For the calculation of NO_x emissions from road transport, this study used emission factors based on the Dutch national emissions inventory; for details and the full dataset, see . The methodology is vehicle-specific and uses a bottom-up approach introduced in 2019, which calculates emissions at the level of individual vehicles using annual odometer readings from the RDW (Netherlands Vehicle Authority). Each vehicle is assigned to one of approximately 350 VERSIT+ vehicle classes, defined by vehicle type, weight, fuel type, emission legislation category (i.e., Euro standards), and exhaust after-treatment technologies . Emission factors for NO_x are expressed in grams per vehicle kilometre and are road-type specific, distinguishing between urban, rural, and highway conditions. These emission factors are derived annually from both laboratory testing and real-world driving measurements, and are adjusted for vehicle aging using odometer data. NO_x temperature effects are not included in the Dutch national emissions inventory. Applying vehicle kilometres and vehicle type information from COPERT to our emission factors dataset, we calculated the national emission totals for each country. In a next step, we derived weighted average emission factors per sector and vehicle kilometre. For this, the national emissions were divided by the total sector vehicle kilometres from COPERT. The COPERT dataset supplies yearly annual data on national vehicle fleet composition, and can readily be used to divide the dataset into relative shares for each vehicle category.

For each road link, the corresponding weighted emission factor was multiplied with the road's AADT value and road length. The weighted emission factor is dependent on the location (country) of the road, as well as the environment (urban, rural, highway) and vehicle class (see Sect. ), resulting in an annual emission per year and vehicle class. In previous works, the urban–rural split was performed with gridded land use or population density data, resulting in all roads in an area sharing the same emission factors. However, emission factors of roads depend on the road conditions, maximum speed and congestion levels , and not on the location of a road within an urban boundary. In an effort to choose the appropriate emission factor on a link level, we used urban emission factors for all roads with a speed limit of ≤50 km h⁻¹, and rural emission factors for all roads with a speed limit of >50 km h⁻¹. Maximum speed information was preferentially taken from OSM where available, or from OTM as a fallback. Highways were identified by road class and received their own emission factor independent of their speed limit.

The resulting dataset is referred to in Fig. as bottom-up emissions. The term bottom-up emissions stands for the dataset which was based directly on our activity dataset. We then scaled bottom-up emissions with reported national totals (for more details, see ) and gridded with 0.05° × 0.1° resolution to generate our final results for CAMS-REG v8.1 in line with the reported data. Both datasets aligned closely, with bottom-up emissions overestimating domain totals by 3 %.

We used a combination of random forest (RF) models (see Sect. ) and spatial gap filling (see Sect. ) to create a complete dataset of AADT and maximum-speed values for most roads in the study area. This was done to generate a complete activity dataset. On this basis, the road-level emissions are calculated in a next step. Gap filling AADT data with machine learning approaches among them, random forest is a common choice among traffic modellers, especially when working with mixed and incomplete data. AADT values were later used to calculate absolute NO_x emissions per road. A complete set of speed limits is necessary to choose the appropriate emission factor per road.

Based on the introduced methodology and datasets, CAMS-REG v8.1 includes the first major update on the spatial distribution of road emissions since v4.2, which was published in 2022 . At the core, both methods are based on the activity data distribution from OTM in combination with OSM shapes and a methodology to fill up missing data (see Fig. ). In v4.2, the link-based activity data is first filled up by taking an average of the road type within each corresponding NUTS3 area, or, if not available, a global average. Then, emission factors from COPERT were applied, and the spatial distribution was gridded to a fixed grid of 0.05° × 0.1° resolution. Lastly, empty grid cells with no available data; for example in non-EU Eastern European countries were filled up using a regression approach based on Landscan population density data, per road class. The resulting spatial dataset was then used to distribute national total emissions per country.

The spatial distribution, as well as large parts of the data handling within this version, is dependent on the exact grid definition, and an increase of grid resolution is not possible beyond the resolution of Landscan for large parts of the study area. If city scale or higher resolution inventories need to be derived from this approach, additional tools and proxies are always necessary. So far, this has been done by either tools such as UrbEm , or proxies such as local road geometries or other distributions.

Here, we describe the evaluation of our intermediate results and the final dataset.

RF gap filling model performance was tested with 10 % reserved test data and the coefficient of determination (R2), mean absolute error (MAE) and root mean square error (RMSE) as performance metrics.

Due to the scaling with national emission totals (Fig. ), national totals of the final emission datasets are bound to be similar to previous versions on a national level, despite the base year difference of 2017 (v4.2) and 2018 (v8.1). National totals used to scale emissions for the two CAMS-REG versions used may be slightly different due to updates in the national methodologies.

We then compare our results to the 8 made-available city scale inventories (see Sect. ). For this, the boundary shapes of the city inventories were used to extract annual emission totals from CAMS-REG versions, which were then compared to the city inventories. The areas of these boundary shapes included regions of different sizes, which are available as described in Sect. . The largest city boundary was for the Paris-Ile de France region (ca. 12 470 km²).

For a wider picture, we included 16 other European cities for a comparison between CAMS-REG versions. As different national totals between the CAMS-REG versions can also affect city allocation, comparisons were also done on a “Share of urban emissions to national totals” basis.

For London and Milan, in addition to city totals also a high-resolution spatial distribution is available from LAEI and ARPA Lombardia, which enables a case-study comparison of the spatial distribution between different methods. We gridded our new distribution to grid of the local inventory, and performed an UrbEm downscaling of CAMS-REG v4.2 to the same grid. We then performed a spatial correlation between the local inventory and both CAMS inventories, as well as spatial cross-correlation. Spatial cross-correlation has been proposed by as a way to assess the relationship between one variable at a location and another variable at other locations. It is an extension of the commonly used Moran's I index for spatial autocorrelation over another variable . Possible values reach from -1 to 1, with -1 denoting perfect negative cross-correlation, 1 denoting perfect positive cross-correlation, and 0 denoting no cross-correlation.

RF Gap filling performance was dependent on model and road type. Model 2 (see Table ) reaches R2=0.63, whereas Model 1 (trained also with OTM data) reaches R2=0.74. This performance decreases along decreasing road size, with primary roads achieving R2=0.64, secondary roads R2=0.51 and tertiary roads R2=0.44 for Model 2 and R2=0.47, R2=0.39 and R2=0.29 for Model 1, respectively. The MAE and RMSE for Model 2 are MAE = 2028.3 and RMSE = 4407.2. Errors increase with road class (highway MAE = 5182.3, tertiary roads MAE = 619.7). For the Model 1, errors were MAE = 1570.2 and RMSE = 3702.4.

For motorways, the highway models achieve R2=0.66 and R2=0.76 for Highway Model 2 and Highway Model 1, respectively (see also Fig. ).

We further calculated variable importance according to . For Model 2, the most important predictor variables were the OSM highway key, and then population density and land use class. For Model 1, the OTM road class was the most important predictor, followed by population density and the OSM highway key. For both models, OSM data on maximum road speed were of low importance.

We compared our complete activity dataset to a recent dataset published by . This dataset provides measured, annual averaged traffic data for a number of European cities between 2015 to 2024 depending on availability. The locations of traffic counts were matched with the OSM network by Hidden Markov Models (in case of line geometries) and nearest neighbour approach (in case of point data). The performed matching with the OSM network provided a straightforward way for comparison with our dataset.

For the year 2018, data was available for 13 cities, for a total number of 6219 traffic counting stations. The number of stations per city varied strongly, with the smallest number in Copenhagen (n=17) and the largest number in London (n=2207). Motorways (motorway + trunk) accounted for 1056 stations, primary (primary + primary_link) for 1570 stations, secondary (secondary + secondary_link) for 825 stations, tertiary (tertiary + tertiary_link) for 1217 stations and residential (residential + service + living_street) for 1430 stations. Descriptive statistics were (min: 5; 25 % quantile: 3775; median: 10 288; mean: 15 405; 75 % quantile: 18 530; max: 163 045), compared to our generated dataset: (min: 0; 25 % quantile: 221; median: 1449; mean: 4508; 75 % quantile: 3841; max: 107 656). Frequent high values for residential streets in the dataset from hint to a possible mismatch of some sensor locations. For example, the mean AADT of service roads was 21 572, which is likely be explained by a location mismatch. are aware of this source of error.

Correlation between both datasets was found at R2=0.17, p<0.01 with a slope of b=0.84. mention higher certainty of their matching algorithm with reduced distance between sensor and matched roads. We therefore performed the analysis again in two steps. First, we only took into account sensors with matched roads close to the sensor location (distance < 1 m; n = 3476), as suggested by the authors to help reduce matching uncertainty. Secondly, we only took into account sensors that came with a matched line geometry, increasing location certainty even further (n=2249). In the first case, correlation increased to R2=0.20, and in the latter case to R2=0.38, which is still below R2=0.5, a value seen satisfactory by . Our RF gap filling methodology did not seem to negatively impact correlation with the validation dataset. Using only gap filled data, correlation increases from R2=0.17 to R2=0.27.

The statistics show a large underestimation in our dataset. The underestimation is the largest for small roads (by factors of 210 for service roads and 18 for residential roads, with likely reasons as outlined before). Amongst other road classes, there is an underestimation of our dataset by a factor ranging from 2–6 for different per road class. As road traffic volume in Europe still generally continues to grow , a part of the underestimation may be explained by OTM's 2015 base year compared to the measured data from 2018. However, there seems to exist an additional systematic underestimation of AADT values in the OTM dataset for urban areas compared to the measured data.

Our findings of a substantial increase in correlation with decreasing geolocation uncertainty is in line with previous results by , who explain weak correlation with a validation datasets due to uncertainty in geolocation of sensor data. For the final purpose of generating a relative spatial distribution, the low correlation values between between our dataset and the measured data are a limitation to our results, highlighting the need for an updated and consistent AADT dataset in Europe.

As absolute emissions per country were scaled by reported country totals, emissions on the country levels between CAMS-REG versions differ only due to changes in country reporting methodology for a given year. Figure gives an overview of changes in country totals. The NO_x domain total for CAMS-REG v4.2 was 3.67×109 kg, and 4.03×109 kg in v8.1 for 2018. The largest absolute increases in reported emissions were for Turkey and Russia and the largest decrease, for Poland. We further calculated the changes of urban core emissions between the versions. Urban core areas were taken from the Global Human Settlement Layer . Throughout the domain, urban emissions increased by 26 %. Large increases can be found in non-EU countries such as Georgia, Russia, Serbia and Turkey (Fig. ). Strong decreases can also be found, for example in Estonia and Finland, which occur due to the spatial redistribution of emissions.

A distribution of absolute emissions by OSM class is given in Table . Over 65 % of all emissions occurs on trunk, motorway and primary roads, with another roughly 15 % of emissions occurring on secondary and tertiary roads. Despite their large number, smaller roads only account to 3.7 % of all emissions in the domain.

Figure gives an overview of the spatial distribution for France, Russia and Ukraine. France shows a higher allocation to urban centres, with a largely unchanged spatial distribution for the rest of the country. Russia and Ukraine show vastly different spatial distributions, with more emissions attributed to cities, visible urban centres and highways, as well as a reduction in artifacts.

As city inventories compiled by local institutes or authorities are prepared with the most detailed local knowledge, they are here seen as the gold standard with which to compare our European emission dataset. Nonetheless, there could be also significant errors in the spatial distribution and absolute emission estimates of local city inventories. We compared the absolute NO_x estimations for CAMS-REG v4.2 and CAMS-REG v8.1 to the data of eight cities for which independent city inventories was made available to us (Sect. ).

Absolute emission comparisons are given in Fig. . The mean absolute percentage error of CAMS-REG v4.2 in comparison with local city inventories was 35 %, with the smallest error for Paris (18 %) and the largest error for Bologna (53 %). All cities showed underestimations in CAMS-REG v4.2 compared with local inventories, which we explain by the generally too-low urban AADT values from OTM-based estimation (Sect. ), as well as the more basic gap filling approach employed in v4.2.

Using CAMS-REG v8.1 emissions, the average difference was 18 % compared with the city scale inventories. All estimates improved except for Helsinki, and improvements were largest for Barcelona and Milan. CAMS-REG v8.1 largely underestimates emissions for Helsink (-26 %), and overestimates emissions for Milan (+26 %).

Higher emission totals in urban areas were also estimated for most of the cities for which no locally-made city inventory was available for comparison (see right side of Fig. ). Here, Kiev and Istanbul saw strong increases compared to CAMS-REG v4.2 (+84 %, +360 %, respectively).

Absolute emission estimates are impacted not only by the spatial distribution of country totals, but also by the country totals themselves. Between CAMS-REG v4.2 and v8.1, there has been a change in reported country totals for some countries (see Sect. ). To understand the separate effects of the spatial distribution, we compared the relative shares of urban NO_x emission to country totals between both versions (Fig. ). Here, the relative shares of urban emissions increased for most cities, with the exception of Helsinki, Athens and Porto. The case of Helsinki is the only city showing a decreasing performance compared to the local inventory. In CAMS-REG v4.2, a large proportion of Finnish national emissions were allocated to the capital city (Fig. ), in line with the population-based method used (Sect. ). In Finland, over 30 % of the population lives in Helsinki, which is a high value for Europe .

The absolute emission changes in each city follow the changes of relative urban emission shares (Figs. , ). Therefore, the changes between CAMS-REG versions can be attributed to the updated spatial distribution. Across all cities, the mean increase of urban emission share was 34 %. Istanbul, Milan and Kiev saw high increases of relative shares (160 % and 100 %, 90 %, respectively) (see Fig. ).

Figure compares the spatial distribution for London between the urban inventory (LAEI) and the previous and recent CAMS-REG estimates in 1 × 1 km resolution, normalized by total urban emissions. The original 0.05° × 0.1° resolution of the CAMS-REG v4.2 dataset was downscaled to 1 × 1 km using the UrbEm tool . In the local and CAMS-REG v8.1 estimates, major roads such as the outer M25 ring or the North Circular Ring are clearly visible. Compared to the local inventory, CAMS-REG v8.1 seems to overestimate emissions at certain highways. Spatial correlation between the local inventory and CAMS-REG v8.1 reaches R2=0.62, with p<0.001, and spatial cross-correlation was calculated at I=0.06, p<0.001. Spatial correlation between the local inventory and CAMS-REG v4.2 reaches R2=0.33, with p<0.001 (downscaled with UrbEm), and spatial cross-correlation at I=0.11, p<0.01. Spatial autocorrelation of the local inventory (Moran's I) is I=0.07.

To derive a local inventory for Milan, started with a complete road graph that had been simplified to include the fewest oriented arcs capable of representing the most significant motions. Data from motorway companies, ANAS (National Autonomous Roads Corporation) and local authorities of vehicular traffic data (from traffic counters, cameras, passages at toll booths and motorway barriers) were used in a flow assignment model for estimating the origin and destination matrices over the entire network. To extend the spatial extension of the detailed estimates and avoid the calculation of diffuse traffic emissions, the simplified road graph was used to train and test (with a data split of 75 % and 25 %) a RF model for predicting emissions by road arch, according to the following variables: vehicles (cars, high-duty, low-duty and motorcycles) and 12 variables describing road characteristics. The ML performances are confirmed for training and testing in the range of an R2 of: 0.8–0.6 for high duty, 0.9–0.8 for light duty, 0.8–0.7 for motorcycles and 0.9–0.7 for passenger cars. For a detailed description of the Milan local inventory, see .

An overview of the spatial distribution of road transport emissions from the local Milan inventory and CAMS-REG versions are shown in Fig. . Like to London, the CAMS-REG v4.2 inventory was downscaled using the UrbEm tool to match the spatial resolution of the local inventory. The Milan local inventory places most emissions on the outer ring road of Milan, while also estimating emissions for small roads. CAMS-REG v8.1 places more emissions on the inner ring road, and less emissions on local roads in general. Ring roads and highways are less visible in CAMS-REG v4.2. Spatial correlation between the local inventory and CAMS-REG v4.2 (downscaled with UrbEm) inventories reaches R2=0.25, with p<0.001, and spatial cross-correlation is at I=0.08 with p<0.001. The spatial correlation between the local inventory and CAMS-REG v8.1 is R2=0.59, with p<0.001, and spatial cross-correlation reaches I=0.06 with p<0.001. Moran's I (spatial autocorrelation) for the local inventory is at I=0.07. Low spatial autocorrelation is captured in both versions of CAMS-REG.

Our emission factor set differentiates between urban roads, rural roads and highways. The allocation to highways was straightforward, and is done via OSM classes (see Table ).

We further tested the impact of the methodology to determine whether a road receives an urban or rural emission factor. In the previous version of this dataset, the emission factor of roads (or of gridded road proxies) was determined by land use class or population density . In this update, we set the road status by the maximum driving road speed allowed on the road (see Sect. ). This was thought to better represent real-world emission factors than the land use class around the road and align the method with the approach of the COPERT emission inventory model . For the first method, we gave an urban status to roads within an urban CORINE grid cell (CORINE categories 1.1.1 or 1.1.2). For the second method, we attributed urban status for roads with a maximum speed of ≤50 km h⁻¹.

Figure shows a comparison of urban and rural allocation for both methods. It is visible that the allocation by maximum speed leads to more emissions being classified as urban, both inside and outside urban areas. These roads subsequently receive urban (and therefore higher) emission factors compared to rural roads. Over the whole domain, the ratio of urban to rural emissions is greatly different for both approaches. Using a speed-based approach, the ratio between urban and rural emissions is approximately 4 : 1, whereas it is approximately 1 : 2 when using a land-use–based approach. This leads to a wider use of higher, urban emission factors in the speed-based approach (see Fig. ). We tested the impact of both methods on overall city emissions (Sect. ). For each city, the difference was very small and typically less than 1 % of the final result.