Field observations were continuously conducted from 4–26 October 2023 at the Guangdong Atmospheric Supersite of China in Heshan City, located in northern Jiangmen, Guangdong Province (112.93° E, 22.73° N). The supersite is situated in the downwind area of Guangzhou, Foshan, and Dongguan, a region characterized by active secondary reactions and serving as a receptor for pollution transported from the industrial and urban centers (Luo et al., 2025; Huang et al., 2020). The surrounding area is primarily composed of farmland conservation zones and forested regions, with no major industrial sources. The supersite sits on a small mountain ∼ 3 km from the nearest area heavy traffic corridor; at the observed mean wind speed of 2.8 m s⁻¹, the air mass from the corridor takes ∼ 17 min to arrive. This separation limits spatial heterogeneity in both emissions and chemical composition, making the site well-suited for comprehensive monitoring and research on complex regional air pollution in the PRD (Mazaheri et al., 2019). The geographical location is shown in Fig. S1 in the Supplement.

The P(O₃)_net detection system (NPOPR), based on the dual-reaction chamber technique, was used to monitor the P(O₃)_net and OFS. This system has been successfully applied in multiple field observation campaigns (Hao et al., 2023; Zhou et al., 2024a, b). The detection system consists of a sampling unit, a monitoring unit, and a data acquisition unit. Ambient air passes through a Teflon particulate filter (7592-104, Whatman, UK) to remove particles larger than 2 µm before entering the dual chambers. The reaction chamber and the reference chamber are made of two identical quartz tubes (inner diameter: 190.5 mm, length: 700 mm, wall thickness: 5 mm). Unlike the reaction chamber, which allows ultraviolet light to penetrate and initiate photochemical reactions, the reference chamber is covered with an ultraviolet protective film (SH2CLAR, 3M, Japan) to block light with wavelengths below 390 nm, thereby preventing O₃ formation in the reference chamber. A custom circuit control system alternates the gas flow between the reaction chamber and the reference chamber into the NO reaction tube every 2 min, where the O₃ is converted to NO₂, which is then introduced into a Cavity Attenuated Phase Shift (CAPS)-NO₂ analyzer (Aerodyne Research, Inc., Billerica MA, USA). The gas not introduced into the NO reaction tube is expelled through an auxiliary pump. The data acquisition system detects NO₂, including both ambient NO₂ and NO₂ converted from O₃. By combining the average residence time (τ) of the gas in the chambers and the difference in O_x (O_x = (O₃ + NO₂)) between the two chambers, the P(O₃)_net_Mea can be calculated as Eq. (5): 5P(O3)net_Mea=P(Ox)=ΔOxτ=[Ox]reaction-[Ox]referenceτ The mean residence time in the reaction chamber is 0.15 h at the air flow rate of 2.1 L min⁻¹, and the limit of detection (LOD) of the NPOPR detection system is 0.86 ppbv h⁻¹ at the sampling air flow rate of 2.1 L min⁻¹, which is obtained as three times the measurement error of P(O₃)_net (Hao et al., 2023). The time resolution of the P(O₃)_net measurement is 4 min. Our previous study demonstrated that P(O₃)_net more directly reflects the photochemical O₃ formation potential from local precursors and is less affected by transport processes compared to O₃ concentrations (Zhou et al., 2024b). The measurement error of P(O₃)_net is determined by the uncertainty in the O_x mixing ratio estimated for both the reaction and reference chambers. This uncertainty combines (i) the measurement uncertainty of the CAPS-NO₂ monitor used to derive O_x and (ii) the error induced by light-enhanced O₃ loss inside the chambers. Taken together, these contributions define the measurement precision of the NPOPR detection system. In addition, the measurement accuracy of the NPOPR detection system is 13.9 %, corresponding to the maximum systematic error arising from photochemical O₃ production in the reference chamber (Hao et al., 2023; Zhou et al., 2024b); details are given in Sect. S1 in the Supplement.

An additional system for the addition of NO or VOCs was added to the NPOPR sampling unit to assess OFS. The OFS was assessed by measuring the changes in P(O₃)_net induced by the addition of NO or VOCs, enabling the direct measurement of OFS. A schematic diagram of the detection system is shown in Fig. S2. In the experiments for determining OFS through direct measurements (conducted daily from 08:00–18:00 LT), each cycle lasted 1 hour. The first 20 min involved the addition of NO (denoted as P(O₃)_net_Mea^+NO), the next 20 min measured the ambient baseline (P(O₃)_net_Mea), and the final 20 min involved the addition of VOCs (denoted as P(O₃)_net_Mea^+VOCs). Following Carter et al. (1995) and Wu et al. (2022), we select VOCs surrogates for the OFS measurement on the basis of ambient measurements previous to the measurements. From 4–11 October, the tracer mixture was formulated from the average daytime total VOC reactivity measured during 20 September–3 October 2023, and isopentane served as the alkane surrogate, ethylene and isoprene as the alkene surrogates, and toluene as the aromatic surrogate. For 13–26 October 2023, we used the average daytime total VOC reactivity obtained during 4–11 October 2023; ethylene represented non-methane hydrocarbons (NMHCs) and formaldehyde represented oxygenated VOCs (OVOCs). Each surrogate was mixed in proportion to its category's share of the ambient reactivity, and the effective precursor strength (NO or VOCs) should increase by 20 % relative to the original ambient level. For data treatment, we first interpolated P(O₃)_net_Mea^+NO, P(O₃)_net_Mea, and P(O₃)_net_Mea^+VOCs to 4 min resolution and then averaged them over 1 h to suppress data fluctuations. We caution that this 1 h averaging may smooth out transient responses in the measured P(O₃)_net. The sensitivity of O₃ production to precursor changes was quantified using the measured OFS, derived from the incremental reactivity (IR) index. IR is defined as the change in P(O₃)_net per unit change in precursor concentration (ΔS(X)): a negative IR value indicates that reducing the precursor concentration increases O₃ production (e.g., decrease NO_x would increase O₃ through OH mediate effect), while a larger absolute IR value suggests higher sensitivity of O₃ production to changes in the precursor. The IR was calculated as:

6IR=P(O3)net_Mea+X-P(O3)net_MeaΔS(X)=ΔP(O3)net_Mea+XΔS(X) where X represents VOCs or NO, ΔP(O₃)net+X represents the P(O₃)_net values measured during the NO or VOCs addition period minus the P(O₃)_net values measured when only injecting ambient air. ΔS(X) represents the concentration of the NO or VOCs precursor changed during the corresponding measurement period. We define the transition regime as the region over which the IR shows a simultaneous increase or decrease upon addition of both VOCs and NO.

In addition to P(O₃)_net and OFS, hourly data such as PM_2.5, O₃, NO, NO₂, SO₂, carbon monoxide (CO), photolysis rates (jO1D, jNO2, jH2O2, jNO3_M, jNO3_R, jHONO, jHCHO_M, jHCHO_R), HONO, and VOCs concentrations were monitored (more details about the measurements are shown in Table S1). Hourly observations of conventional meteorological parameters, such as temperature, pressure, relative humidity, wind direction, and wind speed, were sourced from the European Centre for Medium-Range Weather Forecasts (ECMWF). The planetary boundary layer height (PBLH) data used in the model here was obtained from the web portal of the Real-time Environmental Applications and Display sYstem (READY) of the National Oceanic and Atmospheric Administration (NOAA) Air Resource Laboratory (https://ready.arl.noaa.gov/READYamet.php, last access: 26 June 2024).

This study employed an observation-constrained zero-dimensional photochemical reaction model (Observed 0-D box model) to simulate atmospheric photochemical processes. The chemical mechanism module is the core of the box model, and most mainstream studies use the Master Chemical Mechanism (MCM) nested within the model, incorporating processes such as solar radiation, boundary layer height, atmospheric photochemistry, and dry deposition (Zhang et al., 2022). The OBM model used in this study is AtChem2 (https://atchem.york.ac.uk/, last assess: 18 July 2024), which is equipped with the Master Chemical Mechanism (MCM v3.3.1: https://mcm.york.ac.uk/MCM, lase assess: 18 August 2024) to simulate O₃ and radical chemistry and analyze their budgets (Wang et al., 2022a; Sommariva et al., 2020). The model includes approximately 143 VOCs, 6700 chemical species, and over 17 000 reactions. Hourly resolution observational data of O₃, NO, NO₂, CO, SO₂, HONO, VOCs (in total 82 species), meteorological parameters (e.g., temperature, relative humidity, pressure, and boundary layer height), and photolysis rates were used as model constraints. The constraints are applied to the model every 1 h, with no free concentration evolution in between. Photolysis rates for unmeasured species were calculated using the Tropospheric Ultraviolet and Visible Radiation Model (TUV v5.3) (Table S2). Additionally, to avoid unreasonable increases in the concentrations of constrained species, a dilution rate of 1 / 86 400 s⁻¹ was applied. Before the simulation, the model underwent a 48 h pre-run to stabilize unmeasured species (e.g., radicals).

The configuration of model mechanisms was informed by previous research, with a particular focus on the dry deposition processes of key species (e.g., O₃, NO₂, SO₂, H₂O₂, HNO₃, PAN, and HCHO), the heterogeneous uptake reactions of HO₂ and N₂O₅, and the Cl⚫ chemistry mechanism. Dry deposition is a critical pathway for the transfer of atmospheric pollutants from the gas phase to the Earth's surface, significantly influencing the concentration distribution and removal of regional pollutants. Many models have already incorporated this atmospheric physical process (Ma et al., 2022; Chen et al., 2020a). Although the heterogeneous uptake of HO₂ is not the dominant loss pathway of HO₂, it accounts for approximately 10 %–40 % of global HO₂ loss (Li et al., 2019); as a termination reaction, its direct impact on photochemical O₃ production is non-negligible. Studies have shown that including the heterogeneous uptake mechanism of HO₂ in simulations reduces P(O₃)_net concentration and alters the sensitivity to VOCs (Zhou et al., 2021; Dyson et al., 2023). Additionally, Cl⚫ enhances atmospheric oxidation, accelerating the OH-HO₂-RO₂ reaction cycle (Ma et al., 2023). By incorporating these mechanisms, this study aims to more accurately simulate the atmospheric chemical processes and their impacts on pollutant concentrations in the PRD region (Zhou et al., 2024a). The configurations of each scenario are as follows: Case A considers only the simplified chemical reaction mechanism from the MCM, excluding dry deposition and heterogeneous reactions; Case B incorporates the HO₂ uptake by ambient aerosols based on Case A; Case C further includes the dry deposition processes of key species on top of Case B; and Case D₁ extends Case C by adding the N₂O₅ uptake mechanism and Cl⚫ related photochemical reactions. Detailed simulation parameter settings can be found in our previous study (Zhou et al., 2024a) and the Supplement (Table S3).

The Index of Agreement (IOA) was used to evaluate the simulation performance (Li et al., 2021). 7IOA=1-∑i=1n(Oi-Si)2∑i=1n(|Oi-O‾|-|Si-O‾|)2 where Oi and Si represent the observed and simulated values, respectively, O‾ denote the mean of the observed values, and n is the number of samples. The IOA ranges from 0 to 1, with higher values indicating better agreement between observed and simulated values. In addition to the IOA, the Pearson correlation coefficient (R), mean bias (MB), normalized mean bias (NMB), root mean square error (RMSE), mean fractional bias (MFB) and mean fractional error (MFE) were used to evaluate the consistency between observed and simulated values (Table S7).

Total OH reactivity (kOH) is a crucial indicator of atmospheric chemical cycling and oxidative capacity (Gilman et al., 2009). kOH is defined as the sum of the products of the concentrations of all reactive species Xi that can react with OH radicals and their respective reaction rate constants, calculated as follows: 8kOH=∑ikOH+Xi⋅[X]i where Xi includes CO, NO_x, and VOCs, among others, and kOH+Xi is the reaction rate constant (s⁻¹) between reactive species Xi and OH radicals.

O₃ Formation Potential (OFP) is an indicator used to measure the relative contribution of different VOC species to ground-level O₃ formation (Wu et al., 2020). The formula for OFP is as follows: 9OFP=[VOCs]i×MIRi where [VOCs]_i represents the concentration of a specific VOC species i (µg m⁻³), and MIR represents the maximum incremental reactivity of the VOC species i (g_O3 gVOC-1). MIR is used to characterize the increase in O₃ production per unit increase in VOCs under conditions where O₃ formation is most sensitive to VOCs.

We calculated the modelled OFS using the absolute P(O₃)_net sensitivity, adapted from the logarithmic derivative approach of Sakamoto et al. (2019). It is defined as the change in P(O₃)_net with respect to the natural logarithm of O₃ precursor concentrations. This method facilitates the quantitative assessment of how reductions in O₃ precursors contribute to the overall reduction of P(O₃)_net over a period or within a region. The formula is as follows: 10AbsoluteP(O3)net=dP(O3)netdln⁡[X] In the equation, [X] represents NO_x or VOCs. A positive absolute P(O₃)_net sensitivity indicates that reducing the precursor will lead to a decrease in the P(O₃)_net. In contrast, a negative value indicates that reducing the precursor will lead to an increase in the P(O₃)_net (Dyson et al., 2023). In this study, the analysis of absolute P(O₃)_net sensitivity was conducted using the box model through an analytical calculation approach that does not involve artificial perturbation of precursor concentrations.

The Supplement (Figs. S3, S4, and Tables S4, S5) provides the time series plots, diurnal variation, and daytime averages (daytime: 06:00–18:00 LT) of meteorological parameters, conventional pollutants, photolysis rate constants, NO, P(O₃)_net and hourly VOCs concentrations from 4–26 October 2023, at the Guangdong Atmospheric Supersite of China. The site was located downwind of the Guangzhou-Foshan area, with atmospheric pollutants primarily originating from the northeast. To access daily O₃ pollution levels, the maximum daily 8 h average O₃ concentration (MDA8) was employed, in accordance with the Technical Specification for Ambient Air Quality Evaluation (Trial) (HJ 663-2013). In this study, days with MDA8-O₃ concentration exceeding the Class II limit stipulated by the Ambient Air Quality Standards (GB3095-2012) were defined as O₃ pollution days (with MDA8-O₃ concentration limit of 160 µg m⁻³ (equivalent to approximately 81.6 ppbv at 25 °C), while others were defined as normal days.

During the whole observation period, there were 6 O₃ pollution days (15–17 and 24–26 October 2023). The maximum O₃ mixing ratio (136.5 ppbv) occurred at 15:00 LT on 25 October 2023, while the maximum P(O₃)_net (53.7 ppbv h⁻¹) occurred at 10:00 LT on 24 October 2023. Diurnal variation plots show that O₃ and P(O₃)_net exhibited single-peak patterns, with O₃ peaking at 15:00 LT and P(O₃)_net peaking between 09:00–10:00 LT. On O₃ pollution days, the daytime average mixing ratios concentrations of O₃ and P(O₃)_net during the observation period were 63.2 ± 37.6 and 14.4 ± 13.8 ppbv h⁻¹, respectively, both approximately twice as high as on normal days (daytime average O₃: 30.9 ± 22.9 ppbv; daytime average P(O₃)_net: 7.2 ± 9.4 ppbv h⁻¹). The maximum values of directly measured P(O₃)_net in different ambient environments in previous studies are listed in Table S6, ranging from 10.5 to 100 ppbv h⁻¹, and the measured P(O₃)_net values in this study fall within this range, demonstrating the reasonableness of the values measured in this study.

As shown in Fig. S4, the diurnal variation of parameters on O₃ pollution days and normal days indicates that the nighttime background concentrations/mixing ratios of O₃ precursors (TVOC and NO_x) are higher on O₃ pollution days. However, during the period of strongest sunlight (11:00–14:00 LT), the concentrations/mixing ratios of TVOC and NO_x on O₃ pollution days are lower than those on normal days. Specifically, on O₃ pollution days, the TVOC concentration is 11.4 µg m⁻³, and the NO_x concentration is 13.5 ppbv, while on normal days, the TVOC concentration is 13.7 µg m⁻³, and the NO_x concentration is 14.8 ppbv. As the PBLH on O₃ pollution days and normal days does not differ statistically during the period of strongest solar radiation (11:00–14:00 LT, t-test, p = 0.45, see Fig. S4k), the lower daytime concentrations / mixing ratios of O₃ precursors on O₃ pollution days than on normal days may be due to higher photolysis rates on O₃ pollution days (see Fig. S4a). The diurnal variation of NO concentration on O₃ pollution days showed an early morning peak at 08:00 LT, rising to 12.2 ppbv and then decreasing to 1.6 ppbv. By comparing the diurnal variation data between O₃ pollution days and normal days, we found that both O₃ mixing ratios and P(O₃)_net values were significantly higher on O₃ pollution days, particularly during the daytime (06:00–18:00 LT). This phenomenon aligns with the conclusion that high temperatures, low humidity, strong radiation, and stable weather conditions favor O₃ pollution formation.

This study analyzed 110 VOC species, examining the contributions of different categories to TVOC concentrations, kOH, and daily OFP. We also identified the top 10 VOC species contributing to these three indicators (Fig. S5), aiming to explore the atmospheric presence, chemical reactivity, and environmental impact of VOCs. Additionally, this study used two classification methods to group VOC species. Method 1 divided VOCs into alkynes (1 species), alkanes (27 species), alkenes (11 species), aromatic hydrocarbons (17 species), OVOCs (20 species), halogenated hydrocarbons (33 species), and sulfur-containing VOCs (1 species). Method 2 categorized VOCs into BVOC (Biogenic Volatile Organic Compounds), OVOCs (Oxygenated Volatile Organic Compounds), and AVOCs/NMHC (Anthropogenic Volatile Organic Compounds), with specific classifications shown in Table S4.

During the observation period, the daily average TVOC concentration ranged from 7.2 to 28.9 µg m⁻³. OVOCs contributed the most (40.8 %), followed by halogenated hydrocarbons (20.8 %), aromatic hydrocarbons (18.3 %), alkanes (17.9 %), alkenes (1.7 %), and alkynes (0.5 %). The kOH average value was 12.1 ± 3.9 s⁻¹, primarily contributed by OVOCs (62.9 %), followed by halogenated hydrocarbons (10.8 %), alkenes (10.4 %), aromatic hydrocarbons (9.8 %), alkanes (6.0 %), and alkynes (0.1 %). Among the alkenes in the known MCM mechanism, ethylene, as an indicator of VOCs, had the highest proportion, accounting for 10.7 % of alkeneskOH and 2.8 % of NMHC kOH. Formaldehyde, another VOCs indicator, was the most dominant species in OVOCskOH, contributing about 13.3 %. Among VOC species, OVOCs contributed the most to OFP (51.6 %), followed by aromatic hydrocarbons (32.9 %), alkenes (8.0 %), alkanes (6.9 %), halogenated hydrocarbons (0.5 %), and alkynes (0.2 %). The analysis results show that although halogenated hydrocarbons dominate VOCs concentration emissions, their contribution to O₃ pollution is low. In contrast, alkenes, despite their lower contribution to VOCs concentration emissions, are important precursors for O₃ formation. Based on the comprehensive analysis of VOCs concentration, kOH, and OFP, OVOCs and aromatic hydrocarbons significantly contribute to O₃ formation and should be prioritized as key VOC species for O₃ pollution control in the PRD region. This result aligns with other related studies in the PRD, such as those in Shenzhen (Yu et al., 2020), Guangzhou (Pei et al., 2022), and Jiangmen (Jing et al., 2024), which indicate that OVOCs and aromatic hydrocarbons are key VOC species for O₃ formation. As OVOCs arise from both direct (anthropogenic and natural) emissions and secondary atmospheric formation (Lyu et al., 2024; Yuan et al., 2012), precluding a direct quantification of their respective contributions to O₃ formation. Nevertheless, our previous work showed that anthropogenic primary VOCs correlate most closely with instantaneous P(O₃)_net on O₃ pollution days, and urban anthropogenic OVOC emissions markedly enhance both oxidative capacity and O₃ production (Qian et al., 2025; Wang et al., 2024b).

Overall, toluene, m/p-xylene, formaldehyde, 2-hexanone, ethyl acetate, and tetrahydrofuran consistently ranked in the top 10 VOC species in terms of concentration, kOH and OFP contribution. These VOC species mainly originate from human activities, such as industrial production, solvent use, traffic emissions, and fuel combustion, highlighting the significant impact of anthropogenic sources on O₃ pollution (Cai et al., 2010; Yang et al., 2023; Zheng et al., 2019).

Figure 1 shows the correlation between P(O₃)_net_Mea and kOH and OFP (calculated using the daytime average data during the observation period). Data outside the confidence interval may be due to the fact that the calculation of kOH and OFP did not fully consider the environmental conditions and atmospheric chemistry complexity at the observation site (Zhang et al., 2024; Yadav et al., 2024). The color of the scatter points represents the TVOC concentration. The r2 values between P(O₃)_net measurements and kOH and OFP are 0.6 and 0.5, respectively, indicating that VOCs with higher kOH and OFP significantly enhance the P(O₃)_net.

Based on our previous research (Zhou et al., 2024a), we named the scenario considering only the current chemical reaction mechanism from the MCM v3.3.1 in the box model as Case A. Subsequently, we gradually incorporated the HO₂ uptake by ambient aerosols, dry deposition, N₂O₅ uptake, and ClNO₂ photolysis mechanisms into the MCM mechanism in the box model, implemented as modelling scenarios labeled Case B, Case C, and Case D₁. The specific parameter settings for each scenario are shown in Table S3. The time series and diurnal variations of the P(O₃)_net_Mea and P(O₃)_net_Mod for Cases A–D₁ are shown in Fig. S7. To evaluate the model's performance, P(O₃)_net_Mea and P(O₃)_net_Mod data were used to calculate IOA, R, MB, NMB, RMSE, MFB and MFE values under different scenarios (Table S7). The IOA values between P(O₃)_net_Mod and P(O₃)_net_Mea was > 0.86 for all cases, and R ranged from 0.84 to 0.98, indicating that the model can reasonably reproduce the variations in P(O₃)_net. However, MB and NMB were -3.0 to -2.4 ppbv h⁻¹ and -30.5 % to -24.9 %, respectively, revealing a systematic underestimation of P(O₃)_net. RMSE ranged from 7.0 to 7.2 ppbv h⁻¹, while MFB and MFE ranged from -3.1 % to -1.7 % and 53.8 % to 55.5 %, respectively. These results suggest that, although the model captures the overall trends well, there is room to reduce simulation biases.

In all modelling scenarios from Case A–Case D₁, P(O₃)_net_Mod values were generally lower than P(O₃)_net_Mea (see Fig. 3). Although the correlation between P(O₃)_net_Mea and P(O₃)_net_Mod was good (Fig. S9, r2 = 0.73), even after incorporating mechanisms that may affect O₃ production simulation biases into to the box model (labeled as Case D₁), the simulated daytime average P(O₃)_net_Mod was still 3.4 ppbv h⁻¹ lower than P(O₃)_net_Mea (26.3 % bias), with a peak deviation of up to 13.3 ppbv h⁻¹ (44.8 %), as shown in Fig. 2. We defined the difference between P(O₃)_net_Mea and P(O₃)_net_Mod as P(O₃)_net_Missing, and its distribution of each day is shown in Fig. S10. Due to the measurement error of HONO by MARGA in this study, the modelled P(O₃)_net tends to be underestimated (as shown in Sect. S2); thus, we define the P(O₃)_net_Missing obtained from all simulation cases as the upper-limit values. During the observation period, 7–10 and 18–22 October were rainy days, with a median P(O₃)_net_Missing < 1.1 ppbv h⁻¹; therefore, these days were excluded when calculating the diurnal variations of different O₃ production and consumption pathways. On non-rainy days, the averaged daytime P(O₃)_net_Missing reached 4.5 ± 7.6 ppbv h⁻¹, accounting for 31 % of the total measured P(O₃)_net. Furthermore, the enlarged days in Fig. 3 reveal day-to-day variations in P(O₃)_net_Mod across the different cases, underscoring that the overall diurnal pattern described above does not resolve this variability. The averaged daytime P(O₃)_net_Missing values on O₃ pollution days were statistically higher than those on normal days (t-test, p < 0.05), suggesting that while the supplementary mechanisms explored in the model may contribute to some extent, they are unlikely to be the dominant cause of the P(O₃)_net_Missing.

We further explore the possible reasons for the discrepancies between P(O₃)_net_Mea and P(O₃)_net_Mod using the modelling results of Case D₁. The ratio of cumulative P(O₃)_net_Mea and P(O₃)_net_Mod derived from Case D₁ was 1.4, calculated by summing the daytime data with 1 h resolution during the observation period. This result is consistent with previous findings: Cazorla and Brune (2010) reported a ratio of 1.3, and Ren et al. (2013) and Hao et al. (2023) both reported 1.4. As shown in Fig. 2, the HO₂ + NO reaction dominates O₃ production, accounting for 71.4 % of total O₃ production pathways. In contrast, the main O₃ loss pathways were OH + NO₂ and RO₂ + NO₂, accounting for 67.9 % and 16.5 % of total O₃ consumption pathways, respectively. The importance of the HO₂ / RO₂ reaction pathways indicates that simulation biases in HO₂ or RO₂ will propagate into P(O₃)_net_Mod.

To explore the possible drivers of P(O₃)_net_Missing, we correlated it with TVOC, NO_x, JO1D, T, and O_x separately for O₃ pollution days and normal days (Fig. S11). On O₃ pollution days, P(O₃)_net_Missing exhibited a moderate positive correlation with VOCs (r2 = 0.4, R = 0.2, t = 2.9) and NO_x (r2 = 0.5, R = 0.2, t = 3.8), confirming that the P(O₃)_net_Missing is larger at higher precursor concentrations/mixing ratios (both t > critical 2.0, p < 0.05), consistent with earlier box-model studies (Whalley et al., 2021; Ren et al., 2013; Zhou et al., 2024a). A moderate positive correlation is also found with JO1D on both O₃ pollution days and normal days, with r2 values of 0.5 and 0.4, respectively. On normal days all correlations collapse (r2 < 0.2, p > 0.1), implying that the model deficit is not tied to the measured precursors under low-NO_x conditions and may instead related to the missing mechanisms for unmeasured photolabile VOCs. Wang et al. (2022b) indicates that constraining OVOCs in the model is crucial for the accuracy of P(O₃)_net_Mod, and photochemical models without OVOCs constraints significantly underestimate P(O₃)_net. In our previous study on the industrial city of Dongguan (Zhou et al., 2024a), we used parameter equations developed by Wang et al. (2024a, b) to quantify the impact of missing kOH on P(O₃)_net_Missing and qualitatively tested the potential compensating effects of unmeasured OVOCs on P(O₃)_net_Missing. This study measured more VOC species compared to the Dongguan campaign (Table S4). Therefore, we further compensate for the Case D₁ scenario by constraining more measured VOC species compared to the study in Dongguan (e.g., OVOCs, halogenated hydrocarbons) to explore their impact on P(O₃)_net_Mod. The specific simulation scenario settings are described in Table S3.

Figure 3 shows the time series and diurnal variations of P(O₃)_net_Mea and P(O₃)_net_Mod (under Case D₁–D₄) during the observation period. Specifically, we added constraints for measured acetaldehyde, acrolein, acetone, and butanone (OVOCs, which were considered as potential contributors for P(O₃)_net_Missing in Dongguan) to the model based on Case D₁, which is labeled as Case D₂. However, the daytime mean P(O₃)_net_Mod in Case D₂ decreased by 0.5 % compared with Case D₁, indicating that the dominant OVOC species responsible for P(O₃)_net_Missing may differ between Heshan and Dongguan. We further constrained all measured OVOC species in Heshan (which included additional OVOCs species compared to that added to Case D₂, such as propionaldehyde, butyraldehyde, and valeraldehyde) that could be input into the box model in the Case D₃ simulation scenario (more details can be found in Table S8). The results showed that the averaged daytime P(O₃)_net_Mod from Case D₃ increased by 4.4 % compared to that in Case D₂. Notably, in Case D₃, constraining all OVOC species significantly improved P(O₃)_net_Mod during the morning period (08:00–09:00 LT), with an increasing rate of approximately 10.2 % (∼ 1.3 ppbv h⁻¹). Additionally, Case D₄ scenario added constraints for chlorine-containing VOCs (i.e., all measured VOC species listed in Table S8 that could be input into the OBM model were constrained). The daytime average P(O₃)_net_Mod values from Case D₄ changed by only 1.1 % compared to those derived from Case D₃, indicating that the potential contribution of OVOCs to compensating P(O₃)_net_Missing is greater than that of chlorine-containing VOCs. The negligible (or even negative) change in P(O₃)_net_Mod when OVOCs are constrained in Cases D1-D4 may arise because the OVOC constraint masks deficiencies in the model's chemical mechanism and artificially suppresses diagnostic signals of missing secondary formation pathways. Until the underlying chemical mechanisms are improved, observational nudging of OVOCs offers a practical compromise – it helps maintain concentration accuracy while limiting unrealistic chemical feedbacks (more details can be found in Sect. S5). However, in modelling scenario Case D₄, the daytime average P(O₃)_net_Mod still showed a 22.2 % underestimation compared to the measured values. Accurate quantification of P(O₃)_net missing is possible here because the diurnal patterns of measurement uncertainty and the modelling bias responsible for the P(O₃)_net missing do not co-vary; consequently, measurement uncertainty is much smaller than modelling bias for most of the daytime, especially around noon.

The diurnal variations of O₃ production pathways in Case D₄ are shown in Fig. S12. Compared to Case D₁, the RO₂ + NO reaction rate in Case D₄ was higher by 0–2.1 ppbv h⁻¹ in the diurnal variations during the whole measurement period (excluded the rainy days). The RO₂ species with higher contributions to this pathway included CH₃O₂, HO₂C₄O₂, HO₁₃C₄O₂, HOCH₂CH₂O₂, HO₃C4O₂, CH₃COCH₂O₂, and COCCOH₂CO₂. This indicates that the constraints on additional OVOCs in Case D₄ (such as aldehyde and ketone compounds with specific functional groups, e.g., carbonyl and hydroxyl) increased the intermediate RO₂ products, leading to a significant enhancement in the RO₂ + NO reaction rate. This suggests their large potential to contribute to P(O₃)_net_Missing.

The modelling results of scenarios Case D₁–D₄ show that although constraining the measured VOC species in the box model mechanism can reduce P(O₃)_net_Missing to some extent, there is still a significant gap between the simulated and measured P(O₃)_net values. Previous studies have shown that the RO₂ isomerization (Crounse et al., 2012), autoxidation (Wang et al., 2017a), and the accretion reactions (Berndt et al., 2018) can also effect modelled P(O₃)_net, but these processes have not been investigated here. Also, the potential contribution of unmeasured VOC species to compensating P(O₃)_net_Missing in the box model mechanism cannot be ignored. Yang et al. (2017) and Tan et al. (2019) conducted radical measurements at the Guangdong Atmospheric Supersite of China in autumn of 2014, revealing missing kOH contributions of approximately 32 % and 50 %, respectively. Yang et al. (2017) pointed out that the missing kOH contributions in the Heshan region may originate from OVOCs such as aldehydes, acids, and dicarbonyls. Tan et al. (2019) indicated that about 60 % of the O₃ produced in the Heshan region was contributed by unmeasured VOCs. We hypothesize that the remaining P(O₃)_net_Missing is caused by unknown VOCs that are not constrained in the box model.

The method of estimating missing VOC concentrations through the empirical linear relationship between OH reactivity (kOH) and P(O₃)_net is used in this study, the scientific basis lies in the fact that P(O₃)_net is closely related to the production rate of RO_x radicals (P(RO_x)), which are primarily formed through the reaction of OH with VOCs. Since P(RO_x) is directly influenced by the OH reactivity (kOH), P(O₃)_net is consequently correlated with kOH. Previous study has shown that P(O₃)_net exhibits a linear relationship with both P(HO_x) and kOH when O₃ formation is located in VOCs-limited regime (Baier et al., 2017), and this approach reflects nearly actual atmospheric chemistry if P(O₃)_net missing is driven by VOCs reactivity missing (Wang et al., 2024b). Furthermore, we examined whether unconstrained secondary products affect P(O₃)_net missing – and thus the linear relationship between P(O₃)_net missing and kOH – by analysing its dependence on the ethylbenzene/m,p-xylene ratio. Because this ratio increases with the degree of air-mass aging (de Gouw et al., 2005; Yuan et al., 2013), the observed decrease in the P(O₃)_net missing with increasing ratio (Fig. S11f) indicates that the P(O₃)_net missing is not likely caused by unaccounted secondary production. By quantifying the relationship between kOH and P(O₃)_net, the contribution of missing kOH (kOH_Missing) to P(O₃)_net_Missing can be assessed, and compensating for kOH_Missing in the box model can help reduce P(O₃)_net_Missing. Figure 4 shows the relationship between kOH and P(O₃)_net_Mod calculated under the Case D₁ scenario, which can be expressed as: 11PO3net_Missing=3.4×kOH_Missing-2.7 where P(O₃)_net_Missing and kOH_Missing in the equation represent the daytime averaged values for each day. Based on this relationship, we calculated kOH_Missing according to calculated P(O₃)_net_Missing for each day. This value was then used to compensate for the unmeasured VOCs in the model (with a daytime kOH compensation range of 1.2–2.4 s⁻¹, approximately 27.6 %–45.1 % of missing values). Based on the significant contribution of OVOCs to P(O₃)_net_Missing mentioned earlier, we designed three modelling scenarios to compensate for kOH_Missing, with the specific multiples varying each day. We note that these scenarios are idealized sensitivity tests to explore potential bounds of OVOCs' contribution to P(O₃)_net_Missing compensation, rather than realistic emission assumptions. Specifically, we tested how much the P(O₃)_net_Missing could be accounted for if the kOH were attributed to different VOCs categories. The specific scenarios include: (1) Case E₁: by expanding the constrained overall VOCs concentrations in Case D₁ (daily mean compensation range for TVOCs: 0.5–2.8 µg m⁻³) the daily TVOC concentration was increased by 1.1 to 1.7 times; (2) Case E₂: according to kOH ratio of NMHC to OVOCs in the constrained VOCs of Case D₁, the concentrations of ethylene (a representative NMHC species) and formaldehyde (OVOCs indicator) were expanded separately. The ethylene concentration (daily mean compensation range for TVOCs: 0.5–2.8 µg m⁻³) was increased by 5.9 to 85.6 times, and the formaldehyde concentration (daily mean compensation range for TVOCs: 0.0–0.5 µg m⁻³) was increased by 1.4 to 2.0 times; (3) Case E₃: by expanding only the formaldehyde concentration to compensate for kOH_Missing, in this case, the daily formaldehyde concentration (daily mean compensation range for TVOCs: 0.6–1.4 µg m⁻³) was increased by 1.8 to 9.2 times, to verify the role of OVOCs in compensating for P(O₃)_net_Missing. The time series and overall diurnal variations of modelled Cases E1-E3 are presented alongside Case D1 in Fig. 5.

In Case E₁, where the overall TVOC concentration was increased to compensate for kOH_Missing without distinguishing VOCs categories, the compensation effect was limited due to the dilution effect of low-reactivity VOCs, resulting in a reduction of the daytime average P(O₃)_net_Missing proportion from 26.3 % (calculated as P(O₃)_net_Missing / P(O₃)_net_Mea) to 10.3 %. In Case E₂, where the concentrations of ethylene and formaldehyde were expanded to compensate for kOH_Missing, the daytime average P(O₃)_net_Missing proportion reduced from 26.3 % to 17.2 %. This proportion is higher than that obtained from Case E1, which may be due to the relatively low reactivity of ethylene limited the overall compensation effect. In contrast, Case E₃ compensated for kOH_Missing solely by expanding the formaldehyde concentration. More details concerning the cases settings are shown in Table S3. Since formaldehyde, as a representative high-reactivity OVOC species, contributes more directly and significantly to O₃ generation through photochemical pathways (Mousavinezhad et al., 2021), it achieved the best compensation effect, reducing the daytime average of P(O₃)_net_Missing from 26.3 % to 5.1 %. However, P(O₃)_net_Missing during the peak period of diurnal variation remained at 9.0 ppbv h⁻¹. This result confirms the critical role of high-reactivity OVOCs (especially those with the same photochemical reaction characteristics as formaldehyde) in compensating for P(O₃)_net_Missing. Further, it suggests the potential presence of other unmeasured high-reactivity VOC species in the ambient atmosphere. Constraining these species could help further improve the model's simulation accuracy (Lyu et al., 2024; Wang et al., 2024b). Overall, the degree of compensation for P(O₃)_net_Missing follows the order Case E₃ > Case E₁ > Case E₂, which may be related to the reactivity of the selected VOCs. However, we observe a slight difference in the diurnal trends of P(O₃)_net across different days (enlarged view in Fig. 5); this depicts the overall pattern for the observation period described above does not capture day-to-day variability.