A study on the impact of street trees on PM10 dispersion in urban areas using the Graz Lagrangian Model

Abstract

Urban air pollution, particularly from PM10, presents significant health risks, especially in rapidly growing cities. This study utilizes the Graz Lagrangian Model to analyze PM10 dispersion along Avenida da Liberdade in Lisbon, an area characterized by high traffic, tall buildings, and a dense canopy of street trees. The study examines how wind patterns, atmospheric stability, urban characteristics, and vegetation influence pollutant distribution. The results show that, in the current scenario with trees, PM10 concentrations were significantly higher at points near the emission source, indicating that, in this specific study of an avenue with extensive tree coverage, trees impede ventilation and hinder PM10 dispersion. In contrast, in a hypothetical scenario without trees, pollutant dispersion was less obstructed, leading to lower concentrations but a broader spatial distribution, particularly at more distant points. The study also found that increased traffic did not significantly elevate PM10 concentrations during periods of atmospheric instability. Limitations of the model, including its inability to accurately represent individual trees background pollutant levels, are acknowledged. These findings contribute to a deeper understanding of urban pollutant dynamics and can inform air quality management strategies, particularly in areas with dense street tree coverage.

Introduction

Urban air pollution presents serious health risks, particularly in fast-growing cities. Air pollutants have been linked to various health issues, including respiratory illnesses, cardiovascular conditions, and effects on the nervous and endocrine systems¹. Particulate matter (PM10) is especially concerning, with research indicating strong correlations between its levels and increased mortality and morbidity rate².

In Europe, the severity of air pollution’s impact is evident, with 389,000 deaths recorded in 2021 due to exposure to pollution levels exceeding World Health Organization (WHO) guideline^3,4. Additionally, 97% of the European Union’s population was exposed to PM10 levels above the daily limit of 45 μg/m³, underscoring the widespread nature of the issue^3,4.

Urban air quality is heavily influenced by wind patterns and emissions, both of which determine pollutant concentrations in cities. The primary atmospheric pollutants have shifted over time; initially, sulfur compounds from coal combustion were the major concern, but today, photochemical smog resulting from traffic, industrial activities, power generation, and solvent use has become the dominant issue⁵. The highest pollutant concentrations are often found near high-traffic roads, where air quality monitoring is limited or absent, exacerbating the exposure of urban populations (Anjos et al.⁶). In this context, understanding how wind conditions impact pollutant dispersion is essential for air quality management.

Wind flow in urban areas is influenced by various factors, including the porosity and roughness of buildings and trees, which in turn affects the transport and dispersion of pollutants⁷. Trees, especially street trees, play a dual role in this process. While they can filter pollutants and improve air quality, they also alter wind flow dynamics, which can sometimes lead to localized increases in pollutant concentration^8,9. For example, street trees with dense canopies can reduce wind speed at pedestrian level, promoting comfort in some cases but potentially hindering air renewal in heavily vegetated areas^10,11. Furthermore, the influence of trees on air quality also depends on factors like tree arrangement and the orientation of streets, which can either facilitate or impede the effective movement of air^12,13.

In addition to vegetation, traffic flow patterns significantly impact air quality in street canyons. Free-flow traffic generally reduces pollutant concentrations due to increased turbulence, while congested traffic leads to higher concentrations, particularly on the leeward side during perpendicular winds¹⁴. These interactions between wind patterns, traffic, and urban infrastructure highlight the complexity of urban air pollution dynamics.

The dispersion of pollutants in urban canyons has been the subject of numerous studies exploring how street geometry, building height, and the presence of vegetation influence urban air quality. Studies highlight that tall buildings create pollutant accumulation zones, while tree-lined avenues can even increase concentrations compared to tree-free streets^15,16,17. Other works emphasize the critical role of aspect ratio (height/width) in controlling urban ventilation and pollutant dispersion, with taller buildings hindering the natural removal of pollutants¹⁸. Additionally, other studies demonstrate that variability in building height significantly alters airflow and pollutant removal efficiency, while vegetation can reduce wind speed, increasing turbulence and affecting pollution levels. These studies indicate that urban design, including the use of vegetation and variation in building heights, must be considered to mitigate the impacts of air pollution in urban areas^19,20.

Several studies indicate that street trees have a significant influence on natural ventilation by modifying airflow patterns in urban areas, particularly through characteristics such as height, canopy density, and spatial arrangement within the urban fabric. Trees with dense and continuous canopies can reduce wind speed at pedestrian level, thereby enhancing comfort in overly exposed environments, but they may also hinder air renewal in densely vegetated areas^10,12,21. Street orientation also affects airflow behavior: north–south-oriented streets, when combined with tall and well-spaced canopies, tend to promote more effective wind corridors, whereas streets oriented northwest–southeast have shown lower performance in terms of air renewal^12,13.

Studies have reinforced this perspective, demonstrating that dense street tree cover can increase PM10 levels in summer due to high leaf density, while areas without vegetation tend to exhibit lower concentrations in this season due to greater atmospheric instability²². Additionally, the morphology of urban street canyons—including depth, orientation, and building height—affects the concentration of suspended particulate matter at pedestrian level²³.

The promotion and preservation of natural ventilation has been identified as one of the most effective strategies for mitigating heat and improving air quality in both indoor and outdoor environments²⁴. In Lisbon, natural ventilation conditions have deteriorated in recent decades due to the aggressive expansion of urban development²⁵. These conditions directly affect air quality and the dispersion of atmospheric pollutants. Understanding and quantifying this impact is essential for enhancing the efficiency of urban planning and design processes.

The Graz Lagrangian Model (GRAMM/GRAL) is a simulation tool for atmospheric pollutant dispersion in urban environments. It can generate high-resolution pollutant fields while accounting for building effects at relatively low computational costs²⁶. Given the importance of street trees in modifying wind flow and pollutant distribution, this study incorporates GRAL simulations to assess their specific impact on PM10 dispersion. GRAL has been successfully applied in various urban settings, including Sofia, Modena, Zurich, and Krasnoyarsk, demonstrating its ability to capture spatial and temporal variations in air pollution^27,28,29. The model has shown strong performance in reproducing seasonal cycles, short-term pollution events, and diurnal pollutant concentration patterns²⁸. However, the accuracy of these simulations depends on the implementation of appropriate boundary conditions. Specifically, transient boundary conditions—conditions that change over time—play an important role in refining the model’s capacity to replicate real-world air pollution dynamics. Recent studies, such as ref. ³⁰, have highlighted the importance of incorporating transient boundary conditions in pollutant dispersion models to better simulate the time-dependent nature of urban air quality, particularly in complex urban environments where pollution levels vary rapidly due to factors like traffic fluctuations and meteorological changes.

This study aims to analyze the dispersion patterns of PM10, with GRAMM/GRAL simulation, within an urban canyon environment, providing insights into pollutant dispersion dynamics in densely built areas. The selected urban canyon is Avenida da Liberdade in Lisbon—a central avenue characterized by high vehicle traffic, buildings averaging 14.53 m in height, and a high density of street trees. Environmentally, this avenue is one of the most polluted locations in Lisbon and has frequently exceeded European Union air quality standards, leading to recurrent fines and heightened regulatory pressure. The urban morphology of Avenida da Liberdade makes it a particularly relevant case for assessing how vegetation and street layout influence pollutant dispersion and pedestrian exposure. Moreover, its features are comparable to those of other major European boulevards, enhancing the transferability of the findings.

This study focuses on a single-day simulation (7 October 2022), which represents a limitation regarding the temporal generalization of the results. However, this day was selected due to its representativeness of typical autumn meteorological conditions in Lisbon—mild temperatures, stable atmospheric conditions, and moderate easterly winds—alongside elevated PM10 concentrations recorded at nearby Liberdade monitoring stations³¹. Additionally, the date coincided with a weekday characterized by high traffic intensity³² allowing for the assessment of dispersion under realistic emission scenarios. While single-day simulations cannot capture seasonal variability, they are useful for understanding short-term pollution dynamics in critical scenarios and serve as a basis for future studies involving multi-day or seasonal comparisons.

By focusing on this specific site, the study aims to generate evidence that can support targeted interventions and urban planning strategies for improving air quality and public health in Lisbon and beyond. More specifically, the goal is to answer the following questions:

• How does pollutant dispersion behave on Avenida da Liberdade during periods of high concentration?

• Which areas on Avenida da Liberdade are most prone to pollutant accumulation?

• What is the impact of street trees on PM10 dispersion in this urban canyon?

Results and discussion

Atmospheric condition stability

The classification of atmospheric stability on 7 October 2022 in Lisbon was determined using the Pasquill–Gifford method³³, incorporating from solar radiation and cloud cover data obtained from the ERA5 reanalysis³⁴ and wind speeds provided by Meteostat³⁵. Table 1 summarizes the hourly atmospheric conditions, indicating the dynamic behavior of atmospheric stability throughout the day. Stability ranged from relatively stable (Classes F and G) in the early morning, to unstable (Classes A and B) during the afternoon—favoring dispersion—and back to moderate stability (Classes C and D) by evening, which reduced dispersion efficiency.

Table 1 Atmospheric stability classification in Lisbon on 7 October 2022 using the Pasquill–Gifford method

During the night (12 a.m. to 6 a.m.), Classes F and G prevailed, reflecting stable atmospheric conditions with minimal cloud cover and light winds—typical of nocturnal radiative cooling and potential thermal inversion. These stable conditions generally hinder vertical mixing, reducing pollutant dispersion.

As solar radiation increased from 7 a.m., atmospheric instability intensified, leading to classifications B and A/B. Between 10 a.m. and 4 p.m., instability peaked (Classes A and B), associated with high solar radiation and convective activity near the surface—conditions favorable to pollutant dilution and dispersion. After 5 p.m., with declining solar radiation, the atmosphere gradually stabilized again. By night (from 9 p.m. onward), stability classes transitioned to E and F, indicating the reestablishment of nocturnal stability, which again restricted pollutant dispersion.

PM10 dispersion along Avenida da Liberdade

Dispersion of PM10 along Avenida da Liberdade was simulated using the GRAMM and GRAL models for two scenarios: (i) the current configuration with street trees and (ii) a hypothetical configuration without trees. The results, presented in Fig. 1, reveal notable spatial and temporal differences in PM10 concentration between the two scenarios.

Fig. 1: Comparison of PM10 concentrations in Av.

da Liberdade with and without vegetation at different times of the day. This figure presents hourly spatial maps comparing the simulated PM10 concentrations (µg/m³) for the current scenario, which includes existing urban vegetation, and a hypothetical scenario without trees. The maps cover the entire 24-h period on 7th October 2022, showing both the PM10 concentrations in the current scenario and the concentration differences resulting from vegetation removal (expressed as “Without trees - Current scenario”). Black arrows in each panel indicate the prevailing wind direction at each hour, providing context for pollutant dispersion patterns. Code and Data Availability: PM10 simulations were conducted using GRAL (version 23.09.0 d).

In the current scenario, with street trees, higher PM10 concentrations were observed in specific areas of the avenue. The high density of street trees in Av. da Liberdade was found to reduce airflow and inhibit pollutant dispersion, generating accumulation zones. Conversely, in the tree-free scenario, dispersion was more homogeneous, with lower concentrations but broader spatial distribution.

The hourly analysis shows that from 12 a.m. to 6 a.m., under stability classes F and G and northwesterly winds (2–2.8 m/s), the atmosphere remained stable, limiting dispersion capacity. In the tree-without scenario, average PM10 concentrations along Av. da Liberdade ranged from 55 µg/m³ at 12 a.m. to 54.26 µg/m³ at 6 a.m. In contrast, the vegetated scenario showed slightly higher values during the same period, starting at 77.3 µg/m³ at 12 a.m. and remaining above 69.9 µg/m³ until 6 a.m.—indicating that vegetation further limited dispersion, enhancing accumulation under already stable nighttime conditions Girotti et al. This suggests that airflow, while insufficient even in the absence of trees, was further obstructed by vegetation, aggravating pollutant buildup.

As solar radiation increased from 7 a.m. to 3 p.m., atmospheric instability rose (Classes A and B), improving pollutant dispersion—despite increased traffic emissions. During this period, PM10 concentrations in the tree-free scenario reached 69.9 µg/m³ at 8 a.m. and 55.3 µg/m³ at 2 p.m., while the vegetated scenario registered higher peaks of 86.56 µg/m³ and 79.88 µg/m³ at the same times, respectively. Values in the tree-free case, although elevated, were generally more evenly distributed, whereas the presence of trees led to localized hotspots.

At 4 p.m., a sudden wind direction shift (to the south) and an increase in speed (3.19 m/s) disrupted the established dispersion pattern, resulting in a short-term spike in PM10 along the avenue. In the tree-free scenario, this peak reached 56.92 µg/m³, whereas in the vegetated scenario it climbed to 89.33 µg/m³. Despite the unstable Class B conditions, this episode illustrates how abrupt directional changes can override favorable dispersion conditions, leading to reaccumulation by modifying airflow pathways within the canyon—especially in the presence of vegetation.

Following this episode, from 5 p.m. onward, solar radiation declined, atmospheric stability increased (Classes C–F), and the wind gradually returned to a northwesterly pattern. Although wind speeds remained above 2 m/s, dispersion efficiency decreased again due to increasing stabilization. During this evening transition, the vegetated scenario maintained higher average PM10 concentrations—around 64 µg/m³ to 56.1 µg/m³—while the tree-without scenario showed concentrations between 51 µg/m³ and 49.1 µg/m³. These results support the premise that, while vegetation plays an important role in urban climate regulation, it can promote local pollutant accumulation when airflow is already weak. Although wind speed increased, the complex interaction between wind direction shifts and the physical obstruction caused by vegetation limited the effective dispersion of pollutants.

These patterns underscore the importance of wind direction and atmospheric stability in shaping urban pollutant dynamics. The results corroborate previous findings²⁶, which emphasize the influence of built morphology on pollutant distribution and the impact of stability conditions on local air quality, as well as those by authors²², who demonstrated how stable conditions hinder dispersion at the microscale.

The simulations further confirm the role of vegetation in altering pollutant patterns. In line with other studies^8,16, trees were shown to obstruct both horizontal and vertical airflow, potentially promoting pollutant accumulation in certain configurations. Similarly, other author¹⁷ demonstrated through computational modeling that urban vegetation often leads to increased local pollutant concentrations due to its significant aerodynamic effect in reducing street-level ventilation, a mechanism that tends to outweigh the pollutant removal capacity of vegetation. The hypothetical no-tree scenario consistently displayed lower PM10 levels, albeit with a wider spatial spread across the canyon.

Despite the robustness of the GRAMM/GRAL system for urban dispersion modeling, limitations must be acknowledged. The models may overestimate concentrations near complex geometries²⁸. Furthermore, GRAL currently does not represent individual trees volumetrically, instead treating vegetation as drag-inducing surfaces—potentially underestimating their influence on turbulence and deposition. These aspects should be considered when interpreting results and designing urban air quality strategies.

Statistical analysis

For the statistical analysis, PM10 concentration data were collected at nine points along Avenida da Liberdade, considering two scenarios: current (with trees) and without trees. Figure 2 illustrates the location of the sampling points along the avenue.

Fig. 2: Sampling points for PM10 concentration along Avenida da Liberdade.

This figure shows the spatial distribution of the nine PM10 sampling points (P1–P9) strategically located along and around Avenida da Liberdade, Lisbon. The red points indicate the specific collection locations where hourly PM10 concentration data (µg/m³) were extracted from the model simulations. Code and Data Availability: The selection of sampling points and spatial analysis were performed using QGIS.

Figure 3 compares PM10 concentrations at different positions (P1–P9) in two scenarios: with and without trees.

Fig. 3: Comparative analysis of PM10 concentration – current scenario vs. without trees.

This figure presents a comparative analysis of simulated PM10 concentrations (µg/m³) at the nine monitoring points (P1–P9) along Avenida da Liberdade, contrasting the current scenario (with existing vegetation) and a hypothetical scenario without trees. The green line represents PM10 levels under current vegetative conditions, while the red line illustrates PM10 concentrations in the absence of trees. The shaded areas around each line correspond to the variability (standard deviation) of PM10 concentrations at each sampling point. Code and Data Availability: The analysis was performed using Python (pandas, seaborn, and matplotlib libraries) to process simulation outputs and visualize the results.

Figure 3 shows that at points P1 and P2—located at the beginning of the avenue—the PM10 concentration is higher in the current scenario (with trees). This suggests that the presence of trees at these points may act as a barrier, limiting wind circulation and reducing the dispersion of pollutants. Similarly, at locations closer to the emission source, such as P5, the concentration of PM10 is also higher in the current scenario, reinforcing the idea that trees can hinder pollutant dispersion.

Conversely, at points farther from the emission source—such as P7, P9, P4, and P6—an opposite pattern emerges. In these areas, the absence of trees leads to a slight increase in PM10 concentrations, indicating that, without vegetation, pollutants disperse over a larger area.

The analysis of the PCA reveals notable differences between the current scenario with trees and the scenario without trees. In the current scenario, the first two principal components, PCA1 and PCA2, explain 58.7% of the data variance, with PCA1 accounting for 37.5% and PCA2 for 21.2%, as shown in Fig. 4.

Fig. 4: PCA of PM10 concentrations — current scenario vs. without trees.

This figure presents the results of a PCA applied to the simulated PM10 concentration dataset under two scenarios: with trees (current scenario) and without trees. Each point represents a specific observation, with green markers indicating PM10 levels under the current scenario (with trees) and red markers representing the scenario without trees. Methodological note: PCA was conducted using the scikit-learn library in Python.

In the current scenario, the presence of trees results in greater data dispersion, suggesting that vegetation significantly influences the variability of environmental conditions and pollutant dispersion. The data points are spread across both positive and negative values for PCA1 and PCA2, reflecting considerable variability. This variability is likely driven by the trees, which impact factors such as wind speed, generating varied effects. For example, trees can less wind speed (reflected in negative PCA1 values) or enhance pollutant dispersion (reflected in positive PCA1 values), depending on how they interact with local wind dynamics and traffic distribution.

In contrast, the scenario without trees shows a much more homogeneous distribution of data. This reduction in variability suggests that the absence of trees leads to a less dynamic environment, where pollutant dispersion and wind effects become more consistent and predictable. Without trees, factors like wind speed and traffic distribution may exert a less variable influence on pollutant behavior, resulting in a more controlled, uniform dispersion pattern. This implies that trees play a important role in modulating environmental conditions, contributing to a greater diversity and complexity in pollutant behavior.

Statistically, the presence of trees in the current scenario introduces greater variability in environmental conditions, as seen in the spread of data points across both positive and negative PCA values. Trees seem to influence pollutant dispersion, atmospheric stability, and wind effects in a nonlinear manner. Conversely, the absence of trees leads to a more predictable and controlled pollutant distribution, as indicated by the concentration of data points in the negative regions of the PCA. This shift in variability highlights the important role trees play in shaping local environmental conditions and modulating pollutant behavior. Without trees, the environment becomes more uniform, suggesting that vegetation has a significant impact on the dynamics of local air quality.

The simulation of PM10 dispersion on Avenida da Liberdade in Lisbon, using the GRAMM/GRAL model, provided valuable insights into pollutant behavior throughout the day. The results show that, despite an increase in traffic volume, PM10 concentrations did not significantly increase during the hours of highest atmospheric instability, suggesting that efficient dispersion helped mitigate pollution levels. However, a change in wind direction led to a rise in pollutant concentrations, underscoring the role of wind dynamics and urban configuration in pollutant dispersion.

The presence of street trees also influenced pollutant distribution by altering wind flow patterns. In the current scenario with trees, PM10 concentrations were higher in certain areas due to reduced ventilation and pollutant accumulation. In contrast, in the scenario without trees, dispersion was less restricted, leading to lower concentrations but a wider spatial distribution of pollutants. This indicates that while urban vegetation offers various environmental benefits, its impact on air quality requires careful consideration in planning strategies.

Quantitative analysis showed that, in the current scenario with trees, PM10 concentrations were higher at points closer to the emission source suggesting trees act as barriers to wind and pollutant dispersion. At more distant points the removal of trees resulted in higher concentrations of PM10, implying that the absence of vegetation allows pollutants to spread more widely. Additionally, PCA analysis revealed that the presence of trees led to greater variability in pollutant dispersion, accounting for 58.7% of the data variance, while the absence of trees resulted in a more uniform and predictable dispersion pattern.

While the model demonstrated high accuracy in reproducing the spatial distribution of pollutants, several limitations were identified. The inability to incorporate individual trees in the model may compromise the analysis of their effects on pollutant dispersion. Future models should integrate more detailed representations of vegetation and background pollutant level to improve data accuracy. These findings can inform urban planning and air quality management strategies, promoting more effective interventions to reduce pollution levels and improve urban air quality.

Methods

Study area

Lisbon spans an area of 84 km² and is home to around 547,000 residents. Situated on the western coast of the Iberian Peninsula, the city borders the Tagus estuary to the east, southeast, and south, while the Atlantic Ocean lies to the west. Lisbon’s location supports a temperate climate, characterized by mild, rainy winters and hot, dry summers, a season that has recently been extending into autumn³⁶.

At the center of Lisbon lies Liberdade Avenue, an important avenue characterized by buildings averaging 14.53 m in height, heavy traffic, and a dense canopy of tall trees. These trees form a “green tunnel” over the avenue. The combination of high traffic volume and dense vegetation limits airflow, creating physical barriers that hinder the natural dispersion of pollutants^16,17. In areas of dense urban construction, such as Liberdade Avenue, these barriers amplify the complexity of modeling pollutant dispersion due to interactions between buildings and trees.

For this study, the high-resolution dispersion modeling system GRAMM/GRAL-SCI was applied, focusing on a domain centered on Avenida da Liberdade (38°44′33″N, 09°08′49″W), situated 40 meters above sea level. This location was selected due to its combination of heavy traffic, dense vegetation, and available air quality monitoring data.

Figure 5 shows the simulation domain and the location of the air quality monitoring station (Liberdade QualAr)³⁷.

Fig. 5: Location of the study area, the simulation domain, and the air quality monitoring station.

This figure illustrates the geographical context and specific features relevant to the study conducted in Lisbon, Portugal. The figure is composed of three panels: a A set of three maps locating the study area at multiple spatial scales. The upper map shows the national context within Portugal, highlighting Lisbon in dark gray. The middle map zooms into the Lisbon Northern Metropolitan Area, indicating Lisbon city in dark gray. The bottom map further zooms into Lisbon city, showing the study area in purple within the city’s administrative boundaries in light gray. b A high-resolution satellite image of the study area in Av. da Liberdade -Lisbon, bounded by a red solid line that delineates the GRAL computational domain used in the PM10 dispersion simulations. The black open circle marks the location of the Liberdade air quality monitoring station, which provided observational data for model validation. c Two ground-level photographs of Avenida da Liberdade. The upper photograph depicts a general view of the avenue with dense tree cover on both sides and visible vehicular and pedestrian traffic under clear sky conditions. The lower photograph shows a closer view of the avenue with multiple vehicles in transit, also highlighting the vegetation and urban setting characteristic of the area. Code and Data Availability: The satellite imagery used in this figure is derived from publicly available sources (Google Earth/QGIS software). The ground-level photographs are original and were taken by the authors.

Regarding the characteristics of the Liberdade urban canyon, it presents a height-to-width (H/W) ratio of 0.17, with an average building height of 14.53 m and an inter-building distance of 82.5 m. The building density (λ) is 0.54, indicating a moderately dense urban configuration. Figure 6 illustrates the building height, street trees, and NDVI in the Liberdade urban canyon.

Fig. 6: Building height, street trees, and NDVI in the Liberdade urban canyon.

This figure presents three key spatial datasets describing the urban morphology and vegetation in the Av. da Liberdade urban canyon, Lisbon. The figure is composed of three panels: a Map of building height, showing variations in building elevation within the study area. The color gradient ranges from light orange for lower buildings (3–6 m), to medium orange (16–19 m), and dark orange for taller buildings reaching up to 32 m. b Map of street trees, depicting the spatial distribution of trees represented by solid green circles across the urban street network. The tree data highlights the characteristic linear vegetation along Avenida da Liberdade. c NDVI map, illustrating vegetation density based on satellite imagery analysis. NDVI values are shown using a green color gradient, with lighter shades indicating lower vegetation density (values near −1.0) and darker shades indicating higher vegetation density (values approaching 1.0). All spatial data layers were processed using QGIS software. The building height and street trees data were sourced from ref. ⁵², while the NDVI data was derived from satellite imagery processed following the methodology described in ref. ³⁸. Code and Data Availability: All spatial datasets used to create this figure are openly available. Building height and street tree datasets can be accessed through ref. ⁵². NDVI data were derived following the methodology in ref. ³⁸. All geospatial analyses and visualizations were performed using QGIS.

As shown in Fig. 6, the canyon features a well-defined tree-lined street layout, which contributes to local microclimatic conditions and influences pollutant dispersion patterns. The NDVI map (October 2022) from Sentinel-2³⁸ highlights the presence of vegetation, predominantly aligned along Liberdade Avenue. Within the analyzed segment of Avenida da Liberdade, a total of 1009 trees were identified across an area of ~98,317 m², yielding a tree density of ~103 trees per hectare. Additionally, ~72.3% of the total area is covered by vegetation, as indicated by the NDVI analysis, emphasizing the significant role of street trees in the urban environment.

In the current scenario, a total of 2326 street trees were considered. Tree data were extracted from the Lisbon open data portal³⁹, which provides georeferenced records of tree species and locations. Table 2 presents the predominant tree species and their respective percentages within the study area.

Table 2 Tree species and percentage of each in the study area

Graz mesoscale scientific model (GRAMM-GRAL)

The GRAMM-SCI model applies a Lagrangian approach to simulate particle motion. The position of each particle is updated using the following fundamental Eq. (1).

$${x}_{i,{new}}={x}_{i,{old}}+\left(\overline{{u}_{i}}+\acute{{u}_{i}}\right)\cdot \Delta \,t$$

(1)

Where ${x}_{i,{new}}$ represents the updated spatial position (with i = 1, 2, 3), and ${x}_{i,{old}}$ is the previous position, $\bar{{u}_{i}}$ is the mean velocity component and $\acute{u}$ is the fluctuating (random, stochastic) fluctuation, and $\triangle t$ is a time step. The rate at which particles cross a counting grid allows for the connection between the Lagrangian and Eulerian modeling frameworks⁴⁰.

In this framework, GRAL models airflow around obstacles by solving the Reynolds-Averaged Navier-Stokes (RANS) equations, expressed as Eq. (2).

$$\frac{\partial \bar{{u}_{i}}}{\partial t}+\bar{{u}_{j}}\frac{\partial \bar{{u}_{i}}}{\partial {x}_{j}}=-\frac{1}{\rho }\frac{\partial \bar{\rho }}{\partial {x}_{i}}+\frac{\partial }{\partial {x}_{j}}\left[K\left(\frac{\partial \bar{{u}_{i}}}{\partial {x}_{j}}+\,\frac{\partial \bar{{u}_{j}}}{\partial {x}_{i}}\right)-\frac{2}{3}{\delta }_{ij}k\right]$$

(2)

Here, ${u}_{i}$ corresponds to the mean wind velocity components in both horizontal and vertical directions, ρ is the air density, $\frac{\partial \bar{\rho }}{\partial {x}_{i}}$ refers to the mean pressure gradient force, k is the turbulent kinetic energy, and K is the eddy viscosity⁴⁰.

This approach enables the model to resolve mean wind fields, while the turbulent fluctuations, expressed as Reynolds stresses, are parameterized through turbulence modeling. Specifically, GRAMM utilises a turbulent viscosity approach, grounded in eddy viscosity theory, and also incorporates an algebraic turbulence model based on mixing length theory, as described by Blackadar et al.^41,42. The turbulent viscosity is computed using an algebraic formulation that depends on parameters such as geostrophic wind speed or friction velocity⁴³. Enhanced to incorporate reanalysis data from ERA5 for initialization and to allow transient boundary conditions³⁴. As a non-hydrostatic model, GRAMM-SCI solves the fundamental equations of atmospheric dynamics using a vertically terrain-following coordinate system and a tetrahedral mesh structure⁴⁴. This setup is particularly effective for simulating atmospheric phenomena in densely built urban areas and mountainous regions, where topographical variations are pronounced.

The model employs a no-slip boundary condition for wind velocity at the lower boundary, representing zero wind speed relative to the ground surface. Turbulent fluxes at the surface are computed using Monin–Obukhov similarity theory, applying scaling variables such as friction velocity and surface potential temperature. These surface-layer formulations ensure realistic representation of atmospheric turbulence near the ground⁴³.

At the lateral boundaries, GRAMM-SCI offers two treatments for horizontal wind components: a homogeneous Neumann condition, where the spatial gradient normal to the boundary is set to zero, and a nudging approach that gradually forces the model solution toward prescribed large-scale values from reanalysis data. The strength of the nudging is modulated by the number of grid points from the boundary, with influence limited to six grid points. Other meteorological variables at the lateral boundaries use homogeneous Neumann conditions by default⁴³.

The upper boundary also applies a nudging scheme for the wind components, using a hyperbolic tangent function to modulate the relaxation strength based on vertical distance from the top of the domain, with influence limited to the top three vertical levels. For all other scalar fields at the upper boundary—such as temperature and humidity—homogeneous Neumann conditions are applied⁴³.

For land use representation, the model utilizes the European Corine Land Cover dataset⁴⁵, which provides spatial resolution data at 100 m. The GRAMM–GRAL modeling system combines meteorological and microscale simulations to model the dispersion of atmospheric pollutants, applying a catalog-based approach. GRAMM is responsible for solving the conservation equations for mass, enthalpy, momentum, and moisture, while accounting for variations in land use and the associated surface fluxes²⁸.

Large-scale meteorological conditions, including wind speed and direction as well as stability class, are transformed into parameterized vertical profiles of wind, temperature, and pressure, based on Pasquill–Gifford stability classification^33,46. This enables GRAMM to accurately simulate the dynamics of atmospheric flow in complex urban areas. The GRAL model, coupled with GRAMM, operates in a diagnostic mode that interpolates the GRAMM wind fields onto a fine Cartesian grid, assuming a logarithmic wind profile close to building surfaces. This methodology ensures mass conservation by applying a Poisson equation to establish a pressure field that corrects atmospheric flow velocities²⁸.

For this study, a nesting approach with multiple modeling domains was implemented, including domain resolution of 4 km, 1 km, and 200 m for GRAMM, and 200 m for GRAL - with a grid resolution of 1 m. This approach allows the model to simulate both regional and local-scale meteorological dynamics effectively. This choice of multiple resolution scales was informed by previous GRAMM-SCI simulations in urban environments^28,47, as illustrated in Table 3 and Fig. 7.

Fig. 7: Modeling domains and spatial resolutions used in the PM10 dispersion simulations in Avenida da Liberdade.

This figure illustrates the nested modeling domains and their respective spatial resolutions applied in the simulations of PM10 dispersion in Avenida da Liberdade. The figure is composed of two panels: a Map showing the three nested computational domains over the Lisbon metropolitan region. The largest domain (GRAMM) is delimited by a red solid line, representing a spatial resolution of 4000 by 4000 m. Nested within it, the intermediate domain (GRAMM) is shown with an orange solid line, corresponding to a resolution of 1000 by 1000 m. The smallest domain (GRAL), focused on the Liberdade area, is represented by a green solid line, with a higher spatial resolution of 200 by 300 m. b Detailed map of the innermost modeling domain (GRAL – 200 by 300 m), overlaid on the urban fabric of the Liberdade area. Code and Data Availability: All geospatial data used to define the modeling domains are derived from GRAMM (version 23.09.0 d).

Table 3 GRAMM/GRAL-SCI models description

To capture the influence of urban morphology and vegetation on pollutant dispersion, the GRAMM–GRAL modeling system combines a nesting approach and high-resolution land cover data. For land use classification, the model uses the Corine Land Cover dataset⁴⁸, which offers 100 m spatial resolution and is used to assign surface roughness lengths, albedo, and heat fluxes across the domain. GRAMM simulates mesoscale meteorological dynamics using a terrain-following tetrahedral mesh, while GRAL operates in diagnostic mode with a Cartesian grid that explicitly resolves buildings and tree canopies. Within GRAL, building geometries are represented as solid obstacles, and vegetation can be treated as porous volumes with drag and attenuation properties. The model assumes a logarithmic wind profile near surfaces and applies mass conservation through a Poisson pressure solver²⁸.

Trees were implemented in GRAL as solid polygonal areas using the “vegetation” module, which treats vegetation as porous volumes influencing wind flow and turbulence. In the GRAL software, trees were represented as a continuous area rather than individual points, as in other software. To achieve this, a polygon was drawn to encompass the region corresponding to the vegetation along Avenida da Liberdade. This polygon-based approach was adopted due to software limitations and to simplify the aerodynamic representation of vegetation. In order to represent the predominant species, Celtis australis (28.1%) and Platanus × hybrida (19.2%), the following specifications were adopted: a total height of 10 m, with the trunk zone accounting for 10% of this height. The leaf area density was set at 0.1 m²/m³ in the trunk zone and 0.5 m²/m³ in the crown zone.

Vehicle count and emissions

Vehicle counting on Avenida da Liberdade was carried out using hourly traffic data from TomTom’s historical database³², considering the hourly average for weekdays in October 2022. Although the free version of TomTom imposes some limitations, the data provides adequate temporal granularity and broader spatial coverage compared to traditional on-site surveys. Figure 8 presents the average vehicle count on Avenida da Liberdade for October 2022.

Fig. 8: Average vehicle counts on Avenida da Liberdade from TomTom³².

This figure presents the average hourly vehicle counts on Avenida da Liberdade, derived from TomTom traffic data. The stacked bar chart differentiates between two directional flows: South Western (green) and North Western (orange). The x-axis represents the time of day in hourly intervals, while the y-axis indicates the average number of vehicles recorded. Code and Data Availability: The traffic data were obtained from the TomTom³².

The rush hour occurred between 9 p.m. and 10 p.m., with the total number of vehicles reaching 11,419. This can be attributed to the central location of Avenida da Liberdade and the evening activity in the surrounding area. The peak period was preceded by a gradual increase in traffic throughout the day, with flow intensifying consistently from 10 a.m. onwards and remaining high until reaching its maximum at 9 p.m.

During this peak, traffic in the Southwest and Northwest regions was significant, with the Northwest registering a similar volume to the Southwest, at 5737 vehicles in circulation. After the peak, the number of vehicles gradually decreased, falling to 10,248 by 10 p.m. and continuing to decline steadily through the night.

For this study, only transport-related emissions were considered, estimated from traffic on four main source lines (Fig. 9), using vehicle count data as input for the GRAL model. PM10 emissions from vehicles were calculated through a methodological adaptation that incorporated both primary emissions and the contribution from background concentrations. Initially, emissions were estimated using the GRAL line source model, based on traffic data from the TomTom platform. The emission factors were defined from values in the technical literature, specifically 0.0198 g/km for Light Duty Vehicles (LDV), consistent with the average values for paved urban roads under dry conditions and moderate traffic, as recommended by the EMEP/EEA Guidebook⁴⁹.

Fig. 9: Location of the source lines and air quality monitoring station.

This figure displays the emission source lines along Avenida da Liberdade, categorized by traffic direction and lane position, overlaid on a high-resolution satellite image. The South Western direction is represented by two lines: lateral (light green) and central (green). Similarly, the North Western direction includes a central (orange) and lateral (light orange) line. The red star marks the location of the air quality monitoring station (Liberdade QualAr), used for model validation. Code and Data Availability: The monitoring station location was obtained from the Portuguese national air quality monitoring network (QualAr). Data processing and visualization were performed using QGIS.

The emission factors and methodological approach adopted in this study are consistent with the Tier 1 methodologies recommended by the EMEP/EEA Air Pollutant Emission Inventory Guidebook⁵⁰. The effective emission rate for each road segment was calculated using Eq. (3):

$$Q=\frac{(T\cdot {EF})}{1000\cdot N}$$

(3)

where Q is the emission rate (kg/h/km), T is the traffic volume (vehicles per hour), EF is the emission factor (g/km), and N is the number of lanes. This formulation allowed the translation of vehicle counts into standardized emission rates compatible with the GRAL input requirements.

Additionally, to account for the influence of background concentrations—which are not directly incorporated by the dispersion model—the observed average background PM₁₀ concentration was converted into an equivalent emission rate in the units required by the model (kg/h/km). This conversion was performed by multiplying the background concentration (58.49 µg/m³, converted to g/m³ for calculation) by the characteristic parameters of the simulation domain—namely, the average wind speed (U) and the width of the modeled road segment (W)—resulting in a background emission value (Q_background) that represents the mass flow of pollutants corresponding to the observed background concentration. This value was then added to the initial traffic-related emission rate (Q), yielding the adjusted total emission rate (Q_total), as expressed in Eq. (4):

$${Q}_{{total}}=Q+({{\rm{C}}}_{\mathrm{background}}\cdot {\rm{U}}\cdot {\rm{W}})$$

(4)

where Q_total is the adjusted emission rate (kg/h/km); Q is the initial traffic-related emission rate (kg/h/km); C_background is the average background concentration (g/m³); U is the average wind speed (m/s); and W is the width of the model domain or the road segment considered (m).

This approach ensured a more comprehensive representation of pollutant levels within the model by conservatively incorporating background contributions.

Validation

The GRAL simulation uses meteorological data collected from the Liberdade QualAr, located directly on Avenida da Liberdade³¹. Climatic data correspond to the 7th October 2022, a day characterized by high concentrations of atmospheric pollutants (PM10: 73.32 µg/m³) and adverse dispersion conditions. This date was selected due to the intensity of pollution and the availability of continuous hourly monitoring data.

The validation of the simulation (Fig. 10) was performed using hourly PM10 data collected on October 7, 2022, from the Liberdade QualAr localized³¹.

Fig. 10: Hourly validation of PM10 on 7th October 2022.

This figure presents the hourly validation of PM10 concentrations at Avenida da Liberdade for 7th October 2022. The blue bars represent the observed PM10 concentrations (µg/m³), measured at the Liberdade QualAr monitoring station. The red line with markers indicates the PM10 concentrations simulated by the GRAL model for the same period. Code and Data Availability: Observed PM10 data were retrieved from the QualAr database³⁷, while the GRAL model outputs were generated using GRAL (version 23.09.0 d).

Figure 10 presents the comparison between the simulated PM10 concentrations obtained from the GRAL model and the observed PM₁₀ data throughout the day of 07/10/2022. The observed values, represented by the blue bars, show a relatively stable concentration pattern with a slight decline in the late evening. The GRAL-simulated values, illustrated by the red line, closely follow the general trend of the observations, capturing the peaks and troughs during different hours of the day. Although some discrepancies are noticeable at specific times, the overall agreement between the model and the observed data suggests that the model adequately represents the temporal variation of PM₁₀ concentrations for this case study.

Multivariate statistical analysis: principal component analysis (PCA)

In order to assess the influence of environmental variables on the dispersion of atmospheric pollutants under different urban conditions, Principal Component Analysis (PCA) was applied. PCA is a multivariate statistical technique used to reduce the dimensionality of complex datasets while retaining as much of the original variance as possible. It transforms the original variables into a new set of uncorrelated variables called principal components. These components are ordered according to the amount of variance they explain. In simple terms, PCA seeks to identify patterns in the variables, allowing for a clearer and more simplified visualization of the data, which facilitates the interpretation of the results⁵¹.

The simulations were carried out using the coupled GRAMM/GrAL model, considering two distinct scenarios: (i) with the presence of tree vegetation (“Current” scenario) and (ii) without trees (“No Trees” scenario). The simulation results were organized as hourly PM10 concentration values at nine monitoring points distributed along Avenida da Liberdade, in addition to relevant environmental variables.

The PCA included the following independent variables: Atmospheric condition stability, Wind Speed (m/s), Vehicle Count, and the presence or absence of trees (scenario). These variables were selected based on their relevance to the dynamics of pollutant dispersion, as highlighted in the literature.

The principal component analysis was performed using two components (PC1 and PC2), which together explained the majority of the total variance in the dataset.