Hajima et al. Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-020-00350-2(2020) 7:40

Progress in Earth andPlanetary Science

RESEARCH ARTICLE

Open AccessMillennium time-scale experiments on
climate-carbon cycle with doubled CO2
concentration
Tomohiro Hajima* , Akitomo Yamamoto, Michio Kawamiya, Xuanming Su, Michio Watanabe, Rumi Ohgaito andHiroaki Tatebe

Abstract
Earth system models (ESMs) are commonly used for simulating the climate–carbon (C) cycle and for projecting
future global warming. While ESMs are most often applied to century-long climate simulations, millennium-longsimulations, which have been conducted by other types of models but not by ESM because of the computationalcost, can provide basic fundamental properties of climate–C cycle models and will be required for estimating thecarbon dioxide (CO2) concentration and subsequent climate stabilization in the future. This study used two ESMs
(the Model for Interdisciplinary Research on Climate, the Earth system model version (MIROC-ESM) and the MIROC
Earth system version 2 for long-term simulation (MIROC-ES2L)) to investigate millennium-scale climate and C cycle
adjustment to external forcing. The CO2 concentration was doubled abruptly at the beginning of the model
simulations and kept at that level for the next 1000 or 2000 years; these model simulations were compared withtransient simulations where the CO2 was increased at the rate of 1% year−1 for up to 140 years (1pctCO2). Model
simulations to separate and evaluate the C cycle feedbacks were also performed. Unlike the 1pctCO2 experiment,
the change in temperature–cumulative anthropogenic C emission (ΔT–CE) relationship was non-linear over themillennium time-scales; there were differences in this nonlinearity between the two ESMs. The differences in ΔT–CE
among existing models suggest large uncertainty in the ΔT and CE in the millennium-long climate-C simulations.
Ocean C and heat transport were found to be disconnected over millennium time-scales, leading to longer timescale of ocean C accumulation than heat uptake. Although the experimental design used here was highly idealized,
this long-lasting C uptake by the ocean should be considered as part of the stabilization of CO2 concentration andglobal warming. Future studies should perform millennium time-scale simulations using a hierarchy of models toclarify climate-C cycle processes and to understand the long-term response of the Earth system to anthropogenic
perturbations.
Keywords: Global warming, Earth system models, Millennium time-scales, Carbon cycle feedbacks, Transient climate
response to cumulative carbon emission, Anthropogenic emission* Correspondence: hajima@jamstec.go.jp
Research Institute for Global Change, Japan Agency for Marine-Earth Scienceand Technology, 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
permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

(2020) 7:40

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Introduction
It is clear that anthropogenic carbon dioxide (CO2) emission via fossil fuel burning and land-use change is themain cause of the current global warming; nations aroundthe world have agreed to make efforts to try to limit global
warming well below 2 °C. The global warming induced byanthropogenic CO2 emission involves a series of physicalclimate and carbon (C) cycle processes—anthropogenically emitted C is partly absorbed by land and ocean, andthe CO2 remaining in the atmosphere has changed the atmospheric radiation balance resulting in radiative forcing,leading to the current warming.
To understand the complex nature of the climate–C
cycle systems and to make climate projections, Earthsystem models (ESMs) have been developed; thesemodels have land and ocean biogeochemical components embedded or overlaid onto physical climate
models (e.g., Hajima et al. 2014; Kawamiya et al. 2020).
Recent studies using ESMs have revealed that the anthropogenically induced global warming can be well explained by the cumulative anthropogenic CO2 emission;
global warming is almost linear in relation to the cumulative amount of anthropogenic C emission regardless ofthe choice of future emission scenario (Allen et al. 2009;
Matthews et al. 2009; Gillett et al. 2013). The ratio of
global warming to cumulative C emission is called transient climate response to cumulative CO2 emission(TCRE), usually evaluated at the time when the total
emission reaches 1000 PgC. This relationship between
global warming and anthropogenic CO2 emission helps
to estimate the C budget required to not exceed a specific warming target, like the 2 °C target promised in the
Paris agreement (United Nations 2015).
Although the findings on TCRE have provided clear
perspective on future cumulative emissions and global
warming, the near constancy of TCRE irrespective of
scenario choice holds in limited conditions. For example,
Stocker et al. (2013) suggested that the constant TCRE
is valid for cumulative emissions up to about 2000 GtC
and until temperatures peak. After that, the characteristics of TCRE have been intensively examined: for example, MacDougall (2017) suggested that there likely
exists a limited range for anthropogenic emissions to result in TCRE being independent of scenario choice;Tachiiri et al. (2019) examined TCRE in various types ofidealized scenarios and confirmed that TCRE is stable
under scenarios of increasing or stable CO2 concentration. Another example of the typical condition that has
not been well examined is the period after net zero anthropogenic emission is achieved. Although Rogelj et al.
(2018) assumes, in the calculation of the total amount of
CO2 that can be emitted to not exceed a specific warming target “remaining carbon budget”, that thetemperature change after zero emission (the temperaturechange is called “zero-emission commitment”, ZEC)
would be almost zero, it has not been systematically examined how models project the ZEC (Jones et al. 2019;
MacDougall et al. 2020).
Another condition that should be further examined
and the main purpose of this study is the long-term response of the climate–C cycle to anthropogenic perturbation. In particular, the long-term stabilization ofgreenhouse gases and the subsequent climate
stabilization correspond to the framework of the United
Nations Framework Convention on Climate Change(UN 1992). In addition, the final goal of our attempts inrelation to the Paris agreement, beyond the urgent necessity to curb anthropogenic emissions to avoid exceeding a specific warming target, should be the eventual
climate stabilization and concentration stabilization ofgreenhouse gases at a certain level. The eventual
stabilization of CO2 concentration can be realized by reducing anthropogenic emissions to the same level as thetotal natural C sink or by net zero emission of anthropogenic C (in this case, the CO2 concentration would
slowly decline over hundreds or thousands of years andthen the stabilization of concentration and global
temperature will be eventually realized (Eby et al. 2009;
MacDougall et al. 2020)). In both cases, the climate–C
system continues to change for a long time to adjust to
the new external forcing, likely from century to millennium time-scale (Archer et al. 2009; Li et al. 2013; Frölicher et al. 2013; Joos et al. 2013; Yamamoto et al. 2018;
Rugenstein et al. 2019).
In the physical climate science field, the degree of eventual warming and the time period necessary to reach a
new equilibrium state have been intensively examined in
the context of “equilibrium climate sensitivity (ECS)”. ECS
is defined as the eventual warming after doubling of theCO2 concentration from the pre-industrial state and isusually evaluated by applying regression analysis to climate model simulations of 150 years to reduce the computational cost of performing simulations over thousandsof years (Gregory et al. 2004; Andrews et al. 2012). To accurately estimate ECS, recent studies actually performed
simulations of running climate models over thousands ofyears until they reach the new equilibrium state (e.g.,
Danabasoglu and Gent 2009; Li et al. 2013; Paynter et al.
2018; Saint-Martin et al. 2019; Mauritsen et al. 2019), anda multi-model comparison study was conducted by
Rugenstein et al. (2019).
When compared with physical climate research, there
are few studies that examine how long the C cycle continues to change in response to external forcing andhow much anthropogenic C eventually accumulates onland and in the ocean on the millennium time-scale. In
particular, the feedback strength of C cycle processes
has been examined in century-scale simulations where

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the CO2 concentration is gradually increased by 1%
year−1, and thus the feedback strengths have been evaluated as the transient C cycle response against changing
magnitude of external forcing. In addition to such
century-scale simulations, the quantification of C cycle
processes in millennium time-scale simulations, as in theexperiments for evaluating ECS, will provide perspective
on our long-term climate and CO2 concentration
stabilization. Although the long-term simulations beyond centuries and the analysis on climate–C cycle processes have been performed by ESMs of Intermediate
Complexity (EMICs) (e.g., Archer et al. 2009; Eby et al.
2013; Zickfeld et al. 2013; Joos et al. 2013), there are few
ESM-based studies on the climate–C cycle because of
the computational costs (e.g., Frölicher et al. 2013; Jooset al. 2013). Such millennium time-scale experiments by
ESMs will reveal the detailed processes on how climate–
C cycle processes continue to change toward a new
equilibrium state and can provide fundamental understanding on our long-term climate and CO2 concentration stabilization.
In this study, we performed millennium time-scale experiments using ESMs to investigate long-term climate
and C cycle adjustment to external forcing. As in theevaluation of ECS, the C cycle process was quantified
based on experiments where CO2 concentration was
abruptly doubled and kept at that level over 1000 or2000 years, using two ESMs. By using the simulation results, the relationship between global warming and cumulative anthropogenic C emission can be analyzed.
The models and experimental configurations are described in the “Methods” section, and the simulation results are shown in the “Results and discussion” section.
We first compare the simulation results of global
temperature, ocean, and land C amount, and diagnosed
fossil fuel emission, and then the simulation results areanalyzed in terms of global warming and cumulative anthropogenic C emission, by comparing with that of transient simulations where the CO2 concentration wasincreased at the rate of 1% year−1. Such analysis is also
applied to existing simulation results performed by
EMICs. To explore the mechanisms that produce different patterns between the two types of experiments,
ocean heat and C uptakes are analyzed together with thediscussion on the limitation of near constancy of TCRE.
Finally, the summary and conclusions are described in
the corresponding sections.

Climate, the Earth system model version (MIROC-ESM)
developed by Watanabe et al. (2011) and the MIROC
Earth system version 2 for long-term simulation(MIROC-ES2L), developed by Hajima et al. (2020). The
former is a model that was intensively used for the
Coupled Model Intercomparison Project phase 5(CMIP5, Taylor et al. 2012). This model is based on
MIROC3.2 coupled with a land C cycle model, aspatially explicit individual-based dynamic global vegetation model (SEIB-DGVM; Sato et al. 2007) and an ocean
biogeochemical component including ocean C cycle
model and nutrient-phytoplankton-zooplankton-detritus
type ocean ecosystem model. The atmospheric grid system employs a T42 horizontal grid with 80 verticallayers, and the ocean has a grid system that consists oflongitudinal spacing of about 1.4° and latitudinal grid intervals that gradually become finer close to the equator,
with 44 levels of vertical coordinates. The latter model,
MIROC-ES2L, is the latest generation of MIROC-based
ESM and is expected to be intensively used for CMIP6(Eyring et al. 2016). The physical core is MIROC5.2, andthe horizontal resolution of the atmosphere is the sameas that of MIROC-ESM but with reduced vertical layers(40; up to 3 hPa). The ocean grid has the longitudinal
grid spacing of 1°, and the meridional grid spacing varies
from about 0.5° near the Equator to 1° in the midlatitudes. This model has a land biogeochemical component
model, the Vegetation Integrative Simulator for Tracegases model (VISIT; Ito and Inatomi 2012), extended for
the ESM and embeds an updated ocean biogeochemicalcomponent named OECO2 (Hajima et al. 2020).

Hajima et al. Progress in Earth and Planetary Science

Methods
Earth system models

To examine the long-term climate–C cycle response toexternal forcing, we used two types of ESMs based on
Atmosphere-Ocean
GeneralCirculation
Models(AOGCM): the Model for Interdisciplinary Research on

Simulations

Using the two ESMs, we performed several types of millennium time-scale experiments in addition to other experiments performed in CMIP (Table 1). The first was acontrol run “CTL”, where external forcing like CO2 concentration was fixed at pre-industrial levels. The control
run was performed over 2000 years by MIROC-ESM and1000 years by MIROC-ES2L. These experiments wereoriginally performed for CMIP5/CMIP6 experiments,
but in this study, the simulations were extended up to
1000 and 2000 years.
The second type of experiment was the “FULL2 × CO2”
experiment, where the atmospheric CO2 concentration
was abruptly doubled (hereafter presented by “2 ×CO2”) and held at that level during the same period asin the CTL runs. These experiments were similar to an
idealized experiment of CMIP5/CMIP6, where the CO2
concentration abruptly quadrupled over a few centuries,
but in this study, the simulation period was extended to1000 or 2000 years, and the CO2 concentration was doubled, not quadrupled.

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Table 1 Models, experimental configurations, and time periods of simulation used in this study
Experiment name

CTL

FULL2 × CO2

Experimental configuration on CO2 concentration

Fix at pre-industrial level

Abruptly doubled and fixed

Simulation years: MIROC-ESM

2000 years

2000 years

2000 years

2000 years

140 years

Simulation years: MIROC-ES2L

1000 years

1000 years––

140 years

The third and fourth experiments, named “BGC2 ×” and “RAD2 × CO2”, respectively, were special simulations to evaluate the C cycle feedbacks. These two experiments were performed by MIROC-ESM only. The
former experiment was designed to isolate the C cyclechange in response to CO2 increase. In this experiment,
CO2 concentration change was only detected by C cycle
processes, and the atmospheric radiation process wasmaintained at the pre-industrial level concentration.
Thus, in the BGC2 × CO2 experiment, there was no global warming induced by CO2 concentration increase,and direct stimulation of CO2 increase was the main
driver of C cycle change. The RAD2 × CO2 experiment,in contrast, was designed to evaluate the C cycle changesolely in response to climate change. In this experiment,
the atmospheric radiation process detected the CO2 increase, but there was no direct stimulation of CO2 increase on land and ocean C cycle processes. Thus,
climate change was the main driver of C cycle change inthis experiment. These two types of experiments wereoriginally devised in the multi-model comparison on
climate-C cycle models in the Coupled Carbon Cycle
Climate Model Intercomparison Project (C4MIP, Aroraet al. 2013; Jones et al. 2016), but the CO2 concentrationin the original C4MIP experiment was increased by 1%
year−1 over 140 years (named “1pctCO2”).
Finally, to analyze the relationship between global
temperature change and cumulative anthropogenic C emission, the 1pctCO2 simulation results from MIROC-ESM
and MIROC-ES2L were also compared with the millennium time-scale experiment. The 1pctCO2 experiments
were performed as one of the experiments of CMIP5/
CMIP6 and already reported in several places (e.g., Hajima
et al. 2012; Gillett et al. 2013; Hajima et al. 2020).
All experiments performed in this study were based onprescribed CO2 concentration, and thus the anthropogenic C emissions were diagnosed from the prescribed
CO2 concentration and simulated C uptake by land andocean, as shown below:

CO2

E ¼ dC A =dt þ dC L =dt þ dC O =dt
where E is the annual anthropogenic emission; CA, CL,
and CO are changes in the C amount in the atmosphere,
land, and ocean, respectively; and the time derivatives ofthe land and ocean C amounts corresponded to their net
C uptake.

BGC2 × CO2

RAD2 × CO2

1pctCO2
Increased by 1% year−1

Simulations by EMICs

When compared with ESMs, EMICs have less complexity of climate-C cycle processes in some component
models, and thus the models can effectively be run overmillennium time-scales. Eby et al. (2013) and Zickfeld
et al. (2013) performed various types of long-term simulations using multiple EMICs (named “EMIC-AR5”), andwe obtained the simulation results from eight of the
EMICs (Bern3D, DCESS, GENIE, IGSM, MESMO,MIROC3-lite-LCM, UMD, and UVic ESCM) for
1pctCO2 (140 years) and FULL2 × CO2 (1000 years) experiments. The results of global temperature and C
fluxes were compared with those of MIROC-ESM and
MIROC-ES2L simulations.

Results and discussion
Global changes in temperature and C storages

The results of global mean surface air temperaturechange (ΔT) and changes in land and ocean C amountare shown in Fig. 1 and Table 2, after removing thetrends that were found in CTL (the successful removalof the trends can be confirmed in the gray lines in Fig. 1,
and the result before the detrending operation is shownin Fig. S1). In the FULL2 × CO2 experiment by MIROCESM, there was a temperature increase of about 3 °C in
the first few centuries. Then, slight warming started ataround 600–700 years, and in the latter half of the simulation, ΔT was almost stabilized and finally reached
3.2 °C above the warming when compared with CTL.
This number is much smaller than the ECS estimates of
4.7 °C by Andrews et al. (2012), in which linear regression analyses using 150 year simulations, the so called“Gregory method,” were used for the ECS evaluation.
One of the likely reasons for the ECS discrepancy between the actual warming in FULL2 × CO2 and the resultof Andrews et al. (2012) is the strong and non-linear
warming trend found in the CTL experiment by
MIROC-ESM (Fig. S1); although Andrews et al. (2012)
considers such global temperature drift in the control
run, the analysis relies on 150 year simulation results,
which might be insufficient to capture the strong andnon-linear drift of MIROC-ESM. Additionally, similar to
the MIROC-ESM result, Li et al. (2013) also suggested
an overestimation of ECS by the linear regression
method; their 6000 year simulation using a climate
model also showed smaller global warming than the ECS
estimated by the Gregory method. Throughout the

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Fig. 1 Change in temperature (ΔT) (top) and changes in cumulative land (middle) and ocean (bottom) carbon (C) uptake in the millennium timescale experiments. Left a–c panels present the simulation results from MIROC-ESM; FULL2 × CO2 (black), BGC2 × CO2 (blue), and RAD2 × CO2 (red),
where atmospheric CO2 concentrations are abruptly doubled and held constant over 2000 years. Right d–f panels present the results from
MIROC-ES2L with the results from FULL2 × CO2 over 1000 years. The control experiment of each model is shown by the gray line. All simulation
results were detrended by the control run of each model, by fitting spline curves over 1000/2000 years

simulation period, most of the global warming was realized in the first half of the 2000 year simulation. As expected from the experimental designs, ΔT in BGC2 ×
CO2
was almost constant and very close to zero because
abrupt CO2 doubling does not affect atmospheric radiative processes; ΔT in the RAD2 × CO2 experiment almost
overlapped with that of FULL2 × CO2.
In the FULL2 × CO2 experiment by MIROC-ESM, land
showed quite a small change in C amount. Althoughatmospheric CO2 increase actually stimulates land ecosystems (Fig. 1b, results from BGC2 × CO2 experimentshown by the blue line), most of this land C sink induced by CO2 stimulation was opposed by the large C
loss that was induced by global warming and the resultant increase in ecosystem respiration (confirmed by the
results of the RAD2 × CO2 experiment shown by the redline in the panel). This weak land C sink in the FULL2 ×
CO2experiment is consistent with the results of theHajima et al. Progress in Earth and Planetary Science(2020) 7:40

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Table 2 The simulation results of FULL2 × CO2, BGC2 × CO2, and RAD2 × CO2 by MIROC-ESM and MIROC-ES2L
1000th year
MIROC-ESM

MIROC-ES2L

2000th year

ΔT* [K]CL† [PgC]

CO‡ [PgC]

CE§ [PgC]

ΔT* [K]CL† [PgC]

CO‡ [PgC]

CE§ [PgC]

2 × CO2

3.2

180

1121

1904

3.2

167

1435

2205

2 × CO2

BGC

0.1

800

1357

2761

0.0

836

1691

3131

RAD2 × CO2

3.3

− 487

− 196

− 79

3.2

− 527

− 272

− 195

FULL2 × CO2

2.5

497

1072

2172

–

–

–

–

FULL

The values presented are 20 year averages (e.g., the average of years 981–1000 is used for the value of year 1000). All results are calculated after the detrending
as in Fig. 1. Please refer to Table 1 for descriptions of models, model configurations, and time periods of simulations*ΔT, Global mean surface air temperature change†CL, Cumulative land carbon (C) uptake‡CO, Cumulative ocean C uptake§CE, Cumulative anthropogenic C emission

1pctCO2 experiment (Arora et al. 2013). The C amountin vegetation and soil kept changing beyond 1000 years(Fig. S2) because (1) the vegetation C kept increasing because of the spatial redistribution of vegetation (e.g., theboreal forest invasion into the tundra region) and (2) soil
C kept declining in the northern hemisphere high latitude areas because of the lag in response behind climatechange. In contrast, the ocean component showed astrong and long-lasting C sink (black line in Fig. 1c),which was mainly caused by CO2 stimulation of ocean
biogeochemistry (blue line in the panel). Although theocean C sink was somewhat reduced by the global
warming effect (red line), the C reduction induced by
global warming was smaller than that of land, as confirmed in a previous study (Arora et al. 2013). When
compared with land, the ocean continued to accumulate
C throughout the simulation period, although the rate ofincrease gradually declined.
The ΔT in MIROC-ES2L was relatively small compared with that in MIROC-ESM, and the ΔT after 1000
years was about 2.5 °C (Fig. 1d; Table 2). This reduced
warming in MIROC-ES2L as opposed to MIROC-ESM
was already confirmed by comparing the transient climate response in each model (Hajima et al. 2020:
MIROC-ESM is 2.2 K while MIROC-ES2L is 1.5 K), andby comparing ECSs based on the Gregory method (4.7 K
for MIROC-ESM by Andrews et al. 2012 and 2.7 K for
MIROC-ES2L by Tsutsui 2020). When compared with
MIROC-ESM, MIROC-ES2L shows a stronger land C
sink of about 500 PgC accumulation (Fig. 1e; Table 2),
by increasing the CO2-induced C accumulation and reducing warming-induced C loss (Hajima et al. 2020). Although the global land C change almost ceased within a
few hundred years, regional soil C change was stillpresent at around year 1000, and soil C reduction in
boreal forest and in other warmer regions was partly
compensated by the soil C accumulation in the tundra
region. The ocean C sink in MIROC-ES2L was slightly
smaller than that of MIROC-ESM at year 1000 (Fig. 1f;
Table 2), as expected from the almost unchanged
strength of C cycle feedback of the ocean in the twomodels (Hajima et al. 2020). As in MIROC-ESM, theocean in MIROC-ES2L continued to show C accumulation over the 1000 year period while the land C was almost stabilized within a few centuries. We note that
although MIROC-ES2L explicitly simulates the C removal by the ocean sedimentation process of about 0.07
PgC year−1 (this can be confirmed by the linear ocean C
uptake found in CTL, Fig. S1), the contribution of thesedimentation process to ocean C change is excluded inFig. 1 and in other results displayed herein.
Diagnosed annual anthropogenic emission

The annual mean anthropogenic C emissions diagnosed
from the FULL2 × CO2 simulation by two models areshown in Fig. 2 (and the cumulative anthropogenic C
emissions are shown in Fig. S2). To maintain consistency
with the abrupt CO2 concentration doubling, more than
500 PgC year−1 emission should be added to the atmosphere in the first year of the simulation. In addition, because the land and the ocean start to accumulate C in
response to the abrupt CO2 concentration increase, thetotal annual emissions in the first year exceeded 600 PgC(Fig. 2 a and f) in both models.
After the second year, because the CO2 concentration
was fixed at 2 × CO2 level, there should be no change in
the atmospheric C concentration. Thus, the annual compatible emission should be identical to the sum of the Cchanges in land and ocean hereafter. In the first decades,
the annual emissions were more than 10 PgC year−1, but
the emission rates gradually reduced. Contributions
from land and ocean to the annual emission were almost
comparable, but the contribution from land was different between the two models—MIROC-ES2L showed larger land contribution than MIROC-ESM because of theintensified land C sink, as mentioned above. After 50
years, although both the natural C sink of land andocean resulted in anthropogenic emissions exceeding 2
PgC year−1 (Fig. 2 d and i), the land contribution gradually reduced and almost vanished after 250 years;
MIROC-ESM showed a slight negative contribution ofland to anthropogenic emissions over this time-scale.

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Fig. 2 Changes in atmospheric carbon (C) pool, annual land/ocean C uptake, and diagnosed anthropogenic emission in the FULL2 × CO2
experiments: the 2000 years simulation by MIROC-ESM (top) and the 1000 years simulation by MIROC-ES2L (bottom). The annual C emission isdiagnosed as the sum of C changes in the atmosphere, land, and the ocean, and presented in the figure as black dotted lines. Color bars
represent changes in C storages of atmosphere (orange) and annual C uptake by ocean (light blue) and land (green). In panels c and h, d and i,and e and j, the annual C fluxes were calculated as the averages of 5-, 25-, and 250 year intervals, respectively

Even after 1000 years have passed, both models projected positive anthropogenic emission originating fromthe ocean C uptake, but the emission rates were lessthan 1 PgC year−1. The slight C uptake by the ocean wasmaintained even after 2000 years, as simulated by
MIROC-ESM.
Relationship between global temperature rise andcumulative emission

To understand the relationship between global warming
and anthropogenic emission on the millennium timescale, ΔT and cumulative anthropogenic C emission(CE) in the experiments were examined (Fig. 3; Table 2).
The ΔT–CE relationship is well-known to be almost linear in simulations of 1pctCO2 or historical to future climate projections (Allen et al. 2009; Matthews et al.
2009; Gillett et al. 2013), and this was also confirmed in
the 1pctCO2 experiments by the two models (green
dots, Fig. 3). In the FULL2 × CO2 experiment, because atmospheric CO2 concentration is instantaneously doubled in the first year, the ΔT–CE plots do not start fromthe origin of the plot (black dots, Fig. 3). As CE increased, ΔT in FULL2 × CO2 by the two models showed
an almost linear increase, overlapping the result on theplot for 1pctCO2. However, after 400 years, the global
temperature in the FULL2 × CO2 experiment by MIROCESM was almost stabilized at around 3 °C while the CEcontinued to increase. As a result, the ΔT–CE plot of
FULL2 × CO2 started to deviate from that of the 1pctCO2
experiment at around year 400, and this deviation was
more clearly recognized in MIROC-ESM than in
MIROC-ES2L. As mentioned above, at around 600–700
years the two models showed a slight increase in ΔT(Fig. 1), and this slight warming was confirmed in the
ΔT–CE plot (Fig. 3).
The BGC2 × CO2 and RAD2 × CO2 simulation resultsfrom MIROC-ESM are also presented in Fig. 3 (blue andred dots, respectively). In the BGC2 × CO2 experiment, because the CO2 increase only stimulates the C cycle without CO2-induced global warming, the ΔT–CE plot lies on
the horizontal axis, showing CE exceeding 3000 PgC. In
the RAD2 × CO2 experiment, because the CO2 increase
does not stimulate the C cycle but perturbs the atmospheric radiation balance, CO2-induced global warming occurs as in the FULL2 × CO2 experiment. This global
warming reduced the CE in the RAD2 × CO2 experimentto − 195 PgC. The synthesis of the final condition of the
BGC2 × CO2 and RAD2 × CO2 simulations (blue circle filled
by red in Fig. 3) is close to the final condition of the
FULL2 × CO2 experiment (black circle), although there is amismatch between the FULL2 × CO2 and BGC2 × CO2 plus
RAD2 × CO2 in terms of CE. In summary, if the CO2 concentration was doubled without producing radiative forcing, there would be a total C emission of about 3100 PgC

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Fig. 3 Relationships between cumulative carbon (C) emission and changes in global mean near surface air temperature in two Earth systemmodels. The top panel presents 2000 year simulations by MIROC-ESM; FULL2 × CO2 (black), BGC2 × CO2 (blue), and RAD2 × CO2 (red) experiments
where the CO2 concentration is abruptly doubled. The result from the 1pctCO2 experiment is shown in green. The bottom panel presents 1000
year simulations by MIROC-ES2L with the FULL2 × CO2 configuration, together with the result from the 1pctCO2 experiment. Circles presents the
final condition of experiments (the last 50 year average). Transient conditions in the Xth year (50 year average centering on the Xth year) arepresented by cross marks in whiteby the C cycle response to CO2 increase, but this cumulative C emission should be reduced by about 900 PgC because of the warming effect on natural C uptake, leading
to the cumulative emission of about 2200 PgC in the
FULL2 × CO2 experiment (Table 2).
Quantifying the dissimilarity of ΔT and CE relationshipbetween 1pctCO2 and FULL experiments

In the sections above, we confirmed that the ΔT–CE relationship in the FULL2 × CO2 experiments was not

linear, unlike the case of 1pctCO2, and that this nonlinearity was more evident in MIROC-ESM than MIROCES2L—the degree of nonlinearity of the ΔT–CE relationship in FULL2 × CO2 was different between the twomodels. MIROC-ESM showed strong nonlinearity, which
was illustrated as a large deviation of the FULL2 × CO2
experiment from 1pctCO2 in the latter period of the2000 year simulation (top panel of Fig. 3). In contrast,
MIROC-ES2L showed limited nonlinearity in the FULL2
× CO2
experiment, with close positioning of the FULL2 ×(2020) 7:40

Page 9 of 19

result in relation to that of 1pctCO2 (bottom panelof Fig. 3). To quantitatively discuss the difference between the models, we first define several quantities forevaluating temperature, C, and temperature-C, as summarized in Fig. 4.
For discussing global temperature change in models,some quantities have been conventionally utilized in the
climate science field: transient climate response (TCR),
equilibrium climate sensitivity (ECS), and unrealized
warming (presented here as “ΔTUNR”). TCR is defined as
the global temperature rise when the CO2 concentration
reaches the 2 × CO2 level in the 1pctCO2 experiment.
ECS is an equilibrium temperature rise: this can be realized by providing abruptly doubled CO2 concentration
to models and running models over thousands of years
until they reach a new steady state; in many cases, theECS values in models are usually estimated by a linear
regression method, as mentioned above. As suggested byprevious studies, > 2000 years and up to 10,000 years ofsimulation will be necessary to obtain the real equilibrium state (e.g., Li et al. 2013). Indeed, the global temperatures at the end of the simulations in this study still
have some variations or trends, and thus, we define theglobal temperature rise at the time of year 1000 as aquasi-ECS “qECS”. The unrealized warming, ΔTUNR, isusually defined as the difference between ECS and TCR.
However, since we cannot obtain a real ECS, we thus define ΔTUNR as qECS–TCR.
Similarly, we define C-related quantities for quantifying the ΔT–CE relationship in experiments: transient
cumulative emission (TCE), quasi-equilibrium cumulative emission (qECE), unrealized C uptake (ΔCUNR), andadditional C uptake (ΔCADD). Analogous to TCR, TCE
is defined here as the cumulative C emission when CO2reaches 2 × CO2 level in the 1pctCO2 experiment (if the
cumulative airborne fraction of emitted carbon (AF, defined as CA/CE) of 1pctCO2 in existing models is available, TCE can be estimated by: TCE = CA2 × CO2/AF,
where CA2 × CO2 is the atmospheric carbon change atthe doubled CO2 concentration level). qECE is definedas the cumulative emission of year 1000 of the FULL2 ×
CO2experiment. The difference between the two, qECE–
TCE, is defined here as the unrealized carbon uptake
ΔCUNR. Thus, ΔCUNR reflects the difference in CE between the final condition of the FULL2 × CO2 experiment, and the condition where CO2 concentration isdoubled in 1pctCO2. ΔCADD is similar to ΔCUNR, but
this quantity is defined as the CE difference between thetwo experiments when ΔT reaches qECS in each experiment (as shown by the orange arrow in Fig. 4).

Hajima et al. Progress in Earth and Planetary Science

CO2

Fig. 4 Definitions of quantities for evaluating temperature and carbon (C) in 1pctCO2 and FULL2 × CO2 experiments, illustrated in the context ofglobal surface air temperature change (ΔT)–cumulative anthropogenic C emission (CE): transient climate response (TCR); transient C emission(TCE); quasi-equilibrium climate sensitivity (qECS); quasi-equilibrium C emission (qECE); unrealized warming (ΔTUNR); unrealized C uptake (ΔCUNR);
additional C uptake (ΔCADD); transient climate response to cumulative C emission (TCRE); quasi-equilibrium climate response to cumulative Cemission (qECRE); and the ratio of unrealized warming to unrealized C uptake (RUNR). Note that TCRE is usually defined as the ratio of ΔT to CE
when CE reaches 1000 PgC, but we evaluate it here when the CO2 concentration in the 1pctCO2 experiment reaches 2 × CO2 level(2020) 7:40

Page 10 of 19

The ratio of ΔT to CE is called the transient climate response to cumulative C emission (TCRE), which is usually
evaluated when CE reaches 1000 PgC. In this study, TCRE
is evaluated at the time when the CO2 concentration
reaches the 2 × CO2 level in the 1pctCO2 experiment.
Similarly, the ratio of qECS to qECE is named here as thequasi-equilibrium climate response to cumulative C emission (qECRE). In addition, the ratio of unrealized warming(ΔTUNR) to unrealized C uptake (ΔCUNR) is named here
as RUNR. If a model has a value for RUNR that is perfectly
identical to the TCRE, the relationship TCRE = RUNR =qECRE holds, presenting no difference between the
1pctCO2 and FULL2 × CO2 experiments.
The ΔTUNR and ΔCUNR of MIROC-ESM were 1.0 °C and
910 PgC, respectively, and thus RUNR of the model was about
1.13 °C/EgC (Table 3, Fig. 5). This RUNR only accounts for
51% of the TCRE, which is visualized in Fig. 5 as the decreasing slope of the ΔT–CE curve in the latter period of the
FULL2 × CO2 experiment; the dissimilarity of the ΔT–CE relationship between the FULL2 × CO2 and 1pctCO2 experiments is captured by the relatively small value of RUNR whencompared with TCRE. This suggests that in the model, global warming in the FULL2 × CO2 experiment is almost
ceased/realized in the first 500–1000 years but cumulative Cemission still continues beyond this time-scale—natural C
uptake, in particular by the ocean, still continues even after
the global warming is almost ceased. In MIROC-ES2L (Table
3, Fig. 5), ΔTUNR and ΔCUNR were respectively 0.94 °C and1024 PgC, and thus RUNR of this model becomes 0.91. The

RUNR of MIROC-ES2L is 67% of the TCRE, indicating thatΔT–CE is relatively similar between 1pctCO2 and FULL2 ×
CO2experiments, compared with MIROC-ESM. This suggests that the global warming and cumulative emission projected by MIROC-ES2L almost proceed in pace with eachother in the FULL2 × CO2 experiment, as in the 1pctCO2
experiment.

Hajima et al. Progress in Earth and Planetary Science

Comparison with other models: EMICs

The two types of ESMs showed quite different values of
RUNR and TCRE although both models belong to thesame family of MIROC. To examine how RUNR and
TCRE are uncertain in existing models, the same analyses was applied to the simulation results of EMICAR5. Analysis of the results of the eight EMICs is shownin Fig. 5 and Table 3. Five of the eight EMICs (DCESS,GENIE, IGSM, MESMO, and UMD) showed the reduction in slope of ΔT–CE plot in the latter period of the
FULL2 × CO2 experiment—these models have lower
RUNR than TCRE values, as in the MIROC-ESM simulations. Two of the models (Bern3D and MIROC3-liteLCM) showed almost similar values for both RUNR and
TCRE, thus the final condition of the 1000 year simulation dropped onto the ΔT–CE line of the 1pctCO2
simulation. One model, UVic ESCM, showed larger
RUNR than TCRE. On average, all ten models including
two ESMs and eight EMICs showed 1.87 ± 0.38 °C/EgC
for TCRE, 1.11 ± 0.51 °C/EgC for RUNR, and 1.48 ±0.37 °C/EgC for qECRE (Table 3). The quantification of

Table 3 Comparison of temperature, carbon, and temperature-carbon quantities in two Earth system models and eight Earthsystems Models of Intermediate Complexity
Quantity category

Temperature quantities

Quantity name
[Unit]

TCR
[K]

qECS
[K]

ΔTUNR
[K]

Carbon quantities
TCE
[PgC]

MIROC-ESM

2.21

3.23

1.03

MIROC-ES2L

1.56

2.49

0.94

Bern3D

1.98

3.32

DCESS

2.07

2.83

GENIE

2.47

IGSM

1.52

MESMO
MIROC3-lite-LCM

Temperature–Carbon quantities

qECE
[PgC]

ΔCUNR
[PgC]

ΔCADD
[PgC]

TCRE [K/EgC]

qECRE [K/EgC]

RUNR [K/EgC]

RUNR/TCRE
[–]

994

1904

910

392

2.22

1.70

1.13

0.51

1148

2172

1024

262

1.36

1.15

0.91

0.67

1.34

1002

1849

848

42

1.98

1.80

1.58

0.80

0.76

1006

2214

1207

629

2.05

1.28

0.63

0.31

3.98

1.51

1079

2354

1275

464

2.29

1.69

1.19

0.52

1.91

0.39

963

1888

925

647

1.58

1.01

0.42

0.27

2.41

3.70

1.29

968

1830

862

225

2.49

2.02

1.50

0.60

1.58

2.84

1.26

1031

2038

1006

45

1.53

1.39

1.25

0.82

UVic-ESCM

1.94

3.49

1.55

1183

1959

776

− 326

1.64

1.78

2.00

1.22

UMD

1.60

2.23

0.63

1009

2387

1378

669

1.59

0.94

0.46

0.29

Mean

1.93

3.00

1.07

1038

2060

1021

305

1.87

1.48

1.11

0.60

S.D.

0.36

0.66

0.39

75

209

201

322

0.38

0.37

0.51

0.30

Max

2.47

3.98

1.55

1183

2387

1378

669

2.49

2.02

2.00

1.22

Min.

1.52

1.91

0.39

963

1830

776

− 326

1.36

0.94

0.42

0.27

S.D./Mean

0.19

0.22

0.36

0.07

0.10

0.20

1.05

0.20

0.25

0.46

0.49

The quantities are defined in Fig. 4

Hajima et al. Progress in Earth and Planetary Science(2020) 7:40

Page 11 of 19

Fig. 5 Relationships between cumulative carbon (C) emission and changes in global mean surface air temperature in the experiments of abruptly
doubled CO2 concentration (FULL2 × CO2 1000 years; black) and that where CO2 concentration is increased by 1 % year−1 (1pctCO2; 140 years;gray) by two ESMs (MIROC-ESM and MIROC-ES2L) and eight EMICs from EMIC-AR5 (Eby et al. 2013; Zickfeld et al. 2013). Gray-filled circles
represent the time when the CO2 concentration reaches about 2 × CO2 level in 1pctCO2 (calculated as the average of years 61–80); black-filled
circles represent the final condition of the FULL2 × CO2 experiment (calculated as the average of years 981–1000). Red, blue, and orange arrows
indicate the unrealized warming (ΔTUNR), unrealized C uptake (ΔCUNR), and additional C uptake (ΔCADD), as defined in Fig. 4

TCRE, RUNR, and qECRE also revealed that the standard
deviation relative to multi-model mean (the coefficientof variation, Table 3) was the largest for RUNR (0.46),
followed by that of qECRE (0.25), and TCRE (0.20), suggesting the importance of constraining the long-term climate and C cycle responses beyond century time-scale
in models. Although year 1000 was used in this study forcalculating RUNR and qECRE, the values are likely to become smaller in many models if we extend the simulation (e.g., up to more than a few thousands of years) and
use the result for calculating the RUNR and qECRE because oceanic C uptake likely persists beyond 1000 years.
If RUNR is smaller than TCRE, it should be accompanied by positive ΔCADD, as indicated by the orange arrows

in Figs. 4 and 5. The positive ΔCADD means that the Cemission that is eventually achieved by the end of 1000
years simulation should be larger than the cumulativevalue that is estimated from 1pctCO2. This is owing to
the long-lasting C uptake by the ocean, and the ΔCADD
was 305 ± 322 PgC (Table 3; a demonstration by a simple climate model to estimate ΔCADD in other climate
stabilization scenarios can be found in Fig. S7).
Difference in ocean heat and C uptake

In the above discussion, we have confirmed that both
ESMs showed smaller RUNR than TCRE, particularly for
MIROC-ESM (Table 3); this was also confirmed in many
(five of eight) EMICs. In MIROC-ESM, much of the(2020) 7:40

Page 12 of 19

global warming was already realized by around year 250,
and the global warming almost ceased after 1000 years(Fig. 1a). However, ocean C uptake was still present beyond 1000 years (Fig. 1c), leading to the long-lasting anthropogenic C emission (Fig. 2) and increase incumulative emission (Fig. 3; Fig. S2). As a result, theΔT–CE relationship, which is usually visualized as an almost linear line on the ΔT–CE plot when using the
1pctCO2 experiment or other historical/future simulation results, became non-linear in the 2000-year simulation (Fig. 3). These results suggest that long-lasting
ocean C uptake will be a key for understanding the ΔT–
CE relationship in millennium time-scale simulations.
In addition to the important role of the ocean in thelong-term C budget, the ocean has been implicated in
the control of long-term global warming by absorbing
excess heat from the atmosphere, until the outgoing
longwave radiation into space counterbalances radiative
forcing. Previous studies have suggested that these heat
and C uptakes by the ocean likely proceed in pace witheach other because both processes are controlled by thesame oceanic processes such as wintertime deep convection in polar regions and deep ocean circulation that

distributes absorbed excess heat and anthropogenic C
over the global oceans (e.g., Jones et al. 2016; MacDougall 2017). Indeed, a multi-model study using CMIP5
ESMs demonstrated the almost similar spatiotemporal
pattern of ocean heat and C uptake (Frölicher et al.
2015). Ehlert and Zickfeld (2017) noted in their longterm simulation study on ZEC that thermal equilibrium
is likely faster than biogeochemical equilibrium, but they
attributed it to the long time-scales of sediment C cycle
processes. This widespread understanding appears to becontradictory to the results of this study, which showsthat C uptake by the ocean likely continues longer than
ocean heat uptake. Indeed, the shape of the curve of annual ocean heat uptake plotted against cumulative ocean
C uptake is quite similar to the shape of the ΔT–CE
curve in the FULL2 × CO2 experiments in the two ESMs
and seven EMICs (Fig. 6, in which one EMIC (UMD) isomitted because the data on ocean heat uptake of themodel was not available). This suggests that the longterm response of the ocean forms the shape of the ΔT–
CE plots and that the ocean heat uptake and C uptake
beyond centuries proceed at different paces, resulting in
relatively smaller RUNR than TCRE values.

Hajima et al. Progress in Earth and Planetary ScienceFig. 6 The relationship between cumulative oceanic carbon uptake (CO) and (1) changes in global mean air temperature (red dots, T2) and (2)annual ocean heat uptake (black dots, OHU) in the experiments of abruptly doubled CO2 concentration during 1000 years by two ESMs (MIROCESM and MIROC-ES2L) and seven EMICs from EMIC-AR5. The UMD model shown in Fig. 5 was omitted because the data on ocean heat uptake ofthe model was not available(2020) 7:40

Page 13 of 19

To explore the mechanism behind the different rate of
the two processes, we examined the propagation of heat
and C in the ocean in the FULL2 × CO2 experiment by
MIROC-ESM. Figure 7 shows the result in the Atlantic.
Note that the RAD2 × CO2 experiment is used for the

analysis of heat transport and that the BGC2 × CO2 experiment is used for C, so as to separately discuss the effect of CO2 doubling on the ocean heat and C uptakes(the figures for the FULL2 × CO2 experiment can befound in Figs. S3 and S4, respectively).

Hajima et al. Progress in Earth and Planetary ScienceFig. 7 Atmosphere-ocean heat and carbon dioxide (CO2) fluxes (plots) and vertical distributions of ocean temperature and dissolved inorganiccarbon (DIC) (TO and tCO2; shades) in the Atlantic ocean (30°W): the first and third columns show the absolute magnitudes of the fluxes andsystem states (ocean temperature and DIC), and the second and fourth columns show the anomalies from the control run. The units are: W m−2
for ocean net heat flux (FH; negative means ocean uptake), °C for TO, gC m−2 year−1 for ocean net carbon flux (FC; negative means ocean uptake),and mmol m−3 for tCO2. Counter lines in panels show isopycnic surfaces with an interval of 0.5 σθ. The RAD2 × CO2 result by MIROC-ESM is used
for the FH and TO analyses, and BGC2 × CO2 for FC and tCO2. All analyses were made based on 30 year averages and anomalies. Red, orange, andmagenta arrows represent the anthropogenic C transport by the Antarctic intermediate water (AAIW), Antarctic bottom water (AABW), and North
Atlantic deep water (NADW), respectively

(2020) 7:40

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In the pre-industrial condition (top panels in Fig. 7), theocean temperature above the 1000 m depth is relatively
warm in the region 40°S–40°N and stratified as characterized by the thermocline, which is roughly located between
the 26.5–27.0 σθ isopycnal surfaces; the ocean C is relatively poor above the thermocline. One hundred years
after the abrupt CO2 doubling, the surface ocean above
the thermocline in the region 40°S–40°N was filled withwarmed waters (2nd row in Fig. 7). As schematically explained by Goodwin et al. (2015), this relatively fast uptakeof heat is likely based on the processes of the surface turbulent mixed layer development and the warmed watersubduction from surface into thermocline along with theisopycnal surfaces. As time passes, the heat is furthertransported downward, seemingly attributed to both of
the above-mentioned warmed water subduction processes
and the ocean heat uptake associated with the formationof North Atlantic deep water (NADW) and Antarctic bottom water (AABW). Additionally, diapycnal mixing andresultant downward heat flux across isopycnal surfaces
could accelerate the warming above and around thethermocline. Deep-ocean warming became apparent in
the Southern Ocean until year 500 (3rd row in Fig. 7),
which was likely related to the recovery of deep convection in the Weddell Sea (Yamamoto et al. 2015; Obaseet al. 2017). Finally, at the end of the 2000 year-long simulation, the entire Atlantic was warmed.
When compared with the heat transport, the spatial
and temporal change in C transport into deeper ocean
showed a distinct pattern (the third and fourth columnsof Fig. 7), particularly beyond a few centuries. In the first
100 years, the upper ocean, where seawater is well mixed
and ventilated, was filled by the anthropogenic C similarly to that of heat uptake. In addition, the North Atlantic also showed moderate anthropogenic C uptake. This
relatively fast (decadal to centennial) uptake of anthropogenic C into the thermocline and deeper layers in
the North Atlantic was also confirmed in the observational study on ocean C inventory (Sabine et al. 2004;
Gruber et al. 2019) and in centennial simulations by
CMIP5 and CMIP6 ESMs (Frölicher et al. 2015; Aroraet al. 2020). After that, unlike the heat transport, a largepart of the anthropogenic C remained above the thermocline in the region 40°S–40°N, while the anthropogenic
C absorbed in the high-latitude formation region of
NADW was transported into intermediate/deep layers
mainly along the lower equatorward branch of the Atlantic Meridional Overturning Circulation (magenta arrows in the third to fifth row of Fig. 7). Again, we notethat the BGC2 × CO2 simulation was used for this C uptake analysis, and thus the warming effects on the ocean
dynamics can be ignored here.
Like the Atlantic, the surface water in the Pacific also
quickly accumulated and transported the anthropogenic

C into the thermocline within a century, and the structure where much of the anthropogenic C was trapped in
the upper ocean persisted afterwards (Fig. 8). Unlike theAtlantic, there was less anthropogenic C transport into
intermediate/deep layers in the Northern hemispherebecause there was no deep water formation in the subarctic North Pacific. As a result, the content of anthropogenic C in the intermediate and deep layers wasmaintained for a long time at levels that were not largely
different from those in the pre-industrial condition. The
anthropogenic C was gradually transported into deeper
layers along the northward intrusion of AABW, but evenafter 2000 years, the ocean still had potential for anthropogenic C uptake.

Hajima et al. Progress in Earth and Planetary Science

The possible reasons for non-linear T-CE relationship inmillennium-scale experiments

Our simulations show that, on a centennial time-scale,ocean heat and C uptake both proceeded in a similar manner—they occurred in the well-ventilated upper ocean,likely relying on the processes of surface mixing, andwarmed, C-rich water subduction into the thermocline, assuggested by previous studies (e.g., Goodwin et al. 2015;
Frölicher et al. 2015; Williams et al. 2016; Arora et al.
2020). Additionally, the formation of NADW and associated equatorward flow are also confirmed to play an important role for C transport on this time-scale. Within a
few centuries, ocean heat and C uptakes proceeded in asimilar manner and at similar rates, but they were notexactly the same; thus, partially opposing effects of oceanic
uptake of heat and C act to remain the almost constant
TCRE on multi-decadal to centennial time-scales (Goodwin et al. 2015; Williams et al. 2016). Over centuries tomillennia, however, the behavior of ocean heat and C uptake is found to be decoupled, and the dominant process
in this time-scale changes to the slow ventilation of theintermediate and deep ocean (Figs. 7 and 8; Goodwin
et al. 2015). This suggest that the key process to understand the different pace of ocean heat and C uptake beyond centuries exists in the ventilation processes of theintermediate and deep ocean.
One of the possible reasons for such different behaviorof ocean heat and C transport into deeper ocean overcenturies could be explained by the difference in thetime-scales of air-sea exchange of heat and C. The ocean
surface water reaches the equilibrium of air-sea heat exchange within a month, while air-sea CO2 exchange,
which is buffered by CO2 dissolution and carbonate
chemistry in the seawater, occurs over months or abouta year (Frölicher et al. 2015; Jones et al. 2014). As a result of the slow air-sea exchange of CO2, a large part ofthe surface water is subducted into the ocean interior
before reaching air-sea CO2 equilibrium, producing alarge C deficit between the actual C amount in seawaterHajima et al. Progress in Earth and Planetary Science(2020) 7:40

Page 15 of 19

Fig. 8 Atmosphere-ocean heat and carbon dioxide (CO2) fluxes (plots) and vertical distributions of ocean temperature and dissolved inorganiccarbon (TO and tCO2; shades) in the Pacific Ocean (150°W). See Fig. 7 legend for further details

and the amount of C that can potentially be contained
under air-sea equilibrium. Thus, the C deficit, called the“C disequilibrium” or “unsaturated C” component (Itoand Follows 2005; Jones et al. 2014; Schwinger and Tjiputra 2018; Arora et al. 2020), mainly reflects how longthe ocean surface is exposed to the atmosphere. A study
based on centennial time-scale simulations by Aroraet al. (2020) compared this C disequilibrium component
among CMIP6 ESMs, and they clearly showed that C
disequilibrium is the main driver to keep anthropogenic

C in intermediate and deep water at relatively low levels.
Although their study was based on much shorter simulations (150 years) than ours, the C disequilibrium component, which is originally derived from the slow rate of
air-sea CO2 exchange, could also explain the low level ofanthropogenic C in intermediate and deep layers beyond
centuries to millennia.
Another possible mechanism could be associated withthe heat and C uptake in the Southern Ocean. The
Southern Ocean is the dominant region for global heat(2020) 7:40

Page 16 of 19

and C uptake, and about 75% and 43% of heat and C, respectively, are estimated to be absorbed there based on
CMIP5 simulations (Frölicher et al. 2015). This significant contribution of the Southern Ocean is maintained
by upwelling of cold and low anthropogenic C waterfrom deeper layers to the surface; the upwelled water istransported northwards mainly by the surface winddriven Ekman flow, with uptake of heat and anthropogenic C from the atmosphere; a certain fraction of thesurface water is subducted again into the ocean interior;this provides a pathway of warmed and C-rich surface
water into the ocean interior, making the thermocline
the main storage mechanism of excess heat and anthropogenic C in decadal to centennial time-scales; theformation of Antarctic intermediate water in the region
around 50°S–40°S transports the anthropogenic C into
intermediate layers of around 1000 m depth; the anthropogenic C can also be transported into deeper layers
by AABW (Sabine et al. 2004; Iudicone et al. 2016; Joneset al. 2014; Gruber et al. 2019). The C uptake from theatmosphere into the Southern Ocean, however, only accounts for 43% of global ocean C uptake—this contribution is large but much less than that of heat uptake inthis region (75%; Frölicher et al. 2015), suggesting a low
efficiency of oceanic C uptake in this region comparedwith heat uptake. Indeed, the amount of anthropogenic
C on the transport pass of the Antarctic intermediatewater (AAIW; the red arrows in Figs. 7 and 8, which almost corresponded to the potential density of AAIW of
27.0σθ–27.55σθ) is clearly lower than that in the above
layers; in particular, the anthropogenic C minimum of
AAIW is found clearly in the Atlantic Ocean, at year
500 and later in the FULL2 × CO2 (rightmost column in
Fig. 7); in the Pacific, the anthropogenic C of AAIW andof the layers below clearly maintains a lower amount ofanthropogenic C over the whole 2000 years (Fig. 8).
Similarly, the AABW (shown by orange arrows in Figs. 7
and 8) also contains low levels of anthropogenic C.
These low levels of anthropogenic C in the intermediate
and deep layers are also confirmed in the FULL2 × CO2
by MIROC-ES2L (Figs. S5 and S6).
The low level of anthropogenic C in the water massformed in the Southern Ocean (AAIW and AABW)
might be attributable to the C disequilibrium component
as discussed above, which is further associated with themixed layer depth, buffering effect of C chemistry, existence of sea ice, and other factors like residence time of
upwelled water in this region (Jones et al. 2014). In
addition, because the upwelled water in the Southern
Ocean is cold but already contains abundant C becauseof the long-term biological effects, the upwelled cold
water could more effectively take up the heat from theatmosphere than C. For more detail, we need further
examination of the mechanism to produce the low levelof anthropogenic C in the Southern Ocean, hopefully
based on multi-model comparison. In particular, the regenerated C component, which is one of the oceanic inorganic C components caused by biological regenerationof organic C, might be associated with the millenniumlong processes; the regenerated C can contribute to C
accumulation in intermediate and deeper layers and thus
it may partly accelerate the C uptake, in particular underthe effect of global warming (e.g., Schwinger and Tjiputra 2018; Arora et al. 2020).
In the section above, to explain the situation when
RUNR is smaller than TCRE (Figs. 3 and 5), we have discussed the decoupled behavior of the ocean heat and C
uptake beyond centuries, by attributing it to the C disequilibrium component and the role of the Southern
Ocean. Additionally, MacDougall (2017) suggested basedon a theoretical framework that constant TCRE can berealized for a limited range of emission rates and that
constant TCRE cannot be maintained when emission
rates are very high or very low. Indeed, in the FULL2 ×
CO2
and 1pctCO2 simulations, the two experiments
overlap when diagnosed emissions are in the mid-rangeof emission rates and diverge when the emission rates
are very high (> 20 PgC year−1) and very low (< 1 PgC
year−1). Thus, even if the ocean heat and C uptake processes remained tightly coupled beyond centuries, wemight expect the relationship between global warming
and cumulative C emission to be non-linear based on
the emission rate (MacDougall 2017; Seshadri 2017).

Hajima et al. Progress in Earth and Planetary Science

Summary and conclusions
In this study, by using two ESMs, we performed idealized climate–C cycle simulations where the atmospheric
CO2 concentration was abruptly doubled from preindustrial state and fixed at that level over a millennial
time-scale (FULL2 × CO2, BGC2 × CO2, and RAD2 × CO2);
the analysis mainly focused on the relationship between
global temperature change and diagnosed anthropogenic
emission. The results were compared with another idealized experiment, 1pctCO2, where the CO2 concentration
is increased by 1% per year, and we confirmed that the
ΔT–CE relationship was not linear in the FULL2 × CO2
experiment when compared with that of 1pctCO2, although the degree of similarity of the ΔT–CE plot between the two experiments was dependent on themodel. One model, MIROC-ESM, showed a relatively
large discrepancy on the ΔT–CE plot between FULL2 ×
CO2
and 1pctCO2 experiments, which was quantitatively
captured by the relatively smaller RUNR (the ratio of
unrealized warming to unrealized C uptake in the latterpart of the FULL2 × CO2 experiment) than the TCRE
(which was evaluated at the doubled CO2 level in the
1pctCO2 experiment). This smaller RUNR than TCRE
was also confirmed in EMICs, but the degree of(2020) 7:40

Page 17 of 19

mismatches between RUNR and TCRE was dependent on
the models, suggesting that large uncertainty exists inboth ΔT and CE in the long-term climate–C cycle simulations by existing models. On average, all 10 models including two ESMs and eight EMICs showed 1.87 ±0.38 °C/EgC for TCRE, 1.11 ± 0.51 °C/EgC for RUNR, and1.48 ± 0.37 °C/EgC for qECRE.
In the latter period of the millennium time-scale experiment, RUNR became relatively smaller than TCRE because in this period global warming is almost ceased but
the ocean continues to take up C. By considering that
long-term global temperature is tightly associated withocean heat uptake, it is interesting that the small RUNR
relative to TCRE suggests that the ocean continues totake up C longer than it takes up heat. However, this iscontradictory to the widespread understanding of therole of the ocean in long-term climate and C cycles—theocean continues to take up heat and C in pace with eachother because deep ocean circulation dominates bothprocesses, and thus global warming and ocean C uptake
are expected to continue/cease with the same pace. In
our study, ESMs showed that the ocean heat propagatedinto deeper ocean in a straight downward manner, while
ocean C transport seemed strongly dominated by themeridional overturning circulations. Because of this,ocean C transport into the deeper ocean slowed, taking
more time to dominate and saturate with anthropogenic
C throughout the depth of the water column, and leading to the time-lag of ceasing of ocean C uptake behindthe ceasing of global warming. We raised two possibilities (C disequilibrium component and the role of theSouthern Ocean) to explain this decoupled behavior ofocean heat and C uptake beyond centuries, but further
multi-model analysis would be necessary to clarify thedetailed mechanism behind this difference.
If models have relatively smaller RUNR than TCRE,
they should have larger CE at the end of 1000 years
simulation than CE that is evaluated when global warming reaches qECS in the 1pctCO2 experiment. This deficit was quantified as ΔCADD, and many models
projected positive values for ΔCADD, indicating that if
we aim to stabilize the CO2 concentration and the subsequent climate stabilization over centuries to millennia,
we can emit C by ΔCADD in addition to the CE estimated from the linear ΔT–CE plot of 1pctCO2.
The experimental design employed in this study was
highly idealized (abruptly doubling CO2 concentration
over 1000–2000 years), and thus the direct translation of
the simulation results to policy-relevant messages might
be difficult. However, performing such experiments byusing ESMs can lead us to a fundamental understanding
on how the climate–C cycle system proceeds on the millennium time-scale, as partly performed in this study. In
particular, the examination of (quasi)equilibrium statesof the climate–C cycle system, which were evaluated by
qECS, qECE, and qECRE in this study, might provide
more basic properties of models because these indices
are independent of the choice of scenario (the pathway
to reach the doubled CO2 level) and rely on the magnitude of external forcing (and simulation length), as traditionally examined in the physical climate science field.
The examination revealed that larger uncertainty exists
in RUNR than TCRE, suggesting the importance of constraining the long-term response of the climate–C cycle
system in models.
In this study, only two ESMs were used for the analysis, but to confirm the robustness of the conclusions, it
is desirable to perform similar simulations by multiple
ESMs, as performed by a model intercomparison project“LongRunMIP” by Rugenstein et al. (2019). Although
the simulations proposed in this study are computationally expensive and other possible experimental designs
exist (e.g., a pulse emission scenario as used in Archer
et al. 2009; Frölicher et al. 2013; Joos et al. 2013), the experiments performed in this study are quite simple. Because the abrupt increase in CO2 (quadrupling) scenario
was already embedded as one of the fundamental experiments of CMIP5 and CMIP6, extending the simulation
up to 1000 years was not difficult and thus this simple
design might be favored by modeling centers. Furthermore, a part of the simulations can be performed by offline models (e.g., the BGC2 × CO2 simulation could be
performed by off-line land/ocean models with biogeochemistry; the RAD2 × CO2 experiment could be performed by AOGCMs). Performing millennium timescale simulations by a hierarchy of climate models(ESMs, AOGCMs, EMICs, and simplified climate
models) and comparison of the results will help to obtain further insight on climate-C cycle processes and tounderstand the long-term response of the Earth system
to anthropogenic perturbations.

Hajima et al. Progress in Earth and Planetary Science

Supplementary information
Supplementary information accompanies this paper at https://doi.org/10.
1186/s40645-020-00350-2.
Additional file 1:. Supplemental Materials

Abbreviations
AABW: Antarctic bottom water; AAIW: Antarctic intermediate water;
AOGCMs: Atmosphere-ocean general circulation models; CMIP: Coupledmodel intercomparison project; C4MIP: The Coupled Carbon Cycle Climate
Model Intercomparison Project; ECS: Equilibrium climate sensitivity;
EMICs: Earth systems models of intermediate complexity; ESMs: Earth systemmodels; MIROC: The Model for Interdisciplinary Research on Climate; MIROCESM: The Model for Interdisciplinary Research on Climate, the Earth System
Model; MIROC-ES2L: The Model for Interdisciplinary Research on Climate, theEarth System model version2 for Long-term simulations; NADW: North
Atlantic deep water; qECS: Quasi-equilibrium climate sensitivity; qECE: Quasiequilibrium cumulative emission; qECRE: Quasi-equilibrium climate response
to cumulative carbon emission; TCE: Transient cumulative emission;

Hajima et al. Progress in Earth and Planetary Science(2020) 7:40

TCR: Transient climate response; TCRE: Transient climate response tocumulative emission; ZEC: Zero emission commitment
Acknowledgements
We greatly appreciate the valuable comments from the two reviewers –Chris Jones and an anonymous referee. The authors appreciate the data
providers/modelers participating in EMIC-AR5, and data archiving support by
M. Abe and O. Arakawa. The Super Computing System in JAMSTEC, the Earth
Simulator, was used for the simulations. Kaoru Tachiiri, Junichi Tsutsui, andTomoo Ogura provided helpful and encouraging comments. We thank Catherine Dandie, PhD, from Edanz Group (https://en-author-services.edanzgroup.
com/expert/soil-sciences/catherine-dandie) for editing a draft of this manuscript and helping to draft the abstract.
Authors’ contributions
TH designed the experiments, performed simulations and analysis, anddrafted the entire document. AY and MK contributed to the analysis anddrafting. RO performed a part of the simulation of the CTL run. MW and HT
contributed the physical oceanic analysis. XS supported the analysis of longterm global warming and natural carbon uptake. All authors read and approved the final manuscript.
Funding
This work was supported by TOUGOU/SOUSEI, the “Integrated Research
Program for Advancing Climate Models (grant number JPMXD0717935715)”/“Program for Risk Information on Climate Change”, by the Ministry of
Education, Culture, Sports, Science, and Technology of Japan.
Availability of data and materials
The simulation outputs of the CTL, FULL2 × CO2, and 1pctCO2 simulations by
MIROC-ESM and MIROC-ES2L are distributed and made freely available
through the Earth System Grid Federation (ESGF). Details on the ESGF can befound on the website of the CMIP Panel (https://www.wcrp-climate.org/
wgcm-cmip/). Readers are requested to contact the corresponding author ifthey wish to obtain the outputs of the BGC2 × CO2 and RAD2 × CO2 simulations. The simulation results of EMICs were obtained from the EMIC-AR5
website (http://climate.uvic.ca/EMICAR5/).
Competing interests
The authors declare that they have no competing interest.
Received: 30 December 2019 Accepted: 8 July 2020

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