The estimates of global and national fossil CO2 emissions (EFF) 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 fertilisers). The estimates of EFF rely primarily on energy consumption data, specifically data on hydrocarbon fuels, collated and archived by several organisations (Andres et al., 2012). We use four main data sets for historical emissions (1750–2018).

We use global and national emission estimates for coal, oil, natural gas, and peat fuel extraction from CDIAC for the time period 1750–2016 (Gilfillan et al., 2019), as it is the only data set that extends back to 1750 by country.

CDIAC. The CDIAC estimates have been updated annually to the year 2016, derived primarily from energy statistics published by the United Nations (UN, 2018). 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).

UNFCCC. Estimates from the UNFCCC national inventory reports follow the IPCC guidelines (IPCC, 2006), but they have a slightly larger system boundary than CDIAC by including emissions coming from carbonates other than in cement manufacturing. We reallocate the detailed UNFCCC 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 China and Saudi Arabia, the most recent version of CDIAC introduces what appear to be spurious interannual variations for these two countries (IEA, 2018); therefore we use data from the 2018 global carbon budget (Le Quéré et al., 2018b). For Norway, the CDIAC's method of apparent consumption results in large errors for Norway, and we therefore overwrite emissions before 1990 with estimates based on official Norwegian statistics.

BP. For the most recent period when the UNFCCC and CDIAC estimates are not available, we generate preliminary estimates using energy consumption data from the BP Statistical Review of World Energy (Andres et al., 2014; BP, 2019; Myhre et al., 2009). We apply the BP growth rates by fuel type (coal, oil, natural gas) to estimate 2018 emissions based on 2017 estimates (UNFCCC Annex I countries) and to estimate 2017–2018 emissions based on 2016 estimates (remaining countries). 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 subregion the country belongs to. For the most recent years, natural gas flaring is assumed constant from the most recent available year of data (2017 for Annex I countries, 2016 for the remainder).

Cement. Estimates of emissions from cement production are taken directly from Andrew (2019). Additional calcination and carbonation 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 former East and West Germany into 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 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. This is different to last year, where we used the independent global total estimated by CDIAC (combined with cement from Andrew, 2018). 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-oxidised carbon (e.g. as solvents, lubricants, feedstocks) at the global level is assumed to be fixed at the 1970's 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, 2019), 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-oxidised carbon (IEA, 2018). To remove this discrepancy we now calculate the global total as the sum of the countries and international bunkers.

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 developing countries such as China have uncertainties of around ±10 % (for ±1σ; Gregg et al., 2008). 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.

We assign a medium confidence to the results presented here because they are based on indirect estimates of emissions using energy data (Durant et al., 2011). There is only limited and indirect evidence for emissions, although there is high agreement among the available estimates within the given uncertainty (Andres et al., 2012, 2014), and emission estimates are consistent with a range of other observations (Ciais et al., 2013), even though their regional and national partitioning is more uncertain (Francey et al., 2013).

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 they reflect the trade-driven movement of emissions across the Earth's surface in response to human activities.

We estimate consumption-based emissions from 1990 to 2016 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 Analysis Project (GTAP; Narayanan et al., 2015), and we make detailed estimates for the years 1997 (GTAP version 5), 2001 (GTAP6), 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 (2016 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, 2017) 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 per cent per year) by calculating the difference between the two years and then normalising to the emissions in the first year: (EFF(t0+1)-EFF(t0))/EFF(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 (1/365) and causes growth rates to go up approximately 0.3 % if the first year is a leap year and down 0.3 % if the second year is a leap year.

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

To gain insight into emission trends for 2019, we provide an assessment of global fossil CO2 emissions, EFF, 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 2019 estimate for China uses (1) the sum of monthly domestic production of raw coal, crude oil, natural gas and cement from the National Bureau of Statistics (NBS, 2019c), (2) monthly net imports of coal, coke, crude oil, refined petroleum products and natural gas from the General Administration of Customs of the People's Republic of China (2019); and (3) annual energy consumption data by fuel type and annual production data for cement from the NBS, using final data for 2000–2017 (NBS, 2019c) and preliminary data for 2018 (NBS, 2019b). We estimate the full-year growth rate for 2019 using a Bayesian regression for the ratio between the annual energy consumption data (3 above) from 2014 through 2018 and monthly production plus net imports through September of each year (1+2 above). The uncertainty range uses the standard deviations of the resulting posteriors. Sources of uncertainty and deviations between the monthly and annual growth rates include lack of monthly data on stock changes and energy density, variance in the trend during the last 3 months of the year, and partially unexplained discrepancies between supply-side and consumption data even in the final annual data. Note that in recent years, the absolute value of the annual growth rate for coal energy consumption, and hence total CO2 emissions, has been consistently lower (closer to zero) than the growth suggested by the monthly, tonnage-based production and import data, and this is reflected in the projection. This pattern is only partially explained by stock changes and changes in energy content. It is therefore not possible to be certain that it will continue in the current year, but it is made plausible by a separate statement by the National Bureau of Statistics on energy consumption growth in the first half of 2019, which suggests no significant growth in energy consumption from coal for January–June (NBS, 2019a). Results and uncertainties are discussed further in Sect. 3.4.1.

For the USA, we use the forecast of the U.S. Energy Information Administration (EIA) for emissions from fossil fuels (EIA, 2019). This is based on an energy forecasting model which is updated monthly (last update with data through October 2019) and takes into account heating-degree days, household expenditures by fuel type, energy markets, policies, and other effects. We combine this with our estimate of emissions from cement production using the monthly US cement data from USGS for January–July 2019, assuming changes in cement production over the first part of the year apply throughout the year. While the EIA's forecasts for current full-year emissions have on average been revised downwards, only 10 such forecasts are available, so we conservatively use the full range of adjustments following revision, and additionally we assume symmetrical uncertainty to give ±2.3 % around the central forecast.

For India, we use (1) monthly coal production and sales data from the Ministry of Mines (2019), Coal India Limited (CIL, 2019), and Singareni Collieries Company Limited (SCCL, 2019), combined with import data from the Ministry of Commerce and Industry (MCI, 2019) and power station stock data from the Central Electricity Authority (CEA, 2019a); (2) monthly oil production and consumption data from the Ministry of Petroleum and Natural Gas (PPAC, 2019b); (3) monthly natural gas production and import data from the Ministry of Petroleum and Natural Gas (PPAC, 2019a); and (4) monthly cement production data from the Office of the Economic Advisor (OEA, 2019). All data were available for January to September or October 2019. We use Holt–Winters exponential smoothing with multiplicative seasonality (Chatfield, 1978) on each of these four emissions series to project to the end of India's current financial year (March 2020). This iterative method produces estimates of both trend and seasonality at the end of the observation period that are a function of all prior observations, weighted most strongly to more recent data, while maintaining some smoothing effect. The main source of uncertainty in the projection of India's emissions is the assumption of continued trends and typical seasonality.

For the EU, we use (1) monthly coal supply data from Eurostat for the first 6–9 months of 2019 (Eurostat, 2019) cross-checked with more recent data on coal-generated electricity from ENTSO-E for January through October 2019 (ENTSO-E, 2019); (2) monthly oil and gas demand data for January through August from the Joint Organisations Data Initiative (JODI, 2019); and (3) cement production assumed to be stable. For oil and natural gas emissions we apply the Holt–Winters method separately to each country and energy carrier to project to the end of the current year, while for coal – which is much less strongly seasonal because of strong weather variations – we assume the remaining months of the year are the same as the previous year in each country.

For the rest of the world, we use the close relationship between the growth in GDP and the growth in emissions (Raupach et al., 2007) to project emissions for the current year. This is based on a simplified Kaya identity, whereby EFF (GtC yr-1) is decomposed by the product of GDP (USD yr-1) and the fossil fuel carbon intensity of the economy (IFF; GtC USD-1) as follows: 3EFF=GDP×IFF. Taking a time derivative of Eq. (3) and rearranging gives 41EFFdEFFdt=1GDPdGDPdt+1IFFdIFFdt, where the left-hand term is the relative growth rate of EFF, and the right-hand terms are the relative growth rates of GDP and IFF, respectively, which can simply be added linearly to give the overall growth rate.

As preliminary estimates of annual change in GDP are made well before the end of a calendar year, making assumptions on the growth rate of IFF allows us to make projections of the annual change in CO2 emissions well before the end of a calendar year. The IFF is based on GDP in constant PPP (purchasing power parity) from the International Energy Agency (IEA) up to 2016 (IEA/OECD, 2018) and extended using the International Monetary Fund (IMF) growth rates through 2018 (IMF, 2019a). Interannual variability in IFF is the largest source of uncertainty in the GDP-based emissions projections. We thus use the standard deviation of the annual IFF for the period 2009–2018 as a measure of uncertainty, reflecting a ±1σ as in the rest of the carbon budget. In this year's budget, we have extended the rest-of-the-world method to fuel type to get separate projections for coal, oil, natural gas, cement, flaring, and other components. This allows, for the first time, consistent projections of global emissions by both countries and fuel type.

The 2019 projection for the world is made of the sum of the projections for China, the USA, the EU, India, and the rest of the world, where the sum is consistent if done by fuel type (coal, oil, natural gas) or based on total emissions. The uncertainty is added in quadrature among the five regions. The uncertainty here reflects the best of our expert opinion.

Land use change CO2 emissions and uptake fluxes are calculated by two bookkeeping models. Both 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 they also include forest management practices such as wood harvests.

The bookkeeping models do not include land ecosystems' transient response to changes in climate, atmospheric CO2, and other environmental factors, and the carbon densities are based on contemporary data reflecting stable environmental conditions at that time. Since carbon densities remain fixed over time in bookkeeping models, the additional sink capacity that ecosystems provide in response to CO2 fertilisation and some other environmental changes is not captured by these models (Pongratz et al., 2014; see Sect. 2.7.4). The H&N2017 and BLUE models differ in (1) computational units (country-level vs. spatially explicit treatment of land use change), (2) processes represented (see Table A1), and (3) carbon densities assigned to vegetation and soil of each vegetation type. A notable change of H&N2017 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 the FAO is assumed to represent a concurrent expansion and abandonment of cropland. In contrast, the BLUE model includes sub-grid-scale transitions at the grid level between all vegetation types as indicated by the harmonised land use change data (LUH2) data set (10.22033/ESGF/input4MIPs.1127; Hurtt et al., 2011, 2019). Furthermore, H&N2017 assume conversion of natural grasslands to pasture, while BLUE allocates pasture proportionally on all natural vegetation that exists in a grid cell. This is one reason for generally higher emissions in BLUE. For both H&N2017 and BLUE, we add 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) to the output of their bookkeeping model for the countries of Indonesia and Malaysia. Peat burning and emissions from the organic layers of drained peat soils, which are not captured by bookkeeping methods directly, need to be included to represent the substantially larger emissions and interannual variability due to synergies of land use and climate variability in Southeast Asia, in particular during El Niño events.

The two bookkeeping estimates used in this study differ with respect to the land use change data used to drive the models. H&N2017 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 countries reporting to the 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 the FAO (FAOSTAT, 2015). H&N2017 was extended here for 2016 to 2018 by adding the annual change in total tropical emissions to the H&N2017 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). On the other hand, BLUE uses the harmonised land use change data LUH2 covering the entire 850–2018 period (10.22033/ESGF/input4MIPs.1127; Hurtt et al., 2011, 2019), which describes land use change, also based on the FAO data as well as the HYDE data set (Klein Goldewijk et al., 2017; Goldewijk et al., 2017), but downscaled at a quarter-degree spatial resolution, considering sub-grid-scale transitions between primary forest, secondary forest, cropland, pasture, and rangeland. The LUH2 data provide a distinction between rangelands and pasture, based on inputs from HYDE. To constrain the models' interpretation on whether rangeland implies the original natural vegetation to be transformed to grassland or not (e.g. browsing on shrubland), a forest mask was provided with LUH2; forest is assumed to be transformed, while all other natural vegetation remains. This is implemented in BLUE.

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

Land use change CO2 emissions have also been estimated using an ensemble of 15 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 they 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 fertilisers (Table A1). The DGVMs are independent from the other budget terms except for their use of atmospheric CO2 concentration to calculate the fertilisation effect of CO2 on plant photosynthesis.

Many DGVMs used the HYDE land use change data set (Klein Goldewijk et al., 2017; Goldewijk et al., 2017), which provides annual (1700–2018), 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. Last year's HYDE version used FAO statistics until 2012, which are now supplemented using the annual change anomalies from FAO data for the years 2013–2015 relative to the 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 2018. Some models also use the LUH2 data set, an update of the more comprehensive harmonised land use data set (Hurtt et al., 2011), that 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., 2011, 2019; 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, new representation of shifting cultivation, crop rotations, and management information including irrigation and fertiliser 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 over last year's version use 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.

DGVMs implement land use change differently (e.g. an increased cropland fraction in a grid cell can either be at the expense of either 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 area 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 CRU and 6-hourly 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 2018 (Harris et al., 2014). 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, 2019), and gridded, time-dependent N deposition and N fertilisers (as used in some models; Table A1).

Two sets of simulations were performed with 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, and 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 (around 0.4±0.3 GtC yr-1; 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, 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 from the bookkeeping method, and we use the resulting variations as a way to characterise the uncertainty in ELUC.

The ELUC estimate from the DGVMs 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 two bookkeeping models (average difference of 0.7 GtC yr-1), and between the current estimate of H&N2017 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 a 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 to quantify some of the processes in DGVMs.

We project the 2019 land use emissions for both H&N2017 and BLUE, starting from their estimates for 2018 and adding observed changes in emissions from peat drainage (update on Hooijer et al., 2010) as well as emissions from peat fires, tropical deforestation, and degradation as estimated using active fire data (MCD14ML; Giglio et al., 2016). Those from degradation 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. While the degree to which the fires in 2019 in the Amazon are related to land use change requires more scrutiny, initial analyses based on fire radiative power (FRP) of the fires detected indicate that many fires were associated with deforestation (http://www.globalfiredata.org/forecast.html, last access: 31 October 2019). Most fires burning in Indonesia were on peatlands, which also represent a net source of CO2.

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, 2019), 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 programme at Scripps Institution of Oceanography (Keeling et al., 1976). For the 1980–2018 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 (2019) 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 parts per million per year is converted to units of gigatonnes of carbon per year 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. The first is the long-term reproducibility of reference gas standards (around 0.03 ppm for 1σ from the 1980s; Dlugokencky and Tans, 2019). 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 randomising both the duration and the magnitude (determined from the existing evidence) in a Monte Carlo procedure. The third is 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, 2019). The latter uncertainty was estimated by NOAA ESRL with a Monte Carlo method by constructing 100 “alternative” networks (Masarie and Tans, 1995; NOAA/ESRL, 2019). The second and third uncertainties, summed in quadrature, add up to 0.085 ppm on average (Dlugokencky and Tans, 2019). The fourth is 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) as 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 1980–2018, when a larger set of stations was available as provided by Dlugokencky and Tans (2019), but we recognise 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 to 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 2019 based on the monthly calculated global atmospheric CO2 concentration (GLO) through August (Dlugokencky and Tans, 2019) and bias-adjusted Holt–Winters exponential smoothing with additive seasonality (Chatfield, 1978) to project to January 2020. The assessment method used this year differs from the forecast method used last year (Le Quéré et al., 2018b), which was based on the observed concentrations at Mauna Loa (MLO) only, using the historical relationship between the MLO and GLO series. 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 use the observational constraints assessed by IPCC of a mean ocean CO2 sink of 2.2±0.4 GtC yr-1 for the 1990s (Denman et al., 2007) to verify that the GOBMs provide a realistic assessment of SOCEAN. 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). The IPCC confirmed this assessment in 2013 (Ciais et al., 2013). The observational-based estimates use the ocean–land CO2 sink partitioning from observed atmospheric O2 and N2 concentration trends (Manning and Keeling, 2006; updated in Keeling and Manning, 2014), an oceanic inversion method constrained by ocean biogeochemistry data (Mikaloff Fletcher et al., 2006), and a method based on a penetration timescale 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 three estimates of the ocean CO2 sink and its variability based on interpolations of measurements of surface ocean fugacity of CO2 (pCO2 corrected for the non-ideal behaviour of the gas; Pfeil et al., 2013). We refer to these as pCO2-based flux estimates. The measurements are from the Surface Ocean CO2 Atlas version 2019, which is an update of version 3 (Bakker et al., 2016) and contains quality-controlled data to 2018 (see data attribution Table A4). The SOCAT v2019 data were mapped using a data-driven diagnostic method (Rödenbeck et al., 2013; referred to here as Jena-MLS), a combined self-organising map and feed-forward neural network (Landschützer et al., 2014; MPI-SOMFFN), and an artificial neural network model (Denvil-Sommer et al., 2019; Copernicus Marine Environment Monitoring Service, CMEMS). The global pCO2-based flux estimates were adjusted to remove the pre-industrial ocean source of CO2 to the atmosphere of 0.78 GtC yr-1 from river input to the ocean (Resplandy et al., 2018), per our definition of SOCEAN. Several other ocean sink products based on observations are also available but they continue to show large unresolved discrepancies with observed variability. Here we used, as in our previous annual budgets, the two pCO2-based flux products that had the best fit to observations for their representation of tropical and global variability (Rödenbeck et al., 2015), plus CMEMS, which has a similarly good fit with observations. 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 % of the observed total ocean area, so two products are effectively corrected upwards by a factor of 1.126.

We further use results from two diagnostic ocean models of 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 as about ±30 % for the annual values (Khatiwala et al., 2009).

The ocean CO2 sink for 1959–2018 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 their horizontal and vertical resolutions (Table A2). GOBMs do not include the effects of anthropogenic changes in nutrient supply, which could lead to an increase in the ocean sink of up to about 0.3 GtC yr-1 over the industrial period (Duce et al., 2008). They also do not include the perturbation associated with changes in riverine organic carbon (see Sect. 2.7.3).

The annual mean air–sea CO2 flux from the GOBMs is corrected for any model bias or drift by subtracting the time-dependent model bias. The time-dependent model bias is calculated as a linear fit to the annual CO2 flux from a control simulation with no climate variability and change and constant pre-industrial CO2 concentration. The absolute biases per model in the 1990s vary between 0.005 and 0.362 GtC yr-1, with some models having positive and some having negative biases. The bias correction reduces the model mean ocean carbon sink by 0.06 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 97 % to 101 % of the total ocean area, so the effect of this correction is small. All models fell within the observational constraint for the 1990s before and after applying the corrections.

The mean ocean CO2 sink for all GOBMs falls within 90 % confidence of the observed range, or 1.6 to 2.8 GtC yr-1 for the 1990s. Here we have adjusted the confidence interval to the IPCC confidence interval of 90 % to avoid rejecting models that may be outliers but are still plausible.

The GOBMs and flux products have been further evaluated using air–sea CO2 flux (fCO2) from the SOCAT v2019 database (Bakker et al., 2016, updated). We focused this evaluation on the root-mean-square error (RMSE) between observed fCO2 and modelled pCO2 and on a measure of the amplitude of the interannual variability of the flux (Rödenbeck et al., 2015). The amplitude of the SOCEAN interannual variability (A-IAV) is calculated as the temporal standard deviation of a 12-month running mean over the CO2 flux time series (Rödenbeck et al., 2015). The RMSE is only calculated for open-ocean (water depth >400 m) grid points on a 1∘×1∘ monthly grid where actual observations exist. 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 uncertainty around the mean ocean sink of anthropogenic CO2 was quantified by Denman et al. (2007) for the 1990s (see Sect. 2.4.1). To quantify the uncertainty around annual values, we examine the standard deviation of the GOBM ensemble, which averages 0.3 GtC yr-1 during 1959–2018. We estimate that the uncertainty in the annual ocean CO2 sink is about ±0.5 GtC yr-1 from the combined uncertainty of the mean flux based on observations of ±0.4 GtC yr-1 (Denman et al., 2007) and the standard deviation across GOBMs of up to ±0.4 GtC yr-1, reflecting the uncertainty in both the mean sink from observations during the 1990s (Denman et al., 2007; Sect. 2.4.1) and in the interannual variability as assessed by GOBMs.

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 the standard deviation) of the three pCO2-based flux products for 1985–2018 (where they overlap) is ±0.37 GtC yr-1 (Jena-MLS), ±0.46 GtC yr-1 (MPI-SOMFFN), and ±0.51 GtC yr-1 (CMEMS). The inter-annual variability in the mean of the pCO2-based flux estimates is ±0.41 GtC yr-1 for the 1985–2018 period, compared to ±0.31 GtC yr-1 for the GOBM ensemble. The standard deviation includes a component of trend and decadal variability in addition to interannual variability, and their relative influence differs across estimates. Individual estimates (both GOBM and flux products) generally produce a higher ocean CO2 sink during strong El Niño events. The annual pCO2-based flux products correlate with the ocean CO2 sink estimated here with a correlation of r=0.75 (0.55 to 0.79 for individual GOBMs), r=0.86 (0.70 to 0.87), and 0.93 (0.83 to 0.93) for the pCO2-based flux products of Jena-MLS, MPI-SOMFFN, and CMEMS, respectively (simple linear regression). The averages of the GOBM estimates and of the data-based estimates have a mutual correlation of 0.91. 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 for the annual ocean CO2 sink and its uncertainty because it is based on multiple lines of evidence, and the results are consistent in that the interannual variability in the GOBMs and data-based estimates is 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 fertilisation 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 exactly attribute CO2 fluxes on land between SLAND and ELUC (Erb et al., 2013).

SLAND is estimated from the multi-model mean of 16 DGVMs (Table 4). As described in Sect. 2.2.2, DGVM simulations include all climate variability and CO2 effects over land, with some DGVMs also including the effect of N inputs. The DGVMs do 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) net land fluxes (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 mentioned in Sect. 2.2.2. All 16 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 from 1959 to 2018. 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).

The three inversion systems used in this release are the CarbonTracker Europe (CTE; Van Der Laan-Luijkx et al., 2017), the Jena CarboScope (Rödenbeck, 2005, with updates from Rödenbeck et al., 2018), and the Copernicus Atmosphere Monitoring Service (CAMS; Chevallier et al., 2005). See Table A3 for version numbers. The inversions are based on Bayesian inversion principles with prior information on fluxes and their uncertainty that interpret the same, for the most part, observed time series (or subsets thereof), but use different methodologies (Table A3). These differences mainly concern the selection of atmospheric CO2 data, the used prior fluxes, spatial breakdown (i.e. grid size), assumed correlation structures, and mathematical approach. The details of these approaches are documented extensively in the references provided above. Each system uses a different transport model, which was demonstrated to be a driving factor behind differences in atmospheric-based flux estimates and specifically their distribution across latitudinal bands (e.g. Gaubert et al., 2019).

The inversions use atmospheric CO2 observations from various flask and in situ networks, as detailed in Table A3. They prescribe global fossil fuel emissions, which is already scaled to the present estimate of EFF for CAMS, while CTE and CarboScope used slightly different EFF values (<0.39 GtC yr-1) based on alternative emissions compilations. Since this is known to result in different total CO2 uptake in atmospheric inversions (Peylin et al., 2013; Gaubert et al., 2019), we adjusted the land sink of each inversion estimate (where most of the fossil fuel emissions occur) by its fossil fuel difference to the CAMS model. These differences amount to up to 0.5 GtC for certain years in the Northern Hemisphere and are thus an important consideration in an inverse flux comparison.

The land–ocean CO2 fluxes from atmospheric inversions contain anthropogenic perturbation and natural pre-industrial CO2 fluxes. Natural pre-industrial fluxes are primarily land CO2 sinks and ocean CO2 sources corresponding to carbon taken up on land, transported by rivers from land to ocean, and outgassed by the ocean. These pre-industrial land CO2 sinks are thus compensated for over the globe by ocean CO2 sources corresponding to the outgassing of riverine carbon inputs to the ocean. We apply the distribution of land-to-ocean C fluxes from rivers in three latitude bands using estimates from Resplandy et al. (2018), which are constrained by ocean heat transport to a total land-to-ocean carbon transfer of 0.78 GtC yr-1. The latitude distribution of river-induced ocean CO2 sources (north: 0.20 GtC yr-1; tropics: 0.19 GtC yr-1; south: 0.38 GtC yr-1) is derived from a simulation of the IPSL GOBM using as an input the river flux constrained by heat transport of Resplandy et al. (2018). To facilitate the comparison, we adjusted the inversion estimates of the land and ocean fluxes per latitude band with these numbers based on these results to produce historical perturbation CO2 fluxes from inversions.

The atmospheric inversions are also evaluated using vertical profiles of atmospheric CO2 concentrations (Fig. B3). More than 30 aircraft programmes over the globe, either regular programmes or repeated surveys over at least 9 months, have been used in order to draw a robust picture of the model performance (with space-time data coverage irregular and denser in the 0–45∘ N latitude band). The three models are compared to the independent aircraft CO2 measurements between 2 and 7 km above sea level between 2001 and 2017. Results are shown in Fig. B3 and discussed in Sect. 3.1.3.

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 oxidised 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 carbon budget are the fugitive emissions of coal, oil, and gas upstream sectors (see below). These emissions of CO and CH4 contribute a net addition of fossil carbon to the atmosphere.

In our estimate of EFF we assumed (Sect. 2.1.1) that all the fuel burned is emitted as CO2; thus CO anthropogenic emissions associated with incomplete combustion and their atmospheric oxidation into CO2 within a few months are already counted implicitly in EFF and should not be counted twice (same for ELUC and anthropogenic CO emissions by deforestation fires). Anthropogenic emissions of fossil CH4 are not included in EFF because these fugitive emissions are not included in the fuel inventories. Yet they contribute to the annual CO2 growth rate after CH4 gets oxidised into CO2. Anthropogenic emissions of fossil CH4 represent 15 % of total CH4 emissions (Kirschke et al., 2013), that is 0.072 GtC yr-1 for the past decade. Assuming steady state, these emissions are all converted to CO2 by OH oxidation, and thus they explain 0.06 GtC yr-1 of the global CO2 growth rate in the past decade, or 0.07–0.1 GtC yr-1 using the higher CH4 emissions reported recently (Schwietzke et al., 2016).

Other anthropogenic changes in the sources of CO and CH4 from wildfires, vegetation biomass, wetlands, ruminants, or permafrost 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., 2016; Zheng et al., 2019).

The contribution of fossil carbonates other than cement production is not systematically included in estimates of EFF, 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 and the reabsorption of CO2 by the rocks and concrete from carbonation through their lifetime (Xi et al., 2016). Carbonates are used in various industries, including in iron and steel manufacture and in agriculture. They are found naturally in some coals. Carbonation from the cement life cycle, including demolition and crushing, was estimated by one study to be around 0.25 GtC yr-1 for the year 2013 (Xi et al., 2016). Carbonation emissions from the cement life cycle would offset calcination emissions from lime and limestone production. The balance of these two processes is not clear.

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 summarised in two points of relevance for the anthropogenic CO2 budget. First, the anthropogenic perturbation 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. The increase in storage of land-derived organic carbon in the LOAC and open ocean combined is estimated by Regnier et al. (2013) at 0.65±0.35 GtC yr-1. We do not attempt to incorporate the changes in LOAC in our study.

The inclusion of freshwater fluxes of anthropogenic CO2 affects the estimates of, and partitioning between, SLAND and SOCEAN in Eq. (1) but does not affect the other terms. This effect is 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 sink capacity”, is calculated as the difference between the actual land sink under changing land cover and the counterfactual land sink under pre-industrial land cover. An efficient protocol has yet to be designed to estimate the magnitude of the loss of additional sink capacity in DGVMs. Here, we provide a quantitative estimate of this term to be used in the discussion. Our estimate uses the compact Earth system model OSCAR whose land carbon cycle component is designed to emulate the behaviour of DGVMs (Gasser et al., 2017). We use OSCAR v2.2.1 (an update of v2.2 with minor changes) in a probabilistic setup identical to the one of Arneth et al. (2017) but with a Monte Carlo ensemble of 2000 simulations. For each, we calculate SLAND and the loss of additional sink capacity separately. We then constrain the ensemble by weighting each member to obtain a distribution of cumulative SLAND over 1850–2005 close to the DGVMs used here. From this ensemble, we estimate a loss of additional sink capacity of 0.4±0.3 GtC yr-1 on average over 2005–2014 and of about 20±15 GtC when accumulated between 1850 and 2018 (using a linear extrapolation of the trend to estimate the last few years).

Global fossil CO2 emissions have increased every decade from an average of 3.0±0.2 GtC yr-1 in the 1960s to an average of 9.5±0.5 GtC yr-1 during 2009–2018 (Table 6, Figs. 2 and 5). The growth rate in these emissions decreased between the 1960s and the 1990s, from 4.4 % yr-1 in the 1960s (1960–1969) to 2.8 % yr-1 in the 1970s (1970–1979), 1.9 % yr-1 in the 1980s (1980–1989), and 0.9 % yr-1 in the1990s (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 0.9 % yr-1 for 2010–2018, with 1.3 % yr-1 for the last decade (2009–2018). In contrast, CO2 emissions from land use, land use change, and forestry have remained relatively constant, at around 1.3±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 2.0±0.5 GtC yr-1. However, there is no agreement on this recent increase between the two bookkeeping models, each suggesting an opposite trend (Fig. 6).

The growth rate in atmospheric CO2 level increased from 1.8±0.07 GtC yr-1 in the 1960s to 4.9±0.02 GtC yr-1 during 2009–2018 with important decadal variations (Table 6 and Fig. 2). 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±0.6 GtC yr-1 in the 1960s to 2.5±0.6 GtC yr-1 during 2009–2018, with interannual variations of the order of a few tenths of gigatonnes of carbon per year generally showing an increased ocean sink during large El Niño events (i.e. 1997–1998) (Fig. 7; Rödenbeck et al., 2014). There is coherence among the GOBMs and pCO2-based flux products regarding the mean and the patterns of temporal variability; however, the ocean models underestimate the magnitude of decadal variability (Sect. 2.4.3 and Fig. 7; DeVries et al., 2019).

The terrestrial CO2 sink increased from 1.3±0.4 GtC yr-1 in the 1960s to 3.2±0.7 GtC yr-1 during 2009–2018, 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 2009–2018 compared to the 1960s is reproduced by all the DGVMs in response to the combined atmospheric CO2 increase and the changes in climate and 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±0.8 GtC yr-1 source in the 1960s to a 1.7±0.9 GtC yr-1 sink during 2009–2018 (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 (EFF-GATM-SOCEAN, Table 5), except during 2009–2018, where the DGVM ensemble estimates a total atmosphere-to-land flux of 1.0±0.8 GtC yr-1, likely below both our estimate of 1.7±0.9 GtC yr-1 and the carbon budget constraint of 2.1±0.7 GtC yr-1 but still within the range of the inversions (1.1–2.2 GtC yr-1) (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 a RMSE of 15 to 17 µatm for the three pCO2-based flux products over the globe, relative to the pCO2 observations from the SOCAT v2019 database for the period 1985–2018. The GOBM RMSEs are a factor of 2 to 3 larger and range between 29 and 49 µatm. The RMSEs are generally larger at high latitudes compared to the tropics, for both the flux products and the GOBMs. The three flux products have similar RMSEs of around 12 to 14 µatm in the tropics, around 17 to 18 µatm in the north, and 17 to 24 µatm in the south. Note that the flux products are based on the SOCAT v2019 database; hence these are no independent data sets for the evaluation of the flux products. The GOBM RMSEs are more spread across regions, ranging from 21 to 34 µatm in the tropics, 32 to 48 µatm in the north, and 31 to 77 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) shows generally high skill scores across models for runoff, and to a lesser extent for vegetation biomass, gross primary productivity (GPP), and ecosystem respiration (Fig. B2, left panel). Skill score was lowest for leaf area index and net ecosystem exchange, with the 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 better 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 (e.g. Houweling et al., 2015). Such model- and campaign-specific performance will be analysed separately.

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 2018 is small (average of 0.17 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 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, early 1990s, and in the last decade suggests that either the emissions were overestimated or the sinks were underestimated during these periods. The reverse is true for the 1970s and around 1995–2000 (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 has been 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). Decadal and semi-decadal variability in the ocean sink has also been reported recently (DeVries et al., 2019, 2017; Landschützer et al., 2015), with the pCO2-based ocean flux products and a decadal ocean inverse model suggesting 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). 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), or by internal variability, which is not captured by single realisations of coarse resolution model simulations (Li and Ilyina, 2018) The decadal variability is thought to be largest in regions with strong seasonal and interannual climate variability, i.e. the high latitude ocean regions (poleward of the subtropical gyres) and the equatorial Pacific (Li and Ilyina, 2018; McKinley et al., 2016). 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 have grown at a rate of 1.3 % yr-1 for the last decade (2009–2018). China's emissions increased by +2.2 % yr-1 on average (increasing by +0.063 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 EU28 by -1.4 % yr-1 (decreasing by -0.010 GtC yr-1) and in the USA by -0.5 % yr-1 (decreasing by -0.002 GtC yr-1). In the past decade, fossil CO2 emissions decreased significantly (at the 95 % level) in 19 growing economies: Belgium, Croatia, Czech Republic, Denmark, Finland, France, Italy, Latvia, Luxembourg, Republic of Macedonia, Malta, the Netherlands, Romania, Slovenia, Sweden, Switzerland, the United Kingdom, the USA, and Uzbekistan. The drivers of recent decarbonisation 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), though the data are very uncertain, with only one of the two bookkeeping estimates showing a positive trend over the last decade. Larger emissions are increasingly expected over time for DGVM-based estimates as they include the loss of additional sink capacity, while the bookkeeping estimates do not. The LUH2 data set also features large dynamics in land use in particular in the tropics in recent years, causing higher emissions in DGVMs and BLUE than in H&N.

The growth rate in atmospheric CO2 concentration increased during 2009–2018, in contrast to more constant levels in the previous decade and reflecting a similar decrease in the land sink compared to an increase in the previous decade, albeit with large interannual variability (Fig. 4). During the same period, the ocean CO2 sink appears to have intensified, an effect which is particularly apparent in the pCO2-based flux products (Fig. 7) and a decadal ocean inverse model (DeVries et al., 2019). The GOBMs show the same patterns of decadal variability as the mean of the pCO2-based flux products, but of weaker magnitude (Fig. 7). 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).

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 account 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 (SLAND+SOCEAN-ELUC) according to the multi-model average of the process models in the ocean and on land (GOBMs and DGVMs) and to the atmospheric inversions. 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 2009–2018 is 3.5±0.9 GtC yr-1. This is below but still within the uncertainty range of a global mean atmosphere-to-surface flux of 4.6±0.5 GtC yr-1 inferred from the carbon budget (EFF-GATM in Eq. 1; Table 6). The total atmosphere-to-surface CO2 fluxes from the three inversions are very similar, ranging from 4.6 to 4.9 GtC yr-1, consistent with the carbon budget as expected from the constraints on the inversions and the adjustments to the same EFF distribution (See Sect. 2.6).

In the south (south of 30∘ S), the atmospheric inversions suggest an atmosphere-to-surface flux for 2009–2018 around 1.7–2.0 GtC yr-1, slightly above the process models' estimate of 1.4±0.3 GtC yr-1 (Fig. 8). The higher flux in the pCO2-based flux products than in the ocean models might be explained by a known lack of surface ocean pCO2 observations in winter, when CO2 outgassing occurs south of the Polar Front (Gray et al., 2018).

The interannual variability in the south 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 oceanic variability in the south is estimated to be significant in the three pCO2-based flux products, with decadal variability of 0.18 to 0.22 GtC yr-1 (Fig. B1). The GOBMs show slightly lower interannual variability (0.11 to 0.18 GtC yr-1, Fig. B1).

In the tropics (30∘ S–30∘ N), both the atmospheric inversions and process models suggest the total carbon balance in this region has been close to neutral on average over the past decade. The three inversion models suggest an atmosphere-to-surface flux between -0.5 and +0.3 GtC yr-1 for the 2009–2018 period, which is within the range of the process models' estimates of 0.1±0.4 GtC yr-1. The agreement between inversions and models is significantly better for the last decade than for any previous decade, although the reasons for this better agreement are still unclear. Both the process models and the inversions consistently allocate more year-to-year variability of CO2 fluxes to the tropics compared to the north (north of 30∘ N; Fig. 8). The split between the land and ocean indicates the land is the origin of most of the tropical variability, consistently among models (both for the land and for the ocean) and inversions. The oceanic variability in the tropics is similar among the three ocean flux products (A-IAV 0.12 to 0.14 GtC yr-1) and the models, although the model spread is larger (A-IAV 0.08 to 0.19 GtC yr-1, Sect. 3.1.3, Fig. B1). While the inversions indicate that atmosphere-to-land CO2 fluxes are more variable than atmosphere-to-ocean CO2 fluxes in the tropics, the correspondence between the inversions and the ocean flux products or GOBMs is much poorer, partly caused by a substantial tropical ocean carbon sink produced by one of the three inversions.

In the north (north of 30∘ N), 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 variability in the pCO2-based flux products (A-IAV: 0.12 to 0.13 GtC yr-1) than in the models (A-IAV: 0.03 to 0.08 GtC yr-1, Fig. B1). Atmospheric inversions and process models show less agreement on the magnitude of the atmosphere-to-land flux, with the ensemble mean of the process models suggesting a total Northern Hemisphere sink for 2009–2018 of 2.1±0.5 GtC yr-1, below the estimates from the inversions ranging from 2.5 to 3.4 GtC yr-1 (Fig. 8). The discrepancy in the northern tropics distribution of CO2 fluxes between the inversions and models arises from the differences in mean fluxes over the northern land. This discrepancy is also evidenced over the previous decade and highlights not only persistent issues with the quantification of the drivers of the net land CO2 flux (Arneth et al., 2017; Huntzinger et al., 2017) but also the distribution of atmosphere-to-land fluxes between the tropics and higher latitudes that is particularly marked in previous decades, as highlighted previously (Baccini et al., 2017; Schimel et al., 2015; Stephens et al., 2007).

Differences between inversions may be related for example to differences in their interhemispheric transport and other inversion settings (Table A3). Separate analysis has shown that the influence of the chosen prior land and ocean fluxes is minor compared to other aspects of each inversion, while fossil fuel inputs were adjusted to match those of EFF used in this analysis (see Sect. 2.6), therefore removing differences due to fossil emissions prior. Differences between inversions and the ensemble of process models in the north cannot be simply explained. They could either reflect a bias in the inversions or missing processes or biases in the process models, such as the lack of adequate parameterisations for land management for the DGVMs. The estimated contribution of the north and its uncertainty from process models is sensitive both to the ensemble of process models used and to the specifics of each inversion.

Resolving the differences in the Northern Hemisphere land sink 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. Moreover, effective use of such information would demand a more process-based approach to land-surface exchange of CO2 than currently employed in inverse models. Such a process-based approach would represent constraints on carbon exchange derived from local observations and biogeochemical relations on multiple timescales, which in turn would be constrained by the regional- to continental-scale mass balance of atmospheric CO2. Some of these near-surface data are now becoming available but are not used in the current inverse models sometimes due to the short records and sometimes because the coarse transport models cannot adequately represent these time series. Improvements in model resolution and atmospheric transport realism together with expansion of the observational record (also in the data-sparse boreal Eurasian area) will help anchor the mid-latitude fluxes per continent. In addition, new metrics could potentially differentiate between the more and less realistic realisations of the Northern Hemisphere land sink shown in Fig. 8.

The budget imbalance was +0.4 GtC yr-1 on average over 2009–2018. Although the uncertainties are large in each term, the sustained imbalance over this last decade suggests an overestimation of the emissions and/or an underestimation of the sinks. An origin in the land and/or ocean sink may be more likely, given the large variability of the land sink and the suspected underestimation of decadal variability in the ocean sink. An underestimate of SLAND would also reconcile model results with inversion estimates for fluxes in the total land during the past decade (Fig. 8, Table 5). An underestimation of SOCEAN is also possible given slightly higher estimates for SOCEAN from ocean interior carbon observations over the period 1994 to 2007 (2.6±0.3 GtC yr-1; Gruber et al., 2019) compared to the estimate from GOBMs of 2.1±0.5 GtC yr-1 over the same period, although uncertainties overlap. However, we cannot exclude that the budget imbalance over the last decade could partly be due to an overestimation of CO2 emissions, in particular from land use change, given their large uncertainty, as has been suggested elsewhere (Piao et al., 2018). 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 2.1 % between 2017 and 2018 to reach 10.0±0.5 GtC in 2018 (Fig. 5), distributed among coal (40 %), oil (34 %), natural gas (20 %), cement (4 %), and others (1.3 %). Compared to the previous year, emissions from coal increased by 1.4 %, while emissions from oil, natural gas, and cement increased by 1.2 %, 5.4 %, and 2.1 %, respectively. All growth rates presented are adjusted for the leap year, unless stated otherwise.

In 2018, the largest absolute contributions to global CO2 emissions were from China (28 %), the USA (15 %), the EU (28 member states; 9 %), and India (7 %). These four regions account for 59 % of global CO2 emissions, while the rest of the world contributed 41 %, which includes aviation and marine bunker fuels (3.4 % of the total). Growth rates for these countries from 2017 to 2018 were 2.3 % (China), 2.8 % (USA), -2.1 % (EU28), and 8.0 % (India), with 1.8 % for the rest of the world. The per capita CO2 emissions in 2018 were 1.3 tC per person per year for the globe and were 4.5 (USA), 1.9 (China), 1.8 (EU28) and 0.5 (India) tC per person per year for the four highest emitting countries (Fig. 5).

The growth in emissions of 2.1 % in 2018 is within the range of the projected growth of 2.7 % (range of 1.8 % to 3.7 %) published in Le Quéré et al. (2018b) based on national emissions projections for China, the USA, and India and projections of gross domestic product corrected for IFF trends for the rest of the world. The growth in emissions in 2018 for China, the USA, EU28, India, and the rest of the world were all within their previously projected range (Table 7).

In 2016 (the last year available), the largest absolute contributions to global CO2 emissions from a consumption perspective were China (25 %), the USA (16 %), the EU (12 %), and India (6 %). The difference between territorial and consumption emissions (the net emission transfer via international trade) has generally increased from 1990 to around 2005 and remained relatively stable afterwards until the last year available (2016; Fig. 5).

The global CO2 emissions from land use change are estimated as 1.5±0.7 GtC in 2018, close to the previous decade but with low confidence in the annual change. This brings the total CO2 emissions from fossil fuel plus land use change (EFF+ELUC) to 11.5±0.9 GtC (42.5±3.3 GtCO2).

The growth rate in atmospheric CO2 concentration was 5.1±0.2 GtC in 2018 (2.42±0.08 ppm; Fig. 4; Dlugokencky and Tans, 2019). This is near the 2009–2018 average of 4.9±0.02 GtC yr-1.

The estimated ocean CO2 sink was 2.6±0.6 GtC in 2018. The multi-model mean agrees with the mean of the pCO2-based flux products on an average increase of 0.1 GtC in 2018. Six models and two flux products show an increase in SOCEAN (up to +0.38 GtC), while three models and one flux product show no change or a decrease in SOCEAN (down to -0.15 GtC) (Fig. 7).

The terrestrial CO2 sink from the DGVM model ensemble was 3.5±0.7 GtC in 2018, slightly above the decadal average (Fig. 4) and consistent with constraints from the rest of the budget (Table 5). The budget imbalance was +0.3 GtC in 2018, consistent with its average over the last decade (Table 6). This imbalance is indicative only, given the large uncertainties in the estimation of the BIM.

Based on the available data as of 14 November 2019 (see Sect. 2.1.5), fossil CO2 emissions (EFF) for 2019 are projected to increase by +0.6 % (range of -0.2 % to +1.5 %; Table 7). Our method contains several assumptions that could influence the estimate beyond the given range, and as such it has an indicative value only. Within the given assumptions, global emissions would be 10.0±0.5 GtC (36.8±1.8 GtCO2) in 2019.

For China, the expected change is for an increase in emissions of +2.6 % (range of +0.7 % to +4.4 %) in 2019 compared to 2018. This is based on estimated growth in coal (+0.8 %, the main fuel source in China), oil (+6.9 %), and natural gas (+9.1 %) consumption and cement production (+6.3 %). The uncertainty range considers the variations in the difference between preliminary January–September data and final full-year data, lack of monthly data on stock changes, variances in the discrepancies between supply-side and demand data, the uncertainty in the preliminary data used for the 2018 base, and uncertainty in the evolution of the average energy density of each of the fossil fuels.

For the USA, the EIA emissions projection for 2019 combined with cement data from USGS gives a decrease of -1.7 % (range of -3.7 % to +0.3 %) compared to 2018. This is based on separate projections for coal -10.5 %, oil -0.5 %, natural gas +3.5 %, and cement +0.7 %.

For the European Union, our projection for 2019 is for a decrease of -1.7 % (range of -3.4 % to +0.1 %) over 2018. This is based on separate projections for coal of -10.0 %, oil of +0.5 %, natural gas of +3.0 %, and stable cement emissions. Uncertainty is largest in coal, where two alternative methods give divergent estimates.

For India, our projection for 2019 is for an increase of +1.8 % (range of +0.7 % to +3.7 %) over 2018. This is based on separate projections for coal (+2.0 %), oil (+1.5 %), natural gas (+2.5 %), and cement (+0.0 %). The wide uncertainty range reflects an anomalous year: the 2019 monsoon year produced above-average rainfall, particularly in September, with 52 % higher rainfall than the long-term average (IMD, 2019). This heavier rainfall led to both flooded coal mines (Varadhan, 2019) and high hydropower generation (CEA, 2019b). In addition, the Indian economy has slowed rapidly during the year (IMF, 2019b). Furthermore, our forecast for India covers its financial year, April 2019 to March 2020, reflecting the underlying emissions data, adding to uncertainty.

For the rest of the world, the expected growth for 2019 is +0.5 % (range of -0.8 % to +1.8 %). This is computed using the GDP projection for the world excluding China, the USA, the EU, and India of 1.9 % made by the IMF (IMF, 2019a) and a decrease in IFF of -1.4 % yr-1, which is the average from 2009 to 2018. The uncertainty range is based on the standard deviation of the interannual variability in IFF during 2009–2018 of ±0.8 % yr-1 and our estimates of uncertainty in the IMF's GDP forecast of ±0.5 %. The methodology allows independent projections for coal, oil, natural gas, cement, and other components, which add to the total emissions in the rest of the world. The 2019 growth rates for coal were +0.1 % (range -2.9 % to +3.2 %), oil +0.1 % (range -0.9 % to +1.2 %), natural gas +1.3 % (range -0.7 % to +3.4 %), and cement +1.3 % (range -1.2 % to +3.9 %).