A modified version of the WRF-Chem model (Grell et al., 2005) is used in this study, which is developed by Li et al. (2010, 2011a, b, 2012) at the Molina Center for Energy and the Environment. A new flexible gas-phase chemical module has been developed and implemented into the version of the WRF-Chem model, which can be utilized with different chemical mechanisms, including CBIV, RADM2, and SAPRC. The gas-phase chemistry is solved by an Eulerian backward Gauss–Seidel iterative technique with a number of iterations, inherited from NCAR-HANK (Hess et al., 2000). In the study, the SAPRC99 chemical mechanism is used based on the available emission inventory. For the aerosol simulations, the CMAQ/Models-3 aerosol module (AERO5) developed by U.S. EPA has incorporated into the model (Binkowski and Roselle, 2003). Briefly, wet deposition uses the method in the CMAQ module and dry deposition of chemical species is parameterized following Wesely (1989). The photolysis rates are calculated using the Fast Tropospheric Ultraviolet and Visible (FTUV) radiation model (Tie et al., 2003; Li et al., 2005), with the aerosol and cloud effects on the photochemistry (Li et al., 2011a).

ISORROPIA (version 1.7) is used to predict the thermodynamic equilibrium between the ammonia–sulfate–nitrate–chloride–water aerosols and their gas-phase precursors of H2SO4–HNO3–NH3–HCl–water vapor (Nenes et al., 1998). It is worth noting that the most recent extension of ISORROPIA, known as ISORROPIA II, has incorporated a larger number of aerosol species (Ca, Mn, K salts) and is designed to be a superset of ISORROPIA (Fountoukis and Nenes, 2007). Considering that crustal species are not considered in the study, ISORROPIA (version 1.7) is still used to calculate inorganic components and ISORROPIA II is imperative to be incorporated into the WRF-Chem model in future studies. In addition, a parameterization of sulfate heterogeneous formation involving aerosol liquid water (ALW) has been developed and implemented into the model, which has successfully reproduced the observed rapid sulfate formation during haze days (Li et al., 2017). The sulfate heterogeneous formation from SO2 is parameterized as a first-order irreversible uptake by ALW surfaces, with a reactive uptake coefficient of 0.5×10-4 assuming that there is enough alkalinity to maintain the high iron-catalyzed reaction rate.

The organic aerosol (OA) module is based on the volatility basis set (VBS) approach with aging and detailed information can be found in Li et al. (2011b). The POA components from traffic-related combustion and biomass burning are represented by nine surrogate species with saturation concentrations (C∗) ranging from 10-2 to 106 µg m-3 at room temperature (Shrivastava et al., 2008), and assumed to be semi-volatile and photochemically reactive (Robinson et al., 2007). The secondary organic aerosol (SOA) formation from each anthropogenic or biogenic precursor is calculated using four semi-volatile organic compounds (VOCs) with effective saturation concentrations of 1, 10, 100, and 1000 µg m-3 at 298 K. The SOA formation via the heterogeneous reaction of glyoxal and methylglyoxal is parameterized as a first-order irreversible uptake by aerosol particles with an uptake coefficient of 3.7×10-3 (Liggio et al., 2005; Zhao et al., 2006; Volkamer et al., 2007). The OA module has reasonably reproduced the POA and SOA concentration against measurements, and detailed model performance can be found in Li et al. (2011b), Feng et al. (2016), and Xing et al. (2019).

The anthropogenic emission inventory with a horizontal resolution of 6 km is developed by Zhang et al. (2009), with the base year of 2013, including industry, transportation, power plant, residential, and agriculture sources. The Model of Emissions of Gases and Aerosols from Nature (MEGAN) is used to calculate the biogenic emissions online (Guenther et al., 2006).

A heavy haze episode from 10 to 27 February 2014 in BTH is simulated in association with the field observation of air pollutants and secondary inorganic aerosols. Detailed model configuration can be found in Table 1 and the simulation domain is presented in Fig. 1.

The reaction of N2O5 heterogeneous hydrolysis on the surface of deliquescent aerosols to form HNO3 can be represented as 1N2O5+H2O→2⋅HNO3. This reaction is usually implemented into air quality transport models as a first-order loss: 2∂[N2O5]∂t=-kN2O5⋅[N2O5]. [N2O5] represents the N2O5 concentration in the atmosphere. The loss rate constant, kN2O5, is parameterized in the following way: 3kN2O5=14⋅cN2O5⋅S⋅γN2O5, where cN2O5 is the average molecular velocity of N2O5, and S is the available aerosol surface area density.

In this study, the parameterization of γN2O5 follows Riemer03 and Riemer09. In the parameterization, primary emission compounds such as elemental carbon, insoluble organic matter (mostly part of POA), insoluble inorganic matter, and mineral dust particles are assumed to serve as a nucleus of aerosols. Condensation of soluble chemical components and further water vapor on the surface of the nucleus forms an aqueous layer. The nucleus and the aqueous layer are assumed to be a unified “core” (aqueous core) in the Riemer03 and Riemer09 parameterizations. In the Riemer03 parameterization, soluble inorganic components including sulfate and nitrate are taken into consideration for suppressing the N2O5 heterogeneous hydrolysis uptake in the aqueous core, and the parameterization of γN2O5 is defined as 4γN2O5=f⋅γ1+1-f⋅γ2, with γ1=0.02 and γ2=0.002, and f is defined as 5f=mSO42-mSO42-+mNO3-. mSO42- and mNO3- are the aerosol mass concentrations of soluble sulfate and nitrate.

In the Riemer09 parameterization, unreactive organic layers are further considered for the suppression of N2O5 hydrolysis by covering the aqueous core. Organic layers may be formed by secondary organic aerosols, and such layers may consist of a single layer of molecules (monolayered coatings) or of several molecule layers (multilayered coatings) on the surface of the aqueous core. These organic layers are assumed to be an organic “coating” (shell) in the Riemer09 parameterization. The resistor scheme to calculate γN2O5 in the Riemer09 parameterization is parameterized as follows: 61γN2O5=1γN2O5,core+1γN2O5,coat, where γN2O5,core is the reaction probability of the aqueous core, which is calculated using Eq. (4), and γN2O5,coat is the pseudo-reaction probability of the organic coating calculated by the following formulation: 7γN2O5,coat=4⋅R⋅T⋅Horg⋅Dorg⋅RccN2O5⋅l⋅Rp, where R is the universal gas constant, T is temperature, Horg is the Henry's law constant for N2O5 in the organic coating, and Dorg is the diffusion coefficient for N2O5 in the organic coating. Horg and Dorg depend on the physicochemical properties of the compounds comprising the organic coating. In the Riemer09 scheme, Horg⋅Dorg is defined as 0.03⋅Haq⋅Daq. Haq is the Henry's law constant of N2O5 for the aqueous phase (Haq=5000 M atm-1) and Daq is the diffusion coefficient of N2O5 in the aqueous phase (Daq=10-9 m2 s-1). Rp, Rc, and l are the radius of the particle, radius of the inorganic core, and thickness of the coating, respectively. Rp, Rc, and l are calculated as follows: 8Rp=Rc+l,9l=Rp⋅1-β13,10β=VinorgVinorg+Vorg, where Vinorg and Vorg are the volume of inorganic and organic materials, respectively.

In this study, the mean bias (MB), root-mean-square error (RMSE), the index of agreement (IOA), mean fractional bias (MFB), and mean fractional error (MFE) are used to evaluate the model performance in simulating air pollutants. 11MB=1N∑i=1NPi-Oi12RMSE=1N∑i=1NPi-Oi21213IOA=1-∑i=1NPi-Oi2∑i=1NPi-O‾+Oi-O‾214MFB=1N∑i=1NPi-OiPi+Oi/215MFE=1N∑i=1NPi-OiPi+Oi/2 Here Pi and Oi are the simulated and observed variables, respectively. N is the total number of the simulations for comparisons, and O‾ donates the average of the observation. The IOA ranges from 0 to 1, with 1 showing a perfect agreement of the simulation with the observation.

Simulations are compared to available meteorological and air pollutant observations to evaluate the model performance. The meteorological parameters including temperature, RH, wind speed, and direction are obtained from the website http://www.meteomanz.com (last access: 20 June 2019). The hourly observations of PM2.5, O3, SO2, NO2, and CO concentrations are released by the China National Environmental Monitoring Center and can be downloaded from the website http://106.37.208.233:20035 (last access: 20 June 2019).

Additionally, hourly organic carbon (OC) and elemental carbon (EC) concentrations are measured using a thermal–optical reflectance carbon analyzer (OCEC RT-4, Sunset Lab, USA) at the Chinese Research Academy of Environmental Sciences (CRAES, 40.04∘ N, 116.40∘ E) in Beijing (Wei et al., 2014; Liu et al., 2018). Hourly sulfate, nitrate, ammonium, and other inorganic ions are sampled and analyzed by ion chromatography (URG 9000S, Thermo Fisher Scientific, USA).

The OC / EC ratio approach is used to derive the SOA mass concentrations from EC and OC filter measurements as follows (Strader, 1999; Cao et al., 2004): 16POC=EC×POCEC,17SOC=OC-POC,18SOA=SOC×SOASOC, where POC and SOC are the primary OC and secondary OC, respectively. In the present study, POC/EC and SOA/SOC are assumed to be 2.4 and 1.6, respectively, based on previous studies (Cao et al., 2007; Aiken et al., 2008; Yu et al., 2009), and detailed information about the approach can be found in Feng et al. (2016). It is worth noting that those assumed POC/EC and SOA/SOC could potentially affect the model–measurement comparisons.

Based on the NCEP FNL reanalysis data (https://rda.ucar.edu/datasets/ds083.2, last access: 20 June 2019), we have initially performed the analysis of synoptic conditions using the wind, temperature, relative humidity, and geopotential height fields at 500 and 850 hPa averaged from 10 to 27 February 2014 over China (Fig. 2). At 500 hPa, flat westerly winds prevail over BTH and its surrounding area, indicating stagnant atmospheric circulation conditions (Fig. 2a). Moreover, the flat isotherm distribution is similar to that of the isobar at 500 hPa, showing that there is no obvious exchange of cold and warm air masses, which together with the flat westerly leads to weak turbulent mixing in the vertical direction and stable weather conditions (Fig. 2b). At 850 hPa, the southeast coastal areas of China are controlled by the anticyclone, whose center is located over the South China Sea (Fig. 2c). In eastern China influenced by the anticyclone, the weak southerly wind prevails over the BTH and its surrounding regions, providing a favorable condition for stagnant weather conditions and the formation of air pollution. With the prevailing southerly wind, the warm and humid air flow and the polluted air mass are subject to being transported from south to north, aggravating the air pollution in BTH. In addition, high-relative-humidity conditions facilitate heterogeneous reactions for secondary aerosol formation (Fig. 2d).

In order to quantify effects of the N2O5 heterogeneous hydrolysis and organic coating on the nitrate formation, three experiments have been performed in the study. In the base case, the Riemer09 parameterization is used to take into consideration the organic coating effect on the N2O5 heterogeneous hydrolysis by assuming that all the SOA is involved in coating (hereafter referred to as the B-case). In the first sensitivity case, the contribution of N2O5 heterogeneous hydrolysis to nitrate formation is not considered (hereafter referred to as the H0-case). In the second sensitivity case, the organic coating effect is not considered in the Riemer09 parameterization (hereafter referred to as the C0-case). The simulation results in the B-case are compared to observations in BTH.

Figure 8 provides the nitrate temporal variations in the three cases against observations at CRAES site in Beijing from 10 to 27 February 2014. When the N2O5 heterogeneous hydrolysis is not considered in the H0-case, although the model tracks the observed nitrate variations well with an IOA of 0.91, it considerably underestimates nitrate concentration against the measurement, with a MB of -17.0 µg m-3. When the N2O5 heterogeneous hydrolysis is taken into consideration based on the Riemer09 parameterization without organic coating in the C0-case, the nitrate simulation is improved compared to that in the H0-case, with an IOA of 0.95. However, the model begins to overestimate the nitrate concentration compared to the measurement, with a MB of 5.4 µg m-3. In the B-case, when all the SOA is assumed to be involved in coating to suppress the N2O5 heterogeneous uptake on surfaces of deliquescent aerosols, the model performs best in simulating the nitrate variation compared to the measurement, with a MB and IOA of 0.1 µg m-3 and 0.96, respectively. The remarkable consistency of the simulated nitrate in the B-case with the measurement indicates that the organic coating plays an important role in improving the nitrate simulation. It is worth noting that the MB for nitrate aerosols at the CRAES site in the B-case is close to zero, but the RMSE is still rather large, reaching 19.0 µg m-3, showing considerable underestimation and overestimation, caused by uncertainties of meteorological fields and emissions. For example, the model overestimates nitrate concentrations on 11, 13, and 14 February and underestimates on 24 February against measurements. In addition, the early occurrence of intensified winds in the morning on 16 February in simulations causes rapid falloff of nitrate concentrations, leading to substantial model biases.

Figure 9a presents the distribution of contributions of the N2O5 heterogeneous hydrolysis to the nitrate formation averaged during the episode by differentiating simulations in the B-case and H0-case. The contribution of the N2O5 heterogeneous hydrolysis to the nitrate formation is substantial in BTH, exceeding 15 µg m-3 in the plain area. Although the O3 concentration is fairly low in BTH during the episode (Fig. 6b), particularly during nighttime (Fig. 5b), the elevated NO2 level still facilitates the N2O5 formation to warrant occurrence of the N2O5 heterogeneous hydrolysis. Previous studies have revealed that N2O5 heterogeneous hydrolysis is vital in nitrate formation. For example, Wang et al. (2017) calculated the daily average nitrate formation potential from the N2O5 heterogeneous hydrolysis in Beijing, showing that the reaction accounts for 52 % of the total nitrate formation. Su et al. (2017) investigated the contribution of N2O5 heterogeneous hydrolysis to the nitrate formation in Beijing during autumn in 2015 and found that the reaction causes a 21.0 % enhancement of nitrate concentrations. In the present study, the nitrate contribution of the N2O5 heterogeneous hydrolysis is 29.4 % in Beijing during the episode on average, which is close to the result in Su et al. (2017) but much lower than that in Wang et al. (2017). The average nitrate contribution of the reaction in BTH is about 30.1 %, showing that the reaction constitutes an important nitrate source during the haze pollution episode. Additionally, the N2O5 heterogeneous hydrolysis contributes 11.6 % of the PM2.5 concentration on average, playing a considerable role in the haze formation in BTH.

However, it is worth noting that the brute force method (BFM) is used to quantify the contribution of the N2O5 heterogeneous hydrolysis to the nitrate formation (Dunker et al., 1996). The BFM is generally used to assess the importance of some source, but it lacks consideration of interactions of the complicated physical and chemical processes in the atmosphere (Zhang and Ying, 2011). Therefore, in the study, the contribution of the N2O5 heterogeneous hydrolysis to the nitrate formation might be underestimated, considering the competition of inorganic cations from HNO3 formed through gas-phase reactions and sulfate aerosols in the atmosphere. It is imperative to use the source-oriented base module to evaluate the nitrate contribution of the reaction.

Figure 9b shows the distribution of the average decrease in nitrate concentrations due to suppression of organic coating during the episode by differentiating simulations in the B-case and C0-case. The organic coating reduces the nitrate concentration by more than 5 µg m-3 in the plain area of BTH, and on average the decrease in nitrate aerosols is 4.7 µg m-3 or 8.4 % in BTH during the episode. Riemer et al. (2009) have shown that when the nitrate levels are high (above 15 µg m-3), the organic coating decreases nitrate concentrations by 10 %–15 % over Europe. However, Chen et al. (2018) have demonstrated that the suppression of organic coating is negligible over western and central Europe, with an influence on nitrate concentrations of less than 2 % on average and 20 % at the most significant moment. Apparently, except for N2O5 and water-soluble OA in the atmosphere, the effect of organic coating is also dependent on NH3, RH, and temperature. Hence, the inconsistency between the model results about the organic coating effect can be attributed to the variation in simulation conditions. For example, in order to obtain substantial effects of the organic coating, N2O5, SOA, and NH3 need to be present when RH is high and temperature is low. However, those conditions are rarely fulfilled simultaneously over western and central Europe, causing a negligible effect of organic coating (Chen et al., 2018). Additionally, Wang et al. (2017) have indicated that the evaluated nitrate level with the N2O5 heterogeneous hydrolysis in Beijing is much higher than the observation, which they have attributed to atmospheric dilution and deposition. It is worth noting that the organic coating effect might constitute one of the most possible reasons for the overestimation of nitrate concentrations, considering the elevated SOA level in Beijing, which suppresses the N2O5 heterogeneous hydrolysis and results in high observed N2O5 concentrations (Wu et al., 2017). Figure 10 presents the temporal variation in the simulated γN2O5 in Beijing during the episode. The simulated γN2O5 fluctuates between 0.009 and 0.02 when organic coating is included, with an average of 0.013. The estimated γN2O5 in Beijing by Wang et al. (2017) ranges from 0.025 to 0.072 without consideration of the suppression of organic coating, indicating that organic coating substantially hinders the N2O5 heterogeneous hydrolysis, likely causing the observed high level of N2O5 during nighttime.

It is worth noting that, in the study, the assumption of metastable aerosols is used or the water-soluble aerosol is assumed to be only in a liquid state in simulations. However, Wang et al. (2008) have highlighted the effect of the hysteresis of particle-phase transitions on the distribution of solid and aqueous aerosols. The aerosol phase is generally regulated by the hysteresis loop. Atmospheric particles containing inorganic salts remain solid until the RH reaches the DRH (deliquescence relative humidity). At the DRH, the solid particle spontaneously absorbs water to become a saturated aqueous solution. However, the liquid particle does not crystallize when the RH is below the DRH (Seinfeld and Pandis, 2006). Therefore, another possible pathway exists to suppress the N2O5 hydrolysis; i.e., the inorganic particles might be in solid phase without organic coating. Further studies need to be conducted to evaluate the hysteresis effect on the N2O5 hydrolysis and organic coating.

In Sect. 3.3, the WRF-Chem model considerably improves nitrate simulations when considering the N2O5 heterogeneous hydrolysis and organic coating effects. Organic aerosols (OAs) are broadly classified as primary OA (POA) directly emitted and SOA formed in the atmosphere, some of which are water soluble. In order to explore the effects of different OA coatings on the nitrate formation, an additional four sensitivity studies are conducted, in which half of SOA (C1-case), all SOA (C2-case), all SOA and half of POA (C3-case), and all SOA and POA (C4-case) are involved in coating.

Figure 11 shows the Taylor diagram (Taylor, 2001) to present the variance, bias, and correlation of the observed and simulated nitrate concentrations in the four sensitivity cases at the CRAES site during the episode. In the C1-case, when half of SOA is considered to be involved in coating, the simulated nitrate concentration is the most consistent with the observation, with a correlation coefficient of 0.96. In the C2-case with all SOA assumed to be engaged in coating, the correlation coefficient decreases to 0.95. The normalized standardized deviation (NSD) is 1.02 for the C1-case and C2-case, showing the model overestimation in these two cases. With half of POA involved in coating, the NSD is very close to 1.0 (0.99), indicating the simulated nitrate concentration in the C3-case is almost the same as the observation on average, but the correlation coefficient of 0.94 is less than those in the C1-case and C2-case. When all of OA is assumed as the coating, the bias between simulated and observed nitrate concentrations is the largest, and the effect of POA on suppressing the N2O5 heterogeneous hydrolysis might be overestimated in the C4-case.

Sensitivity results show that the effects of different organic compounds on suppressing the N2O5 heterogeneous hydrolysis to form nitrate vary, depending on the content of water-soluble OA. Laboratory and field measurements have revealed that OA becomes progressively oxidized and more hygroscopic during the aging process in the atmosphere (Jimenez et al., 2009). The OA hygroscopicity constitutes a necessary prerequisite for accurately representing the organic coating effect on the N2O5 heterogeneous hydrolysis. According to the simulations in the present study, in BTH, not all SOA can serve as the coating to suppress the nitrate formation, and the effect of POA on coating might be neglected. Xing et al. (2019) have shown that in BTH, the heterogeneous SOA formed by irreversible uptake of glyoxal and methylglyoxal on wet aerosol surfaces contributes about 30 % of the SOA mass during haze days. Considering the possible heterogeneous SOA contribution of other carbonyl compounds and the atmospheric aging of OA, about half of SOA should likely be hygroscopic and involved in coating.