Intercomparisons of global greenhouse gas (GHG) emission inventories were carried out (e.g. Cong et al., 2019; Petrescu et al., 2020) to better understand discrepancies and missing or lesser-known sources. The United Nations Framework Convention on Climate Change (UNFCCC) experts, reviewing national GHG inventories on a yearly basis, are keen to know which sectors or fuels need extra attention for an inventory that complies with the principles of transparency, accuracy, consistency, completeness, and comparability (TACCC principles). Discrepancies are often related to the different interpretations of definitions or to missing information (statistics and/or measurements). When focussing on global emission datasets, which are calculated bottom-up following the Intergovernmental Panel on Climate Change (IPCC) 2006 Guidelines for National Greenhouse Gas Inventories, then the discrepancy using different definitions disappears, while the lack of information becomes strongly apparent for certain regions. More information costs time and effort when compiling a global dataset in a consistent way. Therefore, it is of paramount importance to prioritize the additional information needs and the weaknesses in the inventory with sources of large uncertainty in intensity or variability.

The IPCC has been addressing uncertainty from the beginning. Methodology, data, and data sources in this paper were taken from IPCC (2006) guidelines and their refinements (IPCC, 2019). Also, the assumptions are based on IPCC (2006), so all emissions are considered to be fully uncorrelated with activity (and so with sector and type) (i.e. all activities from IPCC (2006) are fully uncorrelated with each other) for the calculation of the uncertainty as well as of the covariance matrices.

While the UNFCCC sticks to national inventories, the atmospheric modelling community needs spatially distributed data. This adds an extra uncertainty to the emission grid maps, not evaluated with the uncertainty in the proxy data but which needs an assessment of the representativeness of the selected proxies for distributing the emissions. The point sources, leading to large plumes, were prioritized for being treated separately with more data. These consisted of super power plants, which are defined as a large power plant or a group of closely located power plants (operating at maximum capacity and availability), causing CO2 plumes from a single grid cell with a CO2 flux ≥ 7.9 × 10-6 kgm-2s-1. According to expert knowledge, the upper-half range of uncertainty for super power plants is not larger than +3.0 %, whereas for small plants whose operation is decided based on day-to-day needs, this can reach up to +15.0 %. In this paper, 30 grid cells of 0.1∘ × 0.1∘ from 12 countries were identified, representing these super power generators (896.7 Mt of the energy sector) and including large plants from China, Russia, and India (for the detailed ranking of the power plant sites as a function of their emission intensity, refer to the Supplement, Sect. S1). The power plant coordinates were checked to avoid the need for an uncertainty related to their positioning. The remaining power plants (not super power generators), over 30 000, could not be checked to the same extent and therefore are recommended in a second emission group.

The uncertainty calculation methodology and initial uncertainty values (i.e. activity data and emission factor uncertainties per CO2-emitting activity) are both taken from IPCC (2006) and its refinements (IPCC, 2019). The following terminology is used to ease the explanation: “activity” – IPCC (2006) activities which result in anthropogenic CO2 emissions in the yearly budget (a long-cycle carbon), “sector” – combination of different activities that are measured or reported together (that have emission budget data), “group” – combination of different sectors that have emission budget data purely for modelling or comparison needs.

In general, uncertainties are calculated in three steps: (i) sector uncertainties (based on emission factors and activity data uncertainties), (ii) annual grouped uncertainties, and (iii) monthly grouped uncertainties. By default, all calculations are performed separately for upper- and lower-half ranges of uncertainties and sector and/or group combined uncertainties, where upper- and lower-half ranges of uncertainty are in percent.

In this example, 2015, the year of the Paris Agreement and reference for several Nationally Determined Contributions, is chosen as a base year to analyse anthropogenic CO2 budgets (i.e. global, regional, national) from different sources (i.e. global statistics, national reports), benefitting the availability of observations (both in situ ground and spaceborne) as well as reported and verified emission inventories.

Following IPCC (2006) and its refinements (IPCC, 2019), starting from the global fossil CO2 grid maps of EDGAR inventory versions 4.3.2 (Janssens-Maenhout et al., 2019) and 4.3.2_FT2015 (Olivier et al., 2016a), for 2012 and 2015, respectively, an updated emission dataset CHE_EDGAR-ECMWF_2015

CHE stands for the CO2 Human Emissions project (CHE, 2021).

The operational IFS model is used to provide global CO2 forecasts using the gridded prior emissions previously described (Agusti-Panareda et al., 2014; Agusti-Panareda et al., 2019). A prototype 4D-Var inverse modelling system is currently under development to monitor anthropogenic CO2 emission using the IFS. There is also an ongoing development to extend the window length beyond 24 h using an ensemble-based methodology.

The uncertainties derived for the seven groups described here have been used to generate an ensemble of forecasts for 2015 based on the operational IFS ensemble system (McNorton et al., 2020). This provides a representation of the model uncertainty and an estimation of the expected signal-to-noise ratio for a future inverse modelling system. Random seeds for each group and country were applied to the normalized log-normal mean μln⁡ and standard deviation σln⁡ to generate emission scaling factors, which were then used for 50 ensemble members.

Primarily, the derived emission uncertainties presented here are envisaged for use as prior errors within atmospheric inversion frameworks. Aggregation of emission sectors into seven groups is required for computational efficiency and to reduce the dimensions of the inverse problem. To resolve collocated emissions, further information is required about spatial correlations and/or co-emitted species (e.g. nitrogen oxides, NOx). Within the IFS inversion prototype, the log-normal normalized standard deviation outlined in the previous section is used to provide the uncertainty values to prevent negative scaling factors.

The new CHE_EDGAR-ECMWF_2015 dataset with anthropogenic fossil CO2 emissions and their uncertainties was compiled and tested at ECMWF. The fossil CO2 emissions include all long-cycle carbon emissions from human activities, such as fossil fuel combustion, industrial processes (e.g. cement), and product use, but excludes emissions from land-use change and forestry. Human CO2 emission inventories were processed into gridded 0.1∘ × 0.1∘ resolution maps to provide an estimate of prior CO2 emissions, aggregated in seven main emissions groups: (1) energy production by super-emitters, (2) energy production by standard emitters, (3) manufacturing, (4) settlements, (5) aviation, (6) other transport at ground level, and (7) others, with an estimation of their uncertainty and covariance. Aggregation of the IPCC activities and sectors into groups was based on similarities between the magnitude of uncertainty, the spatiotemporal correlation, and co-emission factors of each sector. It is assumed that each emission group is fully correlated with itself and fully uncorrelated with any other group (only diagonal values of the 7 × 7 group covariance matrix for the atmospheric transport model are non-zero and equal to log-normal variance). The CHE_EDGAR-ECMWF_2015 data are freely available (10.5281/zenodo.3967439; Choulga et al., 2020) and consist of 11 grid maps in NetCDF format and one Excel file with information on anthropogenic CO2 emissions and their uncertainties. For detailed information on each file see Table 3.

Table 4 shows a step-by-step example of how yearly uncertainties are calculated, and Fig. 2 shows plotted probability density functions based on computed log-normal parameters. The example shows calculations for the TRANSPORT group that consists of several emission sectors. The example shows two countries with different statistical infrastructure development levels (the country with well-developed statistical infrastructure is Germany, and the country with less well-developed statistical infrastructure is the Russian Federation) and significant differences in emission budgets.

Calculated yearly and monthly uncertainties per country and emission group were assigned to each grid box on the global map. National uncertainties were applied uniformly across each country. Figure 3 shows an example of the upper and lower uncertainty limits of anthropogenic CO2 emission flux for the TRANSPORT group. It should be noted that uncertainties related to the spatial distribution (representativeness of the proxy data and their uncertainty) should be much higher than the ones presented in this study. This research does not address uncertainties related to the spatial distribution. In the future it is planned to address these uncertainties too, for example by following Oda et al. (2019) to characterize spatial patterns of the disaggregation errors in the emission maps.

Calculated emissions and uncertainties in fossil CO2 have been compared to other global datasets based on the country-specific data reported to UNFCCC and on fuel-specific data reported in the energy statistics of IEA. The global values and their uncertainty at a 2σ range for the CHE_EDGAR-ECMWF_2015 dataset show a lowest value of -4.7 %/+9.6 %, or ±7.1 %; see Table 5. This result might be attributed to the methodology, in particular considering that (i) all calculations were done at the country level and then aggregated to the global level assuming no correlation following IPCC (2006); (ii) all calculations were done separately for upper- and lower-half ranges of uncertainty to preserve original information with asymmetric confidence intervals for large uncertainties (not required for the Approach 1 described in IPCC (2006), in which only the higher uncertainty value of the asymmetric interval should be used, leading to artificial inflation of uncertainty upper or lower limit); and (iii) in this study proxy grid map uncertainties are not considered.

The contribution of each emission group to the total uncertainty per grid cell is assessed. Figures 4–7 show which group contributes the most to the total uncertainty per grid cell. The TRANSPORT group contributes most to the grid cell uncertainty over the Unites States of America (due to road and off-road transport) and over the ocean (due to shipping). The AVIATION group contributes most over main flight routes all over the globe. The OTHER group contributes the most over agricultural areas and regions with oil refineries and transformation industry and fuel exploitation. The MANUFACTURING group contributes most over industrial areas (e.g. in Vietnam and Bangladesh). The ENERGY_A (and ENERGY_S) group contributes the most over power plant (and super power plant) location grid cells (e.g. South Africa). The SETTLEMENTS group contributes the most to the grid cell uncertainty over either very densely or very sparsely populated areas.

Also, some specific geographical areas are analysed: chosen to be among the most emitting in total or per emission group and the most typical or most influential for a certain region. A list of these geographical entities and development levels of their statistical infrastructures is presented in Table 6.

In order to see how the development level of country's or geographical entity's statistical infrastructure influences the emission uncertainty in that country or geographical entity itself and (possibly) the globe, uncertainty calculations for selected entities were performed twice – with their original and switched types (i.e. a country with a well-developed statistical infrastructure becomes a country with a less well-developed statistical infrastructure and vice versa). More details on a geographical entity's statistical infrastructure development level (e.g. how it was determined) are given in the Supplement, Sect. S5. Figure 8 shows sectoral emission budgets, uncertainties, and contributions in percentage to the total uncertainty in a country or geographical entity with its original and switched statistical infrastructure development levels. The biggest impact of development level change occurs for countries with larger emission budgets. On average, total uncertainties in selected countries (see Table 6) changed by 1 %–2 %; group uncertainties changed in line with prior uncertainties and countries' emission budgets, as reported in Table 7.

Alterations in some countries' (e.g. Germany, France) statistical infrastructure's development levels lead to changes in uncertainties in Europe (28 members until end of 2019), with the most substantial change for the SETTLEMENTS group (e.g. 2.5 % and 1.0 %, respectively). Huge changes (> 10.0 %) in Europe's (28 members until end of 2019) AVIATION group's uncertainty percentage value can be due to the variation in statistical infrastructure development level for Germany, United Kingdom, France, or Spain, though this group's contribution to Europe's total uncertainty remains negligible. Alterations in statistical infrastructure development levels for China or the United States of America modify even global uncertainties because these countries substantially contribute to the total global emission budget; e.g. China emits ∼ 1/3 of the global anthropogenic CO2 budget and can change global total uncertainty up to 0.5 %.

To increase the emission temporal resolution, monthly emissions and their uncertainties were calculated combining yearly emissions, monthly multiplication factors, and adapted uncertainty calculation methodology (see Sect. 2.2). Prior yearly uncertainties were multiplied by a dimensionless uncertainty-boosting parameter α (same value for each month) to compute prior monthly uncertainties, which were further used together with monthly emission budgets for countries' monthly uncertainty calculation. Monthly uncertainties (just like yearly uncertainties) are determined by empirical formulas from IPCC (2006) with monthly emission budgets (weighted with the total number of days in a month). The dimensionless uncertainty-boosting parameter α is applied; see Table 8 for most common values for countries with well- and less well-developed statistical infrastructures per sector. Boosting parameters become active (α≠1) when absolute uncertainty values are ≥ 25.0 %, and α increases with the increase in absolute uncertainty following a third-order polynomial. For lower-half ranges of uncertainty, α has larger values and steeper growth than for upper-half ranges of uncertainty (e.g. -25.0 %  α = 1.5 and -124.0 %  α = 2.6, +25.0 %  α = 0.8 and +124.0 %  α = 1.2;  means “corresponds to”), and α behaves in the same way for countries with well- and less well-developed statistical infrastructures. Discrepancies in a different geographical entity's (country's) boosting parameters might be for several reasons. The main ones are (i) sector emissions were zero (e.g. super power plant emissions of the energy sector had no emissions), and (ii) sector uncertainties were ≥ 50.0 % and needed to be adapted accordingly to log-normal distribution (this is the case for the agricultural soils sector with prior uncertainties -70.7/+0.0 % for countries with well- and less well-developed statistical infrastructures; discrepancies from Table 8 for agricultural soils are France – α = 1.8/3.1, UK – 1.8/7.2, China – 1.8/8.4, Japan – 1.8/10.8, Brazil – 1.8/0.0, and the Russian Federation – 1.8/5.6, where the first value is for the lower-half range of uncertainty, and the second value is for the upper-half range of uncertainty).

In general, Brazil, Indonesia, and India have a very weak yearly cycle with quite high monthly uncertainties throughout the year. The globe, Europe (28 members until end of 2019), Germany, Spain, France, United Kingdom, Poland, China, Japan, the Russian Federation, and the United States of America have more pronounced yearly cycles, most significant for the SETTLEMENTS and ENERGY_A (and ENERGY_S where present) groups and less significant for the AVIATION, TRANSPORT, and MANUFACTURING groups. This is in line with the monthly profiles applied in EDGARv4.3.2 for northern and southern temperate zones and the Equator; see Janssens-Maenhout et al. (2019). In the summer months for the northern temperate zone, a strong decrease in SETTLEMENTS and ENERGY_A (and ENERGY_S where present) group emissions was observed, with a light decrease in MANUFACTURING group emissions and a light increase in AVIATION and TRANSPORT group emissions. This corresponds rather well to the assumption that most of the population in the Northern Hemisphere heat their houses during winter and take holidays and travel more during summer.

The CHE_EDGAR-ECMWF_2015 dataset containing seven global gridded fossil CO2 emission flux maps and country- and group-specific emission budgets and uncertainties have been assessed with independent data. Global emission budget values from different datasets are almost never the same; therefore it is important to first identify why estimates differ between datasets. Datasets might use the same country-level information as primary input, though differences in inclusion, interpretation, and treatment of that data lead to diverse results in emissions. It is necessary to try to harmonize data inclusion or omission across datasets to have more clarity in the discrepancies.

For Europe (28 members until end of 2019), Germany, Spain, France, United Kingdom, Poland, Japan, the Russian Federation, and the United States of America, emission and uncertainty data were collected from UNFCCC NIR. The aggregation of the IPCC (2006) activity-specific emissions and uncertainties into seven groups was done assuming no correlation, following IPCC (2006). Although IPCC (2006) has a standard table to report GHG emissions, uncertainties can be reported in less detail by a more general category (e.g. 2.D only instead of 2.D.1, 2.D.2, 2.D.3, 2.D.4), meaning information “harmonization” required lots of careful time-consuming country-specific technical work by the authors of this paper.

The Netherlands Organisation for Applied Scientific Research (TNO) has prepared the first version of their GHG and co-emitted species emission database (TNO_GHGco_v1.1) that covers the entire European domain (at 0.1∘ × 0.05∘ resolution), including CO2 (distinguishing between fossil fuel and biofuel). Initial emission data are from the UNFCCC (common reporting format, CRF, tables) and the European Monitoring and Evaluation Programme (EMEP) of the Centre on Emission Inventories and Projections (CEIP) for air pollutants. These data were harmonized; checked for gaps, errors, and inconsistencies; and (where needed) replaced or completed using emission data from the Greenhouse Gas and Air Pollution Interactions and Synergies (GAINS) model (Amann et al., 2011). Moreover, inland shipping emissions were replaced with the TNO's own estimates, and sea shipping is based on automatic identification system (AIS)-based tracks. Expert judgement is used to assess the quality of each data source and to make choices on which source to use. The resulting emissions were checked in detail regarding their absolute value and trends (Kuenen et al., 2014). In this study emission budgets from 30 TNO sectors (Ingrid Super, Jeroen Kuenen, Antoon Visschedijk, and Hugo Denier van der Gon​​​​​​​, personal communication, February 2020), and prior uncertainties calculated from IPCC (2006) and its refinements (IPCC, 2019) are used. In addition, the TNO has provided Tier 2 (Monte Carlo approach) uncertainties based on the same budgets and uncertainties from submitted NIR reports based on a Tier 1 approach. The Monte Carlo simulations were done at the highest detail level (nomenclature for reporting (NFR) sector and fuel type) assuming correlations between certain sectors (for more information see Super et al., 2020), and then emissions were aggregated to groups assuming no correlation.

Figure 9 shows emission budgets and uncertainties in megatonnes and contributions in percent to the total geographical entity's uncertainty for Europe (28 members until end of 2019), Germany, France, and United Kingdom with their original statistical infrastructure development types based on data from CHE_EDGAR-ECMWF_2015 (in pink), UNFCCC (in yellow), and TNO_GHGco_v1.1 Tier 1 (in blue) and Tier 2 (in green); plots for Spain and Poland are not shown here. Out of the four different sources, usually UNFCCC and TNO_GHGco_v1.1 Tier 2 uncertainties are the lowest ones and CHE_EDGAR-ECMWF_2015 the highest one. It should be noted that (i) UNFCCC uncertainties were aggregated to groups individually per country as uncertainties are reported in a rather free form and thus could be aggregated from different levels of precision; (ii) uncertainties for Europe (28 members until end of 2019) from CHE_EDGAR-ECMWF_2015 are rather low as they were calculated by aggregating information from 28 countries; and (iii) differences in uncertainties in CHE_EDGAR-ECMWF_2015 with other sources, especially in fuel-dependent emission groups, might be due to biofuels or other fuels (e.g. wood and/or coal for residential heating). Differences in uncertainties between CHE_EDGAR-ECMWF_2015 and TNO_GHGco_v1.1 Tier 1 show additional value in more detailed emission budget knowledge (i.e. where absence of the uncertain glass production activity in the non-metallic mineral production sector decreases overall uncertainty). Differences in uncertainties between TNO_GHGco_v1.1 Tier 1 and TNO_GHGco_v1.1 Tier 2 show additional value in an advanced calculation technique using a more sophisticated, data-demanding Monte Carlo approach instead of simple error propagation. Overall, there is quite good agreement in emission budgets and uncertainties from different sources of emission data.

Emission budgets, Tier 1 uncertainties, and contributions in percentage to the total geographical entity's uncertainty for Japan, the Russian Federation, and the United States of America from CHE_EDGAR-ECMWF_2015 could be compared only with UNFCCC data (plots not shown here). UNFCCC uncertainties are usually lower than the ones calculated in this study. The main reason for that is the use of country-specific emission data and activity data uncertainties, which are lower than default values suggested by IPCC (2006) and its refinements (IPCC, 2019). Only for the fuel-dependent groups (e.g. AVIATION) might UNFCCC uncertainties be higher than in this study as rather uncertain biofuels might be taken into account (note: CHE_EDGAR-ECMWF_2015 does not take biofuels into account). Also, emission budgets reported to the UNFCCC show some differences from the ones from CHE_EDGAR-ECMWF_2015. For Japan, group budgets agree rather well, and the total budget difference is ∼ 1.0 %. For the Russian Federation, major differences are in the ENERGY_A (and ENERGY_S) and MANUFACTURING groups, which results in a ∼ 6.0 % higher total budget of CHE_EDGAR-ECMWF_2015. For the United States of America, major differences are ∼ 200 Mt and ∼ 100 Mt for the SETTLEMENTS and OTHER groups, respectively, which results in a ∼ 4.0 % higher total budget than based on UNFCCC data. Recent comparison of different gridded global datasets by Andrew (2020) pointed out that only a few of these datasets provide quantitative uncertainty assessment; see the summary in Table 5. Compared to other global emission uncertainty values, CHE_EDGAR-ECMWF_2015 shows the lowest values mainly due to the aggregation technique.

As mentioned above, for transport-related emission uncertainty calculations only the most typical fuel type (for aviation, railways, shipping) and emission factor uncertainty (for road and off-road transport) were used because detailed fuel consumption information per IPCC activity was not available for this study. The EDGAR dataset development team do have specific fuel information globally, which could be used for uncertainty calculation. The EDGAR dataset with incorporated fuel-specific activity data and emission factor uncertainties and Tier 1 approach for uncertainty calculation (see Supplement, Sect. S6) is hereinafter referred to as EDGAR-JRC. Country budget uncertainties were calculated by considering “full fuel” splitting and by taking into consideration the assumption that the emission factors, from sectors sharing the same fuel, are fully correlated. This latter assumption transformed the sum in quadrature of Eq. () into a linear summation (Bond et al., 2004; Bergamaschi et al., 2015). The uncertainty in activity data was set in accordance with IPCC (2006) guidelines, in the range of 5.0 % to 10.0 % for combustion activities; 10.0 % to 20.0 % for combustion in the residential sector; 25.0 % for bunker fuels in marine transport; and 35.0 % for industrial processes of cement, lime, glass, and ammonia (the range of uncertainty values refers to the 95 % confidence interval of the mean, assigned separately to countries with well- and less well-developed statistical infrastructures). Uncertainties from the EDGAR-JRC dataset aggregated to the group level were compared with the ones from CHE_EDGAR-ECMWF_2015; see Table 9 for Europe (28 members until end of 2019) and all world countries and Table S8 from the Supplement, Sect. S6, for all the remaining geographical entities from Table 6. Emission uncertainties from EDGAR-JRC reflect the share of fuel composing the emission of each country and are in line with the estimates by CHE_EDGAR-ECMWF_2015 for those countries where the fuel-composite uncertainty is closer to the average value assigned. Uncertainties calculated with fuel-specific data are usually smaller; when prevailing fuel coincides with a typical fuel type from CHE_EDGAR-ECMWF_2015, emission group uncertainties from both sources are quite similar. It should be noted that (i) countries' total uncertainty is higher in EDGAR-JRC due to the aggregation technique (full correlation is assumed), and (ii) AVIATION group uncertainties are higher in EDGAR-JRC due to prior aggregation of all three aviation connected sectors (cruise, climbing and descent, and landing and take-off).

The uncertainties derived in this study are an upper bound of the uncertainty estimation compared to the uncertainties calculated with more detailed information, as done by the countries and reported to UNFCCC or to the uncertainties calculated with fuel-specific data. Even though sometimes differences might be quite high in percentage values, they are usually quite small in megatonnes.

The gridded emissions are required input to the ECMWF IFS model used to simulate atmospheric CO2 globally (Agusti-Panareda et al., 2014; Agusti-Panareda et al., 2019). Ideally, uncertainties at a grid cell level would be preferred by the models in general, which is a difficult time-consuming task. To check the usefulness of the information-intensive derivation of uncertainties at a grid cell level, it was decided to run some experiments. High-resolution (∼ 25 km horizontal resolution, 137 vertical levels) simulations with the ECMWF IFS model have been performed to assess the atmospheric sensitivity to fully resolved emissions compared to nationally smoothed (global emission budget is conserved); see Fig. 10.

Model simulations were performed for January 2015 with 3-hourly output. Anthropogenic, fire, ocean, and biogenic fluxes (large-scale model bias mitigated by the biogenic CO2 flux adjustment scheme, BFAS) were considered. For the full model configuration description see McNorton et al. (2020). It was noted that point sources (e.g. power plants, factories) can be easily detected if they comprise a substantial part of countries' total emission budget (e.g. in South Africa). If point sources are distributed homogeneously over the country, and other areal sources are rather high as well, it becomes difficult to detect one extra or missing emitting hotspot (e.g. in Germany). China is a very good example for both cases as its western part has very few hotspots, and they are easy to detect over the low-emitting background. Its eastern part, however, has lots of hotspots and high-emitting areal sources, making it almost impossible to disentangle emissions from a single power plant or factory from the high-emitting background. Differences of several parts per million are detected over multiple regions, highlighting the importance of using high-resolution spatially resolved emissions. With increase in both flux and transport model resolutions, these differences are expected to increase further with steeper atmospheric CO2 gradients.