The estimates of global and national fossil CO2 emissions (EFOS) include the combustion of fossil fuels through a wide range of activities (e.g. transport, heating and cooling, industry, fossil industry own use, and natural gas flaring), the production of cement, and other process emissions (e.g. the production of chemicals and fertilizers) as well as CO2 uptake during the cement carbonation process. The estimates of EFOS in this study rely primarily on energy consumption data, specifically data on hydrocarbon fuels, collated and archived by several organizations (Andres et al., 2012; Andrew, 2020a). We use four main data sets for historical emissions (1750–2019):

Global and national emission estimates for coal, oil, natural gas, and peat fuel extraction from the Carbon Dioxide Information Analysis Center (CDIAC) for the time period 1750–2017 (Gilfillan et al., 2020), as it is the only data set that extends back to 1750 by country.

CDIAC. The CDIAC estimates have been updated annually up to the year 2017, derived primarily from energy statistics published by the United Nations (UNSD, 2020). Fuel masses and volumes are converted to fuel energy content using country-level coefficients provided by the UN and then converted to CO2 emissions using conversion factors that take into account the relationship between carbon content and energy (heat) content of the different fuel types (coal, oil, natural gas, natural gas flaring) and the combustion efficiency (Marland and Rotty, 1984; Andrew, 2020a). Following Andrew (2020a), we make corrections to emissions from coal in the Soviet Union during World War II, amounting to a cumulative reduction of 53 MtC over 1942–1943, and corrections to emissions from oil in the Netherlands Antilles and Aruba prior to 1950, amounting to a cumulative reduction of 340 MtC over 23 years.

UNFCCC. Estimates from the national greenhouse gas inventory reports submitted to the United Nations Framework Convention on Climate Change (UNFCCC) follow the IPCC guidelines (IPCC, 2006, 2019) but have a slightly larger system boundary than CDIAC by including emissions coming from carbonates other than in cement manufacture. We reallocate the detailed UNFCCC sectoral estimates to the CDIAC definitions of coal, oil, natural gas, cement, and others to allow more consistent comparisons over time and between countries.

Specific country updates. For India, the data reported by CDIAC are for the fiscal year running from April to March (Andrew, 2020a), and various interannual variations in emissions are not supported by official data. Given that India is the world's third-largest emitter and that a new data source is available that resolves these issues, we replace CDIAC estimates with calendar-year estimates through 2019 by Andrew (2020b). For Norway, CDIAC's method of apparent energy consumption results in large errors, and we therefore overwrite emissions before 1990 with estimates derived from official Norwegian statistics.

BP. For the most recent year(s) for which the UNFCCC and CDIAC estimates are not yet available, we generate preliminary estimates using energy consumption data (in exajoules, EJ) from the BP Statistical Review of World Energy (Andres et al., 2014; BP, 2020; Myhre et al., 2009). We apply the BP growth rates by fuel type (coal, oil, natural gas) to estimate 2019 emissions based on 2018 estimates (UNFCCC Annex I countries), and to estimate 2018–2019 emissions based on 2017 estimates (remaining countries except India). BP's data set explicitly covers about 70 countries (96 % of global energy emissions), and for the remaining countries we use growth rates from the sub-region the country belongs to. For the most recent years, natural gas flaring is assumed to be constant from the most recent available year of data (2018 for Annex I countries, 2017 for the remainder). We apply two exceptions to this update using BP data. The first is for China's coal emissions, for which we use growth rates reported in official preliminary statistics for 2019 (NBS, 2020b). The second exception is for Australia, for which BP reports a growth rate of natural gas consumption in Australia of almost 30 %, which is incorrect, and we use a figure of 2.2 % derived from Australia's own reporting (Department of the Environment and Energy, 2020).

Cement. Estimates of emissions from cement production are updated from Andrew (2019). Other carbonate decomposition processes are not included explicitly here, except in national inventories provided by Annex I countries, but are discussed in Sect. 2.7.2.

Country mappings. The published CDIAC data set includes 257 countries and regions. This list includes countries that no longer exist, such as the USSR and Yugoslavia. We reduce the list to 214 countries by reallocating emissions to currently defined territories, using mass-preserving aggregation or disaggregation. Examples of aggregation include merging East and West Germany to the currently defined Germany. Examples of disaggregation include reallocating the emissions from the former USSR to the resulting independent countries. For disaggregation, we use the emission shares when the current territories first appeared (e.g. USSR in 1992), and thus historical estimates of disaggregated countries should be treated with extreme care. In the case of the USSR, we were able to disaggregate 1990 and 1991 using data from the International Energy Agency (IEA). In addition, we aggregate some overseas territories (e.g. Réunion, Guadeloupe) into their governing nations (e.g. France) to align with UNFCCC reporting.

Global total. The global estimate is the sum of the individual countries' emissions and international aviation and marine bunkers. The CDIAC global total differs from the sum of the countries and bunkers since (1) the sum of imports in all countries is not equal to the sum of exports because of reporting inconsistencies, (2) changes in stocks, and (3) the share of non-oxidized carbon (e.g. as solvents, lubricants, feedstocks) at the global level is assumed to be fixed at the 1970s average while it varies in the country-level data based on energy data (Andres et al., 2012). From the 2019 edition CDIAC now includes changes in stocks in the global total (Dennis Gilfillan, personal communication, 2020), removing one contribution to this discrepancy. The discrepancy has grown over time from around zero in 1990 to over 500 MtCO2 in recent years, consistent with the growth in non-oxidized carbon (IEA, 2019). To remove this discrepancy we now calculate the global total as the sum of the countries and international bunkers.

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 as the average of two studies in the literature (Cao et al., 2020; Guo et al., 2020). Both studies use the same model, developed by Xi et al. (2016), with different parameterizations and input data, with the estimate of Guo and colleagues being a revision of Xi et al. (2016). The trends of the two studies are very similar. 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, of cement waste after demolition, and the volumetric properties of structures, among others (Xi et al., 2016). Lifetime is an important parameter because demolition results in the exposure of new surfaces to the carbonation process. The most significant 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. In the present budget, we include the cement carbonation carbon sink in the fossil CO2 emission component (EFOS), unless explicitly stated otherwise.

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 the 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 per cent (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 of emissions are likely to be mainly systematic errors related to underlying biases of energy statistics and to the accounting method used by each country.

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 = territorial - exports + 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 1990–2018 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) and 2001 (GTAP6) as well as 2004, 2007, and 2011 (GTAP9.2), covering 57 sectors and 141 countries and regions. The detailed results are then extended into an annual time series from 1990 to the latest year of the gross domestic product (GDP) data (2018 in this budget), using GDP data by expenditure in the current exchange rate of US dollars (USD; from the UN National Accounts Main Aggregates Database; UN, 2019) and time series of trade data from GTAP (based on the methodology in Peters et al., 2011b). We estimate the sector-level CO2 emissions using the GTAP data and methodology, include flaring and cement emissions from CDIAC, 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, but based on model comparisons and sensitivity analysis, they are unlikely to be significantly different than for the territorial emission estimates (Peters et al., 2012a).

We report the annual growth rate in emissions for adjacent years (in percent per year) by calculating the difference between the two years and then normalizing to the emissions in the first year: (EFOS(t0+1)-EFOS(t0))/EFOS(t0)×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 % yr-1 (1/366) and causes calculated growth rates to go up by approximately 0.3 % if the first year is a leap year and down by 0.3 % if the second year is a leap year.

The relative growth rate of EFOS over time periods of greater than 1 year can be rewritten using its logarithm equivalent as follows: 21EFOSdEFOSdt=d(ln⁡EFOS)dt. Here we calculate relative growth rates in emissions for multi-year periods (e.g. a decade) by fitting a linear trend to ln⁡(EFOS) in Eq. (2), reported in percent per year.

To gain insight into emission trends for 2020, we provide an assessment of global fossil CO2 emissions, EFOS, by combining individual assessments of emissions for China, the USA, the EU, India (the four countries/regions with the largest emissions), and the rest of the world. Our analysis this year is different to previous editions of the Global Carbon Budget, as there have been several independent studies estimating 2020 global CO2 emissions in response to restrictions related to the COVID-19 pandemic, and the highly unusual nature of the year makes the projection much more difficult. We consider three separate studies (Le Quéré et al., 2020; Forster et al., 2020; Liu et al., 2020), in addition to building on the method used in our previous editions. We separate each method into two parts: first we estimate emissions for the year to date (YTD) and, second, we project emissions for the rest of the year 2020. Each method is presented in the order it was published.

YTD. Le Quéré et al. (2020) estimated the effect of COVID-19 on emissions using observed changes in activity using proxy data (such as electricity use, coal use, steel production, road traffic, aircraft departures, etc.), for six sectors of the economy as a function of confinement levels, scaled to the globe based on policy data in response to the pandemic. The analyses employed baseline emissions by country for the latest year available (2018 or 2019) from the Global Carbon Budget 2019 to estimate absolute daily emission changes and covered 67 countries representing 97 % of global emissions. Here we use an update through to 13 November. The parameters for the changes in activity by sector were updated for the industry and aviation sectors, to account for the slow recovery in these sectors observed since the first peak of the pandemic. Specific country-based parameters were used for India and the USA, which improved the match to the observed monthly emissions (from Sect. “Global Carbon Budget Estimates”). By design, this estimate does not include the background seasonal variability in emissions (e.g. lower emissions in Northern Hemisphere summer; Jones et al., 2020), nor the trends in emissions that would be caused by other factors (e.g. reduced use of coal in the EU and the US). To account for the seasonality in emissions where data are available, the mean seasonal variability over 2015–2019 was calculated from available monthly emissions data for the USA, EU27, and India (data from Sect. “Global Carbon Budget Estimates”) and added to the UEA estimate for these regions in Fig. B5. The uncertainty provided reflects the uncertainty in activity parameters.

Projection. A projection is used to fill the data from 14 November to the end of December, assuming countries where confinement measures were at level 1 (targeted measures) on 13 November remain at that level until the end of 2020. For countries where confinement measures were at more stringent levels of 2 and 3 (see Le Quéré et al., 2020) on 13 November, we assume that the measures ease by one level after their announced end date and then remain at that level until the end of 2020.

YTD. Forster et al. (2020) estimated YTD emissions based primarily on Google mobility data. The mobility data were used to estimate daily fractional changes in emissions from power, surface transport, industry, residential, and public and commercial sectors. The analyses employed baseline emissions for 2019 from the Global Carbon Project to estimate absolute emission changes and covered 123 countries representing over 99 % of global emissions. For a few countries – most notably China and Iran – Google data were not available and so data were obtained from the high-reduction estimate from Le Quéré et al. (2020). We use an updated version of Forster et al. (2020) in which emission-reduction estimates were extended through 3 November.

Projection. The estimates were projected from the start of November to the end of December with the assumption that the declines in emissions from their baselines remain at 66 % of the level over the last 30 d with estimates.

YTD. Liu et al. (2020) estimated YTD emissions using emission data and emission proxy activity data including hourly to daily electrical power generation data and carbon emission factors for each different electricity source from the national electricity operation systems of 31 countries, real-time mobility data (TomTom city congestion index data of 416 cities worldwide calibrated to reproduce vehicle fluxes in Paris and FlightRadar24 individual flight location data), monthly industrial production data (calculated separately by cement production, steel production, chemical production, and other industrial production of 27 industries) or indices (primarily the industrial production index) from the national statistics of 62 countries and regions, and monthly fuel consumption data corrected for the daily population-weighted air temperature in 206 countries using predefined heating and temperature functions from EDGAR for residential, commercial, and public buildings' heating emissions, to finally calculate the global fossil CO2 emissions, as well as the daily sectoral emissions from power sector, industry sector, transport sector (including ground transport, aviation, and shipping), and residential sector respectively. We use an updated version of Liu et al. (2020) with data extended through the end of September.

Projection. Liu et al. (2020) did not perform a projection and only presented YTD results. For purposes of comparison with other methods, we use a simple approach to extrapolating their observations by assuming the remaining months of the year change by the same relative amount compared to 2019 in the final month of observations.

Previous editions of the Global Carbon Budget (GCB) have estimated YTD emissions and performed projections, using sub-annual energy consumption data from a variety of sources depending on the country or region. The YTD estimates have then been projected to the full year using specific methods for each country or region. This year we make some adjustments to this approach, as described below, with detailed descriptions provided in Appendix C.

China. The YTD estimate is based on monthly data from China's National Bureau of Statistics and Customs, with the projection based on the relationship between previous monthly data and full-year data to extend the 2020 monthly data to estimate full-year emissions.

USA. The YTD and projection are taken directly from the US Energy Information Agency.

EU27. The YTD estimates are based on monthly consumption data of coal, oil, and gas converted to CO2 and scaled to match the previous year's emissions. We use the same method for the EU27 as for Carbon Monitor described above to generate a full-year projection.

India. YTD estimates are updated from Andrew (2020b), which calculates monthly emissions directly from detailed energy and cement production data. We use the same method for India as for Carbon Monitor, described above, to generate a full-year projection.

Rest of the world. There is no YTD estimate, while the 2020 projection is based on a GDP estimate from the IMF combined with average improvements in carbon intensity observed in the last 10 years, as in previous editions of the Global Carbon Budget (e.g. Friedlingstein et al., 2019).

In the results section we present the estimates from the four different methods, showing the YTD estimates to the last common historical data point in each data set and the projections for 2020.

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 also include forest management practices such as wood harvests.

BLUE and HandN2017 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 separate bookkeeping of land-use emissions and the loss of additional sink capacity. Only the former is included here, while the latter is discussed in Sect. 2.7.4. The bookkeeping models differ in (1) computational units (spatially explicit treatment of land-use change for BLUE, country-level for HandN2017, 10 regions and 5 biomes for OSCAR), (2) processes represented (see Table A1), and (3) carbon densities assigned to vegetation and soil of each vegetation type (literature-based for HandN2017 and BLUE, calibrated to DGVMs for OSCAR). A notable change of HandN2017 over the original approach by Houghton (2003) used in earlier budget estimates is that no shifting cultivation or other back and forth transitions at a level below country are included. Only a decline in forest area in a country as indicated by the Forest Resource Assessment of the FAO that exceeds the expansion of agricultural area as indicated by FAO is assumed to represent a concurrent expansion and abandonment of cropland. In contrast, the BLUE and OSCAR models include sub-grid-scale transitions between all vegetation types. Furthermore, HandN2017 assume conversion of natural grasslands to pasture, while BLUE and OSCAR allocate pasture 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, in particular during El-Niño events, nor emissions from the organic layers of drained peat soils. To correct for this, HandN2017 includes carbon emissions from peat burning based on the Global Fire Emission Database (GFED4s; van der Werf et al., 2017), and peat drainage based on estimates by Hooijer et al. (2010) for Indonesia and Malaysia. We add GFED4s peat fire emissions to BLUE and OSCAR output but use the newly published global FAO peat drainage emissions 1990–2018 from croplands and grasslands (Conchedda and Tubiello, 2020). We linearly increase tropical drainage emissions from 0 in 1980, consistent with HandN2017's assumption, and keep emissions from the often old drained areas of the extra-tropics constant pre-1990. This adds 8.6 GtC for 1960–2019 for FAO compared to 5.4 GtC for Hooijer et al. (2010). Peat fires add another 2.0 GtC over the same period.

The three bookkeeping estimates used in this study differ with respect to the land-use change data used to drive the models. HandN2017 base their estimates directly on the Forest Resource Assessment of the FAO, which provides statistics on forest-area change and management at intervals of 5 years currently updated until 2015 (FAO, 2015). The data are based on country reporting to FAO and may include remote-sensing information in more recent assessments. Changes in land use other than forests are based on annual, national changes in cropland and pasture areas reported by FAO (FAOSTAT, 2015). On the other hand, BLUE uses the harmonized land-use change data LUH2-GCB2020 covering the entire 850–2019 period (an update to the previously released LUH2 v2h data set; 10.22033/ESGF/input4MIPs.1127; Hurtt et al., 2020), which was also used as input to the DGVMs (Sect. 2.2.2). It describes land-use change, also based on the FAO data as well as the HYDE data set (Klein Goldewijk et al., 2017a, b), but provided at a quarter-degree spatial resolution, considering sub-grid-scale transitions between primary forest, secondary forest, primary non-forest, secondary non-forest, cropland, pasture, rangeland, and urban land (Hurtt et al., 2020). LUH2-GCB2020 provides a distinction between rangelands and pasture, based on inputs from HYDE. To constrain the models' interpretation of 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-GCB2020; 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-GCB2019 850–2018 (as used in Friedlingstein et al., 2019) and FAO/FRA (as used by Houghton and Nassikas, 2017), where the latter was extended beyond 2015 with constant 2011–2015 average values. The best-guess OSCAR estimate used in our study is a combination of results for LUH2-GCB2019 and FAO/FRA land-use data and a large number of perturbed parameter simulations weighted against an observational constraint. HandN2017 was extended here for 2016 to 2019 by adding the annual change in total tropical emissions to the HandN2017 estimate for 2015, including estimates of peat drainage and peat burning as described above as well as emissions from tropical deforestation and degradation fires from GFED4.1s (van der Werf et al., 2017). Similarly, OSCAR was extended from 2018 to 2019. Gross fluxes for HandN2017 and OSCAR were extended to 2019 based on a regression of gross sources (including peat emissions) to net emissions for recent years. BLUE's 2019 value was adjusted because the LUH2-GCB2020 forcing for 2019 was an extrapolation of earlier years, thus not capturing the rising deforestation rates occurring in South America in 2019 and the anomalous fire season in equatorial Asia (see Sects. 2.2.4 and 3.2.1). Anomalies of GFED tropical deforestation and degradation and equatorial Asia peat fire emissions relative to 2018 are therefore added. Resulting dynamics in the Amazon are consistent with BLUE simulations using directly observed forest cover loss and forest alert data (Hansen et al., 2013; Hansen et al., 2016).

For ELUC from 1850 onwards we average the estimates from BLUE, HandN2017, and OSCAR. For the cumulative numbers starting 1750 an average of four earlier publications is added (30 ± 20 PgC for 1750–1850, rounded to the nearest 5; Le Quéré et al., 2016).

For the first time we provide estimates of the gross land-use change fluxes from which the reported net land-use change flux, ELUC, 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 after clearing of natural vegetation for agricultural purposes, wood harvesting, emissions from peat drainage and peat burning, and, for BLUE, additionally from degradation from primary to secondary land through usage of natural vegetation as rangeland. Gross removals stem from regrowth after agricultural abandonment and wood harvesting.

Land-use change CO2 emissions have also been estimated using an ensemble of 17 DGVM simulations. The DGVMs account for deforestation and regrowth, the most important components of ELUC, 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 concentration and to climate variability and change. Some models explicitly simulate the coupling of carbon and nitrogen cycles and account for atmospheric N deposition and N fertilizers (Table A1). The DGVMs are independent from the other budget terms except for their use of atmospheric CO2 concentration to calculate the fertilization effect of CO2 on plant photosynthesis.

Many DGVMs used the HYDE land-use change data set (Klein Goldewijk et al., 2017a, b), which provides annual (1700–2019), half-degree, fractional data on cropland and pasture. The data are based on the available annual FAO statistics of change in agricultural land area available until 2015. HYDE version 3.2 used FAO statistics until 2012, which were supplemented using the annual change anomalies from FAO data for the years 2013–2015 relative to year 2012. HYDE forcing was also corrected for Brazil for the years 1951–2012. After the year 2015 HYDE extrapolates cropland, pasture, and urban land-use data until the year 2019. Some models also use the LUH2-GCB2020 data set, an update of the more comprehensive harmonized land-use data set (Hurtt et al., 2011), which further includes fractional data on primary and secondary forest vegetation, as well as all underlying transitions between land-use states (1700–2019) (10.22033/ESGF/input4MIPs.1127, Hurtt et al., 2017; Hurtt et al., 2011, 2020; Table A1). This new data set is of quarter-degree fractional areas of land-use states and all transitions between those states, including a new wood harvest reconstruction and 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 the pasture–rangeland split discussed before. Wood harvest patterns are constrained with Landsat-based tree cover loss data (Hansen et al., 2013). Updates of LUH2-GCB2020 over last year's version (LUH2-GCB2019) are using the most recent HYDE/FAO release (covering the time period up to and including 2015), which also corrects an error in the version used for the 2018 budget in Brazil. The FAO wood harvest data have changed for the years 2015 onwards and so those are now being used in this year's LUH-GCB2020 data set. This means the LUH-GCB2020 data are identical to LUH-GCB2019 for all years up to 2015 and differ slightly in terms of wood harvest and resulting secondary area, age, and biomass for years after 2015.

DGVMs implement land-use change differently (e.g. an increased cropland fraction in a grid cell can either be at the expense of grassland or 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 areas and other forest product pools into carbon, and different choices are made regarding the allocation of rangelands as natural vegetation or pastures.

The DGVM 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, both providing observation-based temperature, precipitation, and incoming surface radiation on a 0.5∘×0.5∘ grid and updated to 2019 (Harris and Jones, 2019; Harris et al., 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. The forcing data also include global atmospheric CO2, which changes over time (Dlugokencky and Tans, 2020), and gridded, time-dependent N deposition and N fertilizers (as used in some models; Table A1).

Two sets of simulations were performed with each of the DGVMs. Both applied historical changes in climate, atmospheric CO2 concentration, and N inputs. The two sets of simulations differ, however, with respect to land use: one set applies historical changes in land use, the other a time-invariant pre-industrial land cover distribution and pre-industrial wood harvest rates. By difference of the two simulations, the dynamic evolution of vegetation biomass and soil carbon pools in response to land-use change can be quantified in each model (ELUC). Using the difference between these two DGVM simulations to diagnose ELUC means the DGVMs account for the loss of additional sink capacity (see Sect. 2.7.4), while the bookkeeping models do not.

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

Differences between the bookkeeping models and DGVM models originate from three main sources: the different methodologies, which among other things lead to inclusion of the loss of additional sink capacity in DGVMs (Sect. 2.7.4), the underlying land-use and land-cover data set, and the different processes represented (Table A1). We examine the results from the DGVM models and of the bookkeeping method and use the resulting variations as a way to characterize the uncertainty in ELUC.

Despite these differences, the ELUC estimate from the DGVM multi-model mean is consistent with the average of the emissions from the bookkeeping models (Table 5). However there are large differences among individual DGVMs (standard deviation at around 0.5 GtC yr-1; Table 5), between the bookkeeping estimates (average difference BLUE-HN2017 of 0.7 GtC yr-1, BLUE-OSCAR of 0.3 GtC yr-1, OSCAR-HN2017 of 0.5 GtC yr-1), and between the current estimate of HandN2017 and its previous model version (Houghton et al., 2012). The uncertainty in ELUC of ±0.7 GtC yr-1 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 ELUC was taken from the standard deviation of the DGVMs. We assign low confidence to the annual estimates of ELUC because of the inconsistencies among estimates and of the difficulties in quantifying some of the processes in DGVMs.

We project the 2020 land-use emissions for BLUE, HandN2017, and OSCAR, starting from their estimates for 2019 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). Those latter scale almost linearly with GFED over large areas (van der Werf et al., 2017) and thus allow for tracking fire emissions in deforestation and tropical peat zones in near-real time. During most years, emissions during January-September cover most of the fire season in the Amazon and Southeast Asia, where a large part of the global deforestation takes place and our estimates capture emissions until 31 October. By the end of October 2020 emissions from tropical deforestation and degradation fires were estimated to be 227 TgC, down from 347 TgC in 2019 (313 TgC 1997–2019 average). Peat fire emissions in equatorial Asia were estimated to be 1 TgC, down from 117 TgC in 2019 (68 TgC 1997–2019 average). The lower fire emissions for both processes in 2020 compared to 2019 are related to the transition from unusually dry conditions for a non-El Niño year in Indonesia in 2019, which caused relatively high emissions, to few fires due to wet conditions throughout 2020. By contrast, fire emissions in South America remained above-average in 2020, with the slight decrease since 2019 estimated in GFED4.1s (van der Werf et al., 2017) being a conservative estimate. This is consistent with slightly reduced deforestation rates in 2020 compared to 2019 (note that often Amazon deforestation is reported from August of the previous to July of the current year; for such reporting, 2020 deforestation will tend to be higher in 2020 than in 2019 by including strong deforestation August–December 2019). Together, this results in pantropical fire emissions from deforestation, degradation, and peat burning of about 230 TgC projected for 2020 as compared to 464 TgC in 2019; this is slightly above the 2017 and 2018 values of pantropical fire emissions. Overall, however, we have low confidence in our projection due to the large uncertainty range we associate with past ELUC, the dependence of 2020 emissions on legacy fluxes from previous years, uncertainties related to fire emissions estimates, and the lack of data before the end of the year that would allow deforested areas to be quantified accurately. Also, an incomplete coverage of degradation by fire data makes our estimates conservative, considering that degradation rates in the Amazon increased from 2019 to 2020 (INPE, 2020).

The rate of growth of the atmospheric CO2 concentration is provided by the US National Oceanic and Atmospheric Administration Earth System Research Laboratory (NOAA/ESRL; Dlugokencky and Tans, 2020), which is updated from Ballantyne et al. (2012). For the 1959–1979 period, the global growth rate is based on measurements of atmospheric CO2 concentration averaged from the Mauna Loa and South Pole stations, as observed by the CO2 Program at Scripps Institution of Oceanography (Keeling et al., 1976). For the 1980–2019 time period, the global growth rate is based on the average of multiple stations selected from the marine boundary layer sites with well-mixed background air (Ballantyne et al., 2012), after fitting each station with a smoothed curve as a function of time, and averaging by latitude band (Masarie and Tans, 1995). The annual growth rate is estimated by Dlugokencky and Tans (2020) from atmospheric CO2 concentration by taking the average of the most recent December–January months corrected for the average seasonal cycle and subtracting this same average 1 year earlier. The growth rate in units of ppm yr-1 is converted to units of GtC yr-1 by multiplying by a factor of 2.124 GtC ppm-1 (Ballantyne et al., 2012).

The uncertainty around the atmospheric growth rate is due to four main factors: first, the long-term reproducibility of reference gas standards (around 0.03 ppm for 1σ from the 1980s; Dlugokencky and Tans, 2020); second, small unexplained systematic analytical errors that may have a duration of several months to 2 years come and go – they have been simulated by randomizing both the duration and the magnitude (determined from the existing evidence) in a Monte Carlo procedure; third, the network composition of the marine boundary layer with some sites coming or going, gaps in the time series at each site, etc. (Dlugokencky and Tans, 2020) – this uncertainty was estimated by NOAA/ESRL with a Monte Carlo method by constructing 100 “alternative” networks (Masarie and Tans, 1995; NOAA/ESRL, 2020) and added up to 0.085 ppm when summed in quadrature with the second uncertainty (Dlugokencky and Tans, 2020); fourth, the uncertainty associated with using the average CO2 concentration from a surface network to approximate the true atmospheric average CO2 concentration (mass-weighted, in three dimensions) is needed to assess the total atmospheric CO2 burden. In reality, CO2 variations measured at the stations will not exactly track changes in total atmospheric burden, with offsets in magnitude and phasing due to vertical and horizontal mixing. This effect must be very small on decadal and longer timescales, when the atmosphere can be considered well mixed. Preliminary estimates suggest this effect would increase the annual uncertainty, but a full analysis is not yet available. We therefore maintain an uncertainty around the annual growth rate based on the multiple stations' data set ranges between 0.11 and 0.72 GtC yr-1, with a mean of 0.61 GtC yr-1 for 1959–1979 and 0.17 GtC yr-1 for 1980–2019, when a larger set of stations were available as provided by Dlugokencky and Tans (2020), but recognize further exploration of this uncertainty is required. At this time, we estimate the uncertainty of the decadal averaged growth rate after 1980 at 0.02 GtC yr-1 based on the calibration and the annual growth rate uncertainty, but stretched over a 10-year interval. For years prior to 1980, we estimate the decadal averaged uncertainty to be 0.07 GtC yr-1 based on a factor proportional to the annual uncertainty prior and after 1980 (0.02×[0.61/0.17] GtC yr-1).

We assign a high confidence to the annual estimates of GATM because they are based on direct measurements from multiple and consistent instruments and stations distributed around the world (Ballantyne et al., 2012).

In order to estimate the total carbon accumulated in the atmosphere since 1750 or 1850, we use an atmospheric CO2 concentration of 277 ± 3 ppm or 286 ± 3 ppm, respectively, based on a cubic spline fit to ice core data (Joos and Spahni, 2008). The uncertainty of ±3 ppm (converted to ±1σ) is taken directly from the IPCC's assessment (Ciais et al., 2013). Typical uncertainties in the growth rate in atmospheric CO2 concentration from ice core data are equivalent to ±0.1–0.15 GtC yr-1 as evaluated from the Law Dome data (Etheridge et al., 1996) for individual 20-year intervals over the period from 1850 to 1960 (Bruno and Joos, 1997).

We provide an assessment of GATM for 2020 based on the monthly calculated global atmospheric CO2 concentration (GLO) through August (Dlugokencky and Tans, 2020), and bias-adjusted Holt–Winters exponential smoothing with additive seasonality (Chatfield, 1978) to project to January 2021. Additional analysis suggests that the first half of the year shows more interannual variability than the second half of the year, so that the exact projection method applied to the second half of the year has a relatively smaller impact on the projection of the full year. Uncertainty is estimated from past variability using the standard deviation of the last 5 years' monthly growth rates.

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 SOCEAN. We further test that GOBMs and data products fall within 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). The IPCC estimates are based on the observational constraint of the mean 1990s sink and trends derived mainly from models and one data product (Ciais et al., 2013). This is based on indirect observations with seven different methodologies and their uncertainties, using the 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 timescales for chlorofluorocarbons (McNeil et al., 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 also use four estimates of the ocean CO2 sink and its variability based on surface ocean pCO2 maps obtained by the interpolation of measurements of surface ocean fugacity of CO2 (fCO2, which equals pCO2 corrected for the non-ideal behaviour of the gas; Pfeil et al., 2013). These estimates differ in many respects: they use different maps of surface pCO2, different atmospheric CO2 concentrations, wind products, and different gas-exchange formulations as specified in Table A3. We refer to them as pCO2-based flux estimates. The measurements underlying the surface pCO2 maps are from the Surface Ocean CO2 Atlas version 2020 (SOCATv2020; Bakker et al., 2020), which is an update of version 3 (Bakker et al., 2016) and contains quality-controlled data through 2019 (see data attribution Table A5). Each of the estimates uses a different method to then map the SOCAT v2020 data to the global ocean. The methods include a data-driven diagnostic method (Rödenbeck et al., 2013; referred to here as Jena-MLS), a combined self-organizing map and feed-forward neural network (Landschützer et al., 2014; referred to here as MPI-SOMFFN), an artificial neural network model (Denvil-Sommer et al., 2019; Copernicus Marine Environment Monitoring Service, referred to here as CMEMS), and an ensemble average of six machine learning estimates of pCO2 using a cluster regression approach (Gregor et al., 2019; referred to here as CSIR). The ensemble mean of the pCO2-based flux estimates is calculated from these four mapping methods. Further, we show the flux estimate of Watson et al. (2020) whose uptake is substantially larger, owing to a number of adjustments they applied to the surface ocean fCO2 data and the gas-exchange parameterization. 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 also included a further adjustment to account for the cool surface skin temperature effect. They then used the MPI-SOMFFN method to map the adjusted fCO2 data to the globe. 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, which, if correct, should be applied to all pCO2-based flux estimates. So far this adjustment is based on a single line of evidence and hence associated with low confidence until further evidence is available. The Watson et al. (2020) flux estimate presented here is therefore not included in the ensemble mean of the pCO2-based flux estimates. This choice will be re-evaluated in upcoming budgets based on further lines of evidence.

The global pCO2-based flux estimates were adjusted to remove the pre-industrial ocean source of CO2 to the atmosphere of 0.61 GtC yr-1 from river input to the ocean (the average of 0.45 ± 0.18 GtC yr-1 by Jacobson et al. ,2007, and 0.78 ± 0.41 GtC yr-1 by Resplandy et al., 2018), to satisfy our definition of SOCEAN (Hauck et al., 2020). The river flux adjustment was distributed over the latitudinal bands using the regional distribution of Aumont et al. (2001; north: 0.16 GtC yr-1, tropics: 0.15 GtC yr-1, south: 0.30 GtC yr-1). The CO2 flux from each pCO2-based product is scaled by the ratio of the total ocean area covered by the respective product to the total ocean area (361.9×106 km2) from ETOPO1 (Amante and Eakins, 2009; Eakins and Sharman, 2010). In products where the covered area varies with time (MPI-SOMFFN, CMEMS) we use the maximum area coverage. The data products cover 88 % (MPI-SOMFFN, CMEMS) to 101 % (Jena-MLS) of the observed total ocean area, so two products are effectively corrected upwards by a factor of 1.13 (Table A3, Hauck et al., 2020).

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).

The ocean CO2 sink for 1959–2019 is estimated using nine 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 in their horizontal and vertical resolutions (Table A2). All GOBMs except one (CESM-ETHZ) 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. 2.7.3).

Two 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. In order to derive SOCEAN from the model simulations, we subtracted 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) which is often a major source of biases. Simulation B of IPSL had to be treated differently as it was forced with constant atmospheric CO2 but observed historical changes in climate. For IPSL, we fitted a linear trend to the simulation B and subtracted this linear trend from simulation A. This approach ensures 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 0.35 GtC yr-1, with six models having positive and three models having negative biases. This correction reduces the model mean ocean carbon sink by 0.07 GtC yr-1 in the 1990s. The CO2 flux from each model is scaled by the ratio of the total ocean area covered by the respective GOBM to the total ocean area (361.9×106 km2) from ETOPO1 (Amante and Eakins, 2009; Eakins and Sharman, 2010). The ocean models cover 99 % to 101 % of the total ocean area, so the effect of this correction is small.

The mean 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) and within the derived constraints for the 2000s and 2002–2011 (see Sect. 2.4.1) before and after applying corrections. The GOBMs and flux products have been further evaluated using the fugacity of sea surface CO2 (fCO2) from the SOCAT v2020 database (Bakker et al., 2016, 2020). The fugacity of CO2 is 3 ‰–4 ‰ smaller than the partial pressure of CO2 (Zeebe and Wolf-Gladrow, 2001). We focused this evaluation on the root mean squared error (RMSE) between observed fCO2 and modelled pCO2 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 annually and regionally averaged time series calculated from GOBM and data product pCO2 subsampled to open ocean (water depth > 400 m) SOCAT sampling points to measure the misfit between large-scale signals (Hauck et al., 2020) as opposed to the RMSE calculated from binned monthly data as in the previous year. The amplitude of the SOCEAN interannual variability (A-IAV) is calculated as the temporal standard deviation of the detrended CO2 flux time series (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 SOCEAN on interannual timescales. We apply these metrics globally and by latitude bands (Fig. B1). Results are shown in Fig. B1 and discussed in Sect. 3.1.3.

The 1σ uncertainty around the mean ocean sink of anthropogenic CO2 was quantified by Denman et al. (2007) for the 1990s to be ±0.5 GtC yr-1. Here we scale the uncertainty of ±0.5 GtC yr-1 to the mean estimate of 2.2 GtC yr-1 in the 1990s to obtain a relative uncertainty of ± 18 %, which is then applied to the full time series. To quantify the uncertainty around annual values, we examine the standard deviation of the GOBM ensemble, which varies between 0.2 and 0.4 GtC yr-1 and averages to 0.30 GtC yr-1 during 1959–2019. We estimate that the uncertainty in the annual ocean CO2 sink increases from ±0.3 GtC yr-1 in the 1960s to ±0.6 GtC yr-1 in the decade 2010–2019 from the combined uncertainty of the mean flux based on observations of ±18 % (Denman et al., 2007) and the standard deviation across GOBMs of up to ±0.4 GtC yr-1, reflecting both the uncertainty in the mean sink from observations during the 1990s (Denman et al., 2007; Sect. 2.4.1) and the uncertainty in annual estimates from the standard deviation across the GOBM ensemble.

We examine the consistency between the variability of the model-based and the pCO2-based flux products to assess confidence in SOCEAN. The interannual variability of the ocean fluxes (quantified as A-IAV, the standard deviation after detrending; Fig. B1) of the four pCO2-based flux products plus the Watson et al. (2020) product for 1992–2019 ranges from 0.16 to 0.25 GtC yr-1 with the lower estimates by the two ensemble methods (CSIR, CMEMS). The inter-annual variability in the GOBMs ranges between 0.11 and 0.17 GtC yr-1; hence there is overlap with the lower A-IAV estimates of two data products.

Individual estimates (both GOBM and flux 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 SOCEAN with a global stagnation in the 1990s and an extra-tropical strengthening in the 2000s (McKinley et al., 2020; Hauck et al., 2020).

The annual pCO2-based flux products correlate with the ocean CO2 sink estimated here with a correlation coefficient r ranging from 0.80 to 0.97 (1985–2019). The central estimates of the annual flux from the GOBMs and the pCO2-based flux products have a correlation r of 0.97 (1985–2019). The agreement between the models and the flux products reflects some consistency in their representation of underlying variability since there is little overlap in their methodology or use of observations. We assess a medium confidence level to the annual ocean CO2 sink and its uncertainty because it is based on multiple lines of evidence, it is consistent with ocean interior carbon estimates (Gruber et al., 2019; see Sect. 3.1.2), and the results are consistent in that the interannual variability in the GOBMs and data-based estimates are all generally small compared to the variability in the growth rate of atmospheric CO2 concentration.

The terrestrial land sink (SLAND) is thought to be due to the combined effects of fertilization by rising atmospheric CO2 and N inputs on plant growth, as well as the effects of climate change such as the lengthening of the growing season in northern temperate and boreal areas. SLAND does not include land sinks directly resulting from land use and land-use change (e.g. regrowth of vegetation) as these are part of the land-use flux (ELUC), although system boundaries make it difficult to attribute CO2 fluxes on land exactly between SLAND and ELUC (Erb et al., 2013).

SLAND is estimated from the multi-model mean of 17 DGVMs (Table 4). As described in Sect. 2.2.2, DGVM simulations include all climate variability and CO2 effects over land, with 12 DGVMs also including the effect of N inputs. The DGVMs estimate of SLAND does not include the export of carbon to aquatic systems or its historical perturbation, which is discussed in Sect. 2.7.3.

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 (SLAND – ELUC) that is an atmosphere-to-land carbon flux over the 1990s ranging between -0.3 and 2.3 GtC yr-1, within 90 % confidence of constraints by global atmospheric and oceanic observations (Keeling and Manning, 2014; Wanninkhof et al., 2013); and (3) global ELUC that is a carbon source to the atmosphere over the 1990s, as already mentioned in Sect. 2.2.2. All 17 DGVMs meet these three criteria.

In addition, the DGVM results are also evaluated using the International Land Model Benchmarking system (ILAMB; Collier et al., 2018). This evaluation is provided here to document, encourage, and support model improvements through time. ILAMB variables cover key processes that are relevant for the quantification of SLAND and resulting aggregated outcomes. The selected variables are vegetation biomass, gross primary productivity, leaf area index, net ecosystem exchange, ecosystem respiration, evapotranspiration, soil carbon, and runoff (see Fig. B2 for the results and for the list of observed databases). Results are shown in Fig. B2 and discussed in Sect. 3.1.3.

For the uncertainty for SLAND, we use the standard deviation of the annual CO2 sink across the DGVMs, averaging to about ±0.6 GtC yr-1 for the period 1959 to 2019. We attach a medium confidence level to the annual land CO2 sink and its uncertainty because the estimates from the residual budget and averaged DGVMs match well within their respective uncertainties (Table 5).

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. It omits, however, any other anthropogenic carbon-containing gases that are eventually oxidized in the atmosphere, such as anthropogenic emissions of CO and CH4. An attempt is made in this section 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 EFOS we assumed (Sect. 2.1.1) that all the fuel burned is emitted as CO2, and thus CO anthropogenic emissions associated with incomplete fossil fuel combustion and its atmospheric oxidation into CO2 within a few months are already counted implicitly in EFOS and should not be counted twice (same for ELUC and anthropogenic CO emissions by deforestation fires). Anthropogenic emissions of fossil CH4 are, however, not included in EFOS, because these fugitive emissions are not included in the fuel inventories. Yet they contribute to the annual CO2 growth rate after CH4 gets oxidized into CO2. Emissions of fossil CH4 represent 30 % of total anthropogenic CH4 emissions (Saunois et al., 2020; their top-down estimate is used because it is consistent with the observed CH4 growth rate), which is 0.083 GtC yr-1 for the decade 2008–2017. Assuming a steady state, an amount equal to this fossil CH4 emission is all converted to CO2 by OH oxidation and thus explains 0.083 GtC yr-1 of the global CO2 growth rate with an uncertainty range of 0.061 to 0.098 GtC yr-1 taken from the minimum and maximum of top-down estimates in Saunois et al. (2020). If this minimum–maximum range is assumed to be 2σ because Saunois et al. (2020) did not account for the internal uncertainty of their min and max top-down estimates, it translates into a 1σ uncertainty of 0.019 GtC yr-1.

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).

This year we account for cement carbonation (a carbon sink) for the first time. The contribution of emissions of fossil carbonates (carbon sources) other than cement production is not systematically included in estimates of EFOS, except at the national level where they are accounted for in the UNFCCC national inventories. The missing processes include CO2 emissions associated with the calcination of lime and limestone outside 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 are estimated to amount to about 1 % of EFOS (Crippa et al., 2019), though some of these carbonate emissions are included in our estimates (e.g. via UNFCCC inventories).

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 significant 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. 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) to be 0.65 ± 0.35 GtC yr-1. The inclusion of LOAC-related anthropogenic CO2 fluxes should affect estimates of SLAND and SOCEAN 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.

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. 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 ELUC estimates are only used to quantify the uncertainty around the bookkeeping models' ELUC we do not add the loss of additional sink capacity to the bookkeeping estimate.

Global fossil CO2 emissions have increased every decade from an average of 3.0 ± 0.2 GtC yr-1 for the decade of the 1960s to an average of 9.4 ± 0.5 GtC yr-1 during 2010–2019 (Table 6, Figs. 2 and 5). The growth rate in these emissions decreased between the 1960s and the 1990s, from 4.3 % yr-1 in the 1960s (1960–1969), 3.1 % yr-1 in the 1970s (1970–1979), 1.6 % yr-1 in the 1980s (1980–1989), to 0.9 % yr-1 in the 1990s (1990–1999). After this period, the growth rate began increasing again in the 2000s at an average growth rate of 3.0 % yr-1, decreasing to 1.2 % yr-1 for the last decade (2010–2019).

In contrast, CO2 emissions from land use, land-use change, and forestry have remained relatively constant, at around 1.4 ± 0.7 GtC yr-1 over the past half-century (Table 6) but with large spread across estimates (Table 5, Fig. 6). These emissions are also relatively constant in the DGVM ensemble of models, except during the last decade when they increase to 2.1 ± 0.5 GtC yr-1. However, there is no agreement on this recent increase between the bookkeeping estimates, with HandN2017 suggesting a downward trend as compared to a weak and strong upward trend in OSCAR and the BLUE estimates respectively (Fig. 6).

ELUC is a net term of various gross fluxes, which comprise emissions and removals (see Sect. 2.2.1). Gross emissions are on average 2–3 times larger than the net ELUC emissions, increasing from an average of 3.5 ± 1.2 GtC yr-1 for the decade of the 1960s to an average of 4.4 ± 1.6 GtC yr-1 during 2010–2019 (Fig. 6, Table 5), showing the relevance of land management such as harvesting or rotational agriculture. They differ more across the three bookkeeping estimates than net fluxes, which is expected due to different process representation; in particular explicit inclusion of shifting cultivation (BLUE, OSCAR) increases both gross emissions and removals.

The uptake of CO2 by cement via carbonation has increased with increasing stocks of cement products, from an average of 20 MtC yr-1 in the 1960s to an average of 190 MtC yr-1 during 2010–2019 (Fig. 5). The growth rate declined from 6.7 % yr-1 in the 1960s to 3.3 % yr-1 in the 1980s, rising again to 6.2 % yr-1 in the 2000s, before declining again to 3.5 % yr-1 in the 2010s.

The growth rate in atmospheric CO2 level increased from 1.8 ± 0.07 GtC yr-1 in the 1960s to 5.1 ± 0.02 GtC yr-1 during 2010–2019 with important decadal variations (Table 6 and Fig. 3). Both ocean and land CO2 sinks have increased roughly in line with the atmospheric increase, but with significant decadal variability on land (Table 6 and Fig. 6), and possibly in the ocean (Fig. 7).

The ocean CO2 sink increased from 1.0 ± 0.3 GtC yr-1 in the 1960s to 2.5 ± 0.6 GtC yr-1 during 2010–2019, with interannual variations of the order of a few tenths of GtC yr-1 generally showing an increased ocean sink during large El Niño events (i.e. 1997–1998) (Fig. 7; Rödenbeck et al., 2014; Hauck et al., 2020). The GOBMs show the same patterns of decadal variability as the mean of the pCO2-based flux products, but of weaker magnitude (Sect. 2.4.3 and Fig. 7; DeVries et al., 2019; Hauck et al., 2020). The pCO2-based flux products and the ocean inverse model highlight different regions as the main origin of this decadal variability, with the pCO2-based flux products placing more of the weakening trend in the Southern Ocean and the ocean inverse model suggesting that more of the weakening trend occurred in the North Atlantic and North Pacific (DeVries et al., 2019). Both approaches also show decadal trends in the low-latitude oceans (DeVries et al., 2019).

Although all individual GOBMs and data products fall within the observational constraint, the ensemble means of GOBMs and data products adjusted for the riverine flux diverge over time with a mean offset of 0.15 GtC yr-1 in the 1990s to 0.55 GtC yr-1 in the decade 2010–2019 and ≥ 0.70 GtC yr-1 since 2017. The GOBMs' best estimate of SOCEAN over the period 1994–2007 is 2.1 ± 0.5 GtC yr-1 and is in agreement with the ocean interior estimate of 2.2 ± 0.4 GtC yr-1 when taking into account the interior ocean carbon changes of 2.6 ± 0.3 GtC yr-1 due to the increase in atmospheric CO2 and -0.4 ± 0.24 GtC yr-1 due to anthropogenic climate change and variability effects on the natural CO2 flux (Gruber et al., 2019) to match the definition of SOCEAN used here (Hauck et al., 2020). The discrepancy between GOBMs and data products stems from the southern and northern extra-tropics prior to 2005, and mostly from the Southern Ocean since the mid-2000s. Possible explanations for the discrepancy in the Southern Ocean could be missing winter observations or uncertainties in the regional river flux adjustment (see Sect. “Regionality”, Hauck et al., 2020).

The terrestrial CO2 sink increased from 1.3 ± 0.4 GtC yr-1 in the 1960s to 3.4 ± 0.9 GtC yr-1 during 2010–2019, with important interannual variations of up to 2 GtC yr-1 generally showing a decreased land sink during El Niño events (Fig. 6), responsible for the corresponding enhanced growth rate in atmospheric CO2 concentration. The larger land CO2 sink during 2010–2019 compared to the 1960s is reproduced by all the DGVMs in response to the combined atmospheric CO2 increase and the changes in climate and is consistent with constraints from the other budget terms (Table 5).

The total atmosphere-to-land fluxes (SLAND – ELUC), calculated here as the difference between SLAND from the DGVMs and ELUC from the bookkeeping models, increased from a 0.2 ± 0.9 GtC yr-1 source in the 1960s to a 1.9 ± 1.1 GtC yr-1 sink during 2010–2019 (Table 5). Estimates of total atmosphere-to-land fluxes (SLAND – ELUC) from the DGVMs alone are consistent with our estimate and also with the global carbon budget constraint (EFOS-GATM-SOCEAN, Table 5). Over the last decade, the land use emission estimate from the DGVMs is significantly larger than the bookkeeping estimate, mainly explaining why the DGVMs total atmosphere-to-land flux estimate is lower than the other estimates.

The evaluation of the ocean estimates (Fig. B1) shows an RMSE from annually detrended data of 0.5 to 1.6 µatm for the five pCO2-based flux products over the globe, relative to the fCO2 observations from the SOCAT v2020 database for the period 1985–2019. The GOBM RMSEs are larger and range from 3.5 to 6.9 µatm. The RMSEs are generally larger at high latitudes compared to the tropics, for both the flux products and the GOBMs. The five flux products have RMSEs of 0.4 to 1.9 µatm in the tropics, 0.6 to 1.9 µatm in the north, and 1.5 to 2.8 µatm in the south. Note that the flux products are based on the SOCAT v2020 database, and hence the latter is no independent data set for the evaluation of the flux products. The GOBM RMSEs are more spread across regions, ranging from 2.7 to 4.0 µatm in the tropics, 3.1 to 7.3 µatm in the north, and 6.6 to 11.4 µatm in the south. The higher RMSEs occur in regions with stronger climate variability, such as the northern and southern high latitudes (poleward of the subtropical gyres).

The evaluation of the DGVMs (Fig. B2) generally shows high skill scores across models for runoff, and to a lesser extent for vegetation biomass, GPP, and ecosystem respiration (Fig. B2a). Skill score was lowest for leaf area index and net ecosystem exchange, with a widest disparity among models for soil carbon. Further analysis of the results will be provided separately, focusing on the strengths and weaknesses in the DGVM ensemble and its validity for use in the global carbon budget.

The evaluation of the atmospheric inversions (Fig. B3) shows long-term mean biases in the free troposphere lower than 0.4 ppm in absolute values for each product. These biases show some dependency on latitude and are different for each inverse model, which may reveal biases in the surface fluxes (Gaubert et al., 2019, Houweling et al., 2015). Despite tracking surface and in situ CO2 observations, the systems reproduce NOAA's global annual CO2 growth rate (Sect. 2.3.1) with mixed skill: where decadal biases are typically small for all systems (< 0.08 ppm yr-1), interannual differences are larger (1σ: 0.10–0.25 ppm yr-1, N=19 years) but can be as large as 0.6 ppm yr-1 for the model or year with the worst performance on this metric.

The carbon budget imbalance (BIM; Eq. 1) quantifies the mismatch between the estimated total emissions and the estimated changes in the atmosphere, land, and ocean reservoirs. The mean budget imbalance from 1959 to 2019 is small (average of -0.03 GtC yr-1) and shows no trend over the full time series. The process models (GOBMs and DGVMs) have been selected to match observational constraints in the 1990s and derived constraints for the 2000s and 2002–2011, but no further constraints have been applied to their representation of trend and variability. Therefore, the near-zero mean and trend in the budget imbalance is indirect evidence of a coherent community understanding of the emissions and their partitioning on those timescales (Fig. 4). However, the budget imbalance shows substantial variability of the order of ±1 GtC yr-1, particularly over semi-decadal timescales, although most of the variability is within the uncertainty of the estimates. The positive carbon imbalance during the 1960s, and early 1990s, suggests that either the emissions were overestimated or the sinks were underestimated during these periods. The reverse is true for the 1980s and late 1990s (Fig. 4).

We cannot attribute the cause of the variability in the budget imbalance with our analysis; we only note that the budget imbalance is unlikely to be explained by errors or biases in the emissions alone because of its large semi-decadal variability component, a variability that is untypical of emissions and has not changed in the past 50 years in spite of a near tripling in emissions (Fig. 4). Errors in SLAND and SOCEAN are more likely to be the main cause for the budget imbalance. For example, underestimation of the SLAND by DGVMs was reported following the eruption of Mount Pinatubo in 1991 possibly due to missing responses to changes in diffuse radiation (Mercado et al., 2009) or other yet unknown factors, and DGVMs are suspected to overestimate the land sink in response to the wet decade of the 1970s (Sitch et al., 2008). Quasi-decadal variability in the ocean sink has also been reported recently (DeVries et al., 2019, 2017; Landschützer et al., 2015), with all methods agreeing on a smaller than expected ocean CO2 sink in the 1990s and a larger than expected sink in the 2000s (Fig. 7; DeVries et al., 2019; McKinley et al., 2020). The decadal variability is possibly caused by changes in ocean circulation (DeVries et al., 2017) not captured in coarse-resolution GOBMs used here (Dufour et al., 2013), but also by external forcing from decadally varying atmospheric CO2 growth rates and cooling effects through the eruption of Mount Pinatubo in 1991 which is captured by GOBMs (McKinley et al., 2020).

The decadal variability is thought to be largest in the high-latitude ocean regions (poleward of the subtropical gyres) and the equatorial Pacific (Li and Ilyina, 2018; McKinley et al., 2016, 2020). Some of these errors could be driven by errors in the climatic forcing data, particularly precipitation (for SLAND) and wind (for SOCEAN) rather than in the models.

Global fossil CO2 emissions grew at a rate of 1.2 % yr-1 for the last decade (2010–2019), with a decadal average of 9.6 ± 0.5 GtC yr-1 excluding the cement carbonation sink (9.4 ± 0.5 GtC yr-1 when the cement carbonation sink is included) (Fig. 5, Table 6). China's emissions increased by +1.2 % yr-1 on average (increasing by +0.046 GtC yr-1 during the 10-year period), dominating the global trend, followed by India's emissions increase by +5.1 % yr-1 (increasing by +0.025 GtC yr-1), while emissions decreased in EU27 by -1.4 % yr-1 (decreasing by -0.014 GtC yr-1) and in the USA by -0.7 % yr-1 (decreasing by -0.01 GtC yr-1). In the past decade, fossil CO2 emissions decreased significantly (at the 95 % level) in 24 growing economies: Barbados, Belgium, Croatia, Czech Republic, Denmark, Finland, France, Germany, Israel, Italy, Japan, Luxembourg, Malta, Mexico, the Netherlands, Norway, Romania, Slovakia, Slovenia, the Solomon Islands, Sweden, Switzerland, the United Kingdom, and the USA. The drivers of recent decarbonization are examined in Le Quéré et al. (2019).

In contrast, there is no clear trend in CO2 emissions from land-use change over the last decade (Fig. 6, Table 6), though the data are very uncertain, with partly diverging trends over the last decade (Sect. 3.1.1). Larger emissions are expected increasingly over time for DGVM-based estimates as they include the loss of additional sink capacity, while the bookkeeping estimates do not. The LUH2-GCB2020 data set also features large dynamics in land use in particular in the tropics in recent years, causing higher emissions in DGVMs, BLUE, and the OSCAR best-guess, which includes simulations based on LUH2-GCB2020, than in HandN2017.

The growth rate in atmospheric CO2 concentration increased during 2010–2019, with a decadal average of 5.1 ± 0.02 GtC yr-1, albeit with large interannual variability (Fig. 4). Averaged over that decade, the ocean and land sinks amount to 2.5 ± 0.6 GtC yr-1 and 3.4 ± 0.9 GtC yr-1 respectively. During 2010–2017, the ocean CO2 sink appears to have intensified in line with the expected increase from atmospheric CO2 (McKinley et al., 2020). This effect is stronger in the pCO2-based flux products (Fig. 7, McKinley et al., 2020). The reduction of -0.16 GtC yr-1 (range: -0.43 to +0.03 GtC yr-1) in the ocean CO2 sink in 2017 is consistent with the return to normal conditions after the El Niño in 2015–2016, which caused an enhanced sink in previous years.

The budget imbalance (Table 6) and the residual sink from global budget (Table 5) include an error term due to the inconsistency that arises from using ELUC from bookkeeping models, and SLAND from DGVMs. This error term includes the fundamental differences between bookkeeping models and DGVMs, most notably the loss of additional sink capacity. Other differences include an incomplete accounting of LUC practices and processes in DGVMs, while they are all accounted for in bookkeeping models by using observed carbon densities, and bookkeeping error of keeping present-day carbon densities fixed in the past. That the budget imbalance shows no clear trend towards larger values over time is an indication that the loss of additional sink capacity plays a minor role compared to other errors in SLAND or SOCEAN (discussed in Sect. 3.1.4).

Figure 8 shows the partitioning of the total atmosphere-to-surface fluxes excluding fossil CO2 emissions (SOCEAN+SLAND-ELUC) according to the multi-model average estimates from process models (GOBMs and DGVMs), atmospheric inversions and ocean pCO2-based products. Figure 8 provides information on the regional distribution of those fluxes by latitude bands. The global mean total atmosphere-to-surface CO2 flux from process models for 2010–2019 is 3.8 ± 0.7 GtC yr-1, below the global mean atmosphere-to-surface flux of 4.3 ± 0.5 GtC yr-1 inferred by the carbon budget (EFOS – GATM in Eq. 1; Table 6). The total atmosphere-to-surface CO2 flux from the inversions (4.5 ± 0.1 GtC yr-1) almost matches the value inferred by the carbon budget, which is expected due to the constraint on GATM incorporated within the inversion approach and the adjustment of the fossil emissions prior to a value consistent with the EFOS budget term (Jones et al., 2020; see Sect. 2.6).

In the southern extra-tropics (south of 30∘ S), the atmospheric inversions suggest a total atmosphere-to-surface sink (SOCEAN+SLAND-ELUC) for 2010–2019 of 1.4 ±  0.3 GtC yr-1, similar to the process models' estimate of 1.4 ± 0.3 GtC yr-1 (Fig. 8). An approximately neutral total land flux (SLAND-ELUC) for the southern extra-tropics is estimated by both the DGVMs (0.0 ± 0.1 GtC yr-1) and the inversion models (sink of 0.1 ± 0.2 GtC yr-1). The GOBMs (1.4 ± 0.3 GtC yr-1) produce a lower estimate for the ocean sink than the inversion models (1.6 ± 0.2 GtC yr-1) or pCO2-based flux products (1.7 ± 0.1 GtC yr-1; discussed further below).

In the tropics (30∘ S–30∘ N), both the atmospheric inversions and process models suggest that the total carbon balance in this region (SOCEAN+SLAND-ELUC) is close to neutral over the past decade. The inversion models indicate a small tropical source to the atmosphere of -0.2 ± 0.6 GtC yr-1, whereas the process models indicate a small sink of 0.2 ± 0.7 GtC yr-1. The GOBMs (-0.1 ± 0.2 GtC yr-1 source), inversion models (-0.1 ± 0.2 GtC yr-1 source), and pCO2-based flux products (-0.05 ± 0.02 GtC yr-1 source) all indicate an approximately neutral tropical ocean flux, meaning that the difference in sign of the total fluxes stems from the land component. Indeed, the DGVMs indicate a total land sink (SLAND-ELUC) of 0.2 ± 0.7 GtC yr-1, whereas the inversion models indicate a small land source of -0.1 ± 0.7 GtC yr-1, though with high uncertainty in both cases. Overall, the GOBMs, pCO2-based flux products, and inversion models suggest either a neutral ocean flux or a small ocean source, while the DGVMs and inversion models suggest either a small sink or source on land. The agreement between inversions and process models is significantly better for the last decade than for any previous decade (Fig. 8), although the reasons for this better agreement are still unclear.

In the northern extra-tropics (north of 30∘ N) the atmospheric inversions suggest an atmosphere-to-surface sink (SOCEAN+SLAND-ELUC) for 2010–2019 of 2.9 ± 0.6 GtC yr-1, which is higher than the process models' estimate of 2.3 ± 0.6 GtC yr-1 (Fig. 8). The difference derives from the total land flux (SLAND-ELUC) estimate, which is 1.1 ± 0.6 GtC yr-1 in the DGVMs compared with 1.7 ± 0.8 GtC yr-1 in the inversion models. The GOBMs (1.2 ± 0.2 GtC yr-1), inversion models (1.2 ± 0.2 GtC yr-1) and pCO2-based flux products (1.2 ± 0.2 GtC yr-1) produce consistent estimates of the ocean sink.

The noteworthy differences between the annual estimates produced by different data sources are as follows: i.

The southern SOCEAN flux in the pCO2-based flux products and inversion models is higher than in the GOBMs. This might be explained by the data products potentially underestimating the winter CO2 outgassing south of the polar front (Bushinsky et al., 2019), or by the uncertainty in the regional distribution of the river flux adjustment (Aumont et al., 2001, Lacroix et al., 2020) applied to pCO2-based flux products to isolate the anthropogenic SOCEAN flux.

The interannual variability in the southern extra-tropics is low because of the dominance of ocean area with low variability compared to land areas. The split between land (SLAND-ELUC) and ocean (SOCEAN) shows a small contribution to variability in the south coming from the land, with no consistency between the DGVMs and the inversions or among inversions. This is expected due to the difficulty of separating exactly the land and oceanic fluxes when viewed from atmospheric observations alone. The interannual variability, calculated as the standard deviation from detrended time series around the mean, was found to be similar in the pCO2-based flux products including Watson et al. (2020) (0.05 to 0.10 GtC yr-1) and GOBMs (0.06 to 0.17 GtC yr-1) in 2010–2019 (Fig. B1).

Both the process models and the inversions consistently allocate more year-to-year variability of CO2 fluxes to the tropics compared to the northern extra-tropics (Fig. 8). The land is the origin of most of the tropical variability, consistently among the process models and inversions. The interannual variability in the tropics is similar among the ocean flux products (0.03 to 0.09 GtC yr-1) and the models (0.02 to 0.09 GtC yr-1; Sect. 3.1.3, Fig. B1). The inversions indicate that atmosphere-to-land CO2 fluxes are more variable than atmosphere-to-ocean CO2 fluxes in the tropics and produce slightly higher IAV than the ocean flux products or GOBMs. With a sparsity of tropical atmospheric measurements, an aliasing of the large land flux variations onto the tropical ocean fluxes in the inversions is one likely cause of this difference.

In the northern extra-tropics, the models, inversions, and pCO2-based flux products consistently suggest that most of the variability stems from the land (Fig. 8). Inversions, GOBMs, and pCO2-based flux products agree on the mean of SOCEAN, but with a higher interannual variability in the pCO2-based flux products (0.05 to 0.08 GtC yr-1) than in the GOBMs (0.04 to 0.10 GtC yr-1; Fig. B1).

The expanded ensemble of atmospheric inversions (from N=3 to N=6) allows a more representative sample of model–model differences, e.g. in latitudinal transport and other inversion settings (Table A4). When assessed for their tropical or northern land+ocean fluxes we see a dipole arise, where three models estimate a northern extra-tropical sink close to 2.5 GtC yr-1, and the other three a sink of close to 3.5 GtC yr-1. The inversions resulting in a large northern sink also estimate a tropical source. Both groups of models perform equally well on the evaluation metric of the misfit of optimized CO2 from inversions against independent aircraft data in Fig. B3 though, and resolving this difference will require the consideration and inclusion of larger volumes of semi-continuous observations of concentrations, fluxes, and auxiliary variables collected from (tall) towers close to the surface CO2 exchange. Improvements in model resolution and atmospheric transport realism together with expansion of the observational record (also in the data-sparse boreal Eurasian area) may help anchor the mid-latitude NH fluxes per continent. In addition, new metrics could potentially differentiate between the more and less realistic realizations of the Northern Hemisphere land sink shown in Fig. 8.

In previous versions of this publication, another hypothesized explanation was that differences in the prior data set used by the inversion models, and related adjustments to posterior estimates, drove inter-model disparity. However, separate analysis has shown that the influence of the chosen prior land and ocean fluxes is minor compared to other aspects of each inversion, and the majority (5 of 6) of the inversion models presented in this update now use a consistent prior for fossil emissions (Jones et al., 2020; see Sect. 2.6).

Finally, in the 2020 effort, two inverse systems (UoE and CAMS) used column CO2 products derived from GoSAT and OCO-2, respectively. Their estimated fluxes and performance on the metrics evaluated in this work were similar to their counterparts driven by in situ and flask observations, and hence these solutions were not included separately (as noted by Chevallier et al., 2019). Nevertheless, this convergence of solutions is an important prerequisite for the use of longer remote sensing CO2 time series in the future and could help to further study differences driven by observational coverage and/or sparseness of the current network. Also, column-CO2 products are likely to be less sensitive to vertical transport differences between models, believed to be a remaining source of uncertainty (Basu et al., 2018).

The budget imbalance (BIM) was low, -0.1 GtC yr-1 on average over 2010–2019, although the BIM uncertainty is large (1.4 GtC yr-1 over the decade). Also, the BIM shows significant departure from zero on yearly timescales (Fig. 4), highlighting unresolved variability of the carbon cycle, likely in the land sink (SLAND), given its large year-to-year variability (Figs. 4e and 6b), while the decadal variability could originate from both the land and ocean sinks, given unresolved discussions on the strength of the ocean carbon sink (Bushinsky et al., 2019; Watson et al., 2020) and its decadal variability (DeVries et al., 2019).

Although the budget imbalance is near zero for the recent decades, it could be due to compensation of errors. We cannot exclude an overestimation of CO2 emissions, in particular from land-use change, given their large uncertainty, as has been suggested elsewhere (Piao et al., 2018), combined with an underestimate of the sinks. A larger SLAND would reconcile model results with inversion estimates for fluxes in the total land during the past decade (Fig. 8; Table 5). Likewise, a larger SOCEAN is also possible given the higher estimates from the data products (see Sect. 3.1.2, Figs. 7 and 8) and the recently suggested upward correction of the ocean carbon sink (Watson et al., 2020; Fig. 7). If data products with the Watson et al. (2020) adjustment were to be used instead of GOBMs to estimate SOCEAN, this would result in a BIM of the order of -1 GtC yr-1 indicating that a closure of the budget could only be achieved with either anthropogenic emissions being larger and/or the net land sink being smaller than estimated here.

More integrated use of observations in the Global Carbon Budget, either on their own or for further constraining model results, should help resolve some of the budget imbalance (Peters et al., 2017; Sect. 4).

Preliminary estimates of global fossil CO2 emissions are for growth of only 0.1 % between 2018 and 2019 to remain at 9.7 ± 0.5 GtC in 2019 (Fig. 5), distributed among coal (39 %), oil (34 %), natural gas (21 %), cement (4 %), and others (1.5 %). Compared to the previous year, emissions from coal decreased by 1.8 %, while emissions from oil, natural gas, and cement increased by 0.8 %, 2.0 %, and 3.2 %, respectively. All growth rates presented are adjusted for the leap year, unless stated otherwise.

In 2019, the largest absolute contributions to global fossil CO2 emissions were from China (28 %), the USA (14 %), the EU (27 member states; 8 %), and India (7 %). These four regions account for 57 % of global CO2 emissions, while the rest of the world contributed 43 %, which includes aviation and marine bunker fuels (3.5 % of the total). Growth rates for these countries from 2018 to 2019 were +2.2 % (China), -2.6 % (USA), -4.5 % (EU27), and +1.0 % (India), with +1.8 % for the rest of the world. The per capita fossil CO2 emissions in 2019 were 1.3 tC per person per year for the globe and were 4.4 (USA), 1.9 (China), 1.8 (EU27), and 0.5 (India) tC per person per year for the four highest-emitting countries (Fig. 5).

The growth in emissions of 0.1 % in 2019 is within the range of the projected growth of 0.6 % (range of -0.2 % to 1.5 %) published in Friedlingstein et al. (2019) based on national emissions projections for China, the USA, the EU27, and India and projections of gross domestic product corrected for IFOS trends for the rest of the world. The growth in emissions in 2019 for China, the USA, EU27, India, and the rest of the world were all within their previously projected range (Table 7).