Tachiiri Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-020-00392-6(2020) 7:74

Progress in Earth andPlanetary Science

RESEARCH ARTICLE

Open Access

Relationship between physical andbiogeochemical parameters and thescenario dependence of the transient
climate response to cumulative carbon
emissions
Kaoru Tachiiri

Abstract
The transient climate response to cumulative carbon emissions (TCRE) is a key metric in estimating the remaining
carbon budget for given temperature targets. However, the TCRE has a small scenario dependence that can be
non-negligible for stringent temperature targets. To investigate the parametric correlations and scenario
dependence of the TCRE, the present study uses a 512-member ensemble of an Earth system model ofintermediate complexity (EMIC) perturbing 11 physical and biogeochemical parameters under scenarios with steadyincreases of 0.25%, 0.5%, 1%, 2%, or 4% per annum (ppa) in the atmospheric CO2 concentration (pCO2), or an initial
increase of 1% followed by an annual decrease of 1% thereafter. Although a small difference of 5% (on average) in
the TCRE is observed between the 1-ppa and 0.5-ppa scenarios, a significant scenario dependence is found for theother scenarios, with a tendency toward large values in gradual or decline-after-a-peak scenarios and small values in
rapidly increasing scenarios. For all scenarios, correlation analysis indicates a remarkably large correlation between
the equilibrium climate sensitivity (ECS) and the relative change in the TCRE, which is attributed to the longer
response time of the high ECS model. However, the correlations of the ECS with the TCRE and its scenario
dependence for scenarios with large pCO2 increase rates are slightly smaller, and those of biogeochemicalparameters such as plant respiration and the overall pCO2–carbon cycle feedback are larger, than in scenarios with
gradual increases. The ratio of the TCREs under the overshooting (i.e., 1-ppa decrease after a 1-ppa increase) and 1ppa increase only scenarios had a clear positive relation with zero-emission commitments. Considering the scenario
dependence of the TCRE, the remaining carbon budget for the 1.5 °C target could be reduced by 17 or 22%(before and after considering the unrepresented Earth system feedback) for the most extreme case (i.e., the 67th
percentile when using the 0.25-ppa scenario as compared to the 1-ppa increase scenario). A single ensemble EMIC
is also used to indicate that, at least for high ECS (high percentile) cases, the scenario dependence of the TCRE
should be considered when estimating the remaining carbon budget.
Keywords: Transient climate response to cumulative carbon emissions, Scenario dependence, Earth system models
of intermediate complexity, Equilibrium climate sensitivity, Zero-emission commitment, Carbon budget

Correspondence: tachiiri@jamstec.go.jp
Research Center for Environmental Modeling and Application, ResearchInstitute for Global Change, Japan Agency for Marine-Earth Science andTechnology, 3173-25 Showamachi, Kanazawaku, Yokohama, Kanagawa
236-0001, Japan© The Author(s). 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,
which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give
appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate ifchanges were made. The images or other third party material in this article are included in the article's Creative Commonslicence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commonslicence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain
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Tachiiri Progress in Earth and Planetary Science(2020) 7:74

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1 Introduction
Although a large inter-model uncertainty remains, discussions on future carbon emission pathways are
assisted by the observation that the transient climate response to cumulative carbon emissions (TCRE) is largely
unaffected by time and pathways (e.g., Collins et al.
2013). For example, in searching for pathways to maintain a given temperature target, one can first estimate
the total allowable carbon emissions and then consider
how to distribute the emissions for each year.
According to Rogelj et al. (2019), the remaining carbon
budget (Blim) can be calculated from the TCRE using Eq.
(1):
Blim ¼ ðT lim − T hist − T nonCO2 − T ZEC Þ=TCRE - E esfb
ð1Þ
where Tlim, Thist , TnonCO2, and TZEC are thetemperature change limit, the historical human-induced
warming to-date, the non-CO2 contributions to a futuretemperature increase, and the zero-emissions commitment (ZEC), respectively, and Eesfb is an adjustment
term for sources of unrepresented Earth system
feedback.
In the Special Report on Global Warming of 1.5 °C by
the Intergovernmental Panel on Climate Change (IPCC)(SR1.5; Rogelj et al. 2018), experts calculated theremaining carbon budget from Eq. (1) using TCRE
values that were estimated in the IPCC AR5 (i.e., 0.8–2.5
K/GtC; Collins et al. 2013). Although this estimate was
the result of expert judgment based on various existingstudies using stabilizing, overshooting, and increasing
scenarios, the TCRE range of 0.8–2.4 K/GtC estimatedby Gillet et al. (2013) using Earth systems models(ESMs) seems remarkably influential. In addition, Gillet
et al. (2013) used a scenario with a monotonic increaseof 1% per annum (ppa) in the atmospheric CO2 concentration (pCO2). This corresponding to the threshold exceedance budgets (TEBs), or total carbon emissions of
the underlying scenarios up to the time of exceeding thethreshold, as defined by Rogelj et al. (2016). In otherwords, only transient warming is considered. The
remaining carbon budget is more closely related to another type of budget, which was termed the threshold
avoidance budget (TAB) by Rogelj et al. (2016) for the
non-overshooting case, and which reflects the total carbon emissions of the underlying scenarios up to the timeof peak warming (i.e., slow warming is also considered).
For the average value, however, the results of the Zero
Emissions Commitment Model Inter-comparison Project(ZEC-MIP; MacDougall et al. 2020) indicated thatwarming after the cessation of CO2 emissions (i.e., theZEC) can be approximately estimated as zero (TZEC = 0).

In that case, the TAB can be considered to be equal to
the TEB.
Tachiiri et al. (2015) demonstrated that the uncertainty of the TCRE increases (i.e., large TCREs get larger
and small TCREs get smaller) when the pCO2 is stabilized, although the average (or median) TCRE remains
unchanged. Hence, the TABs can be smaller than the
TEB if we need to achieve the target with a high probability, whereas the TABs and TEBs are expected to be
similar when considering approximately the 50th
percentile.
Although the initial main focus of researchers was thequasi-constancy of the TCRE, the scenario dependenceof the TCRE has been previously reported (Hajima et al.
2012; Krasting et al. 2014). More recently, MacDougall(2017) concluded that the TCRE is only nearly constant(i.e., < 5% change) when changes in the pCO2 are 0.3–
1.2% p.a. at 400 ppm (or 0.5–2.5% p.a. at > 1000 ppm).
For overshooting scenarios, Zickfeld et al. (2016) indicated some increase in the TCRE and Tachiiri et al.
(2019) quantified a 10–20% increase in the TCRE undera decline-after-a-peak pCO2 (i.e., declining part of an
overshooting) scenario. By contrast, MIROC-ES2L(Hajima et al. 2020), which is the new model in the
MIROC-ESM series, has shown a non-increase in the
TCRE in the decline part of an overshooting scenario(Hajima, personal communication). Thus, whether the
TCRE increases in the declining part of overshooting
scenarios (i.e., the existence of a scenario dependence)
depends on the model. While the quasi-constancy of the
TCRE is obviously interesting and helpful, TCRE
changes, which have not been the focus thus far, could
be important when estimating the remaining carbon
budget. Therefore, investigating the magnitude of scenario dependence, and identifying those cases in which
the scenario dependence is enhanced, can be importantfor estimating the remaining carbon budget for given
temperature targets.
The present study aims to (1) confirm the magnitudeof the scenario dependence of the TCRE and (2) investigate in which cases the TCRE has a high (or low) scenario dependence. To achieve these aims, a single model
ensemble perturbing physical and biogeochemical parameters using an Earth system model of intermediate
complexity (EMIC) is conducted to investigate the magnitude of the scenario dependence of the TCRE and its
correlations with each parameter. In addition, the mechanism of scenario dependence and its impact on the estimation of the remaining carbon budget are discussed.

2 Methods
The present study uses the MIROC-lite/JUMP-LCM(Tachiiri et al. 2010, 2013) model, which contains a fully
coupled core general ocean circulation model, with aTachiiri Progress in Earth and Planetary Science(2020) 7:74

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EMIC-AR5 (Weaver et al. 2012; Eby et al. 2013; Zickfeld
et al. 2013) and ZEC-MIP (MacDougall et al. 2020).
For the model, 512 parameter sets were developed byusing the Latin hypercube method to perturb the 11 parameters listed in Table 1 (i.e., parameter sets were generated with equal distribution in the 11-dimension
parameter space). These parameters include the Gent–
McWilliams thickness parameter that measures the
eddy-induced velocity of the ocean (Gent and McWilliams 1990). In addition, a freshwater flux adjustment isnecessary in order to realistically represent the meridional overturning circulation. For measuring the marine
carbon cycle response, changing the photosynthesis parameters proved ineffective at varying the carbon cycle
sensitivity to pCO2 and temperature. Therefore, an atmosphere–ocean gas exchange coefficient was implemented as a perturbation parameter.
The ranges of the parameters perturbed were selectedon the basis of the original ranges given in Table B1 of
Tachiiri et al. (2013) rather than the final range in Table
1 of the same work. Whereas Tachiiri et al. (2013) considered the representability of the Coupled Climate Carbon Cycle Model Inter-comparison Project (C4MIP)
models (Friedlingstein et al. 2006), the ranges of parameter perturbation in the present work are based on previous studies. In particular, the range of horizontal
diffusivity is determined on the basis of Collins et al.
(2007) and Roach et al. (2018), and is significantly narrowed. The reasons for the varying ranges of the parameters are given in more detail in the Supplementarybiogeochemical nutrition–phytoplankton–zooplankton–
detritus (NPZD) component, and an energy moisturebalance atmosphere model (Oka et al. 2011). In addition,
MIROC-lite uses a simple, one-layer-bucket land model
to close the water budget by considering precipitation(snow and rain), snowmelt, evaporation, and runoff.
However, the spatial distribution of climatic variables isinsufficiently represented by this model—especially precipitation, which is difficult to represent with a twodimensional atmosphere model. This was compensatedfor when calculating the land carbon uptake by using
the loosely coupled Sim-CYCLE model, a process-based
land ecosystem model that includes vegetation and soil
(Ito and Oikawa 2002) in combination with once-yearlydata interactions with the global mean surface airtemperature (GMSAT). First, the annual mean GMSAT
for the year in question was calculated from the output
of MIROC-lite. In addition, a dataset was prepared fromthe output of the 1-ppa scenario using the mediumresolution version of MIROC3.2 (K-1 model developers
2004). The annual mean GMSAT data for the year inquestion were then examined, and the most similar
datum to that of the MIROC-lite output was called fromthe prepared MIROC3.2 dataset. This information wasthen input to Sim-CYCLE. The variables called to run
the vegetation model were cloud cover, precipitation,
specific humidity, shortwave radiation, air temperature,and soil temperature at depths of 10 cm and 200 cm.
This combined model has been employed in international model inter-comparison projects such as

Table 1 Nature and ranges of the parameters perturbed in the present study
Parameter

Component

Default

Climate sensitivity

Atmosphere

1.7

Range

High weight
range

Ref.

1–6 K

2–4.5 Ka

Vertical diffusivity

Ocean

0.1–2.5 cm /s*

0.5–2.0 × default–

b–g

Horizontal diffusivity

Ocean

1 × 107 cm2/s

0.35–1.5 × default

–

h, i

Gent–McWilliams thickness

Ocean

6

7 × 10 cm /s

6

1–10 ×10 cm s–

J

Magnitude of freshwater flux adjustment

Ocean

1.0 (ratio to thevalues by Oort 1983)

0.5–2.0–k

Coefficient for marine CO2 uptake

Marine carbon 1

0.4–1.0

–

l, m,
n

Maximum photosynthetic rate

Land carbon

8.0–13.5 μmolCO2/(m2 s)**0.8–3.0 × default

0.8–2.0 × default oSpecific leaf area

Land carbon

110–170 cm2/(g dry matter)**

0.5–2.5 × default

0.5–1.5 × default p, q

Minimum temperature for photosynthesis

Land carbon− 5.0–11.0 °C **− 3.0–+ 3.0 °C
of default–r

Coefficient for temperature dependency of plant
respiration

Land carbon

2.0 (dimensionless)1.5–3.0–s, tParameter of temperature dependency of soil
respiration

Land carbon

46.02 K

40–60 K

–

r

2

2

2 −1

* Depth-dependent; **biome-dependent; a: Bindoff et al. (2013); b: Huber and Zanna (2017); c: Hasumi and Suginohara (1999); d: Tatebe et al. (2018); e: Meletet al. (2016); f: Simmons et al. (2004); g: Waterhouse et al. (2014); h: Collins et al. (2007); i: Roach et al. (2018); j: Visbeck et al. (1997); k: Talley (2008); l: Denman
et al. (2007); m: Ciais et al. (2013); n: Tachiiri et al. (2013); o: Peterson et al. (1999); p: Kattge et al. (2011); q: Gong and Gao (2019); r: Verbeeck et al. (2011); s:
Bolstad et al. (1999); t: Tjoelker et al. (2001)

Tachiiri Progress in Earth and Planetary Science(2020) 7:74

Information (SI_201015_1126.docx). In addition, while a
temporally unchanged but spatially varying wind speed(namely, the average value from the ERA5 reanalysis for
1979–2020 (Copernicus Climate Change Service 2017))
is used to calculate marine ocean uptake, the coefficientof aerosol forcing is not applicable here since the scenarios only consider the pCO2 change.
As indicated in Fig. 1 and Table 2, the following concentration pathways were applied to the study scenarios:(a) I-1%: 1 ppa increase to 2 × CO2 (dark blue line)(b) I-0.5%: 0.5 ppa increase to 2 × CO2 (green line)(c) I-0.25%: 0.25 ppa to 2 × CO2 (red line)(d) I-2%: 2 ppa to 2 × CO2 (light blue line)(e) I-4%: 4 ppa for 40 years, up to around 4.5 × CO2(purple line)(f) D-1%: 1 ppa decrease from 2 × CO2 after (a) (blackline)
In addition, a biogeochemically coupled run was performed for the I-1% scenario and a zero-emission experiment was initiated from the end of the I-1%
scenario.
Before the experiments, as spin-up, all members of theatmosphere-ocean and land ecosystem parts were runfor 3000 and 2000 years, respectively. The TCRE foreach scenario was the average for years 21–280 for theI-0.25% scenario, 21–140 for the I-0.5% scenario, 21–70
for the I-1% scenario, 21–40 for the I-2% scenario, 15–
24 for the I-4% scenario, and 1–50 for the D-1% scenario. Years 1–20 and the final 20 years of the D-1% scenario were removed to avoid the instability caused byvery small cumulative carbon emissions. The average ofthe 10-year period for the I-4% scenario was centered on
year 19, where the CO2 concentration level was doubled.
Note that the TCRE for the D-1% scenario was calculated from the temperature anomaly and cumulative

Fig. 1 Plots of pCO2 levels against time (years) for the various study
scenarios: I-1% (dark blue line); I-0.5% (green line); I-0.25% (red line); I2% (light blue line); I-4% (Purple line); D-1% (black line)

Page 4 of 12

carbon emissions at the start of the precedent I-1% scenario so a combination of I-1% and D-1% could provide
an example of an overshooting scenario.
To investigate the correlation between the CO2–carbon cycle and climate–carbon cycle feedback to the
TCRE and its scenario dependence, a biogeochemicallycoupled run of the I-1% scenario was performed inwhich ecosystems were subject to an increasing pCO2
but the CO2 did not function as a greenhouse gas. The
TCRE can be decomposed to Eq. (2):α=ð1 þ β þ αγ Þð2Þwhere α[K/GtC], β [GtC/GtC], and γ [GtC/K] are thelinear transient climate sensitivity to pCO2 increase, theCO2–carbon cycle feedback, and the climate–carbon
cycle feedback, respectively (Friedlingstein et al. 2006;
Gregory et al. 2009). Hence, these are assumed to directly influence the change in the TCRE. Here, in calculating β and γ, the effects of temperature change on thebiogeochemically coupled run is confirmed to be small,and β and γ are simply calculated using Eqs. (3) and (4)(Arora et al. 2020):
β¼

ΔC b
ΔCA

ð3Þ

γ¼

ΔC f − ΔC b
ΔT f

ð4Þ

where ΔCb and ΔCf are the total change in land andocean carbon storage in the biogeochemically and fully
coupled runs, respectively; ΔCA is the change in the atmospheric carbon, and ΔTf is the temperature change inthe fully coupled run. Here, values for the 70th year wereused.
To examine the relationship between the scenario dependence of the TCRE and the ZEC, a ZEC experiment
was performed. In contrast to ZEC-MIP (MacDougall
et al. 2020), which starts the zero-emission period when
the cumulative emissions reach their given levels (i.e.,
750, 1000, and 2000 GtC), the start of the zero-emission
period in the present study is the 70th year of the I-1%
scenario. Moreover, the ZEC values up to thetemperature peak (the same as Eq. (1)), the 25th (theaverage of the 20th–29th), and the 50th (the average ofthe 45th–54th) years are used for the analysis, whereas
ZEC-MIP uses the averages of 10 years centering on the
25th, 50th, and 90th.
For three parameters, namely the equilibrium climate
sensitivity (ECS), the maximum photosynthetic rate, andthe specific leaf area, values near the edges of the ranges
are given smaller weights, as shown in Figure S1. Thus,
for the ECS, the weight linearly increases from 0 to 1 asthe ECS increases from 1 to 2; the weight then remains
at 1 throughout the 2–4.5 K range before linearlyTachiiri Progress in Earth and Planetary Science(2020) 7:74

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Table 2 Study scenarios
Scenario

pCO2 change rate

Start CO2 level

End CO2 level

Duration (years)

I-1%

1% p.a. increase

1 × CO2 (Initial)

2 × CO270

I-0.25%

0.25% p.a. increase

1 × CO2 (Initial)

2 × CO2

280

I-0.5%

0.5% p.a. increase

1 × CO2 (Initial)

2 × CO2140

I-2%

2 % p.a. increase

1 × CO2 (Initial)

2 × CO240

I-4%

4% p.a. increase

1 × CO2 (Initial)

4.5 × CO2

40

D-1%

1% p.a. decrease

2 × CO2 (after I1.0%)

1 × CO270

decreasing to 0 beyond that range (Figure S1a). The coefficient of maximum photosynthetic rates of between 2
and 3 have smaller weights (Figure S1b), and specific leaf
areas of between 1.5 and 2.5 have smaller weights (Figure S1c). The total weight is calculated as the product of
the weights for these three parameters. For the members
which develop negative cumulative carbon emissions
during the experiments (as happens for two members in
the D-1% scenario), the end of the period for calculating
the average TCRE is moved to 20 years prior to the year
in which the TCRE becomes negative.

3 Results and discussion
3.1 Scenario dependence of the TCRE

The distribution in the TCRE change for each scenario
relative to that of the I-1% scenario is presented in Fig. 2.
Here, many members under the I-0.5% scenario (greenline) have similar (slightly larger) TCRE values than thoseunder the I-1% scenario; the average ratio of the TCRE tothat of I-1% is 1.05, the peak is in the 1.0–1.1 bin, and
50% of the members are within the range of ± 5% difference from those of the I-1% scenario. Under the I-2% scenario (light blue line), the distribution is shifted toward
small TCREs with a peak in the 0.9–1.0 bin; the average isFig. 2 Weighted probability distributions of the relative change in
the TCRE from that of the I-1% scenario. The numbers inparentheses indicate the average among all members and thepercentages of the members within a ± 5% difference from thevalue under the I-1% scenario: I-0.5% (green line); I-0.25% (red line); I2% (light blue line); I-4% (purple line); D-1% (black line; starting froma non-equilibrium state)

0.91, and 12% are within the range of ± 5% difference fromthose under the I-1% scenario. The other peaks occur at
0.7–0.8, 1.0–1.1, and 1.1–1.2 for the I-4% (purple line), I0.25% (red line), and D-1% (black line) scenarios, respectively, with corresponding averages of 0.79, 1.09, and 1.12.
The corresponding fractions of members within the rangeof ± 5% difference from the I-1% scenario are 0.5%, 29%,
and 21%, respectively. These results clearly indicate that
the TCRE tends to increase under scenarios with a slowly
increasing pCO2 and decrease under scenarios with a rapidly increasing pCO2. In the case of D-1%, with a 1-ppa
decease from the non-equilibrium 2 × CO2 level, theTCRE is even larger than that of the I-0.25% scenario. The
large similarity between I-1% and I-0.5% is consistent withthe results of MacDougall (2017), who concluded that the
TCRE is only close to constant (i.e., < 5% change) at apCO2 of 0.3–1.2% p.a. at 400 ppm.
3.2 Correlations of the parameters to the scenario
dependence of the TCRE

The coefficients of correlation between each parameterand the TCRE for the I-1% scenario are presented inTable 3. Also shown are the correlations between eachparameter and ratio of the TCRE value of each alternative scenario to that of the I-1% scenario. Unsurprisingly,
the correlations of many parameters display opposite
signs depending on whether the specific scenario has alarger or smaller rate of increase in the pCO2 relative tothat of the I-1% scenario. This is a direct result of using
the ratio of the specific scenario TCRE to that of the I1% scenario as the metric.
An examination of Table 3 indicates that the ECS parameter is especially strongly correlated to the TCRE
value of the I-1% scenario and to the ratio of the TCRE
values of all other scenarios to that of the I-1% scenario.
Among the other parameters, relatively large correlations with the scenario dependence of the TCRE are observed for the plant respiration parameter, thecoefficient for marine carbon uptake, the maximum
photosynthetic rate, and the specific leaf area, particularly for rapid pCO2 increase scenarios. Among thephysical parameters, the vertical diffusivity of the ocean
displays a significant correlation. For the D-1% scenario,
the maximum photosynthetic rate and plant respiration

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Table 3 Correlation between each parameter, and TCRE in the I-1% scenario and the relative TCRE change from the I-1% scenario
Parameter

I-1%

D-1%

I-0.25%

I-0.5%

I-2%

I-4%

Equilibrium climate sensitivity (ECS)

0.829
0.835***

0.865
0.891***

0.762
0.791***

0.775
0.785***− 0.742− 0.743***− 0.776− 0.773***

Vertical diffusivity− 0.199− 0.191***− 0.144− 0.135***− 0.084− 0.079− 0.140− 0.129**0.176
0.172**

0.193
0.192***

Horizontal diffusivity

0.035
0.047

0.080
0.076

0.091
0.082

0.090
0.085

− 0.050− 0.060− 0.043− 0.051

Gent–McWilliams thickness

0.066
0.072

0.000
0.007

− 0.009− 0.008− 0.005− 0.008− 0.018− 0.025− 0.004− 0.006

Freshwater flux adjustment− 0.024− 0.019

0.020
0.031

0.010
0.016

0.004
0.007

0.023
0.023

0.022
0.019

Marine CO2 uptake− 0.294− 0.288***

0.018
0.038

− 0.110− 0.097− 0.091− 0.092

0.152
0.160**

0.164
0.178***

Maximum photosynthetic rate

0.026
0.046

0.239
0.207***

0.113
0.089

0.109
0.094

− 0.127− 0.135***− 0.131− 0.154***

Specific leaf area

− 0.205− 0.186***

0.072
0.045

− 0.114− 0.121*− 0.138− 0.139**0.184
0.170**

0.173
0.153**

Minimum temperature for photosynthesis− 0.032− 0.036− 0.026− 0.018− 0.097− 0.092− 0.083− 0.081

0.084
0.086

0.057
0.066

Temperature dependency of plant respiration

0.233
0.235***

0.219
0.213***

0.347
0.349***

0.367
0.371***− 0.393− 0.399***− 0.364− 0.376***

Temperature dependency of soil respiration− 0.032− 0.031− 0.047− 0.025− 0.008
0.002− 0.0280.030− 0.066− 0.049− 0.040− 0.018

CO2–carbon cycle feedback (β )− 0.346− 0.324***− 0.040− 0.047− 0.239− 0.261***− 0.306− 0.313***0.386
0.379***

0.354
0.339***

Climate–carbon cycle feedback (γ )

0.053
0.014

0.001
0.029

− 0.026
0.033

0.064
0.050

0.039
0.002

0.031
0.026

TCRE of I-1%

–

0.810
0.835***

0.831
0.863***

0.869
0.885***− 0.922− 0.928***− 0.943− 0.949***

In each cell, the upper and lower lines show the weighted Pearson’s product-moment correlation and the weighted Spearman’s rank correlation, respectively(weights are considered in calculating the variance and co-variance for the independent and dependent variables). For the latter, *, **, and *** indicate statisticalsignificance at the 10%, 5%, and 1% levels, respectively (the sum of the weights for all members, i.e., 222.17, is used as the sample size in the statisticalsignificance test)

parameter display relatively large correlations with thescenario dependence of the TCRE.
For comprehensive sensitivities, the CO2–carbon cycle
feedback (β) is fairly strongly correlated with the TCRE
under the I-1% scenario and is relatively unchanged
under all other scenarios except for the D-1% scenario.
The climate–carbon cycle feedback (γ) displays a weakcorrelation to the TCRE and its scenario dependence, although the unweighted case shows a statistically significant correlation in slow pCO2 increase scenarios (notshown). For fast pCO2 increase scenarios, the correlationof the ECS is slightly reduced and β instead displays aslightly larger correlation relative to that in slow scenarios. When the TCRE is large under the I-1% scenario,
the TCRE is seen to increase under slower scenarios (D1%, I-0.25%, and I-0.5%) and to decrease under faster
scenarios (I-2% and I-4%), with very large absolute coefficients of correlation (0.81–0.94 and 0.84–0.95 for Pearson’s and Spearman’s coefficients, respectively).
The correlation between the ECS and the TCRE underthe I-1% scenario, and between the ECS and the ratio of

the TCRE value of each alternative scenario to that ofthe I-1% scenario, are indicated by the scatter plots in
Fig. 3. The TCRE is seen to be almost independent of
scenarios that are slower than the I-1% scenario formodels with an ECS of 2–3 K (i.e., the ratio of the TCRE
to that of the I-1% scenario was is close to 1) and has avalue of approximately 1.5–1.6 K/1000 GtC (see also
Figure S2a, which shows that the deviation from the I1% scenario is smallest for an ECS of 2–3 K under slow
scenarios). For the I-2% and I-4% scenarios, a smaller
ECS results in a lesser scenario dependence. The ECS
correlation is seen to decrease under fast scenarios, andthis is attributed to the relatively small variation in thetemperature anomaly among the members in rapid scenarios, particularly when the ECS is high (Fig. 3e, f).
The ECS dependences of the temperature and cumulative carbon emissions for the various scenarios are presented in Figure S3a-d. The large correlation between
the ECS and the TCRE change results from the combined influence of temperature and cumulative carbon
emissions. High ECS models have previously been

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Fig. 3 The correlation between the ECS and a the TCRE under the I-1% scenario, and b–f the relative change in the TCRE from that of the I-1%
for the other scenarios: b D-1% (starting from a non-equilibrium state), c I-0.25%, d I-0.5%, e I-2%, and f I-4%. The red, blue, and black circles
indicate members with weights of > 0.5, 0.1–0.5, and < 0.1, respectively. Note that each sub-figure has a different y-axis

shown to have low transient climate responses (TCRs)
to the ECS ratio (Millar et al. 2015, Tsutsui 2017, 2020);
i.e., these models are prone to longer responses. Thistendency is confirmed in the present study (Figure S3f).
Thus, members of high ECS respond more slowly thanmembers of low ECS, generating a smaller temperaturerise for a given level of emission (smaller TCRE) in fast
pCO2 increase scenarios than in slow pCO2 increase scenarios. This higher realized fraction (i.e., ratio to thevalue when the system is equilibrated for a given pCO2
condition) for warming in slow scenarios becomes evenmore remarkable in the declining part of overshooting
scenarios (Fig S3c); in overshooting, the system iswarmed up when it experiences a high pCO2 condition,
causing high realized warming fraction in the following
period. Actually, a similar effect occurs for CO2 too (Fig
S3d), but as the temperature is more sensitive, the TCRE
rise in the declining part of the overshooting scenarios
becomes the highest among the scenario consideredhere. This is regarded as the mechanism by which the
ECS correlates with the scenario dependence of theTCRE. Indeed, Tachiiri et al. (2015) also showed a positive relationship between the ECS and TCRE, and this
proposed mechanism probably explains their observationthat stabilization of the pCO2 resulted in enhanced
TCRE increases during the pCO2-increasing period forhigh-TCRE models and TCRE decreases for low-TCRE
models. In brief, the results presented herein can explain
why the use of a high ECS model (MIROC-ESM, 4.7K;
Andrews et al. 2012) revealed an increase in the TCREs

under overshooting scenarios (Tachiiri et al. 2019),
whereas the relatively low climate sensitivity of the
MIROC-ES2L model (ECS = 2.7 K; MacDougall et al.
2020) did not give that outcome.
For each scenario, the deviations (root-mean-squareerrors) of the TCREs from that of the I-1% scenario are
related to the ECS, CO2–carbon cycle feedback (β), andclimate–carbon cycle feedback (γ) in Figure S2, while
the correlations between the TCRE and the β and γ are
indicated by the scatter plots in Figures S4 and S5, respectively. Thus, a larger β is seen to result in a relatively
small scenario dependence for the TCRE, as does a large(small negative) γ value (Figure S2). Here, it is worth
noting that the members with γ<−300 PgC/K have small
ECS, thus resulting in small weights and a small
temperature rise.
Care should be exercised on the limitations of EMICs
or differences in the behaviors between EMICs and full
ESMs. Tokarska et al. (2016) found that the TCRE wasstable for the Representative Concentration Pathway 8.5
scenario, but tended to decrease for EMICs, when the
cumulative carbon emissions were large. In addition,
MacDougall et al. (2020) identified a positive relationship between the ZEC and the ECS in ESMs, but thistendency disappeared when EMICs were added. Moreover, although the correlation between the ECS and ZEC
was small, the same study showed a clear positive relationship between these values when different ECS versions of the same EMICs were compared, thus
demonstrating that the use of a single-model ensemble

Tachiiri Progress in Earth and Planetary Science(2020) 7:74

Page 8 of 12(with varying parameters) can provide different resultsfrom those of a multi-model study.
3.3 Implications for carbon budget estimation

The values of the weighted 1st–99th TCRE percentiles
for each scenario are plotted in Fig. 4. Thus, for the ensemble members of the lowest TCRE values, the scenario dependence of the TCRE is small. Among the 33rd,
50th, and 67th percentiles, which present the remaining
carbon budget in SR1.5 (Rogelj et al. 2018), the 33rd percentile is relatively stable except for a slight decrease in
the I-4% scenario. For the 50th and 67th percentiles, theTCRE is slightly increased under I-0.25% (by 8% and13%, respectively), while 12% and 20% increases are observed under the D-1% scenario. For higher percentiles,
the scenario dependence of the TCRE is significant, witha tendency toward low values under rapidly increasing
pCO2 scenarios, high values under slowly increasing
pCO2 scenarios, and even higher values under the
decline-after-a-peak (D-1%) scenario. In this experiment,
the 50th percentile in the dataset corresponds to the 1.6
K/1000GtC for the I-1% scenario. The 95% ranges (2.5–
97.5 percentiles) are 0.9–1.6, 1.0–2.0, 1.0–2.3, 1.0–2.6,
0.9–3.0, and 0.9–3.3 K/TtC for the I-4%, I-2%, I-1%, I0.5%, I-0.25%, and D-1% scenarios, respectively. Although the sample size is small, a linear regression is
attempted in Figure S6 in order to estimate the TCRE
using the ECS and the rate of increase in the pCO2. This
enabled the derivation of Eq. (5):TCRE½K=TtC ¼ ð − 0:091 ln ðI Þ þ 0:26ÞECS½K
þ maxð0; minð0:77; 0:22 ln ðI Þ þ 0:76ÞÞ

ð5Þ
where I is the rate of increase in pCO2 [ppa].
The remaining carbon budget calculated from the TCRE
for at the 33rd, 50th, and 67th percentile of the I-1%, I0.5%, and I-0.25% scenarios, along with the ratio of theFig. 4 Weighted values of the 1st–99th percentiles of the TCRE undereach scenario. D-1% scenario starts from a non-equilibrium stateremaining carbon budget to that of the I-1% at the same
percentile, are presented in Table 4. The two remaining
carbon budget values quoted for each scenario are thoseobtained before (left) and after (right) subtracting the estimated contribution of unpresented Earth system feedback(100 GtCO2 = 27.3 GtC; Rogelj et al. 2018). The I-2% andI-4% scenarios are not included because they are too fast
for practical carbon budget estimation for temperaturetargets such as 1.5 °C and 2 °C. Meanwhile, the D-1% scenario is excluded because Eq. (1) is not applicable to it(Rogelj et al. 2019). Here, the method of Tachiiri et al.
(2019) was used to estimate the remaining carbon budget
for the 1.5 °C target, i.e., using Tlim−Thist = 0.53 °C in Eq.
(1), assuming that the non-CO2 greenhouse gas contribution was 30%, and that the 2011–2017 emissions were
79.4 PgC. The TZEC was expected to be scenario
dependent but since only one scenario was assessed in thisstudy, its value was assumed to be zero, following MacDougall et al. (2020). In this study, for the I-1% scenario,
the ZEC is found to be 0.07, 0.11, and 0.15 °C for the 33rd,
50th, and 67th percentile, respectively. Due to the scenario
dependence of the TCRE, the remaining carbon budget
could be reduced by 18% and 22% before and after subtracting the estimated contribution of unpresented Earthsystem feedback for the most extreme case (i.e., the 67th
percentile I-0.25% scenario).
The ratio of the TCREs under the D-1% and I-1% scenarios is used as an indicator of the scenario dependence of
the TCRE, and its relationship to the ZEC at the peaktemperature is plotted in Fig. 5. Similar plots at 25 and 50
years after starting the zero-emission period are presented
in Figure S7. In each case, a positive relationship between
the ZEC and the scenario dependence of the TCRE can beobserved. This is expected because the warming in thezero-emission period is an indicator of scenario dependence
in terms of the temperature and the TCRE, as shown in
Figure S8. Note that the ratio of the TCRE under the D-1%
and I-1% scenarios is used in this analysis because the extreme scenario of D-1% generates a large spread in TCRE.
Although the ZEC was considered in Eq. (1), the TCRE
was assumed constant (having no scenario dependence).
Nevertheless, as shown in Fig. 5, a non-zero ZEC is associated with the scenario dependence of the TCRE. Thus, forcases with no scenario dependence for the TCRE, and no
ZEC, the ZEC term can be omitted from Eq. (1) and carbon budget estimation becomes relatively trivial. However,when a ZEC and scenario dependence of the TCRE occur,
inclusion of the ZEC term may be insufficient. It is necessary to consider what specific scenario was used to estimate the TCRE and, if the scenario is significantly
different, the TCRE value must be adjusted. This is particularly important when the ECS is large.
The pathways for maintaining the 2 °C target were previously analyzed with a realistic magnitude of overshoot byTachiiri Progress in Earth and Planetary Science(2020) 7:74

Page 9 of 12

Table 4 Remaining carbon budget (RCB) for the 1.5 °C target based on the TCREs for the I-1%, I-0.5%, and I-0.25% scenarios
33rd percentile

Scenario
I-1%

I-0.5%

I-0.25%50th percentile

67th percentile

TCRE (K/TtC)

1.44

1.59

1.72

RCB

178/151

154/127

136/109

Relative to I-1%

1.00/1.00

1.00/1.00

1.00/1.00

TCRE (K/TtC)

1.48

1.67

1.84

RCB

171/144

143/115

122/95

Relative to I-1%

0.961/0.954

0.927/0.912

0.897/0.871

TCRE (K/TtC)

1.48

1.72

1.94

RCB

171/144

136/109

112/85

Relative to I-1%

0.961/0.954

0.885/0.861

0.821/0.776

Tokarska et al. (2019) to indicate identical cumulative CO2
emissions for both overshooting and non-overshooting
pathways. They concluded that no corrections are needed
for ambitious mitigation scenarios with the low levels ofovershoot presented in SR1.5. The present study confirms
their output (which is available at http://data.iac.ethz.ch/
Tokarska_et_al_2019_Overshoot_UVicESCM/, and wasaccessed on May 8, 2020) and found that the TCRE isslightly larger in the negative emission period, moderate in
the slow emission period, and small in the rapid emission
period. More importantly, however, the differences in the
TCREs between the scenarios and periods were small (<5%), which is presumed to lead to almost identical cumulative carbon emissions for both pathways. For the experiments described herein, the relationship between the ECS
and the scenario dependence of the cumulative carbon
emission for the 1.5 °C target shown in Fig. 6 indicates that
this outcome only occurs when the ECS is low. By contrast,
when the ECS is high, an overshooting scenario could generate a significant reduction in the carbon budget. Thus,

Fig. 5 The relationship between the ZEC and the scenario
dependence of the TCRE. The ZEC is presented at the peaktemperature after the cessation of CO2 emissions. Ratio of TCREs forD-1% (starting from a non-equilibrium state) to that of I-1%
scenarios is used as an indicator of the scenario dependence. The
red, blue, and black circles indicate members with weights of > 0.5,
0.1–0.5, and < 0.1, respectively

more research is needed to determine whether a correction
is required in carbon budget estimation methods for overshooting pathways.

4 Conclusions
Considering the importance of the TCRE in estimating
the remaining carbon budget, the magnitude of scenario
dependence and its relation to physical and biogeochemical parameters were investigated via ensemble experiments using an EMIC. The results indicated that, on
average, the TCRE decreases in scenarios with a rapid
rate of CO2 increase, and increases in scenarios with aslow rate of CO2 increase. Moreover, the declining partof an overshooting scenario was shown to generate aneven larger TCRE than the slow CO2 increase scenario.
Among the parameters considered, the ECS displayedby far the strongest correlation with the scenario

Fig. 6 Relationship between the ECS and the scenario dependenceof the cumulative carbon emission for the 1.5°C target: D-1% to I-1%
(black), D-1% to I-0.5% (red), and D-1% to I-0.25% (blue). Memberswith a low ECS (approximately < 2.5 K) do not reach the 1.5 °C
warming level from the initial stateTachiiri Progress in Earth and Planetary Science(2020) 7:74

dependence of the TCRE. This is attributed to the longer
response time in the high ECS model and can explain why
the use of a high ECS model (MIROC-ESM, 4.7 K; Andrews et al. 2012) revealed an increase in the TCRE underovershooting scenarios (Tachiiri et al. 2019), whereas thiswas not observed when using the MIROC-ES2L (ECS =2.7 K). Here, when the ECS was high, the ECS correlation
was reduced for fast scenarios, and the correlations of thebiogeochemical parameters were strengthened comparedto those in slow scenarios.
In the slower scenarios, the TCRE increase wasfound to be more significant when the ECS was high.
As such, the remaining carbon budget for the 1.5 °C
target could be significantly reduced in the slow
pCO2 scenarios. For example, the 67th percentile
values for the I-0.25% scenario before and after subtracting the estimated contribution of the unpresented
Earth system feedback were reduced by 18% or 22%
relative to the case using the value for the I-1% scenario, respectively, thus indicating that the scenario
dependence of the TCRE could cause non-negligible
changes in the remaining carbon budget. For an overshooting scenario (i.e., I-1% + D-1%), the cumulative
carbon emission to 1.5 °C warming was found to be
reduced compared to the slow increasing (e.g., I0.25%) scenarios for high ECS cases. In the present
study, the scenario dependence of the realized warming fraction demonstrated that the ZEC is also likely
to be scenario dependent, and could therefore be included in calculating the carbon budget. However, theincorporation of the ZEC term into the carbon
budget estimation remains as future work because thespecifics are beyond the scope of the present study.
The quasi-constant TCRE concept is both scientificallyinteresting and practically helpful, and there are manyother uncertainties in carbon budget estimation (e.g.,
GMST observation). However, an investigation of the subtle differences in the TCRE is meaningful for both attaining
a deeper understanding of the climate–carbon cycle systemand for more practical carbon budget estimation.
Notably, the present study was conducted using a single EMIC. The difference in the behaviors between
ESMs and EMICs is sometimes non-negligible and theresults of a single-model ensemble can differ from thoseof a multi-model ensemble. The methods used to simplify the EMIC and select the range of parameter variation could also affect the results. However, considering
the significance of the impact, and the tendency for
Coupled Model Inter-comparison Project Phase6(CMIP6) models to have larger ECS values than previous
versions (Zelinka et al. 2020; Meehl et al. 2020), an investigation into the scenario dependency of the TCRE instate-of-the-art ESMs could be very important future
work.

Page 10 of 12

5 Supplementary Information
The online version contains supplementary material available at https://doi.
org/10.1186/s40645-020-00392-6.
Additional file 1: Figure S1. Weights used for the parameters: (a) ECS,(b) maximum photosynthetic rate, and (c) specific leaf area (see Table 1).
Figure S2. The weighted relationships between the deviations (rootmean-square errors) of the ratios of the TCRE to that of the I-1% scenarioand (a) the ECS, (b) β, and (c) γ. D-1% scenario starts from a nonequilibrium state. “All” indicates the total (root-mean-square) of all
scenarios, and “Slow” indicates that for D-1%, I-0.25% and I-0.5%
scenarios. Figure S3. The ECS dependence of (a, c) the temperature, (b,d) the cumulative carbon emissions for (a, b) 2 × CO2, (c, d) 1.5 × CO2, (e)transient warming at the 2 × CO2 level, and (f) the realized warming fraction (i.e., the ratio of the transient warming at the 2 × CO2 level to the
ECS). D-1% scenario starts from a non-equilibrium state. Figure S4. The
correlation between the CO2-carbon cycle feedback (β) and (a) the TCRE
under the I-1% scenario and (b-f) the relative change in the TCRE fromthat under I-1% for (b) the D-1% (starting from a non-equilibrium state),(c) the I-0.25%, (d) the I-0.5%, (e) the I-2%, and (f) the I-4% scenarios. The
red, blue, and black circles indicate members with weights of >0.5, 0.1–
0.5, and <0.1, respectively. Figure S5. Correlations between the climatecarbon cycle feedback (γ) and (a) the TCRE under the I-1% scenario, and(b-f) the relative change in the TCRE from that of the I-1% for (b) the D1% (starting from a non-equilibrium state), (c) the I-0.25%, (d) the I-0.5%,(e) the I-2%, and (f) the I-4% scenarios. The red, blue, and black circles indicate members with weights of >0.5, 0.1–0.5, and <0.1, respectively. Figure S6. The slopes (a) and intercepts (b) of the linear regressions of the
TCRE for the ECS under each scenario plotted against the rate of increase
in pCO2 for each scenario. The D-1% scenario, starting from a nonequilibrium state, is indicated by the orange circle but is excluded fromthe regression. Figure S7. The relationship between (a) the ZEC25 and(b) the ZEC50 and the scenario dependence of the TCRE. Ratio of TCREs
for D-1% (starting from a non-equilibrium state) to that of I-1% scenarios
is used as an indicator of the scenario dependence. The red, blue, andblack circles indicate members with weights of >0.5, 0.1–0.5, and <0.1, respectively. Figure S8. Schematic relationship between the ZEC and thescenario dependence of the TCRE: (a) initial scenario, (b) same scenario
followed by a 70-year ZEC period.
Abbreviations
AR5: The Fifth Assessment Report (of IPCC); ECS: Equilibrium climate
sensitivity; EMIC: Earth system model of intermediate complexity; ESM: Earthsystem model; GMSAT: Global mean surface air temperature;
IPCC: Intergovernmental Panel on Climate Change; pCO2: Atmospheric CO2
concentration; SR1.5: Special Report on Global Warming of 1.5°C (of IPCC);
TAB: Threshold avoidance budget; TCRE: Transient climate response tocumulative carbon emissions; TEB: Threshold exceedance budget; ZECMIP: Zero-emission commitment model inter-comparison project;
β: Magnitude of the CO2–carbon cycle feedback; γ: Magnitude of
the climate–carbon cycle feedback
Acknowledgements
The author would like to thank Dr. Hiroaki Tatebe of the Japan Agency for
Marine-Earth Science and Technology (JAMSTEC) for his helpful comments
on uncertainty in ocean physics parameters and Dr. Akira Oka of the University of Tokyo for his additional helpful comments on the same topic and on
the treatment of wind speed. I would also like to thank Dr. Junichi Tsutsui ofCentral Research Institute of Electric Power Industry for his helpful commentson the relationship between transient climate response and equilibrium climate sensitivity. This work was supported by TOUGOU, the “Integrated Research Program for Advancing Climate Models” (Grant Number
JPMXD0717935715) of the Ministry of Education, Culture, Sports, Science andTechnology of Japan. The experiments were carried out using Data Analyzer
System of the Japan Agency for Marine-Earth Science and Technology.
Author’s contributions
KT designed and carried out the experiments, analyzed the results, andprepared the manuscript. The author read and approved the final
manuscript.

Tachiiri Progress in Earth and Planetary Science(2020) 7:74

Author information
KT is the leader of the Earth System Model Development and Application
Group at the Research Center for Environmental Modeling and Applicationof the Japan Agency for Marine-Earth Science and Technology.
Funding
This work was supported by TOUGOU, the “Integrated Research Program for
Advancing Climate Models” of the Ministry of Education, Culture, Sports,
Science and Technology of Japan. (Grant Number JPMXD0717935715).
Availability of data and materials
The datasets used and/or analyzed during the current study are available
from the corresponding author on reasonable request.
Competing interests
The authors declare that they have no competing interest.
Received: 31 December 2019 Accepted: 10 November 2020

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