the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Interpretation of NO_{3}–N_{2}O_{5} observation via steady state in highaerosol air mass: the impact of equilibrium coefficient in ambient conditions
Xiaorui Chen
Steadystate approximation for interpreting NO_{3} and N_{2}O_{5} has large uncertainty under complicated ambient conditions and could even produce incorrect results unconsciously. To provide an assessment and solution to the dilemma, we formulate datasets based on in situ observations to reassess the applicability of the method. In most of steadystate cases, we find a prominent discrepancy between K_{eq} (equilibrium coefficient for reversible reactions of NO_{3} and N_{2}O_{5}) and correspondingly simulated $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\left[{\mathrm{NO}}_{\mathrm{2}}\right]\times \left[{\mathrm{NO}}_{\mathrm{3}}\right]\right)$, especially under highaerosol conditions in winter. This gap reveals that the accuracy of K_{eq} has a critical impact on the steadystate analysis in polluted regions. In addition, the accuracy of γ (N_{2}O_{5}) derived by steadystate fit depends closely on the reactivity of NO_{3} (kNO_{3}) and N_{2}O_{5}(kN_{2}O_{5}). Based on a complete set of simulations, air mass of kNO_{3} less than 0.01 s^{−1} with high aerosol and temperature higher than 10 ^{∘}C is suggested to be the best suited for steadystate analysis of NO_{3}–N_{2}O_{5} chemistry. Instead of confirming the validity of steady state by numerical modeling for every case, this work directly provides appropriate concentration ranges for accurate steadystate approximation, with implications for choosing suited methods to interpret nighttime chemistry in highaerosol air mass.
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The nitrate radical (NO_{3}), an extremely reactive species prone to buildup at night, is an ideal candidate for steadystate analysis in combination with dinitrogen pentoxide (N_{2}O_{5}) due to fast equilibrium reactions between them (Reaction R1).
Under the steadystate condition, the lifetime of NO_{3} (denoted as τ_{ss}(NO_{3})) can be calculated as the ratio of NO_{3} concentration over the production rate (${k}_{{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right])$ or over the removal rate of both NO_{3} and N_{2}O_{5}, as indicated in Eq. (1). A similar representation of N_{2}O_{5} steadystate lifetime is also shown in Eq. (2). The loss frequencies of various sink pathways of NO_{3} and N_{2}O_{5} are integrated as total first order in the following equations, represented by the kNO_{3} and kN_{2}O_{5} terms. Briefly, kNO_{3} is contributed by the reaction of the NO_{3} radical with NO and hydrocarbons and uptake on particles at night, ranging from hundredths of reciprocal seconds to several reciprocal seconds depending on the air mass. Due to its large rate constant with NO, the concentration usually dominates the lifetime of the NO_{3} radical in urban areas with fresh NO emission. Otherwise, the reactions with hydrocarbons, especially unsaturated hydrocarbons, are preferential for NO_{3} in rural areas. The K_{eq} denotes the equilibrium coefficient for Reactions (R1a) and (R1b), derived by Eq. (3).
Numerous works have taken advantage of the steadystate calculation to quantify the total firstorder loss rate for NO_{3} or N_{2}O_{5} such that they drew conclusions about the oxidation capacity and reactive nitrogen budgets contributed by this chemical system (Allan et al., 1999, 2000; Carslaw et al., 1997; Platt et al., 1984; Vrekoussis et al., 2007; Wang et al., 2013). Since the steadystate approximation was used to interpret atmospheric observation of NO_{3}–N_{2}O_{5} (Brown et al., 2003; Platt et al., 1981), this method was also widely implemented to quantify the N_{2}O_{5} uptake coefficient (γ (N_{2}O_{5})) (Brown et al., 2009, 2003; Li et al., 2020; McDuffie et al., 2019; Phillips et al., 2016; Wang et al., 2017a, c, 2020a).
However, with the influence induced by complicated atmospheric conditions and emission, steady state in ambient air mass will not always be the case (as illustrated in Sect. S1 and Fig. S1 in the Supplement). These situations are prevalent in nocturnal boundary layer (Phillips et al., 2016; Stutz et al., 2004; Wang et al., 2017a, c) and therefore increase the difficulty of applying steady state directly to NO_{3}–N_{2}O_{5} observation data, whereas few studies have systematically characterized the error source and application conditions of this method (Brown et al., 2009).
Due to a faster approach to equilibrium than steady state, the application of K_{eq} in the calculation of steadystate equations seems to be reasonable (Brown et al., 2003). For example, the ambient NO_{3} concentration was usually calculated based on ambient N_{2}O_{5} concentration with K_{eq}×[NO_{2}] when determining their budgets or characterizing the lifetime or sink attribution of these two reactive nitrogen compounds (Brown et al., 2011; Osthoff et al., 2006; Wang et al., 2018, 2017c, d; Yan et al., 2019). In addition, the mathematical conversion between NO_{3} and N_{2}O_{5} concentration via K_{eq} coefficient can simplify the calculation in the iterative box model, which derives γ(N_{2}O_{5}) by iterating its value in the model until the predicted N_{2}O_{5} concentration matches the observation (Wagner et al., 2013; Wang et al., 2020b). However, considerable uncertainty could be associated with the quantification of K_{eq} and its different parameterizations (Cantrell et al., 1988; Pritchard, 1994). The impact of K_{eq} value on steadystate fit or concentration conversion has not been explored to date in the analysis of NO_{3}–N_{2}O_{5} steady state.
In this study, we formulate a half artificial dataset with expected properties based on field campaigns. Specifically, most of the species contained in the dataset are observed values while only NO_{3} and N_{2}O_{5} were calculated by the steadystate model (illustrated in the Sect. 2.2). With the dataset, we illustrate the reasons for deviation of parameterized K_{eq} from $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\right[{\mathrm{NO}}_{\mathrm{2}}]\times [{\mathrm{NO}}_{\mathrm{3}}\left]\right)$ in ambient conditions, the possible uncertainties of linear fit based on steadystate Eqs. (4) and (5) (the related variables are explained in Sect. 2.1) that resulted from different K_{eq} values, and the influence of relevant atmospheric variables on γ (N_{2}O_{5}) derivation via the steadystate method. Furthermore, a series of ambient condition tests specify the exact ranges suited for steadystate analysis according to not only the validity of steady state but also K_{eq} values, which optimize the validity check by numerical modeling in previous research (Brown et al., 2009, 2003) and develop complete standard for data filtering.
2.1 γ (N_{2}O_{5}) derivation by steadystate approximation
The framework of steadystate approximation for the NO_{3}–N_{2}O_{5} system is basically built on its chemical production and removal pathways, in case of extremely weak physical processes (e.g., transport, dilution, and deposition) relative to its chemical processes. With simultaneous measurements of NO_{3}, N_{2}O_{5}, and relevant precursor concentrations, the steadystate lifetime τ_{ss}(NO_{3}) and τ_{ss}(N_{2}O_{5}) can be quantified for a targeted period as shown in Eqs. (1) and (2). By substituting the kN_{2}O_{5} with $\mathrm{0.25}\times c\times {S}_{\mathrm{a}}\times \mathit{\gamma}$ (N_{2}O_{5}), the γ(N_{2}O_{5}) and the reactivity of NO_{3} (kNO_{3}, including the reactions of NO_{3} with NO and hydrocarbons) can therefore be determined by Eqs. (4) and (5).
Here c represents the mean molecular velocity of N_{2}O_{5}, S_{a} represents the aerosol surface area, and K_{eq} is calculated from the rate constant of reversible Reactions (R1a) (k_{R1a}) and (R1b) (k_{R1b}), which is a temperaturedependent parameter. It should be noted that the photolysis of NO_{3} is not considered in the kNO_{3} due to weak radiation at night, and the homogeneous hydrolysis was also ignored due to its small contribution in comparison to the heterogeneous pathway. A similar presumption was also implemented in previous studies (Brown et al., 2009; Mentel et al., 1996; Wahner et al., 1998). In the form of these two equations, the potential covariance between S_{a} and NO_{2} concentration can be avoided to decrease the uncertainty (Brown et al., 2009). By being fit to these two equations, γ (N_{2}O_{5}) can be directly derived from slope of the plot of ${\mathit{\tau}}_{\mathrm{ss}}^{\mathrm{1}}\left({\mathrm{NO}}_{\mathrm{3}}\right)$ against 0.25c S_{a}K_{eq}[NO_{2}] or from the intercept of the plot of ${\left(\mathrm{0.25}c\phantom{\rule{0.125em}{0ex}}{S}_{\mathrm{a}}{\mathit{\tau}}_{\mathrm{ss}}\left({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)\right)}^{\mathrm{1}}$ against ${\left(\mathrm{0.25}c\phantom{\rule{0.125em}{0ex}}{S}_{\mathrm{a}}{K}_{\mathrm{eq}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\right)}^{\mathrm{1}}$ respectively. In the following analysis, the linear fit based on Eq. (5) is preferred in steadystate approximation.
2.2 Steadystate model and halfartificial datasets
The steadystate model is reformed from a zerodimensional box model to produce NO_{3} and N_{2}O_{5}, which are in steady state as far as possible. It is constrained by measurements of NO, NO_{2}, O_{3}, CO, CH_{4}, VOCs, HCHO, S_{a}, relative humidity (RH), temperature (T), and pressure, coupled with the Regional Atmospheric Chemistry Mechanism, version 2 (RACM2). Each data point is treated as an independent air mass, aging 10 h and keeping input constraint unchanged. As NO_{3}–N_{2}O_{5} chemistry, the interest of this work, usually shows marked impacts during the night, only the time periods with negligible photolysis frequency are under consideration. In the standard simulation (herein referred to as Mod0), the uptake coefficient of N_{2}O_{5} is set to 0.02, as a reasonable value of literature (Brown et al., 2006; Chen et al., 2020; McDuffie et al., 2018; Morgan et al., 2015; Phillips et al., 2016; Wagner et al., 2013; Wang et al., 2017c; Yu et al., 2020).
Two halfartificial datasets are derived from PKU2017 and TZ2018 field campaigns (see Sect. S2) based on the steadystate model for analysis in the following sections. The simulated NO_{3} and N_{2}O_{5} and other observed values used for the constraints of the steadystate model jointly formulate these halfartificial datasets. Specifically, the NO_{3} and N_{2}O_{5} concentrations in this dataset are the output of the steadystate model simulation and guaranteed to be in steady state with respect to other observed precursors. To verify the steady state of NO_{3} and N_{2}O_{5} for each data point, we filtered the dataset according to the deviation between the steadystate lifetime of N_{2}O_{5} (${\mathit{\tau}}_{\mathrm{ss}}\left({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)=\frac{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}{{k}_{\mathrm{R}\mathrm{1}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right]})$ and calculated lifetime of N_{2}O_{5} (${\mathit{\tau}}_{\mathrm{calc}}\left({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)=({k}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}+\frac{{k}_{{\mathrm{NO}}_{\mathrm{3}}}}{{K}_{\mathrm{eq}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]}{)}^{\mathrm{1}})$. If the deviation exceeds 10 % for a data point, it will be excluded from the following analysis. We presume that if any data point output from the model is still out of steady state in terms of NO_{3} and N_{2}O_{5}, the sink rate constant of air mass represented by this data point should be too weak for steadystate analysis within a reasonable timescale. In addition, the data higher than 5 ppbv NO are filtered out in the following calculation, since the resulting large variation in kNO_{3} can bias the linear fit even though NO_{3} and N_{2}O_{5} approach steady state rapidly under high NO (discussed in Sect. 3.2). The fraction of excluded data is less than 8 %, and they are expected to have little influence on our results. The calculated nighttime loss fraction accounted for by NO_{3} and N_{2}O_{5} show large discrepancy (see Sect. S3 and Fig. S2) between these two halfartificial datasets, which provide us a good opportunity to investigate the factors impacting steadystate approximation across different conditions.
Rather than using observation data directly, a halfartificial dataset can provide a larger amount of valid data for steadystate analysis with a known γ (N_{2}O_{5}) value. In addition, this method avoids the impacts from steadystate deviation, which helps to analyze the factors influencing γ (N_{2}O_{5}) quantification via steadystate approximation backwards from a known steadystate condition.
3.1 Varying equilibrium coefficient under steady state
The rates of NO_{3}–N_{2}O_{5} reversible reactions are expected to be equal for the steadystate case, so that the equilibrium coefficient K_{eq} can be determined from either the rate constant ratio of Reactions (R1a) and (R1b) or the ratio of $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\right[{\mathrm{NO}}_{\mathrm{2}}]\times [{\mathrm{NO}}_{\mathrm{3}}\left]\right)$. Although this approach is reasonable under ideal conditions, the exact same rates between reversible reactions and the following calculation based on K_{eq} scaling are not so appropriate for ambient atmosphere where the removal pathway for NO_{3}–N_{2}O_{5} is not negligible, especially under the highaerosolloading condition. NO_{3} and N_{2}O_{5} achieve steady state after 1.5 h evolution, when concentration and rates remain constant (Fig. 1). In this simulation, the starting mixing ratios of NO_{2} and O_{3} are 10 and 23 ppbv, respectively, which is the average level for the nighttime conditions in PKU2017. The concentrations of these two precursors are held constant in the simulation to better illustrate the influence of removal rates. This result will stay almost the same no matter whether these starting values are initialized to be constant or allowed to vary. Under steady state, the net equilibrium reaction rate in Fig. 1b and c stays negative and positive for NO_{3} and N_{2}O_{5}, respectively. In addition, the absolute values and difference of the forward and backward reaction rates remain unchanged after achieving steady state. This result is similar to a previous numerical calculation study (Brown et al., 2003), while the deviation between reversible reaction rates becomes larger in our case.
In this case, the original equilibrium is imperfectly realized (a perfect realization of the original equilibrium condition is that K_{eq} and the ratio of $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\right[{\mathrm{NO}}_{\mathrm{2}}]\times [{\mathrm{NO}}_{\mathrm{3}}\left]\right)$ are equivalent as in Eq. 6), leading to errors on the projection of NO_{3} and N_{2}O_{5} concentration via K_{eq}×[NO_{2}]. In fact, we note that a new equilibrium between NO_{3} and N_{2}O_{5} is developed with constant but unequal rates. Under this new equilibrium condition, the ratio of (R1b) reaction rate (the red dashed line in Fig. 1d) over (R1a) reaction rate (the black dashed line in Fig. 1d) can be regarded as the degree of approaching original equilibrium (the blue line in Fig. 1d). In addition, this value is also the ratio of $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\right[{\mathrm{NO}}_{\mathrm{2}}]\times [{\mathrm{NO}}_{\mathrm{3}}\left]\right)$ against original K_{eq}; therefore we defined this ratio as a correction factor ε, implemented to calculate accurate $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\right[{\mathrm{NO}}_{\mathrm{2}}]\times [{\mathrm{NO}}_{\mathrm{3}}\left]\right)$ with significant N_{2}O_{5} removal pathways. The value of K_{eq} after scaled by ε can be used for converting the concentration of NO_{3} and N_{2}O_{5} via Eq. (6):
Sensitivity tests are conducted to demonstrate the dependence of ε on relevant variables based on the steadystate model. The averages ambient conditions observed at the wintertime Peking University (PKU) site and summertime Tai Zhou (TZ) site are taken as two basic constraints for sensitivity tests (Table S2 in the Supplement). By separately altering variables, such as NO_{2}, O_{3}, kN_{2}O_{5}, kNO_{3}, and T, the sensitivity of the ε value can be obtained as shown in Figs. 2 and S4. The ε value depends primarily on kN_{2}O_{5} and T in both scenarios, where ε increases with T (approaching 1 under relatively high T) and decreases with kN_{2}O_{5}. In comparison, the ε value behaves insensitively to kNO_{3} as well as NO_{2} and O_{3} concentration, at least within the range of reasonable ambient conditions. High kN_{2}O_{5} results from highaerosol events, usually occurring in winter accompanied by low temperature and high relative humidity in some populated areas (Baasandorj et al., 2017; Huang et al., 2014; Wang et al., 2017b, 2014), further decreasing the accuracy of original K_{eq} values. It can be inferred that in order to accurately interpret the relationship of NO_{3} and N_{2}O_{5}, calculation relying on the equilibrium equation and steadystate approximation should consider the dependence of ε on ambient conditions.
Even if the K_{eq} value serves as a good representation of the ratio of $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\right[{\mathrm{NO}}_{\mathrm{2}}]\times [{\mathrm{NO}}_{\mathrm{3}}\left]\right)$ or ε can be readily quantified in the field, the discrepancy among different databases in calculating K_{eq} still increases the uncertainties of NO_{3}–N_{2}O_{5} calculation through steadystate approximation or equilibrium, which has not been carefully considered. Here, we apply a set of uniform formulas to describe k_{R1a} and k_{R1b} (see Sect. S4) from preferred values of several popular atmospheric chemistry mechanisms (Mozart, CB05, Saprc07, RACM2 and kinetic databases JPL2015 as well as IUPAC2017) and finally calculating K_{eq}. As is shown in Figs. S5 and S6, K_{eq} variations derived from these six different databases reflect considerable discrepancy from each other, especially in colder conditions. Because parameterized K_{eq} values are only dependent on ambient temperature, they continuously increase with time due to the decrease in temperature. In addition to the discrepancy between different K_{eq} parameterizations, the ε value varies dissimilarly with each K_{eq}, ranging from 70 % to 90 %. All these results demonstrate that, in most cases, K_{eq} values simply derived from an existing database would fail to reproduce an accurate relationship between NO_{3} and N_{2}O_{5}.
To further elucidate the impact of K_{eq} on deriving γ (N_{2}O_{5}) via steadystate approximation (hereafter defined as γ_{ss} (N_{2}O_{5})), Fig. S6 shows the steadystate fit based on all six databasederived K_{eq} values and in the same time periods as Fig. S5 through Eqs. (4) and (5), respectively (both equations can derive a pair of γ_{ss} (N_{2}O_{5}) and kNO_{3}). K_{eq} (corrected with ε) is calculated with NO_{3} and N_{2}O_{5} concentration simulated based on RACM2. Fits based on Eq. (4) could lead to 11 %–46 % underestimation of γ_{ss} (N_{2}O_{5}), as indicated by varying slopes in Fig. S7b and d, when using the databasederived K_{eq}. Conversely, fit by Eq. (5) (shown in Fig. S7a and c) biases the result of kNO_{3} as the slopes without much influence on γ_{ss}(N_{2}O_{5}) as the intercept. Previous research ascribed inconsistent fit results between two equations to measurement uncertainty (Brown et al., 2009, 2006). However, fit with the original K_{eq} might be the primary reason for such inconsistent results and even differentiates the derived γ_{ss} (N_{2}O_{5}) and kNO_{3} from true values. Therefore, steadystate fit based on Eq. (5) might be the best choice for γ (N_{2}O_{5}) derivation via steadystate approximation. Similarly, Eq. (4) is preferred to be applied when kNO_{3} is the final objective.
3.2 Impacts of NO_{3}–N_{2}O_{5} reactivity on steady state
In order to further explore the impacting factors on the steadystate fit method, γ_{ss} (N_{2}O_{5}) results are derived for each 2 h time period of the PKU2017 and TZ2018 datasets based on output from the steadystate model. Since the preset γ (N_{2}O_{5}) in this model is 0.02, the degree of deviation from this value is supposed to reflect the accuracy of the fitted result.
It can be noticed from Eq. (5) that the variability of kNO_{3} during the same time period leads data points to scatter on lines with different slopes, which could bias the resulted γ_{ss} (N_{2}O_{5}) from the model preset value. As is shown in Fig. 3, the absolute percentages of γ_{ss} (N_{2}O_{5}) deviation grow dramatically with the increase in relative standard deviation of kNO_{3} (kNO_{3} RSD) in both winter and summer datasets. The positive correlation even gives rise to extreme deviation in the summer dataset, with up to almost 10 times of model setting γ (N_{2}O_{5}). In fact, there remain accurate γ_{ss}(N_{2}O_{5}) values derived in each range of kNO_{3} RSD, indicating a not strictly positive correlation between γ_{ss} (N_{2}O_{5}) deviation and kNO_{3} RSD. This implies that large variation in kNO_{3} only enhances the possibilities of inaccurate results from steadystate fit rather than hinder the γ_{ss} (N_{2}O_{5}) quantification all the time.
In addition to the large variation in kNO_{3} in a short time period, the absolute level of kNO_{3} and kN_{2}O_{5} could influence the possibilities of inaccurate γ_{ss} (N_{2}O_{5}) from different aspects. Although the enhancement of kNO_{3} and kN_{2}O_{5} boosts the approach to steady state (Sect. S5 and Fig. S8), higher levels of kNO_{3} amplify the bias of γ_{ss} (N_{2}O_{5}), contrary to kN_{2}O_{5}, with the same relative variation in kNO_{3} (Sect. S6 and Fig. S10). This indicates that the region with plural emissions (e.g., strong biogenic or vehicular emission) might not be suited for steadystate fit due to the high kNO_{3}. Therefore, a tradeoff between the variation in kNO_{3} and the high level of kNO_{3} (fast approach to steady state) should be made when deriving γ_{ss} (N_{2}O_{5}).
3.3 Implication for accurate steadystate analysis of NO_{3}–N_{2}O_{5}
While a few studies have examined the validity of steady state under certain conditions via numerical modeling when interpreting the ambient data (Brown et al., 2009, 2003), a clear range well suited to steadystate analysis of NO_{3}–N_{2}O_{5}, taking both K_{eq} and validity of steady state into consideration, has not been determined to date.
Here almost 20 000 simulations are displayed in the parallel plot of Fig. 4, where each line connects five constraint parameters to the calculated steadystate time and ε (the correction factor for K_{eq} parameterization to match the exact ratio of $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\right[{\mathrm{NO}}_{\mathrm{2}}]\times [{\mathrm{NO}}_{\mathrm{3}}\left]\right)$, detailed in Eq. 6). The gray traces represent the simulations that could not match steady state within 600 s and were defined as less valid cases here. By this definition, we intend to indicate that it is also viable to apply steadystate approximation on air mass, which requires more than 600 s to match steady state, whereas the uncertainty caused therefrom could increase to some extent. The pink and blue traces together represent the simulations that could match valid steady state within 600 s without consideration of K_{eq} deviation (in other words the value of ε). Furthermore, the criteria to apply steadystate approximation appropriately is approach to steady state within 600 s and ε larger than 0.9, which are indicated as pink traces. While the levels of T, NO_{2}, and O_{3} have a minor effect on the approach to steady state, simultaneous low kN_{2}O_{5} (indicated as low S_{a} in the plot) and kNO_{3} prevent the NO_{3}–N_{2}O_{5} system from developing steady state. For example, when kNO_{3} is lower than 0.01 s^{−1}, the air mass will be valid only if S_{a} increases to at least 3000 µm^{2} cm^{−3} with γ (N_{2}O_{5}) of 0.02. This implies that clean air mass is not suited for steady state in any cases, whereas the highaerosol condition provides more possibilities to approach steady state even with low kNO_{3}. However, in order to interpret NO_{3}–N_{2}O_{5} chemistry with an accurate K_{eq} coefficient, the ε larger than 0.9 is additionally taken into consideration, which excludes 50 % of valid steadystate cases mainly with high aerosol and lower than 10 ^{∘}C. These cases could bias $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\right[{\mathrm{NO}}_{\mathrm{2}}]\times [{\mathrm{NO}}_{\mathrm{3}}\left]\right)$ from original K_{eq} (also indicated in Fig. 2), leading to inaccurate results of calculation based on K_{eq}.
In this study, we found that the parameterized K_{eq} coefficient deviates much from the ratio of $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\right[{\mathrm{NO}}_{\mathrm{2}}]\times [{\mathrm{NO}}_{\mathrm{3}}\left]\right)$ in some cases where steady state is valid. The indicator of the deviation, ε, is relatively sensitive to N_{2}O_{5} reactivity and ambient temperature. It implies that conditions suited for steadystate analysis should be determined according to not only the validity of steady state but also K_{eq}, especially under highaerosol conditions, like some regions in India, China, Europe, and the US (Baasandorj et al., 2017; Cesari et al., 2018; Huang et al., 2014; Mogno et al., 2021; Petit et al., 2017; Wang et al., 2017b). Considering that a high level of kNO_{3} might amplify the bias of γ_{ss} (N_{2}O_{5}) yield from steadystate fit and appears to be accompanied by fast variations, air mass of kNO_{3} less than 0.01 s^{−1} with high aerosol and T higher than 10 ^{∘}C are therefore the best suited for steadystate analysis of NO_{3}–N_{2}O_{5} chemistry, which indicates that this method would be more applicable in polluted regions with high aerosol loading during summertime. If the restriction of ε is relaxed to 30 %, some winter conditions will also be applicable. Our results provide an insight into improving the accuracy of the steadystate approximation method and finding suited areas to interpret nighttime chemistry. Further improvement of in situ NO_{3}–N_{2}O_{5} budget quantification might rely on the direct measurements via flow tube system or machine learning prediction based on ancillary parameters.
The datasets used in this study are available from the corresponding author upon request (wanghch27@mail.sysu.edu.cn; k.lu@pku.edu.cn).
The supplement related to this article is available online at: https://doi.org/10.5194/acp2235252022supplement.
KL and HW designed the study. XC and HW analyzed the data and wrote the paper with input from KL.
The contact author has declared that neither they nor their coauthors have any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Thanks for the data contributed by field campaign team.
This research has been supported by the National Natural Science Foundation of China (grant nos. 21976006 and 42175111), the Beijing Municipal Natural Science Foundation (grant no. JQ19031), the State Key Joint Laboratory of Environmental Simulation and Pollution Control (grant no. 21K02ESPCP), the National Key Basic Research Program For Youth (grant nos. DQGG010301 and 2019YFC0214800), and the National State Environmental Protection Key Laboratory of Formation and Prevention of Urban Air Pollution Complex (grant no. CX2020080578).
This paper was edited by Qiang Zhang and reviewed by two anonymous referees.
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