The observational experiment was conducted at the Station of Rural Environment, Research Center for Eco-Environmental Sciences (SRE-RCEES; 38°42^′ N, 115°15^′ E), located in Dongbaituo village, Wangdu county, Hebei province. Situated approximately 180 km southwest of Beijing, the station is surrounded primarily by farmland with no nearby industrial facilities, making it an ideal site for studying typical rural atmospheric conditions. This location has historically served as a key site for numerous large-scale observational campaigns (Tan et al., 2017; Peng et al., 2021). The experiment took place from 6 July to 12 August 2016, with the primary objective of investigating the underlying causes of photochemical pollution in the rural North China Plain.

H₂O₂ concentrations were measured using the AL-2021 H₂O₂ monitor (Aero-Laser) (Lazrus et al., 1986). The instrument operates on the following principle: gas-phase peroxides in ambient air are collected by the buffered solution in a glass stripping coil. The trapped peroxides then react with p-hydroxyphenyl acetic acid (POPHA) under the catalysis of peroxidase, producing a fluorescent dimer. This dimer exhibits maximal light absorption at a characteristic wavelength of 320 nm and emits fluorescence with a central wavelength of 400 nm. By continuously monitoring the intensity of this fluorescence signal, the instrument enables online quantitative detection of atmospheric peroxides. To differentiate between H₂O₂ and organic peroxides, a dual-channel measurement approach was employed. Channel A measures the total peroxide content, while channel B incorporates catalase into the absorbent solution to selectively decompose H₂O₂, thereby measuring only organic peroxides. The H₂O₂ concentration is determined by the difference in signals between the two channels. Although channel B provides an approximation of organic peroxides, it is important to note that the percentage of organic peroxides reported in this study represents a lower limit, as the collection efficiency of the stripping coil technique varies significantly among different organic peroxide species. While H₂O₂ is efficiently trapped due to its high solubility (Henry's law constant of ∼ 10⁵ M atm⁻¹), many organic peroxides such as methyl hydroperoxide (MHP) have substantially lower solubilities (Henry's law constant of 3 × 10² M atm⁻¹), resulting in lower collection efficiencies. Additionally, the catalase used to differentiate between H₂O₂ and organic peroxides may not completely discriminate between certain hydroperoxide species, further contributing to uncertainty in organic peroxide quantification. The detection limit of the H₂O₂ measurement instrument is 50 ppt, with an uncertainty of 10 %. To ensure the stability of the instrument's operation, regular calibrations are performed at fixed intervals. In several previous field experiments (Ye et al., 2018, 2021b, a; Liu et al., 2021), this instrument has been successfully utilized to measure atmospheric H₂O₂, demonstrating high reliability and consistent operational stability.

NO_x, O₃, SO₂, PM_2.5, CO, and total reactive nitrogen (NO_y) were measured using commercial instruments from Thermo Electron. Volatile organic compounds (VOCs) were quantified by gas chromatography with a flame ionization detector (GC-FID), while nitrous acid (HONO) was measured using a long-path absorption photometer (LOPAP) from QUMA. The aerosol surface area density was calculated by combining data from a scanning mobility particle sizer (SMPS) and an aerodynamic particle sizer (APS). PAN was analyzed using gas chromatography with electron capture detection (GC-ECD). Gas-phase meteorological data were collected using a portable meteorological station (Model WXT520, Vaisala, Finland). The photolysis rate constant of NO₂ (j(NO₂)) was measured directly, and other photolysis rate constants were derived using the tropospheric ultraviolet and visible (TUV) radiation model, scaled based on j(NO₂) measurements. Detailed information on the experimental instruments is provided in Table S1 in the Supplement.

A zero-dimensional box model based on the RACM2-LIM1 mechanism was employed to investigate the sources and removal mechanisms of H₂O₂. This model is widely recognized for its ability to accurately model HO_x radicals (Tan et al., 2017; Ma et al., 2022). Given that the HO₂ is a critical precursor for H₂O₂ formation, the model's strong performance in simulating free radicals provides confidence in its ability to reliably simulate H₂O₂ concentrations. The model was constrained using input parameters including photolysis rate constants (j(NO₂), j(O¹D), j(HONO), j(H₂O₂), j(HCHO)), VOCs, NO, NO₂, O₃, HONO, methane (CH₄), CO, and meteorological data (temperature, relative humidity, and pressure). VOCs were categorized into different reactivity-based groups according to their reaction rates with OH, as detailed in Table S2. The dry deposition rate constant for H₂O₂ was set to 3 × 10⁻⁵ s⁻¹, and boundary layer heights were derived from the hybrid single-particle Lagrangian integrated trajectory (HYSPLIT) model.

The simulation focused on the period from 24 July to 3 August, selected for its stable meteorological conditions that were characterized by low wind speeds and predominantly static weather. During this period, the observed trends in H₂O₂ concentrations exhibited consistent patterns, suggesting that local photochemical processes were the primary source of H₂O₂. This makes the selected time frame ideal for exploring H₂O₂ sources using the box model. Additionally, elevated PM_2.5 concentrations during this period provided an opportunity to investigate the potential influence of particle uptake on H₂O₂ removal. The rate coefficient of H₂O₂ uptake by particles was parameterized as Eq. (1): 1k=0.25×c×γ×Sa. Here c is mean molecular speed of H₂O₂, γ is the H₂O₂ uptake coefficient, and Sa is aerosol surface area density.

To assess the contributions of different precursors to H₂O₂ production, a relative incremental reactivity (RIR) analysis was conducted. RIR was calculated using the following equation: 2RIRX=ΔH2O2XH2O2ΔCXCX. In Eq. (2), X represents the primary pollutants that may influence H₂O₂ concentrations. H₂O₂ represents modeled H₂O₂ in the base case. ΔC(X)/C(X) represents the relative change in primary pollutants. ΔH₂O2(X)/H₂O₂ represents the relative change in modeled H₂O₂ concentrations induced by the reduction in X. Considering the variations in simulated radical concentrations and the deviations in the RIR, a 20 % reduction scenario was selected for further analysis. This approach allowed for the quantification of the sensitivity of H₂O₂ production to variations in precursor concentrations, providing insights into the key drivers of H₂O₂ formation in the rural North China Plain.

Figure 1 depicts H₂O₂, other related chemical species, and meteorological parameters during the observation period. Throughout the observation period, meteorological conditions were characterized by high temperature and relative humidity. High temperature generally increased the rate constants of photochemical reactions, while abundant water vapor enhanced the recombination rate of HO₂ and the reaction rate between O(¹D) and water vapor (H₂O). The maximum O₃ concentration reached 120 ppb, with the maximum daily 8 h average (MDA8) frequently exceeding the National Ambient Air Quality Standard (NAAQS) class-II standard of 82 ppb (25°, 1013 kPa). High-O₃-pollution events often coincided with elevated H₂O₂ concentrations (>2 ppb), suggesting that O₃ production at this site may be sensitive to NO_x. This hypothesis will be further investigated using the H2O2/NOz and O3/NOz ratios in Sect. 3.6 on O₃ sensitivity. NO_x concentrations peaked in the morning, driven by factors such as traffic emissions and lower boundary layer height. Daytime NO concentrations were generally below 1 ppb, while daily peak H₂O₂ concentrations exhibited significant day-to-day variability, ranging from approximately 0.2 ppb to 4 ppb. Higher H₂O₂ concentrations were observed during periods of intense solar radiation, indicating that local photochemical reactions play a significant role in H₂O₂ production. Notably, elevated H₂O₂ levels were only observed when NO concentrations were low, consistent with the known mechanism of H₂O₂ formation under low-NO_x conditions.

The average H₂O₂ concentration during the whole observation period was 0.62 ± 0.80 ppb, significantly higher than wintertime concentrations (0.19 ppb) at the same site (Ye et al., 2021b), as summer conditions with high solar radiation intensity and relative humidity are more conducive to H₂O₂ production. This average concentration also exceeded summer H₂O₂ levels reported in urban areas such as Beijing (0.27 ppb) (Qin et al., 2018) and Hong Kong (0.32 ppb) (Guo et al., 2014), likely due to lower NO_x levels at the rural site, which favor H₂O₂ formation. Compared to the H₂O₂ concentrations reported at rural sites in other countries, the levels observed in this study were lower than those in Kinterbish (Watkins et al., 1995) and Whiteface Mountain (1.61 ppb) (Balasubramanian and Husain, 1997). It is worth mentioning that an average H₂O₂ concentration of 0.51 ± 0.90 ppb was reported at the same site in summer 2014 (Wang et al., 2016), lower than the current study's findings, reflecting a potential increasing trend in H₂O₂ concentrations over time. In addition, multiyear measurements at the summit of Mount Tai revealed an increasing trend in H₂O₂ concentrations in cloud water from 2014 to 2018 (Li et al., 2020), indirectly indicating rising gas-phase H₂O₂ levels in the North China Plain. The significant reduction in NO_x emissions in the North China Plain over recent years, while VOC levels remained relatively high or decreased less sharply, has likely shifted the atmospheric chemistry towards conditions more favorable for HO₂ recombination, potentially contributing to the observed increasing trend in H₂O₂ concentrations. This aligns with the known sensitivity of H₂O₂ formation to NO_x levels.

Elevated H₂O₂ concentrations and high relative humidity in rural areas facilitate the oxidation of SO₂ by H₂O₂ in both aerosol water and cloud water, contributing to sulfate formation and increased PM_2.5 levels. During the observation period, the average PM_2.5 concentration reached 57 µg m⁻³, and the co-occurrence of PM_2.5 and O₃ pollution was frequently observed. This dual pollution phenomenon suggests that high concentrations of oxidants may play a significant role in driving secondary aerosol formation. PAN, another key secondary oxidant measured in this study, reached a maximum concentration of 2.9 ppb. Similar to H₂O₂ and O₃, PAN is a product of photochemical pollution, and its temporal trends closely mirrored those of H₂O₂ and O₃. These trends will be analyzed in detail in Sect. 3.2. As strong oxidizing agents, H₂O₂, O₃, and PAN are proven to be damaging to vegetation and human health. Given the high concentrations of these oxidants observed in this study, photochemical pollution in rural areas poses serious risks to agricultural productivity and human health.

The average diurnal trends in H₂O₂, PAN, and O₃ exhibited pronounced daily variations, with concentrations peaking during the daytime and declining at night (Fig. 2). These trends closely followed solar radiation patterns, highlighting the significant contribution of photochemical reactions to their formation. In addition, the pronounced daily variations also indicated the presence of abundant precursors in the region facilitating the production of H₂O₂, PAN, and O₃. In the early morning, as solar radiation intensified, the photolysis of HONO initiated daytime photochemical reactions (Reaction R1), generating peroxyl radicals (Reaction R2). These radicals reacted with NO to produce O₃ (Reactions R3–R6), HO₂ recombination underwent bimolecular recombination to produce H₂O₂ (Reaction R7), and peroxyacetyl radicals (PA) reacted with NO₂ to form PAN (Reaction R8). These processes led to a rapid increase in the concentrations of all three oxidants, with peak concentrations reaching 1.8, 1.2, and 84 ppb for H₂O₂, PAN, and O₃, respectively.

Despite sharing similar photochemical formation pathways, the peak times of the three oxidants differed due to variations in their production and removal rates. PAN concentrations peaked around 12:00 LT (all subsequent times are in local time, LT), approximately 2–3 h earlier than H₂O₂ and O₃, a phenomenon also observed in previous studies (Lee et al., 2008a). This earlier peak in PAN can be attributed to its higher thermal decomposition rate at midday. In contrast, the peaks for H₂O₂ and O₃ both occurred around 16:00. Notably, in urban areas, H₂O₂ peaks often lag behind O₃ peaks. For example, observations at the urban Tai'an site in the North China Plain revealed that H₂O₂ peaks occurred approximately 2 h after O₃ peaks (Ye et al., 2021a). This delay can be explained by HO₂ chemistry under varying NO_x conditions. Under high-NO_x conditions, HO₂ primarily reacts with NO (reaction rate constant of 8.9 × 10⁻¹² cm³ molecule⁻¹ s⁻¹ at 298 K), whereas under low-NO_x conditions, HO₂ undergoes bimolecular recombination to form H₂O₂ (reaction rate constant of 1.5 × 10⁻¹² cm³ molecule⁻¹ s⁻¹ at 298 K). In urban settings, H₂O₂ peaks only occur when NO concentrations drop to around 100 ppt, allowing HO₂ recombination to dominate, thus delaying the H₂O₂ peak relative to O₃. However, at this rural site, daytime NO concentrations were consistently low, resulting in simultaneous peaks for O₃ and H₂O₂. R1HONO+hυ→OH+NOR2VOCs+OH→RO2+H2OR3RO2+NO→HO2+RO2+OVOCR4HO2+NO→NO2+OHR5NO2+hυ→NO+O3PR6O3P+O2→O3R7HO2+HO2+M→H2O2+H2O+MR8CH3COOO+NO2+M→CH3COOONO2PAN+H2O+M Following their peaks, the concentrations of all three oxidants declined rapidly. For H₂O₂, this decrease was primarily driven by dry deposition and, in the evening, enhanced uptake by liquid aerosols formed as relative humidity increased. O₃ concentrations dropped due to a combination of dry deposition and NO titration, while PAN levels decreased mainly through thermal decomposition. At night, the absence of photochemical reactions caused all three oxidants to maintain low concentrations.

Figure 3 illustrates the average diurnal trends in ROOH and H₂O₂. The trends in total peroxides closely align with those of H₂O₂, indicating similar production and removal mechanisms. H₂O₂ accounts for 69 % of the total peroxides on average, while ROOH (0.28 ppb) constitutes 31 %. This demonstrates that peroxides in rural areas are predominantly dominated by H₂O₂, consistent with the findings of Wang et al. (2016) at this site. However, it is important to note that the percentage of ROOH reported in this study represents a lower limit, as not all ROOH is fully captured by the measurement technique. In contrast, Liang et al. (2013) reported that ROOH accounted for 80 % of total peroxides in urban areas such as Beijing. The difference in organic peroxide proportions between Beijing and Wangdu can likely be attributed to variations in chemical conditions, such as differences in VOC compositions, which influence the types and abundances of the peroxyl radicals formed.

The diurnal variation in the relative contributions of H₂O₂ and ROOH to total peroxides reflects their distinct production and loss mechanisms. H₂O₂ dominates (over 90 %) around 19:00 due to strong photochemical production via HO₂ recombination during the day, while its contribution drops to ∼ 25 % by 05:00 due to nighttime losses (e.g., heterogeneous uptake and dry deposition) without replenishment. In contrast, ROOH contributes more significantly in the early morning, likely due to slower loss rates compared to H₂O₂. ROOH molecules such as CH₃OOH (methyl hydroperoxide) have much lower dry-deposition rates – approximately 30 times lower than that of H₂O₂ – leading to less nighttime loss and a higher relative contribution to total peroxides during early-morning hours. The minimum in ROOH concentration observed around 19:00 represents a transitional point. By this time, daytime photochemical production has largely ceased due to diminishing solar radiation, leading to a decline from its afternoon peak as the removal processes continue. The subsequent increase in ROOH concentration after 19:00, which makes 19:00 a local minimum, may be attributed to nighttime chemical production primarily through (a) the ozonolysis of alkenes (O3+ alkenes →…→ RO₂ → ROOH) and (b) NO₃ radical-initiated oxidation of VOCs (NO₂ + O₃ → NO₃; NO₃ + VOCs →…→ RO₂ → ROOH). These processes become major sources of RO₂ (and subsequently ROOH) during the night. In contrast, H₂O₂ typically continues to decrease throughout the night. Although ozonolysis can also be a source of H₂O₂, H₂O₂ generally has a higher dry-deposition velocity than many ROOH species, leading to more efficient net removal overnight. These differences highlight the distinct photochemical dynamics and loss mechanisms of H₂O₂ compared to ROOH, influenced by diurnal variations in radiation, precursor concentrations, and meteorological conditions.

The formation of H₂O₂, O₃, and PAN is closely linked to VOCs, NO_x, and solar radiation. Consequently, their concentrations are typically elevated and well-correlated during photochemical pollution episodes. Here, we investigate the relationships among these oxidants. Figure 4 illustrates the correlations between the daily maximum concentrations of H₂O₂, O₃, and PAN. A good correlation (r2=0.55) was observed between PAN and O₃, consistent with previous studies (Lee et al., 2008a; Zhang et al., 2014; Xu et al., 2021; Sun et al., 2020). In contrast, the correlation between H₂O₂ and O₃ was weak (r2=0.19). Prior research has shown positive correlations between H₂O₂ and O₃ during photochemical pollution due to their shared dependence on VOC and NO_x photochemistry (Hua et al., 2008; Takami et al., 2003; Ye et al., 2021a; Guo et al., 2022), while negative correlations have been reported in the clean marine boundary layer where O₃ photolysis dominates radical production (Ayers et al., 1992). The lack of a positive correlation between O₃ and H₂O₂ in this rural polluted environment may indicate additional factors influencing H₂O₂ concentrations. Notably, heterogeneous uptake by particles has been shown to affect H₂O₂ levels (de Reus et al., 2005; Qin et al., 2018), and given the relatively high PM_2.5 concentrations during the observation period, we hypothesize that heterogeneous loss reduces gas-phase H₂O₂, weakening its correlation with O₃. Additionally, aqueous-phase reactions in aerosol water or cloud droplets, facilitated by high relative humidity during the campaign, could further reduce gas-phase H₂O₂ without affecting O₃, contributing to the decoupling of their peak values. While the focus on daytime maxima limits the direct relevance of nighttime chemistry, processes such as alkene ozonolysis or nocturnal deposition could influence background H₂O₂ levels, indirectly affecting daytime peaks.

To test this hypothesis, we analyzed the O3/H2O2 ratio on polluted (daily average PM_2.5 < 50 µg m⁻³) and clean days (daily average PM_2.5 ≥ 50 µg m⁻³). While O₃ and H₂O₂ share similar photochemical formation pathways, O₃ is less affected by particle uptake. O₃ lifetime was estimated to be 13 d with respect to heterogeneous uptake for dust mass concentrations of 1000 µg m⁻³, highlighting the minor role of particle uptake on O₃ removal (Tang et al., 2017). If the O3/H2O2 ratio remains stable across polluted and clean conditions, heterogeneous uptake likely has minimal impact on H₂O₂. However, if the ratio is higher during polluted periods, it is possible that PM_2.5 may scavenge H₂O₂ by heterogeneous uptake. As shown in Fig. 5, the O3/H2O2 ratio during peak photochemical hours (09:00–18:00) was markedly higher on polluted days compared to clean days, supporting the hypothesis that heterogeneous uptake by PM_2.5 significantly reduces H₂O₂ concentrations. It is important to note that this method provides only a preliminary assessment, as uncertainties exist due to differences in the dependence of H₂O₂ and O₃ on peroxyl radical concentrations and their respective responses to radiation intensity. In addition, differences in photochemical regimes, potentially driven by varying VOC/NOx ratios between clean and polluted days, could also influence the O3/H2O2 relationship independently of particle uptake effects. In the following section, we further examine the impact of PM_2.5 on H₂O₂ budget using a box model.

To better understand the sources and removal mechanisms of H₂O₂, we employed a box model to simulate its concentrations. As shown in Fig. 6, base simulations using the model's default H₂O₂ source and removal mechanisms overestimated H₂O₂ concentrations compared to observations, with a simulated-to-measured ratio of 2.7. This discrepancy suggests an unaccounted removal pathway, consistent with our earlier hypothesis of H₂O₂ removal by particle uptake. When a parameterized uptake mechanism with an uptake coefficient of 6 × 10⁻⁴ was incorporated into the box model, the simulated H₂O₂ concentrations and trends aligned well with observed values (Fig. 6), confirming the significant role of particle uptake in H₂O₂ removal in rural areas. This uptake coefficient is comparable with the value (5 × 10⁻⁴) estimated during a dense Saharan dust event (de Reus et al., 2005) and lower than the value of 1 × 10⁻³ reported by Wang et al. (2016), which may be likely due to differences in particulate matter composition. Sensitivity tests indicated that an uptake coefficient of 1 × 10⁻³ resulted in underestimation (Fig. S1), supporting 6 × 10⁻⁴ as the optimal value for our study. This coefficient falls within the range (10⁻⁴–10⁻³) determined in laboratory studies for H₂O₂ uptake on ambient particles collected on filters or artificial particles (Pradhan et al., 2010; Romanias et al., 2012; Qin et al., 2022). We believe that this value represents a reasonable estimate for the conditions at our sampling site, although we acknowledge that a more dynamic treatment of heterogeneous processes that accounts for variations in aerosol composition, phase state, and ambient RH would be valuable in future studies.

It should be mentioned that previous studies have demonstrated that considering HO₂ uptake by particles can partially explain the discrepancy between observed and modeled HO₂ concentrations under low-NO_x conditions (Kanaya et al., 2007a, b; Whalley et al., 2010; Ma et al., 2022), as well as the phenomenon of increasing O₃ concentrations with decreasing particulate matter levels (Li et al., 2019). Since HO₂ is a precursor to H₂O₂, its uptake by particles naturally reduces H₂O₂ concentrations. However, laboratory-measured HO₂ uptake coefficients exhibit significant variability, ranging from 10⁻⁵ to 0.82, and are strongly influenced by the composition of the particulate matter (Thornton et al., 2008; Taketani et al., 2012; George et al., 2013; Lakey et al., 2015). Through analysis of the measured radical budget and related parameters, Tan et al. (2020) showed that the HO₂ uptake was not important in the North China Plain in 2014, with an uptake coefficient of 0.08. Given that our observational experiments were conducted at the same site with a similar particulate matter composition, we also assumed an HO₂ uptake coefficient of 0.08 to investigate its impact on the H₂O₂ budget. Under this assumption, we found that an H₂O₂ uptake coefficient of 4.5 × 10⁻⁴ resulted in good agreement between modeled and observed H₂O₂ concentrations (Fig. S1). The results indicate that considering HO₂ uptake reduces the H₂O₂ uptake coefficient by 25 %. Therefore, uncertainties in the HO₂ uptake coefficient significantly affect the accurate simulation of H₂O₂ concentrations and the estimation of the H₂O₂ uptake coefficient. A more precise parameterization scheme for HO₂ uptake is critical for models to accurately assess the global distribution of H₂O₂ concentrations and their environmental impacts.

Figure 7 depicts the H₂O₂ production rates and removal rates by different pathways. The percentage contribution of different pathways is shown in Fig. S2. HO₂ bimolecular recombination was identified as the dominant H₂O₂ production pathway, contributing 91 % of the H₂O₂ production, with a maximum yield of 1.0 ppb h⁻¹ at noon. This highlighted rapid photochemical production as the primary driver of H₂O₂ pollution at the rural site. In contrast, the reaction of O₃ with alkenes accounted for 9 % of H₂O₂ production (Fig. S2), with a maximum yield of 0.07 ppb h⁻¹, primarily from O3+OLI reactions. This mechanism was found to be significant during winter pollution due to high alkene and NO concentrations inhibiting HO₂ recombination (Qin et al., 2018). Heterogeneous uptake dominated H₂O₂ removal, accounting for 69 %, with a maximum removal rate of 0.7 ppb h⁻¹, underscoring its importance during summer pollution periods. Dry deposition, photolysis, and reaction with OH radicals contributed 25 %, 2 %, and 4 % H₂O₂ losses, respectively. These findings provide a comprehensive understanding of H₂O₂ sources and sinks in rural environments, emphasizing the critical role of particle uptake in the H₂O₂ budget.

It is evident that photochemical pollution in rural areas is associated with elevated concentrations of H₂O₂, necessitating urgent measures to mitigate H₂O₂ pollution by regulating its precursor compounds. Given the diversity of precursors involved in H₂O₂ formation, a critical objective is to quantify the relative contribution of each precursor of H₂O₂ pollution to establish prioritized control strategies. In this study, the RIR method was employed to identify the most effective pollutants for H₂O₂ control (Fig. 8). Here it should be noted that the RIR analysis was performed using the adjusted model with an H₂O₂ uptake coefficient of 6 × 10⁻⁴ that showed good agreement with observations. The results demonstrate that reducing NO concentrations leads to an increase in H₂O₂ levels, as the reaction between NO and HO₂ inhibits H₂O₂ production. However, under realistic conditions, a decrease in NO also results in reduced NO₂ levels. Since the NO₂ heterogeneous reaction is a significant source of HONO, which serves as a key precursor for OH that influences H₂O₂ formation, a decline in NO₂ consequently reduces H₂O₂ concentrations. To validate this hypothesis, RIR values for NO_x were calculated. Although the absolute RIR values for NO_x remained negative (-0.06), they were significantly lower than those for NO (-0.9), indicating that the reduction in H₂O₂ due to decreased NO₂ partially offsets the increase in H₂O₂ caused by reduced NO.

Furthermore, the negative RIR value for alkanes (-0.06) suggests that lowering alkane concentrations enhances H₂O₂ production, likely due to their lower photochemical reactivities with OH. When alkane levels are reduced, OH radicals preferentially react with more reactive alkenes and aromatics, leading to increased HO₂ and hence more H₂O₂ formation. The RIR values for alkenes (0.51), aromatics (0.15), and CO (0.26) were consistently positive, indicating that reducing these pollutants is effective in reducing H₂O₂ concentrations, with alkenes exhibiting the most pronounced effect. Consequently, controlling alkene concentrations within anthropogenic VOCs should be prioritized, aligning with findings from previous studies (Wang et al., 2016; Ye et al., 2021a). Coal combustion and gasoline exhaust were identified as the primary sources of alkenes in the region, underscoring the importance of regulating these emissions to mitigate H₂O₂ pollution. Additionally, the RIR value for HONO was 0.12, indicating that reducing HONO concentrations can further diminish H₂O₂ levels by limiting the primary radical source. Elevated HONO concentrations have been observed across various sites in China, contributing over 40 % of the primary radical production. Thus, reducing HONO emissions represents a potential mitigating strategy for H₂O₂. Ye et al. (2022) reported that HONO emissions due to fertilizer use significantly increase H₂O₂ levels in rural areas, suggesting that reducing excessive fertilizer use could mitigate H₂O₂ pollution. Moreover, NO₂ heterogeneous reactions at various interfaces and nitrate photolysis are additional sources of HONO (Xue et al., 2020; Xue et al., 2022), highlighting the potential to reduce H₂O₂ by decreasing NO₂ concentrations and subsequently limiting HONO production.

The RIR value for PM_2.5 (-0.6) was found to be negative, as reducing PM_2.5 decreases the uptake of H₂O₂, thereby increasing its gas-phase concentration. Recent studies have extensively examined the impact of PM_2.5 reduction on O₃ concentrations, attributing this phenomenon to diminished HO₂ radical uptake and enhanced photolysis rates, both of which elevate O₃ levels (Wang et al., 2019; Song et al., 2022). These mechanisms similarly contribute to increased H₂O₂ concentrations, yet the effect of particulate matter reduction on H₂O₂ has been largely overlooked. This study demonstrates that PM_2.5 reduction also decreases H₂O₂ uptake, further exacerbating its gas-phase concentration. This increase in H₂O₂ could enhance sulfate formation efficiency and pose greater threats to human health and ecosystems. Given the critical role of H₂O₂ in an atmospheric oxidation capacity, in global sulfate aerosol formation, and on human health, further research is warranted to investigate H₂O₂ trends, environmental impacts, and mitigation strategies.

H₂O₂ measurements serve as a valuable indicator of O₃ production sensitivity. Under NO_x-poor conditions, the HO₂ recombination to form H₂O₂ represents the primary radical termination pathway. Conversely, under NO_x-sufficient conditions, the reaction between NO₂ and OH to form nitric acid (HNO₃) constitutes the dominant termination mechanism. Sillman (1995) identified the H2O2/HNO3 ratio as a robust indicator of O₃ sensitivity, with model simulations revealing that a ratio between 0.2 and 0.3 corresponds to a transitional regime, while values exceeding 0.3 indicate NO_x-limited conditions and values below 0.2 suggest VOC-limited conditions. In the absence of direct gaseous HNO₃ measurements, alternative metrics such as the H2O2/NOy or H2O2/NOz ratios can be employed to assess O₃ sensitivity (Sillman et al., 1998), where NO_z encompasses HNO₃, PAN, HONO, and alkyl nitrates, and NO_y is defined as NO_z + NO_x.

In this study, simultaneous measurements of H₂O₂ and NO_z enabled the determination of O₃ sensitivity using the H2O2/NOz ratio, with a transitional range identified at 0.15–0.20 (Sillman et al., 1998). The analysis focused on the period of intense photochemical activity between 10:00 and 17:00. As illustrated in Fig. 9, over 82 % of measured H2O2/NOz values exceeded 0.15, indicating that the rural study area predominantly exhibited NO_x-limited or transitional conditions during most of the observed period. It is important to note that this metric can be influenced by additional factors. For instance, significant uptake of H₂O₂ by particles was observed in this study, suggesting that the actual photochemical production of H₂O₂ is higher than the measured concentrations. Consequently, the theoretical H2O2/NOz ratio is likely greater than the observed values, implying that O₃ production is more strongly aligned with NO_x-limited or transitional regimes.

To corroborate these findings, the O3/NOz ratio was also utilized to evaluate O₃ sensitivity (Fig. 10). The relationship between peak O₃ concentrations and peak NO_z concentrations demonstrated a good positive correlation (r2=0.71), with a regression slope of 4.98. This slope is comparable with the value (3.3–7.6) reported in a mountainous area north of Beijing (Wang et al., 2006) but lower than those (6–11) observed in Houston (Daum et al., 2004). Notably, the positive correlation persisted up to NO_z concentrations of 12 ppb, differing from observations at other sites where the slope typically decreased for NO_z levels above 10 ppb (Trainer et al., 1993). This deviation can be attributed to reduced O₃ production efficiency under VOC-limited conditions. However, the sustained positive correlation across the entire study period suggests that the generation of NO_z is consistently accompanied by O₃ production, further supporting the prevalence of NO_x-sensitive or transitional regimes. These results align with those derived from the H2O2/NOz ratio, affirming the utility of H2O2/NOz as a reliable indicator of O₃ sensitivity.

The findings underscore the importance of controlling NO_x concentrations to mitigate photochemical pollution in rural areas. Tan et al. (2017) similarly reported that O₃ production in the rural North China Plain is primarily NO_x-limited. As NO_x emissions continue to decline due to regulatory efforts, an increasing number of regions may transition to NO_x-limited or transitional regimes, highlighting the potential benefits of stringent NO_x reduction strategies for future O₃ pollution control. However, given the need for synergistic management of H₂O₂ and O₃, a dual approach targeting both NO_x and VOC emissions remains essential. This integrated strategy will be critical to achieve effective and sustainable air quality improvements.