3.1 Field-measured ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and influencing factors

During the field measurements at Heshan and Mt. Tai, the air was characterized as moderately polluted for O₃ (43±22 ppbv at Heshan and 63±14 ppbv at Mt. Tai), NO_x (14.0±11.5 ppbv at Heshan and 2.2±2.1 ppbv at Mt. Tai), and PM_2.5 (66.7±41.9 µg m⁻³ at Heshan and 33.7±26.7 µg m⁻³ at Mt. Tai), as summarized in Table S2 and shown in Fig. 1b. ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$, which was directly measured using the aerosol flow tube, showed a large variation ranging from 0.002 to 0.067 with an average of 0.020±0.019 at Heshan and from 0.001 to 0.019 with an average of 0.011±0.005 at Mt. Tai. These values are within the range of 10⁻⁵ to > 0.1 derived from the ambient N₂O₅ concentrations around the world (e.g., Brown et al., 2006; Bertram et al., 2009b; Riedel et al., 2012; Morgan et al., 2015; Z. Wang et al., 2017; Tham et al., 2018; McDuffie et al., 2018a) but slightly lower than the previous results in the polluted regions in China (0.021 to 0.102) (Z. Wang et al., 2017; X. Wang et al., 2017; H. Wang et al., 2017). The field-measured ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and relevant pollutants at the two sites as well as those derived from three previous studies in China are summarized in Fig. 1b, covering diverse atmospheric conditions from moderately humid to humid conditions and from clean to polluted conditions.

Figure 2 shows the relationship between the field-measured ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and the aerosol composition during five campaigns at those four sites in China. It can be seen that the ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ had a good positive correlation with the aerosol water content (r²=0.65) (Fig. 2a), suggesting a common controlling role of aerosol water in the reactivity of N₂O₅ in both northern and southern China. Although the positive correlation of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ with the humidity or aerosol water has been observed in the low range in previous laboratory studies, the ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ reached plateaus at a value around 0.036 at RH > 50 % or [H₂O] > 15 M (Hallquist et al., 2003; Thornton et al., 2003; Bertram and Thornton, 2009). In contrast, other laboratory studies also measured higher ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ values on NH₄HSO₄ particles. For example, Mozurkewich and Calvert (1988) reported an upper limit of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ of 0.056 at RH = 55 % at 293 K, which increased to around 0.1 at 274 K. Kane et al. (2001) observed a strong RH-dependent ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$, increasing from 0.018 to 0.069 with RH from 56 % to 99 %, which is largely consistent with the field results in the present study. Moreover, several field measurements also observed ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ values exceeding 0.04 at high RH or water molarity (e.g., Phillips et al., 2016; McDuffie et al., 2018a; H. Wang et al., 2017; Tham et al., 2018), and some of them also found the similar positive relationship between ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and water molarity (McDuffie et al., 2018a). Although uncertainties may exist in the calculation of aerosol surface and uptake coefficient at high ambient RH conditions, our results with a consistently increasing trend of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ with [H₂O] from below 10 M up to 50 M suggest that the aerosol water content strongly affects the activity of N₂O₅ uptake, and that N₂O₅ hydrolysis is always limited by aerosol water content under all the encountered ambient conditions. Since limited measurement data of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ from laboratory and field studies are available at the RH > 80 % condition, it is unclear what exact mechanism or process (e.g., a phase change different from laboratory-made particles or acidity involved) promotes more effective uptake on ambient aerosols at higher aerosol water content conditions. Therefore, more detailed investigations of N₂O₅ uptake on nanosized water or aerosol droplets in the real (or close to real) ambient conditions are clearly warranted. For nitrate, a clear suppression effect can be found at the Chinese sites (Fig. 2b), which is similar to most of the previous field and laboratory studies. The decrease of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ with increasing nitrate concentration seems to be better captured by an “exponential-decay” curve, with almost linear suppression for [${\mathrm{NO}}_{\mathrm{3}}^{-}$] below 5 M. The observed ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ under high nitrate condition (> 5 M) was generally below 0.025 and became nitrate independent as the nitrate levels further increased.

The ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ variation was affected by the additive effects from both [${\mathrm{NO}}_{\mathrm{3}}^{-}$] and [H₂O], which could not be easily isolated because of their competing reactions with the reactive intermediate ${\mathrm{H}}_{\mathrm{2}}{\mathrm{ONO}}_{\mathrm{2}}^{+}$. This is further supported by the positive dependence of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ on the molar ratio of $\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]/\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]$ (Fig. 2c). Different from the previously reported plateauing of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ with increasing $\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]/\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]$ ratio in laboratory studies (Hallquist et al., 2003; Bertram and Thornton, 2009), no decrease in ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ suppression was found in the present study for $\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]/\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]$ ratio of up to 60. The more scattered data at higher $\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]/\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]$ ranges imply that the variation of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ becomes more sensitive to other factors in the diluted aqueous aerosols. Although the ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ measured at two mountain sites showed a positive relationship with $\left[{\mathrm{Cl}}^{-}\right]/\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]$, the overall results from five sites did not exhibit an obvious pattern (Fig. 2d). These results suggest that chloride concentration may not play a critical role in ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ during our observations as laboratory studies have observed (Bertram and Thornton, 2009), possibly due to the complex effect of aerosol mixing state. Though the measured ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ exhibited a nonlinear relationship and complex dependence on different factors at a single site, the general consistent patterns at different sites in this study suggests the feasibility of a common parameterization representing the N₂O₅ uptake in these regions.

Table 1Statistical summary and comparison of the observed parameters (N₂O₅ uptake coefficient, ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$; ClNO₂ yield, ${\mathrm{\Phi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$) with values predicted from different parameterizations.

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3.2 Comparison to parameterizations

Current regional air quality models such as WRF-Chem and CMAQ mainly use the ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ parameterization recommended by Bertram and Thornton (2009) (hereafter referred to as BT09), which links ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ to aerosol water content, nitrate, and chloride as well as the aerosol size and ambient temperature. The BT09 parameterization based on the abovementioned reaction mechanism (Reactions R1–R5) was expressed as follows:

where V_a∕S_a is the measured aerosol volume to surface area ratio, ranging from $\mathrm{3.30}\times {\mathrm{10}}^{-\mathrm{8}}$ to $\mathrm{9.29}\times {\mathrm{10}}^{-\mathrm{8}}$ m in the five campaigns; K_H is Henry's law coefficient, taken as 51 (Bertram and Thornton, 2009; Fried et al., 1994); $\mathit{\beta }=\mathrm{1.15}\times {\mathrm{10}}^{\mathrm{6}}$; $\mathit{\delta }=-\mathrm{0.13}$. The parameters $k_{\mathrm{3}}/k_{\text{2b}}(=\mathrm{0.06})$ and $k_{\mathrm{4}}/k_{\text{2b}}(=\mathrm{29})$ represent the relative rates of competing reactions of intermediate ${\mathrm{H}}_{\mathrm{2}}{\mathrm{ONO}}_{\mathrm{2}}^{+}\left(\mathrm{aq}\right)$ with H₂O (Reaction R3) and Cl⁻ (Reaction R4) over ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Reaction R2), respectively. [H₂O], [${\mathrm{NO}}_{\mathrm{3}}^{-}$], and [Cl⁻] are the aerosol water content, aerosol nitrate, and chloride molarity, respectively, calculated by the E-AIM model with the measured ionic compositions of PM_2.5 and RH (http://www.aim.env.uea.ac.uk/aim/aim.php, last access: 8 April 2020) (Wexler and Clegg, 2002).

We calculate the ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ values from BT09 with the measured aerosol composition at the five sites. The parameterized ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ ranged from 0.021 to 0.075, with an average of 0.047±0.015, which overestimates the observed values by a factor of 1.8. When the chloride effect was excluded, the parameterized ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ mean value decreased to 0.020±0.018, which was better correlated with but underestimated (by 30 %) the measurements (Table 1). Figure 3 compares the observation-derived and parameterized ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ at five sites in China and in different parts of the world. The BT09 parameterization (blue markers in Fig. 3) generally overestimates the observed ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ values in the range of 0.001 to 0.03, but it is closer (within a factor of 1.5) to the observed value for ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ above 0.03 in Germany (Phillips et al., 2016) and Mt. Tai (Z. Wang et al., 2017). The BT09 parameterization excluding chloride effects (orange markers) gives much better agreement, with more values located in the range within a factor of 2, though the ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ was still overpredicted in most of the studies in North America (Bertram et al., 2009b; Riedel et al., 2012; McDuffie et al., 2018a) except for Boulder (Wagner et al., 2013). The improvement indicates that the efficiency of chloride in competing for the ${\mathrm{H}}_{\mathrm{2}}{\mathrm{ONO}}_{\mathrm{2}}^{+}$ intermediate and the effects on N₂O₅ uptake on ambient aerosols might be overestimated, possibly due to the existence of other nucleophiles competing with Cl⁻ (McDuffie et al., 2018b; Staudt et al., 2019) or different mixing states of particle and nonuniform distribution of available chlorine in the aerosols.

Organic matter or coatings on the aerosols can suppress the uptake of N₂O₅ (Thornton and Abbatt, 2005; McNeill et al., 2006; Park et al., 2007), and previous studies have attempted to account for this effect by treating organics as a coating on the inorganic core (Anttila et al., 2006; Riemer et al., 2009). However, significant underpredictions were found from the parameterization of BT09 combined with the organic effect (Morgan et al., 2015; McDuffie et al., 2018a; Tham et al., 2018) (green and red markers in Fig. 3). One reason could be that the parameterization does not differentiate the water-soluble organic fractions and simplifies the morphology, and phase state, which leads to the underestimation of the solubility and/or diffusivity of N₂O₅ in the organics. The complex effects of organic matter on N₂O₅ uptake remain poorly quantified (McDuffie et al., 2018a), and the prediction of composition, morphology and phase state of the organic fractions are still difficult in current air quality models. Therefore, we do not consider the organic effect in deriving a new parameterization in the next section.

Figure 3Summary of the comparisons of field-measured or derived ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and values estimated from parameterizations from the literature. Blue, orange, green, and red markers represent the results calculated from parameterizations of original BT09, BT09 excluding chloride effect, BT09 plus organic effect, and BT09 excluding chloride but with organic effect, respectively.

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3.3 Observation-based empirical parameterization of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$

Based on the above discussion and comparison, we attempt to derive a new empirical parameterization of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ following the BT09 framework (Eq. 2) and using the measurement data from five field campaigns in China. The variables in the parameterization (i.e., reaction rates) were fitted with multiple regressions to obtain the best representation of observations in China. The derived empirical parameterization of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ is shown as Eq. (4) and the fitted ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ values are summarized in Table 1.

In view of the linear dependence of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ on the aerosol water content in this study and reaction mechanism (Bertram and Thornton, 2009), the second-order reaction rate coefficient with water (refer to ${k^{\prime }}_{\text{2f}}$ in Eqs. 2 and 3) was fitted as a linear function of [H₂O], as $(\mathrm{3.0}\pm \mathrm{0.4})\times {\mathrm{10}}^{\mathrm{4}}\times \left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]$. This value is in reasonable agreement with the values of (2.7–3.8) ×10⁴, $\sim \mathrm{3.9}\times {\mathrm{10}}^{\mathrm{4}}$, and 2.6×10⁴ M⁻¹ s⁻¹ determined from ammonium bisulfate, ammonium sulfate (Gaston and Thornton, 2016), and aqueous organic acid particles (Thornton et al., 2003), respectively. Compared to original BT09 (Eq. 3), the newly fitted ${k^{\prime }}_{\text{2f}}$ is smaller for [H₂O] < 38 M, but it become higher with the increasing of aerosol water content (Fig. S2). Different dimensionless K_H values have been used in previous studies, e.g., ∼ 50 (e.g., Hallquist et al., 2003; Bertram and Thornton, 2009) or ∼ 120 (e.g., Gaston et al., 2014; Gaston and Thornton, 2016; Griffiths et al., 2009), which correspond to a Henry's law constant of 2 or 5 M atm⁻¹ at 298 K. As ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ in the parameterization is linearly dependent on the K_H, an increase of K_H value would proportionally increase the ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ value, but it cannot account for the large variability of measured ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ values. Given the lack of an explicit function of effective Henry's law constant for N₂O₅ to include the different processes (e.g., “salting-in” effect and surface processes), we use the value of 51 suggested by Bertram and Thornton (2009) and enclose those effects from the aerosol composition in the last “chemical” term. The derived empirical ratios in the last chemical term not only represent the competing ratio of these reactions but also include other unspecified effects or processes (organic coating, mixing state, other nucleophiles reactions, etc.). The fitted relative rates of competing reactions, i.e., k₃∕k_2b and k₄∕k_2b, were 0.033±0.017 and 3.4±1.4, respectively, which are smaller than the original BT09 parameters by factors of 1.8 and 8.5, respectively. The smaller ratios of the reaction rates indicate a smaller enhancement effect of chloride or a larger suppression effect by nitrate, which is consistent with the abovementioned relationship of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ with the aerosol composition. Other suppression effects such as organic coating and mixing state that were not specified in the parameterization also may contribute to, and are reflected in, the smaller fitted values. As compared in Fig. 4 and Table 1, the new empirical parameterization can better reproduce the average values and the large variability of the observed ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ than the original BT09 both with and without considering Cl⁻ effects.

Figure 4Comparison of the field-measured or derived ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ with the values estimated from parameterizations for the five sites in the present study. The dashed line represents the 1 : 1 line. Blue circles, orange triangles, and red squares are results estimated by BT09 parameterization, BT09 excluding chloride effect and the derived observation-based empirical parameterization, respectively.

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Table 2Statistical summary and comparison of the observed species (nitrate and NO₂ concentrations) with values predicted from different parameterization. NMB represents the normalized mean bias.

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As suggested by the previous studies, the production yield of ClNO₂ (${\mathrm{\Phi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$) from N₂O₅ uptake is also a function of competing reactions of H₂O and Cl⁻ content in aerosols, and they can be estimated from ${\mathrm{\Phi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}=\mathrm{1}/(\mathrm{1}+k_{\mathrm{3}}/k_{\mathrm{4}}\times [{\mathrm{H}}_{\mathrm{2}}\mathrm{O}]/[{\mathrm{Cl}}^{-}\left]\right)$ (Bertram and Thornton, 2009). Based on the abovementioned fitting results for ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$, k₄∕k₃ is determined to be 105±37 for the five sites, which is smaller than the values of 450±100 (Roberts et al., 2009), 483±175 (Bertram and Thornton, 2009) and 836±32 (Behnke et al., 1997) derived from laboratory experiments and used in previous parameterizations. As compared in Fig. S3 and Table 1, although the newly fitted values improve the estimated ClNO₂ yield comparing to the original BT09 (with k₄∕k₃ of 483), overestimation remains, and the large variability of observed ${\mathrm{\Phi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$ in different campaigns still cannot be well captured. As shown in Fig. 5, the new fits can better catch the ${\mathrm{\Phi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$ trend at $\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]/\left[{\mathrm{Cl}}^{-}\right]>\mathrm{750}$, but a discrepancy is still obvious at $\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]/\left[{\mathrm{Cl}}^{-}\right]<\mathrm{750}$. The discrepancy could be due to aqueous-phase competition reactions of intermediate ${\mathrm{H}}_{\mathrm{2}}{\mathrm{ONO}}_{\mathrm{2}}^{+}$ with other compounds (e.g., phenol) (Heal et al., 2007) and ClNO₂ loss or reaction mechanisms (e.g., reaction with Cl⁻ to form Cl₂) (Roberts et al., 2008, 2009). A recent laboratory study (Staudt et al., 2019) has reported that sulfate and acetate can suppress ${\mathrm{\Phi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$ for Cl⁻-containing solutions, but such a sulfate suppression effect was not observed in our results. Further studies are needed to identify and quantify these effects for better parameterizing the heterogeneous ClNO₂ production. Nonetheless, the revised k₃∕k₄ from fitting the field data has improved the estimates of ${\mathrm{\Phi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$ at our study sites.

Figure 5Relationship between the ClNO₂ yield, ${\mathrm{\Phi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$, and the molarity ratio of H₂O to Cl⁻. Gray diamond symbols, blue circles, and red squares represent the observed ${\mathrm{\Phi }}_{{\mathrm{ClNO}}_{\mathrm{2}}}$, values from BT09 parameterization, and those fitted from the empirical parameters derived in the present study, respectively.

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3.4 Evaluation of the empirical parameterization

To further evaluate the representativeness and validity of the newly fitted empirical parameterization of ${\mathit{\gamma }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ in predicting N₂O₅ heterogeneous process in air quality models, simulation tests were performed with the WRF-CMAQ model. The simulations were conducted with the incorporation of newly fitted and original BT09 parameterizations, respectively. The simulated concentrations of NO₂ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$, as the key precursor and a product of the N₂O₅ uptake, were compared with the observed daily ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations at 28 sites and hourly NO₂ concentrations at 472 sites in the North China Plain during December of 2017. As summarized in Table 2 and shown in Fig. S4, the simulation with original BT09 parameterization overestimated the regionally averaged ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations by 18.7 % compared to the observations, whereas the new parameterization gave more consistent results with the observations (20.98±18.77 µg m⁻³ vs. 20.94±17.16 µg m⁻³), reducing the normalized mean bias (NMB) of simulated ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentration from 18.72 % to 0.19 %. The simulated NO₂ concentrations were also in better agreement with the observations, with the NMB changing from −12.25 % to −8.06 %. In addition to NO₂ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$, we also compared the simulated N₂O₅ concentrations for December 2017 with those observed in the wintertime at various locations in China, including two in the North China Plain (Beijing and Wangdu in Hebei Province) and two in southern China (Tai Mo Shan and Heshan). As shown in Fig. 6, with the new parameterization, the WRF-CMAQ model can better simulate the average concentration and variation range of N₂O₅ at these locations. Overall, the new parameterization has significantly reduced the discrepancies between the modeled and observed concentrations of NO₂, N₂O₅, and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ at our study sites and periods in both northern and southern China. More tests of this empirical parameterization are warranted for other locations and seasons in China and other parts of the world.

Figure 6Comparison of simulated N₂O₅ concentrations by the CMAQ model for December 2017 with the wintertime observation results from four sites in China. The field observations were conducted in Wangdu (Hebei Province) in December 2017, Beijing in January 2018, Heshan (Guangdong Province) in January 2017, and Tai Mo Shan (Hong Kong) in November 2013. The columns and error bars represent the average value and standard deviation, respectively.

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