Gas-particle partitioning process contributes more to nitrate dominated air pollution than oxidation process in northern China

Abstract Nitrate has been recognized as a key aerosol component in regional haze formation in China. However, reducing nitrate aerosol concentration remains a major challenge. Generally, the formation of particulate nitrate (NO3-) is mainly affected by two processes: oxidation (to generate gaseous HNO3 or particulate NO3-) and gas-particle partitioning (HNO3-NO3- partition). Here, we proposed a new method to explore the contributions of above two processes (COxiobs (%) and CG/Pobs (%)) to nitrate formation based on field observation, and combined theoretical calculation and modeling to verify it. Quantitative results showed that gas-particle partitioning process (average CG/Pobs (%) was 64.90%) always contributed more than oxidation process (average COxiobs (%) was 35.10%) for particulate nitrate formation under different pollution scenarios in the ambient environment. We argued that this phenomenon was mainly caused by high aerosol pH (>4.5). Nevertheless, as pollution level rose, the COxiobs (%) will also increase (contributing to 32%, 38%, 40% and 41% under clean, light, medium and heavy pollution levels) which may be attributed to the increased HNO3 production rate and relatively enhanced heterogeneous reaction pathway. The results indicate future strategies for prevention and control of nitrate pollution should both consider reducing precursors emission and regulating aerosol acidity, in order to increase the effectiveness of reducing nitrate dominated pollution. Copyright © 2023 American Association for Aerosol Research Graphical Abstract

etc.) were the predominant component of PM 2.5 , with a mass proportion of approximately 30%-60% (Fu et al. 2020;Tao et al. 2017;Zheng et al. 2015).Since the promulgation of China's Clean Air Action in 2013, primary emissions of nitrate and sulfate precursors have been strictly controlled, such as NO x which saw a 21% reduction and a 59% reduction for SO 2 in 2017 compared to those in 2013 (Shi et al. 2022;Zheng et al. 2018).Numbers of studies have found that sulfate decreased remarkably during the period, while nitrate did not (Wang et al. 2013;Zhai et al. 2019).The proportion of nitrate in SIA increased considerably, and it has surpassed sulfate becoming the dominant secondary inorganic component of PM 2.5 (Fu et al. 2020;Shang et al. 2021;Tian et al. 2019;Xu et al. 2019a).Therefore, the control of nitrate is critical for alleviation of haze pollution.
High level of nitrate concentration may be due to its complicated formation processes under ambient environment which include valence and phase transition (Seinfeld and Pandis 2016;Shi et al. 2019b;Wang et al. 2009;Xue et al. 2014).Generally, particulate nitrate formation in the atmosphere is mainly affected by two processes.One is the oxidation process, that is, oxidants (for example O 3 , �OH, �NO 3 ) oxidize NO 2 to form gaseous HNO 3 /particulate NO 3 − in which the valence of N changes from positive tetravalent N(IV) to positive pentavalent N(V).And the HNO 3 /NO 3 − oxidization production pathways are different during daytime and nighttime (Chang et al. 2011).More specifically, OH radical oxidize NO 2 in gas phase to produce HNO 3 is the major oxidization pathway during daytime (R1), and the heterogeneous hydrolysis of N 2 O 5 which originated from the reactions between NO 2 and NO 3 radical is the dominant pathway for nighttime nitrate formation (R2-R4) (Fu et al. 2020).The other process is the gas-particle partitioning process, that is, the partition between gaseous HNO 3 and particulate NO 3 − (R5-R6), in which the valence of N remains consistent, and only phase transition occurs (Guo et al. 2017;Kaneyasu et al. 1999;Ma et al. 2003;Seinfeld and Pandis 2016).Both processes are significant for the formation of nitrate, which likely lead to the inconsistent decline of nitrate and precursor concentration.
Oxidation process-gaseous N(IV) convert to gaseous/particulate N(V): Gas-particle partitioning process-gaseous N(V) convert to particulate N(V): In previous studies, some researchers suggested that the increased production of HNO 3 or NO 3 − which was supported by increased oxidants could be the key process for persistent NO 3 − pollution in northern China (Fu et al. 2020;Lu et al. 2019;Zhang et al. 2021b).Others suggested that high NH 3 concentration in NCP and increased NH 3 availability for nitrate production were the key factor that caused nitrate pollution in the NCP area, due to the fact that gas-particle partitioning process is also important for NO 3 − formation (Xu et al. 2019b;Zhai et al. 2021).
However, most previous studies were based on laboratory or model simulation, while actual reactions in the ambient environment are likely to be more complex due to the impact of environmental factors such as temperature, relative humidity, and physical and chemical properties of aerosol (Guo et al. 2016;Patel et al. 2023;Seinfeld and Pandis 2016;Shi et al. 2019b).Moreover, most existing works studied the two processes separately when analyzing the drivers of nitrate production.Generally, there are two forms of oxidization products, gaseous and particulate (HNO 3 and NO 3 − ), produced by oxidation process; and the contribution of these two products to the particulate nitrate is then determined by the gas-particle partitioning process.The reduction of precursor concentration could lead to the decline in oxidization products, but it is inconsistent with the variation of the ultimate proportion of particulate nitrate in oxidization products due to the gas-particle partitioning process.Therefore, the above two processes should be studied together to reveal their effects on nitrate formation.In our recent study, the effect of liquid phase processes (including oxidation and gas-particle partitioning process for nitrate) on secondary particles has been quantitatively analyzed based on observational data (Gao et al. 2021).However, quantitative apportioning of the contributions of oxidation process and gas-particle partitioning process has not been achieved.In order to better understand the formation mechanism of nitrate in ambient atmosphere, revealing the quantitative contributions of the two processes is important.
In this work, we proposed a new process-contribution apportionment method which can quantify the impacts of oxidation and partitioning processes on nitrate formation, based on online observation and an empirical theoretical approach.For the first time, we quantitatively apportioned the normalized contributions of the above mentioned two processes on nitrate formation; and identified the drivers that shifted the impacts of the two processes among different pollution levels by applying thermodynamic model and chemical box model.The quantitative findings on the key processes of nitrate formation from this work provide guidelines for designing effective control strategies for nitrate and haze pollution.

Sampling site and instrumentation
The sampling site in this work is the Air Quality Research Supersite at Nankai University (NKAQRS, 38 � 59 0 N and 117 � 20 0 E), which is located at the south of Tianjin (�25 km southeast of downtown).The site is away from high traffic zone (except for a nearby highway and entrance ramp) and is surrounded by several universities (online supplementary information [SI], Figure S1).It represents a typical suburban area with relatively low population density (Dai et al. 2020).The sampling inlet is about 5 m from the ground.The sampling period spanned an entire year, from 1 January to 31 December 2018.
Online aerosol and gaseous measurements with 1-h time resolution were made.PM 2.5 were measured by beta ray particulate matter automatic monitors Focused Photonics Inc.).Mass concentrations of major water-soluble ions (NO 3 ) and semi-volatile species in the gas phase (HNO 3 , NH 3 , HCl) were measured by URG9000B samplers (AIM, URG Corporation) with two ICs.Concentrations of trace gases (NO 2 , SO 2 , CO, O 3 , NH 3 ) were measured in hourly temporal resolution by Teledyne-API instruments.Concentrations of VOCs were measured by a GC955-611/811 (manufacturer).Meteorological data (Temperature [T] and Relative Humidity [RH]) were measured by a miniature weather station (WS600-UMB, LUFFT).

Aerosol pH calculation
In this work, the ISORROPIA-II model (http://isorropia.eas.gatech.edu) was used to calculate aerosol liquid water content and H þ concentration (Fountoukis and Nenes 2007) − -Cl − -H 2 O aerosol system in ISORROPIA-II was adopted (Fountoukis and Nenes 2007;Hennigan et al. 2015).Two modes (forward and reverse) and two aerosol states (metastable and stable) are available in this model.Based on previous studies, we chose the forward mode and metastable state (Shi et al. 2019b;Song et al. 2018).The inputs are the hourly measurement data, including water-soluble ions in PM 2.5 , semi-volatile components in gas phase (HCl, HNO 3 and NH 3 ), and meteorological data (RH and T) during the entire sampling period.The output parameters include aerosol liquid water content (lg/m 3 ) (ALWC) and concentrations of H þ (lg/m 3 ).Aerosol pH was calculated by Equation (1) (Chan et al. 2021). (1)

Box-model simulation
To investigate the variation of the daytime and nighttime NO x oxidation level, a zero-dimension chemical box model named F0AM (The Framework for 0-D Atmospheric Modeling), which is a flexible software interface for simulating chemical systems relevant to atmospheric composition, was used in this study (Chen et al. 2020;Wen et al. 2018;Yun et al. 2018).The chemical mechanism we selected was MCM 3.3.1.This new version has been improved in several key areas, including HO x recycling, NO x recycling, and the formation of species which are involved in secondary organic aerosol (SOA) formation mechanisms (Dewald et al. 2020;Jenkin, Young, and Rickard 2015;Mehra et al. 2020;Yun et al. 2018).The simulation period was the entire year.And the model time step we chose was an hour.The input data included 5 inorganic species, 43 organic species and meteorological data at hourly resolution (full list see SI, Table S1).The output variables include meteorological constraints, modeled concentrations (ppb), chemistry parameters, model options, etc.

Normalized contributions for oxidation and gas-particle partitioning processes
Here, we called the oxidation process as Oxi-process, and the gas-particle partitioning process as G/P-process in the next text.In order to further explore the impacts of the above two processes on nitrate formation, we first proposed a principle (Equation ( 2)) to represent the formation process of nitrate based on observational data.In the principle, we used R obs NO − 3 to represent the ratio of particulate nitrate (NO 3 − ) generating from total N (N total ) (Equation ( 3)); and R obs NO −

was divided into two parts (R obs
Oxi and R obs G=P ) (Equation ( 2)).We defined R obs Oxi to represent the ratio of oxidization product (calculated by TN oxi ) generating from precursor (calculated by N total ) by Oxi-process (as shown in Equation ( 4)); and R obs G=P to represent the ratio of particulate nitrate to oxidization product after G/P-process (as shown in Equation ( 5)).

R obs NO
where, total oxidized N (TN Oxi ) equals to the sum (mol/m 3 ) of HNO 3 and NO 3 Here, based on the N conservation assumption, we let the sum of the observed concentrations (mol/ m 3 ) of HNO 3 and NO 3 − as the total oxidized N at the observation site.It represents the secondary products generated by NO 2 through the oxidation process, including gaseous and particulate forms.Of course, we know that this assumption is inaccurate, because there are many sinks of N, but we found that the influence of other processes was relatively weak in our study.Such as deposition process, the lifetime of (HNO 3 þNO 3 − ) calculated against deposition was 7.5h in this work, so the deposition process had weak impact in our study (details are provided in the SI (Text I)).Similarly, total N (N total ) is the sum of observed HNO 3 , NO 3 3 ), which includes precursors, and oxidation products generated by corresponding reactions during nitrate formation.NO 3 − is the observed concentration (mol/m 3 ) of particulate nitrate.The details of R obs NO −

, R obs
Oxi and R obs G=P are further described in Supporting Information (Text II).
Based on the formation process of particulate nitrate (Equation ( 2)), we proposed a method (Equations ( 8)-( 12)) to calculate the contributions from the Oxi-process and G/P-process on nitrate formation based on observational data.Firstly, to normalize the contributions of the two processes on nitrate formation, we transformed Equation ( 2) to obtain Equation ( 8).Similar mathematical methods have been used to explore the contributions of different factors in pervious study (Tao et al. 2022;Tao and Murphy 2021).Secondly, since the values of R obs

R obs
Oxi and R obs G=P were all less than one, to ensure that the index is positive, we normalized them for comparison purposes (Equation ( 9)).We chose the appropriate normalizing factor (nf) 100 by simulation tests (details are provided in the SI (Text III)).

Observations for pollutants
Figure 1 shows the hourly concentration of NO 3 − , HNO 3 and NO 2 in 2018 based on high temporal resolution (1-hr) data collected from online instruments.Overall, the average annual concentrations of NO 3 − , HNO 3 and NO 2 were 8.21 ± 10.20 lg/m 3 , 1.07 ± 1.06 lg/m 3 and 27.07 ± 15.03 ppb, respectively.Although the annual average concentration of NO 3 − was relatively low, the annual maximum hourly concentration of NO 3 − and HNO 3 reached as high as 76.3 lg/m 3 and 12.19 lg/m 3 , respectively.Time series plots of other inorganic ions, gaseous pollutants and meteorological data are shown in Figure S3 (SI).
Concentration variation of NO 2 was somewhat inconsistent with the variations of HNO 3 and NO 3 − , especially in the period when HNO 3 and NO 3 − concentrations showed peaks (12.19 lg/m 3 and 76.33 lg/ m 3 ), while NO 2 concentration was close to the annual average (27.03ppb).It shows that there was a nonlinear response of nitrate concentration to gaseous precursor decline.Monthly average concentrations of the three species are shown in Figure S4 (SI).NO 3 − concentration was generally higher in winter and spring (January-April, November-December, with an average of 11.16 lg/m 3 ), while lower in summer and autumn (May-October, averaging 5.23 lg/m 3 ).The highest NO 3 -concentration (18.34 lg/m 3 ) was observed in November (early winter) (SI, Figure S4), which was significantly higher than in other months.The concentration of HNO 3 was higher in spring and summer (March-June, averaging 1.78 lg/m 3 ), and lower in autumn and winter (July-December, January-February) with an average of only 0.62 lg/m 3 .And NO 2 was higher in winter, the highest concentration appeared in December.The above observations showed that the concentration variation of NO 3 − and HNO 3 was inconsistent with that of NO 2 , indicating that the increase in gaseous precursors was not the only reason for the elevation of NO 3 − level, which was in line with previous studies.For example, Ren et al. (2021) found that the nonlinear response of nitrate to NO x reduction in China during the COVID-19 pandemic.And Fu et al. (2020) found that the about 30% reduction of NO x emissions during 2010-2017 in the NCP lowered nitrate by only 0.2% and even increased nitrate in some polluted periods (Chan et al. 2021;Fu et al. 2020;Li et al. 2021;Ren et al. 2021).
We further found weak correlation between NO 3 − and NO 2 (r ¼ 0.44), HNO 3 and NO 2 (r ¼ 0.06), HNO 3 and NO 3 − (r ¼ 0.13) (SI, Figure S5), which also confirmed that the change of precursor concentration was not the primary reason for the variation of particulate nitrate concentration.Therefore, we suggest that the poor correlation between NO 2 and NO 3 − concentration variations may be more influenced by the complex internal process of NO 2 conversion into NO 3 − in ambient atmospheric condition.Of course, air mass transport processes can also influence nitrate pollution, but in recent studies, it found that their impacts on nitrates in this study area were relatively weak (Fu et al. 2020;Zhou et al. 2022).Additionally, previous studies suggested that chemical processes were important to nitrate formation (Cheng et al. 2019;Xie et al. 2022); meanwhile, NO 2 and NO 3 − were observed at the same observation site in our study, and the wind speed was relatively weak (except in spring) (SI, Figure S6), the average wind speed was 1.58 m/s, so the above weak correlation was likely less affected by meteorological disturbance (Zhou et al. 2022).Therefore, we will focus our discussion on the internal chemical mechanism processes from NO 2 to NO 3 − in this work.

Increased oxidation and gas-particle partitioning processes at high PM 2.5
In order to further understand the formation mechanism of particulate matter pollution events, we next classified the sampling data of PM 2.5 concentrations into four categories: clean (0 � 75 lg/m 3 ) (C), lightpollution (75 � 115 lg/m 3 ) (LP), medium-pollution (115 � 150 lg/m 3 ) (MP) and heavy-pollution (>150lg/m 3 ) (HP).The cut-points were based on ambient air quality standards in China (GB3095-2012) (Xu et al. 2019a).We observed that the proportion (%) of NO 3 − in PM 2.5 increased gradually with the increase of PM 2.5 pollution level (SI, Figure S7), thus the impacts from Oxi-process and G/P-process would vary among different pollution episodes.
From Figure 2a, Oxi-process and G/P-process were both enhanced when the concentration of PM 2.5 was high.After further exploring the relationships of TN Oxi vs. N total and NO 3 − vs. TN Oxi (Figure 2b and c), we found the concentrations of initiator (N total ) and product (TN Oxi ) of Oxi-process were nonlinear during the oxidation process, while the initiator (TN Oxi ) and product (NO 3 − ) of G/P-process exhibited linear relationship during the gas-particle partitioning process.This phenomenon showed that the response of the Oxi-process efficiency and G/P-process efficiency to the variation of PM 2.5 level and the concentration of TN Oxi and N total is quite different.It can be clearly seen that TN Oxi increased with the PM 2.5 concentrations, but sometimes higher values of TN Oxi did not appear together with high N total (Figure 2b), which was consistent with the phenomenon observed in Figure 1.Furthermore, Figure 2b shows the oxidation ratio continued to increase with the aggravation of pollution.In contrast, Figure 2c shows the gas-particle partitioning ratio increased obviously during the transition from clean to light pollution, and tended to be flat when the pollution continued to aggravate and stayed at a high level.Therefore, a quantitative method is urgently needed to estimate the contributions of Oxi-process and G/P-process to nitrate formation under different pollution characteristics, and to explore their relative importance in particulate nitrate concentration growth.

Apportionment of Oxi-process and G/Pprocess
Applying the Equations ( 2)-( 12), we were surprised to find that the G/P-process contributed higher (average C obs G=P (%) ¼ 64.90%) to the production of nitrate in particulate form from precursor than the Oxi-process (average C obs Oxi (%) ¼ 35.10%) during the entire study period.Next, we calculated contributions of the two processes on particulate nitrate formation under different pollution levels.The classification has been described in detail above.Surprisingly, we found the C obs G=P (%) was consistently higher than C obs Oxi (%) across all levels (Figure 3a), which were 68%, 62%, 60% and 59%, respectively.We also calculated C obs Oxi (%) and C obs G=P (%) for each month of the whole year and found similar results that the C obs G=P (%) (62%-73%) was greater than C obs Oxi (%) (27%-38%) in different months (SI, Figure S8).These quantitative results suggest that gas-particle partitioning exhibits a more important impact on particulate nitrate formation from the purpose of eliminating air pollution which influences the proportion of particulate NO 3 − in total N.Note that the normalized contributions mentioned in this work are not actual contributions of the two processes to nitrate formation, they are rather quantitative indicators for evaluating the relative importance of the two processes to nitrate formation.
We then calculated the enhancement factors (R pollution /R Clean ) of the two processes when pollution occurred (SI, Figure S9).It can be found that the efficiency of both oxidation process and gas-particle partitioning process enhanced when pollution occurred.As the pollution level increased, the efficiency of the Oxiprocess enhanced more significantly compared to the G/P-process, in which the enhancement factor of the Oxi-process was 3.13 and that of the G/P-process was only 1.17 in heavy-pollution.It can be seen that the oxidation process aggravated the nitrate-dominated pollution more significantly.The result corresponded to the above findings that C obs Oxi (%) increased and C obs G=P (%) decreased as pollution worsened.

Empirical theoretical analysis of Oxi-process and G/P-process
In order to understand why the G/P-process had greater effects on particulate nitrate formation than the Oxi-process, we further analyzed the impacts of Oxi-process and G/P-process using empirical theoretical calculation and modeling.
For the Oxi-process, NO 2 is oxidized by OH radical to produce HNO 3 in daytime and by O 3 to form NO 3 radical in nighttime, respectively.It can be seen from empirical kinetics equations (Equations ( 13) and ( 14)) that different driving factors affect the oxidation reactions during daytime and nighttime, including precursors (NO 2 ), oxidants (�OH, O 3 ) and kinetics rate coefficients (Seinfeld and Pandis 2016): In order to comprehensively evaluate the impact from the Oxi-process, we proposed a theoretical oxidation ratio (R theo Oxi ) (physical meaning is same as R obs Oxi ), which can roughly estimate hourly average oxidation level, as follows: where, NO 2(day) and OH (day) are average concentrations of observed NO 2 and simulated OH (molecule/cm 3 ) (by box model, see method section) during daytime; NO 2(night) and O 3(night) are average concentrations of observed NO 2 and O 3 (molecule/cm 3 ) during nighttime; the NO 2 value used in the denominator was the diel average NO 2 (molecule/cm 3 ) concentration.k (OH�NO2) and k (O3�NO2) are the rate coefficients (cm 3 molecule −1 s −1 ) of ( R1) and (R2) (details are provided in the SI (Text IV)); 3600 is a constant for converting second to hour.
Applying the Equation ( 15), we found the R theo Oxi to be 0.05, which meant that theoretically only about 5% of NO 2 were oxidized per hour through the Oxi-process.And R theo Oxi was in line with the R obs Oxi whose average was 0.1.This relatively low ratio suggested that even though oxidants had increased in recent years, given the small value of R theo Oxi , the proportion of oxidized NO 2 involved in the oxidation reaction was still very low compared to the total NO 2 .We also calculated the theoretical contribution percentage (%) from the Oxi-process (C theo Oxi (%)) (25.6%) on nitrate formation (Equation ( 16)), and the results were similar with observations as follows: For the G/P-process, we found aerosol pH, temperature and aerosol liquid content water (ALWC) are the key parameters for gas-particle partitioning of HNO 3 /NO 3 − , based on empirical thermodynamical equations in our previous works (Shi et al. 2019b;Zhao et al. 2020).Generally, aerosol pH and R obs G=P (or e(NO 3 − )) usually exhibits a "S-curve" relationship (Guo et al. 2016;Shi et al. 2019b).Here we estimated aerosol pH (by ISORROPIA-II) and found that the average aerosol pH was 4.77.Most of aerosol samples were found to be in the non-sensitive zone of the "Scurve" (4-8) (SI, Figure S10), which was constructed by fitting e(NO 3 − ) as a function of pH using the Boltzmann equation (y (Shi et al. 2019b).At this time, the G/P-process is very efficient.In this work, we calculated a theoretical nitrate particulate phase conversion ratio (R theo G=P ) (physical meaning is same as R obs G=P ) by using the empirical thermodynamical formula which was proposed in our previous work (Shi et al. 2019b), to estimate the partitioning level, as follows: where I TL ¼ 3.2RTL (Shi et al. 2019b); R is the idealgas constant equal to 0.08205 atm L mol −1 K −1 ; T is the temperature in K; and L is the aerosol liquid water content in g/m 3 (estimated by ISORROPIA-II).In this work, I TL and H þ had an average value of 0.0078 and 0.0002 mol/L, and R theo G=P was estimated to be 0.88.It was in line with the R obs Oxi whose average was 0.77.Such high value of R theo G=P indicated that about 88% TN Oxi (produced by Oxi-process) existed in the particulate phase, which suggested the partitioning process contributed significantly to the formation of particulate nitrate.We also calculated the theoretical contribution percentage (%) of the G/P-process (C theo G=P (%)) (74.4%) on nitrate formation (Equation ( 18)), which was similar to the observed result, as follows: Based on the above theoretical analysis, the reason why the G/P-process had a greater impact on nitrate formation may be due to the relatively higher aerosol pH in recent years (Fu et al. 2017;Guo et al. 2018;Liu et al. 2018;Wang et al. 2013).Aerosol pH is influenced by cations and anions in aerosol liquid phase.Recent data showed substantial NH 3 emissions in China, and cations content (Ca 2þ , Mg 2þ , etc.) in aerosol were relatively high as a result of fugitive road dust, construction dust and others sources (SI, Figure S11c) (Huang et al. 2012;Liu et al. 2018;Vasilakos et al. 2018) ) > 0 under four pollution levels (0.17, 0.48, 0.70, and 0.94), it indicated that the aerosol was ammonium-rich condition (SI, Figure S11b) (Huang et al. 2011;Shi et al. 2019a).More cations and high NH 3 emission are responsible for the relative high aerosol pH (Ding et al. 2019;Jia et al. 2020;Liu et al. 2017).Some studies also showed that HNO 3 mainly relied on reacting with NH 3 (NH 3 þ HNO 3 $ NH 4 NO 3 ) to enter particle phase.If so, the level of NH 3 is a key factor affecting the concentration of nitrate (Hildemann, Russell, and Cass 1984;Moya, Ansari, and Pandis 2001).Therefore, ammonium-rich condition may be a main reason for the high contribution of the G/P-process to nitrate formation.
There is no doubt that the Oxi-process is prerequisite to form nitrate, but because the G/P-process is highly efficient, nitrate pollution is mainly due to the reason that more oxidization products enter particle phase by gas-particle partitioning.Hence, the impact of the Oxi-process on nitrate is relatively lower compared to the G/P-process.This finding was consistent with aforementioned observations on increased nitrate levels despite NO x decrease.

Drivers for Oxi-process and G/P-process during pollutions
As for the Oxi-process, despite the contribution percentage (%) of the G/P-process (C obs G=P (%)) was higher, the contribution percentage (%) of the Oxi-process (C obs Oxi (%)) did grow with the aggravation of pollution, from 32% under clean conditions to 41% under HP (Figure 3a).Considering the different formation pathways of nitrate during daytime and nighttime, the contributions of Oxi-process and G/P-process were calculated separately (Figure 3b and c).It was found that C obs Oxi (%) exhibited similar variation patterns in both daytime and nighttime, but the reasons for such variation may be different.By using a box-model constrained by observational data, we simulated the concentrations of OH radical and N 2 O 5 under different pollution levels.
During daytime, OH radical concentration decreased from clean to LP and from MP to HP, and remained basically unchanged from LP to MP, which was similar to the simulation results of Xue et al. (2020) (Figure 4a).However, because NO 2(day) concentration increased, the HNO 3 production rate (k OH�NO2 �OH (day) �NO 2(day) ) showed an upward trend from clean to higher pollution levels.The concentration of NO 2(day) in different pollution levels was 19.30, 32.48, 34.62, and 41.46 ppb, respectively.This finding may be due to the weakening solar radiation during heavy pollution periods, which inhibited the production of OH radical (see reactions RS1-RS5 in SI (Text V)) (Wu et al. 2021;Yun et al. 2018).It could also be possible that the complex environment conditions during heavy pollution periods are so complex that model simulation are inaccurate (Xue et al. 2020).Moreover, with the aggravation of pollution, the concentrations of N 2 O 5 showed an increasing trend during daytime (Wang et al. 2017a).Usually, diminished solar radiation could weaken the photolysis of NO 3 and thermal decomposition of N 2 O 5 during pollution periods (Wu et al. 2021).The relative humidity and heterogeneous reactions interface will also increase which are favorable for the heterogeneous hydrolysis of N 2 O 5 into nitrate in daytime (SI, Figure S12) (Wu et al. 2020;Wu et al. 2018).Therefore, N 2 O 5 heterogeneous hydrolysis could exist in the daytime especially during heavy pollution period which helped to enhance the impact of the Oxi-process on nitrate formation (Chan et al. 2021;Liu et al. 2020;Wu et al. 2021;Yun et al. 2018).In the nighttime, N 2 O 5 concentrations increased significantly during the transition from clean to light pollution, though such increasing trend slowed considerably with the further aggravation of pollution (Figure 4), which enhanced the impact of Oxi-process (Kim et al. 2014;McDuffie et al. 2019;Prabhakar et al. 2017).The simulated N 2 O 5 concentrations in our study were similar with the nighttime N 2 O 5 concentrations observed near the urban surface in Chen et al. (Chen et al. 2020).Because of the accumulated NO x , O 3 , and NO 3 were titrated rapidly by NO, the production of NO 3 and N 2 O 5 were consequently suppressed (Chen et al. 2020;Wang et al. 2017b;Yan et al. 2021).More details are given in the SI (Text V).In conclusion, the increase of the HNO 3 production rate and the enhancement of the N 2 O 5 heterogeneous hydrolysis drove the increase of C obs Oxi (%) together during the pollutions.What's more, we performed a series of sensitivity simulation to study the evolution of MDA8 (maximum daily 8-h average) O 3 and OH concertation with varying NO x levels (in 20% increment) by chemical box model (SI, Figure S13).We found that MDA8 O 3 and OH concertation will both increase with NO x reduction.And we next calculated the theoretical contribution percentages (%) of the Oxi-process and G/P-process under different situations.The results showed that the C theo Oxi (%) will increase and the C theo G=P (%) will decrease with NO x reduction that were in line with previous studies.
As for the G/P-process, although the contribution percentages (%) of the G/P-process (C obs G=P (%)) to nitrate formation decreased with the increase of pollution levels (from 68% to 59% (Figure 3a)), its ratio of particulate nitrate formed from oxidization product (R obs G=P ) was in fact increased from 0.82 to 0.97.We estimated that aerosol pH among the four pollution levels were 4.74, 4.71, 4.85, and 4.90 (SI, Figure S7a), respectively.According to the S-curve of nitrate gasparticle partition (SI, Figure S10), when aerosol pH is low (2-4), the partitioning efficiency is sensitive to the change of pH and increases rapidly with the increase of pH value, but when pH is high (>4), the growth of partitioning efficiency tends to be flat with the increase of pH value, and maintains at a high level.It is because that higher pH meaning low [H þ ] and thus its impact on R theo G=P is weak, as shown in the theoretical thermodynamic formula (Equation ( 17)).Therefore, when aerosol pH is high, the research shows that the influence of temperature and relative humidity on the change of partitioning efficiency is strengthened (Shi et al. 2019b).In light of Equation ( 17), I TL play an important role in determining the changes of R theo G=P (when [H þ ] is low).Thus, in this work, the variation of G/P-process during different pollution levels may be mainly affected by temperature and ALWC (I TL is calculated from temperature and ALWC).Low temperature and high humidity conditions are favorable for nitric acid to partition to particle phase.The continuous increase in liquid water content (especially during the period of heavy pollution) and decreased temperature were responsible for the enhanced G/Pprocess with the aggravation of pollution (Figure 4c).What's more, we calculated I TL during different pollution levels, and found a clear increasing trend of I TL (Figure 4d) which could help better explain the growth of R obs G=P :

Conclusions and implications
Particulate nitrate has become the main driving factor for the formation of PM 2.5 pollution in China.Even during the COVID-19 lockdown period, the level of secondary nitrate remained high, leading to the occurrence of pollution events (Ren et al. 2021).Our work quantitatively analyzed the impacts of two dominant processes on nitrate formation (the Oxi-process and the G/P-process) based on ambient observation and empirical theoretical analysis, which could innovate a new insight for understanding this complex problem of environmental nitrate production.This paper provided quantitative evidences that the G/P-process was more important than the Oxi-process for the formation of particulate nitrate in the North China Plain, although the atmospheric oxidant in this region have increased in recent years.This result was due to high aerosol pH caused by higher cations concentration (NH 4 þ , Ca 2þ , Mg 2þ , etc.), according to the "S-curve," more nitrate enters particulate phase.During different pollution levels, we found that oxidants and precursors were the drivers that influenced the oxidation process, while temperature and ALWC were the drivers of the partitioning process.For the purpose of effectively reducing nitrate pollution, ignoring the partitioning between HNO 3 and NO 3 − will be less effective.Relatively lower aerosol pH is beneficial for the partitioning of particulate nitrate to gas phase which can alleviate pollution.Therefore, in order to scientifically prevent and control nitrate pollution, attentions should not only focus on reducing the emissions of precursors and oxidants, but also on the regulation of aerosol pH.For example, to control the aerosol pH under complex environmental conditions, it is necessary to strengthen the control of NH 3 emissions, continue to control dust source pollution, and pay attention to the impact of sea salt in coastal areas.However, although the lower aerosol pH will greatly reduce the efficiency of HNO 3 -NO 3 − partitioning, it is necessary to beware of environmental problems such as acid rain.
At present, the NO x emissions are largely controlled in the study area.Therefore, we should pay more attention to the partitioning process, so current success on emission reduction of precursors and oxidants can be retained.We can further control the emission sources of NH 3 , Ca 2þ , and Mg 2þ that cause aerosol pH increase, such as relevant industry, fertilization and dust, especially during the heavy pollution period.The coordinated control of precursor and the emission sources of cation for raising aerosol pH may be more effective in reducing particulate nitrate.Additional filed observations and model simulations will be beneficial for further understanding this research topic (Jin 2011).

Figure 2 .
Figure 2. (a) R obs Oxi vs. R obs G=P , (b) TN Oxi vs. N total , and (c) NO 3 − vs. TN Oxi .Sample points were coded by PM 2.5 concentration and circle A indicated PM 2.5 at a higher concentration.