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## Appendix B ATom flights

An overview of the full flight paths of the three analyzed ATom campaigns (ATom-2: Jan-Feb 2017, ATom-3: Sep-Oct 2017, and ATom-4: April-May 2018) is shown in Figure B1.

<figure><img src="image_17.png" /></figure>

**Figure B1.** Overview of the three analyzed ATom campaigns. The altitude versus latitude of the flight track, as well as the mean observations at that respective altitude and latitude, is shown for each campaign. The bottom right figure shows a map of the flight track of the three campaigns.
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## Appendix C Site locations

An overview of the *in situ* observation site locations in the ObsPack products used in GCB2024 (Schuldt et al., 2023, 2024) is shown in Figure C1.

<figure><img src="image_18.png" /></figure>

**Figure C1.** Surface site locations in ObsPack GLOBALVIEWplus9.1 in black (Schuldt et al., 2023). The 23 sites that are used to calculate the global growth rate (Sect. 3.1.2) are shown in red. These are ASC, AZR, BMW, BRW, CBA, CGO, CHR, CRZ, GMI, HBA, ICE, KEY, KUM, MHD, MID, PSA, RPB, SHM, SMO, SPO, SYO, and ZEP, see https://gml.noaa.gov/dv/site/ (last access 21-05-2025) for the abbreviations.
## Appendix D Seasonal cycle depth and carbon uptake period analysis

Figure D1 shows an overview of how we calculate the seasonal cycle amplitude (SCA), carbon uptake period (CUP, calculated as the period during which the fitted harmonic is less than 70% of the maximum and decreasing (i.e. drawdown of atmospheric CO₂ at the surface)), and zero crossing time (ZC, calculated as the time during which the harmonic fit is smaller than 0). Note that both CUP and ZC are not used in the analyses. The left-most panel shows the observed atmospheric mole fraction (blue) and the CCG curve fit (with default parameters, orange) at site Puijo (PUI) in Finland as an example. The harmonics from the fit are shown in the middle panel. The harmonics from one year are shown in the right-most panel. The seasonal cycle depth is indicated in the black arrow and the carbon uptake period is indicated by the red box.

<figure><img src="image_19.png" /></figure>

**Figure D1.** Overview of the fit and calculation of SCA (black arrow), CUP (red box) and ZC (orange line). The left figure shows observations of atmospheric mole fractions of CO₂ at PUI (Finland) in blue, and a CCG-Curvefit fitted function in orange. The middle panel shows the repeating harmonics. In the right panel, a zoom is made over one year of the harmonics. The seasonal cycle amplitude is shown in the black arrow, and is calculated as the difference between the maximum and the minimum of the harmonic fit. The CUP is shown in the red box and the ZC in the orange line. Although only one year is shown in the right panel, the harmonics repeat so the CUP and SCA will be the same for all years.

The correlation between the SCA and ZC from the atmospheric mole fractions and the flux estimates tends to be negative for most sites and CCG-CurveFit settings. This is shown in Figure D2, and validates our rationale to use this metric. It should be noted that the SCA, ZC and CUP correlation in other regions do not show such as skewed correlation distribution. This indicates that the correlation between these metrics in other regions is random. We attribute this to the smaller number and less dense spatial coverage of observation sites in other regions. Therefore, these metrics are not used as constraints in regions other than Europe.

To analyse the robustness of these constraints, we fitted the harmonics of the observed and optimised mole fractions with CCG-curve fit (Thoning et al., 1989) with different settings for the short- and long-term cutoffs and a different number of harmonics, all centered around the default settings. The values tested are shown in Table D1. The standard deviation of the metrics for a site, calculated using different settings, is generally about 100 times smaller than the mean metric for that respective site, indicating a high signal-to-noise ratio (not shown).
<figure><img src="image_20.png" /><figcaption>**Figure D2.** Left: Kernel density estimate (KDE) of the correlation coefficient between the metrics (SCA (blue), ZC (green) and CUP (orange)), and flux estimates from different systems over Europe. Different settings for the CurveFit (D1) are treated as independent ‘observations’ for this plot, but differences due to the CCG settings are small. Right: KDE of the estimated fluxes based on the SCA (blue), CUP (orange), ZC (green) and the ensemble of inversions (red). Each datapoint included in the distribution represents one site with one set of CCG settings.</figcaption></figure>

<table><caption>**Table D1.** Parameter combinations tested in the curve fitting of the seasonal harmonics.</caption><thead><tr><th>Setting</th><th>Parameters used</th></tr></thead><tbody><tr><td>Short-term cutoff</td><td>60, 70, 80, 90, 100, 110</td></tr><tr><td>Long-term cutoff</td><td>500, 550, 600, 650, 700, 750</td></tr><tr><td>Number of harmonics</td><td>3, 4, 5</td></tr></tbody></table>

## Appendix E Amazon Anomalies

We analyzed the anomalies of the inverse flux estimates both compared to anomalies from direct flux observations from eddy-covariance (EC) and anomalies in independent atmospheric CO₂ observations at the ATTO site (see Section 2.4.8). Flux anomalies from the ensemble mean and CarboScope, CAMS, NISMON, CT-NOAA, CMS-Flux, COLA, and NTFVAR show a strong correlation to anomalies in the observed mole fractions; and flux anomalies from the ensemble mean and CAMS-Satellite, COLA and CTE correlate well to anomalies in the EC-observed NEE (see Figure E2). As stated in the methods, we do not expect global inverse systems to be able to replicate the highly localized eddy-covariance towers, and we only use the eddy-covariance observations as reference point for the presence of larger-scale anomalies.

The inversions, however, do not show agreement on the magnitude of the anomalies in the El Niño years of 2016 (end of the event) and 2023 (onset of the event). This is shown in Figure E1, in which the inversions that correlate well to observed atmospheric anomalies are shown in thicker lines. Similar behavior of the ensemble is observed for selecting on correlation with eddy-covariance observations (systems *p*-value shown in Figure E2; resulting fluxes not shown). Thus, currently, no improved selection for analysis of Amazonian anomalies is available. This can both be attributed to the limited observation capacity in the Amazon and the scale on which these anomalies occur.
<figure><img src="image_21.png" /><figcaption>**Figure E1.** Simulated anomalies in the footprint of the ATTO tower (Botía et al., 2022) for 2016 (left) and 2023 (right). Inverse systems that correlate well to observed anomalies (Figure E2) are shown in the thicker lines. The box plots show the ensemble mean spread and the spread of the sub-selected systems for both years.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Figure E2.** *p* values for: the correlation between footprint-convolved flux anomalies and observed anomalies of atmospheric CO₂ mole fractions at ATTO (left), and correlation between the optimized flux estimates at the ATTO grid cell and eddy-covariance observations at ATTO for the different systems (right). 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>

## Appendix F CONTRAIL analysis

An overview of the CONTRAIL observations used to constrain the East Asian flux is shown in Figure F1. We use the mismatch with observations in the vertical profile, as shown in the right panel of Figure F1. It should be noted that with the ATom analysis we performed (Figure 7), we found differences in the vertical distribution that we could explain due to the transport model used in the inversion. However, over East Asia we did not find differences related to the transport model.

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<figure><img src="image_23.png" /></figure>

**Figure F1.** Left: CONTRAIL observations over the selected domain (between 80 and 135°E and 20 and 50°N used in this analysis. Right: the corresponding average mismatch with observed values per system in 500 m altitude bins. The grey lines (at 1 km and 12 km altitude) indicate the altitude range used for the analysis (Figure 13).

## Appendix G Region overviews

Here we show an overview of the fluxes (Luijkx et al., 2024) in the 15 land and 11 ocean extended RECCAP2 regions. The region mask is shown in panels a, and the prior and optimized mean flux estimates in panel b. Panel c shows the monthly flux estimates for 2015-2023 for all systems. Panels d and e show the mean and trend over the same time period. Panel f shows the mean seasonal cycle, separated by satellite and *in situ* systems. Panel g shows the interannual variability, also separated by satellite and *in situ* systems.

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<figure><img src="image_24.png" /><figcaption>**Figure G1.** Factsheet for global flux estimates</figcaption></figure>
<figure><img src="image_25.png" /><figcaption>**Figure G2.** Factsheet for land flux estimates</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>**Figure G3.** Factset for ocean flux estimates</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>**Figure G4.** Factsheet for North (>30°N) flux estimates</figcaption></figure>
<figure><img src="image_28.png" /><figcaption>**Figure G5.** Factsheet for Tropical (<30°N > °S) flux estimates</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>**Figure G6.** Factsheet for South (<30°S) flux estimates</figcaption></figure>
<figure><img src="image_30.png" /><figcaption>**Figure G7.** Factsheet for Boreal North American flux estimates</figcaption></figure>
<figure><img src="image_31.png" /><figcaption>**Figure G8.** Factsheet for Temperate North American flux estimates</figcaption></figure>
<figure><img src="image_32.png" /><figcaption>**Figure G9.** Factsheet for European flux estimates</figcaption></figure>
<figure><img src="image_33.png" /><figcaption>**Figure G10.** Factsheet for Russian flux estimates</figcaption></figure>
<figure><img src="image_34.png" /><figcaption>**Figure G11.** Factsheet for Central Eurasian flux estimates</figcaption></figure>
<figure><img src="image_35.png" /><figcaption>**Figure G12.** Factsheet for East Asian flux estimates</figcaption></figure>

<caption>**Figure G13.** Factsheet for global flux estimates</caption>
<figure><img src="image_36.png" /><figcaption>**Figure G14.** Factsheet for Brazilian flux estimates</figcaption></figure>
<figure><img src="image_37.png" /><figcaption>**Figure G15.** Factsheet for North African flux estimates</figcaption></figure>
<figure><img src="image_38.png" /><figcaption>**Figure G16.** Factsheet for Central African flux estimates</figcaption></figure>
<figure><img src="image_39.png" /><figcaption>**Figure G17.** Factsheet for South African flux estimates</figcaption></figure>
<figure><img src="image_40.png" /><figcaption>**Figure G18.** Factsheet for Oceanian flux estimates</figcaption></figure>
<figure><img src="image_41.png" /><figcaption>**Figure G19.** Factsheet for Temperate South American flux estimates</figcaption></figure>
<figure><img src="image_42.png" /><figcaption>**Figure G20.** Factsheet for Central American flux estimates</figcaption></figure>
<figure><img src="image_43.png" /><figcaption>**Figure G21.** Factsheet for Indian flux estimates</figcaption></figure>
<figure><img src="image_44.png" /><figcaption>**Figure G22.** Factsheet for Southeast Asian flux estimates</figcaption></figure>
<figure><img src="image_45.png" /><figcaption>**Figure G23.** Factsheet for North Pacific flux estimates</figcaption></figure>
<figure><img src="image_46.png" /><figcaption>**Figure G24.** Factsheet for West Pacific flux estimates</figcaption></figure>
<figure><img src="image_47.png" /><figcaption>**Figure G25.** Factsheet for East Pacific flux estimates</figcaption></figure>
<figure><img src="image_48.png" /><figcaption>**Figure G26.** Factsheet for Southern Ocean flux estimates</figcaption></figure>
<figure><img src="image_49.png" /><figcaption>**Figure G27.** Factsheet for Northern ocean flux estimates</figcaption></figure>
<figure><img src="image_50.png" /><figcaption>**Figure G28.** Factsheet for North Atlantic flux estimates</figcaption></figure>
<figure><img src="image_51.png" /><figcaption>**Figure G29.** Factsheet for Tropical Atlantic flux estimates</figcaption></figure>
<figure><img src="image_52.png" /><figcaption>**Figure G30.** Factsheet for South Atlantic flux estimates</figcaption></figure>
<figure><img src="image_53.png" /><figcaption>**Figure G31.** Factsheet for Southern Ocean flux estimates</figcaption></figure>
<figure><img src="image_54.png" /><figcaption>**Figure G32.** Factsheet for Tropical Indian Ocean flux estimates</figcaption></figure>
<figure><img src="image_55.png" /><figcaption>**Figure G33.** Factsheet for South Indian Ocean flux estimates</figcaption></figure>