Prediction and Source Contribution Analysis of PM_2.5 Using a Combined FLEXPART Model and Bayesian Method over the Beijing-Tianjin-Hebei Region in China

Abstract

Fine particulate matter (PM_2.5) has a serious impact on human health. Forecasting PM_2.5 levels and analyzing the pollution sources of PM_2.5 are of great significance. In this study, the Lagrangian particle dispersion (LPD) model was developed by combining the FLEXPART model and the Bayesian inventory optimization method. The LPD model has the capacity for real-time forecasting and determination of pollution sources of PM_2.5, which refers to the contribution ratio and spatial distribution of each type of pollution (industry, power, residential, and transportation). In this study, we applied the LPD model to the Beijing-Tianjin-Hebei (BTH) region to optimize the a priori PM_2.5 emission inventory estimates during 15–20 March 2018. The results show that (1) the a priori estimates have a certain degree of overestimation compared with the a posteriori flux of PM_2.5 for most areas of BTH; (2) after optimization, the correlation coefficient (R) between the forecasted and observed PM_2.5 concentration increased by an average of approximately 10%, the root mean square error (RMSE) decreased by 30%, and the IOA (index of agreement) index increased by 16% at four observation sites (Aotizhongxin_Beijing, Beichenkejiyuanqu_Tianjin, Dahuoquan_Xintai, and Renmingongyuan_Zhangjiakou); and (3) the main sources of pollution at the four sites mainly originated from industrial and residential emissions, while power factory and transportation pollution accounted for only a small proportion. The concentration of PM_2.5 forecasts and pollution sources in each type of analysis can be used as corresponding reference information for environmental governance and protection of public health.

1. Introduction

Over the past several decades, industrialization and urbanization have caused serious PM_2.5 pollution in China. PM_2.5 refers to atmospheric particulates with aerodynamic diameters less than 2.5 μm in ambient air [1,2]. Ambient particles can affect air quality and climate by absorbing and scattering solar irradiation [3,4,5,6], and they also have adverse effects on human health. Studies have shown that high concentrations of PM_2.5 not only increase the morbidity and mortality of the public but also affect the cardiovascular system [7,8,9,10]. PM_2.5 is more harmful to human health than PM₁₀ because PM_2.5 has a smaller particle size and a larger specific surface area, which makes it easier to absorb toxic chemicals [11,12]. Therefore, increasing attention has been given to PM_2.5 in China, not only from the scientific community but also from the public. Overall, it is particularly important to accurately predict the PM_2.5 concentration. In addition, to reduce PM_2.5 concentrations, it is essential to understand the relative contributions to PM_2.5 from various sources, and effective management and control strategies can only be developed for major emission sources when this information is obtained.

Generally, environmental pollution prediction methods are divided into two categories: deterministic and statistical methods [13]. Deterministic methods use mathematical methods to approximate the physical-chemical mechanisms of reaction, transport, and deposition processes to predict the concentration of pollutants. Using the atmospheric model to simulate PM_2.5 for predicting air quality is a hot research topic at present. For example, the WRF-Chem and CMAQ models have been used to evaluate the responses of the surface PM_2.5 level to emission mitigation. Because the model structure and parameter estimation are excessively dependent on ideal theoretical assumptions and large databases, the nonlinearity and heterogeneity of multiple factors cannot be well evaluated by the deterministic method [11,14]. With the continuous improvement in the air quality detection network and the continuous increase in the hourly concentration monitoring data of various pollutants, it is more convenient to use statistical methods to predict regional air quality. Huang et al., (2021) developed an integration method of gated recurrent unit neural networks based on empirical mode decomposition (EMD-GRU) for predicting PM_2.5 concentrations [15]. Wen et al., (2019) constructed a convolutional long short-term neural network to predict the PM_2.5 concentration in Beijing [16]. Zhu et al., (2021) proposed an attention-based parallel network (APNet) to predict PM_2.5 concentrations in the subsequent 72 h [17]. There are also multiple linear regressions (MLRs) [18,19,20], neural networks (NNs) [21,22], fuzzy logic (FL) [23], autoregressive moving averages (ARIMAs) [24,25], machine learning (ML) [11,26,27,28,29], graph convolutional networks, and long short-term memory networks (GC-LSTMs) [30]. Compared with deterministic methods, statistical methods have the advantages of higher operational and simple model structure settings. In addition, related research shows that statistical methods have better forecasting effects than deterministic methods [31,32].

Effective management and control strategies rely on high-precision pollutant forecasts; however, these strategies also need to fully understand the emission sources of pollutants. Qie et al., (2018) used the principal component analysis (PCA) method combined with the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model and potential source contribution function (PSCF) to analyze the distribution and sources of PM_2.5 [33,34]. Caili et al., (2021) built a comprehensive framework based on a horizontal 2-dimensional transport model to optimally estimate the initial concentrations and emission sources of PM_2.5 with 4D-Var [35]. Guo et al., (2018) used the FLEXPART-WRF model combined with the Bayesian optimization method to retrieve and optimize the emission inventory of PM_2.5 [36]. An emission database for global atmospheric research (EDGAR) was developed by scientists at the Netherlands Organization for Applied Scientific Research (TNO) and the National Institute for Public Health and the Environment (RIVM) [37]. Zhang et al., (2009) established an inventory of air pollutant emissions in Asia for 2006 to support the Intercontinental Chemical Transport Experiment-Phase B (INTEX-B) [38]. Yan et al., (2020) used the PMF (positive matrix factorization) model to analyze the main contribution source of PM_2.5 when the AQI exceeds 200 in urban residential areas [39]. Fan et al., (2018) used diagnostic ratios to invert the source of PM_2.5 pollution in Guiyang [40]. Hu et al., (2017) used the PCA method to study the main pollution sources in Hefei from 2014 to 2015 [41].

However, there are a few studies that simultaneously analyze the pollution sources during the process of pollutant forecasting, which can help clearly understand the pollution source distribution during a pollution process and propose targeted solutions. Therefore, the main objective of this study is to develop an LPD (i.e., the FLEXPART model combined with the Bayesian method) model for real-time forecasting of PM_2.5 concentrations and emission source analysis. In this model, to improve the hourly prediction accuracy of PM_2.5, the Bayesian optimization method was used to calibrate the monthly inventory of PM_2.5 emissions and to analyze the contribution and spatial distribution of each type of pollution source (industry, power, residence, and transportation) to the site concentration based on the posterior inventory.

2. Study Area

The Beijing-Tianjin-Hebei (BTH) region is located on the North China Plain. This region is the country’s main high-tech and heavy industry base, and it is also the location of China’s political and cultural center. These cities include Beijing, Tianjin, and 11 prefecture-level cities of the Hebei Province. The land area is 218,000 square kilometers, and the resident population is approximately 110 million people, of which 17.5 million are from outside areas. Economic development in the BTH region is accompanied by serious air pollution. Some studies have found that the BTH region is the most seriously polluted region in China [42,43,44,45]. According to China’s 2015 and 2016 Environmental Status Bulletin [46], PM_2.5, as the main pollutant, has the largest number of days exceeding the standard in the BTH region, accounting for 68.4% and 63.1%, respectively [47]. Figure 1 is a sketch map of the study area in this research, and this area covers from 113.5° E to 119.8° E and from 36.0° N to 42.6° N.

3. Materials and Methods

3.1. Model Development

The LPD model is developed based on the FLEXPART-WRF model, which employs the FLEXPART model to calculate the forward Lagrangian particle dispersion with driving data from the WRF model [48,49,50]. Compared with an adjoint Eulerian model, the advantage of the LPD model is that there is no initial diffusion due to the release of the adjoint tracer into a finite-size grid cell, which is independent from the computational grid. Furthermore, long-range transport can be simulated more accurately as no artificial numerical diffusion is present. The LPD model does not consider dry deposition or chemical reactions in the simulation of PM_2.5, so it has low computational costs. The trajectories of individual particles are computed using a zero-acceleration scheme, in which particle movements are dependent on the grid scale winds and the turbulent fluctuations, which is shown as follows:

$$X\left(t+\Delta t\right)=X\left(t\right)+v\left(X,t\right)\Delta t$$

(1)

This equation is accurate to the first-order to integrate the trajectory equation [48]

$$\frac{dX}{dt}=v\left[X\left(t\right)\right]$$

(2)

where t is the time step, $\Delta t$ is the time increment, X is the position vector, and $v=\overline{v}+v_t+v_m$ is the wind vector that is composed of the grid scale wind $\overline{\mathrm{v}}$, the turbulent wind fluctuations $v_t$, and the mesoscale wind fluctuations $v_m$.

The LPD model makes it possible to obtain the contribution rate of each grid emission source to the receptors (observation sites), which provides the possibility to improve the prediction accuracy and analyze the contribution and spatial distribution of each type of pollution source (industry, power, residential, and transportation) to the site concentration of PM_2.5. In addition, the forecast accuracy of the LPD model and the validity of the inventory inversion results have been verified and analyzed in previous studies, the prediction and inversion results are proved good [36,51]. In the following discussion, the receptors refer to the observation stations.

3.2. Methods

This section mainly includes two parts: inversion of the emission inventory of PM_2.5 and the pollution source analysis of receptors of PM_2.5, and the flowchart is shown in Figure 2. The a priori emission inventory and grid emission ratio (industry, power, transportation, and residential) of PM_2.5 are from the Multiresolution emission inventory for China (MEIC) with a horizontal resolution of 0.25° $\times$ 0.25° (http://www.meicmodel.org/ accessed on 22 March 2021). The PM_2.5 observations were collected from the air quality observation datasets issued by the Ministry of Environmental Protection of China. The LPD drive data were provided by the Advanced Research WRF (WRW) version 4.0 modelling system.

3.2.1. Inventory Inversion

In this research, the spatial distribution of the source-receptor relationship (SRR) was determined by the FLEXPART model. The SRR represents the contribution of each potential source to the receptors. In the present study, 30-day SRR was determined by releasing 10,000 particles from the potential sources per hour [51]. The Bayesian inversion method was used to combine the receptor observations to inverse the PM_2.5 inventory. The principle of inversion is to optimize the emission flux density by minimizing the mismatch between the observed and simulated concentrations. The basic equation of the inversion approach can be written as follows:

$$Y_m=M_{m\times n} . X_n$$

(3)

where M is the matrix of SRR, $y$ is a vector of PM_2.5 concentrations (μg/m³) at the receptor, and $\mathrm{x}$ is the emission flux vector (Mg/grid/month). The equation can be written as follows:

$$M_{mn}=\left[\begin{array}{c}\begin{array}{c}{s}_{11 }, s_{12, }\dots .., s_{1n}\\ s_{21 }, s_{22, }\dots ‥, s_{2n}\\ \dots \dots \dots \dots \dots \dots \dots \end{array}\\ s_{m1 }, s_{m2, }\dots ‥, s_{mn}\end{array}\right]$$

(4)

$$Y_m=\left[\begin{array}{c}{y}_1\\ y_2\\ \begin{array}{c}\dots \dots \\ y_m\end{array}\end{array}\right]$$

(5)

$$X_n=\left[x_1,x_2,\dots \dots .x_n\right]$$

(6)

where m is the time series of observations at the receptor and n is the number of emission grids. $Y_m$ is a matrix that has m rows. Presuming that $\tilde{x}=x-x^a$ and $\tilde{y}=y^o-M.x^a$ where $x^a$, $x,$ and $y^o$ are referred to as a priori, a posteriori source vector, and observation vector, the cost function is described as follows:

$$J={\left(M\tilde{x}-\tilde{y}\right)}^{T}diag\left({\delta }_0^{-2}\right)\left(M\tilde{x}-\tilde{y}\right)+{\tilde{x}}^{T}diag\left({\delta }_x^{-2}\right)\tilde{x}$$

(7)

The best estimate $\mathrm{x}$ was obtained by solving equation ${\nabla }_{\mathrm{x}}\mathrm{J}\left(\mathrm{x}\right)=0$ as follows:

$$x={\left[M^{T}diag\left({\delta }_o^{-2}\right)M+diag\left({\delta }_x^{-2}\right)\right]}^{-1}{M}^{T}diag\left({\delta }_o^{-2}\right)\left(y^o-M{x}^a\right)+x^a$$

(8)

where ${\delta }_o$ and ${\delta }_x$ represent the standard errors related to the observations and a priori values, respectively. Considering that the inventory cannot be a negative, we need to have the condition $\min \left(x\right)\ge 0$. To reduce the unrealistic emissions in the posteriori region, the calculation was iterated until all negative emissions were greater than or equal to 0. Finally, the posteriori inventory was used to predict the PM_2.5 concentration of receptors.

where t represents the time series of simulations in the future.

$$\left[\begin{array}{c}{y}_{m+1}\\ y_{m+2}\\ \begin{array}{c}\dots \dots \\ y_{m+t}\end{array}\end{array}\right]=\left[\begin{array}{c}\begin{array}{c}{s}_{m+1,1 }, s_{m+1,2, }\dots ‥, s_{m+1,n}\\ s_{m+2,1 }, s_{m+22, }\dots ‥, s_{m+2n}\\ \dots \dots \dots \dots \dots \dots \dots \end{array}\\ s_{m+t,1 }, s_{m+t,2, }\dots ‥, s_{m+t,n}\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ \begin{array}{c}\dots \dots \\ x_n\end{array}\end{array}\right]$$

(9)

3.2.2. Source Analysis

The LPD model can simulate the contribution of each potential source of pollution to the receptor sites in real time. The PM_2.5 emission inventory uses the 2016 MEIC products, which are divided into industrial, power, transportation, and residential emissions. The emission proportion of each source in each grid is calculated based on the MEIC PM_2.5 emission inventory of 2016 (Figure 3), and the time resolution is monthly; that is, it is assumed that the emissions proportion of each source does not change within one month. The contribution of each pollution source (industry, electricity, transportation, and residential emission ratio) and the source spatial distribution of those pollutants to the receptors can be analyzed through the pollution emission source contribution of the receptors multiplied by the emission ratio of each grid point, which is described as follows:

$$Ft=F{t}_{ind}+F{t}_{pow}+F{t}_{res}+F{t}_{tra}$$

(10)

where $Ft$ represents the forecasted concentration of PM_2.5 at time t; $F{t}_{ind}$ represents the contribution of industrial sources to the forecasted concentration of the receptors at time t; $F{t}_{pow}$ represents the contribution of power sources to the forecasted concentration of the receptors at time t; $F{t}_{res}$ represents the contribution of residential sources to the forecasted concentration of the receptors at time t; and $F{t}_{tra}$ represents the contribution of transportation sources to the forecasted concentration of the receptors at time t, where $F{t}_{ind}$, $F{t}_{pow}$, $F{t}_{res},$ and $F{t}_{tra}$ can be obtained by Formula (11) as follow:

$$\left[\begin{array}{c}F{t}_{ind}\\ F{t}_{pow}\\ \begin{array}{c}F{t}_{res}\\ F{t}_{tra}\end{array}\end{array}\right]=\left[\begin{array}{c}\begin{array}{c}Pe{r}_{ind,1 }, Pe{r}_{ind,2, }\dots ‥, Pe{r}_{ind,n}\\ Pe{r}_{pow,1 }, Pe{r}_{pow,2, }\dots ‥, Pe{r}_{pow,n}\\ Pe{r}_{res,1 }, Pe{r}_{res,2, }\dots ‥, Pe{r}_{res,n}\end{array}\\ Pe{r}_{tra,1 }, Pe{r}_{tra,2, }\dots ‥, Pe{r}_{tra,n}\end{array}\right]\left[\begin{array}{c}S{t}_1\\ S{t}_2\\ \begin{array}{c}\dots \dots \\ S{t}_n\end{array}\end{array}\right]$$

(11)

where $Pe{r}_{ind,n}$ represents the proportion of industrial emissions from the nth emission grid, $Pe{r}_{pow,n}$ represents the proportion of power emissions from the nth emission grid, $Pe{r}_{res,n}$ represents the proportion of residential emissions from the nth emission grid, $Pe{r}_{tra,n}$ represents the proportion of transportation emissions from the nth emission grid, and $S{t}_n$ represents the contribution of the nth emission grid to the concentration of receptors at time t, where $Pe{r}_{ind,n}$, $Pe{r}_{pow,n}$, $Pe{r}_{res,n},$ and $Pe{r}_{tra,n}$ can be obtained by the MEIC PM_2.5 emission inventory in 2016, and $S{t}_n$ can be obtained from the LPD model.

3.3. Statistical Analysis Methods

To evaluate the accuracy of the concentration forecast and inventory inversion of the LPD model for PM_2.5, the main statistical methods used in this article include the Pearson product-moment coefficient of linear correction, the root mean square error (RMSE) [52,53], and the index of agreement (IOA). The IOA index is defined as follows:

$$IOA=1-\frac{{{\displaystyle \sum }}_{i=1}^N{\left(C_{\left(m,i\right)}-C_{\left(o,i\right)}\right)}^2}{{{\displaystyle \sum }}_{i=1}^N{(\left|{\widehat{C}}_{\left(m,i\right)}\right|+{\widehat{|C}}_{\left(o,i\right)}|)}^2}$$

(12)

$${\widehat{C}}_{\left(m,i\right)}=C_{\left(m,i\right)}-{\overline{C}}_o$$

(13)

$${\widehat{C}}_{\left(o,i\right)}=C_{\left(o,i\right)}-{\overline{C}}_o$$

(14)

where $\mathrm{i}$ is the $\mathrm{i}$th paired (model-observation) data point, $N$ is the total number of paired data points, and $C_{\left(m,i\right)}$ and $C_{\left(o,i\right)}$ are the $\mathrm{i}$th modelled and observed mixing ratios, respectively. Additionally, ${\overline{C}}_o$ is the mean observed mixing ratio. The IOA value varies between 0.0 and 1.0, representing the limits of complete disagreement to perfect agreement, respectively, between the observations and simulations.

4. Results and Discussion

4.1. Evaluation of the Posteriori Inventory

The inversion results of the PM_2.5 inventory from the LPD model in January and February of 2018 will be used as the spin-up time and will not be part of the discussion of the results. The following series of discussions are based mainly on the results of the March 2018 period. Figure 4b shows the PM_2.5 emission inventory in March 2018 retrieved by the LPD model for the BTH region, whose spatial distribution is basically consistent with the a priori inventory (Figure 4a), and the emissions have a certain degree of reduction compared with the a priori inventory. To show the spatial difference before and after the optimization inventory in the BTH region, the spatial difference between the posterior inventory and the a priori inventory is processed (Figure 4c), where blue and red represent the negative and positive differences between the two, respectively. The green column in Figure 5 is the posteriori inventory of PM_2.5 statistics for the BTH region in March 2018, and the statistical results are basically consistent with the inventory of MEIC products (red column) in the corresponding months of 2016, which were 6.29 × 104 Mg and 6.13 × 104 Mg, respectively. In addition, Figure 5 shows that the annual emissions of PM_2.5 pollution increased year by year from 2008 to 2012 and reached the maximum in 2012 [54]. In contrast, the annual emissions of PM_2.5 decreased year by year from 2012 to 2018 and then reached a stable level in 2016. This result is mainly because the “Air Pollution Prevention and Control Action Plan” was issued by the State Council in 2013, and strict control measures have made the emissions of PM_2.5 pollution decrease year by year since 2013 [55,56,57].

To verify the rationality of the posteriori inventory of PM_2.5 inversion by the LPD model in March 2018, we analyzed the observations of the PM_2.5 concentration in 2016 and 2018 (http://www.pm25.in/ accessed on 22 March 2021), and the results showed that the average hourly observations of the PM_2.5 concentration in the BTH region in March 2018 changed in the same way as those in 2016 (Figure 6), which had values of 76.36 and 75.07 ug/m³ in March 2016 and March 2018, respectively. Ignoring the interannual differences in PM_2.5 concentration caused by meteorological conditions, the variation trend and magnitude of the PM_2.5 concentration were approximately the same as those in March 2016, which also verifies the rationality that the a posteriori inventory of PM_2.5, that is, the a posteriori inventory of PM_2.5 in 2018, is basically consistent with the MEIC inventory production in March 2016 (Figure 5). Notably, all the times used in this paper are Beijing Time (BJT).

4.2. Evaluation of Site Forecasts

To evaluate the forecast effect of the LPD model after inventory optimization, the 6-day forecast results from 15–20 March 2018, were compared and analyzed with the observations (Figure 7) based on four observation sites in the BTH region (Aotizhongxin_Beijing, Beichenkejiyuanqu_Tianjin, Dahuoquan_Xintai, Renmingongyuan_Zhangjiakou). In Figure 7, Sim_Raw represents the hourly average concentration of PM_2.5 that forecasts from the FLEXPART model based on the a priori inventory, Sim_Opt represents the hourly average concentration of PM_2.5 that forecasts from the LPD based on the a posteriori inventory, and Obs represents the hourly average concentration of PM_2.5 from the observation sites. The results show that the forecasted concentration of PM_2.5 after inventory optimization is significantly better than that before inventory optimization. In Figure 7, the forecasted PM_2.5 concentrations of the Aotizhongxin_Beijing and Beichenkejiyuanqu_Tianjin sites before inventory optimization are significantly higher than the observations. The Dahuoquan_Xingtai and Renmingongyuan_Zhangjiakou results are opposite, and their forecast concentrations of PM_2.5 are significantly lower than the observations. The statistical results in

Table 1. Statistical analysis between the simulations of PM_2.5 concentration based on the a priori inventory and the posteriori inventory and observations.

Name	Raw_R	Opt_R	Raw_RMSE (μg/m3)	Opt_RMSE (μg/m3)	Raw_IOA	Opt_IOA
Aotizhongxin-Beijing	0.70	0.81	39.44	25.80	0.73	0.83
Beichenkejiyuanqu-Tianjin	0.73	0.79	33.30	25.18	0.73	0.85
Dahuoquan-Xingtai	0.75	0.83	32.65	25.06	0.74	0.84
Renmingongyuan-Zhangjiakou	0.80	0.83	26.03	17.60	0.71	0.86

show that the correlation between the forecast concentration of PM_2.5 of the LPD model after the inventory optimization and observations is increased by 9.66% compared to before optimization on average, the RMSE is reduced by 28.74%, and the IOA index is increased by 16.26%. In Table 1, the prefix RAW represents before the optimization of the inventory, and the prefix OPT represents after the optimization of the inventory, where INCREMENT = (OPT-RAW)/RAW. This result is mainly due to the Bayesian optimization method, which makes the PM_2.5 emission inventory more reasonable and corrects part of the errors in the model simulation.

Additionally, we compared the prediction effect of the LPD model with the research results of other scholars. For example, Liu et al., (2020) evaluated the 5-day PM_2.5 forecast results of three models on a daily scale: the CEEMD-GWO-SVR model proposed by Zhu et al., (2019), which combines the complementary ensemble empirical mode decomposition (CEEMD), grey wolf optimizer (GWO), and support vector regression (SVR) [58]; the wavelet-Ann model developed by Cheng et al., (2019) [59]; the WPD-PSO-BPNN-Adaboost model proposed by Liu et al., (2019), which contains the wavelet packet decomposition (WPD); and the prediction of a backpropagation neural network (BPNN) optimized by the particle swarm optimization (PSO) and adaptive boosting (Adaboost) algorithm [60]; the RMSEs of these three model forecast concentrations of PM_2.5 in the BTH region are 37.4061 μg/m³, 34.8185 μg /m³, 27.8686 μg/m³, respectively [61]. These errors are higher than the results of concentrations of PM_2.5 predicted by the LPD model using the posteriori inventory, in which RMSE with the observations is 23.41 μg/m³ on average. In addition, the LPD model can capture the concentration change information of PM_2.5 at the hourly scale, which is more targeted for prevention and treatment. Guo et al., (2020) also compared the LPD forecasting model with the WRF-Chem and Camx models using data from monitoring stations in Xingtai, China, and the LPD forecasting model had higher accuracy than those models [51].

4.3. Analysis of the Spatiotemporal Forecasts of Pollution Sources

The LPD model improves the accuracies of the PM_2.5 concentration forecasts at stations and predicts the pollution sources (industry, power, residence, and transportation) at the stations and their spatial distributions. Figure 8 shows the main pollution sources that caused the change in the PM_2.5 concentrations at the stations from 15–20 March 2018. The black rendering represents the contribution of pollution sources outside the BTH region, and the red, blue, pink, and green renderings represent the contribution of industrial sources, power sources, residential sources, and transportation sources to the PM_2.5 concentrations at the stations (Aotizhongxin_Beijing, Beichenkejiyuanqu_Tianjin, Dahuoquan_Xintai, Renmingongyuan_Zhangjiakou) in the BTH region, respectively. Figure 8 and the statistical analysis table (

Table 2. Contribution rate of each pollution source to the PM_2.5 concentration at each site.

Name	Base (%)	Industry (%)	Power (%)	Residential (%)	Transportation (%)
Aotizhongxin-Beijing	10.36	33.25	3.54	44.27	8.58
Beichenkejiyuanqu-Tianjin	7.62	35.52	7.00	42.73	7.13
Dahuoquan-Xingtai	16.44	32.41	1.72	42.95	6.48
Renmingongyuan-Zhangjiakou	19.39	26.06	1.39	45.66	7.50

) show that the main pollution sources from 15–20 March 2018 originated from industrial and residential emissions, which are consistent with the previous sectoral analyzing results for other cities in BTH region [62]. In particular, residential emission sources contributed as much as 43.9% to the PM_2.5 concentration at four stations in the BTH region, which was similar to a previous report that used the WRF-CMAQ model in December 2015, representing 46% of the monthly average concentration [63]. In addition, the results are consistent with the analytical results of modelling methods, and show that emissions from the residential contribute more to the PM_2.5 concentration than the industrial sectors [64,65,66]. The result is reasonable and could be explained by an increase in residential coal usage due to heating during these colder seasons. In contrast, the power and transportation emission sources accounted for only a small proportion, especially the two monitoring stations in the Hebei Province (Dahuoquan_Xintai and Renmingongyuan_Zhangjiakou stations), which had little influence from power sources, and the rates were 1.72% and 1.39%, respectively. The contribution rates of the surrounding pollution sources to the two monitoring stations (Dahuoquan_Xintai and Renmingongyuan_Zhangjiakou) in the Hebei Province for the PM_2.5 concentration were 16.44% and 19.39%, respectively, which were 8.9% higher than the Aotizhongxin_Beijing and Beichenkejiyuanqu_Tianjin sites, and the rates were 10.36% and 7.62%, respectively. A similar phenomenon was previously reported; for example, Zhang et al., (2017) used the WRF-Chem model to analyze the impact of the surrounding pollution sources on the BTH region, and the results showed that the surrounding pollution sources contributing to the PM_2.5 concentration in the BTH region were approximately 9.3% [67]. Although different models, simulation times, and input data have a great influence on the analytical results, the research results of previous studies and this paper show that the PM_2.5 concentration contribution in the BTH region mainly originates from local pollution sources, and this information can be targeted to control and prevent the occurrence of pollution events.

Figure 9 shows the spatial distribution of each type of pollution source that led to the PM_2.5 concentration change at the Aotizhongxin_Beijing station from 15–20 March 2018, simulated by the LPD model. This distribution map is the ratio between the grid contribution of the corresponding pollution source to the Aotizhongxin_Beijing station and the maximum grid contribution to the Aotizhongxin_Beijing station of this type of pollution source in the BTH region, with a spatial resolution of 0.25° × 0.25°. Red represents the grid values where the corresponding pollution sources (industry, power, residence, and transportation) contribute more to the site concentration of PM_2.5, and blue represents the corresponding types of pollution sources that contribute less to the site concentration of PM_2.5. During this forecast period (15–20 March 2018), the surrounding industrial and residential emission sources have a greater influence on the Aotizhongxin_Beijing station over a wide range. In contrast, the power and transportation sources have a small influence on the Aotizhongxin_Beijing station. In particular, the influence of the power source on the Aotizhongxin_Beijing station is relatively scattered (Figure 9b).

5. Conclusions

LPD can improve PM_2.5 concentration forecast accuracy by optimizing the PM_2.5 emission inventory and by obtaining real-time analyses of the temporal and spatial distributions and pollution source contributions that lead to changes in the PM_2.5 concentration at the receptors. This model was applied to the BTH region, which has severe pollution, and the hourly forecast values over 6 days from 15–20 March 2018 were analyzed. The results show that the average correlation between the forecasted concentrations of PM_2.5 after the emission inventory was optimized and that the observations were as high as ~0.82 at four observation sites (Aotizhongxin_Beijing, Beichenkejiyuanqu_Tianjin, Dahuoquan_Xintai, Renmingongyuan_Zhangjiakou); the RMSE was ~23.41, and the IOA index was ~0.84, which was significantly improved compared to the values obtained before inventory optimization.

During this period (15–20 March 2018), the main pollution sources that led to the changes in the concentrations of PM_2.5 at the four observation sites originated from industrial and residential emissions, and power and transportation pollution sources accounted for only a small proportion, especially the Dahuoquan_Xintai and Renmingongyuan_Zhangjiakou stations in the Hebei Province; power pollution sources had little influence on these stations, and the values were 1.72% and 1.39%, respectively. The influence of the surrounding pollution sources from outside BTH on the Dahuoquan_Xintai and Renmingongyuan_Zhangjiakou stations in the Hebei Province was 16.44% and 19.39%, respectively. Compared with the Aotizhongxin_Beijing and Beichenkejiyuanqu_Tianjin sites, the average influence ratio increased by 8.9%.

Considering the actual situation and operating efficiency of the LPD model, the concentration forecast of PM_2.5 and the analysis of each type of pollution source are only at the site scale, without considering dry and wet sedimentation and chemical reactions of the particles, and this part of the error is attributed to the uncertainties in both the model and emission inventory. The reader should keep in mind that inverse approaches still have large uncertainties due to the limited observation sites and the method bias. Therefore, the LPD model needs to be further optimized and expanded in future research for the development of forecasting surface-level distributions of PM_2.5 concentration and each type of pollution source analysis at a regional scale. In addition, at present, we only quantitatively evaluate the reliability of the LPD model and input the parameters through indirect or by comparison with observations, and we need to further verify and analyze its reliability and adaptability.