as a monograph of the American Geophysical Union [6]. Paleoclimate data and global climate modeling together led to an inference that climate sensitivity is in the range 2.5–5°C for 2 × CO 2 and that climate response time to a forcing is of the order of a century, not 15 years [7]. Thus, the concept that a large amount of additional human-made warming is already ‘in the pipeline’ was introduced. E.E. David, Jr, President of Exxon Research and Engineering, in his keynote talk at the symposium insightfully noted [8]: ‘The critical problem is that the environmental impacts of the CO 2 buildup may be so long delayed. A look at the theory of feedback systems shows that where there is such a long delay, the system breaks down, unless there is anticipation built into the loop.’

Thus, the danger caused by climate’s delayed response and the need for anticipatory action to alter the course of fossil fuel development was apparent to scientists and the fossil fuel industry 40 years ago.2 Yet industry chose to long deny the need to change energy course [9], and now, while governments and financial interests connive, most industry adopts a ‘greenwash’ approach that threatens to lock in perilous consequences for humanity. Scientists will share responsibility if we allow governments to rely on goals for future global GHG levels, as if targets had meaning in the absence of policies required to achieve them.

The Intergovernmental Panel on Climate Change (IPCC) was established in 1988 to provide scientific assessments on the state of knowledge about climate change [10] and almost all nations agreed to the 1992 United Nations Framework Convention on Climate Change [11] with the objective to avert ‘dangerous anthropogenic interference with the climate system’. The current IPCC Working Group 1 report [12] provides a best estimate of 3°C for equilibrium global climate sensitivity to 2 × CO 2 and describes shutdown of the overturning ocean circulations and large sea level rise on the century time scale as ‘high impact, low probability’ even under extreme GHG growth scenarios. This contrasts with ‘high impact, high probability’ assessments reached in a paper [13]—hereafter abbreviated Ice Melt—that several of us published in 2016. Recently, our paper’s first author (JEH) described a long-time effort to understand the effect of ocean mixing and aerosols on observed and projected climate change, which led to a conclusion that most climate models are unrealistically insensitive to freshwater injected by melting ice and that ice sheet models are unrealistically lethargic in the face of rapid, large climate change [14].

Eelco Rohling, editor of Oxford Open Climate Change, invited a perspective article on these issues. Our principal motivation in this paper is concern that IPCC has underestimated climate sensitivity and understated the threat of large sea level rise and shutdown of ocean overturning circulations, but these issues, because of their complexity, must be addressed in two steps. Our present paper addresses climate sensitivity and warming in the pipeline, concluding that these exceed IPCC’s best estimates. Response of ocean circulation and ice sheet dynamics to global warming—already outlined in the Ice Melt paper—will be addressed further in a later paper.

The structure of our present paper is as follows. Climate sensitivity section makes a fresh evaluation of Charney’s equilibrium climate sensitivity (ECS) based on improved paleoclimate data and introduces Earth system sensitivity (ESS), which includes the feedbacks that Charney held fixed. Climate response time section explores the fast-feedback response time of Earth’s temperature and energy imbalance to an imposed forcing, concluding that cloud feedbacks buffer heat uptake by the ocean, thus increasing the delay in surface warming and making Earth’s energy imbalance an underestimate of the forcing reduction required to stabilize climate. Cenozoic era section analyzes temperature change of the past 66 million years and infers the Cenozoic history of CO 2 , thus providing insights about climate change. Aerosols section addresses the absence of aerosol forcing data via inferences from paleo data and modern global temperature change, and we point out potential information in ‘the great inadvertent aerosol experiment’ provided by recent restrictions on fuels in international shipping. Summary section discusses policy implications of high climate sensitivity and the delayed response of the climate system. Warming in the pipeline need not appear. We can take actions that slow and reverse global warming; indeed, we suggest that such actions are needed to avoid disastrous consequences for humanity and nature. Reduction of greenhouse gas emissions as rapidly as practical has highest priority, but that policy alone is now inadequate and must be complemented by additional actions to affect Earth’s energy balance. The world is still early in this ‘vast geophysical experiment’—as far as consequences are concerned—but time has run short for the ‘anticipation’ that E.E. David recommended.

Climate sensitivity (ECS and ESS)

This section gives a brief overview of the history of ECS estimates since the Charney report and uses glacial-to-interglacial climate change to infer an improved estimate of ECS. We discuss how ECS and the more general Earth system sensitivity (ESS) depend on the climate state.

Charney defined ECS as the eventual global temperature change caused by doubled CO 2 if ice sheets, vegetation and long-lived GHGs are fixed (except the specified CO 2 doubling). Other quantities affecting Earth’s energy balance—clouds, aerosols, water vapor, snow cover and sea ice—change rapidly in response to climate change. Thus, Charney’s ECS is also called the ‘fast-feedback’ climate sensitivity. Feedbacks interact in many ways, so their changes are calculated in global climate models (GCMs) that simulate such interactions. Charney implicitly assumed that change of the ice sheets on Greenland and Antarctica—which we categorize as a ‘slow feedback’—was not important on time scales of most public interest.

ECS defined by Charney is a gedanken concept that helps us study the effect of human-made and natural climate forcings. If knowledge of ECS were based only on models, it would be difficult to narrow the range of estimated climate sensitivity—or have confidence in any range—because we do not know how well feedbacks are modeled or if the models include all significant real-world feedbacks. Cloud and aerosol interactions are complex, e.g. and even small cloud changes can have a large effect. Thus, data on Earth’s paleoclimate history are essential, allowing us to compare different climate states, knowing that all feedbacks operated.

Climate sensitivity estimated at the 1982 Ewing Symposium

] for the Ewing Symposium monograph using the feedback framework implied by E.E. David and employed by electrical engineers [ ]. The climate forcing caused by 2 × CO 2 —the imposed perturbation of Earth’s energy balance—is ∼4 W/m2. If there were no climate feedbacks and Earth radiated energy to space as a perfect black surface, Earth’s temperature would need to increase ∼1.2°C to increase radiation to space 4 W/m2 and restore energy balance. However, feedbacks occur in the real world and in GCMs. In our GCM the equilibrium response to 2 × CO 2 was 4°C warming of Earth’s surface. Thus, the fraction of equilibrium warming due directly to the CO 2 change was 0.3 (1.2°C/4°C) and the feedback ‘gain’, g, was 0.7 (2.8°C/4°C). Algebraically, ECS and feedback gain are related by ECS = 1.2 ° C / ( 1 - g ) (1) Climate sensitivity was addressed in our paper [ 7 ] for the Ewing Symposium monograph using the feedback framework implied by E.E. David and employed by electrical engineers [ 15 ]. The climate forcing caused by 2 × CO—the imposed perturbation of Earth’s energy balance—is ∼4 W/m. If there were no climate feedbacks and Earth radiated energy to space as a perfect black surface, Earth’s temperature would need to increase ∼1.2°C to increase radiation to space 4 W/mand restore energy balance. However, feedbacks occur in the real world and in GCMs. In our GCM the equilibrium response to 2 × COwas 4°C warming of Earth’s surface. Thus, the fraction of equilibrium warming due directly to the COchange was 0.3 (1.2°C/4°C) and the feedback ‘gain’, g, was 0.7 (2.8°C/4°C). Algebraically, ECS and feedback gain are related by

We evaluated contributions of individual feedback processes to g by inserting changes of water vapor, clouds, and surface albedo (reflectivity, literally whiteness, due to sea ice and snow changes) from the 2 × CO 2 GCM simulation one-by-one into a one-dimensional radiative-convective model [16], finding g wv = 0.4, g cl = 0.2, g sa = 0.1, where g wv , g cl , and g sa are the water vapor, cloud and surface albedo gains. The 0.2 cloud gain was about equally from a small increase in cloud top height and a small decrease in cloud cover. These feedbacks all seemed reasonable, but how could we verify their magnitudes or the net ECS due to all feedbacks?

We recognized the potential of emerging paleoclimate data. Early data from polar ice cores revealed that atmospheric CO 2 was much less during glacial periods and the CLIMAP project [17] used proxy data to reconstruct global surface conditions during the Last Glacial Maximum (LGM), which peaked about 20 000 years ago. A powerful constraint was the fact that Earth had to be in energy balance averaged over the several millennia of the LGM. However, when we employed CLIMAP boundary conditions including sea surface temperatures (SSTs), Earth was out of energy balance, radiating 2.1 W/m2 to space, i.e. Earth was trying to cool off with an enormous energy imbalance, equivalent to half of 2 × CO 2 forcing.

Something was wrong with either assumed LGM conditions or our climate model. We tried CLIMAP’s maximal land ice—this only reduced the energy imbalance from 2.1 to 1.6 W/m2. Moreover, we had taken LGM CO 2 as 200 ppm and did not know that CH 4 and N 2 O were less in the LGM than in the present interglacial period; accurate GHGs and CLIMAP SSTs produce a planetary energy imbalance close to 3 W/m2. Most feedbacks in our model were set by CLIMAP. Sea ice is set by CLIMAP. Water vapor depends on surface temperature, which is set by CLIMAP SSTs. Cloud feedback is uncertain, but ECS smaller than 2.4°C for 2 × CO 2 would require a negative cloud gain. g cl ∼ 0.2 from our GCM increases ECS from 2.4°C to 4°C (Equation 1) and accounts for almost the entire difference of sensitivities of our model (4°C for 2 × CO 2 ) and the Manabe and Stouffer model [18] (2°C for 2 × CO 2 ) that had fixed cloud cover and cloud height. Manabe suggested [19] that our higher ECS was due to a too-large sea ice and snow feedback, but we noted [7] that sea ice in our control run was less than observed, so we likely understated sea ice feedback. Amplifying feedback due to high clouds increasing in height with warming is expected and is found in observations, large-eddy simulations and GCMs [20] Sherwood et al. [21] conclude that negative low-cloud feedback is ‘neither credibly suggested by any model, nor by physical principles, nor by observations.’ Despite a wide spread among models, GCMs today show an amplifying cloud feedback due to increases in cloud height and decreases in cloud amount, despite increases in cloud albedo [22]. These cloud changes are found in all observed cloud regimes and locations, implying robust thermodynamic control [23].

CLIMAP SSTs were a more likely cause of the planetary energy imbalance. Co-author D. Peteet used pollen data to infer LGM tropical and subtropical cooling 2–3°C greater than in a GCM forced by CLIMAP SSTs. D. Rind and Peteet found that montane LGM snowlines in the tropics descended 1 km in the LGM, inconsistent with climate constrained by CLIMAP SSTs. CLIMAP assumed that tiny shelled marine species migrate to stay in a temperature zone they inhabit today. But what if, instead, these species partly adapt over millennia to changing temperature? Based on the work of Rind and Peteet, later published [24], we suspected but could not prove that CLIMAP SSTs were too warm.

Based on GCM simulations for 2 × CO 2 , on our feedback analysis for the LGM, and on observed global warming in the past century, we concluded that ECS was in the range 2.5–5°C for 2 × CO 2 . If CLIMAP SSTs were accurate, ECS was near the low end of that range. In contrast, our analysis implied that ECS for 2 × CO 2 was in the upper half of the 2.5–5°C range, but our analysis depended in part on our GCM, which had sensitivity 4°C for 2 × CO 2 . To resolve the matter, a paleo thermometer independent of biologic adaptation was needed. Several decades later, such a paleo thermometer and advanced analysis techniques exist. We will use recent studies to infer our present best estimates for ECS and ESS. First, however, we will comment on other estimates of climate sensitivity and clarify the definition of climate forcings that we employ.

IPCC and independent climate sensitivity estimates

Reviews of climate sensitivity are available, e.g. Rohling et al. [25], which focuses on the physics of the climate system, and Sherwood et al. [26], which adds emphasis on probabilistic combination of multiple uncertainties. Progress in narrowing the uncertainty in climate sensitivity was slow in the first five IPCC assessment reports. The fifth assessment report [26] (AR5) in 2014 concluded only—with 66% probability—that ECS was in the range 1.5–4.5°C, the same as Charney’s report 35 years earlier. The broad spectrum of information on climate change—especially constraints imposed by paleoclimate data—at last affected AR6 [12], which concluded with 66% probability that ECS is 2.5–4°C, with 3°C as their best estimate (Supplementary Fig. TS.6).

Sherwood et al. [21] combine three lines of evidence: climate feedback studies, historical climate change, and paleoclimate data, inferring S = 2.6–3.9°C with 66% probability for 2 × CO 2 , where S is an ‘effective sensitivity’ relevant to a 150-year time scale. They find ECS only slightly larger: 2.6–4.1°C with 66% probability. Climate feedback studies, inherently, cannot yield a sharp definition of ECS, as we showed in the cloud feedback discussion above. Earth’s climate system includes amplifying feedbacks that push the gain, g, closer to unity than zero, thus making ECS sensitive to uncertainty in any feedback; the resulting sensitivity of ECS to g prohibits precise evaluation from feedback analysis. Similarly, historical climate change cannot define ECS well because the aerosol climate forcing is unmeasured. Also, forced and unforced ocean dynamics give rise to a pattern effect: [27] the geographic pattern of transient and equilibrium temperature changes differ, which affects ECS inferred from transient climate change. These difficulties help explain how Sherwood et al. [21] could estimate ECS as only 6% larger than S, an implausible result in view of the ocean’s great thermal inertia. An intercomparison of GCMs run for millennial time scales, LongRunMIP [28], includes 14 simulations of 9 GCMs with runs of 5000 years (or close enough for extrapolation to 5000 years). Their global warmings at 5000 years range from 30% to 80% larger than their 150-year responses.

Our approach is to compare glacial and interglacial equilibrium climate states. The change of atmospheric and surface forcings can be defined accurately, thus leading to a sharp evaluation of ECS for cases in which equilibrium response is assured. With this knowledge in hand, additional information can be extracted from historical and paleo climate changes.

Climate forcing definitions

Attention to climate forcing definitions is essential for quantitative analysis of climate change. However, readers uninterested in radiative forcings may skip this section with little penalty. We describe our climate forcing definition and compare our forcings with those of IPCC. Our total GHG forcing matches that of IPCC within a few percent, but this close fit hides larger differences in individual forcings that deserve attention.

Δ Ts ∼ F × ECS = F × λ , (2) S is the global mean equilibrium surface temperature change in response to climate forcing F, which is measured in W/m2 averaged over the entire planetary surface. There are alternative ways to define F, as discussed in Chapter 8 [ ] of AR5 and in a paper [ ] hereafter called Efficacy. Objectives are to find a definition of F such that different forcing mechanisms of the same magnitude yield a similar global temperature change, but also a definition that can be computed easily and reliably. The first four IPCC reports used adjusted forcing, F a , which is Earth’s energy imbalance after stratospheric temperature adjusts to presence of the forcing agent. F a usually yields a consistent response among different forcing agents, but there are exceptions such as black carbon aerosols; F a exaggerates their impact. Also, F a is awkward to compute and depends on definition of the tropopause, which varies among models. F s , the fixed SST forcing (including fixed sea ice), is more robust than F a as a predictor of climate response [ 30, ], but a GCM is required to compute F s . In Efficacy, F s is defined as F s = F o + δ T o λ , (3) o is Earth’s energy imbalance after atmosphere and land surface adjust to the presence of the forcing agent with SST fixed. F o is not a full measure of the strength of a forcing, because a portion (δT o ) of the equilibrium warming is already present as F o is computed. A GCM run of about 100 years is needed to accurately define F o because of unforced atmospheric variability. That GCM run also defines δT o , the global mean surface air temperature change caused by the forcing with SST fixed. λ is the model’s ECS in °C per W/m2. δT o /λ is the portion of the total forcing (F s ) that is ‘used up’ in causing the δT o warming; radiative flux to space increases by δT o /λ due to warming of the land surface and global air. The term δT o /λ is usually, but not always, less than 10% of F o . Thus, it is better not to neglect δT o /λ. IPCC AR5 and AR6 define effective radiative forcing as ERF = F o . Omission of δT o /λ was intentional [ ] and is not an issue if the practice is followed consistently. However, when the forcing is used to calculate global surface temperature response, the forcing to use is F s , not F o . It would be useful if both F o and δT o were reported for all climate models. Equilibrium global surface temperature change is related to ECS bywhere λ is a widely used abbreviation of ECS, ΔTis the global mean equilibrium surface temperature change in response to climate forcing F, which is measured in W/maveraged over the entire planetary surface. There are alternative ways to define F, as discussed in Chapter 8 [ 29 ] of AR5 and in a paper [ 30 ] hereafter called Efficacy. Objectives are to find a definition of F such that different forcing mechanisms of the same magnitude yield a similar global temperature change, but also a definition that can be computed easily and reliably. The first four IPCC reports used adjusted forcing, F, which is Earth’s energy imbalance after stratospheric temperature adjusts to presence of the forcing agent. Fusually yields a consistent response among different forcing agents, but there are exceptions such as black carbon aerosols; Fexaggerates their impact. Also, Fis awkward to compute and depends on definition of the tropopause, which varies among models. F, the fixed SST forcing (including fixed sea ice), is more robust than Fas a predictor of climate response [ 31 ], but a GCM is required to compute F. In Efficacy, Fis defined aswhere Fis Earth’s energy imbalance after atmosphere and land surface adjust to the presence of the forcing agent with SST fixed. Fis not a full measure of the strength of a forcing, because a portion (δT) of the equilibrium warming is already present as Fis computed. A GCM run of about 100 years is needed to accurately define Fbecause of unforced atmospheric variability. That GCM run also defines δT, the global mean surface air temperature change caused by the forcing with SST fixed. λ is the model’s ECS in °C per W/m. δT/λ is the portion of the total forcing (F) that is ‘used up’ in causing the δTwarming; radiative flux to space increases by δT/λ due to warming of the land surface and global air. The term δT/λ is usually, but not always, less than 10% of F. Thus, it is better not to neglect δT/λ. IPCC AR5 and AR6 define effective radiative forcing as ERF = F. Omission of δT/λ was intentional [ 29 ] and is not an issue if the practice is followed consistently. However, when the forcing is used to calculate global surface temperature response, the forcing to use is F, not F. It would be useful if both Fand δTwere reported for all climate models.

A further refinement of climate forcing is suggested in Efficacy: effective forcing (F e ) defined by a long GCM run with calculated ocean temperature. The resulting global surface temperature change, relative to that for equal CO 2 forcing, defines the forcing’s efficacy. Effective forcings, F e , were found to be within a few percent of F s for most forcing agents, i.e. the results confirm that F s is a robust forcing. This support is for F s , not for F o = ERF, which is systematically smaller than F s . The Goddard Institute for Space Studies (GISS) GCM [32, 33] used for CMIP6 [34] studies, which we label the GISS (2020) model,3 has higher resolution (2° × 2.5° and 40 atmospheric layers) and other changes that yield a moister upper troposphere and lower stratosphere, relative to the GISS model used in Efficacy. GHG forcings reported for the GISS (2020) model [32, 33] are smaller than in prior GISS models, a change attributed [33] to blanketing by high level water vapor. However, part of the change is from comparison of F o in GISS (2020) to F S in earlier models. The 2 × CO 2 fixed SST simulation with the GISS (2020) model yields F o = 3.59 W/m2, δTo = 0.27°C and λ = 0.9°C per W/m2. Thus F S = 3.59 + 0.30 = 3.89 W/m2, which is only 5.4% smaller than the F S = 4.11 W/m2 for the GISS model used in Efficacy.

e , was obtained in two steps. Adjusted forcings, F a , were calculated for each gas for a large range of gas amount with a global-mean radiative-convective model that incorporated the GISS GCM radiation code, which uses the correlated k-distribution method [ ] and high spectral resolution laboratory data [ ]. The F a are converted to effective forcings (F e ) via efficacy factors (E a ; of Efficacy) based on GCM simulations that include the 3-D distribution of each gas. The total GHG forcing is F e = F a C O 2 + 1.45 F a C H 4 + 1.04 F a N 2 O + 1.32 F a MPTGs + OTGs + 0.45 F a ( O 3 ) (4) Our GHG effective forcing, F, was obtained in two steps. Adjusted forcings, F, were calculated for each gas for a large range of gas amount with a global-mean radiative-convective model that incorporated the GISS GCM radiation code, which uses the correlated k-distribution method [ 35 ] and high spectral resolution laboratory data [ 36 ]. The Fare converted to effective forcings (F) via efficacy factors (E Table 1 of Efficacy) based on GCM simulations that include the 3-D distribution of each gas. The total GHG forcing is

Table 1. Greenhouse gas radiative forcings Gas . Radiative Forcing . CO 2 F = f(c) – f(c o ), where f(c) = 4.996 ln (c + 0.0005c2) CH 4 F = 0.0406(√m − √m o ) − [g(m, n o ) – g(m o , n o )] N 2 O F = 0.136(√n – √n o ) – [g(m o , n) – g(m o , n o )] where g(m, n) = 0.5 ln [1 + 2 × 10–5(mn)0.75] CFC-11 F = 0.264(x − x o ) CFC-12 F = 0.323(y − y o ) Gas . Radiative Forcing . CO 2 F = f(c) – f(c o ), where f(c) = 4.996 ln (c + 0.0005c2) CH 4 F = 0.0406(√m − √m o ) − [g(m, n o ) – g(m o , n o )] N 2 O F = 0.136(√n – √n o ) – [g(m o , n) – g(m o , n o )] where g(m, n) = 0.5 ln [1 + 2 × 10–5(mn)0.75] CFC-11 F = 0.264(x − x o ) CFC-12 F = 0.323(y − y o ) Open in new tab

Table 1. Greenhouse gas radiative forcings Gas . Radiative Forcing . CO 2 F = f(c) – f(c o ), where f(c) = 4.996 ln (c + 0.0005c2) CH 4 F = 0.0406(√m − √m o ) − [g(m, n o ) – g(m o , n o )] N 2 O F = 0.136(√n – √n o ) – [g(m o , n) – g(m o , n o )] where g(m, n) = 0.5 ln [1 + 2 × 10–5(mn)0.75] CFC-11 F = 0.264(x − x o ) CFC-12 F = 0.323(y − y o ) Gas . Radiative Forcing . CO 2 F = f(c) – f(c o ), where f(c) = 4.996 ln (c + 0.0005c2) CH 4 F = 0.0406(√m − √m o ) − [g(m, n o ) – g(m o , n o )] N 2 O F = 0.136(√n – √n o ) – [g(m o , n) – g(m o , n o )] where g(m, n) = 0.5 ln [1 + 2 × 10–5(mn)0.75] CFC-11 F = 0.264(x − x o ) CFC-12 F = 0.323(y − y o ) Open in new tab

The CH 4 coefficient (1.45) includes the effect of CH 4 on O 3 and stratospheric H 2 O, as well as the efficacy (1.10) of CH 4 per se. We assume that CH 4 is responsible for 45% of the O 3 change [37]. Forcing caused by the remaining 55% of the O 3 change is based on IPCC AR6 O 3 forcing (Fa = 0.47 W/m2 in 2019); we multiply this AR6 O 3 forcing by 0.55 × 0.82 = 0.45, where 0.82 is the efficacy of O 3 forcing from Table 1 of Efficacy. Thus, the non-CH 4 portion of the O 3 forcing is 0.21 W/m2 in 2019. MPTGs and OTGs are Montreal Protocol Trace Gases and Other Trace Gases [38]. A list of these gases and a table of annual forcings since 1992 are available as well as the earlier data [39].

The climate forcing from our formulae is slightly larger than IPCC AR6 forcings (Fig. 1). In 2019, the final year of AR6 data, our GHG forcing is 4.00 W/m2; the AR6 forcing is 3.84 W/m2. Our forcing should be larger, because IPCC forcings are F o for all gases except O 3 , for which they provide F a (AR6 section 7.3.2.5). Table 1 in Efficacy allows accurate comparison: δT o for 2 × CO 2 for the GISS model used in Efficacy is 0.22°C, λ is 0.67°C per W/m2, so δT o /λ = 0.33 W/m2. Thus, the conversion factor from F o to F e (or F s ) is 4.11/(4.11−0.33). The non-O 3 portion of AR6 2019 forcing (3.84−0.47 = 3.37) W/m2 increases to 3.664 W/m2. The O 3 portion of the AR6 2019 forcing (0.47 W/m2) decreases to 0.385 W/m2 because the efficacy of F a (O 3 ) is 0.82. The AR6 GHG forcing in 2019 is thus ∼4.05 W/m2, expressed as Fe ∼ Fs, which is ∼1% larger than follows from our formulae. This precise agreement is not indicative of the true uncertainty in the GHG forcing, which IPCC AR6 estimates as 10%, thus about 0.4 W/m2. We concur with their error estimate and employ it in our ECS uncertainty analysis (Equilibrium climate sensitivity section).

Figure 1. Open in new tabDownload slide IPCC AR6 Annex III greenhouse gas forcing [12], which employs F a for O 3 and F o for other GHGs, compared with the effective forcing, F e , from Equation (4). See discussion in text.

We conclude that the GHG increase since 1750 already produces a climate forcing equivalent to that of 2 × CO 2 (our formulae yield F e ∼ F s = 4.08 W/m2 for 2021 and 4.13 W/m2 for 2022; IPCC AR6 has F s = 4.14 W/m2 for 2021). The human-made 2 × CO 2 climate forcing imagined by Charney, Tyndall and other greenhouse giants is no longer imaginary. Humanity is now taking its first steps into the period of consequences. Earth’s paleoclimate history helps us assess the potential outcomes.

Glacial-to-interglacial climate oscillations

In this section we describe how ice core data help us assess ECS for climate states from glacial conditions to interglacial periods such as the Holocene, the interglacial period of the past 12 000 years. We discuss climate sensitivity in warmer climates in Cenozoic era section.

Air bubbles in Antarctic ice cores—trapped as snow piled up and compressed into ice—preserve a record of long-lived GHGs for at least 800 000 years. Isotopic composition of the ice provides a measure of temperature in and near Antarctica [40]. Changes of temperature and CO 2 are highly correlated (Fig. 2). This does not mean that CO 2 is the primal cause of the climate oscillations. Hays et al. [42] showed that small changes of Earth’s orbit and the tilt of Earth’s spin axis are pacemakers of the ice ages. Orbital changes alter the seasonal and geographical distribution of insolation, which affects ice sheet size and GHG amount. Long-term climate is sensitive because ice sheets and GHGs act as amplifying feedbacks: [43] as Earth warms, ice sheets shrink, expose a darker surface, and absorb more sunlight; also, as Earth warms, the ocean and continents release GHGs to the air. These amplifying feedbacks work in the opposite sense as Earth cools. Orbital forcings oscillate slowly over tens and hundreds of thousands of years [44]. The picture of how Earth orbital changes drive millennial climate change was painted in the 1920s by Milutin Milankovitch, who built on 19th century hypotheses of James Croll and Joseph Adhémar. Paleoclimate changes of ice sheets and GHGs are sometimes described as slow feedbacks [45], but their slow change is paced by the Earth orbital forcing; their slow change does not mean that these feedbacks cannot operate more rapidly in response to a rapid climate forcing.

Figure 2. Open in new tabDownload slide Antarctic Dome C temperature for past 800 ky from Jouzel et al. [40] relative to the mean of the last 10 ky and Dome C CO 2 amount from Luthi et al. [41] (kyBP is kiloyears before present).

We evaluate ECS by comparing stable climate states before and after a glacial-to-interglacial climate transition. GHG amounts are known from ice cores and ice sheet sizes are known from geologic data. This empirical ECS applies to the range of global temperature covered by ice cores, which we will conclude is about –7°C to + 1°C relative to the Holocene. The Holocene is an unusual interglacial. Maximum melt rate was at 13.2 kyBP, as expected [45] and GHG amounts began to decline after peaking early in the Holocene, as in most interglacials. However, several ky later, CO 2 and CH 4 increased, raising a question of whether humans were affecting GHGs. Ruddiman [46] suggests that deforestation began to affect CO 2 6500 years ago and rice irrigation began to affect CH 4 5000 years ago. Those possibilities complicate use of LGM-Holocene warming to estimate ECS. However, sea level, and thus the size of the ice sheets, had stabilized by 7000 years ago (Evidence of aerosol forcing in the Holocene section). Thus, the millennium centered on 7 kyBP provides a good period to compare with the LGM. Comparison of the Eemian interglacial (Fig. 2) with the prior glacial maximum (PGM) has potential for independent assessment.

LGM-Holocene and PGM-Eemian evaluation of ECS

In this section we evaluate ECS by comparing neighboring glacial and interglacial periods when Earth was in energy balance within less than 0.1 W/m2 averaged over a millennium. Larger imbalance would cause temperature or sea level change that did not occur [48].4 Thus, we can assess ECS from knowledge of atmospheric and surface forcings that maintained these climates.

Recent advanced analysis techniques allow improved estimate of paleo temperatures. Tierney et al. [49] exclude microbiology fossils whose potential to adapt makes them dubious thermometers. Instead, they use a large collection of geochemical (isotope) proxies for SST in an analysis constrained by climate change patterns defined by GCMs. They find cooling of 6.1°C (95% confidence: 5.7–6.5°C) for the interval 23–19 kyBP. A similarly constrained global analysis by Osman et al. [50] finds LGM cooling at 21–18 kyBP of 7.0 ± 1°C (95% confidence). Tierney (priv. comm.) attributes the difference between the two studies to the broader time interval of the former study, and concludes that peak LGM cooling was near 7°C.

Seltzer et al. [51] use the temperature-dependent solubility of dissolved noble gases in ancient groundwater to show that land areas between 45°S and 35°N cooled 5.8 ± 0.6°C in the LGM. This cooling is consistent with 1 km lowering of alpine snowlines found by Rind and Peteet [24]. Land response to a forcing exceeds ocean response, but polar amplification makes the global response as large as the low latitude land response in GCM simulations with fixed ice sheets (Supplementary Material Fig. S3). When ice sheet growth is added, cooling amplification at mid and high latitudes is greater [7], making 5.8°C cooling of low latitude land consistent with global cooling of ∼7°C.

LGM CO 2 , CH 4 and N 2 O amounts are known accurately with the exception of N 2 O in the PGM when N 2 O reactions with dust in the ice core corrupt the data. We take PGM N 2 O as the mean of the smallest reported PGM amount and the LGM amount; potential error in the N 2 O forcing is ∼0.01 W/m2. We calculate CO 2 , CH 4 , and N 2 O forcings using Equation (4) and formulae for each gas in Supplementary Material for the periods shown by green bars in Fig. 3. The Eemian period avoids early CO 2 and temperature spikes, assuring that Earth was in energy balance. Between the LGM (19–21 kyBP) and Holocene (6.5–7.5 kyBP), GHG forcing increased 2.25 W/m2 with 77% from CO 2 . Between the PGM and Eemian, GHG forcing increased 2.30 W/m2 with 79% from CO 2 .

Figure 3. Open in new tabDownload slide Dome C temperature (Jouzel et al. [40]) and multi-ice core GHG amounts (Schilt et al. [47]). Green bars (1–5, 6.5–7.5, 18–21, 120–126, 137–144 kyBP) are periods of calculations.

Glacial-interglacial aerosol changes are not included as a forcing. Natural aerosol changes, like clouds, are fast feedbacks. Indeed, aerosols and clouds form a continuum and distinction is arbitrary as humidity approaches 100%. There are many aerosol types, including VOCs (volatile organic compounds) produced by trees, sea salt produced by wind and waves, black and organic carbon produced by forest and grass fires, dust produced by wind and drought, and marine biologic dimethyl sulfide and its secondary aerosol products, all varying geographically and in response to climate change. We do not know, or need to know, natural aerosol properties in prior eras because their changes are feedbacks included in the climate response. However, human-made aerosols are a climate forcing (an imposed perturbation of Earth’s energy balance). Humans may have begun to affect gases and aerosols in the latter Holocene (Aerosols section), but we minimize that issue by using the 6.5–7.5 kyBP window to evaluate climate sensitivity.

Earth’s surface change is the other forcing needed to evaluate ECS: (1) change of surface albedo (reflectivity) and topography by ice sheets, (2) vegetation change, e.g. boreal forests replaced by brighter tundra, and (3) continental shelves exposed by lower sea level. Forcing by all three can be evaluated at once with a GCM. Accuracy requires realistic clouds, which shield the surface. Clouds are the most uncertain feedback [52]. Evaluation is ideal for CMIP [53] (Coupled Model Intercomparison Project) collaboration with PMIP [54] (Paleoclimate Modelling Intercomparison Project); a study of LGM surface forcing could aid GCM development and assessment of climate sensitivity. Sherwood et al. [21] review studies of LGM ice sheet forcing and settle on 3.2 ± 0.7 W/m2, the same as IPCC AR4 [55]. However, some GCMs yield efficacies as low as ∼0.75 [56] or even ∼0.5 [57], likely due to cloud shielding. We found [7] a forcing of −0.9 W/m2 for LGM vegetation by using the Koppen [58] scheme to relate vegetation to local climate, but we thought the model effect was exaggerated as real-world forests tends to shake off snow albedo effects. Kohler et al. [59] estimate a continental shelf forcing of −0.67 W/m2. Based on an earlier study [60] (hereafter Target CO 2 ), our estimate of LGM-Holocene surface forcing is 3.5 ± 1 W/m2. Thus, LGM (18–21 kyBP) cooling of 7°C relative to mid-Holocene (7 kyBP), GHG forcing of 2.25 W/m2, and surface forcing of 3.5 W/m2 yield an initial ECS estimate 7/(2.25 + 3.5) = 1.22°C per W/m2. We discuss uncertainties in Equilibrium climate sensitivity section.

PGM-Eemian global warming provides a second assessment of ECS, one that avoids concern about human influence. PGM-Eemian GHG forcing is 2.3 W/m2. We estimate surface albedo forcing as 0.3 W/m2 less than in the LGM because sea level was about 10 m higher during the PGM [61]. North American and Eurasian ice sheet sizes differed between the LGM and PGM [62], but division of mass between them has little effect on the net forcing (Supplementary Fig. S4 [60]). Thus, our central estimate of PGM-Eemian forcing is 5.5 W/m2. Eemian temperature reached about +1°C warmer than the Holocene [63], based on Eemian SSTs of +0.5 ± 0.3°C relative to 1870–1889 [64], or +0.65 ± 0.3°C SST and +1°C global (land plus ocean) relative to 1880–1920. However, the PGM was probably warmer than the LGM; it was warmer at Dome C (Fig. 2), but cooler at Dronning Maud Land [65]. Based on deep ocean temperatures (Cenozoic Era section), we estimate PGM-Eemian warming as 0.5°C greater than LGM-Holocene warming, that is 7.5°C. The resulting ECS is 7.5/5.5 = 1.36°C per W/m2. Although PGM temperature lacks quantification comparable to that of Seltzer et al. [51] and Tierney et al. [49] for the LGM, the PGM-Eemian warming provides support for the high ECS inferred from LGM-Holocene warming.

We conclude that ECS for climate in the Holocene-LGM range is 1.2°C ± 0.3°C per W/m2, where the uncertainty is the 95% confidence range. The uncertainty estimate is inherently subjective, as it depends mainly on the ice age surface albedo forcing. The GHG forcing and glacial-interglacial temperature change are well-defined, but the efficacy of ice age surface forcing varies among GCMs. This variability is likely related to cloud shielding of surface albedo, which reaffirms the need for a focus on precise cloud observations and modeling.

State dependence of climate sensitivity

ECS based on glacial-interglacial climate is an average for global temperatures −7°C to +1°C relative to the Holocene and in general differs for other climate states because water vapor, aerosol-cloud and sea ice feedbacks depend on the initial climate. However, ECS is rather flat between today’s climate and warmer climate, based on a study [66] covering a range of 15 CO 2 doublings using an efficient GCM developed by Gary Russell [67]. Toward colder climate, ice-snow albedo feedback increases nonlinearly, reaching snowball Earth conditions—with snow and ice on land reaching sea level in the tropics—when CO 2 declines to a quarter to an eighth of its 1950 abundance (Fig. 7 of the study) [66]. Snowball Earth occurred several times in Earth’s history, most recently about 600 million years ago [68] when the Sun was 6% dimmer [69] than today, a forcing of about –12 W/m2. Toward warmer climate, the water vapor feedback increases as the tropopause rises [70], the tropopause cold trap disappearing at 32 × CO 2 (Fig. 7) [66]. However, for the range of ECS of practical interest—say from half preindustrial CO 2 to 4 × CO 2 —state dependence of ECS is small compared to state dependence of ESS.

Earth system sensitivity (ESS) includes amplifying feedbacks of GHGs and ice sheets [71]. When we consider CO 2 change as a known forcing, other GHGs provide a feedback that is smaller than the ice sheet feedback, but not negligible. Ice core data on GHG amounts show that non-CO 2 GHGs—including O 3 and stratospheric H 2 O produced by changing CH 4 —provide about 20% of the total GHG forcing, not only on average for the full glacial-interglacial change, but as a function of global temperature right up to +1°C global temperature relative to the Holocene (Supplementary Fig. S5). Atmospheric chemistry modeling suggests that non-CO 2 GHG amplification of CO 2 forcing by about a quarter continues into warmer climate states [72]. Thus, for climate change in the Cenozoic era, we approximate non-CO 2 GHG forcing by increasing the CO 2 forcing by one-quarter.

Ice sheet feedback, in contrast to non-CO 2 GHG feedback, is highly nonlinear. Preindustrial climate was at most a few halvings of CO 2 from runaway snowball Earth and LGM climate was even closer to that climate state. The ice sheet feedback is reduced as Earth heads toward warmer climate today because already two-thirds of LGM ice has been lost. Yet remaining ice on Antarctica and Greenland constitutes a powerful feedback, which humanity is about to bring into play. We can illuminate that feedback and the climate path Earth is now on by examining data on the Cenozoic era—which includes CO 2 levels comparable to today’s amount—but first we must consider climate response time.

Climate response time

In this section we define response functions for global temperature and Earth’s energy imbalance that help reveal the physics of climate change. Cloud feedbacks amplify climate sensitivity and thus increase eventual heat uptake by the ocean, but cloud feedbacks also have the potential to buffer the rate at which the ocean takes up heat, thus increasing climate response time.

Climate response time was surprisingly long in our climate simulations [7] for the 1982 Ewing Symposium. The e-folding time—the time for surface temperature to reach 63% of its equilibrium response—was about a century. The only published atmosphere-ocean GCM—that of Bryan and Manabe [73]—had a response time of 25 years, while several simplified climate models referenced in our Ewing paper had even faster responses. The longer response time of our climate model was largely a result of high climate sensitivity—our model had an ECS of 4°C for 2 × CO 2 while the Bryan and Manabe model had an ECS of 2°C.

The physics is straightforward. If the delay were a result of a fixed source of thermal inertia, say the ocean’s well-mixed upper layer, response time would increase linearly with ECS because most climate feedbacks come into play in response to temperature change driven by the adjusted forcing, not in direct response to the forcing. Thus, a model with ECS of 4°C takes twice as long to reach full response as a model with ECS of 2°C, if the mixed layer provides the only heat capacity. However, while the mixed layer is warming, there is exchange of water with the deeper ocean, which slows the mixed layer warming. The longer response time with high ECS allows more of the ocean to come into play. If mixing into the deeper ocean is approximated as diffusive, surface temperature response time is proportional to the square of climate sensitivity [74].

Slow climate response accentuates need for the ‘anticipation’ that E.E. David, Jr spoke about. If ECS is 4.8°C (1.2°C per W/m2), more warming is in the pipeline than widely assumed. GHG forcing today already exceeds 4 W/m2. Aerosols reduce the net forcing to about 3 W/m2, based on IPCC estimates (Aerosols section), but warming still in the pipeline for 3 W/m2 forcing is 2.4°C, exceeding warming realized to date (1.2°C). Slow feedbacks increase the equilibrium response even further (Summary section). Large warmings can be avoided via a reasoned policy response, but definition of effective policies will be aided by an understanding of climate response time.

Temperature response function

] at the 2008 American Geophysical Union meeting, JEH argued that the ocean in many GCMs had excessive mixing, and he suggested that GCM groups all report the response function of their models—the global temperature change versus time in response to instant CO 2 doubling with the model run long enough to approach equilibrium. The response function characterizes a climate model and enables a rapid estimate of the global mean surface temperature change in response to any climate forcing scenario: T G t = ∫ [ d T G ( t ) / dt ] dt = ʃ λ × R t d F e / dt dt . (5) In the Bjerknes lecture [ 75 ] at the 2008 American Geophysical Union meeting, JEH argued that the ocean in many 5 GCMs had excessive mixing, and he suggested that GCM groups all report the response function of their models—the global temperature change versus time in response to instant COdoubling with the model run long enough to approach equilibrium. The response function characterizes a climate model and enables a rapid estimate of the global mean surface temperature change in response to any climate forcing scenario:

T G is the Green’s function estimate of global temperature at time t, λ (°C per W/m2) the model’s equilibrium sensitivity, R the dimensionless temperature response function (% of equilibrium response), and dF e the forcing change per unit time, dt. Integration over time begins when Earth is in near energy balance, e.g. in preindustrial time. The response function yields an accurate estimate of global temperature change for a forcing that does not cause reorganization of ocean circulation. Accuracy of this approximation for temperature for one climate model is shown in Chart 15 in the Bjerknes presentation and wider applicability has been demonstrated [76].

We study ocean mixing effects by comparing two GCMs: GISS (2014) [77] and GISS (2020) [33], both models6 described by Kelley et al. [32].Ocean mixing is improved in GISS (2020) by use of a high-order advection scheme [78], finer upper-ocean vertical resolution (40 layers), updated mesoscale eddy parameterization, and correction of errors in the ocean modeling code [32]. The GISS (2020) model has improved variability, including the Madden-Julian Oscillation (MJO), El Nino Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO), but the spectrum of ENSO-like variability is unrealistic and its amplitude is excessive, as shown by the magnitude of oscillations in Fig. 4a. Ocean mixing in GISS (2020) may still be excessive in the North Atlantic, where the model’s simulated penetration of CFCs is greater than observed [79].

Figure 4. Open in new tabDownload slide (a) Global mean surface temperature response to instant CO 2 doubling and (b) normalized response function (percent of final change). Thick lines in Figs 4 and 5 are smoothed (yr1 no smoothing; yr2 3-yr mean; yr3–12 5-yr mean, yr13–300 25-yr mean; yr301–5000 101-yr mean).

Despite reduced ocean mixing, the GISS (2020) model surface temperature response is no faster than in the GISS (2014) model (Fig. 4b): it takes 100 years to reach within 1/e of the equilibrium response. Slow response is partly explained by the larger ECS of the GISS (2020) model, which is 3.5°C versus 2.7°C for the GISS (2014) model, but something more is going on in the newer model, as exposed by the response function of Earth’s energy imbalance.

Earth’s energy imbalance (EEI)

When a forcing perturbs Earth’s energy balance, the imbalance drives warming or cooling to restore balance. Observed EEI is now of order +1 W/m2 (more energy coming in than going out) [80]. High accuracy of EEI is obtained by tracking ocean warming—the main repository for excess energy—and adding heat stored in warming continents and heat used in net ice melt [80]. Heat storage in air adds a small amount. Radiation balance measured from Earth-orbiting satellites cannot by itself define the absolute imbalance, but, when anchored to an in situ EEI value for a sufficient interval (e.g. 10 years), satellite Earth radiation budget observations [81] provide invaluable EEI data on finer temporal and spatial scales than the in situ data.

After a step-function forcing is imposed, EEI and global surface temperature must each approach a new equilibrium, but EEI does so more rapidly, especially for the GISS (2020) model (Fig. 5). EEI in GISS (2020) needs only a decade to reach within 1/e of full response (Fig. 5b), but global surface temperature requires a century (Fig. 4b). Rapid decline of EEI—to half the forcing in 5 years (Fig. 5a)—has practical implications. First, EEI defines the rate heat is pumped into the ocean, so if EEI is reduced, ocean warming is slowed. Second, rapid EEI decline implies that it is wrong to assume that global warming can be stopped by a reduction of climate forcing by the amount of EEI. Instead, the required reduction of forcing is larger than EEI. The difficulty in finding additional reduction in climate forcing of even a few tenths of a W/m2 is substantial [63]. Calculations that help quantify this matter are discussed in Supplementary Material section SM8.

Figure 5. Open in new tabDownload slide (a) Earth’s energy imbalance (EEI) for 2 × CO 2 , and (b) EEI normalized response function.

What is the physics behind the fast response of EEI? The 2 × CO 2 forcing and initial EEI are both nominally 4 W/m2. In the GISS (2014) model, the decline of EEI averaged over the first year is 0.5 W/m2 (Fig. 5a), a moderate decline that might be largely caused by warming continents and thus increased heat radiation to space. In contrast, EEI declines 1.3 W/m2 in the GISS (2020) model (Fig. 5a). Such a huge, immediate decline of EEI implies existence of an ultrafast climate feedback. Climate feedbacks are the heart of climate change and warrant discussion.

Slow, fast and ultrafast feedbacks

Charney et al. [4] described climate feedbacks without discussing time scales. At the 1982 Ewing Symposium, water vapor, clouds and sea ice were described as ‘fast’ feedbacks [7] presumed to change promptly in response to global temperature change, as opposed to ‘slow’ feedbacks or specified boundary conditions such as ice sheet size, vegetation cover, and atmospheric CO 2 amount, although it was noted that some specified boundary conditions, e.g. vegetation, in reality may be capable of relatively rapid change [7].

The immediate EEI response (Fig. 5a) implies a third feedback time scale: ultrafast. Ultrafast feedbacks are not a new concept. When CO 2 is doubled, the added infrared opacity causes the stratosphere to cool. Instant EEI upon CO 2 doubling is only F i = +2.5 W/m2, but stratospheric cooling quickly increases EEI to +4 W/m2 [82]. All models calculate a similar radiative effect, so it is useful to define an adjusted forcing, F a , which is superior to F i as a measure of climate forcing. In contrast, if cloud change—the likely cause of the present ultrafast change—is lumped into the adjusted forcing, each climate model has its own forcing, losing the merit of a common forcing.

Kamae et al. [83] review rapid cloud adjustment distinct from surface temperature-mediated change. Clouds respond to radiative forcing, e.g. via effects on cloud particle phase, cloud cover, cloud albedo and precipitation [84]. The GISS (2020) model alters glaciation in stratiform mixed-phase clouds, which increases supercooled water in stratus clouds, especially over the Southern Ocean [Fig. 1 in the GCM description [32]]. The portion of supercooled cloud water drops goes from too little in GISS (2014) to too much in GISS (2020). Neither model simulates well stratocumulus clouds, yet the models help expose real-world physics that affects climate sensitivity and climate response time. Several models in CMIP6 comparisons find high ECS [84]. For the sake of revealing the physics, it would be useful if the models defined their temperature and EEI response functions. Model runs of even a decade can define the important part of Figs 4a and 5a. Many short (e.g. 2-year) 2 × CO 2 climate simulations with each run beginning at a different point in the model’s control run, can define cloud changes to an arbitrary accuracy.

Cenozoic era

In this section, we use ocean sediment core data to explore climate change in the past 66 million years. This allows us to study warmer climates that are relevant to human-made climate forcing.

High equilibrium climate sensitivity that we have inferred, ECS = 1.2°C ± 0.3°C per W/m2, may affect interpretation of warmer climates. GCMs have difficulty in producing Pliocene warmth [85], especially in the Arctic, without large—probably unrealistic—CO 2 amounts. In addition, a coupled GCM/ice sheet model needs 700–840 ppm CO 2 for transition between glaciated and unglaciated Antarctica [86]. Understanding of these climate states is hampered by uncertainty in the forcings that maintained the climate, as proxy measures of CO 2 have large uncertainty.

Theory informs us that CO 2 is the principal control knob on global temperature [87]. Climate of the past 800 000 years demonstrates (Fig. 2) the tight control. Our aim here is to extract Cenozoic surface temperature history from the deep ocean oxygen isotope δ18O and infer Cenozoic CO 2 history. Oxygen isotope data has high temporal resolution for the entire Cenozoic, which aids understanding of Cenozoic climate change and resulting implications for future climate. Our CO 2 analysis is a complement to proxy CO 2 measurements. Despite progress in estimating CO 2 via carbon isotopes in alkenones and boron isotopes in planktic foraminifera [88], there is wide scatter among results and fossil plant stomata suggest smaller CO 2 amounts [89].

Deep ocean temperature and sea level from δ18O

2 oscillations ( ) involve exchange of carbon among surface carbon reservoirs: the ocean, atmosphere, soil and biosphere. Total CO 2 in the reservoirs also can vary, mainly on longer time scales, as carbon is exchanged with the solid Earth. CO 2 then becomes a primary agent of long-term climate change, leaving orbital effects as ‘noise’ on larger climate swings. Oxygen isotopic composition of benthic (deep ocean dwelling) foraminifera shells provides a starting point for analysis of Cenozoic temperature. includes the recent high-resolution record of Westerhold et al. [ ] and data of Zachos et al. [ ] that have been used for many studies in the past quarter century. When Earth has negligible ice sheets, δ18O (18O amount relative to a standard), provides an estimate of deep ocean temperature (right scale in ) [ ]. T do ° C = - 4 δ 18 O + 12. (6) Glacial-interglacial COoscillations ( Fig. 2 ) involve exchange of carbon among surface carbon reservoirs: the ocean, atmosphere, soil and biosphere. Total COin the reservoirs also can vary, mainly on longer time scales, as carbon is exchanged with the solid Earth. COthen becomes a primary agent of long-term climate change, leaving orbital effects as ‘noise’ on larger climate swings. Oxygen isotopic composition of benthic (deep ocean dwelling) foraminifera shells provides a starting point for analysis of Cenozoic temperature. Figure 6 includes the recent high-resolution record of Westerhold et al. [ 90 ] and data of Zachos et al. [ 44 ] that have been used for many studies in the past quarter century. When Earth has negligible ice sheets, δO (O amount relative to a standard), provides an estimate of deep ocean temperature (right scale in Fig. 6 ) [ 44 ].

Figure 6. Open in new tabDownload slide Global deep ocean δ18O. Black line: Westerhold et al. [90] data in 5 kyr bins until 34 MyBP and subsequently 2 kyr bins. Green line: Zachos et al. [44] data at 1 Myr resolution. Lower left: velocity [91] of Indian tectonic plate. PETM = Paleocene Eocene Thermal Maximum; EECO = Early Eocene Climatic Optimum; Oi-1 marks the transition to glaciated Antarctica; MCO = Miocene Climatic Optimum; NAIP = North Atlantic Igneous Province.

This equation is used for the early Cenozoic, up to the large-scale glaciation of Antarctica at ∼34 MyBP (Oi-1in Fig. 6). At larger δ18O (colder climate), lighter 16O evaporates preferentially from the ocean and accumulates in ice sheets. In Zachos data, δ18O increases by 3 between Oi-1 and the LGM. Half of this δ18O change is due to the 6°C change of deep ocean temperature between Oi-1 (5°C) and the LGM (–1°C) [92]. The other 1.5 of δ18O change is presumed to be due to the ∼180 m sea level (SL) change between ice-free Earth and the LGM, with ∼60 m from Antarctic ice and 120 m from Northern Hemisphere ice. Thus, as an approximation to extract both SL and T do from δ18O, Hansen et al. [66] assumed that SL rose linearly by 60 m as δ18O increased from 1.75 to 3.25 and linearly by 120 m as δ18O increased from 3.25 to 4.75.

18O time series differ ( ) mainly because of different sites of the sediment cores and the way multiple sites are stacked to obtain a time series for the full Cenozoic. For example, mid-Holocene (6–8 kyBP) values of δ18O in the Z and W data sets are δ18 O H Z = 3.32 and δ18 O H W = 3.88. Thus, the Z and W δ18O time series require separate equations for sea level (SL) and deep ocean temperature (T do ) [ ]: S L Z m = 60 - 38.2 δ 18 O - 1.75 ( δ 18 O < 3.32 , maximum SL = + 60 m ) , (7) S L W m = 60 - 25.2 δ 18 O - 1.5 ( δ 18 O < 3.88 , maximum SL = + 60 m ) , (8) S L Z m = - 120 δ 18 O - 3.32 1.58 ( δ 18 O > 3.32 ) , (9) S L W m = - 120 δ 18 O - 3.88 1.42 ( δ 18 O > 3.88 ) , (10) 18O midpoints at the Oi-1 transition for the Z and W data sets. and are based on δ18 O LGM Z = 4.9 and δ18 O LGM W = 5.3 with SL = 0 today. T do equations are based on specified Holocene and LGM T do of 1°C [ ] and −1°C [ ], respectively. Coefficients in the T do equations are calculated as shown by the example. T do Z ° C = 5 - 2.55 δ 18 O - 1.75 1.75 < δ 18 O < 3.32 , (11) T do Z ° C = 1 - 2 δ 18 O - 3.32 / ( 4.9 - 3.32 ) = 1 - 1.27 ( δ 18 O - 3.32 ) 3.32 < δ 18 O , (12) T do W ° C = 6 - 2.10 δ 18 O - 1.5 1.5 < δ 18 O < 3.88 , (13) T do W ° C = 1 - 1.41 δ 18 O - 3.88 3.88 < δ 18 O . (14) The Zachos (Z) and Westerhold (W) δO time series differ ( Fig. 6 ) mainly because of different sites of the sediment cores and the way multiple sites are stacked to obtain a time series for the full Cenozoic. For example, mid-Holocene (6–8 kyBP) values of δO in the Z and W data sets are δ= 3.32 and δ= 3.88. Thus, the Z and W δO time series require separate equations for sea level (SL) and deep ocean temperature (T) [ 66 ]:where 1.75 and 1.5 are δO midpoints at the Oi-1 transition for the Z and W data sets. Equations (9) and (10) are based on δ= 4.9 and δ= 5.3 with SL = 0 today. Tequations are based on specified Holocene and LGM Tof 1°C [ 93 ] and −1°C [ 92 ], respectively. Coefficients in the Tequations are calculated as shown by the Equation (12) example.

Zachos and Westerhold δ18O, SL and T do for the full Cenozoic, Pleistocene, and the past 800 000 years are graphed in Supplementary Material and sea level is compared to data of Rohling et al. [94]. We focus on the finer resolution W data. Differences between the W and Z data and interpretation of those differences are discussed in Paleocene Eocene Thermal Maximum section.

Cenozoic T S

In this section we combine the rich detail in T do provided by benthic δ18O with constraints on the range of Cenozoic T S from surface proxies to produce an estimated history of Cenozoic T S .

We expect T do change, which derives from sea surface temperature (SST) at high latitudes where deepwater forms, to approximate T S change when T do is not near the freezing point. Global SST change understates global T S (land plus ocean) change because land temperature response to a forcing exceeds SST response [95], e.g. the equilibrium global SST response of the GISS (2020) GCM to 2 × CO 2 is 70.6% of the global (land plus ocean) response. However, polar amplification of the SST response tends to compensate for SST undershoot of global T S change. Compensation is nearly exact at latitudes of North Atlantic deepwater formation for 2 × CO 2 climate change in the GISS (2020) climate model (Fig. 7a), but Southern Hemisphere polar amplification does not fully cover the 60–75°S latitudes where Antarctic bottom water forms.

Figure 7. Open in new tabDownload slide (a) Ratio of ΔSST (latitude) to global T S change for all ocean and the Atlantic Ocean, based on equilibrium response (years 4001–4500) in 2 × CO 2 simulations of GISS (2020) model. (b) ΔT, the amount by which T S change exceeds T do change, based on an exponential fit to the two data points provided by the Holocene and LGM (see text).

do nears the freezing point, ice forms, adhering to the Antarctic continent, extending today to a depth of about 2 km, and also forming floating ice shelves. From the Holocene toward colder climate, the effect on temperature change is large: T S declines 7°C between the Holocene and LGM, but T do declines only 2°C (from 1°C to –1°C). From the Holocene toward hotter climate, we expect a smaller effect that we quantify by first neglecting the effect and finding how far we underestimate EECO temperature. Thus, as an initial approximation we assume ΔT S = ΔT do : T S ∼ T do - T doH + 14 ° C = T do + 13 ° C , ( δ 18 O < δ 18 O H ) (15) S as 14°C and T doH as 1°C. In this initial approximation, we interpolate linearly for climate colder than the Holocene, the LGM being ∼7°C cooler than the Holocene: T S = 14 ° C - 7 ° C × ( δ 18 O - δ 18 O H ) / ( δ 18 O LGM - δ 18 O H ) ( δ 18 O > δ 18 O H ) (16) As Tnears the freezing point, ice forms, adhering to the Antarctic continent, extending today to a depth of about 2 km, and also forming floating ice shelves. From the Holocene toward colder climate, the effect on temperature change is large: Tdeclines 7°C between the Holocene and LGM, but Tdeclines only 2°C (from 1°C to –1°C). From the Holocene toward hotter climate, we expect a smaller effect that we quantify by first neglecting the effect and finding how far we underestimate EECO temperature. Thus, as an initial approximation we assume ΔT= ΔTwhere we take Holocene Tas 14°C and Tas 1°C. In this initial approximation, we interpolate linearly for climate colder than the Holocene, the LGM being ∼7°C cooler than the Holocene:

S is ∼27°C ( ). As expected, this initial approximation undershoots EECO T S , which Zhu et al. [ ] infer to be 29°C from a proxy-constrained full-field analysis using a GCM to account for the pattern of temperature change. Moderate undershoot (ΔT = 2°C) of EECO T S is consistent with expectation that global warming of a few degrees would remove Antarctic ice shelves and allow polar amplification to fully cover regions of deepwater formation. Moreover, ΔT of 2°C at the Holocene and 5°C more between the Holocene and LGM are fit well by an exponential function between Antarctic glaciation and the LGM, as needed for ΔT to asymptote at the freezing point ( ). Thus, we take T S as T S = T do - Δ T + 15 ° C = T do - 0.35 e 0.8 X - 1 + 15 ° C , (17) 18O − δ18O Oi-1 and T S is normalized to 14°C in the Holocene. Resulting EECO (Early Eocene Climatic Optimum) Tis ∼27°C ( Fig. 8a ). As expected, this initial approximation undershoots EECO T, which Zhu et al. [ 96 ] infer to be 29°C from a proxy-constrained full-field analysis using a GCM to account for the pattern of temperature change. Moderate undershoot (ΔT = 2°C) of EECO Tis consistent with expectation that global warming of a few degrees would remove Antarctic ice shelves and allow polar amplification to fully cover regions of deepwater formation. Moreover, ΔT of 2°C at the Holocene and 5°C more between the Holocene and LGM are fit well by an exponential function between Antarctic glaciation and the LGM, as needed for ΔT to asymptote at the freezing point ( Fig. 7b ). Thus, we take Taswhere X = δO − δand Tis normalized to 14°C in the Holocene.

Figure 8. Open in new tabDownload slide Cenozoic temperature based on linear (Equations 15 and 16) and nonlinear (Equation 17) analyses. Antarctic Dome C data [40] (red) relative to last 1000 years are multiplied by 0.6 to account for polar amplification and 14°C is added for absolute scale.

The result is a consistent analysis of global T S for the entire Cenozoic (Fig. 8b). Oxygen isotope δ18O of deep ocean foraminifera reproduces glacial-interglacial temperature change well; more detailed agreement is not expected as Antarctic ice core data are for a location that moves, especially in altitude. Our interest is in warmer global climate and its relevance to upcoming human-caused climate change. For that purpose, we want to know the forcing that drove Cenozoic climate change. With the assumption that non-CO 2 GHG forcings provide 20% of the total GHG forcing, it is not difficult to infer the CO 2 abundance required to cause the Cenozoic temperature history in Fig. 8b. Considering the large disagreement among proxy CO 2 measures, this indirect measure of CO 2 via global T S may provide the most accurate Cenozoic CO 2 history.

Cenozoic CO 2

2 history required to yield the Cenozoic T S history from the relation Δ F t = T S t - 14 ° C / ECS , (18) 2 forcing by non-CO 2 GHGs and ice sheets. The GHG amplification factor is taken as 1.25 throughout the Cenozoic (State dependence of climate sensitivity section). The amplification applies to solar forcing as well as CO 2 forcing because it is caused by temperature change, not by CO 2 . Solar irradiance is increasing 10% per billion years [ ]; thus solar forcing (240 W/m2 today) increases 2.4 W/m2 per 100 million years. Thus, Δ F t = 1.25 × Δ F CO 2 t + Δ F Sol t × A S . ( δ 18 O > δ 18 O H ) (19) We obtain the COhistory required to yield the Cenozoic Thistory from the relationwhere ΔF(t) (0 at 7 kyBP) includes changing solar irradiance and amplification of COforcing by non-COGHGs and ice sheets. The GHG amplification factor is taken as 1.25 throughout the Cenozoic (State dependence of climate sensitivity section). The amplification applies to solar forcing as well as COforcing because it is caused by temperature change, not by CO. Solar irradiance is increasing 10% per billion years [ 69 ]; thus solar forcing (240 W/mtoday) increases 2.4 W/mper 100 million years. Thus,

S , surface albedo amplification, is smaller in moving from the Holocene to warmer climate—when the main effect is shrinking of Antarctic ice—than toward colder climate. For δ18O > δ18O H , we take A S as its average value over the period from the Holocene to the LGM: A S = F Ice + F GHG F GHG = 3.5 + 2.25 2.25 = 2. 55. ( δ 18 O > δ 18 O H ) (20) , surface albedo amplification, is smaller in moving from the Holocene to warmer climate—when the main effect is shrinking of Antarctic ice—than toward colder climate. For δO > δ, we take Aas its average value over the period from the Holocene to the LGM:

Δ F t = 3.19 × Δ F CO 2 t + Δ F Sol t . ( δ 18 O > δ 18 O H ) (21) Thus, for climate colder than the Holocene,

18O Oi-1 < δ18O < δ18O H , Δ F t = 1.25 × Δ F CO 2 t + Δ F Sol t + F IceH × δ 18 O H - δ 18 O δ 18 O H - δ 18 O Oi - 1 . (22) For climate warmer than the Holocene up to Oi-1, i.e. for δ< δO < δ

IceH , the (Antarctic plus Greenland) ice sheet forcing between the Holocene and Oi-1, is estimated to be 2 W/m2 ( Supplementary Fig. S4 2 ). For climate warmer than Oi-1 Δ F t = 1.25 × [ Δ F CO 2 ( t ) + Δ F Sol ( t ) + Δ F IceH ] (23) , the (Antarctic plus Greenland) ice sheet forcing between the Holocene and Oi-1, is estimated to be 2 W/m, Target CO). For climate warmer than Oi-1

All quantities are known except ΔF CO2 (t), which is thus defined. Cenozoic CO 2 (t) for specified ECS is obtained from T S (t) using the CO 2 radiative forcing equation (Table 1, Supplementary Material). Resulting CO 2 (Fig. 9) is about 1,200 ppm at the EECO, 450 ppm at Oi-1, and 325 ppm in the Pliocene for ECS = 1.2°C per W/m2. For ECS = 1°C—about as low as we believe plausible—Pliocene CO 2 is near 350 ppm, rising only to ∼500 ppm at Oi-1 and ∼1500 ppm at EECO.

Figure 9. Open in new tabDownload slide Cenozoic CO 2 estimated from δ18O of Westerhold et al. (see text). Black lines are for ECS = 1.2°C per W/m2; red and green curves (ECS = 1.0 and 1.4°C per W/m2) are 1 My smoothed. Blue curves (last 800 000 years) are Antarctica ice core data [41].

Assumed Holocene CO 2 amount is also a minor factor. We tested two cases: 260 and 278 ppm (Fig. 9). These were implemented as the CO 2 values at 7 kyBP, but Holocene-mean values are similar—a few ppm less than CO 2 at 7 kyBP. Holocene = 278 ppm increases CO 2 about 20 ppm between today and Oi-1, and about 50 ppm at the EECO. However, Holocene CO 2 278 ppm causes the amplitude of inferred glacial-interglacial CO 2 oscillations to be less than reality (Fig. 9b), providing support for the Holocene 260 ppm level and for the interpretation that high late-Holocene CO 2 was due to human influence. Proxy measures of Cenozoic CO 2 yield a notoriously large range. A recent review [88] constructs a CO 2 history with Loess-smoothed CO 2 ∼700–1100 ppm at Oi-1. That high Oi-1 CO 2 amount is not plausible without overthrowing the concept that global temperature is a response to climate forcings. More generally, we conclude that actual CO 2 during the Cenozoic was near the low end of the range of proxy measurements.

Interpretation of Cenozoic T S and CO 2

In this section we consider Cenozoic T S and CO 2 histories, which are rich in insights about climate change with implications for future climate.

In Target CO 2 [60] and elsewhere [98] we argue that the broad sweep of Cenozoic temperature is a result of plate tectonic (popularly ‘continental drift’) effects on CO 2 . Solid Earth sources and sinks of CO 2 are not balanced at any given time. CO 2 is removed from surface reservoirs by: (1) chemical weathering of rocks with deposition of carbonates on the ocean floor, and (2) burial of organic matter [99, 100]. CO 2 returns via metamorphism and volcanic outgassing at locations where oceanic crust is subducted beneath moving continental plates. The interpretation in Target CO 2 was that the main Cenozoic source of CO 2 was associated with the Indian plate (Fig. 10), which separated from Pangea in the Cretaceous [101, 102] and moved through the Tethys (now Indian) Ocean at a rate exceeding 10 cm/year until collision with the Eurasian plate at circa 50 MyBP. Associated CO 2 emissions include those from formation of the Deccan Traps7 in western India (a large igneous province, LIP, formed by repeated deposition of large-scale flood basalts), the smaller Rajahmundry Traps [103] in eastern India, and metamorphism and vulcanism associated with the moving Indian plate. The Indian plate slowed circa 60 Mya (inset, Fig. 6) before resuming high speed [91], leaving an indelible signature in the Cenozoic δ18O history (Fig. 6) that supports our interpretation of the CO 2 source. Since the continental collision, subduction and CO 2 emissions continue at a diminishing rate as the India plate underthrusts the Asian continent and pushes up the Himalayan mountains [104]. We interpret the decline of CO 2 over the past 50 million years as, at least in part, a decline of the metamorphic source from continued subduction of the Indian plate, but burial of organic matter and increased weathering due to exposure of fresh rock by Himalayan uplift [105] may contribute to CO 2 drawdown. Quantitative understanding of these processes is limited [106], e.g. weathering is both a source and sink of CO 2 [107].

Figure 10. Open in new tabDownload slide Continental configuration 56 MyBP [97]. Continental shelves (light blue) were underwater as little water was locked in ice. The Indian plate was moving north at about 15 cm per year.

This picture for the broad sweep of Cenozoic CO 2 is consistent with current understanding of the long-term carbon cycle [108], but relative contributions of metamorphism [106] and volcanism [109] are uncertain. Also, emissions from rift-induced Large Igneous Provinces (LIPs) [110, 111] contribute to long-term change of atmospheric CO 2 , with two cases prominent in Fig. 6. The Columbia River Flood Basalt at ca. 17–15 MyBP was a principal cause of the Miocene Climatic Optimum [112], but the processes are poorly understood [113]. A more dramatic event occurred as Greenland separated from Europe, causing a rift in the sea floor; flood basalt covered more than a million square kilometers with magma volume 6–7 million cubic kilometers [111]—the North Atlantic Igneous Province (NAIP). Flood basalt volcanism occurred during 60.5–54.5 MyBP, but at 56.1 ± 0.5 MyBP melt production increased by more than a factor of 10, continued at a high level for about a million years, and then subsided (Fig. 5 of Storey et al. [114]). The striking Paleocene-Eocene Thermal Maximum (PETM) δ18O spike (Fig. 6) occurs early in this million-year bump-up of δ18O. Svensen et al. [115] proposed that the PETM was initiated by the massive flood basalt into carbon-rich sedimentary strata. Gutjahr et al. [116] developed an isotope analysis, concluding that most of PETM carbon emissions were volcanic, with climate-driven carbon feedbacks playing a lesser role. Yet other evidence [117], while consistent with volcanism as a trigger for the PETM, suggests that climate feedback—perhaps methane hydrate and peat CO 2 release—may have caused more than half of the PETM warming. Berndt et al. [118] describe extensive shallow-water vents that likely released CH 4 as well as CO 2 during the NAIP activity. We discuss PETM warming and CO 2 levels below, but first we must quantify the mechanisms that drove Cenozoic climate change and consider where Earth’s climate was headed before humanity intervened.

The sum of climate forcings (CO 2 and solar) and slow feedbacks (ice sheets and non-CO 2 GHGs) that maintained EECO warmth was 12.5 W/m2 (Fig. 11). CO 2 forcing of 9.1 W/m2 combined with solar forcing of—1.2 W/m2 to yield a total forcing8 8 W/m2. Slow feedbacks were 4.5 W/m2 forcing (ice albedo = 2 W/m2 and non-CO 2 GHGs = 2.5 W/m2). With today’s solar irradiance, human-made GHG forcing required for Earth to return to EECO warmth is 8 W/m2. Present human-made GHG forcing is 4.6 W/m2 relative to 7 kyBP.9 Equilibrium response to this forcing includes the 2 W/m2 ice sheet feedback and 25% amplification (of 6.6 W/m2) by non-CO 2 GHGs, yielding a total forcing plus slow feedbacks of 8.25 W/m2. Thus, equilibrium global warming for today’s GHGs is 10°C.10 If human-made aerosol forcing is −1.5 W/m2 and remains at that level indefinitely, equilibrium warming for today’s atmosphere is reduced to 8°C. Either 10°C or 8°C dwarfs observed global warming of 1.2°C to date. Most of the equilibrium warming for today’s atmosphere has not yet occurred and need not occur (Earth’s energy imbalance section).

Figure 11. Open in new tabDownload slide Climate forcings and slow feedbacks relative to 7 kyBP from terms in Equations (21–23).

Prospects for another snowball Earth

We would be remiss if we did not comment on the precipitous decline of Earth’s temperature over the last several million years. Was Earth falling off the table into another Snowball Earth?

Global temperature plummeted in the past 50 million years, with growing, violent, oscillations (Figs 6 and 7). Glacial-interglacial average CO 2 declined from about 325 ppm to 225 ppm in the past five million years in an accelerating decline (Fig. 9a). As CO 2 fell to 180 ppm during recent glacial maxima, an ice sheet covered most of Canada and reached midlatitudes in the U.S. Continents in the current supercontinent cycle [101] are now dispersed, with movement slowing to 2–3 cm/year. Emissions from the last high-speed high-impact tectonic event—collision of the Indian plate with Eurasia—are fizzling out. The most recent large igneous province (LIP) event—the Columbia River Flood Basalt about 15 million years ago (Fig. 6)—is no longer a factor, and there is no evidence of another impending LIP. Snowball conditions are possible, even though the Sun’s brightness is increasing and is now almost 6% greater [69] than it was at the last snowball Earth, almost 600 million years ago [68]. Runaway snowball likely requires only 1–2 halvings [66] of CO 2 from the LGM 180 ppm level, i.e. to 45–90 ppm. Although the weathering rate declines in colder climate [119], weathering and burial of organic matter continue, so decrease of atmospheric CO 2 could have continued over millions of years, if the source of CO 2 from metamorphism and vulcanism continued to decline.

Another factor that may have contributed to cooling in the Pliocene is uplift and poleward movement of Greenland that accelerated about 5 MyBP [120], which likely enhanced glaciation of Greenland and should be accounted for in simulations of Pliocene climate change. We conclude that, in the absence of human activity, Earth may have been headed for snowball Earth conditions within the next 10 or 20 million years, but the chance of future snowball Earth is now academic. Human-made GHG emissions remove that possibility on any time scale of practical interest. Instead, GHG emissions are now driving Earth toward much warmer climate.

Paleocene eocene thermal maximum (PETM)

The PETM event provides a benchmark for assessing the potential impact of the human-made climate forcing and the time scale for natural recovery of the climate system.

Westerhold [90] data have 10°C deep ocean warming at the PETM (Figs 8 and 12a), which exceeds proxy-derived surface warming. Low latitude SST data have 3–4°C PETM warming [121]. Tierney et al. [122] obtain PETM global surface warming 5.6°C (5.4–59°C, 95% confidence) via analysis of proxy surface temperature data that accounts for patterns of temperature change. Zachos [44] data have a deep ocean warming similar to the proxy-based surface warming. These warming estimates can be reconciled, but first let’s note the practical importance of the PETM.

Pre-PETM (56–56.4 MyBP) CO 2 is 910 ppm in our analysis for the most likely ECS (1.2°C per W/m2). Peak PETM CO 2 required to yield the 5.6°C global surface warming estimate of Tierney et al. [122] is then 1630 ppm if CO 2 provides 80% of the GHG forcing, thus less than a doubling of CO 2 . (In the unlikely case that CO 2 caused 100% of the GHG forcing, required CO 2 is 1780, not quite a doubling.) CO 2 amounts for ECS = 1.0 and 1.4°C per W/m2 are 1165 and 760 ppm in the pre-PETM and 2260 and 1270 ppm at peak PETM, respectively. In all these ECS cases, the CO 2 forcing of the PETM is less than or about a CO 2 doubling. Our assumed 20% contribution by non-CO 2 GHGs (amplification factor 1.25, Climate sensitivity (ECS and ESS) section), is nominal; Hopcroft et al., e.g. estimate a 30% contribution from non-CO 2 GHGs [123], thus an amplification factor 1.43.

Thus, today’s human-made GHG forcing (4.6 W/m2, growing 0.5 W/m2 per decade) is already at least comparable to the PETM forcing, although the net human-made forcing including aerosols has probably not reached the PETM forcing. However, there are two big differences between the PETM and today. First, there were no large ice sheets on Earth in the PETM era. Ice sheets on Antarctica and Greenland today make Earth system sensitivity (ESS) greater than it was during the PETM. Equilibrium response to today’s GHG climate forcing would include deglaciation of Antarctica and Greenland, sea level rise of 60 m (200 feet), and surface albedo forcing (slow feedback) of 2 W/m2. The second difference between the PETM and today is the rate of change of the climate forcing. Most of today’s climate forcing was introduced in a century, which is 10 times or more faster than the PETM forcing growth. Although a bolide impact [124] has been proposed as a trigger for the PETM, the issue is the time scale on which the climate forcing—increased GHGs—occurred. Despite uncertainty in the carbon source(s), data and modeling point to duration of a millennium or more for PETM emissions [121, 125].

Better understanding of the PETM could inform us on climate feedbacks. Gutjahr et al. [116] argue persuasively that PETM emissions were mostly volcanic, yet we know of no other large igneous province that produced such great, temporally-isolated, emissions. Further, Cenozoic orbitally-driven hyperthermal events [126] testify to large CO 2 feedbacks. Northern peatlands today contain more than 1000 Gt carbon [127], much of which can be mobilized at PETM warming levels [128]. The double peak in deep ocean δ18O (thus in temperature, cf. Fig. 12, where each square is a binning interval of 5000 years) is also found in terrestrial data [129]. Perhaps the sea floor rift occurred in two bursts, or the rift was followed tens of thousands of years later by methane hydrate release as a feedback to the ocean warming; much of today’s methane hydrate is in stratigraphic deposits hundreds of meters below the sea floor, where millennia may pass before a thermal wave from the surface reaches the deposits [130]. Feedback emissions, especially from permafrost, seem to be more chronic than catastrophic, but stabilization of climate may require cooling that terminates growth of those feedbacks (Summary section). The PETM provides perhaps the best empirical check on understanding of the atmospheric lifetime of fossil fuel CO 2 [131], but for that purpose we must untangle as well as possible the time dependence of the PETM CO 2 source and feedbacks. If continuing magma flow or a slow-release feedback is a substantial portion of PETM CO 2 , the CO 2 lifetime inferred from post-PETM CO 2 recovery may be an exaggeration.

Figure 12. Open in new tabDownload slide Temperature and CO 2 implied by Westerhold et al. [90] δ18O, if surface warming equaled deep ocean warming. In reality, the unique PETM event had surface warming ∼5.6°C, which implies a peak PETM CO 2 of about 1630 ppm (see text).

The PETM draws attention to differences between the Westerhold (W) and Zachos (Z) δ18O data. Zachos attributes the larger PETM response in W data to the shallow (less than 1 km) depth of the Walvis Ridge core in the Southeast Atlantic that anchors the PETM period in the W data (see Supplementary Material SM9). Given that the PETM was triggered by a rift in the floor of the North Atlantic and massive lava injection, it is not surprising that ocean temperature was elevated and circulation disrupted during the PETM. Nunes and Norris [132] conclude that ocean circulation changed at the start of the PETM with a shift in location of deep-water formation that delivered warmer waters to the deep sea, a circulation change that persisted at least 40 000 years. With regard to differences in the early Cenozoic, Zachos notes (Supplementary Material SM9) a likely bias in the Z data with a heavy weighting of data from Southern Ocean sites (Kerguelen Plateau and Maud Rise), which were intended for study of climate of Antarctica and the Southern Ocean.

Differences between the W and Z data sets have limited effect on our paper, as we apply separate scaling (Equations 7–14) to W and Z data to match observations at the LGM, mid-Holocene, and Oi-1 points. This approach addresses, e.g. the cumulative effect in combining data splices noted by Zachos in SM9. Further, we set the EECO global temperature relative to the Holocene and the PETM temperature relative to pre-PETM based on proxy-constrained, full-field, GCM analyses of Tierney et al. [122] and Zhu et al. [96] Nevertheless, there is much to learn from more precise study of the Cenozoic in general and the PETM in particular.

Policy implications require first an understanding of the role of aerosols in climate change.

Aerosols

The role of aerosols in climate change is uncertain because aerosol properties are not measured well enough to define their climate forcing. In this section we estimate aerosol climate forcing via aerosol effects on Earth’s temperature and Earth’s energy imbalance.

Aerosol impact is suggested by the gap between observed global warming and expected warming due to GHGs based on ECS inferred from paleoclimate (Fig. 13). Expected warming is from Eq. 5 with the normalized response function of the GISS (2020) model. Our best estimate for ECS, 1.2°C per W/m2, yields a gap of 1.5°C between expected and actual warming in 2022. Aerosols are the likely cooling source. The other negative forcing discussed by IPCC—surface albedo change—is estimated by IPCC (Chapter 7, Table 7.8) to be –0.12 ± 0.1 W/m2, an order of magnitude smaller than aerosol forcing [12]. Thus, for clarity, we focus on GHGs and aerosols.

Figure 13. Open in new tabDownload slide Observed global surface temperature (black line) and expected GHG warming with two choices for ECS. The blue area is the estimated aerosol cooling effect. The temperature peak in the World War II era is in part an artifact of inhomogeneous ocean data in that period [63].

Absence of global warming over the period 1850–1920 (Supplementary Fig. S1 of IPCC AR6 WG1 report [12]) is a clue about aerosol forcing. GHG forcing increased 0.54 W/m2 in 1850–1920, which causes expected warming 0.3–0.4°C by 1920 for ECS = 1.2°C per W/m2 (Equation 5). Natural forcings—solar irradiance and volcanoes—may contribute to lack of warming, but a persuasive case for the required forcing has not been made. Human-made aerosols are the likely offset of GHG warming. Such aerosol cooling is a Faustian bargain [98] because payment in enhanced global warming will come due once we can no longer tolerate the air pollution. Ambient air pollution causes millions of deaths per year, with particulates most responsible [133, 134].

Evidence of aerosol forcing in the Holocene

In this section we infer evidence of human-made aerosols in the last half of the Holocene from the absence of global warming. Some proxy-based analyses [135] report cooling in the last half of the Holocene, but a recent analysis [50] that uses GCMs to overcome spatial and temporal biases in proxy data finds rising global temperature in the first half of the Holocene followed by nearly constant temperature in the last 6000 years until the last few centuries (Fig. 14). Antarctic, deep ocean, and tropical sea surface data all show stable temperature in the last 6000 years (Supplementary Fig. S6 of reference [60]). GHG forcing increased 0.5 W/m2 during those 6000 years (Fig. 15), yet Earth did not warm. Fast feedbacks alone should yield at least +0.5°C warming and 6000 years is long enough for slow feedbacks to also contribute. How can we interpret the absence of warming?

Figure 14. Open in new tabDownload slide Global mean surface temperature change over the past 24 ky, reproduced from Fig. 2 of Osman et al. [50] including Last Millennium reanalysis of Tardif et al. [136].

Figure 15. Open in new tabDownload slide GHG climate forcing in past 20 ky with vertical scale expanded for the past 10 ky on the right. GHG amounts are from Schilt et al. [47]. Formulae for forcing are in Supplementary Material.

Humanity’s growing footprint deserves scrutiny. Ruddiman’s suggestion that deforestation and agriculture began to affect CO 2 6500 year ago and rice agriculture began to affect CH 4 5000 years ago has been criticized [46] mainly because of the size of proposed sources. Ruddiman sought sources sufficient to offset declines of CO 2 and CH 4 in prior interglacial periods, but such large sources are not needed to account for Holocene GHG levels. Paleoclimate GHG decreases are slow feedbacks that occur in concert with global cooling. However, if global cooling did not occur in the past 6000 years, feedbacks did not occur. Earth orbital parameters 6000 years ago kept the Southern Ocean warm, as needed to maintain strong overturning ocean circulation [137] and minimize carbon sequestration in the deep ocean. Maximum insolation at 60°S was in late-spring (mid-November); since then, maximum insolation at 60°S slowly advanced through the year, recently reaching mid-summer (mid-January, Fig. 26b of Ice Melt [13]). Maximum insolation from late-spring through mid-summer is optimum to warm the Southern Ocean and promote early warm-season ice melt, which reduces surface albedo and magnifies regional warming [45].

GHG forcing of –0.2 W/m2 in 10–6 kyBP (Fig. 15) was exceeded by forcing of +1 W/m2 due to ice sheet shrinkage (Supplementary Material in Target CO 2 [60]) for a 40 m sea level rise (Fig. 16). Net 0.8 W/m2 forcing produced expected 1°C global warming (Fig. 14). The mystery is the absence of warming in the past 6000 years. Hansen et al. [45] suggested that aerosol cooling offset GHG warming. Growing population, agriculture and land clearance produced aerosols and CO 2 ; wood was the main fuel for cooking and heating. Nonlinear aerosol forcing is largest in a pristine atmosphere, so it is unsurprising that aerosols tended to offset CO 2 warming as civilization developed. Hemispheric differences could provide a check. GHG forcing is global, while aerosol forcing is mainly in the Northern Hemisphere. Global offset implies a net negative Northern Hemisphere forcing and positive Southern Hemisphere forcing. Thus, data and modeling studies (including orbital effects) of regional response are warranted but beyond the scope of this paper.

Figure 16. Open in new tabDownload slide Sea level since the last glacial period relative to present. Credit: Robert Rohde [138].

Industrial era aerosols

Scientific advances often face early resistance from other scientists [139]. Examples are the snowball Earth hypothesis [140] and the role of an asteroid impact in extinction of non-avian dinosaurs [141], which initially were highly controversial but are now more widely accepted. Ruddiman’s hypothesis, right or wrong, is still controversial. Thus, we minimize this issue by showing aerosol effects with and without preindustrial human-made aerosols.

Global aerosols are not monitored with detail needed to define aerosol climate forcing [142, 143]. IPCC12 estimates forcing (Fig. 17a) from assumed precursor emissions, a herculean task due to many aerosol types and complex cloud effects. Aerosol forcing uncertainty is comparable to its estimated value (Fig. 17a), which is constrained more by observed global temperature change than by aerosol measurements [144]. IPCC’s best estimate of aerosol forcing (Fig. 17) and GHG history define the percent of GHG forcing offset by aerosol cooling—the dark blue area in Fig. 17b. However, if human-made aerosol forcing was −0.5 W/m2 by 1750, offsetting +0.5 W/m2 GHG forcing, this forcing should be included. Such aerosol forcing—largely via effects of land use and biomass fuels on clouds—continues today. Thirty million people in the United States use wood for heating [145]. Such fuels are also common in Europe [146, 147] and much of the world.

Figure 17. Open in new tabDownload slide (a) Estimated greenhouse gas and aerosol forcings relative to 1750 values. (b) Aerosol forcing as percent of GHG forcing. Forcings for dark blue area are relative to 1750. Light blue area adds 0.5 W/m2 forcing estimated for human-caused aerosols from fires, biofuels and land use.

Figure 17b encapsulates two alternative views of aerosol history. IPCC aerosol forcing slowly becomes important relative to GHG forcing. In our view, civilization always produced aerosols as well as GHGs. As sea level stabilized, organized societies and population grew as coastal biologic productivity increased [148] and agriculture developed. Wood was the main fuel. Aerosols travel great distances, as shown by Asian aerosols in North America [149]. Humans contributed to both rising GHG and aerosol climate forcings in the past 6000 years. One result is that human-caused aerosol climate forcing is at least 0.5 W/m2 more than usually assumed. Thus, the Faustian payment that will eventually come due is also larger, as discussed in Summary section.

Ambiguity in aerosol climate forcing

In this section we discuss uncertainty in the aerosol forcing. We discuss why global warming in the past century—often used to infer climate sensitivity—is ill-suited for that purpose.

Recent global warming does not yield a unique ECS because warming depends on three major unknowns with only two basic constraints. Unknowns are ECS, net climate forcing (aerosol forcing is unmeasured), and ocean mixing (many ocean models are too diffusive). Constraints are observed global temperature change and Earth’s energy imbalance (EEI) [80]. Knutti [150] and Hansen [75] suggest that many climate models compensate for excessive ocean mixing (which reduces surface warming) by using aerosol forcing less negative than the real world, thus achieving realistic surface warming. This issue is unresolved and complicated by the finding that cloud feedbacks can buffer ocean heat uptake (Climate response time section), affecting interpretation of EEI.

IPCC AR6 WG1 best estimate of aerosol forcing (Table AIII.3) [12] is near maximum (negative) value by 1975, then nearly constant until rising in the 21st century to –1.09 W/m2 in 2019 (Fig. 18). We use this IPCC aerosol forcing in climate simulations here. We also use an alternative aerosol scenario [151] that reaches –1.63 W/m2 in 2010 relative to 1880 and –1.8 W/m2 relative to 1850 (Fig. 18) based on modeling of Koch [152] that included changing technology factors defined by Novakov [153]. This alternative scenario11 is comparable to the forcing in some current aerosol models (Fig. 18). Human-made aerosol forcing relative to several millennia ago may be even more negative, by about –0.5 W/m2 as discussed above, but the additional forcing was offset by increasing GHGs and thus those additional forcings are neglected, with climate assumed to be in approximate equilibrium in 1850.

Figure 18. Open in new tabDownload slide Aerosol forcing relative to 1850 from IPCC AR6, an alternative aerosol scenario [151] two aerosol model scenarios of Bauer et al. [154].

Many combinations of climate sensitivity and aerosol forcing can fit observed global warming. The GISS (2014) model (ECS = 2.6°C) with IPCC AR6 aerosol forcing can match observed warming (Fig. 19) in the last half century (when human-made climate forcing overwhelmed natural forcings, unforced climate variability, and flaws in observations). However, agreement also can be achieved by climate models with high ECS. The GISS (2020) model (with ECS = 3.5°C) yields greater warming than observed if IPCC aerosol forcing is used, but less than observed for the alternative aerosol scenario (Fig. 19). This latter aerosol scenario achieves agreement with observed warming if ECS ∼4°C (green curve in Fig. 19).12 Agreement can be achieved with even higher ECS by use of a still more negative aerosol forcing.

The issue we raise is the magnitude of the aerosol forcing, with implications for future warming when particulate air pollution is likely to be reduced. We suggest that IPCC reports may have gravitated toward climate sensitivity near 3°C for 2 × CO 2 in part because of difficulty that models have in realistically simulating amplifying cloud feedbacks and a climate model tendency for excessive mixing of heat into the deep ocean. Our finding from paleoclimate analysis that ECS is 1.2°C ± 0.3°C per W/m2 (4.8°C ± 1.2°C for 2 × CO 2 ) implies that the (unmeasured) aerosol forcing must be more negative than IPCC’s best estimate. In turn—because aerosol-cloud interactions are the main source of uncertainty in aerosol forcing—this finding emphasizes the need to measure both global aerosol and cloud particle properties.

The case for monitoring global aerosol climate forcing will grow as recognition of the need to slow and reverse climate change emerges. Aerosol and cloud particle microphysics must be measured with precision adequate to define the forcing [142, 158]. In the absence of such Keeling-like global monitoring, progress can be made via more limited satellite measurements of aerosol and cloud properties, field studies, and aerosol and cloud modeling. As described next, a great opportunity to study aerosol and cloud physics is provided by a recent change in the IMO (International Maritime Organization) regulations on ship emissions.

The great inadvertent aerosol experiment

Sulfate aerosols are cloud condensation nuclei (CCN), so sulfate emissions by ships result in a larger number of smaller cloud particles, thus affecting cloud albedo and cloud lifetime [144]. Ships provide a large percentage of sulfates in the North Pacific and North Atlantic regions (Fig. 20). It has been suggested that cooling by these clouds is overestimated because of cloud liquid water adjustments [159], but Manshausen et al. [160] present evidence that liquid w

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