Introduction

The haze events in winter heating period have aroused great concern (Yi et al., 2014; Zhang et al., 2014). Beijing-Tianjin-Hebei (BTH) region lies between North China and Northeast China, containing Beijing, Tianjin, and 11 prefecture-level cities in Hebei Province (Fig. 1). In 2020, the heavy haze events frequently occurred in BTH region, and the heavy haze days accounted for 3% of the total days (BEES, 2020; TEES, 2020; HPEES, 2020). PM2.5 (particles with aerodynamic equivalent diameter less than 2.5 microns in ambient air) as the main pollutant in the heating season of BTH region, excessive PM2.5 concentration has become an urgent environmental problem (Zhang et al., 2021a; Zhao et al., 2020). In 2020, cities in BTH region accounted for 40% of the top 10 cities with the worst air quality (CEB, 2020).

Fig. 1
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Study domain

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Residential coal was widely used for household heating in rural areas and was considered as an important source of pollutant emission (Zhang et al., 2021b; Zhang et al., 2022a; Wen et al., 2023). Different from the power plants and industrial sectors, there is no corresponding pollutant removal technology in the residential sector. In the use process, residential coal has the characteristics of high pollution intensity, low emission height, and dense population in emission areas, which is considered to be an important reason for the aggravation of air pollution in the heating season (Zhi et al., 2017; Shen et al., 2019). Therefore, it is essential to study the impact of RCC used for household heating on air pollution for formulating scientific and effective pollution prevention and control measures. The current emission inventory uses the statistical data of China Energy Statistical Yearbook to evaluate pollutant emissions in the residential sector (Tian et al., 2018; Shen et al., 2012). However, the existing statistical yearbooks differ greatly from the actual consumption of residential coal, and there is great uncertainty (Pan et al., 2016; Meng et al., 2019). Therefore, it is of great significance to establish the emission inventory of RCC pollutants in residential sector according to the actual survey data.

From 2010 to 2020, many scholars have conducted a series of studies on the energy consumption and pollutant emissions from rural residential sector in BTH region (Zhou et al., 2020; Peng et al., 2019; Cai et al., 2018). However, the traditional time allocation method based on the average annual emissions to monthly, daily, and hourly emissions is not consistent with the actual emission situation of RCC (Liu et al., 2016). Meanwhile, the traditional spatial allocation method with population density as the weight factor is quite different from the actual situation (Fu et al., 2013; Cao et al., 2011; Qi et al., 2017; Liu et al., 2018a; Cheng et al., 2017). This study conducted a series of studies on the use of residential coal. This study established the latest high temporal and spatial resolution emission inventory from RCC in BTH region, and used the Monte Carlo method to analyze the uncertainty of emission inventory. This study provides a reliable pollutant emission database for air quality model to simulate the regional air pollution, which is of great significance to the prevention and control of air pollution in BTH region.

Method and data

Emission inventory

Based on the survey of residential coal consumption activities and the optimal emission factors (EFs) determined in literature, the air pollutant emissions from RCC were calculated by the bottom-up method. The air pollutant emission inventory of RCC developed in this study includes PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs. According to the population of rural residents in Beijing Statistical Yearbook, Tianjin Statistical Yearbook, and Hebei Economic Yearbook in 2020 at the county level, the emission was calculated (NBSC, 2021). The air pollutant emission inventory of RCC was calculated according to the following formula.

$${E}_{\textrm{i}}=A\times \left(B\times {EF}_{\textrm{i},\textrm{j}}+R\times {EF}_{\textrm{i},\textrm{k}}\right)/1000$$
(1)

where Ei represents the RCC emission (t) for pollutant i, including PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs; A represents the residential coal consumption (t); B represents the proportion of briquette utilization (%); EFi, j represents the emission factors (kg/t) for briquette combustion of pollutant i; Rrepresents the proportion of raw coal utilization (%); and EFi, k represents the emission factors (kg/t) for raw coal combustion of pollutant i.

Activity level

Research showed that the actual coal consumption in the household was quite different from the statistical data in the Statistical Yearbook (Liu et al., 2017a; Li et al., 2018). Therefore, this study used the product of the annual per capita residential coal consumption estimated by Back Propagation (BP) neural network and the rural resident population in BTH region to calculate the residential coal consumption (Li et al., 2021). The surveys for the utilization ratio of briquette and raw coal in BTH region were carried out. Table S1 summarizes the use proportion of briquette and raw coal, and the residential coal consumption of counties of BTH region.

Emission factors

Relevant researches have shown that the EFs of air pollutants from RCC depend on the characteristics of coal and stove (Chen et al., 2015; Liu et al., 2018b), and they vary greatly in different combustion stages (Sun et al., 2014). In addition, the coal composition and sampling and testing methods also affect the EFs results. The production of CO is mainly related to the combustion efficiency. The fuller the combustion, the higher the heat load of the stove, the lower the CO concentration (Liang et al., 2017), which is related to the highly volatile content of coal (Carter et al., 2014). The emission of SO2 from RCC is positively correlated with the sulfur content of coal and negatively correlated with the sulfur content of ash (Sun et al., 1988). Table S2 summarizes the air pollutant EFs of some field experiments and published data (Tian et al., 2018; Zhou et al., 2020; Peng et al., 2019; Cai et al., 2018; Cheng et al., 2017), and Table 1 shows the EFs used in this study.

Table 1 EFs of RCC used in this study (g/kg)
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Temporal allocation

The time distribution factor refers to the proportion of pollutants from RCC in the corresponding emission time (Shen et al., 2020). Due to the characteristics of unorganized and low-altitude emissions, it is difficult to carry out real-time monitoring of pollutant emissions from RCC. Considering that the emission of pollutants from RCC is directly related to the consumption of residential coal, this study reflects the proportion of pollutants from RCC in the corresponding time according to the long-term follow-up survey data of residential coal combustion (daily coal addition time and coal addition amount) of households in BTH region, and obtains the emission characteristics of monthly, daily, and hourly variation of pollutants from RCC. The time distribution factor is calculated using the following formula.

$${K}_i=\frac{A_i}{\sum {A}_i}$$
(6)
$${E}_{i,j}={K}_{i,j}\times {E}_{y,j}$$
(7)

where Ki is the i (monthly/daily/hourly) distribution factor, Ai is the i (monthly/daily/hourly) residential coal consumption (t), ∑Ai is the i (monthly/daily/hourly) residential coal consumption in total (t), Ei, j is the j (PM10/PM2.5/BC/OC/CO/NOx/SO2/VOCs) emission (t) corresponding to the i (monthly/daily/hourly) distribution factor, and Ey, j is the annual emission (t) of j (PM10/PM2.5/BC/OC/CO/NOx/SO2/VOCs).

Spatial allocation

The spatial distribution factor refers to the proportion of pollutant emissions from RCC in the total pollutant emissions in each grid (Sun et al., 2019). According to the air pollutant emissions from RCC and the vector map data of cities, districts, and counties in BTH region, the spatial distribution factor is constructed. The air pollutant emissions from RCC are distributed by ArcGIS software, and the spatial distribution characteristics of PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs emission from RCC in BTH region are obtained. The spatial distribution factor is calculated using the following formula.

$${S}_{x,y}=\frac{E_{x,y}}{\sum \limits_{x=1,y=1}^{x=m,y=n}{E}_{x,y}}$$
(8)

where Sx, y is the spatial distribution factor for the grid corresponding to the horizontal and vertical coordinates (x,y), Ex, y is the pollutant emission (t) for the grid corresponding to the horizontal and vertical coordinates (x,y), m and n are the total number of grids in the horizontal and vertical coordinates, respectively, and \(\sum \limits_{x=1,y=1}^{x=m,y=n}{E}_{x,y}\) is the total emission of pollutants (t) from RCC in each grid.

Uncertainty analysis

As shown in Eq. (1), the emission of air pollutants from RCC depends on the EFs of pollutant and the activity levels of residential coal (Zheng et al., 2021). Due to the characteristics of emission sources, the activity level of residential coal is not easy to calculate. In addition, differences exist between yearbook statistics and the actual situation (Tao et al., 2018). Uncertainty inevitably exists in the air pollutant emissions from RCC. In this study, the Monte Carlo method was used to calculate the uncertainty of air pollutant emission from RCC (Zhang et al., 2022b). The principle of Monte Carlo method is to quantify the uncertainty of the corresponding output by repeated random sampling of model input parameters (EPA, 1997). The random sampling error is calculated using the following formula.

$${RSE}_{-}=\left({E}_{5\%}\hbox{-} {E}_{\textrm{ave}}\right)/{E}_{\textrm{ave}}$$
(9)
$${RSE}_{+}=\left({E}_{95\%}\hbox{-} {E}_{\textrm{ave}}\right)/{E}_{\textrm{ave}}$$
(10)

where RSE− is the relatively negative random sampling error, E5% is the emission of pollutant (t) at 5% confidence level, Eave is the average pollutant emission (t), RSE+ is the relatively positive random sampling error, and E95% is the emission of pollutant (t) at 95% confidence level.

Results and discussion

Estimates of air pollutant emissions in 2020

The air pollutant emissions from RCC were calculated according to the method described in the “Emission inventory” section. Table S3 lists the coal consumption and air pollutant emissions of the different cities. In 2020, the residential coal consumption for household heating in BTH region was 2889.04 million tons. It is estimated that the total coal consumptions in Beijing, Tianjin, and Hebei were 377.67, 311.14, and 2200.23 million tons, respectively. They were approximately 11, 13, and 1.7 times higher than the results in the China Energy Statistical Yearbook, respectively (CESY, 2020; CESY, 2021). Many residential energy consumption surveys’ results showed that the current statistical data seriously underestimated the use of residential coal (Zhou et al., 2020; Peng et al., 2019; Cheng et al., 2017). In the study of urban coal consumption of RCC, Shijiazhuang coal consumption is highest, accounting for 14% of the total coal consumption in BTH region. Beijing (13%), Tianjin (11%), and Baoding (12%) also had higher coal consumption. The statistical methods for data collection, reporting, and validation by national statistical offices in China are not always consistent, which causes the difference between the statistical yearbook and the actual situation (Peng et al., 2019).

Figure 2 shows the city-level emission from RCC in BTH region in 2020. The total emissions of PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs were 19.58, 15.67, 2.98, 8.33, 296.96, 3.51, 36.67, and 5.87 million tons in BTH region, respectively. CO and SO2 are the major contributors of emissions from RCC, of which about 76% come from CO and 9% come from SO2, while other emissions are mainly from PM10 and PM2.5. Similar results can also be found in other studies (Zhong et al., 2018a; Bai et al., 2020; Zhu et al., 2020). The incomplete combustion of residential coal leads to high CO emissions. Different from coal consumption in industrial combustion, RCC is still the focus of SO2 emission reduction policy in the future due to the lack of corresponding control measures. From city-level perspective, the total pollutant discharge in Beijing, Tianjin, and Hebei reached 31.68, 39.52, and 318.35 million tons, respectively. Tianjin, Baoding, Chengde, and Shijiazhuang all contributed more than 10% of the total pollutant emissions from RCC in BTH region. It is worth noting that Chengde contributed the most PM2.5, BC, OC, and VOCs in BTH region, which accounted for 11.48%, 13.71%, 11.52%, and 12.72%, respectively, while Shijiazhuang contributed the most PM10, CO, NOx, and SO2 in BTH region, which accounted for 11.55%, 11.60%, 11.55%, and 12.10%, respectively. The results are directly related to the data of residential coal activity level and the proportion of two types of coal used in this study. Specifically, the utilization ratios of briquette and raw coal in BTH region were derived from the survey results (Table S1). The proportion of briquette used in Shijiazhuang is 0.74, which is twice the average proportion of briquette used in BTH region (0.41 in average). The proportion of raw coal used in Chengde is 0.84, which is one time the average proportion of briquette used in BTH region (0.59 in average). As for the activity level, Shijiazhuang contributed the largest residential coal consumption (14%) and Chengde contributed the highest raw coal consumption (13%), which is related to the rural resident population and per capita annual coal consumption. It can be obtained from Table S1 that the population of rural residents in BTH region is 4501.5 million. Among them, Shijiazhuang accounted for 15% (695.5 million) and Chengde accounted for 7% (302.1 million) (NBSC, 2021). In addition, the reason for the large emission of pollutants from RCC may be related to the differences in economic development level, income level, and energy supply in the study area (Wang et al., 2017; Silveira et al., 2017; Qiu et al., 2018). Our 2020 BTH region estimated OC, CO, and NOx emissions were similar to those in 2013 obtained by Cheng et al. (2017), while our estimated PM10, PM2.5, BC, and VOCs emissions were lower than their results. Considering that the base years were too far apart, the emission in this study is much lower than that in other researches (Zhi et al., 2017; Cai et al., 2018; Cheng et al., 2017; Ru et al., 2015). In conclusion, the pollutant emission in various regions was affected by the coal consumption, the use proportion of briquette and raw coal, and the EFs of pollutants, which was the same as the findings of Peng et al. (2019).

Fig. 2
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Air pollutant emissions from RCC in BTH region in 2020

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Table 2 shows the comparison of our estimated emissions of air pollutant from RCC with other results. In 2020, the estimated PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs emissions in Beijing, Tianjin, and Hebei in our study were 1–74, 1–14, and 2–16 times of those in Cheng et al. (2017), respectively. For Beijing, the 2020 estimated OC and SO2 emissions were 92% and 45% higher than the 2010 estimated emissions in Peng et al. (2019), while our VOCs emission was lower than their results. As for PM2.5, BC, and NOx, the emissions were similar to their research results. Except that the emissions of NOx and VOCs in Tianjin were close to those of Peng et al. (2019), the emissions of other pollutant were higher than their research. Unlike Tianjin, the estimated emissions of PM10, PM2.5, BC, OC, CO, NOx, and VOCs in Hebei were 29–68% of the emissions in 2010 in Peng et al. (2019). The main reasons such as the research base years, residential coal consumption, estimation methods, rural population, and coal usage from 2010 to 2020 are equally critical to the emissions of this study and other research results.

Table 2 Comparison of estimated air pollutant emissions from RCC with other studies (10 kt)
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Uncertainty analysis

In order to evaluate the uncertainty of emission inventory of air pollutants from RCC over BTH region, we used the Monte Carlo method to analyze the uncertainty of air pollutant emissions with reference to Zhong et al. (2018b). Firstly, the input parameter (coal consumption ) was set to logarithmic normal distribution function, the standard deviation was set to 0.44 according to Li et al. (2021), the input parameter (use the proportion of briquette and raw coal) was set to logarithmic normal distribution function with a standard deviation of 0.10 (Zhao et al., 2011), and the input parameter (emission factor) was set to triangular distribution function (Hua et al., 2016). Then, the samples were randomly selected from the set probability density distribution function, and the samples were brought into the output of the model. The average and standard deviation of the output results were used to describe the uncertainty of the quantitative results.

After 10,000 repeated calculations, the uncertainty range of air pollutant emission inventory of RCC in BTH region was simulated under the 95% confidence interval, as shown in Table 3. The uncertainty range of PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs were −35.55 to 45.96%, −50.22 to 55.65%, −48.18 to 51.84%, −58.44 to 73.13%, −35.25 to 40.03%, −41.40 to 47.50%, −32.48 to 33.07%, and −51.43 to 59.92%, respectively. The results were similar to the uncertainty results of atmospheric pollutants generated by RCC in BTH region in 2013 of Cheng et al. (2017). The random errors of each pollutant showed slight asymmetry, which was related to the skew distribution of input parameters of the model (Zhang et al., 2019).

Table 3 Uncertainty analysis of emission inventory from RCC in BTH region
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Temporal and spatial distribution

Temporal distribution

According to the time distribution factor obtained based on the long-term follow-up survey data of RCC of households over BTH region, the annual emissions of different cities were distributed to the temporal resolution of monthly, daily, and hourly. The monthly, daily, and hourly distribution factors of pollutants are shown in Table S4–S6. The monthly distribution of air pollutants from RCC over BTH region is shown in Figs. S1–S8. It was found that the highest emissions appeared in January, and the emissions of PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs reached 61,122.76t, 48,851.56t, 9219.32t, 25,980.34t, 927,188.56t, 10,952.88t, 114,686.96t, and 18,217.24t, respectively. Conversely, low emissions occurred from May to October in each city, accounted for less than 14%. Chengde and Qinhuangdao contributed significantly to air pollutant emissions in November and April, which entered the heating period earlier than other cities in the BTH region. The daily emissions of pollutants during the heating period (1 November 2019 to 16 April 2020) are shown in Figs. S9–S15. Pollutant emissions in the heating period mostly concentrated in mid-November to mid-March, and the emission peaks occurred in mid-December, early January, and mid-February. Shijiazhuang, Chengde, Baoding, and Tianjin contributed more to pollutant emissions. The daily emissions of pollutants were highest on February 9, 2019; the total emissions of PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs in BTH region reached 2192.15t, 1756.58t, 337.03t, 934.49t, 33,240.50t, 392.82t, 4095.24t, and 661.10t, respectively. Studies have shown that the temperature change and holiday factors will affect the emission of pollutants (Zhu et al., 2013). The emission characteristics of hourly variations on February 9, 2019 (Fig. S16–S23), showed that peak emission of pollutants appeared at 8:00, 11:00, 18:00, and 21:00 in BTH region, and the total emission of each pollutant reached 4472.52t, 2610.94t, 2849.09t, and 4806.69t. It can be seen that the hourly emission characteristics of RCC are closely related to the living factors such as residential coal usage habits, and working and rest.

Spatial distribution

The spatial distribution of PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs emission from RCC in BTH region in 2020 is shown in Fig. 3. It can be seen that PM10 and PM2.5 emissions in BTH region (Fig. 3(a)–(b)) were mainly concentrated in the northern, eastern, and southern regions, such as Chengde, Beijing, Tianjin, Tangshan, Cangzhou, Shijiazhuang, and Handan. The emission intensity in the western region of BTH was relatively low, and the PM10 and PM2.5 emissions in most counties were not more than 0.08 million tons and 0.10 million tons. The high emission areas of BC and VOCs (Fig. 3(c) and (h)) were mainly concentrated in Chengde, Tianjin, Cangzhou, and some southern counties. The highest OC, CO, and NOx emission areas (Fig. 3(d)–(f)) were Jizhou and Baodi districts of Tianjin, Weichang district of Chengde, and Haigang district of Qinhuangdao. Since Beijing and Tianjin use anthracite balls uniformly sold by the government, the CO emission factor of this coal type is high, resulting in large CO emission after combustion (Shen et al., 2015). The high emission areas of SO2 (Fig. 3(g)) were mainly concentrated in the central and northern of BTH region, such as Tongzhou district of Beijing, Jizhou and Baodi districts of Tianjin, Weichang district of Chengde, and Haigang district of Qinhuangdao. Also noteworthy is that the emissions of PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs in Baodi district of Tianjin were 0.65, 0.52, 0.09, 0.27, 9.86, 0.12, 1.23, and 0.19 million tons, respectively, showing a high intensity of pollutant emission. As described in the “Method and data” section of this study, the emission of pollutants from RCC depends on the level of residential coal activity, the proportion of different coal types, and the pollutant EFs selected in this study. It can be seen from Table S1 that the consumption of residential coal in Beijing, Tianjin, Baoding, Chengde, and Shijiazhuang is very considerable. Especially in Shijiazhuang, the consumption of residential coal reached 402.88 million tons (14%); the consumption of raw coal in Chengde reached 173.43 million tons (13%). Specially, the EFs of each pollutant in raw coal combustion are higher than those in briquette coal combustion, and areas with large raw coal consumption may lead to more pollutant emissions. This has been proved in many studies (Liu et al., 2018a; Tian et al., 2018; Peng et al., 2019). The rural areas with dense population and low temperature in BTH region have a large demand for heating in winter, resulting in relatively high emission intensity of air pollutants in some areas (Chen et al., 2018). Pollutant emissions exhibit a clear consistency with spatial patterns in residential coal consumption (Zhao et al., 2018).

Fig. 3
figure 3

Spatial distribution of pollutant emissions from RCC in BTH region

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Overall, the regional distribution of pollutant emission in BTH region was obvious, and the intensity of pollutant emission was related to factors such as coal consumption and population density (Liu et al., 2017b). The region may produce compound air pollution under adverse weather conditions, thus affecting the ambient air quality of the region and its surrounding areas (Zhong et al., 2018b). As an important input data for the air quality model, high-resolution pollutant emission inventory helps to better understand the real situation of regional air pollution, so as to study the complex pollutant formation mechanism under different meteorological conditions, and formulate accurate pollution prevention and control measures and policies for regional pollution.

Conclusions

In this study, we developed the emission inventory of RCC at the county level in BTH region in 2020. Pollutants including PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs were considered in the emission inventory. The pollutant emissions of each county were distributed into 1-km × 1-km grids. The annual emissions of different cities were allocated according to the temporal resolution of monthly, daily, and hourly, based on the time distribution factor obtained from long-term follow-up survey data of RCC of households in BTH region.

The results showed that the emissions of PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs in BTH region were 19.58, 15.67, 2.98, 8.33, 296.96, 3.51, 36.67, and 5.87 million tons in BTH region, respectively. Chengde contributed the most PM2.5, BC, OC, and VOCs in BTH region, which accounted for 11.48%, 13.71%, 11.52%, and 12.72%, respectively, while Shijiazhuang contributed the most PM10, CO, NOx, and SO2 in BTH region, which accounted for 11.55%, 11.60%, 11.55%, and 12.10%, respectively. The spatial distribution characteristics of pollutants indicated that the higher pollutant emission from RCC concentrated in the northern, eastern, and southern areas of BTH region, such as Chengde, Beijing, Tianjin, Tangshan, Cangzhou, Shijiazhuang, and Handan.

The temporal distribution of emissions in BTH region showed that the higher emissions occurred in mid-November to mid-March. The highest emissions appeared in January, and the emissions of PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs reached 61,122.76t, 48,851.56t, 9219.32t, 25,980.34t, 927,188.56t, 10,952.88t, 114,686.96t, and 18,217.24t, respectively. Conversely, low emissions occurred from May to October in each city, whcih accounted for less than 14%. The emission characteristics of daily showed that emission peaks occurred in mid-December, early January, and mid-February, and the hourly emission characteristics indicated that the peak emission of pollutants appeared at 8:00, 11:00, 18:00, and 21:00.

The uncertainties of the air pollutants from RCC in BTH region were analyzed by the Monte Carlo method. The uncertainty range of PM10, PM2.5, BC, OC, CO, NOx, SO2, and VOCs under 95% confidence intervals was −35.55 to 45.96%, −50.22 to 55.65%, −48.18 to 51.84%, −58.44 to 73.13%, −35.25 to 40.03%, −41.40 to 47.50%, −32.48 to 33.07%, and −51.43 to 59.92%, respectively.