Machine Learning-Based Retrieval of PM_2.5 Concentrations Using Multi-Source Satellite Data in the Beijing–Tianjin–Hebei Region of China

Abstract

Satellite aerosol optical depth (AOD) provides information for surface PM_2.5 retrieval, but its relationship with ground-level concentrations depends on meteorological and environmental conditions. This study evaluated a multi-source PM_2.5 retrieval framework for the Beijing–Tianjin–Hebei (BTH) region during 2019–2021. Four input combinations were compared: AOD alone, AOD with meteorological variables, AOD with additional satellite variables, and all eight predictors. The satellite variables included land surface temperature, NDVI, and tropospheric NO₂. Random forest, support vector regression, XGBoost, and linear stacking were evaluated using the same samples and an 80:10:10 training–validation–test split. The stacking model was trained using out-of-fold predictions. Across the four models, R² increased from 0.51–0.54 with AOD alone to 0.83–0.84 with all predictors. Stacking achieved the best performance with all predictors, with R² = 0.84, RMSE = 12.4 μg/m³, and MAE = 9.7 μg/m³. Annual retrievals showed higher concentrations in southern and southwestern Hebei and lower concentrations in northern BTH, while the 2021 maps showed higher concentrations in winter than in summer. Missing AOD reduced the spatial completeness of PM_2.5 retrievals, and future work should assess gap filling to improve coverage and its effects on retrieval accuracy.

1. Introduction

Reliable regional PM_2.5 retrievals are needed for air-quality assessment, exposure studies, and pollution management. Ground monitoring provides direct measurements at individual locations, but stations cannot fully describe pollution differences between cities, rural areas, and mountainous areas. Satellite observations can complement these measurements and support regional mapping [1,2,3]. This need is important in the Beijing–Tianjin–Hebei (BTH) region, where urban development, industrial activity, agricultural land, and complex terrain create varied conditions for pollutant emissions and dispersion [4,5].

Aerosol optical depth (AOD) is widely used for surface PM_2.5 retrieval because it measures aerosol extinction through the atmospheric column. However, AOD and PM_2.5 describe different properties: AOD measures column optical loading, whereas ground stations measure particle mass near the surface [1,2,6]. Their relationship changes with aerosol height, relative humidity, boundary-layer structure, and aerosol composition [6,7]. These factors support the inclusion of meteorological and environmental variables in AOD-based retrieval models.

Machine learning can combine these variables and represent nonlinear relationships. Previous studies have used tree-based and ensemble models to combine satellite, meteorological, and land-surface information for PM_2.5 retrieval across China [8,9,10,11,12,13,14]. Related applications to pollutant concentrations and emissions in densely populated regions also support the use of environmental observations and complementary modelling approaches [15,16]. These studies provide a basis for testing multi-source inputs and model combinations under regional conditions.

For regional PM_2.5 retrieval, it is important to determine how much information is gained by adding predictors to AOD and whether stacking improves performance beyond individual models. Meteorological variables describe conditions affecting aerosol growth and dispersion [6,17]. Land surface temperature (LST), NDVI, and tropospheric NO₂ provide additional information on surface conditions and pollution-related spatial differences [8,18]. Comparing input combinations using the same observations and data partitions helps identify their added value.

Input availability also affects the usefulness of retrieved maps. Clouds, retrieval failure, and quality screening can leave pixels without valid AOD, while other required inputs may also be missing [19]. Prediction accuracy and spatial completeness therefore need to be considered together. The varied urban, plain, mountain, and coastal environments of BTH provide a useful setting for examining these aspects of regional retrieval.

This study evaluates daily PM_2.5 retrieval in BTH during 2019–2021 using four input combinations and four machine-learning models. The objectives are to assess the added value of meteorological and satellite variables relative to AOD alone; compare RF, SVR, XGBoost, and linear stacking under the same evaluation conditions; describe annual and seasonal PM_2.5 patterns; and examine how missing AOD affects retrieval coverage. This comparison helps clarify the roles of input information, model choice, and data availability in regional PM_2.5 mapping.

2. Materials and Methods

2.1. Study Area and Period

The Beijing–Tianjin–Hebei (BTH) region is located in northern China and comprises Beijing Municipality, Tianjin Municipality, and Hebei Province (Figure 1). It is one of China’s major urban–industrial agglomerations and includes densely populated urban centers, industrial and energy-production areas, major transportation corridors, agricultural plains, coastal zones, and mountainous landscapes. The southern and eastern parts of the region are dominated by the North China Plain, while the Taihang Mountains border the west and the Yanshan Mountains extend across the north. The eastern part of the region is adjacent to the Bohai Sea. These contrasting land-use and topographic conditions produce considerable spatial heterogeneity in emissions, surface characteristics, and atmospheric dispersion.

Figure 1. Location of the Beijing–Tianjin–Hebei region in China.

The region has a temperate continental monsoon climate characterized by hot, relatively humid summers and cold, dry winters. Summer precipitation and stronger atmospheric mixing generally favor pollutant dispersion and removal, whereas winter heating emissions, shallow boundary layers, and stagnant meteorological conditions can promote near-surface pollutant accumulation. The mountains surrounding the western and northern parts of BTH can further influence local circulation and regional pollutant transport. Together with intensive industrial activity, energy consumption, traffic emissions, and seasonal residential heating, these conditions make BTH a challenging and representative region for evaluating satellite-based PM_2.5 retrieval models.

The study period extended from January 2019 to December 2021, providing three complete annual cycles and a consistent temporal window for the satellite, meteorological, and ground-monitoring datasets. All input data were restricted to this common period prior to preprocessing and spatial matching. During preprocessing, records with missing values or failing the specified quality-control criteria were excluded to ensure the reliability and consistency of the final dataset. The basic unit used for supervised learning was a valid station-day record, defined as a daily ground-level PM_2.5 observation at a monitoring station matched with the corresponding aerosol optical depth (AOD), meteorological variables, and other satellite-derived predictors. This data structure enabled the models to learn the relationships between multi-source environmental variables and observed ground-level PM_2.5 concentrations and supported the subsequent generation of annual regional PM_2.5 retrievals.

2.2. Data Sources

2.2.1. Ground PM_2.5 Observations

Daily ground-level PM_2.5 observations for monitoring stations in the Beijing–Tianjin–Hebei (BTH) region during 2019–2021 were obtained from the China National Environmental Monitoring Centre (CNEMC) [20]. Station identifiers and geographic coordinates were obtained from the official CNEMC monitoring-station list for spatial matching with the satellite and meteorological datasets. The monitoring network covered approximately 113°27′–119°50′ E and 36°05′–42°40′ N. For each station-day, PM_2.5 was represented by the 24 h mean concentration, recorded as PM_2.5 (μg/m³) in the final modelling dataset. These observations served as the reference response variable for model training and evaluation, while satellite-derived and meteorological predictors were used to estimate the spatial distribution of PM_2.5 across the BTH region.

2.2.2. Satellite Remote Sensing Data

Aerosol Optical Depth (AOD) data were obtained from the MODIS MCD19A2 aerosol product using the Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm [19]. This product provides AOD at 550 nm (AOD550) with a nominal spatial resolution of 1 km. It was selected because of its long-term, stable, and widely validated aerosol observations, which are suitable for regional PM_2.5 retrieval. The MCD19A2 product was used to provide daily AOD information over the study area.

Land Surface Temperature (LST) data were obtained from the Terra MODIS MOD11A2 product, which provides 8-day composite LST at a nominal spatial resolution of 1 km [21]. Daytime LST was used and converted to degrees Celsius for integration with the other modelling variables. The corresponding 8-day composite interval was retained when matching LST values with station-day observations. LST helps represent land–atmosphere thermal conditions that influence boundary layer development and pollutant dispersion.

Normalized Difference Vegetation Index (NDVI) data were obtained from the MODIS vegetation index products MOD13A2, which provide 16-day composite NDVI data at a nominal spatial resolution of 1 km. These products were selected to characterize vegetation conditions across the study area. The NDVI represents vegetation and land-surface characteristics, which are associated with surface reflectance, land use, and spatial differences in emission and deposition environments. The NDVI data were spatially matched with ground-level PM_2.5 observations and other satellite-derived and meteorological variables and incorporated as an environmental predictor in the machine learning models.

Nitrogen dioxide (NO₂) data were obtained from the Sentinel-5P satellite equipped with the TROPOMI (TROPOSpheric Monitoring Instrument). The OFFL Level-3 NO₂ product was used, with tropospheric NO₂ column number density as the target variable, expressed in mol/m². The product has a nominal spatial resolution of 1.11 km. Only observations with a quality assurance (QA) value > 0.75 were retained to ensure reliable retrievals. NO₂ was included as an emission-related satellite proxy because it is closely associated with combustion sources, traffic activity, and industrial emissions that also contribute to PM_2.5 formation. The NO₂ data were spatially matched with ground-level PM_2.5 observations and other predictor variables for machine learning-based retrieval of PM_2.5 concentrations.

2.2.3. Meteorological Variables

Meteorological data were obtained from the ERA5 reanalysis product provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) on a regular 0.25° × 0.25° grid [22]. Hourly reanalysis fields were aggregated to daily values. The selected meteorological predictors included near-surface air temperature, relative humidity, wind speed, and planetary boundary layer height (PBLH). These variables were selected to characterize atmospheric thermodynamic conditions, horizontal dispersion, and vertical mixing, which influence the distribution of PM_2.5. The ERA5 fields were interpolated or extracted to the monitoring-station locations for model development and to the common spatial grid for regional PM_2.5 mapping. The data sources, spatial and temporal resolutions, and roles of all variables used in this study are summarized in Table 1.

Table 1. Multi-source variables used in the BTH retrieval framework.

Data Type	Variables	Platform/Data Source	Product/Sensor	Spatial Resolution	Temporal Resolution	Unit	Role in PM2.5 Retrieval
Ground observation	PM2.5	CNEMC	CNEMC ground monitoring data	Station observations in BTH	Daily, 24 h mean	μg/m3	Response variable for model training, validation, testing, and performance evaluation
Satellite aerosol	AOD at 550 nm	NASA/Terra and Aqua	MCD19A2/MODIS	1 km	Daily	—	Core satellite proxy for aerosol loading and PM2.5 retrieval
Satellite thermal	Daytime LST	NASA/Terra	MOD11A2/MODIS	1 km	8-day composite	°C	land-surface thermal
Satellite vegetation	NDVI	NASA/Terra	MOD13A2/MODIS	1 km	16-day composite	—	vegetation and land-surface conditions
Satellite trace gas	Tropospheric NO2 column	Google Earth Engine/Sentinel-5P	OFFL L3 NO2/TROPOMI	1.11 km	Near-daily	mol/m2	Combustion, traffic and industry related satellite proxy
Meteorology	Temperature, RH, wind speed, PBLH	ECMWF	ERA5 reanalysis	0.25° × 0.25°	Hourly, aggregated to daily	°C, %, m/s, m	Characterize meteorological influences on PM2.5 formation, transport, dispersion, and vertical mixing

Table 1. Multi-source variables used in the BTH retrieval framework.

Data Type	Variables	Platform/Data Source	Product/Sensor	Spatial Resolution	Temporal Resolution	Unit	Role in PM2.5 Retrieval
Ground observation	PM2.5	CNEMC	CNEMC ground monitoring data	Station observations in BTH	Daily, 24 h mean	μg/m3	Response variable for model training, validation, testing, and performance evaluation
Satellite aerosol	AOD at 550 nm	NASA/Terra and Aqua	MCD19A2/MODIS	1 km	Daily	—	Core satellite proxy for aerosol loading and PM2.5 retrieval
Satellite thermal	Daytime LST	NASA/Terra	MOD11A2/MODIS	1 km	8-day composite	°C	land-surface thermal
Satellite vegetation	NDVI	NASA/Terra	MOD13A2/MODIS	1 km	16-day composite	—	vegetation and land-surface conditions
Satellite trace gas	Tropospheric NO2 column	Google Earth Engine/Sentinel-5P	OFFL L3 NO2/TROPOMI	1.11 km	Near-daily	mol/m2	Combustion, traffic and industry related satellite proxy
Meteorology	Temperature, RH, wind speed, PBLH	ECMWF	ERA5 reanalysis	0.25° × 0.25°	Hourly, aggregated to daily	°C, %, m/s, m	Characterize meteorological influences on PM2.5 formation, transport, dispersion, and vertical mixing

2.3. Data Preprocessing

All datasets were quality-controlled and harmonized before model development. Daily ground-level PM_2.5 observations were organized by station and date, and invalid records were removed. For satellite variables, MCD19A2 AOD, MOD11A2 daytime LST, and MOD13A2 NDVI were screened using the corresponding product quality information. LST and NDVI were scaled according to product specifications, with LST further converted to °C. Sentinel-5P TROPOMI Level-3 tropospheric NO₂ data obtained through Google Earth Engine were filtered according to the product quality criteria.

Hourly ERA5 temperature, relative humidity, wind speed, and planetary boundary layer height were aggregated to daily values. All satellite and meteorological variables were then spatially matched to the monitoring stations and temporally aligned with the corresponding station-day observations. For composite products, LST and NDVI were assigned according to the composite period covering each observation date. Records with missing values in the variables required for modelling were excluded.

The final dataset consisted of daily PM_2.5 as the target variable and AOD, LST, NDVI, tropospheric NO₂, temperature, relative humidity, wind speed, and planetary boundary layer height as predictors.

2.4. Model Development, Hyperparameter Optimization, and Validation

Daily mean ground-level PM_2.5 concentration was used as the target variable. Four predictor groups were compared (Figure 2): AOD-only, AOD with meteorological variables, AOD with other satellite variables, and all predictors combined. Meteorological variables included temperature, relative humidity, wind speed, and planetary boundary-layer height. Other satellite variables included LST, NDVI, and NO₂. All groups used the same samples after quality screening and the same data splits. Coordinates and dates were used to match and identify records but were not used as model inputs.

RF, SVR, and XGBoost were implemented as base learners, representing bagging-based, kernel-based, and boosting-based approaches, respectively [23,24,25]. Each learner was fitted separately for each predictor configuration using the same hyperparameter search space. SVR employed a radial basis function kernel, and its predictors were standardized using means and standard deviations estimated exclusively from the corresponding training subset. RF and XGBoost used unstandardized predictors. Samples were randomly divided into training, validation, and test sets at an 80:10:10 ratio, with similar year proportions maintained across the three sets. A fixed random seed was used to ensure reproducibility.

Hyperparameters were selected by grid search with three-fold cross-validation within the training set. For each model, the three parameter settings with the lowest cross-validation RMSE were tested on the validation set. The setting with the lowest validation RMSE was selected. The test set was used only for final evaluation. Each model used the same search range across the four predictor groups. RF used 200 trees, maximum depths of unlimited or 12, minimum leaf sizes of 1, 3, or 6, and a feature fraction of 0.8. SVR used C values of 10, 100, or 500, ϵ values of 0.1 or 1, and γ settings of “scale” or 0.03. XGBoost used 300 boosting rounds, maximum depths of 2, 4, or 6, learning rates of 0.03 or 0.1, row and column sampling fractions of 0.8, and L₂ regularization of 5.

The stacking model combined predictions from RF, SVR, and XGBoost [26]. The training set was divided into five folds. In each fold, the base models were tuned by three-fold cross-validation using the other four folds and then used to predict the held-out fold. These out-of-fold predictions were used to train a linear-regression meta-learner with an intercept. The selected base models were then trained on the full training set. Their predictions for the validation and test sets were combined by the meta-learner. The validation and test observations were not used to train the meta-learner.

Model performance was evaluated using the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE):

$$R^2=1-{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n}{\left(y_i-{\widehat{y}}_i\right)}^2}{{\displaystyle {\sum }_{i=1}^n}{\left(y_i-\overline{y}\right)}^2}}$$

(1)

$$\mathit{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n}{\left(y_i-{\widehat{y}}_i\right)}^2}$$

(2)

$$\mathit{MAE}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n}\left|y_i-{\widehat{y}}_i\right|$$

(3)

Here, y_i and ${\widehat{y}}_i$ are the observed and predicted PM_2.5 concentrations, $\overline{y}$ is the mean observed concentration in the evaluated set, and n is the sample size.

The models were built in Python 3.12 using pandas 2.2.3, NumPy 2.3.5, scikit-learn 1.8.0, and XGBoost 3.4.1 [25,27]. Records from the same station could appear in different sets. The test results therefore show performance for randomly held-out station-day records, rather than for new stations or future years.

Figure 2. Machine learning workflow for ground-level PM_2.5 retrieval across four predictor groups.

Figure 2. Machine learning workflow for ground-level PM_2.5 retrieval across four predictor groups.

2.5. Cloud-Affected AOD Availability Case

AOD availability can limit the spatial completeness of PM_2.5 retrieval because cloud cover, retrieval failure, and quality screening may leave pixels without valid AOD [19].

To examine this limitation, a local case study was conducted for Shijiazhuang and its surrounding areas on 13 April 2021. The date was selected because cloud cover occurred over part of the study area while valid satellite observations remained available elsewhere, allowing cloud-affected and relatively clear areas to be compared within the same scene. The PM_2.5 surface was generated using the same preprocessing and retrieval procedures applied in the regional analysis. Pixels without valid AOD were retained as missing values rather than being spatially or temporally interpolated.

MODIS true-color imagery acquired between 10:00 and 14:00 local time, covering the approximate daytime overpass periods of Terra and Aqua, was used to provide visual information on cloud distribution. The true-color image and retrieved PM_2.5 surface were displayed over the same geographic extent and compared qualitatively. Particular attention was given to whether cloud-covered areas in the MODIS imagery corresponded to missing or spatially discontinuous PM_2.5 retrievals.

3. Results

3.1. Model Performance Across Predictor Groups

Model performance improved as meteorological and additional satellite variables were added to AOD (Table 2). The AOD-only models achieved test R² values of 0.506–0.543, with RMSE ranging from 21.196 to 22.022 μg/m³. Adding meteorological variables increased R² to 0.715–0.742 and reduced RMSE to 15.928–16.734 μg/m³. Adding other satellite variables produced higher R² values of 0.793–0.807 and lower RMSE values of 13.755–14.259 μg/m³.

Table 2. Performance of RF, SVR, XGBoost, and stacking under four predictor groups in the BTH region.

Predictor Group	Model	R2	RMSE (μg/m3)	MAE (μg/m3)
AOD-only	Random Forest	0.506	22.022	17.481
	SVR	0.537	21.321	17.227
	XGBoost	0.543	21.196	16.914
	Stacking	0.541	21.236	17.145
AOD + Meteorology	Random Forest	0.715	16.734	13.073
	SVR	0.737	16.078	12.907
	XGBoost	0.742	15.928	12.647
	Stacking	0.738	16.033	12.811
AOD + Satellite	Random Forest	0.793	14.259	11.040
	SVR	0.807	13.755	10.830
	XGBoost	0.799	14.059	10.903
	Stacking	0.805	13.826	10.703
All	Random Forest	0.834	12.787	10.009
	SVR	0.837	12.656	9.902
	XGBoost	0.836	12.685	9.868
	Stacking	0.842	12.444	9.731

Combining all predictors gave the best performance for each model. Stacking achieved the highest R² (0.842) and the lowest RMSE (12.444 μg/m³) and MAE (9.731 μg/m³) in this group. However, stacking did not lead in every predictor group: XGBoost performed best with AOD-only and AOD plus meteorology, while SVR had the highest R² and lowest RMSE with AOD plus satellite variables.

Training, validation, and test performance are reported in Table 3. With all predictors, R² decreased from 0.947 to 0.834 for RF and from 0.916 to 0.836 for XGBoost. Stacking showed a smaller decrease, from 0.900 to 0.842, while SVR changed from 0.851 to 0.837. Validation and test performance were similar under the full-input configuration.

Table 3. Training, validation, and test performance of four models across four input combinations.

Input Combination	Model	Training	Validation	Test
		R2/RMSE/MAE	R2/RMSE/MAE	R2/RMSE/MAE
AOD-only	Random Forest	0.639/17.560/14.139	0.487/21.121/16.958	0.506/22.022/17.481
	SVR	0.559/19.415/15.699	0.539/20.022/16.095	0.537/21.321/17.227
	XGBoost	0.588/18.753/15.202	0.526/20.300/16.271	0.543/21.196/16.914
	Stacking	0.566/19.258/15.585	0.538/20.034/16.101	0.541/21.236/17.145
AOD + Meteorology	Random Forest	0.864/10.764/8.448	0.712/15.814/12.623	0.715/16.734/13.073
	SVR	0.758/14.368/11.361	0.732/15.254/12.310	0.737/16.078/12.907
	XGBoost	0.797/13.169/10.536	0.716/15.703/12.618	0.742/15.928/12.647
	Stacking	0.801/13.027/10.350	0.730/15.313/12.237	0.738/16.033/12.811
AOD + Satellite	Random Forest	0.863/10.802/8.451	0.751/14.727/11.432	0.793/14.259/11.040
	SVR	0.780/13.704/10.686	0.763/14.352/11.482	0.807/13.755/10.830
	XGBoost	0.806/12.890/10.086	0.747/14.837/11.893	0.799/14.059/10.903
	Stacking	0.816/12.554/9.806	0.761/14.413/11.441	0.805/13.826/10.703
All	Random Forest	0.947/6.740/5.228	0.818/12.568/10.024	0.834/12.787/10.009
	SVR	0.851/11.265/8.733	0.835/11.973/9.567	0.851/11.265/8.733
	XGBoost	0.916/8.484/6.660	0.816/12.634/9.877	0.836/12.685/9.868
	Stacking	0.900/9.260/7.214	0.833/12.057/9.587	0.842/12.444/9.731

3.2. Spatial Distribution of Retrieved PM_2.5

Figure 3 presents the annual mean PM_2.5 concentrations retrieved by the stacking model across the BTH region during 2019–2021. The results revealed a pronounced and persistent north–south spatial gradient, with higher concentrations mainly occurring in southern and southwestern Hebei and lower concentrations in the northern mountainous areas, particularly around Zhangjiakou and Chengde. Beijing and Tianjin generally exhibited intermediate concentrations, with gradual spatial transitions toward surrounding high- and low-concentration areas. Although the overall spatial pattern remained consistent across the three years, variations were observed in the magnitude and extent of high-concentration areas. Overall, the stacking model captured the major regional PM_2.5 gradients and provided spatially continuous estimates across the BTH region.

Figure 3. Annual mean PM_2.5 concentrations retrieved by the stacking model in the BTH region from 2019 to 2021.

Figure 3. Annual mean PM_2.5 concentrations retrieved by the stacking model in the BTH region from 2019 to 2021.

3.3. Temporal and Seasonal Variation in PM_2.5

3.3.1. Interannual Variation from 2019 to 2021

The annual PM_2.5 maps showed a persistent north–south spatial gradient across the BTH region during 2019–2021, with higher concentrations mainly occurring in southern Hebei and lower concentrations in northern BTH. Although the overall spatial pattern remained stable, the intensity and spatial extent of high-concentration areas varied among the three years. These results indicate that the retrieval framework captured both persistent regional patterns and interannual variability in PM_2.5 concentrations.

3.3.2. Seasonal Variation in the Beijing–Tianjin–Hebei Region

Figure 4 compares the spatial distribution of retrieved PM_2.5 concentrations between summer and winter 2021. PM_2.5 concentrations were generally lower and more spatially limited in summer, whereas higher and more extensive concentrations occurred in winter, particularly across southern and southwestern Hebei. The north–south gradient persisted in both seasons, but seasonal differences were more pronounced in southern Hebei. Overall, the results demonstrate that the retrieval framework captured both persistent spatial gradients and seasonal variation in PM_2.5 concentrations.

Figure 4. Seasonal distribution of PM_2.5 concentrations retrieved by the stacking model in the BTH region in 2021.

3.4. AOD Availability and Retrieval Gaps

Figure 5 shows gaps in the PM_2.5 retrieval for Shijiazhuang and its surrounding areas on 13 April 2021. Large blank areas in the western and northwestern parts of the map broadly coincided with visible cloud cover in the MODIS true-color image. Retrievals were more complete in the eastern and southeastern areas, where less cloud cover was visible. This pattern is consistent with cloud-related limits on AOD availability, although missing inputs and quality screening may also explain some gaps. Blank pixels represent unavailable retrievals rather than low PM_2.5 concentrations or prediction errors.

Figure 5. Fine-scale PM_2.5 Retrieval Under Cloud-affected and Missing-AOD Conditions in Shijiazhuang, BTH region: (a) Retrieved PM_2.5 Concentration Distribution in Shijiazhuang on 13 April 2021; (b) MODIS True Color Satellite Image of Shijiazhuang and Surrounding Areas on 13 April 2021.

No gap filling was applied, so the map retained gaps where required inputs were unavailable. Gap filling could increase spatial coverage, but errors in the filled inputs could affect PM_2.5 predictions and smooth local concentration differences. These effects were not quantified in this study. Future work should compare filled and unfilled retrievals using independent observations, with accuracy assessed separately for pixels with observed and filled inputs.

4. Discussion

4.1. Added Value of Multi-Source Inputs

The four input combinations show that AOD alone provided limited information for daily surface PM_2.5 retrieval, with R² ranging from 0.51 to 0.54. Adding meteorological variables increased R² to 0.71–0.74, while adding LST, NDVI, and NO₂ increased it to 0.79–0.81. All eight predictors produced the highest performance for every model, with R² ranging from 0.83 to 0.84. These results show that the additional variables supplied useful information beyond AOD.

The improvement after adding meteorological variables is consistent with the effects of humidity and boundary-layer structure on the AOD–PM_2.5 relationship [6,7,17]. Relative humidity affects aerosol water uptake and optical extinction, while boundary-layer height describes the vertical space available for pollutant mixing [6,7,17]. Temperature and wind speed provide information on atmospheric conditions and dispersion.

The satellite-variable combination also improved retrieval performance. LST and NDVI describe surface thermal and vegetation conditions, while tropospheric NO₂ provides additional information associated with combustion-related pollution. Their combined use with meteorological variables produced the strongest results, supporting the integration of different environmental data sources.

4.2. Performance of the Stacking Ensemble

With all predictors, stacking achieved R² = 0.84, RMSE = 12.4 μg/m³, and MAE = 9.7 μg/m³. Based on the unrounded results, its RMSE and MAE were approximately 1.9% and 1.4% lower than those of XGBoost, respectively. Stacking therefore provided a small improvement under the full-input configuration.

However, stacking was not the best model for every input combination. XGBoost had the highest R² and lowest RMSE with AOD alone and with AOD plus meteorology, while SVR performed best on these metrics with the satellite-variable combination. The benefit of stacking therefore depended on the available inputs. These results support using stacking to combine complementary model predictions, while retaining individual models as useful alternatives. Previous hybrid-model research also supports combining different learners for PM_2.5 retrieval [13,14,26].

The larger training–test gaps for RF and XGBoost suggest greater fitting to the training data and possible overfitting. Stacking showed a smaller gap, although its training performance was also better than its test performance. SVR showed the smallest gap under the full-input configuration. These comparisons show that strong training performance does not guarantee better held-out performance.

4.3. Spatial and Seasonal PM_2.5 Patterns

The annual retrievals showed higher PM_2.5 concentrations in southern and southwestern Hebei and lower concentrations in northern BTH. The persistence of this pattern indicates stable regional differences during 2019–2021. Urban and industrial activity, regional transport, terrain, and atmospheric dispersion provide possible explanations for the spatial contrast [4,5,28].

The 2021 maps showed higher concentrations in winter than in summer. Winter heating and weaker atmospheric mixing can favor pollutant accumulation, while summer conditions can support dispersion and wet removal [17,29]. Similar winter–summer differences have been reported in previous PM_2.5 retrieval studies [14].

Data availability should also be considered when interpreting annual and seasonal maps. Differences in the number and timing of valid daily retrievals may affect the mapped averages. Valid-day counts can help describe the observational support for each mapped area.

4.4. AOD Availability and Gap Filling

The Shijiazhuang case showed that missing required inputs reduced the spatial completeness of PM_2.5 retrievals. Cloud cover in the true-color image provided qualitative evidence for one possible cause of missing AOD. Retrieval failure, quality screening, and missing auxiliary inputs may also produce blank pixels. These gaps indicate unavailable retrievals rather than prediction errors. No gap filling was applied.

Future work should assess whether gap filling improves coverage while maintaining retrieval accuracy and local concentration differences [18,30,31]. Additional meteorological, aerosol-profile, and emission data could also support retrieval improvement.

5. Conclusions

This study compared four input combinations and four machine-learning models for PM_2.5 retrieval in the BTH region during 2019–2021. Multi-source inputs improved performance over AOD alone, with R² increasing from 0.51–0.54 to 0.83–0.84. With all predictors, stacking achieved the best results, with R² = 0.84, RMSE = 12.4 μg/m³, and MAE = 9.7 μg/m³. Its improvement over individual models was small and depended on the input combination.

The retrieved maps showed higher concentrations in southern and southwestern Hebei, lower concentrations in northern BTH, and higher winter than summer concentrations in 2021. Missing required inputs reduced map completeness. Future research should assess gap filling using independent observations and report accuracy separately for filled and originally valid pixels. The framework provides a basis for regional PM_2.5 retrieval and air-quality assessment.