Retrieval and Evaluation of NO_X Emissions Based on a Machine Learning Model in Shandong

Abstract

Nitrogen oxides (NO_X) are important precursors of ozone and secondary aerosols. Accurate and timely NO_X emission estimates are essential for formulating measures to mitigate haze and ozone pollution. Bottom–up and satellite–constrained top–down methods are commonly used for emission inventory compilation; however, they have limitations of time lag and high computational demands. Here, we propose a machine learning model, WOA-XGBoost (Whale Optimization Algorithm–Extreme Gradient Boosting), to retrieve NO_X emissions. We constructed a dataset incorporating satellite observations and conducted model training and validation in the Shandong region with severe NO_X pollution to retrieve high spatiotemporal resolution of NO_X emission rates. The 10–fold cross–validation coefficient of determination (R²) for the NO_X emission retrieval model was 0.99, indicating that WOA-XGBoost has high accuracy. Validation of the model for the other year (2019) showed high agreement with MEIC (Multi–resolution Emission Inventory for China), confirming its strong robustness and good temporal transferability. The retrieved NO_X emissions for 2021–2022 revealed that emission rate hotspots were located in areas with heavy traffic flow. Among 16 prefecture–level cities in Shandong, Zibo exhibited the highest NO_X rate (>1 μg/m²/s), explaining its high NO₂ pollution levels. In the future, priority areas for emission reduction should focus on heavy industry clusters such as Zibo and high traffic urban centers.

1. Induction

Nitrogen oxides (NO_X = NO + NO₂) are important gaseous pollutants in the troposphere [1,2]. They actively participate in the formation of tropospheric ozone (O₃) and secondary aerosols, causing significant impacts on human health and the atmospheric environment. Accurate and timely information on NO_X emissions is essential for predicting air quality, adjusting environmental policies, and mitigating air pollution [3]. However, both bottom–up and top–down methods for compiling emission inventories have some limitations, such as time lags and large computational costs. Therefore, there is an imperative need to develop an efficient, low cost, and sufficiently accurate method for compiling grid–based emission inventories.

The bottom–up approach calculates emissions based on sectoral activity levels and emission factors [4,5]. Due to the extensive data collection and measurement efforts required by this method, the compiled emission inventory cannot be promptly updated to reflect recent/current accurate emission profiles, especially for air quality forecasting [6,7]. The top–down approach is another established method for estimating emissions, which constrains emission estimations by results from ground–based monitoring data and satellite observations [8]. Compared with ground observation stations, satellite remote sensing has the advantages of wide spatial coverage, high spatial resolution, and daily monitoring [9,10], providing reliable data support for top–down emission constraints [11]. The primary challenge for emissions retrieval through satellite–based top–down approach lies in accurately quantifying the nonlinear relationship between environmental NO₂ concentration and NO_X emissions. The nonlinear relationship becomes complicated due to the coupled atmospheric transport, chemical transformation, and physical processes [12]. Atmospheric chemical transport models (CTM) [13,14,15] have been widely adopted to establish emission–concentration relationships, with data assimilation techniques like Kalman filtering [16] and 4D-Var [17] enhancing their precision. However, CTMs exhibit inherent limitations, including systematic biases [18,19] and huge calculation resource consumption [20]. Additionally, the statistical exponentially modified Gaussian model along with meteorological elements can be used to convert NO₂ VCD to NO_X emissions, but most of these models are only applicable to isolated point source emissions [21,22,23].

To overcome the limitations of the model in emission retrieval, Qin et al. [24] and Li et al. [20] developed a new model–free NO_X inversion estimation approach based on the mass conservation equation. This approach quantifies daily NO_X emissions and their uncertainties through linear regression of three key parameters, including temporal rate of change in column loadings, first–order chemical loss of NO_X, and gradient transport of NO_X. Notably, although this approach was free from the limitations of the CTMs, it constrains the nonlinear NO_X chemical loss and transport to first–order processes [25].

As a transformative tool in interdisciplinary science, machine learning has been widely used in the field of atmospheric science, which can automatically extract key features of input data and capture the behavior of target data [26,27,28]. Machine learning can capture the nonlinear relationship between emissions and pollutant concentrations well, with high computational efficiency [7]. For example, Wei et al. [28,29] used machine learning to construct near surface PM, SO₂, CO, and NO₂ concentrations based on a variety of data, including ground observations, satellites, and reanalysis. Relevant studies on estimating NO_X emissions using machine learning have been conducted.

Huang et al. [7] proposed a novel emission inventory estimation framework (neural network, NN) based on dual learning. The framework first employs a neural network model to investigate the complex relationships between emissions and atmospheric pollution as a substitute for CTMs, followed by implementing a backpropagation–based optimization algorithm to iteratively update the emission inventory. Xing et al. [12] and Chen et al. [8] proposed a physically informed variational autoencoder (VAE) and an ensemble backpropagation neural network (eBPNN), respectively, for NO_X emission retrieval. However, both methods still required CTMs to generate training datasets. Although He et al. [30] did not use CTM results in training the model built with a convolutional neural network (CNN) and long short–term memory (LSTM), the retrieved NO_X emissions results lacked sufficient refinement, exhibiting a spatial resolution of only 1.1° × 1.1°.

Table 1. Summary of previous studies on machine learning used for NO_X emission retrieval.

Ref.	Model	Contributions	Limitations
[7]	NN	The updated emissions by the model can improve the accuracy of CTM simulation.	Requires backpropagation algorithm to update emission inventory.
[30]	CNN + LSTM	The retrieved total NOX emissions in 2019 were highly consistent with prior emissions.	Insufficient spatial refinement.
[12]	VAE	Successfully corrected NOX emission underestimation in rural areas and overestimation in urban areas.	Requires CTM results to generate training datasets.
[8]	eBPNN	The proposed framework is sufficiently flexible to correct emissions.	Requires CTM results to generate training datasets.

summarizes relevant studies using machine learning algorithms, including models, contributions, and limitations.

In order to address the shortcomings of current emission inventory compilation methods, we proposed a new method for retrieving NO_X emissions using machine learning techniques. We established a nonlinear relationship between multi–source data and NO_X emissions using extreme gradient boosting (XGBoost), with hyperparameters optimized via the whale optimization algorithm (WOA) to improve prediction accuracy. The method can provide near–real–time NO_X emission characteristics at a low cost. The training dataset, constructed independently of CTM results, enables high spatial resolution (0.05° × 0.05°) for NO_X emission retrieval. This method provides highly efficient and accurate technical support for atmospheric pollution monitoring and governance. This paper is structured as follows. Section 2 outlines the multi–source data, data processing methods, and machine learning model. Section 3 outlines the long-term spatial and temporal variation of NO₂ VCD in Shandong Province, the validation in the NO_X emissions retrieval model, and the prediction of NO_X emissions. Section 4 draws the main conclusions of this study.

2. Data and Methods

2.1. Study Area

Shandong Province is located on the coast of East China and downstream of the Yellow River, with most areas below 50 m in elevation, and it has a warm–temperate monsoon climate. Southeast winds dominate in spring and summer, while northwest winds dominate in fall and winter. As shown in Figure 1, it comprises 16 prefecture–level cities, which are geographically categorized into Northwest Shandong region (Liaocheng, Dezhou, Binzhou, and Dongying), Central Shandong region (Jinan, Taian, Zibo, and Weifang), South Shandong region (Heze, Jining, Zaozhuang, Linyi, and Rizhao), and Jiaodong Peninsula region (Qingdao, Yantai, and Weihai). Due to the developed heavy industry and high consumption of fossil fuels in Shandong Province, it has become one of the areas with the most severe air pollution in China. Establishing an accurate and timely NO_X emission inventory is crucial for implementing differentiated pollution control and emission reduction strategies. In this study, we explore the spatiotemporal variation of NO₂ pollution in Shandong Province and carry out NO_X emission retrieval research.

2.2. NO₂ Tropospheric Vertical Column Measurements

NO₂ tropospheric vertical column density (VCD) measurements were derived from OMI and TROPOMI. OMI, onboard the Aura satellite, was launched by NASA on 15 July 2004, with a local equator overpass time of 13:45 ± 0:15 [31]. As a nadir-viewing imaging spectrometer, it measures direct and atmospheric backscattered sunlight in the UV/vis ranges from 270 to 500 nm. The daily NO₂ VCD data (OMI-Aura_L3-OMNO₂d) were acquired from NASA Goddard Earth Sciences Data & Information Services center (GES-DISC), featuring a spatial resolution of 0.25° × 0.25°.

TROPOMI, onboard the Sentinel-5 Precursor (S5P) satellite, was launched by the European Space Agency (ESA) on 13 October 2017, with a local equatorial overpass time at 13:30. Its NO₂ observations achieve a spatial resolution of 3.5 km × 7 km [32], representing a significant improvement over OMI’s capabilities. This improved resolution enables finer scale spatial analysis. The daily tropospheric NO₂ VCD data were obtained from POMINO-TROPOMI v1.2.2, which was developed for the Asian region by Liu et al. [33]. POMINO-TROPOMI v1.2.2 has a spatial resolution of 0.05° × 0.05° and has undergone stringent quality control, including but not limited to qa_value ≥ 0.5, CF (cloud fraction) ≤ 0.5, and AOD (aerosol optical thickness) < 5.

2.3. Meteorological Reanalysis Data

ERA5 is the latest meteorological dataset from the European Center for Medium-Range Weather Forecasts (ECMWF) (https://cds.climate.copernicus.eu/, accessed on 14 May 2025). It provides hourly data of multiple meteorological variables on a global scale with a spatial resolution of 0.25° × 0.25°. The meteorological elements used in this study include 2 m_temperature, 2 m_dewpoint temperature, BLH (Boundary Layer Height), SNDSF (Surface Net Downward Shortwave Flux), 10 m_U wind, and 10 m_V wind. The meteorological elements were spatially resampled onto 0.05° × 0.05° grids via bilinear interpolation to ensure consistency with other datasets.

2.4. Prior Emissions

The Multi–resolution Emission Inventory model for Climate and air pollution research (MEIC) provides bottom–up pollutant emission inventories for five sectors (agriculture, industry, power, residential, transportation) in mainland China [34,35]. MEIC provides monthly total emissions on 0.25° × 0.25° grids (http://meicmodel.org.cn, accessed on 14 May 2025), which were temporally disaggregated to daily totals using sector–specific emission time allocation coefficients. For spatial refinement, we employed the nighttime light remote sensing dataset from Harvard University [36] to downscale emissions from 0.25° to 0.05°grids. Grid cells contributing less than 2.5% of total emissions were excluded based on established thresholds [24]. The resulting NO_X emission rate was calculated in units of μg/m²/s and served as a prior value for daily emissions.

2.5. Machine Learning (ML) Model and Input Variables

The ML model used in this study was built based on the Whale Optimization Algorithm (WOA) and Extreme Gradient Boosting (XGBoost) algorithm.

2.5.1. WOA

WOA is a metaheuristic optimization algorithm proposed by Mirjalili and Lewis [37], inspired by the hunting behavior of humpback whales. WOA mainly simulates the bubble net predation behavior of humpback whales, and its main components include representation of whale populations, whale behavior and interaction, and adaptability evaluation. WOA has many advantages, such as fast convergence speed, strong global search ability, and easy implementation [38]. It incorporates three steps: encircling prey, bubble net attack, and searching for prey. It is widely used in support vector machines, artificial neural networks, complex function optimization, and feature selection [39].

2.5.2. XGBoost

XGBoost is a powerful machine learning algorithm that improves the boosting algorithm based on GBDT (Gradient Boosting Decision Tree). The algorithm integrates multiple Classification Regression Trees (CARTs) to compensate for the insufficient prediction accuracy of a single CART, and the prediction result is equal to the sum of the scores of all CARTs [40]. It has the advantage of fast training speed, and its algorithm core is as follows:

$${\widehat{y}}_i={\sum }_{k=1}^K{f}_k\left(x_i\right),f_k\in F,\left(i=1,2,3,\dots \dots ,n\right)$$

(1)

where $n$ is the number of samples, ${\widehat{y}}_i$ is the predicted value at the $i$th sample; $K$ is the number of decision trees; $f_k$ is the prediction result at the $k$th decision tree; $F$ is the CARTs collective space; $x_i$ is the feature vector at the $i$th sample. The objective function of XGBoost includes a loss function and regularization term, and the formula is as follows:

$$O^k={\sum }_{i=1}^{n}l\left(y_i,{\widehat{y}}_i^k\right)+{\sum }_{k=1}^K\Omega \left(f_k\right)$$

(2)

where $l\left(y_i,{\widehat{y}}_i^k\right)$ is the loss function, representing the difference between $y_i$ and ${\widehat{y}}_i^k$; $y_i$ is the true value of sample $i$; ${\widehat{y}}_i^k$ is the predicted value of sample $i$ at the $k$th decision tree; $\Omega \left(f_k\right)$ is the regularization term, composed of the number of nodes and the weights of each node. XGBoost performs a second-order Taylor expansion of the cost function. By using the first and second order derivatives, the model can converge faster on the training set, which increases the training speed effectively. And, adding regularization terms to the loss function can reduce the complexity of the model and the risk of overfitting. XGBoost is widely used in the field of atmospheric science, such as in the predictions of PM_2.5 mass concentration [41,42].

The retrieval of NO_X emissions based on satellite remote sensing is inherently a nonlinear regression process. As an efficient ensemble learning machine learning model, XGBoost demonstrates high precision in addressing nonlinear problems and is widely applied to tasks such as classification, regression, ranking, anomaly detection, and model interpretation. XGBoost has been extensively utilized in energy systems [43], including forecasting energy consumption or demand in buildings or microgrids, predicting renewable energy generation, and evaluating the reliability and durability of energy infrastructure components [44,45]. These studies highlight the advantages of the XGBoost model in solving similar regression and prediction tasks.

2.5.3. WOA-XGBoost Modeling Procedure

The hyperparameters for the XGBoost algorithm were optimized by WOA to improve the accuracy of the model in simulating the NO_X emission rate. Seven important hyperparameters were selected for optimization in the XGBoost model (see

Table 2. Hyperparameters optimized using WOA for XGBoost.

Hyperparameters	Description	Range	Optimization Value
learning_rate	Boosting learning rate	[0.01, 0.5]	0.12
max_depth	Maximum tree depth for base learners	[5, 20]	20
subsample	Subsample ratio of the training instance	[0.01, 1]	1
colsample_bytree	Subsample ratio of columns when constructing each tree	[0.5, 1]	1
gamma	Minimum loss reduction required to make a further partition on a leaf	[0, 5]	0
reg_alpha	$l_1$ regularization term on weights	[0, 5]	0.006
reg_lambda	$l_2$ regularization term on weights	[0, 5]	0

). These parameters are all core parameters of XGBoost, and their selection was based on prior literature, such as Song et al. [46] and Qian et al. [47]. Some research results have confirmed that the simulation results of the WOA-XGBoost were better than the combination with other optimization algorithms, such as gray wolf optimization, Bayesian optimization, and butterfly optimization [48,49]. The initial parameters of the WOA algorithm are set as follows. The population size (number of whales) is set to 5, and the maximum number of iterations is set to 50. The iteration terminates when the maximum number of iterations is reached or when the best fitness value of the whale population shows no improvement for 10 consecutive iterations. At this point, the parameters obtained are considered the optimal parameters.

The Schematic of the WOA-XGBoost hybrid model is shown in Figure 2. WOA-XGBoost modeling includes the following five steps [47].

(1)

The population and iteration times are initialized in the WOA algorithm, and the optimization range for each hyperparameter of XGBoost is set.

(2)

The training data is inputted into the XGBoost model, and the fitness of each whale individual in the population is computed based on the score of the respective XGBoost model regarding 10–fold cross–validation (CV) on the training dataset.

(3)

The position of each individual whale is updated, which provides a new set of hyperparameters.

(4)

Steps (2) and (3) are repeated iteratively until the termination criteria are satisfied. At the end of the iteration, WOA outputs the optimal whale position, which is the optimal hyperparameter for the XGBoost model.

(5)

The optimal hyperparameters are inputted into the XGBoost model for simulation, and its performance is evaluated.

2.5.4. Training Dataset for WOA-XGBoost

In this study, we constructed training data for the NO_X emission retrieval model. Variable selection for the training dataset was based on the mass conservation equation [24].

$$\mathrm{d}C=E-L+T$$

(3)

The temporal change in NO_X column concentration ($\mathrm{d}C$) in the troposphere results from NO_X emissions ($E$), NO_X atmospheric chemical/physical losses ($L$), and NO_X atmospheric transport processes ($T$). NO₂ VCD values for days t and days t − 1 are used to characterize the NO_X concentration temporal changes [30]. NO_X chemical/physical losses involve wet deposition, photolytic transformation, and heterogeneous reactions, primarily influenced by meteorological elements including relative humidity, temperature, and solar radiation intensity. NO_X transport processes include vertical and horizontal diffusion mechanisms, with dominant meteorological elements being wind speed/direction and boundary layer height [50].

Table 3. Input variable for WOA-XGBoost.

WOA-XGBoost Input Variable	Unit	Data Source	Description
NO2 VCD from days t and days t − 1	1015 molec/cm2	POMINO-TROPOMI	Variation in NOX column concentration
Boundary layer height	m	ERA5	Influencing NOX vertical diffusion
Surface net downward shortwave flux	J/m2	ERA5	Influencing NOX photolytic transformation
10 m_U wind	m/s	ERA5	Influencing NOX advective diffusion
10 m_V wind	m/s	ERA5	Influencing NOX advective diffusion
2 m_temperature	K	ERA5	Influencing NOX photolytic and heterogeneous reactions
2 m_relative humidity	%	ERA5	Influencing NOX heterogeneous reactions and wet deposition
NO2 horizontal flux divergence	s/m	POMINO-TROPOMI and ERA5	NOX advective diffusion

lists a detailed description of the input variables. As a short–lived species, NO_X daytime lifetimes are ~4 h at low– and mid–latitudes [21]. Given the weak correlation between prior day meteorological parameters and current day NO_X concentrations, we exclusively selected concurrent meteorological parameters as model input variables. In order to better characterize the advective loss of NO_X, we calculated NO₂ horizontal flux divergence using four neighboring grids of the computed grid in both radial and latitudinal directions.

The true values for WOA-XGBoost training come from MEIC prior emissions, which were matched with the data in Table 3 in time and space to obtain a daily NO_X emission retrieval dataset with grids of 0.05° × 0.05°. The 2020 dataset is used to train and validate WOA-XGBoost.

2.6. Model Evaluation Metrics

The WOA-XGBoost model performance was evaluated using the 10–fold cross–validation (CV) method. This method evenly divides the dataset into 10 subsets, using 9 of them as training data and 1 as testing data for validation. The WOA-XGBoost model metrics include root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R²), and correlation coefficient (r). RMSE and MAE are used to quantify the error between predicted values and true values, with small values indicating high accuracy of the model. R² denotes the goodness of fit, with values ranging from 0 to 1. A larger value of R² indicates a better fit. The correlation coefficient r quantifies both the strength and direction of a linear relationship between two variables. The formulas for the evaluation metric are given below.

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(y_i-x_i)}^2}$$

(4)

$$\mathrm{MAE}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n\left|y_i-x_i\right|$$

(5)

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

(6)

$$r={\displaystyle \frac{{\sum }_{i=1}^n{(x}_i-\overline{x}){(y}_i-\overline{y})}{\sqrt{{\sum }_{i=1}^n{(x_i-\overline{x})}^2{\sum }_{i=1}^n{(y_i-\overline{y})}^2}}}$$

(7)

where $n$ is the total amount of evaluated data; $y_i$ is the true value from MEIC; $x_i$ is the predicted value from WOA-XGBoost; $\overline{x}$ is the average of the predicted value; $\overline{y}$ is the average of the true value.

3. Results and Discussion

3.1. Variation in NO₂ VCD and NO_X Emissions in Shandong

Figure 3 presents the interannual variation in NO₂ VCD and NO_X emissions, using data from OMI/Aura observations and MEIC, respectively. The interannual variation in NO₂ VCD closely paralleled the NO_X emissions. NO₂ VCD in Shandong exhibited a trend of initially rising and subsequently declining, reaching its peak in 2011 at 1.78 × 10¹⁶ molec/cm². A notable transient decrease in NO₂ VCD occurred in 2008, attributable to stringent emission control measures implemented by Shandong Province during the Beijing Olympics [51]. After 2011, NO₂ VCD decreased at an average rate of 7.26 × 10¹⁴ molec·cm⁻²/yr, with significant decreases in 2014 and 2015, consistent with NO_X emissions. This was related to China’s release of the Action Plan for Air Pollution Prevention and Control (APAPP) in September 2013 to improve air quality.

Figure 4 illustrates the seasonal and monthly patterns of NO₂ VCD. The NO₂ VCD monthly variation exhibits a distinct “U–shaped” profile (Figure 4b), contrasting with the absence of clear seasonal or monthly trends in NO_X emissions (Figure S1). NO₂ VCD seasonal variation was consistent with observations from other Eastern Chinese provinces [51]. The highest and most fluctuating level of NO₂ pollution was observed in winter (Figure 4a), with VCD of 2.07 × 10¹⁶ molec/cm², which was attributed to a stable atmospheric structure [52]. Conversely, owing to wet deposition and loss of NO₂ photochemical reactions caused by strong solar radiation [53], NO₂ VCD in summer reached their minimum (0.63 × 10¹⁶ molec/cm²), representing less than one–third of the winter concentrations.

Figure 5 depicts the average spatial distribution of NO₂ VCD in Shandong from 2005 to 2023, revealing a clear decline from west to east. On the one hand, this decline was related to the emissions from the heavy industrial centers in Central and Northwestern Shandong (Figure S2). On the other hand, compared with the eastern coastal areas, the atmosphere in the central and western parts of Shandong is relatively stable due to topography and climate, which is not conducive to pollutants diffusion [54]. For example, Huang et al. [55] found that the annual averaged air stagnation days decreased from west to east in Shandong. A persistent NO₂ pollution hotspot emerged in Zibo and adjacent Central Shandong, reaching 1.98 × 10¹⁶ molec/cm². And the hotspot has not migrated in the last 20 years, with an annual maximum exceeding 2.5 × 10¹⁶ molec/cm² during the peak pollution year (Figure S3). Due to its location in the hilly terrain of Central Shandong, Zibo’s urban area is surrounded by mountains, forming a semi–enclosed topography that significantly restricts the horizontal dispersion capacity of pollutants. Furthermore, MEIC emission inventory data reveals that Zibo is one of the high NO_X emission centers in Shandong Province (Figure S2), with emissions primarily originating from industrial boilers (steelmaking), building material production (cement and ceramics), and road transportation [56]. Low NO₂ VCD was found in Yantai and Weihai in the Jiaodong Peninsula region, below 1.1 × 10¹⁶ molec/cm². In particular, Weihai had the lowest NO₂ pollution, with VCD less than 0.9 × 10¹⁶ molec/cm², which was related to the favorable dispersion conditions caused by its coastal location.

In terms of seasonal spatial distribution (Figure 6), as mentioned above, Shandong had the highest pollution level of NO₂ in winter, with NO₂ VCD exceeding 1.9 × 10¹⁶ molec/cm² across most regions except the Jiaodong Peninsula. In addition to the pollution hotpot in Zibo, most areas in Central and South Shandong also showed high NO₂ pollution levels. Autumn maintained a comparable spatial pattern to winter, while the NO₂ VCD was about 0.8 × 10¹⁶ molec/cm² lower than that in winter. In spring, NO₂ levels were above 1.1 × 10¹⁶ molec/cm² in most parts of the province, except for parts of Yantai, Weihai, Rizhao, and Heze. The lowest NO₂ pollution level was observed in summer, with NO₂ concentrations below 0.7 × 10¹⁶ molec/cm², except for some areas in central Shandong.

3.2. Evaluations for NO_X Emission Rate Retrieval

The main cause of NO₂ pollution is NO_X emissions. Using the WOA-XGBoost model introduced in Section 2.5, NO_X emissions were retrieved on 0.05° × 0.05° grids in Shandong. We trained and validated the XGBoost and WOA-XGBoost models based on the data from 2020. We applied 10–fold CV to evaluate the model’s performance, and the results are given in

Table 4. Ten–fold CV results of XGBoost and WOA-XGBoost.

	R2	RMSE (μg/m2/s)	MAE (μg/m2/s)
XGBoost	0.97	0.11	0.06
WOA-XGBoost	0.99	0.03	0.007

. Both the XGBoost and WOA XGBoos models had good performance. Compared with XGBoost, the R² for the WOA-XGBoost model increased by 0.02, and RMSE and MAE decreased by 0.08 μg/m²/s and 0.053 μg/m²/s, respectively, indicating the improvement in accuracy and performance of the WOA-XGBoost model.

We evaluated the performance of the WOA-XGBoost model using data from 11 November 2020, which was not included in the training, and the result is shown in Figure 7. The predicted results were highly consistent with the MEIC, with almost all samples distributed around the 1:1 line and a correlation coefficient (r) of 0.99. Both RMSE and MAE were extremely low, with neither exceeding 0.004 μg/m²/s. Figure 8 shows a spatial comparison between the predicted results and MEIC, and the blank areas indicate missing retrieval values. NO_X emission rates predicted from WOA-XGBoost exhibited high spatial consistency with MEIC, effectively reproducing the high value center of emission rates. Approximately 99.5% of the grid exhibited absolute differences between predicted values and the MEIC inventory within 0.03 μg/m²/s, and the maximum difference was only 0.083 μg/m²/s.

To further evaluate the robustness and temporal transferability of the model, we predicted the NO_X emission rate for 2019 and evaluated it by matching with MEIC. As shown in Figure 9, the yellow area represents high data density. The majority of the data were distributed between 0 and 1 μg/m²/s. The correlation coefficient between the predictions from WOA-XGBoost and MEIC was 0.93, which denotes that the WOA-XGBoost model can effectively capture the nonlinear relationship between multi–source fusion data and NO_X emission rates. The MAE and RMSE were less than 0.3 μg/m²/s, suggesting that the WOA-XGBoost model successfully reproduces NO_X emission rates with strong robustness and good temporal transferability. Notably, as evidenced by the fitting line, the predictions were lower than MEIC, with increasing underestimation at higher emission rates, indicating that the model performs optimally under low to moderate emission scenarios.

Figure 10a compares the monthly mean NO_X emission rates between model predictions and MEIC data for 2019. Both datasets exhibited stable monthly averages (~0.8 μg/m²/s), with minor discrepancies (all <0.035 μg/m²/s). The comparison between prediction and MEIC for 16 cities in Shandong is shown in Figure 10b. The WOA-XGBoost predictions demonstrated strong agreement with MEIC estimates in capturing both absolute emission levels and inter–city variations. As mentioned above, systematic underestimation occurred for high emission cities (e.g., Jinan, Qingdao, Zaozhuang, and Zibo), with Qingdao showing the largest discrepancy (0.15 μg/m²/s). Notably, Zibo exhibited the highest predicted NO_X emissions, consistent with its observed NO₂ VCD. In summary, the proposed model demonstrates robust capability in quantifying NO_X emission rates with high precision, thereby facilitating the development of near–real–time high–resolution grid–based emission inventories for dynamic environmental monitoring.

3.3. NO_X Emission Rate Retrieval for 2021 and 2022

Based on the trained and validated WOA-XGBoost model integrated with multi–source data, daily NO_X emission rates in Shandong Province were quantitatively retrieved for 2021 and 2022, with annual average spatial distributions depicted in Figure 11. The average NO_X emissions rates for 2021 and 2022 were 0.807 μg/m²/s and 0.806 μg/m²/s, respectively, with a slight decrease in 2022. The high-value centers of NO_X emissions were located in areas with high traffic flow, similar to the results from He et al. [57]; for example, Huaiyin, Shizhong, Lixia, and Changqing in Jinan, Shinan, Shibei, and Licang in Qingdao, as well as Weicheng and Kuiwen in Weifang. Transportation emissions are the main source of NO_X, and previous statistics have found that on-road vehicles contribute 68.9% to total NO_X emissions in Shandong [58]. The NO_X emission rates in high emission centers such as Jinan and Zaozhuang showed a downward trend in 2022 (Figure 11c), with some grids decreasing by up to 0.1 μg/m²/s. The downward trend results from the combined effects of industrial pollution control, transportation restructuring, and enhanced policy oversight. For example, Jinan achieved precise emission reductions through mobile source regulation and ultra–low emission transformation, while Zaozhuang accomplished a leapfrog reduction by implementing chemical industry cluster remediation and substituting highway freight with railway transportation.

Figure 12 presents averaged NO_X emissions rate for 16 cities in Shandong Province from 2021 to 2022. The mean NO_X emission rate values of the 16 cities exhibited minimal interannual variation, with the difference around 0. Jinan recorded the most notable reduction in 2022, decreasing by 0.02 μg/m²/s. Consistent with historical patterns in 2019, Zibo maintained the highest emission intensity throughout both years (>1 μg/m²/s), while Dongying exhibited the lowest regional values. These results underscore two critical priorities for emission reduction. Firstly, heavy industrial hubs such as Zibo require sector-specific controls targeting the steel and petrochemical industries. Secondly, high traffic urban areas must accelerate the electrification of freight fleets and optimize logistics routes.

4. Conclusions

The long–term (2006–2023) spatiotemporal variations in NO₂ VCD in Shandong showed that the interannual variation of NO₂ VCD closely paralleled the NO_X emissions. The highest and most fluctuating level of NO₂ pollution was observed in winter, with VCD of 2.07 × 10¹⁶ molec/cm², which was attributed to a stable atmospheric structure. The consumption of NO₂ photochemical reactions caused by strong solar radiation resulted in the lowest NO₂ VCD in summer, representing less than one–third of the winter concentrations. Spatial analysis reveals a distinct west–to–east decreasing gradient in NO₂ VCD, with pollution hotspots persisting in Zibo and surrounding areas of central Shandong Province, where numerous high emission industries cluster and terrain–induced atmospheric stagnation impedes pollutant dispersion.

The NO_X emission rate retrieval model (WOA-XGBoost) was trained and evaluated based on multi–source fusion data from 2020. The 10–fold CV results showed that the WOA-XGBoost model has high accuracy, with R², RMSE, and MAE of 0.99, 0.03 μg/m²/s, and 0.007 μg/m²/s, respectively. The 2019 NO_X emissions retrieved by WOA-XGBoost had high consistency with MEIC (r = 0.93, RMSE = 0.28 μg/m²/s and MAE = 0.21 μg/m²/s), confirming its strong robustness and good temporal transferability. Statistical analysis for 2019 revealed nearly identical monthly mean values between both datasets at approximately 0.8 μg/m²/s. And, the WOA-XGBoost model effectively captured intercity emission heterogeneity. However, the model exhibited a systematic underestimation bias relative to the MEIC. The underestimation increased with the increase in emission rate, demonstrating that the model has optimal predictive accuracy within low–to–moderate emission scenarios.

The NO_X emission rates in 2021 and 2022 were predicted using WOA-XGBoost, and the average NO_X emissions rates for 2021 and 2022 were 0.807 μg/m²/s and 0.806 μg/m²/s, respectively, with a slight decrease in 2022. The high value centers of NO_X emissions rate were located in areas with high traffic flow. The NO_X emission rates in high emission centers such as Jinan and Zaozhuang showed a downward trend in 2022, owing to the combined effects of industrial pollution control, transportation restructuring, and enhanced policy oversight. Similar to 2019, the NO_X emission rate in Zibo was the highest in 2021 and 2022, above 1 μg/m²/s, which explains its high NO₂ VCD. In the future, priority areas for emission reduction should focus on heavy industry clusters such as Zibo and high traffic urban centers.

The MEIC has inherent uncertainties due to systematic errors in activity levels and emission factors. Utilizing MEIC data as the ground “true” data for model training and evaluation introduces biases in the retrieved NO_X emissions. Furthermore, the TROPOMI–derived NO₂ VCD used in our model retrieval reflects the comprehensive influence of emissions from all sectors. Consequently, our model could not distinguish the sectoral origin of NO_X emissions. In the future, we will collect CEMS (Continuous Emission Monitoring System) data and continue to improve our model to reduce its uncertainties. Sector–specific models will be developed to differentiate emissions from various sectors. Furthermore, the models will be extended to other regions to support environmental monitoring.