Patra et al. Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-021-00420-z(2021) 8:25

Progress in Earth andPlanetary Science

RESEARCH ARTICLE

Open Access

Evaluation of earth system model andatmospheric inversion using total column
CO2 observations from GOSAT and OCO-2
Prabir K. Patra1,2* , Tomohiro Hajima1, Ryu Saito3, Naveen Chandra1,4, Yukio Yoshida4, Kazuhito Ichii2,
Michio Kawamiya1, Masayuki Kondo4, Akihiko Ito4 and David Crisp5

Abstract
The measurements of one of the major greenhouse gases, carbon dioxide (CO2), are being made using dedicatedsatellite remote sensing since the launch of the greenhouse gases observing satellite (GOSAT) by a three-way
partnership between the Japan Aerospace Exploration Agency (JAXA), the Ministry of Environment (MoE) and the
National Institute for Environmental Studies (NIES), and the National Aeronautics and Space Administration (NASA)
Orbiting Carbon Observatory-2 (OCO-2). In the past 10 years, estimation of CO2 fluxes from land and ocean using
the earth system models (ESMs) and inverse modelling of in situ atmospheric CO2 data have also made significant
progress. We attempt, for the first time, to evaluate the CO2 fluxes simulated by an earth system model (MIROCES2L) and the fluxes estimated by an inverse model (MIROC4-Inv) using in situ data by comparing with GOSAT and
OCO-2 observations. Both MIROC-ES2L and MIROC4-Inv fluxes are used in the MIROC4-atmospheric chemistrytransport model (referred to as ACTM_ES2LF and ACTM_InvF, respectively) for calculating total column CO2 mole
fraction (XCO2) that are sampled at the time and location of the satellite measurements. Both the ACTM simulations
agreed well with the GOSAT and OCO-2 satellite observations, within 2 ppm for the spatial maps and time
evolutions of the zonal mean distributions. Our results suggest that the inverse model using in situ data is moreconsistent with the OCO-2 retrievals, compared with those of the GOSAT XCO2 data due to the higher accuracy of
the former. This suggests that the MIROC4-Inv fluxes are of sufficient quality to evaluate MIROC-ES2L simulated
fluxes. The ACTM_ES2LF simulation shows a slightly weaker seasonal cycle for the meridional profiles of CO2 fluxes,
compared with that from the ACTM_InvF. This difference is revealed by greater XCO2 differences for ACTM_ES2LF
vs GOSAT, compared with those of ACTM_InvF vs GOSAT. Using remote sensing–based global products of leaf areaindex (LAI) and gross primary productivity (GPP) over land, we show a weaker sensitivity of MIROC-ES2L biosphericactivities to the weather and climate in the tropical regions. Our results clearly suggest the usefulness of XCO2
measurements by satellite remote sensing for evaluation of large-scale ESMs, which so far remained untested by
the sparse in situ data.
Keywords: Carbon dioxide (CO2), Global and regional carbon cycle, Earth system model, Inverse model,
Atmospheric chemistry transport model* Correspondence: prabir@jamstec.go.jp
1
Research Institute for Global Change, Japan Agency for Marine-Earth
Science and Technology (JAMSTEC), Yokohama 236-0001, Japan
2
Center for Environmental Remote Sensing (CeRES), Chiba University, Chiba
263-8522, Japan
Full list of author information is available at the end of the article© The Author(s). 2021 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
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Patra et al. Progress in Earth and Planetary Science(2021) 8:25

1 Introduction
Carbon dioxide (CO2) is the most important anthropogenically produced greenhouse gas (Myhre et al. 2013).
During 2009–2018, CO2 emissions associated with human activities, such as the burning of fossil fuel and cement manufacturing contributed about 100 PgC (1 Pg =1015 g) or about 10 PgC/year to the atmosphere (Friedlingstein et al. 2020). Based on available statistics (Janssens-Maenhout et al. 2019), about 60% of theseemissions originate from the northern extratropics,
mainly by the Annex 1 countries of the UN Framework
Convention on Climate Change (UNFCCC), signatories
to the Kyoto Protocol subject to caps on greenhousegases (GHGs) emissions. The inventory emissions fromthe non-Annex I countries are rising quickly due to theirrapid economic growth and shifting manufacturing fromthe Annex I or Organisation for Economic Co-operation
and Development (OECD) member countries to the socalled BRICS countries (i.e. Brazil, Russia, India, China,
and South Africa). Uncertainties in the emissions are larger for non-Annex I counties relative to the Annex I
countries (Andres et al. 2012). This leads to lower confidence of our knowledge of the changes in terrestrial biospheric fluxes in response to climate change and climate
variabilities, and CO2 fertilisation feedbacks (Ainsworth
and Rogers 2007; Keenan et al. 2013; Saeki and Patra
2017; Bastos et al. 2020).
CO2 emissions to the atmosphere from land-use
change (LUC), predominantly caused by human-driven
deforestation and cropland development, is estimated to
be in the range of 1–2 PgC/year for the period 2009–2018 (Hansis et al. 2015; Houghton and Nassikas 2017;
Kondo et al. 2020; Friedlingstein et al. 2020). The uncertainties in LUC CO2 emission estimations are originatedfrom the treatment of various terrestrial carbon pools ofabove and below ground biomass and soil carbon(Houghton and Nassikas 2017; Kondo et al. 2020). Dueto an increase in these anthropogenic emissions, the atmospheric CO2 concentration is rising at an average rateof 3 ppm/year during 2009–2018 (Tans and Keeling2019). This is less than half of the rate that is expectedfrom all anthropogenic emissions. About 29% of the anthropogenic emissions are taken up by the land ecosystems due to the greater availability of CO2 in theatmosphere thereby increasing water use efficiency by
the plants (Keeling et al. 2017). About 23% is being
absorbed by the oceans as the partial pressure of CO2
increases faster in the atmosphere than in the surface
ocean (DeVries et al. 2019). Uncertainties prevail on theregions and process of CO2 uptakes by the land andocean ecosystems (Graven et al. 2013; Zeng et al. 2014;
Forkel et al. 2016; McKinley et al. 2020).
In the Paris Agreement, parties to the UNFCCC
reached a landmark agreement to combat climate

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change and to accelerate and intensify efforts to reduce
the rate of atmospheric CO2 build-up to limit the increase of the Earth’s global-mean surface air temperature
to below 2 °C by 2100 ( https://www.un.org/en/
climatechange/paris-agreement). Meeting this goal will
depend very strongly on the land-ocean-atmosphere
feedbacks in the future (Ciais et al. 2013). One of the urgent questions is whether or not the terrestrial biosphereand the oceanic systems will continue to absorb andstore CO2 from the atmosphere in the future, particularly when the emission mitigation goals of net-zero or
negative emissions are achieved in the later-half of the
century (Jones et al. 2019). For this purpose, comprehensive Earth System Models (ESMs) have been developedthat account for the past behaviours of the terrestrial
and oceanic climate systems, coupled with the carbon
and nutrients cycles (Jones et al. 2016; Arora et al. 2019;
Hajima et al. 2020). The ESM simulated land/ocean-atmosphere CO2 fluxes are relatively untested in comparison with the atmospheric constraints (Wenzel et al.
2016), while the CO2 fluxes simulated by the dynamic
global vegetation models (DGVMs) are recently benchmarked with the global remote sensing CO2 data products or climate parameters (Calle et al. 2019; Collier
et al. 2018).
The main goal of this study is thus to evaluate theCO2 fluxes simulated using one such ESMs, the Japan
Agency for Marine-Earth Science and Technology (JAMSTEC)’s Model for Interdisciplinary Research on Climate(MIROC)-based Earth System Simulation version 2 (referred to as MIROC-ES2L) (Hajima et al. 2020). As thein situ measurements are often affected by local weather
conditions and spatial coverage is sparse, the global ESM
simulations of CO2 will not be adequately assessed bycomparing with in situ data. With the advent of satellite
remote sensing by the dedicated instruments for CO2
measurements, we now have global coverage of CO2
concentrations since 2009 (Yoshida et al. 2013). In
addition, the overall consistency of ACTM simulations
with total column measurements and in situ measurements has already been established (Patra et al. 2017).
This has allowed us here to check the performance of
MIROC-ES2L simulations for the recent 5 years (2009–2014) using the historical Coupled Model Intercomparison Project Phase 6 (CMIP6) climate drivers, which areavailable only up to 2014 as per the CMIP6 protocol.
We also compare the MIROC-ES2L simulation resultswith an inversion estimation of CO2 fluxes using in situ
CO2 measurements and the MIROC4-ACTM simulation(Saeki and Patra 2017; Patra et al. 2018; Friedlingstein
et al. 2020). We reiterate that the in situ data have superior accuracy than the satellite retrievals of XCO2, andthe satellite retrievals, while perfectly suitable for the objectives of this paper, are still maturing.

Patra et al. Progress in Earth and Planetary Science(2021) 8:25

The details of the materials and method for MIROCES2L evaluation are given in Section 2. In Section 3 (Results and discussion), we first compare the fluxes from
MIROC4-Inv and MIROC-ES2L. Then XCO2 simulations by using both the fluxes are evaluated using
GOSAT and OCO-2 observations, in order to evaluate
the quality of MIROC4-Inv fluxes based on sparse in situ
observations and check the applicability for evaluating
the MIROC-ES2L simulations. Recently, the GOSAT
XCO2 measurements are being used for the evaluationof the ESM simulation results at monthly time intervals(Gier et al. 2020), but our analysis uses a common transport model for simulating the fluxes before comparison.
Here, the model XCO2 is constructed by sampling the
MIROC4-ACTM simulated CO2 vertical profiles at theobservation location and time, and by applying the satellite a priori corrections and column averaging kernels(Section 2). Conclusions are given in Section 4.

2 Methods
2.1 Greenhouse gases observing SATelite, retrieval
version 02.81

The Greenhouse gases Observing SATelite (GOSAT),
nicknamed “Ibuki”, was launched on 23 January 2009
(Hamazaki et al. 2004; Yokota et al. 2009). GOSAT has
been making measurements of XCO2 since April 2009.
GOSAT measurement precision and the retrieved XCO2
accuracy have been improving since the first set of retrievals was released (Yoshida et al. 2013). We have used
the latest retrievals, version General User 02.81(GOSAT_v2.81; https://data2.gosat.nies.go.jp/index_en.
html), which are bias uncorrected, but validated using
XCO2 from upward-looking FTS network (TCCON—
Total Carbon Column Observing Network) (Wunch
et al. 2017) (see updates in https://data2.gosat.nies.go.jp/
doc/documents/ValidationResult_FTSSWIRL2_V02.81_
GU_en.pdf). GOSAT data are provided for XCO2, apriori profiles, and column averaging kernels (both at 15pressure layers). Although the bias-corrected data should
be more comparable with the model simulations (earlier
retrieval version 02.72), we have preferred to use thenewest retrieval version which has better physical characteristics. The single-shot precision of GOSAT measurements is estimated to be 2.17 ppm.
2.2 Orbiting carbon observatory, retrieval version 9r

The Orbiting Carbon Observatory-2 (OCO-2) was
launched on 04 July 2014 and retrievals are available
since September 2014 (Crisp et al. 2017; Eldering et al.
2017). We have used bias-corrected retrievals, version 9r(OCO-2_v9r) (Updated Lite files from https://co2.jpl.
nasa.gov/#mission=OCO-2) (O’Dell et al. 2018). OCO-2
data are available for XCO2, a priori profiles (20 levels),and column averaging kernels (20 pressure levels). Data

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with a quality flag of 0 (best data) are used in the analysis. The data coverage of OCO-2 (approximately 10
million data points annually) is much greater than thatof GOSAT (approximately 0.1 million data points annually). The single-shot accuracy of OCO-2 retrievals is estimated to be 1.3 ppm over land and 1 ppm over ocean(Kulawik et al. 2020). The better quality of the XCO2
data from OCO-2 (compared with bias uncorrected
GOSAT_v2.81), although without an overlap with the
MIROC-ES2L simulation, provides us an assessment of
the retrieval data quality on evaluation of the CO2 flux
models.
In this article, the GOSAT and OCO-2 XCO2 retrievals are referred to as XCO2 observations, which are
retrieved from a remote sensing signal and rely on a radiative transfer model with uncertainties.
2.3 MIROC earth system model version 2 for long-term
simulations and evaluation using remote sensing
observations

MIROC-ES2L is the latest generation of earth systemmodel (ESM) that is developed at the JAMSTEC, in collaboration with Tokyo University and the National Institute for Environment Studies (NIES). The ESM has fully
coupled terrestrial-ocean-atmosphere model components for simulating the evolutions of carbon-nitrogen
cycles and climate for the past centuries and centuries tomillennium-term future projection (Hajima et al. 2020).
The horizontal resolution of the atmosphere is T42
spectral truncation (approximately 2.8° intervals for latitude and longitude) and the vertical resolution is 40
layers up to 3 hPa with a hybrid σ–p coordinate; theocean grid system consists of horizontally 360 × 256
grids with 62 vertical layers.
The terrestrial carbon cycle component covers major
processes relevant to the global carbon cycle, with vegetation (leaf, stem, and root), litter (leaf, stem, and root),and humus (active, intermediate, and passive) pools andwith a static biome distribution. Photosynthesis or grossprimary productivity (GPP) is simulated based on theMonsi–Saeki theory (Monsi and Saeki 1953), and the allocation of photosynthate between carbon pools in vegetation (e.g. leaf, stem, and root) is regulated dynamicallyfollowing phenological stages. The transfer of vegetation
carbon into litter–soil pools is simulated using constantturnover rates, and in deciduous forests, seasonal leaf
shedding occurs at the end of the growing period. The
perturbation from the land-use change on the terrestrial
carbon cycle is simulated by the transition of 5 types ofland-use tiles (primary vegetation, secondary vegetation,
urban, crop, and pasture) in a grid; e.g. deforestation
processes are represented by the reduction in area fraction of primary/secondary vegetation (and increase ofless-vegetated land-use tile like urban), and deforested

Patra et al. Progress in Earth and Planetary Science(2021) 8:25

carbon is gradually lost to the atmosphere. Details on
carbon cycle processes in the model can be found elsewhere (Ito and Oikawa 2002; Hajima et al. 2020).
In the Ocean ecosystem component Embedded within
the ocean circulation model (OECO2), ocean biogeochemical dynamics are simulated with 13 biogeochemical tracers (three types of nutrients, four biologicaltracers, four carbon and/or calcium, and other two inorganic tracers). The carbon cycle processes are simulated
following the biogeochemical dynamics of the tracers,
assuming that all organic materials have an identicalelemental stoichiometric ratio. Ocean ecosystem dynamics are simulated based on the nutrient cycles of nitrate,
phosphorous, and iron. The nutrient concentration, in
conjunction with the controls of seawater temperatureand the availability of light, regulates the primary productivity of the phytoplankton. In the model, zooplankton
is assumed to be independent of abiotic conditions (e.g.
seawater temperature) and dependent on biotic conditions (phytoplankton and zooplankton concentrations).
Detritus contains nitrate, phosphorus, iron, and carbon,
most of which is remineralized while sinking downward.
A fraction of the detritus that reaches the ocean floor isremoved from the system. The formulations of atmosphere–ocean gas exchange, carbon chemistry, and related parameters follow protocols from the Ocean
Model Intercomparison Project (OMIP) (Orr et al.
2017).
The basic performance of the land and ocean carbon
cycle is assessed by comparing the simulated spatial patterns with observation data for land (gross primary production, vegetation carbon, and soil carbon for the landcomponent) and ocean (primary production, export production, atmosphere-ocean CO2 flux, dissolved inorganiccarbon) (Hajima et al. 2020). Hajima et al. (2020) also
showed that atmosphere-land or ocean CO2 fluxes in cumulative value (i.e. the changes in land or ocean
amount) in the period of 1850–2014 are within the estimated range suggested by Le Quéré et al. (2018), although the GPP seasonality in land tropics and CO2 flux
seasonality in the Southern Ocean and the North Atlantic Ocean requires improvement. The feedback strengths
of carbon cycle processes, which are associated with themagnitude of natural carbon sinks in response to atmospheric CO2 concentration and climate change, are also
quantified and compared with other ESMs, showing
MIROC-ES2L has the intermediate values for the feedback parameters (Arora et al. 2020).
The original historical simulation of MIROC-ES2L isobtained from the CMIP6 exercise (Eyring et al. 2016;
Hajima et al. 2020), where the model is driven by anthropogenic fossil fuel CO2 emission, other GHGs andaerosol emissions/concentrations, natural forcing likesolar irradiance change and volcanic events, and land-

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use change. The CO2 concentration is explicitly simulated by the model based on the external forcing of anthropogenic CO2 emission, simulated land and ocean
CO2 sink, and simulated LUC-derived CO2 emission(the experimental configuration in which CO2 concentration is prognostically simulated by models is called“emission-driven” mode, while the configuration inwhich CO2 concentration is prescribed as forcing data iscalled “concentration-driven” mode) (Jones et al. 2016).
The simulation period was 1850–2014, following a continuous 2483 spin-up years by the “concentrationdriven” mode and 691 years by the “emission-driven”
mode. The accuracy of future prediction by the ESMs islikely to depend on the quality of the historical simulation of the carbon-nitrogen-climate feedbacks and themodel response to external forcing (e.g. terrestrial response to land-change forcing). However, the sparse insitu measurements and smaller flux footprint of the surface sites limited the evaluation of the historical simulations by the ESMs. The situation has now changed
because of the global coverage of XCO2 measurementsfrom space (GOSAT and OCO-2), which are explored inthis study for an evaluation of the MIROC-ES2L historical simulation.
2.4 MIROC atmospheric chemistry transport model

The MIROC (version 4)-based atmospheric chemistrytransport model (MIROC4-ACTM) simulations are conducted at horizontal resolution of T42 spectral truncations with 67 hybrid pressure layers in vertical. The
greater number of vertical layers covering the altitude
range from Earth’s surface to 0.0128 hPa or about 80
km, and closely spaced levels in the upper troposphereand lower stratosphere region is designed for better representation of the vertical profiles of long-lived gases inthe Earth’s atmosphere. MIROC4-ACTM (Patra et al.
2018; Watanabe et al. 2011) simulated horizontal winds
and temperature are nudged to the Japanese 55 year reanalysis or JRA55 (Kobayashi et al. 2015), is well validated for large-scale interhemispheric transport using
sulphur hexafluoride (SF6) and the Brewer-Dobson circulation patterns using the age of air derived from CO2
and SF6 (Patra et al. 2018). Thus we expect better simulations of XCO2 by accounting for the accurate meridional and vertical profiles of CO2. However, theconvective (weekly or shorter time scale) transportremained invalidated due to the lack of appropriate observational parameters, e.g. Radon-222 with a radioactive
decay lifetime of 3.8 days (Patra et al. 2018).
We use monthly mean CO2 fluxes from JAMSTEC’stime-dependent inversion model for this analysis (Saeki
and Patra 2017; Friedlingstein et al. 2020). The inverse
model estimated CO2 fluxes (referred to as MIROC4_
Inv) for 84 regions of the globe using the MIROC4-

Patra et al. Progress in Earth and Planetary Science(2021) 8:25

ACTM simulations and in situ CO2 observations at 30
sites around the globe (Fig. 1). The atmospheric data areprovided by the National Oceanic and Atmospheric Administration (NOAA) Cooperative Air
Sampling Network (Dlugokencky and Tans 2019),
and the Japan Meteorological Agency (JMA) (Tsuboi et al. 2013). A priori MIROC4-ACTM simulations are conducted using interannually varying
emissions due to fossil-fuel and cement production (FFC) from the global carbon project (Friedlingstein et al. 2020), climatological monthly
mean terrestrial and oceanic fluxes from theCarnegie-Ames-Stanford Approach (CASA) landmodel, and upscaling model of air-sea CO 2 flux
measurements, respectively (Randerson et al.
1997; Takahashi et al. 2009). Thus, the interannual variabilities in the land and ocean regional
fluxes estimated by the inverse model are driven
entirely by the signals in observed CO 2 variabilities at 30 sites. The simulated CO 2 concentrations from the MIROC4_Inv fluxes compare wellwith the other atmospheric inversion models
when evaluating against independent airborne
measurements (Friedlingstein et al. 2020).

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2.5 Preparation of model XCO2 data and processing of
the gridded maps and time series

Here, in order to simultaneously evaluate both the
XCO2 and CO2 fluxes simulated by MIROC-ES2L, we
first made two types of MIROC4-ACTM simulations—one is driven by the CO2 fluxes of MIROCES2L and the other is by MIROC4_Inv flux; the simulations are referred to as ACTM_ES2LF and ACTM_
InvF, respectively. Thus, the atmospheric CO2 transport, driven by JRA55 reanalysis, is common for both
simulations. This experimental setting allows us tomake a direct comparison of XCO2 in both simulations with that of satellite monitoring. The model
simulations by MIROC4-ACTM are archived athourly time resolution and sampled for the GOSAT
and OCO-2 measurement locations by linear interpolations in horizontal grid and time (Patra et al. 2017).
The model simulations are then convolved with satellite a priori (CO2prior) and column averaging kernels(Ai) after calculating their respective pressure levels(Pi; where i is the index for retrieval pressure layers;
20 for OCO-2 and 15 for GOSAT) from the original
ACTM vertical grids (67 hybrid). Thus, the ACTM
simulated XCO2 are

Fig. 1 Regional divisions of land (15) and ocean (11), along with their names, for time series analysis shown by the map. The in situ
measurement sites used in the MIROC4-ACTM inversion are shown by triangles and marked by their 3-letter site abbreviation, as per the World
Meteorological Organisation – World Data Centre for Greenhouse Gases (WMO-WDCGG). CO2 data for 28 sites are taken from NOAA (https://www.esrl.noaa.gov/gmd/ccgg/flask.php), and data for YON and MNM are taken from JMA (https://gaw.kishou.go.jp/)(2021) 8:25

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X

X
 X
CO2 priori ∵dP i þA ∵dPi
CO2 ACTM i − i CO2 prior ii ii

et al. 2016) and GPP from FLUXCOM, a CO2 flux
upscaling inter-comparison project (Tramontana et al.
2016). The MODIS LAI product with the original 500 m
resolution was aggregated globally based on the same
quality control with Ichii et al. (2017) and averaged over
the T42 spatial resolution for comparison with MIROCES2L results. The FLUXCOM GPP product (Jung et al.
2020) was generated by an ensemble of estimations bymultiple machine-learning algorithms with eddycovariance CO2 flux observation network (FLUXNET)
and MODIS land products (Tramontana et al. 2016).
The original 1/12 degree resolution data were converted
to the T42 spatial resolution.

Patra et al. Progress in Earth and Planetary Science

XCO2 ACTM ¼

X
i

ð1Þ
where dPi is the pressure weighting function (Rodgers
and Connor 2003).
Both the simulations using MIROC4-Inv and MIROCES2L fluxes are spin-up from 1996–2009, so that theCO2 concentration responses to the flux changes near
the Earth’s surface propagates throughout the atmosphere, as high as the model top of about 90km. This isimportant because the XCO2 measurements capture thetotal columns and there are systematic CO2 gradients inthe stratosphere and mesosphere that are season
dependent, and lags more than 6 years for the concentration increase rate in the troposphere. Both the model
concentrations are adjusted for initial values so that the
global mean concentrations agree with the GOSAT observations on 01 January 2010. This is a valid approximation because we do not consider any chemical
production or loss of CO2 in the models, thus the concentration increases are consistent with the flux evolution (Basu et al. 2018). The initial value adjustment
helps to put all plots on identical XCO2 scales.
All the XCO2 results are gridded to a 2.5° × 2.5° latitude–longitude grid for further analysis (Patra et al.
2017). Time series analyses are conducted by further aggregating XCO2 data for the 15 partitions of the landand 11 ocean regions as marked by the maps in Fig. 1.
The model data differences and agreements are quantified by comparing the growth rates and seasonal cycles
between the observed and simulated XCO2, following
decomposition of the time series using a harmonic analysis (Thoning et al. 1989). We fitted 4 harmonics toeach of the regionally aggregated time series for deriving
a long-term trend and a fitted time series. The seasonal
cycles are calculated as fitted–trend time series, and thegrowth rate is calculated as a time derivative of the trend
time series.
2.6 Leaf area index and gross primary productivity

The LAI, one-sided green leaf area per unit horizontal
ground surface (m2 m−2), is one of the main drivers ofprimary production in the ESMs (Anav et al. 2015). LAI
defines the canopy structure and functions of the biosphere, influenced by the weather and climate of the region. Thus, the LAI and GPP together allow us todiagnose basic ecosystem functioning for carbon assimilation in MIROC-ES2L. Although solar-induced chlorophyll fluorescence data can be used as an indicator of
GPP (Wu et al. 2016; Doughty et al. 2019), we did notuse it since the data cannot be compared with GPP directly. We used LAI from the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 6 (Yan

3 Results and discussion
Figure 2 shows the time series of CO2 fluxes for the land
biosphere, ocean exchange, and FFC emissions. We also
show the time evolution of the meridional land andocean CO2 fluxes as simulated by the MIROC-ES2L and
MIROC4-Inv (right column). The results show global
total land and ocean CO2 fluxes are increasing with timeand offset about 44 ± 6% of the FFC emissions during
the period 2009–2018, as seen from the latest Global
Carbon Budget (GCB) (Friedlingstein et al. 2020). In
general, the cumulative fluxes by MIROC-ES2L (− 16.0,− 10.1, and 46.7 PgC for land, ocean, and FFC, respectively) and MIROC4-Inv (− 14.4, − 8.1, and 46.3 PgC for
land, ocean, and FFC, respectively) are in good agreement for the overlapping GOSAT observation period of
2010-2014. These fluxes are also in good agreement with
the GCB’s cumulative flux estimates − 13.3, − 8.4, and47.0 PgC for land (land sink – land-use source + riverine
export), ocean (ocean sink – riverine export), and FFC,
respectively, during 2009–2014. For this comparison, we
have corrected the GCB land and ocean fluxes for riverine export (Resplandy et al. 2018), i.e. 0.78 PgC year−1 isadded to the land sink and removed from the ocean sink
for this comparison because the inversion and ESM
fluxes are used in the ACTM simulations for atmospheric CO2 without any spatial adjustment for riverine
export flux. While the GCB underestimate sinks(“budget imbalance”) (Saeki and Patra 2017; Bastos et al.
2020), we find here that the MIROC-ES2L fluxes marginally overestimate the cumulative sink compared with
the inversion estimated CO2 sink. The inversion fluxes
by design reproduce the observed growth rates in atmospheric CO2. In the ACTM simulation of atmosphericCO2, a bias of 1 ppm is produced per 2.12 PgC of flux
imbalance.
The magnitude of interannual variations and trends in
CO2 fluxes are in good agreement between the 3 different estimations for the global land but are at a lower
agreement for the global ocean (Fig. 2a, b). Nevertheless,the land and ocean show similar increasing long-term

Patra et al. Progress in Earth and Planetary Science(2021) 8:25

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Fig. 2 Time series of global (left column) and semi-hemispheric (right column) total CO2 fluxes for land and ocean at annual intervals as
estimated by the MIROC4-Inv and MIROC-ES2L (panels a and b, respectively). The FFC emissions from independent data sources are also
compared (panel c). The global total results are compared with GCP-CO2 budgets (Friedlingstein et al. 2020). The semi-hemispheric biosphericfluxes of land and ocean regions as well as the FFC emissions are shown (right column), for the northern hemisphere (NH) extratropics, tropics,
and southern hemisphere (SH) extratropics (panels d–f, respectively). Please note the different y-axis range for each panel (the ocean flux
variability in panel b may appear deceivingly large compared with the land flux variability in panel a)trends in CO2 uptake (more negative flux in the recent
years), except for the anomalous period of 1996–2002
for MIROC4-Inv. Although this anomalous period is included in the ACTM simulation spin-up, the simulated
CO2 concentrations for 2009 and later will be largely unaffected. The agreements between mean fluxes from
MIROC4-InvF and MIROC-ES2L at 3 broad latitude
bands (Fig. 2d–f) are excellent except for the land in thesouthern hemisphere (SH) extratropics. The SH land
flux is estimated at about − 0.5 PgC year−1 by MIROCInvF during 2009–2014 compared with very weak negative flux by MIROC-ES2L (Fig. 2f). It has to be seen
whether or not such differences in fluxes are validated/invalidated by the GOSAT and OCO-2 observations.
Please bear in mind that the phase of interannual variability of CO2 fluxes by MIROC-ES2L is not expected tomatch the phasing of interannual climate variability of
the real world (e.g. El Niño–Southern Oscillation). Thus,
MIROC4-Inv and MIROC-ES2L disagree on the phasesof interannual variability of CO2 fluxes. However, themagnitude of land flux interannual variabilities for

MIROC4-Inv (0.86 PgC year−1, 1-σ standard deviation
for the period 1996–2014 after detrending) and MIROCES2L (0.85 PgC year−1) are in good agreement, but the
global ocean flux interannual variabilities are underestimated largely by MIROC-ES2L (0.09 PgC year−1) compared with that for MIROC4-Inv (0.32 PgC year−1).
The seasonal variation of fluxes at different latitude
grid are more variable in the case of the MIROC4-Inv
and MIROC-ES2L (Fig. 3). We find that the CO2 flux
seasonalities are in a good match in the latitudes northof 30°N, but the cycle of outgassing and uptake in thelatitude bands of 30°S-Eq and Eq-30°N are contrasting
between the two flux models. The MIROC-ES2L underestimates CO2 uptake in the latitude band of 55°S–30°S
and shows no CO2 degassing in cold season around 60°S
along the coast of Antarctica, when compared with the
MIROC4-Inv fluxes. For the simulation of XCO2, we expect to see different phasing and amplitude of seasonal
cycle simulated using the inversion and ESM fluxes, particularly over the tropical and southern hemisphericregions.

Patra et al. Progress in Earth and Planetary Science(2021) 8:25

Page 8 of 18

Fig. 3 Zonal mean meridional and seasonal variations in CO2 fluxes as estimated by atmospheric inversion (MIROC4-Inv) and simulated by theearth system model (MIROC-ES2L)

Figure 4 shows examples of XCO2 distributions as observed by GOSAT and OCO-2 for the year 2014 and2016, respectively. Note that OCO-2 does not have fullyear coverage of measurements for 2014. The data density has been significantly increased in the case of OCO-2
retrievals. We also see that the model–observation differences are generally lower for OCO-2 and ACTM_
InvF compared with the differences between GOSAT
and ACTM_InvF, particularly over the ocean regions.
The GOSAT sun glint observations are known to haveadditional retrieval bias relative to those over the land
surfaces and produce greater inconsistency when compared with transport model simulations (Patra et al.
2017; Schuh et al. 2019; Yoshida et al. 2013). Both ourmodels systematically overestimated XCO2 concentrations over Asia around the latitude 45°N, which could either arise from high bias in FFC CO2 emissions over
China (Saeki and Patra 2017) or underestimation ofsinks over the regions (Wang et al. 2020). For both thesimulations, XCO2 over the tropical land regions, except
over India, are underestimated (negative differences)while the XCO2 over the ocean basins are systematicallyoverestimated (positive differences) (Fig. 4b, c). The
overestimations over ocean are more prominent in thesouthern extratropics.
Figure 5 shows the latitude–time distributions ofzonal-mean XCO2 for the period of GOSAT and OCO-2
measurement period. Both models are compared withGOSAT for the period 2009–2014 and only ACTM_
InvF results are compared with OCO-2 due to the unavailability of ACTM_ES2LF simulations for the recent
years. In general, the model simulations are within 2

ppm of the observed XCO2 concentrations. The fact that
the ACTM_InvF simulation better agrees with GOSAT
XCO2 suggests an overall consistency of the in situ measurements with those from the satellites. Figure 5 c ande show that the model-observation agreements have improved compared with those using earlier versions of retrievals for both GOSAT and OCO-2, especially at thehigh-latitude edges (Patra et al. 2017). The ACTM_InvF
better simulates the time evolution because the fluxes
are optimised using in situ data, while the free-running
fluxes in ACTM_ES2LF marginally underestimated the
XCO2 increase rate with time due to slightly stronger
global total CO2 sinks in the years 2010–2014, comparedwith the inversion fluxes (Fig. 2). In the latitude range
around 20°S, the seasonal bias in ACTM_ES2L simulated
XCO2 is maximum with positive values in austral autumn and negative values in the austral spring, reflecting
tendencies of weaker sink to source and weaker source
to sink during the two seasons, respectively, in the
MIROC-ES2L fluxes compared with the MIROC4_Inv
fluxes (Fig. 3).
We find that the ACTM_InvF–GOSAT shows greater
differences in the periods since 2015, which may arise
from insufficient accuracy of the degradation correctionof the TANSO-FTS without accounting for switching of
the pointing system in January 2015 (Kuze et al. 2016).
The differences are greater over the water surface thanthe land surface (Figs. S1 and S2). The instrumental degradation correction is suspected more than the retrieval
physics uncertainties because the characteristics of surface reflectance are better modelled over the water bodies than that over the land.

Patra et al. Progress in Earth and Planetary Science(2021) 8:25

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Fig. 4 Spatial maps of XCO2 for GOSAT only in comparison with ACTM_InvF and ACTM_ES2LF simulations for 2014 (left column), and OCO-2(and GOSAT) in comparison with ACTM_InvF only for 2016 (right column). Results are shown for a full calendar year

The model-observed regional biases in XCO2 (Table 1)
provide an indication of how well the flux models simulated the regional fluxes. Because the GOSAT_v2.81 data
are not bias corrected, the agreement between ACTM_
InvF with GOSAT (biases greater than 0.12 ppm for 16
out of 26 regions and are less than 1 ppm) is much greaterthan those for ACTM_InvF and OCO-2 (biases typicallybelow 0.12 ppm except for 3 out of 26 regions). Generally,
the regional biases are greater for ACTM_ES2LF andGOSAT_v2.81 (only 6 out of 26 regions have bias lessthan 0.12 ppm). The biases are systematically positive for
Boreal America and Asia, in contrast to strongly negative

for the Southern Ocean (poleward of 45°S). These biases
will be better assessed in the future by using newer simulations by MIROC-ES2L and updated GOSAT/GOSAT2
and OCO-2/OCO-3 retrievals.
The mean growth rates for the model and observed
time series (not shown in Table 1 for clarity) suggestthat the ACTM_ES2LF simulation (2.01 ± 0.09 ppm
year−1 for 2010–2014) slightly underestimated the
GOSAT growth rates (2.13 ± 0.25 ppm year−1 for 2010–2014) over all the regions. This growth rate mismatch of
0.11 ppm year−1 is equivalent to a sink bias of 0.25 PgC
year−1 for MIROC-ES2L fluxes (1 ppm = 2.12 PgC inPatra et al. Progress in Earth and Planetary Science(2021) 8:25

Page 10 of 18

Fig. 5 Time evolution of zonal mean meridional gradients of XCO2 as measured by GOSAT, OCO-2 in comparison with two ACTM_InvF and
ACTM_ES2LF simulations. The plots by using data over land only and water only are shown in Fig. S1 and Fig. S2, respectively

MIROC4-ACTM). As the inversion fluxes are optimisedusing the surface CO2 measurements the mean growthrate from ACTM_InvF (2.32 ± 0.04 ppm year−1 for
2010–2018) agrees well with that of the GOSAT (2.27 ±0.09 ppm year−1 for 2010–2018). The differences ingrowth rates between the regions are small because CO2
is well mixed in the atmosphere, and also the region-toregion differences are greater over a shorter time period,e.g. for the case of GOSAT during 2010–2014, becauseof the impacts of regional climate variabilities on theCO2 flux (Patra et al. 2005).
Figure 6 shows the importance of greater observational
data coverage, for conducting better inversion of regional CO2 sources and sinks, e.g. the mismatch between
the seasonal cycle phase and amplitude over Southern
Africa is more evident than Temperate North America.

Assuming that the XCO2 are strongly sensitive to the regional and hemispheric flux gradients we find the
ACTM_ES2LF simulation shows large mismatches inthe seasonal cycle phase and amplitudes in the tropicalsouthern hemisphere to the southern extratropics (Table
1; Animation S1 and S2 for GOSAT and OCO-2, respectively). The seasonal cycle correlations are found tobe the smallest over Southern Africa (r = 0.04), Tropical
Africa (r = 0.24), and Brazil (0.38). This suggests that the
MIROC-ES2L fluxes are not simulated well over thetropical land regions and southern hemisphere in general (seen as the contrast between the MIROC4-Inv and
MIROC-ES2L CO2 fluxes in Fig. 3). Since the transport
is common in both the ACTM simulations, we attribute
the ACTM_ES2LF–GOSAT mismatches to the surface
fluxes rather than the model transport uncertainty, due(2021) 8:25

Patra et al. Progress in Earth and Planetary Science

Page 11 of 18

Table 1 Statistics of XCO2 time series simulations in comparison with GOSAT and OCO-2 measurements. Correlation coefficients arecalculated for the mean seasonal cycles of the time series as calculated by harmonic analysis. Mean XCO2 biases are calculated as
the differences for the overlapping periods between two data records. The regions are arranged from North to South latitudes
within each of the continents and ocean basins, as much as possible
Region name

ACTM_ES2LF–GOSAT (2010–2014)

ACTM_InvF–GOSAT (2010–2014)

ACTM_InvF–GOSAT (2015–2018)

ACTM_InvF–OCO2 (2015–2018)

Seasonal
cycle (r)Regional bias
(ppm)

Seasonal
cycle (r)Regional bias
(ppm)

Seasonal
cycle (r)Regional bias
(ppm)

Seasonal
cycle (r)Regional bias
(ppm)

Boreal N.
America

0.76

0.74

0.89

− 0.09

0.93

0.01

0.97

0.05

Temperate N.
America

0.91− 0.250.98− 0.08

0.95

0.09

0.99

0.03

TropicalAmerica

0.96− 0.040.98− 0.11

0.96

0.28

0.98

− 0.07

Brazil

0.38

0.60

0.76

0.22

0.65

0.47

0.72

− 0.04Temperate S.
America

0.44− 0.200.84− 0.31

0.83

0.29

0.89

0.04

Europe0.93− 0.160.97− 0.14

0.97

0.08

0.99

− 0.01

Northern Africa

0.91− 0.08

0.96

0.06

0.97

0.32

0.99

− 0.12Tropical Africa

0.24

0.50

0.81

0.19

0.69

0.63

0.96

− 0.01

Southern Africa

0.04

0.25

0.91

0.03

0.75

0.31

0.87

0.01

Boreal Asia

0.86

1.00

0.94

− 0.09

0.93

0.03

0.99

− 0.21

West Asia

0.94− 0.250.96− 0.18

0.96

0.29

0.99

− 0.02South Asia

0.60

− 0.280.84− 0.460.72− 0.450.95− 0.33

East Asia

0.95− 0.16

0.95

0.07

0.96

0.34

0.99

− 0.04Southeast Asia

0.79

0.40

0.83

0.14

0.88

0.48

0.96

0.01

Oceania− 0.19− 0.420.52− 0.35

0.62

0.29

0.30

0.02

North Pacific0.92− 0.170.93− 0.84

0.95

0.06

0.99

− 0.01

West Pacific0.91− 0.010.94− 0.19

0.88

0.22

0.93

− 0.03

East Pacific0.90− 0.240.91− 0.37

0.80

0.08

0.84

− 0.07

South Pacific0.75− 0.050.78− 0.630.79− 0.150.71

0.01

Northern Ocean 0.93

− 0.110.93− 0.880.93− 0.570.99− 0.23

North Atlantic

0.89

Tropical Atlantic 0.63

0.02

0.92

− 0.670.90− 0.190.99− 0.01− 0.230.78− 0.31

0.55

0.08

0.89

− 0.040.65− 0.520.87− 0.770.91− 0.410.85

0.01Southern Ocean 0.92

− 1.620.91− 0.970.68− 0.490.86

0.01

Tropical Indian
Ocean

0.93

− 0.100.94− 0.30

0.93

0.10

0.91

0.01

South Indian
Ocean

0.39

0.40

0.84

− 0.370.87− 0.140.78

0.07

Mean of all
regions0.71− 0.040.88− 0.28

0.84

0.08

0.90

− 0.04South Atlantic

to the deep cumulus convection in the tropics (Remaud
et al. 2018).
Better seasonal cycle correlations for South Asia (r =0.60) or Southeast Asia (r = 0.79) could arise due to the
far-field influence from the northern extratropics, where
the fluxes are better modelled. It is typical that the terrestrial biosphere models are better parameterised forbiogeochemical cycles of the temperate regions(temperature/radiation controlled), compared with theregions over tropical regions, where the carbon cycle isvery strongly limited by water availability under the
weaker seasonal temperature variations (Gloor et al.
2012; Patra et al. 2013; Haverd et al. 2013; Sitch et al.
2015; Jones et al. 2020). The tropical and temperate regions also have different characteristics of nitrogen andphosphorus limitations (Zaehle et al. 2010; Fleischer

Patra et al. Progress in Earth and Planetary Science(2021) 8:25

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Fig. 6 Time series XCO2 for 4 selected parts of the world. Values are aggregated over the regions highlighted by yellow. The detailed results for
15 land and 11 ocean regions are shown for the time series, ACTM_InvF/ACTM_ES2L-GOSAT, and their detrended seasonal cycles (GIF Animation
S1). Comparisons with OCO-2 data are also shown in supporting materials (GIF Animation S2)

et al. 2019). The issue of poor seasonal cycle simulation
by MIROC-ES2L is addressed later using empirically derived LAI and GPP.
Further, we checked the meridional variations ofmulti-year mean peak-to-trough seasonal cycle amplitudes (SCAs) for XCO2 over the land and ocean regions
separately (Fig. 7). The interannual variabilities, seen as
the vertical error bars, are generally smaller than 0.5
ppm in most latitudes, except over the ocean in the latitudes poleward of 40°N which show persistently greaterthan 1 ppm (Fig. 7d). We find distinct features for thecomparisons over the land and ocean which helps us to
identify the possible link between the surface CO2 fluxes
over the land and ocean on XCO2. ACTM_InvF simulation
generally compares well with GOSAT observations in the
period 2010–2014 and OCO-2 observations in the period
2015–2018. The ACTM_ES2LF simulation shows better
agreement with GOSAT observation over the land compared with the ACTM_InvF simulation except over the tropics and northern extratropics (5°S to 40°N) (Fig. 7a). The
ACTM_ES2LF simulation systematically underestimates
SCAs by about 50% in the northern hemisphere (north of
the Equator) compared with those observed by GOSAT
over the ocean in all years. The ACTM_ES2LF andGOSAT XCO2 SCA agreement over land in the latitudes
poleward of 45oN support the results for the CMIP5 model(MIROC-ESM) and aircraft measurements showed reasonably good agreement, at about 11 ppm and 14 ppm, respectively (Graven et al. 2013). The aircraft data (Graven
et al. 2013) observe a combined effect of land and oceanic

fluxes; thus, the separation of land and ocean flux signals
using XCO2 SCA from a large amount of data provides us
additional information.
While the ACTM_InvF simulation shows systematically lower SCAs than those observed by GOSAT by 1.52.0 ppm at all latitudes over the land, the systematic disagreements of ACTM_InvF SCAs with those of OCO-2
are smaller by half (Fig. 7c). These disagreements in
SCAs over land are outside the range of the interannual
variability in the southern hemisphere (Fig. 7c). The
SCA differences over the ocean are more striking between GOSAT_v2.81 and the other 3 estimations in thesouthern hemisphere (Fig. 7d). This suggests a differencein the quality of XCO2 retrievals by the two satellites, especially over the ocean (i.e. glint observations on water
bodies). It is not clear whether the post-retrieval bias
correction (ref. O’Dell et al. 2018) is the only reason for
the improved agreement between OCO-2 and ACTM_
InvF.
To explain the weaker seasonal cycle correlations(Table 1) and smaller seasonal cycle amplitudes (Fig. 7a)simulated by ACTM_ES2LF in the tropical regions ofAfrica, America, and Asia, we compare two of the important terrestrial biosphere variables GPP and LAI from
MIROC-ES2L with those from the FLUXCOM experiment and MODIS satellite (Fig. 8). In the tropics (10°S10°N), comparisons of the two observed products(MODIS LAI and FLUXCOM GPP) show that the
MODIS LAI exhibits less seasonality as the region consists of mostly evergreen forests, while FLUXCOM GPPPatra et al. Progress in Earth and Planetary Science(2021) 8:25

Page 13 of 18

Fig. 7 Seasonal cycle amplitude of zonal mean XCO2, shown for land (top row) and ocean (bottom row) surfaces separately. The comparisons of
XCO2 SCAs for both the ACTM_InvF and ACTM_ES2LF simulations are compared with GOSAT observations for the 2010–2014 period (leftcolumn), while the ACTM_InvF simulation only is compared with GOSAT and OCO-2 observations for the 2015–2018 period (right column). The
error bars represent 1-σ standard deviations over 5 years in the left column and over 4 years in the right column. The ACTM_invF(GOSAT) and
ACTM_invF(OCO-2) in panels c and d show the ACTM_InvF results when sampled at the location and time of GOSAT and OCO-2
measurements, respectively

shows distinct seasonality (Fig. 8a, c). The GPP is observed to be the highest in the late summer in bothhemispheres. This suggests that GPP seasonality in thisregion is controlled strongly by abiotic processes, suchas precipitation or soil water, radiation, and airtemperature (Jung et al. 2017; Patra et al. 2005).
MIROC-ES2L shows less seasonality in LAI, as in thecase of MODIS LAI, but the simulated GPP shows muchlesser agreement with the FLUXCOM GPP. This led us
to conclude that the abiotic controls on CO2 exchangeby the terrestrial ecosystem, as modelled in MIROCES2L, requires further attention; it is suspected that lesssoil water seasonality in tropics is associated with thisproblem, which needs further clarification through theevaluation of the model in terms of both biogeochemicaland hydrological processes (Eyring et al. 2016; Hoffman
et al. 2017).
At around 30°S, both MODIS LAI and FLUXCOM
GPP show similar seasonality, suggesting LAI is thedominant controlling factor in the region. In MIROCES2L, the simulated LAI clearly shows weaker seasonality, leading to rather flat GPP throughout the year, suggesting problems in the biotic process model. In thenorthern midlatitudes (~ 40°N), it is clear that the growing season is longer in MIROC-ES2L than theobservation-based products, i.e. too early leaf onset andtoo late leaf shedding. This suggests room for improving
the phenology scheme in the model (Hajima et al. 2020).
However, the problematic issues in the midlatitude regions are not tracked well in this study, and further sophistications in the atmospheric (XCO2) metric are
required.

4 Conclusions
We have compared the simulated total column CO2
concentrations (XCO2) by JAMSTEC’s ACTM, using
CO2 fluxes from an atmospheric CO2 inversion(ACTM_InvF) and an ESM (ACTM_ES2LF), with the
XCO2 observed by GOSAT and OCO-2. Based on theanalyses following major conclusions can be drawn.
(1)We show that the forward transport model simulation of CO2 fluxes from various methods can be tested
well for all regions over the globe using the XCO2 measurements from the satellites, with conditions that thetransport model realistically represents the interhemispheric exchange and age of air in the stratosphere(see also Schuh et al. 2019; Calle et al. 2019). Note thatthe atmospheric CO2 inversions lack in situ data coverage over much of the globe, and the ESMs are in theirPatra et al. Progress in Earth and Planetary Science(2021) 8:25

Page 14 of 18

Fig. 8 Comparisons of MODIS satellite–derived LAI with that simulated by MIROC-ES2L (a, b; top row), and flux tower–based FLUXCOM GPP with
MIROC-ES2L simulated GPP (c, d; bottom row)developmental phase for simulating the carbon cycle ina general circulation modelling framework.
(2)The inversion results using surface sites are consistent with the XCO2 measurements over different parts ofthe globe within 1 ppm (or more often within 0.5 ppm)
(Table 1). Although this method of comparing MIROCES2L simulated fluxes with inversion and XCO2 observations is only valid for the simulation period where abundant in-situ or satellite measurements are available (e.g.
2009–2014 in this study), this can be a powerfulconstraint to test the contemporary CO2 flux simulated
by ESMs. Hajima et al. (2020) suggested the MIROCES2L is likely to underestimate the contemporary CO2
concentration, and this study revealed that the contemporary CO2 fluxes by the ESM are comparable with thefluxes estimated by state-of-the-art inverse models witha sink bias of 0.25 PgC year−1.
(3)We also propose a metric to evaluate carbon cycle
processes by using seasonal cycles of CO2—the inversion
CO2 fluxes and satellite XCO2 suggested the ESM

Patra et al. Progress in Earth and Planetary Science(2021) 8:25

should be improved for seasonal amplitude and phasingof CO2 fluxes in different latitude bands. Using theobservation-based leaf area index and gross primary
productivity are compared with those simulated by the
MIROC-ES2L, which suggest that the carbon-cycle processes in MIROC-ES2L need to be improved in theextratropical regions while it was suggested over thetropical regions the weather and soil water dynamics(and its ecological response) are inadequately simulated.
(4)A more sophisticated analysis is needed for removing the far-field effects on the XCO2 over individual regions for accurately judging how well (or badly) the
ESM or inversion CO2 fluxes are modelled, as seen by
the satellites. At the moment, it is not very clear whether
the model–observation mismatches we find over theSouthern Africa region (Fig. 6c) are caused by what fraction due to regional flux error or arising from the wrong
flux seasonality in other continents in the same latitude
range or propagated model data mismatches from theregions north or south of Southern Africa.
(5)More of these questions will be answered better as
the quality of the retrievals continues to improve andlonger time series of remote sensing observations aregathered, while the ESMs account for more complex
processes occurring in the earth’s environment due toboth anthropogenic and natural causes. As demonstrated
in this study, the evaluation of CO2 fluxes over the globe
will be a help to specify the region with large biases andto improve the model performance on reproducing CO2
concentration, both of which are essential to make more
realistic future climate projections.
Abbreviations
ACTM: Atmospheric chemistry transport model; BRIC: Brazil, Russia, India andChina; CASA: Carnegie-Ames-Stanford Approach; CO2: Carbon dioxide;
CMIP6: Coupled Model Intercomparison Project Phase 6; DGVM: Dynamic
global vegetation model; ESM: Earth system model; ES2L: Earth System
Simulation version 2; FFC: Fossil-fuel and cement production; FTS: Fouriertransform spectrometer; GHG: Greenhouse gas; GPP: Gross primary
productivity; GCB: Global carbon budget; GOSAT: Greenhouse Gases
Observing Satellite; JAMSTEC: Japan Agency for Marine-Earth Science andTechnology; JAXA: Japan Aerospace Exploration Agency; JMA: Japan
Meteorological Agency; LAI: Leaf-area index; LUC: Land-use change;
MIROC: Model for Interdisciplinary Research on Climate; MODIS: Moderate
Resolution Imaging Spectroradiometer; MoE: Ministry of Environment; Japan;
NASA: National Aeronautics and Space Administration; NIES: National
Institute for Environmental Studies; NOAA: National Oceanic andAtmospheric Administration; OECD: Organisation for Economic Co-operation
and Development; OCO-2: Orbiting Carbon Observatory (series 2);
OMIP: Ocean Model Intercomparison Project; SF6: Sulphur hexafluoride;
TCCON: Total Carbon Column Observing Network; UNFCCC: United Nations
Framework Convention on Climate Change

5 Supplementary Information
The online version contains supplementary material available at https://doi.
org/10.1186/s40645-021-00420-z.
Additional file 1: Figure S1: Same as Fig. 5 but for data over land
surface only. Figure S2: Same as Fig. 5, but for the observations overPage 15 of 18

water bodies only. Animation S1: Same as Fig. 6 for the time series of
XCO2 for all the 15 land regions and 11 ocean regions for the period of
2009-2018. Note that these plots consist of 2 additional panels showing
the model-measurement differences and the detrended seasonal cycles,
for which the statistics are presented in Table 1. (https://ebcrpa.jamstec.
go.jp/~prabir/data/Pubctn/XCO2model/Animation_S1.gif). Animation
S2: Same as Animation S1, but for the OCO-2 measurement period(2014-2018). (https://ebcrpa.jamstec.go.jp/~prabir/data/Pubctn/XCO2
model/Animation_S2.gif). Animation S3: Same as Fig. 7 for XCO2 seasonal cycle amplitudes for different years, and those for ACTM_InvF and
OCO-2 only for the period 2014 to 2018. (https://ebcrpa.jamstec.go.jp/~prabir/data/Pubctn/XCO2model/Animation_S3.gif). Animations are alsoavailable at: https://doi.org/10.6084/m9.figshare.14343383.v1.

Acknowledgements
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, through the Ministry of
Education, Culture, Sports, Science, and Technology of Japan. We thank
Masayuki Takigawa and Shingo Watanabe, JAMSTEC for helping with the
MIROC4-ACTM development. This work was first presented at the Earth Information Day, an event organised by the The Subsidiary Body for Scientificand Technological Advice (SBSTA) at the 25th Conference of the Parties(COP-25) Madrid, Spain (https://unfccc.int/topics/science/events-meetings/
systematic-observation/earth-information-day-2019). This article was first submitted to the SPEPS/Article Collection “Projection and impact assessment of
global change” (05 Feb 2020). We thank Dr. Marine Remaud and two anonymous reviewers for valuable comments in the review process.
Authors’ contributions
PKP and MKa proposed the research topic and conceived the analysis. TH, AI,
NC, KI conducted the model simulations. RS, NC and PKP performed data
analysis. TH, MKa, MKo, KI, DC joined the discussions. All authors contributed
in preparation of the manuscript. The author(s) read and approved the final
manuscript.
Funding
This work was supported by TOUGOU/SOUSEI, the “Integrated Research
Program for Advancing Climate Models”/“Program for Risk Information on
Climate Change”, by the Ministry of Education, Culture, Sports, Science, andTechnology of Japan (grant number JPMXD0717935715). The Earth Simulator
and JAMSTEC Super Computing System were used for the simulations, andthe administration staff provided much supports.
Availability of data and materials
The dataset(s) supporting the conclusions of this article is(are) available in
JAMSTEC’s webdata server [https://ebcrpa.jamstec.go.jp/~prabir/data/Pubctn/
XCO2model/].
The code of MIROC-ES2L and MIROC4-ACTM are not publicly archived because of the copyright policy of MIROC community. Readers are requested
to contact the modelling group if they wish to validate the model configurations of MIROC-ES2L and MIROC4-ACTM.

Declarations
Competing interests
The authors declare that they have no competing interests.
Author details
1
Research Institute for Global Change, Japan Agency for Marine-Earth
Science and Technology (JAMSTEC), Yokohama 236-0001, Japan. 2Center for
Environmental Remote Sensing (CeRES), Chiba University, Chiba 263-8522,
Japan. 3Disaster Risk Reduction and Environ. SBU, Kokusai Kogyo Co., Ltd.,Tokyo 183-0057, Japan. 4Center for Global Environmental Research, National
Institute for Environmental Studies (NIES), Tsukuba 305-8506, Japan. 5NASA
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA
91109, USA.

Patra et al. Progress in Earth and Planetary Science(2021) 8:25

Received: 2 August 2020 Accepted: 25 March 2021

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