2.2.1 Radicals

OH and HO₂ radicals were measured by the Peking University laser-induced fluorescence system (PKU-LIF), which was built by Forschungszentrum Jülich (FZJ). OH radicals are detected by laser-induced fluorescence (LIF) at 308 nm in a gas expansion inside a low-pressure (4 hPa) measurement cell (Hofzumahaus et al., 1996; Holland et al., 2003). In a second cell, HO₂ radicals are chemically converted with NO, yielding OH, which is detected by LIF (Fuchs et al., 2011). The PKU-LIF instrument was applied first at Wangdu in the North China Plain in summer 2014 (Tan et al., 2017). It was then moved to the Heshan site for the present study. At both sites, the PKU-LIF system was complemented by devices from FZJ to measure RO₂ (ROxLIF) and OH reactivity (k_OH). In the RO_x LIF system, the radicals RO₂, HO₂, and OH are quantitatively converted to HO₂ in a pre-reactor by addition of 0.7 ppmv of NO and 0.11 % of CO at a total pressure of 25 hPa. In a second stage at lower pressure (4 hPa), the HO₂ is further converted by a large excess of 0.5 % NO to OH, which is then detected by LIF (Fuchs et al., 2008). RO₂ concentrations are calculated from the total sum of RO_x (from ROxLIF) by subtracting the contributions of OH and HO₂ measured in the other two detection chambers. A detailed description of the whole measurement system is given by Tan et al. (2017). Due to a technical problem, the integration time for the radical measurements in Heshan was increased to 5 min to achieve 1σ detection limits of 3.9×10⁵ cm⁻³ for OH, 1.2×10⁷ cm⁻³ for HO₂, and 0.6×10⁷ cm⁻³ for RO₂ (Table S1). The accuracy of the calibrations depends on the uncertainty of the calibration source (10 %; 1σ) and the reproducibility of the calibrations, resulting in total accuracies of ±13 %, ±20 %, and ±26 % for OH, HO₂, and RO₂, respectively (Table S1).

As outlined by Tan et al. (2017), attention was paid to possible interferences in the measurement of HO_x. Like in the Wangdu campaign, chemical modulation was applied on several occasions to test whether the OH measurements obtained normally by laser wavelength modulation are perturbed by artificial OH formation in the detection cell. Such kind of interference has been detected in some LIF instruments by applying chemical modulation in field campaigns (Mao et al., 2012; Novelli et al., 2014; Feiner et al., 2016). The chemical modulation system used at Wangdu and Heshan consisted of a flow tube in front of the OH measurement cell and allowed the scavenging of ambient OH by addition of propane in the sampled air flow. Switching between propane and nitrogen additions allows discriminating ambient OH from instrumental OH. For nitrogen, we used research-grade purity (>99.9990 %). A gas chromatograph (GC) analysis of the nitrogen showed no significant contamination by VOCs, which would scavenge OH in the chemical modulation system. In the OH detection cell, scavenging of artificially produced OH by the added propane is calculated to be less than 0.3 %. A description of the prototype chemical-modulation reactor used with PKU-LIF is given by Tan et al. (2017). Results of the chemical modulation experiments during the PRIDE-PRD2014 campaign are presented in Sect. 3.3.

The detection of HO₂ by chemical conversion with NO has two known interferences. First, particular RO₂ radicals (called ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$) from large alkanes (>C₄), alkenes (including isoprene), and aromatics can be converted to OH in the HO₂ detection cell, leading to a systematic positive bias of the HO₂ measurement (Nehr et al., 2011; Fuchs et al., 2011; Whalley et al., 2013; Lew et al., 2018). The interference is most effective when the amount of added NO is high enough to convert most of the atmospheric HO₂ to OH in the LIF cell. In the campaigns in Wangdu and Heshan, the concentration of the NO reagent was lowered by more than a factor of 10, thereby reducing the interference in the HO₂ cell to less than 5 % (Tan et al., 2017).

On the other hand, the chemical conversion of ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$ can be used intentionally for ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$ concentration measurements (Whalley et al., 2013). For that purpose, ROxLIF was operated in an additional measurement mode where the NO addition in the pre-reactor was temporarily turned off and replaced by nitrogen (N₂; Tan et al., 2017). In this mode, the sum of HO₂ and ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$ is detected in the connected LIF cell, which is operated with a large amount of NO for chemical conversion. The concentration of ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$ is then determined as the difference of ${\mathrm{HO}}_{\mathrm{2}}+{\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$ (ROxLIF) and HO₂ (HO₂ cell). The experimental error of the difference is quite large and occasionally exceeds 100 % in the present study because ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$ was much smaller than HO₂ (see Fig. 1). Also, the calibration error of ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$ is larger than that of HO₂. The detection sensitivity for individual ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$ species lies in the range of 0.8±0.2 times the detection sensitivity for HO₂ (Fuchs et al., 2011; Lu et al., 2012). As the speciation of atmospheric ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$ is not exactly known, the possible range of sensitivities causes an additional error of 25 % that has to be added to the normal calibration error, yielding a total accuracy of ±32 % (1σ).

The second NO-related artifact, which is relevant for measurements in the HO₂ cell and ROxLIF system, comes from spurious OH signals generated by the addition of NO in the LIF cells. The signal was regularly determined in humidified synthetic air during calibration and found to be stable over the campaign. It is equivalent to $(\mathrm{2}\pm \mathrm{1})\times {\mathrm{10}}^{\mathrm{7}}$ and $(\mathrm{1}\pm \mathrm{1})\times {\mathrm{10}}^{\mathrm{7}}$ cm⁻³ for HO₂ and RO₂, respectively, and is routinely subtracted from the measurements.

The total OH reactivity was measured by an instrument based on laser-flash photolysis laser-induced fluorescence (LP-LIF; Fuchs et al., 2017; Lou et al., 2010). Ambient air is sampled and pulled through a laminar flow tube at ambient conditions. Artificial OH is produced in the sampled air by pulsed laser photolysis (266 nm wavelength; 10 ns pulse duration) of ozone, which produces OH in nanoseconds according to Reaction (R2). The OH decay due to the reaction with atmospheric trace gases is then monitored in real time by LIF. k_OH is determined as a pseudo-first-order rate coefficient from the decay curves. The precision of the measured k_OH data is ±0.3 s⁻¹ (1σ) and the accuracy is 10 % (Table S1) at an integration time of 180 s.

2.2.2 Trace gases and photolysis frequencies

As summarized in Table S1, the instrumentation used in the PRIDE-PRD2014 campaign was similar to that used in Wangdu (Tan et al., 2017; Fuchs et al., 2017). Photolysis frequencies were determined from spectral actinic photon-flux density measurements (Bohn et al., 2008). Meteorological parameters, including relative humidity, ambient pressure and temperature, and wind speed and direction, were also regularly measured at the site.

NO and NO₂ were measured by a commercial chemiluminescence instrument (Thermo Scientific Model 42i). NO₂ was converted to NO by a custom-built photolytic converter instead of an original molybdenum converter. O₃, SO₂, CO, and CO₂ measurements were also measured by commercial instruments from Thermo Scientific (model 49i, 43i-TLE, 48i-TLE, and 410i). Greenhouse gases, including CO, CO₂, CH₄, and H₂O, were measured by a cavity ring-down spectroscopy instrument (Picarro model G2401). The CO and CO₂ measurements from the Thermo Scientific and Picarro instruments agreed within the instrumental accuracies. The Picarro measurements were used in this work due to the better data coverage. HONO measurements were performed using a custom-built long-path absorption photometer (LOPAP) from PKU (Liu et al., 2016). Measurements of non-methane hydrocarbons (NMHCs) were performed by a GC using a flame ionization detector (FID) and mass spectrometer (MS) for detection. The GC-FID–MS system provided measurements of C₂–C₆ alkanes, C₂–C₆ alkenes, and C₆–C₈ aromatics (Wang et al., 2014). Formaldehyde was measured by a commercial Hantzsch fluorimeter instrument (Aero-Laser GmbH model AL4021). A list of the measured VOCs is given in the Supplement (Table S2).

2.3.1 RO_x budget equations

The RO_x budget is entirely controlled by initiation and termination reactions. RO_x is primarily produced by photolysis of HONO (Reaction R1), O₃ (Reaction R2), HCHO (Reaction R3), and ozonolysis of alkenes (Reaction R4). The total production rate is calculated as

In case of ozone photolysis, φ_OH is the yield of OH from the reaction of O(¹D) with H₂O, which competes with collisional deactivation of O(¹D) with air molecules N₂ and O₂. In the ozonolysis reactions, the yields ${\mathit{\phi }}_{\mathrm{OH}}^i$, ${\mathit{\phi }}_{{\mathrm{HO}}_{\mathrm{2}}}^i$, and ${\mathit{\phi }}_{{\mathrm{RO}}_{\mathrm{2}}}^i$ are specific for each alkene species i. The summation of the radical production from ozonolysis is performed over all measured alkenes. This sum may be not complete if relevant alkenes are not measured (see discussion in Sect. 4.2).

The total destruction rate of RO_x is given by the reactions of OH with NO_x (Reactions R12, R13), RO₂ with NO (Reaction R14), and self-reactions of peroxy radicals (Reactions R15–R17):

Since RO₂ is measured as a sum of organic peroxy radicals, it is treated as a single species. The generalized rate coefficients are adopted from MCMv3.3.1 (see footnotes in Table 1). Reaction (R14), leading to the formation of organic nitrates, competes with Reaction (R8), which produces HO₂ radicals. The branching ratio between Reactions (R8) and (R14) depends on the carbon chain lengths and structure (Atkinson et al., 1982; Lightfoot et al., 1992). The organic nitrate yield generally increases with carbon number and lies typically between 1 % for ethyl RO₂ and 35 % for RO₂ of C₈ alkanes. Here, a nitrate yield of 5 % is assumed. The impact of larger nitrate yields is discussed in Sect. 4.

The thermal decomposition of HO₂NO₂ into HO₂ and NO₂ (an initiation reaction) and the back reaction to HO₂NO₂ (a termination reaction) are not explicitly considered in the budget equations. The two reactions reach a thermal equilibrium within seconds under the conditions of the campaign and have no net effect on the RO_x balance. Likewise, equilibrium is assumed between thermal decomposition of PAN and its formation by the reaction of acetyl peroxy radicals with NO₂. Also, this equilibrium is not explicitly considered in the budget Eqs. (1) and (2).

2.3.2 OH budget equations

As explained above, the total OH destruction rate can be directly quantified as the product of the OH concentration and the OH reactivity, both of which were measured during the PRIDE-PRD2014 campaign:

The total OH production rate is calculated from the primary (Reactions R1, R2, R4) and secondary (Reactions R9, R10) sources of OH. The primary sources are treated in the same way as in the RO_x budget. The secondary sources include OH recycling from the reaction of HO₂ with NO (Reaction R9) and O₃ (Reaction R10):

2.3.3 HO₂ budget equations

The total production rate of HO₂ is calculated from primary sources, i.e. photolysis of HCHO (Reaction R3) and ozonolysis of alkenes (Reaction R4), and secondary sources which involve the conversion of OH and RO₂ to HO₂. The treatment of the primary production by Reactions (R3) and (R4) is explained in Sect. 2.3.1. In addition to the photolysis of HCHO, the photolysis of other oxygenated VOCs (OVOCs) could contribute to the HO₂ production, but this is not considered here due to the absence of OVOC measurements.

Conversion from OH to HO₂ can occur by reaction of OH with CO, HCHO, H₂, and O₃. Under the conditions of the campaign, the reaction rates for H₂ and O₃ were at least 2 orders of magnitude smaller than those for the reactions with HCHO (Reaction R6) and CO (Reaction R7). Therefore, only Reactions (R6) and (R7) are considered in the budget analysis. Also, the reaction of RO₂ with NO (Reaction R8) constitutes an important secondary source of HO₂. Reaction (R8) competes with the radical termination Reaction (R14), for which a nitrate yield of 5 % is assumed (see Sect. 2.3.1). Accordingly, an HO₂ yield of 95 % is taken for Reaction (R8). The total HO₂ production rate is then calculated as

HO₂ is chemically removed by reaction with NO, O₃, HO₂, and RO₂, all of which were measured in this campaign. It should be noted that the effective rate constant k₁₇ for the self-recombination of HO₂ has a water vapor dependence which is taken into account in k₁₇ (Table 1). The total HO₂ destruction rate is then given by

As explained in Sect. 2.3.1, the thermal equilibrium between HO₂+NO₂ and HO₂NO₂ is not explicitly considered in the budget equations.

2.3.4 RO₂ budget equations

Primary RO₂ production is possible by the ozonolysis of alkenes and the photolysis of OVOCs. Owing to the lack of OVOC measurements (except HCHO) in this study, only ozonolysis is considered to be a primary source. It is treated as described in Sect. 2.3.1.

In a broader sense, also reactions of hydrocarbons with NO₃ radicals and chlorine atoms can be considered primary production processes because they do not consume RO_x species. However, neither NO₃ nor Cl were measured. NO₃ is produced by reaction of NO₂ with ozone. It is generally assumed that during the bright hours of the day, NO₃ is predominantly destroyed by photolysis and reaction with NO. Recently, Liebmann et al. (2018) reported measurements in a forested environment in southern Germany, demonstrating that more than 25 % of daytime NO₃ was removed by biogenic VOCs. The possible role of NO₃ reactions with VOCs at Heshan is discussed in Sect. 3.

Cl atoms may play a role in the morning. Gaseous ClNO₂ can be formed at night by heterogeneous reaction of N₂O₅ with Cl⁻ ions and photolyze quickly after sunrise producing Cl atoms (Osthoff et al., 2008; Tham et al., 2016; Li et al., 2018). This mechanism, followed by the reaction of Cl with VOCs, made some contribution to the early morning RO₂ production in a previous campaign in summertime in the North China Plain (Tan et al., 2017) and will be discussed in Sect. 4.2.

The main secondary source of RO₂ is the reaction of OH with VOCs. As it is generally difficult to measure all reactive organic compounds in the atmosphere, we follow two different approaches to determine the RO₂ production from OH reactions. The first approach calculates the RO₂ production rate as the sum of the reaction rates of OH with all measured hydrocarbon species, denoted VOC(1). The resulting total RO₂ production rate can be considered a lower limit:

Here, the first sum represents the primary production by ozonolysis, and the second term represents the RO₂ production rate by OH reactions.

Another approach estimates the total atmospheric amount of organic reactants, here denoted VOC(2), from the measured OH reactivity (e.g., Shirley et al., 2006; Whalley et al., 2016). For this purpose, the reactivity of measured CO, NO, NO₂, HCHO, SO₂, and O₃ is subtracted from the measured k_OH to determine the total reactivity of VOCs that can potentially form RO₂. This reactivity is called k_OH(VOC(2)). This approach makes the implicit assumption that the missing OH reactivity found in the present study (see Sect. 3.2) is caused by unmeasured VOCs. The RO₂ production rate is then given by

The RO₂ destruction is determined by the reaction with NO (Reactions R8, R14) and with other peroxy radicals (Reactions R15, R16). These reactions and the thermal equilibrium of PAN are treated as in the RO_x budget analysis (Sect. 2.3.1). Accordingly, the total destruction rate of RO₂ can be calculated as

Equations (7) and (9) can be adapted for the budget analysis of ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$ radicals. In this case, the second term in Eq. (7) contains only OH reactions of VOCs that are known to produce ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$. In Eq. (9), only the concentration of RO₂ at the end of the equation has to be replaced by ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$, assuming that all ${\mathrm{RO}}_{\mathrm{2}}^{\mathrm{\#}}$ reacts with RO₂.

4.2.1 OH interference

The non-closure in the OH and RO₂ budgets could be explained, for example, by experimental artifacts as recently reported for OH measurements in some LIF instruments (Mao et al., 2012; Novelli et al., 2014; Feiner et al., 2016). An experimental overestimation of the OH concentration would result in reaction rates that are too high being calculated for the OH destruction (k_OH×[OH]) and the RO₂ production from the reactions of VOCs with OH. However, the chemical modulation tests carried out under low NO conditions (<1 ppbv) do not show a significant interference. This result is consistent with other tests that were performed with our LIF technique in field campaigns in China (Tan et al., 2018b, 2017) and in laboratory and chamber experiments (Fuchs et al., 2016, 2012). For this reason, we consider OH interference to be an unlikely explanation here, although we cannot strictly exclude the possibility that there were OH interferences only at times when the chemical modulation system was not used.

4.2.2 OH regeneration mechanisms

An alternative explanation for the non-closure in the OH and RO₂ budgets would be a chemical mechanism that effectively converts RO₂ to OH. Unimolecular isomerization and decomposition reactions of RO₂ can be such an OH source when the competing reaction with NO is slow. This chemistry has been known for a long time as autoxidation, for example, in low-temperature combustion (e.g., Cox and Cole, 1985; Glowacki and Pilling, 2010). Its potential relevance to atmospheric chemistry at ambient temperatures has only recently been recognized (e.g., Peeters et al., 2009; da Silva et al., 2010; Crounse et al., 2013; Praske et al., 2018). Autoxidation involves an intramolecular H shift in the RO₂ molecule leading to a hydroperoxy alkyl radical, which is often named QOOH. This radical can generally undergo various types of reactions, such as a reaction with O₂ producing an oxygenated VOC+HO₂, or decomposition to an oxygenated VOC by elimination of OH from the -OOH group (e.g., Peeters et al., 2009; da Silva et al., 2010; Crounse et al., 2013; Praske et al., 2018). Another path is the addition of O₂ forming a hydroperoxy peroxy radical (O₂)QOOH. This new peroxy radical can then react with NO, HO₂, and RO₂ or undergo another internal H-shift reaction. Repetitive sequential H-shift reactions followed by O₂ addition lead to highly oxidized RO₂ radicals which produce highly oxidized molecules (HOMs) by radical termination reactions (e.g., Ehn et al., 2014, 2017; Jokinen et al., 2014). Due to their low vapor pressure, HOMs are efficient precursors for organic particles, which are produced from the original VOCs with yields in the low percent range (e.g., Ehn et al., 2014; Jokinen et al., 2015).

RO₂ isomerization producing HO_x radicals is known to occur in the oxidation of isoprene ((Peeters et al., 2014, 2009; Peeters and Muller, 2010; da Silva et al., 2010; Crounse et al., 2011; Fuchs et al., 2013; Teng et al., 2017) and methacrolein (Crounse et al., 2012; Fuchs et al., 2014). In Heshan, the production rate of isoprene peroxy radicals from the reaction of isoprene with OH never exceeded 0.5 ppbv h⁻¹. Even if every isoprene-derived RO₂ radical regenerated one OH molecule (which is not likely because of the competing reaction with NO), the process could explain only a small fraction of the missing OH production rate. The concentration of MACR was not measured but is generally not larger than that of isoprene (Karl et al., 2009; Shao et al., 2009). Since the OH rate constant is smaller than that for isoprene, OH regeneration by unimolecular reactions of MACR-derived RO₂ is expected to be even less important.

Other than for isoprene and methacrolein, autoxidation of RO₂ leading to HO_x formation has been experimentally studied for only a few other VOCs, including 3-pentanone (Crounse et al., 2013), glyoxal (Lockhart et al., 2013), n-hexane and 2-hexanol (Praske et al., 2018), hydroxymethyl hydroperoxides (Allen et al., 2018), and 2-hydroperoxy-2-methylpentane (Praske et al., 2019). While isoprene and methacrolein chemistry is especially important in biogenically controlled environments, the new studies demonstrate that autoxidation can also be expected to play a role in urban atmospheres when NO concentrations are as low as 500 pptv (see Praske et al., 2018). Systematic theoretical studies have shown that the rates of H shifts in RO₂ depend very much on their chemical structure (e.g., Crounse et al., 2013; Otkjær et al., 2018; Møller et al., 2019) and range from 10⁻⁴ to 10 s⁻¹ at ambient temperatures. Low rate coefficients can be expected, for example, for 1,5-H or 1,6-H shift reactions in linear alkyl radicals, whereas the presence of (multiple) functional groups like -OH, -OOH, or -CHO may increase the H-shift rate by orders of magnitude. The possible yield of OH, HO₂, or higher-oxidized RO₂ radicals from a hydrogen shift depends on the chemical structure and functionality. Elimination of OH or HO₂ is generally supported by the presence of functional groups (e.g., -OH, -OOH, or -CHO).

In the present campaign, the potential conversion of RO₂ to OH by a unimolecular reaction would require a rate of about 0.08 s⁻¹ to close the budgets of OH and RO₂ if all measured RO₂ radicals could produce OH from H-shift reactions (Fig. S4). Although the rate is in the possible range of H-shift reactions, it is questionable if a major fraction of RO₂ was structurally capable of undergoing a fast H shift leading to OH formation. As approximately half of the measured OH reactivity is likely due to unmeasured VOCs with unknown speciation and owing to the general lack of kinetic and mechanistic studies for specific RO₂ radicals, it is not possible to be more quantitative here. If the missing reactivity at Heshan was caused by photochemically aged, functionalized oxygenated VOCs, there is a chance that RO₂ radicals from these compounds could have contributed significantly to the missing RO₂ sink or missing OH source. If autoxidation played a significant role, additional HO₂ formation from H-shift reactions would also be expected. However, the closed HO₂ budget gives no indication for this.

Another possibility for converting RO₂ to OH under low NO conditions is the reaction of RO₂ with HO₂. The reaction is generally considered to be chain terminating, but in the case of acyl peroxy and α-carbonyl peroxy radicals, a parallel reaction channel can produce OH with yields up to 80 % (Fuchs et al., 2018; Winiberg et al., 2016; Praske et al., 2015; Groß et al., 2014; Hasson et al., 2012, 2004; Dillon and Crowley, 2008; Jenkin et al., 2008). With reaction rate constants in the range of (1–2) $\times {\mathrm{10}}^{-\mathrm{11}}$ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$, the OH production would be less than 0.1 ppbv h⁻¹ even if all measured RO₂ species produce OH. In conclusion, the mechanisms already known for conversion of RO₂ to HO₂ are not sufficient in explaining the missing RO₂ sink and missing OH source.

The observations in Heshan resemble qualitatively those of the previous PRIDE-PRD 2006 campaign in Backgarden (Hofzumahaus et al., 2009), where the experimental OH budget indicated a missing OH source (28 ppbv h⁻¹) in the afternoon, when NO was less than 1 ppbv. Box model simulations underestimated the measured OH concentrations by a factor 3–5 at low NO but agreed well with measured HO₂ concentrations. In that study, the isoprene concentrations were considerably higher, reaching several parts per billion by volume. Isomerization reactions of isoprene peroxy radicals could explain only a small part (max 20 %) of the missing OH source (Lu et al., 2012; Fuchs et al., 2013). The observed behavior of OH and HO₂ could be reproduced by assuming a hypothetical mechanism in which RO₂ is converted to HO₂ and HO₂ is converted to OH by an unknown reactant X with a concentration equivalent to 0.8 ppbv NO. Owing to the lack of RO₂ measurements, the mechanism could not be directly tested for RO₂. In Heshan, the same mechanism would be able to close both the RO₂ and OH budgets if an equivalent of 0.4 ppbv NO is assumed (Fig. S4). Here, the NO concentration of 0.4 ppbv corresponds to the rate coefficient of 0.08 s⁻¹ discussed above. When using the X mechanism, the closure of the HO₂ and RO_x budgets remains unaffected.. Therefore, the X mechanism is one possibility for describing all radical budgets at Heshan consistently, although its chemical nature remains unresolved.

4.2.3 Additional uncertainties in the budget analyses

As pointed out in Sect. 4.1, unmeasured VOCs were most likely responsible for the observed missing OH reactivity. This not only considerably influences the radical chain propagation from OH to RO₂ (Fig. 3e, g) but can also affect the primary production of radicals by ozonolysis and photolysis (see Supplement). Furthermore, Cl reactions with measured and unmeasured VOCs may have initiated RO_x chain reactions in the early morning. These reactions could have slightly influenced the RO_x budget but are of minor importance compared to the radical chain propagation reactions (Supplement).

Reactions of NO₃ with VOCs are an additional RO₂ source which are neglected in the budget calculation in Sect. 2.3.4. The relevance can be estimated from the production rate of NO₃, which is calculated from the reaction of NO₂ with O₃ ($k({\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}})=\mathrm{1.47}\times {\mathrm{10}}^{-\mathrm{13}}\times \exp (-\mathrm{2470}/T$); MCM3.3.1). In this campaign, the NO₃ production rate was on the order of 1.4 and 0.7 ppbv h⁻¹ during the daytime and nighttime, respectively. Because NO₃ is efficiently photolyzed in the bright hours of the day, it is generally assumed that it plays a negligible role as an oxidant during the daytime. Liebmann et al. (2018) recently showed that this is not always the case. They reported measurements in a forested environment in southern Germany, demonstrating that more than 25 % of the daytime NO₃ reacted with biogenic VOCs. Under the conditions at Heshan 2014, the main loss process during the daytime is the reaction with NO. If we neglect unmeasured VOCs, the percentage removal of NO₃ in the morning is 96 % by NO, 3 % by photolysis, and 1 % by measured VOCs. In the afternoon, the corresponding values are 72 %, 21 %, and 7 %. Thus, the estimated RO₂ production rate from NO₃ reactions with known VOCs was probably not more than 0.1 ppbv h⁻¹ during the daytime. It is conceivable that unmeasured VOCs, which probably accounted for 50 % of the OH reactivity, contributed by a similar magnitude. During the daytime, these contributions are relatively small compared to the total production rate of RO₂. The tendency is to slightly increase the imbalance between the production and destruction rate of RO₂ observed in the afternoon (Fig. 3). At sunset and in the night, the NO₃ production rate of 0.7 ppbv h⁻¹ can be considered an upper limit for the RO₂ production. This value can possibly explain, at least partly, the imbalance of about 0.5 ppbv h⁻¹ in the RO_x budget after sunset (Fig. 2).

Another uncertainty is caused by the measurement and incomplete representation of the RO₂ chemistry. Due to the measurement principle of the ROxLIF instrument, only those RO₂ species are measured which are converted in the instrument to HO₂ by reaction with NO. This measurement is suitable to quantify the HO₂ production rate (Eq. 5). Among the RO₂ radicals which are not completely captured by ROxLIF are those species which produce a new RO₂ radical when they react with NO. As these reactions are neutral with respect to the total RO₂, the RO₂ budget (D-P) is not sensitive to the RO₂ measurement bias caused by these species (see Supplement).

Other uncertainties in the RO₂ budget are caused by the rate constants for the reactions of RO₂ with NO (Reactions R8, R14), RO₂ (Reaction R15), and HO₂ (Reaction R16) that are given in Table 1 as effective values for the lumped RO₂ radicals (Jenkin et al., 2019). In this work, the uncertainty of the rate coefficients for Reactions (R15) and (R16) plays only a minor role because the daytime loss of the peroxy radicals was largely dominated by the reaction with NO (see Supplement). The relevant range for the reaction rate constants of different RO₂ species with NO (Reactions R8, R14) is between $\mathrm{8}\times {\mathrm{10}}^{-\mathrm{12}}$ and $\mathrm{1.1}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ s⁻¹ (see Supplement). As a sensitivity test, Figs. S5 and S6 show the budgets of RO_x, RO₂, and HO₂ for a rate constant of $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ s⁻¹. The results are essentially the same as in Figs. 2 and 3, where a rate constant of $\mathrm{9}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ s⁻¹ was applied for Reactions (R8) and (R14). Thus, an increased rate constant cannot explain the missing RO₂ sink in the RO₂ budget.

Also the unknown branching ratio in the reaction of RO₂ with NO, which can produce HO₂ (Reaction R8, chain propagating) or organic nitrates (Reaction R14, chain terminating), is uncertain (see Sect. 2.3.1 and Supplement). Changing the yields for organic nitrates from 5 % to 20 % has a small but notable influence on the RO_x budget, reversing the slightly negative bias (D<P) to a lightly positive one (D>P; Fig. S7). In both limits, the RO_x budget remains closed within experimental errors. The influence of the different HO₂ yields on the production rate of HO₂ is small (Fig. S8). For the range of tested yields, the HO₂ budget remains balanced within experimental uncertainties.