Experimental chemical budgets of OH, HO₂, and RO₂ radicals in rural air in western Germany during the JULIAC campaign 2019

Photochemical processes in ambient air were studied using the atmospheric simulation chamber SAPHIR at Forschungszentrum Jülich, Germany. Ambient air was continuously drawn into the chamber through a 50 m high inlet line and passed through the chamber for 1 month in each season throughout 2019. The residence time of the air inside the chamber was about 1 h. As the research center is surrounded by a mixed deciduous forest and is located close to the city Jülich, the sampled air was influenced by both anthropogenic and biogenic emissions. Measurements of hydroxyl (OH), hydroperoxyl (HO₂), and organic peroxy (RO₂) radicals were achieved by a laser-induced fluorescence instrument. The radical measurements together with measurements of OH reactivity (k_OH, the inverse of the OH lifetime) and a comprehensive set of trace gas concentrations and aerosol properties allowed for the investigation of the seasonal and diurnal variation of radical production and destruction pathways. In spring and summer periods, median OH concentrations reached 6 × 10⁶ cm⁻³ at noon, and median concentrations of both HO₂ and RO₂ radicals were 3 × 10⁸ cm⁻³. The measured OH reactivity was between 4 and 18 s⁻¹ in both seasons. The total reaction rate of peroxy radicals with NO was found to be consistent with production rates of odd oxygen (O_x= NO₂+ O₃) determined from NO₂ and O₃ concentration measurements. The chemical budgets of radicals were analyzed for the spring and summer seasons, when peroxy radical concentrations were above the detection limit. For most conditions, the concentrations of radicals were mainly sustained by the regeneration of OH via reactions of HO₂ and RO₂ radicals with nitric oxide (NO). The median diurnal profiles of the total radical production and destruction rates showed maxima between 3 and 6 ppbv h⁻¹ for OH, HO₂, and RO₂. Total RO_X (OH, HO₂, and RO₂) initiation and termination rates were below 3 ppbv h⁻¹. The highest OH radical turnover rate of 13 ppbv h⁻¹ was observed during a high-temperature (max. 40 ^∘C) period in August. In this period, the highest HO₂, RO₂, and RO_X turnover rates were around 11, 10, and 4 ppbv h⁻¹, respectively. When NO mixing ratios were between 1 and 3 ppbv, OH and HO₂ production and destruction rates were balanced, but unexplained RO₂ and RO_X production reactions with median rates of 2 and 0.4 ppbv h⁻¹, respectively, were required to balance their destruction. For NO mixing ratios above 3 ppbv, the peroxy radical reaction rates with NO were highly uncertain due to the low peroxy radical concentrations close to the limit of NO interferences in the HO₂ and RO₂ measurements. For NO mixing ratios below 1 ppbv, a missing source for OH and a missing sink for HO₂ were found with maximum rates of 3.0 and 2.0 ppbv h⁻¹, respectively. The missing OH source likely consisted of a combination of a missing inter-radical HO₂ to OH conversion reaction (up to 2 ppbv h⁻¹) and a missing primary radical source (0.5–1.4 ppbv h⁻¹). The dataset collected in this campaign allowed analyzing the potential impact of OH regeneration from RO₂ isomerization reactions from isoprene, HO₂ uptake on aerosol, and RO₂ production from chlorine chemistry on radical production and destruction rates. These processes were negligible for the chemical conditions encountered in this study.

1 Introduction

The hydroxyl (OH) radical is the dominant daytime atmospheric oxidant. It reacts with most trace gases in the troposphere and thereby controls the rate of their removal and chemical transformation. In the lower troposphere, OH is primarily produced by solar photolysis of ozone (O₃) and nitrous acid (HONO). The reaction of OH with trace gases leads to the formation of hydroperoxy (HO₂) or organic peroxy (RO₂, with R= organic group) radicals, which undergo further radical reactions. Generally, these reactions are cyclic chain reactions, in which OH, HO₂, and RO₂ are converted into each other, while at the same time emitted pollutants are oxidized and converted into secondary pollutants such as ozone and oxygenated volatile organic compounds (OVOCs). Because the conversion of radicals occurs on a timescale of seconds to minutes, they are often referred to as the RO_X family (OH + HO₂+ RO₂). The most important radical reactions in the lower atmosphere are summarized in Table 1. Understanding radical chemistry is the basis for reliable predictions of the atmospheric lifetime and chemical transformation of air pollutants and climate-relevant gases by atmospheric chemistry models (Stone et al., 2012).

The level of agreement between simulated and observed radical concentrations in various environments shows the degree of understanding of the underlying radical chemical mechanism. Even though good agreement is found in some cases (Tan et al., 2001; Konrad et al., 2003; Mihelcic et al., 2003; Lelieveld et al., 2008; Kubistin et al., 2010; Whalley et al., 2011), there are significant unexplained discrepancies between modeled and measured OH in forested regions (Wolfe et al., 2011; Griffith et al., 2013; Kim et al., 2013; Hens et al., 2013; Wolfe et al., 2014) and of HO₂ and RO₂ in polluted areas (Ren et al., 2003, 2006; Kanaya et al., 2007; Dusanter et al., 2009; Chen et al., 2010; Ren et al., 2013; Brune et al., 2016; Tan et al., 2018; Slater et al., 2020; Whalley et al., 2021), while different results are found depending on the abundance of nitric oxide (NO) in rural environments (Hofzumahaus et al., 2009; Lou et al., 2010; Elshorbany et al., 2012; Kanaya et al., 2012; Tan et al., 2017).

A chemical budget analysis using measured OH, HO₂, and RO₂ radical concentrations can help assess the strength of different radical production and loss paths. This allows identifying possible missing chemical processes by comparing the total production and destruction rates for the different radicals as concentrations are expected to be in steady state due to their short chemical lifetime. A large number of measurements needs to be available (e.g., OH reactivity, OH, peroxy radicals); therefore, there have only been a few studies focusing on the analysis of the chemical budget for OH radicals so far (Handisides et al., 2003; Hofzumahaus et al., 2009; Brune et al., 2016; Whalley et al., 2018; Tan et al., 2019; Whalley et al., 2021).

Results from field campaigns in China showed a larger OH radical destruction rate compared to its production rate in the afternoon, which points to an OH radical source that is unaccounted for. Discrepancies were highest when NO mixing ratios were lower than 2 ppbv (Hofzumahaus et al., 2009; Tan et al., 2019; Whalley et al., 2021). On the other hand, studies in urban areas in California (Brune et al., 2016) and in London (Whalley et al., 2018) as well as in a rural area in Hohenpeissenberg (Handisides et al., 2003) showed no significant gap between the OH production and destruction rates. Recently, radical measurements including RO₂ enabled the investigation of HO₂, RO₂, and RO_X production and destruction rates in field campaigns in China (Tan et al., 2019; Whalley et al., 2021). Tan et al. (2019) showed that an RO₂ loss process was required in a campaign in Wangdu in summer, while HO₂ production and destruction rates were balanced. This suggests a missing conversion of RO₂ to OH in addition to the reaction of peroxy radicals with NO. Furthermore, Whalley et al. (2021) found large imbalances between peroxy radical production and destruction rates in Beijing, indicating substantially slower propagation of RO₂ to HO₂ radicals than anticipated.

In this study, OH, HO₂, and RO₂ radical concentrations as well as OH reactivity, the inverse of the OH radical lifetime, were measured in the atmospheric simulation chamber SAPHIR on the campus of Forschungszentrum Jülich (FZJ), Germany, in the Jülich Atmospheric Chemistry project (JULIAC) campaign. Ambient air was sampled from 50 m height into the SAPHIR chamber. From this dataset, a chemical budget analysis of OH, HO₂, RO₂ radicals, and their sum (RO_X) was done using measured concentrations allowing the investigation of whether all radical production and destruction processes were accounted for during spring and summer.

2 Methodology

2.1 JULIAC

The Jülich Atmospheric Chemistry (JULIAC) project campaign was conducted at Forschungszentrum Jülich (FZJ, 50.9^∘ N, 6.4^∘ E), Germany. The project consisted of four 1-month-long intensive campaigns studying atmospheric chemistry in ambient air in each season throughout 2019. The location is surrounded by a deciduous forest and is located in a rural environment near a town, Jülich (33 000 inhabitants), 25 km northeast, 40 km west, and 43 km southwest from the three large cities of Aachen, Cologne, and Düsseldorf, respectively. Therefore, ambient air is influenced by both biogenic and anthropogenic emission sources.

Table 1 Chemical reactions and rate constants used for the analysis of the chemical budgets of radicals. Values of reaction rate constants are given for standard conditions (298 K, 1 atm). Actual numbers are used for the calculations.

^a 1σ uncertainty. ^b Measured photolysis frequencies. ^c Yield for OH: 0.36, HO₂: 0.10, RO₂: 0.42 from Novelli et al. (2021). ^d Yield for OH: 0.36, HO₂: 0.15, RO₂: 0.51 from Novelli et al. (2021). ^e Yield for OH: 0.32, HO₂: 0.09, RO₂: 0.37 from Novelli et al. (2021). ^f Yield for OH: 0.48, HO₂: 0.11, RO₂: 0.59 from Novelli et al. (2021). ^g Yield for OH: 0.26, HO₂: 0.26 from Malkin et al. (2010). ^h Yield for OH: 0.8 from Cox et al. (2020). ⁱ At 1 % water vapor mixing ratio. ^j Highly variable depending on the specific VOC.

Table 2 Specification of instruments used in the JULIAC campaign for the analysis in this work.

^* NO₂ was converted to NO before detection using a custom-built photolytic converter. NA: not available.

The investigation of the photochemistry was performed in the SAPHIR chamber, which was equipped with a large set of instruments measuring radicals, trace gases, and aerosol (Table 2). The SAPHIR chamber has a cylindrical shape and is made of a double-wall Teflon (FEP) film. A slight overpressure (35 Pa) is maintained in the chamber, and the space between the two films is permanently flushed with pure nitrogen (Linde, purity: > 99:99990 %) to prevent outside air from penetrating the inner chamber. The chamber is equipped with a shutter system allowing the air to be either shielded from or exposed to solar radiation.

In the JULIAC campaign, ambient air was sampled at a high flow rate of 660 m³ h⁻¹ from a 50 m high inlet line (104 mm inner diameter, SilcoNert^® coated stainless steel) by means of an oil-free turbo blower (Aerzener Maschinenfabrik, AERZEN Turbo G3, type TB 50–0.6 S). Large particles (> 10 µm diameter) were removed by a SilcoNert^®-coated cyclone (LTG, ZSB-6). The temperatures in the inlet line and cyclone were controlled to be slightly higher than ambient temperature (+1 to 2 ^∘C) to avoid water vapor condensation in the inlet system. A $\mathrm{3}/\mathrm{2}$-way valve directed some of the air (flow rate of 250 m³ h⁻¹) into the chamber. Two fans inside the chamber ensured fast mixing on a timescale of a few minutes. As a result, the chamber behaved as a continuously stirred photochemical flow reactor with a mean residence time of air of 1.1 h. During the transition time of 3.5 s from the tip of the inlet to the SAPHIR chamber, atmospheric RO_X radicals are lost on walls, but concentrations are rapidly re-established in the sampled ambient air inside the sunlit chamber.

The use of the chamber as a flow reactor has advantages compared to field measurements in the open air. Perturbations of the studied chemistry due to local emissions of VOCs or NO_x can be avoided. Transient fluctuations of reactants in the sampled air, for example due to spikes of NO from passing cars, are smoothed out in the chamber. Due to the homogeneous mixing, instruments connected to the chamber measure the same air composition, and segregation effects on reaction rates are insignificant.

The air composition could be influenced by the inlet line and chamber surfaces. As the whole inlet line is heated and chemically inert due to the SilcoNert^® coating, no relevant wall loss or desorption of trace gases is expected from the inlet. This assumption was confirmed by comparing OH reactivity measured at several positions of the inlet line. No significant differences were found between measurements whether the air was sampled upstream of the cyclone or downstream of the blower. Wall losses of trace gases (VOCs, NO_x, O₃) inside the SAPHIR chamber were found to be negligible in previous experiments (e.g., Kaminski et al., 2017, Rolletter et al., 2020).

Nitrous acid (HONO) and formaldehyde (HCHO) are known to be emitted from the chamber film when it is exposed to solar radiation (Rohrer et al., 2005). These emissions significantly increase the concentrations of HONO and HCHO in the chamber. Due to the transmission through the Teflon film and shading from construction elements of the chamber, the absolute actinic flux density is reduced by 20 % to 40 % compared to outside the chamber. It is worth noting, however, that the relative spectral distribution of the solar radiation is not changed by the transmission through the chamber film (Bohn and Zilken, 2005).

The floor underneath the chamber is heated by the solar radiation. Although it is not in direct contact with the foil, the air temperature in the chamber was on average 0.7 ^∘C higher during winter and autumn and 1.9 ^∘C higher during spring and summer than the temperature outside the chamber in daytime. Since photochemistry was studied in the chamber, all data for chemical and physical conditions shown in this work refer to conditions inside the chamber.

The measurements in the campaign were interrupted at least once a week for calibration and maintenance of instruments. Some days were also excluded from the analysis in this work because the chamber shutter system was kept closed to protect the chamber film during bad weather from strong wind gusts and/or precipitation. Reference experiments with clean synthetic air were performed to investigate possible changes in the strength of chamber emissions and to check for instrumental backgrounds. In addition, chemical actinometry experiments, in which NO₂ was photolyzed in synthetic air, were performed before and after each intensive period. The comparison of actinometric and spectroradiometric $j_{{\mathrm{NO}}_{\mathrm{2}}}$ values was used to track and correct for changes in light transmission due to aging of the chamber wall (Bohn et al., 2005).

2.2 Instrumentation

2.2.1 OH, HO₂, and RO₂ radical and OH reactivity (k_OH) measurements

OH, HO₂, and RO₂ radicals were measured by the FZJ laser-induced fluorescence (LIF) instrument, which included a newly developed chemical modulation reactor (CMR) for interference-corrected measurements of OH radicals (Cho et al., 2021). The signals of the instrument were calibrated against well-defined radical concentrations that were produced from water photolysis in synthetic air at a wavelength of 185 nm using radiation from a mercury lamp. A detailed description of the LIF instrument and its calibration can be found in previous publications (Holland et al., 2003; Fuchs et al., 2008, 2011, 2012).

The OH radical is sampled through a nozzle with a 0.4 mm diameter pinhole and is excited by a pulsed laser at a wavelength of 308 nm in a low-pressure (4 hPa) fluorescence cell. The emitted resonant fluorescence is detected with a time delay by a time-gated micro-channel plate detector (MCP). In the JULIAC campaign, a chemical modulation reactor (CMR) was implemented on top of the OH cell to quantify potential interferences. This is achieved by periodically removing ambient OH by an OH scavenger that is injected in the reactor (propane, Air Liquide, purity > 99.95 %, (5.0 ± 0.1) % mixture in nitrogen) before the air enters the fluorescence cell. During the campaign, the observed interference could be fully explained by the well-characterized interference from the photolysis of ozone in humid air inside the detection cell. No evidence for unexplained interference was found (Cho et al., 2021). The limit of detection for OH was 0.7 × 10⁶ cm⁻³ and the accuracy was 18 % (1σ).

OH radical concentrations were also measured by differential optical absorption spectroscopy (DOAS) using a multiple folded light path for absorption inside along the chamber. The DOAS technique is a calibration-free technique (Hausmann et al., 1997; Schlosser et al., 2007, 2009). The limit of detection was 0.8 × 10⁶ cm⁻³ and the 1σ accuracy was 6.5 %. Due to a technical laser problem, the DOAS instrument was not available in spring.

HO₂ radicals were detected by the LIF instrument in a separate detection cell, where HO₂ is chemically converted to OH radicals in the reaction with NO (Air Liquide, 1 % NO in N₂, purity > 99.5 %) that is injected in the fluorescence cell (Fuchs et al., 2011). During the JULIAC campaign, two different concentrations (2.5×10¹³ and 1.0×10¹⁴ cm⁻³) of NO in the fluorescence cell were used to observe possible interference from specific RO₂ radicals as highlighted by Fuchs et al. (2011). No difference between HO₂ measurements at high and low NO concentrations was found, suggesting that there was no significant interference from RO₂.

In addition, the sum of OH, HO₂, and RO₂ (RO_X) was measured by the RO_X–LIF system. Air is sampled into a chemical converter (pressure of ∼ 25 hPa), where a mixture of NO (Air Liquide, 500 ppmv NO in N₂, purity > 99.5 %) and CO (Air Liquide, 10 % CO in N₂, purity > 99.997 %) is injected. The NO converts RO₂ radicals to HO₂ radicals, and CO converts OH radicals formed from the reaction of HO₂ radicals with NO back to HO₂. Therefore, an equilibrium between OH and HO₂ is established. Concentrations are chosen so that the equilibrium is on the side of HO₂. In a low-pressure cell downstream of the converter HO₂ radicals are converted to OH radicals by injecting excess NO (Air Liquide, pure NO, purity > 99.5 %) (Fuchs et al., 2008) that shifts the equilibrium between OH and HO₂ to OH. The RO₂ concentration is obtained from the difference between the sum measurement of RO_X and measurements of OH and HO₂ concentrations in the other two detection cells. The RO₂ detection sensitivity was calibrated for methyl peroxy radicals (CH₃O₂), which are produced from the reaction of OH with methane (CH₄) in the calibration system. The resulting calibration is also applicable to the majority of other atmospheric alkyl peroxy radicals (Fuchs et al., 2008, 2011), and recent laboratory tests performed with a variety of VOCs including monoterpenes and chained alkanes for the CO and NO mixing ratios applied in the RO_X converter during the JULIAC campaign showed a decrease of less than 15 % sensitivity compared to methyl peroxy radicals, which is within the accuracy of the instrument.

The signals in the HO₂ and RO₂ detection systems contain a background signal observed when NO is injected into the detection cells, even if no radicals are present in the air sampled. The background signal can be characterized when the inlet of the detection system is overflown with synthetic air, which is part of the calibration procedures. During the JULIAC campaign the background varied from calibration to calibration and was often larger than the smallest signals measured in ambient air from the chamber (Table S1). The highest background signals obtained from calibrations are therefore regarded as an upper limit, and the variability is considered to be an additional uncertainty in the measured HO₂ and RO₂ concentrations. HO₂ and RO₂ background signals, which are subtracted in the evaluation of HO₂ and RO₂ measurements, were taken from reference experiments in the dark clean chamber, when no HO₂ or RO₂ radicals are expected. The subtracted signals for each period are available in Table S1 and in most cases were equivalent to concentrations lower than 1 × 10⁷ cm⁻³ for both HO₂ and RO₂ measurements.

The total OH reactivity (k_OH), the inverse of the chemical lifetime of OH radicals, was measured in ambient air by a laser-flash photolysis LIF instrument (Lou et al., 2010; Fuchs et al., 2017). A high concentration of OH radicals is produced by flash photolysis (266 nm, 1 Hz repetition rate) of ozone in humid air (Reaction R2 in Table 1) in a flow tube that is on top of an OH fluorescence cell. The pseudo-first-order decay of OH in the chemical reactions with atmospheric reactants is measured, directly giving the OH reactivity.

2.2.2 Other trace gas, aerosol property, and photolysis frequency measurements

A comprehensive set of instruments operated during the JULIAC campaign (Table 2) analyzed the air composition inside the chamber. Photolysis frequencies inside the chamber were derived from solar actinic flux densities measured by a spectroradiometer mounted on the roof of the nearby institute building. Chamber values were calculated using a model approach considering shading effects and the influence of the chamber film (Bohn et al., 2005; Bohn and Zilken, 2005). Formaldehyde (HCHO) was detected by cavity ring-down spectroscopy (Picarro, G2307, Glowania et al., 2021). NO and NO₂ were measured by chemiluminescence (Eco Physics, TR780, NO₂ conversion by a custom-built photolytic converter). In addition, HONO was measured by long-path absorption photometry (LOPAP, Kleffmann et al., 2006; Häseler et al., 2009), CO, CO₂, CH₄, and H₂O by cavity ring-down spectroscopy (Picarro, G2401), and O₃ by UV absorption (Ansyco-41M and Thermo scientific-49I). Volatile organic compounds (VOCs) were detected by a proton-transfer-reaction time-of-flight mass spectrometer (PTR-TOF-MS, Ionicon) (Jordan et al., 2009) and a VOCUS PTR-TOF-MS instrument (Aerodyne). The VOCs included in this study are listed in Table S2 and include isoprene and some carbonyl compounds. Total aerosol surface area was determined from measurements by a scanning mobility particle sizer (SMPS). In the summer and autumn periods, nitryl chloride (ClNO₂) was detected by a chemical ionization mass spectrometer using iodine as the reagent ion (I-CIMS) (Sommariva et al., 2018; Tan et al., 2022).

In addition to measurements in the chamber, concentrations of O₃ and NO_x were also measured in the inlet system before the air flowed into the SAPHIR chamber. For these measurements, a combined system (Eco Physics, CraNO_X) consisting of an ozone photometer and a chemiluminescence instrument for NO_x was deployed. Measurements were used to determine the photochemical ozone production in the JULIAC campaign. The measurement setup and concept of the evaluation will be discussed in detail in a further publication.

2.3 Chemical budget calculations

A chemical budget analysis, similar to that in Tan et al. (2019) and Whalley et al. (2021), was applied for OH, HO₂, RO₂, and the sum of all three radicals (RO_X) to the dataset from the JULIAC campaign. All reactions typically considered to be relevant for the generation and destruction of these radicals are considered (Table 1). Rate constants and their uncertainties were mainly taken from IUPAC recommendations (Atkinson et al., 2004, 2006; Cox et al., 2020) or more recent studies. If not otherwise specified, radical production and destruction rates are calculated from measured concentrations of reactants.

2.3.1 Chemical budget of OH radicals

The production rate of OH radicals includes primary production reactions (Reactions R1, R2, and R5) and radical interconversion reactions (Reactions R10 and R11):

$$\begin{array}{}\text{(1)}& \begin{array}{rl}{P}_{\mathrm{OH}}& =j_{\mathrm{HONO}}\left[\mathrm{HONO}\right]+{\mathit{\phi }}_{\mathrm{OH}}{j}_{{\mathrm{O}}^{\mathrm{1}}\mathrm{D}}\left[{\mathrm{O}}_{\mathrm{3}}\right]\\ & +k_{\mathrm{10}}\left[\mathrm{NO}\right]\left[{\mathrm{HO}}_{\mathrm{2}}\right]+k_{\mathrm{11}}\left[{\mathrm{O}}_{\mathrm{3}}\right]\left[{\mathrm{HO}}_{\mathrm{2}}\right]\\ & +\mathrm{\Sigma }\left\{{\mathit{\phi }}_{\mathrm{OH}}^i{k}_{\mathrm{5}}^i{\left[\mathrm{alkene}\right]}^i\left[{\mathrm{O}}_{\mathrm{3}}\right]\right\}+{\mathrm{P}}_{\mathrm{OH},\mathrm{Isop}.}\end{array}\end{array}$$

Here, φ_OH is the effective OH yield of the ozone photolysis including the reaction of excited oxygen atoms O(¹D) with H₂O, producing two OH radicals. ${\mathit{\phi }}_{\mathrm{OH}}^i$ is the OH yield of the ozonolysis reaction of alkenes, and $k_{\mathrm{5}}^i$ represents the rate constants of the corresponding reactions.

P_OH,Isop is the effective production of OH radicals from unimolecular reactions (1,6-hydrogen shift reactions) of isoprene–RO₂ radicals (Z-δ-RO₂-I and II, Peeters et al., 2014) and the subsequent chemistry of products. As there was no measurement of speciated RO₂ radicals, isoprene–RO₂ radical concentrations are estimated from steady-state conditions considering their production from the reaction of isoprene with OH and their destruction in bimolecular reaction (reaction rate k_bi) as well as unimolecular reactions (bulk reaction rate k_{bulk 1,6-H} as defined in Peeters et al., 2014).

$$\begin{array}{}\text{(2)}& {\displaystyle }{\left[{\mathrm{RO}}_{\mathrm{2}}(\mathrm{isop}.)\right]}_{\mathrm{SS}}={\displaystyle \frac{k_{\mathrm{18}}\left[\mathrm{Isoprene}\right]\left[\mathrm{OH}\right]}{k_{\mathrm{bi}}+k_{\text{bulk 1,6-H}}}}\text{(3)}& {\displaystyle }{k}_{\mathrm{bi}}=\left(k_{\mathrm{9}}+k_{\mathrm{14}}\right)\left[\mathrm{NO}\right]+k_{\mathrm{15}}\left[{\mathrm{RO}}_{\mathrm{2}}\right]+k_{\mathrm{16}}\left[{\mathrm{HO}}_{\mathrm{2}}\right]\end{array}$$

Bimolecular loss reactions include reactions with NO (Reactions R9 and R14), RO₂ (Reaction R15), and HO₂ (Reaction R16). The OH production from isoprene–RO₂ isomerization reactions is simplified in the calculation of the total OH production in this work by assuming that each isomerization reaction rapidly produces one OH radical from the subsequent reactions of products such as photolysis of hydroxy-peroxy aldehyde (HPALD). In this case, the radical production rate is equal to the loss rate of the isoprene–RO₂ due to isomerization reactions ($D_{Z-\mathit{\delta }-{\mathrm{RO}}_{\mathrm{2}},\mathrm{Isop}.}$).

$$\begin{array}{}\text{(4)}& P_{\mathrm{OH},\mathrm{Isop}.}=D_{Z-\mathit{\delta }-{\mathrm{RO}}_{\mathrm{2}},\mathrm{Isop}.}=k_{\text{bulk 1,6-H}}{\left[{\mathrm{RO}}_{\mathrm{2}}(\mathrm{isop}.)\right]}_{\mathrm{SS}}\end{array}$$

The total loss rate of OH radicals for the chemical budget analysis is determined by the product of the total OH reactivity (k_OH) and the OH radical concentration.

$$\begin{array}{}\text{(5)}& D_{\mathrm{OH}}=k_{\mathrm{OH}}\left[\mathrm{OH}\right]\end{array}$$

2.3.2 Chemical budget of HO₂ radicals

The production rate of HO₂ radicals includes primary reactions (Reactions R3, R4, and R5) and interconversion reactions (Reactions R6, R7, and R9, Table 1).

$$\begin{array}{}\text{(6)}& \begin{array}{rl}{P}_{{\mathrm{HO}}_{\mathrm{2}}}& =\mathrm{2}{j}_{\mathrm{HCHO}}\left[\mathrm{HCHO}\right]+k_{\mathrm{6}}\left[\mathrm{HCHO}\right]\left[\mathrm{OH}\right]\\ & +k_{\mathrm{7}}\left[\mathrm{CO}\right]\left[\mathrm{OH}\right]+k_{\mathrm{9}}\left[\mathrm{NO}\right]\left[{\mathrm{RO}}_{\mathrm{2}}\right]\\ & +\mathrm{\Sigma }\left\{{\mathit{\phi }}_{{\mathrm{HO}}_{\mathrm{2}}}^i{k}_{\mathrm{5}}^i{\left[\mathrm{alkene}\right]}^i\left[{\mathrm{O}}_{\mathrm{3}}\right]\right\}\end{array}\end{array}$$

Here, the photolysis frequency of HCHO (j_HCHO) includes only paths generating radicals. ${\mathit{\phi }}_{{\mathrm{HO}}_{\mathrm{2}}}^i$ is the HO₂ yield from the ozonolysis of alkenes. The reactions of OH with H₂ and O₃ are not considered due to their negligible contributions to the HO₂ production.

The loss rate of HO₂ is determined by the reactions with NO (Reaction R10), O₃ (Reaction R11), RO₂ (Reaction R16), and HO₂ (Reaction R17).

$$\begin{array}{}\text{(7)}& \begin{array}{rl}{D}_{{\mathrm{HO}}_{\mathrm{2}}}& =(k_{\mathrm{10}}\left[\mathrm{NO}\right]+k_{\mathrm{11}}\left[{\mathrm{O}}_{\mathrm{3}}\right]+k_{\mathrm{16}}\left[{\mathrm{RO}}_{\mathrm{2}}\right]\\ & +\mathrm{2}{k}_{\mathrm{17}}\left[{\mathrm{HO}}_{\mathrm{2}}\right])\left[{\mathrm{HO}}_{\mathrm{2}}\right]\end{array}\end{array}$$

Here, the humidity dependence of k₁₇ was taken into account. The reaction of HO₂ radicals with NO₂ is not included as the thermal decomposition of peroxynitric acid (HO₂NO₂) forming back HO₂ radicals and NO₂ is instantaneous for the temperatures experienced during the JULIAC campaign.

In a sensitivity calculation (Sect. 4.2.3), potential loss of HO₂ due to heterogeneous uptake on aerosol is investigated. The first-order loss rate (k_het.) can be described as

$$\begin{array}{}\text{(8)}& k_{\mathrm{het}.}={\displaystyle \frac{{\mathit{\gamma }}_{\mathrm{eff}.}\cdot {\mathit{\nu }}_{{\mathrm{HO}}_{\mathrm{2}}}\cdot \left[\mathrm{AS}\right],}{\mathrm{4}}}\end{array}$$

where ${\mathit{\nu }}_{{\mathrm{HO}}_{\mathrm{2}}}$ is the mean molecular velocity of HO₂ (4.44 × 10⁵ cm s⁻¹ at 298 K), [AS] is the measured aerosol surface area concentration, and γ_eff. is the effective uptake coefficient.

2.3.3 Chemical budget of RO₂ radicals

Primary sources of RO₂ radicals include all oxidation reactions of VOCs with OH, Cl, NO₃ radicals, and O₃. As the number of measured VOC species in this study was limited (Table S2) and because it is generally difficult to capture the entire spectrum of atmospheric VOCs (Goldstein and Galbally, 2007; Lou et al., 2010), the measured total OH reactivity (k_OH) can be used to calculate the RO₂ radical production from the reactions of VOCs with OH. First, the contributions from CO, NO, NO₂, HCHO, and O₃ are removed from the measured OH reactivity as these species do not form RO₂ radicals in the reaction with OH. It is then assumed that the remaining fraction can be attributed to organic compounds (VOC reactivity (k_VOC)) including measured and unmeasured VOCs, which produce RO₂ radicals in their reaction with OH.

For some aromatics, such as toluene, benzene, and xylene, the prompt formation of HO₂ is expected from their reaction with OH (Nehr et al., 2011, 2014; Jenkin et al., 2019). However, in this campaign, their concentrations were small and their average contributions to the OH reactivity from VOCs were only 2.8 %. Therefore, their potential impacts on the RO₂ production are negligible (less than 1 %).

In addition, RO₂ production from ozonolysis needs to be included. In this work, only the reactions of measured organic compounds are considered. The contribution to the RO₂ production from the oxidation of VOCs by the NO₃ radical was negligible during daytime due to the low VOC load (low OH reactivity), so NO₃ destruction by photolysis and reaction with NO dominated.

Reactions of chloride (Cl) also produce RO₂ radicals, but the concentration was not measured in the JULIAC campaign. However, one of the most important precursor species, nitryl chloride (ClNO₂), was detected during the campaign (except in spring, Tan et al., 2022). ClNO₂ can accumulate during nighttime, but it is photolyzed after sunrise, yielding NO₂ and Cl atoms (Reaction R20). Assuming as an upper limit that each Cl atom reacts with a VOC (Tanaka et al., 2003), the RO₂ production rate from Cl radicals can be calculated as

$$\begin{array}{}\text{(9)}& P_{{\mathrm{RO}}_{\mathrm{2}},\mathrm{Cl}}=j_{{\mathrm{ClNO}}_{\mathrm{2}}}\left[{\mathrm{ClNO}}_{\mathrm{2}}\right].\end{array}$$

The total RO₂ production rate is then calculated as

$$\begin{array}{}\text{(10)}& \begin{array}{rl}{P}_{{\mathrm{RO}}_{\mathrm{2}}}& =k_{\mathrm{VOC}}\left[\mathrm{OH}\right]+\sum \left({\mathit{\phi }}_{{\mathrm{RO}}_{\mathrm{2}}}^i{k}_{\mathrm{R}\mathrm{5}}^i{\left[\mathrm{alkene}\right]}^i\left[{\mathrm{O}}_{\mathrm{3}}\right]\right)\\ & +P_{{\mathrm{RO}}_{\mathrm{2}},\mathrm{Cl}}.\end{array}\end{array}$$

Here, ${\mathit{\phi }}_{{\mathrm{RO}}_{\mathrm{2}}}^i$ is the RO₂ yield from the ozonolysis of alkenes species (Table 1).

With respect to the destruction rate of RO₂, its reactions with NO, HO₂, and other RO₂ as well as unimolecular reactions of specific isoprene–RO₂ radicals ($D_{Z-\mathit{\delta }-{\mathrm{RO}}_{\mathrm{2}},\mathrm{Isop}.}$) (Eq. 4) are considered in this work:

$$\begin{array}{}\text{(11)}& \begin{array}{rl}{D}_{{\mathrm{RO}}_{\mathrm{2}}}& =\left(\right(k_{\mathrm{9}}+k_{\mathrm{14}})\left[\mathrm{NO}\right]+\mathrm{2}{k}_{\mathrm{15}}\left[{\mathrm{RO}}_{\mathrm{2}}\right]\\ & +k_{\mathrm{16}}\left[{\mathrm{HO}}_{\mathrm{2}}\right])\left[{\mathrm{RO}}_{\mathrm{2}}\right]+D_{Z-\mathit{\delta }-{\mathrm{RO}}_{\mathrm{2}},\mathrm{Isop}.}\end{array}\end{array}$$

2.3.4 Chemical budget of RO_X radicals

In the chemical budget of the sum of OH, HO₂, and RO₂ (RO_X), inter-radical conversion reactions cancel out, and only initiation and termination reactions are included. Therefore, the RO_X radical budget analysis allows investigating whether primary radical source reactions or termination processes are missing in the chemical mechanism used (Table 1).

The production rate of the RO_X radicals is given by the sum of rates from radical initiation reactions (Reactions R1–R5, R20–R22, Table 1).

$$\begin{array}{}\text{(12)}& \begin{array}{rl}{P}_{{\mathrm{RO}}_x}& =j_{\mathrm{HONO}}\left[\mathrm{HONO}\right]+{\mathit{\phi }}_{\mathrm{OH}}{j}_{{\mathrm{O}}^{\mathrm{1}}\mathrm{D}}\left[{\mathrm{O}}_{\mathrm{3}}\right]\\ & +\mathrm{2}{j}_{\mathrm{HCHO}}\left[\mathrm{HCHO}\right]\\ & +\sum \left(\left({\mathit{\phi }}_{\mathrm{OH}}^i+{\mathit{\phi }}_{{\mathrm{HO}}_{\mathrm{2}}}^i+{\mathit{\phi }}_{{\mathrm{RO}}_{\mathrm{2}}}^i\right)k_{\mathrm{5}}^i{\left[\mathrm{alkene}\right]}^i\left[{\mathrm{O}}_{\mathrm{3}}\right]\right)\\ & +P_{{\mathrm{RO}}_{\mathrm{2}},\mathrm{Cl}}\end{array}\end{array}$$

Radicals can additionally be produced from the photolysis of other oxygenated organic compounds (OVOCs, e.g., Reaction R4) not included in Eq. (12). Their potential impact is further discussed in Sect. 4.2.2.

The loss rate of the RO_X radical is calculated by the sum of rates from radical termination reactions (Reactions R12–R17).

$$\begin{array}{}\text{(13)}& \begin{array}{rl}{D}_{{\mathrm{RO}}_x}& =\left(k_{\mathrm{13}}\left[\mathrm{NO}\right]+k_{\mathrm{12}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\right)\left[\mathrm{OH}\right]+k_{\mathrm{14}}\left[\mathrm{NO}\right]\left[{\mathrm{RO}}_{\mathrm{2}}\right]\\ & +\mathrm{2}{k}_{\mathrm{15}}{\left[{\mathrm{RO}}_{\mathrm{2}}\right]}^{\mathrm{2}}+\mathrm{2}{k}_{\mathrm{16}}\left[{\mathrm{HO}}_{\mathrm{2}}\right]\left[{\mathrm{RO}}_{\mathrm{2}}\right]\\ & +\mathrm{2}{k}_{\mathrm{17}}{\left[{\mathrm{HO}}_{\mathrm{2}}\right]}^{\mathrm{2}}\end{array}\end{array}$$

2.3.5 Uncertainties in the calculated production and destruction rates

The uncertainty of each production or loss rate is calculated by Gaussian summation of the 1σ errors of the measured quantities (Table 2) and the uncertainties of the reaction rate constants (Table 1).

For reactions of RO₂ with NO (Reactions R9, R14), HO₂ (Reaction R16), and RO₂ (Reaction R15), generic rate constants are used for the sum of RO₂ radicals (Table 1, Jenkin et al., 2019). Rate constants of the NO reaction with RO₂ derived from hydrocarbons (< C₅) and with oxygenated peroxy radicals range from $\mathrm{7.7}\times {\mathrm{10}}^{-\mathrm{12}}$ to $\mathrm{1.1}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ s⁻¹ (Jenkin et al., 2019). The 1σ uncertainty of the rate constants varies from 6 % to 30 %. In the error calculations here, an upper limit value of 30 % is applied. However, for reactions of RO₂ with HO₂ and with RO₂, the range of rate constants varies by more than an order of magnitude. In the calculations, an uncertainty of 50 % is used for the reaction rate constants of RO₂ with HO₂ and with RO₂.

As there are no measurements of speciated RO₂ radicals, a yield of 5 % for the formation of organic nitrates is assumed for all RO₂, but the yield can vary between 1 % for methyl peroxy radicals (CH₃O₂) and more than 20 % for RO₂ from monoterpene species. This simplification can introduce systematic errors in the calculations (Sect. 4.2.1).

2.4 Odd oxygen production rate

In the troposphere, ozone is formed exclusively by the oxidation of NO to NO₂ through reaction with RO₂ (Reaction R9) and HO₂ (Reaction R10), followed by NO₂ photolysis (Fishman and Carney, 1984; Sillman et al., 1990; Kleinman et al., 2002).

During the day, the photolysis of NO₂ and the back reaction of NO with O₃ form a rapid photochemical equilibrium between O₃ and NO₂. The sum of O₃ and NO₂ is therefore defined as odd oxygen (O_x) (Han et al., 2011; Goldberg et al., 2015). The relative composition of O_x depends on the NO₂ photolysis frequency and the NO concentration. For the conditions of the spring and summer periods in the JULIAC campaign, O_x consisted predominantly (> 85 %) of O₃.

In this work, the net production rate of O_x ($P_{{\mathrm{O}}_x}$) was determined experimentally from the increase in O_x in the sunlit SAPHIR chamber. Furthermore, measurements of radicals and NO_x were used to calculate $P_{{\mathrm{O}}_x}$ from the rate of O_x formation reactions (Reactions R9, R10) and O_x loss by the reaction of NO₂ with OH (Reaction R12) (Mihelcic et al., 2003; Cazorla et al., 2012).

$$\begin{array}{}\text{(14)}& \begin{array}{rl}{P}_{{\mathrm{O}}_X,\mathrm{net}}& =k_{\mathrm{9}}\left[\mathrm{NO}\right]\left[{\mathrm{RO}}_{\mathrm{2}}\right]+k_{\mathrm{10}}\left[\mathrm{NO}\right]\left[{\mathrm{HO}}_{\mathrm{2}}\right]\\ & -k_{\mathrm{12}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\left[\mathrm{OH}\right]\end{array}\end{array}$$

This calculation neglects minor O_x destruction processes such as the reaction of O₃ with NO₂, OH, HO₂, Cl, or alkenes since they did not play a notable role during the day in this campaign.

3 Results

3.1 Data quality of radical measurements

Performing measurements in the SAPHIR chamber allowed testing the accuracy of radical measurements in different ways that are typically not available in field experiments. First, OH radicals was measured by two independent instruments, the OH DOAS and LIF instruments (Cho et al., 2021). Second, the O_x production rate calculated from measured concentrations of HO₂ and RO₂ could be compared to the observed increase in O_x concentrations in the chamber, which can be solely attributed to chemical reactions. This is possible because other factors typically impacting the O_x concentration in field experiments such as transportation processes are not effective.

OH concentrations were measured by the LIF instrument by applying the chemical modulation scheme and the DOAS in the winter, summer, and autumn periods of the campaign. As OH concentrations were close to the limit of detection in autumn and winter, a meaningful comparison of measurements was only possible for the summer period. A detailed comparison of measurements can be found in Cho et al. (2021). In general, the OH measurements of the two instruments agreed within their measurement errors (Table 1), giving a slope of 1.1 ± 0.02 in a linear regression analysis. The good agreement confirms that the newly developed chemical modulation system of the LIF instrument allowed for interference-free OH concentration measurements for conditions of the campaign. Only in the period from 22 to 26 August, which was characterized by exceptionally high temperatures (30 to 40 ^∘C), were OH concentrations measured by the LIF instrument systematically higher by 25 % than those measured by the DOAS instrument for unknown reasons (Cho et al., 2021). OH concentrations measured by the DOAS instrument were used for the analysis of the radical budgets in this period.

Net O_x production rates were determined from the measured increase in O_x concentrations in the chamber and compared to calculations from the turnover rates of HO₂ and RO₂ reactions with NO. This calculation also takes the NO₂ loss due to its reaction with OH into account (Eq. 14). The odd oxygen production rate did not exceed 1 ppbv h⁻¹ in winter and autumn due to the generally low photochemical activity in these seasons. In spring and summer, the O_x production rate showed clear diurnal variations with noontime maxima that reached up to 16 ppbv h⁻¹. In these seasons, both methods for determining the O_x production rate agreed within ± 15 % (1σ). Observed discrepancies were less than 1 ppbv h⁻¹ when NO mixing ratios were lower than 1 ppbv but reached values of 3 ppbv h⁻¹ for NO mixing ratios of 3–4 ppbv NO. The largest discrepancy of 8.5 ppbv h⁻¹ was found in the morning on 29 April, when the NO mixing ratio exceeded 9 ppbv. High NO values suppressed HO₂ and RO₂ concentrations to values below 2.0 ×10⁷ cm⁻³, which is within the range of the background corrections for the HO₂ and RO₂ measurements (Table S1). Under these conditions, an erroneous background subtraction may have caused the observed discrepancies.

Figure 1 Time series of temperature and trace gas concentrations during the spring period of the JULIAC campaign. Vertical dashed lines denote midnight. Grey shaded areas indicate calibration days when no measurements were done and days when the chamber roof was closed due to bad weather conditions.

3.2 Meteorological and chemical conditions during the JULIAC campaign

A broad range of meteorological and chemical conditions was encountered during the JULIAC campaign. During the winter and autumn periods (Figs. S1 and S2), the sky was often overcast and it rained frequently. Temperatures were generally below 10 ^∘C and the photolysis frequencies of ozone ($j_{{\mathrm{O}}_{\mathrm{1}}\mathrm{D}}$) and nitrogen dioxide ($j_{{\mathrm{NO}}_{\mathrm{2}}}$) mostly remained below $\mathrm{1.5}\times {\mathrm{10}}^{-\mathrm{6}}$ and $\mathrm{2}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹, respectively. During spring and summer, temperatures in the chamber were up to 35 ^∘C in mid-April and 40 ^∘C between 24 and 31 August (Figs. 1 and 2). Photolysis frequencies in the chamber were $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹ ($j_{{\mathrm{O}}_{\mathrm{1}}\mathrm{D}}$) and $\mathrm{4}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹ ($j_{{\mathrm{NO}}_{\mathrm{2}}}$).

The air was sampled at all times from 50 m above the ground. The temperature at different heights measured between 5 m and 120 m at a meteorological tower near the SAPHIR chamber showed that the air was well mixed within this height range during the day. Therefore, it can be assumed that the chemical composition of the air sampled into the chamber is representative of the air within the atmospheric boundary layer. At night, vertical temperature profiles showed atmospheric stratification below 100 m. The air at 50 m can be assumed to be isolated from the ground and therefore not affected by surface emissions or deposition on surfaces at the ground level.

Overall, relatively clean air was sampled during the whole of the JULIAC campaign, as indicated by CO and NO mixing ratios below 0.3 ppmv and 2 ppbv, respectively. Concentrations of anthropogenic organic compounds (e.g., benzene and toluene) were low with mixing ratios of less than 0.5 ppbv. Even though the measurement site is surrounded by a deciduous forest, the concentrations of biogenic organic compounds such as isoprene and monoterpenes were also low (median 0.8 ppbv and 0.15 ppbv, respectively) compared to previously reported values measured on the campus of FZJ in summer, when isoprene concentrations ranged between 0.5 and 4 ppbv (Komenda et al., 2003; Spirig et al., 2005; Kanaya et al., 2012). A possible reason for the low values could be damage to trees from severe droughts in the previous year (BMEL, 2021).

Figure 2 Time series of temperature and trace gas concentrations during the summer period of the JULIAC campaign. Vertical dashed lines denote midnight. Grey shaded areas indicate calibration days when no measurements were done and days when the chamber roof was closed due to bad weather conditions.

Figure 3 Time series of OH, HO₂, and RO₂ radical concentration measured by the FZJ LIF–CMR instrument and measurements of the OH reactivity (k_OH) measured in the spring period of the JULIAC campaign (Cho et al., 2022). Vertical bars represent 1σ statistical errors. Vertical dashed lines denote midnight. Grey shaded areas indicate calibration days when no measurements were done and days when the chamber roof was closed due to bad weather conditions.

3.3 OH, HO₂, and RO₂ radical concentrations and OH reactivity during the winter and autumn periods of the JULIAC campaign

During winter (Fig. S3) and autumn (Fig. S4), daytime OH radical concentrations were below 1×10⁶ cm⁻³, mainly due to low primary radical production. Daytime peroxy radical (HO₂ and RO₂) concentrations during these periods were also very low with average values below 2×10⁷ cm⁻³ (Fig. S5), which is close to the limit of detection of RO₂ radicals (Table 2) and within the uncertainty of the background corrections for HO₂ and RO₂ (Table S1). During winter and autumn, HO₂ concentrations typically increased in the morning and reached peak concentrations of 2×10⁷ cm⁻³ at noon. Concentrations decreased in the evening and night with minimum values right before sunrise. In contrast, nighttime RO₂ concentrations increased to values between 3 and 4×10⁷ cm⁻³ after sunset, when the chemical loss due to their reaction with NO became negligible, while RO₂ radicals were still produced from reactions of VOCs with NO₃ and O₃. NO concentrations were essentially zero at that time because NO production by the photolysis of NO₂ stopped and NO rapidly reacted with ozone. RO₂ radical concentrations decreased in the morning to values that were similar to those of HO₂ radicals as can be expected for conditions with high NO mixing ratios, which led to a fast loss of RO₂ and HO₂ in their reactions with NO.

The measured OH reactivity (k_OH) ranged between 4 and 33 s⁻¹ during winter and autumn periods. The highest value was observed on 21 January, when a highly polluted plume containing 50 ppbv of NO was sampled.

The measured OH reactivity can be compared to OH reactivity calculated by summing up the product between measured OH reactant concentrations and their reaction rate constants with the OH radical. On average, 1.3 s⁻¹ (18 %) of the measured OH reactivity could not be explained by the measured OH reactants during the winter and autumn periods (Fig. S5). NO_x, CH₄, CO, and VOCs contributed approximately 43 %, 3 %, 20 %, and 13 %, respectively, to the measured OH reactivity.

Figure 4 Time series of OH, HO₂, and RO₂ concentration measured by the FZJ LIF–CMR instrument and measurements of the OH reactivity (k_OH) in the summer period of the JULIAC campaign (Cho et al., 2022). Vertical bars represent 1σ statistical errors. Vertical dashed lines denote midnight. Grey shaded areas indicate calibration days when no measurements were done and days when the chamber roof was closed due to bad weather conditions.

Figure 5 Median values of the diurnal profiles of OH, HO₂, RO₂, k_OH, $j_{{\mathrm{O}}_{\mathrm{1}}\mathrm{D}}$, NO, and O₃ measured in the spring and summer periods of the JULIAC campaign. Colored areas represent the contributions of measured reactants to the total OH reactivity. Vertical lines give 25th and 75th percentile values.

3.4 OH, HO₂, and RO₂ radical concentrations and OH reactivity during the spring and summer periods of the JULIAC campaign

During spring and summer (Figs. 3, 4 and 5), maximum daytime OH concentrations were between 6 and 8 × 10⁶ cm⁻³. The highest OH concentration (1.2 ×10⁷ cm⁻³) occurred on 31 August. The diurnal OH concentration profile shows a high correlation with the ozone photolysis frequency ($j_{{\mathrm{O}}^{\mathrm{1}}\mathrm{D}}$) as observed in previous field campaigns (e.g., Ehhalt and Rohrer, 2000; Handisides et al., 2003; Holland et al., 2003).

Unfortunately, the measurements of HO₂ and RO₂ radicals were not available for the first 2 weeks of the spring campaign due to a malfunction of the instrument. Daily maximum HO₂ and RO₂ concentrations were in the range of 2 to 4 ×10⁸ cm⁻³ during the spring period and the first half of the summer period. Maximum HO₂ and RO₂ concentrations were 8.0 ×10⁸ and 7.0 ×10⁸ cm⁻³, respectively, during the second half of summer period. In spring and summer, peroxy radical concentrations showed a distinct diurnal pattern. Both HO₂ and RO₂ radical concentrations were suppressed in the early morning (between 04:00 and 07:00 UTC) due to the reaction with elevated NO mixing ratios of up to 1.5 ppbv. Maximum peroxy radical concentrations were usually reached in the afternoon (∼ 14:00), when NO concentrations were lowest.

The measured OH reactivity values were in the range of 4 to 18 s⁻¹. High values were observed between 23 and 31 August due to high emissions of biogenic volatile organic compounds (BVOCs) from plants at high ambient temperatures. The OH reactivity that cannot be attributed to the measured OH reactants was on average 2.5 s⁻¹ (40 %), which is much higher than observed in the winter and autumn periods (Fig. S5). CO and CH₄ contributed 10 % and 4 %, respectively. Due to the high emissions of biogenic organic compounds in spring and summer, the attributed contribution of organic compounds to the total measured OH reactivity was 20 % and the contribution of NO_x was only 19 %, which is much less compared to the winter and autumn periods. Isoprene had the largest contribution among all VOCs, accounting for up to 5 % of the total measured OH reactivity. Unfortunately, the number of detected VOC species in the JULIAC campaign was small (Table S2).

In the JULIAC campaign, nighttime OH concentrations were clearly below the limit of detection of the FZJ CMR–LIF instrument (0.7 ×10⁶ cm⁻³). When all nighttime data are averaged, mean OH concentrations with 1σ standard errors of $(\mathrm{3}\pm \mathrm{1})\times {\mathrm{10}}^{\mathrm{4}}$ and $(\mathrm{5}\pm \mathrm{3})\times {\mathrm{10}}^{\mathrm{4}}$ cm⁻³ are obtained for the spring and summer periods, respectively. These low values support the absence of instrumentally produced OH and indicate very low nocturnal OH production at 50 m height in the absence of NO and solar UV.

Figure 6 Time series of total production and destruction rates of OH, HO₂, RO₂, and RO_X radicals in the spring period of the JULIAC campaign. Vertical dashed lines denote midnight. Grey areas indicate calibration days and days when the chamber roof was closed.

Figure 7 Time series of total production and destruction rates of OH, HO₂, RO₂, and RO_X radicals in the summer period of the JULIAC campaign. Vertical dashed lines denote midnight. Grey areas indicate calibration days and days when the chamber roof was closed. The red boxes denote periods that are discussed in more detail (Case 1 and Case 2).

3.5 Chemical budgets of OH, HO₂, RO₂, and RO_X radicals in the spring and summer periods

Due to the very low photochemical activity observed in autumn and winter, which resulted in radical concentrations close to the detection limit of the instrument, the chemical budget analysis is only discussed for data from the spring and summer periods. It focuses on daytime conditions.

Time series of turnover rates of reactions involving OH, HO₂, RO₂, and RO_X radicals in the spring and summer periods are presented in Figs. 6 and 7, respectively, and median diurnal profiles in Fig. 8. Typical daytime turnover rates of OH, HO₂, and RO₂ radicals were between 3 and 10 ppbv h⁻¹. The rates of RO_X production and destruction ranged from 1 to 3 ppbv h⁻¹, which is 2 to 4 times lower than those of OH, HO₂, and RO₂ because radical conversion reactions cancel out. The highest OH turnover rate of 13 ppbv h⁻¹ was observed on 31 August, when the air temperature in the chamber reached up to 40 ^∘C. Unusually high turnover rates for HO₂, RO₂, and RO_X radicals occurred on 29 April with values of 14, 15, and 4 ppbv h⁻¹, respectively, when the NO mixing ratio exceeded 9 ppbv. For the reasons stated in Sect. 3.1, the HO₂ and RO₂ data on this date are considered highly uncertain and were excluded from further analysis of the chemical budgets.

Diurnal variations of total radical production and destruction rates, as well as of the contributions of the most important reactions, are shown as median values for the entire spring and summer period in Fig. 8. For OH, the reaction of HO₂ with NO (Reaction R10) was the dominant production pathway, contributing more than 70 % to the total production rate in both spring and summer periods. The photolysis of HONO (Reaction R1) was the most important primary OH source during daytime, contributing approximately 20 % to the total OH production. The reaction of HO₂ with ozone (Reaction R11), the photolysis of ozone (Reaction R2), and the ozonolysis of alkenes (Reaction R5) contributed less than 3 % to the total OH production. The maximum median total OH production rate of 3.5 ppbv h⁻¹ was observed in the morning shortly after the peak NO concentration in both spring and summer (Fig. 5). Values gradually decreased until sunset. Median total OH destruction rates were higher than production rates and reached up to 5 and 6 ppbv h⁻¹ at noon in spring and summer, respectively. The contributions of different reactions to the total OH destruction rate are described by the contribution of OH reactants to the OH reactivity (Sect. 3.4, Fig. 5).

Short-lived radicals are expected to be in a steady state, and therefore radical production and destruction rates must be balanced. An imbalance between the calculated rates indicates inaccurate data or a missing radical production or destruction process. The daily peak of the OH production rates was typically lower than the destruction rate by approximately 1.8 ppbv h⁻¹ in the spring and 2.5 ppbv h⁻¹ in the summer period (36 % and 43 % of the total OH destruction rate). These discrepancies are higher than the uncertainty of the calculation (Fig. 8).

80 % of the HO₂ production rate consisted of the reaction of RO₂ with NO (Reaction R9). The remaining part of the HO₂ production rate was due to the photolysis of formaldehyde (9 %) and the reaction of formaldehyde with OH (10 %). Other reactions producing HO₂ played a minor role (<1 %). The HO₂ destruction was mostly due to the reaction of HO₂ with NO (Reaction R10), contributing on average 88 % to the total production rate. The loss due to reaction of HO₂ with RO₂ radicals (Reaction R16) contributed on average 9 % to the total loss.

Median values of the total HO₂ destruction and production rates were well balanced in the spring period, with the production rate being slightly higher than the destruction rate. The maximum difference of 1 ppbv h⁻¹, however, was insignificant compared to the uncertainty of the calculation. A similar tendency but more pronounced feature was observed in summer. Here, the median value of the production rate was higher than that of the destruction rate by 1.8 ppbv h⁻¹ (38 % of the total HO₂ production rate), but differences were variable (Fig. 7). This aspect is discussed in more detail for two periods (Sect. 3.7 and 3.8), which exhibited different degrees of imbalance in the radical budgets.

The RO₂ production rate was dominated by the reaction of VOCs with OH (Reaction R8). The contributions of ozonolysis of measured alkenes to the RO₂ production were very small (less than 1 %). The reaction of RO₂ with NO (Reaction R9) dominated the RO₂ destruction and contributed more than 90 % to the total loss rate. In the late afternoon, the RO₂ termination reaction with HO₂ gained importance with contributions of up to 10 %. Although slight imbalances of up to 1 ppbv were observed in the early morning, the RO₂ production and destruction rates were generally balanced within the uncertainty of calculations in both spring and summer.

Figure 8 Median values of production and destruction rates of OH, HO₂, and RO₂ radicals in the spring and summer periods of the JULIAC campaign, with data from 29 April excluded. In addition, the differences between the destruction and production rates are shown. Grey areas indicate the 1σ uncertainty derived from experimental errors of the measured quantities (Table 2) and of the reaction rate constants (Table 1). The reactions that have insignificant contributions to the production or destruction rates are not shown.

Figure 9 shows the calculated RO_X production and destruction rates. The photolysis of HONO (Reaction R1), HCHO (Reaction R3), and O₃ (Reaction R2) was the dominant process initiating radical chemistry and contributed 45 %, 38 %, and 15 %, respectively, to the total RO_X production rate on average in both periods. In the morning, the reaction of OH with NO₂ (Reaction R12) was the most important radical termination process, contributing up to 65 % to the total RO_X destruction rate. In addition, due to relatively high NO mixing ratios in the early morning, the reactions of OH with NO (Reaction R13) and RO₂ with NO, which yields organic nitrate (Reaction R14), were also significant radical termination processes, contributing 13 % and 17 % to the total RO_X destruction rate, respectively. In the afternoon, radical self-reactions (Reactions R15–R17) and, in particular, the reaction of RO₂ with HO₂ (Reaction R16) dominated the RO_X destruction due to the low NO and NO₂ mixing ratios. In both the spring and summer periods , the total RO_X destruction rate was slightly higher than the production rate, in particular in the afternoon. The imbalance was up to 0.5 ppbv h⁻¹, which is higher than the uncertainty of the calculations.

Meteorological and chemical conditions were variable, especially in the summer period, causing variations in the balance between radical production and destruction rates (Fig. 7 and Table S3). In the following, the chemical budgets with the largest and smallest observed imbalances are discussed: 5–8 August (Case 1) and 22–31 August (Case 2).

Figure 9 Median values of production and destruction rates of RO_X radicals during the spring and summer periods of the JULIAC campaign. In addition, the differences between the destruction and production rates are shown. Grey areas indicate the 1σ uncertainty derived from experimental errors of the measured quantities (Table 2) and of the reaction rate constants (Table 1). The reactions that have insignificant contributions to the production or destruction rates are not shown.

3.5.1 Case 1: 5–8 August 2019

For the period between 5 and 8 August, relatively low NO mixing ratios (maximum: 1 ppbv, median: 0.26 ppbv) and typical summer temperatures for this region (median: 27 ^∘C) were observed (Fig. 10 and Table S3).

As for the whole summer period (Fig. 8), the reactions of peroxy radicals with NO (Reactions R9, R10) dominated the inter-radical conversion reactions of OH, HO₂, and RO₂ in this period (Fig. 10). A significant imbalance between the OH production and destruction rates of up to 3.0 ppbv h⁻¹ (51 % of the total OH destruction rate) is found, which cannot be explained by the uncertainty of the calculations. The total HO₂ production rate was 2.0 ppbv h⁻¹ higher than the destruction rate (48 % of the total HO₂ production rate), whilst the RO₂ production and destruction rates were well balanced. Relatively small but nevertheless significant differences between RO_X production and destruction rates (0.5 ppbv h⁻¹) were observed during daytime (Fig. 11).

Figure 10 Production and destruction rates of OH, HO₂, and RO₂ radicals for Case 1 (5–8 August 2019) and Case 2 (22–31 August 2019). In addition, the differences between the destruction and production rates are shown. Grey areas give the 1σ uncertainty derived from experimental errors of the measured quantities (Table 2) and of the reaction rate constants (Table 1). The reactions that have insignificant contributions to the production or destruction rates are not shown.

3.5.2 Case 2: 22–31 August 2019

During the period from 22 to 31 August, the temperature was generally high and reached a maximum value of 42 ^∘C inside the chamber. The concentrations of the radical precursors (HONO, HCHO, and O₃) were higher than those observed in Case 1 (Table S3). Ozone mixing ratios reached values up to 100 ppbv, while daytime NO mixing ratios were similar as in Case 1 (<1.5 ppbv, median value of 0.22 ppbv). The conditions outside the chamber were characterized by stagnant air (wind speed <4 m s⁻¹ at 50 m height) with no precipitation. At these conditions, vigorous biogenic emissions can be expected (Vilà-Guerau de Arellano et al., 2009; Sarkar et al., 2020). Enhanced biogenic VOC emissions and their photochemical degradation can therefore explain the higher VOC and HCHO concentrations in Case 2 compared to the cooler period at the beginning of the month (Table S3). The larger VOC reactivity and comparable OH concentrations resulted in HO₂ and RO₂ concentrations that were approximately 2 to 3 times higher than in Case 1 (Table S3).

Imbalances between the radical production and destruction rates were a factor of 2 smaller in the warmer and more photochemically active period of Case 2 compared to Case 1. OH destruction rates were up to 1.5 ppbv h⁻¹ (25 % of the total OH destruction rate) higher than the total production rate (Fig. 10). The HO₂ production and destruction rates agree within ± 1 ppbv h⁻¹. The contributions from photolysis of HCHO and the reaction of HCHO with OH to the HO₂ production rate were larger compared to other periods with values of up to 15 % and 13 %, respectively, due to high HCHO mixing ratios of up to 8 ppbv (Fig. 2). The RO₂ production and destruction rates showed imbalances up to 1.5 ppbv h⁻¹ in the late afternoon.

While HONO photolysis was the dominating RO_X source most of the time in spring and summer (Fig. 9), HO₂ production from the photolysis of HCHO was the most important primary radical source in Case 2 due to the high concentration of HCHO (Fig. 11). Although the chemical budgets for each radical species were essentially closed within the experimental uncertainty, the total loss rate of RO_X was consistently higher than the production rate during daytime. The deviation was higher than the experimental uncertainty and reached a maximum value of 1.4 ppbv h⁻¹ at noontime.

Figure 11 Production and destruction rates of RO_X for the periods of the case studies (Case 1 and Case 2). In addition, the differences between the destruction and production rates are shown. Grey areas indicate the 1σ uncertainty derived from experimental errors of the measured quantities (Table 2) and of the reaction rate constants (Table 1). The reactions that have insignificant contributions to the production or destruction rates are not shown.

3.5.3 NO dependence of radical production and destruction rates

One of the most influential parameters for the radical chemistry is the concentration of NO, since the reaction with NO dominates the conversion rate of RO₂ to HO₂ (Reaction R10) and HO₂ to OH (Reaction R9) (Fig. 10). Figure 12 shows the NO dependence of median values of the calculated production and destruction rates for the different radicals for the spring and summer period.

For OH, the production rates are consistently lower than the destruction rates by about 1.5 ppbv h⁻¹ for NO mixing ratios lower than 1 ppbv NO. At higher NO, the OH budget is balanced within the experimental uncertainty. For HO₂, an inverse pattern is observed. Below 1 ppbv NO, the production rate is higher than the destruction rate by about 1 ppbv h⁻¹. Only for lowest NO mixing ratios are the production and destruction rates balanced. For NO mixing ratios above 1 ppbv, the chemical budget of HO₂ is essentially closed. For NO mixing ratios of 3.5 ppbv, the difference between the production and destruction rate is noticeably high (more than 4 ppbv h⁻¹) but also has large uncertainty. For RO₂ radicals, the chemical budget is closed for NO mixing ratios below 1 ppbv, but an increasing discrepancy between the loss and production rates is observed with increasing NO mixing ratios. While the production rate is relatively constant at a value of 2.5 ppbv h⁻¹, the loss rate increases to values of up to 7.5 ppbv h⁻¹ at 3.5 ppbv NO. The budget of RO_X, in which radical interconversion reactions cancel out, is mostly balanced over the whole range of NO. Only for the lowest and highest NO mixing ratios is the destruction rate 0.6 ppbv h⁻¹ higher than the production rate.

Figure 12 NO dependence of median production and destruction rates of OH, HO₂, RO₂, and RO_X radicals. Median values include all data from the spring and summer periods of the JULIAC campaign (NO intervals: ln(NO) = 0.4 ppbv). Vertical bars represent the 1σ uncertainty from experimental errors of the measured quantities (Table 2) and of the reaction rate constants (Table 1). The number of data points in each NO bin is represented on the top panel.

4 Discussion

4.1 Discrepancies in the chemical budgets of radicals

The highest imbalances in the chemical budgets of radicals are found for OH radicals. In spring and summer, their production rate was consistently lower than the loss rate (Fig. 8). This deficit was largest at the beginning of August (Case 1, Fig. 10) when the discrepancy reached (3.0 ± 1) ppbv h⁻¹.

Imbalances in the radical budgets can be observed for different reasons. They can be caused by missing processes or incorrect rate constants in the calculations of the production or destruction rates (Sect. 4.2). It is also possible that measured concentrations that are used for the calculation contain unknown errors. The technically difficult radical measurements have a large potential for artifacts (Hofzumahaus and Heard, 2016). Precautions were taken to minimize measurement interferences for OH and HO₂ in this campaign.

• The measurements of OH by the LIF instrument were interference-corrected using chemical modulation and agreed with simultaneous OH measurements by the DOAS instrument within the experimental uncertainties. The measured OH reactivity quantifies the total chemical loss rate of OH caused by atmospheric reactants and has a total accuracy of 10 %. Thus, the destruction rate of OH, which is the product of the concentration and reactivity of OH, is known within 20 % and is unlikely to be biased by unknown OH interferences or unknown atmospheric reactants.

• The O_x production rate calculated from the reaction of peroxy radicals with NO agrees with the measured increase in O_x concentrations within ± 1 ppbv h⁻¹ for most conditions (Sect. 3.1). As more than 70 % of the OH production is due to the reaction of HO₂ with NO (Reaction R10), a bias of more than 1 ppbv h⁻¹ due to an HO₂ measurement error that is unaccounted for seems unlikely.

• The analysis of the chemical budget of OH in previous chamber experiments performed at various chemical conditions showed no evidence for a missing OH source originating from chamber wall effects (Kaminski et al., 2017; Fuchs et al., 2018; Novelli et al., 2018; Rolletter et al., 2019; Rolletter et al., 2020).

Thus, there is no evidence for instrumental errors that are not included in the estimated errors of the calculated turnover rates. The observed imbalances in the OH budget of up to 3 ppbv h⁻¹ are therefore most likely due to a missing OH source.

The missing OH production is correlated with the imbalance in the HO₂ budget, for which the production rate is larger than the loss rate at low NO mixing ratios (Fig. 12). This is most clearly seen in the period of Case 1, when the discrepancy reaches (2.0± 1) ppbv h⁻¹ (Fig. 10). The production rate of HO₂ is nearly equal to the RO₂ loss rate ($P_{{\mathrm{HO}}_{\mathrm{2}}}\approx D_{{\mathrm{RO}}_{\mathrm{2}}}$) because both are controlled by the reaction of RO₂ with NO (Reaction R9). Furthermore, the RO₂ loss rate is well balanced by the RO₂ production rate within the experimental uncertainty of ± 1 ppbv h⁻¹ (Figs. 8 and 10). Thus, there is no hint that the calculated turnover rate of the RO₂+ NO reaction had a bias higher than 1 ppbv h⁻¹. In addition, turnover rates of the reactions of HO₂ and RO₂ with NO, producing ozone, are consistent with the observed O_x increase in the chamber (Sect. 3.1). This suggests that these rates are correct in the chemical budget analysis. For the above reasons, the discrepancy between HO₂ production and destruction rates is most likely due to a missing HO₂ loss process and not measurement errors of HO₂, RO₂, or NO.

RO_X destruction rates are generally higher than the production rates, but differences are on average lower than 0.5 ppbv h⁻¹ (Fig. 9). In the periods of Case 1 and Case 2, the corresponding discrepancies reach 0.5 and 1.4 ppbv h⁻¹, respectively (Fig. 10). If these discrepancies were due to a missing primary OH source, they could also explain a small part (17 %) of the imbalance in the chemical OH budget in Case 1 and the complete imbalance in the OH budget in Case 2.

It is difficult to identify the exact cause of the differences in OH and HO₂ budgets observed for Case 1 and 2 with only the available data. Case 2 was characterized by high temperature with increased BVOC emissions and high levels of HCHO (Table S3). No clear correlation was found between the ratio of the production and destruction rates of the radicals and the concentration of chemical species such as NO, NO₂, O₃, and HCHO. A weak correlation was observed with temperature with an improved balance in the budgets the higher the temperature was. This could indicate that the processes that are unaccounted for become less competitive for high radical turnover rates with chemical conditions being dominated by organic compounds from biogenic emissions.

In conclusion, the radical budget analysis suggests the presence of a missing OH source and a missing HO₂ loss process with a similar turnover rate at NO mixing ratios below 1 ppbv for typical temperatures in summer. The opposing imbalances in the OH and HO₂ budgets could be due to an unknown mechanism that converts HO₂ to OH, or they could indicate a missing primary OH source and a similar fast, but independent, termination reaction removing HO₂. The remaining imbalance in the RO_X budget would be consistent with a primary OH source that is unaccounted for. This fits the observations best in Case 2, which is characterized by high temperatures and VOC emissions.

For NO mixing ratios that are higher than 1 ppbv, production and destruction rates of OH and HO₂ radicals are generally balanced (Fig. 12). An exception is observed for HO₂ for the highest NO mixing ratios of 3.5 ppbv, for which the production rate is 3.5 ppbv h⁻¹ higher than the loss rate.

For RO₂, the radical budget is not closed, but the loss rate increases with NO in contrast to the production rate. The difference reaches a value of 5 ppbv h⁻¹ at 3.5 ppbv NO. In the same range of NO mixing ratios, the odd oxygen production rate ($P_{{\mathrm{O}}_x}$) calculated by peroxy radicals (Eq. 14) overestimates the observed increase in the O_x mixing ratio by about 3 ppbv h⁻¹. This difference points to a systematic error in the peroxy radical measurements, explaining a considerable part of the imbalance in the RO₂ budget. A reduction of the RO₂ concentration by 3 ×10⁷ cm⁻³ would reduce the HO₂ production rate by 3 ppbv h⁻¹ and resolve the discrepancy in the odd oxygen production calculations for the highest NO mixing ratio. The presumed bias in the RO₂ measurement may be caused by an incorrect background subtraction that becomes most relevant at high NO concentrations (Sect. 3.1). However, even after correction of this bias a discrepancy in the RO₂ budget would remain, requiring an additional RO₂ source of approximately 2 ppbv h⁻¹ to be balanced.

Further information on the nature of the missing RO₂ source can be obtained from the chemical budget of RO_X, for which the production rate is 0.5 ppbv h⁻¹ smaller than the loss rate at 3.5 ppbv NO (Fig. 12). This discrepancy cannot be explained by the instrumental uncertainties in HO₂ and RO₂ measurements because the RO_X budget at high NO in the morning was dominated by OH reactions with NO₂ and (Fig. 9). Thus, the imbalance in the RO_X budget at high NO indicates a missing primary radical source, which on a single day (29 April) even reached 3 ppbv h⁻¹ (Fig. 6). As the OH budget is balanced most of the time and the corresponding HO₂ budget does not require an additional HO₂ source, a missing primary RO₂ source is a likely explanation for the discrepancy in the RO_X budget. This would also explain part of the imbalance in the RO₂ budget at high NO concentrations.

4.2 Potentially missing chemical processes

The above discussion shows that imbalances between calculated production and destruction rates are highly variable over time and change with chemical conditions. As main general features in spring and summer, the radical budget analysis indicates OH production processes that are unaccounted for with a typical strength of 1.5–3 ppbv h⁻¹ at low NO concentrations, which coincides with a missing HO₂ sink of 1–2 ppbv h⁻¹. At high NO mixing ratios (> 1 ppbv), the radical budgets for OH and HO₂ radicals are relatively well balanced, but RO₂ production processes of about 2 ppbv h⁻¹ appear to be missing in the RO₂ radical budget. In the following, potential reasons for the observed discrepancies in the radical budgets are discussed.

4.2.1 Differences in the chemical behavior of specific RO₂ radicals

As no speciated RO₂ radicals were detected but the sum of all RO₂ species, effective rate coefficients for the reaction of all RO₂ species with NO (Reactions R9, R14), RO₂ (Reaction R15), and HO₂ (Reaction R16) are used from the structure–activity relationship (SAR) by Jenkin et al. (2019) for the calculations of turnover rates. Potential systematic errors due to this simplification for reactions of RO₂ with RO₂ and HO₂ are expected to be negligible due to their small contributions to the total turnover rates.

In contrast, the reaction of RO₂ with NO plays an important role in the chemical budgets of HO₂ and RO₂. The reaction has one channel that converts RO₂ to HO₂ (Reaction R9) and one radical termination channel that produces organic nitrates (RONO₂) (Reaction R14). The unknown speciation of RO₂ causes uncertainty with respect to the total rate constant of the RO₂+ NO reaction (k₉+k₁₄). An effective value of $\mathrm{9}\times {\mathrm{10}}^{-\mathrm{12}}$ cm⁻³ s⁻¹ was taken from Jenkin et al. (2019). A high limit for the total rate coefficient of RO₂+ NO (for example, $\mathrm{1.1}\times {\mathrm{10}}^{-\mathrm{11}}$ cm⁻³ s⁻¹ at 298 K for c-C₅H₉O₂) would slightly increase the imbalances between production and destruction rates for HO₂ and RO₂ radicals by 13 % for both spring and summer. A lower limit would be the rate constant of the reaction of methyl peroxy radicals (CH₃O₂) with NO having a value of $\mathrm{7.7}\times {\mathrm{10}}^{-\mathrm{12}}$ cm⁻³ s⁻¹ (298 K). Applying this number in the calculations for HO₂ production and RO₂ destruction rates (Fig. S6) for the period when observed discrepancies in the HO₂ budget were highest (Case 1) further improves the already well-balanced budget of RO₂ radicals. This also reduces the imbalance between HO₂ destruction and destruction rates, but the effect is rather small (approximately 10 %) and not sufficient to explain the total difference. For the other periods such as the spring period and the period of Case 2, a reduced reaction rate would worsen the observed imbalances.

An additional uncertainty in the HO₂ production rate comes from the assumed yield of organic nitrates in the reaction of RO₂ with NO. Typical organic nitrate yields range from 5 % to 20 % (Jenkin et al., 2019). The low-limit value is applied in the calculations above. Using a value of 20 % decreases the discrepancy between HO₂ production and destruction rates from 2.0 to 1.5 ppbv h⁻¹ for the period of Case 1.

It is worth noting that the organic nitrate yield is generally higher for larger hydrocarbons, but the rate constant for the RO₂+ NO reaction is also often higher so that there are compensating effects in the production efficiency of HO₂. In addition, it is expected that only a fraction of RO₂ radicals produced from large hydrocarbons due to the major composition of RO₂ would be methyl peroxy radicals.

For the above reasons, the unknown speciation of RO₂ is unlikely to be the reason for the observed imbalances in the HO₂ budget that are most prominent in the period of Case 1.

4.2.2 Missing primary radical sources

Primary RO_X radical production that may not be appropriately accounted for in the calculations could be OH, HO₂, and RO₂ production from the ozonolysis of alkenes. Only a few alkene compounds were measured in the JULIAC campaign. The contribution from the ozonolysis of these alkenes to the radical production was very small with values in the range of 0.005 to 0.03 ppbv h⁻¹ (Sect. 3.5). The ozonolysis of small alkenes such as propene and cis-2-butene that were not measured but are often abundant, for example, in forested areas (Goldstein et al., 1996; Rhew et al., 2017) may have significantly contributed to the radical production.

The potential impact of unmeasured alkenes on the primary radical production is tested by assuming that the OH reactivity that cannot be explained by measured OH reactants (on average, 2.5 s⁻¹) originates from 1.5 ppbv propene and 1.0 ppbv cis-2-butene. The radical production by ozonolysis of the additional propene and cis-2-butene increases the production from ozonolysis of measured species by more than an order of magnitude in both the spring and summer periods of the JULIAC campaign (Fig. S7). The discrepancies between the total RO_X production and destruction rates are significantly decreased for the period of 2 Case by approximately 0.2 ppbv h⁻¹. However, the additional OH production is by far insufficient to explain the missing OH source that was generally found during the JULIAC campaign. In addition, the corresponding OH and O₃ reactivity from the additional alkene compounds is about a factor of 6 larger than of alkenes (e.g., ethene, propene, trans-2-butene, cis-2-pentene) that were measured in ambient air next to the SAPHIR chamber in the HOxComp campaign in July 2005 (Elshorbany et al., 2012; Kanaya et al., 2012).

The photolysis of oxygenated organic compounds is another source for radicals that could be underestimated in the calculations. Only the photolysis of HCHO is included in the production rate of HO₂ and RO_X at all times of the campaign. In addition, acetaldehyde (CH₃CHO), methyl vinyl ketone (MVK), methacrolein (MACR), and methylglyoxal were measured during part of the campaign and were not included in the analysis in Sect. 3. Calculations show that the radical production rate from their photolysis was less than 0.1 ppbv h⁻¹. Thus, photolysis of unmeasured OVOCs was very likely unimportant in the present study. This is consistent with similar small contributions from photolysis of OVOCs other than HCHO found in the HOxComp campaign (Kanaya et al., 2012). In addition, during the HOxComp campaign the modeled OH reactivity could be matched with the measured reactivity by including either additional primary emissions (Kanaya et al., 2012) or model-produced oxygenated secondary products (Elshorbany et al., 2012). Neither of the additional species contributed enough to close the radical budgets. If it is assumed that the missing OH reactivity (2.5 s⁻¹) is all due to glyoxal (9 ppb), additional OH production of 0.3 ppb h⁻¹ could be expected. This would still not be enough to close the radical budget, suggesting that unmeasured OVOCs do not play a large role.

The photolysis of ClNO₂ constitutes a primary radical source (Reactions R20, R22) that can be found in coastal environments (e.g., Osthoff et al., 2008) and mid-continental regions (e.g., Thornton et al., 2010). The availability of ClNO₂ data during the summer period allowed assessing the potential impact of its photolysis on the RO₂ radical production (Eq. 9). Due to the low mixing ratio of ClNO₂ of less than 0.4 ppbv (Tan et al., 2022), the RO₂ production from Cl oxidation processes was insignificant (<0.1 ppbv h⁻¹) and cannot explain the observed discrepancies in the primary production and destruction rates of radicals in the summer period and in the case studies. The instrument detecting ClNO₂ was not available in the spring period of the campaign. Therefore, the extent to which ClNO₂ photolysis contributed in spring, for example to the large missing RO_x source (up to 3 ppbv h⁻¹) on 29 April, remains unknown.

4.2.3 Missing radical termination reactions

Heterogeneous uptake of HO₂ on aerosol is a potential termination reaction that is not included in the HO₂ and RO_X destruction rates above. However, the impact of including the heterogeneous HO₂ loss on an aerosol surface (Reaction 8) on the total loss rate is insignificant (less than 1 %), even if a high effective uptake coefficient of 0.2 is assumed (Fig. S7).

As HO₂ uptake is a radical termination process, its relative contribution to the total RO_X loss rate can be higher compared to the relative contribution to the total HO₂ loss rate. However, the only notable influence would be for the period of Case 2 (8 % of total RO_X loss rate), when the aerosol surface area concentration was high with values of up to 3.0 ×10² µm² cm⁻³.

The estimate for the heterogeneous HO₂ loss rate has high uncertainty because the uptake coefficient highly depends on the aerosol properties that were not fully characterized in this campaign. Previous laboratory investigations showed large variability for the uptake coefficient with values ranging from 0.08 to 0.6 depending on the aerosol chemical composition and the physical state (George et al., 2007; Taketani et al., 2008, 2009; George et al., 2013; Lakey et al., 2015; Song et al., 2020; Tan et al., 2020). Even the largest reported HO₂ uptake coefficients cannot explain the observed differences in the chemical budget of HO₂ radicals. Therefore, heterogeneous HO₂ reactions can be ruled out as an explanation for the unexplained HO₂ loss rate.

4.2.4 Missing radical interconversion reactions

In the last decade, it has been discovered that unimolecular reactions of RO₂ can significantly increase atmospheric OH concentrations in low-NO environments where they can compete with the reaction of RO₂ with NO. The most important, atmospherically relevant example is the production of OH from the isomerization of isoprene–RO₂ radicals (Peeters et al., 2009; da Silva et al., 2010; Peeters and Müller, 2010; Crounse et al., 2011; Fuchs et al., 2013; Peeters et al., 2014; Teng et al., 2017; Novelli et al., 2020). The SAPHIR chamber is surrounded by a deciduous forest that emits isoprene, especially in summer. Compared to previous campaigns on the campus wherein up to several parts per billion by volume of isoprene were measured (Komenda et al., 2003; Spirig et al., 2005; Kanaya et al., 2012), concentrations were relatively low during the JULIAC campaign (<0.4 ppbv on average).

The effect of the conversion of RO₂ to OH by the isomerization of isoprene–RO₂ (Eq. 4) is tested in the analysis of the OH and RO₂ budgets. In the afternoon of days in the spring period and the period of Case 2, the total OH production increases only 1 % due to the low isoprene mixing ratios (<0.2 ppbv) and the competition of unimolecular reactions with bimolecular reactions of RO₂ with NO. Even in the summer period, when isoprene mixing ratios were up to 0.8 ppbv, the contribution of isomerization reactions from isoprene–RO₂ radicals to the total turnover rate of RO₂ is still small with values of less than 4 %. This implies that unimolecular decomposition reactions of isoprene–RO₂ radicals made a minor contribution to the RO₂ destruction and OH production rates.

Another known isomerization process that produces OH applies to RO₂ formed by OH oxidation of methacrolein (MACR) (Crounse et al., 2012; Fuchs et al., 2014), which is an oxidation product of isoprene. MACR mixing ratios were up to 0.5 ppbv in the JULIAC campaign. Because the rate constant for the OH reaction of MACR is smaller than for isoprene, OH regeneration from MACR-RO₂ radicals is even less important than from isoprene–RO₂.

For acyl and carbonyl peroxy radicals it was shown that the reaction of RO₂ with HO₂, which mainly forms hydroperoxides (ROOHs) (Reaction R16), can produce OH with yields up to 80 % (Hasson et al., 2004; Dillon and Crowley, 2008; Groß et al., 2014; Praske et al., 2015; Winiberg et al., 2016; Fuchs et al., 2018; Jenkin et al., 2019). It is also noteworthy that the rate constant for the reaction of HO₂ with this class of RO₂ species is almost a factor of 2 higher than for other RO₂ species (Jenkin et al., 2019). However, even if it is assumed that all the measured RO₂ constitutes acyl and carbonyl peroxy radicals, the formation of OH from their reaction with NO could only explain up to 0.5 ppbv h⁻¹ of the imbalances in both OH and HO₂ budgets.

Studies in the remote marine boundary layer show that HO₂ to OH conversion mediated by halogen oxides (XO, X= Cl, Br, I) (e.g., Bloss et al., 2005; Sommariva et al., 2006; Kanaya et al., 2007; Stone et al., 2018; Fan and Li, 2022) can significantly contribute to the interconversion of radicals and destroy ozone.

$$\begin{array}{}\text{(R23)}& {\displaystyle }{\mathrm{HO}}_{\mathrm{2}}+X\mathrm{O}& {\displaystyle }\to \mathrm{HO}X+{\mathrm{O}}_{\mathrm{2}}\text{(R24)}& {\displaystyle }\mathrm{HO}X+hv& {\displaystyle }\to \mathrm{OH}+X\text{(R25)}& {\displaystyle }X\mathrm{O}+\mathrm{NO}& {\displaystyle }\to {\mathrm{NO}}_{\mathrm{2}}+X\text{(R26)}& {\displaystyle }X+{\mathrm{O}}_{\mathrm{3}}& {\displaystyle }\to X\mathrm{O}\end{array}$$

This conversion mechanism would only be effective at low NO, when the consumption of XO by NO (Reaction R25) is comparatively slow and when X is not depleted by other reactions as in the case of Cl by reactions with VOCs (Reaction R22).

For BrO, the rate constants for Reactions (R23) and (R25) are about the same ($\mathrm{2.1}\times {\mathrm{10}}^{-\mathrm{11}}$ cm⁻³ s⁻¹ at 298 K; Burkholder et al., 2019). Thus, the reaction of BrO with HO₂ would only be dominant if the NO concentration were smaller than the concentration of HO₂, i.e., less than 10 pptv in this campaign. For IO, the situation is similar and NO mixing ratios would need to be less than 40 pptv. Such low NO mixing ratios were not observed during daytime and rule out significant halogen-oxide-mediated HO₂ to OH conversion. The required XO concentrations to achieve an HO₂ loss rate of 1 ppbv h⁻¹ at an HO₂ concentration of 2 ×10⁸ cm³ would be 66 pptv of BrO or 16 pptv of IO, which exceeds the abundances reported for marine environments, where halogen sources are known to exist, by more than an order of magnitude. For these reasons, halogen oxide chemistry cannot explain the missing HO₂ sink and missing OH source in this study.

4.3 Comparison with results from other field campaigns

Although the chemical and physical conditions were partly influenced by the chamber properties (Sect. 2.1), the radical concentrations observed during spring and summer were within the range of values that have been observed in other field studies in summertime in urban and suburban areas (Tan et al., 2001; Ren et al., 2003; Kanaya et al., 2007; Mao et al., 2010; Lu et al., 2013; Brune et al., 2016; Tan et al., 2017; Whalley et al., 2018; Tan et al., 2019). The impact of the decreased solar radiation by the chamber transmission on the radical production was compensated for by the radical production from the photolysis of HONO and HCHO emitted from the chamber film.

This effect is also shown in the relationship between the OH concentration and the photolysis frequencies of ozone, $j_{{\mathrm{O}}^{\mathrm{1}}\mathrm{D}}$ (Sect. 3.4). The slope (8.0 ×10¹¹ cm⁻³ s⁻¹) of the correlation for the data from the JULIAC campaign is much higher than obtained for data in other field campaigns in similar environments (Ehhalt and Rohrer, 2000; Handisides et al., 2003; Holland et al., 2003; Tan et al., 2017) due to the high OH production by the photolysis of chamber-produced HONO (Reaction R1). This is further confirmed by the similarity in OH and HO₂ radical concentrations between this campaign and what was observed in the HOxComp campaign when measurements were performed in front of the SAPHIR chamber for 3 d in July 2005 (Elshorbany et al., 2012).

In contrast, daytime OH concentrations observed during winter and autumn in the JULIAC campaign were lower than OH concentrations observed in previous wintertime field campaigns (Heard et al., 2004; Ren et al., 2006; Kanaya et al., 2007; Tan et al., 2018; Ma et al., 2019). This is due to the lower photolysis frequencies in the chamber compared to outside, which is not compensated for by chamber-produced HONO in wintertime because the emission strength is low at low temperature and low solar radiation.

The very low nighttime OH concentration in all seasons of the JULIAC campaign (Sect. 3.4) is consistent with observations in previous field campaigns in rural areas in Germany (Ehhalt and Rohrer, 2000; Handisides et al., 2003; Holland et al., 2003), in which nighttime OH concentrations were less than 1 ×10⁵ cm⁻³. However, in several other field studies performed in urban areas, nighttime OH concentrations were in the range of 0.2 to 3 ×10⁶ cm⁻³, for example in China (Lu et al., 2014; Rohrer et al., 2014; Tan et al., 2017, 2018; Ma et al., 2019; Tan et al., 2019; Wang et al., 2019; Whalley et al., 2021), in the US (Martinez et al., 2003; Brune et al., 2016; Griffith et al., 2016), and in the UK (Ren et al., 2003; Vaughan et al., 2012). In these studies, the high nighttime OH concentrations could not be explained by model predictions and raised questions about the presence of potential interference in nighttime OH signals measured by LIF instruments (Mao et al., 2012; Lu et al., 2014; Novelli et al., 2014).

Similar studies investigating the chemical budgets of OH, HO₂, RO₂, and RO_X radicals like in this study were performed for data from field campaigns in a suburban area in the Pearl River Delta (PRD), China, in autumn 2014 (Tan et al., 2019), and in central Beijing, China (Whalley et al., 2021), in summer 2017.

Tan et al. (2019) observed median values of turnover rates of OH, HO₂, and RO₂ radicals ranging from 10 to 15 ppbv h⁻¹, while rates for RO_X initiation and termination were on the order of 3 to 4 ppbv h⁻¹ during daytime for chemical conditions affected by anthropogenic emissions. From the comparison between the radical production and destruction rates, a missing OH source and a missing RO₂ sink with a similar rate up to 7 ppbv h⁻¹ (45 % of the total OH turnover) were found at low NO mixing ratios below 1 ppbv, while HO₂ production and destruction rates were balanced. The authors suggested that an additional chemical mechanism is required that efficiently converts RO₂ to OH without the involvement of NO. One possibility proposed by Tan et al. (2019) is that HO_X radicals are formed from the auto-oxidation of specific RO₂ species which include multifunctional groups such as -OH, -OOH, or -CHO groups.

The analysis of the chemical budget of OH radicals in the JULIAC campaign shows that an OH source that is unaccounted for with a rate ranging between 2 and 3 ppbv h⁻¹ (about 50 % of the total OH destruction rate) is required at low NO mixing ratios to balance OH production and destruction rates. This rate is smaller than the rate determined in Tan et al. (2019). However, considering that the OH radical turnover rates in the JULIAC campaign were about half compared to values in the campaign in the PRD area, the relative importance of the unaccounted for OH source was comparable in both campaigns. However, the mechanism suggested by Tan et al. (2019) is likely not the only explanation for discrepancies in the radical budgets observed in this study. In the JULIAC campaign, to balance the budget of RO₂ radicals requires an additional radical source rather than additional loss processes, particularly at high NO mixing ratios above 1 ppbv, and the missing OH sources likely originate from an HO₂ to OH conversion process and/or a missing primary OH source.

Whalley et al. (2021) also investigated the chemical budgets for radicals over a wide range of NO mixing ratios (0.1 to 104 ppbv) from measurements performed in central Beijing, China. Compared to the results in Tan et al. (2019) and results in this study, the rates of RO_X initiation and termination reactions were 2 to 4 times higher. Also, the rates of radical propagation reactions for OH, HO₂, and RO₂ radicals were 5 to 10 times higher due to fast inter-radical conversion reactions at conditions with high concentrations of NO. Similar to the results in this study, an OH source with a high rate of up to 15 ppbv h⁻¹ (50 % of the total OH destruction) was required to balance OH production and destruction rates for low NO mixing ratios. This unaccounted for OH source is more than 3 times higher than that determined in the JULIAC campaign and in the campaign in China reported by Tan et al. (2019). The HO₂ production rate observed in Beijing largely exceeded the destruction rate by 3 to 5 times for low NO mixing ratios. In contrast, production and destruction of RO₂ and RO_X radicals were well balanced. On the other hand, for results in conditions of low NO concentrations, production and destruction of OH radicals were balanced at high NO mixing ratios, while very high imbalances of up to 50 ppbv h⁻¹ were observed for HO₂ and RO₂ radicals. Whalley et al. (2021) showed that reducing the rate constant of the reaction between RO₂ and NO by a factor of 10 could close the gaps between production and destruction rates. The authors suggested that the presence of a significant fraction of RO₂ radicals from the oxidation of large and multifunctional VOCs such as monoterpenes and long-chain alkanes could explain observations. These radicals can undergo multiple RO₂ to RO₂ conversion reactions by unimolecular isomerization of alkoxy radicals (RO), which are formed from the reaction of RO₂ with NO so that no HO₂ is produced. Such an RO₂ radical reaction chain would be equivalent to an increased chemical lifetime of RO₂ radicals if RO₂ species cannot be distinguished by instruments like in the sum measurements performed by RO_X–LIF instruments. Whalley et al. (2021) showed that RO₂ production by this mechanism would largely reconcile discrepancies between modeled and measured RO₂ concentrations (the model–measurement ratio decreases from 6.2 to 1.8) if the OH reactivity that could not be accounted for by measured OH reactants is attributed to α-pinene.

Applying a reduced rate constant for RO₂ to HO₂ propagation reactions as suggested in Whalley et al. (2021) in the calculations in this study could help explain the observed discrepancies between HO₂ and RO₂ production and destruction rates. The largest effect is expected when high NO mixing ratios up to 10 ppbv like on 29 April are experienced. In this case, a large reduction of the rate constant by a factor of 2 for all measured RO₂ would be required to close the observed gaps between production and destruction rates. Reduced reaction rate constants of the RO₂+ NO reaction could be expected for RO₂ from large VOCs. However, the fraction of these RO₂ species is expected to be small for conditions of this campaign, even if OH reactivity that is not explained by measured OH reactants is attributed to large VOCs. Therefore, it seems unlikely that the mechanism suggested by Whalley et al. (2021) affects the observed discrepancies in the radical budgets in this study.

It is interesting to point out that similar discrepancies in the OH and HO₂ budgets were observed during the HOxComp campaign in July 2005 (Elshorbany et al., 2012). Although measurements were only done for 3 d and despite the fact that these were 14 years earlier than measurements in this work, the chemical composition was similar with comparable values of NO_x, O₃, isoprene concentrations, and OH reactivity. As observed in this study, a missing OH radical source in the range of 2 to 4 ppbv h⁻¹ was needed to close the OH budget for low-NO chemical regimes. The lack of measured RO₂ radicals did not allow performing a measurement-only budget for HO₂ radicals. Nevertheless, model calculations overestimated measured HO₂ radicals after the correction for RO₂ radical interference (Fuchs et al., 2011) by up to 30 % at low NO (Elshorbany et al., 2012; Kanaya et al., 2012). Like in this study, good agreement was found between modeled and measured OH and HO₂ radical concentrations only if an unknown loss process for HO₂ radicals that would recycle OH was introduced.

4.4 Potential role of the missing radical processes in the evaluation of the ozone production rate

The good agreement of the odd oxygen production rates calculated by the two different methods (Sect. 3.1) not only gives high confidence in the measured peroxy radical concentrations but also confirms the current chemical understanding of tropospheric ozone formation from the reaction of peroxy radicals with NO. Therefore, results demonstrate that accurate predictions of radical concentrations in atmospheric models are crucial to accurately predict the surface ozone level.

However, the significant level of missing radical processes found in this study implies difficulties in the prediction of radical concentrations by models without constraining radicals by their measurements. In low NO mixing ratios, there are two opposing effects of the missing radical processes on the O₃ formation. At first, a missing OH source and therefore an underestimation of OH concentrations by the models would lower the loss of NO₂ by the reduced reaction rate with OH and essentially produce more O₃ by its photolysis. Furthermore, the production of RO₂ would be underpredicted due to the lower OH concentrations in the models. At the same time, an unexplained HO₂ sink would result in the overprediction of HO₂ concentrations and thus O₃ production. In high-NO environments, missing RO₂ and RO_X production processes would result in an underestimation of the O₃ production.

5 Summary and conclusions

Ambient measurements of atmospheric radicals, trace gases, and aerosol properties were performed during the Jülich Atmospheric Chemistry (JULIAC) project campaign using the atmospheric simulation chamber SAPHIR at Forschungszentrum Jülich, Germany. Ambient air was continuously drawn at a high rate into the chamber (1 h residence time) through a 50 m high inlet line for 1 month in each season throughout 2019.

For parts of the campaign, measurements of OH concentrations were achieved by two different methods, laser-induced fluorescence with a chemical modulation system for zeroing (FZJ LIF–CMR) and differential optical absorption spectroscopy (FZJ DOAS). Measurements of both instruments agreed within 11 % (Cho et al., 2021).

The production rate of odd oxygen (O_x) was determined by using either measured HO₂ and RO₂ concentrations or O₃ and NO₂ concentrations measured in the chamber and in the incoming flow. Results showed excellent agreement between the two different methods, confirming that HO₂ and RO₂ are responsible for the formation of tropospheric O₃ and giving additional confidence to the reliability of peroxy radical concentration measurements performed in the JULIAC campaign.

An analysis of the chemical budgets of OH, HO₂, RO₂, and RO_X radicals was performed for data obtained in the spring and summer periods of the campaign. On average, daytime radical turnover rates ranged between 3 and 6 ppbv h⁻¹ and between 4 and 10 ppbv h⁻¹ in spring and summer, respectively, for OH, HO₂, and RO₂ radicals, while total rates of RO_X initiation and termination reactions were below 2.0 ppbv h⁻¹. For most conditions, radical production and destruction rates highly depended on the turnover rate of the reaction of peroxy radicals with NO. For the total turnover rate of the sum of all radicals (RO_X), the photolysis of HONO and HCHO contributed most to the primary radical production, and the reactions of OH with NO₂ and RO₂ with HO₂ dominated the radical termination processes.

Differences between radical production and destruction rates were often small and below the accuracy of the calculations in the JULIAC campaign in winter and autumn. However, for both spring and summer, an additional OH source is required to explain the observed discrepancy between production and destruction rates. The OH production rate of this source would need be on average 2 and 3 ppbv h⁻¹ in the spring and summer period, respectively. This discrepancy is in the same range as observed for measurements at the same location during the HOxComp campaign in July 2005 (Elshorbany et al., 2012).

Discrepancies between production and destruction rates of OH radicals were highest for conditions with low NO mixing ratios in this study. This is similar to findings in other field campaigns in China (Tan et al., 2017, 2019; Whalley et al., 2021). The high reliability of radical data in this study gives further confidence that the discrepancies arise from chemical processes that are unaccounted for rather than from instrumental artifacts.

The highest unaccounted for OH source with a rate of 3.0 ppbv h⁻¹ (51 % of the observed total OH destruction rate) is observed in the period from 5 to 8 August (Case 1), when NO mixing ratios were less than 1 ppbv and median maximum temperatures in the chamber were 31 ^∘C. At the same time, an additional HO₂ destruction process with a rate of up to 2.0 ppbv h⁻¹ is required to balance the HO₂ production rate, while production and destruction rates for RO₂ radicals are well balanced. The opposing imbalances in the OH and HO₂ budgets could be due to an unknown mechanism that converts HO₂ to OH, or this could indicate a missing primary OH source and a similar fast, but independent, termination reaction removing HO₂. If an unknown HO₂ to OH conversion mechanism played a major role, it would not explain the complete rate of the missing OH source. Since the missing OH source is slightly larger than the rate of the missing HO₂ sink, part of the missing OH source could have originated from a missing primary OH production process because a small difference between the total RO_X production and destruction rates is also observed. The missing RO_X source was up to 0.5 ppbv h⁻¹ for Case 1 but was even higher with a rate of 1.4 ppbv h⁻¹ in the summer when temperature was highest (Case 2). Since the calculated reaction rates of the HO₂ and RO₂ radicals with NO were able to reproduce the observed O_x production within 1 ppbv h⁻¹, the unknown missing processes do not seem to have a direct impact on net ozone production.

For NO mixing ratios in the range of 1 to 3 ppbv, production and destruction rates for OH and HO₂ radicals were balanced, while additional sources of RO₂ and RO_X having average rates of 1.6 and 0.4 ppbv h⁻¹, respectively, were required to balance their production and destruction rates. Therefore, part of the missing RO₂ source can be explained by a primary radical source, but the remaining RO₂ source is still unresolved.

For high NO mixing ratios above 3 ppbv (4 to 5 ppbv h⁻¹), large discrepancies between production and destruction rates of HO₂ and RO₂ radicals were found, but the calculations for these conditions have a higher uncertainty due to low HO₂ and RO₂ concentrations close to background signals. Whereas the imbalance in the budget for HO₂ radicals is due to a loss process that is unaccounted for, an additional RO₂ production process is required to close the chemical budget for RO₂ radicals. For the same conditions, a primary RO_X source with a rate of 0.5 ppbv h⁻¹ was needed to balance the RO_X destruction rate. Therefore, the missing primary RO_X source is likely a primary RO₂ source that is unaccounted for.

Production of radicals from the oxidation of organic compounds by chlorine could have been one additional source. Unfortunately, the potential impact of chlorine chemistry could not be examined in the spring periods, when these conditions were experienced, because ClNO₂ measurements were not available. During times when ClNO₂ concentrations were measured, chlorine chemistry initiated by the photolysis of ClNO₂ did not significantly contribute to the radical production.

For chemical conditions when the contribution of the reaction of HO₂ with NO to the OH production was reduced, i.e., at lower NO levels, other radical formation pathways such as isomerization reactions of RO₂ radicals, OH formation from ozonolysis of alkenes, or photolysis of multifunctional organic compounds could gain importance and need to be properly accounted for. These processes remain relatively poorly constrained due to the lack of direct measurements of, e.g., multifunctional organic compounds.

Although the exact mechanism for the missing production or destruction processes for OH, HO₂, and RO₂ radicals could not be determined from measurements in this campaign, knowing the magnitudes of the missing radical processes gives indicative information about the disagreements of model simulations and observations for radicals and secondary air pollutants.

More investigations of the chemical budgets of radicals, for example in environments with high NO mixing ratios, including the determination of the impact of chlorine chemistry and with a detailed characterization of the chemical composition of air masses with respect to the presence of complex organic compounds, would be beneficial for the understanding of radical chemistry as well as the formation of secondary air pollution such as ozone.