Estimation of PM_2.5 Vertical Profiles from MAX-DOAS Observations Based on Machine Learning Algorithms

Highlights

What are the main findings?

• Synchronized NO₂ and SO₂ vertical profiles contribute to the estimation of PM_2.5 vertical distribution.
• The proposed model can be used to estimate PM_2.5 concentration in typical regions in China.

What is the implication of the main finding?

• PM_2.5 mass concentration is not significantly impacted by RH in the two northern cities of Beijing and Lanzhou.
• PM_2.5 vertical profile estimation reveals high altitude air pollution transport event in Beijing.

Abstract

The vertical profile of PM_2.5 is important for understanding its secondary formation, transport, and deposition at high altitudes; it also provides important data support for studying the causes and sources of PM_2.5 near the ground. Based on machine learning methods, this study fully utilized simultaneous Multi-Axis Differential Optical Absorption Spectroscopy measurements of multiple air pollutants in the atmosphere and employed the measured vertical profiles of aerosol extinction—as well as the vertical profiles of precursors such as NO₂ and SO₂—to evaluate the vertical distribution of PM_2.5 concentration. Three machine learning models (eXtreme Gradient Boosting, Random Forest, and back-propagation neural network) were evaluated using Multi-Axis Differential Optical Absorption Spectroscopy instruments in four typical cities in China: Beijing, Lanzhou, Guangzhou, and Hefei. According to the comparison between estimated PM_2.5 and in situ measurements on the ground surface in the four cities, the eXtreme Gradient Boosting model has the best estimation performance, with the Pearson correlation coefficient reaching 0.91. In addition, the in situ instrument mounted on the meteorological observation tower in Beijing was used to validate the estimated PM_2.5 profile, and the Pearson correlation coefficient at each height was greater than 0.7. The average PM_2.5 vertical profiles in the four typical cities all show an exponential pattern. In Beijing and Guangzhou, PM_2.5 can diffuse to high altitudes between 500 and 1000 m; in Lanzhou, it can diffuse to around 1500 m, while it is primarily distributed between the near surface and 500 m in Hefei. Based on the vertical distribution of PM_2.5 mass concentration in Beijing, a high-altitude PM_2.5 pollutant transport event was identified from January 19th to 21st, 2021, which was not detected by ground-based in situ instruments. During this process, PM_2.5 was transported from the 200 to 1500 m altitude level and then sank to the near surface, causing the concentration on the ground surface to continuously increase. The sinking process contributes to approximately 7% of the ground surface PM_2.5 every hour.

1. Introduction

Fine particulate matter (PM_2.5), which is defined as particulate matter with an aerodynamic diameter of 2.5 um or less, has complex effects on human health and climate change [1,2,3]. Although PM_2.5 pollution in China has been significantly reduced over the past decade, outdoor PM_2.5 in China still causes approximately 1.2 million premature deaths each year [4]. Atmospheric aerosols are mainly distributed in the troposphere at altitudes of 0–12 km, and those in the 2–4 km altitude layer contribute to over 40% of the total aerosol variation. The long-distance transport of high-altitude aerosols and the vertical deposition of atmospheric aerosols have significant impacts on human health [5,6,7]. Measuring the vertical distribution of PM_2.5 mass concentration in the atmosphere can provide a more comprehensive understanding of its dispersion, transformation, transport, and deposition at different altitudes, which can help to better comprehend the impacts of regional transport and deposition on near-surface PM_2.5 [8,9,10]. The vertical PM_2.5 distribution can help in formulating a target-oriented control strategy for air pollution.

PM_2.5 concentration monitoring mainly relies on in situ monitoring methods, such as the Tapered Element Oscillating Microbalance (TEOM) [11], Beta-Ray Absorption Method [12], Light Scattering Method [13], and Gravimetric Method [14]. However, an in situ observation instrument can only monitor the particulate matter concentration in its vicinity. To obtain the vertical mass concentration distribution of PM_2.5, an in situ instrument is usually mounted on a meteorological observation tower, a balloon, an airplane, or an unmanned aerial vehicle to collect samples at high altitudes. Sun et al. observed the vertical distribution of PM_2.5 mass concentration between 1 August 2009 and 16 August 2009 by mounting three environmental particulate matter monitors (rp1400a) on meteorological observation towers at three different levels (8 m, 120 m, and 280 m) in Beijing [15]. The advantage of mounting an in situ instrument on a meteorological observation tower is the ability to perform long-term monitoring at a relatively low cost. However, the monitoring height is limited by the height of the tower. At present, most such towers in China are no more than 500 m in height and are scarce, being available only in Beijing, Shanghai, and Guangzhou. In situ observations based on tower-mounted instruments have significant gaps in terms of height and geographical coverage. In situ monitoring instruments mounted on balloons or airplanes can measure the vertical distribution of particulate matter from the near surface to the stratosphere, but they have the problem of high cost [16,17,18]. At present, the use of drones equipped with in situ monitoring instruments is an emerging method for vertical distribution monitoring. Compared with balloon and airplane platforms, drones are more flexible and less costly. However, their disadvantage is that the detection height is limited by airspace applications.

In addition to in situ instruments, remote sensing methods are widely used to obtain the vertical distribution of atmospheric aerosols [19,20]. At present, two main approaches can be used for aerosol profile monitoring: lidar and Multi-Axis Differential Optical Absorption Spectroscopy (MAX-DOAS). The satellite-based lidar CALIOP can obtain the vertical distribution of aerosol extinction through backscattering and is often used in research on regional pollutant transport [21]. In addition, ground-based lidar is widely used in the vertical monitoring of aerosol extinction [22]. As a passive remote sensing technique, MAX-DOAS retrieves the vertical distributions of aerosols and trace gases by measuring scattered sunlight at several view elevations [23,24,25]. MAX-DOAS can obtain not only the vertical distribution of aerosol extinction coefficients but also the vertical distributions of NO₂ and SO₂ simultaneously, which are precursors of PM_2.5 [26,27,28,29,30]. In addition, AOD can be obtained using sun photometers and satellite-based imaging spectroradiometers, such as the Moderate-Resolution Imaging Spectroradiometer (MODIS) [31], Himawari-8 [32], the China Aerosol Remote Sensing Network (CARSNET) [33], and the Aerosol Robotic Network (AERONET) [34]. However, all these remote sensing methods merely measure the optical characteristic parameters of aerosols, rather than directly measuring the concentration of particulate matter.

The traditional method assumes a linear relationship between the aerosol extinction coefficient (EC) or aerosol optical depth (AOD) and PM_2.5 at a certain relative humidity at a given spatial location. Given the variation in relative humidity and location, the linear relationships can change between different spatial locations. For example, a linear regression relationship between the measured aerosol extinction coefficient and PM_2.5 mass concentration has been obtained. However, the reported linear relationships have certain differences; the slopes in Hefei and Wuhan are 0.0148 and 0.0067, respectively [35,36]. On the other hand, machine learning methods can be used to establish the relationship between the PM_2.5 mass concentration and aerosol extinction coefficient, and they are widely used in remote sensing [37,38]. Commonly used machine learning models include eXtreme Gradient Boosting (XGBoost), Random Forest (RF), and the back-propagation neural network (BPNN). XGBoost, which is based on the gradient boosting decision tree (GBDT) algorithm, is an efficient gradient boosting decision tree algorithm [39]. The RF model, proposed by Breiman, is an ensemble algorithm based on the bagging algorithm [40,41]. The BPNN model is a multi-layer feedforward neural network trained via error back-propagation [42]. Chen et al. evaluated the performance of Extra Trees (ET), Random Forest (RF), Deep Neural Network (DNN), and Gradient Boosting Regression Tree (GBRT) when generating the vertical distribution of PM_2.5 mass concentration via the aerosol extinction profile obtained using Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) [43]. The ET model showed the best performance in terms of model effectiveness and feature interpretation. Zhu et al. used the relationship between the aerosol extinction coefficient, temperature, relative humidity, and the near-surface PM_2.5 mass concentration to build linear regression, improved linear regression, and Random Forest (RF) models to retrieve the PM_2.5 mass concentration profile [44].

This study fully utilized simultaneous MAX-DOAS measurements of multiple air pollutants in the atmosphere and employed the measured vertical profile of aerosol extinction (which is directly related to particulate matter concentration) as well as the vertical profiles of precursors such as NO₂ and SO₂ (which directly affect the secondary formation of PM_2.5), which were combined with relative humidity and wind information to evaluate the vertical concentration distribution of PM_2.5. The applicability of this estimation model at different geographical locations was studied. Using the estimated PM_2.5 vertical distribution, we analyzed the vertical distribution of particulate matter in four representative cities across China and studied the high-altitude pollutant transport process.

2. Materials and Methods

2.1. Dataset

2.1.1. MAX-DOAS Observations

In this study, four MAX-DOAS sites in typical cities in eastern, western, southern, and northern China—Beijing (BJ, 116.32°E, 39.95°N), Lanzhou (LZ, 103.85°E, 36.14°N), Guangzhou (GZ, 113.36°E, 23.15°N), and Hefei (HF, 117.18°E, 31.78°N)—were used. Beijing, Lanzhou, Hefei, and Guangzhou are typical Chinese cities with different climates and pollution levels and significant differences in the concentrations of PM_2.5 precursors and humidity. Using the data from these four cities for model training, we aimed to obtain a general model that is suitable for most areas of China. The locations of these four sites are shown in Figure 1. MAX-DOAS can provide the vertical distribution of various air pollutants, such as NO₂ and SO₂, and parameters such as the aerosol extinction coefficient (EC). The MAX-DOAS used in the experiment is the SkySpec-2D-200-System manufactured by the Airyx company [28], which consists of a scanning telescope and two spectrometers (Avaspec-UL2048L-USB2, Avantes, The Netherlands). These spectrometers cover the ultraviolet (303–370 nm) and visible bands (390–608 nm). Using a multi-axis scanning method, the instrument can collect scattered sunlight at any elevation and azimuth. A full scan sequence consists of 11 elevation angles (1°, 2°, 3°, 4°, 5°, 6°, 8°, 10°, 15°, 30°, and 90°) at a fixed azimuth. The QDOAS 3.6.0 software (http://uv-vis.aeronomie.be/software/QDOAS/, accessed on 22 December 2022) was used to process the scattered sunlight spectrum and obtain the differential Slant Column Density (dSCD) for O₄, NO₂, and SO₂. The DOAS fitting setting for O₄, NO₂, and SO₂ is as described in previous works [23,24,45]. Then, an optimization estimation (OE) solver was used to retrieve the aerosol extinction coefficient and trace gas (NO₂ and SO₂) profiles from the dSCD of a full scan [46,47,48,49]. Since O₄ concentration is proportional to the square of the oxygen concentration and relatively constant, significant variations in O₄ dSCD are mainly caused by the changes in the optical path resulting from the scattering of sunlight by aerosols. MAX-DOAS thus utilizes the optimal estimation method to invert the scattering and absorption of sunlight by aerosols; that is, optical parameters such as the aerosol extinction coefficient. Using the Levenberg–Marquardt method from OE, the cost function ${\chi }^2$ is minimized. ${\chi }^2$ is as follows:

$${\chi }^2=(y-F(x,b\left){)}^T{S}_{\epsilon }^{-1}\right(y-F(x,b))+(x-x_a{)}^T{S}_a^{-1}(x-x_a)$$

(1)

When minimizing the cost function, the solution of the inversion is given by

$$x_{i+1}=x_i+\left[\right(1+{\gamma }_i)S_a^{-1}+K_i^T{S}_{\epsilon }^{-1}{K}_i{]}^{-1}[K_i^T{S}_{\epsilon }^{-1}(y-F(x_i\left)\right)-S_a^{-1}(x_i-x_a)]$$

(2)

in which $x_a$ is the prior state vector, which imposes a prior constraint on the state vector x. The matrices $S_{\epsilon }$ and $S_a$ represent the observation and prior covariance matrices, respectively. $F(x,b)$ is the forward result of the radiative transfer model, and $x_{i+1}$ and $x_i$ represent the state vectors of the current and previous iterations, respectively. ${\gamma }_i$ is the correction factor, and $K$ is the weighting function matrix. $y$ is the observed dSCD.

The profile ranges from 0 to 4.0 km height, with a layer height of 100 m, was used in the retrieval of aerosol EC, NO₂, and SO₂ profiles. The bottom layer of the profile is regarded as the near-surface observation. The observation time of a full elevation sequence is around 15 min; therefore, the time resolution of the profile is approximately 15 min. To match the time resolution of in situ PM_2.5 measurements, hourly averages of these profiles were calculated. Generally, one hour is divided into four MAX-DOAS observation periods, each lasting 15 min. These four periods overlap with the first, second, third, and fourth quarters of an hour; that is, there will be exactly four MAX-DOAS observations within one hour. The average of these four observations was calculated as the hourly average. The aerosol EC is a physical parameter of particulate matter concentration. NO₂ and SO₂ are considered important precursors of particulate matter. Therefore, the aerosol EC, NO₂, and SO₂ profiles were used as input for the PM_2.5 concentration estimation model.

2.1.2. PM_2.5 In Situ Monitoring

The near-surface PM_2.5 concentration in this study was obtained from the China National Environmental Monitoring Centre (CNEMC) Air Quality Real-time Publicity System “http://www.cnemc.cn/ (accessed on 20 Decemeber 2024)”, which provides air quality measurements from 3866 monitoring sites in China. Four CNEMC sites were used in this study: Beijing (116.34°E, 39.93°N), Lanzhou (103.8400°E, 36.07°N), Guangzhou (113.32°E, 23.13°N), and Hefei (117.19°E, 31.78°N). The distance from each CNEMC site to its nearby MAX-DOAS site is approximately 2.53, 8.09, 4.53, and 0.95 km, respectively. The criteria for data validity judgment specified in HJ 817–2018, the official technical specifications for operation and quality control of ambient air quality automated monitoring system for particulate matter (PM₁₀ and PM_2.5) used by the CNEMC, were strictly followed. The PM_2.5 mass concentrations from CNEMC were used as labels to train the machine learning model for PM_2.5 concentration estimation. Meanwhile, part of the ground-based in situ measurement dataset was used to evaluate the trained model. In addition, the estimated and the measured PM_2.5 profiles were compared; the measured profiles were obtained from the 325-meter-high meteorological observation tower located at the Institute of Atmospheric Physics, Chinese Academy of Sciences (IAP, 39.98°N, 116.39°E), approximately 6 km away from the Chinese Academy of Meteorological Sciences (CAMS). The in situ instruments were placed on the 60, 160, and 280 m platforms of the tower. PM_2.5 concentrations were measured using the beta-ray attenuation method [50]. The tower-based PM_2.5 data were acquired from the Institute of Atmospheric Physics, Chinese Academy of Sciences (IAP/CAS), with quality control procedures independently executed by IAP/CAS [50].

2.1.3. Meteorological Data

Meteorological conditions have a direct impact on the formation, transportation, transformation, and hygroscopic growth of particulate matter in the atmosphere, and thus were incorporated into the PM_2.5 concentration estimation model as important input data. The vertical profiles of meteorological data, including air temperature (T), relative humidity (RH), and wind speed (U, V), were modeled in this study using the Weather Research and Forecasting with Chemistry model version 4.3 (WRF-chem). WRF-chem is used to simulate meteorological fields and air pollutants across the country using a horizontal spatial resolution of 20 km × 20 km and 44 vertical layers [51,52]. Meteorological data with a spatial resolution of 1° × 1° and temporal resolution of 6 h, provided by the National Center for Environmental Prediction (NCEP), were used as the initial meteorological fields and boundary conditions. Furthermore, the emission inventories used in the modeling were obtained from the Multi-resolution Emission Inventory for China (MEIC, http://meicmodel.org/). In this study, the meteorological data were temporally and spatially matched with the vertical grid of the MAX-DOAS profile. In addition, meteorological data at heights less than 20 m were used to represent near-surface meteorological parameters.

2.1.4. Data Preprocessing

The MAX-DOAS profile contains some invalid data due to unavoidable issues such as instrument errors and natural factors. The preprocessing of MAX-DOAS data was performed as follows. Firstly, profiles obtained under cloudy conditions were filtered out according to the Aerosol Robotic Network (AERONET). Secondly, based on the quality control standard of the MAX-DOAS retrieval algorithm [48], invalid data were removed from the aerosol EC and trace gas profiles. Thirdly, as the effective observation time of MAX-DOAS in the daytime is usually from 8:00 to 16:00 (UTC + 8), meteorological data obtained during the daytime were chosen as the model input. Note that all times in this study are Beijing Time (UTC + 8). Finally, the aerosol EC, NO₂, SO₂, and meteorological data were matched with each other in terms of hourly time points. A few near-surface PM_2.5 data points could not be completely matched with the independent variables due to missing data or outliers; these unmatched data were defined as invalid and were removed. After data preprocessing and matching, a total of 6423 aerosol profiles were obtained from the four sites.

2.2. Methodology

2.2.1. XGBoost Model

XGBoost is an efficient gradient boosting decision tree algorithm. The model is based on the gradient boosting decision tree (GBDT) algorithm. As an ensemble algorithm, the core of XGBoost is the boosting algorithm, which integrates multiple weak learners into a strong learner. In other words, it is an additive model that gradually adds classification and regression trees (CART) to minimize the objective function. During the training of the XGBoost model, a CART tree is first trained using the initial training dataset, and then the residual of the former CART tree is taken as the input for the next CART tree. The preceding procedure is repeated numerous times until the stop conditions are satisfied. The estimated result is determined based on the sum of results from all CART trees.

2.2.2. RF Model

The RF model is an ensemble algorithm based on the bagging algorithm. A CART tree is utilized as the base learner, and then multiple CART trees are combined in the RF model. The primary characteristic of the bagging algorithm is its use of the bootstrap resampling technique. Before building a CART tree, each time, some of the samples and features are randomly picked from the initial training dataset and used to train the CART tree. In contrast to the XGBoost model, every CART tree in the RF model is independent of the others. The approach can handle a large number of samples and features while avoiding overfitting. Therefore, the RF model is widely used to solve non-linear problems. Notably, the result for regression problems is usually given by the average of all decision trees’ estimations.

2.2.3. BPNN Model

A back-propagation neural network (BPNN) model is a multi-layer feedforward neural network trained with the error back-propagation. Typically, a BPNN model includes input, hidden, and output layers. The input and output layers each constitute a single network layer, but there may be one to several hidden layers. Each layer of the neural network consists of several neurons, and the connection mode is fully connected. The BPNN learning process consists of two phases. The first phase is forward propagation. The input data are transmitted from the input layer unit to the output layer unit via the hidden layer unit. The second one is back-propagation. An error signal is defined as the difference between the true value and the result of network estimation. During the error back-propagation, the signal is transferred layer-by-layer from the output to the input layer. Meanwhile, the network weights and thresholds are adjusted accordingly [53]. The forward and backward propagation are repeated several times until the difference between the true value and the estimation result meets the requirement.

2.2.4. Model Optimization

In this study, six parameters of the XGBoost model were adjusted: the number of trees, the maximum depth of the tree (max depth), subsample, learning rate, alpha (L1 regularization parameter), and lambda (L2 regularization parameter). For the RF model, there are three parameters to adjust: the number of trees, the maximum depth of the tree (max depth), and the criterion. As a metric for evaluating the quality of decision tree branching, the mean squared error (MSE) was employed as the criterion.

Table 1. Tuning parameters of three models.

Model	Parameters	Values
XGBoost	number of trees (n_estimators)	100
	maximum depth of tree (max_depth)	9
	subsample	0.7
	learning rate	0.1
	alpha	0.1
	lambda	3
RF	number of trees (n_estimators)	90
	maximum depth of tree (max_depth)	10
	criterion	mse
BPNN	hidden layer sizes	8
	solver	adam
	activation	relu
	maximum iterations	1000
	init learning rate	0.06

lists the parameters of the three models. For the BPNN model, five parameters were adjusted accordingly: hidden layer sizes, solver, activation, maximum iterations, and initial learning rate.

2.2.5. Model Evaluation

In this study, the ratio of the training set to the test set was 9:1. Since activation functions are typically used in the training process of BPNNs, the data in the samples are usually mapped to a smaller range (such as [0, 1] or [−1, 1]) for normalization before training. Normalization transforms the data in the dataset to a specific range of values, making it easier for data processing in the neural network. Therefore, before training the BPNN model, the training and testing datasets were normalized to the range of [0, 1] using Equation (3). However, XGBoost and RF models do not require data normalization, because decision tree algorithms are not affected by the scaling or translation of individual features.

$$x^{\mathrm{*}}={\displaystyle \frac{x-min}{max-min}}.$$

(3)

This study used the Pearson correlation coefficient (R) and root mean square error (RMSE) to evaluate the error between the measured and estimated PM_2.5 concentrations. The R and RMSE values were calculated using the following formulas:

$$R={\displaystyle \frac{Cov\left(y,\widehat{y}\right)}{{\sigma }_y{\sigma }_{\widehat{y}}}},$$

(4)

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

(5)

where $n$ is the number of samples; $y_i$ is the observed value and $\widehat{y_i}$ is the estimated value; $Cov(y,\widehat{y})$ represents the covariance between observed and estimated values; and ${\sigma }_y$ and ${\sigma }_{\widehat{y}}$ are the standard deviations of the observed and estimated values, respectively. A 10-fold cross-validation (CV) was used to evaluate model performance. Therefore, ten subsets from the overall datasets were randomly and equitably generated. To evaluate the performance of the model, nine of the ten subsets were chosen as training data, while the remaining subset was used as test data. The evaluation was repeated ten times until all samples had been evaluated [54]. To assess the models’ performance at various sites, a spatial four-fold cross-validation was also applied, in which three MAX-DOAS sites were used for training the models and the remaining site for testing the models.

2.2.6. Feature Importance

The interpretability of the model can also help in understanding the relationship between aerosol extinction, NO₂, SO₂, meteorological conditions, and PM_2.5 concentration, ultimately facilitating model adjustment for required accuracy. In this study, the SHAP (SHapley Additive exPlanations) method was utilized to interpret the contribution of each feature to the three machine learning models, and the SHAP values are provided as the feature importance. SHAP, proposed by Lundberg and Lee, is a post hoc model interpretation method based on cooperative game theory [55]. The method can assist in the interpretation of models by quantifying the importance of each feature variable in each sample. Consequently, for the entire dataset, the SHAP value can be utilized to efficiently and precisely obtain the local interpretation, i.e., the interpretation of each sample. Then, for a certain feature variable, the SHAP values of the corresponding variable in all samples are calculated. The average of the absolute SHAP values represents the feature’s importance for global interpretation. Meanwhile, it also resolves the problem of feature importance being impacted by the multicollinearity of ML model features. To evaluate the impact of each feature on the PM_2.5 concentration estimation, Tree SHAP was applied to the trained XGBoost and RF models, while Kernel SHAP was applied to the trained BPNN model. Tree SHAP and Kernel SHAP were performed using Tree Explainer and Kernel Explainer, respectively [56,57].

2.2.7. Vertical Transport Flux

Transport flux is a critical indicator for evaluating the transport of pollutants [58,59]. In this study, we considered two forms of vertical transport of PM_2.5—vertical transport and vertical diffusion. The first form entails calculating vertical transport using vertical wind speed and PM_2.5 concentration, which is given by

$$W{Flux}_i=C_i{V}_i,$$

(6)

where $C_i$ and $V_i$ represent the PM_2.5 mass concentration (µg/m³) and vertical wind speed (m/s) at a specific height, respectively. The second involves calculating transport diffusion using the turbulence coefficient and PM_2.5, which is given by

$$T{Flux}_i=\left(C_i-C_{i-1}\right){\displaystyle \frac{exch\_h}{h}},$$

(7)

where $C_i$ and $C_{i-1}$ represent the PM_2.5 mass concentrations in two neighboring layers $i^{th}$ and ${(i-1)}^{th}$, respectively; $exch\_h$ is the turbulence coefficient; and $h$ denotes the height difference between neighboring layers $i$ and $i-1$. The contribution rate of the transport flux to the near-surface concentration can then be obtained.

The ratio between accumulated vertical flux and the estimated PM_2.5 concentration represents the contribution of vertical transport to PM_2.5 pollution. Accumulated flux refers to the time-integrated vertical flux of PM_2.5. The PM_2.5 vertical flux mentioned here includes both the vertical transport caused by vertical wind and the turbulent exchange in the atmosphere.

3. Results and Discussion

3.1. Model Comparison

To evaluate the performance of the XGBoost, RF, and BPNN models, the estimated near-surface PM_2.5 mass concentrations of the three models were compared. The test set, 10-fold CV, and spatial 4-fold CV validation were used to evaluate the performance of the three models, and the results are shown in

Table 2. Model performance on the test set, 10-fold CV, and spatial 4-fold CV.

	XGBoost		RF		BPNN
	R	RMSE	R	RMSE	R	RMSE
Test set	0.91	13.37	0.90	13.70	0.87	17.11
10-fold CV	0.98	6.52	0.95	9.83	0.81	18.46
Spatial 4-fold CV	0.61	20.71	0.64	21.05	0.64	21.98

. These results indicate that the performance of XGBoost and RF is similar, and both are superior to the BPNN in the test set and 10-fold CV. Overall, the Pearson correlation coefficient is the highest and the RMSE value is the lowest for XGBoost compared to RF and BPNN. XGBoost, RF, and BPNN have similar performance in the spatial 4-fold CV, which shows the similar spatial extrapolation capabilities of the models. Temperature, wind speed, and wind direction in different regions can affect the diffusion and transport of PM_2.5.

Figure 2 shows the feature importance of the input variables of the three models. The feature importance ranking of six input variables is the same for the XGBoost and RF models, but it is different in the BPNN model. In this study, the correlations of PM_2.5 with EC, NO₂, SO₂, T, RH, and wind were 0.79, 0.39, 0.21, −0.07, 0.08, and −0.25, respectively. The R between the EC and PM_2.5 is the largest. Similarly, the feature importance of the aerosol EC is much larger than that of other features, which suggests that the EC is strongly related to the PM_2.5 mass concentration. They are positively related, so more PM_2.5 usually means a larger aerosol extinction coefficient. Additionally, it is found that the PM_2.5 mass concentration is also affected by RH. This is because high relative humidity can result in the hygroscopic growth of particulate matter. When RH is high, water molecules will condense into water droplets on the surface of aerosol particles, increasing the size of the aerosols and thus increasing aerosol extinction. As the aerosol particle size increases, its settling velocity slows down, resulting in a longer residence time and propagation distance in the atmosphere, thereby exacerbating the concentration of PM_2.5 [9,60,61]. The impacts of NO₂, SO₂, T, and wind speed on the concentration of PM_2.5 slightly differed among the three models. Overall, the three models do not rely on only one feature.

3.2. Near-Surface PM_2.5 Concentration Validation

According to the performance comparison results, the XGBoost model has the best performance. Therefore, the trained XGBoost model was used to estimate the hourly PM_2.5 mass concentration at the four MAX-DOAS sites during 2021. The correlation between hourly observed and estimated PM_2.5 mass concentrations at four MAX-DOAS sites is shown in Figure 3. The results show that the correlation coefficient of in situ measurement and estimated PM_2.5 mass concentrations in Beijing is 0.98, which is better than in the other three sites. The correlation coefficients for Lanzhou, Guangzhou, and Hefei are 0.94, 0.92, and 0.93, respectively. The Lanzhou site RMSE, which is 4.24 μg/m³, is lower than those for the other three sites. The RMSE values for Beijing, Guangzhou, and Hefei are 5.65, 4.63, and 5.98 μg/m³, respectively. Figure 4 shows the correlation between the estimated hourly PM_2.5 mass concentration and the aerosol EC measured by MAX-DOAS at four MAX-DOAS sites. The correlation coefficients for Beijing, Lanzhou, Guangzhou, and Hefei are 0.85, 0.58, 0.74, and 0.51, respectively. Overall, the XGBoost model has the best performance at the Beijing site, and there are two main potential reasons. Firstly, more data were obtained for the Beijing site compared to the other sites, which allows the XGBoost model to learn more information from Beijing. Secondly, affected by meteorological, geographical, and instrumental conditions, the aerosol EC has the highest correlation with the near-surface PM_2.5 mass concentration measurement in Beijing. Among the four cities, Guangzhou has the highest humidity. Therefore, the aerosol particles in Guangzhou tend to increase in size due to hygroscopic growth. Then, as the aerosol particles become larger, their extinction coefficient naturally increases. As a result, as shown in Figure 4, under the same PM_2.5 concentration conditions, the extinction coefficient of aerosols in Guangzhou is significantly higher than those in the other three cities. This also leads to Guangzhou having the largest slope in Figure 4 among the four cities.

Figure 5 shows the hourly variations in near-surface aerosol extinction coefficients, observed PM_2.5 mass concentrations, and estimated PM_2.5 mass concentrations from May to July at four MAX-DOAS sites. The results show that the estimated and observed PM_2.5 concentrations exhibit similar fluctuations. It can also be observed that the estimated PM_2.5 mass concentrations are closer to the observed PM_2.5 mass concentrations than the aerosol extinction coefficient. In addition, the results further verify the strong correlation between the extinction coefficient and surface-level PM_2.5 concentration.

3.3. PM_2.5 Vertical Profile Validation

Next, the XGBoost model was used to estimate the hourly vertical distribution of PM_2.5 mass concentration. The hourly observed vertical distribution of PM_2.5 mass concentration is from the meteorological observation tower at the Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing [45]. The time range of the data is from March to May 2019. Considering that the vertical resolution of the estimated PM_2.5 is 100 m, we used the estimated PM_2.5 concentrations in the first, second, and third layers to compare with the observation results at heights of 60, 160, and 280 m.

Figure 6 shows the correlation between observed and estimated PM_2.5 mass concentrations at different heights. The correlation coefficients at different heights are 0.98, 0.84, 0.76, and 0.71 at the near surface and 60, 160, and 280 m’s height, respectively. The correlation coefficient shows a decreasing trend with the increase in height. The RMSE is the highest at 280 m at 28.78 μg/m³. The RMSE values at the other heights are 9.53 μg/m³ at the near surface, 22.18 μg/m³ at 60 m, and 25.13 μg/m³ at 160 m. The slopes for 60, 160, and 280 m are 0.65, 0.8, and 0.82, respectively. This difference is mainly attributed to the vertical profiles of aerosol extinction coefficients measured by MAX-DOAS due to its different sensitivities to observations at different altitudes. Additionally, when the observed PM_2.5 mass concentration exceeds approximately 100.00 μg/m³, PM_2.5 is underestimated. This underestimation is mainly due to the small sample of high values, such that the models could not learn the connection between the inputs and the observed PM_2.5 concentration under all conditions. In addition, the XGBoost model was trained based on near-surface datasets. When the model is extrapolated to higher heights, it introduces a certain bias. This results in a decrease in the correlation coefficient when the model is applied to higher altitudes. It is still notable that the overall correlation coefficient is larger than 0.71. In conclusion, the results support the feasibility of using the XGBoost model to estimate the vertical distribution of PM_2.5 mass concentration.

3.4. Vertical Distribution of PM_2.5

Figure 7 shows the vertical distribution of the annual hourly average PM_2.5 mass concentrations in 2021 for the four MAX-DOAS sites, as well as the corresponding feature importance ranking for each site. Utilizing the XGBoost model, data on the PM_2.5 mass concentration can be obtained in different areas and at varying altitudes. Unlike the traditional linear extinction–PM_2.5 relationship, which may vary with the study area and height, the XGBoost model achieves uniformity, enabling a horizontal comparison of PM_2.5 mass concentrations at different altitudes and in different study areas. As shown in Figure 7, in 2021, high-altitude PM_2.5 pollution was the most severe in Lanzhou, followed by Beijing and Guangzhou, while Hefei had the least pollution. Lanzhou, Guangzhou, and Beijing exhibit significant diurnal variations in the distribution of PM_2.5 mass concentrations at different altitudes. The boundary layer height is low in the morning and evening, leading to high PM_2.5 mass concentrations at lower altitudes. However, at noon, as the boundary layer height increases, the PM_2.5 mass tends to diffuse to higher altitudes. PM_2.5 in Beijing and Guangzhou can diffuse to high altitudes between 500 and 1000 m; meanwhile, it can diffuse to around 1500 m in Lanzhou, and it is primarily distributed between the near surface and 500 m in Hefei.

Figure 7e–h describe the feature importance ranking of the estimated PM_2.5 mass concentration at each of the four MAX-DOAS sites. The x-axis represents the SHAP value of each feature in each sample, which indicates its importance in the estimation process. The y-axis represents the feature names, with the importance decreasing from top to bottom. Each sample is represented by a point in the figures. The color bar represents the true value of each feature, with the color of the point becoming redder as the true value increases and bluer as the true value decreases. It is found that the aerosol EC has the highest importance in the estimation of PM_2.5 mass concentration at all four MAX-DOAS sites. Furthermore, the impact of the aerosol EC on PM_2.5 mass concentration increases as the value of the EC increases. At the Beijing, Lanzhou, and Guangzhou sites, the importance of nitrogen dioxide ranks second while, at the Hefei site, it ranks fourth. Moreover, the impact of NO₂ on PM_2.5 mass concentration also increases as NO₂ concentration increases. The ranking of SO₂ at all four sites is relatively low, and its impact on PM_2.5 mass concentration is not significant. The effects of temperature and wind speed on PM_2.5 mass concentration are complex; hence, their feature importance rankings vary across the four sites. PM_2.5 mass concentration is not significantly impacted by RH in the two northern cities of Beijing and Lanzhou, while it is heavily influenced by RH in Guangzhou and Hefei. The reason for this is that Lanzhou and Beijing have low humidity and a smaller range of humidity variations, resulting in a lesser impact on PM_2.5 mass concentration. On the other hand, Hefei and Guangzhou experience significant fluctuations in humidity, leading to a greater impact on PM_2.5 mass concentration. In addition, since 2012, China has substantially reduced sulfur and nitrogen emissions. In particular, the reduction in SO₂ has produced significant effects. Currently, the concentration of SO₂ in China is very low, which led to SO₂, as a precursor of PM_2.5, contributing less to the formation of PM_2.5. Although the concentration of NO₂ has decreased since 2012, nitrate is still one of the main components of current aerosols and, so, the impact of NO₂ on PM_2.5 concentration is still significant.

Figure 8 shows a PM_2.5 pollutant event that occurred from January 19th to 21st, 2021 in Beijing, illustrating the high-altitude transport and deposition of PM_2.5. Figure 8a shows the variation in aerosol extinction, HCHO, NO₂, PM_2.5, and wind speed profiles during these three days. Figure 8b shows the measured and estimated ground-surface PM_2.5 concentration, AERONET AOD, and MAX-DOAS aerosol extinction at the ground surface. On 19 January 2021, there was a high-altitude transport process. The pollutants were mainly concentrated at high altitudes between 8:00 and 17:00, with a height range of 0–1.5 km. However, the observed PM_2.5 at the near-surface level was less than 30 μg/m³—a low PM_2.5 concentration. This implies the occurrence of high-altitude transport, accompanied by NO₂ and HCHO transport at heights of around 200–1500 m. On this day, the wind speed reached its highest value during the pollution event, which also contributed to the transport of PM_2.5 in high-altitude areas.

The PM_2.5 mass concentrations started to descend on January 20th, leading to an increase in near-surface PM_2.5 mass concentration and a decrease in the aerosol extinction coefficient at high altitudes. The aerosol extinction coefficient and HCHO both showed high values from around 10:00 to 12:00 at an altitude of approximately 500 to 1000 m, which indicates the potential secondary generation of aerosols. At the same time, NO₂ was also transported at the altitude range of 0.3–0.5 km, with a peak appearing at 16:00. Around 10:00, wind speed decreased, and PM_2.5 mass concentration began to accumulate at high altitudes.

On January 21st, the aerosols descended to the near surface, and the wind speed decreased between 10:00 and 13:00. Following the stabilization of atmospheric conditions, significant deposition of PM_2.5 on the ground surface from high altitudes began to occur. Consequently, high concentrations of PM_2.5, NO₂, and HCHO at the ground surface were observed during this time. The high concentrations of NO₂ and HCHO promoted the secondary generation of PM_2.5. After 13:00, the wind speed increased, and the concentrations of NO₂, HCHO, and PM_2.5 decreased.

As shown in Figure 8b, during this air pollution period, the estimated near-surface PM_2.5 mass concentration was below 30.00 μg/m³ on the 19th, and then gradually increased from the 20th and reached its peak on the 21st. This observation is consistent with the measurement results. Additionally, AERONET and MAX-DOAS AOD have similar decreasing trends during the air pollution period and exhibit the total opposite phenomenon from the near-surface PM_2.5 concentration. This indicates that the aerosols are at high altitudes, which is consistent with the profiles of aerosol extinction and estimated PM_2.5 concentration shown in Figure 8a. As the total AOD decreases, the near-surface PM_2.5 concentration increases. This indicates that the deposition of high-altitude aerosols results in an increase in near-surface PM_2.5 concentration. The AERONET site used in this study is Beijing-CAMS, with a latitude and longitude of 39.9°N, 116.3°E. The Beijing-CAMS site is approximately 6 km from the MAX-DOAS Beijing site.

Figure 9 shows the vertical transport flux during this PM_2.5 pollution event at each height level, calculated separately using the turbulence coefficient and vertical wind speed. The positive values represent upward transport, and negative values represent downward transport. The results show an overall transport of PM_2.5 from higher altitudes towards the near surface. In addition, the vertical diffusion flux is larger than the flux driven by vertical wind. They also show significant diffusion between the near surface and 500 m. Moreover, we find that the vertical transport flux caused by vertical wind decreases rapidly over 1.4 km height.

Furthermore, we adopt the ratio between accumulated vertical flux and the estimated PM_2.5 concentration to represent the contribution of vertical transport to PM_2.5 pollution. The contribution rate of the transport flux at 100 m to the near-surface PM_2.5 concentration is shown in Figure 10. Figure 10a shows the turbulence coefficient at 100 m and the pollutant transport contribution rate calculated using the turbulence coefficient. A positive contribution ratio means downward transport, and a negative value means upward transport. The maximum contribution rate reaches 6%. Figure 10b shows an up to 0.8% contribution rate of the vertical transport flux calculated using the vertical wind speed. The results show that diffusion contributes more than vertical wind transport. In addition, PM_2.5 is mostly brought to the near surface by downward diffusion and vertical wind in the afternoon during PM_2.5 pollution events.

In general, the technological advantage of this method is that it incorporates synchronous MAX-DOAS observations of PM_2.5 precursors. The limitation of the proposed method is that atmospheric meteorological data are required to estimate PM_2.5 concentration, which affects the time efficiency and prevents the acquisition of real-time PM_2.5 concentration estimation results through observation.

4. Conclusions

In this study, we employed machine learning models and integrated the aerosol extinction coefficient, NO₂, SO₂, T, RH, and wind obtained using MAX-DOAS and WRF-chem to estimate the PM_2.5 mass concentration. The performance of the XGBoost, RF, and BPNN models was compared based on the correlation between observed and estimated PM_2.5 mass concentrations. Furthermore, the XGBoost model was chosen to estimate the vertical distribution of the PM_2.5 mass concentration. The model was used to estimate the vertical distribution of the annual average PM_2.5 mass concentration at four MAX-DOAS sites, as well as a specific high-altitude pollutant transport event in Beijing.

The comparison between the XGBoost, RF, and BPNN models for estimating near-surface PM_2.5 mass concentration suggests that the XGBoost model has the best performance among the three models. The R and RMSE values are 0.91 and 13.37 μg/m³, respectively. For a 10-fold CV, the R is 0.98 and the RMSE is 6.52 μg/m³. The RF and XGBoost models showed similar performance. Detailed feature importance analysis suggests that aerosol EC has the greatest effect on the PM_2.5 mass concentration, while relative humidity has a more significant impact on PM_2.5 in Hefei and Guangzhou than in Beijing and Lanzhou. The comparison between tower-based measurements and estimates of the PM_2.5 concentration shows the XGBoost model’s feasibility in estimating the vertical distribution of the PM_2.5 mass concentration.

Finally, the vertical distributions of the annual average PM_2.5 mass concentrations at the four sites in 2021 were compared. The daily variation in the annual average PM_2.5 vertical distribution was obtained for the four MAX-DOAS sites. The PM_2.5 mass concentration is not significantly impacted by RH in the two northern cities of Beijing and Lanzhou, but it is heavily influenced by RH in Guangzhou and Hefei. Lanzhou, being closer to the desert, has the highest PM_2.5 concentration of the four cities. In addition, PM_2.5 in Beijing and Guangzhou can diffuse to high altitudes between 500 and 1000 m; in contrast, it can diffuse to around 1500 m in Lanzhou, and it is primarily distributed between the near surface and 500 m in Hefei. We identified a high-altitude PM_2.5 transport event from January 19th to 21st, 2021, in Beijing. PM_2.5 was transported through the high-altitude area and subsequently descended towards the near surface, with diffusion and vertical wind contribution rates of up to 6% and 0.8%, respectively.

In summary, machine learning methods were utilized to establish a conversion relationship between aerosol extinction measured by MAX-DOAS and the PM_2.5 mass concentration, and the vertical distribution of the PM_2.5 concentration was obtained in four key cities across China. The importance of the influencing factors of particulate matter concentration was evaluated using interpretable machine learning networks. This work used the vertical distribution of MAX-DOAS in combination with the meteorological field to quantitatively analyze the high-altitude transport of particulate matter, as well as the diffusion and vertical transport of particles from high to low altitudes and their contributions to the near-ground concentration. This study expands the methods for monitoring the vertical profile of PM_2.5 and provides data support for future studies on the vertical evolution of atmospheric particulate matter, regional transport, and vertical exchange of air pollutants. Additionally, through the estimation of PM_2.5, we found that precursors, such as NO₂, have significant impacts on PM_2.5 generation.