The presented uncertainties in the reported emissions of the individual countries and the EU27+UK bloc were calculated by using the methods and data used to compile the official GHG emission uncertainties that are reported by the EU under the UNFCCC (2022a). The EU uncertainty analysis reported in the bloc's national inventory report (NIR) is based on country-level, approach 1 uncertainty estimates (IPCC, 2006, Vol. 1, Chap. 3) that are reported by EU member states, Iceland, and the United Kingdom under Article 7(1)(p) of EU (2013). These country-level uncertainty estimates are typically reported at the beginning of a submission cycle and are not always revised with updated CRF submissions later in the submission cycle. Furthermore, the compiled uncertainties of some countries are incomplete (e.g., uncertainties not estimated for LULUCF and/or indirect CO2 emissions; certain subsector emissions are confidential), and the sector and gas resolution at which uncertainties are provided vary between the countries. The EU inventory team therefore implements a procedure to harmonize and gap-fill these uncertainty estimates. A processing routine reads the individual country uncertainty files that are preformatted manually to assign consistent sector and gas labels to the respective estimates of emissions/removals and uncertainties. The uncertainty values are then aggregated to a common sector resolution, at which the emissions and removals reported in the uncertainty tables of the countries are then replaced with the respective values from the final CRF tables of the countries. Due to the issue of incompleteness mentioned above, the country-level data are then screened to identify residual GHG emissions and removals for which no uncertainty estimates have been provided. Where sectors are partially complete, the residual net emission is quantified in CO2 equivalents and incorporated. An uncertainty is then estimated, by calculating the overall sector uncertainty of the sources and sinks that were included in that country's reported uncertainty estimates and assigning this percentage average to the residual net emission. In cases where for certain sectors no uncertainties have been provided at all (e.g., indirect CO2 emissions, LULUCF), an average (median) sector uncertainty in percent is calculated from all the countries for which complete sectoral emissions and uncertainties were reported, and this average uncertainty is assigned to the country's sector GHG total reported in its final CRF tables.

The country-level uncertainties presented in this paper, have been compiled using this same processing routine and using the uncertainties and CRF data reported by the countries in the 2021 submission. However, here the method has been expanded to gap-fill at the individual greenhouse gas level (CO2 emissions and removals only) rather than at the aggregate GHG level. Furthermore, the expanded method here assigns the subsectoral uncertainties to the emissions and removals of the entire time series (1990–2019), rather than just the base year and latest year of the respective time series. This allows uncertainties to be sensitive to the subsectoral contributions to sectoral and national total emissions, which of course change over time. For each year of the time series, uncertainties in the total and sectoral CO2 emissions are calculated using Gaussian error propagation, by summing the respective subsectoral uncertainties (expressed in kt CO2) in quadrature and assuming no error correlation. In contrast, for the EU27+UK bloc, uncertainties in the total and sectoral CO2 emissions were calculated to take into account error correlations between the respective country estimates at the subsector level. This was done by applying the same methods and assumptions described in the 2022 EU NIR (UNFCCC, 2022a). The subsector resolution applied for gap-filling allows the routine to access respective data on emission factors from CRF table “Summary 3” and apply correlation coefficients (r) when aggregating the uncertainties. For a given subsector, it is assumed that the errors of countries using default factors are completely correlated (r=1), while errors of countries using country-specific factors are assumed uncorrelated (r=0). For countries using a mix of default and country-specific factors at the given subsector level, it is assumed that these errors are partially correlated (r=0.5) with one another and with the errors of countries using the default factors only.

Based on these correlation assumptions, the routine then aggregates CO2 emissions/removals and uncertainties for the specified subsector resolution at the EU27+UK level. Uncertainties at sector total level are then aggregated from the subsector estimates assuming no correlation between subsectors. However, for countries reporting very coarse resolution estimates (e.g., total sector CO2 emissions/removals) or where the sector has been partially or completely gap-filled, it is assumed that these uncertainties are partially correlated (r=0.5) with one another and with the other reported subsector level estimates. Level uncertainties on the total EU27+UK CO2 emissions and removals (with and without LULUCF) are then aggregated from the sector estimates assuming no error correlation between sectors.

Note that the above procedure does not apply to LULUCF categories (FL, CL, and GL). Estimates for these values were taken directly from the EU NIR (2021) without gap-filling or consideration of correlations. An uncertainty greater than 100 % implies that either a sink or a source is possible. As the values are given for only 1 single year, this value is applied uniformly across the whole time series.

For further details of all datasets, see Andrew (2020).

The UNFCCC NGHGI CO2 emissions/removals include estimates from five key sectors for the EU27+UK: 1 Energy, 2 Industrial processes and product use (IPPU), 3 Agriculture, 4 LULUCF, and 5 Waste. The tiers method that a country applies depends on the national circumstances and the individual conditions of the land, which explains the variability of uncertainties among the sector itself as well as among EU countries. This annual published dataset includes all CO2 emission sources for those countries, as well as for most countries for the period 1990 to year t-2. Some eastern European countries' submissions began in the 1980s.

Information on uncertainty calculation in the NGHGIs is found above in the general section on the NGHGI.

The first edition of the Emissions Database for Global Atmospheric Research was published in 1995. The dataset now includes almost all sources of fossil CO2 emissions, is updated annually, and reports data for 1970 to year n-1. Estimates for v6.0 are provided by sector. Emissions are estimated fully based on statistical data from 1970 till 2018 https://data.jrc.ec.europa.eu/dataset/97a67d67-c62e-4826-b873-9d972c4f670b (last access: 16 September 2023).

Uncertainties. EDGAR uses emission factors (EFs) and activity data (AD) to estimate emissions. Both EFs and AD are uncertain to some degree, and when combined, their uncertainties need to be combined too. To estimate EDGAR's uncertainties (stemming from a lack of knowledge of the true value of the EF and AD), the methodology devised by IPCC (2006, Chap. 3) is adopted (Solazzo et al., 2021), including the use of default uncertainties. The overall relative uncertainty in emissions is thus given by simple error propagation for the product of two variables, where the overall relative uncertainty is the square root of the sum of squares of the relative uncertainties of the EF and AD. A lognormal probability distribution function is assumed in order to avoid negative values, and uncertainties are reported as the 95 % confidence interval according to IPCC (2006, Chap. 3, Eq. 3.7). For emission uncertainty in the range 50 % to 230 %, a correction factor is adopted as suggested by Frey et al. (2003) and IPCC (2006, Chap. 3, Eq. 3.4). Uncertainties are published in Solazzo et al. (2021).

BP releases its “Statistical Review of World Energy” annually in June, the first report being published in 1952. Primarily an energy dataset, BP also includes estimates of fossil fuel CO2 emissions derived from its energy data (BP, 2011, 2017). The emission estimates are totals for each country starting in 1965 to year n-1.

The original Carbon Dioxide Information Analysis Center included a fossil CO2 emissions dataset that was long known as CDIAC. This dataset is now produced at Appalachian State University and has been renamed CDIAC-FF (CDIAC, 2022). It includes emissions from fossil fuels (including gas flaring) and cement production from 1751 to year n-3. Fossil fuel emissions are derived from UN energy statistics, and cement emissions are from USGS production data.

The US Energy Information Administration publishes international energy statistics and from these derives estimates of CO2 emissions from energy combustion based on energy consumption. Data are currently available for the period 1980–2016.

The International Energy Agency publishes international energy statistics and from these derives estimates of CO2 emissions from energy combustion. In addition, the IEA also estimates emissions from the use of coal in the iron and steel industry, while not providing any other IPPU estimates. Emission estimates start in 1960 for OECD members and 1971 for non-members, and they run through to year n-1 for OECD members' totals and year n-2 for members' details and non-members. Most subsector-level data from the IEA are available for a fee, although some high-level emissions data can be accessed free of charge.

The Global Carbon Project includes estimates of fossil CO2 emissions in its annual global carbon budget publication. These include emissions from fossil fuels and cement production for the period 1750 to year n-1. GCP's fossil CO2 dataset was once entirely derived solely from CDIAC's dataset, with some extension using BP data, but this has since changed as described in Andrew and Peters (2022).

The Community Emissions Data System has included estimates of fossil CO2 emissions since 2018, with an irregular update cycle (CEDS, 2022). Energy data are directly from IEA, but emissions are scaled to higher-priority sources, including national inventories. Almost all emission sources are included, and estimates are published for the period 1750 to year n-1. Estimates are provided by subsector.

The PRIMAP-hist dataset combines several published datasets to create a comprehensive set of greenhouse gas emission pathways for every country and GHG covered by the Kyoto Protocol, covering the years 1850 to 2018, and all UNFCCC (United Nations Framework Convention on Climate Change) member states as well as most non-UNFCCC territories. The data resolve the main IPCC (Intergovernmental Panel on Climate Change) 2006 categories. For CO2, CH4, and N2O, subsector data for Energy, industrial processes and product use (IPPU), and Agriculture are available. Due to data availability and methodological issues, version 2.2 of the PRIMAP-hist dataset does not include emissions from land use, land use change, and forestry (LULUCF). More info is available at https://zenodo.org/record/4479172#.YUsc6p0zbIU (last access: March 2023).

CIF-CHIMERE is used for both CO2 land and CO2 fossil emission estimates, and this section only describes the CO2 fossil estimates. The product is explained in more detail by Fortems-Cheiney and Broquet (2021).

Results from previous atmospheric inversions of the European fossil CO2 emissions indicated that there were much larger uncertainties associated with the assimilation of CO data than with that of NO2 data for such a purpose (Konovalov et al., 2016; Konovalov and Lvova, 2018). In this context, we have developed an atmospheric inversion configuration quantifying monthly to annual budgets of the national emissions of fossil CO2 in Europe based on the assimilation of the long-term series of NO2 spaceborne observations, the Community Inversion Framework (CIF), the CHIMERE regional chemical transport model (CTM), corrections to the TNO-GHGco-v3 inventory of NOx anthropogenic emissions at 0.5∘ horizontal resolution, and the conversion of NOx anthropogenic emission estimates into CO2 fossil emission estimates. For the first time, to our knowledge, variational regional inversions have been performed to estimate the European CO2 fossil emissions using NOx emissions from Ozone Monitoring Instrument (OMI) satellite observations. Particular attention is paid to the analysis assessing the consistency between the fossil CO2 emission estimates from our processing chain with the fossil CO2 emission budgets provided by the TNO-GHGco-v3 inventory based on the emissions reported by countries to UNFCCC, which are assumed to be accurate in Europe. The algorithm first optimizes NOx emissions and then assumes a fixed ratio of NOx to fossil CO2 emissions. However, long-term plans include the simultaneous inversion of all three gasses (CO2, NO2, and CO).

The analysis is conducted over the period 2005 to 2020. CHIMERE is run over a 0.5∘ × 0.5∘ regular grid and 17 vertical layers, from the surface to 200 hPa, with 8 layers within the first 2 km. The domain includes 101 (longitude) × 85 (latitude) grid cells (15.25∘ W–35.75∘ E and 31.75–74.25∘ N) and covers Europe. CHIMERE is driven by the European Centre for Medium-Range Weather Forecasts (ECMWF) meteorological forecast (Owens and Hewson, 2018). The chemical scheme used in CHIMERE is MELCHIOR-2, with more than 100 reactions (Lattuati, 1997; CHIMERE 2017), including 24 for inorganic chemistry. Climatological values from the LMDZ-INCA global model (Szopa et al., 2009) are used to prescribe mole fractions at the lateral and top boundaries and the initial atmospheric composition in the domain. Considering the short NO2 lifetime, we do not consider its import from outside the domain: its boundary conditions are set to zero. Nevertheless, we take into account peroxyacetyl nitrate (PAN) for the large-scale transport of NOx. Due to atmospheric chemistry, it represents an important NOx reservoir, and it has a significant impact on the regional NO2 tropospheric columns observed by OMI.

Several critical aspects of this workflow need to be highlighted: (i) Fortems-Cheiney and Broquet (2021) have not yet reported estimates of the uncertainty in the fossil CO2 emissions (this requires the derivation of the uncertainties in the NOx emission inversions and in the NOx-to-FFCO2 emission conversion) and (ii) the fossil CO2 emission budgets provided by the TNO-GHGco-v3 inventory are based on the emissions reported by countries to UNFCCC, which are assumed to be accurate in Europe; therefore, the NOx inversion prior estimate is consistent with the inventory estimates (with respect to the NOx-to-FFCO2 emission conversion used to infer fossil CO2 emissions from the NOx inversions).

Uncertainty. There is no uncertainty estimate currently available for this product.

For the biogenic CO2 emissions from LULUCF (Sector 4 in the terminology of the NGHGIs), methods for the estimation of CO2 removals differ enormously among countries and land use categories. Each country uses its own country-specific method which takes into account specific national circumstances (as long as they are in accordance with the 2006 IPCC guidelines), as well as IPCC default values, which are a “compromise between the level of detail that would be needed to create the most accurate estimates for each country and the input data likely to be available or readily obtainable in most countries” (Vol. 1, Chap. 3 of IPCC, 2006). They may, therefore, result in higher uncertainties. The EU GHG inventory underlies the assumption that the individual use of national country-specific methods leads to more accurate GHG estimates than the implementation of a single EU-wide approach (UNFCCC, 2018). Key categories for the EU27 are 4.A.1 Forest Land: land use CO2, 4.A.2. Forest Land: land use CO2, 4.B.1 Cropland: land use CO2, 4.B.2 Cropland: land use CO2, 4.C.1 Grassland: land use CO2, 4.C.2 Grassland: land use CO2, 4.D.1 Wetlands: land use CO2, 4.E.2 Settlements: land use CO2, and 4.G Harvested wood products: wood product CO2. The tiered method that a country applies depends on the national circumstances and the individual conditions of the land, which explains the variability of uncertainties among the sector itself as well as among EU countries.

Table A4 shows the mean values of all LULUCF categories for the EU27+UK NGHGI (2021). The contribution is calculated as the percentage of the sum of the absolute values of all the categories, in order to account for differing signs.

Uncertainty. Methodology for the NGHGI UNFCCC submissions are based on Chap. 3 of 2006 IPCC Guidelines for National Greenhouse Gas Inventories and is the same as described in Appendix A2.

ORCHIDEE is a general ecosystem model designed to be coupled to an atmospheric model in the context of modeling the entire Earth system. As such, ORCHIDEE calculates its prognostic variables (i.e., a multitude of carbon, water, and energy fluxes) from the following environmental drivers: air temperature, wind speed, solar radiation, air humidity, precipitation, and atmospheric CO2 mole fraction. As the run progresses, vegetation grows on each pixel, divided into 15 generic types (e.g., broadleaf temperate forests, C3 crops), which cycle carbon between the soil, land surface, and atmosphere through such processes such as photosynthesis, litter fall, and decay. Limited human activities are included through the form of generic wood and crop harvests, which remove aboveground biomass on an annual basis. The version reported here, ORCHIDEE-N v3, includes a dynamic nitrogen cycle coupled to the vegetation carbon cycle which results in, among other things, limitations on photosynthesis in nitrogen-poor environments (Vuichard et al., 2019)

Among other environmental indicators, ORCHIDEE simulates positive and negative CO2 emissions from plant uptake; soil decomposition; and harvests across forests, grasslands, and croplands. Activity data are based on land use and land cover maps. For VERIFY, pixel land cover/land use fractions were based on a combination of the land use map LUH2v2h and the land cover project of the Climate Change Initiative (CCI) program of the European Space Agency (ESA). The latter is based on purely remotely sensed methods, while the former makes use of national harvest data from the UN Food and Agricultural Organization.

LUH2v2-ESA CCI: quoted directly from Lurton et al. (2020):

We describe here the input data and algorithms used to create the land cover maps specific for our CMIP6 [Coupled Model Intercomparison Project Phase 6] simulations using the historical/future reconstruction of land use states provided as reference datasets for CMIP6 within the land use harmonization database LUH2v2h (Hurtt et al., 2020). More details are provided on the devoted web page (https://orchidas.lsce.ipsl.fr/dev/lccci, last access: 16 September 2023) which shows further tabular, graphical and statistical data. The overall approach relies on the combination of the LUH2v2 data with present-day land cover distribution derived from satellite observations for the past decades. The main task consists in allocating the land use types from LUH2v2 in the different PFTs [plant functional types] for the historical period and the future scenarios. The terrestrial biospheric vegetation in each grid cell is defined as the PFT distribution derived from the ESA-CCI land cover product for the year 2010 to which pasture fraction and crop fraction from LUH2v2 (for the year 2010) have been subtracted from grass and crop PFTs. This characterization of the terrestrial biospheric vegetation in terms of PFT distribution is assumed invariant in time and is used for both the historical period and the different future scenarios.

Uncertainty. In the ORCHIDEE model, uncertainty arises from three primary sources: parameters, forcing data (including spatial and temporal resolution), and model structure. Some researchers argue that the initial state of the model (i.e., the values of the various carbon and water pools at the beginning of the production run, following model spinup) represents a fourth area. However, the initial state of this version of ORCHIDEE is defined by its equilibrium state and therefore a strong function of the parameters, forcing data, and model structure, with the only independent choice being the target year of the initial state. Out of the three primary areas of uncertainty, the climate forcing data are dictated by the VERIFY project itself, thus removing that source from explaining observed differences among the models, although it can still contribute to uncertainty between the ORCHIDEE results and the national inventories. The land use/land cover maps, another major source of uncertainty for ORCHIDEE carbon fluxes, have also been harmonized to a large extent between the bottom-up carbon budget models in the project. Parameter uncertainty and model structure thus represent the two largest sources of potential disagreement between ORCHIDEE and the other bottom-up carbon budget models. Computational cost prevents a full characterization of uncertainty due to parameter selection in ORCHIDEE (and dynamic global vegetation models in general), and uncertainties in model structure require the use of multiple models of the same type but including different physical processes. Such a comparison has not been done in the context of VERIFY, although the results from the TRENDY suite of models shown in Fig. 5 give a good indication of this. Figure A3 shows a small influence from the nitrogen forcing, likely because the European nitrogen forcing is only available from 1995–2018 and ORCHIDEE carries out almost 500 years of simulation prior to this point. Many major carbon pools (i.e., woody biomass, soil carbon) have built up a large amount of inertia over that time and are unlikely to undergo dramatic changes for any realistic forcing over the past. A similar conclusion can be reached from simulations ORCHIDEE-V2019 and ORCHIDEE-V2021 in Fig. A3, which only differ in meteorological forcing from 1981–2020.

CABLE-POP (Haverd et al., 2018) is a global terrestrial biosphere model developed around a core biogeophysics module (Wang and Leuning, 1998) and a biogeochemistry module including cycles of nitrogen and phosphorus (Wang et al., 2010). Only nitrogen cycling was turned on for the present simulations. The model also includes modules simulating woody demography (Haverd et al., 2013) as well as land use change and land management (Haverd et al., 2018). The model distinguishes seven plant functional types which can co-occur in a given grid cell. CABLE-POP does not simulate (natural) dynamic vegetation, and the distribution and cover fraction of PFTs is only affected by land use change. Forest demography (establishment, age class distribution, mortality) is accounted for in the simulations, as are natural disturbances and forest management (wood harvest). For the simulations described here, a baseline land cover map was created from the HILDA+ dataset for the year 1901, and vegetation classes in the dataset were reclassified to correspond to PFTs represented in CABLE-POP. Land use transitions and land management (harvest) were prescribed from the LUH2v2h dataset over the entire simulation period. Crops and pastures are treated as C3 grasses but are subject to agricultural harvest fluxes as given by LUH2v2h. The use of HILDA+ data for the land cover distribution and the LUH2v2h for the representation of land cover/land use change likely introduced additional uncertainties resulting from a potential mismatch between the two datasets.

The Carbon Budget Model, developed by the Canadian Forest Service (CBM-CFS3), can simulate the historical and future stand- and landscape-level C dynamics under different scenarios of harvest and natural disturbances (fires, storms), according to the standards described by the IPCC (Kurz et al., 2009). Since 2009, the CBM has been tested and validated by the Joint Research Centre of the European Commission (EC-JRC), and adapted to the European forests. It is currently applied to 26 EU member states, both at country and NUTS2 levels (Pilli et al., 2016).

Based on the model framework, each stand is described by area, age, and land use classes and up to 10 classifiers based on administrative and ecological information and on silvicultural parameters (such as forest composition and management strategy). A set of yield tables define the merchantable volume production for each species, while species-specific allometric equations convert merchantable volume production into aboveground biomass at stand level. At the end of each year, the model provides data on the net primary production (NPP), carbon stocks, and fluxes, as the annual C transfers between pools and to the forest product sector.

The model can support policy anticipation, formulation, and evaluation under the LULUCF sector, and it is used to estimate the current and future forest C dynamics, both as a verification tool (i.e., to compare the results with the estimates provided by other models) and to support the EU legislation on the LULUCF sector (Grassi et al., 2018a). In the biomass sector, the CBM can be used in combination with other models to estimate the maximum wood potential and the forest C dynamic under different assumptions of harvest and land use change (Jonsson et al., 2018).

Uncertainty. Quantifying the overall uncertainty of CBM estimates is challenging because of the complexity of each parameter. The uncertainty in CBM arises from three primary sources: parameters, forcing data (including spatial and temporal resolution), and model structure. It is linked to both activity data and emission factors (area and biomass volume implied by the species-specific equation to convert the merchantable volume to total aboveground biomass (used as a biomass expansion factor)) as well as to the capacity of each model to represent the original values – in this case estimated through the mean percentage difference between the predicted and observed values. A detailed description of the uncertainty methodology is found in Pilli et al. (2017).

Background. We performed a linear extrapolation of forest net biome productivity (NBP) by country (EU25 member states and UK) in the period 2017–2020 based on the correlation between NBP and harvest from the period 2000–2015. Cyprus and Malta are excluded from the analysis because of missing historical data.

Assessment procedure. The extrapolation of the NBP for the period 2017–2020 was obtained throughout the following steps:

Additional notes. Because of biased estimates, values for the year 2016 were excluded from this analysis.

Extrapolated NBP for the Czech Republic, Ireland, and the Netherlands were negative (thus showing emissions) because of an increase in harvest in the corresponding years (2017–2020) compared to the previous period 2000–2015. Estonia shows negative extrapolated NBP only for the year 2018.

The European Forest Information SCENario Model (EFISCEN) is a large-scale forest model that projects forest resource development on a regional to European scale. The model uses aggregated national forest inventory data as a main source of input to describe the current structure and composition of European forest resources. The model projects the development of forest resources, based on scenarios for policy, management strategies, and climate change impacts. With the help of biomass expansion factors, stem wood volume is converted into whole-tree biomass and subsequently to whole-tree carbon stocks. Information on litter fall rates, felling residues, and natural mortality is used as input into the soil module YASSO (Liski et al., 2005), which is dynamically linked to EFISCEN and delivers information on forest soil carbon stocks. The core of EFISCEN was developed by Ola Sallnäs at the Swedish Agricultural University (Sallnäs, 1990). It has been applied to European countries in many studies since then, dealing with a diversity of forest resource and policy aspects. A detailed model description is given by Verkerk et al. (2016), with online information on availability and documentation of EFISCEN at http://efiscen.efi.int (last access: 16 September 2023). The model and its source code are freely available, distributed under the GNU General Public License conditions (http://www.gnu.org/licenses/gpl-3.0.html, last access: 16 September 2023).

In this report the follow-up of the EFISCEN was used, called EFISCEN-Space. EFISCEN-Space simulates the development of the forest at the level of the plots as measured in the national forest inventories, thereby providing a much higher spatial detail. The simulation is based on the distribution of trees over diameter classes rather than age as in the old EFISCEN. This allows for the simulation of a wider variety of stand structures, species mixtures, and management options. Similar to the EFISCEN, biomass expansion factors and the YASSO soil carbon model are used to provide carbon balances for the forest. For use within VERIFY, individual plot results are aggregated to a 0.125∘ grid. For the moment, only 15 European member states are included, partly due to the lack of an appropriate national forest inventory in the other member states or because the data could not be shared. No formal sensitivity and uncertainty analysis has been conducted yet.

Figure 3 shows results which vary from year to year. In practice, the model was initialized with starting years depending on the country, assuming that all data applied to this year. The model then produced stock and flux changes for the subsequent 5-year period, reporting a single mean value per pixel. To compute time series for the EU27+UK, it was further assumed that these values were valid across 2005–2020. As the fluxes were given per square meter of forest, they were scaled by the total area of the forest in each pixel found on the land use/land cover maps used by the ORCHIDEE DGVM. This explains why the numbers vary from year to year; the flux per square meter of forest does not change, but the total amount of forest area changes slightly. It should be noted that country-level values available on the VERIFY website are only available for the 5-year period for which the model produces a mean result.

Uncertainties. A sensitivity analysis of EFISCEN v3 is described in detail in Chap. 6 of the user manual (Schelhaas et al., 2007). Total sensitivity is caused by especially young forest growth, width of volume classes, age of felling, and a few other variables. Scenario uncertainty comes on top of this when projecting in future. Within VERIFY, a full uncertainty analysis has been completed, enabling the estimation of uncertainty ranges of the various output variables (Schelhaas et al., 2022).

The Environmental Policy Integrated Climate (EPIC) model is a field-scale process-based model (Izaurralde et al., 2006; Williams, 1990) which calculates, with a daily time step, crop growth and yield; hydrological, nutrient, and carbon cycling; soil temperature and moisture; soil erosion; tillage; and plant environment control. Potential crop biomass is calculated from photosynthetically active radiation using the radiation-use-efficiency concept modified for vapor pressure deficit and the atmospheric CO2 mole fraction effect. Potential biomass is adjusted to actual biomass through daily stress caused by extreme temperatures, water and nutrient deficiency, or inadequate aeration. The coupled organic C and N module in EPIC (Izaurralde et al., 2006) distributes organic C and N between three pools of soil organic matter (active, slow, and passive) and two litter compartments (metabolic and structural). EPIC calculates potential transformations of the five compartments as regulated by soil moisture, temperature, oxygen, tillage, and lignin content. Daily potential transformations are adjusted to actual transformations when the combined N demand in all receiving compartments exceeds the N supply from the soil. The transformed components are partitioned into CO2 (heterotrophic respiration), dissolved C in leaching (DOC), and the receiving SOC pools. EPIC also calculates SOC loss with erosion.

The EPIC-IIASA (version EU) modeling platform was built by coupling the field-scale EPIC version 0810 with large-scale data on land cover (cropland and grasslands), soils, topography, field size, crop management practices, and grassland cutting intensity aggregated at a 1×1 km grid covering European countries (Balkovič et al., 2018, 2013). In VERIFY, a total of 10 major European crops including winter wheat, winter rye, spring barley, grain maize, winter rapeseed, sunflower, sugar beet, potatoes, soybean, and rice were used to represent agricultural production systems in European cropland. Crop fertilization and irrigation were estimated for NUTS2 statistical regions between 1995 and 2010 (Balkovič et al., 2013). For VERIFY, the simulations were carried out assuming conventional tillage, consisting of two cultivation operations and moldboard plowing prior to sowing and offset disking after harvesting of cereals. Two row cultivations during the growing season were simulated for maize and one ridging operation for potatoes. It was assumed that 20 % of crop residues are removed in the case of cereals (excluding maize), while no residues are harvested for other crops.

A total of five managed grassland types with distinct temperature requirements, biomass productivity, and phenology were used to represent the C cycle in European grasslands. High-productive generic winter pasture and tall fescue-based grasslands were used for Atlantic Europe, low fescue grasslands for the cool climates of Nordic regions and high mountains, high-productive tall fescue-based grasslands and low-productive bluegrass types for continental Europe, and low-productive bromegrass and high-productive winter pastures in the Mediterranean regions. Annual nitrogen and carbon inputs (including inorganic and manure fertilization and atmospheric N deposition) were obtained from ISIMIP3 (Jägermeyr et al., 2021). In this dataset, the annual manure production and the fraction of manure from livestock applied to cropland and rangeland were used from Zhang et al. (2017). The original manure data were regridded to 0.5∘ spatial resolution in ISMIP3. In the model, manure is applied as an organic fertilizer with a C:N ratio of 14.5:1. The organic carbon and nitrogen are added to the fresh organic litter pool where they decompose in a manner identical to the fresh litter from vegetation, while mineral N from manure is added to the soil nitrate and ammonium pools. The distribution of herbage biomass export intensity was constructed based on Chang et al. (2016).

Uncertainty. In EPIC, uncertainties arise from three primary sources which were described in detail by ORCHIDEE. A detailed sensitivity and uncertainty analysis of EPIC-IIASA regional carbon modeling is presented in Balkovič et al. (2020).

ECOSSE is a biogeochemical model that is based on the carbon model RothC (Jenkinson and Rayner, 1977; Jenkinson et al., 1987; Coleman and Jenkinson, 1996) and the nitrogen-model SUNDIAL (Bradbury et al., 1993; Smith et al., 1996). All major processes of the carbon and nitrogen dynamics are considered (Smith et al., 2010a, b). Additionally, in ECOSSE processes of minor relevance for mineral arable soils are implemented as well (e.g., methane emissions) to have a better representation of processes that are relevant for other soils (e.g., organic soils). ECOSSE can run in different modes and for different time steps. The two main modes are site-specific and limited data. In the later version, basic assumptions/estimates for parameters can be provided by the model. This increases the uncertainty but makes ECOSSE a universal tool that can be applied for large-scale simulations even if the data availability is limited. To increase the accuracy in the site-specific version of the model, detailed information about soil properties, plant input, nutrient application, and management can be added as available.

During the decomposition process, material is exchanged between the SOM pools according to first-order rate equations, characterized by a specific rate constant for each pool, and modified according to rate modifiers dependent on the temperature, moisture, crop cover, and pH of the soil. The model includes five pools with one of them being inert. The N content of the soil follows the decomposition of the SOM, with a stable C:N ratio defined for each pool at a given pH, and N being either mineralized or immobilized to maintain that ratio. Nitrogen released from decomposing SOM as ammonium (NH4+) or added to the soil may be nitrified to nitrate (NO3-).

For spatial simulations, the model is implemented in a spatial model platform. This allows users to aggregate the input parameter for the desired resolution. ECOSSE is a one-dimensional model, and the model platform provides the input data in a spatial distribution and aggregates the model outputs for further analysis. While climate data are interpolated, soil data are represented by the dominant soil type or by the proportional representation of the different soil types in the spatial simulation unit (this is in VERIFY a grid cell).

Uncertainty. In ECOSSE, uncertainty arises from three primary sources: parameters, forcing data (including spatial and temporal resolution), and model structure. These uncertainties are not yet quantified.

We make use of data from two bookkeeping models: BLUE (Hansis et al., 2015) and H&N (Houghton and Nassikas, 2017).

The BLUE model provides a data-driven estimate of the net land use change fluxes. BLUE stands for “bookkeeping of land use emissions”. Bookkeeping models (Hansis et al., 2015; Houghton et al., 1983) calculate land use change CO2 emissions (sources and sinks) for transitions between various natural vegetation types and agricultural lands. The bookkeeping approaches keep track of the carbon stored in vegetation, soils, and products before and after the land use change. In BLUE, land use forcing is taken from the Land Use Harmonization, LUH2, for estimates within the annual global carbon budget. The model provides data at annual time steps and 0.25∘ resolution. Temporal evolution of carbon gain or loss, i.e., how fast carbon pools respire or regrow following a land use change, is based on response curves derived from literature. The response curves describe gradual respiration of vegetation and soil carbon, including transfer to product pools of different lifetimes, as well as carbon uptake due to regrowth of vegetation and subsequent refilling of soil carbon pools. In this report we present two versions of BLUE: BLUE-vVERIFY and BLUE-vGCB. The BLUEvVERIFY version is a set of runs made for VERIFY, using the Hilda+ (https://landchangestories.org/hildaplus/, last access: 16 September 2023) product (Ganzenmüller et al., 2022).

The H&N model (Houghton et al., 1983) calculates land use change CO2 emissions and uptake fluxes for transitions between various natural vegetation types and agricultural lands (croplands and pastures). The original bookkeeping approach of Houghton (2003) keeps track of the carbon stored in vegetation and soils before and after the land use change. Carbon gain or loss is based on response curves derived from literature. The response curves describe gradual respiration of vegetation and soil carbon, including transfer to product pools of different life-times, as well as carbon uptake due to regrowth of vegetation and consequent refilling of soil carbon pools. Natural vegetation can generally be distinguished into primary and secondary land. For forests, a primary forest that is cleared can never return back to its original carbon density. Instead, long-term degradation of primary forest is assumed and represented by lowered standing vegetation and soil carbon stocks in the secondary forests. Apart from land use transitions between different types of vegetation cover, forest management practices in the form of wood harvest volumes are included. Different from dynamic global vegetation models, bookkeeping models ignore changes in environmental conditions (climate, atmospheric CO2, nitrogen deposition, and other environmental factors). Carbon densities at a given point in time are only influenced by the land use history but not by the preceding changes in the environmental state. Carbon densities are taken from observations in the literature and thus reflect environmental conditions of the last decades. In this study an updated H&N version submitted to the GCP2021 is used.

Uncertainty. Uncertainties can be captured through simulations varying uncertain parameters, input data, or process representation. A large contribution of uncertainty can be expected from various input datasets. Apparent uncertainties arise from the land use forcing data (Gasser et al., 2020; Hartung et al., 2021; Ganzenmüller et al., 2022), the equilibrium carbon densities of soil and vegetation as well as allocation of material upon a land use transition (Bastos et al., 2021), and the response curves built to reflect carbon pool decay and regrowth after land use transitions. Furthermore, studies have shown that different accounting schemes (Hansis et al., 2015) and initialization settings at the start of the simulations (Hartung et al., 2021) lead to different emission estimates even decades later.

FAOSTAT: the Statistics Division of the Food and Agricultural Organization of the United Nations provides updates for the LULUCF CO2 emissions for the period 1990–2019, available at https://www.fao.org/faostat/en/#data/GT (last access: June 2021), and its subdomains. The FAOSTAT emissions land use database is computed following a Tier 1 approach of IPCC (2006). Geospatial data are the source of AD for the estimates of emissions from cultivation of organic soils, biomass, and peat fires. GHG emissions are provided by countries, regions, and special groups, with global coverage, relative to the period 1990–present (with annual updates). Land use Total contains all GHG emissions and removals produced in the different land use subdomains, representing four IPCC land use categories, of which three are land use categories: forest land, cropland, grassland, and biomass burning. LULUCF emissions consist of CO2 associated with land use and change, including management activities. CO2 emissions/removals are computed at Tier 3 using carbon stock change. To this end, FAOSTAT uses Forest area and carbon stock data from FRA (2015), gap-filled and interpolated to generate annual time series. As a result, CO2 emissions/removals are computed for forest land and net forest conversion, representing, respectively, IPCC categories “Forest Land” and “Forest Land converted to other land uses”. CO2 emissions are provided as by country, regions, and special groups, with global coverage, relative to the period 1990 to the most recent available year (with annual updates), expressed as net emissions/removals as Gg CO2, by the underlying land use emission subdomain and by aggregate (land use total).

Uncertainty. FAOSTAT uncertainties are not available.

The TRENDY (trends in net land–atmosphere carbon exchange over the period 1980–2010) project represents a consortium of dynamic global vegetation models (DGVMs) following identical simulation protocols to investigate spatial trends in carbon fluxes across the globe over the past century. As DGVMs, the models require climate, carbon dioxide, and land use change input data to produce results. In TRENDY, all three of these are harmonized to make the results across the whole suite of models more comparable. In the case of VERIFY, 15 of the 16 models for TRENDY v10 (except for ISAM, which after visual inspection showed several outlier years) were used. While describing the details of all the models used here is clearly not possible, DGVMs calculate prognostic variables (i.e., a multitude of carbon, water, and energy fluxes) from the following environmental drivers: air temperature, wind speed, solar radiation, air humidity, precipitation, and atmospheric CO2 mole fraction. As the run progresses, vegetation grows on each pixel, divided into generic types which depend on the model (e.g., broadleaf temperate forests, C3 crops), which cycle carbon between the soil, land surface, and atmosphere, through such processes such as photosynthesis, litter fall, and decay. Limited human activities are included depending on the model, typically removing aboveground biomass on an annual basis.

Among other environmental indicators, DGVMs simulate positive and negative CO2 emissions from plant uptake; soil decomposition; and harvests across forests, grasslands, and croplands. Activity data are based on land use and land cover maps and generally follows approach 1 as described by the IPCC 2006 guidelines (enabling calculation of only net changes from year to year). For TRENDY, pixel land cover/land use fractions were based on the land use map LUH2 (Hurtt et al., 2020) and the HYDE land use change dataset (Klein Goldewijk et al., 2017a, b). Both of these maps rely on FAO statistics on agricultural land area and national harvest data.

Uncertainty. In TRENDY v10 uncertainties are model specific and described by Friedlingstein et al. (2022). The spread of the 15 TRENDY models used by this study (Fig. 5) gives an idea of the uncertainty due to model structure in dynamic global vegetation models, as the forcing data were harmonized for all models.

Net carbon flux due to lateral transport includes both carbon imported into a country/pixel and respired and carbon assimilated in a country/pixel and then transported to a different country/pixel before respiration.

Production and consumption of carbon do not always occur on the same grid points. This is particularly relevant for the land surface in the case of crops, wood products, and carbon transfers through the inland water network. The purpose of the work here is primarily to convert the flux changes of the top-down inversions into NGHGI-like stock changes. To convert the flux changes of the inversions (where a positive number represents a flux to the atmosphere, i.e., a source) into NGHGI-like stock changes, one needs to add the crop sink and remove the crop source. The crop sink comes from production numbers in the FAO food balance sheets, while the source is estimated by production plus import minus export (all from the FAO food balance sheets), and both terms make use of conversion factors for each commodity. We take the forestry balance sheets of FAO (production, import, and export per commodity) and convert to C mass. For a given year, the fraction of this mass that is released later in the atmosphere in each country is modeled with an e-folding decrease driven by experimental data per country (Mason Earles et al., 2012). Lateral transfers of carbon through inland waters also need to be removed from the inversion results as the terrestrial biospheric CO2 uptake leached into the inland water network represents a carbon sink, while the fraction that is subsequently reemitted as CO2 before reaching the ocean is a carbon source. The inland water CO2 outgassing originates from carbon imported with runoff as dissolved CO2 or produced in situ from the decomposition of terrestrial carbon inputs. Note further that a fraction of the net uptake of atmospheric CO2 over the continents does not accumulate on land but is instead exported through the inland water network to the oceans; this fraction is included in the calculation. For regional carbon budgets, any river carbon export outside the boundaries of the region of interest (in this case, EU27+UK) needs to be known to separate net uptake of atmospheric C from the actual land C sink.

Carbon fluxes to the atmosphere from rivers and lakes were obtained from maps described in Zscheischler et al. (2017). These methods are similar to those described previously in Petrescu et al. (2021). The primary difference is that the updated estimates include smaller lakes and reservoirs not represented in the Global Lakes and Wetland Database through the use of a scaling law, in addition to the older results being created specifically for Europe, while the newer results are part of a global product. The emissions from the previous work totaled 25.5 Tg C yr-1 for the EU27+UK, while those used here are 19.8 Tg C yr-1 (with no variability from year to year). This difference is therefore small compared to the river C export, which is included this year for the first time and averages -73.8 Tg for the period 1990–2020.

One important difference between the fluvial carbon exports reported here and those from a previous work (Ciais et al., 2021) are that those reported here are rescaled to reasonable global flux reflecting bias in inter-hemispheric exchange. Similar to Bastos et al. (2020b), the dissolved organic carbon (DOC) and particulate organic carbon (POC) exports were rescaled per basin to match the estimates of Resplandy et al. (2018). The global total organic C was finally rescaled to 500 Tg C yr-1, which is considered a reasonable global number based on different reviews and synthesis efforts (Regnier et al., 2013).

For the regional inversions, atmospheric observations of CO2 were taken from multiple sources. For CarboScopeRegional, atmospheric observations were taken from the ICOS 2021.1 ATC (ICOS RI, 2021) and the GlobalViewPlus 6.1 product (Schuldt et al., 2021a). For the CIF-CHIMERE inversions, atmospheric observations of CO2 for the period 2005–2020 were taken from the ICOS 2021.1 ATC (ICOS RI, 2021) and SNO_SIFA L2 (SNO-IFA, 2023) releases, along with data distributed through the GlobalViewPlus 6.1 product (Schuldt et al., 2021a). For LUMIA inversions, atmospheric observations of CO2 for the period 2006–2018 were taken from the dataset prepared for the 2018 Drought Task Force initiative (Thompson et al., 2020). For the more recent years, data were used from the ICOS 2021.1 ATC release (ICOS RI, 2021), along with data distributed through the GlobalViewPlus 7.0 product (Schuldt et al., 2021b) and, for four sites, data distributed through the World Data Center for Greenhouse Gases.

CarboScopeRegional (CSR) (Munassar et al., 2022): CSR is a Bayesian framework inversion system that employs a priori knowledge of the surface-atmosphere carbon fluxes to regularize the solution of the ill-posed inverse problem arising from the sparseness of observations sampled over limited geographical locations throughout the domain of interest. Due to the heterogeneity of biogenic fluxes, the convention in CSR is to optimize net ecosystem exchange (NEE) against measurements of CO2 dry model fraction at 3-hourly temporal and 0.5∘ horizontal resolutions, while ocean fluxes and anthropogenic emissions are prescribed given their better knowledge available compared with NEE. The prior flux uncertainty is assumed to have a uniform shape in space and time, and its spatial correlation is fitted to a hyperbolic decay function following the assumption of Kountouris et al. (2018a, b). Model–data mismatch uncertainty is defined weekly in the measurement covariance matrix varying over sites from 0.5 to 4 (ppm) according to the ability for atmospheric transport models to sample the true mole fraction at such locations (Rödenbeck, 2005). This uncertainty implicitly encompasses the combinations of atmospheric transport, representation, and measurement errors and is assumed to be independent at different locations. To separate the lateral influences originating from outside of the regional domain, the two-step scheme inversion (Rödenbeck et al., 2009) is applied to run a global inversion with the Eulerian model TM3 at coarse resolutions to provide the lateral boundary conditions to the regional inversion. In the regional inversion runs, the Lagrangian model STILT (Lin et al., 2003), forced by IFS data from ECMWF, is used to calculate the surface sensitivities “footprints” over the regional site network (receptors) at hourly temporal and 0.25∘ spatial resolutions. Typically, the prior fluxes of CO2 are obtained from bottom-up model estimations. Thus, the diagnostic biosphere model VPRM (Vegetation Photosynthesis and Respiration Model; Mahadevan et al., 2008) calculates the biogenic fluxes at hourly temporal resolution preserving the diurnal cycle. Ocean fluxes are obtained from the CarboScope ocean-based fluxes developed in-house by Rödenbeck et al. (2014). Emissions of fossil fuel are taken from EDGAR_v4.3 inventories updated every year based on the British Petroleum statistics (BP), and are distributed in space and time using the COFFEE approach (Steinbach et al., 2011) according to fuel type and sector.

The v2021 CSR inversions underwent updates in comparison with the previous v2019.

v2019 from Petrescu et al. (2021) excluded observations from two sites: La Muela (LMU) in Spain, because of inconsistent datasets between releases, and Finokalia (FKL) in Greece, due to errors in the dataset. These exclusions resulted in a larger C sink from 2013 onwards (Fig. 5, lower plot). FKL observations start at this time and are the dominant impact over southeast Europe, as it is the only site located there. In v2021 inversions, we included corrected datasets from the FKL site.

Uncertainty. Uncertainties from top-down (TD) estimates can be reported as posterior Bayesian uncertainties. Following the methodology of Chevallier et al. (2007), the CSR inversion system computed maps of uncertainty reductions for 2006 and 2018 (Fig. A4). The reduction is carried out through an ensemble of 40 members of inversions using error realizations following a Monte Carlo (MC) approach. Circles on maps refer to locations of stations. In the inversion system, a MC method is used to generate N ensembles of realizations of prior errors and model–data mismatch errors. The inversion is repeated for each ensemble member starting from each set of prior and model–data mismatch errors to generate posterior fluxes. The posterior uncertainty is calculated as the spread over the optimized fluxes across the whole ensemble. The uncertainty reduction is then calculated as 1-(σpost/σprior). It is clear that larger ensembles will lead to better convergence of the error reduction. However, due to computational limitations, 40 ensemble members were selected as a good compromise.

Figure A4 represents a preliminary attempt at how the inclusion of additional observation stations (additional circles in the right-side figure for Germany, Switzerland, and Finland compared to the left-side figure) might reduce the uncertainty. However, the two different simulation years (2006 and 2018) might also differ in terms of other factors which may lead to lower uncertainties in a given year (e.g., climatological conditions, such as the 2018 drought year).

Several caveats remain. When comparing the uncertainty over pixels or subregions in the domain of interest, the maps of uncertainty reduction should be interpreted together with the maps of posterior uncertainty to give a better illustration of the magnitude of uncertainty. The maps of uncertainty reduction reflect only the random uncertainties. The systematic uncertainties are still poorly characterized, including uncertainties due to atmospheric transport modeling, dependence on the prior fluxes, and the weighting between the prior and observation uncertainties. To improve knowledge of the systematic uncertainties, dedicated studies with controlled comparisons between inversions using different atmospheric transport models (such as planned with the Community Inversion Framework; Berchet et al., 2021) are still needed. Furthermore, the posterior uncertainty and uncertainty reductions between inversions depend on internal parameterizations, e.g., the weighting of prior and observation uncertainties. Future efforts should focus on establishing best practices on how to set up inversions and quantification of systematic uncertainties, including as well tests of the fidelity of models against data (Simmonds et al., 2021).

The LUMIA inversion system (Monteil and Scholze, 2021) is a regional atmospheric inversion system, which was designed to produce estimates of the land–atmosphere carbon exchanges based on in situ CO2 observations from the ICOS network. It relies on the FLEXPART 10.4 Lagrangian transport model (Pisso et al., 2019) to compute the transport of CO2 fluxes within a regional domain (33∘ N to 73∘ N and 15∘ W to 35∘ E) at a 0.5∘, 3-hourly resolution. Boundary conditions are provided in the form of time series of far-field contributions at the observation sites, obtained from a global TM5-4DVAR inversion (using the two-step inversion approach of Rödenbeck et al., 2009). Both transport models were driven by ECMWF ERA-Interim data, up to 2018, and by ECMWF ERA5 data afterwards. The inversions solve for weekly offsets to the prior NEE/NBP estimate, at a variable spatial resolution, highest where the observational coverage is better (up to 0.5∘ upwind of the observation sites). The optimal solution is searched for using a variational inversion approach (preconditioned conjugate gradient). The inversions were constrained by in situ and flask observations from 66 European observation sites, although only a subset of these sites is usually available at a given time. The observation uncertainties were set to 1 ppm per week at all sites (the uncertainty of a single observation is therefore higher, on average 5.2 ppm, and given by √n, with n being the number of assimilated observations at the same site in a ±3.5 d window around the observation time). The prior NEE was produced using the LPJ-GUESS model (Smith et al., 2014), driven by ECMWF ERA5 meteorological data.

The inversion also accounts for (prescribed) anthropogenic CO2 fluxes from the EDGAR/TNO product (10.18160/Y9QV-S113, Karstens, 2019) and for atmosphere–ocean CO2 exchanges from the Jena CarboScope oc_v2021 product (https://www.bgc-jena.mpg.de/CarboScope/oc/oc_v2021.html, last access: 16 September 2023). The uncertainties on the prior NEE were set proportional to the sum of the absolute value of the 3-hourly fluxes in each 7 d optimization interval (so the uncertainty is not zero even if the net flux is zero) and scaled to a total value of 0.45 Pg C yr-1, accounting for covariances based on Gaussian (spatial) and exponential (temporal) correlation decay functions, with correlation lengths of, respectively, 500 km and 1 month (see Monteil and Scholze, 2021, for details).

The main differences from the LUMIA setup used in Thompson and Stohl (2014) are the specification of prior and observation uncertainties (here made, on purpose, more comparable to those used in the CSR inversions) and the implementation of flux optimization at a variable spatial resolution (which has negligible impact on the results but improves the model performance).

CIF-CHIMERE is used for both CO2 land and CO2 fossil emission estimates, and this section only describes the CO2 land estimates.

The CIF-CHIMERE inversions have been generated with the variational mode of the Community Inversion Framework (CIF; Berchet et al., 2021) coupled to the regional Eulerian atmospheric chemical transport model CHIMERE (Menut et al., 2013; Mailler et al., 2017) and to its adjoint code. They are set up in a manner that is close to that of the PYVAR-CHIMERE inversions of Broquet et al. (2013), of Thompson et al. (2020), and of Monteil et al. (2020).

A European configuration of CHIMERE is used; this configuration covers latitudes 31.75–73.25∘ N and longitudes 15.25∘ W–34.75∘ E with a 0.5∘×0.5∘ horizontal resolution and 17 vertical layers up to 200 hPa. Meteorological forcing for CHIMERE is generated using the European Centre for Medium-Range Weather Forecasts (ECMWF) operational forecasts. Initial, lateral and top boundary conditions for CO2 mole fractions are generated from the new CAMS global CO2 inversions v20r2 (Chevallier et al., 2010).

The inversion assimilates in situ CO2 data from continuous measurements stations compiled in the VERIFY Deliverable D3.12 and in the Table A1 from the VERIFY CIF Inversion Protocol (Berchet et al., 2021). More specifically, the inversion assimilates 1 h averages of the measured CO2 mole fractions during the time window 12:00–18:00 UTC for low-altitude stations (below 1000 m a.s.l.) and 00:00–06:00 UTC for high-altitude stations (above 1000 m a.s.l.). The inversion optimizes 6-hourly mean NEE and ocean fluxes at the 0.5∘ × 0.5∘ resolution of CHIMERE. The anthropogenic CO2 emissions, considered as perfect and consequently not optimized in the inversions, are based on the spatial distribution of the EDGAR-v4.2 inventory, on national and annual budgets from the BP (British Petroleum) statistics and on temporal profiles at hourly resolution derived with the COFFEE approach (Steinbach et al., 2011).

The prior estimate of NEE and its uncertainty covariance matrix are specified using ORCHIDEE model simulations of NEE and respiration, respectively, following the general approach of Broquet et al. (2011). The temporal and spatial correlation scales for the prior uncertainty in NEE are set to ∼ 1 month and 200 km (following the diagnostics of Kountouris et al., 2015), with no correlation between the four 6 h windows of the same day. The ocean prior fluxes come from a hybrid product of the University of Bergen coastal ocean flux estimate and the Rödenbeck global ocean estimate (Rödenbeck et al., 2014). Fluxes from biomass burning are ignored. The observation error covariance matrix is set up to be diagonal, ignoring the correlations between errors for different hourly averages of the CO2 measurements (which has been justified by the analysis of Broquet et al., 2011). The variances for hourly data are based on the values from Broquet et al. (2013), which vary depending on the sites and season, and which are derived from radon model–data comparisons.

About 12 iterations are needed to reduce the norm of the gradient of J by 95 %, using the M1QN3 limited memory quasi-Newton minimization algorithm (Gilbert and Lemaréchal, 1989). To cover the whole analysis period (2005–2020), a series of 7-month (including an overlapping of 15 d between consecutive periods) inversions is performed. Posterior estimates of NEE at 1-hourly temporal resolution and 0.5∘ × 0.5∘ spatial resolution are generated for the full period of analysis.

Uncertainty. Estimates of the uncertainty of regional inversions over Europe can be found by comparing against the results of the other regional inversions in this work (the ensembles of EUROCOM, CarboScopeRegional, and LUMIA).

Top-down estimates of land biosphere fluxes are provided by a number of different inverse modeling systems that use atmospheric mole fraction data as input, as well as prior information on fossil emissions, ocean fluxes, and land biosphere fluxes. The land biosphere fluxes, and in some systems the ocean fluxes, are estimated using a statistical optimization involving atmospheric transport models. The inversion systems differ in the transport models used, optimization methods, spatiotemporal resolution, boundary conditions, and prior error structure (spatial and temporal correlation scales), thus using ensembles of such systems is expected to result in more robust top-down estimates.

For this study, the global inversion results are taken from all six of the models reported in the GCB2021: CTE (CarbonTracker Europe), CAMS (Copernicus Atmosphere Monitoring Service), CMS-Flux, JENA, NISMON-CO2, and UoE, with spatial resolutions ranging from 1∘×1∘ for certain regions to 4∘×5∘. For details, see Friedlingstein et al. (2022), in particular Table A4. Atmospheric observations for most model systems are taken from Cox et al. (2021) and Di Sarra et al. (2021). Note that one of the ensemble members (CMS-Flux) only covers the period 2010–2020; therefore, the ensemble results are only shown from 2010 until the last year common between all models (2018).

Top-down estimates at regional scales (up to 0.25∘ × 0.25∘ resolution) for the period 2009–2018 are taken from three models used within EUROCOM (Monteil et al., 2020; Thompson et al., 2020): LUMIA, PYVAR, and CSR. The NAME model was excluded as visual inspection of monthly values identified it as a clear outlier. FLEXINVERT was excluded after visual inspection of annual values identified it as a clear outlier (Fig. A5). These inversions make use of more than 30 atmospheric observing stations within Europe, including flask data and continuous observations. The CarboScopeRegional (CSR) inversion system results were rerun for VERIFY using the extended period 2009–2020 using four different settings: three network configurations using 15, 40, or 46 sites, and one using all 46 sites but a factor of 2 larger prior error correlation length scale (200 instead of 100 km). The CSR results reported to EUROCOM were not used, being instead replaced by the mean of the four updated CSR runs. The observational dataset used for the EUROCOM drought ensemble is accessible on the ICOS Carbon Portal (Drought 2018 Team; ICOS Atmosphere Thematic Centre, 2020).

The ERA5-Land (Muñoz-Sabater, 2019; Muñoz-Sabater et al., 2021) dataset at 0.1∘ resolution over the global land surface at hourly resolution was aggregated to 3-hourly resolution and extracted for a 0.125∘ grid over Europe (35∘ N to 73∘ N and 25∘ W to 45∘ E) to match the grid used in previous efforts within the VERIFY project. The variables extracted are the following: air temperatures, wind components, surface pressure, downwelling longwave radiation, downwelling shortwave radiation, snowfall, and total precipitation. From these, additional variables were calculated: total wind speed, specific humidity, relative humidity, and rainfall. Of these, the air temperature, downwelling shortwave radiation, specific humidity, and total precipitation were realigned with the CRU observation dataset (Harris et al., 2020) from 1901–2020 so that monthly means at 0.5∘ pixels correspond exactly. Variation from observations is therefore present only on sub-monthly temporal scales and sub-0.5∘ spatial scales. At the time of the model intercomparison, ERA5-Land was only available from 1981–2020. Consequently, the years 1901–1980 were taken from the UERRA HARMONIE-V1 dataset from ECMWF realigned with CRU observations under the VERIFY project and used in Petrescu et al. (2021). For both datasets, results were aggregated to daily and monthly temporal resolution for use as needed in some models.

The full Hilda+ dataset is described in detail elsewhere (Winkler et al., 2020, 2021). Hilda+ is available at 1×1 km spatial and annual temporal resolution across the whole globe from 1960–2019 for six land use classes (urban, cropland, pasture/rangeland, forest, unmanaged grass/shrubland, and sparse/no vegetation). The algorithm uses Earth observation data and land use statistics to generate annual land use/cover maps and transitions. Probability maps for land use change categories are generated by using multiple Earth-observation-based data estimates of the extent of a given land cover category on a given pixel. The VERIFY project requires additional work to satisfy the needs of the various modeling groups. For example, the maps were extended back to 1900 to meet the needs of the DGVM groups. As observational data are lacking for the years before 1960, the temporal trend of the probability maps and the FAO land use database were used for extrapolation. In addition, forest areas were further subdivided into six forest types (Evergreen, needleleaf; Evergreen, broadleaf; Deciduous, needleleaf; Deciduous, broadleaf; Mixed; unknown/other) based on the ESA CCI land cover dataset (ESA, 2017). Spatiotemporal forest type dynamics within the forest category were included for 1992–2015. Before 1992 and after 2015, the static forest type distribution as found in the years 1992 and 2015 in the ESA CCI land cover was assumed, respectively.

Wet and dry deposition maps of ammonium and nitrate covering Europe from 1995–2018 were calculated at 0.5∘ spatial and monthly temporal resolution by the European Monitoring and Evaluation Programme (EMEP) MSC-W model (“EMEP model” hereafter). The EMEP model is a 3-D Eulerian chemistry transport model (CTM) developed at the EMEP center MSC-W under the framework of the UN Convention on Long-Range Transboundary Air Pollution (CLRTAP). The EMEP model has traditionally been used to assess acidification, eutrophication, and air quality over Europe, to underpin air quality policy decisions (e.g., the Gothenburg Protocol), and has been under continuous development, reflecting new scientific knowledge and increasing computer power. The model was described in detail by Simpson et al. (2012) and later updated as described in the annual EMEP status reports (Simpson et al., 2022, and references therein). For the VERIFY project, output from the EMEP model version rv4.33 was used (Simpson et al., 2019) and averaged to annual temporal resolution. In these simulations, the model was driven by meteorological data from the ECMWF IFS (European Centre for Medium-Range Weather Forecasts – Integrated Forecast System) version cy40r1. Land use data were taken from the CORINE land cover maps (De Smet and Hettelingh, 2001), the Stockholm Environment Institute at York (SEIY), the Global Land Cover (GLC2000) database, and the Community Land Model (Oleson, 2010; Lawrence et al., 2011). For more details, see Simpson et al. (2017).

Ocean CO2 fluxes were prepared for use as prior estimates in the regional inversions by combining the Rödenbeck global ocean estimate (Rödenbeck et al., 2014) with coastal ocean fluxes for Europe prepared under the VERIFY project. The combined dataset was prepared by choosing the coastal flux map when available and otherwise the open ocean map. The coastal ocean fluxes were generated for an area extending from the western Mediterranean to the Barents Sea and cover shelf areas down to 500 m water depth or 100 km distance from shore. First, surface ocean fCO2 observations are taken from the annually updated SOCAT database (Bakker et al., 2016, 2022) and gridded to a monthly 0.125∘ × 0.125∘ grid. pCO2 maps are created based on fitting a set of driver data (including sea surface temperature, mixed layer depth, chlorophyll concentration, and ice concentration) against the gridded fCO2 observations. Both random forest and multi-linear regressions were used. The general procedure is described elsewhere (Becker et al., 2021), but for the version reported here, random forest regressions were used instead of multi-linear regression, and the region was extended to the south. The dataset was divided into seven subregions (Barents Sea, Norwegian coast, North Sea, Baltic Sea, Northern Atlantic coast/Celtic Sea, Southern Atlantic coast/Bay of Biscay, western Mediterranean), and each region was fitted separately (leaf size: 20, bag size: 500). The root mean square error (RMSE) of the random forest regressions was determined to be between 34 µatm (Baltic Sea) and 10 µatm (Barents Sea). Random forest regressions consist of many regression trees, each based on a random subset of data. Due to this internal structure, the overall RMSE can be seen as an out-of-box error estimate. The final fluxes are calculated from the pCO2 maps with the atmospheric xCO2 in the marine boundary layer and 6-hourly wind speed data using the gas transfer coefficient and the Schmidt number after Wanninkhof (2014), with the coefficient aq of 0.2814 calculated after Naegler (2009) and 6-hourly winds from the NCEP-DOE Reanalysis 2 product (Kanamitsu et al., 2002).