Appendix A: Supplementary tables

<table><caption>**Table A1.** Comparison of the processes included in the bookkeeping method and DGVMs in their estimates of *E*<sub>LUC</sub> and *S*<sub>LAND</sub>. See Table 4 for model references. All models include deforestation and forest regrowth after abandonment of agriculture (or from afforestation activities on agricultural land). Processes relevant for *E*<sub>LUC</sub> are only described for the DGVMs used with land-cover change in this study. Here we use the term “DGVM” in the broadest sense in terms of global vegetation models which are able to dynamically adjust to imposed land use and land-use change (LULCC).</caption><thead><tr><th rowspan="2">Processes relevant for E<sub>LUC</sub></th><th colspan="4">Bookkeeping models</th><th colspan="10">DGVMs</th></tr><tr><th>H&amp;N</th><th>BLUE</th><th>OSCAR</th><th>CABLE-POP</th><th>CLASSIC</th><th>CLMS5.0</th><th>DLEM</th><th>IBIS</th><th>ISAM</th><th>JSBACH</th><th>JULES-ES</th><th>LPJ-GUESS</th><th>LPJ</th><th>LPX-Bem</th><th>OCNv2</th><th>ORCHIDEEv3</th><th>SDGVM</th><th>VISIT</th><th>YIBs</th></tr></thead><tbody><tr><td>Wood harvest and forest degradation<sup>a</sup></td><td>yes</td><td>yes</td><td>yes</td><td>yes</td><td>no</td><td>yes</td><td>yes</td><td>yes</td><td>yes</td><td>yes</td><td>no</td><td>yes</td><td>yes</td><td>no<sup>d</sup></td><td>yes</td><td>yes</td><td>no</td><td>yes</td><td>no</td></tr><tr><td>Shifting cultivation<sup>f</sup></td><td>yes<sup>b</sup></td><td>yes</td><td>yes</td><td>yes</td><td>no</td><td>yes</td><td>no</td><td>yes</td><td>no</td><td>yes</td><td>no</td><td>yes</td><td>yes</td><td>no<sup>d</sup></td><td>no</td><td>no</td><td>no</td><td>yes</td><td>no</td></tr><tr><td>Subgrid scale transitions</td><td>yes(R)<sup>j</sup></td><td>yes(R)<sup>j</sup></td><td>yes(R)</td><td>yes(R)</td><td>yes(L)</td><td>yes(R)</td><td>yes(R)</td><td>yes(R)</td><td>yes(R+L)</td><td>yes(R)</td><td>yes(R)</td><td>yes(L)</td><td>yes(R)</td><td>yes(R+L)</td><td>yes(R)</td><td>yes(R)</td><td>yes(R)</td><td>yes(R)</td><td>yes(L)</td></tr><tr><td>Cropland harvest (removed, R, or added to litter, L)</td><td>yes(R)<sup>j</sup></td><td>yes(R)<sup>j</sup></td><td>yes(R)</td><td>yes(R)</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td></tr><tr><td>Peat fires</td><td>yes</td><td>yes</td><td>yes</td><td>no</td><td>no</td><td>yes</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td></tr><tr><td>Fire as a management tool</td><td>yes<sup>f</sup></td><td>yes<sup>f</sup></td><td>yes<sup>b</sup></td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td></tr><tr><td>N fertilization</td><td>yes<sup>f</sup></td><td>yes<sup>f</sup></td><td>yes<sup>b</sup></td><td>no</td><td>no</td><td>yes<sup>g</sup></td><td>no</td><td>no</td><td>no</td><td>no</td><td>yes<sup>i</sup></td><td>yes</td><td>no</td><td>yes</td><td>yes</td><td>yes</td><td>yes<sup>g</sup></td><td>no</td><td>no</td></tr><tr><td>Tillage</td><td>yes<sup>f</sup></td><td>yes<sup>f</sup></td><td>yes<sup>b</sup></td><td>no</td><td>no</td><td>yes<sup>g</sup></td><td>no</td><td>no</td><td>no</td><td>no</td><td>yes</td><td>yes</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td></tr><tr><td>Irrigation</td><td>yes<sup>f</sup></td><td>yes<sup>f</sup></td><td>yes<sup>b</sup></td><td>no</td><td>no</td><td>yes</td><td>no</td><td>no</td><td>no</td><td>no</td><td>yes</td><td>yes</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td></tr><tr><td>Welland drainage</td><td>yes<sup>f</sup></td><td>yes<sup>f</sup></td><td>yes<sup>b</sup></td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>yes</td><td>yes</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td></tr><tr><td>Erosion</td><td>yes<sup>f</sup></td><td>yes<sup>f</sup></td><td>yes<sup>b</sup></td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td></tr><tr><td>Peat drainage</td><td>yes</td><td>yes</td><td>yes<sup>b</sup></td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td></tr><tr><td>Grazing and mowing</td><td>yes(r)<sup>j</sup></td><td>yes(r)<sup>j</sup></td><td>yes(r)</td><td>yes(r)</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>yes(r)</td><td>yes(l)</td><td>no</td><td>yes(r+1)</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td></tr><tr><td>Harvest (removed, r, or added to litter, l)</td><td>yes(r)<sup>j</sup></td><td>yes(r)<sup>j</sup></td><td>yes(r)</td><td>yes(r)</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td></tr><tr><td colspan="17">Processes also relevant for S<sub>LAND</sub> (in addition to CO<sub>2</sub> fertilization and climate)</td></tr><tr><td>Fire simulation and/or suppression</td><td>n/a</td><td>n/a</td><td>n/a</td><td>no</td><td>yes</td><td>yes</td><td>no</td><td>yes</td><td>no</td><td>yes</td><td>yes</td><td>yes</td><td>yes</td><td>yes</td><td>yes</td><td>no</td><td>no</td><td>no</td><td>no</td></tr><tr><td>Carbon-nitrogen interactions, including N deposition</td><td>n/a</td><td>n/a</td><td>n/a</td><td>yes</td><td>no<sup>f</sup></td><td>yes</td><td>yes</td><td>no</td><td>yes</td><td>no</td><td>yes</td><td>yes</td><td>yes</td><td>no</td><td>yes</td><td>yes</td><td>yes<sup>c</sup></td><td>no</td><td>no<sup>f</sup></td></tr><tr><td>Separate treatment of direct and diffuse solar radiation</td><td>n/a</td><td>n/a</td><td>n/a</td><td>yes</td><td>no</td><td>yes</td><td>no</td><td>no</td><td>no</td><td>no</td><td>yes</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>no</td><td>yes</td></tr></tbody></table>
<table><caption>Table A2. Comparison of the processes and model set-up for the Global Ocean Biogeochemistry Models for their estimates of SOCEAN. See Table 4 for model references.</caption><thead><tr><th></th><th>NEMO-PlankTOM12</th><th>NEMO-PISCES (PSL)</th><th>MICOM-HAMOCC (NofESM1-OCv1.2)</th><th>MPION-HAMOCC6</th><th>FESOM-2.1-RECOAM2</th><th>NEMO3.6-PISCES2-gas (CNRM)</th><th>MOM6-COBALT (Princeton)</th><th>CESM-ETHZ</th><th>MRI-ESM2-1</th><th>CESM2</th></tr></thead><tbody><tr><td>Model specifics</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Physical ocean model</td><td>NEMO3.6-ORCA2</td><td>NEMO3.6-ORCA1L75</td><td>MICOM OCv1.2</td><td>MPION</td><td>FESOM-2.1</td><td>NEMO3.6-GELATOv6-ORCA1L75 PISCES2-gas</td><td>MOM6-SIS2</td><td>CESMv1.3 (ocean model based on POP2)</td><td>MRI-CON4</td><td>CESM2-POP2</td></tr><tr><td>Biogeochemistry model</td><td>PlankTOM12</td><td>PISCES2</td><td>HAMOCC (NofESM1-OCv1.2)</td><td>HAMOCC6</td><td>RECOAM-2-M</td><td>unstructured mesh, 20-120 km resolution (COREM-mesh)</td><td>COBALTv2</td><td>BEC (modified & extended)</td><td>NIPZD</td><td>MARBL</td></tr><tr><td>Horizontal resolution</td><td>2° long, 0.3 to 1.5° lat</td><td>1° long, 0.3 to 1° lat</td><td>1.5°</td><td>51 isopycnic layers + 2 layers representing a bulk mixed layer</td><td>40 levels</td><td>46 levels, 10m spacing in the top 100 m</td><td>0.5° long, 0.25 to 0.5° lat</td><td>1° long, 0.3 to 0.5° lat</td><td>1.125° long, 0.53° to 0.27° lat</td><td>1.125° long, 0.53° to 0.27° lat</td></tr><tr><td>Vertical resolution</td><td>31 levels</td><td>75 levels, 1 m at the surface</td><td></td><td>3.6006E+08</td><td>3.6598E+08</td><td>3.6435E+08</td><td>3.6111E+08</td><td>60 levels</td><td>60 levels with 1 level of bottom boundary layer</td><td>60 levels</td></tr><tr><td>Total ocean area on active grid (km²)</td><td>3.6080E+08</td><td>3.6270E+08</td><td>Orr et al. (2017), but with a = 0.337</td><td>Orr et al. (2017)</td><td>Orr et al. (2017)</td><td>Orr et al. (2017)</td><td>Orr et al. (2017)</td><td>60 levels, hybrid coordinates, 2 m at surface</td><td>60 levels</td><td>60 levels with 1 level of bottom boundary layer</td></tr><tr><td>Gas exchange parameterization</td><td>Wannimhoff (1992)</td><td>Orr et al. (2017)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CO₂ chemistry routines</td><td>following Broecker (1982)</td><td>mocsy</td><td>following Dickson et al. (2007)</td><td>Ilyina et al. (2013) adapted to comply with OMIP protocol (Orr et al., 2017)</td><td>mocsy</td><td>mocsy</td><td>mocsy</td><td>Wannimhoff (1992, coefficient a scaled down to 0.31) OCMIP (Orr et al., 2017)</td><td>mocsy</td><td>OCMIP (Orr et al., 2017)</td></tr><tr><td>River input (pCO₂ yr⁻¹) (organic/morganic DIC)</td><td>0.7237</td><td>0.617</td><td>0</td><td>0.777</td><td>00</td><td>~0.6117</td><td>~0.077~0.15</td><td>0.337</td><td>00</td><td>0.1730/263</td></tr><tr><td>Net flux to sediment (pCO₂ yr⁻¹) (organic/other)</td><td>0.7237</td><td>0.597</td><td>around 0.547</td><td>-0.44</td><td>00</td><td>~0.6567</td><td>~0.117~0.07 (CaCO₃)</td><td>0.217</td><td>00</td><td>0.345/0.110 (CaCO₃)</td></tr><tr><td>Spin-up procedure</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Initialization of carbon chemistry</td><td>GLODAPv1 (pre-industrial DIC)</td><td>GLODAPv2 (pre-industrial DIC)</td><td>GLODAPv1 (pre-industrial DIC)</td><td>initialization from previous simulation</td><td>GLODAPv2 (pre-industrial DIC)</td><td>GLODAPv2 (pre-industrial DIC)</td><td>GLODAPv2 (pre-industrial DIC)</td><td>GLODAPv2 (pre-industrial DIC)</td><td>GLODAPv2 (pre-industrial DIC)</td><td>GLODAPv2 (pre-industrial DIC)</td></tr><tr><td>Pre-industrial spin-up prior to 1850</td><td>spin-up 1750-1947</td><td>spin-up starting in 1836 with 3 loops of JRAS5</td><td>1000 year spin-up</td><td>~2000 years</td><td>189 years</td><td>Long spin-up (> 1000 years)</td><td>spin-up 1655-1849</td><td>166 years with xCO₂ = 284.32</td><td>spin-up 1653-1850. xCO₂ = 278</td><td>spin-up 1653-1850. xCO₂ = 278</td></tr><tr><td>Atmospheric forcing fields and CO₂</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Atmospheric forcing for (i) pre-industrial spin-up (ii) spin-up 1850-1958 for simulation B, (iii) simulation B</td><td>NCEP year 1990 (i, i, iii)</td><td>looping full JRAS5 reanalysis</td><td>looping full JRAS5 reanalysis (i, i, iii)</td><td>CORE-1 (normal-year) forcing (i, i, iii)</td><td>OMIP climatology (i, NCEP year 1957 (i, iii))</td><td>JRAS5-do-v1.50 repeated-year 1961 (i, ii, iii)</td><td>JRAS5-do-v1.50 full reanalysis (i) cycling-year 1958 (i, iii)</td><td>CORE-2 until 1835, 1835-1850. JRAS (i) normal-year forcing created from JRAS5-do version 1.3 (ii, iii)</td><td>JRAS5-do-v1.50 repeat-year 1990/991 (i, ii, iii)</td><td>(i) repeating JRAS 1958-2018 for spin-up for A & D repeating JRAS 1990/1991 repeat-year forcing for spin-up for B & C, (ii) repeat-year forcing xCO₂ of 278 ppm</td></tr><tr><td>Atmospheric CO₂ for control spin-up 1850-1958 for simulation B, and for simulation B</td><td>constant to 278 ppm, converted to pCO₂ temperature formulation (Sarmiento et al., 1992)</td><td>xCO₂ of 286-46 ppm, converted to pCO₂ with constant sea-level pressure and water-vapour pressure</td><td>xCO₂ of 278 ppm, converted to pCO₂ with sea-level pressure and water-vapour pressure</td><td>xCO₂ of 278 ppm, converted to pCO₂ with constant sea-level pressure and water-vapour pressure</td><td>xCO₂ of 278 ppm, converted to pCO₂ with conversion to pCO₂</td><td>xCO₂ of 278 ppm, converted to pCO₂ with constant sea-level pressure and water-vapour pressure</td><td>xCO₂ of 286-46 ppm, converted to pCO₂ with constant sea-level pressure and water-vapour pressure</td><td>xCO₂ of 287 ppm, converted to pCO₂ with sea-level pressure and water-vapour pressure</td><td>xCO₂ of 284-32 ppm (CMIP6 pControl), converted to pCO₂ with water-vapour and sea-level pressure (JRA55-do repeat-year 1990/991)</td><td>(i) repeating JRAS 1958-2018 for spin-up for A & D repeating JRAS 1990/1991 repeat-year forcing for spin-up for B & C, (ii) repeat-year forcing xCO₂ of 278 ppm</td></tr><tr><td>Atmospheric forcing for historical spin-up 1850-1958 for simulation A (i) and for simulation A (ii)</td><td>1750-1947; NCEP year 1990; 1948-2021: NCEP</td><td>looping full JRAS5 reanalysis (i, i, iii)</td><td>looping full JRAS5 reanalysis (i, i, iii)</td><td>CORE-1 (normal-year) forcing: from 1948 onwards: JRAS5-do-v1.4 then 1.5 for 2020-2021 (ii)</td><td>CORE-2 (normal-year) correction (i, i, iii)</td><td>CORE-1 (normal-year) correction (i, i, iii)</td><td>CORE-2 (normal-year) correction (i, i, iii)</td><td>CORE-2 (normal-year) correction (i, i, iii)</td><td>CORE-2 (normal-year) correction (i, i, iii)</td><td>CORE-2 (normal-year) correction (i, i, iii)</td></tr><tr><td>Atmospheric CO₂ for historical spin-up 1850-1958 for simulation A (i) and for simulation A (ii)</td><td>xCO₂ provided by the GCB, converted to pCO₂ temperature formulation (Sarmiento et al., 1992), monthly resolution (i, ii)</td><td>xCO₂ provided by the GCB, converted to pCO₂ with sea-level pressure (taken from the atmospheric forcing) and water-vapour pressure (i, ii)</td><td>xCO₂ provided by the GCB, converted to pCO₂ with sea-level pressure (taken from the atmospheric forcing) and water-vapour pressure (i, ii)</td><td>xCO₂ provided by the GCB, converted to pCO₂ with sea-level pressure (taken from the atmospheric forcing) and water-vapour pressure (i, ii)</td><td>xCO₂ provided by the GCB, converted to pCO₂ with sea-level pressure (taken from the atmospheric forcing) and water-vapour pressure (i, ii)</td><td>xCO₂ provided by the GCB, converted to pCO₂ with sea-level pressure (taken from the atmospheric forcing) and water-vapour pressure (i, ii)</td><td>xCO₂ provided by the GCB, converted to pCO₂ with sea-level pressure (taken from the atmospheric forcing) and water-vapour pressure (i, ii)</td><td>xCO₂ provided by the GCB, converted to pCO₂ with sea-level pressure (taken from the atmospheric forcing) and water-vapour pressure (i, ii)</td><td>xCO₂ provided by the GCB, converted to pCO₂ with sea-level pressure (taken from the atmospheric forcing) and water-vapour pressure (i, ii)</td><td>xCO₂ provided by the GCB, converted to pCO₂ with sea-level pressure (taken from the atmospheric forcing) and water-vapour pressure (i, ii)</td><td>xCO₂ provided by the GCB, converted to pCO₂ with sea-level pressure (taken from the atmospheric forcing) and water-vapour pressure (i, ii)</td></tr></tbody></table>
<table><caption>Table A3. Description of ocean data products used for assessment of SOCEAN. See Table 4 for references.</caption><thead><tr><th></th><th>Jena-MLS</th><th>MPI-SOMFFN</th><th>CMEMS:LSCE-FFNN</th><th>Watson et al</th><th>NIES-NN</th><th>JMA-MLR</th><th>OS-ETHZ-GRaCER</th><th>LDEO HPD</th></tr></thead><tbody><tr><td>Method</td><td>Spatio-temporal interpolation (version oc.2022); Spatiotemporal field of ocean-internal carbon sources and sinks is fit to the SOCAT2022 pCO2 data. Includes a multi-linear regression against environmental drivers to bridge data gaps.</td><td>A feed-forward neural network (FFN) determines the non-linear relationship between SOCAT pCO2 measurements and environmental predictors. The models are used to reconstruct sea surface fugacity of CO2 and convert to air-sea CO2 fluxes.</td><td>An ensemble of neural network models trained on 100 subsampled datasets from SOCAT and environmental predictors. The models are used to reconstruct sea surface fugacity of CO2 and convert to air-sea CO2 fluxes.</td><td>Modified MPI-SOMFFN network model trained on SOCAT2022 pCO2 database. Corrected to the sub-skin temperature of the ocean as measured by satellite (Goddijin Murphy et al., 2015). Flux calculation corrected for the cool and salty surface skin. Monthly climatology for skin temperature correction derived from ESA CCI product for the period 2003 to 2011 (Merchant et al., 2019).</td><td>A feed-forward neural network model trained on SOCAT2021 fCO2 and environmental predictor data. The fCO2 was normalized to the reference year 2000 by a global fCO2 trend. We fitted the dependence of fCO2 on year by linear regression. We subtracted the trend from fCO2 and used the neural network to model the non-linear dependence of the residual on predictors. The trend was added to model predictions to reconstruct fCO2.</td><td>Fields of total alkalinity (TA) were estimated by using a multiple linear regression (MLR) method based on GLO-DAP2.2021 and satellite observation data.</td><td>Geospatial random cluster ensemble regression is a two-step cluster-regression approach, where multiple clustering instances with slight variations are run to create an ensemble of estimates. We use K-means clustering and a combination of gradient-boosted trees and feed-forward neural networks to estimate SOCAT2022 fCO2.</td><td>Based on fCO2 misfit between observed fCO2 and eight of the ocean biogeochemical models used in this assessment. The extreme gradient boosting method links this misfit to environmental observations to reconstruct the model misfit across all space and time, which is then added back to model-based fCO2 estimate. The final reconstruction of surface fCO2 is the average across the eight reconstructions.</td></tr><tr><td>Gas exchange parameterization</td><td>Wanninkhof (1992); transfer coefficient k scaled to match a global mean transfer rate of 16.5 cm h<sup>-1</sup> by Naeiger (2009).</td><td>Wanninkhof (1992); transfer coefficient k scaled to match a global mean transfer rate of 16.5 cm h<sup>-1</sup></td><td>Wanninkhof (2014); transfer coefficient k scaled to match a global mean transfer rate of 16.5 cm h<sup>-1</sup> (Naeiger, 2009)</td><td>Nightingale et al. (2000)</td><td>Mean and mean square wind monthly at 1 × 1° from CCMP, 0.25° × 0.25° × 6-hourly data, 1 × 1°</td><td>Wanninkhof (2014); transfer coefficient k scaled to match a global mean transfer rate of 16.5 cm h<sup>-1</sup> (Naeiger, 2009)</td><td>Wanninkhof (2014); transfer coefficient k scaled to match a global mean transfer rate of 16.5 cm h<sup>-1</sup> (Naeiger, 2009).</td><td>Wanninkhof (1992); averaged and scaled for three reanalysis wind data sets to a global mean 16.5 cm h<sup>-1</sup> (after Naeiger, 2009; Fay et al., 2021)</td></tr><tr><td>Wind product</td><td>JMA55-do reanalysis</td><td>ERA 5</td><td>ERA5</td><td>ERA5</td><td>ERA5</td><td>JRA55</td><td>JRA55, ERA5, NCEP1</td><td>JRA55, ERA5, CCMP2</td></tr><tr><td>Spatial resolution</td><td>2.5° longitude × 2° latitude daily</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td></tr><tr><td>Temporal resolution</td><td>Spatially and temporally varying field based on atmospheric CO2 data from 169 stations (Jena Carbon Scope atmospheric inversion sEXTALL_v2021).</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td></tr><tr><td>Atmospheric CO2</td><td>Spatially and temporally varying field based on atmospheric pCO2-wet calculated from the NOAA GMD marine boundary layer xCO2 and NCEP sea-level pressure with pH₂O. Atmospheric inversion from the Copernicus Atmosphere Monitoring Service and atmospheric dry-air pressure, which is derived from monthly surface pressure (ERA5) and water-vapour pressure fitted by Weiss and Price (1980).</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td><td>1 × 1°</td></tr><tr><td></td><td>3.50E+08</td><td>3.50E+08</td><td>3.50E+08</td><td>3.50E+08</td><td>3.50E+08</td><td>3.50E+08</td><td>3.50E+08</td><td>3.50E+08</td></tr><tr><td>Total ocean area on native grid (km²)</td><td>3.63E+08</td><td>3.63E+08</td><td>3.63E+08</td><td>3.49E+08</td><td>3.49E+08</td><td>3.10E+08</td><td>(2.98E+08 to 3.16E+08, depending on ice cover)</td><td>Method has near-full coverage.</td></tr><tr><td>method to extend product to full global ocean coverage</td><td>Arctic and marginal seas added following Land-schützer et al. (2020). No coastal cut.</td><td></td><td></td><td></td><td></td><td></td><td>Fay et al. (2021)</td><td>Fay et al. (2021) was used, and gaps were filled with monthly climatology. In-terrestrial variability was added to the climatology based on the temporal evolution of five products for the years 1985 through 2020 and then only using this product for the year 2021.</td></tr></tbody></table>
<table><caption>**Table A4.** Comparison of the inversion set-up and input fields for the atmospheric inversions. Atmospheric inversions see the full CO₂ fluxes, including the anthropogenic and pre-industrial fluxes. Hence, they need to be adjusted for the pre-industrial flux of CO₂ from the land to the ocean that is part of the natural carbon cycle before they can be compared with S<sub>OCEAN</sub> and S<sub>LAND</sub> from process models. See Table 4 for references.</caption><thead><tr><th></th><th>Copernicus Atmosphere Monitoring Service (CAMS)</th><th>Carbon-Tracker Europe (CTE)</th><th>Jena CarboScope</th><th>UoE</th><th>NISMON-CO<sub>2</sub></th><th>CMS-Flux</th><th>GONGGA</th><th>THU</th><th>Copernicus Atmosphere Monitoring Service (CAMS) Satellite</th></tr></thead><tbody><tr><td>Versión number</td><td>v21r1</td><td>v2022</td><td>v2022</td><td>UoE v6.1b</td><td>v2022.1</td><td>v2022</td><td>v2022</td><td>v2022</td><td>FT21r2</td></tr><tr><td>Observations</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Atmospheric observations</td><td>Hourly resolution (well-mixed conditions) obspack GLOBALVIEWplus v7.0<sup>a</sup> and NRT_v7.2<sup>b</sup>, WDCGG, RAMCES, and ICOS ATC</td><td>Hourly resolution (well-mixed conditions) obspack GLOBALVIEWplus v7.0<sup>a</sup> and NRT_v7.2<sup>b</sup></td><td>Flasks and hourly resolution from various institutions (outliers removed by 2σ criterion)</td><td>Hourly resolution (well-mixed conditions) obspack GLOBALVIEWplus v7.0<sup>a</sup> and NRT_v7.2<sup>b</sup></td><td>Hourly resolution (well-mixed conditions) obspack GLOBALVIEWplus v7.0<sup>a</sup> and NRT_v7.2<sup>b</sup></td><td>ACOS-GOSAT v9<sup>r</sup>; OCO-2 v10 scaled to WMO 2019 standard; and remote flask observations from ObsPack, GLOBALVIEW plus, v7.0<sup>c</sup>, and NRT_v7.2<sup>b</sup></td><td>OCO-2 v10r data scaled to the WMO 2019 standard</td><td>OCO-2 v10r data scaled to the WMO 2019 standard</td><td>Bias-corrected ACOS GOSAT v9 over land until August 2024 plus bias-corrected ACOS OCO-2 v10 over land, with both rescaled to X2019</td></tr><tr><td>Period covered</td><td>1979-2021</td><td>2001-2021</td><td>1957-2021</td><td>2001-2021</td><td>1990-2021</td><td>2010-2021</td><td>2015-2021</td><td>2015-2021</td><td>2010-2021</td></tr><tr><td>Prior fluxes</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Biosphere and fires</td><td>ORCHIDEE, GFEDv4.1s</td><td>SIB4 and GFAS</td><td>Zero</td><td>CASA v1.0, climatology after 2016 and GFEDv4.0</td><td>VISIT and GFEDv4.1s</td><td>CARDAMOM</td><td>CASA and GFEDv4.1s</td><td>SIB4.2 and GFEDv4.1s</td><td>ORCHIDEE, GFEDv4.1s</td></tr><tr><td>Ocean</td><td>CMEMS-LSCE-FFNN 2021</td><td>CarboScope v2021</td><td>CarboScope v2022</td><td>Takahashi climatology</td><td>JMA global ocean mapping (Iida et al., 2015)</td><td>MOM6</td><td>Takahashi climatology</td><td>Takahashi climatology</td><td>CMEMS-LSCE-FFNN 2021</td></tr><tr><td>Fossil fuels</td><td>GridFED 2021.2<sup>c</sup> with an extrapolation to 2021 based on Carbonmonitor and NO<sub>2</sub></td><td>GridFED 2021.3 + GridFED 2022.2 for 2021</td><td>GridFED v2022.2<sup>c</sup></td><td>GridFED 2022.1<sup>c</sup></td><td>GridFED v2022.2<sup>c</sup></td><td>GridFED2022.2<sup>c</sup></td><td>GridFED 2021.3<sup>c</sup> with an extrapolation to 2021 based on Carbon-monitor</td><td>GridFED v2022.1<sup>c</sup></td><td>GridFED 2021.2<sup>c</sup> with an extrapolation to 2021 based on Carbonmonitor and NO<sub>2</sub></td></tr><tr><td>Transport and optimization</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Transport model</td><td>LMDZ v6</td><td>TM5</td><td>TM3</td><td>GEOs-CHEM</td><td>NICAM-TM</td><td>GEOs-CHEM</td><td>GEOs-CHEM</td><td>GEOs-CHEM</td><td>LMDZ v6</td></tr><tr><td>Weather forcing</td><td>ECMWF</td><td>ECMWF</td><td>NCEP</td><td>MERRA</td><td>JRA55</td><td>MERRA</td><td>MERRA</td><td>GEOS-FP</td><td>ECMWF</td></tr><tr><td>Horizontal resolution</td><td>Global 3.75° × 1.875°</td><td>Global 3° × 2°, Europe 1° × 1°, North America 1° × 1°</td><td>Global 3.83° × 5°</td><td>Global 4° × 5°</td><td>Isosahedral grid ~225 km</td><td>Global 4° × 5°</td><td>Global 2° × 2.5°</td><td>Global 4° × 5°</td><td>Global 3.75° × 1.875°</td></tr><tr><td>Optimization</td><td>Variational</td><td>Ensemble Kalman filter</td><td>Conjugate gradient (re-orthonormalization)<sup>d</sup></td><td>Ensemble Kalman filter</td><td>Variational</td><td>Variational</td><td>Non-linear least squares four-dimensional variation (NLS-4DVar)</td><td>Ensemble Kalman filter</td><td>Variational</td></tr></tbody></table>

<footnote><sup>a</sup> https://doi.org/10.25925/2021.0801 (Schmidt et al., 2021). <sup>b</sup> https://doi.org/10.25925/2022.0624 (Schmidt et al., 2022). <sup>c</sup> GCP-GridFED v2021.2, v2021.3, v2022.1, and v2022.2 (Jones et al., 2022) are updates through the year 2021 of the GCP-GridFED dataset presented by Jones et al. (2021). <sup>d</sup> Ocean prior is not optimized.</footnote>
<table><caption>**Table A5.** Attribution of fCO₂ measurements for the year 2021 included in SOCATv2022 (Bakker et al., 2016, 2022) to inform ocean fCO₂-based data products.</caption><thead><tr><th>Platform name</th><th>Regions</th><th>No. of measurements</th><th>Principal investigators</th><th>No. of datasets</th><th>Platform type</th></tr></thead><tbody><tr><td>1 degree</td><td>North Atlantic, coastal</td><td>71 863</td><td>Tanhua, T.</td><td>1</td><td>Ship</td></tr><tr><td>Alawai_158W_21N</td><td>Tropical Pacific</td><td>387</td><td>Sutton, A.; De Carlo, E. H.; Sabine, C.</td><td>1</td><td>Mooring</td></tr><tr><td>Atlantic Explorer</td><td>North Atlantic, tropical Atlantic, coastal</td><td>34 399</td><td>Bates, N. R.</td><td>16</td><td>Ship</td></tr><tr><td>Atlantic Sail</td><td>North Atlantic, coastal</td><td>27 496</td><td>Steinhoff, T.; Körtzinger, A.</td><td>7</td><td>Ship</td></tr><tr><td>BlueFin</td><td>Tropical Pacific</td><td>60 606</td><td>Alin, S. R.; Feely, R. A.</td><td>11</td><td>Ship</td></tr><tr><td>Cap San Lorenzo</td><td>North Atlantic, tropical Atlantic, coastal</td><td>44 281</td><td>Lefèvre, N.</td><td>7</td><td>Ship</td></tr><tr><td>CCE2_121W_34N</td><td>Coastal</td><td>1333</td><td>Sutton, A.; Send, U.; Ohman, M.</td><td>1</td><td>Mooring</td></tr><tr><td>Celtic Explorer</td><td>North Atlantic, coastal</td><td>61 118</td><td>Cronin, M.</td><td>10</td><td>Ship</td></tr><tr><td>F.G. Walton Smith</td><td>Coastal</td><td>38 375</td><td>Rodriguez, C.; Millero, F. J.; Pierrot, D.; Wanninkhof, R.</td><td>14</td><td>Ship</td></tr><tr><td>Finnmaid</td><td>Coastal</td><td>223 438</td><td>Rehder, G.; Bittig, H. C.; Glockzin, M.</td><td>1</td><td>Ship</td></tr><tr><td>FRA56</td><td>Coastal</td><td>5652</td><td>Tanhua, T.</td><td>1</td><td>Ship</td></tr><tr><td>G.O. Sars</td><td>Arctic, North Atlantic, coastal</td><td>82 607</td><td>Skjelvan, I.</td><td>9</td><td>Ship</td></tr><tr><td>GAKOA_149W_60N</td><td>Coastal</td><td>402</td><td>Monacci, N.; Cross, J.; Musielewicz, S.; Sutton, A.</td><td>1</td><td>Mooring</td></tr><tr><td>Gordon Gunter</td><td>North Atlantic, coastal</td><td>36 058</td><td>Wanninkhof, R.; Pierrot, D.</td><td>6</td><td>Ship</td></tr><tr><td>Gulf Challenger</td><td>Coastal</td><td>6375</td><td>Salisbury, J.; Vandemark, D.; Hunt, C. W.</td><td>6</td><td>Ship</td></tr><tr><td>Healy</td><td>Arctic, North Atlantic, coastal</td><td>28 998</td><td>Sweeney, C.; Newberger, T.; Sutherland, S. C.; Munro, D. R.</td><td>5</td><td>Ship</td></tr><tr><td>Henry B. Bigelow</td><td>North Atlantic, coastal</td><td>67 399</td><td>Wanninkhof, R.; Pierrot, D.</td><td>8</td><td>Ship</td></tr><tr><td>Heron Island</td><td>Coastal</td><td>989</td><td>Tilbrook, B.; Neill, C.; van Oojen, E.; Passmore, A.; Black, J.</td><td>1</td><td>Mooring</td></tr><tr><td>Investigator</td><td>Southern Ocean, coastal, tropical Pacific, Indian Ocean</td><td>120 782</td><td>Tilbrook, B.; Akl, J.; Neill, C.</td><td>6</td><td>Ship</td></tr><tr><td>KC_BUOY</td><td>Coastal</td><td>2860</td><td>Evans, W.; Pocock, K.</td><td>1</td><td>Mooring</td></tr><tr><td>Keifu Maru II</td><td>North Pacific, tropical Pacific, coastal</td><td>10 053</td><td>Kadono, K.</td><td>8</td><td>Ship</td></tr><tr><td>Laurence M. Gould</td><td>Southern Ocean</td><td>2604</td><td>Sweeney, C.; Newberger, T.; Sutherland, S. C.; Munro, D. R.</td><td>1</td><td>Ship</td></tr><tr><td>Marion Dufresne</td><td>Indian Ocean, Southern Ocean, coastal</td><td>9911</td><td>Lo Monaco, C.; Metzl, N.</td><td>1</td><td>Ship</td></tr><tr><td>Nathaniel B. Palmer</td><td>Southern Ocean</td><td>2376</td><td>Sweeney, C.; Newberger, T.; Sutherland, S. C.; Munro, D. R.</td><td>1</td><td>Ship</td></tr><tr><td>New Century 2</td><td>North Pacific, tropical Pacific, North Atlantic, coastal</td><td>198 293</td><td>Nakaoka, S.-I.; Takao, S.</td><td>10</td><td>Ship</td></tr><tr><td>Newrest - Art and Fenetres</td><td>North Atlantic, tropical Atlantic, South Atlantic, coastal</td><td>17 699</td><td>Tanhua, T.</td><td>2</td><td>Ship</td></tr><tr><td>Quadra Island Field Station</td><td>Coastal</td><td>81 201</td><td>Evans, W.; Pocock, K.</td><td>1</td><td>Mooring</td></tr><tr><td>Ronald H. Brown</td><td>North Atlantic, coastal</td><td>31 661</td><td>Wanninkhof, R.; Pierrot, D.</td><td>3</td><td>Ship</td></tr><tr><td>Ryofu Maru III</td><td>North Pacific, tropical Pacific, coastal</td><td>10 464</td><td>Kadono, K.</td><td>8</td><td>Ship</td></tr><tr><td>Sea Explorer</td><td>Southern Ocean, North Atlantic, coastal, tropical Atlantic</td><td>37 027</td><td>Landshützer, P.; Tanhua, T.</td><td>2</td><td>Ship</td></tr><tr><td>Sikuliaq</td><td>Arctic, North Pacific, coastal</td><td>60 549</td><td>Sweeney, C.; Newberger, T.; Sutherland, S. C.; Munro, D. R.</td><td>13</td><td>Ship</td></tr><tr><td>Simon Stevin</td><td>Coastal</td><td>57 055</td><td>Gkritzalis, T.; Theetaert, H.; Cat-trijsse, A.; T'Jampens, M.</td><td>11</td><td>Ship</td></tr><tr><td>Sitka Tribe of Alaska Environmental Research Laboratory</td><td>Coastal</td><td>19 086</td><td>Whitehead, C.; Evans, W.; Laphier, K.; Peterson, W.; Kennedy, E.; Hales, B.</td><td>1</td><td>Mooring</td></tr><tr><td>SOFS_142E_46S</td><td>Southern Ocean</td><td>894</td><td>Sutton, A.; Trull, T.; Shadwick, E.</td><td>1</td><td>Mooring</td></tr><tr><td>Soyo Maru</td><td>Tropical Pacific, coastal</td><td>33 234</td><td>Ono, T.</td><td>3</td><td>Ship</td></tr><tr><td>Station M</td><td>North Atlantic</td><td>447</td><td>Skjelvan, I.</td><td>1</td><td>Mooring</td></tr><tr><td>Statsraad Lehmkuhl</td><td>North Atlantic, tropical Atlantic, coastal</td><td>47 881</td><td>Becker, M.; Olsen, A.</td><td>3</td><td>Ship</td></tr><tr><td>TAO125W_0N</td><td>Tropical Pacific</td><td>241</td><td>Sutton, A.</td><td>1</td><td>Mooring</td></tr><tr><td>Tavastland</td><td>Coastal</td><td>48 421</td><td>Willstrand Wranne, A.; Stein-hoff, T.</td><td>17</td><td>Ship</td></tr><tr><td>Thomas G. Thompson</td><td>North Atlantic, tropical Atlantic, North Pacific, tropical Pacific, coastal</td><td>47 073</td><td>Alin, S. R.; Feely, R. A.</td><td>5</td><td>Ship</td></tr><tr><td>Trans Future 5</td><td>Southern Ocean, North Pacific, tropical Pacific, coastal</td><td>257 424</td><td>Nakaoka, S.-I.; Takao, S.</td><td>22</td><td>Ship</td></tr><tr><td>Tukuma Arctica</td><td>North Atlantic, coastal</td><td>70 033</td><td>Becker, M.; Olsen, A.</td><td>23</td><td>Ship</td></tr><tr><td>Wakataka Maru</td><td>North Pacific, coastal</td><td>13 392</td><td>Tadokoro, K.</td><td>2</td><td>Ship</td></tr></tbody></table>
<table><caption>**Table A6.** Aircraft measurement programmes archived by Cooperative Global Atmospheric Data Integration Project (CGADIP; Schuldt et al., 2021, 2022) that contribute to the evaluation of the atmospheric inversions (Fig. B4).</caption><thead><tr><th>Site code</th><th>Measurement programme name in Obspack</th><th>Specific DOI</th><th>Data providers</th></tr></thead><tbody><tr><td>AAO</td><td>Airborne Aerosol Observatory, Bondville, Illinois</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>ABOVE</td><td>Carbon in Arctic Reservoirs Vulnerability Experiment (CARVE)</td><td>https://doi.org/10.3334/ORNLDAAC/1404</td><td>Sweeney, C., J. B. Miller, A. Karion, S. J. Dinardo, and C. E. Miller. 2016. CARVE: L2 Atmospheric Gas Concentrations, Airborne Flasks, Alaska, 2012-2<br>015. ORNL DAAC, Oak Ridge, Tennessee, USA.</td></tr><tr><td>ACG</td><td>Alaska Coast Guard</td><td></td><td>Sweeney, C.; McKain, K.; Karion, A.; Dlugokencky, E. J.</td></tr><tr><td>ACT</td><td>Atmospheric Carbon and Transport - America</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.; Baier, B; Montzka, S.; Davis, K.</td></tr><tr><td>AIRCORENOAA</td><td>NOAA AirCore</td><td></td><td>Colm Sweeney (NOAA) AND Bianca Baier (NOAA)</td></tr><tr><td>ALF</td><td>Alta Floresta</td><td></td><td>Gatti, L. V.; Gloor, E.; Miller, J. B.; ghgobs@met.kishou.go.jp</td></tr><tr><td>AOA</td><td>Aircraft Observation of Atmospheric trace gases by JMA</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>BGI</td><td>Bradgate, Iowa</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>BNE</td><td>Beaver Crossing, Nebraska</td><td></td><td>Sasaki, N.; Machida, T.</td></tr><tr><td>BRZ</td><td>Berezorechka, Russia</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>CAR</td><td>Briggsdale, Colorado</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>CMA</td><td>Cape May, New Jersey</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>CON</td><td>CONTRAIL (Comprehensive Observation Network for Trace gases by AirLiner)</td><td>https://doi.org/10.17595/20180208.001</td><td>Machida, T.; Matsueda, H.; Sawa, Y.; Niwa, Y.</td></tr><tr><td>CRV</td><td>Carbon in Arctic Reservoirs Vulnerability Experiment (CARVE)</td><td></td><td>Sweeney, C.; Karion, A.; Miller, J. B.; Miller, C. E.; Dlugokencky, E. J.</td></tr><tr><td>DND</td><td>Dahlen, North Dakota</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>ECO</td><td>East Coast Outflow</td><td></td><td>Sweeney, C.; McKain, K.</td></tr><tr><td>ESP</td><td>Estevan Point, British Columbia</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>ETL</td><td>East Trout Lake, Saskatchewan</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>FWI</td><td>Fairchild, Wisconsin</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>GSFC</td><td>NASA Goddard Space Flight Center Aircraft Campaign</td><td></td><td>Kawa, S. R.; Abshire, J. B.; Riris, H.</td></tr><tr><td>HAA</td><td>Molokai Island, Hawaii</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>HFM</td><td>Harvard University Aircraft Campaign</td><td></td><td>Wofsy, S. C.</td></tr><tr><td>HIL</td><td>Homer, Illinois</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>HIP</td><td>HIPPO (HIAPER Pole-to-Pole Observations)</td><td>https://doi.org/10.3334/CDIAC/HIPPO_010</td><td>Wofsy, S. C.; Stephens, B. B.; Elkins, J. W.; Hintsa, E. J.; Moore, F.</td></tr><tr><td>IAGOS-CARIBIC</td><td>In-service Aircraft for a Global Observing System</td><td></td><td>Obersteiner, F.; Boenisch H; Gehrlein, T.; Zahn, A.; Schuck, T.</td></tr><tr><td>INX</td><td>INFLUX (Indianapolis Flux Experiment)</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.; Shepson, P. B.; Turnbull, J.</td></tr><tr><td>LEF</td><td>Park Falls, Wisconsin</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>NHA</td><td>Offshore Portsmouth, New Hampshire (Isles of Shoals)</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>OIL</td><td>Oglesby, Illinois</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>ORC</td><td>ORCAS (O<sub>2</sub>/N<sub>2</sub> Ratio and CO<sub>2</sub> Airborne Southern Ocean Study)</td><td>https://doi.org/10.5065/D6SB445X</td><td>Stephens, B. B, Sweeney, C., McKain, K., Kort, E.</td></tr><tr><td>PFA</td><td>Poker Flat, Alaska</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>RBA-B</td><td>Rio Branco</td><td></td><td>Gatti, L. V.; Gloor, E.; Miller, J. B.</td></tr><tr><td>RTA</td><td>Rarotonga</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>SCA</td><td>Charleston, South Carolina</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>SGP</td><td>Southern Great Plains, Oklahoma</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.; Biraud, S.</td></tr><tr><td>TAB</td><td>Tabatinga</td><td></td><td>Gatti, L. V.; Gloor, E.; Miller, J. B.</td></tr><tr><td>TGC</td><td>Offshore Corpus Christi, Texas</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>THD</td><td>Trinidad Head, California</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr><tr><td>WBI</td><td>West Branch, Iowa</td><td></td><td>Sweeney, C.; Dlugokencky, E. J.</td></tr></tbody></table>
<table><caption>**Table A7.** Main methodological changes in the global carbon budget since first publication. Methodological changes introduced in one year are kept for the following years unless noted. Empty cells mean there were no methodological changes introduced that year.</caption><thead><tr><th>Publication year</th><th>Global</th><th>Fossil fuel emissions</th><th>Country (territorial)</th><th>Country (consumption)</th><th>LUC emissions</th><th>Atmosphere</th><th>Ocean</th><th>Reservoirs</th><th>Uncertainty &amp; other changes</th></tr></thead><tbody><tr><td>2006<sup>a</sup></td><td rowspan="2">Split in regions</td><td rowspan="2"></td><td rowspan="2"></td><td rowspan="2"></td><td rowspan="2">E<sub>LUC</sub> based on FAO-FRA 2005 and constant E<sub>LUC</sub> for 2006</td><td rowspan="2">1959–1979 data from Mauna Loa, data after 1980 are from the global average</td><td rowspan="2">Based on one ocean model tuned to reproduced observed 1990s sink</td><td rowspan="2">Based on four ocean models normalized to observations with constant delta</td><td rowspan="2">±1σ provided for all components</td></tr><tr><td>2007<sup>b</sup></td><td>Constant E<sub>LUC</sub> for 2007</td></tr><tr><td>2008<sup>c</sup></td><td rowspan="2">Split between Annex B and non-Annex B</td><td rowspan="2"></td><td rowspan="2"></td><td rowspan="2">Results from an independent study discussed</td><td rowspan="2">Fire-based emission anomalies used for 2006–2008</td><td rowspan="2"></td><td rowspan="2"></td><td rowspan="2">First use of five DGVMs to compare with budget residual</td><td rowspan="2"></td></tr><tr><td>2009<sup>d</sup></td><td>E<sub>LUC</sub> updated with FAO-FRA 2010</td></tr><tr><td>2010<sup>e</sup></td><td rowspan="2">Projection for current year based on GDP</td><td rowspan="2"></td><td rowspan="2">Emissions for top emitters</td><td rowspan="2"></td><td rowspan="2">Split between Annex B and non-Annex B</td><td rowspan="2">All years from global average</td><td rowspan="2">Based on five ocean models normalized to observations with ratio E<sub>LUC</sub></td><td rowspan="2">10 DGVMs available for S<sub>LAND</sub>. First use of four models to compare with E<sub>LUC</sub></td><td rowspan="2">Confidence levels, cumulative emissions, and budget from 1750</td></tr><tr><td>2011<sup>f</sup></td><td>E<sub>LUC</sub> for 1997–2011 includes interannual anomalies from fire-based emissions</td></tr><tr><td>2012<sup>g</sup></td><td rowspan="2">129 countries from 1959</td><td rowspan="2"></td><td rowspan="2"></td><td rowspan="2">Results from an independent study discussed</td><td rowspan="2">E<sub>LUC</sub> for 2012 estimated from 2001–2010 average</td><td rowspan="2"></td><td rowspan="2">Based on six models compared with two data products to year 2011</td><td rowspan="2">Coordinated DGVM experiments for S<sub>LAND</sub> and E<sub>LUC</sub></td><td rowspan="2"></td></tr><tr><td>2013<sup>h</sup></td><td>E<sub>LUC</sub> for 1997–2013 includes interannual anomalies from fire-based emissions</td></tr><tr><td>2014<sup>i</sup></td><td>3 years of BP data</td><td>3 years of BP data</td><td></td><td></td><td>Extended to 2012 with updated GDP data</td><td></td><td></td><td></td><td></td></tr><tr><td>2015<sup>j</sup></td><td>Projection for current-year-based January–August data</td><td>National emissions from UNFCCC extended to 2014 also provided</td><td></td><td></td><td>Detailed estimates introduced for 2011 based on GTAP9</td><td></td><td></td><td></td><td></td></tr><tr><td>2016<sup>k</sup></td><td rowspan="2">2 years of BP data</td><td rowspan="2">Added three small countries and China's emissions from 1990 from BP data (this release only)</td><td rowspan="2"></td><td rowspan="2"></td><td rowspan="2">Preliminary E<sub>LUC</sub> using FRA-2015 shown for comparison, and use of five DGVMs</td><td rowspan="2"></td><td rowspan="2">Based on eight models</td><td rowspan="2">Based on seven models</td><td rowspan="2">Based on 10 models</td></tr><tr><td>2017<sup>l</sup></td><td>Average of two book-keeping models and use of 12 DGVMs</td><td></td><td></td><td></td></tr><tr><td></td><td>Projection includes India-specific data</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<footnote><sup>a</sup> Rauschen et al. (2007). <sup>b</sup> Camell et al. (2007). <sup>c</sup> GCP (2007). <sup>d</sup> Le Quéré et al. (2009). <sup>e</sup> Friedlingstein et al. (2010). <sup>f</sup> Peters et al. (2012b). <sup>g</sup> Le Quéré et al. (2013). <sup>h</sup> Le Quéré et al. (2014). <sup>i</sup> Le Quéré et al. (2015a); <sup>j</sup> Le Quéré et al. (2015b). <sup>k</sup> Le Quéré et al. (2016). <sup>l</sup> Le Quéré et al. (2018a).</footnote>
<table><caption>**Table A8.** Mapping of global carbon cycle models land flux definitions to the definition of the LULUCF net flux used in national reporting to UNFCCC. Non-intact lands are used here as proxy for “managed lands” in the country reporting; national greenhouse gas inventories (NGHGI) are gap filled (see Sect. C2.3 for details). Where available, we provide independent estimates of certain fluxes for comparison (values are in GtC yr⁻¹).</caption><thead><tr><th></th><th></th><th></th><th>2002–2011</th><th>2012–2021</th></tr></thead><tbody><tr><td colspan="2">E<sub>LUC</sub> from bookkeeping estimates (from Table 5)</td><td></td><td>1.36</td><td>1.24</td></tr><tr><td rowspan="5">S<sub>LAND</sub></td><td>total (from Table 5)</td><td>from DGVMs</td><td>-2.85</td><td>-3.10</td></tr><tr><td>in non-forest lands</td><td>from DGVMs</td><td>-0.74</td><td>-0.83</td></tr><tr><td>in non-intact forest</td><td>from DGVMs</td><td>-1.67</td><td>-1.81</td></tr><tr><td>in intact forests</td><td>from DGVMs</td><td>-0.44</td><td>-0.47</td></tr><tr><td>in intact land</td><td>from ORCHIDEE-MICT</td><td>-1.34</td><td>-1.38</td></tr><tr><td rowspan="2">E<sub>LUC</sub> plus S<sub>LAND</sub> on non-intact lands</td><td>considering non-intact forests only</td><td>from bookkeeping E<sub>LUC</sub> and DGVMs</td><td>-0.31</td><td>-0.56</td></tr><tr><td>considering all non-intact land</td><td>from ORCHIDEE-MICT</td><td>0.90</td><td>0.60</td></tr><tr><td colspan="2">National greenhouse gas inventories (LULUCF)</td><td></td><td>-0.37</td><td>-0.54</td></tr><tr><td colspan="2">FAOSTAT (LULUCF)</td><td></td><td>0.39</td><td>0.24</td></tr></tbody></table>
<table><caption>**Table A9.** Funding supporting the production of the various components of the global carbon budget in addition to the authors' supporting institutions (see the Acknowledgements for further details).</caption><thead><tr><th>Funder and grant number (where relevant)</th><th>Author initials</th></tr></thead><tbody><tr><td>Australia, Integrated Marine Observing System (IMOS)</td><td>BT</td></tr><tr><td>Australian National Environment Science Program (NESP)</td><td>JGC</td></tr><tr><td>Belgium, FWO (Flanders Research Foundation, contract grant no. I001821N)</td><td>ThaG</td></tr><tr><td>BNP Paribas Foundation through Climate &amp; Biodiversity initiative, philanthropic grant for developments of the Global Carbon Atlas</td><td>PC</td></tr><tr><td>Canada, Tula Foundation</td><td>WE, KP</td></tr><tr><td>China, National Natural Science Foundation (grant no. 41975155)</td><td>XY</td></tr><tr><td>China, National Natural Science Foundation (grant no. 42141020)</td><td>WY</td></tr><tr><td>China, National Natural Science Foundation of China (grant no. 41921005)</td><td>BZ</td></tr><tr><td>China, Scientific Research Start-up Funds (grant no. QD2021024C) from Tsinghua Shenzhen International Graduate School</td><td>BZ</td></tr><tr><td>China, Second Tibetan Plateau Scientific Expedition and Research Program (2022QZKK0101)</td><td>TX</td></tr><tr><td>China, Young Elite Scientists Sponsorship Program by CAST (grant no. YESS20200135)</td><td>BZ</td></tr><tr><td>EC Copernicus Atmosphere Monitoring Service implemented by ECMWF</td><td>FC</td></tr><tr><td>EC Copernicus Marine Environment Monitoring Service implemented by Mercator Ocean</td><td>MG</td></tr><tr><td>EC H2020 (4C; grant no. 821003)</td><td>PF, MOS, RMA, SS, GPP, PC, JIK, TI, LB, AJ, PL, LukG, NG, NMa, SZ</td></tr><tr><td>EC H2020 (CoCO2: grant no. 958927)</td><td>RMA, GPP, JIK</td></tr><tr><td>EC H2020 (COMFORT: grant no. 820989)</td><td>LukG, MG, NG</td></tr><tr><td>EC H2020 (CONSTRAIN: grant no. 820829)</td><td>RS, ThoG</td></tr><tr><td>EC H2020 (ESM2025 – Earth System Models for the Future; grant agreement no. 101003536).</td><td>RS, ThoG, TI, LB, BD</td></tr><tr><td>EC H2020 (JERICO-S3: grant no. 871153)</td><td>HCB</td></tr><tr><td>EC H2020 (VERIFY: grant no. 776810)</td><td>MWJ, RMA, GPP, PC, JIK, MJM</td></tr><tr><td>Efg International</td><td>TT, MG</td></tr><tr><td>European Space Agency Climate Change Initiative ESA-CCI RECCAP2 project 655 (ESRIN/4000123002/18/I-NB)</td><td>SS, PC</td></tr><tr><td>European Space Agency OceanSODA project (grant no. 4000137603/22/I-DT)</td><td>LukG, NG</td></tr><tr><td>France, French Oceanographic Fleet (FOF)</td><td>NMe</td></tr><tr><td>France, ICOS (Integrated Carbon Observation System) France</td><td>NL</td></tr><tr><td>France, Institut National des Sciences de l'Univers (INSU)</td><td>NMe</td></tr><tr><td>France, Institut polaire français Paul-Emile Victor(IPEV)</td><td>NMe</td></tr><tr><td>France, Institut de recherche français sur les ressources marines (IFREMER)</td><td>NMe</td></tr><tr><td>France, Institut de Recherche pour le Développement (IRD)</td><td>NL</td></tr><tr><td>France, Observatoire des sciences de l'univers Ecce-Terra (OSU at Sorbonne Université)</td><td>NMe</td></tr><tr><td>Germany, Deutsche Forschungsgemeinschaft (DFG) under Germany's Excellence Strategy – EXC 2037 “Climate, Climatic Change, and Society” – project no. 390683824</td><td>TI</td></tr><tr><td>Germany, Federal Ministry for Education and Research (BMBF)</td><td>HCB</td></tr><tr><td>Germany, Federal Ministry for Education and Research (BMBF) under project “CDRSynTra” (01LS2101A)</td><td>JP</td></tr><tr><td>Germany, German Federal Ministry of Education and Research under project “DArgo2025” (03F0857C)</td><td>TS</td></tr><tr><td>Germany, Helmholtz Association ATMO program</td><td>AA</td></tr><tr><td>Germany, Helmholtz Young Investigator Group Marine Carbon and Ecosystem Feedbacks in the Earth System (MarESys), grant no. VH-NG-1301</td><td>JH, OG</td></tr><tr><td>Germany, ICOS (Integrated Carbon Observation System) Germany</td><td>HCB</td></tr><tr><td>Hapag-Lloyd</td><td>TT, MG</td></tr><tr><td>Ireland, Marine Institute</td><td>MC</td></tr><tr><td>Japan, Environment Research and Technology Development Fund of the Ministry of the Environment (JPMEERF21S20810)</td><td>YN</td></tr><tr><td>Japan, Global Environmental Research Coordination System, Ministry of the Environment (grant no. E1751)</td><td>SN, ST, TO</td></tr><tr><td>Japan, Environment Research and Technology Development Fund of the Ministry of the Environment (JPMEERF21S20800)</td><td>HT</td></tr><tr><td>Japan, Japan Meteorological Agency</td><td>KK</td></tr><tr><td>Kuehne + Nagel International AG</td><td>TT, MG</td></tr><tr><td>Mediterranean Shipping Company (MSc)</td><td>TT, MG</td></tr><tr><td>Monaco, Fondation Prince Albert II de Monaco</td><td>TT, MG</td></tr><tr><td>Monaco, Yacht Club de Monaco</td><td>TT, MG</td></tr><tr><td>Netherlands, ICOS (Integrated Carbon Observation System)</td><td>WP</td></tr></tbody></table>
<table><caption>Table A9. Continued.</caption><thead><tr><th>Funder and grant number (where relevant)</th><th>Author initials</th></tr></thead><tbody><tr><td>Norway, Research Council of Norway (N-ICOS-2, grant no. 296012)</td><td>AO, MB, IS</td></tr><tr><td>Norway, Norwegian Research Council (grant no. 270061)</td><td>JS</td></tr><tr><td>Sweden, ICOS (Integrated Carbon Observation System)</td><td>AW</td></tr><tr><td>Sweden, Swedish Meteorological and Hydrological Institute</td><td>AW</td></tr><tr><td>Sweden, The Swedish Research Council</td><td>AW</td></tr><tr><td>Swiss National Science Foundation (grant no. 200020-200511)</td><td>QS</td></tr><tr><td>Tibet, Second Tibetan Plateau Scientific Expedition and Research Program (SQ2022QZKK0101)</td><td>TX</td></tr><tr><td>UK Royal Society (grant no. RP\R1\191063)</td><td>CLQ</td></tr><tr><td>UK, Natural Environment Research Council (SONATA: grant no. NE/P021417/1)</td><td>RW</td></tr><tr><td>UK, Natural Environmental Research Council (NE/R016518/1)</td><td>PIP</td></tr><tr><td>UK, Natural Environment Research Council (NE/V01417X/1)</td><td>MWJ</td></tr><tr><td>UK, Royal Society: The European Space Agency OCEANFLUX projects</td><td>JDS</td></tr><tr><td>UK Royal Society (grant no. RP\R1\191063)</td><td>CLQ</td></tr><tr><td>USA, BIA Tribal Resilience</td><td>CW</td></tr><tr><td>USA, Cooperative Institute for Modeling the Earth System between the National Oceanic and Atmospheric Administration Geophysical Fluid Dynamics Laboratory and Princeton University and the High Meadows Environmental Institute</td><td>LR</td></tr><tr><td>USA, Cooperative Institute for Climate, Ocean, and Ecosystem Studies (CIOCES) under NOAA Cooperative Agreement no. NA20OAR4320271</td><td>KO</td></tr><tr><td>USA, Department of Energy, Biological and Environmental Research</td><td>APW</td></tr><tr><td>USA, Department of Energy, SciDac (DESC0012972)</td><td>GCH, LPC</td></tr><tr><td>USA, Energy Exascale Earth System Model (E3SM) project, Department of Energy, Office of Science, Office of Biological and Environmental Research</td><td>GCH, LPC</td></tr><tr><td>USA, EPA Indian General Assistance Program</td><td>CW</td></tr><tr><td>USA, NASA Carbon Monitoring System program and OCO Science team program (80NM0018F0583).</td><td>JL</td></tr><tr><td>USA, NASA Interdisciplinary Research in Earth Science (IDS) (80NSSC17K0348)</td><td>GCH, LPC, BP</td></tr><tr><td>USA, National Center for Atmospheric Research (NSF Cooperative Agreement no. 1852977)</td><td>DK</td></tr><tr><td>USA, National Oceanic and Atmospheric Administration, Ocean Acidification Program</td><td>DP, RW, SRA, RAF, AJS, NMM</td></tr><tr><td>USA, National Oceanic and Atmospheric Administration, Global Ocean Monitoring and Observing Program</td><td>DRM, CSw, NRB, CRodr, DP, RW, SRA, RAF, AJS</td></tr><tr><td>USA, National Science Foundation (grant no. 1903722)</td><td>HT</td></tr><tr><td>USA, State of Alaska</td><td>NMM</td></tr><tr><td colspan="2"><strong>Computing resources</strong></td></tr><tr><td>ADA HPC cluster at the University of East Anglia</td><td>MWJ</td></tr><tr><td>CAMS inversion was granted access to the HPC resources of TGCC under the allocation A0110102201</td><td>FC</td></tr><tr><td>Cheyenne supercomputer data were provided by the Computational and Information Systems Laboratory (CISL) at NCAR</td><td>DK</td></tr><tr><td>HPC cluster Aether at the University of Bremen, financed by DFG within the scope of the Excellence Initiative</td><td>ITL</td></tr><tr><td>MRI (FUJITSU Server PRIMERGY CX2550M5)</td><td>YN</td></tr><tr><td>NIES (SX-Aurora)</td><td>YN</td></tr><tr><td>NIES supercomputer system</td><td>EK</td></tr></tbody></table>
Appendix B: Supplementary figures

<figure><img src="image_28.png" /><figcaption>**Figure B1.** Ensemble mean air–sea CO₂ flux from (a) global ocean biogeochemistry models and (b) fCO₂-based data products, averaged over the 2012–2021 period (kgC m⁻² yr⁻¹). Positive numbers indicate a flux into the ocean. (c) Gridded SOCAT v2022 fCO₂ measurements, averaged over the 2012–2021 period (µatm). In (a), model simulation A is shown. The data products represent the contemporary flux, i.e. including outgassing of riverine carbon, which is estimated to amount to 0.65 GtC yr⁻¹ globally.</figcaption></figure>
<figure><img src="image_29.png" /></figure>

**Figure B2.** Evaluation of the GOBMs and data products using the root-mean-squared error (RMSE) for the period 1990 to 2021 between the individual surface ocean fCO₂ mapping schemes and the SOCAT v2022 database. The y axis shows the amplitude of the interannual variability of the air–sea CO₂ flux (A-IAV), taken as the standard deviation of the detrended annual time series. Results are presented for the globe, northern extratropics (≥ 30° N), tropics (30° S–30° N), and southern extratropics (< 30° S) for the GOBMs (see legend, circles) and for the fCO₂-based data products (star symbols). The fCO₂-based data products use the SOCAT database and are therefore not independent of the data (see Sect. 2.4.1).
<figure><img src="image_30.png" /></figure>

**Figure B3.** Evaluation of the DGVMs using the International Land Model Benchmarking system (ILAMB; Collier et al., 2018) (left) absolute skill scores and (right) skill scores relative to other models. The benchmarking is done with observations for vegetation biomass (Saatchi et al., 2011; and global carbon unpublished data; Avitabile et al., 2016), GPP (Jung et al., 2010; Lasslop et al., 2010), leaf area index (De Kauwe et al., 2011; Myneni et al., 1997), ecosystem respiration (Jung et al., 2010; Lasslop et al., 2010), soil carbon (Hugelius et al., 2013; Todd-Brown et al., 2013), evapotranspiration (De Kauwe et al., 2011), and runoff (Dai and Trenberth, 2002). For each model–observation comparison a series of error metrics are calculated. Scores are then calculated as an exponential function of each error metric. Finally, for each variable the multiple scores from different metrics and observational data sets are combined to give the overall variable scores shown in the left panel. Overall variable scores increase from 0 to 1 with improvements in model performance. The set of error metrics vary with data set and can include metrics based on the period mean, bias, root-mean-squared error, spatial distribution, interannual variability and seasonal cycle. The relative skill score shown in the right panel is a Z score, which indicates in units of standard deviation the model scores relative to the multi-model mean score for a given variable. Grey boxes represent missing model data.

<figure><img src="image_31.png" /></figure>

**Figure B4.** Evaluation of the atmospheric inversion products. The mean of the model minus observations is shown for four latitude bands in four periods: (first panel) 2001–2021, (second panel) 2001–2010, (third panel) 2011–2021, and (fourth panel) 2015–2021. The nine systems are compared to independent CO₂ measurements made aboard aircraft over many areas of the world between 2 and 7 km above sea level. Aircraft measurements archived in the Cooperative Global Atmospheric Data Integration Project (Schuldt et al., 2021, 2022) from sites, campaigns, or programmes that have not been assimilated and cover at least 9 months (except for SH programmes) between 2001 and 2021 have been used to compute the biases of the differences in four 45° latitude bins. Land and ocean data are used without distinction, and observation density varies strongly with latitude and time, as seen in the lower panels.
<figure><img src="image_32.png" /></figure>

**Figure B5.** Comparison of the estimates of each component of the global carbon budget in this study (black line) with the estimates released annually by the GCP since 2006. Grey shading shows the uncertainty bounds representing ±1 standard deviation of the current global carbon budget based on the uncertainty assessments described in Appendix C. CO₂ emissions from (a) fossil CO₂ emissions (E fos) and (b) land-use change (E luc) and their partitioning among (c) the atmosphere (G atm), (d) land (S land), and (e) ocean (S ocean). See the legend for the corresponding years and Tables 3 and A7 for references. The budget year corresponds to the year when the budget was first released (all values are in GtC yr⁻¹).
<figure><img src="image_33.png" /></figure>

**Figure B6.** Differences in the HYDE/LUH2 land-use forcing used for the global carbon budgets GCB2020 (Friedlingstein et al., 2021), GCB2021 (Friedlingstein et al., 2022a), and GCB2022 (Friedlingstein et al., 2022b). Shown are year-to-year changes in cropland area (b) and pasture area (c). To illustrate the relevance of the update in the land-use forcing to the recent trends in E_LUC, the top panel shows the land-use emission estimate from the bookkeeping model BLUE (original model output, i.e. excluding peat fire and drainage emissions).
# Appendix C: Extended methodology

## C1 Methodology: fossil fuel CO₂ emissions ($E_{FOS}$)

### C1.1 Cement carbonation

From the moment it is created, cement begins to absorb CO₂ from the atmosphere, a process known as “cement carbonation”. We estimate this CO₂ sink, from 1931 onwards as the average of two studies in the literature (Cao et al., 2020; Guo et al., 2021). The Global Cement and Concrete Association reports a much lower carbonation rate, but this is based on the highly conservative assumption of 0% mortar (GCCA, 2021). Modelling cement carbonation requires estimation of a large number of parameters, including the different types of cement material in different countries, the lifetime of the structures before demolition, the lifetime of cement waste after demolition, and the volumetric properties of structures (Xi et al., 2016). Lifetime is an important parameter because demolition results in the exposure of new surfaces to the carbonation process. The main reasons for differences between the two studies appear to be the assumed lifetimes of cement structures and the geographic resolution, but the uncertainty bounds of the two studies overlap.

### C1.2 Emissions embodied in goods and services

CDIAC, UNFCCC, and BP national emission statistics “include greenhouse gas emissions and removals taking place within national territory and offshore areas over which the country has jurisdiction” (Rypdal et al., 2006) and are called territorial emission inventories. Consumption-based emission inventories allocate emissions to products that are consumed within a country and are conceptually calculated as the territorial emissions minus the “embodied” territorial emissions to produce exported products plus the emissions in other countries to produce imported products (consumption is equal to territorial minus exports plus imports). Consumption-based emission attribution results (e.g. Davis and Caldeira, 2010) provide additional information to territorial-based emissions that can be used to understand emission drivers (Hertwich and Peters, 2009) and quantify emission transfers by the trade of products between countries (Peters et al., 2011b). The consumption-based emissions have the same global total but reflect the trade-driven movement of emissions across the Earth’s surface in response to human activities. We estimate consumption-based emissions from 1990–2020 by enumerating the global supply chain using a global model of the economic relationships between economic sectors within and between every country (Andrew and Peters, 2013; Peters et al., 2011a). Our analysis is based on the economic and trade data from the Global Trade and Analysis Project (GTAP; Narayanan et al., 2015), and we make detailed estimates for the years 1997 (GTAP version 5); 2001 (GTAP6); and 2004, 2007, 2011, and 2014 (GTAP10.0a), covering 57 sectors and 141 countries and re-

gions. The detailed results are then extended into an annual time series from 1990 to the latest year of the gross domestic product (GDP) data (2020 in this budget) using GDP data by expenditure in current exchange rate of US dollars (USD; from the UN National Accounts main aggregates database; UN, 2021) and time series of trade data from GTAP (based on the methodology in Peters et al., 2011a). We estimate the sector-level CO₂ emissions using the GTAP data and methodology, add the flaring and cement emissions from our fossil CO₂ dataset, and then scale the national totals (excluding bunker fuels) to match the emission estimates from the carbon budget. We do not provide a separate uncertainty estimate for the consumption-based emissions; however, based on model comparisons and sensitivity analysis, they are unlikely to be significantly different than for the territorial emission estimates (Peters et al., 2012a).

### C1.3 Uncertainty assessment for $E_{FOS}$

We estimate the uncertainty of the global fossil CO₂ emissions at ±5% (scaled down from the published ±10% at ±2σ to the use of ±1σ bounds reported here; Andres et al., 2012). This is consistent with a more detailed analysis of uncertainty of ±8.4% at ±2σ (Andres et al., 2014) and at the high end of the range of ±5%–10% at ±2σ reported by (Ballantyne et al., 2015). This includes an assessment of uncertainties in the amounts of fuel consumed, the carbon and heat contents of fuels, and the combustion efficiency. While we consider a fixed uncertainty of ±5% for all years, the uncertainty as a percentage of emissions is growing with time because of the larger share of global emissions from emerging economies and developing countries (Marland et al., 2009). Generally, emissions from mature economies with good statistical processes have an uncertainty of only a few percent (Marland, 2008), while emissions from strongly developing economies such as China have uncertainties of around ±10% (for ±1σ; Gregg et al., 2008; Andres et al., 2014). Uncertainties in emissions are likely to be mainly systematic errors related to underlying biases of energy statistics and to the accounting method used by each country.

### C1.4 Growth rate in emissions

We report the annual growth rate in emissions for adjacent years (in percent per year) by calculating the difference between the 2 years and then normalizing to the emissions in the first year: $(E_{FOS}(t_0+1) - E_{FOS}(t_0))/E_{FOS}(t_0) \times 100\%$. We apply a leap-year adjustment where relevant to ensure valid interpretations of annual growth rates. This affects the growth rate by about 0.3% per year (1/366) and causes calculated growth rates to go up approximately 0.3% if the first year is a leap year and down 0.3% if the second year is a leap year.
The relative growth rate of $E_{FOS}$ over time periods of greater than 1 year can be rewritten using its logarithm equivalent as follows:

$$ \frac{1}{E_{FOS}} \frac{dE_{FOS}}{dt} = \frac{d(\ln E_{FOS})}{dt}. \qquad (C1) $$

Here we calculate relative growth rates in emissions for multi-year periods (e.g. a decade) by fitting a linear trend to ln($E_{FOS}$) in Eq. (2), reported in percent per year.

## C1.5 Emissions projection for 2022

To gain insight into emission trends for 2022, we provide an assessment of global fossil CO₂ emissions, $E_{FOS}$, by combining individual assessments of emissions for China, USA, the EU, and India (the four countries/regions with the largest emissions) and the rest of the world.

The methods are specific to each country or region, as described in detail below.

### China

We use a regression between monthly data for each fossil fuel and cement and annual data for consumption of fossil fuels or production of cement to project full-year growth in fossil fuel consumption and cement production. The monthly data for each product consists of the following elements.

- Coal. This product uses a proprietary estimate for monthly consumption of main coal types from SX Coal.

- Oil. The product uses production data from the National Bureau of Statistics (NBS), plus net imports from the China Customs Administration (i.e. gross supply of oil, not including inventory changes).

- Natural gas. This product uses the same source as for oil.

- Cement. This product uses production data from NBS.

For oil, we use data for production and net imports of refined oil products rather than crude oil. This choice is made because refined products are one step closer to actual consumption and because crude oil can be subject to large market-driven and strategic inventory changes that are not captured by available monthly data.

For each fuel and cement, we make a Bayesian linear regression between year-on-year cumulative growth in supply (production for cement) and full-year growth in consumption (production for cement) from annual consumption data. In the regression model, the growth rate in annual consumption (production for cement) is modelled as a regression parameter multiplied by the cumulative year-on-year growth rate from the monthly data through July of each year for past years (through 2021). We use broad Gaussian distributions centred around 1 as priors for the ratios between annual and

through-July growth rates. We then use the posteriors for the growth rates together with cumulative monthly supply or production data through July of 2022 to produce a posterior predictive distribution for the full-year growth rate for fossil fuel consumption and cement production in 2022.

If the growth in supply or production through July were an unbiased estimate of the full-year growth in consumption or production, the posterior distribution for the ratio between the monthly and annual growth rates would be centred around 1. However, in practice the ratios are different from 1 (in most cases below 1). This is a result of various biasing factors such as uneven evolution in the first and second half of each year, inventory changes that are somewhat anti-correlated with production and net imports, differences in statistical coverage, and other factors that are not captured in the monthly data.

For fossil fuels, the mean of the posterior distribution is used as the central estimate for the growth rate in 2022, while the edges of a 68% credible interval (analogous to a 1σ confidence interval) are used for the upper and lower bounds.

For cement, the evolution from January to July has been highly atypical owing to the ongoing turmoil in the construction sector, and the results of the regression analysis are heavily biased by equally atypical but different dynamics in 2021. For this reason, we use an average of the results of the regression analysis and the plain growth in cement production through July 2022, since this results in a growth rate that seems more plausible and in line with where the cumulative cement production appears to be headed at the time of writing.

### USA

We use emissions estimated by the U.S. Energy Information Administration (EIA) in their Short-Term Energy Outlook (STEO) for emissions from fossil fuels to get both year-to-date (YTD) information and a full-year projection (EIA, 2022). The STEO also includes a near-term forecast based on an energy forecasting model that is updated monthly (last update with preliminary data through August 2022) and takes into account expected temperatures, household expenditures by fuel type, energy markets, policies, and other effects. We combine this with our estimate of emissions from cement production using the monthly US cement clinker production data from USGS for January–June 2022, assuming changes in cement production over the first part of the year apply throughout the year.

### India

We use monthly emissions estimates for India updated from Andrew (2020b) through July 2022. These estimates are derived from many official monthly energy and other activity data sources to produce direct estimates of national CO₂ emissions without the use of proxies. Emissions from coal
are then extended to August using a regression relationship based on power generated from coal, coal dispatches by Coal India Ltd., the composite Purchasing Managers' Index, time, and days per month. For the last 3–5 months of the year, each series is extrapolated assuming typical trends.

## EU

We use a refinement to the methods presented by Andrew (2021), deriving emissions from monthly energy data reported by Eurostat. Some data gaps are filled using data from the Joint Organizations Data Initiative (JODI, 2022). Sub-annual cement production data are limited, but data for Germany and Poland, the two largest producers, suggest a small decline. For fossil fuels this provides estimates through July. We extend coal emissions through August using a regression model built from generation of power from hard coal, power from brown coal, total power generation, and the number of working days in Germany and Poland, the two biggest coal consumers in the EU. These are then extended through the end of the year assuming typical trends. We extend oil emissions by building a regression model between our monthly CO₂ estimates and oil consumption reported by the EIA for Europe in its Short-Term Energy Outlook (September edition) and then using this model with EIA's monthly forecasts. For natural gas, the strong seasonal signal allows the use of the bias-adjusted Holt–Winters exponential smoothing method (Chatfield, 1978).

## Rest of the world

We use the close relationship between the growth in GDP and the growth in emissions (Raupach et al., 2007) to project emissions for the current year. This is based on a simplified Kaya Identity, whereby $E_{FOS}$ (GtC yr⁻¹) is decomposed by the product of GDP (USD yr⁻¹) and the fossil fuel carbon intensity of the economy ($I_{FOS}$; GtC USD⁻¹) as follows:

$$E_{FOS} = GDP \times I_{FOS}. \qquad (C2)$$

Taking a time derivative of Eq. (3) and rearranging gives

$$\frac{1}{E_{FOS}} \frac{dE_{FOS}}{dt} = \frac{1}{GDP} \frac{dGDP}{dt} + \frac{1}{I_{FOS}} \frac{dI_{FOS}}{dt}, \qquad (C3)$$

where the left-hand term is the relative growth rate of $E_{FOS}$, and the right-hand terms are the relative growth rates of GDP and $I_{FOS}$, respectively, which can simply be added linearly to give the overall growth rate.

The $I_{FOS}$ is based on GDP in constant PPP (purchasing power parity) from the International Energy Agency (IEA) up to 2017 (IEA/OECD, 2019) and extended using the International Monetary Fund (IMF) growth rates through 2021 (IMF, 2022). Interannual variability in $I_{FOS}$ is the largest source of uncertainty in the GDP-based emissions projections. We thus use the standard deviation of the annual $I_{FOS}$

for the period 2012–2021 as a measure of uncertainty, reflecting a ±1σ as in the rest of the carbon budget. For rest-of-world oil emissions growth, we use the global oil demand forecast published by the EIA less our projections for the other four regions and estimate uncertainty as the maximum absolute difference over the period available for such forecasts using the specific monthly edition (e.g. August) compared to the first estimate based on more solid data in the following year (April).

## World

The global total is the sum of each of the countries and regions.

## C2 Methodology: CO₂ emissions from land-use, land-use change, and forestry ($E_{LUC}$)

The net CO₂ flux from land-use, land-use change, and forestry ($E_{LUC}$, called land-use change emissions in the rest of the text) includes CO₂ fluxes from deforestation, afforestation, logging, and forest degradation (including harvest activity); shifting cultivation (cycle of cutting forest for agriculture, then abandoning); and regrowth of forests following wood harvest or abandonment of agriculture. Emissions from peat burning and drainage are added from external datasets (see Appendix C2.1 below). Only some land-management activities are included in our land-use change emissions estimates (Table A1). Some of these activities lead to emissions of CO₂ to the atmosphere, while others lead to CO₂ sinks. $E_{LUC}$ is the net sum of emissions and removals due to all anthropogenic activities considered. Our annual estimate for 1960–2021 is provided as the average of results from three bookkeeping approaches (Appendix C2.1 below): an estimate using the Bookkeeping of Land Use Emissions model (Hansis et al., 2015; hereafter BLUE), one using the compact Earth system model OSCAR (Gasser et al., 2020), with both BLUE and OSCAR being updated here to new land-use forcing covering the time period until 2021, and an updated version of the estimate published by Houghton and Nassikas (2017) (hereafter updated H&N2017). All three data sets are then extrapolated to provide a projection for 2022 (Appendix C2.5 below). In addition, we use results from dynamic global vegetation models (DGVMs; see Appendix C2.2 and Table 4) to help quantify the uncertainty in $E_{LUC}$ (Appendix C2.4) and thus better characterize our understanding. Note that in this budget, we use the scientific $E_{LUC}$ definition, which counts fluxes due to environmental changes on managed land towards $S_{LAND}$, as opposed to the national greenhouse gas inventories under the UNFCCC, which include them in $E_{LUC}$ and thus often report smaller land-use emissions (Grassi et al., 2018; Petrescu et al., 2020). However, we provide a methodology of mapping of the two approaches to each other further below (Appendix C2.3).
## C2.1 Bookkeeping models

Land-use change CO₂ emissions and uptake fluxes are calculated by three bookkeeping models. These are based on the original bookkeeping approach of Houghton (2003) that keeps track of the carbon stored in vegetation and soils before and after a land-use change (transitions between various natural vegetation types, croplands, and pastures). Literature-based response curves describe decay of vegetation and soil carbon, including transfer to product pools of different lifetimes, as well as carbon uptake due to regrowth. In addition, the bookkeeping models represent long-term degradation of primary forest as lowered standing vegetation and soil carbon stocks in secondary forests and include forest management practices such as wood harvests.

BLUE and the updated H&N2017 exclude land ecosystems' transient response to changes in climate, atmospheric CO₂, and other environmental factors and base the carbon densities on contemporary data from literature and inventory data. Since carbon densities thus remain fixed over time, the additional sink capacity that ecosystems provide in response to CO₂ fertilization and some other environmental changes is not captured by these models (Pongratz et al., 2014). On the contrary, OSCAR includes this transient response, and it follows a theoretical framework (Gasser and Ciais, 2013) that allows separating bookkeeping land-use emissions and the loss of additional sink capacity. Only the former is included here, while the latter is discussed in Appendix D4. The bookkeeping models differ in (1) computational units (spatially explicit treatment of land-use change for BLUE, country-level for the updated H&N2017 and OSCAR), (2) processes represented (see Table A1), and (3) carbon densities assigned to vegetation and soil of each vegetation type (based on literature for BLUE and the updated H&N2017, calibrated to DGVMs for OSCAR). A notable difference between models exists with respect to the treatment of shifting cultivation. The update of H&N2017, introduced for the GCB2021 (Friedlingstein et al., 2022a), changed the approach over the earlier H&N2017 version: H&N2017 had assumed the “excess loss” of tropical forests, i.e. when the Global Forest Resources Assessment (FRA; FAO 2020) indicated that a forest loss larger than the increase in agricultural areas from FAO (FAOSTAT 2021) resulted from converting forests to croplands at the same time older croplands were abandoned. Those abandoned croplands began to recover to forests after 15 years. The updated H&N2017 now assumes that forest loss in excess of increases in cropland and pastures represented an increase in shifting cultivation. When the excess loss of forests was negative, it was assumed that shifting cultivation was returned to forest. Historical areas in shifting cultivation were extrapolated taking into account country-based estimates of areas in fallow in 1980 (FAO/UNEP, 1981) and expert opinion (from Heinemann et al., 2017). In contrast, the BLUE and OSCAR models include sub-grid-scale transitions between all vegetation

types. Furthermore, the updated H&N2017 assumes conversion of natural grasslands to pasture, while BLUE and OSCAR allocate pasture transitions proportionally on all natural vegetation that exists in a grid cell. This is one reason for generally higher emissions in BLUE and OSCAR. Bookkeeping models do not directly capture carbon emissions from peat fires, which can create large emissions and interannual variability due to synergies of land-use and climate variability in Southeast Asia, particularly during El Niño events, nor do they capture emissions from the organic layers of drained peat soils. To correct for this, we add peat fire emissions based on the Global Fire Emission Database (GFED4s; van der Werf et al., 2017) to the bookkeeping models' output. Emissions are calculated by multiplying the mass of dry matter emitted by peat fires with the C emission factor for peat fires indicated in the GFED4s database. Emissions from deforestation fires used to derive $E_{LUC}$ projections for 2022 are calculated analogously. As these satellite-derived estimates of peat fire emissions start in 1997 only, we follow the approach by Houghton and Nassikas (2017) for earlier years, which ramps up from zero emissions in 1980 to $0.04 \text{ Pg C yr}^{-1}$ in 1996, reflecting the onset of major clearing of peatlands in equatorial Southeast Asia in the 1980s. Similarly, we add estimates of peat drainage emissions. In recent years, more peat drainage estimates that provide spatially explicit data have become available, and we thus extended the number of peat drainage datasets considered. We employ FAO peat drainage emissions 1990–2019 from croplands and grasslands (Conchedda and Tubiello, 2020), peat drainage emissions 1700–2010 from simulations with the DGVM ORCHIDEE-PEAT (Qiu et al., 2021), and peat drainage emissions 1701–2021 from simulations with the DGVM LPX-Bern (Lienert and Joos, 2018; Müller and Joos, 2021), applying the updated LUH2 forcing as also used by BLUE, OSCAR, and the DGVMs. We extrapolate the FAO data to 1850–2021 by keeping the post-2019 emissions constant at 2019 levels, by linearly increasing tropical drainage emissions between 1980 and 1990 starting from $0 \text{ GtC yr}^{-1}$ in 1980, consistent with H&N2017's assumption (Houghton and Nassikas, 2017), and by keeping pre-1990 emissions from the often old drained areas of the extratropics constant at 1990 emission levels. ORCHIDEE-PEAT data are extrapolated to 2011–2021 by replicating the average emissions in 2000–2010 (Chunjing Qiu, personal communication, 2022). Further, ORCHIDEE-PEAT only provides peat drainage emissions north of 30°N, and thus we fill the regions south of 30°N using the average peat drainage emissions from FAO and LPX-Bern. The average of the carbon emission estimates by the three different peat drainage datasets is added to the bookkeeping models to obtain net $E_{LUC}$ and gross sources.

The three bookkeeping estimates used in this study differ with respect to the land-use change data used to drive the models. The updated H&N2017 bases its estimates directly on the Forest Resource Assessment of the FAO, which pro-
vides statistics on forest area change and management at in-
tervals of 5 years and is currently updated until 2020 (FAO,
2020). The data are based on country reporting to FAO and
may include remote-sensing information in more recent as-
sessments. Changes in land-use other than forests are based
on annual, national changes in cropland and pasture areas re-
ported by FAO (FAOSTAT, 2021). On the other hand, BLUE
uses the harmonized land-use change data LUH2-GCB2022
covering the entire 850–2021 period (an update to the pre-
viously released LUH2 v2h dataset; Hurtt et al., 2017; Hurtt
et al., 2020), which was also used as input to the DGVMs
(Appendix C2.2). It describes land-use change, also based
on the FAO data as described in Appendix C2.2 and the
HYDE3.3 dataset (Klein Goldewijk et al., 2017a, b), but pro-
vided at a quarter-degree spatial resolution, considering sub-
grid-scale transitions between primary forest, secondary for-
est, primary non-forest, secondary non-forest, cropland, pas-
ture, rangeland, and urban land (Hurtt et al., 2020; Chini et
al., 2021). LUH2-GCB2022 provides a distinction between
rangelands and pasture, based on inputs from HYDE. To
constrain the models’ interpretation on whether rangeland
implies the original natural vegetation to be transformed to
grassland or not (e.g. browsing on shrubland), a forest mask
was provided with LUH2-GCB2021; forest is assumed to
be transformed to grasslands, while other natural vegetation
remains (in case of secondary vegetation) or is degraded
from primary to secondary vegetation (Ma et al., 2020).
This is implemented in BLUE. OSCAR was run with both
LUH2-GCB2022 and FAO/FRA (as used with the updated
H&N2017), where the drivers of the latter were linearly ex-
trapolated to 2021 using their 2015–2020 trends. The best-
guess OSCAR estimate used in our study is a combination of
results for LUH2-GCB2022 and FAO/FRA land-use data and
a large number of perturbed parameter simulations weighted
against a constraint (the cumulative S<sub>LAND</sub> over 1960–2020
of last year’s GCB). As the record of the updated H&N2017
ends in 2020, we extend it to 2021 by adding the difference
of the emissions from tropical deforestation and degradation,
peat drainage, and peat fire between 2020 and 2021 to the
model’s estimate for 2020 (i.e. considering the yearly anoma-
lies of the emissions from tropical deforestation and degra-
dation, peat drainage, and peat fire). The same method is ap-
plied to all three bookkeeping estimates to provide a projec-
tion for 2022.

For E_LUC from 1850 onwards we average the estimates
from BLUE, the updated H&N2017, and OSCAR. For the
cumulative numbers starting 1750, an average of four earlier
publications is added (30 ± 20 PgC 1750–1850, rounded to
the nearest 5; Le Quéré et al., 2016).

We provide estimates of the gross land-use change fluxes
from which the reported net land-use change flux, E_LUC,
is derived as a sum. Gross fluxes are derived internally by
the three bookkeeping models. Gross emissions stem from
decaying material left dead on site and from products af-
ter clearing of natural vegetation for agricultural purposes

or wood harvesting, emissions from peat drainage and peat
burning, and, for BLUE, additionally from degradation from
primary to secondary land through usage of natural vegeta-
tion as rangeland. Gross removals stem from regrowth after
agricultural abandonment and wood harvesting. Gross fluxes
for the updated H&N2017 for 2020 and for the 2022 pro-
jection of all three models were calculated by the change in
emissions from tropical deforestation and degradation and
peat burning and drainage as described for the net E_LUC
above. As tropical deforestation and degradation and peat
burning and drainage all only lead to gross emissions to the
atmosphere, only gross (and net) emissions are adjusted this
way, while gross sinks are assumed to remain constant over
the previous year.

This year, we provide an additional split of the net E_LUC
into component fluxes to better identify reasons for diver-
gence between bookkeeping estimates and to give more in-
sight into the drivers of sources and sinks. This split dis-
tinguishes between fluxes from deforestation (including due
to shifting cultivation); fluxes from organic soils (i.e. peat
drainage and fires); afforestation, reafforestation, and wood
harvest (i.e. fluxes in forests from slash and product decay
following wood harvesting, regrowth associated with wood
harvesting or after abandonment, including reforestation and
in shifting cultivation cycles, and afforestation); and fluxes
associated with all other transitions.

C2.2 Dynamic global vegetation models (DGVMs)

Land-use change CO₂ emissions have also been estimated
using an ensemble of 16 DGVM simulations. The DGVMs
account for deforestation and regrowth, the most important
components of E_LUC, but they do not represent all processes
resulting directly from human activities on land (Table A1).
All DGVMs represent processes of vegetation growth and
mortality, as well as decomposition of dead organic matter
associated with natural cycles, and include the vegetation and
soil carbon response to increasing atmospheric CO₂ concen-
tration and to climate variability and change. Most models
explicitly simulate the coupling of carbon and nitrogen cy-
cles and account for atmospheric N deposition and N fertil-
izers (Table A1). The DGVMs are independent of the other
budget terms except for their use of atmospheric CO₂ con-
centration to calculate the fertilization effect of CO₂ on plant
photosynthesis.

All DGVMs use the LUH2-GCB2022 dataset as input,
which includes the HYDE cropland/grazing land dataset
(Klein Goldewijk et al., 2017a, b), and additional information
on land-cover transitions and wood harvest. DGVMs use an-
nual, half-degree (regridded from 5 min resolution) fractional
data on cropland and pasture from HYDE3.3.

DGVMs that do not simulate subgrid-scale transitions (i.e.
net land-use emissions; see Table A1) used the HYDE infor-
mation on agricultural area change. For all countries, with
the exception of Brazil and the Democratic Republic of the
Congo, these data are based on the available annual FAO statistics of change in agricultural land area available from 1961 up to and including 2017. The FAO retrospectively revised their reporting for the Democratic Republic of the Congo, which was newly available until 2020. In addition to FAO country-level statistics, the HYDE3.3 cropland/grazing land dataset is constrained spatially based on multi-year satellite land cover maps from ESA CCI LC (see below). After the year 2017, LUH2 extrapolates, on a grid cell basis, the cropland, pasture, and urban data linearly based on the trend over the previous 5 years to generate data until the year 2021. This extrapolation methodology is not appropriate for countries that have experienced recent rapid changes in the rate of land-use change, e.g. Brazil, which has experienced a recent upturn in deforestation. Hence, for Brazil we replace FAO state-level data for cropland and grazing land in HYDE by those from in-country land cover dataset MapBiomas (collection 6) for 1985–2020 (Souza et al., 2020). ESA-CCI is used to spatially disaggregate as described below. Similarly, an estimate for the year 2021 is based on the MapBiomas trend 2015–2020. The pre-1985 period is scaled with the per capita numbers from 1985 from MapBiomas, and thus this transition is smooth.

HYDE uses satellite imagery from ESA-CCI from 1992–2018 for more detailed yearly allocation of cropland and grazing land, with the ESA area data scaled to match the FAO annual totals at country level. The original 300 m spatial resolution data from ESA were aggregated to a 5 arcmin resolution according to the classification scheme as described in Klein Goldewijk et al. (2017a).

DGVMs that simulate subgrid scale transitions (i.e. gross land-use emissions; see Table A1) use more detailed land-use transition and wood harvest information from the LUH2-GCB2022 data set. LUH2-GCB2022 is an update of the more comprehensive harmonized land-use data set (Hurtt et al., 2020) that further includes fractional data on primary and secondary forest vegetation, as well as all underlying transitions between land-use states (850-2020; Hurtt et al., 2011, 2017, 2020; Chini et al., 2021; Table A1). This data set is of quarter-degree fractional areas of land-use states and all transitions between those states, including a new wood harvest reconstruction, new representation of shifting cultivation, crop rotations, and management information, including irrigation and fertilizer application. The land-use states include five different crop types in addition to splitting grazing land into managed pasture and rangeland. Wood harvest patterns are constrained with Landsat-based tree cover loss data (Hansen et al., 2013). Updates of LUH2-GCB2022 over last year's version (LUH2-GCB2021) are using the most recent HYDE release (covering the time period up to 2017, revision to Brazil and the Democratic Republic of the Congo as described above). We use the same FAO wood harvest data as last year for all dataset years from 1961 to 2019 and extrapolate to the year 2022. The HYDE3.3 population data are also used to extend the wood harvest time series

back in time. Other wood harvest inputs (for years prior to 1961) remain the same in LUH2. These updates in the land-use forcing are shown in comparison to the more pronounced version change from the GCB2020 (Friedlingstein et al., 2020) to GCB2021, which was discussed in Friedlingstein et al. (2022a) in Fig. B6, and their relevance for land-use emissions is discussed in Sect. 3.2.2. DGVMs implement land-use change differently (e.g. an increased cropland fraction in a grid cell can either be at the expense of grassland, shrubs, or forest, the latter resulting in deforestation; land cover fractions of the non-agricultural land differ between models). Similarly, model-specific assumptions are applied to convert deforested biomass or deforested area and other forest product pools into carbon, and different choices are made regarding the allocation of rangelands as natural vegetation or pastures.

The difference between two DGVM simulations (see Appendix C4.1 below), one forced with historical changes in land use and a second with time-invariant pre-industrial land cover and pre-industrial wood harvest rates, allows quantification of the dynamic evolution of vegetation biomass and soil carbon pools in response to land-use change in each model ($E_{LUC}$). Using the difference between these two DGVMs simulations to diagnose $E_{LUC}$ means the DGVMs account for the loss of additional sink capacity (around $0.4 \pm 0.3 \text{ GtC yr}^{-1}$; see Sect. 2.7 and Appendix D4), whereas the bookkeeping models do not.

As a criterion for inclusion in this carbon budget, we only retain models that simulate a positive $E_{LUC}$ during the 1990s, as assessed in the IPCC AR4 (Denman et al., 2007) and AR5 (Ciais et al., 2013). All DGVMs met this criterion, although one model was not included in the $E_{LUC}$ estimate from DGVMs as it exhibited a spurious response to the transient land cover change forcing after its initial spin-up.

### C2.3 Mapping of national GHG inventory data to $E_{LUC}$

An approach was implemented to reconcile the large gap between land-use emissions estimates from bookkeeping models and from national GHG inventories (NGHGI) (see Table A8). This gap is due to different approaches to calculating “anthropogenic” CO₂ fluxes related to land-use change and land management (Grassi et al., 2018). In particular, the land sinks due to environmental change on managed lands are treated as non-anthropogenic in the global carbon budget, while they are generally considered anthropogenic in NGHGIs (“indirect anthropogenic fluxes”; Eggleston et al., 2006). Building on previous studies (Grassi et al., 2021), the approach implemented here adds the DGVM estimates of CO₂ fluxes due to environmental change from countries’ managed forest area (part of $S_{LAND}$) to the $E_{LUC}$ flux. This sum is expected to be conceptually more comparable to LU-LUCF than $E_{LUC}$.

$E_{LUC}$ data are taken from bookkeeping models, in line with the global carbon budget approach. To determine $S_{LAND}$
on managed forest, the following steps were taken: spa-
tially gridded data of “natural” forest net biome productiv-
ity (NBP) (S<sub>LAND</sub>, i.e. due to environmental change and ex-
cluding land-use change fluxes) were obtained with S2 runs
from DGVMs up to 2021 from the TRENDY v11 dataset.
Results were first masked with a forest map that is based on
Hansen (Hansen et al., 2013) tree cover data. To do this con-
version (“tree” cover to “forest” cover), we exclude grid cells
with less than 20% tree cover and isolated pixels with maxi-
mum connectivity less than 0.5 ha following the FAO defini-
tion of forest. Forest NBPs are then further masked with the
“intact” forest map for the year 2013, i.e. forest areas char-
acterized by no remotely detected signs of human activity
(Potapov et al., 2017). This way, we obtained the S<sub>LAND</sub> in
“intact” and “non-intact” forest area, which previous studies
(Grassi et al., 2021) indicated to be a good proxy, respec-
tively, for “unmanaged” and “managed” forest area in the
NGHGI. Note that only four models (CABLE-POP, CLAS-
SIC, JSBACH and YIBs) had forest NBP at grid-cell level.
For the other DGVMs, when a grid cell had forest, all the
NBP was allocated to forest. However, since S2 simulations
use pre-industrial forest cover masks that are at least 20%
larger than today’s forest (Hurtt et al., 2020), we corrected
this NBP using a ratio between observed (based on Hansen et
al., 2013) and prescribed (from DGVMs) forest cover. This
ratio is calculated for each individual DGVM that provides
information on prescribed forest cover (LPX-Bern, OCN,
JULES, VISIT, VISIT-NIES, SDGVM). For the others (IBIS,
CLM5.0, ORCHIDEE, ISAM, DLEM, LPJ-GUESS), a com-
mon ratio (median ratio of all the 10 models that provide in-
formation on prescribed forest cover) is used. The details of
the method used are explained in Alkama (2022).

LULUCF data from NGHGIs are from Grassi et al. (2022a). While Annex I countries report a complete time series 1990–2020, for non-Annex I countries gap-filling measures were applied through linear interpolation between two points and/or through extrapolation backward (till 1990) and forward (till 2020) using the single closest available data point. For all countries, the estimates of the year 2021 are assumed to be equal to those of 2020. These data include all CO2 fluxes from land considered managed, which in principle encompasses all land uses (forest land, cropland, grassland, wetlands, settlements, and other land), changes among them, and emissions from organic soils and fires. In practice, although almost all Annex I countries report all land uses, many non-Annex I countries report only on deforestation and forest land, and only few countries report on other land uses. In most cases, NGHGIs include most of the natural response to recent environmental change because they use direct observations (e.g. national forest inventories) that do not allow for separating direct and indirect anthropogenic effects (Eggleston et al., 2006).

To provide additional, largely independent assessments
of fluxes on unmanaged vs. managed lands, we include a
DGVM that allows diagnosing fluxes from unmanaged vs.

managed lands by tracking vegetation cohorts of different
ages separately. This model, ORCHIDEE-MICT (Yue et al.,
2018), was run using the same LUH2 forcing as the DGVMs
used in this budget (Sect. 2.5) and the bookkeeping models
BLUE and OSCAR (Sect. 2.2). Old-aged forest was classi-
fied as primary forest after a certain threshold of carbon den-
sity was reached again, and the model-internal distinction be-
tween primary and secondary forest was used a proxy for un-
managed vs. managed forests; agricultural lands are added to
the latter to arrive at total managed land.

Table A8 shows the resulting mapping of global carbon cycle models’ land flux definitions to that of the NGHGI (discussed in Sect. 3.2.2). ORCHIDEE-MICT estimates for S<sub>LAND</sub> on intact forests are expected to be higher than based on DGVMs in combination with the NGHGI managed and unmanaged forest data because the unmanaged forest area, with about 27 × 10<sup>6</sup> km<sup>2</sup>, is estimated to be substantially larger by ORCHIDEE-MICT than by the NGHGI (less than 10 × 10<sup>6</sup> km<sup>2</sup>), while managed forest area is estimated to be smaller (22 compared to 32 × 10<sup>6</sup> km<sup>2</sup>). Related to this, E<sub>LUC</sub> plus S<sub>LAND</sub> on non-intact lands is a larger source estimated by ORCHIDEE-MICT compared to NGHGI. We also show FAOSTAT emissions totals (FAO, 2021) as a comparison, which include emissions from net forest conversion and fluxes on forest land (Tubiello et al., 2021) and CO<sub>2</sub> emissions from peat drainage and peat fires. The 2021 data were estimated by including actual 2021 estimates for peatland drainage and fire and a carry forward from 2020 to 2021 for the forest land stock change. The FAO data shows a global source of 0.24 GtC yr<sup>-1</sup> averaged over 2012–2021, in contrast to the sink of –0.54 GtC yr<sup>-1</sup> of the gap-filled NGHGI data. Most of this difference is attributable to different scopes: a focus on carbon fluxes for the NGHGI and a focus on area and biomass for FAO. In particular, the NGHGI data includes a larger forest sink for non-Annex 1 countries resulting from a more complete coverage of non-biomass carbon pools and non-forest land uses. NGHGI and FAO data also differ in terms of underlying data on forest land (Grassi et al., 2022a).

C2.4 Uncertainty assessment for E<sub>LUC</sub>

Differences between the bookkeeping models and DGVMs
models originate from three main sources: the different
methodologies, which among others lead to inclusion of
the loss of additional sink capacity in DGVMs (see Ap-
pendix D1.4), the underlying land-use or land-cover data set,
and the different processes represented (Table A1). We ex-
amine the results from the DGVMs models and of the book-
keeping method and use the resulting variations as a way to
characterize the uncertainty in E<sub>LUC</sub>.

Despite these differences, the E_LUC estimate from the
DGVMs multi-model mean is consistent with the average of
the emissions from the bookkeeping models (Table 5). How-
ever, there are large differences among individual DGVMs
(standard deviation at around 0.5 GtC yr⁻¹; Table 5), between the bookkeeping estimates (average difference 1850–2020 BLUE-updated H&N2017 of 0.8 GtC yr⁻¹, BLUE-OSCAR of 0.4 GtC yr⁻¹, OSCAR-updated H&N2017 of 0.3 GtC yr⁻¹), and between the updated estimate of H&N2017 and its previous model version (Houghton et al., 2012). A factorial analysis of differences between BLUE and H&N2017 attributed them particularly to differences in carbon densities between natural and managed vegetation or primary and secondary vegetation (Bastos et al., 2021). Earlier studies additionally showed the relevance of the different land-use forcing as applied (in updated versions) also in the current study (Gasser et al., 2020). Ganzenmüller et al. (2022) recently showed that *E*<sub>LUC</sub> estimates with BLUE are substantially smaller when the model is driven by a new high-resolution land-use dataset (HILDA+). They identified shifting cultivation and the way it is implemented in LUH2 as a main reason for this divergence. They further showed that a higher spatial resolution reduces the estimates of both sources and sinks because successive transitions are not adequately represented at coarser resolution, which has the effect that – despite capturing the same extent of transition areas – overall less area remains pristine at the coarser compared to the higher resolution.

The uncertainty in *E*<sub>LUC</sub> of ±0.7 GtC yr<sup>-1</sup> reflects our best value judgement that there is at least 68 % chance (±1σ) that the true land-use change emission lies within the given range for the range of processes considered here. Prior to the year 1959, the uncertainty in *E*<sub>LUC</sub> was taken from the standard deviation of the DGVMs. We assign low confidence to the annual estimates of *E*<sub>LUC</sub> because of the inconsistencies among estimates and of the difficulties in quantifying some of the processes in DGVMs.

## C2.5 Emissions projections for E_LUC

We project the 2022 land-use emissions for BLUE, the updated H&N2017, and OSCAR, starting from their estimates for 2021 assuming unaltered peat drainage, which has low interannual variability, and the highly variable emissions from peat fires, tropical deforestation and degradation as estimated using active fire data (MCD14ML; Giglio et al., 2016). These latter variables scale almost linearly with GFED over large areas (van der Werf et al., 2017), and thus they allow for tracking fire emissions in deforestation and tropical peat zones in near-real time.

# C3 Methodology: ocean CO₂ sink

## C3.1 Observation-based estimates

We primarily use the observational constraints assessed by IPCC of a mean ocean CO₂ sink of 2.2 ± 0.7 GtC yr⁻¹ for the 1990s (90 % confidence interval; Ciais et al., 2013) to verify that the GOBMs provide a realistic assessment of S<sub>OCEAN</sub>. This is based on indirect observations with seven

different methodologies and their uncertainties and further use of the three of these methods that are deemed most reliable for the assessment of this quantity (Denman et al., 2007; Ciais et al., 2013). The observation-based estimates use the ocean–land CO₂ sink partitioning from observed atmospheric CO₂ and O₂/N₂ concentration trends (Manning and Keeling, 2006; Keeling and Manning, 2014), an oceanic inversion method constrained by ocean biogeochemistry data (Mikaloff Fletcher et al., 2006), and a method based on penetration timescale for chlorofluorocarbons (McNeil, 2003). The IPCC estimate of 2.2 GtC yr⁻¹ for the 1990s is consistent with a range of methods (Wanninkhof et al., 2013). We refrain from using the IPCC estimates for the 2000s (2.3 ± 0.7 GtC yr⁻¹) and the period 2002–2011 (2.4 ± 0.7 GtC yr⁻¹, Ciais et al., 2013), as these are based on trends derived mainly from models and one data product (Ciais et al., 2013). Additional constraints summarized in AR6 (Canadell et al., 2021) are the interior ocean anthropogenic carbon change (Gruber et al., 2019) and ocean sink estimates from atmospheric CO₂ and O₂/N₂ (Tohjima et al., 2019), which are used for model evaluation and discussion, respectively.

We also use eight estimates of the ocean CO₂ sink and its variability based on surface ocean fCO₂ maps obtained by the interpolation of surface ocean fCO₂ measurements from 1990 onwards due to severe restrictions on data availability prior to 1990 (Fig. 10). These estimates differ in many respects: they use different maps of surface fCO₂, atmospheric CO₂ concentrations, wind products, and gas exchange formulations as specified in Table A3. We refer to them as fCO₂-based flux estimates. The measurements underlying the surface fCO₂ maps are from the Surface Ocean CO₂ Atlas version 2022 (SOCATv2022; Bakker et al., 2022), which is an update of version 3 (Bakker et al., 2016) and contains quality-controlled data through 2021 (see data attribution Table A5). Each of the estimates uses a different method to then map the SOCAT v2022 data to the global ocean. The methods include a data-driven diagnostic method combined with a multi-linear regression approach to extend back to 1957 (Rödenbeck et al., 2022; referred to here as Jena-MLS), three neural network models (Landschützer et al., 2014; referred to as MPI-SOMFFN; Chau et al., 2022; Copernicus Marine Environment Monitoring Service, referred to here as CMEMS-LSCE-FFNN; and Zeng et al., 2014; referred to as NIES-NN), a cluster regression approach (Gregor and Gruber, 2021, referred to as OS-ETHZ-GRaCER), a multi-linear regression method (Iida et al., 2021; referred to as JMA-MLR), and a method that relates the fCO₂ misfit between GOBMs and SOCAT to environmental predictors using the extreme gradient-boosting method (Gloege et al., 2022). The ensemble mean of the fCO₂-based flux estimates is calculated from these seven mapping methods. Further, we show the flux estimate of Watson et al. (2020), who also use the MPI-SOMFFN method to map the adjusted fCO₂ data to the globe, resulting in a substantially larger ocean sink esti-
mate owing to a number of adjustments they applied to the surface ocean fCO₂ data. Concretely, these authors adjusted the SOCAT fCO₂ downward to account for differences in temperature between the depth of the ship intake and the relevant depth right near the surface, and they included a further adjustment to account for the cool surface skin temperature effect. The Watson et al. (2020) flux estimate hence differs from the others by their choice of adjusting the flux to a cool, salty ocean surface skin. Watson et al. (2020) showed that this temperature adjustment leads to an upward correction of the ocean carbon sink, up to 0.9 GtC yr⁻¹, that, if correct, should be applied to all fCO₂-based flux estimates. A reduction of this adjustment to 0.6 GtC yr⁻¹ was proposed by Dong et al. (2022). The impact of the cool skin effect on air-sea CO₂ flux is based on established understanding of temperature gradients (as discussed by Goddijn-Murphy et al 2015) and laboratory observations (Jähne and Haußecker, 1998; Jähne, 2019), but in situ field observational evidence is lacking (Dong et al., 2022). The Watson et al. (2020) flux estimate presented here is therefore not included in the ensemble mean of the fCO₂-based flux estimates. This choice will be re-evaluated in upcoming budgets based on further lines of evidence.

Typically, data products do not cover the entire ocean due to missing coastal oceans and sea ice cover. The CO₂ flux from each fCO₂-based product is already at or above 99% coverage of the ice-free ocean surface area in two products (Jena-MLS, OS-ETHZ-GRaCER) and filled by the data provider in three products (using the Fay et al., 2021, method for JMA-MLR and LDEO-HPD and the Landschützer et al., 2020, methodology for MPI-SOMFFN). The products that remained below 99% coverage of the ice-free ocean (CMEMS-LSCE-FFNN, MPI-SOMFFN, NIES-NN, UOx-Watson) were scaled by the following procedure.

In previous versions of the GCB, the missing areas were accounted for by scaling the globally integrated fluxes by the fraction of the global ocean coverage (361.9 × 10⁶ km² based on ETOPO1, Amante and Eakins, 2009; Eakins and Sharman, 2010) with the area covered by the CO₂ flux predictions. This approach may lead to unnecessary scaling when the majority of the missing data are in the ice-covered region (as is often the case), where flux is already assumed to be zero. To avoid this unnecessary scaling, we now scale fluxes regionally (north, tropics, south) to match the ice-free area (using NOAA's OISSTv2; Reynolds et al., 2002):

$$FCO_2^{\text{reg-scaled}} = \frac{A_{(1-\text{ice})}^{\text{region}}}{A_{\text{FCO}_2}^{\text{region}}} \cdot FCO_2^{\text{region}}. \quad (C4)$$

In Eq. (C4), A represents area, (1−ice) represents the ice-free ocean, AregionFCO₂ represents the coverage of the data product for a region, and FCO₂region is the integrated flux for a region.

We further use results from two diagnostic ocean models, Khatiwala et al. (2013) and DeVries (2014), to estimate

the anthropogenic carbon accumulated in the ocean prior to 1959. The two approaches assume constant ocean circulation and biological fluxes, with SOCEAN estimated as a response in the change in atmospheric CO₂ concentration calibrated to observations. The uncertainty in cumulative uptake of ±20 GtC (converted to ±1σ) is taken directly from the IPCC's review of the literature (Rhein et al., 2013) or about ±30% for the annual values (Khatiwala et al., 2009).

## C3.2 Global ocean biogeochemistry models (GOBMs)

The ocean CO₂ sink for 1959–20121 is estimated using 10 GOBMs (Table A2). The GOBMs represent the physical, chemical, and biological processes that influence the surface ocean concentration of CO₂ and thus the air-sea CO₂ flux. The GOBMs are forced by meteorological reanalysis and atmospheric CO₂ concentration data available for the entire time period. They mostly differ in the source of the atmospheric forcing data (meteorological reanalysis), spin-up strategies, and horizontal and vertical resolutions (Table A2). All GOBMs except two (CESM-ETHZ, CESM2) do not include the effects of anthropogenic changes in nutrient supply (Duce et al., 2008). They also do not include the perturbation associated with changes in riverine organic carbon (see Sect. 2.7 and Appendix D3).

Four sets of simulations were performed with each of the GOBMs. Simulation A applied historical changes in climate and atmospheric CO₂ concentration. Simulation B is a control simulation with constant atmospheric forcing (normal-year or repeated-year forcing) and constant pre-industrial atmospheric CO₂ concentration. Simulation C is forced with historical changes in atmospheric CO₂ concentration but repeated-year or normal-year atmospheric climate forcing. Simulation D is forced by historical changes in climate and constant pre-industrial atmospheric CO₂ concentration. To derive SOCEAN from the model simulations, we subtracted the slope of a linear fit to the annual time series of the control simulation B from the annual time series of simulation A. Assuming that drift and bias are the same in simulations A and B, we thereby correct for any model drift. Further, this difference also removes the natural steady-state flux (assumed to be 0 GtC yr⁻¹ globally without rivers), which is often a major source of biases. This approach works for all model set-ups, including IPSL, where simulation B was forced with constant atmospheric CO₂ but observed historical changes in climate (equivalent to simulation D). This approach assures that the interannual variability is not removed from IPSL simulation A.

The absolute correction for bias and drift per model in the 1990s varied between < 0.01 and 0.41 GtC yr⁻¹, with seven models having positive biases, two having negative biases, and one having essentially no bias (NorESM). The MPI model uses riverine input and therefore simulates outgassing in simulation B. By subtracting simulation B, the ocean carbon sink of the MPI model also follows the defi-
nition of S<sub>OCEAN</sub>. This correction reduces the model mean ocean carbon sink by 0.04 GtC yr<sup>-1</sup> in the 1990s. The ocean models cover 99% to 101% of the total ocean area so that area scaling is not necessary.

### C3.3 GOBM evaluation and uncertainty assessment for S<sub>OCEAN</sub>

The ocean CO₂ sink for all GOBMs and the ensemble mean falls within 90% confidence of the observed range, or 1.5 to 2.9 GtC yr⁻¹, for the 1990s (Ciais et al., 2013) before and after applying adjustments. An exception is the MPI model, which simulates a low ocean carbon sink of 1.38 GtC yr⁻¹ for the 1990s in simulation A owing to the inclusion of riverine carbon flux. After adjusting to the GCB's definition of S<sub>OCEAN</sub> by subtracting simulation B, the MPI model falls into the observed range with an estimated sink of 1.69 GtC yr⁻¹.

The GOBMs and data products have been further evaluated using the fugacity of sea surface CO₂ (fCO₂) from the SOCAT v2022 database (Bakker et al., 2016, 2022). We focused this evaluation on the root-mean-squared error (RMSE) between observed and modelled fCO₂ and on a measure of the amplitude of the interannual variability of the flux (modified after Rödenbeck et al., 2015). The RMSE is calculated from detrended, annually and regionally averaged time series calculated from GOBMs and data product fCO₂ subsampled to SOCAT sampling points to measure the misfit between large-scale signals (Hauck et al., 2020). To this end, we apply the following steps: (i) subsample data points for which there are observations (GOBMs or data products and SOCAT), (ii) average spatially, (iii) calculate annual mean, (iv) detrend both time series (GOBMs or data products and SOCAT), and (v) calculate RMSE. This year, we do not apply an open-ocean mask of 400 m but instead a mask based on the minimum area coverage of the data-products. This ensures a fair comparison over equal areas. The amplitude of the S<sub>OCEAN</sub> interannual variability (A-IAV) is calculated as the temporal standard deviation of the detrended annual CO₂ flux time series after area scaling (Rödenbeck et al., 2015; Hauck et al., 2020). These metrics are chosen because RMSE is the most direct measure of data-model mismatch, and the A-IAV is a direct measure of the variability of S<sub>OCEAN</sub> on interannual timescales. We apply these metrics globally and by latitude bands. Results are shown in Fig. B2 and discussed in Sect. 3.5.5.

We quantify the 1σ uncertainty around the mean ocean sink of anthropogenic CO₂ by assessing random and systematic uncertainties for the GOBMs and data-products. The random uncertainties are taken from the ensemble standard deviation (0.3 GtC yr⁻¹ for GOBMs, 0.3 GtC yr⁻¹ for data-products). We derive the GOBMs systematic uncertainty by the deviation of the DIC inventory change 1994–2007 from the Gruber et al. (2019) estimate (0.4 GtC yr⁻¹) and suggest these are related to physical transport (mix-

ing, advection) into the ocean interior. For the data products, we consider systematic uncertainties stemming from uncertainty in fCO₂ observations (0.2 GtC yr⁻¹, Takahashi et al., 2009; Wanninkhof et al., 2013), gas transfer velocity (0.2 GtC yr⁻¹, Ho et al., 2011; Wanninkhof et al., 2013; Roobaert et al., 2018), wind product (0.1 GtC yr⁻¹, Fay et al., 2021), river flux adjustment (0.3 GtC yr⁻¹, Regnier et al., 2022, formally 2σ uncertainty), and fCO₂ mapping (0.2 GtC yr⁻¹, Landschützer et al., 2014). Combining these uncertainties as their squared sums, we assign an uncertainty of ±0.5 GtC yr⁻¹ to the GOBM ensemble mean and an uncertainty of ±0.6 GtC yr⁻¹ to the data product ensemble mean. These uncertainties are propagated as σ(S<sub>OCEAN</sub>) = (1/2² × 0.5² + 1/2² × 0.6²)½ GtC yr⁻¹ and result in an ±0.4 GtC yr⁻¹ uncertainty around the best estimate of S<sub>OCEAN</sub>.

We examine the consistency between the variability of the model-based and the fCO₂-based data products to assess confidence in S<sub>OCEAN</sub>. The interannual variability of the ocean fluxes (quantified as A-IAV, the standard deviation after detrending, Fig. B2) of the seven fCO₂-based data products plus the Watson et al. (2020) product for 1990–2021 ranges from 0.12 to 0.32 GtC yr⁻¹, with the lower estimates coming from the two ensemble methods (CMEMS-LSCE-FFNN, OS-ETHZ-GRaCER). The interannual variability in the GOBMs ranges between 0.09 and 0.20 GtC yr⁻¹; hence, there is overlap with the lower A-IAV estimates of two data products.

Individual estimates (both GOBMs and data products) generally produce a higher ocean CO₂ sink during strong El Niño events. There is emerging agreement between GOBMs and data products on the patterns of decadal variability of S<sub>OCEAN</sub>, with a global stagnation in the 1990s and an extratropical strengthening in the 2000s (McKinley et al., 2020; Hauck et al., 2020). The central estimates of the annual flux from the GOBMs and the fCO₂-based data products have a correlation r of 0.94 (1990–2021). The agreement between the models and the data products reflects some consistency in their representation of underlying variability since there is little overlap in their methodology or use of observations.

## C4 Methodology: land CO₂ sink

### C4.1 DGVM simulations

The DGVMs model runs were forced by either the merged monthly Climate Research Unit (CRU) and 6-hourly Japanese 55-year Reanalysis (JRA-55) data set or by the monthly CRU data set, with both providing observation-based temperature, precipitation, and incoming surface radiation data on a 0.5° × 0.5° grid updated to 2021 (Harris et al., 2014, 2020). The combination of CRU monthly data with 6-hourly forcing from JRA-55 (Kobayashi et al., 2015) is performed with methodology used in previous years (Viovy, 2016) adapted to the specifics of the JRA-55 data.
Introduced in GCB2021 (Friedlingstein et al., 2022a), in-
coming short-wave radiation fields are used to take into ac-
count aerosol impacts and the division of total radiation into
direct and diffuse components as summarized below.

The diffuse fraction dataset offers 6-hourly distributions
of the diffuse fraction of surface short-wave fluxes over the
period 1901–2021. Radiative transfer calculations are based
on monthly averaged distributions of tropospheric and strato-
spheric aerosol optical depth and 6-hourly distributions of
cloud fraction. Methods follow those described in the Meth-
ods section of Mercado et al. (2009) but with updated input
datasets.

The time series of speciated tropospheric aerosol optical depth is taken from the historical and RCP8.5 simulations by the HadGEM2-ES climate model (Bellouin et al., 2011). To correct for biases in HadGEM2-ES, tropospheric aerosol optical depths are scaled over the whole period to match the global and monthly averages obtained over the period 2003–2020 by the CAMS reanalysis of atmospheric composition (Inness et al., 2019), which assimilates satellite retrievals of aerosol optical depth.

The time series of stratospheric aerosol optical depth is taken from the climatology of Sato et al. (1993), which has been updated to 2012. The years 2013–2020 are assumed to be background years and thus replicate the background year 2010. That assumption is supported by the Global Space-based Stratospheric Aerosol Climatology time series (1979–2016; Thomason et al., 2018). The time series of cloud fraction is obtained by scaling the 6-hourly distributions simulated in the Japanese Reanalysis (Kobayashi et al., 2015) to match the monthly averaged cloud cover in the CRU TS v4.06 dataset (Harris et al., 2020). Surface radiative fluxes account for aerosol–radiation interactions from both tropospheric and stratospheric aerosols and for aerosol–cloud interactions from tropospheric aerosols (except mineral dust). Tropospheric aerosols are also assumed to exert interactions with clouds.

The radiative effects of those aerosol–cloud interactions are assumed to scale with the radiative effects of aerosol–radiation interactions of tropospheric aerosols using regional scaling factors derived from HadGEM2-ES. Diffuse fraction is assumed to be 1 in cloudy sky. Atmospheric constituents other than aerosols and clouds are set to a constant standard mid-latitude summer atmosphere, but their variations do not affect the diffuse fraction of surface short-wave fluxes.

In summary, the DGVMs forcing data include time-
dependent gridded climate forcing, global atmospheric CO₂
(Dlugokencky and Tans, 2022), gridded land cover changes
(see Appendix C2.2), and gridded nitrogen deposition and
fertilizers (see Table A1 for specific models details).

Four simulations were performed with each of the
DGVMs. Simulation 0 (S0) is a control simulation that
uses fixed pre-industrial (year 1700) atmospheric CO₂ con-
centrations, cycles early 20th century (1901–1920) climate,
and applies a time-invariant pre-industrial land cover distri-

bution and pre-industrial wood harvest rates. Simulation 1 (S1) differs from S0 by applying historical changes in atmospheric CO₂ concentration and N inputs. Simulation 2 (S2) applies historical changes in atmospheric CO₂ concentration, N inputs, and climate, while applying time-invariant pre-industrial land cover distribution and pre-industrial wood harvest rates. Simulation 3 (S3) applies historical changes in atmospheric CO₂ concentration, N inputs, climate, land cover distribution, and wood harvest rates.

S2 is used to estimate the land sink component of the global carbon budget ($S_{LAND}$). S3 is used to estimate the total land flux but is not used in the global carbon budget. We further separate $S_{LAND}$ into contributions from CO₂ (= S1–S0) and climate (= S2 – S1 + S0).

C4.2 DGVM evaluation and uncertainty assessment for $S_{LAND}$

We apply three criteria for minimum DGVM realism by
including only those DGVMs with (1) steady state after
spin up, (2) global net land flux (S<sub>LAND</sub> − E<sub>LUC</sub>), i.e. an
atmosphere-to-land carbon flux over the 1990s ranging be-
tween −0.3 and 2.3 GtC yr<sup>−1</sup> within 90% confidence of
constraints by global atmospheric and oceanic observations
(Keeling and Manning, 2014; Wanninkhof et al., 2013), and
(3) global E<sub>LUC</sub> that is a carbon source to the atmosphere
over the 1990s, as already mentioned in Appendix C2.2. All
DGVMs meet these three criteria.

In addition, the DGVMs results are also evaluated us-
ing the International Land Model Benchmarking system (IL-
AMB; Collier et al., 2018). This evaluation is provided
here to document, encourage, and support model improve-
ments through time. ILAMB variables cover key processes
that are relevant for the quantification of S<sub>LAND</sub> and result-
ing aggregated outcomes. The selected variables are vege-
tation biomass, gross primary productivity, leaf area index,
net ecosystem exchange, ecosystem respiration, evapotran-
spiration, soil carbon, and runoff (see Fig. B3 for the results
and for the list of observed databases). Results are shown in
Fig. B3 and discussed in Sect. 3.6.5.

For the uncertainty for $S_{LAND}$, we use the standard devia-
tion of the annual CO₂ sink across the DGVMs, averaging to
about ±0.6 GtC yr⁻¹ for the period 1959 to 2021. We attach
a medium confidence level to the annual land CO₂ sink and
its uncertainty because the estimates from the residual bud-
get and averaged DGVMs match well within their respective
uncertainties (Table 5).

C5 Methodology: atmospheric inversions

C5.1 Inversion system simulations

Nine atmospheric inversions (details of each are given in Ta-
ble A4) were used to infer the spatio-temporal distribution
of the CO₂ flux exchanged between the atmosphere and the
land or oceans. These inversions are based on Bayesian in-
version principles with prior information on fluxes and their
uncertainties. They use very similar sets of surface measure-
ments of CO₂ time series (or subsets thereof) from various
flask and in situ networks. One inversion system also used
satellite xCO₂ retrievals from GOSAT and OCO-2.

Each inversion system uses different methodologies and input data but is rooted in Bayesian inversion principles. These differences mainly concern the selection of the atmospheric CO₂ data, prior fluxes, spatial resolution, assumed correlation structures, and mathematical approaches of the models. Each system uses a different transport model, which was demonstrated to be a driving factor behind differences in atmospheric inversion-based flux estimates and specifically their distribution across latitudinal bands (Gaubert et al., 2019; Schuh et al., 2019).

The inversion systems all prescribe similar global fos-
sil fuel emissions for E fos; specifically, the GCP's
Gridded Fossil Emissions Dataset version 2022 (GCP-
GridFEDv2022.2; Jones et al., 2022), which is an update
through 2021 of the first version of GCP-GridFED pre-
sented by Jones et al. (2021), or another recent version of
GCP-GridFED (Table A4). All GCP-GridFED versions scale
gridded estimates of CO emissions from EDGARv4.3.2
(Janssens-Maenhout et al., 2019) within national territo-
ries to match national emissions estimates provided by the
GCP for the years 1959-2021, which are compiled fol-
lowing the methodology described in Appendix C1. GCP-
GridFEDv2022.2 adopts the seasonality of emissions (the
monthly distribution of annual emissions) from the Carbon
Monitor (Liu et al., 2020a, b; Dou et al., 2022) for Brazil,
China, all EU27 countries, the United Kingdom, the USA,
and shipping and aviation bunker emissions. The seasonality
present in Carbon Monitor is used directly for years 2019-
2021, while for years 1959-2018 the average seasonality of
2019 and 2021 are applied (avoiding the year 2020 during
which emissions were most impacted by the COVID-19 pan-
demic). For all other countries, seasonality of emissions is
taken from EDGAR (Janssens-Maenhout et al., 2019; Jones
et al., 2022), with a small annual correction to the seasonality
present in year 2010 based on heating or cooling degree days
to account for the effects of interannual climate variability
on the seasonality of emissions (Jones et al., 2021). Earlier
versions of GridFED used Carbon Monitor-based seasonal-
ity only from 2019 onwards. In addition, we note that GCP-
GridFEDv2022.1 and v2022.2 include emissions from ce-
ment production and the cement carbonation CO₂ sink (Ap-
pendix C1.1), whereas earlier versions of GCP-GridFED did
not include the cement carbonation CO₂ sink.

The consistent use of recent versions of GCP-GridFED for
E fos ensures a close alignment with the estimate of E fos
used in this budget assessment, enhancing the comparability
of the inversion-based estimate with the flux estimates de-
riving from DGVMs, GOBMs, and fCO₂-based methods.
To ensure that the estimated uptake of atmospheric CO₂ by

the land and oceans was fully consistent with the sum of the
fossil emissions flux from GCP-GridFEDv2022.2 and the at-
mospheric growth rate of CO₂, small corrections to the fossil
fuel emissions flux were applied to inversions systems using
other versions of GCP-GridFED.

The land and ocean CO₂ fluxes from atmospheric inver-
sions contain anthropogenic perturbation and natural pre-
industrial CO₂ fluxes. On annual timescales, natural pre-
industrial fluxes are primarily land CO₂ sinks and ocean CO₂
sources corresponding to carbon taken up on land, trans-
ported by rivers from land to ocean, and outgassed by the
ocean. These pre-industrial land CO₂ sinks are thus compen-
sated over the globe by ocean CO₂ sources corresponding to
the outgassing of riverine carbon inputs to the ocean, using
the exact same numbers and distributions as described for the
oceans in Sect. 2.4. To facilitate the comparison, we adjusted
the inverse estimates of the land and ocean fluxes per latitude
band with these numbers to produce historical perturbation
CO₂ fluxes from inversions.

C5.2 Inversion system evaluation

All participating atmospheric inversions are checked for con-
sistency with the annual global growth rate, as both are de-
rived from the global surface network of atmospheric CO2
observations. In this exercise, we use the conversion factor
of 2.086 GtC ppm⁻¹ to convert the inverted carbon fluxes to
mole fractions, as suggested by Prather (2012). This number
is specifically suited for the comparison to surface observa-
tions that do not respond uniformly (or immediately) to each
year’s summed sources and sinks. This factor is therefore
slightly smaller than the GCB conversion factor in Table 1
(2.142 GtC ppm⁻¹, Ballantyne et al., 2012). Overall, the in-
versions agree with the growth rate, with biases between 0.03
and 0.08 ppm (0.06–0.17 GtC yr⁻¹) on the decadal average.

The atmospheric inversions are also evaluated using ver-
tical profiles of atmospheric CO₂ concentrations (Fig. B4).
More than 30 aircraft programmes over the globe, either reg-
ular programmes or repeated surveys over at least 9 months,
have been used in order to draw a robust picture of the sys-
tem performance (with space–time data coverage that is ir-
regular and denser in the 0–45° N latitude band; Table A6).
The nine systems are compared to the independent aircraft
CO₂ measurements between 2 and 7 km above sea level be-
tween 2001 and 2021. Results are shown in Fig. B4, where
the inversions generally match the atmospheric mole frac-
tions to within 0.7 ppm at all latitudes, except for CT Eu-
rope in 2011–2021 over the more sparsely sampled Southern
Hemisphere.
# Appendix D: Processes not included in the global carbon budget

## D1 Contribution of anthropogenic CO and CH₄ to the global carbon budget

Equation (1) only partly includes the net input of CO₂ to the atmosphere from the chemical oxidation of reactive carbon-containing gases from sources other than the combustion of fossil fuels, such as (1) cement process emissions, since these do not come from combustion of fossil fuels, (2) the oxidation of fossil fuels, and (3) the assumption of immediate oxidation of vented methane in oil production. However, it omits any other anthropogenic carbon-containing gases that are eventually oxidized in the atmosphere, forming a diffuse source of CO₂, such as anthropogenic emissions of CO and CH₄. An attempt is made here to estimate their magnitude and identify the sources of uncertainty. Anthropogenic CO emissions are from incomplete fossil fuel and biofuel burning and deforestation fires. The main anthropogenic emissions of fossil CH₄ that matter for the global (anthropogenic) carbon budget are the fugitive emissions of coal, oil, and gas sectors (see below). These emissions of CO and CH₄ contribute a net addition of fossil carbon to the atmosphere.

In our estimate of E<sub>FOS</sub>, we assumed (Sect. 2.1.1) that all the fuel burned is emitted as CO<sub>2</sub>, and thus CO anthropogenic emissions associated with incomplete fossil fuel combustion and its atmospheric oxidation into CO<sub>2</sub> within a few months are already counted implicitly in E<sub>FOS</sub> and should not be counted twice (same for E<sub>LUC</sub> and anthropogenic CO emissions by deforestation fires). The diffuse atmospheric source of CO<sub>2</sub> deriving from anthropogenic emissions of fossil CH<sub>4</sub> is not included in E<sub>FOS</sub>. In reality, the diffuse source of CO<sub>2</sub> from CH<sub>4</sub> oxidation contributes to the annual CO<sub>2</sub> growth. Emissions of fossil CH<sub>4</sub> represent 30% of total anthropogenic CH<sub>4</sub> emissions (Saunois et al., 2020; their top-down estimate is used because it is consistent with the observed CH<sub>4</sub> growth rate), i.e. 0.083 GtC yr<sup>-1</sup> for the decade 2008–2017. Assuming steady state, an amount equal to this fossil CH<sub>4</sub> emission is all converted to CO<sub>2</sub> by OH oxidation, and this therefore explains 0.083 GtC yr<sup>-1</sup> of the global CO<sub>2</sub> growth rate, with an uncertainty range of 0.061 to 0.098 GtC yr<sup>-1</sup> taken from the min-max of top-down estimates in Saunois et al. (2020). If this min-max range is assumed to be 2σ because Saunois et al. (2020) did not account for the internal uncertainty of their minimum and maximum top-down estimates, it translates into a 1σ uncertainty of 0.019 GtC yr<sup>-1</sup>.

Other anthropogenic changes in the sources of CO and CH₄ from wildfires, vegetation biomass, wetlands, ruminants, or permafrost changes are similarly assumed to have a small effect on the CO₂ growth rate. The CH₄ and CO emissions and sinks are published and analysed separately in the global methane budget and global carbon monoxide

budget publications, which follow a similar approach to that presented here (Saunois et al., 2020; Zheng et al., 2019).

## D2 Contribution of other carbonates to CO₂ emissions

Although we do account for cement carbonation (a carbon sink), the contribution of emissions of fossil carbonates (carbon sources) other than cement production is not systematically included in estimates of E<sub>FOS</sub>, except for Annex I countries and lime production in China (Andrew and Peters, 2021). The missing processes include CO₂ emissions associated with the calcination of lime and limestone outside of cement production. Carbonates are also used in various industries, including in iron and steel manufacture and in agriculture. They are found naturally in some coals. CO₂ emissions from fossil carbonates other than cement not included in our dataset are estimated to amount to about 0.3% of E<sub>FOS</sub> (estimated based on Crippa et al., 2019).

## D3 Anthropogenic carbon fluxes in the land-to-ocean aquatic continuum

The approach used to determine the global carbon budget refers to the mean, variations, and trends in the perturbation of CO₂ in the atmosphere, referenced to the pre-industrial era. Carbon is continuously displaced from the land to the ocean through the land-ocean aquatic continuum (LOAC) comprising freshwaters, estuaries, and coastal areas (Bauer et al., 2013; Regnier et al., 2013). A substantial fraction of this lateral carbon flux is entirely “natural” and is thus a steady-state component of the pre-industrial carbon cycle. We account for this pre-industrial flux where appropriate in our study (see Appendix C3). However, changes in environmental conditions and land-use change have caused an increase in the lateral transport of carbon into the LOAC – a perturbation that is relevant for the global carbon budget presented here.

The results of the analysis of Regnier et al. (2013) can be summarized in two points of relevance for the anthropogenic CO₂ budget. First, the anthropogenic perturbation of the LOAC has increased the organic carbon export from terrestrial ecosystems to the hydrosphere by as much as 1.0 ± 0.5 GtC yr⁻¹ since pre-industrial times, mainly owing to enhanced carbon export from soils. Second, this exported anthropogenic carbon is partly respired through the LOAC, partly sequestered in sediments along the LOAC, and to a lesser extent transferred to the open ocean where it may accumulate or be outgassed. The increase in storage of land-derived organic carbon in the LOAC carbon reservoirs (burial) and in the open ocean combined is estimated by Regnier et al. (2013) at 0.65 ± 0.35 GtC yr⁻¹. The inclusion of LOAC-related anthropogenic CO₂ fluxes should affect estimates of S<sub>LAND</sub> and S<sub>OCEAN</sub> in Eq. (1) but does not affect the other terms. Representation of the anthropogenic perturbation of LOAC CO₂ fluxes is, however, not included
in the GOBMs and DGVMs used in our global carbon budget analysis presented here.

## D4 Loss of additional land sink capacity

Historical land-cover change was dominated by transitions from vegetation types that can provide a large carbon sink per area unit (typically, forests) to others less efficient in removing CO₂ from the atmosphere (typically, croplands). The resultant decrease in land sink, called the “loss of additional sink capacity”, can be calculated as the difference between the actual land sink under changing land cover and the counterfactual land sink under pre-industrial land cover. This term is not accounted for in our global carbon budget estimate. Here, we provide a quantitative estimate of this term to be used in the discussion. Seven of the DGVMs used in Friedlingstein et al. (2019) performed additional simulations with and without land-use change under cycled pre-industrial environmental conditions. The resulting loss of additional sink capacity amounts to 0.9 ± 0.3 GtC yr⁻¹ on average over 2009–2018 and 42 ± 16 GtC accumulated between 1850 and 2018 (Obermeier et al., 2021). OSCAR, emulating the behaviour of 11 DGVMs, finds values of the loss of additional sink capacity of 0.7 ± 0.6 GtC yr⁻¹ and 31 ± 23 GtC for the same time period (Gasser et al., 2020). Since the DGVM-based E_LUC estimates are only used to quantify the uncertainty around the bookkeeping models’ E_LUC, we do not add the loss of additional sink capacity to the bookkeeping estimate.

**Author contributions.** PF, MOS, MWJ, RMA, LukG, JH, CLQ, ITL, AO, GPP, WP, JP, CIS, and SS designed the study, conducted the analysis, and wrote the paper with input from JGC, PC, and RBJ. RMA, GPP and JIK produced the fossil fuel emissions and their uncertainties and analysed the emissions data. MH and GM provided fossil fuel emission data. JP, ThoG, CIS, and RAH provided the bookkeeping land-use change emissions with synthesis by JP and CIS. JH, LB, ÖG, NG, TI, KL, NMa, LR, JS, RS, HiT, and ReW provided an update of the global ocean biogeochemical models. MG, LucG, LukG, YI, AJ, ChR, JDS, and JZ provided an update of the ocean fCO₂ data products, with synthesis on both streams by JH, LukG, and NMa. SRA, NRB, MB, HCB, MC, WE, RAF, ThaG, KK, NL, NMe, NMM, DRM, SN, TO, DP, KP, ChR, IS, TS, AJS, CoS, ST, TT, BT, RiW, CW, and AW provided ocean fCO₂ measurements for the year 2021, with synthesis by AO and KO. AA, VKA, SF, AKJ, EK, DK, JK, MJM, MOS, BP, QS, HaT, APW, WY, XY, and SZ provided an update of the dynamic global vegetation models, with synthesis by SS and MOS. WP, ITL, FC, JL, YN, PIP, ChR, XT, and BZ provided an updated atmospheric inversion. WP, FC, and ITL developed the protocol and produced the evaluation. RMA provided predictions of the 2022 emissions and atmospheric CO₂ growth rate. PL provided the predictions of the 2022 ocean and land sinks. LPC, GCH, KKG, TMR, and GRvdW provided forcing data for land-use change. RA, GG, FT, and CY provided data for the land-use change NGHGI mapping. PPT provided key atmospheric CO₂ data. MWJ produced the model atmospheric

CO₂ forcing and the atmospheric CO₂ growth rate. MOS and NB produced the aerosol diffuse radiative forcing for the DGVMs. IH provided the climate forcing data for the DGVMs. ER provided the evaluation of the DGVMs. MWJ provided the emission priors for use in the inversion systems. ZL provided seasonal emissions data for most recent years for the emission prior. MWJ and MOS developed the new data management pipeline, which automates many aspects of the data collation, analysis, plotting, and synthesis. PF, MOS, and MMJ coordinated the effort and revised all figures, tables, text, and/or numbers to ensure the update was clear from the 2021 edition and in line with the http://globalcarbonatlas.org (last access: 25 September 2022).

**Competing interests.** At least one of the (co-)authors is a member of the editorial board of *Earth System Science Data*. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.

**Disclaimer.** Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Acknowledgements.** We thank all people and institutions who provided the data used in this Global Carbon Budget 2022 and the Global Carbon Project members for their input throughout the development of this publication. We thank Nigel Hawtin for producing Figs. 2 and 14. We thank Thomas Hawes for technical support with the data management pipeline. We thank Ed Dlugokencky for providing atmospheric CO₂ measurements. We thank Ian G. C. Ashton, Fatemeh Cheginig, Trang T. Chau, Sam Ditkovsky, Christian Ethé, Amanda R. Fay, Lonneke Goddijn-Murphy, Thomas Holding, Fabrice Lacroix, Enhui Liao, Galen A. McKinley, Shijie Shu, Richard Sims, Jade Skye, Andrew J. Watson, David Willis, and David K. Woolf for their involvement in the development, use, and analysis of the models and data products used here. Daniel Kennedy thanks all the scientists, software engineers, and administrators who contributed to the development of CESM2. We thank Joe Salisbury, Doug Vandemark, Christopher W. Hunt, and Peter Landschützer, who contributed to the provision of surface ocean CO₂ observations for the year 2021 (see Table A5). We also thank Benjamin Pfeil, Rocío Castaño-Primo, and Stephen D. Jones of the Ocean Thematic Centre of the EU Integrated Carbon Observation System (ICOS) Research Infrastructure; Eugene Burger of NOAA’s Pacific Marine Environmental Laboratory; and Alex Kozyr of NOAA’s National Centers for Environmental Information for their contribution to surface ocean CO₂ data and metadata management. This is PMEL contribution 5434. We thank the scientists, institutions, and funding agencies responsible for the collection and quality control of the data in SOCAT and the International Ocean Carbon Coordination Project (IOCCP), the Surface Ocean Lower Atmosphere Study (SOLAS), and the Integrated Marine Biosphere Research (IMBeR) program for their support. We thank data providers ObsPack GLOBALVIEWplus v7.0 and NRT v7.2 for atmospheric CO₂ observations. We thank the individuals and institutions that provided the databases used for the model evaluations used here. We thank Fortunat Joos, Samar Khatiwala,
and Timothy DeVries for providing historical data. Matthew J. McGrath thanks the whole ORCHIDEE group. Ian Harris thanks the Japan Meteorological Agency (JMA) for producing the Japanese 55-year Reanalysis (JRA-55). Anthony P. Walker thanks ORNL, which is managed by UT-Battelle, LLC, for the DOE under contract DE-AC05-1008 00OR22725. Yosuke Niwa thanks CSIRO, EC, EMPA, FMI, IPEN, JMA, LSCE, NCAR, NIES, NILU, NIWA, NOAA, SIO, and TU/NIPR for providing data for NISMON-CO₂. Xiangjun Tian thanks Zhe Jin, Yilong Wang, Tao Wang, and Shilong Piao for their contributions to the GONGGA inversion system. Bo Zheng thanks the comments and suggestions from Philippe Ciais and Frédéric Chevallier. Frédéric Chevallier thanks Marine Remaud, who maintained the atmospheric transport model for the CAMS inversion. Paul I. Palmer thanks Liang Feng and acknowledges ongoing support from the National Centre for Earth Observation. Junjie Liu thanks the Jet Propulsion Laboratory, California Institute of Technology. Wiley Evans thanks the Tula Foundation for funding support. Australian ocean CO₂ data were sourced from Australia's Integrated Marine Observing System (IMOS); IMOS is enabled by the National Collaborative Research Infrastructure Strategy (NCRIS). Margot Cronin thanks Anthony English, Clynt Gregory, and Gordon Furey (P&O Maritime Services) for their support. Nathalie Lefèvre thanks the crew of the Cap San Lorenzo and the US IMAGO of IRD Brest for technical support. Henry C. Bittig is grateful for the skilful technical support of Michael Glockzin and Bernd Sadkowiak. Meike Becker and Are Olsen thank Sparebanken Vest/Agenda Vestlandet for their support for the observations on the Statsraad Lehmkuhl. Thanos Gkritzalis thanks the personnel and crew of Simon Stevin. Matthew W. Jones thanks Anthony J. De-Gol for his technical and conceptual assistance with the development of GCP-GridFED. FAOSTAT is funded by FAO member states through their contributions to the FAO Regular Programme; data contributions by national experts are gratefully acknowledged. The views expressed in this paper are the authors' only and do not necessarily reflect those of FAO. Finally, we thank all funders who have supported the individual and joint contributions to this work (see Table A9), the reviewers of this manuscript and previous versions, and the many researchers who have provided feedback.

**Financial support.** For a list of all funders that have supported this research, please refer to Table A9.

**Review statement.** This paper was edited by David Carlson and reviewed by H. Damon Matthews, Hélène Peiro, Ana Maria Roxana Petrescu, Michio Kawamiya, and one anonymous referee.

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