On the understanding of tropospheric fast photochemistry: airborne 1 observations of peroxy radicals during the EMeRGe-Europe campaign 2

. In this study, airborne measurements of the sum of hydroperoxyl (HO 2 ) and organic peroxy (RO 2 ) radicals that react 14 with NO to produce NO 2 , i.e. RO 2* , coupled with actinometry and other key trace gases measurements, have been used to test the 15 current understanding of the fast photochemistry in the outflow of major population centres (MPCs). All measurements were 16 made during the airborne campaign of the EMeRGe ( E ffect of M egacities on the transport and transformation of pollutants on 17 the R egional to G lobal scal e s) project in Europe on-board the H igh A ltitude Lo ng range research aircraft (HALO). The on-board 18 measurements of RO 2* were made using the in-situ instrument P eroxy R adical C hemical E nhancement and A bsorption 19 S pectrometer (PeRCEAS). RO 2* mixing ratios up to 120 pptv were observed in air masses of different origins and composition 20 under different local actinometrical conditions during seven HALO research flights in July 2017 over Europe. 21 The range and variability of the RO 2* measurements agree reasonably well with radical production rates estimated using 22 photolysis frequencies and RO 2* precursor concentrations measured on-board. RO 2* is primarily produced following the 23 photolysis of ozone (O 3 ), formaldehyde (HCHO), glyoxal (CHOCHO), and nitrous acid (HONO) in the airmasses investigated. 24 The suitability of p hotostationary s teady- s tate (PSS) assumptions to estimate the mixing ratios and the variability of RO 2* during 25 the airborne observations is investigated. The PSS assumption is robust enough to calculate RO 2* mixing rations for most 26 conditions encountered in air masses measured. The similarities and discrepancies between measured and calculated RO 2* 27 mixing ratios are analysed stepwise. The parameters, which predominantly control the RO 2* mixing ratios under different 28 chemical and physical regimes, are identified during the analysis. The dominant removal processes of RO 2* in the airmasses 29 measured up to 2000 m are the loss of OH and RO through the reaction with NO x during the radical interconversion. Above 2000 30 m, HO 2 – HO 2 and HO 2 – RO 2 reactions dominate RO 2* loss reactions. RO 2* calculations underestimated (< 20 %) the 31 measurements by the analytical expression inside the pollution plumes probed. The underestimation is attributed to the 32 limitations of the PSS analysis to take into account the production of RO 2* through oxidation and photolysis of the OVOCs not 33 measured during EMeRGe. 113 2019 and Whalley et al., 2021 reported experimental radical budget calculations based on the published reaction rate coefficients 114 of fundamental reactions (R1 to R26) controlling OH, HO 2 and RO 2 in the lower troposphere and ground-based measurements of 115 all relevant reactants and photolysis frequencies. In this study, a similar approach has been used to calculate the amount of 116 peroxy radicals in the air masses measured on-board of the H igh A ltitude Lo ng range (HALO) research aircraft over Europe 117 during the first campaign of the EMeRGe ( E ffect of Me gacities on the transport and transformation of pollutants on the Regional 118 to Global scal e s) project. The available on-board measurements of RO 2* are defined as the total sum of OH, RO and peroxy 119 radicals reacting with NO to produce NO 2 (i.e., RO 2 * = OH + ∑RO + HO 2 + ∑RO 2 , where RO 2 are the organic peroxy radicals 120 reacting with NO to produce NO 2 ). Since the amount of OH and RO is much smaller, RO 2* to a good approximation is the sum 121 of HO 2 and those RO 2 radicals that react with NO to produce NO 2 . For the calculation, RO 2* is assumed to be in PSS, and an 122 analytical expression is developed with a manageable degree of complexity to estimate the concentration and mixing ratios of 123 RO 2* . The simultaneous on-board measurements of trace gases and photolysis frequencies are used to constrain the estimate of 124 the RO 2* concentration. number of assumptions gain a deeper insight into the source and sink reactions of RO 2* and the applicability of the PSS assumption for the different pollution regimes and related weather conditions in the free troposphere. well-mixed the differences in sampling and temporal and spatial resolution in the in-situ reasonable 10 12 molecules cm -3 for 60 % of the 235 measurements during the IOP, as a first approximation, the production of OH from H 2 O 2 photolysis is assumed to be negligible 236 for the dataset considered in this study. Similarly, the VOC photolysis was assumed to dominate the RO 2* production over the 237 oxidation by OH and ozonolysis of alkenes. The most abundant and reactive oxygenated volatile organic compounds (OVOCs) 238 the air NO 2 ≤ 100 pptv, RO 2* ≤ 40 pptv 417 and HCHO ≤ 1 ppbv, the rate of reaction R18, which forms H 2 O and O 2 from OH and HO 2 , is about 4 times faster than the rate 418 of the OH oxidation reaction of the dominant OVOCs (R12) considered in this study or the rate of formation of HONO (R19). 419 RO 2*m is systematically underestimated for ∑VOCs greater than 7 ppbv. The composition of these air masses is quite different, 420 as reflected by the  VOCs/NO ratios. This implies that Eq. 9 does not capture the peroxy radical production adequately from 421 VOCs in these cases. The underestimation of RO 2*m may be explained in part by a) OH recycling through additional VOC 422 oxidation processes, which are not in Eq. 9 and/or b) RO 2* production from the photolysis of carbonyls, which were not 423 measured and/or c) RO 2* ratio of NO is < 1 ppbv. This study exploits the airborne measurements of various atmospheric constituents on-board the HALO research aircraft over 559 Europe in summer 2017 to investigate radical photochemistry in the probed airmasses. RO 2* are calculated by assuming a 560 p hotostationary s teady- s tate (PSS) of RO 2* and compared with the actual measurements. The calculation is constrained by the 561 simultaneous airborne measurements of radical precursors, photolysis frequencies and reactants of RO 2 * such as NO x and O 3 . 562 The significance and the importance of selected production and loss processes in the RO 2* chemistry are investigated by 563 gradually increasing the complexity of the analytical expression. The agreement of the calculations with the measurements over a 564 wide range of chemical composition and insolation conditions improves when the analytical expression is extended to account 565 for oxy–peroxy radical interconversion reactions and loss of OH and RO during the interconversion. The RO 2* measured is 566

by solar actinic radiation, and on the concentration of the precursors, such as carbon monoxide (CO), volatile organic compounds 48 (VOCs), and peroxides. It also strongly depends on the amounts of nitrogen monoxide (NO) and nitrogen dioxide (NO 2 ) due to 49 the gas-phase reactions of NO and NO 2 with the OH and organic oxy (RO) radicals formed during the radical interconversion.

50
The main production and loss processes of HO 2 and RO 2 in the troposphere are summarised as follows:

89
R23 is one of the most important reactions in the troposphere as it leads to O 3 formation through R27 and R28.

90
Provided that there is sufficient insolation to ensure rapid photochemical processing and all species involved are known, the sum 91 of HO 2 and RO 2 that react with NO to produce NO 2 can be estimated from a photochemical steady-state (PSS) assumption in 92 which production and loss mechanisms are equally important. The HO 2 + RO 2 concentrations and mixing ratios can be estimated 93 using the PSS assumption for NO 2 by considering the following reactions:

101
where j NO 2 is the photolysis frequency of NO 2 ; k NO+O 3 (1.9×10 -14 cm 3 molecules -1 s -1 ) is the rate coefficient of the reaction of 102 NO with O 3 and k NO+(HO 2 +RO 2 ) is the weighted average rate coefficient assumed for the reactions of peroxy radicals with NO.

103
The comparison of [HO 2 + RO 2 ] PSS calculated using Eq.1 with ground-based (e.g. Ridley et al., 1992;Cantrell et al., 1997; 104 Carpenter et al., 1998;Volz-Thomas et al., 2003), and airborne measurements, has shown in the past different degree of 105 agreement. The underestimations and overestimations found in air masses with different chemical compositions are not well 106 understood. In the case of airborne measurements, the PSS calculation generally overestimates that measured peroxy radicals 107 (Cantrell et al., 2003a(Cantrell et al., , 2003b. The differences observed could not be attributed to systematic changes in NO, altitude, water 108 vapour and temperature, although these variables are often correlated.
109 Ground-based (Mihelcic et al., 2003;Kanaya et al., 2007Kanaya et al., , 2012Elshorbany et al., 2012;Lu et al., 2012Lu et al., , 2013Tan et al., 2017Tan et al., , 110 2018Whalley et al., 2018Whalley et al., , 2021Lew et al., 2020) and airborne (Crawford et al., 1999;Tan et al., 2001;Cantrell et al., 2003b) 111 measurements have also been compared with model simulations of HO 2 and RO 2 . The discrepancies encountered depend upon  chemical reactor and detector, which operate alternatively in both background and amplification modes, i.e. without and with the 157 addition of CO, to account for the rapid background variations during airborne measurements. In the amplification mode, the 158 sum of the NO 2 produced from ambient RO 2 * through the chain reaction, the ambient NO 2 , the NO 2 produced from the ambient 159 O 3 -NO reagent gas reaction and the NO 2 produced in the inlet from any other sources (e.g. thermal decomposition of PAN) is 160 measured. In the background mode, the sum of the ambient NO 2 , the NO 2 produced from the ambient O 3 -NO reagent gas 161 reaction and NO 2 produced in the inlet from any other sources is measured. The RO 2 * is retrieved by dividing the difference in 162 NO 2 concentration (∆NO 2 ) between amplification and background mode by the conversion efficiency of RO 2 * to NO 2 , which is 163 referred to as eCL (effective chain length). The PeRCEAS instrument and its specifications have been described in detail 164 elsewhere (Horstjann et al., 2014, George et al., 2020.

165
The two chemical reactors for sampling the ambient air are part of the DUal channel Airborne peroxy radical Chemical

174
Although the DUALER pressure is kept constant below the ambient pressure, variations in dynamical pressure > 10 mbar during 175 the flight can change the residence time and induce turbulences inside the inlet (Kartal et al., 2010;George et al., 2020). These 176 may lead to different physical losses of radicals before amplification and affect the eCL. In the measurements presented in this 177 study, variations in dynamical pressure of this magnitude were only encountered during flight level changes of the aircraft. When 178 used during the analysis, these data sets are either excluded or flagged (P_flag). The effect of the ambient air humidity on eCL 179 (Mihele and Hastie, 1998;Mihele et al., 1999;Reichert et al., 2003) has been accounted for by a calibration procedure reported 180 in George et al. (2020).

181
In addition to the measurement of RO 2 * from PeRCEAS, other in-situ and remote-sensing measurements and basic aircraft data 182 from HALO are used in this study. Details of the corresponding instruments are summarised in Table 1. Concerning the data 183 obtained by the remote sensing instruments, the miniDOAS retrieves the Slant Column Density (SCD) of the target gas and a 184 scaling gas (O 4 ) towards the horizon at the flight altitude. From this, mixing ratios of the targeted gas within the line of sight is 185 estimated using RT modelling (Stutz et al., 2017;Hüneke et al., 2017;Kluge et al., 2020;Rotermund et al., 2021). The HAIDI 186 instrument retrieves SCDs below the aircraft. The SCDs from HAIDI are then converted to mixing ratios using the 187 corresponding geometric Air Mass Factor (AMF) under a well-mixed NO 2 layer assumption. As a result of this assumption, the 188 calculated mixing ratios for HAIDI target gases are lower limits and close to the actual values while flying within and close to a 189 well-mixed boundary layer. Despite the differences in sampling volume and temporal and spatial resolution in the in-situ and remote sensing measurement techniques, the concentration of common and related species obtained are in reasonable agreement

200
RO 2 * mixing ratios up to 120 pptv were measured during the campaign, as shown in Fig. 2. Typically, the highest RO 2 * mixing 201 ratios were observed below 3000 m over Southern Europe. This is attributed to the higher insolation and temperatures favouring 202 the rapid production of RO 2 * from the photochemical oxidations of CO and VOCs.

206
The origin and thus the composition of the air sampled during the seven flights over Europe were different and heterogeneous.

207
Typically, the air masses measured were influenced by emissions from MPCs and their surroundings, and sometimes by biomass 208 burning transported over short or long distances. The concentration and mixing ratio of RO 2 * depends on the insolation and the 209 chemical composition of the air masses probed, particularly on the abundance of RO 2 * precursors. Provided that insolation 210 conditions and a sufficient number of key participating precursors are comparable, the air mass origin is irrelevant for calculating 211 RO 2 * concentrations and mixing ratios. This is because the RO 2 * concentration is controlled by fast chemical and photochemical 212 processes. Thus, the RO 2 * variability and production rates provide insight into the photochemical activity of the air masses

226
The H 2 O concentration in the air masses decreases steadily with altitude as expected. The higher relative variability in H 2 O 227 observed at 3000 m and the increase at 5000 m is associated with measurements under stormy conditions, often over the Alps. The total production rate of OH and RO 2 * (P OH+HO 2 +RO 2 ) can be estimated from the reactions R1 to R13 as follows: In this work, Eq. 2 has been applied to the measurements taken within the EMeRGe campaign in Europe. There were no H 2 O 2 233 measurements available for EMeRGe IOP. However, from the results reported by Tan et al. (2001), the OH production from the 234 H 2 O 2 photolysis become significant at low NO x conditions. Since the [NO x ] > 8 × 10 12 molecules cm -3 for 60 % of the measured have been taken as a surrogate for the sum of VOCs. These assumptions lead to Eq. 3, which estimates the RO 2 * 239 production rate (P RO 2 * ) as: Eq. 3 yields the rate of production of RO 2 * molecules. The production rate can be expressed in units of mixing ratio of RO 2 * by 243 dividing with the air concentration at each altitude, estimated from the pressure and temperature measurements. Figure 4 shows 244 the composite averaged vertical profile of all measured RO 2 * mixing ratios colour-coded with the estimated P RO 2 * . Small circles

245
show the 1-minute measurements binned for P RO 2 * up to 0.8 pptv s -1 in 0.1 pptv s -1 intervals. The production rates above 0.8 pptv 0.1 ppts -1 intervals. Larger circles result from a further binning over 500 m altitude steps. All the production rates below 0.1 pptv Figure 5 shows the fractional contribution of the production rate from each radical precursor reaction included in Eq. 3 as a 260 function of altitude. The data are classified into three groups according to the rate of change of production of the RO 2 * mixing 261 ratio P RO 2 * < 0.07 pptv s -1 (5a), 0.07< P RO 2 * < 0.8 pptv s -1 (5b), and P RO 2 * > 0.8 pptv s -1 (5c) to show the lowest, most common,

263
while the rest of the data are equally distributed in the other two P RO 2 * ranges. The data in each group are always binned over 500 264 m when available.

271
The vertical changes of the precursor mixing ratios and photolysis frequencies used to calculate P RO 2 * in Fig

300
where k RO 2 * +RO 2 * is the effective RO 2 * self-reaction rate coefficient, which is defined as the weighted average rate coefficient 301 between HO 2 -HO 2 , HO 2 -RO 2 and RO 2 -RO 2 reactions.

302
Consequently, the RO 2 * concentrations are expected to correlate with the square root of the P RO 2 * . indicates the presence of other radical loss processes and/or missing production 307 terms in the P RO 2 * calculation. Apart from this, the spread in the diagram confirms that the effective RO 2 * self-reaction rate 308 k RO 2 * +RO 2 * [RO 2 * ] 2 varies widely in the air masses probed due to the effect of changes in HO 2 and ∑RO 2 concentrations in the 309 individual loss reaction rate coefficients. As mentioned in section 4.1, photochemical processing was expected to be enhanced 310 over Southern Europe due to the prevailing high insolation and temperatures during the measurements. This is also reflected in 311 the higher P RO 2 * and [RO 2 * ] observed in Southern Europe as compared to those in Northern Europe (Fig. 7b).

324
The relationship between RO 2 * and P RO 2 * is further investigated to identify the dominant RO 2 * loss process in the air masses 325 considered in this study. As stated in section 3, HO 2 and RO 2 are not speciated but retrieved as RO     Table 2.

354
The PSS data presented in Fig, 9  reactions with OH (k OH+HCHO = 8.5 × 10 -12 cm 3 molecule -1 s -1 and k OH+CH 3 CHO = 1.5 × 10 -11 cm 3 molecule -1 s -1 ). Despite the 369 high mixing ratios measured, CH 3 C(O)CH 3 is a less important source of RO 2 * . This is because the rate coefficient 370 k(T) OH+CH 3 C(O)CH 3 is significantly slower than k OH+HCHO and k OH+ CH 3 CHO (see Table S1 in the supplement). Similarly, the 371 RO 2 * production rate of CHOCHO and CH 3 OH through oxidation is an order of magnitude lower than that of HCHO and 372 CH 3 CHO. Since k HO 2 +O 3 is almost four orders of magnitude smaller than k HO 2 +NO and the NO concentrations remained about 373 three orders of magnitude smaller than the O 3 measured, the HO 2 reaction with O 3 had a negligible effect in Eq. 8.

374
The   ratios approximately above 50 pptv (see Fig. 11 for  = 0.5). The y-axis intercept is below the instrumental detection limit for 392 most measurement conditions. 393 Table 2: Linear regression parameters from RO 2 * m versus RO 2 * c using Eq. 7 and Eq. 9 from Fig. 9 and Fig.10   407 Figure 12 shows the data for δ = 0.5 colour-coded with NO, NO x , the sum of HCHO, CH 3 CHO, CHOCHO, CH 3 OH, and 408 CH 3 C(O)CH 3 (from now on referred to as VOCs), as a surrogate for the amount of OVOCs acting as RO 2 * precursors, and the 409 VOCs to NO ratio. The largest differences between RO 2 * m and RO 2 * c is observed for the bins around 50 pptv. The RO 2 * m < 25 410 pptv observed above 4000 m are overestimated for air masses with low insolation, i.e. j O( 1 D) < 2 × 10 -5 s -1 (Fig. 11)

419
RO 2 * m is systematically underestimated for ∑VOCs greater than 7 ppbv. The composition of these air masses is quite different, 420 as reflected by the VOCs/NO ratios. This implies that Eq. 9 does not capture the peroxy radical production adequately from

421
VOCs in these cases. The underestimation of RO 2 * m may be explained in part by a) OH recycling through additional VOC 422 oxidation processes, which are not in Eq. 9 and/or b) RO 2 * production from the photolysis of carbonyls, which were not 423 measured and/or c) RO 2 * production from the ozonolysis of alkenes.

430
Spatial and temporal differences in the in-situ measurements of the key trace gases (O 3 , NO, H 2 O, CO, CH 4 , VOCs) with respect 431 to remote sensing observations (NO 2 and HONO) used in Eq. 9 may also contribute to the overall spread observed in Fig. 12.

432
Although the temporal evolution and the amount of the trace gases measured using in-situ and remote sensing instruments agree 433 reasonably well, as shown for HCHO in Fig.13, the remote sensing instruments have, in general, larger air sampling volumes 434 compared to that of in-situ instruments. This may occasionally lead to significant differences depending on the location of the 435 pollutant layers with respect to HALO. In addition, PTR-MS measurements of HCHO might include interferences from 436 molecular fragments of other compounds in the sample air (Inomata et al., 2008). Further details about the accuracy and 437 comparability of the instrumentation on-board during the campaign can be found elsewhere (Schumann, 2020).

446
The ratio of RO 2 * m to RO 2 * c (RO 2 * m /RO 2 * c ) has been used to assess the applicability of Eq. 9 for the calculation of RO 2 * in the air 447 masses probed (Fig. 14). In Fig. 14

459
The applicability of Eq. 9 for calculating the in-flight measurements of RO 2 * along the track of the E-EU-03 flight on 11 July 460 2017 is shown in Fig. 16. The E-EU-03 flight investigated the outflow of selected MPCs in Italy (i.e., Po Valley and Rome).

461
Consequently, the flight track was routed along the western coast of Italy and included vertical profiling over the Tyrrhenian Sea 462 upwind of Rome (Fig. 15). As can be seen in

471
The measurements of VOCs used in Eq. 9 may not be representative of the actual complex VOC composition in the plume 472 measured from 12:05 to 12:25 UTC. Consequently, the RO 2 to HO 2 ratio and the RO intermediates involved in the radical 473 interconversion processes, the branching ratios and effective rate coefficients for RO 2 * -RO 2 * reactions might not be well 474 represented in Eq. 9. Taking CH 3 O 2 as a surrogate for all RO 2 might lead to uncertainties in the RO 2 * calculations in the presence

475
of OVOCs with larger organic chains. On the experimental side, changes in the HO 2 to RO 2 ratio affect the accuracy of the 476 PeRCEAS retrieval of the total sum of radicals. As noted in section 3, in this study RO 2 * = HO 2 + 0.65 × RO 2 , and the eCL is 477 determined for a 1:1 mixture of HO 2 :CH 3 O 2 , i.e. δ = 0.5 is used for the RO 2 * retrieval. However, the HO 2 to CH 3 O 2 ratio is not 478 expected to remain constant in all the air masses probed. For a 3:1 ratio of HO 2 :RO 2 , the RO 2 * m would decrease by 10 %.

479
Similarly, a HO 2 :RO 2 ratio of 1:3 would lead to an increase of 10 % in the reported RO 2 * m . This uncertainty is well below the in-

488
NO y , and HONO mixing ratios.

489
The OH concentrations in Fig. 16

514
The least-square fitting in Eq. 12 is applied to RO 2 * m and RO 2 * c from the EMeRGe measurements in Europe binned in 0.1 pptv s -515 1 P RO 2 * intervals as shown in Fig. 17. The fit parameters for Fig. 17a and Fig. 18b are k RR = 7 × 10 -5 ; k RN = 9 × 10 -6 . is not linear. This indicates that more complex non-linear processes are 525 involved in the air masses investigated than those considered in Eq. 11 (see Fig.17d).   The O 3 production rate (P O 3 ) is calculated from the EMeRGe Europe dataset using the reaction of RO 2 * with NO in a similar 533 manner to that used in previous studies of photochemical processes in urban environments (e.g. Kleinman et al., 1995;534 Thomas et al., 2003;Mihelcic et al., 2003;Cantrell et al., 2003b; and references herein).   Beijing (Whalley et al., 2021) and similar ranges of peroxy radicals and NO mixing ratios. In previous work, Whalley et al.

548
(2018) calculated P O 3 to be about an order of magnitude lower than that found in this study from observations in central London

549
for about an order of magnitude lower amount of HO 2 + RO 2 . For NO > 1 ppbv, the P O 3 estimated from the measurement of HO 2 550 and RO 2 , or from the assumptions of an HO 2 to RO 2 ratio were underestimated by the models in other studies in the urban 551 atmosphere (e.g. Martinez et al., 2003;Ren et al., 2003;Kanaya et al., 2008;Mao et al., 2010;Kanaya et al., 2012;Ren et al., 552 2013;Brune et al., 2016;Griffith et al., 2016). This is generally attributed to underestimating large RO 2 concentrations , which 553 likely undergo multiple bimolecular reactions with NO before forming an HO 2 radical.

554
During the EMeRGe IOP in Europe, the NO mixing ratios were < 1 ppbv (approximately < 3 × 10 10 molecules cm -3 ). The ozone 555 production rates obtained for both measured and calculated RO 2 * are in reasonable agreement with other modelling studies in 556 urban environments where the mixing ratio of NO is < 1 ppbv.

558
This study exploits the airborne measurements of various atmospheric constituents on-board the HALO research aircraft over 559 Europe in summer 2017 to investigate radical photochemistry in the probed airmasses. RO 2 * are calculated by assuming a usually overestimated when NO is < 50 pptv in the air probed. This is attributed to RO 2 * loss processes involving reactions with 567 OH, which are not considered in the analytical expression. The reactions are excluded from the analytical expression to constrain 568 it with on-board measurements. These reactions become significant RO 2 * loss processes at low NO concentrations.

569
The results indicate that the steady-state calculations mostly underestimated the RO 2 * measurements in polluted plumes of urban 570 origin at altitudes below 2000 m. Changes in the HO 2 to RO 2 ratios in different plumes partly account for the disagreement in 571 particular cases. In pollution plumes with the sum of the OVOCs measured mixing ratios > 7 ppbv, the underestimation of the 572 measurements can reach up to 80 %. In these plumes, the oxidation and/or photolysis of non-measured VOCs and the ozonolysis 573 of alkenes might be significant, limiting the accuracy of the analytical expression. The overestimation of the OH concentration 574 calculated based on the measured reactants also indicates missing oxy-peroxy radical interconversion reactions in the analytical 575 PSS expression. More information about peroxy radical speciation and VOC partitioning is required to better describe the fast 576 photochemistry in these pollution plumes.

577
The analytical expression developed is robust enough to simulate the radical chemistry in most of the conditions in the free 578 troposphere encountered during EMeRGe IOP in Europe. Speciated radical and VOC measurements in future campaigns would 579 facilitate the estimation of radical loss reactions in air masses with NO < 50 pptv and improve radical production rates 580 estimations in pollution plumes with a high amount of VOCs, where non-linear complex chemistry is involved. Comparing RO 2 * 581 measurements with RO 2 * calculations from the analytical expression helps to identify different chemical and physical regimes, 582 which can be used to constrain future model studies.

583
The calculated O 3 production rates for NO < 1 ppbv are in the same order of magnitude as those previously reported for urban 584 environments. This indicates that the selected RO 2 * production and loss processes and observations of the radical precursors on-

585
board are, to a good approximation, adequate for the estimation of the O 3 production in the measured airmasses in the free 586 troposphere over Europe.