Assessment of negative and positive CO 2 emissions on global warming metrics using large ensemble Earth system model simulations

The benefits of implementing negative emission technologies for a century (years 2070-2170) on the global warming response to cumulative carbon emissions until year 2420 are assessed with a comprehensive set of 25 intermediate complexity Earth system model integrations. Model integrations include 82 different model realisations covering a wide range of plausible climate states. The global warming response is assessed in terms of two key climate metrics: the effective transient climate response to cumulative CO 2 emissions (eTCRE), measuring the surface warming response to cumulative carbon emissions and associated non-CO 2 (RCP4.5) forcing, and the zero emissions commitment (ZEC), measuring the extent of any continued warming after net zero 30 is reached. The TCRE is approximated from eTCRE by removing the contributions of non-CO 2 forcing as 2.15 °C EgC -1 (with a 10-90 % range of 1.6 to 2.8 °C EgC -1 ). During the net positive emission phases, the eTCRE decreases from 2.62 (1.90 to 3.65) to 2.30 (1.73 to 3.23) °C EgC -1 due to a weakening in the increase in radiative forcing with an increase in atmospheric carbon, which is partly opposed by an increasing fraction of the radiative forcing warming the surface as the ocean stratifies. During the negative and zero emission phases, a progressive reduction 35 of the eTCRE to 2.0 (1.4 to 2.8) °C EgC -1 is driven by the reducing airborne fraction as CO 2 is drawn down by the ocean. The model uncertainty in the slopes of warming versus cumulative CO 2 emissions varies from being controlled by the radiative feedback parameter during positive emissions to also being affected by ocean circulation and carbon-cycle parameters during zero or net-negative emissions. There is hysteresis in atmospheric CO 2 and surface warming, where atmospheric CO 2 and surface temperature are higher after peak emissions compared with 40 before peak emissions. The continued warming after emissions cease defining the ZEC for the model mean without carbon capture is -0.01 o C at 25 years and decreases in time to -0.15 °C at 90 years after emissions cease. However, there is a spread in the ensemble with a temperature overshoot occurring in 50 % of the ensemble members at year 25. The ZEC only becomes


Introduction
There is an increasing need to adopt negative emission technologies (Luderer et al., 2013;Rogelj et al., 2015; 50 Beerling et al., 2020) to enhance the chance of meeting the Paris climate agreement targets of global warming of 1.5 °C or less than 2 °C given the ongoing growth in greenhouse gas concentrations (Boucher et al. 2012;Jeltsch-Thömmes et al., 2020). For a 1.5 °C target, there is 66 % chance of meeting this target only if post-2019 cumulative carbon emissions are limited to less than ~400 GtCO2 (IPCC 2021). How much carbon may be emitted while remaining within the warming target is inversely proportional to the amount of surface warming resulting from 55 cumulative carbon emissions. The increase in the mean-global surface air temperature relative to cumulative CO2 emission is defined as the transient climate response to cumulative CO2 emissions (TCRE) (Matthews et al., 2009;Zickfeld et al., 2012;IPCC, 2013;Gillett et al., 2013;Zickfeld et al., 2013;Friedlingstein et al., 2014;Matthews et al., 2017). Climate model projections reveal a simple near-linear relationship between the global surface air temperature change and cumulative CO2 emissions between 0 and ~2000 PgC (MacDougall, 2016). However, 60 despite a similar linear dependence, there is a wide inter-model range in TCRE values (Williams et al., 2017;Spafford and MacDougall, 2020), varying from 1.4 to 2.5 °C TtC -1 in intermediate-complexity Earth system models (Eby et al., 2013), 0.8 to 2.4 °C TtC -1 in full-complexity Earth system models (Matthews et al., 2018), and 0.7 to 2 °C TtC -1 (90 % confidence interval) in observationally-constrained TCRE estimates from a 15-member CMIP5 ensemble (Gillett et al., 2013). 65 For the case of radiative forcing exclusively from atmospheric CO2, the TCRE can be related to the dependence of the global mean temperature on the radiative forcing, the dependence of the radiative forcing on the atmospheric CO2 and the airborne fraction (Sect. 2; Williams et al., 2016;Ehlert et al., 2017;Katavouta et al., 2018;Williams et al., 2020). Applying this framework to 7 CMIP5 and 9 CMIP6 models following a 1 % annual increase in atmospheric CO2, the TCRE is affected by a large inter-model spread in the climate feedback parameter 70 for CMIP6 (Williams et al., 2020) as well as by a larger inter-model spread in the land carbon system for CMIP5 (Jones and Friedlingstein, 2020). The inclusion of non-CO2 radiative forcing is able to alter the relationship between emissions and surface warming through both direct warming and carbon feedback effects (Tokarska et al., 2018). For the more realistic case including non-CO2 radiative forcing contributions, the TCRE may be estimated by approximately removing the warming linked to non-CO2 radiative forcing (Matthews et al., 2021). 75 Alternatively, an effective TCRE (eTCRE) may be defined to include non-CO2 warming and the non-CO2 radiative forcing (Williams et al., 2016;Williams et al., 2017).
Here we apply the eTCRE framework developed by Williams et al. (2016) to the intermediate complexity 2 Theoretical framework 95 We first introduce the framework under the assumption of only CO2 forcing. A climate metric TCRE (°C PgC -1 ) is defined as the surface warming response to cumulative CO2 emissions where ∆ is the change since year 850 CE, ∆ ( ) is the global mean change in surface air temperature (in °C) and ( ) is the cumulative CO2 emissions (in PgC) from the sum of fossil-fuel emissions and land use changes.
The TCRE may be viewed as a product of two terms, the change in global mean air temperature divided by 100 the change in the atmospheric carbon inventory, ∆ ( )/∆ ( ), and the airborne fraction, ∆ ( )/ ( ), given by the change in the atmospheric carbon inventory (in PgC) divided by the cumulative CO2 emissions (Matthews et al., 2009;Solomon et al., 2009;Gillett et al., 2013;MacDougall, 2016) where ∆ ( )/∆ ( ) is related to the transient climate response, defined by the temperature change at the time of doubling of atmospheric CO2 (Matthews et al., 2009). The TCRE is defined in terms of this surface warming 105 response to CO2 forcing, usually following a 1 % annual rise in atmospheric CO2.
Alternatively, the TCRE may be linked to an identity involving a thermal dependence on radiative forcing, defined by the change in temperature divided by the change in radiative forcing, ∆ ( ) (in Wm -2 ), and the radiative forcing dependence on CO2 emissions, defined by the change in radiative forcing divided by the cumulative CO2 emissions (Goodwin et al., 2015;Williams et al., 2016;Williams et al., 2017) such that These two viewpoints can be rationalized by rewriting the radiative forcing dependence to CO2 emissions in Eq. 3 in terms of the radiative forcing dependence on atmospheric CO2 and the airborne fraction (Ehlert et al., 2017;Katavouta et al., 2018;Williams et al., 2020).
The TCRE is then defined by the product of the thermal dependence, the radiative dependence between radiative forcing and atmospheric carbon, and the carbon dependence involving the airborne fraction: The thermal response may be further understood from an empirical global radiative balance (Gregory et al., 2004;Forster et al., 2013). The increase in radiative forcing, ∆ ( ), drives an increase in planetary heat uptake, ( ) (in Wm -2 ), plus a radiative response, which is assumed to be equivalent to the product of the increase in global mean surface air temperature, ∆ ( ), and the climate feedback parameter, ( ) (in °C -1 Wm -2 ): The thermal dependence in Eq. 4 given by the dependence of surface warming on radiative forcing, 120 ∆ ( )/ ( ), is then given by the product of the inverse of the climate feedback, ( ), and the planetary heat uptake divided by the radiative forcing, ( )/Δ ( ), where 1 − ( )/Δ ( ) represents the fraction of the radiative forcing that warms the surface rather than the ocean interior.
The carbon dependence in Eq. 4 involving the airborne fraction, ∆ ( )/ ( ), is related to the changes 125 in the ocean-borne, land-borne and sediment-borne fractions (Jones et al., 2013), where the changes in the ocean, land and sediment inventories are denoted by ∆ ( ) , ∆ ( ) and The TCRE is formally defined in terms of the climate response to cumulative CO2 emissions following a 1 % 130 annual rise in atmospheric CO2 (Matthews et al., 2009). As the rise in anthropogenic radiative forcing is currently dominated by the radiative forcing from atmospheric CO2, the TCRE is a useful climate metric to understand future climate projections. However, in the more realistic framework we apply here, the warming response includes In order to allow for possible changes in the thermal and carbon responses from the non-CO2 forcing, we prefer to define an effective TCRE (eTCRE) including the effect of the radiative forcing from non-CO2 and CO2 radiative components using a series of mathematical identities (Williams et al., 2016 and, where By including the effect of the non-CO2 radiative forcing, the eTCRE in Eq. 9 is larger than the TCRE with non-CO2 radiative forcing removed in Eq. 8 whenever the positive radiative effect of non-CO2 greenhouse gases From the year 2005, the model is forced with CO2 emissions consistent with RCP4.5 until 2100 (Meinshausen et al., 2011), held constant until 2120 and then set to zero for the remainder of the simulation to year 2420 ( Fig.1). 165 In the carbon capture and storage (CCS) scenario, CO2 emissions are reduced by 2 PgC from year 2070 to 2170, so applying net negative emissions from 2120 to 2170. In both scenarios, land use change and non-CO2 forcing were held fixed at RCP4.5 values from year 2020. The land use change emissions in Fig. 1 were diagnosed as the difference in land carbon relative to a third 850 to 2420 ensemble that applied RCP4.5 forcing with no land-use change (i.e. natural vegetation everywhere).

175
To quantify the uncertainty in climate and carbon-cycle responses, we used an ensemble of 86 members generated from different combinations of 28 model parameters (Foley et al., 2016). These parameters were selected for their importance for climate, ocean dynamics and carbon cycle and create diverse plausible climate states by varying over the entire range of possible inputs rather than the best values (Holden et al., 2013a(Holden et al., , 2013b.

Carbon feedback
The distribution of carbon between carbon inventories is diagnosed (Fig. 3), and carbon conservation ensures that at all times the sum of the change in the carbon content of the atmosphere, ∆ ( ), ocean, ∆ ( ), land, ∆ ( ), and ocean sediment, ∆ ( ), equals the cumulative CO2 emissions from both land use change and fossil fuels, ( ), with all inventories in PgC, Aside from the ocean sediments, which lose carbon, there is an increase in the carbon content of all inventories between the years 2020 and 2120, the positive emission phase in both the baseline and carbon capture and storage scenarios (Fig. 3). inventory until year 2170. During the post-emissions phase, in both scenarios, the increase in ocean storage is associated with a decrease in carbon content in the atmosphere, land and sediment.
The ocean heat uptake is used to estimate the planetary heat uptake, given that 90 % of the Earth's total energy increase is due to the ocean warming (Church et al., 2011). The climate feedback parameter, ( ) (°C -1 225 (Wm -2 )) is diagnosed from the ocean heat uptake and the change in surface air temperature (Eq. 5). Most of the radiative forcing drives a radiative response involving a rise in surface air temperature, rather than an increase in ocean heat uptake (Fig. 4).
The model ensemble for both baseline and carbon capture scenarios reveals a decrease in eTCRE from the median value of 2.62 °C EgC -1 in year 2020 to 1.96 °C EgC -1 in year 2420 (with 10-90 % range of 1.90 to 3.65 and 1.43 to 2.78 °C EgC -1 respectively) (Fig. 6a). During the positive emission phase (to year 2120) this reduction is driven by a weakening in the increase in radiative forcing with an increase in atmospheric carbon (Fig. 6b), which 260 dominates over the increase in the thermal dependence (Fig. 6d). During the negative and zero emission phases (from year 2120), the eTCRE reduction is driven by the reducing airborne fraction as CO2 is drawn down by the ocean (Fig. 6e).
The eTCRE is scenario dependent and varies with both CO2 and non-CO2 portions of the total radiative forcing. Following the analysis of Matthews et al. (2021), we quantify the spread of the non-CO2 fraction of total 265 anthropogenic forcing, (from Eq. 8), between 2020 and 2100 for RCP4.5 as well as the other three RCP scenarios (2.6, 6.0 and 8.5) (Table S1) to investigate the extent of scenario dependency of the eTCRE. The results showed that the change in across all RCP scenarios and times ranges from ~6 % to ~17 % (25 to 75 % range) with the mean and median value of ~11 % (Table S1). The results could be in part due to the fixed non-CO2 radiative forcing from 2020 onwards in the calculations which diminishes the effect of non-CO2 radiative 270 forcing. The TCRE diagnosed by removing the non-CO2 warming factor (from Eq. 8) varies from 1.6 to 2.8 °C EgC -1 (10 to 90 % range) with a median value of 2.2 °C EgC -1 between the years 2020 to 2100 (Fig. S1).
The uncertainty in the eTCRE, and its dependencies for the model ensemble, is assessed based on the nondimensional coefficient of variation, given by the inter-model standard deviation divided by the ensemble mean (Williams et al., 2020). The uncertainty in the eTCRE varies from 0.23 to 0.27 over the course of the model 275 integrations and is marginally larger by 0.01 for the negative emissions (Table S2).
In both scenarios, the coefficients of variation for the thermal dependence and airborne fraction provide the dominant contributions to the eTCRE uncertainty, with their values ranging from 0.17 to 0.20 and 0.18 and 0.21 respectively (Table S2). These contributions are larger than the coefficient of variation for the fractional radiative forcing contribution from atmospheric CO2, ∆ ( )/∆ ( ), ranging from 0.11 to 0.14, and the dependence of

Carbon dependence for the effective TCRE
The fraction of emitted CO2 that remains in each carbon inventory (based on Eq. 7) varies over the course of the integration. The carbon dependence for the eTCRE is given by the airborne fraction of carbon emissions, 290 ∆ ( )/ ( ). In both scenarios, the airborne fraction strengthens by ~7 % (based on the median values) from years 2020 to 2070 (Fig. 7a), likely as a result of increasing CO2 emissions and weakening terrestrial carbon sinks. After year 2070 and a cessation of CO2 emissions, the ocean becomes the dominant carbon sink with an increase in the ocean-borne fraction, ∆ ( )/ ( ), to ~65 % (median value) by 2420 (Fig. 7b). The landborne fraction, ∆ ( )/ ( ) decreases from ~0.24 (median value) in 2020 to the minimum value of ~16 % in 295 2420 (Fig. 7c). The sediment-borne fraction, ∆ ( )/ ( ), remains negative at ~-0.03 (median value) over the entire period (Fig. 7d), and therefore acts as a weak carbon source.
The coefficient of variation is the largest for the land-borne fraction (~0.7), followed by the sediment-borne fraction (~-0.5) and then the airborne and ocean-borne fractions (~0.2) (

Radiative forcing dependence on atmospheric CO2 for the effective TCRE
By year 2120, the radiative forcing dependence on atmospheric CO2 emissions, ∆ ( )/∆ ( ), weakens due to a saturation in the radiative forcing with an increase in atmospheric CO2 (Gillett et al. 2013;William et al., 2020) ( Fig. 8a-b). Over the next few centuries from year 2120 onwards, ∆ ( )/∆ ( ) rises again due to a decrease in atmospheric CO2 associated with the decrease in the airborne fraction (Fig. 8c).

Thermal dependence for the effective TCRE
For both scenarios, the thermal dependence of the eTCRE, involving the dependence of the surface warming on the radiative forcing, ∆ ( )/∆ ( ), increases in all emissions phases (Fig. 9a) due to the reinforcing contributions of the inverse of the climate feedback parameter, ( ) (Fig. 9b) and the fraction of the radiative forcing warming 320 the surface, 1 − ( )/∆ ( ) (Fig. 9c). The increase in ( ) is equivalent to a slight decrease in the climate feedback ( ). The temporal evolution of the climate feedback parameter is mirrored in other climate model studies as climate feedbacks evolve on different timescales for a myriad of reasons (e.g., Gregory et al. 2004;Armour et al., 2013;Knutti and Rugenstein, 2015;Goodwin, 2018).  The relationship between the surface air temperature and atmospheric CO2 exhibits hysteresis behaviour in most 345 ensemble members, consistent with climate change reversibility studies ( Fig. 10a-b) (Tokarska and Zickfeld, 2015;Jeltsch-Thömmes et al., 2020). The temperature remains at high levels after high atmospheric CO2 concurrent with a decrease in the ocean heat uptake, N(t) (Fig. 10c-d). The ability of the ocean interior in taking up heat diminishes in time, probably due to increasing stratification and weakening ventilation. The fraction of the radiative forcing warming the ocean interior, /∆ ( ) (Fig. 10e-f) then continues to decrease after the peak in atmospheric CO2 350 leading to higher surface air temperatures even after the lower CO2 concentrations are restored.
In the carbon capture and storage scenario, the atmospheric CO2 declines during the negative emissions phase from year 2070 (Fig. S6) (associated with the cumulative CO2 emissions of ~1050 PgC (Figs. 1 and 11b). After the cessation of the emissions, the atmospheric CO2 continues to decrease in both scenarios ( Fig. 11a-b) mainly due to uptake by the ocean and to a lesser extent the land (Fig. 11c-f). The ocean carbon uptake is governed by the   omitted as outliers because they were undergoing substantial re-organisation of ocean circulation during the period of negative emissions (Fig. S7), significantly perturbing ocean heat uptake.
During the positive emissions phase, uncertainty in ∆ /∆ is dominated by the radiative feedback parameter (OL1) (R 2~6 4 %) (Table 1), which perturbs outgoing longwave radiation proportionally to ∆ 395 (Matthews and Caldeira, 2007). This parameter is primarily designed to capture unmodelled cloud responses to global average temperature change, and it has previously been shown to drive 81 % of the variance in GENIE-1 climate sensitivity (Holden et al., 2010). Although radiative forcing uncertainty dominates, carbon cycle parameters also drive ∆ /∆ variance via the land use change soil carbon parameter (KC) (R 2~1 2 %) through its control on soil carbon losses under land use change that continue after land use change is held fixed from 2020 400 due to the long (multi-decadal) soil time scales. The fractional vegetation parameter (VFC) (R 2~1 0 %) drives additional carbon cycle uncertainty through its control on terrestrial carbon surface density.
During net negative emissions within the carbon capture and storage experiment (2120-2170), uncertainty in ∆ /∆ is affected again by the radiative feedback parameter (OL1, ~15 %) but now also by the effects of ocean transport and the carbon cycle. In the ocean, uncertainty is dominated by the wind stress scaling parameter (WSF, 405 ~16 %), which drives circulation strength and is the dominant control of uncertainty in ocean carbon uptake (Holden et al 2013b

The Zero Emissions Commitment
The climate response after net zero emissions is an important climate metric, encapsulated in the zero emissions commitment (ZEC) given by the mean surface air temperature change after CO2 emissions cease (Hare and Meinshausen, 2006;Caldeira, 2008, Froelicher andPaynter, 2015;MacDougall et al., 2020). 420 Quantification of the ZEC is critical for calculating the remaining carbon budget. Whether there is continued surface warming depends on a competition between a cooling effect from the reduction of the radiative forcing from atmospheric CO2 as carbon is taken up by the ocean and terrestrial biosphere versus a surface warming effect from a decline in the heat uptake by the ocean interior (Williams et al., 2017b). In an analysis of Earth system model responses, MacDougall et al (2020) found that the model mean for the ZEC was close to zero, but that there 425 was a wide spread in continued warming and cooling responses from individual models.
Our baseline experiment, which applies RCP4 We additionally consider ZEC metrics for the ensemble including carbon capture and storage. In contrast to 445 the baseline, surface temperatures decrease in all the ensemble members after cessation of positive emissions. We consider two alternative interpretations of the ZEC, the warming after the cessation of net positive emissions (in 2120) and the warming after the cessation of net negative emissions (in 2170). The former may be more relevant from a policy perspective (as the time of likely peak warming), while the latter is theoretically useful to quantify committed warming when emissions are precisely zero. 450 The blue bars in Fig. 12  All ZEC values are again robustly negative, varying between -0.14 and -0.05 for ZEC25, -0.33 and -0.14 for ZEC50, and -0.49 and -0.2 for ZEC90 (10 %-90 % percentile values), confirming that no ensemble member exhibits a temperature overshoot after the cessation of positive emissions in the carbon capture and storage scenario.  can be extended to projections with moderate amounts of carbon capture and storage. 485 The comparison of the coefficient of variation for the effective TCRE and its dependencies show that the thermal dependence and airborne fraction almost equally contribute to the uncertainty in the effective TCRE. Our results differ from the analysis of CMIP6 ensembles in which the radiative forcing response and thermal response were the main contributors to the uncertainty in the TCRE (Williams et al., 2020). These inferences are consistent with a model parameter correlation analysis attributing the weakening in warming slopes versus emissions to 490 radiative feedbacks during net positive emissions, and also affected by changes in the airborne fraction of CO2 during the negative and zero emission phases The relationship between thermal and carbon feedbacks with an increase in atmospheric CO2 exhibits hysteresis behaviour. The fraction of the radiative forcing warming the surface continues to increase after peak atmospheric CO2 as the ocean is stratified, leading to higher surface air temperatures after lower atmospheric CO2 495 values are restored. The increase in the ocean and terrestrial carbon storage after the peak in atmospheric CO2 is associated with the long-term response of each of these carbon sinks as well as the carbon storage from their past carbon uptake.
The zero emission commitment given by the warming after net emissions is close to zero, in the model mean of integrations excluding carbon capture, the ZEC is -0.01 o C at 25 years and decreases in time to -0.15 °C at 90 500 years after emissions cease. However, in this case without carbon capture, the distribution of ZEC after 25 years from the cessation of emissions shows warming in ~50 % of ensemble members. Including modest levels of carbon capture and storage avoids this continued warming after net zero with all ensemble members exhibiting a ZEC close to or below zero. Hence, implementing net negative emissions is required to reduce the risk of over-shoot and continued warming after net zero is reached, and so increase the probability of meeting the Paris targets. 505 Negative emissions technologies with naturally long CO2 removal lifetimes, such as agricultural enhanced rock weathering (Beerling et al., 2020) may be especially well suited for this purpose as the legacy effects of the repeated application of this technology increase the rate of carbon drawdown per unit area for years after implementation at no incremental cost (Beerling et al., 2020;Vakilifard et al., 2021). Data availability. The data that support the findings of this study are available from the corresponding author upon reasonable request.
Author contributions. NV undertook model experimental design, all simulations, and analyses. All authors were involved in the design of the model experiments, led by NV and RGW. All authors contributed to writing, led by 515 NV and RGW.
Competing interests. The authors declare that they have no conflict of interest.