Observation and modeling of atmospheric OH and HO₂^∗ radicals at a subtropical rural site and implications for secondary pollutants

HO_x radicals (OH and HO₂) are crucial oxidants that determine atmospheric oxidation capacity and the production of secondary pollutants; however, their sources and sinks remain incompletely understood in certain rural, forest, and maritime environments. This study measured ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ (HO₂ + contribution from RO₂, organic peroxyl radicals) and OH concentrations using a chemical ionization mass spectrometer at a subtropical rural site in southern China from 12 November to 19 December 2022. The average peak concentrations were 3.50 ± 2.47 × 10⁶ cm⁻³ for OH and 1.34 ± 0.93 × 10⁸ cm⁻³ for ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$. Model-estimated contribution from RO₂ to HO₂ during the measurement period ranged from 44 % to 69 % of ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$. Calculations based on an observation-constrained chemical model revealed an overestimation of HO₂ and OH concentrations during warm periods of the field study. Sensitivity tests suggest that adding HO_x sinks or an HO₂ recycle process to the model could improve the model performance. Over-simulation of HO_x in the model resulted in overestimations of midday (10:00–15:00 UTC) production rates by more than 79 % for ozone and a factor of 1.88 for nitric acid. Our study highlights the need for further improving understanding of the sources and sinks of OH and HO₂ and representation of them in air quality models.

1 Introduction

The HO_x family, comprising hydroxyl (OH) and peroxy radicals (HO₂), plays a pivotal role in the Earth's atmosphere by driving photochemical processes that influence the air composition and chemistry. OH radicals are primarily produced by the photolysis of ozone (O₃), nitrous acid (HONO), and ozonolysis of alkenes. They initiate the oxidation of CO and most volatile organic compounds (VOCs), producing HO₂ and other organic peroxyl radicals (RO₂, where R represents an organic group such as alkyl, acyl, or aryl). HO₂ is also generated from the photolysis of oxygenated VOCs (OVOCs) and by reactions between OVOCs and OH. In the presence of NO, RO₂ radicals are converted to HO₂ and then to OH radicals, buffering OH concentrations and maintaining atmospheric oxidation capacity (Stone et al., 2012). These interactions are crucial in the formation of photochemical smog and secondary organic aerosol (SOA), which generate NO₂, O₃, and highly oxygenated molecules. HO_x (OH + HO₂) radicals are removed through reactions of OH with inorganic trace gases, self-reactions among radicals, peroxyacetyl nitrate (PAN) formation, and the heterogeneous uptake by aerosols. These processes subsequently contribute to atmospheric acidification and aerosol formation through the production of H₂SO₄ and HNO₃. See Fig. S1 and Table S1 in the Supplement for detailed processes and chemical reactions.

The accuracy of model-predicted OH is a crucial indicator for assessing our understanding of atmospheric processes (Heard and Pilling, 2003). There is a long-standing debate regarding the discrepancies between simulated and observed radical concentrations under low-NO_x conditions, which remains a significant issue (Hofzumahaus et al., 2009; Stone et al., 2012; Zou et al., 2023). Previous studies have shown that models generally predict OH levels well in polluted conditions (NO > 1 ppb), but notable overestimations were observed under low-NO and aged conditions, such as in coastal areas (Kanaya et al., 2007; Zou et al., 2023), marine boundary layers (Berresheim et al., 2002; Carslaw et al., 1999), and rural areas (Bottorff et al., 2023; Kanaya et al., 2012). Missing OH sinks from both measurements and chemical mechanisms were proposed as the primary reason for the overestimation (Lou et al., 2010; Yang et al., 2016; Hansen et al., 2014; Thames et al., 2020). Underestimations of OH concentrations were also observed in high-biogenic-VOC (BVOC) and low-NO (< 1 ppb) conditions, which generally happen in subtropical or tropical areas (Hofzumahaus et al., 2009; Lelieveld et al., 2008; Tan et al., 2001; Whalley et al., 2011). After considering a new OH regeneration mechanism (Wennberg et al., 2018; Novelli et al., 2020) and measurement interference (Feiner et al., 2016; Hens et al., 2014; Mao et al., 2012; Novelli et al., 2014; Woodward-Massey et al., 2020), daytime OH concentrations could be reasonably reproduced by the model in high-BVOC conditions, with some unresolved underestimation in the evening (Jeong et al., 2022; Lew et al., 2020; Tan et al., 2019). Those results call for more measurement and modeling in subtropical and tropical rural areas.

HO₂ concentrations were consistently underpredicted in polluted urban sites (Ma et al., 2019, 2022; Yang et al., 2021), with no clear trends in relatively clean regions. Some studies reported good agreement between measurement and model prediction (Feiner et al., 2016; Lew et al., 2020), whereas others indicated model overprediction (Bottorff et al., 2023; Griffith et al., 2013) and underprediction (Whalley et al., 2010; Kim et al., 2013; Mallik et al., 2018; Tan et al., 2017). These discrepancies may be attributed to several factors, including measurement interference caused by RO₂ recycling in environments rich in BVOCs or aromatics (Fuchs et al., 2011), uncertainties associated with heterogeneous uptake in box models (Yang et al., 2022), and the outflow (or entrainment) of reservoir species like PAN (Griffith et al., 2013; Whalley et al., 2010). Despite these advances, it remains difficult to pin down the exact causes of the model–measurement discrepancies in some of the previous studies.

In the present study, we measured concentrations of OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ (HO₂ + contribution from RO₂) using a quadrupole chemical ionization mass spectrometer (PolyU-CIMS) from November to December 2022 at a subtropical rural site in southern China. We tested the model's capability in reproducing the radical concentrations and elucidating factors contributing to discrepancy under varying temperatures, VOCs, and NO_x conditions. The Methodology section describes the measurement site, the principles and the configuration of PolyU-CIMS, and the setup of chemical box models. The “Results and discussion” section details our findings, providing an analysis of the radical concentrations and exploring the discrepancies between observed data and model predictions. By employing an observation-constrained box model, we analyzed the radical budgets and investigated potential causes for these discrepancies. The study concludes with a discussion of the implications of these findings.

2 Methodology

2.1 Measurement site

The field campaign was conducted at the Conghua Liangkou Air Monitoring Station (23°44^′47^′′ N, 113°47^′06^′′ E; 200 m above sea level) from 12 November to 19 December 2022 (Fig. 1). The site is located at the northern part of the Pearl River Delta (PRD), approximately 80 km from densely populated areas. It is nestled within the Liuxi River National Forest Park (an evergreen broadleaf forest). The site is situated just north of the G105 national highway and around 0.5 km east of Liangkou. Even though it is close to the road, traffic was generally limited during the observation period due to the coronavirus disease (COVID-19) pandemic. The site is subject to BVOC emissions, predominantly isoprene, from the surrounding forest when the daytime temperatures exceeds 20 °C and NO emissions from the nearby national highway, particularly during periods of low wind speeds. The measurements included trace gases such as O₃, NO, NO₂, CO, HONO, VOCs, and OVOCs and meteorological data such as relative humidity (RH), temperature, and photolysis frequencies of HONO, NO₂, O₃, H₂O₂, and HCHO. Details about the instruments are shown in Table S2.

Figure 1 Geographic location of the measurement site (Liangkou Air Monitoring Station; 23°44^′47^′′ N, 113°47^′06^′′ E; 200 $\mathrm{m}\mathrm{a}.\mathrm{s}.\mathrm{l}.$; marked by the inverted red triangle) in Conghua, Guangdong Province, southern China. The map is sourced from © Google Earth and © Amap.

2.2 Radical measurement principle

OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ radicals were measured using the Hong Kong Polytechnic University's quadrupole chemical ionization mass spectrometer (PolyU-CIMS), which had been used in a previous study for OH measurement (Zou et al., 2023). The use of CIMS for OH measurement was pioneered by Eisele and Tanner (1991), with subsequent enhancements in measurement accuracy (Eisele and Tanner, 1993; Tanner et al., 1997; Tanner and Eisele, 1995) and the adoption of inlets for simultaneous measurements of HO₂ and RO₂ (Edwards et al., 2003; Sjostedt et al., 2007), H₂SO₄ (Mauldin et al., 2004), and OH reactivity (Muller et al., 2018).

Figure 2 Flowchart depicting the relationship between measurement species and signal intensity at $m/z$ 97 (S₉₇) with various gas injections. The color-filled grids label the ambient species, while the oval shapes label the species injected into the sample flow. Signal intensities with different gas additions to the sample flow are represented by S_97w/o, $S_{\mathrm{97}{\mathrm{SO}}_{\mathrm{2}}}$, S_97NO, $S_{\text{97Sca}{\mathrm{SO}}_{\mathrm{2}}}$, and S_97ScaNO. The signals correspond to ambient OH, HO₂, H₂SO₄, and noise from OH measurement, HO₂ measurement, and the CIMS are denoted as S_OH, $S_{{\mathrm{HO}}_{\mathrm{2}}}$, $S_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}$, S_NoiseOH, $S_{\text{Noise}{\mathrm{HO}}_{\mathrm{2}}}$, and S_NoiseCIMS, respectively.

Figure 2 illustrates the measurement principle of PolyU-CIMS used in this campaign. Briefly, the ambient OH radicals are converted to H₂SO₄ in the sample inlet system by reacting with SO₂ (Reaction SR21 in Table S1). These are then transformed to ${\mathrm{HSO}}_{\mathrm{4}}^{-}$ ion clusters in the ionization chamber by the reactions with a reagent gas in sheath flow (HNO₃, Reactions SR24 to SR27 in the Supplement) and are ultimately dissociated (Reaction SR29) for detection by the mass spectrometer system at $m/z$ 97 ($S_{\mathrm{97}{\mathrm{SO}}_{\mathrm{2}}}$ in Fig. 2). To mitigate interference and noise, scavenger gases (C₃F₆ in this study) were introduced to scavenge the ambient OH, creating a background signal (Reaction SR23, $S_{\text{97Sca}{\mathrm{SO}}_{\mathrm{2}}}$ in Fig. 2). See Text S1 in the Supplement for details about scavenging efficiency. The ambient OH radical signal (S_OH) is then determined by subtracting $S_{\text{97Sca}{\mathrm{SO}}_{\mathrm{2}}}$ from $S_{\mathrm{97}{\mathrm{SO}}_{\mathrm{2}}}$. The OH concentration is calculated using the following equation:

$$\begin{array}{}\text{(1)}& \left[\mathrm{OH}\right]={\displaystyle \frac{\mathrm{1}}{C_{\mathrm{OH}}}}\times {\displaystyle \frac{S_{\mathrm{OH}}}{S_{\mathrm{62}}}},\end{array}$$

where C_OH represents the calibration factors of OH, and S₆₂ is the signal corresponding to the reagent ion (${\mathrm{NO}}_{\mathrm{3}}^{-}$). A detailed calibration procedure for OH is outlined in previous studies (Kürten et al., 2012; Zou et al., 2023) and also in Text S2. Ambient and injected NO can interfere with OH measurements through reaction of NO + HO₂. The interference by ambient NO is estimated using a model (within a range of 10⁴–10⁵ cm⁻³) and is subtracted from the ambient OH measurements (see Text S3). The interference from the injected NO after HO₂ measurement is discussed in Text S3 and is mitigated through the duty cycle configuration described in Text S4.

To measure ambient HO₂, NO is injected into the sample flow, converting HO₂ to OH (Reaction SR11). This converted OH then follows the same reaction pathway (Reactions SR21, SR24 to SR27, and SR29) and is measured at $m/z$ 97 (S_97NO in Fig. 2). Similar to the OH measurement, the background signal for HO₂ (S_97ScaNO in Fig. 2) is determined by introducing the scavenger gas. The corresponding signal for ambient HO₂ ($S_{{\mathrm{HO}}_{\mathrm{2}}}$, as shown in Fig. 2) is determined by subtracting S_97ScaNO and S_OH from S_97NO. The HO₂ concentration is calculated using an equation similar to Eq. (1) by replacing S_OH and C_OH with $S_{{\mathrm{HO}}_{\mathrm{2}}}$ and $C_{{\mathrm{HO}}_{\mathrm{2}}}$, respectively (Eq. 2).

$$\begin{array}{}\text{(2)}& \left[{\mathrm{HO}}_{\mathrm{2}}\right]={\displaystyle \frac{\mathrm{1}}{C_{{\mathrm{HO}}_{\mathrm{2}}}}}\times {\displaystyle \frac{S_{{\mathrm{HO}}_{\mathrm{2}}}}{S_{\mathrm{62}}}}\end{array}$$

The procedure for determining the HO₂ calibration factor, $C_{{\mathrm{HO}}_{\mathrm{2}}}$, is akin to that for C_OH (Text S2). The calibration tube generates equal amounts of radicals (Reaction SR30 in the Supplement, $\left[\mathrm{OH}\right]/\left[{\mathrm{HO}}_{\mathrm{2}}\right]=\mathrm{1}$), allowing for simultaneous calibration of HO₂ and OH with and without NO addition to the sample flow.

In addition to HO₂, the added NO can also react with RO₂ and produce HO₂, which is a potential interference, leading to an overestimation of ambient HO₂ levels (Edwards et al., 2003; Hanke et al., 2002; Fuchs et al., 2011, 2014; Whalley et al., 2013). For our CIMS configuration, the model-estimated daytime interference from RO₂ ranged from 44 % to 69 % of the ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ during the field study (Text S3). Considering the uncertainties in RO₂ mechanisms in the MCM model, we opted not to use model results to correct RO₂ interference, and we denote our HO₂ measurement hereafter as ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, which is the maximum value of the ambient HO₂ concentrations.

Compared to the configuration of PolyU-CIMS in the previous campaign (Zou et al., 2023), the instrument has been upgraded for simultaneous ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ measurements. Refer to Fig. S2 and Text S5 for the modification to the ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ measurement and to Text S4 for the measurement duty cycle. Apart from these modifications, the settings and configurations of PolyU-CIMS remained the same as those in the previous campaign (see Table S3). With the updated configuration, PolyU-CIMS achieved simultaneous measurement of OH, ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, and H₂SO₄.

The calibration factors, detection limits, and uncertainties were 1.09 × 10⁻⁸, 3 × 10⁵ cm⁻³, and 44 % for OH and 1.07 × 10⁻⁸, 2 × 10⁶ cm⁻³, and 222 % for ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, respectively (Table S3). The large uncertainty in ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ reflects the possible contribution of RO₂ interference, as discussed previously.

2.3 Box model

HO_x concentrations in this study were simulated using the Framework for 0-D Atmospheric Modelling (F0AM; Wolfe et al., 2016) with the Master Chemical Mechanism (MCM) v3.3.1 (https://mcm.york.ac.uk/MCM/, last access: 24 July 2025), which encompasses over 6700 species and 17 000 reactions. MCM v3.3.1 features a near-explicit chemical mechanism that includes isoprene degradation and OH regeneration mechanisms. This mechanism has previously been employed to investigate HO_x chemistry and conduct budget analyses (Slater et al., 2020; Tan et al., 2018; Zou et al., 2023). The gas-phase chlorine chemistry described by Xu et al. (2015) and Wang et al. (2019) was included in the model (Chen et al., 2022).

Figure 3 Time series of ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ and OH radicals from 12 November to 19 December 2022, showing measured weather conditions (temperature, RH, wind speed, and wind direction), primary sources of HO_x radicals (ozone, HONO), important sinks of the radicals (CO, isoprene, and VOCs), and photolysis frequencies of NO₂ ($J_{{\mathrm{NO}}_{\mathrm{2}}}$) and ozone (J_O1D). Non-continuous days during the campaign are delineated by the black line. The PRD, CEC, and CNC periods for further analysis are labeled in red, orange, and blue, respectively. The x axis is in local time (+08:00 UTC).

In the baseline scenario, the observation data were aggregated into 1 h intervals to provide input for the model, initially constraining it without incorporating observed OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ data. For the assessment of ozone formation rates, the model was adjusted to include constraints based on the actual measured concentrations of OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$. Observed VOCs were categorized into anthropogenic origin (AVOCs), including species from petroleum gas and industrial solvent evaporation (alkanes, alkenes, benzene, and TEX – toluene, ethylbenzene, and xylene), and OVOCs, comprising aldehydes, ketones, and acids. The sole BVOC measured in this study was isoprene. Physical processes like deposition and entrainment in the model were represented by a first-order physical loss with a 24 h lifetime for all species (Chen et al., 2022; Wolfe et al., 2016; Zou et al., 2023). The model also included the heterogeneous uptake of HO₂ by aerosols, represented as a pseudo-first-order loss (Jacob, 2000):

$$\begin{array}{}\text{(3)}& {\displaystyle }& {\displaystyle \frac{\mathrm{d}\left[{\mathrm{HO}}_{\mathrm{2}}\right]}{\mathrm{d}t}}=-k_{{\mathrm{HO}}_{\mathrm{2}}}\left[{\mathrm{HO}}_{\mathrm{2}}\right],\text{(4)}& {\displaystyle }& {\displaystyle }{k}_{{\mathrm{HO}}_{\mathrm{2}}}={\displaystyle \frac{V_{{\mathrm{HO}}_{\mathrm{2}}}\times S_{\mathrm{a}}\times {\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}}{\mathrm{4}}},\text{(5)}& {\displaystyle }& {\displaystyle }{v}_{{\mathrm{HO}}_{\mathrm{2}}}=\sqrt{{\displaystyle \frac{\mathrm{8}RT}{\mathit{\pi }\times M_{{\mathrm{HO}}_{\mathrm{2}}}}}}.\end{array}$$

Here, $k_{{\mathrm{HO}}_{\mathrm{2}}}$ represents the first-order loss rate coefficient of HO₂ by aerosol uptake, determined by the effective HO₂ uptake coefficient ${\mathit{\gamma }}_{{\mathrm{HO}}_{\mathrm{2}}}$ (0.1, Guo et al., 2019), the mean molecular velocity of HO₂ ($v_{{\mathrm{HO}}_{\mathrm{2}}}$), the aerosol surface area concentration (S_a) measured by a scanning mobility particle sizer (SMPS), and the molecular mass of HO₂ ($M_{{\mathrm{HO}}_{\mathrm{2}}}$ = 17 g mol⁻¹). As aerosol- and aqueous-phase chemistry was not included in the model, it was assumed that the heterogeneous HO₂ loss would not lead to further reactions (Guo et al., 2019). For each day, a 3 d spin-up was performed with constant inputs to establish stable model chemistry and reduce the uncertainty in unconstrained species. Refer to Text S3 for details on the model setup for interference assessment.

Table 1 Average values and standard deviations of measured species and parameters throughout the entire campaign (Total) and the selected 3 d cases from each cluster (PRD, CEC and CNC).

Note: OVOCs – oxygenated VOCs; AVOCs – anthropogenic VOCs; TEXS – toluene, ethylbenzene, xylene, and styrene. For the average mixing ratio of each measured VOC, refer to Table S4.

3 Results and discussion

3.1 Results from observations

3.1.1 Overview

Figure 3 illustrates a time series showing observed concentrations of radical and trace gases, along with meteorological parameters, from 12 November to 19 December 2022. In November, the conditions were characterized by warm temperatures ranging from 29 to 19 °C and high relative humidity averaging 86 %. In contrast, December witnessed a significant decrease in temperature (ranging from 20 to 9 °C) and a reduction in relative humidity (averaging 72 %). Wind speeds during the campaign were generally low, averaging 0.9 ± 0.6 m s⁻¹ and typically remaining below 3.0 m s⁻¹, with higher speeds occurring towards the end of December. In November, daytime winds predominantly blew from the south, while nighttime winds came from the north. In December, northerly winds predominated both day and night. Detailed hourly wind speed and direction data are illustrated in Fig. 3, and wind roses are shown in Fig. S3. On days with low wind speeds (less than 0.5 m s⁻¹), NO_x emissions from the G105 national highway significantly influenced chemical measurements at the monitoring site, causing morning NO levels to peak at several parts per billion (ppb). Isoprene concentrations peaked in the afternoons, ranging from 0.2 to 1.7 ppb in November and dropping to less than 0.1 ppb in December. Other trace gases and particulate matter levels were higher in November than in December.

Throughout the campaign, the daytime concentrations of OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ consistently exceeded detection limits and showed distinct diurnal patterns. OH concentrations typically peaked around midday (10:00–15:00 UTC, referred to hereafter in this paper), while ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ levels reached their maximum approximately 1 to 2 h later (Fig. S4). The daily maximum concentration of OH varied significantly, ranging from 8.00 × 10⁶ cm⁻³ to nearly the detection limit of 2.54 × 10⁵ cm⁻³, with an average of 3.50 ± 2.47 × 10⁶ cm⁻³ (Table 1). Similarly, the daily maximum concentration of ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ varied from 3.42 × 10⁸ to 2.17 × 10⁷ cm⁻³, averaging 1.34 ± 0.93 × 10⁸ cm⁻³ (Table 1). At nighttime, while ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ levels generally remained above the detection threshold, OH concentrations frequently approached the threshold. The average nighttime concentrations were 3.92 × 10⁷ cm⁻³ for ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ and 1.64 × 10⁵ cm⁻³ for OH. We compared the observed OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ concentrations with those reported in previous studies conducted in urban, suburban, rural forest, and coastal sites. As illustrated in Fig. S5, OH concentrations were generally lower than those found in urban settings but similar to levels observed in suburban, rural, and forest environments. This suggests a moderate level of anthropogenic activity typical of mixed rural settings. In contrast, ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ concentrations during these periods were significantly lower than earlier observations in rural and forest environments, likely owing to reduced photochemical activity during our measurement period.

Figure 4 illustrates the results of the 24 h backward-trajectory analysis, revealing three distinct but sequentially occurring phases. In the initial phase (Fig. 4a), air masses originated from the urban and industrial zones of the Pearl River Delta (PRD). This phase was characterized by intense photochemical activity, with ambient temperatures exceeding 20 °C and relative humidity levels surpassing 70 %. During this period, notably high concentrations of VOCs, ozone, and radicals were observed, with the average daily maximum concentrations of OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ radicals reaching 6.50 ± 1.19 × 10⁶ and 2.20 ± 0.27 × 10⁸ cm⁻³, respectively. The subsequent phase was characterized by air masses originating from central eastern China (CEC; Fig. 4b). This phase showed reduced photochemical reactivity and lower concentrations of the measured trace gases. The average daily maximum concentrations of OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ during this phase were 4.35 ± 2.19 × 10⁶ and 1.96 ± 0.90 × 10⁸ cm⁻³, respectively. The final phase was influenced by air masses from central northern China (CNC; Fig. 4c), which exhibited the lowest concentrations of trace gases and the least pronounced average daily maximum concentrations in OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ concentrations, measured at 2.23 ± 1.95 × 10⁶ and 7.63 ± 7.66 × 10⁷ cm⁻³, respectively. This phase coincided with an increase in cloudy days and a decrease in temperatures, indicating reduced photochemical conditions.

Figure 4 The 24 h back trajectories for the (a) Pearl River Delta (5 d), (b) central eastern China (4 d), and (c) central northern China (14 d) cases. The 3 d selected from each cluster for model simulation is distinguished by different colors.

3.1.2 Selection of cases

For each phase, a representative 3 d period was selected for detailed analysis based on the availability of comprehensive data and sunny conditions (colored trajectories in Fig. 4). In the subsequent analysis, PRD, CEC, and CNC refer to the selected periods corresponding to the air masses originating from these regions. The average daily maximum concentrations of OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ radicals for these periods are presented in Table 1. The average daily max OH concentrations were 6.89 ± 1.10 × 10⁶ cm³ in PRD, 4.90 ± 1.47 × 10⁶ cm³ in CEC, and 5.27 ± 0.89 × 10⁶ cm³ in CNC, with a pronounced decrease from PRD to CEC (of 1.99 × 10⁶ cm³). The average daily max ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ concentrations were 2.32 ± 1.25 × 10⁸ cm³ in PRD, 2.36 ± 0.92 × 10⁸ cm³ in CEC, and 1.82 ± 1.02 × 10⁸ cm³ in CNC, with a slight increase of 0.04 × 10⁸ cm³ from PRD to CEC and a more substantial decrease of 0.54 × 10⁸ cm³ from CEC to CNC. These trends suggest a declining atmospheric oxidation capacity from PRD to CNC.

Figure 5 Average diurnal variations in (a) temperature, (b) relative humidity, (c) J_O1D, (d) OH, (e) ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, (f) ozone, (g) NO, (h) NO₂, (i) HONO, (j) isoprene, (k) AVOCs, and (l) OVOCs. The solid-colored lines represent the selected cases: orange for PRD, green for CEC, and blue for CNC. The light band represents the standard deviations of the mean. The increase in the standard deviations of VOCs and OVOCs during the PRD case is a result of an absence of data on the afternoon of 15 November and large variations on 12 and 13 November.

The precursor concentrations and meteorological parameters also varied across cases in terms of statistics (Tables 1 and S4) and diurnal variations (Fig. 5). In the PRD case, the average mixing ratios are characteristic of a rural environment, with AVOCs at 9.70 ± 5.00 ppb, OVOCs at 3.20 ± 2.30 ppb, isoprene at 0.26 ± 0.34 ppb, NO₂ at 6.3 ± 2.5 ppb, and NO at 0.73 ± 1.09 ppb. The NO concentration was affected by traffic sources, as there were no other fresh emission sources nearby, and the diurnal variation in NO showed a morning peak in all three cases (Fig. 5). In the CEC case, a general reduction in anthropogenic influence is evident. AVOCs, OVOCs, isoprene, and NO₂ drop significantly to 6.90 ± 1.80, 1.70 ± 0.38, 0.16 ± 0.20, and 4.84 ± 2.23 ppb, respectively. Meanwhile, NO levels remain close to PRD levels at 0.69 ± 1.00 ppb. In the CNC case, the air mass was more aged with reduced biogenic emissions, reflected in further decreases in isoprene and NO₂ to 0.03 ± 0.04 and 4.52 ± 1.97 ppb, respectively, due to colder weather conditions. The temperature decreased significantly from PRD to CNC, whereas the average peak photolysis frequency was comparable between PRD and CNC, as shown in Table 1.

Figure 6 Chemical budgets of OH and HO₂ for PRD (a, d), CEC (b, e), and CNC (c, f) simulated using a chemical box model.

3.2 Chemical budgets of OH and HO₂

To investigate the OH and HO₂ chemical budgets during the three distinct periods, we employed a box model constrained by observed concentrations of NO_x, VOCs, and relevant meteorological parameters in the selected cases (base scenario in which OH and HO₂ concentrations were not constrained by the measurements). The resulting OH and HO₂ budgets, displaying typical bell-shaped patterns, are illustrated in Fig. 6. During midday, the recycling of RO species becomes the dominant pathway for HO₂ production, with rates of 3.22 ppb h⁻¹ for PRD, 2.09 ppb h⁻¹ for CEC, and 1.08 ppb h⁻¹ for CNC. Additionally, HCHO photolysis contributed 0.75, 0.46, and 0.26 ppb h⁻¹ for PRD, CEC, and CNC, respectively. The sinks of HO₂ varied among the cases, with a minor contribution from the uptake process, driven by radical termination mechanisms. The rate of radical self-reactions decreased from PRD to CNC. In contrast, NO_x radical reactions between CEC and CNC were comparable, with respective rates of 0.39 and 0.33 ppb h⁻¹, indicating a shift in radical termination mechanisms.

Figure 7 Observed and simulated OH, observed ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, and simulated HO₂ time series for the PRD case. The “Obs” subscript denotes the observation data. “Base” denotes the result of the baseline scenario, as described in Sect. 2.3. “Cons” denotes the results with additional constrained species compared to the baseline scenario.

OH formation was predominantly driven by the HO₂ + NO reaction, contributing 5.18, 3.51, and 1.81 ppb h⁻¹ (midday average for 10:00–15:00 UTC, referred to hereafter in this section) for PRD, CEC, and CNC, respectively. Additionally, contributions from ozone photolysis and HONO increased from PRD to CEC and then to CNC, with rates of 21.4 %, 22.7 %, and 24.6 %, respectively. The primary sinks for OH included reactions with VOCs to produce RO₂, with rates of 3.31, 2.02, and 1.13 ppb h⁻¹, and reactions with CO and other VOCs to generate HO₂, contributing 1.55, 1.06, and 0.38 ppb h⁻¹ for PRD, CEC, and CNC, respectively. These findings highlight the critical role of OH + VOC reactions in the chemical budget of OH.

Figure 8 Observed and simulated OH, observed ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, and simulated HO₂ time series for the CEC case. The “Obs” subscript denotes the observation data. “Base” denotes the result of the baseline scenario, as described in Sect. 2.3. “Cons” denotes the results with additional constrained species compared to the baseline scenario.

Figure 9 Observed and simulated time series of OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ for the CNC case. “Base” denotes the results of the baseline scenario, as described in Sect. 2.3.

3.3 Comparison of model with observation results

Modeled OH and HO₂ concentrations were evaluated by comparing them against observations. The observed ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ serves as an upper limit for ambient HO₂ due to the interference from RO₂. According to model simulations (Text S3), RO₂ interference was estimated to account for 56 %, 54 %, and 59 % of the observed ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ signal for the PRD, CEC, and CNC cases, respectively. In the PRD case (Fig. 7), which represents the most polluted and warmest environment among the three cases, the model slightly overestimated OH concentrations. However, the modeled HO₂ concentration was substantially higher than the observed ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, indicating an overprediction of HO₂. Similar overestimations have been reported at a rural site (Kanaya et al., 2012). For the CEC case (Fig. 8), the modeled OH and HO₂ concentrations were moderately higher than the observed values during the daytime, consistent with findings from a rural forest site (Bottorff et al., 2023). In the CNC case (Fig. 9), the model generally reproduced the observed OH trend, with HO₂ comparable to the observed ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$. However, on 7 December, it exhibited daytime overestimation of HO_x, similar to the PRD case. At night, both CNC and CEC showed lower modeled HO₂ concentrations compared to observed ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, which can be explained by the expected contribution of RO₂ interference to ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ in the observations. To further investigate the possible reasons for the model–observation discrepancies, sensitivity tests were conducted. The modeled RO₂ interference ratio was used to correct ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ values, roughly estimating ambient HO₂ as input for the tests.

3.3.1 Substantial overestimation of HO₂ in PRD case

To explain the HO₂ overprediction by the base model, we constrained OH or corrected ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ and compared these to the base case (without constraining OH and HO₂). Results show that constraining corrected ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ (blue line in Fig. 7a) causes the model to underestimate OH, while constraining OH still leads to a substantially higher modeled HO₂ concentration (blue line in Fig. 7b) than the observed ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$. This result suggests that to align the modeled OH and HO₂ with observations, it may be necessary to introduce a strong, unknown process for HO₂ that efficiently recycles OH with a high yield (Kanaya et al., 2012).

3.3.2 Moderate overestimation of both OH and HO₂ radicals in CEC case

Unlike the PRD case, constraining either OH or corrected ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ in the CEC case generally reduces the daytime overestimation of both HO₂ and OH. These results indicate an additional sink for both OH and HO₂, as suggested by Bottorff et al. (2023). However, the OH concentration is overestimated in the morning when the corrected ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ is constrained, suggesting that some OH sinks may be missing in the model during this period or that the corrected ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ values that were used to constrain the model are still higher than the true HO₂ values. To further investigate the underlying causes, we examined the correlations between various pollutants. The significant negative correlation between CO and NO (R² = 0.49, p = 0.01, Fig. S6b) suggests that morning conditions in the CEC case may have been influenced by emission from fresh complete combustion during the CEC case, while correlations in the PRD and CNC cases are not significant (Fig. S6a and c). This indicates that the missing OH reactivity in the CEC case during the morning hours is possibly related to fresh vehicle emissions.

Figure 10 O_x (O₃ + NO₂) photochemical production rates in three comparative cases: (a) PRD, (b) CEC, and (c) CNC. The orange, green, and blue lines represent rates modeled by excluding OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, including OH with corrected ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, and including OH with uncorrected ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, respectively.

Figure 11 Modeled HNO₃ production rates in three comparative cases: (a) PRD, (b) CEC, and (c) CNC. The orange, green, and blue lines represent rates modeled by excluding OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, including OH with corrected ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, and including OH with uncorrected ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, respectively. (The blue lines are covered by the green lines as the daytime HNO₃ production rates are determined by the constrained OH.)

4 Implication for model overestimation of HO_x

OH and HO₂ are key species that determine the atmosphere's oxidative processes. Inaccurate modeling of their sinks can lead to significant overestimations of oxidation capacity, which may skew assessments of the impact of HO_x on air pollution and climate change. This problem is particularly pronounced in the case of ozone, a widespread photochemical pollutant. To demonstrate this issue, we compared results from two modeling scenarios: the first scenario was the base case (as described in Sect. 3.2), while the second scenario included constraints from all observational parameters, including measurements of OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$. Results for the scenario constrained by OH and corrected ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ measurements are also shown in Figs. 10 and 11.

As illustrated in Fig. 10, not constraining free-radical measurement data in the chemical model (the orange lines) led to overestimates of ozone's photochemical production rates. Compared to scenarios constrained by OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, in the PRD case, simulated midday O_x (O₃ + NO₂) formation rates in the base case were overestimated by 33 % on average and 32 % at peak O_x rates. In the CEC case, the overestimation was 79 % on average and 89 % at peak O_x rates, while in the CNC case, the smallest overestimation was 17 % on average and 25 % at peak. Since the ambient HO₂ concentration is lower than the constrained ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ concentration, the impact of the overestimated HO_x on ozone production rates might be even larger in such environments (the green lines in Fig. 10).

The overestimation of HO_x also significantly affected the simulated concentration of nitric acid (HNO₃), which is crucial for new particle formation and growth (Wang et al., 2020). Figure 11 illustrates that the chemical model moderately overestimated nitric acid production rates without the constraints of free-radical measurements (the orange lines). Compared to the scenarios constrained by OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$, the midday production rates of nitric acid were overestimated by 25 %, 88 %, and 31 % in the PRD, CEC, and CNC cases, respectively. Such overestimations can considerably impact assessments of new particle formation and growth processes and their impact on air pollution and climate change. On the other hand, the impact on HNO₃ production is dominated by OH radicals; therefore, measurement interference of HO₂ is negligible.

5 Conclusion

${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ and OH concentrations were measured using a chemical ionization mass spectrometer at a subtropical rural site in southern China from 12 November to 19 December 2022. The measurements indicated generally lower concentrations of OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ than those observed in previous studies at various sites. The model estimated that interferences from RO₂ contributed to 44 %–69 % of the ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ throughout the campaign. Backward-trajectory analysis revealed three distinct phases characterized by sequentially decreasing pollution levels and temperatures. During the cold, clean period, model simulations closely matched the observed OH and ${\mathrm{HO}}_{\mathrm{2}}^{\ast }$ concentrations. However, during the warm, polluted period, the models overestimated HO₂ or both radicals. Model sensitivity analysis indicates that adding an OH cycling reaction from HO₂ or additional sinks of OH and HO₂ would largely reduce the model–observation discrepancy in different cases of this study. However, the exact chemical reactions remain to be identified. Our results are in line with previous studies, indicating substantial gaps in our understanding of the sources and sinks of OH and HO₂ in certain environments. Our study provides additional evidence of the current incomplete understanding of HO_x sources and sinks and calls for more research to resolve the model–observation mismatch found in this work and in previous studies.

The overprediction of HO_x resulted in significant overestimation of the production rates of other secondary pollutants at the site, such as ozone and nitric acid. It is critical to evaluate the capability of OH and HO₂ simulations in major chemical transport models and Earth system models, as inaccurate simulations of OH and HO₂ may misguide the development of air pollution and global warming control strategies.