A Data Assimilation Method Combined with Machine Learning and Its Application to Anthropogenic Emission Adjustment in CMAQ

Abstract

Anthropogenic emissions play an important role in air quality forecasting. To improve the forecasting accuracy, the use of nudging as the data assimilation method, combined with extremely randomized trees (ExRT) as the machine learning method, was developed and applied to adjust the anthropogenic emissions in the Community Multiscale Air Quality modeling system (CMAQ). This nudging–ExRT method can iterate with the forecast and is suitable for linear and nonlinear emissions. For example, an episode between 15 and 30 January 2019 was simulated for China’s Beijing–Tianjin–Hebei (BTH) region. For PM_2.5, the correlation coefficient of the site averaged concentration (Ra) increased from 0.85 to 0.94, and the root mean square error (RMSEa) decreased from 24.41 to 9.97 µg/m³. For O₃, the Ra increased from 0.75 to 0.81, and the RMSEa decreased from 13.91 to 12.07 µg/m³. These results showed that nudging–ExRT can significantly improve forecasting skills and can be applied to routine air quality forecasting in the future.

1. Introduction

The air quality in China has improved rapidly over the past decades due to the development of action plans for controlling air pollution [1] and the Blue Sky Protection Campaign [2]. Fine particulate matter (PM_2.5) pollution has also followed a decreasing trend in recent years. However, ozone (O₃) pollution has had an increasing tendency since the 1990s [3,4,5,6]. Regional atmospheric environmental problems will damage human health and affect social harmony and stability. Existing studies have shown that air pollution is related to increasing mortality and hospitalizations that have been caused by respiratory and cardiovascular diseases [7,8,9]. Currently, the cooperative control of PM_2.5 and O₃ is becoming increasingly important, and demands a more accurate and efficient operational forecasting system for both PM_2.5 and O₃.

Uncertainties in anthropogenic emissions are a major factor that influence forecasting accuracy. Bottom-up and top-down are the two main methods that can establish an emission inventory. The bottom-up method mainly uses a series of statistical data, including human activities, population density, industrial output, road networks, vehicle numbers, and other emission factors, to calculate the averaged emission inventories over a long period. Many bottom-up emission inventories have been established in China [10,11,12,13]. However, the problems caused by these uncertainties and a delay of the statistical data in the bottom-up method are difficult to solve. Therefore, top-down methods are carried out to estimate the uncertainties in these bottom-up emission inventories and they usually use observed data, including ground-based stations and satellite and radar data, to establish real-time emission inventories.

Many top-down studies on linear emission sources have been carried out [14,15,16,17]. Four-dimensional variational (4DVAR) and ensemble Kalman filter (EnKF) are two of the major methods that are used to establish an inversion model to adjust the emission inventories. In addition, nudging has been proven to be another method for adjusting these linear emission sources [18,19]. However, these inversion models for emissions, which have nonlinear reactions with pollutants and insufficient observation data, such as volatile organic compounds (VOCs) and NO, still have some limitations that need to be studied [20]. Owing to the lack of VOC observations and the complex O₃-VOCs-NO_x photochemical reactions, inversing VOCs from O₃ observations has been the subject of numerous research efforts [21,22]. To solve this problem, Ma et al. used O₃ observations and ensemble methods to update the NO_x and VOC state variables and emissions [23,24]. However, this method costs considerable computing resources and is hard to adapt within operational forecasting.

Machine learning is one of the most popular methods for solving nonlinear problems and can usually be more effective with the growth of databases, though it has not yet been adopted for emission data assimilation. The extremely randomized trees (ExRT) method is a stable and effective method that has been used in air quality forecasting [25,26,27]. Our previous CMAQ (Community Multiscale Air Quality) model output statistics study also proved that ExRT is a better method than multiple linear regression and gradient boosted regression trees [28]. In this paper, we attempted to adopt ExRT in the nudging method and adjust the anthropogenic emissions within an operational CMAQ forecasting simulation. This is an attempt to combine data assimilation and machine learning.

2. Materials and Methods

2.1. Model and Dataset

The observational data from 255 air quality stations in the Beijing–Tianjin–Hebei (BTH) region from the China National Environmental Monitoring Center were used (Figure 1b). The final operational global analysis (FNL) 1° × 1° data can be downloaded from https://rda.ucar.edu/datasets/ds083.2/, accessed on 1 March 2020, and they are produced by the National Centers for Environmental Prediction (NCEP) [29]. An FNL was used in this simulation to initialize the weather research and forecasting model (WRF) [30,31]. The geographical input data, which provide static geographical data for the WRF preprocessing system (WPS) input, can be downloaded from https://www2.mmm.ucar.edu/wrf/users/download/get_sources_wps_geog.html accessed on 15 June 2019. The 2017 emission inventory from the Multi-resolution Emission Inventory for China (MEIC) was developed and maintained by Tsinghua University [12], and can be downloaded from http://meicmodel.org/, accessed on 1 February 2022. The MEIC provided the monthly total emissions for the species in different mechanisms, and these were used in all of the domains in our study through temporal allocation, spatial allocation, and speciation.

2.2. Model Configurations

This study applied a WRF-CMAQ modeling system to simulate the variations in PM_2.5 and O₃. The WRF was developed by the National Center for Atmospheric Research (NCAR) and the University Corporation for Atmospheric Research (UCAR) [30,31]. WRFv3.7.1 was used to generate the meteorological driver for the air quality simulation. The CMAQ modeling system is an active open-source development project of the United States Environmental Protection Agency, which consists of a suite of programs for model simulations of air quality [32]. We used CMAQv5.3.2 [33] to simulate the spatial distribution and temporal variation of the PM_2.5, O₃, and NO₂ concentrations within the study region between 2 and 30 January 2019. All the simulations were restarted every 24 h, using the last simulation as the initial conditions and simulated 72 h concentration. There were 3 simulation cycle spin-ups before 2 January 2019. The boundary conditions of domain 1 and the initial conditions of the first simulation cycle used the mean value of the climate state. The detailed WRF-CMAQ model configurations are listed in

Table A1. WRF simulation configurations.

WRFv3.7.1
Simulation period	3–30 January 2019
Vertical resolution	33 Vertical levels
Microphysics scheme	WSM 3-class simple ice scheme [37]
Boundary layer scheme	YSU scheme [38]
Surface layer scheme	MM5 scheme [39]
Land-surface scheme	Unified Noah land-surface model [40]
Longwave radiation scheme	rrtm scheme [41]
Shortwave radiation scheme	Dudhia scheme [42]
Grid-nudging fdda	on
Domain center	39.1248°N, 116.5657°E
Domain id	1	2	3
Domain size	64 × 75	69 × 81	102 × 96
Starting IJ-indices from the parent domain	×	(30, 19)	(38, 23)
Horizontal resolution	81 km	27 km	9 km

and

Table A2. CMAQ simulation configurations.

CMAQv5.3.2
Horizontal advection	Yamo [32]
Vertical advection	WRF
Horizontal diffusion	Multiscale
Vertical diffusion	ACM2
Deposition	M3Dry [43]
Chemistry solver	EBI
Aerosol module	AERO7 [44]
Cloud module	ACM [45]
Mechanism	cb6r3_ae7_aq [44,46]
Domain ID	1	2	3
Domain size	62 × 73	67 × 79	100 × 94

. The model simulation domain and topographic height are shown in Figure 1.

2.3. The Combination of Nudging and ExRT

The nudging method [34] has been widely used for improving air quality forecasting [18,19]. The nudging form can be expressed as

$$\frac{\partial P_n}{\partial t}=F\left(P_n,x,t\right)+N(P_n,P^{*},Q^{*}+{∆Q}_n)$$

(1)

$${∆Q}_{n+1}={∆Q}_n\times \frac{[P^{*}-P_n-\beta \left(P_n-P_{n-1}\right)]}{P_n-P_{n-1}}$$

(2)

$$Q_{n+1}=Q^{*}+{∆Q}_{n+1}$$

(3)

where $P_n$ is the concentration of the pollution in n iterations, t is the time, F is the array of the forcing function, N is the nudging terms, $P^{*}$ is the concentration of the observations, $Q^{*}$ is the original emission inventories, ${∆Q}_n$ is the emission innovation vector (the differences between the original emissions and assimilated emissions), and $\beta$ is the empirical nudging coefficients.

The nudging used the original emissions ($Q^{*}$), observations ($P^{*}$), and simulated concentrations of the CMAQ ($P_n$) to calculate the differences between the assimilated and original emissions (innovations) (${∆Q}_{n+1}$). Then, the assimilated emissions ($Q_{n+1}$) were calculated using the emission innovations and original emissions to improve the CMAQ forecasts.

Firstly, the CMAQ predicted the concentration of $P_1$, and the observed concentration of $P_1^{*}$ and original emission data of $Q_1$ from the MEIC were used to derive the first emission innovation vector, ${∆Q}_1$, ${∆Q}_1=\beta \times Q1\times \frac{[P_1^{*}-P_1]}{P_1}$. Then, the new emission $Q_2=Q_1+{∆Q}_1$ was used to predict the concentration of $P_2$ using the CMAQ. $P_1$ and $P_2$ were used to estimate ${∆Q}_2$ using Equation (2). In this study, the iteration of the nudging went with the simulation circle, which meant that we only ran one nudging in a single simulation every 24 h.

While there were adequate data, we used all the simulations (the CMAQ-predicted concentrations) and corresponding emission innovation vectors in the database (which grew with the simulation circle) to train the ExRT model, and we used the trained ExRT model and the observations to calculate the prediction emission innovation vector. The training and prediction of the ExRT model can be expressed as:

$$\left[\begin{array}{ccc}{∆Q}_1& \cdots & {∆Q}_n\end{array}\right]=M_n\left(\left[\begin{array}{c}\begin{array}{ccc}{P}_{\mathrm{1,1}}& \cdots & P_{n,1}\end{array}\\ \begin{array}{ccc}⋮& \ddots & ⋮\end{array}\\ \begin{array}{ccc}{P}_{1,s}& \dots & P_{n,s}\end{array}\end{array}\right]\right)$$

(4)

$${∆Q}_{n+1}=M_n\left(\left[\begin{array}{c}\begin{array}{ccc}{P}_{\mathrm{1,1}}^{*}& \cdots & P_{n,1}^{*}\end{array}\\ \begin{array}{ccc}⋮& \ddots & ⋮\end{array}\\ \begin{array}{ccc}{P}_{1,s}^{*}& \dots & P_{n,s}^{*}\end{array}\end{array}\right]\right)$$

(5)

where $M_n$ is the ExRT model in simulation n, trained in Equation (4) and used in Equation (5);$P_{n,s}$ is the simulated concentration of the pollutant s in iteration n; and $P_{n,s}^{*}$ is the observed concentration of the pollutant s in iteration n. As for PM_2.5, s = 1, the PM_2.5 emission innovations, ${∆Q}_{n+1}$, were calculated using the simulated observed PM_2.5 concentration and the corresponding PM_2.5 emission innovations. As for the VOCs, s = 2, the VOC emission innovations were calculated using the simulated observed O₃ and NO₂ concentrations and the corresponding VOC emission innovations. The calculation of NO_x was similar to that of the VOCs.

The extremely randomized trees method was developed by Geurts et al. [35], which is an improved version of the original decision tree models using the classical top-down procedure. A nonlinear solution can be found in the basic decision tree models. The entropy in probability theory is used in a decision tree to measure the uncertainty of information, and can be calculated as follows:

$$H\left(X\right)=-{\sum }_{i=1}^{n}p\left(x_i\right){log}_{b}p\left(x_i\right)$$

(6)

where H(X) is the entropy of X, n is the number of samples, $p\left(x_i\right)$ is the probability that $x_i$ occurs, and ${log}_{b}p\left(x_i\right)$ is the logarithm of $p\left(x_i\right)$ to base b.

Figure 2 shows the framework of the ExRT, and the construction of the ExRT is mainly divided into three parts. The first step was the feature selection. The database of simulations corresponded to the nudging emission innovations in the chronological order of spatial conversion, unit conversion, and chemical species. The entropy was automatically calculated and sorted to obtain the selected training samples. The second step was the modeling of the ExRT. In order to comprehensively train all of the samples and enhance the independence of the basic regression tree, part of the basic regression tree used all of the training samples, while the other part used the resampling training samples. If the input sample passed the given criteria, a leaf node was generated; otherwise, several candidate attributions were randomly calculated to generate several candidate sample subsets. When selecting the eigenvalues of the node splitting, the split was according to the attribute with the highest regression score, until the given criteria were met. The construction process of the k-times regression tree was repeated to form the ExRT model. The third step was the prediction, which was based on the ExRT model that was trained in the previous step and combined with the observations, and finally, the corresponding nudging emission innovation results were obtained.

The main innovations of the ExRT are as follows: (1) the randomly selected cut points are transformed into split nodes; and (2) the decision tree is constructed from the whole training dataset. This means that the ExRT generally does not use random sampling, and that each decision tree uses the original training samples. The partition points of the eigenvalues are randomly selected instead of using the most advantageous ones, and the size of the decision tree will generally be larger than the common random forest. In other words, the variance of the model is further reduced and the generalization ability, stability, and availability of the ExRT are better. A comparison of the ExRT, GBRT (gradient boosting regression tree), and MLS (multiple linear regression) was carried out in our previous MOS (model output statistics) study [28]. In a study of Xuzhou from 1 January 2016 to 31 March 2016, the WRF-CMAQ-MOS, using the ExRT, increased the correlation coefficient of the NO₂ and O₃ from 0.35 and 0.39 to 0.63 and 0.79, and the root mean square error decreased from 0.0346 mg/m³ and 0.0447 mg/m³ to 0.0243 mg/m³ and 0.0367 mg/m³. The scikit-learn machine learning package in Python was used here to accomplish the ExRT within nudging, and is available at http://scikit-learn.org/stable/index.html, accessed on 1 February 2022.

Figure 3 shows the framework of the nudging–ExRT methods that were used for the emission adjustment in the CMAQ. The nudging method was used to create a database of the nudging innovation vectors, using simulations of the CMAQ and ground-based observations. Then, these data were employed to train a machine learning model that used the ExRT, and to store the relationships between the nudging innovation vectors and the simulations in the trees. Using the trained machine learning model, the observations were used again to determine the proper nudging–ExRT innovation vector. The nudging–ExRT emission inventories were calculated using the original emission inventories and the nudging–ExRT innovation vector.

In the operational forecast of the emission data assimilation in the CMAQ simulation, we used nudging to calculate the hourly emission innovation vector between 2 and 14 January 2019, and created a database of the observations, simulations, and innovation vectors. Iterative nudging was performed every 24 h using all of the databases from the previous iterations to assimilate the emissions, and then used the assimilated emissions in the CMAQ to simulate the next 72 h of the pollutant concentrations. Then, we performed nudging (Nud) and nudging–ExRT (NudEx) experiments to adjust the anthropogenic emissions of the PM_2.5, VOCs, and NO_x between 15 and 30 January 2019. The proportion of the components did not change for PM_2.5, VOCs, or NO_x after the data assimilation. All the simulations of the PM_2.5, O₃, and NO₂, and the innovation vectors of the emission database were used to train the machine learning model every 24 h. Finally, the machine learning model was used with the previous 72 h of observations to obtain the NudEx innovation vector for the next simulation. All the CMAQ simulations, including NODA (the CMAQ simulations without data assimilation), Nud, and NudEx, were restarted every 24 h, using the last simulation as their initial conditions. It should be noted that Nud could only use the database of O₃ to adjust the emission of the VOCs, and that NudEx could use the databases of O₃ and NO₂ in the ExRT to adjust the emissions of the VOCs. As shown in Equations (1), (2), (4) and (5), the simulated concentration of the $P_n$ and the emission innovation of ${∆Q}_n$ were in a one-to-one correspondence for a pollutant species in Nud, and the VOC emission innovations were calculated by using the simulated observed O₃ and NO₂ concentrations and the corresponding VOC emission innovations in the NudEx.

3. Results

3.1. Anthropogenic Emission Adjustment

Figure 4 shows the daily change comparison in the NODA, Nud, and NudEx experiments of the PM_2.5, O₃, and NO₂ concentrations and the PM_2.5, VOC, and NO_x emission inventories. The data in Figure 3 were calculated using the average of the 255 station locations in the BTH region and the 15 days between 15 and 30 January 2019. In Figure 3a, the daily change in the PM_2.5 in the Nud and NudEx was closer to the observation than that of the NODA; meanwhile, the NudEx was closest around the leak at approximately 10 LST (Local Standard Time, UTC+8). In Figure 3b, the daily change in the O₃ of the NudEx was closest to the observation around the leak at approximately 15 LST. The results expressed that the daily change in the NudEx emissions could better simulate the concentrations of PM_2.5 and O₃. All of the times used in this paper are expressed in LST.

Figure 5 shows the PM_2.5, VOC, and NO_x differences between the NODA, Nud, and NudEx emissions in the CMAQ as the hourly average of 15–30 January 2019. For the emission sources of PM_2.5, the Nud reduced the emissions in Beijing and southern Hebei, and increased the emissions in western Shanxi, southeastern Liaoning, and western Shandong. The NudEx reduced the emissions in Beijing, southern Hebei, and northern Shandong. The largest differences between the Nud and NudEx were in Shandong and Liaoning. For the emission sources of the VOCs, Nud and NudEx both had an increasing tendency around Beijing, Tianjin, and Shijiazhuang. However, the NudEx had a larger adjustment in Beijing and a smaller adjustment in Tianjin and Shijiazhuang. For the emission sources of NO_x, Nud and NudEx both had a decreasing tendency around Beijing and Tianjin, and had an increasing tendency in northeastern Hebei. The emissions of PM_2.5, VOCs, and NO_x in the NODA, Nud, and NudEx experiments can be found in Figure A1.

3.2. Emission Data Assimilation Results

Figure 6 shows the PM_2.5 and O₃ concentrations using the NODA, Nud, and NudEx emission inventories as the average of 15–30 January 2019. For PM_2.5, the nudging methods could decrease the differences throughout the region, and NudEx had a better performance. For O₃, owing to the fact that the Nud method was unable to deal with the nonlinear reaction of O₃-VOCs-NO_x, it had an even worse performance than NODA in the emission data assimilation of the VOCs. NudEx used machine learning methods and an increasing database to build a machine learning model of the observation, simulation, and emission innovations every 24 h. This machine learning model could partly replace the O₃-VOCs-NO_x nonlinear reactions in the emission data assimilation, using the existing O₃ and NO₂ observations to invert the emissions of the VOCs. These results showed that the nudging–ExRT method could improve the spatial accuracy of PM_2.5 and O₃ in the CMAQ. The concentrations of PM_2.5 and O₃ in the observations and the NODA, Nud, and NudEx experiments can be found in Figure A2.

To assess the performance of the NODA CMAQ simulation and the Nud and NudEx emission data assimilation results, the simulated PM_2.5 and O₃ concentrations were compared to the observations from the 255 air quality stations from the China National Environmental Monitoring Center. The hourly averaged spatial correlation coefficient ($\stackrel{-}{Rs}$), hourly averaged spatial root mean squared error ($\stackrel{-}{RMSEs}$), hourly averaged spatial normalized mean bias ($\stackrel{-}{NMBs}$), hourly averaged spatial normalized mean error ($\stackrel{-}{NMBs}$), correlation coefficient of the site averaged concentration (Ra), root mean squared error of the site averaged concentration (RMSEa), normalized mean bias of the site averaged concentration (NMBa), and the normalized mean error of the site averaged concentration (NMEa) were used to validate the results. These statistical parameters were divided into two different types: spatial ($\stackrel{-}{Rs}$, $\stackrel{-}{RMSEs}$, $\stackrel{-}{NMBs}$, and $\stackrel{-}{NMBs}$) and temporal (Ra, RMSEa, NMBa, and NMEa). The spatial statistics first calculated the statistical parameters for the 255 stations for each hour, and then calculated the average of these parameters. The temporal statistics first calculated the average for the 255 stations, and then used the averaged concentration to calculate the statistical parameters.

$$Rs(t)=\frac{{\sum }_{s=1}^m\left(C\right(t,s)-\stackrel{-}{C(t,s)})\left(C_0\right(t,s)-\stackrel{-}{C_0(t,s)})}{\sqrt{\sum _{s=1}^m{\left(C\right(t,s)-\stackrel{-}{C(t,s)})}^2}\sqrt{\sum _{s=1}^m{\left(C_0\right(t,s)-\stackrel{-}{C_0(t,s)})}^2}}$$

(7)

$$RMSEs(t)=\sqrt{\frac{\sum _{s=1}^m\left(C\right(t,s)-C_0(t,s){)}^2}{m-1}}$$

(8)

$$NMBs(t)=\frac{{\sum }_{s=1}^m\left(C\right(t,s)-C_0(t,s\left)\right)}{{\sum }_{s=1}^m{C}_0(t,s)}\times 100\%$$

(9)

$$NMEs(t)=\frac{{\sum }_{s=1}^m\left|C(t,s)-C_0(t,s)\right|}{{\sum }_{s=1}^m{C}_0(t,s)}\times 100\%$$

(10)

$$Ra=\frac{{\sum }_{t=1}^n\left(C_a\right(t)-\stackrel{-}{C_a\left(t\right)})\left(C_{0a}\right(t)-\stackrel{-}{C_{0a}(t,m)})}{\sqrt{\sum _{t=1}^n{\left(C_a\right(t)-\stackrel{-}{C_a\left(t\right)})}^2}\sqrt{\sum _{t=1}^n{\left(C_{0a}\right(t)-\stackrel{-}{C_{0a}(t,m)})}^2}}$$

(11)

$$RMSEa=\sqrt{\frac{\sum _{t=1}^n\left(C_a\right(t)-C_{0a}(t){)}^2}{n-1}}$$

(12)

$$NMBa=\frac{{\sum }_{t=1}^n\left(C_a\right(t)-C_{0a}(t\left)\right)}{{\sum }_{t=1}^n{C}_{0a}\left(t\right)}\times 100\%$$

(13)

$$NMEa=\frac{{\sum }_{t=1}^n\left|C_a\left(t\right)-C_{0a}\left(t\right)\right|}{{\sum }_{t=1}^n{C}_{0a}\left(t\right)}\times 100\%$$

(14)

Here, C(n,m) is the simulated concentration matrix of n hours and m stations, C₀(n,m) is the observed concentration matrix of n hours and m stations, $Rs\left(t\right)$ is the spatial correlation coefficient at time t, and $\stackrel{-}{Rs}=\frac{1}{n}\sum _{t=1}^{n}Rs\left(t\right)$. Similarly, $\stackrel{-}{RMSEs}=\frac{1}{n}\sum _{t=1}^{n}RMSEs\left(t\right)$, $\stackrel{-}{NMBs}=\frac{1}{n}\sum _{t=1}^{n}NMBs\left(t\right)$, and $\stackrel{-}{NMEs}=\frac{1}{n}\sum _{t=1}^{n}NMEs\left(t\right)$. $C_a\left(t\right)$ and $C_{0a}\left(t\right)$ are the site-averaged simulated and observed concentrations, respectively, and $C_a\left(t\right)=\frac{1}{m}\sum _{s=1}^{m}C\left(t,s\right) \mathrm{a}\mathrm{n}\mathrm{d} C_{0a}\left(t\right)=\frac{1}{m}\sum _{s=1}^m{C}_0(t,s)$.

Figure 7 and

Table 1. Assessment of PM_2.5 and O₃ in the NODA, Nud, and NudEx simulations.

	PM2.5			O3
	NODA	Nud	NudEx	NODA	Nud	NudEx
$\stackrel{-}{Rs}$	0.47	0.54	0.54	0.33	0.16	0.28
$\stackrel{-}{RMSEs}$ (µg/m3)	56.44	38.23	32.2	24.6	36.61	19.51
$\stackrel{-}{NMBs}$	29%	−4%	9%	−21%	19%	−9%
$\stackrel{-}{NMEs}$	67%	44%	47%	72%	92%	74%
$Ra$	0.85	0.91	0.94	0.75	0.81	0.81
$RMSEa$ (µg/m3)	24.41	10.59	9.97	13.91	14.86	12.07
$NMBa$	28%	−6%	8%	−23%	17%	−8%
$NMEa$	32%	13%	13%	33%	31%	31%

show the assessments of PM_2.5 and O₃ in the NODA, Nud, and NudEx simulations. For PM_2.5, all the assessments of the PM_2.5 were improved in the Nud experiments and were better in the NudEx. For O₃, the assessments of the O₃ showed that the Nud decreased the correlation coefficient and increased the root mean squared error, which meant the Nud made the simulation worse. The reason for this was that the Nud reckoned without the nonlinear reactions of O₃-VOCs-NO_x and only considered the direct reaction between O₃ and the VOCs. All the assessments, except the $\stackrel{-}{Rs}$ of the NudEx, showed a better performance for O₃, and the NudEx could partly take the place of nonlinear reactions. The $\stackrel{-}{Rs}$ of the O₃ in the NudEx decreased mainly because the low Rs at night were caused by the low O₃ concentration after the assimilation. These results showed that the nudging–ExRT method could improve both the temporal and spatial accuracy of PM_2.5 and O₃ in the CMAQ.

Using the assessment data of the PM_2.5 and O₃, Figure 8 shows a Taylor diagram of the hourly averaged spatial and site-averaged PM_2.5 and O₃ comparison of the observations and simulations, using the NODA, Nud, and NudEx emission inventories in China between 15 and 30 January 2019. The scattered points in the Taylor chart represent the simulations using different emissions, the radiation line represents the correlation coefficient, and the horizontal and vertical axes represent the normalized standard deviation. These results directly point out that NudEx had more significant improvements than Nud.

4. Conclusions

In this paper, we established an efficient and extensible data assimilation method that was combined with machine learning to adjust the anthropogenic emissions in the CMAQ. The framework of nudging–ExRT was efficient, and the key point is that we only performed one iteration in every forecast and used all the data in the increasing database to build the machine learning model. In the experiment of this paper, a total of four Linux servers that were connected through optical fiber were used. Each server had two Intel (R) Xeon (R) E5-2620 v4 16-core CPUs, a total of 128 cores, 16 G of memory, 6 T of storage space, and 100 T of separate shared disk storage. It only took approximately half an hour before the forecasting and could be widely used for operational forecasting. The framework is extensible for adoption by other air quality models, because it only uses changeable emission sources and their corresponding simulations. The data assimilation and machine learning methods are both changeable and can be better extended in the future.

The results proved that the nudging method without the ExRT could improve the forecasting accuracy in linear emission sources, but could not eliminate nonlinear errors, and that the nudging–ExRT method, based on ensemble methods and probability theory, could significantly improve both the linear and nonlinear emission sources. We used O₃ observations and simulations to adjust the VOC emissions in the Nud experiment. The nudging method attributed all of the errors in O₃ to the VOCs, which was wrong, since it only considered the direct reaction between O₃ and the VOCs. In the NudEx experiment, the machine learning model of the VOCs was established using O₃ and NO₂ observations and simulations. The ExRT model used the database to create the nonlinear relationships between the O₃ and NO₂ simulations and the VOC emissions, which could replace the real reactions. The reactions of the O₃-VOCs-NO_x in the CMAQ can be found in a study by Sarwar et al. [36].

This attempt to combine data assimilation and machine learning has proven to be a good way to invert both linear and nonlinear anthropogenic emission sources. In our experiments from 15 to 30 January 2019, in the BTH region of China, for the PM_2.5, the $\stackrel{-}{Rs}$ increased from 0.47 to 0.54, the $\stackrel{-}{RMSEs}$ decreased from 56.44 µg/m³ to 32.20 µg/m³, the Ra increased from 0.85 to 0.94, and the RMSEa decreased from 24.41 µg/m³ to 9.97 µg/m³. For the O₃, the $\stackrel{-}{Rs}$ decreased from 0.33 to 0.28, the $\stackrel{-}{RMSEs}$ decreased from 24.60 µg/m³ to 19.51 µg/m³, the Ra increased from 0.75 to 0.81, and the RMSEa decreased from 13.91 µg/m³ to 12.07 µg/m³. These results showed that the nudging–ExRT method could improve both the temporal and spatial accuracy of the PM_2.5 and O₃ in the CMAQ.

The results of the nudging–ExRT show good prospects for combining data assimilation and machine learning. This study can help researchers to gain more knowledge on the relationship between nonlinear emission sources and pollution. The accuracy of the operational air quality model can benefit from this framework and its extension.