category: literaturenote citekey: sheehandevelopmentevaluationstatisticalmodels2026 title: Development and evaluation of statistical models for international-scale road traffic flow estimation authors: "Sheehan, Annalisa; Jephcote, Calvin; Gulliver, John" year: 2026 date: 2026-04-01 2026-04-01 doi: 10.1016/j.envint.2026.110231 publication: Environment International url: "https://www.sciencedirect.com/science/article/pii/S0160412026001893" zotero_key: KC3X9H5H zotero_storage: XXVXNNX5 collections: magistritöö / kohalikud teed folder: 001_artiklid firstAuthor: "Sheehan, Annalisa"

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Environment International

journal homepage: www.elsevier.com/locate/envint

Full length article

Development and evaluation of statistical models for international-scale road traffic flow estimation

Annalisa Sheehan a,\* , Calvin Jephcote ^b , John Gulliver ^a

^a Department of Population Health and Policy, School of Health and Medical Sciences, City St George's, University of London, London, United Kingdom
^b Centre for Environmental Health and Sustainability, University of Leicester, Leicester, United Kingdom

ARTICLE INFO

Keywords: Road traffic flows Machine learning Geographic Information Systems (GIS) Road traffic modelling Environmental modelling

ABSTRACT

A major shortcoming of air pollution and road traffic noise models is a lack of traffic data, especially for local roads. We aimed to increase the coverage and accuracy of data on annual average daily traffic (AADT) flows on all road types to support the development of emission inventories. We developed statistical machine learning approaches (Random Forest – RF; extreme gradient boosting − XGB; generalised linear mixed model – GLMM) to model AADT, using open-data on measured traffic flows from 4744 sites, covering 12 areas in 7 European Countries. Traffic flow predictor variables (N = 51) described the types of roads, road network connectivity, population, drive-time, land use and topography. A 1000-fold cross-validation procedure was used in model training and testing, where a randomly stratified (by road type and area) selection of 80% of traffic counting sites were used to train models, with the remaining 20% of sites reserved for model testing. The predictions for all reserved sites from the 1000 iterations were pooled to provide an 'ensemble' prediction for each site. For performance evaluation, we compared 'single' models developed using the whole dataset with models 'combined' from road-type sub-models (highways, local, residential). RF and XGB performed similarly overall (R² 0.85–0.86) and outperformed GLMM (R² : 0.69–0.73). The 'combined' method slightly outperformed 'single' models overall, with notably better performance for residential roads by using sub-models. For transferability to other areas, we recommend testing the need for local calibration of the models (i.e., regression) using measurements of AADT covering different road types.

1. Introduction

Road traffic has for several decades been the main source of air pollution and environmental noise in many urban areas (World Health Organization, 2019; European Environment Agency, 2020) and is increasingly a problem in rural areas. Understanding spatial and temporal patterns of traffic is an important aspect for both the management of environmental impacts and understanding the health effects relating to traffic pollution. There are two options for data acquisition to assist with this inquiry: 1) observations of traffic for specific roads or groups of roads either by automatic or manual counting, and 2) simulation models of traffic flow/distribution. Traffic counting is generally sparse with many countries lacking a national approach to traffic monitoring; these may exist but are often not presented for open access. The United Kingdom (UK) is unusual in that it has a comprehensive network of automatic monitors, supplemented with estimated counts, and includes some counting on minor roads (Department for Transport, 2025a). Even in well-developed networks such as in the UK, traffic counting represents a small fraction of the road network (*<*1%) and does not provide sufficient coverage for widespread geographical assessments. There are open-access national- and city-region-scale datasets covering different road types, but these are not readily available for many locations.

Traffic flow modelling has traditionally focussed on simulation (i.e., 'traffic assignment') approaches based on origin–destination matrices (i. e., trip generation). Traffic assignment models (e.g. SATURN) may be used by consultants to generate traffic flows across a connected road network, or used for data blending with count data, but this is not cost effective and potentially not computationally feasible for largegeographical-scale applications. Alternatively, statistical traffic modelling has been developed in recent years to estimate annual average daily traffic (AADT) flows. Statistical models are based around regression techniques where traffic flows (in the form of counts) are used as the response (i.e., dependent) variable to train a model based on a series of predictors derived from geographical data on the road network, land

E-mail address: asheehan@sgul.ac.uk (A. Sheehan).

https://doi.org/10.1016/j.envint.2026.110231

^* Corresponding author.

use, population and topography. Examples include, the first UK-wide approach (Morley and Gulliver, 2016), with similar approaches developed elsewhere (Apronti et al., 2016; Fu et al., 2017; Jung et al., 2017; Sfyridis and Agnolucci, 2020), a study in Australia informed by the UK approach (Alvarado-Molina et al., 2023), and recently approaches that involve machine learning (Shen et al., 2024). Traffic flow estimates have been used to enhance air pollution modelling in national studies (Alvarado-Molina et al., 2023; Jephcote and Gulliver, 2025) and on an international-scale (Shen et al., 2024).

In this study, we present results of developing statistical models to predict AADT on an international scale, motivated by a study on the health effects of environmental noise as part of an international, multicohort health study including 7 different countries in Europe (van Kamp et al., 2022). The first known attempt to model traffic flow estimate at international-scale was by Shen et al. (2024), who applied the data to enhance European-wide air pollution models. Random Forest models were shown to provide good cross-validation (CV) performance overall (CV-R2 = 0.82), with good performance for estimates on main roads (CV-R2 = 0.60–0.69), but weaker estimates on minor roads (CV-R2 < 0.5), especially residential roads where models performed poorly (CV-R2 = 0.02). One potential reason limiting model performance is the reliance on predictor variables that use relatively simple measures of proximity (e.g., Euclidean distance and circular buffers) to summarise the influence of geographical features on the variance in AADT. We aimed therefore to create alternative, 'smart' predictor variables to improve the performance of models in general and especially on minor roads. Our vision being to increase the density and accuracy of data that is used in environmental models for estimating emissions (e.g., air pollution, sound). Potential beneficiaries of better traffic flow estimation include: 1) reduction of exposure misclassification in epidemiological studies, 2) potentially in generating data or gap filling data in regulatory modelling (e.g., 'strategic noise mapping' as part of the European Noise Directive), 3) road maintenance and resource planning.

2. Methods

To train and evaluate statistical models to estimate annual average daily traffic (AADT) we sought openly available traffic count data within Europe to act as the dependent variable. We associated the traffic count sites with their corresponding road link using the provided locational coordinates. We then used open, geographical data to generate a range of complementary predictor variables to train and test models using machine learning (ML) and supervised regression. Finally, we used cross-validation to compare the performance of different approaches. We also compared the performance of models with a simplified approach where we applied the median measured observation for each road type as a 'constant' to represent a 'worst-case-scenario' where modelled data were not available.

2.1. Data

2.1.1. Road traffic counts (dependent variable)

To source data on traffic counts, we used prior knowledge of some of the datasets used in this study from our involvement in the development of traffic models in Shen et al. (2024). The strategy for model development was to achieve broad geographical representativeness by obtaining traffic count data from different countries and representing different road types (e.g., motorways, local roads, residential roads). In this study, we aimed to produce models for a single year relating to the observed traffic counts (AADT). We found only a few national datasets, with most relating to city-regions. Where national datasets were available for relatively large areas (e.g., UK) we selected subsets of the data with the aim of not oversampling from one data-location.

Traffic counts were collected for 12 areas in 7 countries. The number of traffic count locations by country, year of data collection, and source of data is shown in Supplementary information Table S1. For most of the

sites, AADT data for the year 2019 was chosen, however, if data for this year was unavailable, the closest available year was chosen. In the case of the UK, we chose a predominantly urban area in the north-west covering Liverpool and Manchester and the south-west covering Bristol and South Wales.

Table S2 (Supplementary Information) shows the number of sites by road type and location yielded from the sources in Table S1. We subsequently capped the maximum number of sites by road type in any location to 200 to achieve a better balance across the whole dataset. Where the number of sites exceeded 200 by road type in a location, we split the data into quintiles by traffic count and randomly selected 40 sites from each quintile to obtain a total of 200 sites. Following Tukey's (1977) statistical guidance for the detection and removal of outlier we increased the standard value of 1.5*IQR to 2*IQR for outlier detection given the high level of right skewness (2.8) in the traffic count data (i.e., limit lower values of Q1 − 2*IQR and upper values of Q3 + 2*IQR), resulting in the removal of 544 sites from the dataset, resulting 4744 sites remaining for model training and testing.

We used IQR*2 to remove outliers (stratified by road type) rather than IQR*1.5, removing 93 (1.9%) traffic measurement sites; IQR*1.5 would have yielded removal of an additional 76 sites (1.5%), 3.5% in total. The number of sites removed varied by road type and area. The greatest difference between IQR*1.5 compared to IQR*2 was on primary (n = 25) and secondary roads (n = 24), with *<*10 sites removed for each of the other road types. In 10 out of 12 areas, the difference was ≤ 8 sites removed from applying values of 1.5 and 2 for the outlier multiplier. Only in Barcelona (n = 28) and Greater Manchester (n = 18) were there relatively large differences between these two outlier removal thresholds. We chose to remove outliers rather than reassigning values (i.e., winsorizing based on upper (e.g., 95th) and lower (5th) percentiles of AADT) because of the relatively small number of sites being removed from the dataset. The final selection of traffic counter sites by location is shown in Table 1. We used a Kruskal-Wallis test to study overall differences in AADT by site type between areas, and a post-hoc Dunn's test, of 'Holm-Bonferroni' type, to study differences between pairs of areas. Comparison of distributions of AADT between areas by site type showed statistically significant differences (p < 0.05) with a large average effect size (0.40). From the Dunn's test, 143 out of 269 (53%) pairwise comparisons (i.e., between areas by site type) showed no significant difference in distributions of AADT.

2.1.2. Preparation of the road network

Line features (i.e., road links) without a motorized vehicle denomination were removed. The OSM feature class (i.e., 'fclass') types attributed to the road network then included: motorway, motorway link, trunk, trunk link, primary, primary link, secondary, secondary link, tertiary, tertiary link, residential, living street and unclassified. The 'link' roads were renamed after their main road type e.g. 'primary links' were renamed 'primary'. We used boxplots and non-parametric tests to further group the road classes, resulting in six categories of 'fclass': motorway, primary, secondary, tertiary, residential (including residential, living street and unclassified).

The road network was prepared for the needs of generating different types of variables. Some variables, for example, required the network to be "routable" (i.e., network analysis). We used tools in a geographical information system (GIS) to clean (i.e., snapping links to road junctions and removing links that could not be resolved) to provide a topologically connected road network. The main steps to topologically clean the road network included: splitting road links where they intersect with other road links, joining two road links which have the same road type and no road intersections, and removing unconnected roads links. These steps ensured a topologically connected road network, with road links split at intersections.

The traffic count sites were initially assigned to their nearest OSM road link and the record linkage was deemed valid if the following sequence of steps was passed: 1) The matched road link is less than 10 m

Table 1 The number of AADT traffic counter sites by city and road type used in the analysis after data reduction.

Area / Country	Motorway	Trunk	Primary	Secondary	Tertiary	Residential*
Nantes, France	1	7	190	200	171	112
Lyon, France	62	118	199	200	200	90
Loiret, France	0	5	68	197	200	17
Toulouse, France	0	0	76	111	113	2
Frankfurt, Germany	162	25	78	0	2	0
Cologne, Germany	126	10	87	0	1	0
Ireland	106	100	84	19	0	0
Sicily, Italy	19	3	99	59	3	0
Barcelona, Spain	0	3	18	79	113	16
Switzerland	200	34	89	30	0	0
Liverpool and Manchester, UK	108	115	48	53	31	141
Bristol and South Wales, UK	16	37	47	39	31	174
TOTALS	800	457	1083	987	865	552

^* Residential road type includes living streets and unclassified roads, please see Section 2.1.2 for more information.

away (i.e. the upper local geographic discrepancy threshold between projection systems); 2) Major roads (i.e., motorway, trunk, and primary) record more than 2 vehicles per minute; 3) Counts on minor roads (i.e., secondary, tertiary, and residential) are less than the median AADT value of the sites assigned to major roads; 4) Sites assigned to link roads are less than the median AADT value of the same road type AADT (i.e., "primary link" < median AADT on "primary" roads); 5) Sites within the major and minor road groups are not deemed as outliers (i.e., Tukey's 1.5*IQR rule). Invalid site assignments from this first data pass were flagged and assigned to the 'best' road link within 50 m (i.e., smallest absolute percent error between the count site and the median AADT value of the road class). A final manual check was conducted on count sites which had an available site name or location to check it matched the OSM road link name. Less than 1% of roads were flagged and checked.

2.1.3. Predictor variables

We used open data to provide a harmonised basis for developing international-scale models. Most of the variables were derived from the Open Street Maps (OSM) road network, along with population data on a 100 m resolution grid from 'WorldPop' and elevation data on a 25 m resolution grid from the EEA European Digital Elevation Model, as show in Table 2.

We generated a range of predictor variables related to the distance to and density of road links and junctions, road network connectivity, population distribution, urbanicity, and topography. Instead of using circular buffers to measure proximity we measured distance along the connected road network. In total 51 predictor variables were tested in the traffic model (Table 2). Further explanation for some of these variables follows.

2.1.3.1. Static population. A population estimate ('rd_pop') was assigned to the road network, and thus also traffic counting sites, by intersecting road junctions (i.e., nodes) with the 100x100m population grid (i.e., WorldPop) and distributing the extracted population values to the road links connecting to each node. The final value for each road link is the sum of the values assigned to its start and end nodes.

2.1.3.2. Drive-time population. This variable required the 100x100m 'worldpop' data assigned to road links (see above). 'Drive-time population' (e.g., 't_05_min') is the number of people that can reach each road link within a 5-, 10-, or 15-minute 'drive-time' given the traffic speed assigned to the network; it is broadly equivalent to a service area function in GIS. For each road link, the population ('rd_pop') was routed across the road network using the data on the speed (i.e., limit) values assigned to the network (e.g., 70mph on motorways and trunk roads, 60 mph on primary, secondary and tertiary roads, and 30mph on residential roads). The final estimate for each road link (the target) was the sum of people associated with all source links that could reach a target link within a given drive-time. We also generated the drive-time variables using half of the speed limit for each road type, to reflect a potentially (i. e., unknown) more congested or speed-managed traffic situation (e.g., 'ht_05_min'). Previous studies have shown that half the national speed limit is a good approximation of vehicle speed, through comparisons to satellite-derived vehicle speed estimates (Sheehan et al, 2025a) and Google's Directions API traffic speed data (Sheehan et al, 2025b). The GIS processing was undertaken in R using the 'cppRouting' package developed by others not involved in this study (Larmet, 2022). To account for traffic flows from outside of the study area, we enlarged the 'bounding box' by 3 km.

2.1.3.3. Gradient. The gradient of each road link was derived from the EEA European Digital Elevation Model (EU_DEM) 25x25m grid data set. The elevation for each (start and end) node and road centroid was extracted from the DEM, and the minimum and maximum elevation for the road link calculated. The road link 'rise' was calculated as the difference between the maximum and minimum elevation; the maximum value (i.e., a proxy for remoteness) was used as 'elev_max'. The 'gradient' was calculated by dividing the rise by the road link length, which was capped at 10%.

2.1.3.4. Road junction connectivity. We devised 'connectivity' measures based on the number of road links at each road junction ('con_n' – connectivity number) and a measure of road class (dis)similarity between connected links at each junction ('con_diff' – connectivity difference). 'Con_n" is simply the average of the number of roads connected to each pair of (start and end) nodes (i.e., junctions) and assigned to the corresponding road link. 'Con_diff' aims to describe road links that are likely to experience higher or lower than average volumes of traffic given the class of road link being considered (e.g., two connecting roads of the same class will have a value of zero; e.g., a residential road connecting to a tertiary road will have a value of '1′; a residential road connecting to a motorway will have a value of '6′, etc.). For each (start and end) node associated with a road link the maximum and minimum value of 'road class difference' is determined, and the average of these differences is assigned to the road link as 'con_diff'.

2.1.3.5. Terminal. Road 'dead-ends' (i.e., cul-de-sac) are often located in residential areas and therefore may represent roads with low traffic. The 'terminal' variable is found from the 'con_n' variable where one of the nodes associated with a link returns a value of zero. If both nodes return a value of zero, then the road link is not connected within the network (see above step on preparation of the road network).

2.1.3.6. Betweenness centrality. The basis of 'betweenness centrality' is roads which are more central in an area and often traversed in calculating the shortest route between two locations, are more likely to have

Table 2 Description of the variables.

| Variable
name | Description | | | | |------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--|--|--| | aadt* | Response variable: annual average daily traffic count. | | | | | scheme_2† | Seven classes of road type: 'motorway', 'trunk', 'primary', | | | | | | 'secondary', 'tertiary', 'residential', 'living_street'. | | | | | scheme_1† | Two classes of road type: 'Major', 'Minor'. | | | | | rdpop†‡ | Estimated count of the population living on each road link. | | | | | | WorldPop 100x100m population count points were assigned to the
nearest non-motorway road nodes. These counts were then equally
split amongst the roads connected to the node in question. The road
population count is the total of its two (i.e., the start and end nodes)
road-by-nodes population counts. | | | | | RUC†‡ | Urbanisation index – on a continuous scale from 0 (large open | | | | | | natural spaces) to 1 (highly populated urban spaces) constructed | | | | | | from the thresholding of focal statistics on WorldPop 100 × 100 m | | | | | | population surfaces (Jephcote and Gulliver, 2025). | | | | | end'X'm† | Number of terminal nodes within Xm. | | | | | mway'X'm† | Distance (m) to nearest motorway junction. | | | | | maj'X'm† | Distance (m) to nearest major road junction ('motorway'/'trunk'/ | | | | | | 'primary'). | | | | | t_05_min†‡ | Sum of the population within 5 min driving (using average traffic
speeds associated with each road type). (cppRouting R package:
Larmet, 2022). | | | | | ht_05_min†‡ | Sum of the population within 5 min driving (using half national | | | | | | traffic speeds associated with each road type). (cppRouting R
package: Larmet, 2022). | | | | | elev_min | Minimum elevation of road link derived from EU-DEM. | | | | | elev_max | Maximum elevation of road link derived from EU-DEM. | | | | | gradient†§ | Slope of road link (degrees) derived from EU-DEM. | | | | | con_diff† | A measure of dissimilarity between connected links (e.g., two
connecting roads of the same class will have a value of zero; a
residential or unclassified road connecting to a tertiary road will
have a value of '1′; a residential or unclassified road connecting to a
secondary road will have a value of '2′; a residential or unclassified
road connecting to a primary road will have a value of '3′, etc.). | | | | | con_n† | A measure of connectivity. The count of road links each road link is
connected to. | | | | | terminal† | Denotes road link as 'dead end'. Where 0 is not a terminal node, and
1 is a terminal node. | | | | | slip_rd | A measure of whether a motorway, trunk or primary road link is a | | | | | | slip road based on a connectivity difference value of >0. | | | | | oneway | Denotes whether traffic flows along road link in either one direction | | | | | | (0) or both directions (1) derived from OSM roads data set. | | | | | btwn_maj† | A measure of centrality of a major road link (its amount of | | | | | | influence) relative to other major road links in a connected network
(Brandes, 2008). Using NetworkX python package's function | | | | | | 'edge_betweenness_centrality' (Hagberg et al., 2007). | | | | | bus_route† | A measure of whether a road is likely to be a bus route. Using
NetworkX python package's function 'shortest_path' function and
OSM bus stop data set. | | | |

Data sources and references:

* AADT references are shown for each area in Table S1 in Supplementary information.
† OpenStreetMap: Roads (OpenStreetMap contributors, 2024).
‡ WorldPop 100x100m population grid (WorldPop, 2025; Bondarenko et al., 2020).
§ EEA European Digital Elevation Model (EU_DEM) 25x25m grid data set (European Environment Agency, 2016).
- || OpenStreetMap: Transport (OpenStreetMap contributors, 2024).

more traffic. The 'edge betweenness centrality' metric from graph theory (Brandes, 2001; Brandes, 2008), is a measure of how frequently a road link appears on the shortest path between other road links in the connected road network. We created a betweenness variable 'btwn_maj' for major roads by constructing a primal graph using the 'momepy' python package (Fleischmann, 2019). 'NetworkX' python package function 'edge betweenness centrality' was then used to calculate the road betweenness centrality using the road length as a weight (i.e., impedance) (Hagberg et al., 2007). The road betweenness centrality variable was only generated for major roads due to computational constraints and the large size of some of the study area road networks (e.g. Cologne study area had more than 1.2 million road links). To limit the influence of edge effects on the betweenness centrality estimates, we enlarged the 'bounding box' by 30 km (Gil, 2017).

2.1.3.7. Bus links. The premise, especially for local/residential roads, is that road links trafficked by buses are likely to be a marker for higher levels of within-road-class traffic. The aim was to create routes between bus stops, to create bus routes suggesting where the buses travel through the network. To create a 'bus_route' data set, the bus stop locations from the OSM transport data set were used alongside the OSM road network. Network analysis was used to derive bus routes across the connected road network implemented using 'Network X's' python package 'shortest_path' function. To do this, the bus stops were snapped to the nearest point on the OSM roads data set and the OSM roads were split at the point of intersection with the snapped bus stop. This was to enable bus stops to coincide with nodes in the network Graph. The 'shortest_path' function was then used to find the shortest route along the OSM road network between all the bus stops. The bus routes were then transposed onto the OSM road network to create the 'bus route' data set. There are two sources of uncertainty in this data set: 1) the bus stop may not be snapped to the correct road link, 2) road links between bus stops via shorted path method may not represent real-world bus routes.

2.1.4. Data normalisation

All predictor variables were assessed for normality and then logtransformed, using the 'neglog' function described by Whittaker et al. (2005), where required. Subsequently, to avoid issues with scale inflation and to allow direct comparison of the influence/contribution of each predictor variable to estimation of traffic flows, the whole dataset was normalised to values between 0 and 1 (by the minimum and range of the vector, or defined limits) to revalue variables to a common scale, except where already measured in this range (e.g., urbanicity).

2.2. Model development

2.2.1. Overview of approach

The variable list was compiled in a single data frame containing 51 predictor variables (i.e., features) for model development. We used two ML approaches (Random Forests and extreme gradient boosting) and one supervised approach (generalised linear mixed model) to estimate AADT.

Random Forests (RF) and extreme gradient boosting (XGB) are from the family of 'regression tree' methods, where decision trees are grown to recursively reduce the standard error of the estimate (SEE) in estimating the dependent variable (i.e., AADT). RF extends the principle of decision trees by using bootstrap samples (i.e. random selection of the training data with replacement) to build multiple trees (Breiman, 2001). A further element of randomness relates to how the trees are split at each node in the tree. Splits at each node are formed on the best predictor from a random selection of variables (mtry) from the full list of variables (p). The final set of predictions for the model is the average of predictions across all trees, hence RF is referred to as 'ensemble learning' method.

The XGB method (Kuhn and Johnson, 2013) differs from RF in the way that the trees are constructed and in the way that the predictions are combined. In XGB, each tree reflects the 'loss' (i.e., the error) from the previous tree to develop a more accurate prediction in the current tree. Rather than estimating the dependent variable separately for n trees, each new tree in XGB is a regression formed on the residual from the previous tree with the aim of reducing the residual (i.e., measured as the gradient) over the minimum number of trees.

The generalised linear mixed model (GLMM), a supervised method, is an extension of the generalised linear model (GLM) to include fixed and random effects (Jiang and Nguyen, 2021). We used GLMM in this study to consider random intercepts, as exploratory data analysis showed that traffic counts separated strongly into groups of road class (i. e., 'fclass' in OSM). Exploratory analysis also showed that traffic counts separated by study area, but we did not further consider it as the aim was to develop a generalisable (i.e., transferable to other locations) approach. In addition, we experimented with quantile regression for GLMM and RF to reflect the needs of a skewed response variable (AADT). Where standard regression methods focus on predicting the mean, quantile-based methods are able to predict a range of values (mean, median, percentiles), not bound by Gaussian assumption for the error distribution, allowing models to be fine-tuned for specific settings and types of roads. However, we were unable to produce a robust solution due to the relatively low number of sites for low-flow (i.e., residential) roads.

We were interested in whether a single model would provide parity in predictive performance across the range of traffic counts (i.e., for different types of roads). We therefore used two approaches to modelling using each statistical method (RF, XGB, GLMM): 1) a single model was developed for all road types, 2) a combined model was developed by initially splitting the data into three groups of road types: a) Highways (motorways, trunk), b) Local roads (primary, secondary, tertiary), c) Residential roads (i.e., renamed as 'residential' from the previous step combining residential, unclassified roads, and living streets). These groups were determined by analysis of variance using the measured traffic counts. Fig. 1 shows the boxplots of traffic counts by road type and Tables S3–S8 (Supplementary information) shows descriptive statistics of traffic counts by location and road type. We compared the performance of the single and combined models on the reconstructed data by combining the predictions from the 3 road-type sub-models. Following model development, we also separated the predictions from the single model into same three groups used in the combined approach to see if the separate models from the combined approach provided a stronger basis for predicting across the range of measured AADT.

2.2.2. Model parameters

The hyperparameters used for Random Forest were identified through experimentation on the full data set. The main parameters to consider are the number of trees (ntrees) and the number of variables in the subset at each split (mtry). For ntrees we started by multiplying the number of features (X) by 10 (Boehmke and Greenwell, 2020) and then varied the number of trees by +/- 50 trees. We observed the impact of varying values of ntrees on the 'out-of-bag' (OOB) error (i.e., RMSE) generated by RF as part of this process using plots in R. A value of 500 for ntrees was used in subsequent model development. The number of

Fig. 1. Traffic counts used for modelling by road type. Boxplot show the median, ◆ symbol represents the mean and ○ represent outliers.

predictors randomly sampled at each split (mtry) was calculated using the number of features in the data set divided by 3, which is the default for regression (Boehmke and Greenwell, 2020). Varying values of mtry did not lead to notable differences in the explained variance.

To find the best hyperparameters for the XGB model, a randomised grid search was conducted on the full dataset, using 10-fold crossvalidation and 500 rounds (with early stopping after 20 rounds to prevent overfitting (Wade, 2020)). The randomised grid search was run 30 times on random parameter sets, selecting a random number from ranges for each parameter. For the 'learning rate', the value was randomly selected between 0.01 and 0.2. The 'maximum depth of a tree' was selected between 3 and 10. The 'fraction of observations to sample' for each tree (subsample) was selected between 0.6 and 1.0. The 'fraction of features to sample' when building each tree (colsample_bytree) was selected between 0.6 and 1.0. The 'minimum sum of instance weights' needed in a child (min_child_weight) was selected between 1 and 10. The 'gamma' (minimum loss reduction required to make a split) was selected between 0 and 2.

The final hyperparameters used in the XGB model were: objective = "reg:squarederror", learning rate = 0.078, maximum depth of a tree = 10, subsample = 0.832, colsample_bytree = 0.633, min_child_weight = 10, gamma = 0.762, best_iter = 66.

The GLMM models were constructed using Poisson (log link function) as the model family (i.e., for count data). For the GLMM single model we applied random intercepts using the variable with six classes of road type (i.e., notation: '1 | scheme_2′). We also applied random intercepts for 'scheme_2′ in the sub-models for the combined model approach, except for the residential model which had a single road type. In combination with 'scheme_2′ we also experimented with other categorical variables. For example, we tried an interaction between road type and urbanicity (i.e., '1 | scheme_2:ruc') on the basis that roads of the same class in rural areas would likely have lower traffic flows than those in urban areas. For fixed effects in the model, we used a forward supervised approach by firstly creating a correlation matrix between the predictors and response variables and then taking the variable with the highest correlation first, and so on. The correlation matrix for the variables is shown in Fig. S1 (Supplementary information).

2.3. Model performance evaluation

Some ML methods have built-in cross-validation by design. This is via the bootstrapping sample where a user-defined proportion of the data can be used for creating the ntrees with the remaining data, referred to as OOB, being used in cross validation. RF, for example, randomly selects two-thirds of the data without stratification to develop each model and retains one third of the data to obtain the OOB error (Breiman, 2001; Liaw and Wiener, 2002). It is possible to override the default OOB sample selection to impose a different percentage of the data selected for the OOB sample or impose a user-defined approach. We took the latter option and programmed our own function for model development and evaluation for two specific reasons: 1) we wanted to develop models with a random stratified sample by quintiles of traffic counts within each of road type group, and 2) to have a consistent basis for comparing results between the different methods (ML and GLMM). We therefore adopted a 'Monte-Carlo' type (Picard and Cook, 1984), sometimes referred to as Monte-Carlo Cross Validation (MCCV) (Xu and Liang, 2001; Haddad et al., 2013) approach by creating 1000 models in each case, where in each model run the data were split into 80% for training and 20% for testing by randomly selecting traffic sites stratified by area name, road type and AADT quintile. The final model prediction for each traffic site was therefore the average, 'ensemble' prediction from the 1000 model runs.

For model performance evaluation we used the following statistical tests: 1) coefficient of determination (R2 ), 2) Root Mean Square Error (RMSE), 3) Factor-of-Two (FAC2 − the % of values within half or double the measurement), 4) RMSE normalised by the range of measurements

(NRMSErange), 5) RMSE normalised by the mean of the measurements (NRMSEmean) (shown in Supplementary information Eqs. S1–S5). For each set of predictions, we analysed the distribution and normality of the residuals. For XGB, we also interpreted variable importance plots to gain insight into the contribution of individual variables to model prediction and the difference in types of variables used in the model by road type group in the combined approach. We produced standardised residuals for each approach and area (i.e., city/region) and studied their scale using plots and spatial variability using Spatial Dependence: Weighting Schemes, Statistics (spdep) R package (Bivand and Wong, 2018) in R for Moran's I and 'hot spot' mapping using the Getis-Ord 'G' statistic in ArcGIS Pro (ESRI Inc., 2024).

3. Results

Table 3 shows performance results from 1000-fold cross-validation (CV) for the three statistical modelling approaches and the approach using a 'constant', where a fixed value for AADT was applied from the median measured value for each of six road classes. Results are shown for each single model and for each of three road type groups within the single model. Results for sub-models (i.e., separate models for each road type group) were 'combined' by appending the predictions for each submodel. For each model in full and sub-setting of the data, the number of sites used in model development and CV is shown. For the single model and each of the three sub-models in the combined model, the results are based on the average of 1000 CV iterations. Fig. S2 shows a distribution of the number of times sites were used for model testing (i.e., included in the 20% of reserved data for each model developed). Scatterplots of estimated versus measured AADT are shown in Fig. 2 for each of the models (XGB, RF and GLMM) from the combined approach, with plots for the single models shown in Fig. S3. Fig. S4 shows scatterplots of estimated versus measured AADT for each of the sub-models in the 'combined' approach. Boxplots of measured and predicted AADT separated by the six OSM road classes are shown in Fig. 3 for the XGB combined model, with results for other models shown in Figs. S5–S9. Descriptive statistics of the measured and estimated AADT separated by the six OSM road classes and the combined and single models are shown in Tables S9–S14. Standardised residuals for each of the models are shown in Figs. S10–S12 by road type and in Figs. S13–S15 by area/ country name, with the number (and %) of sites exceeding ± 3 σ (i.e., standard control limits for data with a skewed response variable) shown in Tables S15–S20. The variables included in the GLMM models are shown in Table S21 along with coefficients for fixed effects. Table S22 shows Global Moran's I (z-scores and Moran's I values) of the standardised residuals by area and each of the 6 models. Table S23 shows the average variable importance for the XGB 1000 MC model runs.

As Table 3 shows, the combined XGB model performed best overall (R2 = 0.86; RMSE = 9999; FAC2 = 83%) and by sub-model, with the exception of the sub-model for residential roads where performance between RF and XGB methods was the same except for slight differences in values of RMSE. Overall, there were only small performance differences between the RF and XGB methods. Single and combined models had similar performance overall, but for residential roads the performance of the single model approach was notably weaker (e.g., R2 = 0.40; RMSE = 1142 in RF) than in the combined approach (R2 = 0.56; RMSE = 979 in RF) where sub-models by road type were used.

Models for residential roads performed less well than for other road groupings in the RF and XGB single and combined models in terms of R2 , whereas there was more parity in performance in the GLMM models between road type groups. As expected, values of R2 are lower for each of the sub models (R2 : 0.44–0.72) than in the combined models (R2 0.73–0.86). The application of a 'Constant' value for each road type yielded the weakest result (R2 = 0.59). Although overall correlation with measurements of AADT was moderate, the performance within each road type was poor (R2 : 0.00–0.2).

The values of NRMSE provide a basis for comparing performance between the single model, the single model separated by road group, the combined model and its sub-models. Values of NRMSErange and NRMSEmean for the RF and XGB methods further show that sub-models for residential roads (NRMSErange: 14%; NRMSEmean: 58%) were generally weaker than models for the other road types (NRMSErange: 11%; NRMSEmean: 41–47%), but not in the case of GLMM.

As shown via the regression fit lines and equations in Fig. 2, and

Table 3 Performance results from 1000-fold cross-validation (CV) for the three statistical approaches and the 'constant' model.

Method*	Metric	Single model	Estimates from single model separated by road type		Combined model†	Separate models by road type‡
			Highways (H)	Local (L)	Residential (R)	H + L + R	Highways (H)	Local (L)	Residential (R)
Training	N	3834	1005	2383	446	3834	1005	2383	446
HOV§	N	910	252	552	106	910	252	552	106
RF	R2	0.85	0.71	0.64	0.40	0.85	0.71	0.64	0.56
	RMSE	10,237	19,434	2719	1142	10,233	19,445	2724	979
	NRMSErange (%)	6	11	11	16	6	11	11	14
	NRMSEmean (%)	63	42	46	68	63	42	47	58
	%FAC2	82	87	84	63	83	86	84	66
XGB	R2	0.85	0.72	0.64	0.48	0.86	0.72	0.65	0.56
	RMSE	10,058	19,079	2720	1070	9999	19,028	2678	981
	NRMSErange (%)	6	11	11	15	6	11	11	14
	NRMSEmean (%)	62	41	46	63	62	41	46	58
	%FAC2	82	87	83	63	83	87	85	66
GLMM	R2	0.69	0.41	0.40	0.40	0.73	0.47	0.44	0.48
	RMSE	14,525	27,696	3495	1146	13,735	26,173	3376	1067
	NRMSErange (%)	8	15	15	16	8	15	14	15
	NRMSEmean (%)	90	59	60	68	85	56	58	63
	%FAC2	71	75	72	61	72	75	73	63
Constant	R2	0.59	0.20	0.20	0.00
	RMSE	16,812	32,053	4049	1529
	NRMSErange (%)	9	18	17	21
	NRMSEmean (%)	104	69	69	91
	% FAC2	61	67	62	41

^* Methods: RF (Random Forest); XGB (eXtreme Gradient Boosting); GLMM (generalised linear mixed model).

^† Combination (appending) of predicted AADT from separate models by road type (H- Highways; L – Local; R – Residential).

^‡ Models by road type: Highways (motorways and trunk roads); Local (primary, secondary, and tertiary roads); Residential (residential roads).

^§ HOV – Hold-out-validation (i.e. a target of 20% of the data reserved for model performance testing).

Fig. 2. Estimated versus measured AADT for each of the 'Combined' models.

similarly in Figs. S3 − S4, models overall tend to under-predict measured AADT. This is more notable for higher levels of AADT associated with highway and trunk count sites (e.g., Fig. 2). Overall, however, mean predicted AADT and mean measured AADT are similar by road type, as shown in Fig. 3 for the XGB combined models, and in Figs. S5–S9 for the other methods. Models tended to result in higher median AADT than found in measured data. Fig. 3 can also be used to supplement the results in Table 3 in terms of showing that models did not fully capture the explained variability in measured AADT. Descriptive statistics for these comparisons can be found in Tables S9–S14.

For the XGB Combined model, 97% of the standardised residuals fell within ± 3 σ (Fig. S10). The 3% of standardised residuals > ± 3 σ were predominantly motorway roads (2.9%) and a few trunk roads. The pattern is similar for the other methods (GLMM and RF) as shown in Figs. S11 and S12. There were no outlier residuals for primary, secondary, tertiary or residential roads. The outlier residuals for motorway roads were mainly in the German cities (Frankfurt and Cologne), Switzerland, and Liverpool and Manchester (Figs. S13–S15 and Tables S15–S20). This is unsurprising as these are the areas with the majority of data on motorway AADT. Between 16% and 18%, depending on the method (XGB, RF, or GLMM), of standardised residuals for

motorways were > ± 3 σ. For trunks roads, *<*1% to *<*2% of standardised residuals were > ± 3 σ. The analysis of standardised residuals revealed systematic (i.e., trend) under-prediction and over-prediction (Figs. S10–S12) but not strongly linked to specific locations (Figs. S13- S15). We subsequently modified the various approaches to address the outlier residuals (i.e., under- and over-prediction). Firstly, we ran all models with log-transformed values of measured AADT (i.e., response variable). This resulted in ~5% reduction in values of R2 for the Single models, ~4% reduction in R2 for the Combined models, and increases in values of RMSE by 12–16%. We also applied regularisation which aims to balance bias and avoid over-fitting of models. For the ML approaches this was achieved by tuning additional hyperparameters using 'Grid-Search' for XGB (L1 – alpha; L2 – lambda) and the Regularised Random Forest 'RRF' package with the coefficient for regularisation ('coefReg') (Deng, 2013). Regularisation reduced the number of outliers (*>*3σ) in standardised residuals by about 1% but we also found a slight loss in performance. We therefore did not revise the original approaches.

As summarised in Table S22, in terms of Global 'Moran's I' we found geographical clustering of standardised residuals in some of the locations (i.e., cities/regions). Clustering was more prevalent from the GLMM approach than from RF and XGB. For GLMM, in only 2 out of 12

Fig. 3. Boxplots showing the measured and predicted AADT by road type using the XGB Combined Model. Boxplot show the median, ◆ symbol represents the mean and ○ represent outliers.

locations for the Combined model and in only 3 out of 12 locations for the Single model was there no or weak spatial autocorrelation. Conversely, for RF we found no or weak spatial autocorrelation for standardised residuals in 10 out of 12 locations for the Combined model and 9 out of 12 locations for the Single model; for XGB there was no or weak spatial autocorrelation in 9 out of 12 locations for both the Combined and Single models. For RF and XGB the highest degree of spatial autocorrelation was moderate and related to between 1 and 3 of localised clusters of sites per location and found either in city centres or around major road junctions, as noted by mapping the Getis-Ord G statistic via the 'hot spot' analysis tool in ArcGIS Pro (ESRI Inc., 2024).

Table S23 shows the average variable importance for the XGB 1000 MC model runs. For the XGB Single model, the drive-time variables (e.g. t_10_min, ht_15_min) distance to nearest motorway junction, whether a road type was a motorway or trunk road, elevation and major road betweenness had high importance in the model. For the XGB Highways sub-model, variable importance was similar to. the single model with drive-time, distance to nearest motorway junction and elevation variables ranking highest. A similar variable importance pattern was found for the XGB Local sub-model, with the addition of whether a road is a major road (scheme1: major road). Similarly, for XGB Residential submodel, the drive-time variables had high importance, in addition to distance to terminal node (end_m) and estimated count of the population living on each road link (rd_pop19).

We noted that the XGB Single model produced negative predicted values in one or more of the 1000 iterations for 3% of the training/ testing sites used. Some negative predictions were also found in iterations of the XGB Combined approach (*<*1%) but this did not result in negative predictions overall (i.e., the 'ensemble' average of all predicted values from 1000 iterations of prediction). The negative predictions for the XGB Single model were predominately on tertiary roads and residential roads, whereas for the XGB Combined model negative predictions occurred on most road types (motorways = 4 sites, residential roads = 5 sites, tertiary roads = 2 sites, trunk = 1 site). No negative

values were found from the RF or GLMM methods.

Following model performance evaluation, we applied the XGB Combined models, as the best performing method, to all areas used in model development. Fig. 4 shows predicted AADT from the XGB Combined model for the connected road network in A) Lyon, and B) Liverpool and Manchester. For the XGB Combined model, it took 13 s to apply in Lyon on 97,948 road links and 21 s to apply in Liverpool and Manchester on 235,304 road links. For the RF Combined model, it took 38 s to apply in Lyon on 97,948 road links and 47 s to apply in Liverpool and Manchester on 235,304 road links. For the ~3.73 million road links across the 12 study areas we found negative predictions for 355 road links (0.0095%), relating to low-flow (residential and tertiary) roads; 7 out of 12 areas did not have any negative values. We corrected negative values by reassigning them (i.e., truncation) as the lowest measured value of AADT for each road type (residential = 50; tertiary = 58) from all areas. We did not reassign values based on AADT for specific areas due to these road categories not being represented everywhere.

4. Discussion

We developed statistical approaches to modelling AADT using open data on observed traffic flows and a range of predictor variables describing the types of roads, road network connectivity, population, drive-time, land use and topography. ML approaches produced 1000 fold cross-validation R2 of 0.85–0.86 depending on the method and outperformed the supervised approach (GLMM). By including sufficient numbers of traffic counting sites covering 12 areas in 7 countries, and undertaking thorough cross-validation, we suggest the models could be transferred to other locations not used in model development.

Due to differences in traffic intensity between areas for some types of roads (i.e., motorways), our study showed that data on measured AADT, if available, could be used to test the need for local calibration (i.e., regression calibration) of the models developed here. Procuring existing localised traffic measurements or undertaking bespoke surveys for a

Fig. 4. Predicted AADT from the XGB Combined model in A) Lyon, France and B) Liverpool and Manchester study area, UK.

relatively modest number of sites may be sufficient to capture the variability in local traffic by road type to then calibrate the models locally (i.e., regression-based adjustment), or partial retraining of models with local data. It may be the case that users should consider using this work as guidance to adapt our approach and develop new models that better fit the local area.

Despite mixed findings on differences in distributions of AADT between locations, we produced models combing all areas to study the potential for a unified model for estimation of AADT. Although we used a relatively large dataset with the aim of a unified and generalisable approach to creating models, this is not without shortcomings. The results highlight the challenge of compiling a dataset with a balance of site types and with representative values of AADT.

Our motivation for developing traffic flow data was to undertake road traffic noise exposure assessment as part of an EU-funded (Horizon 2020) project looking at environmental quality and life-course mental health effects in children and adolescents (van Kamp et al., 2022). We modelled road traffic flows and subsequently noise exposures for 11 cohorts across Europe. Our approach will be of interest to others aiming to enhance data for environmental noise and air quality models as part of epidemiologic and related analyses. The approach may also be of interest to countries undertaking strategic noise mapping (e.g., as part of the European Noise Directive (Directive 2002/49/EC, 2002)) wishing to generate completely new datasets or fill gaps in existing traffic data.

4.1. Choice of statistical approaches

We considered four different approaches to traffic count modelling: Random Forests (RF), extreme gradient boosting (XGB), Generalised Linear Mixed Model (GLMM), and the median observed traffic flow value for each of six road types (motorway, trunk, primary, secondary, tertiary, residential), referred to as 'Constant'. Although GLMM was the weakest performing statistical approach, it was by no means poor, and a substantial improvement over using a fixed value ('constant') for each road type.

We limited the training and testing of AADT models to GLMM, RF and XGB. We may have overlooked methods that could have provided equivalent and better performance in our study. Other ML methods that have seen use in estimating AADT or environmental models where traffic data have been involved, including, for example, gradient boosted machines (GBM), k-nearest neighbours (KNN), support vector machines (SVM), and artificial neural networks (ANN). The number of studies comparing the performance of different methods for estimating AADT is relatively small, but they all point to RF being one of the strongest options. In a study estimating AADT in Hong Kong, for example, Pun et al. (2019) found that RF outperformed ANN, SVM, and linear regression. Das and Tsapakis (2020) showed that in modelling AADT in Vermont, USA, RF outperformed KNN, SVM, and standard regression approaches (linear and generalised linear models). In the UK, Syfridis and Agnolucci (2020) showed that RF outperformed multiple linear regression. Shen et al. (2024) only used RF based on its strength of performance in estimating AADT in previous studies. Studies in related fields have shown that boosted machine methods (GBM, XGB) are also promising. Chen et al. (2019), in developing European-scale models for air pollution, found that many of the methods (16 in total) compared have similar performance for nitrogen dioxide (NO2), with RF and GBM yielding the best results for fine particulates (PM2.5). We chose to use XGB, in addition to RF, as a more advanced and optimisable option than GBM in our study on estimating AADT.

4.2. Structure and performance of models

GLMM models (i.e., one single model and three separate models for the combined approach) were parsimonious in terms of the number variables included (1 to 2 random effects and up to 7 fixed effect variables). Being a supervised approach, the feedback from the iterative process of manually adding variables showed the dominance of road type as a random effect along with the 'drive-time' variable as the main fixed effect. We were able to determine the importance of the drive-time variable by comparing the size of the coefficients as all variables were normalised. Although the GLMM models developed in this study were shown to have good performance compared results from various methods in other studies (Morley and Gulliver, 2016; Apronti et al, 2016; Fu et al, 2017; Shen et al 2024), in terms of explained variability in AADT, the process of obtaining models was laborious and had challenges. We experienced challenges in getting the optimal combination of

variables for random effects in terms of model performance. We initially created GLMM models with different combinations of random intercept variables that had slightly better CV performance, but the models failed in application to the testing data (i.e., 20% reserved in each CV iteration). This relates to a combination of random effects that were not features of the testing (i.e., held-out) data, despite having thousands of sites for model training. For example, any inclusion of greater than two interactions in the random effects led to 'new levels' in the data.

The ML approaches (RF and XGB) provided superior performance. The performance of RF and XGB models was similar, especially in the combined model approach. The choice of method becomes a trade-off between the following considerations: 1) unlike XGB, RF did not produce negative predictions, 2) RF cannot predict outside the range of measurements used to calibrate the model (i.e., which may be an issue for transfer of models to other locations where AADT may be outside of the range of measurement locations used in this study), 3) XGB performed slightly better than RF overall. Our results slightly favour the Combined XGB model over the Combined RF model in the choice of method. Negative values for XGB Combined models were not found in the overall predictions of the Combined approach at training/testing sites, but a very small number of negative predictions were found, and subsequently corrected, when applying the models to the ~3.73 million road links across the 12 study areas. We applied a universal approach to correct for negative values of AADT (i.e., truncation) for each road type where applicable (i.e., residential = 50; tertiary = 58). This may lead to underestimation of the lowest values of AADT for other areas if the models are transferred. Ideally, negative values would be reassigned using local data on measured AADT to get an area-specific correction rather than the universal correction applied here. One criticism of the XGB method is that it has potential for over-fitting (Friedman, 2001), which is not the case with RF. This is unlikely to be an issue with a relatively large dataset as is the case here but has been noted as a potential pitfall elsewhere (Kuhn and Johnson, 2013).

The rationale for the combined approach was selecting variables for sub-models that were better suited to specific road types. If the objective is to achieve parity in performance for different road types, then a Combined approach like the one devised in this study could be considered. In the case of the RF models, the Combined approach provided notably better performance for residential roads than the Single model. For XGB there was less difference in performance between the Single and Combined approaches when evaluated by road type groups. In GLMM there was slightly better performance for each road type group and overall, by using the Combined approach as opposed to a Single model. The decision on whether to adopt sub-models based on road type should therefore be based on the objective of the exercise and the type of statistical method being used. Although we used ANOVA to determine the road type groups for the Combined approach, we recognise that determining groups by traffic counts is only one consideration. We did not undertake an exhaustive approach to testing model development with many possible combinations of road type, nor did we take an approach whereby distinct models could be created for each of the six major road types (i.e., motorway, trunk, primary, secondary, tertiary, residential) defined in this study based on the initial list of 13 road types by OSM 'fclass'.

We believe our study to be the first example where statistical traffic models for traffic flow estimation have compared Single models with separate models by road type and their recombination. In the main comparator study by Shen et al., (2024), separate models were created for four different road types (highways (motorway, trunk), primary, local (secondary, tertiary), residential) compared to three groups used in our study, the difference being we included primary roads in the 'local' sub-model rather than separately. Shen et al., (2024) did consider a single RF model, but this was dismissed in model development stage because 'the model was dominated by the observed high AADT counts on motorways, and thus the significant difference in AADT patterns on other roads cannot be represented' (Shen et al., 2024). We produced a single RF model and single models for the other approaches without loss of performance, with the exception of modest performance reduction for residential roads in the RF model, and to a lesser extent in the XGB model, noted above. All our models produced better performance overall and by road type that those published in Shen et al., (2024). This may be explained by the partly different data on traffic observations used, different variables, and different treatment of model parameters and evaluation steps. Shen et al (2024) used almost double the number of traffic observations used in our study, but ~70% of sites were UK locations, and nearly all residential sites were UK locations. We used less sites overall but had a more balanced site selection by country and road types. Ideally, we would have equal numbers of sites for each country/ city-region and by road type, but this was not possible with the available data without drastically reducing the numbers of sites used. Consideration is therefore needed on the balancing of with the number of sites overall and the representation of different road types. This is especially pertinent for residential roads, as the under-representativeness of traffic observations on residential roads in traffic data sets is a fundamental challenge for developing traffic models.

4.3. Variables included in models

Our aim was to produce 'smarter' variables than previously used for estimating traffic flows. Rather than measuring proximity by Euclidean distance or summarising features in circular buffers, we measured distance along the road network. Others have adopted similar approaches by using service areas to summarise features based on network distance (Sfyridis and Agnolucci, 2020). We also included 'drive-time' variables (i.e. t_05_min, ht_05_min) by routing the population within specific time limits (5, 10, 15 min). The journey times we used in this study for the drive-time variables represent the vast majority of journeys, especially in urban areas. In the UK, for example, 60% of all journeys by private vehicle are less 5 miles (Department for Transport, 2025b). We did not consider longer drive times (e.g., 30 or 60 min) as the aim was to relate driving time to the potential movement of the general population locally rather than inter-city or inter-regional journeys. A greater search area for drive-time variables would impose a different set of modelling considerations and would greatly increase the computation time. Despite the excellent performance of models overall, greater search distances for drive-time may, however, provide better predictions for Highways, which may help address the unresolved outliers in standardised residuals that mostly relate to motorways. We did not use longer drivetime variables in this study, but given that transformation of measured AADT and attempts to limit bias via regularisation did not provide reduction of the residual outliers, we will look at accommodating routing of longer journey times in future work.

It was notable that the measures we devised for network connectivity (con_n and con_diff) were included in all GLMM models but less important in the ML approaches. We used a relative ranking of road types to produce values of 'con_diff' (0 for no difference in road type, and values of 1 to 6 to incrementally represent the differences between low and higher flow roads). We chose not to test the sensitivity of models to alternative values of 'con_diff' as other representations would have been arbitrary. We could not use an ordered categorical approach in the ML methods (e.g., low to high), except for 'one-hot encoding' to produce independent binary variables for each category which would not have made sense for the application of 'con_diff'. Furthermore, we noted that our variable for defining road links traversed by buses was included in the GLMM sub-model for residential roads. We recognise however that our derivation of bus routes assumes that buses use the shortest path between the road links known to be traversed by buses. Ideally, we would use known bus routes but there is no known dataset with sufficient coverage for our approach. In the GLMM sub-model for residential roads, the 'bus_route' variable added up to 4.1% of explained variability in measured AADT. However, 'bus_route' was not included in the XGB residential sub-model, but was included in the XGB local sub-model,

albeit with low importance. Due to the limited contribution of the 'bus_route' variable and that its derivation involves assumptions that may introduce uncertainty, it should be used with caution. Inclusion in some models, however, suggests that the utility of a validated 'bus_route' variable should be explored in future work.

We included a variable for betweenness centrality but restricted this to major roads. One of the limitations of 'betweenness' is that its derivation is a linked to the bounding box used to define the study area. In other words, roads at the geometric centre of a study area are more central than roads at the edges which will lead to systematic bias in values generated. We limited betweenness to major roads in this study due to computation constraints in variable generation. Betweenness may not be suited to minor roads, however, as these roads reflect more localised traffic rather than trips generated across a network.

The variable importance for the XGB Single and sub-models showed that the 'drive time' variables were important for all models, with the longer time durations (i.e. 10 and 15 min) more important for the Single and Highways sub-models, and the shorter time durations (i.e. 5 min and half speed) were more important for the Local and Residential submodels. The 'betweenness' variable was important for Single, Highways and Local sub-models (not included in the Residential sub-model due to restriction to major roads). We restricted 'betweenness' to major roads as we took the view that centrality of residential roads (i.e., relating to local neighbourhoods) wasn't a basis for distribution of traffic across the network. Interestingly, the 'bus route' variable did not rank highly for variable importance for the Single or Local sub-models (not included in other models). For the RF models, we were unable to calculate variable importance, as variable importance relies on out-ofbag sampling which we did not use for the model runs for reasons explained in Section 2.3.

Although we included 51 variables in the dataset, we recognise that our variable list is not exhaustive. It may be possible then to include, for example, more locally relevant variables in relation to 'points of interest' (e.g., transport hubs, commercial areas, shops, schools) that are associated with local traffic generation. We didn't use land cover (i.e., CORINE) unlike other studies (Apronti et al, 2016; Shen et al, 2024) as in initial experimentation we found it provided no value, especially in ML models. CORINE may not be of sufficient spatial resolution (100 m pixel) to be used for this purpose given other variables used. For example, the drive-time and road connectivity variables also represent the density or urban fabric. We may however get better results with higher resolution, country-specific datasets for land cover. This would however mean using inconsistent approach and for some locations data may not be available as open access. In future work, we will investigate other global highresolution land cover data sets, such as the ESA WorldCover data set (10 m pixel) (European Space Agency, 2025). Higher resolution land cover data may also promote improvements in predictions, which may especially benefit the performance of models for residential roads, by defining local centres of commerce and industry as a measure of attracting higher levels of traffic than other residential areas. It may also help reduce bias in AADT prediction for other road types.

5. Strengths and limitations

The performance of models in this study is underpinned by a relatively large number of traffic observations from different countries and novel approaches to some of the predictor variables. The results benefited from access to code repositories from outside the study to produce the drive-time variables. Creating sub-models by road type was shown to add value to the approach depending on the type of method used, although this could be further refined. We treated road types as equivalent between country although the descriptive statistics generated showed that traffic varied within road types, especially trunk and primary roads. It would be possible to produce models without reference to a pre-defined road type, but we have not tested this approach. The 1000 fold Monte-Carlo cross-validation (MCCV) is a strength of our study in

terms of the extent to which we could demonstrate the robustness of the approaches and the derived models. MCCV with 1000 iterations (or other large quantities of iterations), produces more stable estimates of model performance compared to 5- or 10-fold cross validation (CV) (Xu and Liang, 2001; Haddad et al., 2013). This more rigorous crossvalidation approach is especially pertinent in our study as we recognise some differences in the distributions of AADT between areas in the data set. Although 10-fold CV is a common and efficient default, its limited number of splits can yield unstable results. By averaging over many random train-test splits of the data, high-iteration MCCV offers greater flexibility by allowing more random splits and better exploration of model performance. We chose to use all the available data rather than reserve some of the data exclusively for model testing (i.e. hold-out validation). Ideally, we would have had access to data for areas not included in this study, preferably from other countries not represented, for hold-out validation. We could have used additional data from the UK for further model testing but chose not to as we included two cityregions from the UK and aimed to maintain a balance between countries where possible.

We recognised some limitations or uncertainties with the variables used in the models. For example, we restricted the application of some variables that may have impacted model performance (e.g., drive-time distances, betweenness), as noted above. We were unable to determine the uncertainty in the road links defined as bus routes in our development of the 'bus route' variable due to lack of datasets where bus routes are known for the areas used in this study. Furthermore, we used modelled population from WorldPop and did not have information on its validity for the areas used in this study.

In the study, we did not validate the quality of the OSM roads data with national standard data due to the cost of national standard data and the primary aim of the study being to develop a generalisable method, potentially applicable globally using similar data. There are three main quality considerations in using data from OSM in this context: 1) spatial accuracy, 2) reliability of road classification, and 3) road network connectivity (for network analysis). We did not have the basis to determine the spatial accuracy of OSM and any impacts this may have had on model performance. We were also unable to determine any errors in 'fclass' as it would involve manual work that was not feasible given the very large number (~3.73 million) of road links involved in mapping AADT following model development. The script we created to clean the road network was focused on ensuring that all roads we geometrically attached to at least one node for the network analysis used in variable generation. Other studies have assessed the quality of OSM data to national standard data sets such as Barrington-Leigh and Millard-Ball (2017), who stated that the accuracy and completeness of OSM data varies globally, with OSM road networks more than 80% complete. In a study on Montreal and Quebec City (Canada) Moradi et al (2021) found that OSM roads data had a completeness of 99.82% and 99.53% respectively, and the province of Quebec had a positional accuracy of *<*8 m on 80% of all roads.

In GLMM we tested interactions for random effects with eventual inclusion of these in some of the models (e.g., between road type and urbanicity). For fixed effects in GLMM, we explored interactions between variables such as elevation and urbanicity, and interactions between urbanicity and distance travelled to the nearest major road junction. These experiments did not lead to better cross-validation results, so we did not pursue interactions for fixed effects in GLMM. Our decisions were, however, informed by the correlation matrix for variables, which indicated that high levels of co-linearity existed between many of the stronger variables for fixed effects. This means it was unlikely that performance overall has been limited by the chosen approach. Variable interactions are automatically accounted for in the XGB and RF approaches. These tree-based models can capture interactions through hierarchical splits, provided sufficient data and appropriate tree depth (i.e., by optimizing hyperparameters via a 'Grid Search').

Our analysis revealed cases of clustering (i.e., spatial autocorrelation) of standardised residuals, especially for the GLMM approach, with low levels of clustering overall from the RF and XGB approaches. In this study we did not attempt post-hoc methods for improving performance such as fitting surfaces to residuals, as utilised in other studies (Yuval et al., 2017), as the purpose of our approach was to develop a generalisable model that could potentially be transferred to other locations. The results here suggest that RF and XGB would overall not produce spatial heterogeneity in model errors, as assessed in terms of standardised residuals.

These results further highlight that local testing should be undertaken, and potentially local calibration, by linear or non-linear regression, may be required. Ideally, a larger, more balanced (i.e., by site type) dataset is likely to improve the basis for developing unified models.

5.1. Future work

This study has shown potential for international-scale traffic prediction models using ML approaches, with the need, as noted above, for considering local calibration of models developed. However, it is important to note that we found a high proportion of errors (*>*± 3 σ) for motorways sites in each of the statistical approaches (XGB, RF, and GLMM) and model types (i.e., Single or Combined). We may in future be able to develop other variables to better capture the variability in AADT for highways, which may involve variables representing inter-regional drive-times and population movements (e.g., *>*30 min). In this study, we only addressed drive-times and population movement at the subregional and city-scale (e.g., up to 15 min). Data on road width and more detailed information on the number of traffic lanes per road link may help improve model performance, but this would need to be derived from other products (e.g., satellite data) and may be prohibitively timeconsuming and/or expensive for national and international-scale AADT estimation.

Since we have established that ML methods provide strong potential in estimating values of AADT in this context, in future work we will consider other ML methods. However, other studies, as reported above, and our study suggest that RF and a form of boosted machines (e.g. XGB) are likely to be contenders for the strongest approaches.

Given the noted outliers and the relatively low performance for residential roads, in future developments we will look again at quantile regression in different methods. In this study, due to a relatively small number of residential sites, we could not, in experimentation, resolve quantile models at the margins of the distribution to improve solutions for potential outliers. We believe that with a larger dataset, especially for low-flow roads, we may be able to apply quantile approaches in ML methods.

We aim in a follow-up publication to test the transferability of the models developed in this study to non-European regions. We intend to focus on the performance of the models with and without calibration using measured AADT across the different road types. This will provide insight into on how important local calibration is for transfer of models.

We also aim, in a follow-up publication, to demonstrate the benefits of the data developed in this study for use in air pollution and road traffic noise modelling. For example, evaluating the changes in performance in air pollution models by including enhanced traffic flow estimates (Shen et al, 2024). Using the methods developed here we will, for example, improve the inventory on road traffic emissions as part of a new generation air quality model (HADES: Hybrid Air Dispersion Exposure System) we published recently (Jephcote, et al., 2025). In the follow-up publication, we will evaluate the theoretical improved performance of HADES using routine air pollution measurement data, especially for traffic-related pollutants such as nitrogen dioxide (NO2), within the UK (Department for Environment and Food and Rural Affairs , 2026) and across Europe (European Environment Agency, 2025). Others, using different types of air quality models, will also be able to harness the traffic flow estimation approach presented here. It is not ideal to evaluate noise models for specific sources using empirical evaluation studies as noise measurements provide an integration of all sound sources. We suggest, however, that the increased density in traffic data and representation of roads that would otherwise be missing in models is of great potential benefit for road traffic noise modelling. In 'strategic noise mapping' it's not a requirement to include minor roads but perhaps this will change with the advent of models to predict entire road traffic datasets or those to fill data gaps. We developed models for a nominal year (2019) in this study. The approaches used could be remodelled for other years, or the existing models scaled to other years using regression calibration.

In addition to the other potential OSM-based variables noted above, we also aim to consider the use of satellite data or aerial imagery to derive additional variables. One of the main considerations, however, is the cost of sufficiently resolved images and computational processing required. Furthermore, we could enhance the general approach by adding time-varying components to estimate diurnal or seasonal changes in traffic flows. This would require time-dependent observations which were not available for most sites used in AADT data we sourced in this study.

6. Funding Sources

This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 874724.

CRediT authorship contribution statement

Annalisa Sheehan: Writing – review & editing, Writing – original draft, Visualization, Validation, Resources, Methodology, Formal analysis, Data curation. Calvin Jephcote: Writing – review & editing, Resources, Methodology, Formal analysis, Data curation. John Gulliver: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Resources, Methodology, Funding acquisition, Formal analysis, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors gratefully acknowledge the contribution of all Equal-Life consortium members and the members of the advisory committee (http: //www.equal-life.eu).

Appendix A. Supplementary material

Supplementary data to this article can be found online at https://doi. org/10.1016/j.envint.2026.110231.

Data availability

We have made the modelled AADT estimates for all the study areas openly available here: https://doi.org/10.5281/zenodo.17700124. The code in Python and R programming languages may be requested for noncommercial use.

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