Spatial Modeling of Trace Element Concentrations in PM₁₀ Using Generalized Additive Models (GAMs)

Abstract

GAMs were implemented to evaluate the spatial variation in concentrations of 33 elements in PM₁₀, in their water-soluble and insoluble fractions used as tracers for different emission sources. Data were collected during monitoring campaigns (November 2016–February 2018) in the Terni basin (an urban and industrial hotspot of Central Italy), using an innovative experimental approach based on high-spatial-resolution (23 sites, approximately 1 km apart) monthly samplings and the chemical characterization of PM₁₀. For each element, a model was developed using monthly mean concentrations as the response variable. As covariates, the temporal predictors included meteorological parameters (temperature, relative humidity, wind speed and direction, irradiance, precipitation, planet boundary layer height), while the spatial predictors encompassed distances from major sources, road length, building heights, land use variables, imperviousness, and population. A stepwise procedure was followed to determine the model with the optimal set of covariates. A leave-one-out cross-validation method was used to estimate the prediction error. Statistical indicators (Adjusted R-Squared, RMSE, FAC2, FB) were used to evaluate the performance of the GAMs. The spatial distribution of the fitted values of PM₁₀ and its elemental components, weighted over all sampling periods, was mapped at a resolution of 100 m.

1. Introduction

Exposure to air pollution stands out as a significant risk factor for global health. It is recognized as the primary environmental risk, with well-documented associations with increased mortality and morbidity worldwide [1,2,3,4,5,6,7]. Research has linked air pollution to a variety of health issues, including cardiovascular, respiratory, and neurological diseases, even at minimal exposure levels, underscoring the urgent need for effective public health interventions and policies to mitigate its impact.

Particulate matter (PM) is indeed a significant air pollutant with serious health implications. While extensive exposure assessments for PM concentrations have been conducted at various scales [8,9,10,11,12,13,14], to date, there are still only a few studies aimed to assess spatially resolved population exposure for its main and trace components. It is worth considering that the spatial distribution of different PM components requires specific instrumentation (Smart Samplers or HSRS) for dust sampling on filter membranes and subsequent chemical analysis. These components, such as metals, heavy metals, and organic compounds vary significantly by location and can have different health effects [15,16].

Exposure to potentially toxic elements (PTEs) in PM, such as lead (Pb), cadmium (Cd), arsenic (As), nickel (Ni), chromium (Cr), and manganese (Mn), has been associated with various health outcomes [17].

The inhalation of PM containing heavy metals can exacerbate respiratory diseases, including asthma and chronic obstructive pulmonary disease (COPD). Metals can irritate lung tissues and contribute to inflammation. Research indicates that metal exposure from PM is linked to cardiovascular diseases, including hypertension, heart attacks, and stroke. The mechanisms involve oxidative stress and inflammatory responses that affect vascular health [18]. Certain metals, particularly Pb and Mn, are neurotoxic. They can impact cognitive function and are associated with neurodevelopmental disorders in children [19]. Some PTEs, such as As, Cd, Cr, and Ni are classified as carcinogens by the International Agency for Research on Cancer (IARC). Long-term exposure is associated with the increased risk of lung cancer and other cancers [20]. Moreover, exposure to metals may lead to adverse pregnancy outcomes, including low birth weight and developmental delays in children [21].

A lack of detailed assessments hinders our understanding of their specific impacts on health, especially in epidemiological studies that aim to establish clear links between exposure and health outcomes. Enhanced spatial resolution in exposure assessments would enable more accurate risk assessments and targeted public health interventions, ultimately contributing to better air quality management and improved population health. Addressing this gap is essential for advancing research and policy aimed at mitigating the health risks associated with air pollution.

Indeed, traditional monitoring networks are constrained by a limited number of fixed sampling points since ad hoc monitoring campaigns that rely on deploying numerous sampling devices (whether low or high volume) can become prohibitively expensive and logistically challenging. Moreover, mathematical deterministic models applied at the local level require reliable and up-to-date emission inventories, which are often unavailable or incomplete, leading to poor estimation performance. The knowledge gained from the high spatial characterization of PM trace elements is crucial for both health effect studies and the assessment of the relative burden attributable to different emission sources. Furthermore, in areas characterized by complex mixed-source contexts (such as cities where traffic and domestic heating emissions combine with industrial sources), this information enables better action planning and more effective population exposure reduction and mitigation strategies.

Recent studies have demonstrated the effectiveness of very low-volume samplers for high-spatial-resolution PM monitoring. The results of PM chemical characterizations can be used to generate spatially resolved population exposure data through statistical models. In this context, the most widely used approaches have been land-use regression models, employing a linear regression equation (LM) with multiple regressors to predict a dependent variable (e.g., a PM component or fraction) [22,23,24,25], and machine learning approaches [26,27].

In generalized additive models (GAMs) [28,29], linear predictors are expressed as a sum of smooth functions of covariates, such as penalized splines. This approach allows for the capture of both linear and non-linear relationships between covariates and air pollutant concentrations. GAMs are particularly effective at detecting complex non-linear relationships in data while eliminating the need for preliminary assumptions about the shape of the response curves. A GAM typically combines smoothed functions of predictor variables, commonly represented as polynomials distributed across intervals, known as splines [28,30]. Furthermore, GAMs have demonstrated strong performance in quantitatively distinguishing the effects of specific predictor variables, such as meteorological factors and air emissions, on gaseous and fine particulate concentrations [31,32,33,34,35,36,37,38]. Considering both the primary and trace components of PM, only a limited number of studies have attempted to disentangle the sources contributing significantly to the spatial variability of their concentrations within a given study area. In several studies, to quantitatively assess the effects of the meteorological variables and emission sources on PM levels, GAMs coupled with the Positive Matrix Factorization model (PMF) have been used, to support the policies aimed at improving air quality: emission sources were identified and quantified by applying PMF to PM chemical components, while GAMs were developed to investigate and quantify the factors (temporal and spatial variables) influencing these sources [39,40,41,42].

We aim to illustrate the utility of combining measurement campaigns conducted with a dense network of very low-volume samplers and GAMs to achieve reliable predictions of high spatial resolution of PM elemental components. As a case study, we apply our approach in the Terni basin, an urban and industrial hotspot of Central Italy. This area is characterized by significant urban PM emissions stemming from vehicular traffic, a rail network, and biomass domestic heating, as well as a high density of industrial activities, including a waste treatment power plant and a steel plant. In addition, we evaluate the performance of models developed for the PM components addressed.

Finally, we also aim to delineate across the entire monitoring area the impact of PM emission sources traced by different elements: steelworks, non-exhaust vehicular traffic, and the biomass combustion for domestic and industrial heating. To the best of the authors’ knowledge, there are currently no similar applications in the literature that include an evaluation of the performance of models developed for the PM components addressed in this study.

2. Materials and Methods

2.1. Study Area

The study domain encompasses the city of Terni, which has a population of 107,165 inhabitants (ISTAT—Population and housing census 2021) and covers an area of 211.90 km². Terni is located in a basin within the Umbria Region of Central Italy (42°34′ N; 12°39′ E).

The unique orography of Terni basin, namely, a broad plain surrounded by the Apennine mountains, favors episodes of atmospheric stability, marked by shallow mixing layer heights (MLHs) and low wind speeds, particularly during winter months. These conditions prevent the transport and dispersion of air pollutants [43]. Terni’s climate is classified as temperate mid-latitude, according to the Köppen climate classification [44]. Specifically, the Terni area is characterized by cold, rainy winters; mild, humid springs and autumns; and hot, humid, muggy, and dry summers [45,46,47].

In Terni, primary sources of PM emissions include urban activities such as vehicular traffic, the rail network, and domestic heating, in addition to industrial operations such as a power plant for waste treatment and a steel plant [47,48,49]. Furthermore, in the areas to the south and north of the city center, biomass-burning appliances are frequently utilized for domestic and industrial heating [47].

The spatial distribution of the main PM emission sources within the study area is well established, as previous research examined the spatial variability of PM₁₀ element concentrations in Terni [15,46,47].

2.2. Sampling and Analysis

This study employed concentration data of inhalable PM (aerodynamic diameter ≤ 10 µm, PM₁₀) and its chemical components, encompassing both water-soluble and insoluble fractions of 33 elements (Al, As, Ba, Bi, Ca, Cd, Ce, Co, Cr, Cs, Cu, Fe, Ga, K, La, Li, Mg, Mn, Mo, Na, Nb, Ni, Pb, Rb, Sb, Sn, Sr, Ti, Tl, U, W, Zn, Zr). The chemical fractionation of the elements has already been demonstrated to increase their selectivity as source tracers since the water-soluble and insoluble fractions of many elements are released by different emission sources [50,51,52]. These 33 water-soluble/insoluble elements were already selected based on their analytical uncertainty and suitability as tracers for different local sources of PM₁₀ in the Terni basin [16,46,47]. The PM₁₀ data were collected during monitoring campaigns carried out from November 2016 to February 2018, with 12 sampling periods lasting approximately one month each (Supplementary Materials, Table S1). A total of 23 sampling sites were established within the city of Terni, with each site approximately 1 km apart.

The sampling sites were strategically selected to ensure comprehensive coverage of the entire Terni basin, with a spatial resolution of approximately 1 km, thereby allowing for the identification of areas impacted by various local PM emission sources (Figure 1) [46,47]. Specifically, the sampling locations included the following:

• Two sites (RI, MA) situated near the waste treatment power plant in the western part of the city;
• Three sites (GI, CR, HG) located near the railway in the northwest of the city;
• Six sites (CZ, HV, SA, UC, CA, CO) encompassing the busiest streets in the city center;
• Two sites representing industrial biomass heating (FA and CB, corresponding to carpentry and craftsmanship laboratories) in the southwest of the city;
• Six sites (FR, BR, AR, PI, PV, LG) designated for domestic biomass heating in townhouses located in the northern and southern regions of the city;
• Four sites (RO, OB, PR, CP) surrounding the extensive steel plant to the east of the city.

Figure 1. Map of the 23 sampling sites of PM₁₀ in the study area (Terni, Central Italy).

Figure 1. Map of the 23 sampling sites of PM₁₀ in the study area (Terni, Central Italy).

Further details regarding the characteristics of the sampling sites, as well as the equipment and analytical procedures employed, have been extensively documented in previous studies [46,47] and are available in the Supplementary Materials (Table S2).

2.3. Potential Spatial Explanatory Variables

The following spatial predictor variables were calculated at each sampling site and used for the models’ development:

• Land use, calculated in the domain of interest at a spatial resolution of 10 m:
  • Continuous urban fabric representative of continuous areas with high urban fabric (>80% coverage);
  • Discontinuous urban fabric represented area with varying urban fabric densities: dense (50–80%), medium (30–50%), low (10–30%), and very low (<10%);
  • Industrial commercial public representative of industrial, commercial, and public areas;
  • Imperviousness, which was representative of impervious surfaces.

Data sources were the Urban Atlas 2018 dataset through the Copernicus Land Monitoring Service (CLMS, https://land.copernicus.eu/en/products/urban-atlas/urban-atlas-2018; accessed on 1 January 2024) and, for imperviousness, the Copernicus Imperviousness Density 2018 raster (https://land.copernicus.eu/en/products/high-resolution-layer-imperviousness/imperviousness-density-2018; accessed on 1 January 2024).

2.

Urban morphology:

• Building heights were extracted from the Urban Atlas 2018 section of the CLMS, weighted for the corresponding urban fabric area.
• Road lengths and distances were assessed for main, secondary, tertiary, and local roads, as well as proximity to railways, utilizing Open Street Map layers (https://www.openstreetmap.org; accessed on 1 January 2024).
• Further street configuration variables were included from Urban Atlas 2018, distinguishing between fast transit roads and other roads with associated land.
• Cold and hot areas, along with scrapyard, were identified as primary point sources associated with the Terni steel plant, represented by the minimum distance from each sampling site.

3.

Population:

• The number of inhabitants in 2018 was referenced from the most recent ISTAT census sections of 2011 (https://www.istat.it/it/archivio/104317; accessed on 1 January 2024).

4.

Normalized Vegetation Index (NDVI):

• NDVI was included as a predictor variable, given that it serves as a better proxy for vegetation density compared to Corine Land Cover categories (urban green, natural areas). Daily updates were provided at a spatial resolution of 10 m × 10 m.

Each spatial variable was calculated at the sampling points within buffers of 25, 50, 75, 100, and 200 m radii.

All analyses were performed using R statistical software (v4.4.2; R Core Team 2024) [53].

2.4. Potential Temporal Explanatory Variables—Meteorological Parameters

We obtained time series data for the planetary boundary layer height (PBL) from ERA5 (https://cds.climate.copernicus.eu/datasets/reanalysis-era5-single-levels?tab= download; accessed on 1 January 2024), which provides hourly atmospheric reanalysis products at a resolution of 0.25° × 0.25°. In addition, all other meteorological surface-level variables (temperature, pressure, relative humidity, precipitation, horizontal and vertical wind components, wind speed, solar radiation) were sourced from ERA5-Land (https://cds.climate.copernicus.eu/datasets/reanalysis-era5-land?tab = download; accessed on 1 January 2024), which operates at a finer resolution (0.1° × 0.1°).

For each air quality monitoring station, a time series of meteorological parameters was extracted from the nearest grid centroid. The hourly data related to selected meteorological variables were subsequently aggregated from both datasets, and mean values were calculated corresponding with the sampling periods of the air quality monitoring campaign, which took place from November 2016 to January 2018.

2.5. Generalized Additive Model Development

Generalized additive models (GAMs) were employed to assess the variation in concentrations of PM₁₀ and of 33 water-soluble/insoluble elements in relation to predictor variables.

In this study, the model was implemented considering the dependent variable having a log-normal distribution [31,54]. The response variable consists of concentration data collected from all sampling sites, as described in Section 2.2, for each pollutant, namely, PM₁₀ and its elemental components. Furthermore, smooth covariate functions, such as thin plate splines, were employed for the explanatory variables.

For the spline functions of the spatial explanatory variables, a single calculation interval was imposed to mitigate excessive fluctuations, which might give rise to implausible trends.

For certain elemental tracers, whose air concentrations significantly depend on sources with a markedly seasonal emission profile, the GAMs were implemented by also considering a linear categorical variable, with classes corresponding to the four seasons.

The non-linear effects of both meteorological and spatial explanatory factors were analyzed using a stepwise approach to identify the optimal set of covariates based on the lowest Akaike Information Criterion (AIC), following the methodology of Barmpadimos et al. [33] but using the Bayesian Information Criterion (BIC) instead of the Akaike Information Criterion (AIC), in order to impose a stronger penalty on models with an excessive number of covariates [55]. To address potential collinearity, a maximum Pearson correlation coefficient of 0.7 was established.

Furthermore, for tracers exclusively emitted by steel plant (Cr_i, Mo_s, Ni_i and W_s), a simplified model was implemented, where the only possible spatial covariates, included in the aforementioned selection procedure, were the distance from the cold area and the hot area.

The “mgcv” package in R [56] was utilized for fitting GAMs and for model selection. The significance of the spline terms was evaluated, and residual diagnostics were performed using the “gam.check” function included in the “mgcv” package.

A leave-one-out cross-validation method was employed for accuracy assessment. Finally, statistical performance indicators of the cross-validated models including adj-R2, CV-R2, RMSE, FAC2, FB, and NMSE were calculated [57].

Acceptance criteria for these indicators were established to assess the reliability of the developed GAMs. The values selected for these criteria [58] are reported in

Table 1. Acceptance criteria for statistical performance indicators.

FAC2	|FB|	NMSE
≥0.50	≤0.30	≤3

.

The GAMs developed on the data collected in the sampling points were used to predict the average concentration of PM₁₀ and its selected chemical components over various sampling periods and throughout the computational domain.

A schematic representation of the key concepts and steps underlying the proposed methodology is presented in the following flowchart (Figure 2).

3. Results and Discussion

GAMs, which exhibited a satisfactory goodness of fit based on the statistical performance indicators used, pertain to PM₁₀ and the following 19 water-soluble (“_s”) and/or insoluble (“_i”) elements: Bi_i, Cr_i, Cr_s, Cs_s, Cu_i, Fe_i, K_s, Li_i, Li_s, Mn_i, Mn_s, Mo_s, Ni_i, Pb_i, Sn_i, Tl_s, W_s, Zn_s, and Zr_i.

For all models, the spatial and temporal variables selected using the stepwise procedure described in Section 2.5 are presented in

Table 2. Spatial predictor variables selected in the GAMs.

Variable 1	Description	Unit of Measure
code_12100	Industrial, commercial, and public areas	m2
code_12220	Local street area	m2
bh_index	Height of the buildings weighted on the related area of the urban fabric	m/m2
dist_ferr	Distance from railway	m
imp_200	Impermeable surfaces in a buffer of 200 m	%
pop_200	Number of inhabitants in a buffer of 200 m	n.
dist_strade	Distance of the nearest road	m
ml_200	Lengths of road in a buffer of 200 m	m
cold_area	Distance from cold area of the steel plant	m
hot_area	Distance from the hot area of the steel plant	m

¹ Only spatial predictor variables calculated within a 200 m buffer around the measurement point are included in the models.

and

Table 3. Meteorological parameters selected in the GAMs.

Variable 1	Description	Unit of Measure
t2m_mean	Mean, over the air quality sampling periods, of the air temperature at 2 m from ground level	°C
tmin2m_mean	Mean of the daily minimum air temperature at 2 m from ground level	°C
tmax2m_mean	Mean of the daily maximum air temperature at 2 m from ground level	°C
tp_mean	Mean of the daily accumulated precipitation at 2 m from ground level	mm
rh_mean	Mean of the relative humidity of the air at 2 m from ground	%
u10m_mean	Mean of the eastward horizontal wind component at 10 m height	m/s
v10m_mean	Mean of the northward vertical wind component at 10 m height	m/s
wspeed_mean	Mean of the wind speed intensity at 10 m height	m/s
wspeed_max_mean	Mean of the daily maximum wind speed intensity at 10 m height	m/s
sp_mean	Mean ground level pressure	hPa
nirradiance_mean	Mean solar radiation intensity	W/mq
pbl00_mean	Mean of the planetary boundary layer height at 00:00	km
pbl12_mean	Mean of the planetary boundary layer height at 12:00	km
pblmin_mean	Mean of the minimum planetary boundary layer height	km
pblmax_mean	Mean of the maximum planetary boundary layer height	km

¹ Values averaged over the sampling period of air quality monitoring campaigns.

. GAMs developed for PM₁₀ and its selected elemental fractions are reported in

Table 4. Model formula for PM₁₀ and its selected elemental fractions.

Pollutant	Model Formula *
PM10	value ~ s(pbl00) + s(wspeed_max) + s(pop, k = 1) + s(code_12100, k = 1) + s(sp) + s(rh) + s(hot_area, k = 6)
Bi_i	value ~ s(rh) + s(hot_area, k = 6) + s(code_12100, k = 1) + s(v10m) + s(wspeed) + s(imp, k = 1)
Cr_i	value ~ s(cold_area, k = 6) + s(u10m)
Cr_s	value ~ s(hot_area, k = 6) + s(rh) + s(dist_ferr, k = 1) + s(code_12100, k = 1) + s(dist_strade, k = 1, bs = “gp”) + s(imp, k = 1)
Cs_s	value ~ season + s(u10m) + s(cold_area, k = 6) + s(dist_ferr, k = 1) + s(ml, k = 1) + s(sp) + s(code_12100, k = 1)
Cu_i	value ~ s(u10m) + s(code_12100, k = 1) + s(code_12220, k = 1) + s(v10m) + s(pblmin)
Fe_i	value ~ s(cold_area, k = 6) + s(u10m) + s(code_12100, k = 1) + s(dist_ferr, k = 1) + s(v10m)
K_s	value ~ season + s(pblmax) + s(hot_area, k = 6) + s(dist_ferr, k = 1) + s(bh_index, k = 1)
Li_i	value ~ s(pbl12) + s(imp, k = 1) + s(wspeed_max) + s(bh_index, k = 1)
Li_s	value ~ s(hot_area, k = 6) + s(rh) + s(dist_ferr, k = 1) + s(pop, k = 1) + s(code_12220, k = 1)
Mn_i	value ~ s(cold_area, k = 6) + s(dist_ferr, k = 1) + s(wspeed_max) + s(imp, k = 1) + s(pop, k = 1) + s(pblmin) + s(dist_strade, k = 1, bs = “gp”)
Mn_s	value ~ s(nirradiance) + s(hot_area, k = 6) + s(dist_ferr, k = 1) + s(code_12220, k = 1) + s(pop, k = 1) + s(pbl00)
Mo_s	value ~ s(cold_area, k = 6) + s(wspeed_max) + s(pbl00)
Ni_i	value ~ s(cold_area, k = 6) + s(tmin2m) + s(wspeed_max) + s(tp)
Pb_i	value ~ season + s(hot_area, k = 6) + s(dist_ferr, k = 1) + s(t2m) + s(code_12220, k = 1) + s(pop, k = 1)
Sn_i	value ~ s(pbl12) + s(hot_area, k = 6) + s(dist_ferr, k = 1) + s(bh_index, k = 1) + s(imp, k = 1)
Tl_s	value ~ season + s(hot_area, k = 6) + s(sp) + s(bh_index, k = 1) + s(dist_ferr, k = 1) + s(imp, k = 1)
W_s	value ~ s(cold_area, k = 6) + s(v10m)
Zn_s	value ~ s(pblmax) + s(hot_area, k = 6) + s(dist_ferr, k = 1) + s(code_12220, k = 1) + s(pop, k = 1)
Zr_i	value ~ s(code_12220, k = 1) + s(pblmax) + s(bh_index, k = 1) + s(cold_area, k = 6) + s(imp, k = 1) + s(dist_ferr, k = 1) + s(wspeed_max)

* value = average concentration over the sampling period of air quality monitoring campaigns; s() = spline function.

.

The evaluation parameters (Adjusted-R²) and the statistical indicators of the cross-validation procedure (CV-R², RMSE, FAC2, FB, NMSE) of these models are reported in

Table 5. GAM performance indicators of PM₁₀ and its selected elemental fractions.

Pollutant	Adj R2	CV-R2	RMSE	FAC2	FB	NMSE
PM10	0.80	0.81	6.59	1.00	0.09	0.05
Bi_i	0.79	0.80	0.08	0.84	0.20	0.14
Cd_s	0.74	0.75	0.06	0.87	0.16	0.13
Cr_i	0.68	0.69	19.32	0.78	0.23	0.43
Cr_s	0.70	0.72	0.76	0.89	0.16	0.18
Cs_s	0.86	0.87	0.01	0.91	0.16	0.08
Cu_i	0.63	0.65	3.29	0.94	0.21	0.13
Fe_i	0.56	0.59	223.08	0.90	0.22	0.20
K_s	0.84	0.84	124.49	0.93	0.13	0.09
Li_i	0.56	0.58	0.04	0.92	0.12	0.12
Li_s	0.74	0.76	0.04	0.95	0.14	0.09
Mn_i	0.69	0.71	3.36	0.97	0.12	0.09
Mn_s	0.71	0.73	2.26	0.95	0.16	0.12
Mo_s	0.83	0.82	4.35	0.76	0.26	0.47
Ni_i	0.81	0.81	8.54	0.74	0.27	0.57
Pb_i	0.75	0.77	1.61	0.92	0.20	0.14
Rb_s	0.72	0.73	0.38	0.91	0.14	0.13
Sn_i	0.88	0.89	1.01	0.91	0.23	0.10
Tl_s	0.86	0.87	0.03	0.92	0.18	0.10
W_s	0.85	0.85	0.04	0.77	0.24	0.37
Zn_s	0.73	0.75	10.44	0.91	0.16	0.12
Zr_i	0.56	0.59	0.59	0.21	0.87	0.19

. Among these models, only that related to Zr_i did not meet the criteria for indicators such as FAC2 and FB (see Section 2.5). The very similar values of Adjusted-R² and CV-R² (Table 5) demonstrate the robustness of the implemented GAMs concerning the uncertainty in model predictions.

The plots related to the checking of the basic assumptions for each statistical model are available in the Supplementary Materials (Figures S1a–S20a).

3.1. Spatial Distribution

Spatial mapping of the fitted values for PM₁₀ and its water-soluble/insoluble elements was performed over a model domain with dimensions of 7.6 km × 4.2 km and a spatial resolution of 100 m × 100 m.

Before proceeding with a detailed analysis of the results obtained for the considered models, in order to highlight the significance of the different air emission sources and make them comparable, spatial maps of standardized fitted values are represented in Figure 3.

Spatial mapping of a single water-soluble/insoluble element was selected to represent the contribution of each main local PM₁₀ source across the entire monitoring area: steel plant, biomass heating, road dust, and brake dust, and further results are reported in the Supplementary Materials. Spatial distributions of remaining water-soluble/insoluble elements are available in Supplementary Materials.

3.1.1. PM₁₀

For the PM₁₀ model (Table 4), the selected explanatory variables included the monthly average of the PBL’s height at midnight, atmospheric pressure and relative humidity, the maximum monthly wind speed, population, the extent of industrial, commercial, and public areas, and the distance from the steel plant’s hot area.

The spline functions of the predictor variables are provided in the Supplementary Materials (Figure S1b).

The results support the hypothesis that PM₁₀ sources are various and variable. Specifically, a positive relationship was observed between PM₁₀ levels and the presence of industrial, commercial, and public activities, key sources of PM₁₀ emissions (code_12100, Table 2), as well as population, which reflects the impact of urban density on PM₁₀ concentrations.

For PBL heights above 150 m, PM₁₀ levels decrease as the PBL height increases, according to the theory that higher PBL height provides a larger volume for pollutant dispersion, reducing pollutant concentrations. Conversely, relative humidity contributed positively, suggesting that PM₁₀ concentrations increase with higher humidity, a pattern typically observed during winter periods when atmospheric stability is greater (see Supplementary Materials).

Figure 4 illustrates the spatial distribution of PM₁₀ fitted averaged values, weighted over all sampling periods, as detailed in Table S1.

The spatial variation in the PM₁₀ concentrations aligns with the spline of the main predictor variables, notably highlighting population, as a proxy of high urban density, along with areas characterized by intense commercial, industrial, and public activities as important sources of this pollutant.

3.1.2. Steel Plant

Regarding the elements in PM₁₀ associated with steel composition and production [16,47,59,60], the models that exhibited robust performance (Table 5) were those related to Cr_i, Mo_s, Ni_i, and W_s.

The spline functions of predictor variables selected in the models are provided in the Supplementary Materials (Figures S3b, S13b, S14b and S18b).

In these models, among the spatial variables with the coefficient aligned with the expected direction of effect, distance from the steel plant, specifically from the cold area (cold_area, Table 2), shows a strong decreasing contribution to elemental concentrations as the distance from the source increased (see related spline functions). These results are consistent with previous studies indicating a major role of cold processes (abrasion, brushing, and polishing of rolled steel) for these water-soluble/insoluble elements.

The spatial distributions of fitted values of aforementioned elemental fractions align with the spline function of the main spatial predictor variable (cold_area), thus confirming the role of the steel plant as the primary source of these elements.

As an example, the spatial distribution of Mo_s concentrations, averaged across all sampling periods, is shown in Figure 5. The spatial distribution of the fitted values for the remaining elements associated with the steel plant source is available in the Supplementary Materials (Figures S4c, S14c and S18c).

Furthermore, models related to the other elements associated with the steel plant emissions [16,47], such as Cr_s, Fe_i, Li_s, Mn_i, Mn_s, Pb_i, and Zn_s, also indicate that distance from the steel plant, particularly from the hot area (hot_area, Table 2), has a strong and predominant decreasing contribution to element concentrations (see related spline functions). These results are consistent with previous studies that identified Cr_s, Li_s, Mn_s, Pb_i, and Zn_s as tracers for monitoring combustion emissions from the steel industry [16,48].

3.1.3. Biomass Heating

Regarding the water-soluble/insoluble elements in PM₁₀ recognized as biomass burning tracers [16,51,61,62,63,64], GAMs that yielded satisfactory results (Table 5) were those related to Cs_s, K_s, Pb_i, and Tl_s.

The spline functions for the predictor variables selected in the models are provided in the Supplementary Materials (Figures S5b, S8b, S15b and S17b).

In all the GAMS developed for these elements, one of the variables selected through the stepwise procedure was the distance from the railway (dist_ferr, Table 2): the corresponding spline function exhibits that the contribution to concentration increases with distance. This variable can be considered as a proxy for identifying areas distant from the railway and located north and south of it, where biomass burning sources are known to be present [16,47,65].

In the K_s and Tl_s models, another spatial explanatory variable with the coefficient aligned with the expected direction of effect, is the height of the buildings weighted on the related area of the urban fabric (bh_index, Table 2): the related spline function shows a significant increasing effect on concentrations up to a value of about 5 m/m² and then a decreasing effect.

In the Cs_s model, the spatial explanatory variable with a coefficient consistent with the expected direction of effect, is the presence of industrial, commercial, and public areas (code_12100, Table 2): the related spline function indicates a growing contribution as the values of this variable rise.

The spatial distributions of fitted values for these elements were analyzed over the four seasons to identify the expected seasonal variations in their behavior. For instance, the spatial distribution of Cs_s concentrations averaged over all sampling periods is presented in Figure 6. Detailed spatial distributions for the remaining elements associated with biomass burning sources are available in the Supplementary Materials (Figures S8c, S15c and S17c).

3.1.4. Road Dust

Regarding the elements in PM₁₀ that trace road dust [16,66,67,68], the GAMs that presented good results (Table 5) were those developed for Li_i, Zn_s, and Cr_s. It is worth noting that road dust is characterized by particles released from different local emissions (i.e., vehicular traffic, steel plant, and soil dust) that are deposited and then resuspended from road surfaces, thus containing elements that trace these sources [51,64,69,70,71]. The spline functions of the predictor variables selected in the models are reported in the Supplementary Materials (Figures S4b, S9b and S19b).

In the Li_i model, the impervious surface variable (imp_200, Table 2), where the roads are a significant component, exhibits an increasing effect on the pollutant concentrations as the percentage of impervious surface rises up to 75%, after which concentrations stabilize. However, the Li_i estimated levels indicate that this effect is relatively minor, and the spatial distribution is rather homogeneous across the domain (Figure S9c in the Supplementary Materials).

In the Zn_s model, the spatial variables with coefficients aligned to the expected direction of effect reveal distinct contributions to pollutant concentrations. Specifically, the extent of local roads (code_12220, Table 2) shows a predominantly increasing contribution to Zn_s levels; conversely, the distance to the steel plant’s hot area exhibits a mainly decreasing contribution, with closer proximity correlating with higher Zn_s concentrations: this finding might imply that heavy vehicle traffic within the steel plant area significantly increases Zn_s pollution. Regarding Cr_s, while the steel plant was identified as the primary source, areas characterized by intense commercial, industrial, and public activities (code_12100, Table 2) with busy traffic roads, also emerged as significant contributors.

The spatial variation in Zn_s and Cr_s fitted levels is consistent with the spline function of the main predictor variables, emphasizing roads as important sources of this element. The spatial distribution of Zn_s fitted values averaged over all sampling periods (Table S1) is shown in Figure 7, while the Cr_s map is reported in Supplementary Materials (Figure S4c).

3.1.5. Brake Dust

Regarding the insoluble elements in PM₁₀ considered as tracers of non-exhaust emissions from vehicular and railway traffic [16,47,72,73,74,75,76], the GAMs that exhibited satisfactory performance (Table 5) were those related to Bi_i, Cu_i, Sn_i, and Zr_i.

The spline functions of predictor variables selected in the models are provided in the Supplementary Materials (Figures S2b, S6b, S16b, and S20b).

In Cu_i and Zr_i models, among the spatial explanatory variables displaying coefficients aligned with the expected direction of effect, the areas covered by local streets (code_12220, Table 2) exhibit a robust, mainly growing contribution to the concentrations of these fractionated elements, which increased with this area. In Sn_i, and Zr_i models, distance from the railway (dist_ferr) shows coefficients consistent with the expected direction of effect, i.e., the contribution to concentrations decreased as distance increased.

In the Bi_i model, the presence of industrial, commercial, and public areas (code_12100, Table 2) and the impervious surfaces (imp_200, Table 2) display coefficients aligned with the expected direction of effect, with increasing contributions to concentration as the values of variables increased.

The spatial distributions of fitted values of Bi_i, Cu_i, Sn_i, and Zr_i fractions illustrate the effect of the main explanatory variables, confirming the role of the brake dust as a significant source of these elements. As an example, the spatial distribution of the Sn_i value concentrations averaged across all sampling periods is reported in Figure 8. Spatial distributions for the remaining elements associated with brake dust are available in the Supplementary Materials (Figures S2c, S6c and S20c).

For Fe_i and Mn_i, the steel plant was identified as the primary source; however, they are also associated with the brake dust. In fact, in the corresponding models, in addition to the cold_area variable, other variables with coefficients consistent with the expected direction of effect of this secondary source were selected, such as distance from the railway (dist_ferr, Table 2): the corresponding spline functions show a decreasing contribution to element concentrations for distances greater than 750 m. The influence of these variables is clearly depicted in the resultant maps (see Supplementary Materials, Figures S7c and S11c).

4. Conclusions

In this study, GAMs were applied to PM₁₀ concentration data and to water-soluble and/or insoluble elements in PM₁₀ used as tracers of different emission sources. A model for each elemental tracer was developed and, as the response variable, mean concentrations of PM₁₀ and its elemental components were used.

For each model, the best set of covariates was determined through a stepwise procedure, while the performance was evaluated by statistical indicators. Thanks to their intrinsic characteristics and the selection procedure used, which allows for the identification of significant covariates without prior assumptions, the implemented GAMs allowed the identification of the most relevant air emission sources for a total of 19 soluble and/or insoluble elements, even in the most complex cases where the element turned out to be a tracer for multiple sources. Spatial mapping of each element mean concentration was generated by associating it with the main emission local PM sources present across the entire study: steel plant, biomass heating, road dust, and brake dust.

Typically, LUR models or GAMs are applied exclusively to PM concentration measured using counters or low-cost sensors, which provide high spatial resolution. In this case, however, GAMs were applied to PM components that act as tracers of different emission sources because an innovative approach based on sampling and, consequently, the chemical analysis of particulate matter with high spatial resolution was used.

Furthermore, our results demonstrate that GAMs for PM components outperform traditional LUR models. In our study, the CV-R² values for GAMs range from 0.59 to 0.89, whereas LUR models reported in the literature show R² values ranging from 0.34 to 0.55 [25], 0.24 to 0.67 [22], and 0.46 to 0.80 [23], as summarized in the most recent review of LUR approaches [77]. Similar conclusions are also evident when comparing our results with those obtained through machine learning (ML) techniques. Specifically, the largest study conducted in a single urban area [27] found that ML models generally performed worse than spatio-temporal linear regression models for most PM elements: in this study, neural networks achieved CV-R² values ranging from 0.24 to 0.71, random forests from 0.08 to 0.63, and extreme gradient boosting from 0.09 to 0.63.

A limitation of GAMs, as implemented in the present study, lies in their inability to capture the contribution attributable to regional or long-range PM transport processes. To overcome this limitation, explanatory variables capable of describing such processes should be included in the model, typically derived from Chemical Transport Models. A GAM approach allowed us to achieve this study’s objective of obtaining high-resolution predictions of PM elemental components even in locations where no monitoring data were available. This provides a solid basis for evaluating population exposure to these pollutants, assessing health risks, and supporting air quality management strategies aimed at mitigating the adverse effects of PM and its components on human health.