Young People's Burden: Requirement of Negative CO2 Emissions

Global temperature is a fundamental climate metric highly correlated with sea level, which implies that keeping shorelines near their present location requires keeping global temperature within or close to its preindustrial Holocene range. However, global temperature excluding short-term variability now exceeds +1degC relative to the 1880-1920 mean and annual 2016 global temperature was almost +1.3degC. We show that global temperature has risen well out of the Holocene range and Earth is now as warm as during the prior interglacial, when sea level reached 6-9 meters higher than today. Further, Earth is out of energy balance with present atmospheric composition, implying more warming is in the pipeline, and we show that the growth rate of greenhouse gas climate forcing has accelerated markedly in the past decade. The rapidity of ice sheet and sea level response to global temperature is difficult to predict but is dependent on the magnitude of warming. Targets for limiting global warming should aim to avoid leaving global temperature at Eemian or higher levels for centuries. Such targets require"negative emissions", extraction of CO2 from the air. If phasedown of fossil fuel emissions begins soon, improved agricultural and forestry practices may provide much of the extraction, and the magnitude and duration of global temperature excursion above the natural range of the current interglacial could be limited and irreversible impacts minimized. In contrast, continued high emissions place a burden on young people to undertake massive technological CO2 extraction to limit climate change and its consequences. Proposed methods of extraction have minimal estimated costs of 89-535 trillion dollars this century and have large risks and uncertain feasibility. Continued high emissions unarguably sentences young people to a massive, implausible cleanup, growing deleterious climate impacts or both.

Global temperature is a fundamental climate metric highly correlated with sea level, which implies that keeping shorelines near their present location requires keeping global temperature within or close to its preindustrial Holocene range. However, global temperature excluding short-term variability now exceeds +1°C relative to the 1880-1920 mean and annual 2016 global temperature was almost +1.3°C. We show that global temperature has risen well out of the Holocene range and Earth is now as warm as it was during the prior (Eemian) interglacial period, when sea level reached 6-9 meters higher than today. Further, Earth is out of energy balance with present atmospheric composition, implying that more warming is in the pipeline, and we show that the growth rate of greenhouse gas climate forcing has accelerated markedly in the past decade. The rapidity of ice sheet and sea level response to global temperature is difficult to predict, but is dependent on the magnitude of warming. Targets for limiting global warming thus, at minimum, should aim to avoid leaving global temperature at Eemian or higher levels for centuries. Such targets now require "negative emissions", i.e., extraction of CO 2 from the air. If phasedown of fossil fuel emissions begins soon, improved agricultural and forestry practices, including reforestation and steps to improve soil fertility and increase its carbon content, may provide much of the necessary CO 2 extraction. In that case, the magnitude and duration of global temperature excursion above the natural range of the current interglacial (Holocene) could be limited and irreversible climate impacts could be minimized. In contrast, continued high fossil fuel emissions today place a burden on young people to undertake massive technological CO 2 extraction if they are to limit climate change and its consequences. Proposed methods of extraction such as bioenergy with carbon capture and storage (BECCS) or air capture of CO 2 have minimal estimated costs of 89-535 trillion dollars this century and also have large risks and uncertain feasibility. Continued high fossil fuel emissions unarguably sentences young people to either a massive, implausible cleanup or growing deleterious climate impacts or both.

Introduction
The United Nations 1992 Framework Convention on Climate Change (UNFCCC, 1992) stated its objective as "…stabilization of GHG concentrations in the atmosphere at a level that would prevent dangerous anthropogenic interference with the climate system." The 15 th Conference of the Parties (Copenhagen Accord, 2009) concluded that this objective required a goal to "…reduce global emissions so as to hold the increase of global temperature below 2°C…." The 21 st Conference of the Parties (Paris Agreement, 2015), currently ratified by 120 nations representing 80% of today's greenhouse gas emissions, aims to strengthen the global response to the climate change threat by " [h]olding the increase in the global average temperature to well below 2°C above the pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5°C above the pre-industrial levels." Global surface temperature has many merits as the principal metric for climate change, but additional metrics, such as atmospheric CO 2 amount and Earth's energy imbalance, help refine targets for avoiding dangerous human-made climate change. Paleoclimate data and observations of Earth's present energy imbalance led Hansen et al. (2008Hansen et al. ( , 2013a to recommend reducing CO 2 to less than 350 ppm, with the understanding that this target must be adjusted as CO 2 declines and empirical data accumulates. The 350 ppm CO 2 target is moderately stricter than the 1.5°C warming target. The near planetary energy balance anticipated at 350 ppm CO 2 implies a global temperature close to recent values, i.e., about +1°C relative to preindustrial. We advocate pursuit of this goal within a century to limit the period with global temperature above that of the current interglacial period, the Holocene. 1 Limiting the period and magnitude of temperature excursion above the Holocene range is crucial to avoid strong stimulation of slow feedbacks. Slow feedbacks include ice sheet disintegration and thus sea level rise, which is probably the most threatening climate impact, and release of greenhouse gases (GHGs) via such mechanisms as thawing tundra and loss of soil carbon. Holocene climate stability allowed sea level to be stable for the past several millennia  as civilizations developed. But there is now a danger that temperature rises so far above the Holocene range that slow feedbacks consistent with knowledge of changing climate forcings, Earth's measured energy imbalance, and the canonical estimate of climate sensitivity 3 , i.e., about 3°C global warming 4 for doubled atmospheric CO 2 . For clarity we make global temperature calculations with our simple climate model, which we show (Appendix A2) has a transient climate sensitivity near the midpoint of the sensitivity of models illustrated in Fig. 10.20a of IPCC (2013). The standard climate sensitivity and climate model do not include effects of "slow" climate feedbacks such as change of ice sheet size. There is increasing evidence that some slow feedbacks can be triggered within decades, so they must be given major consideration in establishing the dangerous level of human-made climate interference. We thus incorporate consideration of slow feedbacks in our analysis and discussion, even though precise specification of their magnitude and time scales is not possible. We present updates of GHG observations and find a notable acceleration during the past decade of the growth rate of GHG climate forcing. For future fossil fuel emissions we consider both the Representative Concentration Pathways (RCP) scenarios used in Climate Model Intercomparison Project 5 (CMIP5) IPCC studies, and simple emission growth rate changes that help evaluate the plausibility of needed emission changes. We use a Green's function calculation of global temperature with canonical climate sensitivity for each emissions scenario, which yields the amount of CO 2 that must be extracted from the air -effectively the climate debt -to return atmospheric CO 2 to less than 350 ppm or limit global warming to less than 1.5°C above preindustrial levels. We discuss alternative extraction technologies and their estimated costs, and finally we consider the potential alleviation of CO 2 extraction requirements that might be obtained via special efforts to reduce non-CO 2 GHGs.

Global Temperature Change
The framing of human-caused climate change by the Paris Agreement uses global mean surface temperature as the metric for assessing dangerous climate change. We have previously argued the merits of additional metrics, especially Earth's energy imbalance von Schuckmann et al., 2016) and atmospheric CO 2 amount . Earth's energy imbalance integrates over all climate forcings, known and unknown, and informs us where climate is heading, because it is this imbalance that drives continued warming. The CO 2 metric has merit because CO 2 is the dominant control knob on global temperature (Lacis et al., 2010(Lacis et al., , 2013, including paleo temperature change (cf. Fig. 28 of . Our present paper uses these alternative metrics to help sharpen determination of the dangerous level of global warming, and to quantify actions that are needed to stabilize climate. We here use global temperature as the principal metric because several reasons of concern are scaled to global warming (O'Neill et al., 2017), including specifically the potential for slow feedbacks such as ice sheet melt and permafrost thaw. The slow feedbacks, whose time scales depend on how strongly the climate system is being forced, will substantially determine the magnitude of climate impacts and affect how difficult the task of stabilizing climate will be.
Quantitative assessment of both ongoing and paleo temperature change is needed to define acceptable limits on human-made interference with climate, with paleo climate especially helpful 3 Climate sensitivity is the response of global average surface temperature to a standard forcing, with the standard forcing commonly taken to be doubled atmospheric CO 2 , which is a forcing of about 4 W/m 2 . 4 IPCC (2013) finds that 2×CO 2 equilibrium sensitivity is likely in the range 3 ± 1.5°C, as was estimated by Charney et al. (1979). Median sensitivity in recent model inter-comparisons is 3.2°C (Andrews et al., 2012;Vial et al., 2013). for characterizing long-term ice sheet and sea level response to temperature change. Thus we examine the modern period with near-global instrumental temperature data in the context of the current and prior (Holocene and Eemian) interglacial periods, for which less precise proxy-based temperatures have recently emerged. The Holocene, over 11,700 years in duration, had relatively stable climate, prior to the remarkable warming in the past half century. The Eemian, which lasted from about 130,000 to 115,000 years ago, was moderately warmer than the Holocene and experienced sea level rise to heights 6-9 m (20-30 feet) greater than today.

Modern Temperature
The several analyses of temperature change since 1880 are in close agreement (Hartmann et al., 2013). Thus we can use the current GISTEMP analysis (see Supporting Information), which is updated monthly and available (http://www.columbia.edu/~mhs119/Temperature/).
The popular measure of global temperature is the annual-mean global-mean value (Fig. 2a), which is publicized at the end of each year. However, as discussed by Hansen et al. (2010), the 12-month running mean global temperature is more informative and removes monthly "noise" from the record just as well as the calendar year average. For example, the 12-month running mean for the past 67 years (Fig. 2b) defines clearly the super-El Niños of 1997-98 and 2015-16 and the 3-year cooling after the Mount Pinatubo volcanic eruption in the early 1990s.
Global temperature in 2014, 2015 and 2016 reached successive record high levels for the period of instrumental data (Fig. 2). Temperature in the latter two years was partially boosted by the 2015-16 El Niño, but the recent warming is sufficient to remove the illusion of a hiatus of global surface warming after the 1997-98 El Niño (Appendix A4).
The present global warming rate, based on a linear fit for 1970-present (dashed line in Fig.  2b) is +0.18°C per decade 5 . The period since 1970 is the time with high growth rate of GHG climate forcing, which has been maintained at approximately +0.4 W/m 2 /decade (see section 6 below) 6 causing Earth to be substantially out of energy balance (Cheng et al., 2017). The energy 5 Extreme endpoints affect linear trends, but if the 2016 temperature is excluded the calculated trend (0.176°C/decade) still rounds to 0.18°C/decade. 6 As forcing additions from chlorofluorocarbons (CFCs) and CH 4 declined, CO 2 growth increased (section 6).  (Clark and Huybers, 2009;Turney and Jones, 2010;McKay et al., 2011;Hoffman et al, 2017), (b) centenniallysmoothed Holocene (Marcott et al., 2013) temperature and the 11-year mean of modern data (Fig. 2), as anomalies relative to 1880-1920. Vertical downward arrows indicate likely overestimates (see text).
imbalance drives global warming, so unless and until there is substantial change in the rate of added climate forcing we expect the underlying warming to continue at a comparable rate.
Global temperature defined by the linear fit to temperature since 1970 now exceeds 1°C 7 relative to the 1880-1920 mean (Fig. 2b), where the 1880-1920 mean provides our best estimate of "preindustrial" temperature (Appendix A5). At the rate of 0.18°C/decade the linear trend line of global temperature will reach +1.5°C in about 2040 and +2°C in the late 2060s. However, the warming rate can accelerate or decelerate, depending on policies that affect GHG emissions, developing climate feedbacks, and other factors discussed below.

Temperature during current and prior interglacial periods
Holocene temperature has been reconstructed at centennial-scale resolution from 73 globally distributed proxy temperature records by Marcott et al. (2013). This record shows a decline of 0.6°C from early Holocene maximum temperature to a "Little Ice Age" minimum in the early 1800s [that minimum being better defined by higher resolution data of Abram et al. (2016)]. Concatenation of the modern and Holocene temperature records ( Fig. 3; Appendix A5) assumes that 1880-1920 mean temperature is 0.1°C warmer than the Little Ice Age minimum (Abram et al., 2016). The early Holocene maximum in the Marcott et al. (2013) data thus reaches +0.5°C relative to the 1880-1920 mean of modern data. The formal 95% confidence bounds to Holocene temperature (Marcott et al., 2013) are ±0.25°C (blue shading in Fig. 3b), but total uncertainty is larger. Specifically, Liu et al. (2014) points out a bias effect caused by seasonality in the proxy temperature reconstruction. Correction for this bias will tend to push early Holocene temperatures lower, increasing the gap between today's temperature and early Holocene temperature (Marcott and Shakun, 2015).
We emphasize that comparisons of current global temperature with the earlier Holocene must bear in mind the centennial smoothing inherent in the Holocene data (Marcott et al. 2013). Thus the temperature in an anomalous single year such as 2016 is not an appropriate comparison. However, the temperature in 2016 based on the 1970-present linear trend (at least 1°C relative to the 1880-1920 mean) does provide a meaningful comparison. The trend line reduces the effect of interannual variability, but the more important point is that Earth's energy imbalance assures that this temperature will continue to rise unless and until the global climate forcing begins to decline. In other words, we know that mean temperature over the next several decades will not be lower than 1°C.
We conclude that the modern trend line of global temperature crossed the early Holocene (smoothed) temperature maximum (+0.5°C) in about 1985. This conclusion is supported by the accelerating rate of sea level rise, which approached 3 mm/year at about that date  show a relevant concatenation of measurements in their Fig. 29]. Such a high rate of sea level rise, which is 3 meters per millennium, far exceeds the prior rate of sea level rise in the last six millennia of the Holocene (Lambeck et al., 2014). Note that near stability of sea level in the latter half of the Holocene as global temperature fell about 0.5°C, prior to rapid warming of the Modern Era (Fig. 3), is not inconsistent with that global cooling. Hemispheric solar insolation anomalies in the latter half of the Holocene favored ice sheet growth in the Northern Hemisphere and ice sheet decay in Antarctica (Fig. 27a, , but the Northern Hemisphere did not become cool enough to reestablish ice sheets on North America or Eurasia. There was a small increase of Greenland ice sheet mass (Larsen et al., 2015), but this was presumably at least balanced by Antarctic ice sheet mass loss (Lambeck et al., 2014).
The important point is that global temperature has risen above the centennially-smoothed Holocene range. Global warming is already having substantial adverse climate impacts (IPCC, 2014), including extreme events (NAS, 2016). There is widespread agreement that 2°C warming would commit the world to multi-meter sea level rise (Levermann et al., 2013;Dutton et al., 2015;Clark et al., 2016). Sea level reached 6-9 m higher than today during the Eemian (Dutton et al., 2015), so it is particularly relevant to know how global mean Eemian temperature compares to the preindustrial level and thus to today.
McKay et al. (2011) estimated peak Eemian annual global ocean SST as +0.7°C ± 0.6°C relative to late Holocene temperature, while models, as described by Masson-Delmotte et al. (2013), give more confidence to the lower part of that range. Hoffman et al. (2017) report the maximum Eemian annual global SST as +0.5°C ± 0.3°C relative to 1870-1889, which is +0.65°C relative to 1880-1920. The response of surface air temperature (SAT) over land is twice as large as the SST response to climate forcings in 21 st century simulations with models , in good agreement with observed warming in the industrial era (Appendix A3 this paper, Fig. A3a). The ratio of land SAT change to SST change is reduced only to ~1.8 after 1000 years in climate models (Fig. A6 Clark and Huybers (2009) and Turney and Jones (2010) estimated global temperature in the Eemian as 1.5-2°C warmer than the Holocene (Fig.  3), but Bakker and Renssen (2014) point out two biases that may cause this range to be an overestimate. Bakker and Rennsen (2014) use a suite of models to estimate that the assumption that maximum Eemian temperature was synchronous over the planet overestimates Eemian temperature by 0.4 ± 0.3°C -a feature supported by a lack of synchroneity of warmest conditions in assessments with improved synchronization of records (Govin et al., 2015) -and that they also suggest that a possible seasonal bias of proxy temperature could make the total overestimate as large as 1.1 ± 0.4°C. Given uncertainties in the corrections, it becomes a matter of expert judgment. Dutton et al. (2015) conclude that the best estimate for Eemian temperature  Hansen et al. (2005), which are consistent with estimates of Myhre et al. (2013) in the most recent IPCC report (IPCC, 2013).
Forcings are based on observations of each gas, except simulated CH 4 -induced changes of O 3 and stratospheric H 2 O included in the CH 4 forcing. Aerosols and surface albedo change are estimated from historical scenarios of emissions and land use. Oscillatory and intermittent natural forcings (solar irradiance and volcanoes) are excluded. CFCs include not only chlorofluorocarbons, but all Montreal Protocol Trace Gases (MPTGs) and Other Trace Gases (OTGs). Uncertainties (for 5-95% confidence) are 0.6 W/m 2 for total GHG forcing and 0.9 W/m 2 for aerosol forcing  is +1°C relative to preindustrial. Consistent with these estimates and the discussion of Masson-Delmotte et al. (2013), we assume that maximum Eemian temperature was +1°C relative to preindustrial with an uncertainty of at least 0.5°C.
These considerations raise the question of whether 2°C, or even 1.5°C, is an appropriate target to protect the well-being of young people and future generations. Indeed, Hansen et al. (2008) concluded "If humanity wishes to preserve a planet similar to that on which civilization developed and to which life on Earth is adapted, … CO 2 will need to be reduced … to at most 350 ppm, but likely less than that." And further "If the present overshoot of the target CO 2 is not brief, there is a possibility of seeding irreversible catastrophic effects." A danger of 1.5°C or 2°C targets is that they are far above the Holocene temperature range. If such temperature levels are allowed to long exist they will spur "slow" amplifying feedbacks (Hansen et al., 2013b;Rohling et al., 2013;Masson-Delmotte et al., 2013), which have potential to run out of humanity's control. The most threatening slow feedback likely is ice sheet melt and consequent significant sea level rise, as occurred in the Eemian, but there are other risks in pushing the climate system far out of its Holocene range. Methane release from thawing permafrost and methane hydrates is another potential feedback, for example, but the magnitude and time scale of this is unclear (O'Connor et al., 2010;Quiquet, 2015).
Here we examine the fossil fuel emission reductions required to restore atmospheric CO 2 to 350 ppm or less, so as to keep global temperature close to the Holocene range, in addition to the canonical 1.5°C and 2°C targets. Quantitative investigation requires consideration of Earth's energy imbalance, changing climate forcings, and climate sensitivity.

Global Climate Forcings and Earth's Energy Imbalance
The dominant human-caused drivers of climate change are changes of atmospheric GHGs and aerosols (Fig. 4). GHGs absorb Earth's infrared (heat) radiation, thus serving as a "blanket" warms Earth's surface by reducing heat radiation to space. Aerosols, fine particles/droplets in the air that cause visible air pollution, both reflect and absorb solar radiation, but reflection of solar energy to space is their dominant effect, so they cause a cooling that partly offsets GHG warming. Estimated forcings (Fig. 4), an update of Fig. 28b of Hansen et al. (2005), are similar to those of Myhre et al. (2013) in the most recent IPCC report (IPCC, 2013). 8 Climate forcings in Fig. 4 are the planetary energy imbalance that would be caused by the preindustrial-to-present change of each atmospheric constituent, if the climate were held fixed at its preindustrial state . The CH 4 forcing includes its indirect effects, as increasing atmospheric CH 4 causes tropospheric ozone (O 3 ) and stratospheric water vapor to increase . Uncertainties, discussed by Myhre et al. (2013), are typically 10-15% for GHG forcings. The aerosol forcing uncertainty, described by a probability distribution function (Boucher et al., 2013), is of order 50%. Our estimate of aerosol plus surface albedo forcing (−1.2 W/m 2 ) differs from the −1.5 W/m 2 of Hansen et al. (2005), as discussed below, but both are within the range of the distribution function of Boucher et al. (2013).
Positive net forcing ( Fig. 4) causes Earth to be temporarily out of energy balance, with more energy coming in than going out, which drives slow global warming. Eventually Earth will become hot enough to restore planetary energy balance. However, because of the ocean's great thermal inertia (heat capacity), full atmosphere-ocean response to the forcing requires a long time: atmosphere-ocean models suggest that even after 100 years only 60-75% of the surface warming for a given forcing has occurred, the remaining 25-40% still being "in the pipeline" (Hansen et al., 2011;Collins et al., 2013). Moreover, we outline in the next section that global warming can activate "slow" feedbacks, such as changes of ice sheets or melting of methane hydrates, so the time for the system to reach a fully equilibrated state is even longer.
GHGs have been increasing for more than a century and Earth has partially warmed in response. Earth's energy imbalance is the portion of the forcing that has not yet been responded to. This imbalance thus defines additional global warming that will occur without further change of forcings. Earth's energy imbalance can be measured by monitoring ocean subsurface temperatures, because almost all excess energy coming into the planet goes into the ocean . Most of the ocean's heat content change occurs in the upper 2000 m (Levitus et al., 2012), which has been well measured since 2005 when the distribution of Argo floats achieved good global coverage (von Schuckmann and Le Traon, 2011). Here we update 8 Our GHG forcings, calculated with formulae of Hansen et al. (2000), yield a CO 2 forcing 6.7% larger than the central IPCC estimate [

Climate Sensitivity and Feedbacks
Climate sensitivity has been a fundamental issue at least since the 19 th century when Tyndall (1861) and Arrhenius (1896) stimulated interest in the effect of CO 2 change on climate. Evaluation of climate sensitivity involves the full complexity of the climate system, as all components and processes in the system are free to interact on all time scales. Tyndall and Arrhenius recognized some of the most important climate feedbacks on both fast and slow time scales. The amount of water vapor in the air increases with temperature, which is an amplifying feedback because water vapor is a very effective greenhouse gas; this is a "fast" feedback, because water vapor amount in the air adjusts within days to temperature change. The area covered by glaciers and ice sheets is a prime "slow" feedback; it, too, is an amplifying feedback, because the darker surface exposed by melting ice absorbs more sunlight. Diminishing climate feedbacks also exist. Cloud-cover changes, e.g., can either amplify or reduce climate change (Boucher at al., 2013). Thus it is not inherent that amplifying feedbacks should be dominant, but climate models and empirical data concur that amplifying feedbacks dominate on both short and long time scales, as we will discuss. Amplifying feedbacks lead to large climate change in response to even weak climate forcings such as ice age cycles caused by small perturbations of Earth's orbit, and still larger climate change occurs on even longer time scales in response to gradual changes in the balance between natural sources and sinks of atmospheric CO 2 (Zachos et al., 2001;Royer et al., 2012;Franks et al., 2014).

Fast-Feedback Climate Sensitivity
Doubled atmospheric CO 2 , a forcing of ~4 W/m 2 , is a standard forcing in studies of climate sensitivity. Charney et al. (1979) concluded that equilibrium sensitivity, i.e., global warming after a time sufficient for the planet to restore energy balance with space, was 3°C ± 1.5°C for 2×CO 2 or 0.75°C per W/m 2 forcing. The Charney analysis was based on climate models in which ice sheets and all long-lived GHGs (except for the specified CO 2 doubling) were fixed. The climate sensitivity thus inferred is the "fast-feedback" climate sensitivity. The central value found in a wide range of modern climate models  remains 3°C for 2×CO 2 .
The possibility of unknown unknowns in models would keep the uncertainty in the fastfeedback climate sensitivity high, if it were based on models alone, but as discussed by Rohling et al. (2012a), paleoclimate data allow narrowing of the uncertainty. Ice sheet size and the atmospheric amount of long-lived GHGs (CO 2 , CH 4 , N 2 O) under natural conditions change on multi-millennial time scales. These changes are so slow that the climate is in quasi-equilibrium with the changing surface condition and long-lived GHG amounts. Thus these changing boundary conditions, along with knowledge of the associated global temperature change, allow empirical assessment of the fast-feedback climate sensitivity. The central result agrees well with the model-based climate sensitivity estimate of 3°C for 2×CO 2 (Rohling et al., 2012b), with an uncertainty that is arguably 1°C or less (Hansen et al., 2013b).
The ocean has great heat capacity (thermal inertia), so it takes decades to centuries for Earth's surface temperature to achieve most of its fast-feedback response to a change of climate forcing (Hansen et al., 1985). Thus Earth has only partly responded to the human-made increase of GHGs in the air today, the planet must be out of energy balance with the planet gaining energy (via reduced heat radiation to space), and more global warming is "in the pipeline." A useful check on understanding of ongoing climate change is provided by the consistency of the net climate forcing (Fig. 4), Earth's energy imbalance, observed global warming, and climate sensitivity. Observed warming since 1880-1920 is 1.05°C 9 based on the linear fit to the 132-month running mean (Fig. 2b), which limits bias from short-term oscillations. Global warming between 1700-1800 and 1880-1920 was ~0.1°C (Abram et al., 2016;Hawkins et al., 2017;Marcott et al., 2013), so 1750-2015 warming is ~1.15°C. Taking climate sensitivity as 0.75°C per W/m 2 forcing, global warming of 1.15°C implies that 1.55 W/m 2 of the total 2.5 W/m 2 forcing has been "used up" to cause observed warming. Thus 0.95 W/m 2 forcing should remain to be responded to, i.e., the expected planetary energy imbalance is 0.95 W/m 2 , which is reasonably consistent with the observed 0.75 ± 0.25 W/m 2 . If we instead take the aerosol + surface albedo forcing as −1.5 W/m 2 , as estimated by Hansen et al. (2005), the net climate forcing is 2.2 W/m 2 and the forcing not responded to is 0.65 W/m 2 , which is also within the observational error of Earth's energy imbalance.

Slow Climate Feedbacks
Large glacial-to-interglacial climate oscillations occur on time scales of tens and hundreds of thousands of years, with atmospheric CO 2 amount and the size of ice sheets (and thus sea level) changing almost synchronously on these time scales (Masson-Delmotte et al., 2013). It is readily apparent that these climate cycles are due to small changes in Earth's orbit and the tilt of its spin axis, which alter the geographical and seasonal distribution of sunlight striking Earth. The large climate response is a result of two amplifying feedbacks: (1) atmospheric GHGs (mainly CO 2 but accompanied by CH 4 and N 2 O), which increase as Earth warms and decrease as it cools , thus amplifying the temperature change, and (2) the size of ice sheets, which shrink as Earth warms and grow as it cools, thus changing the amount of absorbed sunlight in the sense that also amplifies the climate change. For example, 20,000 years ago most of Canada and parts of the United States were covered by an ice sheet, and sea level was about 130 m (~400 feet) lower than today. Global warming of ~5°C between the last glacial maximum and the Holocene (Masson-Delmotte et al., 2013) is accounted for almost entirely by radiative forcing caused by decrease in ice sheet area and increase of GHGs (Lorius et al., 1990;Hansen et al., 2007).
The glacial-interglacial time scale is set by the time scale of the weak orbital forcings. Before addressing the crucial issue of the inherent time scale of slow feedbacks, we need to say more about the two dominant slow feedbacks, described above as ice sheets and GHGs.
The ice sheet feedback works mainly via the albedo (reflectivity) effect. A shrinking ice sheet exposes darker ground and warming darkens the ice surface by increasing the area and period with wet ice, thus increasing the ice grain size and increasing the surface concentration of light-absorbing impurities (Tedesco et al., 2016). The ice albedo effect is supplemented by a change of surface albedo in ice-free regions due to vegetation changes. This vegetation albedo effect provides a significant amplification of warming as Earth's temperature increases from its present climate state, because dark forests tend to replace tundra or sparse low-level vegetation in large areas of Eurasia and North America (Lunt et al., 2010).
The GHG feedback on glacial-interglacial time scales is 75-80 percent from CO 2 change; N 2 O and CH 4 account for 20-25 percent (Lorius et al., 1990, Masson-Delmotte et al., 2013. In simple terms, the ocean and land release more of these gases as the planet becomes warmer. Mechanisms that control GHG release as Earth warms, and GHG drawdown as Earth cools, are complex, including many processes that affect the distribution of carbon, among the ocean, atmosphere, and biosphere (Yu et al., 2016;Ciais et al., 2013 and references therein). Release of carbon from methane hydrates and permafrost contributed to climate change in past warm periods DeConto et al., 2012) and potentially could have a significant effect in the future (O'Connor et al., 2010;Schädel et al., 2016). Paleoclimate data help assess the possible time scale for ice sheet change. Ice sheet size, judged from sea level, varies almost synchronously with temperature for the temporal resolution available in paleoclimate records, but Grant et al. (2012) find that sea level change lags temperature change by 1-4 centuries. Paleoclimate forcing, however, is both weak and very slow, changing on millennial time scales. Hansen (2005Hansen ( , 2007 argues on heuristic grounds that the much faster and stronger human-made climate forcing projected this century with continued high fossil fuel emissions, equivalent to doubling atmospheric CO 2 , would likely lead to substantial ice sheet collapse and multi-meter sea level rise on the time scale of a century. Modeling supports this conclusion, as Pollard et al. (2015) found that addition of hydrofracturing and cliff failure to their ice sheet model not only increased simulated sea level rise from 2 m to 17 m in response to 2°C ocean warming, it also accelerated the time for multi-meter change from several centuries to several decades. Ice sheet modeling of Applegate et al. (2015) explicitly shows that the time scale for large ice sheet melt decreases dramatically as the magnitude of warming increases. , based on a combination of climate modeling, paleo data, and modern observations, conclude that continued high GHG emissions would likely cause multi-meter sea level rise within 50-150 years.
The GHG feedback plays a leading role in determining the magnitude of paleoclimate change and there is reason to suspect that it may already be important in modern climate. Rising temperatures increase the rate of CO 2 and CH 4 release from drying soils, thawing permafrost (Schädel et al., 2016;Schuur et al., 2015) and warming continental shelves (Kvenvolden, 1993;Judd et al., 2002), and affect the ocean carbon cycle as noted above. Crowther et al. (2016) synthesize results of 49 field experiments across North America, Europe and Asia, inferring that every 1°C global mean soil surface warming can cause a 30 PgC soil carbon loss and suggesting that continued high fossil fuel emissions might drive 2°C soil warming and a 55 PgC soil carbon loss by 2050. Although this analysis admits large uncertainty, such large soil carbon loss could wreak havoc with efforts to achieve the net soil and biospheric carbon storage that is likely necessary for climate stabilization, as we discuss in subsequent sections.
Recent changes of GHGs result mainly from industrial and agricultural emissions, but they also include any existing climate feedback effects. CO 2 and CH 4 are the largest forcings ( Fig. 4), so it is especially important to examine their ongoing changes. Figure 6. (a) Global CO 2 annual growth based on NOAA data (http://www.esrl.noaa.gov/gmd/ccgg/trends/). Dashed curve is for a single station (Mauna Loa). Red curve is monthly global mean relative to the same month of prior year; black curve is 12-month running mean of red curve. (b) CO 2 growth rate is highly correlated with global temperature, the CO 2 change lagging global temperature change by 7-8 months.

Observed CO 2 and CH 4 Growth Rates
Annual increase of atmospheric CO 2 , averaged over a few years, grew from less than 1 ppm/year 50 years ago to more than 2 ppm/year today ( Fig. 6), with global mean CO 2 now exceeding 400 ppm (Betts et al., 2016). Growth of atmospheric CO 2 is about half of fossil fuel CO 2 emissions as discussed in Appendix A8 and illustrated in Fig. A8. The large oscillations of annual growth are correlated with global temperature and with the El Niño/La Niña cycle, as discussed in Appendix A8. Recent global temperature anomalies peaked in February 2016, so as expected the CO 2 growth rate has been declining for the past several months (Fig. 6a).
Atmospheric CH 4 stopped growing between 1998 and 2006, indicating that its sources were nearly in balance with the atmospheric oxidation sink, but growth resumed in the past decade ( Fig. 7). CH 4 growth averaged 10 ppb/year in 2014-2016, almost as fast as in the 1980s. Likely reasons for the recent increased growth of CH 4 are discussed in Appendix A8.
The continued growth of atmospheric CO 2 and reaccelerating growth of CH 4 raise important questions related to prospects for stabilizing climate. How consistent with reality are scenarios for phasing down climate forcing when tested by observational data? What changes to industrial and agricultural emissions are required to stabilize climate? We address these issues below.

GHG Climate Forcing Growth Rates and Emission Scenarios
Insight is obtained by comparing the growth rate of GHG climate forcing based on observed GHG amounts with past and present GHG scenarios. We examine forcings of IPCC Special Report on Emissions Scenarios (IPCC SRES, 2000) used in the 2001 AR3 and 2007 AR4 reports (Fig. 8a) and Representative Concentration Pathways scenarios (RCP: Moss et al., 2010;Meinshausen et al., 2011a) used in the 2013 IPCC AR5 report (Fig. 8b). We include the "alternative scenario" of Hansen et al. (2000) in which CO 2 and CH 4 emissions decline such that global temperature stabilizes near the end of the century. 10 We use the same radiation equations for observed GHG amounts and scenarios, so errors in the radiation calculations do not alter the comparison. Equations for GHG forcings are from Table 1 of Hansen et al. (2000) with the CH 4 forcing using an efficacy factor 1.4 to include effects of CH 4 on tropospheric O 3 and stratospheric H 2 O .
The growth of GHG climate forcing peaked at ~0.05 W/m 2 /year (5 W/m 2 /century) in 1978-1988, then falling to a level 10-25% below IPCC SRES (2000) scenarios during the first decade of the 21 st century (Fig. 8a). The decline was due to (1) decline of the airborne fraction of CO 2 emissions (Fig. A8), (2) slowdown of CH 4 growth (Fig. 7), and (3) the Montreal Protocol, which initiated phase-out of the production of gases that destroy stratospheric ozone, primarily chlorofluorocarbons (CFCs).

10
This scenario is discussed by Hansen and Sato (2004). CH 4 emissions decline moderately, producing a small negative forcing. CO 2 emissions (not captured and sequestered) are assumed to decline until in 2100 fossil fuel emissions just balance uptake of CO 2 by the ocean and biosphere. CO 2 emissions continue to decline after 2100.  (Moss et al., 2010;van Vuuren et al., 2011;Meinshausen et al., 2011a,b). Numbers on the RCP scenarios (8.5, 6.0, 4.5 and 2.6) refer to the GHG climate forcing (W/m 2 ) in 2100.
Scenario RCP2.6 has the world moving into negative growth (net contraction) of GHG forcing 25 years from now (Fig. 8b), through rapid reduction of GHG emissions, along with CO 2 capture and storage. Already in 2015 there is a huge gap between reality and RCP2.6. Closing the gap (0.01 W/m 2 ) between actual growth of GHG climate forcing in 2015 and RCP2.6 ( Fig.  8b), with CO 2 alone, would require extraction from the atmosphere of more than 0.7 ppm of CO 2 or 1.5 PgC due to the emissions gap of a single year (2015). We discuss the plausibility and estimated costs of scenarios with CO 2 extraction in Section 9.
As a complement to RCP scenarios, we define scenarios with focus on the dominant climate forcing, CO 2 , with its changes defined simply by percent annual emission decrease or increase. Below (Sec. 10.1 and Appendix A13) we conclude that efforts to limit non-CO 2 forcings could keep their growth small or even slightly negative, so a focus on long-lived CO 2 is appropriate. Thus for the non-CO 2 GHGs we use RCP6.0, a scenario with small changes of these gases. For CO 2 we consider rates −6%/year, −3%/year, constant emissions, and +2%/year; emissions stop increasing in the +2%/year case when they reach 25 Gt/year (Fig. 9a). Scenarios with decreasing emissions are preceded by constant emissions for 2015-2020, in recognition that some time is required to achieve policy change and implementation. Note similarity of RCP 2.6 with −3%/year, RCP 4.5 with constant emissions, and RCP 8.5 with +2%/year (Fig. 9).

Future CO 2 for Assumed Emission Scenarios
We must model Earth's carbon cycle, including ocean uptake of carbon, deforestation, forest regrowth and carbon storage in the soil, for the purpose of simulating future atmospheric CO 2 as a function of the fossil fuel emission scenario. Fortunately, the convenient dynamic-sink pulseresponse function version of the well-tested Bern carbon cycle model (Joos et al., 1996) does a good job of approximating more detailed models, and it produces a good match to observed industrial-era atmospheric CO 2 . Thus we use this relatively simple model, described elsewhere (Joos et al., 1996;Kharecha and Hansen, 2008, and references therein), to examine the effect of alternative fossil fuel use scenarios on the growth or decline of atmospheric CO 2 . Assumptions about emissions in the historical period are given in Appendix A9. Figure 10a shows the simulated atmospheric CO 2 for the baseline emission cases (Fig. 9a). These cases do not include active CO 2 removal. Five additional cases including CO 2 removal ( Fig. 10b) achieve atmospheric CO 2 targets of either 350 ppm or 450 ppm in 2100, with cumulative removal amounts listed in parentheses (Fig. 10b). The rate of CO 2 extraction in all cases increases linearly from zero in 2010 to the value in 2100 that achieves the atmospheric CO 2 target (350 ppm or 450 ppm). The amount of CO 2 that must be extracted from the system exceeds the difference between the atmospheric amount without extraction and the target amount, e.g., constant CO 2 emissions and no extraction yields 547 ppm for atmospheric CO 2 in 2100, but to achieve a target of 350 ppm the required extraction is 328 ppm, not 547 -350 = 197 ppm. The well-known reason (Cao and Caldeira, 2010) is that ocean outgassing increases and vegetation productivity and ocean CO 2 uptake decrease with decreasing atmospheric CO 2 , as explored in a wide range of Earth System models .

Simulations of Global Temperature Change
Analysis of future climate change, and policy options to alter that change, must address various uncertainties. One useful way to treat uncertainty is to use results of many models and construct probability distributions . Such distributions have been used to estimate the remaining budget for fossil fuel emissions for a specified likelihood of staying under a given global warming limit and to compare alternative policies for limiting climate forcing and global warming (Rogelj et al., 2016a,b).
Our aim here is a fundamental, transparent calculation that clarifies how future warming depends on the rate of fossil fuel emissions. We use best estimates for basic uncertain quantities such as climate sensitivity. If these estimates are accurate, actual temperature should have about equal chances of falling higher or lower than the calculated value. Important uncertainties in projections of future climate change include climate sensitivity, the effects of ocean mixing and dynamics on the climate response function discussed below, and aerosol climate forcing. We provide all defining data so that others can easily repeat calculations with alternative choices.
One clarification is important for our present paper. The climate calculations in this section include only fast-feedbacks, which is also true for most climate simulations by the scientific community for IPCC (2013). This is not a limitation for the past, i.e., for the period 1850present, because we employ measured GHG changes, which include any GHG change due to slow feedbacks. Also we know that ice sheets did not change significantly in size in that period; there may have been some change in Greenland's albedo and expansion of forests in the Northern Hemisphere (Pearson et al., 2013), but those feedbacks so far have only a small global effect. However, this limitation to fast feedbacks may soon become important; it is only in the past few decades that global temperature rose above the prior Holocene range and only in the past two years that it shot far above that range. This limitation must be borne in mind when we consider the role of slow feedbacks in establishing the dangerous level of warming.
We calculate global temperature change T at time t in response to any climate forcing scenario using the Green's function (Hansen, 2008) t where R(t') is the product of equilibrium global climate sensitivity and the dimensionless climate response function (percent of equilibrium response), dF(t')/dt' is the annual increment of the net forcing, and Fv is the negative of the average volcanic aerosol forcing during the few centuries preceding 1850. Fv ×R(t) is a small correction term that prevents average volcanic aerosol activity from causing a long-term cooling, i.e., it accounts for the fact that the ocean in 1850 was slightly cooled by prior volcanoes. We take Fv = 0.3 W/m 2 , the average stratospheric aerosol forcing for 1850-2015. The assumed-constant pre-1850 volcanic aerosols caused a constant cooling up to 1850, which gradually decreases to zero after 1850 and is replaced by post-1850 time-dependent volcanic cooling; note that T(1850) = 0°C. We use the "intermediate" response function in Fig. 5 of Hansen et al. (2011), which gives good agreement with Earth's measured energy imbalance. The response function is 0.15, 0.55, 0.75 and 1 at years 1, 10, 100 and 2000 with these values connected linearly in log (year). This defined response function allows our results to be exactly reproduced, or altered with alternative choices for climate forcings, climate sensitivity and response function. Forcings that we use are tabulated in Appendix A10.
We take tropospheric aerosol plus surface albedo forcing as −1.2 W/m 2 in 2015, presuming the aerosol and albedo contributions to be −1 W/m 2 and −0.2 W/m 2 , respectively. We assume a small increase this century as global population rises and increasing aerosol emission controls in emerging economies tend to be offset by increasing development elsewhere, so aerosol + surface forcing is −1.5 W/m 2 in 2100. The temporal shape of the historic aerosol forcing curve (Table  A10)   Historic stratospheric aerosol data (Table A10, annual version), an update of Sato et al. (1993), include moderate 21 st century aerosol amounts (Bourassa et al., 2012). Future aerosols, for realistic variability, include three volcanic eruptions in the rest of this century with properties of the historic Agung, El Chichon and Pinatubo eruptions, plus a background stratospheric aerosol forcing −0.1 W/m 2 . This leads to mean stratospheric aerosol climate forcing −0.3 W/m 2 for remainder of the 21 st century, similar to the mean stratospheric aerosol forcing for 1850-2015 (Table A10). Reconstruction of historical solar forcing (Coddington et al., 2015;, based on data in Fig. A11, is extended with an 11-year cycle. Individual and net climate forcings for the several fossil fuel emission reduction rates are shown in Fig. 11a,c. Scenarios with linearly growing CO 2 extraction at rates required to yield 350 or 450 ppm airborne CO 2 in 2100 are in Fig. 11b,d. These forcings and the assumed climate response function define expected global temperature for the entire industrial era considered here (Fig. 12). We extended the global temperature calculations from 2100 to 2200 by continuing the %/year change of CO 2 emissions. In the cases with CO 2 extraction we kept the GHG climate forcing fixed in the 22 nd century, which meant that large CO 2 extraction continued in cases with continuing high emissions, e.g., the case with constant emissions that required extraction of 695 PgC during 2020-2100 required further extraction of ~900 PgC during 2100-2200. Even the cases with annual emission reductions −6%/year and −3%/year required small extractions to compensate for back-flux of CO 2 from the ocean that accumulated there historically. Warming is about 2°C if emissions are constant until 2100. Furthermore, both scenarios launch Earth onto a course of more dramatic change well beyond the initial 2-3°C global warming, because: (1) warming continues beyond 2100 as the planet is still far from equilibrium with the climate forcing, and (2) warming of 2-3°C would unleash strong slow feedbacks, including melting of ice sheets and increases of GHGs.
The most important conclusion from Fig. 12a is the proximity of results for the cases with emission reductions of 6%/year and 3%/year. Although Hansen et al. (2013a) called for emission reduction of 6%/year to restore CO 2 to 350 ppm by 2100, that rate of reduction may have been regarded as implausibly steep by a federal court in 2012 when it declined to decide whether the U.S. was violating the public trust by causing or contributing to dangerous climate change (Alec L v. Jackson, 2012). Such a concern is less pressing for emission reductions of 3% per year. Note that reducing global emissions at a rate of 3%/year (or more steeply) maintains global warming at less than 1.5°C above preindustrial temperature.
However, end-of-century temperature still rises 0.5°C or more above the prior Holocene maximum with consequences for slow feedbacks that are difficult to foresee. Desire to minimize sea level rise spurs the need to get global temperature back into the Holocene range. That goal preferably should be achieved on the time scale of a century or less, because paleoclimate evidence indicates that the response time of sea level to climate change is 1-4 centuries (Grant et al., 2012(Grant et al., , 2014 for natural climate change, and if anything the response should be faster to a stronger, more rapid human-made climate forcing. The scenarios that reduce CO 2 to 350 ppm succeed in getting temperature back close to the Holocene maximum by 2100 (Fig. 12b), but they require extractions of atmospheric CO 2 that range from 153 PgC in the scenario with 6%/year emission reductions to 1630 PgC in the scenario with +2%/year emission growth.
Scenarios ranging from constant emissions to +2%/year emissions growth can be made to yield 450 ppm in 2100 via extraction of 339-1270 PgC from the atmosphere (Fig. 10b). However, these scenarios still yield warming more than 1.5°C above the preindustrial level (more than 1°C above the early Holocene maximum). Consequences of such warming and the plausibility of extracting such huge amounts of atmospheric CO 2 are considered below.

CO 2 Extraction: Estimated Cost and Alternatives
Extraction of CO 2 from the air, also called negative emissions or carbon dioxide removal (CDR), is required if large, long-term excursion of global temperature above its Holocene range is to be averted, as shown above. In estimating the cost and plausibility of CO 2 extraction we distinguish between (1) carbon extracted from the air by improved agricultural and forestry practices, and (2) additional "technological extraction" by intensive negative emission technologies.
We assume that improved practices will aim at optimizing agricultural and forest carbon uptake via relatively natural approaches, compatible with the land delivering a range of ecosystem services (Smith 2016;Smith et al., 2016). In contrast, proposed technological extraction and storage of CO 2 generally does not have co-benefits and remains unproven at relevant scales (NAS, 2015a). Improved practices have local benefits in agricultural yields and forest products and services , which may help minimize net costs. The Intended Nationally Determined Contributions (INDCs) submitted by 189 countries include carbon drawdown through land use plans (United Nations, 2016) with aggregate removal rate of ~2 PgCO 2 /year (~0.55 PgC/year) after 2020. These targets are not the maximum possible drawdown, as they are only about a third of amounts Smith (2016) estimated as "realistic".
Developed countries recognize a financial obligation to less developed countries that have done little to cause climate change (Paris Agreement 2015) 11 . We suggest that at least part of developed country support should be channeled through agricultural and forestry programs, with continual evaluation and adjustment to reward and encourage progress . Efforts to minimize non-CO 2 GHGs can be included in the improved practices program.
Here, we do not estimate the cost of CO 2 extraction obtained via the "improved agricultural and forestry practices 12 ," because that would be difficult given the range of activities it is likely to entail, and because it is not necessary for reaching the conclusion that total CO 2 extraction costs will be high due to the remaining requirements for technological extraction. However, we do estimate the potential magnitude of CO 2 extraction that might be achievable via such improved practices, as that is needed to quantify the required amount of "technological extraction" of CO 2 . Finally, we compare costs of extraction with estimated costs of mitigation measures that could limit the magnitude of required extraction, while admitting that there is large uncertainty in both extraction and mitigation cost estimates. Hansen et al. (2013) suggested a goal of 100 PgC extraction in the 21 st century, which would be almost as large as estimated net emissions from historic deforestation and land use . Hansen et al. (2013a) assumed that 100 PgC was about as much as could be achieved via relatively natural reforestation and afforestation (Canadell and Raupach, 2008) and improved agricultural practices that increase soil carbon (Smith, 2016).

Estimated Cost of CO 2 Extraction
Here we first reexamine whether a concerted global effort on carbon storage in forests and soil might have potential to provide a carbon sink substantially larger than 100 PgC this century. Smith et al. (2016) estimate that reforestation and afforestation together have carbon storage potential of about 1.1 PgC/year. However, as forests mature, their uptake of atmospheric carbon decreases (termed "sink saturation"), thereby limiting CO 2 drawdown. Taking 50 years as the average time for tropical, temperate and boreal trees to experience sink saturation yields 55 PgC as the potential storage in forests this century. Smith (2016) shows that soil carbon sequestration and soil amendment with biochar compare favorably with other negative emission technologies with less impact on land use, water use, nutrients, surface albedo, and energy requirements, but understanding of and literature on biochar are limited (NAS, 2015a). Smith estimates that soil carbon sequestration has potential to store 0.7 PgC/year. However, as with carbon storage in forest, there is a saturation effect. A commonly used 20-year saturation time (IPCC, 2006) would yield 14 PgC soil carbon storage, while an optimistic 50-year saturation time would yield 35 PgC. Use of biochar to improve soil fertility provides additional carbon storage of up to 0.7-1.8 PgC/year (Woolf et al., 2010;Smith 2016). Larger industrial-scale biochar carbon storage is conceivable, but belongs in the category of intensive negative emission technologies, discussed below, whose environmental impacts and costs require scrutiny. We conclude that 100 PgC is an appropriate ambitious estimate for potential carbon extraction via a concerted global-scale effort to improve agricultural and forestry practices with carbon drawdown as a prime objective.
Intensive negative emission technologies that could yield greater CO 2 extraction include (1) burning of biofuels, most commonly at power plants, with capture and sequestration of resulting CO 2 (Creutzig et al., 2015), and (2) direct air capture of CO 2 and sequestration (Keith, 2009;NAS, 2015a), and (3) grinding and spreading of minerals such as olivine to enhance geological weathering (Taylor et al., 2016). However, energy, land and water requirements of these technologies impose economic and biophysical limits on CO 2 extraction .
The popular concept of bioenergy with carbon capture and storage (BECCS) requires large areas, high fertilizer and water use, and may compete with other vital land use such as agriculture (Smith, 2016). Costs estimates are ~$150-350/tC for crop-based BECCS .
Direct air capture has more limited area and water needs than BECCS and no fertilizer requirement, but it has high energy use, has not been demonstrated at scale, and cost estimates exceed those of BECCS (Socolow et al., 2011;Smith et al., 2016). Keith et al. (2006) have argued that, with strong research and development support and industrial-scale pilot projects sustained over decades, it may be possible to achieve costs ~$200/tC, thus comparable to BECCS costs; however other assessments are higher, reaching $1400-3700/tC (NAS, 2015a).
Enhanced weathering via soil amendment with crushed silicate rock is a candidate negative emission technology that also limits coastal ocean acidification as chemical products liberated by weathering increase land-ocean alkalinity flux (Kohler et al., 2010;Taylor et al., 2016). If twothirds of global croplands were amended with basalt dust, as much as 1-3 PgC/year might be extracted, depending on application rate (Taylor et al., 2016), but energy costs of mining, grinding and spreading likely reduce this by 10-25% (Moosdorf et al., 2014). Such large-scale enhanced weathering is speculative, but potential co-benefits for temperate and tropical agroecosystems could affect its practicality, and may put some enhanced weathering into the category of improved agricultural and forestry practices. Benefits include crop fertilization that increases yield and reduces use and cost of other fertilizers, increasing crop protection from insect herbivores and pathogens thus decreasing pesticide use and cost, neutralizing soil acidification to improve yield, and suppression of GHG (N 2 O and CO 2 ) emissions from soils (Edwards et al., 2017;Kantola et al., 2017). Against these benefits, we note potential negative impacts of air and water pollution caused by the mining, including downstream environmental consequences if silicates are washed into rivers and the ocean, causing increased turbidity, sedimentation, and pH, with unknown impacts on biodiversity (Edwards et al., 2017). Cost of enhanced weathering might be reduced by deployment with reforestation and afforestation and with crops used for BECCS; this could significantly enhance the combined carbon sequestration potential of these methods.
For cost estimates, we first consider restoration of airborne CO 2 to 350 ppm in 2100 (Fig.  10b), which would keep global warming below 1.5°C and bring global temperature back close to the Holocene maximum by end-of-century (Fig. 12b). This scenario keeps the temperature excursion above the Holocene level small enough and brief enough that it has the best chance of avoiding ice sheet instabilities and multi-meter sea level rise . If fossil fuel emission phasedown of 6%/year had begun in 2013, as proposed by Hansen et al. (2013a), this scenario would have been achieved via the hypothesized 100 PgC carbon extraction from improved agricultural and forestry practices.
We examine here scenarios with 6%/year and 3%/year emission reduction starting in 2021, as well as scenarios with constant emissions and +2%/year emission growth starting in 2016 (Figs. 10b and 12b). The −6%/year and −3%/year scenarios leave a requirement to extract 153 and 237 PgC from the air during this century. Constant emission and +2%/year emission scenarios yield extraction requirements of 695 and 1630 PgC to reach 350 ppm CO 2 in 2100.
Total CO 2 extraction requirements for these scenarios are given in Fig. 10. Cost estimates here for extraction use amounts 100 Pg less than in Fig. 10 under assumption that 100 PgC can be stored via improved agricultural and forestry practices. Shortfall of this 100 PgC goal will increase our estimated costs accordingly, as will the cost of the improved agricultural and forestry program.
Given a CO 2 extraction cost of $150-350/tC for intensive negative emission technologies (Fig. 3f of Smith et al., 2016), the 53 PgC additional extraction required for the scenario with 6%/year emission reduction would cost $8-18.5 trillion, thus $100-230 billion per year if spread uniformly over 80 years. We cannot rule out possible future reduction in CO 2 extraction costs, but given the energy requirements for removal and the already optimistic lower limit on our estimate, we do not speculate further about potential cost reduction.
In contrast, continued high emissions, between constant emissions and +2%/year, would require additional extraction of 595-1530 PgC (Fig. 10b) at a cost $89-535 trillion or $1.1-6.7 trillion per year over 80 years. 13 Such extraordinary cost, along with the land area, fertilizer and water requirements  suggest that, rather than the world being able to buy its way out of climate change, continued high emissions would likely force humanity to live with climate change running out of control with all the consequences that would entail.

Mitigation Alternative
High costs of CO 2 extraction raise the question of how these costs compare to the alternative: taking actions to mitigate climate change by reducing fossil fuel CO 2 emissions. The Stern Review (Stern, 2006;Stern and Taylor, 2007) used expert opinion to produce an estimate for the cost of reducing emissions to limit global warming to about 2°C. Their central estimate was 1% of gross domestic product (GDP) per year, thus about $800 billion per year. They argued that this cost was much less than likely costs of future climate damage if high emissions continue, unless we apply a high "discount rate" to future damage, which has ethical implications in its treatment of today's young people and future generations. However, their estimated uncertainty of the cost is ±3%, i.e., the uncertainty is so large as to encompass GDP gain. Hsu (2011) and Ackerman and Stanton (2012) argue that economies are more efficient if the price of fossil fuels better reflects costs to society, and thus GDP gain is likely with an increasing carbon price. Mankiw (2009) similarly suggests that a revenue-neutral carbon tax is economically beneficial. Hansen (2009Hansen ( , 2014 advocates an approach in which a gradually rising carbon fee is collected from the fossil fuel industry with the funds distributed uniformly to citizens. This approach provides incentives to business and the public that drive the economy toward energy efficiency, conservation, renewable energies and nuclear power. An economic study of this carbon-fee-and-dividend in the United States (Nystrom and Luckow, 2014) supports the conclusion that GDP increases as the fee rises steadily. These studies refute the common argument that environmental protection is damaging to economic prosperity.
We can also compare CO 2 extraction cost with the cost of carbon-free energy infrastructure. Global energy consumption in 2015 was 12.9 Gtoe, 14 with coal providing 30% of global energy and almost 45% of global fossil fuel CO 2 emissions (BP, 2016). Most coal use, and its increases, are in Asia, especially China and India. Carbon-free replacement for coal energy is expected to be some combination of renewables (including hydropower) and nuclear power. China is leading the world in installation of wind, solar and nuclear power, with new nuclear power in 2015 approximately matching the sum of new solar and wind power (BP, 2016). For future decarbonization of electricity it is easiest to estimate the cost of the nuclear power component, because nuclear power can replace coal for baseload electricity without the need for energy storage or major change to national electric grids. Recent costs of Chinese and South Korean light water reactors are in the range $2000-3000 per kilowatt (Chinese Academy of Engineering, 2015; Lovering et al., 2016). Although in some countries reactor costs stabilized or declined with repeated construction of the same reactor design, in others costs have risen for a variety of reasons (Lovering et al., 2016). Using $2500 per kilowatt as reactor cost and assuming 85% capacity factor (percent uptime for reactors) yields a cost of $10 trillion to produce 20% of present global energy use (12.9 Gtoe). Note that 20% of current global energy use is a huge amount (Fig. 13), exceeding the sum of present hydropower (6.8%), nuclear (4.4%), wind (1.4%), solar (0.4%), and other renewable energies (0.9%).
We do not suggest that new nuclear power plants on this scale will or necessarily should be built. Rather we use this calculation to show that mitigation costs are not large in comparison to costs of extracting CO 2 from the air. Renewable energy costs have fallen rapidly in the past 2-3 decades with the help of government subsidies, especially renewable portfolio standards that  (2016); energy accounting method is the substitution method (Macknick, 2011). require utilities to achieve a specified fraction of their power from renewable sources. Yet fossil fuel use continues to be high, at least in part because fossil fuel prices do not include their full cost to society. Rapid and economic movement to non-fossil energies would be aided by a rising carbon price, with the composition of energy sources determined by competition among all nonfossil energy sources, as well as energy efficiency and conservation. Sweden provides a prime example: it cut per capita emissions by two-thirds since the 1990s while doubling per capita income in a capitalistic framework that embodies free-market principles (Pierrehumbert, 2016).
Mitigation of climate change deserves urgent priority. We disagree with assessments such as "The world will probably have only two choices if it wants to stay below 1.5°C of warming. It must either deploy carbon dioxide removal on an enormous scale or use solar geoengineering" (Parker and Geden, 2016). While we reject 1.5°C as a safe target -it is likely warmer than the Eemian and far above the Holocene range - Figure 12 shows that fossil fuel emission reduction of 3%/year beginning in 2021 yields maximum global warming ~1.5°C for climate sensitivity 3°C for 2×CO 2 , with neither CO 2 removal nor geoengineering. These calculations show that mitigation -reduction of fossil fuel emissions -is very effective. We know no persuasive scientific reason to a priori reject as implausible a rapid phasedown of fossil fuel emissions.

Non-CO 2 GHGs
The annual increment in GHG climate forcing is growing, not declining. The increase is more than 20% in just the past five years (Fig. 8). Resurgence of CH 4 growth is partly responsible, but CO 2 is by far the largest contributor to growth of GHG climate forcing (Fig. 8). Nevertheless, given the difficulty and cost of reducing CO 2 , we must ask about the potential for reducing non-CO 2 GHGs. Could realistic reductions of these other gases substantially alter the CO 2 abundance required to meet a target climate forcing?
We conclude, as discussed in Appendix A13, that a net decrease of climate forcing by non-CO 2 GHGs of perhaps −0.25 W/m 2 relative to today is plausible, but we must note that this is a dramatic change from the growing abundances, indeed accelerating growth, of these gases today. Achievement of this suggested negative forcing requires (i) successful completion of planned phase-out of MPTGs (−0.23 W/m 2 ), (ii) absolute reductions of CH 4 forcing by 0.12 W/m 2 from its present value, and (iii) N 2 O forcing increasing by only 0.1 W/m 2 . Achieving this net negative forcing of −0.25 W/m 2 for non-CO 2 gases would allow CO 2 to be 365 ppm, rather than 350 ppm, while yielding the same total GHG forcing. Absolute reduction of non-CO 2 gases is thus helpful, but does not alter the requirement for rapid fossil fuel emission reductions. Moreover, this is an optimistic scenario that is unlikely to occur in the absence of a reduction of CO 2 , which is needed to limit global warming and thus avoid amplifying GHG feedbacks.

Aerosols and Purposeful Climate Intervention
Human-made aerosols today are believed to cause a large, albeit poorly measured, negative climate forcing (Fig. 4) of the order of −1 W/m 2 with uncertainty of at least 0.5 W/m 2 ( Figure  7. 19 Boucher et al., 2013). Fossil fuel burning is only one of several human-caused aerosol sources (Boucher et al., 2013). Given that human population continues to grow, and that humancaused climate effects such as increased desertification can lead to increased aerosols, we do not anticipate a large reduction in the aerosol cooling effect, even if fossil fuel use declines. Rao et al. (2017) suggest that future aerosol amount will decline due to technological advances and global action to control emissions. We are not confident of such a decline, as past controls have been at least matched by increasing emissions in developing regions, and global population continues to grow. However, to the extent that Rao et al. (2017) projections are borne out, they will only strengthen the conclusions of our present paper about the threat of climate change for young people and the burden of decreasing GHG amounts in the atmosphere.
Recognition that aerosols have a cooling effect, combined with the difficulty of restoring CO 2 to 350 ppm or less, inevitably raises the issue of purposeful climate intervention, also called geoengineering, and specifically solar radiation management (SRM). The cooling mechanism receiving greatest attention is injection of SO 2 into the stratosphere (Budyko, 1974;Crutzen, 2006), thus creating sulfuric acid aerosols that mimic the effect of volcanic aerosol cooling. That idea and others are discussed in a report of the U.S. National Academy of Sciences (NAS, 2015b) and references therein. We limit our discussion to the following summary comments.
Such purposeful intervention in nature, an attempt to mitigate effects of one human-made pollutant with another, raises additional practical and ethical issues. Stratospheric aerosols, e.g., could deplete stratospheric ozone and/or modify climate and precipitation patterns in ways that are difficult to predict with confidence, while doing nothing to alleviate ocean acidification caused by rising CO 2 ; we note that Keith et al. (2016) suggest alternative aerosols that would limit the impact on ozone. However, climate intervention also raises issues of global governance, and introduces the possibility of sudden global consequences if aerosol injection is interrupted (Boucher at al., 2013). Despite these issues, it is apparent that cooling by aerosols, or other methods that alter the amount of sunlight absorbed by Earth, could be effective more quickly than the difficult process of removing CO 2 from the air. Thus we agree with the NAS (2015b) conclusion that research is warranted to better define the climate, economic, political, ethical, legal and other dimensions of potential climatic interventions.
In summary, although research on climate interventions is warranted, the possibility of geoengineering can hardly be seen as alleviating the overall burden being placed on young people by continued high fossil fuel emissions. We concur with the assessment (NAS, 2015b) that such climate interventions are no substitute for the reduction of carbon dioxide emissions needed to stabilize climate and avoid deleterious consequences of rapid climate change.

Discussion
Global temperature is now far above its range during the preindustrial Holocene, attaining at least the warmth of the Eemian period, when sea level reached +6-9 m relative to today. Also Earth is now out of energy balance, implying that more warming will occur, even if atmospheric GHG amounts are stabilized at today's level. Furthermore, the GHG climate forcing is not only still growing, the growth rate is actually accelerating, as shown in Fig. 14, which is extracted from data in our Fig. 8.
This summary, based on real world data for temperature, planetary energy balance, and GHG changes, differs from a common optimistic perception of progress toward stabilizing climate. That optimism may be based on the lowered warming target in the Paris Agreement (2015), slowdown in the growth of global fossil fuel emissions in the past few years (Fig. A1), and falling prices of renewable energies, but the hard reality of the climate physics emerges in Figs. 2,5,8 and 14. Although the scenarios employed in climate simulations for the most recent IPCC study (AR5) include cases with rapidly declining GHG growth, the scenarios do nothing to alter reality, which reveals that GHG growth rates not only remain high, they are accelerating.
The need for prompt action implied by these realities may not be a surprise to the relevant scientific community, because paleoclimate data revealed high climate sensitivity and the dominance of amplifying feedbacks. However, effective communication with the public of the urgency to stem human-caused climate change is hampered by the inertia of the climate system, especially the ocean and the ice sheets, which respond rather slowly to climate forcings, thus allowing future consequences to build up before broad public concern awakens. Some effects of human-caused global warming are now unavoidable, but is it inevitable that sea level rise of many meters is locked in, and, if so, on what time scale? Precise unequivocal answers to such questions are not possible. However, useful statements can be made.
First, the inertia and slow response of the climate system also allow the possibility of actions to limit the climate response by reducing human-caused climate forcing in coming years and decades. Second, the response time itself depends on how strongly the system is being forced; specifically, the response might be much delayed with a weaker forcing.
For example, studies suggesting multi-meter sea level rise in a century assume continued high fossil fuel emissions this century  or at least a 2°C SST increase (DeConto and Pollard, 2016). Ice sheet response time decreases rapidly in models as the forcing increases, because processes such as hydrofracturing and collapse of marine-terminating ice cliffs spur ice sheet disintegration (Pollard et al., 2015). All amplifying feedbacks, including atmospheric water vapor, sea ice cover, soil carbon release and ice sheet melt could be reduced by rapid emissions phasedown. This would reduce the risk of climate change running out of humanity's control and provide time to assess the climate response, develop relevant technologies, and consider further purposeful actions to limit and/or adapt to climate change. Concern exists that large sea level rise may be inevitable, because of numerous ice streams on Antarctica and Greenland with inward-sloping beds (beds that deepen upstream) subject to runaway marine ice sheet instability (Mercer, 1978;Schoof, 2007Schoof, , 2010. Some ice stream instabilities may already have been triggered (Rignot et al., 2014), but the number of ice streams affected and the time scale of their response may differ strongly depending on the magnitude of the forcing (DeConto and Pollard, 2016). Sea level rise this century of say half a meter to a meter, which may be inevitable even if emissions decline, would have dire consequences, yet these are dwarfed by the humanitarian and economic disasters that would accompany sea level rise of several meters (McGranahan et al., 2007). Given the increasing proportion of global population living in coastal areas (Hallegatte et al., 2013), there is potential for forced migrations of hundreds of millions of people, dwarfing prior refugee humanitarian crises, challenging global governance (Biermann and Boas, 2010) and security (Gemenne et al., 2014).
Global temperature is a useful metric, because increasing temperature drives amplifying feedbacks. Global ocean temperature is a major factor affecting ice sheet size, as indicated by both model studies (Pollard et al., 2015) and paleoclimate analyses (Overpeck et al., 2006;. Eemian ocean warmth, probably not more than about +0.7°C warmer than pre-industrial conditions (McKay et al., 2011;Masson-Delmotte et al., 2013; Section 2.2 above), corresponding to global warmth about +1°C relative to preindustrial, led to sea level 6-9 m higher than today. This implies that, on the long run, the El Niño-elevated 2016 temperature of +1.3°C relative to preindustrial temperature, and even the (+1.05°C) underlying trend to date without the El Niño boost, are probably too high for maintaining our present coastlines.
We conclude that the world has already overshot appropriate targets for GHG amount and global temperature, and we thus infer an urgent need for both (1) rapid phasedown of fossil fuel emissions, (2) actions that draw down atmospheric CO 2 , and (3) actions that, at minimum, eliminate net growth of non-CO 2 climate forcings. These tasks are formidable and, with the exception of the Montreal Protocol agreement on HFCs that will halt the growth of their climate forcing (Appendix A13), they are not being pursued globally. Actions at citizen, city, state and national levels to reduce GHG emissions provide valuable experience and spur technical developments, but without effective global policies the impact of these local efforts is reduced by the negative feedback caused by reduced demand for and price of fossil fuels.
Our conclusion that the world has overshot appropriate targets is sufficiently grim to compel us to point out that pathways to rapid emission reductions are feasible. Peters et al. (2013) note that Belgium, France and Sweden achieved emission reductions of 4-5%/year sustained over 10 or more years in response to the oil crisis of 1973. These rates were primarily a result of nuclear power build programs, which historically has been the fastest route to carbon-free energy (Fig. 2 of Cao et al., 2016). These examples are an imperfect analogue, as they were driven by a desire for energy independence from oil, but present incentives are even more comprehensive. Peters et al. (2013) also note that a continuous shift from coal to natural gas led to sustained reductions of 1-2%/year in the UK in the 1970s and in the 2000s, 2%/year in Denmark in 1990-2000s, and 1.4%/year in the USA since 2005. Furthermore, these examples were not aided by the economywide effect of a rising carbon fee or tax (Hsu, 2011;Ackerman and Stanton, 2012;Hansen, 2014), which encourages energy efficiency and carbon-free energies.
In addition to CO 2 emission phase-out, large CO 2 extraction from the air is needed and a halt of growth of non-CO 2 climate forcings to achieve the temperature stabilization of our scenarios. Success of both CO 2 extraction and non-CO 2 GHG controls requires a major role for developing countries, given that they have been a large source of recent deforestation (IPCC, 2013) and have a large potential for reduced emissions. Ancillary benefits of the agricultural and forestry practices needed to achieve CO 2 drawdown, such as improved soil fertility, advanced agricultural practices, forest products, and species preservation, are of interest to all nations. Developed nations have a recognized obligation to assist nations that have done little to cause climate change yet suffer some of the largest climate impacts. If economic assistance is made partially dependent on verifiable success in carbon drawdown and non-CO 2 mitigation, this will provide incentives that maximize success in carbon storage. Some activities, such as soil amendments that enhance weathering, might be designed to support both CO 2 and other GHG drawdown.
Considering our conclusion that the world has overshot the appropriate target for global temperature, and the difficulty and perhaps implausibility of negative emissions scenarios, we would be remiss if we did not point out the potential contribution of demand-side mitigation that can be achieved by individual actions as well as by government policies. Numerous studies (e.g. Hedenhus et al., 2014;Popp et al., 2010) have shown that reduced ruminant meat and dairy products is needed to reduce GHG emissions from agriculture, even if technological improvements increase food yields per unit farmland. Such climate-beneficial dietary shifts have also been linked to co-benefits that include improved sustainability and public health (Bajzelj et al., 2014;Tilman and Clark, 2014). Similarly, Working Group 3 of IPCC (2014) finds "robust evidence and high agreement" that demand-side measures in the agriculture and land use sectors, especially dietary shifts, reduced food waste, and changes in wood use have substantial mitigation potential, but they remain under-researched and poorly quantified.
There is no time to delay. CO 2 extraction required to achieve 350 ppm CO 2 in 2100 was ~100 PgC if 6%/year emission reductions began in 2013 (Hansen et al., 2013a). Required extraction is at least ~150 PgC in our updated scenarios, which incorporate growth of emissions in the past four years and assume that emissions will continue at approximately current levels until a global program of emission reductions begins in four years (in 2021 relative to 2020; see Figs. 9, 10 for reduction rates). The difficulty of stabilizing climate was thus markedly increased by a delay in emission reductions of eight years, from 2013 to 2021. Nevertheless, if rapid emission reductions are initiated soon, it is still possible that at least a large fraction of required CO 2 extraction can be achieved via relatively natural agricultural and forestry practices with other benefits. On the other hand, if large fossil fuel emissions are allowed to continue, the scale and cost of industrial CO 2 extraction, occurring in conjunction with a deteriorating climate and costly dislocations, may become unmanageable. Simply put, the burden placed on young people and future generations may become too heavy to bear.

A1. Fossil Fuel CO 2 Emissions
CO 2 emissions from fossil fuels in 2015 were only slightly higher than in 2014 (Fig. A1). Such slowdowns are common, usually reflecting the global economy. Given rising global population and the fact that nations such as India are still at early stages of development, the potential exists for continued emissions growth. Fundamental changes in energy technology are needed for the world to rapidly phase down fossil fuel emissions.
Emissions are growing rapidly in emerging economies; while growth slowed in China in the past two years, emissions remain high (Fig. 1). The Kyoto Protocol (1997), a policy instrument of the Framework Convention (UNFCCC, 1992), spurred emission reductions in some nations, and the collapse of the Soviet Union caused a large decrease of emissions by Russia (Fig. 1b). However, growth of international ship and air emissions (Fig. 1b) largely offset these reductions and the growth rate of global emissions actually accelerated from 1.5%/year in 1973-2000 to ~2.5%/year after 2000 (Fig. A1). China is now the largest source of fossil fuel emissions, followed by the U.S. and India, but on a per capita historical basis the U.S. is 10 times more accountable than China and 25 times more accountable than India for the increase of atmospheric CO 2 above its preindustrial level . Tabular data for Figs. 1 and A1 are available on the web page www.columbia.edu/~mhs119/Burden.

A2. Transient Climate Response to cumulative CO 2 Emissions (TCRE)
The transient climate response (TCR), defined as the global warming at year 70 in response to a 1%/year CO 2 increase, for our simple Green's function climate model is 1.89°C with energy imbalance of 1.52 W/m 2 at that point; this TCR is in the middle of the range reported in the IPCC AR5 report (IPCC, 2013). We calculate the transient climate response to cumulative carbon emissions (TCRE) of our climate plus carbon cycle model as in Section 10.8.4 of IPCC (2013), i.e., TCRE = TCR × CAF/C 0 , where C 0 = preindustrial atmospheric CO 2 mass = 590 PgC and CAF = Catm/Csum, Catm = atmospheric CO 2 mass minus C 0 and Csum = cumulative CO 2 emissions (all evaluated at year 2100). We find TCRE = 1.54°C per 1000 PgC at 2100 with constant emissions (which yields cumulative emissions of 1180 PgC at 2100, which is near the midpoint of the range assessed by IPCC, i.e., 0.8°C to 2.5°C per 1000 PgC (IPCC, 2013). Our two cases with rapidly declining emissions never achieve 1000 PgC emissions, but TCRE can still be computed using the IPCC formulae, yielding TCRE = 1.31 and 1.25°C per 1000 PgC at 2100 for the cases of −3%/year and −6%/year respective emission reductions. As expected, the rapid emission reductions substantially reduce the temperature rise in 2100.

A3. Observed Temperature Data and Analysis Method
We use the current Goddard Institute for Space Studies global temperature analysis (GISTEMP), described by Hansen et al. (2010). The analysis combines data from: (1) meteorological station data of the Global Historical Climatology Network (GHCN) described by Peterson and Vose (1997) and Menne et al. (2012), (2) Antarctic research station data reported by the Scientific Committee on Antarctic Research (SCAR), (http://www.antarctica.ac.uk/met/READER), and (3) ocean surface temperature measurements from the NOAA Extended Reconstructed Sea Surface temperature (ERSST) (Smith et al., 2008;Huang et al., 2015).
Surface air temperature change over land is about twice SST change (Fig. A3a), and thus global temperature change is 1.3 times larger than the SST change. Note that the Arctic Ocean and parts of the Southern Ocean are excluded in the calculations because of inadequate data, but these regions are also not sampled in most paleo analyses and the excluded areas are small. Land area included covers 29% of the globe and ocean area included covers 65% of the globe. The present analysis uses GHCN.v3.3.0 (Menne et al., 2012) for land data and ERSST.v4 for sea surface temperature (Huang et al., 2015). Update from GHCN.v2 used in our 2010 analysis to GHCN.v3 had negligible effect on global temperature change over the past century (see graph on http://www.columbia.edu/~mhs119/Temperature/GHCN_V3vsV2/). However, the adjustments to SST to produce ERSST.v4 have a noticeable effect, especially in the period 1939-1945, as shown by the difference between the two data sets (lower graph in Fig. A3b). This change is of interest mainly because it increases the magnitude of an already unusual global temperature fluctuation in the 1940s, making the 1939-1945 global temperature maximum even more pronounced than it was in ERSST.v3 data. Thompson et al. (2008) show that two natural sources of variability, the El Niño/Southern Oscillation and (possibly related) unusual winter Arctic warmth associated with advection over high Northern Hemisphere latitudes, partly account for global warmth of 1939-1945, and they suggest that the sharp cooling after 1945 is a data flaw, due to a rapid change in the mix of data sources (bucket measurements and engine room intake measurements) and a bias between these that is not fully accounted for. Huang et al. (2015) justify the changes made to obtain version 4 of ERSST, the changes including more complete input data in ICOADS Release 2.5, buoy SST bias adjustments not present in version 3, updated ship SST bias adjustments using Hadley Nighttime Marine Air Temperature version 2 (HadNMat2), and revised low-frequency data filling in data sparse regions using nearby observations. ERSST.v4 is surely an improvement in the record during the past half century when spatial and temporal data coverages are best. On the other hand, the largest changes between v3 and v4 are in 1939-1945, coinciding with World War II and changes in the mix of data sources. Several hot spots appear in the Southern Hemisphere ocean during WWII in the v4 data, and then disappear after the war (Fig. A3c). These hot spots coincide with the locations of large SST changes between v3 and v4 (Fig. A3c), which leads us to suspect that the magnitude of the 1940s global warming maximum (Fig. 2) is exaggerated; i.e., it is partly spurious. We suggest that this warming spike warrants scrutiny in the next version of the SST analysis. However, the important point is that these data adjustments and uncertainties are small in comparison with the long-term warming. Adjustments between ERSST.v3b and ERSST.v4 increase global warming over the period 1950-2015 by about 0.05°C, which is small compared with the ~1°C global warming during that period. The effect of the adjustments on total global warming between the beginning of the 20 th century and 2015 is even smaller (Fig. A3b).

A4. Recent Global Warming Rate
Recent warming removes the illusion of a hiatus of global warming since the 1997-98 El Niño (Fig. 2). Several studies, including Trenberth and Fasullo (2013), England et al. (2014), Dai et al. (2015), Rajaratnam et al. (2015) and Medhaug et al. (2017), showed that temporary plateaus are consistent with expected long-term warming due to increasing atmospheric GHGs. Other analyses of the 1998-2013 plateau illuminate the roles of unforced climate variability and natural and human-caused climate forcings in climate change, with the Interdecadal Pacific Oscillation (a recurring pattern of ocean-atmosphere climate variability) playing a major role in the warming slowdown (Kosaka and Xie, 2013;Huber and Knutti, 2014;Meehl et al., 2014;Fyfe et al., 2016;Medhaug et al., 2017).

A5. Coincidence of 1880-1920 Mean and Preindustrial Global Mean Temperatures
The Framework Convention (UNFCCC, 1992) and Paris Agreement (2015) define goals relative to 'preindustrial' temperature, but do not define that period. We use 1880-1920, the earliest time with near global coverage of instrumental data, as the zero-point for temperature anomalies. Although human-caused increases of GHGs would be expected to have caused a small warming by then, that warming was at least partially balanced by cooling from larger than average  (Schmidt et al. 2014), which has higher resolution (40-layer atmosphere at 2°×2.5°, 32-layer ocean at 1°×1.25°), (b) version used by , which has coarse resolution (20layer atmosphere at 4°×5°, 12-layer ocean at 4°×5°) and includes two significant improvements to small scale ocean mixing, cf. section 3.2 of  volcanic activity in 1880-1920. Extreme Little Ice Age conditions may have been ~0.1C cooler than the 1880-1920 mean (Abram et al., 2016), but the Little Ice Age is inappropriate to define preindustrial because the deep ocean temperature did not have time to reach equilibrium. Thus preindustrial global temperature has uncertainty of at least 0.1°C, and the 1880-1920 period, which has the merit of near-global data, yields our best estimate of preindustrial temperature.

A6. Land versus Ocean Warming at Equilibrium
Observations (Fig. A3a) show surface air temperature (SAT) over land increasing almost twice as much as sea surface temperature (SST) during the past century. This large difference is likely partly due to the thermal inertia of the ocean, which has not fully responded to the climate forcing due to increasing GHGs. However, land warming is heavily modulated by the ocean temperature, so land temperature too has not achieved its equilibrium response.
We use long climate model simulations to examine how much the ratio of land SAT change over ocean SST change (the observed quantities) is modified as global warming approaches its equilibrium response. This ratio is ~1.8 in years 901-1000 of doubled CO 2 simulations (Fig. A6) for two versions of GISS modelE-R (Schmidt et al., 2014;.  Figure A8. Fossil fuel CO 2 emissions (left scale) and airborne fraction, i.e., the ratio of observed atmospheric CO 2 increase to fossil fuel CO 2 emissions. W/m 2 by Cheng et al. (2017) for the period 1960-2015 and +0.7 ± 0.1 W/m 2 by Dieng et al. (2017) for the period 2005-2013. We conclude that the estimate of +0.75 ± 0.25 W/m 2 for the current Earth energy imbalance averaged over the solar cycle is still valid.

A8. CO 2 and CH 4 Growth Rates
Growth of airborne CO 2 is about half of fossil fuel CO 2 emissions (Fig. A8), the remaining portion of emissions being the net uptake by the ocean and biosphere . Here we use the Keeling et al. (1973) definition of airborne fraction, which is the ratio of quantities that are known with good accuracy: the annual increase of CO 2 in the atmosphere and the annual amount of CO 2 injected into the atmosphere by fossil fuel burning. The data reveal that, even as fossil fuel emissions have increased by a factor of four over the past half century, the ocean and biosphere have continued to take up about half of the emissions (Fig. A8, right-hand scale). This seemingly simple relation between emissions and atmospheric CO 2 growth is not predictive as it depends on the growth rate of emissions being maintained, which is not true in cases with major changes in the emission scenario, so we use a carbon cycle model in Section 7 to compute atmospheric CO 2 as a function of emission scenario.
Oscillations of annual CO 2 growth are correlated with global temperature and with the El Niño/La Niña cycle 15 . Correlations (Fig. 6) are calculated for the 12-month running means, which effectively remove the seasonal cycle and monthly noise. Maxima of the CO 2 growth rate lag global temperature maxima by 7-8 months (Fig. 6b) and lag Niño3.4 [latitudes 5N-5S, longitudes 120-170W] temperature by ~10 months. These lags imply that the current CO 2 growth spike (Fig. 6 uses data through January 2017), associated with the 2015-16 El Niño, is well past its maximum, as Niño3.4 peaked in December 2015 and the global temperature anomaly peaked in February 2016.
CH 4 growth rate has varied over the past two decades, probably driven primarily by changes in emissions, as observations of CH 3 CCl 3 show very little change in the atmospheric sink for 15 One mechanism for greater than normal atmospheric CO 2 growth during El Niños is the impoverishment of nutrients in equatorial Pacific surface water and thus reduced biological productivity that result from reduced upwelling of deep water (Chavez et al., 1999). However, the El Niño/La Niña cycle seems to have an even greater impact on atmospheric CO 2 via the terrestrial carbon cycle through effects on the water cycle, temperature, and fire, as discussed in a large body of literature (referenced, e.g., by Schwalm et al., 2011). CH 4 (Montzka et al., 2011;Holmes et al., 2013). Recent box-model inversions of the CH 4 -CH 3 -CCl 3 system have argued for large fluctuations in the atmospheric sink over this period but there is no identified cause for such changes (Rigby et al., 2017;Turner et al., 2017;Prather and Holmes, 2017). Future changes in the sink could lead to increased atmospheric CH 4 separate from emission changes, but this effect is difficult to project and not included in the RCP scenarios (Voulgarakis et al., 2013).
Carbon isotopes provide a valuable constraint (Saunois et al., 2016) that aids analysis of which CH 4 sources 16 contribute to the CH 4 growth resurgence in the past decade (Fig. 7). Schaefer et al. (2016) conclude that the growth was primarily biogenic, thus not fossil fuel, and located outside the tropics, most likely ruminants and rice agriculture. Such an increasing biogenic source is consistent with effects of increasing population and dietary changes (Tilman and Clark, 2014). Nisbet et al. (2016) concur with Schaefer et al. (2016) that the CH 4 growth is from biogenic sources, but from the latitudinal distribution of growth they conclude that tropical wetlands 17 have been an important contributor to the CH 4 increase. Their conclusion that increasing tropical precipitation and temperature may be major factors driving CH 4 growth suggests the possibility that the slow climate-methane amplifying feedback might already be significant. There is also concern that global warming will lead to a massive increase of CH 4 emissions from methane hydrates and permafrost (O'Connor et al., 2010), but as yet there is little evidence for a substantial increase of emissions from hydrates or permafrost either now or over the last 1,000,000 years (Berchet et al., 2016;Warwick et al., 2016;Quiquet et al., 2015). Schwietzke et al. (2016) use isotopic constraints to show that the fossil fuel contribution to atmospheric CH 4 is larger than previously believed, but total fossil fuel CH 4 emissions are not increasing. This conclusion is consistent with the above studies, and it does not contradict evidence of increased fossil fuel CH 4 emissions at specific locations (Turner et al., 2016). A recent inverse model study, however, contradicts the satellite studies and finds no evidence for increased US emissions (Bruhwiler et al., 2017). The recent consortium study of global CH 4 emissions finds with top-down studies that the recent increase is likely due to biogenic (natural and human sources) sources in the tropics, but it is difficult to attribute the magnitude of the rise to tropical wetlands alone

A9. CO 2 Emissions in Historical Period
For land use CO 2 emissions in the historical period, we use the values labeled Houghton/2 by Hansen et al (2008), which were shown in the latter publication to yield good agreement with observed CO 2 . We use fossil fuel CO 2 emissions data for 1850-2013 from Boden et al. (2016). BP (2016) fuel consumption data for 2013-2015 are used for the fractional annual changes of each nation to allow extension of the Boden analysis through 2015. Emissions were almost flat from 2014 to 2015, due to economic slowdown and increased use of low-carbon energies, but, even if a peak in global emissions is near, substantial decline of emissions is dependent on acceleration in the transformation of energy production and use .
16 Estimated human-caused CH 4 sources  are: fossil fuels (29%), biomass/biofuels (11%), Waste and landfill (23%), ruminants (27%) and rice (11%) 17 Wetlands compose a majority of natural CH 4 emissions and are estimated to be equivalent to about 36% of the anthropogenic source     Table A10b   Annual data are available at http://www.columbia.edu/~mhs119/Burden/. CO 2 , CH 4 and N 2 O forcings are calculated with analytic formulae of Hansen et al. (2000). CH 4 forcing includes the factor 1.4 to convert adjusted forcing to effective forcing, thus incorporating the estimated effect of a CH 4 increase on tropospheric ozone and stratospheric water vapor. Our CH 4 adjusted forcing is significantly (~17%) higher that the values in IPCC (2013), but (~9%) smaller than values of Etminan (2017). Our factor 1.4 to convert direct radiative forcing to effective forcing is in the upper portion of the indirect effects discussed by Myhre et al. (2013), so our net CH 4 forcing agrees with Etminan et al. (2017) within uncertainties. Figure A11. Solar irradiance and sunspot number in the era of satellite data. Left scale is the energy passing through an area perpendicular to Sun-Earth line. Averaged over Earth's surface the absorbed solar energy is ~240 W/m 2 , so the full amplitude of the measured solar variability is ~0.25 W/m 2 .

A11. Solar Irradiance
Solar irradiance has been measured from satellites since the late 1970s. Fig. A11 is a composite of several satellite-measured time series. Data through 28 February 2003 are an update of Frohlich and Lean (1998) obtained from Physikalisch Meteorologisches Observatorium Davos, World Radiation Center. Subsequent update is from University of Colorado Solar Radiation & Climate Experiment (SORCE). Historical total solar irradiance reconstruction is available at http://lasp.colorado.edu/home/sorce/data/tsi-data/ Data sets are concatenated by matching the means over the first 12 months of SORCE data. Monthly sunspot numbers support the conclusion that the solar irradiance in the current solar cycle is significantly lower than in the three preceding solar cycles.
The magnitude of the change of solar irradiance from the prior solar cycle to the current solar cycle is of the order of −0.1 W/m 2 , which is not negligible but is small compared with greenhouse gas climate forcing. On the other hand, the variation of solar irradiance from solar minimum to solar maximum is of the order of 0.25 W/m 2 , so the high solar irradiance in 2011 -2015 contributes to the increase of Earth's energy imbalance between 2005-2010 and 2010-2015.

A12. Alternative Scenario
Simulated global temperature for the climate forcings of the "alternative scenario" discussed in Section 6 are shown in Fig. A12. The climate model, with sensitivity 3°C for doubled CO 2 , is the same as used for Fig. 12.

A13. Non-CO 2 GHGs
CO 2 is the dominant forcing in future climate scenarios. Growth of non-CO 2 GHG climate forcing is likely to be even smaller, relative to CO 2 forcing, than in recent decades (Fig. 8) if there is a strong effort to limit climate change. Indeed, recent agreement to use the Montreal Figure A12. Simulated global temperature with historical climate forcings to 2000 followed by the alternative scenario. Historical climate forcings are discussed in the main text.
Protocol (2016) to phase down production of minor trace gases, the hydrofluorocarbons (HFCs), should cause annually added forcing of Montreal Protocol Trace Gases (MPTGs) + Other Trace Gases (OTGs) (red region in Fig. 8) to become near zero or slightly negative, thus at least partially off-setting growth of other non-CO 2 GHGs, especially N 2 O.
Methane (CH 4 ) is the largest climate forcing other than CO 2 (Fig. 4). The CH 4 atmospheric lifetime is only about 10 years (Prather et al., 2012), so there is potential to reduce this climate forcing rapidly if CH 4 sources are reduced. Our climate simulations, based on the RCP6.0 non-CO 2 GHG scenarios, follow an optimistic path in which CH 4 increases moderately in the next few decades to 1960 ppb in 2070 and then decreases rapidly to 1650 ppb in 2100, yielding a forcing change of −0.1 W/m 2 . However, the IPCC (Kirtman et al., 2013) uses a more modern chemical model projection for the RCP anthropogenic emissions and gives a less beneficial view with a decrease to only 1734 ppb and a forcing change of −0.03 W/m 2 . RCP2.6 makes a more optimistic assumption: that CH 4 will decline monotonically to 1250 ppb in 2100, yielding a forcing of −0.3 W/m 2 (relative to today's 1800 ppb CH 4 ), but the IPCC projections of RCP2.6 reduce this to −0.2 W/m 2 (Kirtman et al., 2013).
Observed atmospheric CH 4 amount ( Fig. A13a) is diverging on the high side of these optimistic scenarios. The downward offset (~20 ppb) of CH 4 scenarios relative to observations (Fig. A13a) is due to the fact that RCP scenarios did not include a data adjustment that was made in 2005 to match a revised CH 4 standard scale (E. Dlugokencky, pers. comm.), but observed CH 4 is also increasing more rapidly than in most scenarios. Reversal of CH 4 growth is made difficult by increasing global population, the diverse and widely distributed nature of agricultural sources, and global warming "in the pipeline," as these trends create an underlying tendency for increasing CH 4 . The discrepancy between observed and assumed CH 4 growth could also be due in part to increased natural sources or changes in the global OH sink Turner et al., 2017). Evidence for increased natural sources in a warmer climate are suggested by glacial-interglacial CH 4 increases of the order of 300 ppb, and contributions to observed fluctuations cannot be ruled out on the basis of recent budgets .
Methane emissions from rice agriculture and ruminants potentially could be mitigated by changing rice growing methods (Epule et al., 2011) and inoculating ruminants (Eckard et al., 2010;Beil, 2015)], but that would require widespread adoption of new technologies at the farmer level. California, in implementing a state law to reduce GHG emissions, hopes to dramatically cut agricultural CH 4 emissions (see www.arb.ca.gov/cc/scopingplan/scopingplan.htm), but California has one of the most technological and regulated agricultural sectors in the world. It is not clear that this level of management can occur in the top agricultural CH 4 emitters like China, India and Brazil. Methane leaks from fossil fuel mining, transportation and use can be reduced, indeed, percentage leakage from conventional fossil fuel mining and fuel use has declined substantially in recent decades (Schwietzke et al, 2016), but there is danger of increased leakage with expanded shale gas extraction (Caulton et al., 2014;Petron et al., 2013;Howarth, 2015;Kang et al., 2016).
Observed N 2 O growth is exceeding all scenarios (Fig. A13b). Major quantitative gaps remain in our understanding of the nitrogen cycle (Kroeze and Bouwman, 2011), but fertilizers are clearly a principal cause of N 2 O growth (Röckmann and Levin 2005; Park et al., 2012). More efficient use of fertilizers could reduce N 2 O emissions (Liu and Zhang, 2011), but considering the scale of global agriculture, and the fact that fixed N is an inherent part of feeding people, there will be pressure for continued emissions at least comparable to present emissions. In contrast, agricultural CH 4 emissions are inadvertent and not core to food production. Given the current imbalance [emissions exceeding atmospheric losses by about 30% (Prather et al., 2012)] and the long N 2 O atmospheric lifetime (116 ± 9 years; Prather et al., 2015) it is nearly inevitable that N 2 O will continue to increase this century, even if emissions growth is checked. There can be no expectation of an N 2 O decline that offsets the need to reduce CO 2 .
The Montreal Protocol has stifled and even reversed growth of specific trace gases that destroy stratospheric ozone and cause global warming (Prather et al., 1996;Newman et al., 2009). The anticipated benefit over the 21 st century is a drop in climate forcing of −0.23 W/m 2 . Protocol amendments that add other gases such as HFCs are important; forcings of these gases are small today, but without the Protocol their potential for growth is possibly as large as +0.2 W/m 2 .
We conclude that a 0.25 W/m 2 decrease of climate forcing by non-CO 2 GHGs is plausible, but requires a dramatic change from the growing abundances of these gases today. Achievement requires (i) successful phase-out of MPTGs (−0.23 W/m 2 ), (ii) reduction of CH 4 forcing by 0.12 W/m 2 , and (iii) limiting N 2 O increase to 0.1 W/m 2 . A net negative forcing of −0.25 W/m 2 for non-CO 2 gases would allow CO 2 to be 365 ppm, rather than 350 ppm, while yielding the same total GHG forcing. Thus potential reduction of non-CO 2 gases is helpful, but it does not alter the need for rapid fossil fuel emission reduction.