2.3.1 State variable and ensemble generations

The state variable used in this study was chosen following our previous multispecies inversion study (Kong et al., 2023b), which included the scaling factors for the emissions of fine-mode unspeciated aerosol (PMF), coarse-mode unspeciated aerosol (PMC), BC, OC, NO_x, SO₂, CO, and NMVOCs as well as the chemical concentrations of PM_2.5, PM_10−2.5 (PM₁₀ minus PM_2.5), NO₂, SO₂, CO, and the daily maximum 8 h O₃ (MDA8h O₃), which are formulated as follows:

where x denotes the vector of the state variable, c denotes the vector of the chemical concentrations of different species, and β denotes the vector of the scaling factors for the emissions of different species. Note that, although the chemical concentration variables are included in the state variable, they are not optimized simultaneously with the emission in the analysis step and are only used to estimate the covariance between the emissions and concentrations. Detailed descriptions of the state variables are available in Table 1.

Table 1Corresponding relationships between the chemical observations and adjusted emissions.

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The ensemble of the scaling factors for different species was generated independently using the same method of Kong et al. (2021), which has a medium size of 50 and considers the uncertainties of major air pollutant emissions in China, including SO₂, NO_x, CO, NMVOCs, ammonia, PM₁₀, PM_2.5, BC, and OC. The uncertainties of these species were considered to be 12 %, 31 %, 70 %, 68 %, 53 %, 132 %, 130 %, 208 %, and 258 %, respectively, according to the estimates of M. Li et al. (2017) and Streets et al. (2003). Note that in this study we did not perturb the emissions of different sectors to reduce the degrees of freedom in the ill-posed inverse estimation problem. Instead, we only perturbed the total emissions of different species. Therefore, only the total emissions of different species were constrained in this study. The ensemble of the chemical concentrations was then generated through an ensemble simulation based on NAQPMS and the perturbed emissions calculated by multiplying the a priori emissions by the ensemble of scaling factors. This treatment implicitly assumes that the uncertainty in the chemical concentration is mainly caused by the emission uncertainty. This makes sense on a monthly or yearly basis, considering that substantial changes in emissions are expected to have taken place during the clean-air action plans, which are subject to large uncertainty. However, the lack of consideration of other error sources, such as those of the meteorological simulation and the model itself, may lead to underestimation of the background error covariance and emission adjustment, which is a potential limitation of this study. In addition, the dust and sea salt emissions were not perturbed and constrained in this study, and thus the errors in the simulated fine- and coarse-dust emissions would influence the inversion of PM_2.5 and PM₁₀ emissions. As a result, the top-down estimated PM_2.5 and PM₁₀ emissions will contain errors in the simulated dust and sea salt emissions. In particular, we did not consider the emissions of coarse dust during the inversion process since there is large uncertainty in the simulated coarse-dust emissions of current dust emission schemes (Zeng et al., 2020; Kang et al., 2011). The large errors in the simulated coarse-dust concentration could significantly influence the inversion results of PM₁₀ emissions. For example, the simulated coarse-dust concentration could sometimes be several orders of magnitude higher than the observed PM₁₀ concentration, leading to overly low values of the inverse PM₁₀ emissions (approximately 0) over the regions that were not typical dust source regions but were influenced by the transportation of coarse dust. Therefore, we only used simulated PM₁₀ concentrations from other sources in the inversion of PM₁₀ emissions to avoid the influences of the overly large errors in the simulations. This is also similar to assuming that the coarse-dust emission is equal to 0 during the assimilation. However, in this way, the top-down estimated PM₁₀ emissions in this study would comprise all coarse-dust emissions, which should be noted by potential users. A detailed description of the ensemble generation is available in Kong et al. (2021).

2.3.2 Inversion algorithm

We used a deterministic form of the EnKF (DEnKF) proposed by Sakov and Oke (2008) to update the scaling factors of the emissions of different species, which is formulated as follows:

where x‾ denotes the ensemble mean of the state variable; the superscripts b and a, respectively, denote the a priori and a posteriori estimates; and X^a denotes the analyzed anomalies that can be used to calculate the uncertainty of the a posteriori emissions. K is the Kalman gain matrix, Beb is the background error covariance matrix calculated by the background perturbation X^b, y^o is the vector of the observation, and R is the observational error covariance matrix. H is the linear observation operator, which maps the model space to the observation space. λ is the inflation factor used to compensate for the underestimation of the background error caused by the limited ensemble size and unaccounted-for error sources and is calculated using the method of Wang and Bishop (2003):

where d is the observation innovation and p is the number of observations. Table S2 in the Supplement summarizes the calculated average value (standard deviation) of the used inflation factor for different species. It shows that the inflation factor over eastern China (including the NCP and SE regions) was generally around 1.0, suggesting that the original ensemble can represent the simulation errors of the different air pollutants well over these regions. The inflation factor is larger over western China (including the SW, NW, and Central regions), especially for PM₁₀ (36.0–78.1) and SO₂ (7.8–176.1), suggesting that the original ensemble may underestimate the simulation errors of the air pollutants. This is associated with the large biases in the simulated air pollutant concentrations over there and shows that the emission uncertainties assumed in our studies may be underestimated over these regions. This also highlights the importance of the use of the inflation method during the inversion; otherwise, it would lead to filter divergency caused by the underestimations of the background error covariance.

In order to reduce the influence of the spurious correlations on the performance of data assimilation, the EnKF was performed locally in this study in that the analysis was calculated grid by grid with the assumption that only measurements located within a certain distance (cutoff radius) from a grid point would influence the analysis results of this grid. The use of this local analysis method also allowed the inflation factor to be calculated locally and to vary in time and space, which can help characterize the spatiotemporal variations in errors, as we illustrated above. Similarly to Kong et al. (2021) and Kong et al. (2023b), the cutoff radius was chosen as 180 km for each species based on the wind speed and the lifespan of the species (Feng et al., 2020). The same local scheme with a buffer area was also employed during the inversion to alleviate the discontinuities in the updated state caused by the cutoff radius. A detailed description of the local analysis scheme is available in Kong et al. (2021).

Table 1 summarizes the corresponding relationships between the emissions and chemical concentrations. Similarly to Ma et al. (2019) and Miyazaki et al. (2012), we did not consider the interspecies correlation during the assimilation to prevent the spurious correlations between unrelated or weakly related variables. In most cases, observations of one particular species were only allowed to adjust emissions of the same species. The assimilation of PM_2.5 mass observation was more complicated as there are multiple error sources in the simulated mass concentrations of PM_2.5, not only from primary emission, but also from secondary production. In this study, the PM_2.5 mass observation was used to constrain the emissions of PMF, BC, and OC but was not used to constrain the emissions of its precursors to avoid the spurious correlations and nonlinear chemistry effects, similar to the scheme used in Ma et al. (2019). This is feasible as the emissions of primary PM_2.5 (i.e., PMF, BC, and OC) and the emissions of PM_2.5 precursors (e.g., SO₂, NO₂) were perturbed independently in our method, and thus the contributions of primary PM_2.5 emissions and secondary PM_2.5 productions to PM_2.5 mass could be isolated through the use of ensemble simulations. Meanwhile, the use of the iteration inversion method (which will be introduced later) can further reduce the influence of the errors in the precursors' emissions on the inversion of primary PM_2.5 emissions, because the errors of the precursors' emissions would be constrained by their own observations during the iterations. However, the lack of assimilation of speciated PM_2.5 observations may lead to uncertainties in the estimated emissions of PMF, BC, and OC, which is a potential limitation in the current work. For example, if the a priori simulated PM_2.5 equals the observations, the emissions of PMF, BC, and OC would not be adjusted by using the current method. However, in such cases, there may still be errors in the proportions of the emissions of different PM_2.5 components. To adjust the emissions of PMC, we used the observations of PM_10−2.5 to avoid the potential cross-correlations between PM_2.5 and PM₁₀ (Peng et al., 2018; Ma et al., 2019). For the NO_x emissions, although the O₃ concentrations are chemically related to the NO_x emissions, we did not use the O₃ concentrations to constrain the NO_x emissions in this study as there is a nonlinear relationship between O₃ concentration and NO_x emission, which would lead to incorrect adjustment of NO_x emissions (Tang et al., 2016).

Figure 3Time series of the a priori bias (blue lines), the a posteriori bias (red lines), and the emission increment (green lines) from 2013 to 2020 for the different species over the six regions of China.

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The inversion of NMVOC emissions is more difficult than that of other species due to the lack of long-term nationwide NMVOC observations and the strong chemical activity. Previous studies usually assimilated satellite observations of formaldehyde and glyoxal to constrain NMVOC emissions, such as Cao et al. (2018) and Stavrakou et al. (2015). However, these inversion studies were hindered by the NO_x–VOC–O₃ chemistry and the inherent uncertainty in satellite observations of formaldehyde and glyoxal. Considering the strong chemical relationship between O₃ and NMVOCs, some pioneering studies also explored the method of assimilating ground-level O₃ concentrations to constrain NMVOC emissions (Ma et al., 2019; Xing et al., 2020) and demonstrated the effectiveness of this approach. For example, Ma et al. (2019) found that the assimilation of O₃ concentrations could adjust NMVOC emissions in the direction of the bottom-up inventories, and the forecast skills of the O₃ concentrations were also improved, indicating that the constrained NMVOC emissions were improved relative to their a priori values. Inspired by these studies, we have made an attempt to constrain NMVOC emissions based on MDA8h O₃. The use of MDA8h O₃ rather than the daily mean O₃ concentration is meant to avoid the effects of the nighttime O₃ chemistry. For example, the simulation errors in the titration effects of NO_x may influence the simulated O₃ concentrations at night and affect the inversion results of the NMVOCs. An important issue that should be noted when using MDA8h O₃ to constrain the NMVOC emissions is the nonlinear interactions between NO_x, NMVOCs, and O₃. On the one hand, the O₃ concentrations are dependent on not only the NMVOC emissions, but also the NO_x emissions. The errors in the a priori emissions of NO_x would also contribute to the simulation errors of O₃ and deteriorate the inversion of the NMVOCs. The iteration inversion scheme could help deal with this issue as the errors in the NO_x emissions will be constrained by the NO₂ observations in the next iteration, which can reduce the influences of errors in the NO_x emission on the inversion of NMVOC emissions based on MDA8h O₃ concentrations. This is in fact similar to the approach used by Xing et al. (2020), who first constrained the NO_x emissions based on observations of NO₂ and then constrained the NMVOC emissions based on O₃ concentrations. Also, in Feng et al. (2024), the NO₂ observations were simultaneously assimilated to constrain the NO_x emissions to account for the influences of errors in the NO_x emissions on the NMVOC emissions, suggesting that the iteratively nonlinear joint inversion of NO_x and NMVOCs is an effective way of addressing the intricate relationship between VOC, NOx, and O₃ (Feng et al., 2024). Similarly, the errors in the CO emissions, which may be significant according to our following analysis, are also constrained in a similar way to reduce the potential influences on the inversion of the NMVOC emissions. On the other hand, the emission adjustments of NMVOCs may exhibit bidirectionality that is dependent on the VOC-limited or NO_x-limited regimes. According to Fig. 3, the NMVOC emissions were adjusted in alignment with the direction of the O₃ errors, suggesting a VOC-limited regime over urban areas in China, given that the O₃ observation sites are predominantly situated in urban areas. This is in agreement with Ren et al. (2022), who diagnosed the NO_x–VOC–O₃ sensitivity based on the satellite retrievals and found that the VOC-limited regimes are mainly located in urban areas in China. This suggests that the relationship between the O₃ concentrations and VOC emissions could be reasonably reflected by our inversion system, providing the feasibility of utilizing the O₃ observations to constrain the VOC emissions. Note that, due to the lack of observations of VOC components, we only optimize the gross emissions of the VOCs during the assimilation.

As we illustrated before, there exist nonlinear effects in the atmospheric chemistry which could influence the inversion results of different species. In addition, since we did not consider the temporal variations in the a priori emissions, it was expected that there would be significant biases in the a priori emissions for the years after 2013, as substantial changes in emissions were expected owing to the implementation of strict emission control measures. Such bias in the a priori emissions does not conform to the unbiased hypothesis of the EnKF, which could lead to incomplete adjustments of the a priori emissions and degrade the performance of the data assimilation (Dee and Da Silva, 1998). To address these issues, an iteration inversion scheme that was used previously in Kong et al. (2023b) was employed in this study. The main ideas of the iteration inversion scheme are to preserve the background perturbation X^b and to update the ensemble mean of the state variable xb¯ based on the model simulations driven by the inversion results of the kth iteration. Therefore, a new single model simulation needs to be conducted by using the a posteriori emission from the previous iteration as the input to update the ensemble mean of the original ensemble. This enables the observational information and the adjusted emissions to be promptly incorporated into the model, thereby providing feedback for the adjustments of emissions in the next iteration. However, we did not reassemble the ensemble simulation for each iteration due to the expensive computational cost of the ensemble simulation. Therefore, in each iteration calculation, the ensemble perturbations that were used to calculate the background error covariance matrix remain the same, with only the ensemble mean being updated based on the inversion results of the previous iteration. The state variable used in the (k+1)th inversions is then formulated as follows:

where c^k represents the model simulations driven by the inversed emissions of the kth iteration, cie represents the ith member of ensemble simulations with an ensemble mean of ce¯, β^k represents the updated scaling factors of the kth iteration, and βie represents the ith member of the ensemble of scaling factors with a mean value of βe¯. In each iteration, all emissions are updated simultaneously, and two rounds of iterations were conducted in this study based on our previous inversion study to maintain a balance between the inversion performance and the computational cost of the long-term inversions (Kong et al., 2023b).

2.3.3 Setup of inversion estimation

Based on this inversion scheme, we constrained the daily emissions of PMF, PMC, BC, OC, NO_x, SO₂, CO, and NMVOCs from 2013 to 2020, based on the daily averaged observations of PM_2.5, PM_10−2.5, NO₂, CO, and MDA8h O₃. However, due to the lack of enough speciated PM_2.5 observations, the model performance driven by the inversed emission for the BC, OC, and primary unspeciated PM_2.5 has not been evaluated thoroughly. It is thus currently unclear for the quality of the inversed emissions of BC, OC, and primary unspeciated PM_2.5. Also, the lack of speciated PM_2.5 observations could lead to uncertainties in the estimated emissions of PMF, BC, and OC, as we mentioned before. Considering this, similar to Kong et al. (2023b), although we made an attempt to estimate the emissions of BC, OC, and primary unspeciated PM_2.5, we have reservations about their inversion results and only provide the emissions of PM_2.5 (PMC + BC + OC) and PM₁₀ (PM_2.5 + PMC) in the current stage. In the future, we will collect more speciated PM_2.5 observations to comprehensively quantify the accuracy of their inversion results, after which the emissions of these species will be released. Meanwhile, the speciated PM_2.5 observations could be assimilated in the current inversion framework. This could provide us with further constraints on the emissions of BC, OC, and primary PM_2.5. Meanwhile, as mentioned in Sect. 2.3.1, the meteorological and model uncertainties were not considered in the ensemble simulation. Thus, the errors in the meteorological simulation would cause fluctuations in the daily emissions that contaminate the inversion results and are difficult to isolate from the inherent variations in emissions (Tang et al., 2013). Considering this, the daily emissions were averaged to monthly values to reduce the influences of random model errors after the assimilation.

4.2.1 Emission changes in particulate matter

Figure 6 shows the top-down estimated emission changes in PM_2.5 and PM₁₀ over China during the two clean-air action periods. Both PM_2.5 and PM₁₀ emissions decreased substantially, by 44.3 % and 21.2 %, respectively, from 2013 to 2020. By contrast, the top-down estimates showed increases in PM_2.5 and PM₁₀ emissions in 2014 and 2015, but this would be a spurious trend caused by the changes in observation sites that we discussed in Sect. S2. Therefore, the emissions in 2013 and 2014 were discarded to prevent the spurious trends. According to Fig. 6, the PM_2.5 emissions decreased by 14.5 % from 2015 (15.0 Tg) to 2017 (12.8 Tg), and the reduction in emissions was roughly uniform throughout the period, which was about 8 % compared to the previous years. The PM₁₀ emissions showed a smaller reduction rate (−7.2 %) than that of PM_2.5, decreasing from 40.1 Tg in 2015 to 37.2 Tg in 2017. Compared with the emission reduction rate during 2015–2017, both PM_2.5 and PM₁₀ showed higher emission reduction rates during 2018–2020, which were estimated to be 27.2 % and 25.5 %, respectively. The emission reductions in each year were also larger, especially for PM₁₀. For example, PM_2.5 and PM₁₀ emissions decreased by about 19.3 % and 14.0 % in 2019 compared to 2018. This may have been due to the fact that, in addition to the strict controls imposed on the industrial and power sectors during the 2013–2017 action period, the residential emissions were strengthened during the 2018–2020 action period. In particular, “coal-to-electricity” and “coal-to-gas” strategies were vigorously implemented in northern China during the 2018–2020 action to reduce coal consumption and related air pollutant emissions (Liu et al., 2016; S. Wang et al., 2020). Thus, our inversion results confirm the effectiveness of the controls on residential emissions in terms of reducing the emissions of PM_2.5 and PM₁₀. In addition, the control of non-point sources, such as blowing-dust emissions, was also strengthened during the 2018–2020 action period, which is consistent with the faster reduction in PM₁₀ emissions during 2018–2020. The annual trends of PM_2.5 and PM₁₀ emissions were also calculated in China using the Mann–Kendall trend test and the Theil–Sen trend estimation method, the results of which are summarized in Table 4. The calculation of emission trends can help extend the existing emission datasets forward in time to produce up-to-date products. The top-down estimated trends of PM_2.5 and PM₁₀ emissions were −1.4 and −2.6 Tg yr⁻¹ during 2015–2020, which is attributable to the strict emission control measures imposed during the two clean-air action plans. As mentioned, the decreasing trends were higher during 2018–2020 (−1.5 and −4.6 Tg yr⁻¹) than during 2015–2017 (−1.1 and −1.5 Tg yr⁻¹).

On the regional scale (Fig. S3 in the Supplement), it can be seen clearly that the PM_2.5 emissions decreased consistently over all the regions (by 59.8 % in NCP, 49.6 % in SE, 39.5 % in NE, 35.8 % in SW, 33.2 % in NW, and 41.0 % in Central) from 2015 to 2020. The NCP region showed the largest reduction in emissions among the six regions, with its emission reduction rate being almost larger than 10 % in each year. This is consistent with the strictest emission control policies having been imposed over the NCP region. The SE region showed a similar emission reduction to the NCP region, with its emission reduction rate being larger than 10 % in most of the years. Obvious increases in PM_2.5 emissions were found over the NW region from 2013 to 2015 owing to the increase in the number of observation sites in those years. After 2015, PM_2.5 emissions generally decreased over the NW region, while there was a slight rebound in PM_2.5 emissions in 2016 and 2018, possibly due to the influences of the errors in fine-dust emission. The Central region showed different characteristics of emission changes to the other regions insofar as it showed little change in PM_2.5 emissions during 2015–2018 but large reductions in 2019. This may be consistent with the control of emissions over the Fenwei Plain area (the part of the Central region where the emission intensity is highest) being weak during the 2013–2017 action plan but strengthened during the 2018–2020 action plan. In terms of the PM_2.5 emission trends over the different regions, the calculated PM_2.5 emission trends were about −0.32 Tg yr⁻¹ in NCP, −0.32 Tg yr⁻¹ in SE, −0.24 Tg yr⁻¹ in NE, −0.21 Tg yr⁻¹ in SW, −0.09 Tg yr⁻¹ in NW, and −0.15 Tg yr⁻¹ in Central from 2015 to 2020.

The changes in PM₁₀ emissions were generally similar to those of PM_2.5, i.e., with decreases in all the regions from 2015 to 2020 (Fig. S4 in the Supplement). The top-down estimated PM₁₀ emission reductions from 2015 to 2020 were about 3.5 Tg (40.0 %) in NCP, 2.6 Tg (35.5 %) in SE, 3.0 Tg (36.6 %) in NE, 2.0 Tg (35.9 %) in SW, 1.0 Tg (25.3 %) in NW, and 1.3 Tg (21.6 %) in Central. The calculated trends were about −0.64, −0.52, −0.51, −0.40, −0.20, and −0.27 Tg yr⁻¹, respectively. However, due to the influences of the changes in the number of observation sites, the PM₁₀ emissions over the NE, SW, and NW regions increased substantially from 2013 to 2015, while they decreased in almost all the years after 2015. Different from the other regions, the Central region showed increases in PM₁₀ emissions from 2015 to 2018 of about 0.92 Tg (14.9 %) but substantial decreases in 2019 and 2020. The result also shows that most PM₁₀ emission reductions were achieved during the 2018–2020 action plan. According to CAQIEI, the PM₁₀ emissions decreased by 0.64–2.3 Tg (17.4 %–31.8 %) from 2018 to 2020, which accounted for 48.4 %–169.0 % of the total reduction in emissions from 2015 to 2020. This again emphasizes the effectiveness of the control of blowing-dust emissions during the 2018–2020 action plan.

Table 5The calculated annual trends of the four gaseous emissions in China based on CAQIEI.

^∗ The trend is significant at the 0.05 significance level.

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Figure 7Emission changes in (a) SO₂, (b) CO, (c) NO_x, and (d) NMVOCs obtained from CAQIEI from 2013 to 2020.

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4.2.2 Emission changes in gaseous air pollutants

SO₂ and CO

Figure 7 shows the emission changes in different gaseous air pollutants in China from 2013 to 2020. Similar to the PM emissions, SO₂ and CO emissions decreased continuously during the two action plan periods, with top-down estimated emission reductions of approximately 9.6 Tg (54.1 %) and 166.3 Tg (35.7 %) for SO₂ and CO from 2015 to 2020, respectively. Meanwhile, both SO₂ and CO showed a significant decreasing trend from 2015 to 2020, with estimated trends of approximately −2.1 and −36.0 Tg yr⁻¹, respectively (Table 5). The reductions in SO₂ and CO emissions are closely consistent with the strict emission control measures imposed during the action plan periods, such as the phasing-out of outdated industrial capacities and high-emitting factories, the strengthening of emission standards for the industrial and power sectors, the elimination of small coal-fired industrial boilers, and the replacement of coal with cleaner energies, which reflect the effectiveness of the emission control measures during the two action plan periods. Reductions in SO₂ emissions were generally steady during the two action plan periods, which were approximately 4.2 Tg (23.8 %) from 2015 to 2017 and 2.5 Tg (23.5 %) from 2018 to 2020. However, CO showed a different emission reduction rate during the two action plan periods, with its emission reductions (67.1 Tg, 18.3 %) during 2018–2020 being larger than those (45.6 Tg, 9.8 %) during 2015–2017. This contrast may reflect the different emission control policies during the two clean-air action periods as well as the different emission distributions among the sectors between SO₂ and CO. According to the estimates of Zheng et al. (2018), the share of emissions from the industrial and power sectors for SO₂ (77 %) is nearly double that for CO (39 %). Thus, the smaller reduction in CO emissions than that of SO₂ during 2015–2017 provides evidence that the 2013–2017 action plan focused mainly on controlling the emissions from the industrial and power sectors. During the 2018–2020 action plan, strict control measures targeting the residential and transportation sectors were also implemented, which together account for 61 % of CO emissions but only 23 % of SO₂ emissions. As a result, CO showed a larger emission reduction rate during 2018–2020, while the emission reduction rate for SO₂ was similar to that during 2015–2017. The calculated trends of SO₂ and CO emissions during the two action plans are presented in Table 4, which are −2.1 and −1.3 Tg yr⁻¹ for SO₂ and −22.8 and −33.5 Tg yr⁻¹ for CO, respectively.

The reduction in SO₂ and CO emissions was also evident on the regional scale (Figs. S5 and S6 in the Supplement). According to the top-down estimation, the reduction in SO₂ emissions ranged from 0.44 to 2.42 Tg (41.7 %–69.9 %) from 2015 to 2020, with the NCP region exhibiting the largest reductions. The calculated decreasing trend of SO₂ emissions was also significant over all the regions, ranging from −0.08 Tg yr⁻¹ over the NW region to −0.57 Tg yr⁻¹ over the NCP region (Table 5). With regards to the emission reduction rate during the different action plans, the results suggest that the emission reduction rate of SO₂ was higher during 2015–2017 (by 20.8 %–39.8 %) than that during 2018–2020 (by 16.6 %–29.0 %) over the NCP, SE, NE, and SW regions. This may have been because, after the strict emission controls imposed upon industrial and power plants during the 2013–2017 action plan, the room for further reductions in SO₂ emissions became smaller during the 2018–2020 action plan over these regions. Although residential and vehicle emissions were controlled more strictly during the 2018–2020 action plan, in total they account for ∼20 % of anthropogenic SO₂ emissions in China (Zheng et al., 2018). Thus, the enhanced reductions in SO₂ emissions from the residential and transportation sectors may not have been able to fully compensate for the weakened reductions from the industrial and power sectors, leading to a smaller SO₂ emission reduction rate over these regions. In contrast, the SO₂ emission reduction rate during 2018–2020 (31.1 %–34.8 %) was higher than that during 2015–2017 (14.1 %–20.4 %) over the NW and Central regions. This may have been due to the fact that the emission controls over the NW and Central regions were relatively weak during the 2013–2017 action plan (as also evidenced by the emission reduction rates of other species) owing to their less-developed economies. During the 2018–2020 action plan, the emission controls over these two regions were strengthened, which led to their higher emission reduction rates. Accordingly, the enhanced SO₂ emission reduction rates over the NW and Central regions compensated for the weakened reduction rates over the other regions, leading to a steady SO₂ emission reduction rate on the national scale.

The reductions in CO emissions from 2015 to 2020 were approximately 14.9–42.3 Tg (21.6 %–51.4 %) over the different regions of China, with significant decreasing trends ranging from −3.0 to −8.7 Tg yr⁻¹ (Fig. S6 and Table 5). Consistent with the comparisons of national CO emission reduction rates between the two action plans, the emission reduction rates during 2015–2017 (4.4 %–24.6 %) were estimated to be smaller than those during 2018–2020 (12.2 %–24.6 %) over all the different regions, except for the Central region, where the CO emission reduction rates were similar during the two action plans (Fig. S6).

NO_x and NMVOCs

The top-down estimated NO_x and NMVOC emissions showed different changes to the other four species by increasing during 2015–2017 but decreasing during 2018–2020. Specifically, NO_x emissions increased slightly by 5.9 % from 2015 (25.2 Tg) to 2017 (26.6 Tg), with a nonsignificant increasing trend of 0.74 Tg yr⁻¹. Then, NO_x emissions began to decrease in 2018, with a top-down estimated emission reduction and a calculated trend of approximately 3.1 Tg (12.7 %) and −1.6 Tg yr⁻¹, respectively, from 2018 to 2020. NMVOCs showed stronger emission increases than did NO_x, with top-down estimated emission increases of approximately 12.7 Tg (27.6 %) and a calculated emission trend of approximately 6.3 Tg yr⁻¹ from 2015 to 2017. Similarly to NO_x, NMVOC emissions began to decrease after 2018, with a top-down estimated reduction of approximately 2.6 Tg (−4.4 %) from 2018 to 2020 and a calculated trend of approximately −1.3 Tg yr⁻¹.

The increases in NO_x and NMVOC emissions during 2015–2017 suggest that the 2013–2017 action plan may not have achieved desirable mitigation effects on these two species. For NO_x emissions, the upward trend may have been associated with the following factors. On the one hand, vehicle exhaust is one of the most important sources of NO_x in China, accounting for 31 % of all NO_x emissions nationally (Zheng et al., 2018). From 2013 to 2017, the number of vehicles in China continued to increase and reached 310 million in 2017, approximately 33.5 % higher than in 2013 (MEE, 2018), which led to increases in NO_x emissions from vehicles in China. On the other hand, although the 2013–2017 action plan was effective in reducing the NO_x emissions from coal-fired power plants by promoting denitrification facilities and an ultra-low emission standard, the mitigation impacts on industrial NO_x emissions may have been relatively small. For example, X. Y. Wang et al. (2019) compiled a unit-based emission inventory for China's iron and steel industry from 2010 to 2015, based on detailed survey results of approximately 4900 production facilities in mainland China. They found that there were almost no NO_x control measures in China's iron and steel industry during 2010–2015, resulting in a 12.4 % increase in China's NO_x emissions from the iron and steel industry in 2015 compared to 2010. In addition, although the penetration rate of denitrification facilities in China's cement industry reached 92 % in 2015, the actual operating rate of denitrification facilities in the cement industry was not desirable, due to the lack of online emission monitoring systems. According to the research results of the Ministry of Ecology and Environment, 800, 1300, and 1400 cement production kilns were equipped with selective non-catalytic denitrification facilities from 2013 to 2015, but the actual operating rates were only 51 %, 54 %, and 73 %, respectively (Liu et al., 2021). In addition, the new precalciner kilns used in the cement industry have a higher NO_x emission factor, such that the shift from traditional vertical kilns to precalciner kilns has to some extent increased the cement industry's emissions of NO_x (Liu et al., 2021). Thus, there is evidence that the mitigation effects of the industrial control measures on NO_x emissions may not be as significant as expected. Overall, the increased number of vehicles may have offset the emission mitigation effects brought about by the control of power plants, and the mitigation effects of controlling industrial NO_x emissions were also undesirable. Consequently, NO_x emissions in China may not have decreased and may even have increased slightly during the 2013–2017 action plan. Figure S7 in the Supplement further shows the changes in NO_x emissions over the different regions of China, revealing that NO_x emissions over the NCP, SE, NE, and SW regions were roughly unchanged (by less than 5 %) from 2015 to 2017, while they increased over the NW (18.6 %) and Central (17.5 %) regions. This is consistent with previous results and indicates that NO_x emissions may have increased over the NW and Central regions, possibly due to their increased human activities and weak emission controls.

In terms of NMVOC emissions, since the inversion results did not differentiate between anthropogenic and biogenic sources, the changes in NMVOC emissions may have been related to both anthropogenic and biogenic emissions. With respect to anthropogenic emissions, previous bottom-up studies suggested that China's NMVOC emissions did not decline during the 2013–2017 action plan due to the lack of effective control measures on the chemical industry and solvent use (Zheng et al., 2018; M. Li et al., 2019). According to the estimates of M. Li et al. (2019), China's NMVOC emissions from solvent use increased by 11.1 % in 2017 compared to those in 2015. Meanwhile, the increase in the number of vehicles in China may also have led to an increase in NMVOC emissions from transportation. Thus, the increases in NMVOC emissions during 2015–2017 estimated by our inversion inventory may be related to the increases in anthropogenic NMVOC emissions from the chemical industry, solvent use, and vehicles. For the trends of biogenic NMVOC emissions, the Copernicus Atmosphere Monitoring Service (CAMS) global emission inventory shows that there were only little changes in the biogenic NMVOC emissions in China from 2013 to 2018 (Sect. 4.3.3), suggesting little contributions of the biogenic sources to the increased NMVOC emissions in China. Figure S8 in the Supplement further shows the changes in NMVOC emissions over the different regions of China, which suggests consistent increases in NMVOC emissions from 2015 to 2017 over the different regions. According to the top-down estimations, NMVOC emissions increased by 30.5 %, 25.2 %, 18.5 %, 10.9 %, 50.5 %, and 63.1 % over the NCP, SE, NE, SW, NW, and Central regions, respectively. Again, the NW and Central regions exhibited the largest emission increases among the six regions, which is consistent with their elevated levels of human activity and weak emission controls.

The decrease in NO_x and NMVOC emissions after 2018 suggests that the emission control strategy of the Chinese government had reached a point of optimization. The 2018–2020 action plan strengthened not only the controls on the industrial and power sectors, but also the transportation sector, especially for diesel vehicles with high NO_x emissions. For example, the Chinese government released the Action Plan for the Control of Diesel Trucks and vigorously promoted an adjustment of the transportation structure of China by gradually improving the availability of rail transport. As a result, there was a downward trend in NO_x emissions in China. The top-down estimated reductions in NO_x emissions were approximately 0.81 Tg (17.2 %) over NCP, 0.98 Tg (14.0 %) over SE, 0.37 Tg (9.4 %) over NE, 0.51 Tg (12.2 %) over SW, 0.13 Tg (11.0 %) over NW, and 0.32 Tg (9.2 %) over the Central region (Fig. S7). The decrease in NMVOC emissions after 2018 may on the one hand have been related to the strengthening of vehicle controls during the 2018–2020 action plan, while on the other hand it may have been related to the promotion of clean heating plans in the northern China region, which reduced the emissions of NMVOCs from residential sources. However, the decreases in NMVOC emissions were smaller than those of NO_x, which were estimated to be 0.84 Tg (6.9 %) over NCP, 0.47 Tg (2.8 %) over SE, 0.98 Tg (10.1 %) over NE, and 0.53 Tg (14.1 %) over NW (Fig. S6). Different from other regions, the NMVOC emissions over the SW and Central regions remained almost unchanged during the 2018–2020 action plan (Fig. S8).

Figure 8Spatial distributions of the emission changes in different species during 2015–2017 (left panels), 2018–2020 (middle panels), and 2015–2020 (right panels) obtained from CAQIEI from 2013 to 2020.

Figure 9Emission distributions of (a) NO_x, (b) SO₂, (c) CO, (d) PM_2.5, (e) PM₁₀, and (f) NMVOCs among the different regions in China obtained from CAQIEI in 2015, 2017, and 2020.

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4.2.3 Changes in the distribution pattern of emissions in China

Due to the different emission control intensities over the different regions of China, the emission distribution patterns of the different species may also have been altered, which could have influenced the distributions of air pollution in China. Based on CAQIEI, we further investigated the emission distribution patterns, as well as their changes, during the two action plans. Maps of the emission changes in different species during 2015–2017 and 2018–2020 are presented in Fig. 8. The shares of emissions in 2015, 2017, and 2020 for each subregion of China are also presented (Fig. 9). It can be seen that the emission changes during 2015–2017 were more heterogenous than those during 2018–2020. The air pollutant emissions after the 2018–2020 action plan showed consistent reductions over most regions of China, while there were obvious emission increases detected from 2015 to 2017. This is consistent with the different emission control effects during the two clean-air action plans, as mentioned in the previous sections. Due to its strict emission control policies, the NCP region showed consistent emission reductions in SO₂, NO_x, CO, PM_2.5, and PM₁₀ during the two clean-air action plans. Accordingly, the shares of emissions in the NCP region continued to decrease during the two action plan periods (Fig. 9). For example, the share of SO₂ emissions in the NCP region decreased from 19.4 % to 15.4 % during the period of 2015–2017 and from 15.4 % to 12.7 % during the 2018–2020 action plan. In contrast, NMVOC emissions increased obviously over the NCP region from 2015 to 2017 and decreased from 2018 to 2020. However, the share did not change significantly, being roughly 20 % throughout both periods. As for the other regions, increases in SO₂, NO_x, PM_2.5, PM₁₀, and NMVOC emissions during 2015–2017 could be found over the Central region. More specifically, the emission increases were mainly located in the Fenwei Plain area of central China, which was due to the fact that this area was not included as a key region of emission controls during the 2013–2017 action plan. However, the Fenwei Plain area was added as a key emission control region during the 2018–2020 action plan, which is consistent with the emission reductions for these species over the Central region (Fig. 8). As a result, the shares of SO₂ and PM_2.5 emissions in the Central region increased during 2015–2017 but decreased during 2018–2020 (Fig. 9). However, the shares of NO_x, PM₁₀, and NMVOC emissions continued to increase over central China during the two clean-air action plans, which suggests larger roles of air pollutant emissions in that region. In contrast, the share of CO emissions in central China continued to decrease in the two action plans, from 17.7 % in 2015 to 13.4 % in 2020.

In terms of the shares of emissions in eastern and western China, the top-down estimation suggests increased shares of NO_x, PM_2.5, PM₁₀, and NMVOC emissions in western China after the two clean-air action plans (Fig. 9), which indicates slower emission reductions for these species in western China. However, the share of CO emissions in western China was reduced after the two clean-air action plans. Although the share of SO₂ emissions in western China increased during 2015–2017, this turned to a decrease during 2018–2020.

4.3.1 Magnitude

NO_x

Figure 10 shows the average emissions of different air pollutants in China during 2015–2018 obtained from CAQIEI and the previous emission inventories plus the natural sources we considered. Comparisons of the emission estimations on the regional scale and gridded scale are also presented (Fig. 11 and Fig. S9 in the Supplement). The results show that CAQIEI has slightly higher NO_x emissions in China than the other inventories. Considering that CAQIEI includes both anthropogenic and natural sources, this discrepancy could be explained by the natural NO_x sources. According to the estimations of CAMS and GFAS, the soil and biomass burning NO_x emissions are approximately 1.9 and 0.08 Tg yr⁻¹, which explains the higher NO_x emissions given by CAQIEI well. After consideration of the natural sources, MEIC, HTAPv3, and EDGARv6 agree well with our inversion results on the national scale, with their differences being within 1.0 %–7.4 %. The NO_x emissions estimated by ABaCAS, CEDS, and TCR-2 are slightly lower than CAQIEI and other emission inventories. However, the differences between CAQIEI and these inventories were found to range from 15.9 % to 21.3 %, which is within the previous estimated uncertainties of NO_x emissions in China (Kurokawa and Ohara, 2020; M. Li et al., 2017; S. Li et al., 2023). These results suggest that the total NO_x emissions in CAQIEI are generally consistent with the current estimations of the anthropogenic and natural NO_x emissions in China. On the regional scale, the top-down estimated NO_x emissions show good agreement with the previous emission inventories over the NCP and SE regions, with their differences ranging from 1.0 % to 26.8 %, suggesting good consistency in the estimations of NO_x emissions over these two regions. This makes sense because NCP and SE are the two most developed regions in China, where surveys and research on emissions are the most sufficient. The differences are larger over the other regions. In the NE region, CAQIEI has higher NO_x emissions than the other inventories by 5 %–70 %, suggesting higher anthropogenic or biomass burning emissions over there. The estimations made by MEIC, CEDS, and TRC-2 are closer to our estimates, with their differences being approximately 5.4 %–23.3 %, while the differences are larger for ABaCAS, HTAPv3, and EDGARv6 (36.7 %–70.0 %). Over the SW and Central regions, there are large diversities in the previous emission inventories, with estimations by HTAPv3 and EDGARv6 almost double those of MEIC, ABaCAS, CEDS, and TCR-2. CAQIEI suggests a middle estimation which is within the range of previous emission inventories. In the NW region, CAQIEI is consistently higher than other inventories, by 22.7 %–64.2 %, which suggests a potential missing source of the NO_x emissions over this region.

SO₂

For SO₂ emissions, since natural sources contribute little (only about 0.02 Tg yr⁻¹) to them in China, the discrepancies between CAQIEI and previous emission inventories are mainly attributable to the differences in anthropogenic emissions. As shown in Fig. 10, CAQIEI agrees well with HTAPv3 and CEDS on the national scale, with their differences being approximately ±2 %, but it is higher than MEIC, ABaCAS, and TCR-2 by 17.4 %–32.9 %. In contrast, EDGARv6 may have a positive bias in its estimated SO₂ emissions, which are roughly double those of CAQIEI and other inventories. On the regional scale, our results agree well with MEIC, ABaCAS, HTAPv3, CEDS, and TCR-2 over the NCP region, with their differences ranging from 1.0 to 18.1 %. In the SE region, CAQIEI suggests lower SO₂ emissions than previous emission inventories, except for TCR-2. The differences are relatively smaller for the MEIC and ABaCAS inventories by around −15 % but are larger for HTAPv3, EDGARv6, and CEDS (ranging from −47.3 % to −113.2 %). In contrast, CAQIEI suggests higher SO₂ emissions than all previous emission inventories over the NE region by about 14.8 %–132.0 %, indicating possible missing sources over there. Similarly, CAQIEI and HTAPv3 suggest higher SO₂ emissions than MEIC, ABaCAS, CEDS, and TCR-2 by 27.0 %–75.6 % in the NW region and by 44.3 %–77.7 % in the Central region.

Table 6The top-down estimated CO emissions in China from the previous inventories.

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CO

For CO emissions, CAQIEI is substantially higher than the previous emission inventories, with the estimated CO emissions of CAQIEI being about 3 times higher than the bottom-up inventories and more than 2 times the top-down estimates made by TCR-2. According to GFAS, the average rate of CO biomass burning emissions in China from 2015 to 2018 was about 3.4 Tg yr⁻¹. Yin et al. (2019), based on MODIS fire radiative energy data, also estimated China's CO biomass burning emissions to be about 5.0 (2.3–7.8) Tg yr⁻¹. The biogenic CO emissions obtained from the CAMS global emission inventory were approximately 2.3 Tg yr⁻¹. According to these estimates, natural CO emissions in China have a magnitude of approximately 10, which is rather small compared with the anthropogenic sources and cannot explain the large discrepancies between CAQIEI and other inventories. Thus, CAQIEI suggests much higher anthropogenic CO emissions in China than in the existing emission inventories. In fact, the potential underestimation of CO anthropogenic emissions has been investigated in previous studies and is regarded as the main reason for the negative bias in global or hemispheric CO simulations (Stein et al., 2014; Gaubert et al., 2020). Regionally, Kong et al. (2020) compared a suite of 13 modeling results from six different CTMs – i.e., NAQPMS, CMAQ, WRF-Chem, NU-WRF, NHM-Chem, and GEOS-Chem – with observations over the NCP and Pearl River Delta regions in the framework of the Model Inter-Comparison Study for Asia III (MICS-Asia III) and found consistent negative biases in the CO simulations of all the models, pointing toward potential underestimations of CO emissions in China. Previous inversion studies have also reported higher a posteriori CO emissions than their a priori emission inventories (Bergamaschi et al., 2000; Miyazaki et al., 2012; Petron et al., 2002, 2004; Tang et al., 2013; Gaubert et al., 2020). For example, the constrained CO emissions reported by Gaubert et al. (2020) are 80 % higher than the CEDS over northern China. Our inversion results are consistent with these inversion studies, suggesting higher anthropogenic CO emissions in China. However, direct evidence in support of such high CO emissions in China reported by our study is still limited currently. Thus, we compiled more inversion results in the period 2013–2020 from previous studies to further validate our inversion results, which are summarized in Table 6. It can be seen clearly that there are large differences in the estimated CO emissions between the inversion results based on surface observations and those based on satellite data. Our inversion results are consistent with the results of Feng et al. (2020), with China's CO emissions in December 2017 estimated at approximately 1500.0 and 1388.1 kt d⁻¹, respectively. In addition, Feng et al. (2020) used the CMAQ model to constrain CO emissions, which is different from the model we used. This may indicate that the model uncertainty would not significantly influence the inversion results of CO emissions. However, the top-down estimated CO emissions based on satellite data (163.6–553.4 kt d⁻¹) are much lower than those based on surface observations, although they are all higher than their a priori emissions. The lower CO emission estimations based on satellite data assimilation may be attributable to the lower sensitivities of satellite data to surface concentrations, suggesting that the assimilation of satellite data alone may not be adequate for correcting the negative biases in the a priori emissions. This deficiency was also shown by Miyazaki et al. (2020a), who found undercorrected surface CO emissions in the extratropics of the Northern Hemisphere in TCR-2. However, the assimilation of surface observations can be influenced by the uncertainties in the modeled vertical mixing, which could lead to the uncertainties in the inversed CO emissions based on surface observations. Therefore, the inversed CO emissions in CAQIEI could be partly supported by previous inversion studies based on surface observations, but more evidence is still needed to justify the magnitude of the inversed CO emissions. Besides anthropogenic sources, the chemical production of CO via oxidation of methane (CH₄) and NMVOCs, together with the CO sinks via the hydroxyl radical (OH) reaction, also influences the simulation of CO (Stein et al., 2014; Gaubert et al., 2020; Müller et al., 2018). Due to the important role of OH in the chemical production and sinks of CO, the inversion of CO emissions is sensitive to the modeled OH abundance and the emissions of CH₄ and NMVOCs. According to the estimation of Müller et al. (2018), the magnitude of inversed CO emissions in China could differ by more than 40 % when different levels of OH concentrations are used in the model. Thus, the much higher estimations of CO emissions in our inversion results may also be partly explained by the underestimation of CO chemical production or the overestimation of the CO sink.

PM_2.5

In terms of PM_2.5, CAQIEI suggests higher emissions than ABaCAS, HTAPv3, and EDGARv6 of about 20 % and 47.7 % higher emissions than MEIC on the national scale. Larger discrepancies mainly occur in the NE and NW regions, where CAQIEI is about 27.2 %–114.9 % and 83.2 %–143.2 % higher than in the previous inventories. The differences in the estimated PM_2.5 emissions may be related to the uncertainties in the biomass burning or anthropogenic sources in the NE region (J. Wu et al., 2020), while in the NW region the errors in the fine-dust emissions may also contribute to the differences in the estimated PM_2.5 emissions there. The differences in the estimated PM_2.5 emissions are relatively smaller in the NCP and SE regions, ranging from −18.9 % to 20.4 %, suggesting better agreement in the estimated PM_2.5 emissions over these two regions. In the SW region, CAQIEI is closer to HTAPv3 and EDGARv6, with their differences being about 6.3 % and −9.5 %, respectively, which is higher than MEIC and ABaCAS by 54.2 % and 28.6 %, suggesting higher uncertainty in the estimated PM_2.5 emissions over there.

PM₁₀

For PM₁₀ emissions, it is difficult to directly compare CAQIEI with previous emission inventories since CAQIEI contains not only anthropogenic and biomass burning emissions, but also coarse-dust emissions. As a result, the estimated emissions of PM₁₀ by CAQIEI are substantially higher than those of previous inventories, especially over the NW, Central, and NE regions (Fig. 11), which are the typical natural windblown dust source regions in China (Zeng et al., 2020). Besides the naturally windblown dust of arid desert regions (Prospero et al., 2002), large amounts of coarse-dust emissions also stem from anthropogenic sources, including anthropogenic fugitive, combustion, and industrial dust (AFCID) from urban sources (Philip et al., 2017) and anthropogenic windblown dust from human-disturbed soils due to changes in land use practices, deforestation, and agriculture (Tegen et al., 1996). Therefore, although the other regions are not typical natural windblown dust source regions in China, there are still high levels of coarse-dust emissions from anthropogenic sources there (also called “urban dust”), which may be the main reason for the large deviation in the estimated PM₁₀ emissions between CAQIEI and the previous inventories. On the one hand, although AFCID is included in MEIC, ABaCAS, HTAPv3, and EDGARv6, it is difficult for current bottom-up emission inventories to completely represent fugitive sources (Philip et al., 2017). On the other hand, the anthropogenic windblown dust emissions have not been included in current bottom-up emission inventories, which is an important source of coarse dust in urban areas according to the estimations of Li et al. (2016) and is another important contributor to the differences between CAQIEI and previous emission inventories.

NMVOCs

For NMVOC emissions, since CAQIEI includes both anthropogenic and natural sources, its estimated NMVOC emissions are much higher than those estimated by previous emission inventories. After consideration of natural sources, CAQIEI suggests close estimations of the NMVOC emissions with the MEIC, HTAPv3, and CEDS inventories on the national scale, with their differences being about 1.5 %–12.5 %. The estimated NMVOC emissions by ABaCAS and EDGARv6 are slightly lower than CAQIEI by 17.8 % and 24.6 %, respectively. On the regional scale, CAQIEI suggests higher NMVOC emissions over northern China (NCP, NE, and NW), with the top-down estimated NMVOC emissions of about 30.4 %–81.4 %, 27.3 %–72.1 %, 79.3 %–116.8 %, and 8.7 %–57.5 % being higher than those of the previous emission inventories. In contrast, CAQIEI suggests lower NMVOC emissions over the SE region, with the estimated NMVOC emissions of CAQIEI being about 21.2 %–27.6 % lower than those of MEIC, ABaCAS, HTAPv3, and CEDS. These results are consistent with the previous inversion results based on the satellite observations, which suggest higher NMVOC emissions over the NCP region and lower NMVOC emissions over southern China (Souri et al., 2020). Over the SW region, CAQIEI shows good agreement with MEIC, ABaCAS, and CEDS, with CAQIEI being slightly lower than these inventories by 1.0 %–8.9 %, but it is lower than HTAPv3 and EDGARv6 by about 38.6 % and 29.1 %, respectively. Again, it should be noted that the comparisons of NMVOC emissions are conducted on the basis of natural emissions estimated by CAMS and GFAS and could be more sensitive to the used natural sources than other species considering the larger contributions of the natural source to the NMVOC emissions.

Figure 12Comparisons of the monthly profiles of (a) NO_x, (b) SO₂, (c) CO, (d) PM_2.5, (e) PM₁₀, and (f) NMVOCs over China averaged from 2015 to 2018 between CAQIEI and previous inventories added with natural sources.

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4.3.2 Seasonality

Figure 12 presents the monthly profiles of different air pollutants obtained from different emission inventories. Note that the natural sources have been added to the previous inventories to facilitate the comparisons. The results show that different emission inventories give similar monthly profiles of NO_x and CO emissions, with higher emissions during wintertime and lower emissions during summertime, which suggests relatively lower uncertainty in the estimated monthly profiles for these two species. For SO₂ emissions, CAQIEI yields a stronger monthly variation than the other inventories, with a higher proportion from January to March and a lower proportion during summertime. Due to the influences of dust emissions, the top-down estimated PM_2.5 and PM₁₀ emissions show higher proportions than the other emission inventories during the spring season, especially for PM₁₀. However, the proportions of emissions during fall and winter are lower than in the other inventories. The monthly profiles of NMVOC emissions are generally consistent, with higher emissions during summer due to the enhanced biogenic emissions. However, the profile of CAQIEI is flatter than the previous inventories and suggests a higher proportion during springtime. In addition, the timings of peak values of NMVOC emissions are also different between CAQIEI and the previous inventories, with CAQIEI showing peak values during May–July but the other inventories suggesting peaks during June–August.

Figure 13Time series of annual emissions of (a) NO_x, (b) SO₂, (c) CO, (d) PM_2.5, (e) PM₁₀, and (f) NMVOCs over China from 2013 to 2020 obtained from CAQIEI and previous inventories. Note that the natural sources were not included in the previous inventories in this figure.

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4.3.3 Emission changes during 2015–2018

The top-down estimated emission changes in different air pollutants during 2015–2018 were also compared with previous emission inventories. Figure 13 shows the time series of the total emissions of different species from 2013 to 2020 obtained from CAQIEI and other emission inventories. Comparisons of the emission changes over the regional scales are also presented in Figs. S10–S15 in the Supplement. Before the comparison, we first analyze the trends of natural sources in China to investigate their influences on the emission changes in different species based on the CAMS emission inventory and GFAS. Note that we only consider the soil, biogenic, and biomass burning emissions for the natural sources; the trends of dust emissions in China are not analyzed, which may lead to uncertainty when comparing the emission changes in PM_2.5 and PM₁₀. As shown in Fig. S16 in the Supplement, the natural sources of NO_x and NMVOC emissions changed little during 2013–2018. The other species had small decreasing trends from 2013 to 2018. However, considering the small contributions of natural sources to their emissions, these small trends would not significantly influence their emission trends. For the dust emissions, previous studies have indicated a declining trend in dust activity in China from 2001 to 2020 (Wu et al., 2022; Wang et al., 2021) due to weakened surface wind and increased vegetation cover and soil moisture. These results suggest that the emission trends in CAQIEI would mainly be driven by the anthropogenic sources of the gaseous air pollutants based on the estimations of CAMS and GFAS, while its estimated emission trends of PM_2.5 and PM₁₀ would be influenced by the declining trends in dust emissions in China, which should be noted when comparing the emission changes in PM_2.5 and PM₁₀.

Figure 14Comparisons of the calculated emission changes in NO_x, SO₂, CO, PM_2.5, PM₁₀, and NMVOCs over China from 2015 to 2018 between CAQIEI and previous inventories. Note that the natural sources were not included in the calculation of the emission changes in this figure.

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As shown in Fig. 14, all the emission inventories agree that the NO_x, SO₂, CO, PM_2.5, and PM₁₀ emissions in China were reduced from 2015 to 2018, except for the increases in CO emissions estimated by TCR-2, which confirms the effectiveness of the emission control policies implemented during the clean-air action plans. Meanwhile, most emission inventories agree that SO₂ is the species with the largest emission reduction rate, followed by PM_2.5, indicating better emission mitigation effects of these two species (Fig. 14). However, CAQIEI suggested lower emission reduction rates than the other emission inventories for most of the species, especially for NO_x, PM₁₀, and NMVOCs (Fig. 14). The estimated emission reduction rate of NO_x obtained from CAQIEI is about −2.7 %, which is lower than the values of MEIC (−9.7 %), ABaCAS (−23.0 %), HTAPv3 (−13.0 %), and CEDS (−9.0 %). As we discussed in Sect. 4.2.2, “NO_x and NMVOCs”, the small reductions in NO_x emissions in CAQIEI would be related to the increased vehicle emissions and the undesirable mitigation effects of the industry control. In fact, these factors have been considered in some bottom-up emission inventories, such as MEIC. The differences between our inversion results and previous inventories thus reflect uncertainty in the quantifications of the effects of these factors on the NO_x emissions due to the lack of sufficient statistics on the mobile vehicle sector or other sectors. Our inversion results suggest larger adverse effects of these two factors on the reductions in NO_x emissions in China. According to Fig. S17 in the Supplement, the differences between CAQIEI and these inventories mainly occur in the SE, SW, NW, and Central regions, with the emission reduction rate estimated by CAQIEI being substantially lower than those estimated by previous inventories. In particular, CAQIEI suggests increases in NO_x emissions over the Central region, which is contrary to the previous emission inventories. Better agreement is achieved over the NCP and NE regions, with the emission reduction rate estimated by CAQIEI being closer to those of MEIC, HTAPv3, and CEDS. The NO_x emission reduction rates estimated by EDGARv6 (−3.3 %) and TCR-2 (−1.7 %) are closer to our results on the national scale, but they estimated a lower NO_x emission reduction rate than our estimate over the NCP and NE regions.

Similarly, the emission reduction rate of PM₁₀ obtained from CAQIEI (−10.8 %) is lower than those estimated by MEIC (−27.9 %), ABaCAS (−33.0 %), and HTAPv3 (−27.8 %) on the national scale (Fig. 14). A lower PM₁₀ emission reduction rate of CAQIEI than these inventories also exists in the different regions of China, except SW (Fig. S17). In particular, and different from previous emission inventories, CAQIEI suggests that PM₁₀ emissions may have actually increased over the Central region. Considering that dust emissions may have decreased from 2015 to 2018 owing to weakened dust events (Wang et al., 2021), the increase in PM₁₀ emissions over the Central region may reflect the increases in anthropogenic sources. Meanwhile, we also found that CAQIEI estimated the emission reduction rate of PM₁₀ to be smaller than that of PM_2.5. This is different from previous emission inventories, which show similar emission reduction rates for PM_2.5 and PM₁₀. Considering that PM₁₀ emissions include PM_2.5 and PMC emissions, the lower emission reduction rate of PM₁₀ than PM_2.5 in CAQIEI suggests that PMC emissions may have decreased more slowly than PM_2.5 emissions from 2015 to 2018.

In terms of NMVOCs, most previous inventories, including MEIC, EDGARv6, and CEDS, suggest a weak decrease in China, with the estimated rates of change in emissions ranging from −0.8 % to −4.6 %. The emission reduction rate estimated by ABaCAS is larger, reaching up to −14.2 %. In contrast, CAQIEI suggests an opposite emission change to these inventories, with the estimated NMVOC emissions increasing by 26.6 % from 2015 to 2018. HATPv3 also suggests an increase in NMVOC emissions but with a much lower rate of increase (2.7 %). Similar results were also found on the regional scale (Fig. S17), especially over the NCP, NE, and Central regions, where NMVOC emissions could have increased by 38.0 %, 38.3 %, and 60.0 %, respectively, according to the estimates of CAQIEI. As we discussed in Sect. 4.2.2, “NO_x and NMVOCs”, the increases in NMVOC emissions estimated in CAQIEI may be related to the increased anthropogenic NMVOC emissions from the chemical industry, solvent use, and vehicles. Therefore, similar to the NO_x emissions, the differences between CAQIEI and the previous inventories reflect the uncertainty in the quantifications of the impacts of these factors and suggest larger adverse effects of these factors on the emission reductions in NMVOC emissions than the previous inventories.

The differences in the estimated emission reduction rates between CAQIEI and previous inventories are relatively smaller for SO₂ and PM_2.5 emissions. The emission reduction rate of SO₂ estimated by CAQIEI is close to that estimated by MEIC and CEDS, ranging from −34.7 % to −44.3 %. ABaCAS and HTAPv3 estimate higher emission reduction rates of approximately −58.5 % and −53.7 %, respectively. EDGARv6 and TCR-2 may underestimate the reduction rate of SO₂, with estimates of only about −7.0 % and −9.1 %, respectively. This may be because EDGARv6 underestimates the FGD (flue-gas desulfurization) device penetration or SO₂ removal efficiencies of FGD in China. On the regional scale (Fig. S17), the top-down estimated SO₂ emission reduction rate agrees reasonably with that of MEIC over the NCP, NE, and SE regions, but these inventories estimate different SO₂ emission reduction rates over the SW, NW, and Central regions. The reduction rates estimated by MEIC over the SW and Central regions are higher than those given by CAQIEI but are lower over the NW region. The other emission inventories also give different emission reduction rates, suggesting large uncertainty in the estimated SO₂ emission reduction rates over these three regions. In terms of PM_2.5, CAQIEI's estimated emission reduction rate agrees well with those of MEIC and HTAPv3 on the national scale, which is about 24 %–27 % from 2015 to 2018. The emission reduction rates of PM_2.5 estimated by EDGARv6 are lower than our estimates and those of other inventories, which were about 9 %. On the regional scale, our results show good consistency with MEIC and HTAPv3 over the NCP, NE, SE, and SW regions, but they have large differences over the NW and SW regions.

Different from the other species, the CO emission reduction rate estimated by CAQIEI (−21.3 %) is higher than in most of the previous inventories, including MEIC (−13.0 %), ABaCAS (−11.6 %), EDGARv6 (−4.7 %), and CEDS (−11.7 %), suggesting larger mitigation effects on CO emissions than in other inventories. HTAPv3 agrees with our results, with an estimated emission reduction rate of approximately −22.0 %. On the regional scale (Fig. S17), our result is consistent with MEIC over the NCP and SE regions, with estimated emission reduction rates for CO of around 24 % and 15 %, respectively, while in the other regions the emission reduction rate estimated by CAQIEI is higher than that estimated by MEIC. TCR-2 shows opposite changes in CO emissions compared with the other inventories insofar as it suggests increases in CO emissions over the different regions of China. Since the emissions in TCR-2 are constrained by satellite observations, the differences between our results and those of TCR-2 highlight that the observations used to constrain the emissions may have a large influence on the estimated emission changes. In this case, the estimated changes in CO emissions by CAQIEI are more consistent with those estimated by other bottom-up inventories. Considering this, TCR-2 may have uncertainties in its estimated changes in CO emissions in China from 2015 to 2017, which could be related to the suboptimal performance of the data assimilation caused by the underestimated background errors of CO or an overly short assimilation window for the CO emission estimates (Miyazaki et al., 2020a).