This is a pilot project designed to start a dialogue between the top-down research community, inventory compilers and the GHG assessment community to identify ways that top-down CO2 flux estimates can help inform country-level carbon budgets (see , for a similar pilot methane dataset). To meet this objective, the primary goal of this work is to provide two products: (1) annual net surface–atmosphere CO2 fluxes and (2) annual changes in terrestrial carbon stocks. These products are provided annually over the 6-year period 2015–2020 both on a 1∘ × 1∘ global grid and as country-level totals with error characterization.

These products are intended to be used to help inform inventory development and identify areas for future research in both top-down and bottom-up approaches, including informing strategies for operational top-down carbon cycle products that can be used for tracking combined changes in managed and unmanaged carbon stocks and that can help quantify the impact of emission reduction activities.

The burning of fossil fuels and cement production release geologic carbon to the atmosphere (40.0±3.3 PgCO2yr−1 or 10.9±0.9 PgCyr−1 over 2010–2019; ). These emissions, along with land-use activities, impact carbon cycling between atmospheric, oceanic and biospheric reservoirs that make up a near-closed system on annual timescales. As a result, roughly half of the emitted CO2 from anthropogenic sources is absorbed by terrestrial ecosystems and oceans , reducing the rate of atmospheric CO2 increase (18.7±0.08 PgCO2yr−1 or 5.1±0.02 PgCyr−1 over 2010–2019; ). Here we briefly review the movement of carbon between the reservoirs and how these processes are modulated by human activities.

Fluxes of carbon between the atmosphere and ocean are driven by the difference in partial pressures of CO2 between seawater and air, resulting in roughly balancing fluxes from the ocean-to-atmosphere and atmosphere-to-ocean of ∼293 PgCO2yr−1 (∼80 PgCyr−1) each way , with a residual net atmosphere-to-ocean flux due to increasing atmospheric CO2 (9.2±2.2 PgCO2yr−1 or 2.5±0.6 PgCyr−1 over 2010–2019; ). Regional variations in the solubility and saturation of CO2 in ocean waters drive net fluxes, with net fluxes to the atmosphere in upwelling regions, such as the eastern boundary of basins and in equatorial zones . Meanwhile, there are net removals by the ocean in western boundary currents and at extratropical latitudes . Within the oceans, circulation patterns, mixing and biologic activity act to redistribute carbon.

On land, terrestrial ecosystems remove atmospheric carbon through photosynthesis, referred to as gross primary production (GPP) (Fig. ). GPP draws roughly 440 PgCO2yr−1 (120 PgCyr−1) from the atmosphere . Roughly half of this carbon is emitted back to the atmosphere by plants through autotrophic respiration, while the remaining carbon is used to generate plant biomass and is referred to as net primary production (NPP). On an annual basis, the carbon sequestered through NPP is roughly balanced by carbon loss through a number of processes. The largest of these processes is heterotrophic respiration, which is the respiratory emission of CO2 (from the dead organic matter and soil carbon pools) by heterotrophic organisms, and accounts for 82 %–95 % of NPP . The combination of heterotrophic and autotrophic respiration is called ecosystem respiration (Reco). The remaining processes have smaller magnitudes but are still critical for determining the carbon balance of ecosystems. Biomass burning, the emission of carbon to the atmosphere through combustion, releases roughly 7.3 Pg CO2 yr−1 (2 Pg C yr−1) to the atmosphere on an annual basis but with considerable interannual variability . Carbon can also be emitted from the terrestrial biosphere to the atmosphere in the form of carbon monoxide (CO), methane (CH4) and other biologic volatile organic compounds (BVOCs), which are oxidized to CO2 in the atmosphere. Rivers move carbon in the form of dissolved inorganic carbon (DIC), dissolved organic carbon (DOC) and particulate organic carbon (POC). This carbon of terrestrial origin is partly transported to the open ocean, partly released to the atmosphere from inland waters and estuaries, and partly buried in aquatic or marine sediments. Finally, anthropogenic activities such as harvesting of crop and wood products result in lateral transport of carbon such that the removal of atmospheric CO2 through NPP and emission of atmospheric CO2 through respiration (e.g., decomposition in a landfill) or combustion (e.g., burning of biofuels) occur in different regions. See Fig.  for an illustration of these fluxes.

Globally, there is a long-term net uptake of atmospheric CO2 by the land (approximately -6.6 PgCO2yr−1 or -1.8 PgCyr−1 over 2010–2019; ), which is the residual of an emission due to net land-use change (5.9±2.6 PgCO2yr−1 or 1.6±0.7 PgCyr−1 over 2010–2019; ) and removal by other terrestrial ecosystems 12.6±3.3 PgCO2yr−1 or 3.4±0.9 PgCyr−1 over 2010–2019;. This removal is partially driven by direct feedbacks between increasing CO2 and the biosphere, such as CO2 fertilization of photosynthesis and increased water use efficiency. Carbon–climate feedbacks also lead to both increases and decreases in terrestrial carbon stocks: for example, warming at high latitudes leads to a more productive biosphere, but it also leads to increased plant and soil respiration . In addition, the release of nitrogen through anthropogenic energy and fertilizer use may drive increased carbon sequestration by the terrestrial biosphere . Regrowth of forests in previously cleared areas, especially in the extratropics, is also thought to be an important uptake term . Currently, the relative impact of each of these contributions to long-term terrestrial carbon sequestration is poorly known and likely varies between biomes and climates.

While the existence of a long-term global land sink is supported through a number of lines of evidence , regional-scale emissions and removals are less well quantified. Regional-scale carbon sequestration can differ substantially from the global mean and can be impacted by the regional climate, disturbance events and anthropogenic activities . The need to better quantify regional-scale emissions and removals of carbon has motivated much of the recent expansion of in situ CO2 observing networks, the launch of space-based CO2 observing systems and the development of CO2 inversion systems.

Atmospheric CO2 inversions estimate the underlying net surface–atmosphere CO2 fluxes from atmospheric CO2 observations, and this is what is meant by the top-down approach . In this approach, an atmospheric chemical transport model (CTM) is employed to relate surface–atmosphere CO2 fluxes to observed atmospheric CO2 mole fractions. As an inverse problem, the upwind CO2 fluxes are estimated from the downwind observed CO2 mole fractions. The surface CO2 fluxes are adjusted so that forward-simulated CO2 mole fractions better match the CO2 measurements while considering the uncertainty statistics on the observations, transport and prior surface fluxes.

The atmospheric CO2 inversion problem is generally ill-posed such that the solution is underdetermined by the observational constraints. In this case, additional information is required to produce a unique solution and prevent overfitting of the data . Typically, this is performed using Bayesian inference, where prior mean fluxes and their uncertainties provide additional information required to estimate fluxes . Prior mean fluxes of net ecosystem exchange are usually obtained from terrestrial biosphere models (such as CASA, ORCHIDEE and CARDAMOM), while prior mean air–sea fluxes are derived from surface water partial pressure of CO2 (pCO2) datasets or from ocean models e.g.,. The resulting posterior flux estimates combine the constraints on surface fluxes from atmospheric CO2 data with the prior knowledge of the fluxes. If there is a high density of assimilated CO2 observations, then the posterior fluxes will be more strongly impacted by the assimilated data, whereas, in regions with sparse observational coverage, the posterior fluxes will generally remain similar to the prior fluxes (assuming similar prior flux uncertainties across regions).

Measurements of atmospheric CO2 best inform diffuse biosphere–atmosphere fluxes on large spatial scales. This is because CO2 has a long atmospheric lifetime such that the perturbation to atmospheric CO2 due to emissions and removals from individual processes and locations gets mixed in the atmosphere . For example, the measurements of CO2 at Mauna Loa, Hawaii, provide a good estimate of the global-scale changes of CO2 surface fluxes. Inferring smaller-scale flux signals requires a high density of CO2 observations (to capture gradients in atmospheric CO2) and accurate modeling of atmospheric transport (to relate the measurements with surface fluxes). The accuracy of flux estimates depends on a number of factors, particularly the accuracy and precision of the data, transport model and prior constraints. Stringent requirements on the accuracy of space-based column-averaged dry-air mole fraction (XCO2) retrievals are required to infer surface fluxes . Biases in XCO2 retrievals from the Orbiting Carbon Observatory (OCO-2) related to spectroscopic errors, solar zenith angle, surface properties, and atmospheric scattering by clouds and aerosols have been identified . However, intensive research has reduced retrieval errors over time . As will be shown in Sect. , biases in OCO-2 XCO2 retrievals over land are thought to be relatively small, although regionally structured biases may be present. However, OCO-2 XCO2 retrievals over oceans may contain more large-scale spatially coherent retrieval errors that can adversely impact flux estimates.

Accurate atmospheric transport is critical for correctly relating surface–atmosphere fluxes to observations. Due to computational constraints, CTMs are typically run offline with coarsened meteorological fields relative to the parent numerical weather prediction model, which has been shown to introduce systematic transport errors in some configurations . In addition, these offline CTMs have been shown to have large-scale systematic differences in transport associated with the implementation of transport algorithms . These errors appear to be of the same order as the retrieval biases, although the patterns in time and space are different. Systematic errors related to model transport (and errors in prior information) can partially be accounted for by performing multiple inversions that differ in CTM and prior constraints employed. This motivates inversion model intercomparison projects (MIPs), such as the OCO-2 MIP project see Sect. ;. From these ensembles of inversions, estimates of both systematic errors (accuracy) and random errors (precision) can be obtained from the model spread.

To aggregate gridded 1∘ × 1∘ flux estimates to country totals we use a country mask . We also provide NCE and ΔCloss estimates for several country groupings. A number of regional intergovernmental organizations are included: the Association of Southeast Asian Nations (ASEAN), the African Union (AU) and each of its sub-regions (North, South, West, East and Central), the Community of Latin American and Caribbean States plus Brazil (CELAC+Brazil), the Economic Cooperation Organization (ECO), the European Union (EU or EU27), and the South Asian Association for Regional Cooperation (SAARC). We also include some geographic regions, specifically North America, the Middle East and Europe. Countries included in these groupings are listed in the Supplement (Text S1).

Gridded 1∘ × 1∘ fossil CO2 emissions, including those from cement production, are calculated as follows. Monthly gridded emissions up to 2019 are taken from the 2020 version of the Open-source Data Inventory for Anthropogenic CO2 (ODIAC2020, 2000–2019) emission data product . The 2020 emissions were not part of ODIAC but were projected using the Carbon Monitor (CM) emission data product (https://carbonmonitor.org/, last access: 19 May 2021). For each month in 2020 and later, the ratio between that month's emissions and the emissions from the same month in 2019 was calculated from the CM emission data. Since CM provides daily emissions per sector for a handful of major emitting countries and the globe, CM emissions are summed over sectors and days in each month to create monthly total emissions per named country and the rest of the world (RoW). The ratio of each (post-2019) month's emission to the same month in 2019 is then calculated per named country and RoW, then distributed over a 1∘ × 1∘ grid assuming homogeneity of the ratio over each named country and RoW. The 2019 ODIAC emissions for that month are then multiplied by the ratio to generate 1∘ × 1∘ monthly emissions after 2019. While this method loses the information of day-to-day variability provided by CM, this is a conscious choice to be consistent over the entire inversion period. Finally, we impose day-of-week and hour-of-day variations on these fluxes following the Temporal Improvements for Modeling Emissions by Scaling (TIMES) diurnal and day-of-week scaling . The 1∘ × 1∘ uncertainty map is based on the combination of the global level FF uncertainty (1σ of 4.2 %, ) and the grid level emission differences due to the different disaggregation methods . Note that these FF uncertainties are not considered in the inversions used for this product development.

Country-level fossil fuel emission estimates are obtained by aggregating the 1∘ × 1∘ estimates using the country mask. Uncertainties on country-level estimates are calculated using the fractional uncertainties of .

We employ results from the v10 OCO-2 MIP, which is an international collaboration of atmospheric CO2 inversion modelers that produces ensembles of CO2 surface–atmosphere flux estimates by assimilating space-based OCO-2 retrievals of XCO2 and in situ CO2 measurements. The v10 OCO-2 MIP is updated from the v9 OCO-2 MIP described in . Updates to the v10 OCO-2 MIP are presented here with additional details available at https://gml.noaa.gov/ccgg/OCO2_v10mip/ (last access: 6 February 2023).

The v10 OCO-2 MIP consists of a number of inversion systems that perform a set of experiments following a standard protocol. Here, we include fluxes from 11 of the 14 MIP models (Table ; CMS-Flux and JHU were excluded due to time constraints, and LoFI was excluded because it employs a non-traditional inversion approach that does not follow the MIP protocol). There are five v10 OCO-2 MIP experiments that each ensemble member performs, which differ by the data that are assimilated (CO2 datasets described in Sect. ):

IS assimilates in situ CO2 mole fraction measurements from an international observational network.

Lateral carbon flux datasets (Table ) include country-level Friversexport (Sect. ), country-level Fcroptrade and country-level Fwoodtrade (Sect. ). Gridded lateral fluxes are estimated using a somewhat different approach and are described in Sect. .

Finally, we calculate ΔCloss using Eq. () with the datasets described above. Assuming that the components contributing to ΔCloss are independent, we calculate the uncertainty on ΔCloss by combining the uncertainties (1 standard deviations) from the component fluxes in quadrature: 6σΔCloss2=σNBE2+σFcroptrade2+σFwoodtrade2+σFriversexport2.

We consider four atmospheric CO2 datasets:

Withheld in situ CO2 measurements. These are measurements contained in the ObsPack collection described in Sect.  but intentionally withheld for evaluation purposes. Independence from the assimilated data is ensured following the steps described in Sect. .

The exchange of CO2 between the atmosphere and the ocean (air–sea flux) can be estimated from measurements of the surface ocean partial pressure of CO2 (pCO2). These pCO2 data are extrapolated to global maps and combined with gas transfer velocity parameterizations to infer global maps of the air–sea CO2 fluxes . Although significant uncertainties remain, particularly in accurately representing the gas transfer velocity , comparisons between the pCO2-based air–sea fluxes and v10 OCO-2 MIP experiments can inform possible biases between estimates and inform potential areas for future research.

Here, we compare v10 OCO-2 MIP air–sea fluxes to an ensemble of air–sea flux estimates from SeaFlux . SeaFlux developed a standardized approach to harmonize and extend six air–sea CO2 flux products from as many surface pCO2 products: JENA-MLS , MPI-SOMFFN , CMEMS-FFN , CSIR-ML6 , JMA-MLR and NIES-FNN . For each pCO2 product, we examine the mean of three air–sea fluxes obtained using different wind reanalysis datasets to estimate the gas transfer parameterization (ERA5, JRA-55 and CCMP2). The spread among these six estimates provides a measure of uncertainty in the extrapolation of pCO2 data to a global grid but does not account for errors in the gas transfer velocity formulation nor the uncertainties in the reanalysis winds used as input . Note that the prior estimates of air–sea CO2 fluxes in v10 OCO-2 MIP experiments are generally pCO2-based flux estimates and therefore not independent from the SeaFlux datasets.

Figure  shows the 2015–2019 mean air–sea fluxes for each of the six SeaFlux products and for the v10 OCO-2 MIP experiments across 30∘ latitude bands and large ocean regions. Over the global ocean, the pCO2-based air–sea fluxes tend to give stronger removals (median=-10.0 PgCO2yr-1 or -2.7 PgCyr-1, range=-9.2 to -12.9 PgCO2yr-1 or -3.5 to -2.5 PgCyr-1) than the v10 OCO-2 MIP, which range from -7.9±1.9 PgCO2yr-1 (-2.1±0.5 PgCyr-1) for the IS experiment to -10.2±1.28 PgCO2yr-1 (-2.8±0.4 PgCyr-1) for the OG experiment. On regional scales, the v10 OCO-2 MIP experiments overlap with the pCO2-based estimates except for the northern high latitudes (60–90∘ N), where pCO2-based estimates suggest systematically larger removals. Similarly, the pCO2-based estimates tend to give greater removals over the southern midlatitudes (20–50∘ S).

The different v10 OCO-2 MIP experiments tend to give similar air–sea fluxes, except for the OG experiment in the tropics. Although not systematic, the OG experiment suggests weaker emissions in the tropics of 0.2±1.3 PgCO2yr-1 (0.05±0.34 PgCyr-1) relative to the median pCO2-based estimate of 1.6 PgCO2yr-1 (0.43 PgCyr-1) with a range of 0.4 to 1.8 PgCO2yr-1 (0.10 to 0.50 PgCyr-1). Thus, similar to the evaluation of posterior CO2 fields, the OG experiment is an outlier among the v10 OCO-2 MIP experiments, further supporting the possibility that residual biases may exist in the ocean glint XCO2 retrievals.

The Z statistic is defined as 7Zstatistic=NCELNLG‾-NCEIS‾SD(NCELNLG-NCEIS), where the denominator represents the standard deviation of NCELNLG-NCEIS across the ensemble members. Differences in NCE and ΔCloss between v10 OCO-2 MIP experiments can be considerable. As an example, Fig. a shows that differences between NCELNLG‾ and NCEIS‾ are notable for South America and Africa. The LNLG experiment gives more positive ΔCloss (carbon loss from land) over northern sub-Saharan Africa and northeast South America but more negative ΔCloss over southern tropical Africa, southern and eastern South America, and southeast Asia. We examine the Z statistic (Fig. b) to quantify the statistical significance of these differences (magnitude greater than 1.96 indicates statistically significant differences at level α=0.05). Most countries do not have statistically significant differences, indicating relatively good agreement between the IS and LNLG ensembles. Significant differences primarily occur in small to mid-sized tropical countries. Canada also shows a systematic difference driven by small uncertainties in the IS and LNLG estimates.

report the uncertainty in NCE as the standard deviation across v10 OCO-2 MIP ensemble members (estimated using Eq. ). This metric incorporates uncertainties related to model transport and aspects of the inversion configuration, such as optimization technique and a priori flux estimates. However, this metric is different to the uncertainty metric usually computed in a Bayesian framework, that is, the Bayesian posterior uncertainty. That uncertainty quantifies the impact of errors in the observations and prior constraints on the posterior flux estimates. The Bayesian posterior uncertainty is not reported for practical reasons, as the majority of contributing models do not calculate this quantity, so it is not possible to calculate this quantity across the ensemble.

In this section, we examine the posterior uncertainty estimates from two contributing inversion systems (CAMS and TM5-4DVar) and compare these estimates to the ensemble-based uncertainty estimate provided with the dataset. Then, we define the FUR metric between the posterior and prior NCE estimates based on the TM5-4DVar model (as CAMS does not estimate uncertainties for the LNLGIS and LNLGOGIS experiments), which can be used to understand the relative impact of assimilated atmospheric CO2 data on estimates of country-level NCE and ΔCloss.

Both CAMS and TM5-4DVar estimate CO2 fluxes using four-dimensional variational assimilation (4D-Var) and estimate posterior uncertainty estimates using a Monte Carlo method derived by . The realism of the prior and posterior CAMS uncertainty estimates has already been the topic of several studies seeand references therein. Figure  shows the ensemble-based uncertainty, prior/posterior uncertainty from CAMS (prior, IS and LNLG only) and prior/posterior uncertainty from TM5-4DVar for four countries. Notably, the magnitudes of the prior/posterior uncertainties from CAMS and TM5-4DVar are quite different, with CAMS uncertainties being 2–8 times larger. Differences in prior/posterior uncertainties of this magnitude are not unusual among inversion systems and highlight the sensitivity of Bayesian uncertainty estimates to choices about prior uncertainties. Both CAMS and TM5-4DVar posterior uncertainties are smaller relative to their prior by similar fractions, driven by the assimilated CO2 data. The magnitude of the ensemble-based uncertainty tends to fall in between the CAMS and TM5-4DVar estimates. However, the CAMS and TM5-4DVar posterior uncertainty estimates decrease as more data are assimilated (as expected), while the ensemble spread does not. In fact, the ensemble spread increases with data density in some cases (e.g., Australia LNLGIS). Thus, overall, we find that the ensemble-based uncertainty estimate is of similar magnitude to the prior/posterior estimate but that the magnitude of posterior uncertainty is quite dependent on the assumed prior uncertainty.

We now calculate the FUR metric in NCE from the TM5-4DVar Bayesian uncertainties (note that we use TM5-4DVar only because CAMS does not report LNLGIS or LNLGOGIS uncertainties). FUR is calculated from the prior flux standard deviation (σprior) and posterior flux standard deviation (σposterior) as 8FUR=1-σposteriorσprior. This quantity ranges between 0 and 1, with larger values indicating that the Bayesian uncertainties have decreased more (relative to the prior) due to the observational constraints from assimilated data. This metric is useful for understanding how the assimilation of data influences the NCE and ΔCloss estimates, which may not be captured by the ensemble spread. For example, Saudi Arabia has a small NCE uncertainty estimate, but this is largely driven by prior knowledge that biosphere CO2 fluxes, while the atmospheric CO2 data have little impact on the NCE estimate.

Figure  shows FUR for the IS, LNLG, LNLGIS and LNLGOGIS experiments. FUR is larger in regions with denser observational coverage. For example, the IS FUR is close to 1 in the USA and parts of Europe, reflecting dense CO2 measurements, but it remains small for many tropical countries, where sampling is sparse. Meanwhile, the LNLG experiment generally has larger FUR values than the IS experiment in the tropics, reflecting denser sampling, but has lower values for some small high-latitude countries, such as in Scandinavia.

In the context of global inversion analyses, annual mean biosphere–atmosphere CO2 fluxes are best informed by measurements of atmospheric CO2 on large spatial scales (e.g., continental-to-global) due to rapid mixing in the atmosphere and gaps in current measurement coverage. The confidence in these top-down estimates decreases as we move to smaller spatial scales, with the minimum spatial scale being dependent on the density, precision and sensitivity of the measurements. Future refinements in top-down CO2 budgets will depend on increasing observational density (Sect. ), improved validation (Sect. ) and data harmonization (Sect. ).

Atmospheric CO2 inversion analyses are a critical tool for estimating surface fluxes from observations of atmospheric CO2. Expanding observational coverage provides both opportunities and challenges for inversion systems. By addressing the current limitations of our inversion systems, we will be able to take full advantage of increasing observations to improve country-level top-down estimates of NCE and ΔCloss. Here we discuss ongoing and planned developments (Sect. ), improving model transport (Sect. ), missing processes and required assumptions (Sect. ), and uncertainty quantification (Sect. ).

Agriculture and LULUCF emissions and removals are generally quantified as terrestrial carbon stock changes in managed lands. A number of challenges remain in estimating this quantity from top-down methods. Firstly, lateral fluxes of carbon remain quite uncertain (and associated uncertainty estimates are themselves quite uncertain). The best constrained lateral fluxes are annual country-level Fwoodtrade and Fwoodtrade, which are reported to the UN Food and Agriculture Organization. These fluxes are more uncertain on sub-national scales and sub-annual timescales. Meanwhile, Friversexport is best quantified on basin scales, where stream gauge measurements inform carbon fluxes. Improving sub-national and sub-annual estimates of lateral fluxes would have several benefits: first, this would allow for better sub-national attribution, where regional fluxes could be better quantified. Second, this would allow for incorporating the atmospheric imprint of these carbon fluxes as prior information within atmospheric CO2 inversion analyses, which may improve flux estimates on sub-national scales.

The GST and Paris Agreement do not consider emissions and removals from unmanaged lands. Separating managed lands from unmanaged lands remains a major challenge, given the smoothed large-scale CO2 flux constraints provided by these top-down methods and the fact that both managed and unmanaged lands can experience considerable stock changes driven by interannual climate variations (e.g., El Niño) and in response to rising CO2 and climate change. In addition, separating managed and unmanaged lands is further complicated by the fact that there is considerable ambiguity in the definitions of managed lands, which can also vary by country . We recommend that each party provide a mask to unambiguously define the plots considered managed from year to year .