Journal cover Journal topic
Atmospheric Chemistry and Physics An interactive open-access journal of the European Geosciences Union
Journal topic
Atmos. Chem. Phys., 19, 8619–8650, 2019
https://doi.org/10.5194/acp-19-8619-2019
Atmos. Chem. Phys., 19, 8619–8650, 2019
https://doi.org/10.5194/acp-19-8619-2019

Research article 08 Jul 2019

Research article | 08 Jul 2019

# The 2015 and 2016 wintertime air pollution in China: SO2 emission changes derived from a WRF-Chem/EnKF coupled data assimilation system

The 2015 and 2016 wintertime air pollution in China: SO2 emission changes derived from a WRF-Chem/EnKF coupled data assimilation system
Dan Chen1, Zhiquan Liu2, Junmei Ban2, and Min Chen1 Dan Chen et al.
• 1Institute of Urban Meteorology, China Meteorological Administration, Beijing, 100089, China
• 2National Center for Atmospheric Research, Boulder, CO 80301, USA

Correspondence: Zhiquan Liu (liuz@ucar.edu) and Dan Chen (dchen@ium.cn)

Abstract

Ambient pollutants and emissions in China have changed significantly in recent years due to strict control strategies implemented by the government. It is of great interest to evaluate the reduction of emissions and the air quality response using a data assimilation (DA) approach. In this study, we updated the WRF-Chem/EnKF (Weather Research and Forecasting – WRF, model coupled with the chemistry/ensemble Kalman filter – Chem/EnKF) system to directly analyze SO2 emissions instead of using emission scaling factors, as in our previous study. Our purpose is to investigate whether the WRF-Chem/EnKF system is capable of detecting the emission deficiencies in the bottom-up emission inventory (2010-MEIC, Multi-resolution Emission Inventory for China), dynamically updating the spatial–temporal emission changes (2010 to 2015/2016) and, most importantly, locating the “new” (emerging) emission sources that are not considered in the a priori emission inventory. The 2010 January MEIC emission inventory was used as the a priori inventory (to generate background emission fields). The 2015 and 2016 January emissions were obtained by assimilating the hourly surface SO2 concentration observations for January 2015 and 2016. The SO2 emission changes for northern, western, and southern China from 2010 to 2015 and from 2015 to 2016 (for the month of January) from the EnSRF (ensemble square root filter) approach were investigated, and the emission control strategies during the corresponding period were discussed. The January 2010–2015 differences showed inhomogeneous change patterns in different regions, including (1) significant emission reductions in southern China; (2) significant emission reductions in larger cities with a wide increase in the surrounding suburban and rural regions in northern China, which may indicate missing raw coal combustion for winter heating that was not taken into account in the a priori emission inventory; and (3) significantly large emission increases in western China due to the energy expansion strategy. The January 2015–2016 differences showed wide emission reductions from 2015 to 2016, indicating stricter control strategies having been fully executed nationwide. These derived emission changes coincided with the period of the energy development national strategy in northwestern China and the regulations for the reduction of SO2 emissions, indicating that the updated DA system was possibly capable of detecting emission deficiencies, dynamically updating the spatial–temporal emission changes (2010 to 2015/2016), and locating newly added sources.

Forecast experiments using the a priori and updated emissions were conducted. Comparisons showed improvements from using updated emissions. The improvements in southern China were much larger than those in northern and western China. For the Sichuan Basin, central China, the Yangtze River Delta, and the Pearl River Delta, the BIAS (bias, equal to the difference between the modeled value and the observational value, representing the overall model tendency) decreased by 61.8 %–78.2 % (for different regions), the RMSE decreased by 27.9 %–52.2 %, and CORR values (correlation coefficient, equal to the linear relationship between the modeled values and the observational values) increased by 12.5 %–47.1 %. The limitation of the study is that the analyzed emissions are still model-dependent, as the ensembles are conducted using the WRF-Chem model; therefore, the performances of the ensembles are model-dependent. Our study indicated that the WRF-Chem/EnSRF system is not only capable of improving the emissions and forecasts in the model but can also evaluate realistic emission changes. Thus, it is possible to apply the system for the evaluation of emission changes in the future.

1 Introduction

China is one of the fastest growing countries in the world and produces a significant amount of air pollutant emissions. To control pollution, a series of strict control strategies has been implemented by the government since 2010, including both long-term pollution control strategies and temporary emergency measures activated under different air pollution alerts, which has led to large spatial–temporal changes in emissions (factory mitigation from urban to rural regions, industries staggering peak production, and so on.). These spatial–temporal emission changes are difficult to reflect in a timely manner in both “bottom-up” emission inventories and air quality models, which creates large uncertainties. A lot of regional air quality modeling work has been conducted to evaluate the emission reduction and air quality response by comparing the simulations of a baseline scenario and an emission reduction scenario. However, there are large uncertainties in those simulations due to the deficiencies of the models, including the meteorological/chemical initial/boundary conditions, the chemistry process parameterization, and, most importantly, the uncertainties of emission inputs from the bottom-up emission inventories. On the one hand, these three aspects lead to error accumulation and large biases compared with those from observations in the baseline scenario simulations. On the other hand, for emission reduction scenarios during special control events, the common approach is to assume that the control policies are executed to different extents, and several emission reduction ratios are calculated and simulated. The ratio producing results best matching the observations is assumed to be the real emission reduction ratio. This methodology is useful for forward simulations to project the effects of emission reduction but is not straightforward for evaluating whether the control policies are strictly implemented and whether reductions are actually achieved. The forward approach using these models can neither accurately evaluate the spatial–temporal emission changes nor locate newly added sources that are missing from the bottom-up emission inventory.

Various data assimilation (DA) and inversion approaches (e.g., Evensen, 1994; Houtekamer et al., 2005; Hunt et al., 2007; Lee et al., 2011; Pagowski and Grell, 2012; Miyakazi et al., 2012, 2013; Dai et al., 2014; McLinden et al., 2016) have been conducted to improve forecast skill and optimize source emissions. The variational data assimilation approach can greatly improve the initial condition by integrating the observational data into the model forecast; however, the benefits quickly disappear due to the inaccurate emissions in the model. The inversion approach (also called the “top-down” approach) has been of great interest, as the observations can be directly used to constrain and optimize emissions. There are various methods by which to implement the top-down emission constraints, including the adjoint approach (e.g., Guerretta and Henze, 2017), the inverse approach combining satellite/surface observational data with regional/global models, and/or the ensemble Kalman filter (EnKF). Because the adjoint method involves a huge amount of 4D-Var code development, its application is rather limited. The inverse approach using regional/global models and/or the ensemble Kalman filter method are much more flexible; thus, they are commonly used (Miyazaki et al., 2012; Tang et al., 2011, 2013, 2016). For the inverse approach using satellite data, due to satellite data availability, monthly data are usually used in studies, which can only provide information on the historical trends of the total emission amount at the regional and national levels. Compared with satellite data, the use of intensive hourly surface observations as constraints can provide more spatial–temporal characteristics of emissions; thus, they can be used to evaluate the spatial–temporal emission changes and to locate newly added sources that are missing from the bottom-up emission inventory.

In our previous study, Peng et al. (2017, 2018) extended the ensemble square root filter algorithm to simultaneously optimize the chemical initial conditions and the emission input, aiming to improve the forecasting of atmospheric PM2.5, SO2, NO2, O3, CO, and PM10 using the WRF-Chem/EnSRF (Weather Research and Forecasting, WRF, model coupled with the chemistry/ensemble square root filter, EnSRF) system. The surface observational data are used as constraints to update the initial conditions and relevant emissions (through emission scaling factors) by minimizing the error variances. The WRF-Chem is used to propagate the initial ensemble forward in time, and the EnSRF is used to assimilate the observations and update the initial chemical conditions and emissions. In air quality models, deficiencies of concentration simulations come from various aspects, including the initial conditions, emissions, meteorology, chemistry, transport, among others. Especially for PM2.5 and PM10 simulations in China, the significant differences between the models and observations possibly stem from the deficiency of the chemistry representation in the model, including missing paths of secondary organic aerosols (e.g., Chen et al., 2016) and heterogeneous reactions (e.g., Zheng et al., 2015), in addition to emissions. However, to reduce the error variance, emission adjustments may compensate for the model error, which leads to unrealistic/excessive emission adjustment. Because the purpose was to improve the forecasting of chemical species, evaluations of emission changes were not conducted in the previous two studies.

In this study, we introduce two different DA techniques to investigate SO2 emission changes. First, we updated the EnSRF system to evaluate SO2 emission changes, for which the chemistry is better understood and represented in the model. The 2010 January MEIC (Multi-resolution Emission Inventory for China) emission inventory (Zhang et al., 2009; Lei et al., 2011; He, 2012; Li et al., 2014) was used as the a priori inventory (to generate emission background fields), and the 2015 and 2016 January emissions were generated by assimilating hourly surface SO2 concentration observations for January 2015 and 2016. Our purpose is to investigate whether the EnKF algorithm is capable of detecting emission deficiencies in the bottom-up emission inventory (2010-MEIC), dynamically updating the spatial–temporal emission changes (2010 to 2015/2016), and, most importantly, locating newly added sources. Our goal is not only to improve the emissions and forecasting in the model but also to understand the extent to which the DA system can accurately evaluate realistic emission changes, thus allowing it to be applied in emission change evaluations in the future. To better detect new emission sources, we updated the system to directly analyze SO2 emissions instead of emission scaling factors, as in Peng et al. (2017, 2018). In addition to the EnSRF DA algorithm, we also applied the Gridpoint Statistical Interpolation (GSI) variational DA (3D-Var) system to generate the SO2 reanalysis fields, which is helpful in diagnosing the a priori emission deficiency and year-to-year emission changes in the model. Finally, to fully utilize the DA system, we investigated the combined effects of improved initial conditions (by 3D-Var) and dynamically updated emissions (by EnSRF) in the forecast experiments. It has always been challenging to verify optimized top-down emissions from the inverse approach due to the uncertainty of the bottom-up emission inventory and the lack of sufficient independent observational data (not used in the DA process). Herein, we designed three groups of comparisons to address this issue, and the details will be discussed in Sect. 2.6.

The paper is organized as follows. In Sect. 2, the DA system, a priori emissions, observational data, and experimental design are described. The reanalysis SO2 fields obtained using the GSI 3D-Var DA system are analyzed in Sect. 3, focusing on the possible indications of a priori emission deficiency and year-to-year (2015–2016) changes. Section 4 describes the results from the emission assimilation experiment using the updated WRF-Chem/EnKF system. This section starts with the evaluation of the ensemble performance to verify the DA system capability. Then, the derived emission changes (2010 to 2015 and 2015 to 2016) obtained by the EnSRF approach are given spatially throughout the whole domain and in eight different regions with inhomogeneous spatial patterns. The temporal factors derived from the assimilation experiment are also given in Sect. 4. To evaluate the accuracy of the analyzed 2015 and 2016 emissions, two sets of forecast experiments with the respective a priori emissions and the analyzed emissions were conducted and discussed. The details are given in Sect. 5, and the conclusions follow in Sect. 6.

2 Model description, observations, and methodology

We applied two different DA techniques. In the first approach, we extended the GSI 3D-Var DA system originally developed by Liu et al. (2011) and recently updated by Chen et al. (2019) to assimilate SO2 observations, aiming to generate SO2 reanalysis fields. In the second approach, we updated the EnKF DA system (that used in Peng et al., 2017) to optimize SO2 emission changes using surface observations as constraints. The WRF-Chem configurations are the same as those in Chen et al. (2019), and the update of the GSI 3D-Var DA system is also built upon Chen et al. (2019); thus, only simple descriptions are given in this section. A further description of the WRF-Chem/EnKF DA system is given, and the a priori emissions, observations, and experimental design are introduced in detail.

## 2.1 WRF-Chem configuration

WRF-Chem model version 3.6.1 was used in this study (Grell et al., 2005; Fast et al., 2006). The parameterizations were identical to those of Chen et al. (2016), and they are listed in Table 1. The model horizontal resolution is 40 km, and the domain covers most of China and the surrounding regions (Fig. 2). There are 57 vertical levels extending from the surface to 10 hPa. It should be noted that uncertainties might be produced in the analysis due to neglecting the rapid urbanization/land use changes from 2010 to 2015/2016.

Figure 1Flow chart of the data assimilation system that simultaneously optimizes the initial chemical conditions and emissions.

Figure 2Spatial distribution of the a priori SO2 emissions used in this study. Regions defined in the red rectangles are (a) NCP (the North China Plain), (b) NEC (northeastern China), (c) EGT (the Energy Golden Triangle), (d) XJ (Xinjiang), (e) SB (the Sichuan Basin), (f) CC (central China), (g) YRD (the Yangtze River Delta), and (h) PRD (the Pearl River Delta). The color coding of the regional plots relates to the color bar of the national plot. (Units are in mol km−2 h−1.)

Table 1WRF-Chem model configuration.

## 2.2 A priori emissions

The Multi-resolution Emission Inventory for China (MEIC) (Zhang et al., 2009; Lei et al., 2011; He, 2012; Li et al., 2014) for January 2010 is used as the a priori emission input. Unlike in other countries, the national emission inventories in China (e.g., NEI05-08-11-14-17) are provided in a timely manner and updated for the public. It has previously been stated that “there are no official data about how much air pollutants are emitted by China every year. The inventories developed by researchers often lag several years behind the present” (Zheng et al., 2018). MEIC is the only publicly available emission inventory dataset released by the Tsinghua University research community. In the MEIC, the total amount of sectoral emissions at the national and provincial levels has generally been estimated based on the bottom-up approach, which relied on available statistical information concerning activities (energy, industrial production, vehicles, and so on.), emission factors, and end-of-pipe control levels. Due to the large burden of work and the availability of statistical data, the MEIC emission inventory is not updated annually (e.g., the public versions are MEIC-2010-2012); thus, there are always a few years of time lag when applying the MEIC EI (emissions inventory) for research studies. In addition, to drive the regional air quality models, the annual/monthly total amounts of emissions at the national and provincial level are allocated spatially and temporally to generate an hourly gridded emission input for the model. Concerning temporal allocation, as many emission sources have large diurnal and weekly variability that is not fully represented, arbitrary hourly/weekly factors were used in preparing the hourly gridded emissions for the air quality models. Thus, both the uncertainties of the statistical information and the spatial–temporal allocation could cause inaccurate representation of the hourly gridded emission input and affect the performance of the model application.

The preprocessing method used to convert the original emission inventory (in 0.25×0.25) to match the model grid spacing (40 km) is the same as that used in Chen et al. (2019). The spatial distribution of a priori SO2 emissions in the simulation domain is shown in Fig. 2. A number of studies have revealed the uncertainties of the bottom-up emission inventories, including the energy statistics at the national and provincial levels (e.g., Hong et al., 2017) and emission factors from different industry sectors (e.g., Zhao et al., 2011, 2017). Our purpose is to investigate not only the uncertainty of the a priori MEIC emissions but also the capability of the DA system to dynamically update the SO2 emissions using surface observations as constraints. For this purpose, the changes of SO2 emissions from the a priori emission year (2010) to our focus years (2015 and 2016) are emphasized.

There are several different driving factors in different regions that may lead to inhomogeneous changing trends during the years examined (especially from 2010 to 2015). As the Chinese government has implemented desulfurization legislation (since 2005–2006 but with stricter control of the actual use of installations since 2008–2009) and strict control strategies to ensure the air quality during winter seasons since 2013, significant SO2 emission reductions are expected to have occurred since 2010. However, there are converse results for certain regions. For example, Cheng et al. (2017) and Zhi et al. (2017) conducted a village energy survey for the rural areas in Hebei Province and revealed a huge amount of missing rural raw coal for winter heating. For Beijing and Baoding, rural emissions from raw coal in winter were higher than those from the industrial and urban household sectors in the two cities in 2013. Considering the living habits of residents in northern China, this may imply an extreme underestimation of rural household coal consumptions by the China Energy Statistical Yearbooks. Additionally, multi-satellite data (Ozone Monitoring Instrument – OMI, the SCanning Imaging Absorption spectroMeter for Atmospheric CartograpHY – SCIAMACHY) revealed increasing SO2 emissions due to energy industry expansion in northwestern China (The central government of the People's Republic of China, 2012, 2014), especially new power plant installations in Xinjiang and Shaanxi, e.g., in Shen et al. (2016) and Koukouli et al. (2016). Eight different regions are illustrated to address this issue. Northern China is divided into two regions, the North China Plain (NCP) and northeastern China (NEC), as the North China Plain is more emission-intensive and may experience stricter control strategies than those in northeastern China during winter haze periods. Northwestern China is also divided into two regions, including the EGT (the Energy Golden Triangle) and XJ (Xinjiang). Southern China is divided into four regions according to its geographic characteristics, including the SB (Sichuan Basin), CC (central China), YRD (the Yangtze River Delta), and PRD (the Pearl River Delta). The spatial distributions of the SO2 emissions in the eight regions are also illustrated in Fig. 2.

In terms of the temporal allocation, we applied predefined functions for the diurnal variations of the a priori SO2 emissions, but the hourly factors are the same for all of the sectors and all of the grids, which is not optimal. Actually, different sectors/regions may have different hourly emission factors. For example, the transportation sector may produce peak emissions during rush hours, and the industry sector may produce emissions during the production period. Thus, it is not optimal to use the same hourly emission factors for all sectors. For regions in different time zones, different hourly emission factors are also expected. The diurnal variability is not publicly released and is highly uncertain, which introduces large uncertainty into the simulations. We also want to investigate whether the DA system can capture the diurnal variations of SO2 emissions using the hourly surface SO2 concentrations as constraints.

## 2.3 GSI 3D-Var DA system

Building upon the GSI 3D-Var DA system used in Chen et al. (2019), we extended the system capability of assimilating surface SO2 observations. The algorithm and methodology for the aerosol DA are described in Chen et al. (2019). Here, only the differences implemented for the SO2 DA are addressed.

The SO2 observation operator is rather simple, and is written as $\prod m={\mathit{\rho }}_{\mathrm{c}}{M}_{{\mathrm{SO}}_{\mathrm{2}}}$. The unit of the model-simulated ${M}_{{\mathrm{SO}}_{\mathrm{2}}}$ is parts per million (ppm); thus, multiplication by the unit conversion ρc was required to convert the units to micro grams per cubic meter (µg m−3) for consistency with the observations. The observation errors are calculated similarly to the process in Chen et al. (2019). In the data quality control process, SO2 observational values larger than 650 µg m−3 or observations leading to innovations/deviations (observations minus the model-simulated observations determined from the first-guess fields) exceeding 100 µg m−3 were not used. The BECs (background error covariance) values were computed using the “National Meteorological Center (NMC)” method (Parrish and Derber, 1992) by taking the differences of the 24 and 12 h WRF-Chem forecasts valid at the same time for 60 pairs of data valid at either 00:00 or 12:00 UTC over January 2015. The standard deviations over the whole domain are shown in Fig. S1 in the Supplement.

## 2.4 WRF-Chem/EnKF DA system

The WRF-Chem/EnKF assimilation system framework (Fig. 1) was used. Similar to other ensemble DA configurations in WRF-Chem, such as WRF-Chem/Dart (Mizzi et al., 2016), WRF-Chem is used to propagate the initial ensemble forward in time. The EnSRF is used to assimilate the observations and update the meteorological conditions, chemical initial conditions, and/or emissions. The differences relative to WRF-Chem/Dart are mainly in the assimilation engine (the ensemble adjustment Kalman filter is used in WRF-Chem/Dart, whereas the ensemble square root filter is used in our study), the structure of the state variables (meteorological and chemical initial/conditions are used in WRF-Chem/Dart, whereas chemical initial condition/emissions are used in our study), the cycling procedures, and so on. The WRF-Chem/EnKF assimilation system framework (Fig. 1) is very similar to that of Peng et al. (2017). Peng et al. (2017) focused on the joint analysis of both the initial conditions and emissions of PM2.5 and addressed the forecasting skill improvement from using the EnKF system. Here, we focus on the estimation of SO2 emissions, aiming to investigate the system capability of reflecting the spatial–temporal emission changes using observational data as constraints. In addition, instead of setting the emission scaling factors as control variables and adjusting the emissions by timing the scaling factors, we attempted to set emissions directly as control variables, which allowed for adjustments to be made by adding absolute emission values. Using this method, the detection of new emission sources would become more flexible. As in the previous approach, the emission scaling factors were extremely large when a new emission source (e.g., a new power plant) occurred in an originally “clean” model grid (a priori emissions close to zero), with the scaling factor being so large that it might be treated as “unrealistic” and be filtered out in the system. The direct analysis of emissions is expected to be more appropriate for this case.

The ensemble square root filter (EnSRF, Whitaker and Hamill, 2002) algorithm is very similar to that in Peng et al. (2017), except for some differences, such as the state variables (changed from aerosols to SO2 concentrations and emissions) and the inflation factor. In addition, the forecast model for emissions is also different from that in Peng et al. (2017). More details on the differences from Peng et al. (2017) are described below.

### 2.4.1 State variables

A similar ensemble square root filter is used in this study to update a 50-member ensemble to that used in Peng et al. (2017). We also applied the state augmentation method (e.g., Miyazaki et al., 2012). The only difference is that the model parameter (SO2 emissions) is directly estimated by including it as part of the state vector along with the model forecast variable (SO2 concentration). The background ensemble is defined as follows:

$\begin{array}{}\text{(1)}& {x}_{i}^{\mathrm{b}}=\left[\begin{array}{l}{C}_{i}^{\mathrm{b}}\\ {E}_{i}^{\mathrm{b}}\end{array}\right],\end{array}$

where ${\mathrm{x}}_{i}^{\mathrm{b}}$ is the ith member's background vector, consisting of model-simulated SO2 concentrations ${C}_{i}^{\mathrm{b}}$ and the SO2 emissions ${E}_{i}^{\mathrm{b}}$. For a grid with zero emissions in the a priori emissions, the absolute emission values would be added into the DA analysis to reflect the new emission sources. Negative emission estimates were not permitted in the system due to mandatory setting of the minimum values (a small positive value close to zero).

In Miyazaki et al. (2012), the state augmentation method was used to estimate NOx emissions using satellite observations (Ozone Monitoring Instrument, OMI, retrieved NO2 column) as constraints with a local ensemble transform Kalman filter (LETKF). The employment of combined state vectors (both NO2 concentrations and NOx emissions) allowed indirect relationships between NO2 concentrations and NOx emissions, causing complex chemical and transport processes to be considered through the use of the background error covariance, which was produced by the ensemble chemical transport model (CTM) forecast. Building upon Miyazaki et al. (2012), we used a similar approach to address the indirect relationships between SO2 concentrations and SO2 emissions caused by chemical and transport processes. The chemical processes include several paths of SO2 oxidation, such as gas-phase reactions with the hydroxyl radical (OH), aqueous-phase reactions with O3 or hydrogen peroxide (H2O2), and heterogeneous reactions in high-relative-humidity environments (e.g., Li et al., 2011; Wang et al., 2012).

To reduce spurious correlations due to sampling errors, covariance localization was applied following Schwartz et al. (2014) and Peng et al. (2017). EnSRF analysis increments were forced to zero 1280 km from an observation in the horizontal direction and to one scale height (in log pressure coordinates) in the vertical direction using a Gaspari and Cohn (2006) polynomial piecewise function.

### 2.4.2 Inflation factor in the EnSRF

During the analysis process, the analyzed emissions of different members converge gradually, and the background emissions (calculated according to Eq. 4) of different members in the DA cycling become similar, leading to a small ensemble spread (variance). To maintain the spread level, an artificial inflation process (the original perturbations times the inflation factor larger than one) was added to increase the perturbations. Further, multiplicative inflation was applied to posterior (after assimilation) perturbations concerning the ensemble mean analyses, following the “relaxing-to-prior spread” approach by Whitaker and Hamill (2012) with an inflation parameter α:

$\begin{array}{}\text{(2)}& \mathit{\delta }{x}_{\mathrm{a}}^{i}←\mathit{\delta }{x}_{\mathrm{a}}^{i}\left(\mathit{\alpha }\frac{{\mathit{\sigma }}_{\mathrm{b}}-{\mathit{\sigma }}_{\mathrm{a}}}{{\mathit{\sigma }}_{\mathrm{a}}}+\mathrm{1}\right).\end{array}$

In this equation, $\mathit{\delta }{\mathrm{x}}_{\mathrm{a}}^{i}$ is the ith member's analyzed perturbation concerning the mean analysis (${\mathrm{x}}_{\mathrm{a}}^{i}-\overline{x}$), α is the inflation factor, and σb and σa are the prior (before assimilation) and posterior standard deviations at each model grid point, respectively. Using the definition of the standard deviation, Eq. (2) can be expressed as

$\begin{array}{}\text{(3)}& {\mathit{\sigma }}_{\mathrm{a}}←\phantom{\rule{0.125em}{0ex}}\mathit{\alpha }{\mathit{\sigma }}_{\mathrm{b}}+\left(\mathrm{1}-\mathit{\alpha }\right){\mathit{\sigma }}_{\mathrm{a}}.\end{array}$

Assimilating observations reduces the ensemble spread; thus, without inflation, σa<σb. From Eq. (3), if α>1, the inflated posterior spread is forced to be larger than the prior spread (σb). Conversely, for α<1, the inflated posterior spread must be less than σb. As no prior or additive inflation was employed, α>1 was necessary to maintain the ensemble spread, and we used the inflation factor of α=1.12.

### 2.4.3 Forecast models for emissions

The forecast model is important, as it propagates observation information, inflates the analysis spread, and determines the quality of the first guess. In Peng et al. (2017), a smoothing operator served as the forecast model for the emission scaling factors. In this study, direct emissions instead of scaling factors were treated as part of the state variables, thus producing a similar method for the forecasting approach to that used in Miyazaki et al. (2012). A linearized forecast model (M) provides a first guess of the state vector for data assimilation based on the background error covariance from the previous analysis time tn to the new analysis time tn+1,

$\begin{array}{}\text{(4)}& {P}_{\left({t}_{n+\mathrm{1}}\right)}^{\mathrm{b}}=\mathrm{0.75}\phantom{\rule{0.125em}{0ex}}×M{P}_{\left({t}_{n}\right)}^{a}{M}^{T}+\mathrm{0.25}×{P}_{\left({t}_{\mathrm{0}}\right)\phantom{\rule{0.125em}{0ex}}}^{\mathrm{b}},\end{array}$

in which a persistent forecast model (M=I) is used for SO2 emissions, and the estimated emissions are used in the next step of ensemble forecasting. To prevent parameter covariance magnitude reduction, we added the initial prior ensemble as random noise. The forecast model for direct emissions is weighted 75 % toward the results from the previous analysis time and 25 % toward the static initial prior ensemble. The initial prior ensemble of SO2 emissions for the first EnSRF analysis was constructed from the a priori emissions by taking Gaussian random draws from a standard Gaussian distribution and varied for each ensemble member as in Peng et al. (2017). This approach incorporates the useful information from the previous time step and the a priori emissions, which propagates the observation information from one step to the next while still keeping some of the characteristics of the a priori features.

### 2.4.4 The initialization and DA cycling procedure

The WRF-Chem/EnKF assimilation system framework is shown in Fig. 1, and the workflow is briefly introduced here. The initialization and spin-up procedures of the 50-member ensemble were conducted using 72 h ensemble forecasts ahead of the focus period via the same method used in Peng et al. (2017, 2018). For the 50 members, the lateral boundary conditions and initial condition of meteorology from GFS were perturbed by adding Gaussian random noise with a zero mean and statistical background error covariances to the meteorological parameters. The emissions of the 50 members were generated by adding random noise to the a priori emissions, similar to the method in Schwartz et al. (2014) and Peng et al. (2017). After the 72 h forecasts, 50-member ensemble SO2 forecasts were generated, which were used as part of the background (${C}_{i}^{\mathrm{b}}$ in Eq. 1) in the first EMIS_DA cycle. The other part of the background (${E}_{i}^{\mathrm{b}}$ in Eq. 1) was the perturbed emissions of the last time step. In the EnSRF assimilation step, the state variables, including both the emissions for the last hour and the concentrations at the current hour, were updated. In the new 1 h cycle, the background field of emissions is forecast through Eq. (4), and the background concentration is from the WRF-Chem 1 h forecast using the updated chemical fields of the previous assimilation cycle as the ICs (initial conditions). With hourly cycling, the hourly analyzed emissions were obtained.

## 2.5 Observations

Hourly surface SO2 concentrations for January 2015 and 2016 were obtained from the China National Environmental Monitoring Center (CNEMC). There are approximately 1600+ sites in our modeling domain (black dots in Fig. 2). As the 1600+ monitoring sites fall into 531 model grids, observations within the same grid are averaged (by latitude and longitude) for the purpose of statistical analysis and verification. The observation sites mostly span northern, central, and eastern China and are relatively sparse in western China. To ensure data quality before use in the DA, SO2 observational values larger than 650 µg m−3 were deemed unrealistic and were not assimilated in the GSI 3D-Var or the EnKF DA system.

## 2.6 Experimental design

To qualitatively evaluate the deficiencies of the a priori SO2 emissions, generate updated emissions for 2015 and 2016, and evaluate the improvements from the DA approach, five sets of experiments were conducted. The corresponding comparisons and purposes are listed in Table 2. The simulated periods were January of 2015 and 2016. The meteorological initial condition (IC) and boundary condition (BC) were updated from GFS analysis data every 6 h (for NO_DA) or 1 h (for CONC_DA and EMIS_DA) to prevent the meteorology simulation drifting. The same WRF-Chem configurations (Table 1) were used in all the experiments.

Table 2Experiments conducted in this study and the three groups of comparisons.

In the NO_DA experiment, a new WRF-Chem forecast was initialized every 6 h starting at 00:00 UTC on 20 December of the previous year to spin up the chemistry fields and was run through until 23:00 UTC on 31 January. The chemistry fields were simply carried over from cycle to cycle. The 2010-MEIC a priori emissions were used, assuming the same emissions as in 2010. For CONC_DA, the hourly surface observations were assimilated by GSI 3D-Var, and the SO2 concentrations were updated every hour starting from 00:00 UTC on 1 January. The background of the first time step is from the NO_DA simulation, and those of the later time steps are all from the 1 h WRF-Chem forecast using the updated chemical fields of the previous assimilation cycle as the ICs. As the concentrations from CONC_DA are very close to the observations, the concentration differences between CONC_DA and NO_DA possibly indicated a model deficiency in reproducing the reality, which was mainly from the emission changes from 2010 to 2015/2016. The assumption is that the GFS 6 h analysis data provide good meteorological IC/BC values and that the model accurately simulated the meteorological conditions; thus, the emissions were the major deficiency in the model.

The EMIS_DA experiment with continuous hourly cycling of the WRF-Chem/EnKF was performed for January of 2015 and 2016. The initialization and spin-up procedures of the 50-member ensemble were conducted starting from 00:00 UTC on 29 December of the previous year to 00:00 UTC on 1 January of the next year. Then, the EMIS_DA cycle started at 00:00 UTC on 1 January. Following the procedure in Fig. 1, the EMIS_DA experiment started with conducting EnSRF analysis and generated both the updated SO2 concentration fields for the current time step and the updated analyzed SO2 emissions for the previous time step. In this hourly cycling approach, 1 h WRF-Chem/EnKF cycling was conducted for January of 2015 and 2016, and hourly analyzed SO2 emissions were then obtained. We compared the 2015 emissions from EMIS_DA to the 2010 a priori emissions, as the emission differences between the 2015 analyzed emissions and the 2010 a priori emissions not only reflected the changes from 2010 to 2015 but also included the deficiencies in the 2010 a priori emission. We also compared the updated emissions between 2015 and 2016, as the differences between the 2016 analyzed emissions and the 2015 analyzed emissions reflected the pure emission changes from 2015 to 2016, as the deficiencies of the 2010 a priori emissions were offset in the subtraction. The emission control policies are discussed to investigate whether the emission changes are reasonable.

To investigate the impact of using analyzed emissions from the EnKF DA system, two forecast experiments (NO_DA_forecast and EMIS_DA_forecast) were conducted for the same period. Twenty-four-hour forecasts were performed at 00:00 UTC of each day from 1 to 31 January for 2015 and 2016. The original a priori emissions and the updated analyzed emissions were used in the NO_DA_forecast and EMIS_DA_forecast experiments, respectively. The chemistry initial conditions for each forecast in the two forecast experiments were from the 1 h cycling GSI 3D-Var (COND_DA) experiment. The meteorological IC and BC were all from GFS analysis and forecast data. The concentration differences between the two sets of 24 h forecasts reflect the effects of the updated emissions.

3 Changes in ambient concentrations

This section presents the simulated SO2 concentration results of NO_DA and CONC_DA. As shown in Chen et al. (2019), 1 h cycling of the GSI 3D-Var DA system produces reliable PM2.5 reanalysis fields. As the methodology and procedure are the same for SO2, we can expect that the improvement of SO2 assimilation will be as good as that of PM2.5, as evidenced by the basic statistics including the mean bias (MEAN/BIAS), standard deviation (SD), and root mean square errors (RMSEs) between NO_DA/CONC_DA and observations, shown in Supplement Fig. S2. Therefore, the purpose of this section is not to verify the performance of the GSI 3D-Var assimilation experiment but to investigate the differences between NO_DA and CONC_DA. As NO_DA is the simulation with the 2010 emission inventory, whereas the results of CONC_DA can serve as gridded reanalysis data from real observations, the differences between the two runs actually reflect the possible deficiencies in the model. As the meteorology data are from the 6 h GFS reanalysis data, we assume that most of the deficiencies come from using the 2010 a priori emissions for the years 2015 and 2016 in the model, and the comparisons also provide an idea of the changing trends of the emissions.

## 3.1 Spatial distribution

Figure 3 shows the observed and modeled monthly average surface SO2 concentrations for January in 2015 and 2016. The observations show great differences between northern and southern China, reflecting the dominant role of heating-related emissions in northern China during the winter season. The high values in northern China also show localized characteristics (no smooth transitions from the high-value region to the surroundings) that reveal the localization of SO2 emissions and transport. The NO_ DA experiment significantly overestimates the surface SO2 in the Sichuan Basin and central China but underestimates it at several locations in northern China and Xinjiang. After GSI 3D-Var hourly cycling of the DA, the CONC_DA experiment results are very close to observations because they corrected most of the biases in NO_DA except for the very high values at some of the “hot spots” in northern China. The fact that the improvements at those locations are not significant may be due to the data filtering process, in which SO2 data with either observed values larger than 650 µg m−3 or innovations/deviations (observations minus the model-simulated values determined from the first-guess fields) exceeding 100 µg m−3 were rejected. The differences between CONC_DA and NO_DA more clearly revealed the inhomogeneous emission changes in different regions. For 2015, a great SO2 decrease from NO_DA to CONC_DA in most of the eastern and southern regions was found, but increases were observed in northeastern China, the Energy Golden Triangle, and Xinjiang, indicating that the 2010 January a priori emissions should be adjusted accordingly (following decreasing/increasing trends, respectively) to reflect the 2015 January status. The negative discrepancies in the eastern and southern regions are even larger for 2016, indicating continuous emission decreases in these areas.

Figure 3Observed and modeled monthly average SO2 concentrations for January in 2015 (left column) and 2016 (right column). (a) Observations, where the ranges of the different colors are the same as those of the color bars of (b) and (c); (b) NO_DA; (c) CONC_DA; and (d) CONC_DA NO_DA. (Units: µg m−3.)

To further investigate the deficiencies of the a priori emissions, the spatial distributions of the statistics (MEAN BIAS, RMSE, and CORR) at each observational site (which had more than two-thirds valid data in the month) in January of 2015 and 2016 for the two experiments are shown in Fig. 4. We start from the 2015 statistics and then address the differences relative to 2016. In NO_DA, consistent with Fig. 3, the surface SO2 in southern China (the Sichuan Basin, central China, the Pearl River Delta, and the Yangtze River Delta) is generally overestimated by 20–50 µg m−3, but it is underestimated in northeastern China and the Energy Golden Triangle. The BIAS also showed localized characteristics with positive biases in megacities (e.g., Beijing), along with negative biases in the surroundings, indicating overestimated/underestimated emissions, respectively. There are also high RMSEs in northeastern China, the North China Plain, and the Energy Golden Triangle, indicating a wide spread of differences between observational data and NO_DA simulations, which may also indicate a model deficiency in reproducing strong temporal fluctuations (with the same daily emissions and fixed hourly factors as in the a priori emissions); the poor correlations (less than 0.5) at most of the sites also support this assumption. From year to year, the biases in 2016 are even more prominent. With GSI 3D-Var hourly cycling, the BIAS, RMSE, and CORR are greatly improved, as expected, while the improvements in northern China are smaller than those in southern China.

Figure 4The spatial distribution of the statistics between the model simulations and the observations for (a) January 2015 and (b) January 2016. The top row shows NO_DA vs. observations, whereas the bottom row shows CONC_DA vs. observations. (Units: µg m−3 for BIAS and RMSE.)

## 3.2 Changes from 2015 to 2016

The differences between the January values of the 2 years (2015–2016) are shown in Fig. 5. Observations (Fig. 5a) mostly show decreases from 2015 to 2016 for most sites, especially in the North China Plain and southern China. In the NO_DA experiment (with the same emissions and different meteorology), some decreases are shown that reflect the meteorology condition differences between the 2 years, but the observed significant decreases in the North China Plain and southern China are not captured. CONC_DA (Fig. 5b) did reproduce the large decreases in the North China Plain and southern China from 2015 to 2016. From the difference between Fig. 5b and c, it can be assumed that factors other than meteorology (e.g., emissions control measures) play important roles in causing the decreases. CONC_DA failed to reproduce the large positive changes at three locations in the Energy Golden Triangle region, as CONC_DA failed to reproduce the high SO2 concentrations in both years due to the data filtering processes.

Figure 5Observed and modeled SO2 ambient concentration changes (January 2016–January 2015). (a) Observations, where the ranges of different colors are the same as those in the color bars of (b) and (c); (b) NO_DA; and (c) CONC_DA. (Units: µg m−3.)

4 Changes in emissions

Before the emission trend analysis, the ensemble performance was evaluated. For comparison with a priori emissions, the analyzed hourly emissions were averaged monthly. Analysis of the total amounts and spatial changes were conducted for the aforementioned eight regions. We focus on the emission trends for two periods: 2010–2015 and 2015–2016. Additionally, the hourly factors (diurnal cycle) of the optimized emissions were given to reflect the values of the hourly DA.

## 4.1 Ensemble performance

In a well-calibrated system, when compared to the observations, the prior ensemble mean root mean square error (RMSE) would equal the prior “total spread”, defined as the square root of the sum of the observation error variance and the ensemble variance of the simulated observations (Houtekamer et al., 2005). The time series of the hourly prior ensemble mean RMSE and the total spread of surface SO2 in the eight regions are shown in Fig. 6. The time series of the two months (January 2015 and January 2016) are given separately. Typically, the statistics at a single site for a certain period reflect the model biases and variances of errors at that site for the whole period. However, herein, the statistics for the eight regions were determined for all sites within the region at a 1 h frequency, which means that the statistics actually reflect the biases and error variances of the model simulations for those sites at every hour. As the emissions and meteorological conditions could be very different at sites in the same region, the RMSE for that region could be large. Due to the spatial–temporal inhomogeneity of emissions and meteorological conditions in different regions, the model shows different performances in terms of the differences in the RMSE. The “total spread” reflects the ensemble variances of the model-simulated values.

Figure 6Regional averaged RMSE and the total spread for (a) January 2015 and (b) January 2016 in eight regions. Time starts from 00:00 UTC. (Units: µg m−3.)

## 4.2 Analyzed 2015 and 2016 emissions

The optimized SO2 emissions obtained from the assimilations for January 2015 and 2016 are shown in Fig. 7. To address the changes from 2010 to 2015 and those from 2015 to 2016, the differences and ratios between the two groups (2010 vs. 2015 and 2015 vs. 2016) are given. For the comparison of 2015 analyzed emissions with 2010 a priori emissions, as real observations were used to constrain the 2015 emissions, the differences between the two sets of emissions actually reflect the adjustments based on the 2010 a priori emissions, which are needed to better capture observations; thus, the comparison not only reflects the changing trends from 2010 to 2015 but may also indicate the deficiencies of the 2010 a priori emissions. It should be noted that the two aspects are mixed when interpreting the results. While the comparison of 2015 analyzed emissions with 2016 analyzed emissions is more straightforward, as they are both produced using observation constraints, the differences between the two reflect the annual changes between the 2 years, and the impacts from a priori emission deficiencies are removed in the subtraction.

Figure 7Analyzed emissions for (a) January 2015 and (b) January 2016. (c) The differences of the 2015–2010 a priori inventory and (d) ratios of the 2015∕2010 a priori inventory. (e) The differences of 2016 2015 and (f) ratios of 2016∕2015. (Units are mol km−2 h−1 for (a), (b), (c), and (e)).

Compared to the 2010 a priori emissions, the analyzed emissions for 2015 show different spatial changes (northern, western, and southern China). Large emission decreases in southern China (the Sichuan Basin, central China, the Yangtze River Delta, and the Pearl River Delta) are shown, but there are also some small emission increases in scattered regions. These increases are relatively small in absolute value (shown using light yellow in Fig. 7c), but the 2015∕2010 ratios can reach large numbers (shown using orange to red in Fig. 7d), as the a priori emissions in those regions are very small (Fig. 2); thus, minor changes lead to large ratios. For northern China (North China Plain and northeastern China), the change pattern is somewhat opposite. Emission increases are shown for most of the regions, with decreases only occurring at scattered points. Large 2015∕2010 increasing ratios are also shown in western China (Xinjiang and The Energy Golden Triangle), while the a priori emissions are very sparse in those two region; thus, the emission increases are more significant, which may indicate new emission sources. For the changes from 2015 to 2016, the pattern is rather homogenous across the whole domain, with decreases in almost all regions.

Figure 8The differences between the analyzed 2015 January emissions and the 2010 a priori emissions in eight regions. Left/top panels are emission differences of 2015 2010 (units: mol km−2 h−1), and right/bottom panels are the ratios of 2015∕2010 in each region.

## 4.3 Changes in different regions

To further illustrate the changes in different regions, the details of eight regions are given in Fig. 8 (2015 vs. 2010) and Fig. 9 (2016 vs. 2015). Similar to Fig. 7, the emission changes in terms of absolute values (left panels) and ratios (right panels) are given for each region. To better understand the geographic changes, the center locations of some large cities (capital cities of provinces and municipal centers at the city level) in those regions are labeled. According to Fig. 7, the change patterns are different in northern, western, and southern China for 2015; thus, discussions are given based on this classification. We start from the comparison of the 2015 analyzed emissions with the 2010 a priori emissions, as there is a 5-year time lag between the two sets of emissions, along with large uncertainties; therefore, large changes are expected.

Figure 9Same as Fig. 8, but for the differences between the analyzed 2016 January emissions and the 2015 January emissions in eight regions. Left/top panels are emission differences of 2016 2015 (units: mol km−2 h−1), and right/bottom panels are the ratios of 2016∕2015 in each region.

It is interesting to see that for northern China (North China Plain and northeastern China), the most significant decreases occur in or around large cities (city center locations are labeled as black dots). The phenomenon is very prominent in the North China Plain, as we can see some “cold” spots (grids with cold colors) in Fig. 8a, which are either overlapped by city center locations (Beijing, Tianjin, Xingtai, and Handan in the Beijing–Tianjin–Hebei region, and Dongying, Jinan, Zibo, and Jining in Shandong Province) or adjacent to the center locations (Shijiazhuang, Linyi, Zaozhuang). As the center locations are represented as latitudes and longitudes that do not cover entire city areas, there might be some shifting produced from interpreting the results when the city areas are too large (e.g., Shijiazhuang, Changchun, and Shenyang) and have been split into two or more grids in the model. While the results still indicate that the emissions in these larger cities decreased due to the strict control strategies from 2010 to 2015 (factory migration from urban regions to remote regions, desulfurized equipment in factories/vehicles, low-sulfur energy, etc.), there are some emission increases in the suburban and rural regions surrounding these larger cities, either due to emission migration from urban regions or new emission sources added due to urbanization development. The results might also indicate that the control strategies were executed at different levels in urban (more strict) and suburban–rural regions during the period from 2010 to 2015. In northeastern China, significant “cold spots” also occur in the three larger cities, including Ha'erbing, Changchun, and Shenyang, but increases mostly occur in other areas, indicating a similar trend to that in the North China Plain, in which large emission decreases occurred in bigger cities and mild emission increases occurred in suburban–rural regions from 2010 to 2015. In addition to the possible aforementioned reasons accounting for the different changes of urban and suburban–rural regions from 2010 to 2015, it should be noted that the month of January is during the heating season for the North China Plain and northeastern China, and the large areas of emission increase might also indicate some heating emissions (from energy that has not been statistically well recorded, e.g., crop combustion and residential coal combustion) that are missing from the a priori emissions.

In western China, where the emission intensities are not as high and the emission sources are relatively sparse, the changing emission trends from 2010 to 2015 are more obvious and are more meaningful for distinguishing new emission sources/regions. As some studies have revealed increasing SO2 emissions due to energy industry expansion and relocation in northwestern China from OMI measurements (Ling et al., 2017), our 2015 analyzed emissions also show large emission increases in the whole area of the Energy Golden Triangle and Xinjiang, except for in very few larger cities (Yinchuan, Wuhai, Lanzhou, and Karamay, which is also known as Kelamayi). The emissions in other areas of the Energy Golden Triangle and Xinjiang almost all show increases from 2010 to 2015. Especially for Xinjiang, the increases in emissions are all attributed to the rapidly developing cities/counties, including Urumqi, Aksu (A'kesu), Korla (Ku'erle), Yecheng, Manas (Manasi), Tacheng, Huocheng, Bachu, Atushi, Shanshan and Shacheng. Koukouli et al. (2016) and Ling et al. (2017) used multi-satellite data to investigate the SO2 load changes from 2004–2014 and 2005–2015, respectively, and identified locations with increases (including U'rumqi in Xinjiang and cities in northwestern China). They reported that “These belong to provinces with emerging economies which are in haste to install power plants and are possibly viewed leniently by the authorities, in favor of growth.” Our findings are also consistent with those of these two studies.

In southern China, decreasing changes are shown for large areas, especially in the Yangtze River Delta and the Pearl River Delta, in which decreasing trends in larger cities are clearly shown, e.g., in Shanghai, Nanjing, and Hangzhou in the Yangtze River Delta and in Guangzhou, Shenzhen, and Foshan in the Pearl River Delta, with relatively larger decreasing ratios in more well-developed cities. In the Sichuan Basin and central China, the decreases in larger cities are also significant, and different extents are achieved in cities of different levels. For Chengdu, Chongqing, Zunyi, Guiyang, and Yunyang in the Sichuan Basin and Wuhan and Changsha in Central China, approximately 40 %–50 % reductions are shown from 2010 to 2015. For other larger cities (municipal centers of cities), 20 %–30 % reductions are shown.

As previously mentioned, the comparisons between the 2015 and 2016 analyzed emissions (Fig. 9) are more straightforward and reflect the necessary emission changes from 2015 to 2016, as the uncertainties in the a priori emissions are subtracted. As expected, decreasing trends are shown for almost all of the labeled cities, indicating the continuing strict execution of control strategies. However, there are still some grids with emission increases (approximately 10 %–30 %) in surrounding regions, especially in the North China Plain, which might reflect the emission increase from January 2015 to January 2016. As shown in Fig. 10 of Chen et al. (2019), the temperature in January 2016 was much colder than that in 2015, and the emission increases at those points may indicate heating-related emissions. Compared with Fig. 8 (2015 vs. 2010), the changes from 2015 to 2016 (both increases and decreases) are much milder in Fig. 9.

Figure 10Hourly factors in the a priori emission inventory and those derived from the EMIS_DA experiment in eight regions.

The regional averages of the 2015 and 2016 January emissions are summarized in Table 3. In northern China (North China Plain and northeastern China) and western China (the Energy Golden Triangle and Xinjiang), the 2015 analyzed emissions are all larger than the 2010 prior emissions. The increase percentages are 12.7 %, 49.4 %, 25.6 %, and 72 % for the North China Plain, northeastern China, the Energy Golden Triangle, and Xinjiang, respectively, indicating an increasing trend from 2010 January to 2015 January, either due to emission increases in reality (possibly in the Energy Golden Triangle and Xinjiang) or uncertainties in the 2010 a priori emissions (possibly in the North China Plain and northeastern China). The largest increase occurred in Xinjiang, reaching 72 %, which is consistent with the previous findings of newly added emission sources in that region. In southern China, the 2015 analyzed emissions are all smaller, and the decreasing ratios are −10.5 %, −9.9 %, −13.8 %, and −22.9 % for the Sichuan Basin, central China, the Yangtze River Delta, and the Pearl River Delta, respectively. For the changes from 2015 to 2016, decreasing trends are shown for all regions, with the ratios ranging from −5.3 % to −16.1 %.

Table 3A priori and analyzed January emissions and the changing ratios for 8 regions (units: 106 kg d−1).

In the recent study by Zheng et al. (2018), the 2010–2017 trends of anthropogenic emissions in China were investigated. According to the bottom-up approach, the annual total amounts of SO2 emissions were calculated to be 27.8, 16.9, and 13.4 Tg for the years 2010, 2015, and 2016, respectively. The 2010 to 2015/2016 decreases were mostly attributed to the power and industry sectors due to the strict pollution control measures implemented for these two sectors. The sectoral distribution of emissions have changed significantly over recent years, and emissions other than those from power and industry have occupied larger portions, especially for the residential sector, as the current control policies have limited effects on reducing emissions from the residential sector. According to Zheng et al. (2018), the national total SO2 emissions decreased by 20.8 % from 2015 to 2016. Our derived changes ratios for the month of January in most of the regions (NEC, XJ, SB, CC, and the PRD) are comparable (13.9 %, 16.1 %, 12.4 %, 15.5 %, and 12.6 %, respectively, see Table 3), but the change ratios for NCP, ETR, and YRD are (relatively) smaller. As discussed in Zheng et al. (2018), bottom-up emission estimates are uncertain due to incomplete knowledge of the underlying data, and uncertainties are larger when emissions are contributed by scattered emission sources. Especially for the residential sector, the effectiveness of the measures (e.g., phasing out of small high-emission stoves and the banning of coal heating) is difficult to validate due to the lack of inspections; thus, higher uncertainties may arise for regions in which residential emissions are relatively important.

## 4.4 Hourly factors

As hourly observations were used to constrain the emissions, analyzed emissions at an hourly frequency were obtained, which provided us an opportunity to investigate the hourly emission factors from observations. To retrieve the hourly factors, the emissions during each hour (24 h) are averaged based on the EMIS_DA experiment for the whole period (2–31 January ). The retrieved hourly factors for 2015 and 2016 and the 2010 a priori emissions are shown in Fig. 10. The a priori hourly factors are given arbitrarily, with two peaks during the day at 01:00 UTC (09:00 BJ time – Beijing time) and 09:00 UTC (17:00 BJ time) to reflect the emissions during rush hours. The retrieved hourly factors in northern and western China showed two peaks at approximately 02:00 UTC (10:00 BJ time) and 12:00 UTC (20:00 BJ time), but the second peak is obscure in southern regions. In addition, the second peak of the hourly factors in the northern and western regions is much lower than the first, which was different from the predefined curve. In Xinjiang, the peaks occurred later than in the other regions, indicating that the time zone differences caused a different energy consumption/emission pattern. It should be noted that the hourly factors were derived from the analyzed emissions constrained from ambient concentration observations; thus, the response times from emissions to ambient concentrations were simplified in the assimilation system. Although the background emissions contain the information from the previous cycles, and may, therefore, help to pass the response information, there might still be some time lag in the retrieved hourly factors, which should be further verified.

5 Forecast improvements

As there are large uncertainties in the bottom-up 2010 a priori emission inventory and in the assimilation process itself, it is difficult to verify the accuracy of the 2015 and 2016 January analyzed emissions. The bottom-up emission inventory for the 2 years is not yet available for comparison. Thus, two sets of forecast experiments using the a priori emissions and the analyzed emissions were conducted (NO_DA_ forecast vs. EMIS_DA_forecast, see details in Sect. 2.5). The forecast differences between the two experiments can reflect, to some extent, the performance/improvement of the analyzed emissions. To show the differences spatially, the statistics at single observational sites in the two forecast experiments are given and compared. In addition, the improvement from the hourly forecast is more meaningful in showing the system capability of hourly emission optimization. Thus, the time series of the regional means in eight regions are also given to show the performance temporally.

## 5.1 Changes of spatial statistics

Figures 11 and 12 show the performances of the NO_DA_forecast and EMIS_DA_forecast experiments for January 2015 and 2016, respectively. Statistics, including the BIAS (bias, equal to the difference between the modeled value and the observational value, representing the overall model tendency), RMSE (the root mean square error/root mean square deviation, equal to the square root of the second moment of the differences between the model values and the observational values, reflecting both model biases and error variances), and CORR (the correlation coefficient, equal to the linear relationship between the modeled values and the observational values), were chosen to evaluate the two forecast experiments with a priori emissions and analyzed emissions, respectively. For a single site, the three statistics (BIAS, RMSE, and CORR) may change in two directions – for example, the BIAS (the bias of the absolute emission amount) may get worse, but the RMSE (error variance) and CORR (in terms of the diurnal or day-to-day emission changes) may get better. To fairly evaluate and show the overall changes, the 531 lumped sites were classified into five different groups to reflect the differences in the statistics. The classification and performance are listed in Table 4. The spatial distributions of the NO_DA_forecast statistics for each site are given in Figs. 11a and 12a. To better illustrate the changes of the statistics after applying the analyzed emissions, the differences (EMIS_DA_forecast NO_DA_forecast), instead of the absolute values, are shown for the five defined groups in Figs. 11b–f and 12b–f. Specifically, the absolute values of the BIAS were used in the difference calculation.

Figure 11The spatial distribution of the error statistics between the model simulations and the observations for January 2015. (a) Statistics between NO_DA_FCST and the observations, with BIAS and RMSE in micrograms per cubic meter; (b–f) the statistics improvements from NO_DA_FCST to EMIS_DA_FCST for different groups of sites (classification in Table 4), with the BIAS and RMSE improvements shown as percentages. The color bars are the same for (b)(f) and are only shown in (c) and (f) to save space.

Figure 12Same as Fig. 11, but for January 2016.

Table 4Overall statistical changes of the EMIS_DA_FCST experiment compared with the NO_DA_FCST experiment.

Concerning single statistics, the BIAS, RMSE, and CORR are improved at 383, 444, and 426 sites, respectively, for the year 2015 (Table 4), while there are 524 total valid sites over the whole domain. That is to say that the ratios of sites improved are 73 %, 85 %, and 81 %, respectively, as determined using BIAS, RMSE, and CORR as the single criterion. When considering the overall performance using the three statistics, 300 sites (57 %) are fully improved (BIAS/RMSE decrease and CORR increase), 138 sites (26 %) are partially improved (either the BIAS and RMSE improved or the RMSE and CORR improved), only 16 sites (3 %) show an overall deterioration of performance, and the remaining approximately 13 % of sites could not be justified. The performance in 2016 is even better than that in 2015, with the fully improved (overall worse sites) being more (less) compared with the 2015 case.

Figure 11b shows that overall improvements are achieved over the whole domain, with the largest BIAS corrections occurring at sites in the Sichuan Basin, central China, the Yangtze River Delta, and the Pearl River Delta (reaching 60 %–70 % reductions) and the largest CORR improvement occurring in Xinjiang (reaching 0.35). The sites that are partially improved (Fig. 11c, d) and unclassified (Fig. 11e) are not in specific regions but are scattered through the whole domain. The sites that showed an overall deterioration of performance (Fig. 11f) are very few, and the variances are relatively small. Consistent with Table 4, the performance in 2016 (Fig. 12) is even better than that in 2015 (Fig. 11), with the BIAS corrections being more significant, especially in the Sichuan Basin, central China, the Yangtze River Delta, and the Pearl River Delta, and the CORR improvements are even larger in Xinjiang.

## 5.2 Time series of the regional mean

Figure 13 shows the time series of the regional mean forecasts (NO_DA_forecast and EMIS_DA_forecast) and the observed SO2 concentrations in eight regions for 2015 and 2016. From the aspect of the regional mean, forecasts with a priori emissions are severely overestimated in southern China (the Sichuan Basin, central China, the Yangtze River Delta, and the Pearl River Delta), and the overestimations are largely corrected in the forecasts with analyzed emissions. For northeastern China, the Energy Golden Triangle, and Xinjiang, forecasts with a priori emissions are underestimated, and forecasts with analyzed emissions helped to correct the biases. It is surprising to see that the regional averages in the North China Plain match well with the observations, although the site-to-site comparisons (Figs. 11, 12) show large biases at single sites. As the sites in one region are averaged, the positive/negative biases among different sites might be offset in the averaged time series. For this reason, the RMSE and CORR of all the hourly data in one region are also calculated for verification.

Figure 13Time series of the regional mean SO2 concentrations from the observations and from model simulations with the a priori and analyzed (posterior) emissions for (a) January 2015 and (b) January 2016 in eight regions. Time starts from 00:00 UTC. (Units: µg m−3.)

The statistics of the BIAS, RMSE, and CORR in the eight regions are given in Table 5. From the aspect of the regional mean, the improvements obtained after applying the analyzed emissions are more significant in southern China than in northern China, with the RMSE decreased by 27.9 %–39.3 %, the BIAS decreased by 63.3 %–78.2 %, and the CORR increased by 16.7 %–45.0 % for the year 2015. For northern China, although the improvements are not as large, the BIAS still decreased (except in the North China Plain), and the decreasing ratio ranged from 6.3 % to 22.9 %, while the RMSE decreased by 4.2 %–8.8 % and the CORR increased by 7.7 % to 366.7 %. The largest CORR increase occurred in Xinjiang, changing from 0.06 to 0.28, indicating that the newly added emission sources in the analyzed emissions are necessary. Compared with 2015, the improvements in 2016 are also larger, which is consistent with previous discussions.

Table 5Statistics of the EMIS_DA_FCST and NO_DA_FCST experiments in eight regions (units: µg m−3 for BIAS and RMSE).

6 Conclusions

Based upon our previous study (Peng et al., 2017), we further updated the WRF-Chem/EnKF DA system to quantitatively estimate gridded hourly SO2 emissions using hourly surface observations as constraints. In contrast to Peng et al. (2017), direct emissions were used as the analysis variables instead of emission scaling factors, which allows for the detection of new emission sources.

The 2010 January MEIC a priori emissions were used to generate 2015 and 2016 January analyzed emissions, applying the hourly surface SO2 observations as constraints. Compared with the 2010 a priori emissions, the analyzed emissions in January 2015 showed inhomogeneous change patterns in different regions. (1) Significant emission reductions were found in southern China, including in the Sichuan Basin, central China, the Yangtze River Delta, and the Pearl River Delta; however, there were still some grids with slight emission increases surrounding larger cities, indicating the emission transition due to urbanization development. The reduction ratios of the total January emissions for the aforementioned four regions were −10.5 %, −9.9 %, −13.8 %, and −22.9 %, respectively. (2) For northern China (the North China Plain and northeastern China), the situation is more complicated during the winter heating season. Comparisons show large emission reductions in larger cities but wide increases in surrounding suburban and rural regions, which may indicate missing raw coal combustion that was not taken into account in the a priori emission inventory. The increase ratios of the total January emissions for the North China Plain and northeastern China were 12.7 % and 49.4 %, respectively. (3) Significantly large emission increases were found in western China (the Energy Golden Triangle and Xinjiang) due to the energy expansion strategy, which is consistent with satellite observations (e.g., Ling et al., 2017). The increase ratio of the total January emissions for the Energy Golden Triangle and Xinjiang were 25.6 %, and 72.0 %, respectively. It should be noted that the comparisons between the 2010 a priori emissions and the 2015 analyzed emissions not only reflect the changes during the 5 years but also include the uncertainties in the a priori emissions (either due to uncertainties in the total annual/monthly emissions or to the allocation process from the provincial emissions to the gridded data). Comparisons of the 2015 and 2016 analyzed emissions show wide emission reductions from 2015 to 2016, which is consistent with a recent study on emission changing trends using the bottom-up approach (Zheng et al., 2018), indicating that stricter control strategies have been fully executed nationwide. These changes coincided with the period of the energy development national strategy in northwestern China and regulations for the reduction of SO2 emissions, indicating that the updated DA system was possibly capable of detecting the emission deficiencies, dynamically updating the spatial–temporal emission changes (2010 to 2015/2016), and locating the newly added sources. The detection of emission changes by the DA system can be localized to the city level, benefitting from the intensive observations and the model grid resolution.

It is difficult to verify the accuracy of the analyzed emissions, as the bottom-up emission inventories for 2015 and 2016 are not yet available for comparison. Two sets of forecast experiments using the a priori emissions and the analyzed emissions were conducted to show the differences and improvements. Among the 531 lumped sites, 300 sites were fully improved (BIAS and RMSE reduced and CORR increased), and only 16 sites were entirely worse for the year 2015. The other 138 sites were partially improved (two statistical measures became better). The improvements were much larger in southern China than in northern and western China. Upon using the analyzed emissions, the BIAS and RMSE were reduced by 61.8 %–78.2 % and 27.9 %–52.2 %, respectively, and the correlation coefficient increased by 12.5 %–47.1 % for southern Chinese regions (the Sichuan Basin, central China, the Yangtze River Delta, and the Pearl River Delta). However, for northern and western China, where the original BIAS and RMSE values were larger, the decreases were (relatively) smaller. Nevertheless, the correlations were indeed improved, especially for Xinjiang, as new emissions were captured in the analyzed emissions. The distinction of the comparisons among different regions (northern/western regions vs. southern regions) indicated the deficiencies in the perturbation procedure in the DA system when applied to the northern/western regions. Further investigations should be conducted to generate larger spreads for those regions in future studies.

Our study serves as an example indicating that the ensemble Kalman filter algorithm combined with the WRF-Chem regional model can be used to optimize model-ready gridded hourly emissions inputs using hourly surface observations as constraints. This approach is useful for assessing emission control strategies and can also improve forecasting skills. The limitation of this study is that the analyzed emissions are still model-dependent, as the ensembles are conducted through the WRF-Chem model, and, thus, the performance of the ensembles is model-dependent. Changes in the model configuration (e.g., the spatial resolution or chemistry options) can cause differences in the DA system. In our study, the model resolution is 40 km, which might be too coarse for SO2, as it is a species with a relatively short lifetime, and the localized characteristics might not be captured by the system. In addition, the reactions of SO2 are only reflected in the WRF-Chem system and not in the EnKF process. Considering the reaction time of SO2 in the ambient atmosphere, there might be some time lag in the hourly emission factors.

Data availability
Data availability.

The observational data are publicly available from http://www.cnemc.cn (last access: 1 July 2019). The simulation data may be obtained from the corresponding author upon request.

Supplement
Supplement.

Author contributions
Author contributions.

ZL and DC designed research, and DC performed the research. JB contributed towards the development of the DA system. MC provided funds. DC wrote the paper, with contributions from all co-authors.

Competing interests
Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements
Acknowledgements.

This work was supported by the National Key R&D Program on Monitoring, Early Warning and Prevention of Major Natural Disasters (grant no. 2017YFC1501406), the National Natural Science Foundation of China (grant no. 41807312), and the Basic R&D special fund for central scientific research institutes (grant no. IUMKYSZHJ201701). NCAR is sponsored by the US National Science Foundation. We would like to thank Zhen Peng for useful discussions and patient guidance regarding the DA system development.

Financial support
Financial support.

This research has been supported by the National Key R&D Program on Monitoring, Early Warning and Prevention of Major Natural Disasters (grant no. 2017YFC1501406), the National Natural Science Foundation of China (grant no. 41807312), and the Basic R&D special fund for central scientific research institutes (grant no. IUMKYSZHJ201701).

Review statement
Review statement.

This paper was edited by Andrea Pozzer and reviewed by two anonymous referees.

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