# A top-down view of global and regional carbon budgets from an ensemble of atmospheric inversions

Auke van der Woude, Ingrid T. Luijkx, Remco de Kok, Wouter Peters, Frederic Chevallier, Christian Rödenbeck, Philippe Ciais, Naveen Chandra, Kai Wang, Rajesh Janardanan Achari, et al.

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Auke van der Woude, Ingrid T. Luijkx, Remco de Kok, Wouter Peters, Frederic Chevallier, et al. A top-down view of global and regional carbon budgets from an ensemble of atmospheric inversions. 2025. hal-05237143

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A top-down view of global and regional carbon budgets from an
ensemble of atmospheric inversions

Auke van der Woude¹, Ingrid T. Luijkx¹, Remco de Kok¹, Wouter Peters¹, Frederic Chevallier², Christian Rödenbeck³, Philippe Ciais², Naveen Chandra⁴, Kai Wang⁵, Rajesh JANARDANAN ACHARI⁶, Hella van Asperen⁷, Ana Bastos⁸, Anne-Wil van den Berg¹, A. Anthony Bloom⁹, Santiago Botía⁷, Kevin W. Bowman¹⁰, Josep G. Canadell¹¹, Rodrigo Augusto Ferreira de Souza¹², Cléo Quaresma Dias-Junior¹³, Liang Feng¹⁴, Pierre Friedlingstein¹⁵, Luciana Vanni Gatti¹⁶, Emanuel Gloor¹⁷, Kentaro Ishijima¹⁸, Fei Jiang¹⁹, Zhe Jin²⁰, Weimin Ju²¹, Xin Lan²², Junjie Liu²³, Zhiqiang Liu²⁴, T. Machida²⁵, Shamil Maksyutov²⁶, Andrew C Manning²⁷, Adrien Martinez²⁸, Girodane Martins²⁹, Kathryn McKain³⁰, John B Miller³¹, Lorna Nayagam¹⁷, Yosuke Niwa²⁶, Britton B. Stephens³², Colm Sweeney³³, Paul Palmer¹⁴, Prabir K. Patra³⁴, Penelope A Pickers³⁵, Benjamin Poulter³⁶, Steven C. C. Wofsy³⁷, Zhendong Wu³⁸, Dongxu Yang³⁹, Jeongmin Yun²³, and Ning Zeng⁴⁰

¹Wageningen University

²Laboratoire des Sciences du Climat et de l'Environnement

³Max Planck Institute for Biogeochemistry

⁴Japan Agency for Marine-Earth Science and Technology

⁵Peking University

⁶National institute for environmental studies

⁷Max-Planck-Institut für Biogeochemie

⁸Leipzig University

⁹Jet Propulsion Laboratory, California Institute of Technology

¹⁰Jet Propulsion Lab (NASA)

¹¹Global Carbon Project, CSIRO Oceans and Atmosphere

¹²Amazonas State University

¹³Federal Institute of Pará (IFPA)

¹⁴University of Edinburgh

¹⁵University of Exeter

¹⁶INPE

¹⁷Unknown

¹⁸Meteorological Research Institute

¹⁹Nanjing University

²⁰College of Urban and Environmental Sciences, Peking University, Beijing 100871, China

²¹International Institute for Earth System Science, Nanjing University

²²CIRES, University of Colorado, NOAA/ESRL/GMD

²³Jet Propulsion Laboratory

²⁴Chongqing Institute of Meteorological Science

²⁵National Institute for Environmental St.

²⁶National Institute for Environmental Studies
<sup>27</sup>Rochester Institute of Technology

<sup>28</sup>LSCE-IPSL

<sup>29</sup>Inst. Nacional de Pesquisa da Amazônia

<sup>30</sup>National Oceanic and Atmospheric Administration (NOAA)

<sup>31</sup>NOAA

<sup>32</sup>National Center for Atmospheric Research (UCAR)

<sup>33</sup>NOAA Global Monitoring Laboratory

<sup>34</sup>JAMSTEC

<sup>35</sup>University of East Anglia

<sup>36</sup>Goddard Space Flight Center

<sup>37</sup>Harvard University

<sup>38</sup>Lund University

<sup>39</sup>Institute of Atmospheric Physics, Chinese Academy of Sciences

<sup>40</sup>University of Maryland, College Park

July 29, 2025

**Abstract**

Atmospheric inversions provide surface CO2 flux estimates, based on in situ observed atmospheric CO2 mole fractions or satellite-based column average CO2 (XCO2). Results from such atmospheric inversions are extensively used in carbon cycle studies such as the Global Carbon Budget (GCB) and the Regional Carbon Cycle Assessment and Processes 2 (RECCAP2) initiative.

Here, we provide a detailed assessment of the fourteen CO2 inversions included in GCB2024. We show that the global atmospheric CO2 growth rate and its interannual variability are reproduced well by all inversions. In contrast to bottom-up models, inversions provide carbon flux estimates directly constrained by observations. Our ensemble mean estimate of the global net land sink for their common period 2015-2023 is 1.41±0.55 PgC/yr and 2.97±0.55 PgC/yr for the global net ocean sink (uncertainties reported as ±1σ estimates include a river flux adjustment to facilitate comparison to bottom-up estimates).

Furthermore, we find a significant spread in flux estimates between the inverse systems across regions, and we present criteria and metrics to assess, improve, and sub-select ensembles of inverse systems. We find that sub-selecting the ensemble based on metrics using independent observations results in improved inverse flux estimates for specific regions.

We provide fact-sheets with flux estimates for a world-wide list of land and ocean regions. Finally, we provide guidelines to assess atmospheric CO2 inversions to 1) improve inverse systems by the CO2 inverse modeling community and 2) use the inverse results in studies on global and regional carbon budgets by the wider carbon cycle community.
# A top-down view of global and regional carbon budgets from an ensemble of atmospheric inversions

A.M. van der Woude*<sup>1,1</sup>, I.T. Luijkx*<sup>1,1</sup>, R.J. de Kok<sup>1,2</sup>, W. Peters<sup>1</sup>,

F. Chevallier<sup>3</sup>, C. Rödenbeck<sup>4</sup>, P. Ciais<sup>3</sup>, N. Chandra<sup>5</sup>, K. Wang<sup>6</sup>,

R. Janardanan<sup>7</sup>, H. van Asperen<sup>4</sup>, A. Bastos<sup>8</sup>, A. van den Berg<sup>1</sup>,

A.A. Bloom<sup>9</sup>, S. Botía<sup>4</sup>, K. Bowman<sup>9</sup>, J.G. Canadell<sup>10</sup>, R.A.F. de Souza<sup>11</sup>,

C.Q. Dias-Junior<sup>12</sup>, L. Feng<sup>13,14</sup>, P. Friedlingstein<sup>15</sup>, L.V. Gatti<sup>16</sup>, E. Gloor<sup>17</sup>,

K. Ishijima<sup>18</sup>, F. Jiang<sup>19</sup>, Z. Jin<sup>20</sup>, W. Ju<sup>19</sup>, X. Lan<sup>21</sup>, J. Liu<sup>9</sup>, Z. Liu<sup>22</sup>,

T. Machida<sup>7,23</sup>, S. Maksyutov<sup>7</sup>, A.C. Manning<sup>24,25</sup>, A. Martinez<sup>3</sup>,

G.A. Martins<sup>26</sup>, K. McKain<sup>21</sup>, J.B. Miller<sup>21</sup>, L. Nayagam<sup>7</sup>, Y. Niwa<sup>7</sup>,

B.B. Stephens<sup>27</sup>, C. Sweeney<sup>21</sup>, P.I. Palmer<sup>13,14</sup>, P.K. Patra<sup>5,28</sup>,

P.A. Pickers<sup>24,29</sup>, B. Poulter<sup>9</sup>, S. Wofsy<sup>30</sup>, Z. Wu<sup>2</sup>, D. Yang<sup>31</sup>, J. Yun<sup>9</sup>,

N. Zeng<sup>32,33</sup>

*Shared first authors

<sup>1</sup>Meteorology and Air Quality, Wageningen University, Droevendaalsesteeg 3a, 6708 PB Wageningen, the Netherlands

<sup>2</sup>ICOS ERIC, Carbon Portal, Geocentrum II, Sölvegatan 12, SE-22362, Lund, Sweden

<sup>3</sup>Laboratoire des Sciences du Climat et de l'Environnement, LSCE/IPSL, CEA-CNRS-UVSQ, Université Paris-Saclay, F-91198 Gif-sur-Yvette, France

<sup>4</sup>Max Planck Institute for Biogeochemistry, Hans-Knöll-Str. 10, 07745 Jena, Germany

<sup>5</sup>Research Institute for Global Change, JAMSTEC, 3173-25 Showa-machi, Kanazawa, Yokohama, 236-0001, Japan

<sup>6</sup>Institute of Carbon Neutrality, Sino-French Institute for Earth System Science, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China

<sup>7</sup>Earth System Division, National Institute for Environmental Studies, 16-2 Onogawa, Tsukuba, Ibaraki, 305-8506, Japan

<sup>8</sup>Institute for Earth System Science and Remote Sensing, Leipzig University, 04103 Leipzig, Germany

<sup>9</sup>Jet Propulsion Laboratory and California Institute of Technology, Pasadena, CA, USA

<sup>10</sup>CSIRO Environment, Canberra, ACT 2601, Australia

<sup>11</sup>School of Technology, State University of Amazonas, 69050-020, Manaus-AM, Brazil

<sup>12</sup>Federal Institute of Pará, Physics department (IFPA), Belém, Pará, Brazil

<sup>13</sup>National Centre for Earth Observation, University of Edinburgh, EH9 3FF, UK

<sup>14</sup>School of GeoSciences, University of Edinburgh, EH9 3FF, UK

<sup>15</sup>Faculty of Environment, Science and Economy, University of Exeter, Exeter, EX4 4QF, UK

<sup>16</sup>General Coordination of Earth Science (CGCT), National Institute for Space Research (INPE), São José dos Campos, Brazil

<sup>17</sup>School of Geography, University of Leeds, Leeds, LS2 9JT, UK

<sup>18</sup>Department of Climate and Geochemistry Research, Meteorological Research Institute, 1-1 Nagamine, Tsukuba, Ibaraki, 305-0052 Japan

<sup>19</sup>Jiangsu Provincial Key Laboratory for Advanced Remote Sensing and Geographic Information

Technology, International Institute for Earth System Science, Nanjing University, Nanjing, 210023, China

<sup>20</sup>State Key Laboratory of Tibetan Plateau Earth System and Resource Environment, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing 100101, China

<sup>21</sup>Cooperative Institute for Research in Environmental Sciences, CU Boulder and NOAA Global Monitoring Laboratory, Boulder, USA

<sup>22</sup>CMA Key Open Laboratory of Transforming Climate Resources to Economy, Chongqing Institute of Meteorological Sciences, Chongqing, 401147, China

<sup>23</sup>Seto Inland Sea Carbon Neutral Research Center, Hiroshima University, Higashi-Hiroshima, Hiroshima, 739-8529 Japan

<sup>24</sup>Centre for Ocean and Atmospheric Sciences, School of Environmental Sciences, University of East Anglia, Norwich NR4 7TJ, UK

<sup>25</sup>National Technical Institute for the Deaf, Rochester Institute of Technology, Rochester, NY, USA

<sup>26</sup>Fundação Amazônica de Defesa da Atmosfera, Brazil

<sup>27</sup>National Center for Atmospheric Research, Boulder, CO, USA

<sup>28</sup>Hiroshima University, Higashi-Hiroshima 739-8529, Japan

<sup>29</sup>National Centre for Atmospheric Science, University of East Anglia, Norwich, NR4 7TJ, UK

<sup>30</sup>Department of Earth and Planetary Sciences, Harvard University, USA

<sup>31</sup>Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

<sup>32</sup>Earth System Science Interdisciplinary Center, University of Maryland, College Park, MD 20740, USA
**Key Points:**

* Global atmospheric CO₂ inversions estimate carbon fluxes that reflect the atmospheric CO₂ growth rate and its year-to-year variability well.

* We find global net land and ocean sinks of 1.41±0.53 PgC yr⁻¹ and 2.97±0.53 PgC yr⁻¹, respectively, for 2015-2023.

* Regionally, we improve our flux estimates by sub-selecting inversions using independent CO₂ mole fraction observations.

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<footnote>Corresponding author: Auke van der Woude, auke.vanderwoude@wur.nl</footnote>

<footnote>Corresponding author: Ingrid Luijkx, ingrid.luijkx@wur.nl</footnote>
**Abstract**

Atmospheric inversions provide surface CO₂ flux estimates, based on in situ observed atmospheric CO₂ mole fractions or satellite-based column average CO₂ (XCO₂). Results from such atmospheric inversions are extensively used in carbon cycle studies such as the Global Carbon Budget (GCB) and the REgional Carbon Cycle Assessment and Processes 2 (RECCAP2) initiative.

Here, we provide a detailed assessment of the fourteen CO₂ inversions included in GCB2024. We show that the global atmospheric CO₂ growth rate and its interannual variability are reproduced well by all inversions. In contrast to bottom-up models, in- versions provide carbon flux estimates directly constrained by observations. Our ensem- ble mean estimate of the global net land sink for their common period 2015-2023 is 1.41±0.55 PgC yr⁻¹ and 2.97±0.55 PgC yr⁻¹ for the global net ocean sink (uncertainties reported as ±1σ; estimates include a river flux adjustment to facilitate comparison to bottom-up estimates).

Furthermore, we find a significant spread in flux estimates between the inverse sys- tems across regions, and we present criteria and metrics to assess, improve, and sub-select ensembles of inverse systems. We find that sub-selecting the ensemble based on metrics using independent observations results in improved inverse flux estimates for specific re- gions.

We provide fact-sheets with flux estimates for a world-wide list of land and ocean regions. Finally, we provide guidelines to assess atmospheric CO₂ inversions to 1) im- prove inverse systems by the CO₂ inverse modeling community and 2) use the inverse results in studies on global and regional carbon budgets by the wider carbon cycle com- munity.

**Plain Language Summary**

Keeping global temperature rise well below 2°C, and pursuing efforts to limit it to 1.5°C, requires monitoring the greenhouse gases balance in the atmosphere. Carbon diox- ide (CO₂) contributes the most to global warming, and is emitted by fossil fuel combus- tion and land-use change, and taken up by the global land biosphere and the ocean. The Global Carbon Project (GCP) annually reports on global CO₂ sources and sinks using process-based models and ocean data products. Furthermore, atmospheric inversions pro- vide biosphere and ocean CO₂ flux estimates based on atmospheric CO₂ observations. In this paper, we present results from an ensemble of 14 inverse systems on both global and regional scales. We show that all atmospheric inversions close the carbon budget well on a global scale, but regional differences exist and the relative contributions of the land and ocean sinks to the total CO₂ uptake is uncertain. We explore which regions contribute the most to these uncertainties. We also present metrics to assess the strengths and weak- nesses of the inverse systems. Finally, we provide guidelines for using atmospheric in- versions in future studies.

**1 Introduction**

To limit global warming to well below 2°C and preferably 1.5°C, as agreed in the United Nations Framework Convention on Climate Change (UNFCCC)'s Paris Agree- ment, parties have committed to reducing greenhouse gas emissions. The collective progress towards these pledged emission reductions is assessed in Global Stocktakes (GST) ev- ery 5 years. These GSTs are based on national greenhouse gas inventories (NGHGIs) for emissions and removals of greenhouse gases (IPCC, 2019). The first GST took place at the 28th UNFCCC Conference of the Parties in 2023, and the next round of climate
action plans (nationally determined contributions, NDCs) will be submitted in 2025 (Deng et al., 2022, 2025).

Global and regional greenhouse gas budgets established by the research community provide additional information on global and regional sources and sinks and can be used in these greenhouse gas assessments. These are for example provided through the annually updated Global Carbon Budgets (GCB, Friedlingstein et al. (2025)), and regionally in the REgional Carbon Cycle Assessment and Processes 2 project (RECCAP2, e.g. Poulter et al. (2022); Ciais et al. (2022); Lauerwald et al. (2024); Ernst et al. (2024); X. Wang et al. (2024); Murray-Tortarolo et al. (2024); Villalobos et al. (2023); Hauck et al. (2023); Hugelius et al. (2024)). Such budgets combine information from observations, inventories, bookkeeping models, process-based models, and atmospheric inversions. In some countries (e.g. Switzerland and the UK, and most recently the Netherlands), estimates from regional atmospheric inversions for certain greenhouse gases are included as validation alongside the NGHGIs in their national reporting (Perugini et al., 2021) and thereby play an increasingly important role in emission reduction strategies.

Atmospheric CO₂ inversions quantify carbon sources and sinks based on atmospheric observations of the CO₂ mole fractions from monitoring stations around the world and/or from satellite-based column-averaged CO₂ (XCO₂) (e.g. Enting (2002)). Typically, inverse systems assume that fossil fuel emissions are well known, allowing optimization of the net land and ocean exchange. For this, atmospheric transport models are used with horizontal resolutions between 4°×5° and 1°×1° globally, or higher for regional systems. In contrast to bottom-up carbon budgets, which are composed of separate exchange estimates for each carbon reservoir from process models, ocean exchange data products, inventories, and bookkeeping models, atmospheric inversions by design close the atmospheric carbon budget, since they match atmospheric CO₂ observations as well as their growth rate. Inversions therefore inherently do not have a remaining budget imbalance, like bottom-up budgets do (Friedlingstein et al., 2025). Therefore, atmospheric inversions are complementary to and can serve as validation for bottom-up budgets and process models by identifying discrepancies between bottom-up and top-down approaches (e.g. Gurney et al. (2002); Peylin et al. (2013); Bastos, O'Sullivan, et al. (2020)).

In recent decades, several groups around the world have developed atmospheric inverse CO₂ systems. Intercomparison efforts have allowed them to be further improved over the years (e.g. Peylin et al. (2013); Gurney et al. (2002)). Special focus has been on improving the different atmospheric transport models used by the inverse systems (e.g. Gurney et al. (2003); Law et al. (1996); Schuh et al. (2019)). Independent atmospheric observations, such as those from aircraft, have allowed for assessment of the quality of the inverse estimates (e.g. Stephens et al. (2007); Gaubert et al. (2019); Long et al. (2021)). These independent evaluations showed that global atmospheric inversions provide robust estimates of carbon fluxes on a global scale, as well as in certain regions such as the Southern Ocean (Long et al., 2021). Recently, atmospheric CO₂ inversions also make use of satellite data products, which provide additional observational constraints next to the surface network (Byrne et al., 2023; Crowell et al., 2019; Peiro et al., 2022; Deng et al., 2025).

With the growing number of inverse systems and their further development to include more sets of observations and cover longer time-periods, new comparisons between them, and further methods to determine their strengths and weaknesses are of increasing importance. Therefore, in this paper, we present an assessment of the ensemble of fourteen global CO₂ inverse systems used in the latest GCB (Friedlingstein et al. (2025), hereafter GCB2024). We first present the derived land and ocean flux estimates and their trends. We start at the global scale and then analyze the flux estimates in the different extended RECCAP2 regions. Furthermore, we introduce independent metrics to evaluate the inverse results, allowing the comparison of the inverse systems on different spatial and temporal scales. Using these metrics, we provide tools for the community to use
our inverse flux estimates in future studies, such as on global and regional carbon bud-
gets. Furthermore, through our inversions, we provide insights into the atmospheric com-
ponent in the global carbon budget by analyzing the calculation of the atmospheric growth
rate. The goals of this paper are twofold: 1) to provide tools for inverse modelers to com-
pare their results, also to facilitate improvements of the systems, and 2) to provide guide-
lines to other users of our inverse results in the wider carbon cycle research community,
including future contributors and users of GCB, RECCAP and the GST. These guide-
lines include special emphasis on selecting inverse systems based on their performance
on independent metrics to derive improved flux estimates for a specific region, as well
as the need for adjustments (e.g. for river fluxes) to allow fair comparison between top-
down and bottom-up methods.

**2 Methods**

In this section, we first introduce atmospheric inversions in general, and then high-
light the philosophies or key ideas behind each of the systems in the GCB2024 ensem-
ble. Subsequently, we discuss the post-processing of the inverse flux estimates as well as
the analysis methods used in this work.

**2.1 Introduction to atmospheric inversions**

Atmospheric inversions provide estimates of CO₂ surface fluxes (sources and sinks) by assimilating atmospheric observations. They adjust a first guess (prior) estimate of fluxes using atmospheric observations through Bayesian mathematics, resulting in optimized or posterior flux estimates. For CO₂, atmospheric inversions typically work with three main flux components: fossil fuel emissions, ocean exchange, and terrestrial biosphere exchange (either separately considering natural fluxes and land-use change or biomass burning emissions or their net total). In all CO₂ inverse systems currently participating in GCP, fixed fossil fuel emissions are prescribed since their relative uncertainties are smaller compared to the other components in the budget, on the timescales considered. Some systems also separately prescribe fixed land-use change or biomass burning emissions, while others include these emissions in a total land exchange term to be optimized. All atmospheric CO₂ inversions result in net land and ocean flux estimates.

The prior flux fields are transported using atmospheric transport models, result-
ing in simulated CO₂ mole fractions. These are compared to observed CO₂ mole frac-
tions, and the differences between these simulated and observed CO₂ values are mini-
mized by adjusting the prior flux estimates, using Bayesian techniques and a cost func-
tion, taking into account the uncertainties assigned to the prior flux estimates and the
observations. These techniques are extensively described in the literature (e.g. Enting
(2002); Tarantola (2005)). Different data assimilation techniques exist, including the en-
semble Kalman filter (Evensen, 2009) and variational approaches (Courtier et al., 1994),
including the conjugate gradient method (L. R. Taylor et al., 1987).

Atmospheric CO₂ observations are fundamental to atmospheric inversions. The global network of *in situ* stations, operated by many laboratories around the world, provide their observations in collaborative ObsPack (Observational Package) products (Masarie et al., 2014), e.g. Schuldt et al. (2023), or data can be directly provided by station PIs or the World Data Centre for Greenhouse Gases (WDCGG), which is part of the Global Atmosphere Watch (GAW) programme of the World Meteorological Organization (WMO). Surface CO₂ observations consist of continuous *in situ* measurements and (often weekly) flask samples analyzed in laboratories. These observations are collected on different platforms, including (tall) towers (e.g. Andrews et al. (2014); Heiskanen et al. (2022)), aircraft (e.g. Sweeney et al. (2015); Machida et al. (2008)), ships (e.g. (Wanninkhof et al., 2019)) and AirCore (e.g. Karion et al. (2010)). Furthermore, satellite-derived column-averaged CO₂ (XCO₂) provide a space-based view of atmospheric CO₂ from different
instruments, including the Orbiting Carbon Observatory (OCO-2 and OCO-3) (Crisp et al., 2017) and the Greenhouse Gases Observing Satellite (GOSAT, Yokota et al. (2009)).

## 2.2 GCB2024 ensemble of CO₂ inversions

In this study, we analyze the results from an ensemble of fourteen atmospheric CO₂ inversions included in the GCB2024 (Friedlingstein et al., 2025). The number of inversions contributing to GCB has steadily grown over the past decade. Up to now, the selection of systems has been based mostly on the match to the atmospheric growth rate and independent aircraft CO₂ mole fraction observations. In this paper, we develop and present further metrics to assess the quality of the inversions (see Section 2.4).

The inverse results in our ensemble are provided by each group according to a protocol that is distributed to participating and interested groups, and are quality-controlled jointly by the contributing groups. The quality-control consists of different metrics which we further develop in this paper, including e.g. a comparison to the CO₂ growth rate and to independent aircraft observations (Friedlingstein et al., 2025). The output includes monthly averaged flux estimates (Luijkx et al., 2024), as well as simulated mole fractions (A. van der Woude et al., 2025) for observation points included in two ObsPack products (in GCB2024: CO₂ GLOBALVIEWplus v9.1 and near-real time (NRT) v9.2) (Schuldt et al., 2023, 2024). A map of the sites is shown in Figure C1. Inverse modelers individually design their preferred setups, and therefore the systems cover a range of different transport models with their meteorological forcing data, prior flux estimates, data assimilation techniques, and assimilated observations (see Table 1 for a summary of the setups and Appendix A for complete overview). The assimilated observations include near-surface observations, based on both flask samples and continuous *in situ* measurements (which we refer to here as ‘*in situ*’) and satellite-based column average CO₂ (XCO₂) (which we refer to as ‘satellite’; generally, the viewing modes Land Nadir and Land Glint are used, and Ocean Glint is not used, see e.g. Peiro et al. (2022)). In the next sections, we provide background information on each inverse modeling system in the ensemble, mainly focusing on the philosophy of their design. Note that CAMS and CAMS-Satellite are described together, as are UoE and IAPCAS, given the similarities in their respective designs.

### 2.2.1 Jena CarboScope (r76nbetEXToc_v2024E)

The Jena CarboScope inverse system specifically targets capturing interannual and decadal variability in CO₂ fluxes, and their relationship to environmental drivers. Therefore, it runs over a multi-decadal period (60+ years) and takes special precautions against spurious variations due to the steep increase in observational coverage over time. In the CarboScope run r76nbetEXToc_v2024E used in the GCB2024 ensemble, a two-stage approach was used: in a first inversion run, 173 *in situ* CO₂ measurement records were used to estimate the relationship between interannual anomalies in net biome exchange (NBE) of CO₂ and in air temperature (Rödenbeck et al., 2018). In a second run, interannual variations not captured by the temperature regression were added explicitly based on a selection of 8 measurement records that completely span the 1976-2023 period of this run. Given the limited capabilities of atmospheric inversions to separate land and ocean signals (discussed later in this study in Section 3.2.1), the ocean CO₂ exchange was not estimated by the atmospheric data, but in a previous step from interpolated surface-ocean pCO₂ data and a gas exchange parameterization ('CarboScope oc v2024E', Rödenbeck et al. (2013, 2022)).
### 2.2.2 Copernicus Atmosphere Monitoring Service (CAMS and CAMS-Satellite)

CAMS and CAMS-Satellite refer here to the CO₂ atmospheric inversion system of the European operational Copernicus Atmosphere Monitoring Service (https://atmosphere.copernicus.eu/, last access 13-03-2025). This system (Chevallier et al., 2005) produces two types of CO₂ inversions for the Copernicus Atmosphere Data Store on a regular basis: one driven by air-sample measurements (the inversion called CAMS hereafter is version v23r1 in this series) and one driven by OCO-2 column retrievals (the inversion called CAMS-Satellite hereafter is version FT24r1 in this series). Each inversion product results from the application of Bayes' theorem to a single inversion window (a decade for CAMS-Satellite, 4.5 decades for CAMS), thereby ensuring long-term consistency, both physically and statistically. Because of the single window, observations at the end of the simulation period are directly linked to fluxes at the beginning of the simulation period. This results in higher sensitivity to 'remote' fluxes (i.e. fluxes from under-observed regions). Therefore, the CAMS systems aim to better constrain long-term carbon fluxes.

### 2.2.3 CarbonTracker Europe (CTE2024)

CarbonTracker Europe (CTE) (Van der Laan-Luijkx et al., 2017; Peters et al., 2005) optimizes weekly net ecosystem exchange and ocean fluxes using *in situ* observations. The optimization is done using a 5-week lagged ensemble Kalman smoother. CTE is designed to optimally use the available data at synoptic scales. The fluxes are scaled on a 1°x1° horizontal resolution over the Northern Hemisphere, where the observational density is high, and over larger scale 'ecoregions' in the rest of the world. Due to these choices on the resolution and the relatively short window, CTE performs best for mid-latitude biosphere flux estimates on synoptic temporal scales.

### 2.2.4 NISMON

The Nonhydrostatic ICosahedral Atmospheric Model (NICAM)-based Inverse Simulation for Monitoring CO₂ (NISMON-CO₂) (Niwa, Fujii, et al., 2017; Niwa et al., 2022) uses the four-dimensional variational method with the atmospheric transport model NICAM-TM (Niwa, Tomita, et al., 2017). In NISMON-CO₂, fluxes are optimized in a 1°×1° latitude-longitude space, though atmospheric transport is simulated at the larger grids of NICAM (they are hexagon-pentagon shaped, and the mean grid interval is 223 km), so that spatial information of the prior flux estimates originally have is retained. For terrestrial biosphere flux estimates, NISMON-CO₂ separately optimizes monthly means of gross primary production (GPP) and respiration (Re), while applying 3-hourly scaling factors to those GPP and Re means, respectively, to account for predominantly large diurnal flux variations over land. To efficiently find an optimal state for a long-term period, NISMON-CO₂ performs several inversions for different periods with some years overlapping in parallel. Then a final inversion is performed for the whole target period with smaller number of iterations to constrain flux estimates consistently with long-term variations of observed mole fractions.

### 2.2.5 CT-NOAA

CarbonTracker (referred to in this paper as CarbonTracker-NOAA in order to distinguish it from its European counterpart CarbonTracker Europe (CTE)) is a quasi-operational analysis of atmospheric CO₂ produced at the NOAA Global Monitoring Laboratory. CarbonTracker-NOAA consists of intermittent full reanalyses released with a periodicity of 1-5 years, and near-real time simulations (CT-NRT) designed to extend a full reanalysis until more recent dates. CarbonTracker was introduced in 2007 by Peters et al. (2007), and has been continuously improved and updated since that time with updates documented at https://gml.noaa.gov/modeling.html (last access 26-05-2025). Among the most significant changes
since the original CarbonTracker configuration are increases in lateral and vertical resolution, extension of the assimilation window from 5 to 12 weeks, assimilation of a wider variety of measurements enabled by the use of an "adaptive" model-data mismatch model, and use of multiple flux prior models. The simulations being used in the current work are the CT2022 release (Jacobson, Schuldt, Tans, Arlyn Andrews, et al., 2023) extended by the CT-NRT.v2023-3 (Jacobson, Schuldt, Tans, Andrews, et al., 2023a) update. For CT2022 multiple prior models are used, with the results being the mean of the two sets of optimized flux estimates. CT-NRT.v2023-3 used one prior model, built on the climatology of CT2022 optimized flux estimates augmented by a statistical flux anomaly model driven by anomalies of shortwave radiation, temperature, and precipitation.

### 2.2.6 CMS-Flux

The Carbon Monitoring System Flux (CMS-Flux) optimizes monthly NBE and ocean carbon fluxes at 4°x5° grid resolution with a 4D-Var inversion system (J. Liu et al., 2021). The underlying transport model is GEOS-Chem driven by MERRA-2 reanalysis. CMS-Flux assimilates *in situ* CO₂ observations as well as satellite observations from ACOS-GOSAT and OCO-2 (V10). The flux inversion spans from January 2010 to December 2023 and is conducted in four temporal segments, each approximately four years in length, with one-year overlaps between adjacent segments to mitigate the influence of initial conditions. The inversion system uses prior biosphere fluxes from CARDAMOM (Bloom et al., 2020), and prior ocean fluxes from either ECCO-Darwin (Carroll et al., 2020) or MOM6 (Liao et al., 2020). The final inversion estimates are the mean of two separate flux versions, each using either one of the two ocean priors.

### 2.2.7 GONGGA

The GONGGA inversion system optimizes net ecosystem exchange and ocean fluxes constrained by OCO-2 column retrievals (Z. Jin et al., 2024a). The fluxes are optimized at a 2° latitude × 2.5° longitude resolution, using a hybrid data assimilation method that integrates the strengths of the four-dimensional variational (4DVar) method and ensemble Kalman filter (EnKF). GONGGA adopts a two-week inversion window, within which initial CO₂ concentrations and surface fluxes are optimized successively to help distinguish model-data mismatches arising from errors in initial concentrations and surface flux estimates. Due to the relatively short window and the strong constraints from satellite retrievals, GONGGA aims at better estimates of seasonal and interannual variations of CO₂ fluxes.

### 2.2.8 COLA

COLA is an ensemble-based system which aims at assimilating both surface and satellite CO₂ observations and estimating the daily gridded carbon fluxes with low computation costs. COLA applies a short assimilation window of 1 day and a long observation window of 7 days. Unlike most inversion systems, COLA updates both fluxes and the atmospheric CO₂ concentration. COLA applies a constrained ensemble Kalman filter (CEnKF) to ensure the global mass balance (Z. Liu et al., 2022). Since atmospheric CO₂ is a long-lived species, and the surface CO₂ observation network is sparse in the tropics and the Southern Hemisphere, the added information from OCO-2 plays an important role in COLA.

### 2.2.9 GCAS

The Global Carbon Assimilation System, version 2 (GCASv2, subsequently referred to as GCAS) optimizes weekly net ecosystem exchange and ocean fluxes using satellite XCO₂ retrievals and the ensemble root-mean-square filtering (EnSRF) algorithm (Jiang
et al., 2021). It uses the MOZART-4 model for atmospheric transport simulations, which runs at 1.875° × 2.5° horizontal resolution and 56 vertical layers, and is driven by the GEOS-5 meteorological fields. In each data assimilation window (1 week), the prior flux estimates are independently perturbed with a Gaussian random distribution at a resolution of 3° × 3°, a 'two-step' strategy is applied to ensure mass conservation between flux and concentration changes, and a 'super-observation' approach is adopted to reduce the representativeness error of observations. GCAS was run from Sep 2014 to Jan, 2024, with the first 4 months are considered as a spin-up run, and the fossil fuel and wildfire emissions are fixed during the inversion.

### 2.2.10 UoE and IAPCAS

The University of Edinburgh (UoE) and Institute of Atmospheric Physics Carbon Inversion System (IAPCAS) systems are highly similar in design and are therefore described together here. These systems use an ensemble transform Kalman filter (ETKF) data assimilation method (Feng et al., 2009; D. Yang et al., 2021), and the GEOS-Chem global chemistry transport model (v12.5 in GCB2024) driven by MERRA2 meteorological re-analyses running at a spatial resolution of 4° × 5° (IAPCAS) or 2° × 2.5° (UoE), with 47 vertical levels. The main difference between the two systems is that IAPCAS uses an improved approach to generate the flux perturbation ensemble, and has a larger model error. The regional monthly CO₂ fluxes for 496 (IAPCAS) and 476 (UoE) regions are optimized in the CO₂ inversion. The assumed error correlation on the prior flux estimates over these sub-regions have a correlation length of 400 km for land sub-regions and 800 km for oceanic regions, respectively.

Due to sparse observation coverage and limitations in prior inventories, a relatively long lag window of four months was applied. To mitigate over-constraining by continuous observations, which are also frequently influenced by local emissions, UoE and IAPCAS assimilate their daytime means and exclude observations that deviated significantly from model forecasts (i.e. deviations greater than four times the corresponding observational uncertainty). Additionally, to address the geographic imbalance of constraints, further filtering was planned to reduce the number of assimilated continuous sites over North America and Europe, so that only high-quality sites with low variability and well-defined seasonal cycles would be used in the assimilation. However, an implementation issue in the current experiments (GCB2024) prevented this approach from being fully realized in both systems. Despite this, their flux estimates in GCB2024 remain a valid ensemble member, based on both the initial quality control in the GCB2024 process and the analysis in this manuscript. In a future version (likely GCB2025) these systems will resolve this issue, preliminary analysis shows that larger scale patterns (e.g. latitude bands) will not change much, but on a regional level (e.g. East Asia) differences can be significant.

### 2.2.11 MIROC4 (MIROC)

The MIROC4 inversion system optimizes the monthly net ecosystem exchange over 54 land regions and ocean fluxes over 30 oceanic regions using *in situ* surface observations (Chandra et al., 2022). Only sites with minimal (≤6 months) data gaps are included in the inversion. Fluxes are optimized with a time-dependent Bayesian approach over a single 25-year window, ensuring robust long-term carbon flux constraints (Chandra et al., 2022). The underlying atmospheric general circulation model (AGCMs)-based chemistry-transport model (ACTMs) is an online CTM of the JAMSTEC institute (MIROC4-ACTM; T42 × 67 hybrid vertical layers; (Patra et al., 2018)), which is nudged with JRA-55 re-analysis. Large-scale transport and Brewer-Dobson circulation in MIROC4-ACTM are validated using SF₆ and CO₂-derived age of air (Bisht et al., 2021; Patra et al., 2018). Note that the MIROC4-ACTM inversion has a relatively coarse resolution due to the lack of measurements in many of the inversion basis regions outside Europe, North America.
ica and East Asia. The model also uses a relatively small number of fixed sites to avoid observational data gaps for deriving consistent interannual variations across different decades. If the site numbers with valid measurements vary with time the regional flux variations are affected by the gaps in atmospheric data. Because the forward transport simulations are also performed at about 2.8° × x 2.8° horizontal resolution, the transport does not have sufficient representativeness for the continental sites near sharp emission gradients, thereby limiting our ability to include more sites in the inversion system.

### 2.2.12 NTFVAR

The NTFVAR variational flux inverse modeling system (Maksyutov et al., 2021; Nayagam et al., 2024, 2025) is built upon the coupled transport model NIES-TM-FLEXPART, which integrates both Eulerian (NIES-TM; Maksyutov et al., 2008) and Lagrangian (FLEX-PART; Stohl et al. (2005)) models. Including a Lagrangian model provides a refined representation of near-field transport during the three days leading up to the observation event. Coupling a medium-resolution Eulerian model with a high-resolution Lagrangian model helps to better represent the impact of local flux heterogeneity, in principle allowing the model to use the full resolution of meteorological reanalysis data at much lower computational cost than the fully Eulerian models. The high-resolution atmospheric transport in the global CO₂ flux inversions is expected to reduce flux noise originating from the forward transport modeling errors especially downwind of large emitters at continental locations and at coastal sites impacted by strong flux gradients. The model represents the land surface fluxes by optimizing the ecosystem respiration and produces the scaling factors at a biweekly timestep, which accounts for the large-scale flux variations. Besides, the combined use of surface and satellite observations helps resolving the regional land fluxes in the data-sparse regions (Nayagam et al., 2025).

## 2.3 Flux post-processing and adjustments

For a direct comparison of the net inverse land and ocean fluxes estimated by the fourteen systems, we adjust them for small remaining differences in the input fossil fuel emissions (Peylin et al., 2013). Most systems use fossil fuel emissions from the Gridded Fossil Emissions Dataset (GridFEDv2024.0 (Jones et al., 2024)), which is also used in Friedlingstein et al. (2025). Where needed, we have adjusted the resulting land carbon flux estimates to account for differences between GridFEDv2024.0 and the fossil fuel emissions used by the systems not using GridFEDv2024.0 (provided also in Luijkx et al. (2024)). GridFEDv2024.0 also includes cement CO₂ emissions and the cement carbonation sink, and this is also accounted for in the adjustment for systems that used other products. The total adjustment (applied on the land flux variable) is typically smaller than 0.2 PgC yr⁻¹ on the global scale. Note that a small fraction of this fossil fuel adjustment is present above the ocean, when the system's fossil fuel emissions deviate from GridFED (e.g. along ship and aircraft tracks).

Furthermore, when comparing our inverse estimates to bottom-up estimates (from land and ocean process models), we apply a second adjustment to our inverse net land and ocean flux estimates to account for the riverine outflow of carbon to the oceans, following the definitions in Friedlingstein et al. (2025) and Hauck et al. (2020). This 'river flux adjustment' removes the pre-industrial ocean source of CO₂ to the atmosphere of 0.65±0.3 PgC yr⁻¹ from river input to the ocean (Regnier et al., 2022) to satisfy the GCB's definition of the ocean sink (SOCEAN, Hauck et al. (2020). Therefore, the adjusted inverse net land flux estimates become smaller and represent the part of the net uptake of CO₂ by vegetation and soils that is not exported by rivers. The adjusted inverse ocean flux estimates become larger (i.e. higher uptake) by the same amount, and now include the river inflow of carbon, and represents the net uptake of anthropogenic CO₂, which is similar to the ocean models' estimates (Friedlingstein et al., 2025). Next to this river flux adjustment, further lateral adjustments can be considered, such as from harvest and
<table><caption>**Table 1.** Summary of the individual inversion setups, including the assimilated observations (*in situ* (IS) or satellite (Sat, subscripts indicates GOSAT (g) or OCO-2 V11 (o)). Only the land nadir and land glint viewing modes are used, and ocean glint is not used (due to uncharacterised biases)), the used transport model with resolution, prior biosphere and ocean flux estimates, and spatiotemporal resolution of the optimization. Further details are provided in the Supplement (Table Appendix A)</caption><thead><tr><th>System</th><th>Observations</th><th>Transport model</th><th>Prior flux estimates</th><th>Flux optimizing resolution</th><th>Reference</th></tr></thead><tbody><tr><td>CarboScope</td><td>in situ</td><td>TM3<br>3.83x 5°</td><td>Zero (land)<br>CarboScope oc-v2024E (not opt.)</td><td>Monthly<br>2°x 2.5°</td><td>Rödenbeck et al. (2018)</td></tr><tr><td>CAMS</td><td>in situ</td><td>LMDZv6<br>~90 km hexagons</td><td>ORCHIDEE<br>CMEMS-LSCE-FFNN 2024</td><td>Weekly<br>Gridded</td><td>Chevallier et al. (2005)</td></tr><tr><td>CTE</td><td>in situ</td><td>TM5<br>global 2°x3°, Europe/North Am. 1°x1°</td><td>SiB4<br>CarboScope oc-v2024E</td><td>Weekly,<br>1°x 1°(NH), Ecoregion (SH)</td><td>Van der Laan-Luijkx et al. (2017)</td></tr><tr><td>NISMON</td><td>in situ</td><td>NICAM-TM<br>~ 223 km</td><td>VISIT<br>JMA Ocean mapping</td><td>Mean + 3-hourly<br>1°x1°</td><td>Niwa et al. (2022)</td></tr><tr><td>CT-NOAA</td><td>in situ</td><td>TM5<br>global 2°x3°, Europe/North Am. 1°x1°</td><td>Multiple,<br>see Sect. 2.2.5</td><td>Weekly,<br>Ecoregions</td><td>Jacobson, Schuldt, Tans, Andrews, et al. (2023b)</td></tr><tr><td>CMS-Flux</td><td>Sat<sub>o+g</sub> + IS</td><td>GEOS-Chem<br>4°x5°</td><td>CARDAMOM<br>ECCO-Darwin and MOM6</td><td>Monthly,<br>4°x5°</td><td>J. Liu et al. (2021)</td></tr><tr><td>CAMS-Sat</td><td>Sat<sub>o</sub></td><td>LMDZv6<br>~90 km hexagons</td><td>ORCHIDEE<br>CMEMS-LSCE-FFNN 2024</td><td>Weekly<br>Gridded</td><td>Chevallier et al. (2005)</td></tr><tr><td>GONGGA</td><td>Sat<sub>o</sub></td><td>GEOS-Chem<br>2°x2.5°</td><td>ORCHIDEE-MICT<br>Takahashi climatology</td><td>Bi-weekly,<br>2°x2.5°</td><td>Z. Jin et al. (2024b)</td></tr><tr><td>COLA</td><td>Sat<sub>o</sub> + IS</td><td>GEOS-Chem<br>2°x2.5°</td><td>VEGAS<br>Jena OC-v2023</td><td>Daily,<br>2°x2.5°</td><td>Z. Liu et al. (2022)</td></tr><tr><td>GCAS</td><td>Sat<sub>o</sub></td><td>MOZART-4<br>2.5°x1.875°</td><td>BEPS<br>JMA Ocean mapping</td><td>Weekly,<br>3° x 3°</td><td>Jiang et al. (2021)</td></tr><tr><td>UoE</td><td>in situ</td><td>GEOS-Chem<br>2°x2.5°</td><td>CASA (clim)<br>Takahashi climatology</td><td>Monthly,<br>302 land and 176 ocean region</td><td>Palmer et al. (2019)</td></tr><tr><td>IAPCAS</td><td>in situ</td><td>GEOS-Chem<br>4°x5°</td><td>CASA (clim)<br>Takahashi climatology</td><td>Monthly,<br>496 regions</td><td>Feng et al. (2016); D. Yang et al. (2021)</td></tr><tr><td>MIROC</td><td>in situ</td><td>MIROC4-ACTM<br>2.8°x2.8°</td><td>CASA<br>Takahashi climatology</td><td>Monthly<br>54 land and 30 ocean regions</td><td>Chandra et al. (2022); Patra et al. (2018)</td></tr><tr><td>NTFVAR</td><td>Sat<sub>g</sub> + IS</td><td>NIES-TM-Flexpart<br>3.75x3.75°; 0.1x0.1°</td><td>Zeng et al. (2020)<br>Zeng et al. (2014)</td><td>Biweekly<br>0.2 x 0.2°</td><td>Maksyutov et al. (2021); Nayagam et al. (2024)</td></tr></tbody></table>
trade or crops and wood products (Ciais et al., 2022; Deng et al., 2025; Hauck et al., 2020),
but we have not applied them in this work.

In our analyses in this study, we develop metrics based on the simulated CO₂ mole
fractions that are the result of the atmospheric transport of the total fluxes. We there-
fore only apply the ‘river flux adjustment’ when comparing posterior flux estimates to
bottom-up estimates in Section 3.1.3. Note that when using these flux estimates in com-
parison to bottom-up models, this adjustment always needs to be applied on both global
and regional scales. We provide further guidelines on the use of these adjustments in Sec-
tion 5.

## 2.4 Analyses

We use the unified, fossil fuel and cement adjusted (see Section 2.3), monthly mean inverse flux estimates provided by Luijkx et al. (2024) for GCB2024. The inverse systems using satellite-retrievals from OCO-2 start at the end of 2014 since that is when these observations became available (GOSAT retrievals started in 2009). As all inversions cover at least the period from 2015 up to and including 2023, we performed our analyses for this period, unless specified otherwise. Throughout this paper, we use a unified color scheme for each inversion. Throughout our analyses, we compare *in situ* to satellite driven inversions. Note that each inversion was free in setting up the systems, and therefore this grouping between *in situ* and satellite systems is not as strict as in e.g. (Byrne et al., 2023). When applicable, satellite systems are indicated by diagonal hatching (bar plots) or an ‘x’ (scatter plots); *in situ* systems are shown without hatching (bar plots) or are indicated by a ‘●’ (scatter plots). Systems that optimize both satellite and *in situ* observations are indicated with crossed hatching and a ‘∧’. When grouped, satellite systems are shown in dark red and *in situ* systems in teal.

In our analyses, the total net land sink is the sum of the natural land sink (i.e. biogenic uptake) and the fire and land-use change emissions. Unless specified otherwise, negative fluxes indicate uptake of CO₂ and positive fluxes indicate net emissions, sinks by definition represent uptake and are indicated with a positive number in the text. We analyze flux estimates for several regions, using an extended version the RECCAP2 mask (Chandra et al., 2022).

### 2.4.1 Atmospheric CO₂ observations

All inverse systems have reported simulated atmospheric CO₂ mole fractions sampled at *in situ* measurement locations and times based on their posterior flux estimates using their respective transport model. We analyze the simulated CO₂ mole fractions for years in which all inversion systems provide data (2015-2023). We base our analyses on the observations from the ObsPack products versions GLOBALVIEWplus v9.1 and near-real time (NRT) v9.2 (Schuldt et al., 2023, 2024; ICOS RI et al., 2023), which include 617 and 236 datasets respectively. In our analyses, we compare simulated and observed CO₂ mole fractions from both assimilated and not-assimilated (independent) data sets. The simulated mole fractions from all systems, including assimilated/independent flags, are available from (A. van der Woude et al., 2025).

### 2.4.2 Global CO₂ growth rate

Global inversions are by design expected to reproduce the atmospheric global growth
rate, i.e. the annual increase in the global mean atmospheric CO₂ mole fraction, as de-
rived from a selection of surface stations. As a first assessment of the inversions’ qual-
ity, we therefore compare the global growth rate of the simulated CO₂ mole fractions with
a global growth rate derived from observations. In practice, it is not trivial to determine
a global mean growth rate from observations, due to the limited coverage of the avail-
able in situ CO₂ measurements. In our analysis, we applied the method of Wu et al. (2024) to determine the global mean growth rate from measured surface CO₂ mole fractions between 2015-2023, as well as from simulated mole fractions at the same sites for all inverse systems. The code of Wu et al. (2024) is freely available and allows for our own selection of data. The method of Wu et al. (2024) is similar to that used by National Oceanic and Atmospheric Administration's Global Monitoring Laboratory (NOAA GML) (Lan et al., 2025), and applies a filtering of the CO₂ mole fraction time series to remove short-term variability. The growth rates for each site are averaged in 30° latitude bins, and then combined with a weight according to the area of the latitude bin to obtain a global mean growth rate (Wu et al., 2024). We use the NOAA selection of marine boundary layer (MBL) sites for our calculation, but instead of extrapolating data to periods without data, we exclude sites that have data coverage for less than half of the period of 2015-2023 or that do not have data coverage for an entire year for growth rate calculations for individual years. We are left with 23 background stations shown in Figure C1. Although the network of sites might not perfectly represent the global mean growth rate, since the network does not cover the full globe, and MBL sites might over-represent local ocean signals (e.g. Wu et al. (2024) and Pandey, Miller, et al. (2024)), they are sufficient for our purpose of evaluating the global performance of inversions in a self-consistent manner. The mean difference between our calculated growth rates from the observed CO₂ mole fractions and those calculated by NOAA is 0.018 ppm yr⁻¹ for 2015-2023. We apply calculated growth rate values for both simulated and observed mole fractions using the same method, allowing them to be compared more consistently than using the inverse global carbon flux estimates in combination with a scaling factor of 1 ppm yr⁻¹ = 2.124 PgC yr⁻¹ (Friedlingstein et al. (2025), see also Sect. 4.1).

### 2.4.3 Large-scale aircraft constraints

We compare the CO₂ mole fractions simulated by the inversions to aircraft observations from different programs. These observations are currently also used to inform on the performance of the inverse systems in the GCB2024 (see Friedlingstein et al. (2025), Figure S5), together with inverse modeling group's expert judgment. The analysis in GCB2024 includes comparison to independent aircraft observations covering different latitudes, with the majority of observations in the Northern Hemisphere.

Large-scale assessment of inverse systems is enabled by vertical aircraft profile observations from the NASA 'Atmospheric Tomography Mission' (ATom, C. R. Thompson et al. (2022)). The ATom campaigns provide vertical cross-sections based on aircraft measurements from the onboard NOAA Picarro instrument (model G2401-m, McKain and Sweeney (2021)). We use the ATom campaigns for which all inverse systems have provided simulated mole fractions. These are ATom campaigns 2, 3 and 4 in Jan-Feb 2017, Sep-Oct 2017, and April-May 2018 respectively (some systems did not provide simulated mole fractions for ATom-1). The ATom aircraft sampled vertical profiles over the Atlantic and Pacific Ocean, spanning all latitude bands. Five different CO₂ instruments (3 in situ systems and 2 flask samplers) were included in the ATom campaigns, and comparisons between these show that potential systematic biases were very small (Gaubert et al., 2023). The ATom flight paths are shown in Figure B1. We removed non-representative data (primarily from take-offs and landings, during which the observations are strongly affected by local fluxes) using the same filter as used in Loechli et al. (2023).

### 2.4.4 Amazon aircraft observations

An important region for the global carbon cycle that remains under-observed is the Amazon basin and tropical forest. There are only a few in situ observation sites over the Amazon, and satellite retrievals of XCO₂ are sparse due to the cloudy conditions over the Amazon basin (Frankenberg et al., 2024; J. Liu et al., 2015). This potentially results in seasonal biases in estimates of Amazon carbon fluxes derived from satellite XCO₂. In
this paper, we analyze the mean and interannual variability of the fluxes in the biogeo-
graphical Amazon region (Terrabrasilis, 2020), rather than the ‘Brazil’ region (see G14),
which covers other biomes in addition to tropical forest.

We analyzed the mean flux estimates of the Amazon basin based on independent
vertical aircraft profiles of CO2 observations included in the GLOBALVIEWplus v9.1
ObsPack product (Schuldt et al., 2023). We took the mean bias between the simulated
and observed mole fractions in the lowest 3000 m of the atmosphere (i.e. column aver-
age) for the sites: Rio Branco (RBA-B), Tefé (TEF), Alta Floresta (ALF), and Man-
aus (MAN). Santarém (SAN) was left out of this analysis because it was found to be non-
representative for the region analyzed (i.e. no correlation between biases and flux esti-
mates was found). To calculate an uncertainty for the mismatch between the simulated
and observed vertical profiles, we bootstrapped by selecting 10% of the data (from the
four aircraft sites) and taking the standard deviation of the mismatch to observations
of 5000 bootstraps as a measure of the uncertainty.

For the RBA-B, TEF and ALF observations, we use water vapor corrected profiles
to minimize the potential bias due to water vapor in the flasks (Gatti, Cunha, et al., 2023;
Botía, Munassar, et al., 2025). We have applied a similar method as the one presented
by Botía, Munassar, et al. (2025) (their section 2.1.5). We do not use the corrected pro-
files by (Botía, Munassar, et al., 2025) directly, as these only cover 2010-2018, while we
use a longer period. We have applied a consistent correction over all years. We use the
water vapor concentration from ERA5 (Hersbach et al., 2020) at the grid cell (x,y,z,t)
where the sample was taken, rather than the water vapor concentration upwind from each
sample location, extracted from EFCMWF-IFS using a Lagrangian atmospheric trans-
port model, as was done by Botía, Munassar, et al. (2025). The difference between the
corrected and uncorrected profiles is between 0 and 1.7 ppm. The difference between the
correction used here and the one by Botía, Munassar, et al. (2025) turns out to be un-
biased and smaller than 0.25 ppm in more than 99% of the 7710 samples analyzed.

2.4.5 *East Asia aircraft observations*

The Comprehensive Observation Network for Trace gases by AlrLiner (CONTRAIL,
Sawa et al. (2008); Machida et al. (2008)) provides regular *in situ* observations from com-
mercial long-range passenger aircraft. Observations from this program are especially dense
over East Asia, and can therefore provide valuable insights in the carbon fluxes in this
region. We selected observations between 80 and 135°E and 20 and 50°N. Furthermore,
we have removed observations for which the difference between the ensemble mean and
the observed CO2 mole fraction is larger than 1 ppm, to remove local influences that we
do not expect the global inverse systems to resolve. For this dataset, there is a large vari-
ability in the density of observations within the selected region (up to a factor of 2.5 be-
tween years and a factor of 48 for individual months). To account for this, we binned
the data integrated over the region to 500 m altitude bins with daily temporal resolu-
tion. We removed data from the lowest 1 km in altitude to account for take-offs and land-
ings (which generally happen in areas with strong fossil fuel emissions), and then take
the column averaged values. The resulting data is shown in Figure F1. Due to the shear
amount of data from the CONTRAIL continuous observations (1.6 million observation
points), a bootstrapping of 10% of the data (as used in our other analyses for the Ama-
zon aircraft profiles and shipboard measurements in the Atlantic) would result in an under-
estimate of the uncertainty. We therefore select 10,000 times 200 random data points,
and calculate the mean bias to observations of these 200 data points and take the stan-
dard deviation of these 10,000 mean biases as the uncertainty.
### 2.4.6 Atlantic shipboard observations

To constrain fluxes over the Atlantic Ocean, we compare the shipboard atmospheric CO₂ mole fraction observations from the ‘Cap San Lorenzo’ line (Pickers et al. (2017), available from 2015 to 2020) to simulated mole fractions. We select all observations that fall within the Atlantic Ocean region (between -35.2°N and 49.5°N). To minimize temporal sampling biases we resample the data to monthly averages. To calculate the uncertainty, we repeat this analysis 1000 times with 10% of the available data.

### 2.4.7 Seasonal cycle amplitude analysis for Europe

Systems that estimate a stronger seasonal cycle over Europe tend to also estimate a stronger mean net uptake over that region (see Appendix D2, cf. J. Liu et al. (2020); Bastos et al. (2019)). The rationale behind this is that an ecosystem with a larger net carbon uptake likely has both higher gross primary productivity in summer and higher ecosystem respiration in winter. To assess flux estimates for Europe, we leverage this relation by comparing the observed and simulated seasonal cycle amplitude (SCA) of atmospheric CO₂ at both assimilated and independent measurement sites. The SCA itself is not optimized by any of the systems, even if they assimilate observations at the measurement sites used in the SCA analysis. In case the mole fractions at a given site are assimilated, the SCA is not necessarily well constrained because of observation and transport uncertainties. We can therefore use it as an independent metric to assess the inverse systems.

We calculate the SCA of atmospheric CO₂ mole fractions using the curve fitting method ‘CCG-CurveFit’ (Thoning et al. (1989), also see Appendix Figure D1). For this, we first fit the observed and simulated mole fractions at different sites in Europe (N=56) with a suite of harmonic equations that were obtained using different settings in CCG-CurveFit, e.g. the amount of fitted harmonics, see Appendix D1. From these curve fits, SCA is the difference between the maximum and minimum of the (repeating) seasonal harmonics. This results in an observed and system-specific simulated SCA for each site. We then apply a linear fit of the simulated SCA to the long-term (9 years) European mean flux estimates from all systems. We find that for most sites, the correlation coefficient (R) is negative (i.e. a larger SCA is related to more uptake, see Figure D2). For measurement sites that have observations at multiple levels (i.e. inlet heights on a tower), we only use the highest level so that we do not bias towards sites with more inlets. We find that the results are robust to choices in both site selection and curve fitting settings. We also tried similar constraints based on the carbon uptake period (CUP, the period during which the fitted harmonics are smaller than 70% of the maximum and decreasing) and the zero crossing time (ZC; the time during which the harmonics are below the mean). Both of these additional constraints are explained in more detail in Figure D1. We do not show the results of these, as the results turned out similar to the SCA constraint. In this paper, we apply the SCA constraint to European flux estimates. In other studies, it could also be used for other regions with a strong seasonal cycle.

### 2.4.8 Amazon flux anomalies

In addition to comparisons to aircraft mole fraction observations over the Amazon, we also analyze the performance of the inversion ensemble in representing flux anomalies in the Amazon using CO₂ mole fraction observations from the Amazon Tall Tower Observatory (ATTO). For this, we use monthly CO₂ mole fraction observations, averaged over a daytime window (13:00-17:00 Local Time) from the 80 m inlet, roughly 50 m above the canopy top (Botía et al., 2022; Botía, Dias-Junior, et al., 2025). We calculate the monthly mean difference with the previous year (e.g. January 2023 minus January 2022) for both the (monthly) CO₂ mole fraction observations and (monthly) flux estimates in the ATTO footprint, using the monthly mean footprint from Botía et al.
(2022). Additionally, we take the optimized flux in the gridcell of ATTO, and compare it to direct (monthly-averaged) eddy-covariance observations of carbon fluxes (Botía, Dias-Junior, et al., 2025). We note here that we do not expect global inverse systems to be able to replicate the fluxes observed from the highly local eddy-covariance towers. We only use the ATTO eddy-covariance observations as a reference point for larger-scale anomalies, which we do not expect to have a similar magnitude, but a comparable sign and timing. We analyze the flux estimates for the El Niño years 2016 (end of El Niño) and 2023 (onset of El Niño). Note that atmospheric CO₂ mole fractions for ATTO are also available (https://www.attodata.org/home/Start, last access 26-03-2025; Botía, Dias-Junior, et al. (2025)), but not included in the ObsPack products for which the inverse systems provide simulated mole fractions. We therefore did not compare the simulated and observed mole fractions at ATTO directly, but use inverse flux anomalies instead.

### 2.4.9 Comparison to bottom-up land flux estimates and budget imbalance

We analyse the global carbon budget's imbalance term by comparing our inverse flux estimates to bottom-up estimates from Dynamic Global Vegetation Models (DGVMs) from the 'Trends and drivers of the regional-scale terrestrial sources and sinks of carbon dioxide' (TRENDY) ensemble (Sitch et al., 2024) as used in GCB2024 (Friedlingstein et al., 2025). These biosphere flux estimates include changing land use and land cover (S3 simulations). To better evaluate interannual variability, we used a longer time series (2003-2023) for this analysis compared to the other analyses in this paper. We used 2003 as the starting year since one of the TRENDY models (CARDAMOM) only has output starting from that year, and hence the TRENDY ensemble is complete for 2003-2023. We calculated ensemble mean and standard deviations per year for both inversions and the GCB2024 TRENDY ensemble, and binned the data per extended RECCAP2 region. We compare the difference between our inverse flux estimates and DGVM flux estimates to the global carbon budget imbalance given by Friedlingstein et al. (2025). We focus on the land sink because it has a larger interannual variability than the ocean sink. This imbalance term in the global carbon budget is the difference between the sources of CO₂ on the one hand (from fossil fuels and land-use change) and the sinks on the other hand (land, ocean and atmosphere). This imbalance is a significant term in the global carbon budget, amounting to -0.5 PgC yr⁻¹ (i.e. too much uptake or too little emissions) on average over the past decade, with variations up to 1.3 PgC yr⁻¹ in certain years (Friedlingstein et al., 2025).

### 2.4.10 Regional covariance analysis

Given that the atmospheric inverse systems suggest similar total fluxes at the global scale, a covariance between global land flux and global ocean flux across inversions is expected. That means that a system suggesting a higher net land flux would show a lower ocean flux and vice versa. We analyze this behavior by calculating the covariance between the mean global land and global ocean flux estimates from the different inverse systems. This covariance tells us the spread of the range of possible land-ocean fluxes. We calculate the total covariance between these two fluxes, and also determine which of the extended RECCAP2 regions contribute most to this covariance by re-calculating the covariance with one region left out. Because covariances add up linearly (K. Wang et al., 2023), the decrease in covariance when one region is left out determines the contribution of that region to the total covariance (K. Wang et al., 2023). This method also takes into account that some regions have larger mean flux estimates than others and therefore are more likely to contribute to the covariance of the larger region for a given relative change of the fluxes.
We performed the same analysis for the covariance between fluxes north and south of 30°N, as well as the covariance between fluxes in the Western Hemisphere and Eastern Hemisphere (as an example of dipoles existing in multiple directions).

### 2.4.11 Near infrared reflectance of vegetation

The near infrared reflectance of vegetation (NIRv) correlates well with gross primary productivity (GPP, Badgley et al. (2017)), a key driver of interannual variability (IAV) of net land carbon fluxes (NEE) (Jung et al., 2017). Therefore, we use NIRv to analyze the IAV of NEE, which changes from year-to-year e.g. due to droughts. Using NIRv assumes that IAV in NEE is mainly driven by GPP, with a relatively limited contribution of total ecosystem respiration (TER) (Piao et al., 2020). We therefore analyze the NIRv anomalies only for non-desert land areas with a strong seasonal cycle, namely Europe, Boreal and Temperate North America and Russia.

We calculated NIRv anomalies (downloaded from https://e4ftl01.cr.usgs.gov/MOTA/MCD43C4.061/, last access 2025-03-08) from MODIS surface reflectance using the Bi-Directional Reflectance Distribution Function (BRDF) correction, based on the retrieval algorithm v6.1 (Schaaf, n.d.) (https://lpdaac.usgs.gov/products/mcd43c4v061/, last access 2025-02-12).

## 2.5 Inversions performance

Finally, we provide an overview of the performance of the inverse systems on different metrics described in the previous section for selected regions. For this overview, we use a system similar to the International Land Model Benchmarking (ILAMB), which is used to assess land surface models or DGVMs (Collier et al., 2018). We rank the inversions using the metrics discussed in this paper. The ranking is defined relative to the ensemble itself, from 'better' to 'worse' in 7 equidistant bins, similar to the method used in ILAMB (Collier et al., 2018). Therefore, systems with a similar performance end up in the same bin, rather than on a full 14-level range. The choice for 7 bins is slightly arbitrary, but provides an intermediate level of detail. Since the bins are defined equidistantly, not all bins are necessarily filled. It is important to note that the best rank does not mean that the system performed perfectly, since the scale is relative. Furthermore, it should be noted that the metrics analyzed here are not exhaustive. Rather, we show examples of metrics that can be used to assess inverse systems' performance, giving guidelines and inspiration for selecting inversions to be included in future studies, depending on their focus on different aspects or regions of the carbon cycle.

# 3 Results

## 3.1 Global carbon flux estimates

### 3.1.1 Global atmospheric carbon budget according to inversions

All inverse systems estimate a similar mean total net natural (land + ocean) sink of 4.4 PgC yr⁻¹, and a mean interannual variability of 0.77 PgC yr⁻¹ over the 2015-2023 period, with only small differences between systems (0.06 PgC yr⁻¹, Figure 1a and Appendix G). This good correspondence on global total flux estimates applies to both the *in situ* and satellite inversions and originates from the fact that all systems assimilate atmospheric CO₂ observations and thereby close the atmospheric carbon budget. The observation-based growth rate is visualized by the black line in Figure 1a, which shows the natural carbon sink as calculated from the observation-based atmospheric growth rate of CO₂ and anthropogenic CO₂ emissions, using the conversion factor of 1 ppm yr⁻¹ = 2.124 PgC yr⁻¹ as used by Friedlingstein et al. (2025). Note that there is some variability in this conversion factor to go from atmospheric mole fractions to surface fluxes
because of incomplete sampling of the atmosphere in the current method. We further
discuss this in Section 4.1.

Also in the year-to-year variability, there is a high degree of agreement between the
systems, with El Niño years having smaller carbon uptake compared to La Niña years
(brown and blue shading in Figure 1a). This agreement with the El Niño-Southern Os-
cillation (ENSO) cycle can be mainly attributed to IAV in the land fluxes (Figure 1b),
which is larger than the IAV in ocean fluxes (Figure 1c). We find a global mean net land
sink (i.e. the biosphere uptake and the fire and land use change emissions) of 2.06±0.55
PgC yr⁻¹ and a global mean net ocean sink of 2.32±0.55 PgC yr⁻¹ during the common
period 2015-2023 (uncertainties reported as ±1σ). Accounting for the river flux adjust-
ment to facilitate comparison to bottom-up estimates (Friedlingstein et al., 2025), these
estimates become 1.41±0.55 PgC yr⁻¹ for land and 2.97±0.55 PgC yr⁻¹ for ocean. Note
that these ensemble values are strongly correlated, which we will discuss in Section 3.2.1.
In comparison to GCB2024's bottom-up estimate (2.0±1.2 PgC yr⁻¹ for land based on
DGVMs and bookkeeping models, and 2.88±0.49 PgC yr⁻¹ for ocean based on ocean
models and ocean data products), our inverse ensemble finds a similar ocean sink and
smaller land sink. However, note that bottom-up total fluxes (land + ocean) result in
a higher total carbon sink of 4.9 PgC yr⁻¹ compared to our 4.4 PgC yr⁻¹, which leads
to a budget imbalance of -0.5 PgC yr⁻¹, implying that the bottom-up budget overesti-
mates the net total sink.

Although inverse systems that use satellite XCO₂ products estimate a slightly larger
ocean sink compared to inverse systems that use only *in situ* observations, there is no
significant difference between *in situ* and satellite systems on the global scale. However,
large differences between individual systems remain, as seen by the wide spread around
the ensemble mean (shading in Figs. 1b and c). This is a result of differences in the in-
dividual system configurations (see Section 2.2).

**3.1.2 Global growth rate**

The global growth rate is generally well reproduced by all inverse systems (see Fig. 1).
The median biases are generally less than 0.1 ppm yr⁻¹ (see Fig. 2). The highest mean
bias over 2015-2023 is less than 0.07 ppm yr⁻¹ (roughly 0.14 PgC yr⁻¹). However, most
inverse systems show some years in which their bias is slightly larger, with values close
to 0.2 ppm yr⁻¹, as seen in the spread in Figure 2.

**3.1.3 Global carbon budget imbalance**

The total net global land flux in GCB2024 is determined from the TRENDY en-
semble of DGVMs together with the land use change emissions from the bookkeeping
models (Friedlingstein et al., 2025). Fig. 3a shows the ensemble mean of the global to-
tal net land flux estimates from GCB2024 and the inversions (including the river flux
adjustment as explained in Section 2.3). The difference between the two ensembles is also
shown together with the budget imbalance from GCB2024. Fig. 3a shows the strong cor-
relation (R=0.8, p=10⁻⁵) between the mean difference of the two ensembles and the bud-
get imbalance, similar to what was demonstrated by Bastos, O'Sullivan, et al. (2020).
Inversions close the carbon budget and the interannual variability of the fluxes is dom-
inated by the land fluxes (see Fig. 1). Therefore, the difference between inversions and
the bottom-up GCB2024 flux estimates implies that the interannual variability of the
imbalance term in the budget is mainly the result of a misrepresentation of the inter-
annual variability in total net land flux estimates of the DGVMs and, to a lesser degree,
of the other budget components. The remaining differences can include uncertainties in
the anthropogenic emissions, which are assumed to be perfectly known in the inversions.
Furthermore, other contributing factors that explain the remaining differences are the
<figure><img src="image_2.png" /></figure>

**Figure 1.** Overview of the global flux estimates derived by our ensemble of the 14 GCB2024 inversions, split into 2 groups, either assimilating only *in situ* observations (N = 8, teal) or satellite XCO₂ observations (N = 6, red, including systems that assimilate both types of observations) (dashed line indicates the GOSAT-only period, solid line the OCO2+GOSAT period). Panel a shows the global total net (land + ocean) fluxes in which land includes emissions from fire and land-use change. The black line indicates the global natural fluxes as calculated from the global mean growth rate derived from *in situ* observed atmospheric CO₂ mole fractions together with the global fossil fuel emissions (Section 2.4.2). Panels b and c show the net global land and ocean flux estimates, respectively (not accounting for the river flux adjustment). The shaded uncertainty bands show the minimum and maximum range of all inversions in both sub-ensembles. The background shading indicates positive (brown for El Niño) and negative (blue for La Niña) El Niño–Southern Oscillation (ENSO) phases (taken from https://psl.noaa.gov/enso/mei/, last access 28-05-2025).

river flux adjustment, ocean fluxes, and the conversion of the observation-based atmospheric growth rate to fluxes (see Sect. 4.1).
<figure><img src="image_3.png" /></figure>

**Figure 2.** Boxplots indicating the spread of yearly values of the difference between simulated CO₂ growth rate in the atmosphere and global mean growth rate derived from atmospheric CO₂ mole fraction observations (see Section 2.4.2) over 2015-2023 for each inverse system, showing the median (horizontal line), interquartile range (box), 1.5× the interquartile range (whiskers) and outliers (circles). Bars without hatching represent *in situ* inversions, diagonal hatching represents satellite systems, and crossed hatching represents systems that assimilate both.

Next, we assess the mean differences between the inversions and the DGVMs by regions, and determine the covariances between the mean difference and the bottom-up budget imbalance when leaving one region out (see Sect. 2.4.9, note that inversions by design do not have a budget imbalance). We can see that the largest contributors to the budget imbalance are east Asia, tropical Africa, and temperate North America, with additional contributions from northern Africa, central America, and central Asia (Fig. 3b). Thus, these regions are important when comparing the interannual variability of DGVMs with that of atmospheric inversions, and contribute more to the existing bottom-up budget imbalance. Boreal regions contribute little to the difference between the ensembles.

Atmospheric inversions result in a smaller net land sink (1.41±0.55 PgC yr⁻¹, with river flux adjustment) than the GCB2024 bottom-up net land sink (2.0±1.2 PgC yr⁻¹) (Fig. 3a). However, the estimates agree better when looking only at managed land (Figure 8 in Friedlingstein et al. (2025)). A plausible explanation for the bias is the lack of age-dependent regrowth flux after disturbance in the DGVMs, as shown by O'Sullivan et al. (2024). Note also that inverse flux estimates have been adjusted with an uncertain river flux adjustment, which is applied as a fixed value every year, whereas in reality it is likely variable. We discuss this further in Section 4.4.

## 3.2 Regional flux estimates

In this section, we discuss the regional flux estimates for the extended RECCAP2 regions. The derived fluxes, separated for *in situ* and satellite inversions, for the 15 land regions are shown in Figure 4 and for the 11 ocean regions in Figure 5. Generally, mean flux estimates from the *in situ* and satellite inversions are statistically similar, except
<figure><img src="image_4.png" /><figcaption>**Figure 3.** a) Net land carbon sink mean and standard deviation from our GCB2024 inversion ensemble (blue) and the GCB2024 bottom-up ensemble (DGVMs S3, green). Note that in this figure, the sinks are defined as positive values as per GCB2024 convention. The difference between the two ensemble means is indicated by the dashed black line and the carbon budget imbalance term is shown by the solid black line. b) Map of the absolute change in covariance by region (calculated similar to the method described in Sect. 2.4.10) between the dashed and solid black lines in panel a when the region is removed from the calculation of the covariance. Larger values indicate that the region contributes more to the budget imbalance.</figcaption></figure>
for Europe and temperate South America, and the East Pacific and Indian Ocean, which show significant differences (t-test *p* < 0.05) (also see Figure 4). *In situ* and satellite systems also agree well on interannual variability in the land flux estimates (*R* > 0.5 in 11 out of 15 regions, also see Figure 1). This indicates that the effect of events that generate interannual variability, such as ENSO events, droughts or fires, are captured similarly by both *in situ* and satellite-based systems. Detailed summaries of our inverse results for each extended RECCAP2 region are presented in Appendix G.

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Yearly mean flux estimates (without river flux adjustment) for all 15 extended RECCAP2 land regions (shown in the central map), split up between *in situ* (N=8 in teal) and satellite-driven (N=6 in red, dashed line indicates the GOSAT-only period, solid line the OCO2+GOSAT period) inversions. The opaque shadings show the 1σ range.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Yearly mean flux estimates (without river flux adjustment) for all 11 ocean regions (shown in the central map), split up between *in situ* (N=8 in teal) and satellite-driven (N=6 in red, dashed line indicates the GOSAT-only period, solid line the OCO2+GOSAT period) inversions. The opaque shadings show the $1\sigma$ range. Note that satellite systems are poorly constrained over the ocean, as there are no reliable satellite $XCO_2$ observations</figcaption></figure>

### 3.2.1 Regional flux covariance

The fluxes estimated by the inversions for each region shown in Figures 4 and 5 are not independent of each other. On the global scale, the sum of the fluxes agrees well between inversion systems, but when the globe is separated into large areas, such as global land and global ocean, inversions show a large spread in each region, with a compensating effect (also called ‘dipoles’). Next, we show three such global dipoles and determine which regions contribute most to these dipoles.

#### 3.2.1.1 Land-ocean dipole
The mean global land and ocean flux estimates of our inverse ensemble, including river flux adjustment, are -1.41±0.55 and -2.97±0.55 PgC yr⁻¹, respectively. There is a significant spread in the global land and ocean flux estimates between different atmospheric inversions (see Fig. 6a, G2, G3, and also Friedlingstein et al. (2025)), although it is of the same order as the spread in the bottom-up land and ocean flux estimates in GCB2024. The spread in the global land-ocean flux estimates is partly driven by a single inversion with a particularly large ocean sink (CT-NOAA), due to choices in their air-sea gas exchange in the transport model that will be changed in future updates. Without CT-NOAA, the standard deviation of the global ocean sink is reduced to 0.39 PgC yr⁻¹. We find no clear distinction between the *in situ* (shown in dots) and the satellite inversions (crosses and triangles) for this land-ocean dipole. This dipole could partially be driven by the prior flux estimates used in each system, however, the effect
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of the priors cannot be assessed as the prior land and ocean fluxes are independent and therefore do not correlate. Note that ocean glint data is not used by the systems that assimilate satellite XCO₂ data, so the constraint on the ocean fluxes are limited in these systems.

<figure><img src="image_7.png" /></figure>

**Figure 6.** Aggregated flux estimates of: a) global ocean versus global land, c) northern land + ocean (>
30°N) versus southern and tropical land + ocean (< 30°N), and e) eastern land +
ocean versus western land + ocean. Global land and ocean flux estimates in panel a include the
river flux adjustment, to allow comparison with bottom-up models. Standard colors are used for
each inverse system, with dots indicating *in situ* inversions, crosses indicating satellite inversions
and triangles indicating systems that assimilate both *in situ* and satellite data. The maps in pan-
els b, d, and f indicate the absolute change in covariance by region (calculated using the method
described in Sect. 2.4.10) when the region is removed from the calculation of the covariance. The
black lines in the maps indicate the borders of the two regions for which the dipole is shown.

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We also analyze which regions contribute most to the dipoles (see Sect. 2.4.10 for
methodological details). Our covariance analysis for the land-ocean dipole shows that
the regions east Asia, north Pacific, and north Atlantic contribute most to the dipole (Fig. 6b).
These regions represent a clear east-west ambiguity in a relatively narrow latitude range.
When fossil fuel emissions are included, East Asia is also the region with the largest fluxes
of all regions (not shown) and the largest spread in inferred land fluxes between the in-
version systems, especially for *in situ* inversions (see Fig. 4). This coincides with a gen-
eral lack of available *in situ* measurements in East Asia and a relatively high uncertainty
in fossil fuel emissions there (Z. Liu et al., 2015). Satellite inversions show a smaller spread
in this region (see Fig. 4). More measurement constraints (i.e. *in situ* observations) for East Asia would be expected to decrease the spread in the global land-ocean division in atmospheric inversions. We discuss this region further in Sect. 3.3.6.

More measurement constraints (both *in situ* and satellite-based) should also help to reduce the spread in the net land and ocean partitioning between the inversions. However, the contributions of these regions are small compared to e.g. East Asia and thus will have a smaller impact on reducing the dipole.

### 3.2.1.2 North versus tropics and south dipole
Other ways of dividing the globe in two regions also give rise to dipoles similar to those for the global land versus the global ocean. The second dipole that we analyze is the one between the land+ocean flux estimates in the Northern Hemisphere (>$30°N) and those in the tropics and Southern Hemisphere (<30°N, also see Figures G4, G5 and G6). Fig. 6c shows that this dipole has a smaller spread (standard deviation 0.43 PgC yr⁻¹) than the global land-ocean dipole. Note that CT-NOAA (in panel c behind the green marker of IAPCAS) is not an outlier here, despite the large fraction of ocean area in the tropics and Southern Hemisphere. There are several land regions (Temperate North America, Russia and Tropical Africa) that contribute to this dipole, with a smaller role for the oceans. The contribution of the regions is not directly related to the size of the fluxes of these regions, but Russia and Tropical Africa are regions with very limited *in situ* observations.

### 3.2.1.3 East versus west dipole
Finally, when the globe is divided in an east-west sense (Figs. 6e-f), the spread between inversion systems is the largest of the three dipoles, with a standard deviation of 0.71 PgC yr⁻¹. This could be caused by the faster mixing of CO₂ in East-West direction or other factors, which would need further analysis. Note here is that satellite inversions generally show more uptake in the Western Hemisphere than the *in situ* inversions, with a mean difference of 0.5 PgC yr⁻¹. This difference can also be seen in Temperate South America, Temperate North America, and the East Pacific in Figs. 4 and 5. The reduced uptake in the Eastern Hemisphere is seen in the satellite inversions for e.g. South Asia, Southeast Asia, and Northern Africa.

East Asia, the North Pacific, and the North Atlantic again contribute to the east-west dipole, similar to the global land-ocean dipole. Furthermore, other regions such as Northern Asia and Temperate North America have a relatively large contribution to this dipole.

## 3.3 Evaluation metrics

In this section, we provide more insight in the performance of different inverse systems. We do so for a selection of regions, based on availability of independent observations, or with open questions in their carbon balance. We showcase several existing and new metrics on different spatial and temporal scales to assess inversions over different regions. These metrics can be used in follow-up studies using inverse results to derive improved flux estimates for certain regions. We provide guidelines to apply these metrics in Section 5. In the next subsections, we start at the large scale with constraints from independent aircraft observations (see Section 2.4.3). We subsequently highlight metrics and carbon flux estimates for several regions. Finally, we provide an overview of the performance of all inverse systems on all metrics.

### 3.3.1 Vertical distribution analysis

We use the ATom observations to analyze the vertical mixing in the transport models of the different systems (also see Section 2.4.3 and Table 1). We analyze the difference between the simulated and observed vertical profiles of atmospheric CO₂ in the Southern and Northern Hemisphere. The vertical and latitudinal distribution of CO₂ observed
on (part of) ATom-3 (Oct 2017) is shown in Figure 7a. Note the high CO₂ mole fractions close to the equator, which are due to biomass burning plume from Africa, encountered on the flight track over the Atlantic ocean. The mismatch between the observed and simulated mole fractions of all analyzed ATom campaigns (2, 3 and 4; Jan-Feb 2017, Sep-Oct 2017, and May-Jun 2018 respectively) over the Southern and Northern Hemispheres is shown in Figure 7b and c, respectively.

In the Southern Hemisphere, CTE, CMS-Flux and MIROC overestimate the atmospheric CO₂ mole fractions, and CAMS-Satellite and GONGGA underestimate them (Fig. 7c). It should be noted that these biases do not appear to be linked to the transport models used (Table 1), but instead seem to come from a selection of choices such as prior models or setup of the statevector, which will be discussed in Section 4.3. Additionally, in the Southern Hemisphere, satellite systems that assimilate OCO2 data (CAMS-Satellite, GONGGA, COLA, GCAS and NTFVAR) tend to be biased lower than the other systems (with the exception of CMS-Flux). The *in situ* version of CAMS does not show the bias that CAMS-Satellite shows in the Southern Hemisphere, with a very similar inverse system, and the bias therefore seems to be influenced more by the assimilated observations than e.g. the transport model or choice of prior flux estimates.

In the Northern Hemisphere, the biases compared to observations tend to be larger than in the Southern Hemisphere, especially at higher altitudes (Fig. 7c). The systems that use TM3 and TM5 as transport models (CarboScope, CTE and CT-NOAA) have a positive bias in higher atmospheric layers, indicating too strong vertical mixing of the surface fluxes into the higher atmospheric layers (Krol et al., 2018; Schuh et al., 2019; Schuh & Jacobson, 2023). In contrast, systems that use GEOS-Chem (CMS-Flux, GONGGA, COLA, UoE, and IAPCAS) tend to be biased low between 2-8 km, indicating too weak vertical mixing. Note that the shown biases are relatively small compared to variability in the atmospheric CO₂ mole fractions in the boundary layer (<1 ppm), and that most of the constraints are near the surface, as satellite retrievals do not resolve vertical profiles of CO₂ but only column-averaged values.

### 3.3.2 Europe

#### 3.3.2.1 Mean flux estimates
In this section, we discuss the European carbon flux estimates, and highlight new metrics to assess the inversions and derive flux estimates, and their anomalies. We first apply the constraint using the seasonal cycle amplitude (SCA) of the atmospheric CO₂ mole fractions (see Section 2.4.7).

Our ensemble mean European flux estimate is 0.23±0.19 PgC yr⁻¹ over 2015-2023, but *in situ* and satellite systems estimate significantly different carbon uptake (t-test; *p*=0.01), although neither compares better to observations than the other (see also Figure G9). With our SCA constraint (see for methodological details Sect. 2.4.7), we find that Europe is a carbon sink of 0.21± 0.10 PgC yr⁻¹ (assuming Gaussian uncertainties, see Figure 8). This SCA-constrained flux estimate coincides with the ensemble mean, but with a 48% smaller uncertainty. Our estimate corresponds well to regional flux estimates for Europe by Lauerwald et al. (2024), who find 0.20 (0.28 to 0.16) PgC yr⁻¹ using regional inversions, although they also provide estimates of 0.26 (0.40 to -0.050) PgC yr⁻¹ for global inversions and 0.38 (±50%) PgC yr⁻¹ for their bottom-up estimate (all values reported without river flux adjustment). Based on our SCA-constraint flux estimate, with a lower uncertainty range compared to that of our ensemble mean, a very large European carbon sink, as estimated by GCAS (0.52 PgC yr⁻¹), or a European carbon source as estimated by CarboScope, MIROC, and CT-NOAA (0.12 to 0.016 PgC yr⁻¹) are now considered outside the likely range. Using the constraints based on two alternative methods (using the carbon uptake period (CUP) and the zero-crossing (ZC), see Section 2.4.7 for details) gives similar results (Figure D2).
<figure><img src="image_8.png" /></figure>

**Figure 7.** a) Selection of longitude-averaged observations from a selected ATom campaign (ATom-3; Oct 2017, to exemplify the observed vertical profiles) with its mean observed CO₂ mole fractions per 5° and 500 m altitude bins. The observation heights are shown in the black dots. The full flight path for this campaign, as well as for ATom-2 and ATom-4 (in Jan-Feb 2017 and May-Jun 2018) is shown in Figure B1; b) Difference between the mean simulated and observed atmospheric CO₂ mole fraction per altitude bin in the Southern Hemisphere for the ATom 2, 3 and 4 campaigns; c) as b, but for the Northern Hemisphere. Systems that assimilate satellite-derived XCO₂ are indicated with an *, and systems that assimilate both satellite-derived XCO₂ and *in situ* observations are indicated by an ^.

3.3.2.2 *Flux anomalies* Next, we analyze the interannual variability (IAV) of the European carbon fluxes, mainly driven by droughts. We specifically focus on comparing the anomalies of our flux estimates with those of NIRv (see Section 2.4.11), as this proxy correlates to GPP (Badgley et al., 2017), which is found to be a main driver of IAV during droughts (e.g. Luyssaert et al. (2007); Mendes et al. (2020); Piao et al. (2020); Jung et al. (2017)). As mentioned in Section 2.4.11 this assumes a relatively limited contribution of total ecosystem respiration (TER), and we therefore compare the inversions to NIRv anomalies only for non-desert land areas with a strong seasonal cycle, elaborated here for Europe.

We find that satellite-informed systems generally perform better at constraining IAV over Europe, as seen from the higher correlation coefficient to NIRv anomalies compared to inversions that only use *in situ* observations (see Figure 9a). A notable exception
<figure><img src="image_9.png" /><figcaption>**Figure 8.** Mean European carbon flux estimates from the individual systems (bars) as well as the mean flux derived using the seasonal cycle amplitude (SCA) constraint from atmospheric CO₂ observations over Europe (box plot), together with the full ensemble mean. The boxplots show the median (orange line), interquartile range (box), 5 and 95 percentiles (whiskers) for the ensemble mean and SCA constraint. Diagonally hatched bars indicate inversions assimilating satellite-derived XCO₂ and crossed hatching indicates systems that optimize both *in situ* observations and satellite-derived XCO₂.</figcaption></figure>

tion is CarboScope, which has the highest correlation of all systems. We attribute this to CarboScope optimizing the response of land carbon fluxes to temperature directly (see Section 2.2). As temperature anomalies and droughts often go hand-in-hand, this system is expected to capture the drought responses better than other systems. The good performance of CarboScope thus shows the added value of such a method, even without the benefits of the higher density of satellite data compared to *in situ* observations. Note that some systems even have a strong negative correlation to NIRv anomalies, indicating that summers with lower NIRv are associated with enhanced uptake, which is unlikely.

Next, we assess the flux anomalies for two recent major droughts in Europe: 2018 (Smith et al., 2020; Bastos, Fu, et al., 2020; Rödenbeck et al., 2020) and 2022 (A. M. van der Woude et al., 2023; Gharun et al., 2024; Segura-Barrero et al., 2025). The land carbon uptake for Europe estimated by the full ensemble was reduced in summer 2018 by 60±55 TgC and increased in 2022 by 19±72 TgC. By selecting only the four systems (that is, the quartile) that perform best on the NIRv correlation, the reduction is estimated to be 48±17 TgC for 2018 and 61±20 TgC for 2022. For the 2018 drought, the systems that perform best in the NIRv correlation estimate a similar mean reduction in carbon uptake as the ensemble mean, although with a significantly reduced uncertainty. In contrast, for the 2022 drought, the full ensemble mean estimates enhanced uptake (19±72 TgC), but the selected ensemble finds a strong reduction in uptake by 61±20 TgC. We attribute the difference between the estimates for the 2022 drought to the lack of atmospheric observations in the region with the largest impact. For the 2018 drought, this was the north of Europe, which is densely observed (Smith et al., 2020). On the other hand, the greatest impact of the 2022 drought was in the south and east of Europe, where systems that use *in situ* observations have limited observational constraints (A. M. van der Woude et al., 2023). We note that for the 2022 anomaly, a reduction in carbon uptake was also observed at eddy-covariance sites (A. M. van der Woude et al., 2023) and in other satellite products (Gharun et al., 2024). This shows the benefit of sub-selecting systems
<figure><img src="image_10.png" /></figure>

**Figure 9.** a: correlation coefficient of flux anomalies to mean summer (JJA) NIRv anomalies over 2015-2023 for Europe. The systems are sorted on correlation coefficient. Hatched bars indicate inversions assimilating satellite-derived XCO₂ and crossed hatching indicates systems that assimilate both *in situ* CO₂ observations and satellite-derived XCO₂. b: flux anomalies from the four selected (white) and ten non-selected systems (gray, also shown in the gray area in the left figure) over the two strong European droughts of 2018 and 2022. The boxplots show the median (orange line), interquartile range (box), 1.5× the interquartile range (whiskers) and outliers (circles). Negative values indicate reduced uptake.

based on their performance on independent metrics, since the full ensemble mean estimate results in an enhanced uptake during the 2022 drought, whereas the selected systems show a more likely reduced uptake.

### 3.3.3 Amazon

#### 3.3.3.1 Mean flux estimates
Compared to Europe, as analyzed in the previous section, the Amazon lacks the dense number of atmospheric CO₂ observations and a strong seasonal cycle, and therefore the SCA-constraint cannot be applied here. The observational gap is partially filled by aircraft profiles over the Amazon (Gatti, Correa, et al., 2023; Miller et al., 2023), as well as by observations at the Amazon Tall Tower Observatory (ATTO) (Botía et al., 2022). We first analyze the mean bias between the simulated atmospheric CO₂ mole fractions and the water vapor corrected observations (Botía, Munassar, et al. (2025), see Section 2.4.4) for the vertical CO₂ profiles (300-3000 m) at the sites: Rio Branco (RBA-B), Tefé (TEF), Alta Floresta (ALF), and Manaus (MAN).

We find that most inverse systems are biased low (in the lowest 3000 m) in their atmospheric CO₂ mole fractions over the Amazon, compared to independent CO₂ observations (see Fig. 10). Systems with a lower (i.e., more negative) mean atmospheric CO₂ bias tend to have higher uptake (i.e. more negative surface fluxes) and vice versa. Only sub-selecting systems of which the bias to the mean observed profiles is small (0.0±2σ ppm), results in a slightly higher flux (source) of 0.15±0.12 PgC yr⁻¹ compared to the full ensemble mean of 0.13±0.25 PgC yr⁻¹. Although the uncertainties overlap, the sub-selection based on the aircraft profiles provides a 48% smaller uncertainty range on the mean flux, indicating that both a very large Amazon sink (e.g. NTFVAR and CTE) and
large Amazon source (e.g. CAMS-Satellite) are unlikely. The sub-selection of the ensemble results in the same selection with or without the water vapor correction applied (not shown).

<figure><img src="image_11.png" /></figure>

**Figure 10.** Mean bias (ΔCO₂ (ppm)) between the simulated and observed vertical CO₂ profile at the sites RBA-b, TEF, ALF and MAN in the Amazon, and their corresponding flux estimates for the Amazon basin (positive for sources to the atmosphere). Circles indicate systems that assimilate *in situ* observations, crosses show satellite systems and triangles show systems that assimilate both. The ensemble mean is shown in gray for the full ensemble, and in black for the sub-selected ensemble. The error bars on the vertical profile biases for the individual systems are based on bootstrapping 10% of the available observations (1000 repetitions). Systems that have a bias larger than 0.0 ppm (±2σ) are shown with lower opacity. The error bars on the full and selected ensemble means are the standard deviation of the biases and flux estimates from the included systems. Note that CarboScope is not shown, since for this system no simulated CO₂ mole fractions were available.

3.3.3.2 *Flux anomalies* In the Amazon, meteorological and climatological variability, such as El Niño events and droughts can strongly affect carbon uptake (Bowman et al., 2017; Koren et al., 2018; Botía, Dias-Junior, et al., 2025). We analyzed the anomalies of the inverse flux estimates compared to 1) direct local eddy-covariance flux observations using the inverse flux estimates in the same grid cell, and 2) to independent atmospheric CO₂ mole fraction observations at the ATTO site, using the inverse flux estimates under the observation footprint. These analyses are shown in Appendix E. The main conclusion from this analysis is that we currently do not have enough constraints to sub-select our ensemble, nor derive an improved estimate of the flux anomalies for the Amazon. This is partially because inversions have not provided simulated CO₂ mole fractions at ATTO (as it is not part of the ObsPack products), so a direct comparison could unfortunately not yet be made. Enhanced observation capacity in the Amazon (especially in the west of the Amazon (Botía, Munassar, et al., 2025)) could improve our ability to estimate the fluxes and their anomalies in this region, and is therefore highly recommended.
### 3.3.4 Southern Ocean

The Southern Ocean (see Figure 5l; G26) is a region for which the carbon flux magnitude, sign, and trend is under intense debate (Long et al., 2021; Y. Jin et al., 2024; Hauck et al., 2015; Gruber et al., 2019). All 14 inversions find the Southern Ocean to be a carbon sink, although there is considerable variation in the estimated magnitude of this sink (see Figure 11a). We do not find a clear explanation of how these flux estimates differ from each other based on e.g. prior flux estimates or the use of *in situ* observations versus satellite-derived XCO₂. All systems also agree that the Southern Ocean carbon sink strengthened between 2015 and 2018 (Figure 11b). However, in the later period (2019-2023), the ensemble mean shows a significant positive trend (p=0.005), indicating that the Southern Ocean was a smaller sink in recent years. Nevertheless, this trend is not agreed on by three out of the fourteen systems, possibly also due to the short time period assessed here. This indicates that additional observational constraints are needed to better understand and quantify current and future changes in the Southern Ocean carbon sink.

<figure><img src="image_12.png" /><figcaption>**Figure 11.** a) Time series of Southern Ocean flux estimates for the different inversions; b) Change in the mean flux (x-axis) and trend (y-axis) in the Southern ocean between the 2015-2018 and 2020-2023 periods (shown in the gray shading in subplot a). Systems that assimilate *in situ* data are indicated by a dot, whereas systems that assimilate satellite-derived XCO₂ are indicated by a cross and systems that assimilate both *in situ* observations and satellite-derived XCO₂ are indicated by a triangle.</figcaption></figure>

The ensemble mean Southern Ocean carbon uptake from 2015-2023, indicated by the black line in Figure 11a, is 0.45±0.13 PgC yr⁻¹. This is in line with Y. Jin et al. (2024), who found 0.36±0.16 PgC yr⁻¹ for a similar region, based on aircraft observations over 2009-2018. The estimated uptake by Y. Jin et al. (2024) suggests that systems at the low end of the ensemble (e.g. NISMON, 0.22 PgC yr⁻¹) are more likely than estimates at the high-uptake end of the ensemble, such as GONGGA (0.71 PgC yr⁻¹). Taking into account a river flux adjustment of 0.041 PgC yr⁻¹ for this region, our ensemble of inversions (now 0.49 ±0.13 PgC yr⁻¹) also agrees with GCB2024's Global Ocean Biogeochemistry Models (GOBM's, 0.57 ± 0.26 PgC yr⁻¹, based on the 'A'-runs for the 10 GOBM's available) and pCO₂ data products (0.38 ± 0.11 PgC yr⁻¹, based on 8 data products) (Friedlingstein et al., 2025). Note that some of the estimates in these bottom-up ensembles are used as prior flux estimates in the inversion, although they are not fixed in most cases.

### 3.3.5 Atlantic ocean

Our ensemble of atmospheric inverse systems find an Atlantic ocean sink (North, Tropical and South, see Figures 5 and 12) of 0.44 ± 0.25 PgC yr⁻¹. Most systems are
biased high compared to shipboard observations from ‘Cap San Lorenzo’, which provides atmospheric CO₂ observations over a large transect over the Atlantic Ocean, (Pickers et al., 2017), as shown in Fig. 12). We sub-select systems that have a mismatch with the observations smaller than 0.0 ppm ±2σ, similar to the analysis in the Amazon (Fig. 10). The six systems that are included in the sub-selected ensemble (CAMS, CT-NOAA, CAMS-Satellite, GONGGA, GCAS, and NTFVAR) estimate a larger Atlantic Ocean sink (i.e., more uptake) than for the full ensemble (0.61±0.23 PgC yr⁻¹ versus 0.44±0.25 PgC yr⁻¹). This shows that the Atlantic Ocean sink is most likely larger than the ensemble mean suggests, and a very small sink (as simulated by IAPCAS and UoE) is unlikely. In particular, four out of the six systems that do not have a statistically significant bias against surface CO₂ observations ingest satellite-derived XCO₂, suggesting enhanced performance by satellite systems over this region, even without ocean glint data. Note that this selection is likely not only influenced by the fluxes in the ocean region analyzed, but also by adjacent land regions. However, the large biases compared to the observations indicate that the excluded systems do not show representative flux estimates in the analyzed region.

<figure><img src="image_13.png" /></figure>

**Figure 12.** Atlantic Ocean flux estimates and simulated mole fractions for atmospheric CO₂ observations from the ship track of Cap San Lorenzo (shown in blue on the map inset). The mean of the observed CO₂ mole fractions (see Section 2.4.6) is shown in the black horizontal line. Circles indicate systems that assimilate *in situ* observations, crosses show satellite systems, and triangles show systems that assimilate both. The ensemble mean is shown in gray for the full ensemble, and in black for the sub-selected ensemble. The error bars on the mole fractions for the individual systems are based on bootstrapping 10% of the available observations (1000 repetitions). Systems that are biased more than ±2σ away from the observations are shown with lower opacity. The error bars on the full and selected ensemble means are the standard deviation of the biases and flux estimates from the included systems. Note that MIROC is not shown, since for this system no simulated CO₂ mole fractions were available.

### 3.3.6 East Asia carbon sink

East Asia is a strong contributor to the covariance of the dipoles between the land and ocean, as well as between the east and west (see Figure 6). This region also has a large spread in the optimized fluxes (see Figure 4, G12). To constrain East Asia's biosphere fluxes, we analyze data from the Comprehensive Observation Network for Trace
gases by AIRliner (CONTRAIL) over East Asia. The bias compared to column-averaged CONTRAIL observations, as well as the flux over East Asia, is shown in Figure 13. Systems with higher uptake in East Asia tend to be biased low compared to the observed CONTRAIL column observations (see Figure 13). Similar to previous analyses, we exclude systems that have mole fractions that differ significantly from observations ($>2\sigma$, based on bootstrapping of the atmospheric mole fractions; see 2.4.5). The nine selected systems estimate the East Asian land carbon sink to be $0.28 \pm 0.24 \text{ PgC yr}^{-1}$, while the full ensemble estimates the land carbon sink to be $0.50 \pm 0.47 \text{ PgC yr}^{-1}$. Note that this spread of $0.47 \text{ PgC yr}^{-1}$ is the largest spread in the inverse flux estimates for all regions, and is nearly as large as the spread in global land carbon flux ($0.53 \text{ PgC yr}^{-1}$, also see Figure 6). This large spread is partly driven by UoE and IAPCAS, two highly similar systems, who in their current inversion setups accidentally assimilated more stations than they intended (specifically continuous records in Europe and North America). This led to an imbalance in their observational constraints between regions, resulting in these outlier estimates. In a future version (likely GCB2025) these systems will resolve this issue, and preliminary analysis shows that their updated flux estimates will be more in line with the rest of the ensemble in East Asia, while larger scale patterns (e.g. latitude bands) will not change much.

<figure><img src="image_14.png" /><figcaption>**Figure 13.** Inverse flux estimates for East Asia and the difference between the CONTRAIL-observed and simulated vertically averaged CO₂ mole fractions between 1 and 12 km altitude over East Asia (80-135°E; 20-50°N). Circles indicate systems that assimilate *in situ* observations, crosses show satellite systems, and triangles show systems that assimilate both. The ensemble mean is shown in gray for the full ensemble, and in black for the sub-selected ensemble. The error bars on the mole fractions for the individual systems are based on bootstrapping 200 of the available observations (3000 repetitions). Systems that have a significant ($\pm 2\sigma$) bias are shown with lower opacity. The error bars on the full and selected ensemble means are the standard deviation of the biases and flux estimates from the included systems. The East Asia region is shown in the green contour, and the used observation locations in the blue region in the inset.</figcaption></figure>

It should be noted that for China, the uncertainty in fossil fuel emissions also plays an important role (Z. Liu et al., 2015; R. L. Thompson et al., 2016; Saeki & Patra, 2017; Oda et al., 2023). When fossil fuel emissions are incorrectly prescribed in the inversions,
the optimized fluxes can be aliased due to this error in fossil fuel emissions. The flux estimate constraints based on the metric presented here is therefore more reliable for the sum of fossil fuel emissions and land flux than the land flux on its own. However, the spread in input fossil fuel products (also see Appendix A1) is 0.5 PgC yr⁻¹ for this region, compared to the spread of approximately 1.5 PgC yr⁻¹ in the land flux estimates. This large spread among inversion results is likely also partly driven by a relatively large spread in prior flux estimates (also see G12b). This can for example be caused by misrepresentation of afforestation. Additionally, ground-based observations in this region are far more limited than in Europe or North America, and satellite-derived XCO₂ is hampered by both persistent cloud cover during the summer monsoon, and high aerosol concentrations.

## 3.4 Inversion Performance

The metrics described above can also be applied to other extended RECCAP2 regions. To give an impression of the performance of the different inverse systems, we summarize the metrics for different regions for which the independent observational constraints are expected to be meaningful. The performance of the systems, ranked in equidistant bins, is shown in Figure 14, following a similar method as for ILAMB (Collier et al., 2018). Because the ranking is in equidistant bins, it can occur that multiple systems are in the same bin, and some bins are not occupied. In the figure, the first 8 systems optimize only *in situ* data, the last 6 optimize satellite-derived XCO₂. Note that the choice in assimilated observations is not the only difference between these systems, as they were free in the design of their setups (in contrast to e.g. (Byrne et al., 2023)).

The figure shows that no single system performs well on all metrics. This indicates that a different selection of systems should be applied, depending on the region of interest when studying that region in depth. Because the performance of the systems depends on the region and metric (i.e. mean or interannual variability), and we do not assess all possible regions or metrics here, we do not provide a final overall ranking.

We note some differences between satellite and *in situ* systems. On the bias w.r.t. independent aircraft observations (the current key evaluation metric for inverse systems participating in GCB), *in situ* systems tend to perform better. We attribute this to potential biases in retrieval algorithms of XCO₂, and the fact that these take column-averaged values, which might not be representative at the aircraft sampling locations. However, we note that all systems match the observation-based atmospheric growth rate well.

Satellite systems tend to perform better on the interannual variability in the Northern Extratropics. This can be seen in the ‘anomalies in NIRv’ (also see Section 3.3.2.2). This shows the added value of satellite-derived XCO₂, also see Feldman, Zhang, Yoshida, Gentine, et al. (2023).

Finally, satellite systems tend to perform less well in the Amazon mean compared to *in situ* systems. We attribute this to biases in the XCO₂ columns or to seasonality in the amount of satellite retrievals due to cloud cover. For the *in situ* systems, CAMS, NISMON, and IAPCAS perform relatively well on the mean flux. CAMS and NISMON use a single window inversion, and are therefore more sensitive to fluxes that are geographically further away from observations compared to e.g. CTE, which uses a 5-week window. Together with a lack of local observations, this leads to a worse performance in this area.

It is noteworthy that we did not find any grouping in this performance overview based on the transport model used, despite the differences shown in Figure 7.
<figure><img src="image_15.png" /></figure>

**Figure 14.** Relative performance of inversions compared to the full ensemble of inversions based on independent observational metrics. The top rows refer to the aircraft constraint by latitude band as used in Friedlingstein et al. (2025) (their Figure S5). The other rows refer to the metrics presented in this paper. Green colors indicate relatively better scores, whereas brown colors indicate relatively worse scores. Gray crosses indicate missing data. Note that the scores are relative to the ensemble, and good scores do not indicate perfect agreement (cf. Collier et al. (2018)). Systems that assimilate satellite-derived XCO₂ are indicated with an *, and systems that assimilate both satellite-derived XCO₂ and *in situ* observations are indicated with a ^.

# 4 Discussion

## 4.1 Atmospheric CO₂ growth rate and conversion to PgC

In GCB2024 (Friedlingstein et al., 2025), and other studies (e.g. Sarmiento et al. (2010); Ballantyne et al. (2012, 2015); Weir et al. (2021); Luo and Keenan (2022)), changes in the atmospheric carbon stock are estimated using the observation-based global CO₂ growth rate. This observation-based CO₂ growth rate is typically estimated based on a selection of *in situ* measurement locations (Lan et al., 2025). Subsequently, the annual increase in the atmospheric mole fraction of CO₂ (in ppm yr⁻¹) is converted to annual

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net fluxes into the atmosphere ($G_{ATM}$ in PgC yr$^{-1}$). Generally, and also in GCB2024, a conversion factor (CF) of 1 ppm = 2.124 PgC yr$^{-1}$ is used (Ballantyne et al., 2012). However, the exact value of CF is debated, and other options have been suggested, specifically 2.086 PgC/ppm (Prather, 2012) and 2.1276 PgC/ppm (Sarmiento et al. (2010), see also Raupach et al. (2011)). The reason why a fixed value for CF cannot be given straightforwardly is that the fluxes that lead to changes in the atmospheric mole fractions do not mix instantly throughout the entire atmosphere. Also, the observation-based growth rate is a best estimate based on the available observations, but those stations do not fully represent the whole atmosphere (Wu et al., 2024; Pandey, Chevallier, et al., 2024). Different station selections will result in different derived growth rates (Wu et al., 2024), and the representativeness of the station selection depends on the horizontal and vertical mixing of the atmospheric CO$_2$. The global growth rate can also be derived from satellite-based XCO$_2$ (Pandey, Miller, et al., 2024), which also does not sample the entire atmosphere, both due to vertical averaging of the profiles and the limited coverage in XCO$_2$, due to e.g. clouds, and incoming solar radiation. To compare how well inversions match the observation-based growth rate, we recommend to: 1) follow our methodology to compare simulated and observatory growth rate at the same locations, or 2) when comparing the sum of the inverse fluxes to an observation-based growth rate to use the satellite-based growth rate as that compares better to the sum of the estimated inverse fluxes (S. Pandey, personal communication).

In Section 3.1.2, we show that atmospheric inversions match the growth rate based on *in situ* observations (as used for $G_{ATM}$ in GCB2024) well, when comparing simulated and observed CO$_2$ mole fractions at the same locations following (Wu et al., 2024). The flux estimates from the inverse systems were transported to the observation sites to obtain these simulated mole fractions, and their combination can thus be used to determine the (variability in) *CF* as found from the results of the different systems. We have calculated *CF* as the ratio of annual global inverse fluxes and the annual simulated growth rate (Fig. 15). We find a median *CF* from our inverse results for 2015-2023 of 2.13 PgC/ppm, which is close to the widely used factors of 2.124 and 2.086 PgC/ppm. However, our analysis shows that *CF* is not a single fixed value for all years. The interannual variations are generally larger than the spread between inversions. This indicates that the growth rate determined from a limited set of *in situ* stations is not fully representative of the total CO$_2$ mass added by the surface fluxes to the atmosphere on an annual scale. Note that processes like mixing with the higher atmospheric layers (e.g. stratosphere) take even longer (Pandey, Miller, et al., 2024).

To demonstrate the effect of the variability of the *CF*, we use a hypothetical year with realistic total anthropogenic emissions of 10 PgC yr$^{-1}$ and an equally realistic atmospheric CO$_2$ growth rate of 2.5 ppm yr$^{-1}$. Without any land or ocean sinks, and a *CF* of 2 PgC/ppm (e.g. 2021, see Fig. 15), the atmospheric growth rate would have been 5 ppm yr$^{-1}$. This means that 2.5 ppm or 5 PgC was taken up by the land and ocean sinks combined. If instead, *CF* was 2.25 PgC/ppm (as in 2022), the combined land and ocean sink would have been 1.5 ppm, or 3.75 PgC, resulting in a difference in the estimated total sink of 1.25 PgC yr$^{-1}$. For comparison, the uncertainty on fossil fuel emissions is estimated to be between 5% and 10%, and therefore on the order of 1 PgC yr$^{-1}$ (Jones et al., 2024), which is smaller than this difference due to the *CF*. We therefore recommend to, where possible, move away from the fixed value of 2.124 PgC/ppm for global carbon budget calculations, but instead use a variable *CF* based on the atmospheric transport, inverse flux estimates and their corresponding mole fractions. We acknowledge that to be able to use such improved *CF* estimates, the atmospheric inverse ensemble needs to provide *CF* estimates for a longer period of time than that shown in Figure 15. The figure is based on 14 inversions that cover the period considered in this study, but several inversions can also provide *CF* before 2015, with some systems going back to before 1980 or even back to 1957 (CarboScope).
<figure><img src="image_16.png" /><figcaption>**Figure 15.** The ratio between the global inverse flux estimates and the simulated atmospheric CO₂ growth rate, which represents the conversion factor (CF). The boxplots indicate the spread among inverse systems, including the median (horizontal line), interquartile range (box), 1.5× interquartile range (whiskers) and outliers (circles). The dotted lines show the CF values of 2.086 and 2.124 PgC/ppm, which are often used in other studies.</figcaption></figure>

## 4.2 Regional challenges

The main aim of this paper was not to provide the best flux estimates for each region, but instead we focus on showing the added value of independent observations and developing evaluation strategies for the inverse systems. Regional flux estimates require dedicated analyses such as was done for RECCAP2 for several regions, or using further emergent constraints such as was done in Gaubert et al. (2023). For some regions however, we have provided flux estimates based on the best knowledge from our ensemble of inversions, which we discuss here.

### 4.2.1 Europe

Even in the densely observed European region, we find large differences between the carbon flux estimates by different inverse systems. Estimated mean European carbon fluxes range from a sink of 0.52 PgC yr⁻¹ to a source of 0.12 PgC yr⁻¹ (Figure 8). Satellite systems estimate a larger sink compared to *in situ* systems, as previously seen with GOSAT retrievals in Reuter et al. (2014, 2017); Feng et al. (2016). The large spread between the flux estimates by the different inverse systems is caused by system specific choices such as prior flux estimates, transport model (including its atmospheric CO₂ sampling scheme), or statevector setup. For *in situ*-only inversions, the number of sites assimilated is also important. For example, the system furthest away from the ensemble mean for Europe (MIROC, with a source of 0.12 PgC yr⁻¹) only assimilates observations from 56 sites globally (out of 617 datasets in ObsPack GlobalviewPlus v9.1 globally).

In addition to the difference among the inversions in their European mean flux estimates, they also show a large spread in the interannual variability (IAV) of their European carbon flux estimates. These differences can also be traced to choices in the setups of the systems. We found that the IAV estimated by satellite systems correlates bet-
ter with the IAV in remotely sensed NIRv (Figure 9), most likely due to the higher num-
ber of observations assimilated. MIROC has the lowest performance on these anoma-
lies and smallest number of observations, combined with a coarse scaling on continen-
tal scale (Table 1), which does not resolve relatively small-scale variability in the car-
bon cycle. Furthermore, the resolution of the statevector, or the number of regions op-
timized, can also lead to differences between the estimated fluxes (see Table 1). Systems
with a limited amount of scaling factors, e.g. only a single one for Europe, will not cap-
ture IAV at the subregional scale at which droughts occur.

4.2.2 *East Asia*

East Asia contributes strongly to the dipoles between the global land and ocean sink and to the East-West dipole (see Fig. 6). This can be attributed to the large spread in the optimized fluxes in East Asia (Figure F1, also see Fig. G12). X. Wang et al. (2024) estimated the carbon budget for this region, using bottom-up and top-down methods. For the years 2000-2019 they found that the East Asian carbon sink was $0.34 \pm 0.12 \text{ PgC yr}^{-1}$ for the top-down methods, and $0.37 \pm 0.043 \text{ PgC yr}^{-1}$ for the bottom-up methods. Our full ensemble mean estimate for the East Asia (2015-2020) carbon sink is slightly larger than these estimates, $0.43 \pm 0.47 \text{ PgC yr}^{-1}$ (including river flux adjustment following X. Wang et al. (2024) ). However, with the CONTRAIL-based sub-selection of the ensemble, we found the East Asian sink to be $0.28 \pm 0.24 \text{ PgC yr}^{-1}$, which is slightly smaller than the central estimates of X. Wang et al. (2024). The large remaining spread in our estimated fluxes, even with the sub-selection, shows that global inversions have difficulty constraining the East Asian sink, and more measurements from this region are highly needed to reduce the impact on global-scale dipoles (see Fig. 6).

Sub-selecting only the nine inverse systems based on the CONTRAIL observations (Fig. 13), our global net land sink estimate decreases from $1.41 \pm 0.53 \text{ PgC yr}^{-1}$ to $1.32 \pm 0.27 \text{ PgC yr}^{-1}$, thus reducing the spread by about 50% (including river flux adjustment). Here, it should be noted that the reduction in the land-ocean dipole range is largely driven by the removal of CT-NOAA. Based on this reduced uncertainty on the land sink (and thus also on the ocean sink, see Figure 6), the large net land sink from the systems UoE, IAPCAS (which both have a large East Asia sink) and COLA is unlikely. Similarly, the spread in the East-West dipole is also reduced using the sub-selection based on the CONTRAIL constraint. The Eastern sink (Figure 6e) changes from $2.8 \pm 0.71$ to $2.6 \pm 0.45 \text{ PgC yr}^{-1}$, thus reducing the spread by more than 35%. This reduced uncertainty in the East-West dipole indicates that UoE and IAPCAS estimate a too strong Eastern sink, and a too small Western sink (Figure 6). Note that in a next version, the future East Asia sink estimates of UoE and IAPCAS are expected to be smaller, and for CT-NOAA the ocean sink is expected to be smaller, due to planned improvements to their systems (see Sect. 2.2.10 and 3.2.1).

4.2.3 *Amazon*

The Amazon is an especially challenging region in carbon cycle research, with large gross fluxes and strong anomalies. For the period 2015 to 2023 (characterized by major droughts in 2015, 2016 and 2023), we find that the full ensemble mean resulted in a slightly smaller net Amazon source ($0.13 \pm 0.25 \text{ PgC yr}^{-1}$, including fire emissions) compared to the sub-selected ensemble ($0.15 \pm 0.12 \text{ PgC yr}^{-1}$), although the estimates have overlapping uncertainty ranges. This larger source is still slightly smaller than the source estimated by Gatti et al. (2021), who used methods based on aircraft observations instead of atmospheric inversions, and covered a different time period (2010 to 2018).

Our analysis in Section 3.3.3.1 focused on the Amazon region (Terrabrasilis, 2020). We note that the aircraft CO₂ mole fraction observations, although sampled over the Amazon basin, could also be influenced by signals from other neighboring regions, such as
the Cerrado (Botía, Munassar, et al., 2025). However, we did not find any evidence of
a substantial influence outside the Amazon, based on analysis of the larger Brazil region
(the flux estimates of which are shown in Figure G14).

Although we found an observational constraint on the long-term mean Amazon flux by sub-selecting inverse ensemble members using aircraft measurements (Section 3.3.3.1), we did not find a constraint on the Amazon anomalies (Section 3.3.3.2). We attribute this to the limited amount of observations over the Amazon (even with satellite retrievals), which is reflected in the large spread in ensemble estimates of Amazonian anomalies. This indicates that analyzing the Amazonian carbon budget would require the use of targeted inversion systems and metrics, as done in Botía, Munassar, et al. (2025); Bowman et al. (2017); Koren et al. (2018).

## 4.3 Common aspects among inversions in our ensemble

As shown in Table 1, some inverse systems in our ensemble have aspects in common, such as transport model, based on choices in the designs of their setups. We will discuss some of these common aspects here. One of the most important aspects is whether the systems assimilate *in situ* observations or satellite-derived XCO₂, or both. In some regions, this results in significantly different derived fluxes, specifically in Europe and temperate South America (see Figures 4 and G9, G19). However, even though the number and density of observations from satellite systems is generally larger than for *in situ* inversions, satellite systems do not necessarily show better performance on the metrics analyzed (see Figure 14). Satellite inversions would be expected to perform especially better in regions with a sparse *in situ* observation network, such as the tropics. However, due to cloud masking, satellite retrievals over the tropics are difficult (cf. Peiro et al. (2022); Byrne et al. (2023)). As cloudiness varies per season, this means that there is a seasonal bias in the amount of satellite retrievals, which could also result in a seasonal bias in the resulting tropical flux estimates. In general, in our ensemble, satellite systems perform worse on the Amazon mean flux, as shown in Figures 10 and 14. In contrast, satellite constraints appear to improve estimate anomalies in the Northern Hemisphere, as shown in Figures 9 and 14, even for Europe, which has a dense *in situ* network. This shows the added value of these satellite retrievals, as also shown by e.g. Feldman, Zhang, Yoshida, Chatterjee, and Poulter (2023); J. Liu et al. (2018), even in densely observed regions. Note that we have not analyzed all regions in detail in this paper, but these assessments between *in situ* or satellite inversions can also be made for other regions, such as Canada, Oceania, or ocean regions. Note that we did not find specific improvements for systems in our ensemble that use both *in situ* and satellite observations.

We also considered other common aspects among (groups of) inversions in our ensemble. Although we did find differences in vertical biases compared to ATom observations (Fig. 7) that we could relate to the transport model used (especially the vertical mixing), we did not see a clear distinction in the resulting flux estimates. Also other choices, such as prior flux estimates, optimization technique (and related choices), and the statevector setup do not seem to result in consistently different resulting flux estimates. This might indicate that the choice of which observations are assimilated is a major driver of the results, and we have not found other design choices that consistently influenced the outcomes between systems. This also means that improvements in inversions need to be sought not only in one key area, but possibly in all choices. However, it should be noted that choices in statevector and assimilated observations are also transport-dependent. For example, higher resolution transport allows for optimization of atmospheric CO₂ observations that are more influenced by local fluxes, which allows the optimization of the biosphere fluxes on higher resolution in both space and time. A notable example of this is NTFVAR, which uses high-resolution (0.1°×0.1°) Lagrangian transport to better represent the impact of local flux heterogeneity. This allowed Nayagam et al. (2024) to op-
timize local anthropogenic emissions, in tandem with global biosphere fluxes (not used in the NTFVAR version included in GCB2024).

## 4.4 Uncertainty in river flux adjustments

To compare inverse flux estimates to bottom-up methods, the inverse flux estimates are adjusted for riverine outflow of carbon from land to ocean (see also Section 5). For the global carbon budget in GCB2024, a static river flux adjustment of 0.65 is used (Friedlingstein et al., 2025; Regnier et al., 2022), which is distributed globally in larger latitude bands, according to the distribution of Lacroix et al. (2020). This adjustment leads to a larger inverse land uptake and a smaller ocean uptake. However, this river flux adjustment is in itself also uncertain due to e.g. modeling limitations. The uncertainty is ± 0.3 PgC yr⁻¹ but is not accounted for when applied on a global scale. And the value is under debate, e.g. in new studies that show alternative estimates (e.g. Planchat et al. (2025); M. Liu et al. (2024)). The value is also variable over time, and depends on runoff variability (Y. Yang et al., 2024) and anthropogenic influences (Yan et al., 2023). Therefore, the river flux adjustment adds extra uncertainty to the land-ocean distribution, although this does not alter the spread between our inversions on a global scale (since the adjustment is applied equally to all inversions). For regional studies, it is important to use high-resolution spatially distributed versions of this adjustment and consider the uncertainty on the estimate in the comparison between top-down and bottom-up estimates (Tian et al., 2023).

## 4.5 Performance metrics

Throughout this paper, we presented new performance metrics based on independent observations of atmospheric CO₂ mole fractions. It is important to note that the atmospheric CO₂ mole fractions are influenced not only by surface fluxes in the region of interest, but also by advected CO₂ from other locations. Due to the long residence time of anthropogenic CO₂ disturbances in the atmosphere, this weakens the link between the mole fractions and the surface fluxes in the region of interest. When developing new constraints for specific regions in future studies, it is thus important to first assess the correlations between the independent mole fractions and flux estimates and establish that these observations can be used for the constraint.

Additionally, although we have performed several uncertainty analyses based on bootstrapping, we have not taken into account the posterior uncertainty on the flux estimates of the individual inversion systems. For GCB2024, only the mean (or most likely) solution from each individual setup is included, without their individual uncertainties. Inverse systems typically provide the uncertainty as a range of several inverse runs with different settings instead of their mathematical estimate of a single inverse run. This approach accounts for choices made (such as the prior flux estimates used, or transport model) that are important for the final uncertainty but cannot be included in the mathematical calculation of the uncertainty of the inverse solution. Therefore, a range of estimates from an ensemble of different inverse systems as we show here gives a good estimate of the uncertainty for inverse flux estimates, and as such are also used in Friedlingstein et al. (2025), and for regional analyses (e.g. (Hugelius et al., 2024; Villalobos et al., 2023; Hauck et al., 2023; Murray-Tortarolo et al., 2024; Ernst et al., 2024; X. Wang et al., 2024; Qin et al., 2025)). It is therefore important to realize that the sub-selection of ensemble members as we do here only takes into account the final results of each individual system, without their internal uncertainty included.
## 4.6 Outlook

### 4.6.1 Improvements to atmospheric inversions

Throughout this paper, we have not found consistent differences between flux solutions that can be related to the transport models used (Section 4.3). Since the previous meta-analysis by Peylin et al. (2013), where three out of the eleven systems repeated yearly wind fields for their transport, improvements in atmospheric transport modeling have been made. However, further improvements in vertical mixing and both horizontal and vertical resolution can be expected to improve agreement between models, and studies indicate that correctly representing atmospheric transport is still a challenge (Schuh et al., 2019; Schuh & Jacobson, 2023; Y. Jin et al., 2024, 2025), although improvements have been made over the past years (Gaubert et al., 2019). To improve atmospheric transport models, novel constraints or methods can be used, such as the ones given by Y. Jin et al. (2024) or Nayagam et al. (2024). Developments in atmospheric transport towards higher resolution modeling offers the potential to assimilate observations that are representative for more local signals, which could aid to resolve also local fossil fuel emissions.

Another avenue to improve atmospheric inverse flux estimates is the use of multi-tracer setups. Tracers that give unique constraints on biospheric fluxes, such as carbonyl sulfide (COS, Remaud et al. (2022); Ma et al. (2024)) and ¹³C (Velde et al., 2018; Peters et al., 2018) have been used to investigate global biosphere fluxes. To separate ocean, biosphere and fossil fuel fluxes, atmospheric oxygen can be used, as has already been shown for regional inversions by Rödenbeck et al. (2023). In addition, satellite products for plant traits can be used as additional constraints. For example, Scholze et al. (2019) use satellite-based vegetation optical depth (VOD) coupled to NEE in a regional CO₂ inversion. Finally, to separate natural CO₂ from CO₂ emitted by combustion of fossil fuels, radio-carbon (¹⁴C) can be used, such as in regional systems by Basu et al. (2020), Y. Wang et al. (2018), and Gómez-Ortiz et al. (2025). Satellite-based NOx can also be used to estimate fossil fuel emissions from hotspots (Z. Liu et al., 2023). Finally, other types of observations can be used, for example by Upton et al. (2025) who use a mix of eddy-covariance and atmospheric CO₂ observations to provide a global dual-constraint flux estimate. With the constraints from such additional sources of information, we expect that atmospheric inversions will be able to constrain both the flux partitioning over land and ocean, fossil fuel emissions, and individual regions better in the near future.

### 4.6.2 Future data constraints

Improved separation of different regions and fluxes will be aided not only by improved transport and multi-tracer setups but also by new and upcoming data constraints such as new satellites and improved monitoring of greenhouse gases. For example, the new installment of the OCO satellites (OCO-3 (Basilio et al., 2019; X. Wang et al., 2025)), the Copernicus CO2M (Sierk et al., 2021) and GOSAT-GW (Tanimoto et al., 2025) missions will provide high-resolution global XCO₂ data. Furthermore, satellites with a Snapshot Area Mode, such as OCO-3 (Basilio et al., 2019) provide detailed information on target areas, helping to quantify fossil fuel emissions (e.g. Hakkarainen et al. (2023)). Furthermore, satellite product retrieval algorithms for the OCO-2 satellite products are continually improved (for example, Payne et al. (2022)), potentially resulting in significant differences between versions. For example, between V9 and V10, a difference of up to ~1.5 ppm was found over ocean regions (T. E. Taylor et al., 2023). With such improved data coverage and quality, remote regions like the Amazon are expected to be better constrained in the future. Here a crucial aspect is to resolve wet and dry season biases (due to cloud cover) in satellite data.

In addition to upcoming and improved satellite retrievals, it is also of crucial importance to continue and expand the global network of *in situ* CO₂ observations, espe-
cially in tropical regions, both for assimilation and validation. Furthermore, we have shown the added value of both airborne observations from commercial aircraft (see Fig. 13) and dedicated global surveys like ATom (Fig. 7), and expansion of such surveys could greatly improve future intercomparisons and flux estimates. Finally, it is important that new observations are made available to the community quickly to allow inclusion in efforts such as GCB2024, preferably through the widely-used ObsPack products.

### 4.6.3 Low latency inversions

The Global Carbon Project's GCB is published every year (around November) including the budget up to the previous year, with an outlook of the current year. The inversions presented in this paper are also updated annually, with a latency of about half a year. However, monitoring the path towards net carbon neutrality requires insights in the global carbon cycle with a lower latency. Therefore, it is important to provide also low-latency updates of these budgets (Weir et al., 2021; Z. Liu et al., 2023; Ke et al., 2024; Pandey, Miller, et al., 2024; Gui et al., 2024). Such analyses now mainly depend on bottom-up models (e.g. Ke et al. (2024)). CT-NOAA provides its CT-NRT version (Jacobson, Schuldt, Tans, Andrews, et al., 2023a) closer to real time than its GCB update, and the inverse system CAMS-Satellite was used in low-latency analyses of global (Ke et al., 2024) and regional Amazon (Botía, Dias-Junior, et al., 2025) carbon flux anomalies. However, as we showed that the spread in estimated biosphere fluxes can be large within an ensemble of 14 systems, we recommend also using an ensemble of low-latency inversions in such low-latency studies instead of relying on a single inverse system. With the wide availability of near real-time observations of not only atmospheric CO₂ mole fractions, but also eddy-covariance fluxes (e.g. Heiskanen et al. (2022), A. M. van der Woude et al. (2023)) and forest information (Zweifel et al., 2023), operational low-latency inversions with CO₂ and additional tracers are possible in the near future.

Recently, WMO initiated the Global Greenhouse Gas Watch (G3W), combining surface and space-based greenhouse gas observations and modeling products with a low latency, and other efforts have started in parallel (e.g. Ke et al. (2024)). These low-latency inversions allow for a more direct coupling between carbon cycle research and political decision making processes, such as the Global Stocktake. Furthermore, another key advantage of low latency inversions is that they for assessment of the impacts of climate extremes close to real-time, which can be highly valuable for society to learn about the impacts of extreme events and mitigation efforts.

## 5 Guidelines for using inversions in regional carbon budgets

By design, global atmospheric inversions match the global growth rate of atmospheric CO₂ well. Due to global mass conservation, their resulting fluxes thus close the carbon budget on a global scale. Inverse systems are therefore well suited to analyze the global carbon budget, including its year-to-year variability, decadal means, and long-term trends. Also on regional scale, global atmospheric inversions can be used to study the carbon budget. This is also a current practice in the regional chapters of RECCAP2, such as for Europe (Lauerwald et al., 2024), Australasia (Villalobos et al., 2023), Mexico (Murray-Tortarolo et al., 2024), Africa (Ernst et al., 2024; Qin et al., 2025), East Asia (X. Wang et al., 2024), the permafrost region (Hugelius et al., 2024), and the Southern Ocean (Hauck et al., 2023). Here, we provide some key guidelines for the future use of inverse fluxes in analyses of regional carbon budgets.

* One advantage of using the inverse method is that it generates flux estimates accompanied by simulated atmospheric CO₂ mole fraction distributions. This allows us to assess the resulting flux estimates using metrics based on independent observations, which were not included in the data assimilation. Due to the large foot-
prints of CO₂ mole fraction measurements, these metrics represent large-scale fluxes. Such independent validation on large-scale is more challenging with bottom-up methods, particularly for DGVMs, which are typically assessed with eddy-covariance measurements at ecosystem scale. Future versions of our atmospheric inversion ensemble for GCB will therefore, along with the gridded fluxes, also provide the simulated mole fractions per system. **We recommend future studies using our inversion results to compare the simulated CO₂ mole fractions against independent observations in the targeted region.**

* We have shown that not all inverse systems perform equally well in each region, and thereby the ensemble mean can be biased at a regional level. The comparison to independent observation allows selection of only ensemble members that perform within a chosen threshold. **For regional carbon budget studies, we recommend using a sub-selection of the ensemble instead of the full ensemble mean, based on the inversion performance in comparison to independent atmospheric mole fractions.**

* In addition to sub-selection of the ensemble, we have also shown other methods to derive an improved regional flux estimate compared to taking the ensemble mean. For this, we have introduced the SCA-constraint as an example of a 'flux-observation relation constraint'. It results in an improved flux estimate for the region of interest by using an independent metric (in this case, the seasonal cycle amplitude) and its relation to the European carbon flux as constraint. **For regional carbon budget studies in which the observational capacity of the region allows this, we recommend creating such 'flux-observation relation constraints' to improve the flux estimate compared to using an ensemble mean.**

* When comparing inverse flux estimates with bottom-up methods, it is important to compare the same quantities. This requires adjustments to either inverse or bottom-up methods for lateral transport, such as by rivers or net trade of crops and wood products. For example, riverine outflow can move carbon from the land to the ocean, with losses along the way (Ciais et al., 2022; C. Wang et al., 2024; Deng et al., 2025). Such a river flux adjustment is necessary to compare top-down and bottom-up estimates. Additionally, inverse systems mostly use similar fossil fuel emission fields, although differences can occur. Adjusting to a common fossil fuel emission product for these small remaining differences makes the ensemble of flux estimates comparable (Peylin et al., 2013), and is by default included in our inverse flux results (Luijkx et al., 2024). Furthermore, fossil fuel emissions are often taken without uncertainty, and the reference product might be different from the actual emissions in certain regions. This can lead to uncertainties in the inverse flux estimates, especially in regions with large and poorly known emissions. **For future studies using our inverse results, we recommend to 1) apply the fossil fuel adjustment to compare inverse systems equally, 2) to apply the river flux adjustment to compare inverse flux estimates to bottom-up estimates, and 3) to evaluate fossil fuel emission uncertainties on regional level.**

Finally, it is important to note that atmospheric inverse systems are constantly improved over time, due to improved knowledge on atmospheric transport, data assimilation techniques and data pre-processing, but also because prior flux estimates improve. The effects of these changes cannot be captured in the overview table of the atmospheric inversions provided by the GCB (Table S4 in GCB2024 (Friedlingstein et al., 2025)). Therefore, we recommend to periodically repeat analyses of region-specific fluxes. Thus, these recommendations apply to the current and future versions of our ensemble of GCB inversions, but can also be applied to other sets of inverse flux estimates, such as OCO2-MIP (Baker et al., 2021).
# 6 Conclusions

In this paper, we have analyzed the ensemble of atmospheric inversions contributing to the current Global Carbon Project (GCB2024, Friedlingstein et al. (2025)). We set out to achieve two goals: 1) to provide tools for inverse modelers to compare inverse results, which also facilitates improvements of the systems, and 2) to provide guidelines to other users of our inverse results in the wider carbon cycle community, including future versions of GCB and RECCAP, and within the GST process.

We show that atmospheric inversions close the atmospheric carbon budget, and therefore our ensemble of inversions serves as a valid alternative to the bottom-up estimates currently used as the main budget in the yearly GCB assessments. The closed atmospheric carbon budget from the inversions allows one to calculate yearly varying conversion factors to recalculate observation-based atmospheric growth rates to fluxes, which we, where possible, recommend to use instead of the fixed conversion factor that is currently used.

Additionally, we show that inversions in our ensemble constrain the global-scale fluxes well, but on a regional level show significant spread. This results in flux dipoles for land versus ocean, north versus south, and east versus west. These dipoles are, to a large extent, driven by fluxes in East Asia, which is a region with a large uncertainty in fossil fuel emissions and spread in the inverse net land flux estimates.

We have presented different tools to assess the quality of the inverse flux estimates on regional levels, and we propose methods to better constrain the regional flux estimates. Using these metrics allows one to sub-select inversions in our ensemble, resulting in improved regional flux estimates. We have provided guidelines on how to use atmospheric inversions for regional studies. These guidelines include the comparison to independent mole fraction observations, sub-selection of the ensemble, developing ‘flux-observation relation constraints’ and adjustments needed to compare top-down and bottom-up estimates. These guidelines allow for improved use of our inverse flux estimates in carbon cycle research and are recommended to be used for each new version of the ensemble of inversions in future global and regional carbon budgets.
# 7 Open Research

The inverse flux estimates for GCB2024 for the 14 inverse systems as used in this paper are available here: https://doi.org/10.18160/4R5W-VNBV (Luijkx et al., 2024). The corresponding atmospheric CO₂ mole fractions sampled at sites included in the analysis are available here: https://doi.org/10.18160/DH3S-99JQ (A. van der Woude et al., 2025). Analysis code is available at: https://zenodo.org/records/16311883.

## Acknowledgments

The authors would like to thank all data providers that contributed CO₂ observations to the ObsPack products GlobalviewPlus v9.1 and NRT9.2, including those from ICOS RI. We furthermore thank the providers of the ATTO observations. We acknowledge the TRENDY modeling community and the global ocean modeling and data product community for providing their results, which we used in comparison to the global-scale land and southern ocean flux estimates from the inversions. The authors acknowledge support of the Global Carbon Project's Regional Carbon Cycle Assessment and Processes 2 (RECCAP2) activity.

The analysis for this paper and the CTE runs were supported by a computing grant from the Dutch national e-infrastructure with the support of the SURF Cooperative (NWO-2023.003). ITL was supported by the Netherlands Organisation for Scientific Research (grant no. VI.Vidi.213.143). FC and AM (CAMS) were granted access to the HPC resources of CCRT under the allocation CEA/DRF, and of TGCC under the allocation A0170102201 made by GENCI. It was funded by the Copernicus Atmosphere Monitoring Service, implemented by ECMWF on behalf of the European Commission (Grant Number: CAMS2 55 bis). YN (NISMON) is supported by the Environment Research and Technology Development Fund of the Environmental Restoration and Conservation Agency (JPMEERF24S12200), provided by Ministry of the Environment of Japan, and by the JSPS KAKENHI (grant no. JP22H05006, JP23H00513). FJ and WJ (GCAS) were supported by the National Key R&D Program of China (Grant No. 2023YFB3907404). DY (IAPCAS) was funded by the Chinese Academy of Science Project for Young Scientists in Basic Research (grant no. YSBR-037). Work of JL, JY and KB (CMS-Flux) was conducted at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). JL acknowledges the funding support from NASA Orbiting Carbon Observatory Science Team and Carbon Monitoring System Science Team programs. The computation of CMS-Flux inversion was carried out at NASA Pleiades supercomputer. NC and PKP (MIROC) acknowledge funding from the Environment Research and Technology Development Fund (grant no. JPMEERF24S12205) project and the Arctic Challenge for Sustainability II (ArCS-II) project (grant no. JPMXD1420318865). RJ, SM and LN (NTFVAR) are supported by the NIES GOSAT project, Japan.

SB and the ATTO project were funded by the German Federal Ministry of Education and Research (BMBF, contracts 01LB1001A and 01LK1602A). The ATTO project is furthermore funded by the Brazilian Ministério da Ciência, Tecnologia e Inovação (MCTI/FINEP contract 01.11.01248.00) and the Max Planck Society. The NSF National Center for Atmospheric Research is sponsored by the U.S. National Science Foundation under Cooperative Agreement No. 1852977. Regular observations of CONTRAIL are financially supported by the Global Environmental Research Coordination System, the Ministry of the Environment, Japan (MOE2151).

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