Increase of the transient climate response to cumulative carbon emissions with decreasing CO2 concentration scenarios

Near-constancy of the transient climate response to cumulative carbon emissions (TCRE) facilitates the development of future emission pathways compatible with temperature targets. However, most studies have explored TCRE under scenarios of temperature increase. We used an Earth system model (MIROC-ESM) to examine TCRE in scenarios with increasing and stable CO2 concentrations, as well as overshoot pathways in which global mean temperatures peak and decline. Results showed that TCRE is stable under scenarios of increasing or stable CO2 concentration at an atmospheric CO2 concentration (pCO2) double the pre-industrial level. However, in the case of overshoot pathways and a stable pCO2 scenario at a quadrupled pCO2 level, the TCRE increases by 10%–50%, with large increases over a short period just after pCO2 starts to decrease. During the period of pCO2 increase, annual ocean heat uptake (OHU) and ocean carbon storage (CO) (or cumulative ocean carbon uptake from the start of the experiment) exhibit similar changes, resulting in a stable TCRE. During the pCO2 decrease period, after a sudden TCRE increase when pCO2 starts to decrease, the OHU decreases and CO increases (relative to the pCO2 increase period) balance each other out, resulting in a stable TCRE. In overshoot pathways, the temperature distribution when the global mean temperature anomaly cools to 1.5 °C reveals small warming over land and large warming over the oceans relative to the 1% per annum pCO2 increasing scenario, particularly in some high-latitude areas of both hemispheres. The increase in TCRE with overshoot pathways decreases the carbon budget for the temperature anomaly targets in such scenarios. Our analysis showed a 16%–35% decrease in the remaining carbon budget for the 1.5 °C global warming target, in comparison with the reference scenario with a 1% per year pCO2 increase, for pathways peaking at the doubled pCO2 level followed by decline to the pre-industrial level.


Introduction
The transient climate response to cumulative carbon emissions (TCRE) is defined as the global mean surface temperature change per 1000 GtC (PgC) of anthropogenic CO 2 emission (Allen et al 2009, Matthews et al 2009, Collins et al 2013. A constant TCRE that is independent of time and pathway implies that global mean temperature rise is approximately proportional to cumulative carbon emissions (C E ). Such proportionality implies that temperature increases are dependent only on the integrated amount of carbon emissions and not on the emission pathway, thereby facilitating the development of future emission pathways compatible with temperature targets. Future warming can be estimated by multiplying the TCRE by the C E (Allen and Stocker 2014). Likewise, a carbon budget for a given temperature target can be calculated by dividing the target temperature anomaly by the TCRE  (2014) found that TCRE has a complex relationship with emission rates and is largest for both low (2 GtC per annum (p.a.)) and high (25 GtC p.a.) emissions. Tachiiri et al (2015) reported that the uncertainty increases when atmospheric CO 2 concentration (pCO 2 ) stabilizes. Using a model of intermediate complexity, Zickfeld et al (2016) found that TCRE in periods of pCO 2 decrease (temperature decrease for decreasing cumulative carbon emissions) is lower than TCRE in scenarios of pCO 2 increase, and indicated some increase in TCRE in overshoot scenarios (see supplementary information ( TCRE. MacDougall (2017) concluded that TCRE is nearly constant (i.e. <5% change), only when changes in pCO 2 are between 0.3% and 1.2% p.a. at 400 ppm (or between 0.5% and 2.5% p.a. at >1000 ppm).
In this study, we assessed the scenario-dependence of TCRE using a full ESM (MIROC-ESM, see below) by exploring pathways with stable pCO 2 as well as those in which pCO 2 peaks and declines (i.e. an overshoot scenario). We determined contributions of the atmosphere, ocean (heat and carbon uptake), and land to TCRE change by examining the change in each term through decomposition, focusing on how TCRE can be kept relatively stable even when each term is changing. Finally, we discuss the influence of the scenario-dependence of TCRE on carbon budget estimation, as well as the scenario-dependence of the spatial temperature distribution, when the global mean temperature anomaly is 1.5°C. The model has nearly average (1.56 PgC ppm −1 ) carbon-concentration feedback and strong (−100.7 PgC K −1 ) carbon-climate feedback (these values are for quadruple the pre-industrial CO 2 level, 4×CO 2 ; Arora et al 2013), resulting in high TCRE. This is because the linearized formulation for TCRE can be written as α/(1+β+αγ) (Gregory et al 2009), where α(K PgC −1 ), β(PgC PgC −1 in this case), and γ(PgC K −1 ) represent linear transient climate sensitivity to C A , carbon sensitivity to C A , and carbon sensitivity to climate change, respectively (i.e. parameters presented by Friedlingstein et al 2006). At the doubled pre-industrial CO 2 level (2×CO 2 ), β and γ of our model are 0.91(PgC PgC −1 ) and −68(PgC K −1 ); combined with an α value of 0.003 676 K PgC −1 calculated from a transient climate response of 2.2°C, we derived a TCRE of 2.2°C/1000 PgC.

Experimental design
The scenarios (sections) used in this study are summarized in table 1 (and figure 1(a)). They represent idealized experiments designed to supply fundamental information, in which rates of increase and decrease are constant, and only CO 2 is taken into account. For each pathway, the pre-industrial control run output was taken at 10 year intervals to initialize three ensemble members, and the ensemble means were analyzed. The D1.0%_4x experiment has been used to investigate the reversibility of the climate system The I1.0% experiment, included in the standard CMIP5 experimental protocol, was also explored in this study. It was used as the reference scenario and the pathway to reach 2×CO 2 which is the initial condition for S_2x, D0.5% and D1.0%_2x; and 4×CO 2 , which is the initial condition for S_4x and D1.0%_4x.  Compared with other models, the MIROC-ESM has a relatively large warming drift (Sueyoshi et al 2013) of about 0.07 K/century in global mean surface air temperature. To minimize its effect, the linear regression of the control run (for a 300 year period) was removed from all variables prior to analysis (however, we still need to be careful in discussing TCRE when anomalies in temperature and cumulative carbon emission are very small).
From model results, carbon emissions each year were calculated as ΔC A +C A→L +C A→O , where ΔC A is the difference between the airborne carbon of the year concerned and that of the previous year, and C A→L and C A→O are the annual total carbon flux from atmosphere to land and to ocean, respectively.

Experimental results
For all experiments listed in table 1, trajectories of changes in global mean surface air temperature (ΔT, figure 1(b)) and C E (figure 1(c)) follow the shapes of CO 2 concentration pathways (figure 1(a)). Consequently, TCREs are similar in magnitude, with values between 2 and 3°C/TtC (or°C/1000 PgC) (figure 1(d); for each member see figure S1).
The I1.0%, I2.0%, S_4x and D1.0%_4x experiments are defined for C E up to 2500 PgC. We could confirm that the variation in TCRE was as large as 30%-40% in comparison with the reference TCRE of the model (2.2°C/1000 PgC) obtained from the I1.0% scenario (Gillet et al 2013). Although the TCRE variation is somewhat enhanced by a small accumulated carbon emission period, TCRE remains quasi-linear in the temperature-cumulative carbon emission plot (figure S2), consistent with results of Zickfeld et al (2016) using an ESM of intermediate complexity.
Relative variation in TCRE is <50% in the scenarios of slow CO 2 increase, stable CO 2 concentration, and overshoot. Considering the averages of each scenario, we found a 10% increase during CO 2 decline in overshoot pathways as well as in the stabilization scenario for 4×CO 2 . This change could be significant when calculating a carbon budget using the TCRE. In scenarios of CO 2 decline (D0.5%, D1.0%_4x, and pCO 2 decrease in part of D1.0%_2x) and stabilization at a 4×CO 2 level (S_4x), TCREs averaged approximately 2.5°C/TtC. Meanwhile, in the scenarios of CO 2 increase, TCREs averaged approximately 2.2°C/TtC (results from the first 30 years were removed because of instability). Generally, when pCO 2 declined (or stabilized at a high level), TCREs increased slightly. In particular, TCREs were larger in the D0.5%, D1.0% _2x, and D1.0%_4x scenarios, when pCO 2 returned to approximately pre-industrial values (285 ppm). Large TCRE variations in D1.0%_2x (figure 1(d)) were caused by C E approaching zero.
3.2. Contributions of the atmosphere, ocean, and land to changes in transient climate response TCREs 3.2.1. Overview TCRE is a result of the contributions of atmosphere, ocean, and land. To discuss their relative contributions to TCRE change, we can rewrite TCRE as equation (1): , and C L (PgC) are carbon storage in the atmosphere, ocean, and land, respectively; λ(W m −2 K −1 ) is the climate feedback parameter; and OHU(W m −2 ) is OHU (which is equal to the top of atmosphere imbalance of the ESM). Herein, we consider the contributions of RF, OHU, C A , C O , C L , and λ to TCRE. Changes in OHU, C L , and C O or ocean carbon uptake (OCU) are presented in figure 2 and discussed below.
If we did not have land carbon uptake or ocean heat and carbon uptake in the Earth system, and if λ=1, then equation (1) could be reduced to RF/C A . Here, C A is prescribed, and RF is assumed to be a log function of C A . When we consider peak and decline scenarios with 1% p.a. of pCO 2 increase and decrease, in which both RF and C A are symmetrical for the periods of pCO 2 increase and decrease, then through a change in λ that is calculated as ΔT/(RF − OHU) for the year concerned (black line in figure 3(a) for the result of I1.0% and D1.0%_4x scenarios), we see that RF/(C A ·λ), i.e. the red line in figure 3(a), stabilizes around peak pCO 2 but remains nearly symmetrical for the periods of pCO 2 increase and decrease. When OHU and C O , and then C L are added to the numerator and denominator in equation (1), the stability of TCRE increases, and an increase within the pCO 2decline period becomes evident ( figure 3(a)). In figure 3(b), the contribution of C L to C E is small and stable, indicating that C L does not play an important role in TCRE change. Thus, we focused on the contributions of OHU and C O in pCO 2 increase, decrease, and stabilization periods. We did not focus on C A because it is given (as pCO 2 ).

pCO 2 increase
In scenarios with pCO 2 increase, TCRE stabilizes at approximately the 30th year (blue, green and dotted black lines in figure 1(d)), although the spread among each ensemble member becomes larger when the rate of increase of pCO 2 is small (figure S1). In the numerator of equation (1), OHU varies almost linearly with time ( figure 2(a)). Approximated by a log function of pCO 2 that increases exponentially in these scenarios, RF also varies linearly with time (not shown). This causes RF − OHU, which is the energy input that causes global atmospheric temperature to increase, also to vary linearly with time ( figure S3). Owing to the quasi-linear decrease during the pCO 2 -increase period in λ ( figure 3(a); a decrease in λ after around the 40th year is common for I0.5%, I2.0% (not shown)), the relationship between ΔT and time has weak nonlinearity ( figure 1(b)).
In the denominator of equation (1), the air-to-sea carbon flux increases during the first several decades and then becomes nearly constant ( figure 2(b)). Ocean carbon storage (C O in equation (1)), which is more directly associated with TCRE, varies almost linearly with time because of the stabilization of the air-to-sea carbon flux ( figure 2(c)). The exponential increase of C A is moderated when C O , which varies quasi-linearly with time ( figure 2(c)), is added. The nonlinearity is further reduced by slightly decreasing the relative contribution of C L over time ( figure 2(d)). Consequently, the trajectory of C E is similar to that of ΔT ( figure 1(c)), resulting in a stable TCRE in scenarios with pCO 2 increase.

pCO 2 decrease
There is a clear increase in TCRE at the point when pCO 2 switches from increase to decrease (red, black, and cyan curves in figure 1(d)). Using D1.0%_4x as an example, we see that C E starts to decrease when pCO 2 starts to decrease. Even though OCU continues initially ( figure 2(b)), it is unable to counteract the C A reduction at a rate of 1% p.a. After pCO 2 reaches its peak, temperature continues to increase for approximately 10 years because RF − OHU continues to increase. Although RF peaks simultaneously with pCO 2 , the rapid decrease in OHU (figure 2(a)) surpasses the decrease of RF. Therefore, temperature continues to rise but C E becomes smaller, resulting in a TCRE increase.
The important role of OHU is confirmed in figure 3   After the first 10 years of pCO 2 decrease, TCRE stabilizes. When pCO 2 increases, OHU and C O both increase approximately linearly with pCO 2 , resulting in a stable TCRE. When pCO 2 decreases, the stability of the TCRE is the result of the cancellation of the instability of OHU and C O ; therefore, TCRE stability might be more robust during periods of pCO 2 increase. This is confirmed by the behavior of trajectories of C O /C E ( figure 3(b)) and −OHU/(RF − OHU) over time ( figure 3(d)).
While the change in OCU is larger than that of OHU during pCO 2 decline, it is weakened through processes of accumulation (C O ) and addition (summing of C A and C L to obtain C E ). In contrast, OHU directly reflects changes in RF − OHU and subsequently in temperature (figure S4).

pCO 2 stabilization
The trajectory of the TCRE after pCO 2 stabilization depends on the pCO 2 pathway prior to stabilization. Both OHU and OCU start to approach zero at pCO 2 stabilization.
If stabilization is reached after a period of pCO 2 increase (like in S_2x, S_4x), then OHU and OCU approach zero from positive values (i.e. by decreasing); OHU decrease leads to increases in RF − OHU and temperature. Positive OCU results in increasing C O (and then C E ), and both the numerator and the denominator of the TCRE increase.
If stabilization is reached after a period of pCO 2 decrease (like in D1.0%_2x), then both OHU and OCU approach zero from negative values (i.e. by increasing); OHU increase leads to decreases in RF − OHU and temperature. Negative OCU results in decreasing C O and then C E , and both the numerator and the denominator of the TCRE decrease. The TCRE becomes relatively stable in both cases but through opposing processes for scenarios starting with 2×CO 2 (i.e. S_2x and D1.0%_2x).
For S_4x starting with 4×CO 2 , a TCRE increase, comparable to the pCO 2 decline, is observed. Figure 2(a) indicates some contribution of OHU change particularly in the first decades (unlike pCO 2 decline scenarios, the rapid TCRE over the first 10 years was not observed). We surmise that the difference from S_2x is mainly related to the repressed increase in C E (figure 1(c)), reflecting cancellation of the increase in C O by the decrease in C L (figure 2(d)). Unlike D1.0%_4x, in which TCRE increases because of pCO 2 decline (decrease in OHU keeps contributing throughout the section ( figure 2(b))), in S_4x, high temperature reduces C L . This reduction can play an important role in the TCRE increase, when changes in C A and C O are small.
3.3. Scenario-dependence of the carbon budget and spatial distribution of the atmospheric temperature anomaly in meeting the 1.5°C global warming target Finally, we compare the cumulative carbon emissions and temperature distributions of different pathways. The cumulative carbon emissions until each of the pathways intersects the 1.5°C global warming target in scenarios I0.5%, I1.0%, I2.0%, D0.5%, D1.0%_2x, and D1.0%_4x vary by 546-722 PgC, showing a tendency for large emissions with quickly increasing pathways and small emissions with overshoot pathways (table 2; corresponding TCREs are also presented). It is not easy to directly compare these values with the total carbon budget of the actual Earth system because the pathways in the current study do not include non-CO 2 greenhouse gas (GHG) and aerosol emission scenarios. Instead, like equation (1) of Rogelj et al (2019), with an assumption that zero emission commitment and unpresented Earth system feedback are zero, we calculated the remaining carbon budget as (T lim − T hist − T nonCO2 )/TCRE, where T lim , T hist , and T nonCO2 are the temperature anomaly target, historical warming to date, and non-CO 2 -induced future warming, respectively. Following Rogelj et al (2018), a T hist value of 0.97°C results in a value of 0.53°C for T lim − T hist . To estimate T nonCO2 , Rogelj et al (2019) suggested using internally consistent evolution. However, as we have no corresponding non-CO 2 GHG emission scenario, we adopted a simpler method that assumes (by considering non-CO 2 -GHG-induced warming) the remaining carbon budget is reduced by 30% (estimated from Forster et al (2018)) and that 79.4 PgC (291 GtCO 2 ) was emitted during 2011-2017 (Rogelj et al 2018). Thus, the carbon budget after 2018, using these TCRE estimates, will be 56-99 PgC (table 2). These values can be compared with the estimates of Rogelj et al (2018) of 229, 158, and 115 PgC (840, 580, and 420 GtCO 2 ) for the 33rd, 50th, and 67th percentiles, respectively. As the TCRE from the MIROC-ESM (2.2°C/1000 PgC) is larger than the value used to calculate the 67th percentile (0.55°C/1000GtCO 2 =2.0°C/1000 PgC), it is not surprising that the estimated remaining carbon budget is smaller than that of the 67th percentile value of Rogelj et al (2018). However, more importantly, TCRE shows some pathway dependence, and if we apply TCREs for overshoot and slowly increasing pathways, the remaining carbon budget is reduced by 16%-41% for pathways with slower pCO 2 increase than I1.0% (i.e. I0.5%) or overshoot patterns. Conversely, for I2.0%, we have a 4% increase in the remaining carbon budget (table 2). As such, scenario dependency of the TCRE, particularly for overshoot pathways, results in different carbon budgets for different pathways.
Spatial distribution of the atmospheric temperature anomaly (ΔT), when the global mean anomaly is 1.5°C, also shows some scenario-dependence (figure 4). Figure 4(a) shows clear polar intensification in the northern high latitudes in the reference scenario of I1.0%. This basic feature is repeated in other scenarios (figures 4(b)-(e)), despite differences in the value between the reference scenario and all other scenarios. The spatial distribution of temperature is maintained, when pCO 2 (and hence, temperature) increases monotonically (figures 4(b), (c)). In overshoot scenarios (figures 4(d)-(f)), temperature anomalies over land are generally smaller than those in the reference scenario, except in northeastern Siberia, where temperature anomalies are large. These features are also visible in scenario I0.5%. Temperature anomalies over the ocean are typically larger than in the reference scenario, which is considered to reflect larger cumulative OHU (i.e. ocean heat content). The strong positive anomaly observed around 0°longitude in the high latitudes of both hemispheres likely reflects sea ice melting (see figure S7). The difference from the reference scenario is significant in overshoot pathways. For instance, in D1.0%_2x, northeast China has less warming (< −40%) in comparison with I1.0%, while northeastern Siberia is warmer (>+40%) than when both scenarios have a 1.5°C anomaly. Although D1.0%_4x is a scenario with an unrealistically large overshoot, results from other overshoot scenarios are more realistic and clearly show that simple pattern scaling is insufficient to describe their dynamics.

Conclusions
We examined the robustness of TCRE using the MIROC-ESM and various CO 2 concentration pathways to confirm the quasi-constancy of TCRE during periods of pCO 2 increase and stable pCO 2 at a 2×CO 2 level. During pCO 2 decrease and stable pCO 2 at a 4×CO 2 level, we found an average TCRE increase of 10%-20% (from 2.2°C to 2.5°C/1000 PgC) and a maximum of 50% (20 year average). Our ESM results for overshoot scenarios are qualitatively consistent with those of Zickfeld et al (2016). In addition, we analyzed the contributions of the atmosphere, ocean, and land to TCRE. In the case of the ocean, the contributions of OHU and OCU were distinct.
In the scenario with increasing pCO 2 , a stabilized OCU is considered critical for stable TCRE because it results in ocean carbon storage that increases linearly, as does OHU, with pCO 2 . When pCO 2 starts to decrease, TCRE increases within a decade, and it then stabilizes because of a balance between OHU decrease and a slight increase in C O (relative to the period of pCO 2 increase). Typically, OCU decreases more rapidly than OHU, but cumulative OCU continues to increase for a certain period. For a stabilization at a 4×CO 2 level, negative C L and a slower increase in C O (related to high temperature) result in a negligible increase in C E , which causes TCRE to increase, comparable to when pCO 2 declines.
The increase of the TCRE during pCO 2 decline will affect the carbon budget, when an overshoot pathway is planned. Indeed, analysis of different pathways to the 1.5°C global warming target shows decreases in the remaining carbon budget in overshoot pathways. Our simulation also shows that, in overshoot pathways, temperature continues to increase for a certain period, despite strong decreases in atmospheric CO 2 concentration. The results suggest that to compensate for this process, we might need extra measures to moderate climate change (e.g. geoengineering).
Changes in the spatial distributions of temperature and other variables are also of interest to climate researchers. Warming over land is smaller and warming over the ocean is larger than those in the reference (1% per annum pCO 2 increase) scenario, and the warming over some parts of the ocean in high latitudes of both hemispheres is significant. These features appear even more strongly in scenarios with a rapid rate of pCO 2 decrease and a high peak pCO 2 . The mechanism of TCRE change during pCO 2 decline should be investigated to better understand the processes associated with achieving ambitious global warming targets.
We note that our study has been conducted using a single ESM, which is known to have relatively high climate sensitivity among CMIP5 models. In such models, overshooting of global temperature and the reduction of the estimated carbon budget in modeled scenarios might be overestimated; thus, TCRE increase might be exaggerated. To evaluate the behavior of TCRE during the decades after peak pCO 2 , intercomparison studies using multiple ESMs and alternative overshoot scenarios are needed. We expect that CDR-MIP will present meaningful results for such comparisons.