The research strategy of this study consists of three main parts: model setup, spatial distribution characteristic analysis, and quantification of meteorological conditions and anthropogenic emission contributions (Fig. 1). In the first part, DEHM was employed to obtain hourly pollutant concentrations, followed by model evaluation, where the Weather Research and Forecasting (WRF) model v4.1 (Skamarock et al., 2008) driven by either ERA5 or global climate data from the Community Earth System Model (CESM) was used as meteorological input to DEHM and with exactly same spatial setup for China as in DEHM. Sensitivity experiments were designed for meteorological conditions, emission inventories, and anthropogenic emission sources. From these simulations, the spatial-scale estimation of OP was estimated by incorporating simulated values of primary and secondary PM2.5 concentrations from various anthropogenic sources into Eq. () (see Sect.  for details).

In the second part, the spatial distribution characteristics of PM2.5 and OP were determined using probability density functions (PDFs) and spatial distribution maps. In the third part, quantitative analysis was conducted based on the simulation results from the sensitivity experiments to determine the extent of the influence of meteorology and emissions on PM2.5 and OP, as well as the primary sources of PM2.5 and OP.

Most current data on OP of PM2.5 in China are obtained by means of measurement, and the research objects are basically limited to specific cities, which to some extent hinders conducting research on OP in a large-scale region. Considering that Liu et al. (2018) collected samples across four seasons from multiple representative locations in China, their developed OP prediction model (Eq. ) can support us in estimating OP (with units of nmolmin-1m-3) in China, thereby exploring the spatial distribution characteristics of OP and the contributions of different anthropogenic sources to OP. In the present study, we have used this relationship, in combination with the sensitivity simulations (Sect. ), to calculate the OP. 1OP=0.088×re+0.076×bi+0.041×se+0.034×in+0.017×tr Here, re, bi, in, and tr represent the primary PM2.5 concentrations (with units of µg m-3) for coal combustion, biomass burning, industry sources, and transportation sources, respectively. The notation se (secondary aerosol formation) refers to the concentrations of secondary organic and inorganic (SOA and SIA, respectively) components (with units of µg m-3). In this study, coal combustion refers to coal heating from the residential sector. Biomass burning includes open burning of agricultural biomass, domestic biomass burning for cooking and heating, and biomass burning from biomass power plants and coal-fired power plants. The industry source is mainly derived from specific industrial processes in iron and steel, metallurgical production plants for non-ferrous metals (e.g., titanium and molybdenum), and so on. The transportation source primarily comes from tailpipe emissions. It is worth mentioning that secondary aerosol formation originates from a series of atmospheric reactions. Some identified sources (i.e., coal combustion, biomass burning, industrial processes, and transportation) may generate secondary inorganic and organic aerosols through the emission of their precursor components. The coefficient (with units of nmolmin-1m-3source-1) reflects the intrinsic OP of each source.

The DEHM can capture many features of PM well and its precursors' changes in large-scale space (Christensen, 1997; Brandt et al., 2012; Im et al., 2019). To date, the DEHM has been widely used in air pollution and health risk assessment research in Europe and Asia (Brandt et al., 2013a b; Zare et al., 2014; Geels et al., 2015, 2021; Im et al., 2018, 2019, 2023; Lehtomäki et al., 2020; Cramer et al., 2020; S. Liu et al., 2021; Thomas et al., 2022), but this will be the first time that DEHM is applied to estimate OP. Thus, the DEHM system was used to simulate the pollutant concentrations in 2014 by using a two-way nested domain in this study (Kumar et al., 2016). A parent domain with a resolution of 150 km × 150 km was employed on a polar stereographic projection, true at 60° N to cover the entire Northern Hemisphere. The nested domain covered the whole of China, consisting of 150 × 150 grid cells with a resolution of 50 km × 50 km, which was used for the analysis. The mother domain provided initial and boundary conditions for the nested domain. Vertically, there were 29 unevenly distributed layers, with the highest level reaching 100 hPa, and the lowest layer was approximately 20 m in height. The meteorological fields were simulated using the WRF model (Skamarock et al., 2008) with the same domain and resolution driven by global meteorological data obtained from the ERA5 dataset and the CESM global model, respectively. The simulations utilized the revised MM5 surface layer scheme, the Yonsei University (YSU) boundary layer parameterization scheme (Hong et al., 2006), the multi-scale Kain–Fritsch cumulus parameterization scheme (Zheng et al., 2016), the CAM longwave radiation scheme, and the CAM shortwave radiation scheme (Skamarock et al., 2021). The gas-phase chemistry module included 66 species, nine primary particles (including natural particles such as sea salt), and 138 chemical reactions and was based on the scheme by Strand and Hov (1994) (Brandt et al., 2012). The gas-phase species considered in this study included SO2, NO2, CH4, and C2H6. PM2.5 was formed by BC, OC, sea salt, ammonium (NH4+), nitrate (NO3-), sulfate (SO42-), and secondary organic aerosols (SOAs), among others (Frohn et al., 2022). Biogenic volatile organic compounds (BVOCs), such as isoprene, contributed to the formation of SOA (Zare et al., 2012). Further details on the configuration of the chemical scheme and the list of chemical reactions are in the literature (Zare et al., 2012; Brandt et al., 2012; Collin, 2020; Frohn et al., 2022). The SOAs were calculated using the volatility basis set (see details in Im et al., 2019). In addition to the anthropogenic emissions, DEHM also includes emissions from biogenic emissions, such as vegetation, sea salt, lightning, and soil. The current version of the DEHM does not include windblown resuspended dust emissions, road dust, or aerosol–radiation or radiation–cloud interactions. The time resolution of the DEHM output is 1 h.

In the current study, the DEHM used anthropogenic emissions from the Emissions Database for Global Atmospheric Research – Hemispheric Transport of Air Pollution (EDGAR-HTAP) and Eclipse V6. The biomass burning emissions are obtained from the Global Fire Assimilation System (GFAS) from ECMWF (Kaiser et al., 2012), which has a horizontal resolution of 0.1° × 0.1° on a daily time basis. Natural emissions for DEHM are based on the Global Emissions InitiAtive (GEIA, Zare et al., 2012; Frost et al., 2013) with monthly inventories for emissions of nitrogen oxides from soil and lightning and annual inventories for emissions of ammonia from natural sources. The production of sea salt (Soares et al., 2016) and biogenic volatile organic compounds (Zare et al., 2014) is calculated online in the model as a function of meteorological parameters like wind speed and temperature (Frohn et al., 2022).

Taking into account the substantial spatial heterogeneity of PM2.5 concentrations and OP, we employ PDF to characterize the statistical distribution characteristics of PM2.5 concentrations and OP across China. This offers a more generalized and robust probability for criteria limits. In this study, all three functional types (lognormal, exponential, and gamma) were tested for annual average PM2.5 concentrations and OP at the monitoring stations. To determine the representative distributions for the datasets, we further performed goodness-of-fit tests such as the sum of squared error (SSE) and the Kolmogorov–Smirnov (K-S) test (de Melo et al., 2000) using the fitter package in Python.

The hourly observation data were obtained from the Ministry of Ecology and Environment of China (MEE, 2014). The MEE website first released PM2.5 measurement data in January 2013. In accordance with Chinese environmental protection standards, the hourly PM2.5 concentrations are measured using the micro-oscillation balance method and beta absorption method, with an uncertainty of less than 5 µg m-3 (Zeng et al., 2021). The PM2.5 monitoring stations are primarily distributed in urban areas, particularly in major metropolitan areas of China (Zeng et al., 2021). In 2014, the observation stations were mainly concentrated in eastern China, while stations in western China were limited. Therefore, in the present study, we also evaluated with the gridded annual mean global reanalysis Dalhousie surface PM2.5 dataset (van Donkelaar et al., 2021), which combines satellite retrievals of aerosol optical depth, chemical transport modeling, and ground-based measurements. The Dalhousie dataset compensated for the nonuniform distribution spatially of observation stations to comprehensively evaluate the performance of the DEHM. The density scatterplot of model performance and evaluation for China in scenario C1 based on annual mean PM2.5 observations from MEE and PM2.5 derived from the Dalhousie dataset are shown in Fig. 3. Overall, the model performance in terms of correlation coefficient (R) and normalized mean error (NME) calculated based on annual mean observations met the performance criteria suggested by Emery et al. (2017) (NME < 0.5, R > 0.4), and the normalized mean bias (NMB) was also close to the performance criteria suggested by Emery et al. (2017) (NMB < ± 0.3). Compared to the observations, the model performance in terms of R, NME, and NMB calculated based on the Dalhousie dataset was slightly poorer than but still close to the performance criteria suggested by Emery et al. (2017). Additionally, this study evaluated the model performance in scenarios C2 and C3 (Fig. S2 in the Supplement). It was found that under scenarios C2 and C3, the model performance in terms of R and NME, calculated based on both annual mean observations and the Dalhousie dataset, met the performance criteria suggested by Emery et al. (2017). The NMB under scenarios C2 and C3 calculated based on both annual mean observations and the Dalhousie dataset were also close to the performance criteria suggested by Emery et al. (2017). Therefore, the simulated annual mean PM2.5 concentrations in scenarios C1, C2, and C3 are considered reliable.

To verify the spatial accuracy, a comparison of simulated and observed PM2.5 from both MEE and Dalhousie was conducted. Table 2 shows the results of the annual mean simulated minus annual mean observed values (denoted as diffsi-ob), as well as the results of the annual mean simulated values minus the Dalhousie dataset (denoted as diffsi-DH). Table 2 indicates that the majority of regions (central and eastern China) exhibited differences ranging from -18 to 0 µg m-3, which is an underestimation of 37 % compared to the average annual observations. The simulated PM2.5 concentrations in eastern, central, northeastern, and western China were 37 %, 21 %, 49 %, and 41 % lower than the observations, respectively; the simulated values were 28 %, -3 %, 54 %, and 48 % lower than the Dalhousie dataset, respectively. The disparities in model performance across regions may be attributed to uncertainties in the simulation of meteorological fields, coupled with insufficient consideration of species in the reaction processes within the model. Considering the existing literature (Huang et al., 2021; Jia and Zhang, 2021), it is known that bias within approximately 50 % is acceptable. For example, the PM2.5 concentrations in eastern China in 2014 simulated by Jia and Zhang (2021) were overestimated by 48 %. Shi et al. (2021) also reported PM2.5 concentrations being overestimated or underestimated by 40 % compared to observed values. Hence, the simulated bias in this study falls within an acceptable range, meeting the research requirements.

Similarly, the model performance over timescales was also investigated. Density scatterplots and distribution characteristics of monthly average observations and simulations for all monitoring sites in 2014 are depicted in Fig. S1 in the Supplement and Fig. 4, respectively. From Fig. 4, it can be observed that the simulated values closely align with the observed values from April to September. However, in other months, there was a slightly poorer alignment between simulated and observed values. Nonetheless, considering the overall performance throughout the year, as analyzed in conjunction with Fig. S1, it can be deduced that both the correlation R and NME met the performance criteria suggested by Emery et al. (2017) for all months except December. Furthermore, the results in Table 2 indicate that the bias across various regions in DEHM is acceptable. Consequently, on an aggregate level for China, the model demonstrates acceptable performance in simulating monthly average PM2.5 concentrations.

To learn about the spatial distributions of PM2.5 concentrations and OP, we quantified the average annual PM2.5 concentrations and OP across different regions of China (Fig. 5). High PM2.5 concentrations and high OP are mainly located in central and eastern urban clusters. Low PM2.5 concentrations and low OP are mainly distributed in northeastern and western China. The results in Fig. 5 indicate that the annual average PM2.5 concentrations and OP in eastern, central, northeastern, and western China are 33 µg m-3 and 1.4 nmolmin-1m-3, 46 µg m-3 and 2.0 nmolmin-1m-3, 19 µg m-3 and 0.8 nmolmin-1m-3, and 12 µg m-3 and 0.5 nmolmin-1m-3, respectively.

Due to differences in city types, pollutant emission intensities, and pollutant chemical components in different regions, there is significant spatial heterogeneity in PM2.5 concentrations and therefore in OP (see Sect.  and Fig. 9 for details). Due to high population density, socioeconomic activities, and winter heating needs, large quantities of anthropogenic emissions, especially from industry, transportation, coal burning, and biomass burning, exacerbate PM2.5 and redox-active component pollution.

To quantitatively analyze the regional distribution characteristics of PM2.5 concentrations and OP in China, we determined the distribution function that is suitable for a specific dataset (Table 3), investigated the frequency histogram (FH) of PM2.5 concentrations and OP, fitted the PDF, and then obtained the cumulative distribution function (CDF) by integrating PDF, as shown in Fig. 6. It was found that the gamma distribution performed the best in fitting PM2.5 concentrations and OP from Table 3. Considering the test results, the gamma distribution was used to explore the spatial distribution characteristics of PM2.5 concentrations and OP. Figure 6a depicts the probability distribution of PM2.5 concentrations, while Fig. 6b depicts the probability distribution of OP. The wide distribution interval indicates that both PM2.5 concentrations and OP have a similar and large spatial heterogeneity. According to the FH, the highest frequency density of PM2.5 concentrations ranges from 10.5 to 12.9 µg m-3; the maximum frequency density of OP ranges from 0.26 to 0.34 nmolmin-1m-3. This reflects the overall pollution levels of PM2.5 and OP in the Chinese region. Taking into account the annual average PM2.5 concentration limits set out in China's ambient air quality standard (AAQS, 2012), we focused on primary (15 µg m-3) and secondary concentration (35 µg m-3) limits. The PDF and CDF results showed that 85 % of the total area was above the primary concentration limit and 40 % was above the secondary concentration limit. In addition, 36 % of regions in China have an OP below 1.00 nmolmin-1m-3, 41 % have an OP between 1.00 and 2.00 nmolmin-1m-3, and 23 % have an OP above 2.00 nmolmin-1m-3.

To determine the sensitivity of PM2.5 pollution and oxidation potential (OP) to meteorological conditions (emission inventories), this study compared scenarios C2 and C3 (C1) and investigated the impacts and contributions from ERA5 and CESM (HTAP and Eclipse V6 emission inventories) regarding PM2.5 and OP. Table 4 illustrates the PM2.5 concentrations and OP in different regions of China under scenarios C1, C2, and C3. Figure 7a presents the annual average PM2.5 concentrations and OP under different scenarios, and Fig. 7b shows the relative contributions of meteorological conditions and emission inventories. From Table 4 and Fig. 7, it can be observed that, compared to scenario C2, PM2.5 concentrations and OP are lower in the western region under scenario C1, primarily due to changes in emission inventories attributed to the inclusion or exclusion of specific local sources during the compilation process. Compared to scenario C3, PM2.5 concentrations are lower in the western region and higher in some eastern areas under scenario C2, primarily attributed to meteorological contributions. For the entire China region, the transition in emission inventories from Eclipse V6 to HTAP resulted in an overall decrease in PM2.5 concentrations of 1.55 µg m-3, which is approximately 7.61 %, and a decrease in OP of 0.0339 nmolmin-1m-3, which is approximately 4.05 %. The shift in meteorological data from CESM to ERA5 led to an increase in PM2.5 concentrations of 1.22 µg m-3, which is approximately 6.4 %, and an increase in OP of 0.0585 nmolmin-1m-3, which is approximately 7.5 %. According to the normalization process using Eqs. () and (), meteorological conditions contributed approximately 45.6 % to the variations in PM2.5 and approximately 65.0 % to the variations in OP. Meanwhile, emission inventories contributed approximately 54.4 % to the variations in PM2.5 and approximately 35.0 % to the variations in OP. Our findings highlight the significance of the quality of model input data, including emission inventories and meteorological data, for model performance.

To determine the impact of anthropogenic emissions on PM2.5 and OP, we quantified their percent contribution (Fig. 8). Secondary aerosol formation, biomass burning, industrial, coal combustion for residential heating, and transportation sources contributed 48 %, 21 %, 21 %, 6 %, and 4 % to PM2.5, respectively. Secondary aerosol formation, biomass burning, coal combustion for residential heating, industrial sources, and transportation sources contributed 58 %, 21 %, 11 %, 9 %, and 1 % to OP, respectively. This means that secondary aerosol formation and biomass burning are the main sources of PM2.5 and OP.

Thus, we explored the spatial distribution characteristics of PM2.5 and OP from different anthropogenic sources to reveal the spatial contributions of PM2.5 concentrations and OP, as shown in Fig. 9. It was observed that the spatial distribution features of PM2.5 concentrations and OP from each emission source are similar to those in Fig. 5, and they all adhere to the principle that the eastern region is higher than the western.

It can be seen from Fig. 9 that the main reason that secondary aerosol formation is the main anthropogenic source of both PM2.5 concentrations and OP in China is due to the higher pollution levels, more contributions to mass, and toxicity in the central and eastern regions. A relevant study (Molina et al., 2023) has highlighted the significant contribution of secondary aerosol formation to particle mass and intrinsic OP.

Chinese crops (especially corn straw), power plants mainly being concentrated in the central and eastern regions as well as the northeast and part of the western region, and the bigger intrinsic OP (Eq. ) result in biomass burning becoming the second contribution.

In this study, coal combustion refers to coal heating from the residential sector. Coal burning increases secondary inorganic and organic aerosols in the air (Liu et al., 2018), which leads to stronger oxidative toxicity. Thus, due to greater heating demand in locations with a high population density and chilly winters (e.g., the northern part of central and eastern China), PM2.5 concentrations and OP linked to coal burning are higher.

Industrial emissions are mainly derived from specific industrial processes in iron and steel, metallurgical production plants for non-ferrous metals (e.g., titanium and molybdenum), and so on. This is one main source for metals. Due to the correlation between these transition metals and OP (Fang et al., 2017; Liu et al., 2018), China's four industrial zones (Liaozhong-South Heavy Industry Base, Beijing–Tianjin–Tangshan Industrial Base, Shanghai–Nanjing–Hangzhou Industrial Base, and Pearl River Delta Light Industry Base) are important contributors to PM2.5 and OP emissions from industrial sources.

The transportation sector in the DEHM only considers tailpipe emissions, excluding non-exhaust emissions from vehicles like road dust, brake dust, and tire wear, which is a main reason that the traffic sources exhibit the lowest contribution to PM2.5 concentrations and OP. Moreover, it can be observed from Fig. 9 that the contribution of this sector is mainly concentrated in the central and eastern regions, which is mainly due to the high transportation emissions in a small number of regions, such as Henan, Hebei, and Shandong. This is valid for the top three provinces in terms of vehicle particulate matter and nitrogen oxide emissions in 2014 according to the China Annual Vehicle Pollution Prevention and Control Report (MEE, 2015).

OP is considered an important indicator of PM2.5 toxicity and is associated with adverse health effects. Linking the predicted health effects of aerosols to OP may be more relevant than considering PM2.5 mass alone (Alwadei et al., 2020). However, previous studies of OP in China have mainly focused on local areas, and OP and its sources are very different in space and time (Wen et al., 2023), which makes health research on OP challenging. At present, there are two kinds of methods for evaluating OP of PM2.5: the cellular method and non-cellular method. The reproducibility of cellular methods is poor, and it is difficult to achieve a large sample size analysis. And the choice of cell type or cell line can significantly affect the OP results (Xing et al., 2023). The non-cellular method has the advantages of fast speed, simple operation, high reproducibility, and low cost. The most common non-cellular methods are DTT, AA, GSH, and 2′, 7′-dichlorofluorescein (DCFH) assays (Pietrogrande et al., 2019). However, standardized experimental methods for evaluating OP have not been established (Song et al., 2021), and it is difficult to provide more consistent data on OP across samples at different locations and times. Moreover, each non-cellular OP assay is specific for ROS, meaning that none of the methods are used as a standard method for assessing the toxicity of environmental particles. Several studies have used a multi-measure approach to compensate for the specificity of a single-probe response to ROS (Calas et al., 2018; Puthussery et al., 2020; Yu et al., 2021; Xu et al., 2021). Xu et al. (2021) used three measurement methods (OPDTT, OPAA, and OPGSH) to estimate the Canadian annual mean OP and found that the sensitivity of the three methods to different components varied widely. Choosing a variety of methods for OP measurement can lead to more comprehensive results, but it can also lead to a significant increase in workload.

For this, we propose a hybrid approach combining existing observations of OP with a CTM. So, using OP from assays and their observed links to sources and chemical constituents can then be parameterized and implemented in a CTM for a comprehensive assessment of OP exposure over large areas and time periods. The method considers the seasonal characteristics of the chemical composition of PM2.5 and the DTT activity measurement of PM2.5. A positive matrix factorization (PMF) model and multiple linear regression (MLR) model were used to quantify the contribution of PM2.5 emission sources to OP (the volume-normalized DTT activity, DTTv). The normalized regression equation in this study provides the sensitivity of OP to each identified source. The advantage is that directly applying predicted and readily available PM2.5 data makes it easy to estimate the OP and assess health risks over large regions and across time and space. This approach enables the exploration of spatial and seasonal variations in aerosol OP across China, providing insight into the contribution of sources, atmospheric processes, and meteorological conditions. There are some main limitations to this study that may lead to uncertainty in predicting OP outcomes. Firstly, the OP prediction considered is incomplete and does not include all sources of OP. For example, the transportation sector refers only to road transport, excluding emissions from ships and other mobile sources. And the transportation sector only considers tailpipe emissions in traffic. These lead to some OP uncertainties. Additionally, this study only considers the intrinsic OP of total SOA due to limited long-term measurements of SOA. Different types of SOA may exhibit varied OP responses due to differences in their sources, formation pathways, and chemical compositions. Aging and fresh SOA may also exhibit varying toxicities (F. Liu et al., 2023). In future research, efforts should be made to comprehensively collect PM2.5 samples from various sources and fully explore the potential relationships between OP and PM2.5 components and sources to further improve OP prediction models and reduce prediction uncertainties. Secondly, the OP prediction model adopted in this paper is based on Liu et al. (2018). The data samples are from DTT experimental measurements conducted in various coastal cities and from different emission sources, with limited data samples. In this study, they are used to predict the OP of cities across the country, which inevitably leads to a slight error in the forecast results. However, due to the spatiotemporal and emission source differences of the data samples were considered, the three cities selected are representative, which reduces the errors caused by the data samples to a certain extent. Thirdly, a significant body of literature also indicates that vertical resolution can reflect atmospheric thermodynamic environments and the evolution processes of mesoscale systems, which are related to the diffusion and transport of PM2.5. Insufficient vertical resolution can hinder the accurate prediction of PM2.5 surface concentrations (Hara, 2011; Li et al., 2022; Li et al., 2023). Therefore, the configuration of the DEHM (e.g., vertical resolution) also introduces uncertainties to this study. In conclusion, the results calculated by the method proposed in this study are compared with existing measurement data (Liu et al., 2014; Liu et al., 2018; Wang et al., 2019), and good agreement is observed. For instance, through DTT measurements, Zhang et al. (2023) reported an average OPVDTT of 1.33 nmolmin-1m-3 from January 2020 to June 2021 in downtown Nanjing, located in the Yangtze River Delta region of China, with a range of 0.82–2.08 nmolmin-1m-3. This is close to our estimated results (Liu et al., 2024) for the Yangtze River Delta region, where the annual mean OP during 2010–2014 was 1.56 nmolmin-1m-3, and the annual mean OP values for 2020 under two emission reduction scenarios were 1.36 nmolmin-1m-3 and 1.25 nmolmin-1m-3, respectively. The relative errors for the two scenarios were 2.3 % and 6.0 %. Another study (Liu et al., 2020) investigating the OP of PM2.5 in Wuhan, located in the central China region, reported a mean OPVDTT of 1.8 nmolmin-1m-3 for the summer of 2012 in downtown Wuhan. This aligns closely with our estimated results (Liu et al., 2024) for the central China region (1.73 nmolmin-1m-3), with a relative error of 3.9 %. Therefore, the method proposed in this study is reliable. The proposed method provides a possibility to solve the difficulty and high cost of OP measurement.