RO2∗ mixing ratios up to 120 pptv were measured during the campaign, as shown in Fig. 2. Typically, the highest RO2∗ mixing ratios were observed below 3000 m over southern Europe.

The origin and thus the composition of the air sampled during the seven flights over Europe were different and heterogeneous. Typically, the air masses measured were influenced by emissions from MPCs and their surroundings and sometimes by biomass burning transported over short or long distances. The concentration and mixing ratio of RO2∗ rather depends on the insolation and the chemical composition of the air probed, particularly on the abundance of RO2∗ precursors, than on the origin of the air masses. Since RO2∗ species are controlled by fast chemical and photochemical processes, the air mass origin and trajectory are not used in the calculation of RO2∗ concentrations and mixing ratios but are of interest as the source of RO2∗ precursors. Thus, the RO2∗ variability and its production rates provide valuable insight into the photochemical activity of the air masses probed.

Changes in RO2∗ as a function of latitude and altitude, as shown in Fig. 2, confirm the heterogeneity of the photochemical activity in the air masses probed. Figure 3 shows the RO2∗ vertical profiles averaged for the EMeRGe flights over Europe in 500 m altitude bins. The error bars are standard errors (i.e. ±1σ standard deviation of each bin). The vertical profiles may be biased as the higher altitudes have fewer measurements than those below 3000 m, as mentioned in Sect. 2. The vertical profiles are a composite from averaging flights with legs carried out at different longitudes and latitudes and are only shown to summarise the variability in the composition of the air masses measured during the campaign.

Most of the EMeRGe measurements below 2000 m were carried out in the outflow of MPCs, which are expected to contain significant amounts of RO2∗ precursors. HALO flew at the lowest altitudes during flight legs over the English Channel, the Mediterranean, and the North Sea. The H2O concentration in the air masses decreased steadily with altitude as expected. The higher relative variability in H2O observed at 3000 m and the increase at 5000 m are associated with measurements under stormy conditions, often over the Alps.

The rate of production of RO2∗ from Reactions (R1) to (R13) is given by 2PRO2∗=2jOD1O3⋅kOD1+H2OH2OkOD1+H2OH2O+kOD1+O2O2+kOD1+N2N2+jHONOHONO+2jH2O2H2O2+2∑ijiOVOCi+∑kO3+alkeneskO3alkeneskγk, where OVOC stands for oxygenated volatile organic compounds, and γ is the effective RO2∗ yield from ozonolysis of alkenes.

In this study, Eq. (2) has been applied to the measurements taken within the EMeRGe campaign in Europe. There were no H2O2 measurements available for EMeRGe. However, the results reported by Tan et al. (2001) indicate that the rate of OH production from the H2O2 photolysis is not significant except when NOx is low. To be more precise, for conditions having NO <50 ppt, the partitioning of HOx is strongly shifted to HO2. HO2 then predominantly reacts with itself or RO2 to form peroxides, which can in turn photolyse. For conditions with NO >50 pptv, the rates of reactions of HOx with NOx are faster than those of HO2 with HO2 and RO2. As the NO mixing ratio was higher than 50 pptv in 75 % of the air masses probed in Europe, the photolysis of H2O2 was as a first approximation assumed not to be a significant source of OH for the EMeRGe data set considered in this study.

Formaldehyde (HCHO), acetaldehyde (CH3CHO), acetone (CH3C(O)CH3), and glyoxal (CHOCHO) were the OVOCs measured in EMeRGe directly forming radicals through photolysis. They are produced in the photolysis and oxidation of VOCs and are likely the most abundant and reactive OVOCs present. In this study they were assumed to be the dominant VOCs in the air masses probed.

There were no measurements of alkenes provided in EMeRGe. Consequently, the ozonolysis term in Eq. (2) was not included in the analysis.

The above assumptions lead to Eq. (3), which calculates the RO2∗ production rate (PRO2∗) for the EMeRGe measurements as follows: 3PRO2∗=2jO(1D)O3⋅kOD1+H2OH2OkOD1+H2OH2O+kOD1+O2O2+kOD1+N2N2+jHONOHONO+2jHCHOHCHO+2jCH3CHOCH3CHO+2jCH3C(O)CH3CH3C(O)CH3+2jCHOCHOCHOCHO. The production rate of RO2∗ molecules can be expressed in units of mixing ratio of RO2∗ by dividing with the air concentration at each altitude, calculated from the pressure and temperature measurements (for the vertical profile and the latitudinal distribution of PRO2∗, see Figs. S2 and S3 in the Supplement). Figure 4 shows the composite averaged vertical profile of all measured RO2∗ mixing ratios colour-coded with the calculated PRO2∗. For the sake of representativeness and comparability, the number of measurements in each altitude bin is shown in Fig. 4b. The higher RO2∗ mixing ratios observed below 4000 m are typically associated with PRO2∗≥0.4 pptv s-1. Above 4000 m, both PRO2∗ and RO2∗ start to decrease with altitude, as expected. This is related to the decrease in H2O and other radical precursor concentrations with altitude, as detailed in Figs. 5 and 6. In previous airborne campaigns at various parts of the world, RO2∗ vertical distributions showed a local maximum between 1500 and 4000 m, as reported by Tan et al. (2001), Cantrell et al. (2003a, b), and Andrés-Hernández et al. (2009). In the present work, this local maximum is more evident for measurements with PRO2∗≥0.5 pptv s-1.

Figure 5 shows the fractional contribution of the production rate from each radical precursor reaction included in Eq. (3) as a function of altitude. The data are classified into three groups according to the rate of change of production of the RO2∗ mixing ratio: PRO2∗<0.07 pptv s-1 (Fig. 5a), 0.07<PRO2∗<0.8 pptv s-1 (Fig. 5b), and PRO2∗>0.8 pptv s-1 (Fig. 5c) to show the lowest, most common, and highest ranges, respectively, encountered during the campaign. For 89 % of the measurements, 0.07<PRO2∗<0.8 pptv s-1 applies, while the rest of the data are equally distributed in the other two PRO2∗ ranges. The data in each group are always binned over 500 m when available.

Typically, the high amount of H2O in the air masses probed leads to the reaction of O1D with H2O (Reactions R1–R2a), being the highest RO2∗ radical production rate (≥50 %) below 4000 m. As the amount of H2O reduces with altitude, the relative contribution from O3 photolysis decreases. Above 4000 m, HCHO, HONO, and CHOCHO photolysis contributions range between 20 % to 40 %, 2.5 % to 30 %, and 5 % to 25 %, respectively. The HCHO contribution increases up to 80 % during measurements above 6000 m. The contributions of CH3CHO and CH3C(O)CH3 photolysis are, in contrast, practically negligible (<5 %).

The vertical changes of the precursor mixing ratios and photolysis frequencies used to calculate PRO2∗ in Fig. 5 are shown in Fig. 6a to f. PRO2∗<0.07 pptv s-1 is associated with measurements under cloudy conditions, towards sunset where the photolysis frequencies are low, or at altitudes above 5000 m in air masses with a low amount of RO2∗ precursors. Values of PRO2∗>0.8 pptv s-1 are found for air masses, measured below 2000 m in the outflow of MPCs over the sea, for conditions having sufficient insolation (jO(1D)>3×10-5 S-1) and a high content of RO2∗ precursors (HCHO >1000 pptv and HONO >100 pptv). The increase in the photolysis frequencies as a function of altitude is concurrent with decreases in precursor concentrations. As a result, the PRO2∗ rates do not significantly vary with altitude in the air masses investigated.

In previous airborne campaigns, Tan et al. (2001) and Cantrell et al. (2003b) reported a reduction of the fractional contribution of the reaction of O(1D) with H2O as the PRO2∗ value decreases. At very low PRO2∗ values (<0.03 pptv s-1), the sum of all other production terms exceeded the fraction from the O(1D) + H2O term. For these conditions, H2O2 and VOCs photolysis dominated PRO2∗. For the EMeRGe data set in Europe, only 6 % of PRO2∗ is below 0.06 pptv s-1.

Under most ambient conditions in the troposphere, the RO2∗ species are short-lived, and the chemical lifetime of RO2∗ is much shorter than the chemical transport time into and out of an air mass being probed. Consequently, pseudo-steady-state conditions prevail, and the radical production and destruction rates are balanced: 4PRO2∗=DRO2∗. The Reactions (R5) to (R7), (R12), (R16b), and (R23) to (R26) are interconversion reactions between OH, RO, HO2, and RO2 and do consequently occur without radical losses. Solving Eq. (4) leads to Eq. (5) if RO2∗–RO2∗ reactions are assumed to be the dominant radical terminating processes. 52jO(1D)O3⋅kOD1+H2OH2OkOD1+H2OH2O+kOD1+O2O2+kOD1+N2N2+jHONOHONO+2jHCHOHCHO+2jCH3CHOCH3CHO+2jCH3C(O)CH3CH3C(O)CH3+2jCHOCHOCHOCHO=kRO2∗+RO2∗RO2∗2, where jHCHO, jCH3CHO, jCH3C(O)CH3, and jCHOCHO are respectively j8, j9, j10, and j11, as in Table S1 in the Supplement, and kRO2∗+RO2∗ represents an effective RO2∗ self-reaction rate coefficient, comprising HO2–HO2, HO2–RO2, and RO2–RO2 reaction rates.

Consequently, the RO2∗ concentrations are expected to correlate with the square root of the PRO2∗.

Figure 7 shows the relationship between the measured [RO2∗] and the calculated PRO2∗2. Generally, both [RO2∗] and PRO2∗2 increase with the photolysis frequency of O3 (jO(1D)). Measurements with [RO2∗] <0.5×1012 molecules cm-3, PRO2∗2<1000, and jO(1D)>5×10-5 were made above 6000 m, where the amount of RO2∗ precursors is low. The relatively weak correlation observed between [RO2∗] and PRO2∗2 indicates the necessity of other radical terminating processes and/or missing radical formation terms in the PRO2∗ calculation. Apart from this, the spread in the diagram confirms that the effective RO2∗ self-reaction rate kRO2∗+RO2∗RO2∗2 varies widely in the air masses probed, likely due to the effect of changes in HO2 and ∑RO2 concentrations in the individual loss reaction rate coefficients. Photochemical processing is expected to be enhanced over southern Europe due to the prevailing conditions of high insolation and temperatures during the EMeRGe flights, which might lead to the rapid production of RO2∗ from the photochemical oxidations of CO and VOCs. This is also reflected in the higher PRO2∗ and [RO2∗] observed in southern Europe as compared to those in northern Europe (Fig. 7b).

The correlation between [RO2∗] and PRO2∗2 improves when the measurements south and north of 47∘ N are separately analysed (Fig. 8). For a given [RO2∗], the PRO2∗ calculated is higher for the measurements north of 47∘ N than south of 47∘ N. The lowest [RO2∗] to PRO2∗2 ratios are associated with higher NOx (NO + NO2), especially north of 47∘ N, indicating the urban character and higher amounts of the RO2∗ precursors of the air probed (Fig. 8d). Please note that these results are only valid for the data set acquired over Europe during EMeRGe flights and do not yield a relationship between [RO2∗] and PRO2∗2, which is generally applicable under all conditions for these two latitude windows.

The relationship between RO2∗ and PRO2∗ is further investigated to identify the dominant RO2∗ loss process in the air masses considered in this study. As stated in Sect. 3, HO2 and RO2 are not speciated but retrieved as RO2∗ by the PeRCEAS instrument. Because not all peroxy radicals are detected equally by the instrument, the comparison of measured and calculated RO2∗ values is complicated. To investigate this, the changes in the HO2 to the total RO2∗ ratios have been taken into consideration by δ (i.e. [HO2] =δ[RO2∗] and [CH3O2] = (1-δ) [RO2∗]) in the analysis. As a first approach, RO2 is assumed to consist only of CH3O2 to reduce the complexity of the calculations by considering only CH3O2 reaction rate constants. The reaction channel (R25b) is not considered in the calculation since the yield of this channel is <5 % (Burkholder et al., 2019) for CH3O2+ NO reaction. Moreover, as mentioned in Sect. 3, the ratio α=eCLCH3O2/eCLHO2 was determined to be 65 % for the measurement conditions (George et al., 2020).

Equation (5) is additionally extended to include RO2∗ effective yields from VOC oxidation and radical losses through HONO and HNO3 formation: 62j1O3β+j3HONO1-ρ+2j8HCHO+2j9[CH3CHO]+2j10a+j10b[CH3C(O)CH3]+2j11CHOCHO=δRO2∗k23NO+k24O3ρ+2k15δ1-δRO2∗2+2k16a1-δRO2∗2+2k14δRO2∗2, where β is the effective yield of OH in the reaction of O(1D) with H2O given by 7β=k2aH2Ok2aH2O+k2bO2+k2cN2. On the left-hand side of Eq. (6), 1-ρ accounts for the effective yield of HO2+RO2 production through the radical initiation Reactions (R2a) and (R3) and Reactions (R5) to (R7) and (R12). As the calculation is constrained with onboard measurements, only the reactions of measured VOCs were considered in Reaction (R12). Similarly, on the right-hand side of Eq. (6), ρ accounts for the radical termination through the OH + NO, OH + NO2, and OH + HONO reactions (Reactions R19 to R21) relative to the radical undergoing OH to peroxy radical conversion.

Consequently, ρ is given by 8ρ=k19NO+k20NO2+k21HONOk5O3+k6CO+k7CH4+k12aHCHO+k12bCH3CHO+k12cCH3COCH3+k12dCH3OH+k12eCHOCHO+k19NO+k20NO2+k21HONO. Measurements of CH4, HCHO, CH3CHO, CHOCHO, CH3OH, and CH3C(O)CH3 on board HALO are available and implemented in Eq. (6). These comprise the most abundant and reactive OVOCs and are considered to be a representative surrogate for the VOCs that act as RO2∗ precursors through oxidation and photolysis. During the EMeRGe campaign in Europe, k12a× [HCHO] and k12b×[CH3CHO] have the highest contribution to 1-ρ from all the OVOC measured. Their impact on the RO2∗ budget is found to be similar, because their respective concentrations compensate for the difference in the rate coefficients of their reactions with OH (k12a=8.5×10-12 cm3 molecule-1 s-1 and k12b=1.5×10-11 cm3 molecule-1 s-1 at 298 K and 1 atm). Despite its high mixing ratios measured, CH3C(O)CH3 is less important in the 1-ρ term. This is because the rate coefficient k(T)12c is significantly slower than k12a and k12b (see Table S1 in the Supplement). Similarly, the contribution of CHOCHO and CH3OH is an order of magnitude lower than that of HCHO and CH3CHO.

Concerning the term δRO2∗k23NO+k24O3ρ on the right-hand side of Eq. (6), the HO2 reaction with O3 has a negligible effect as k24 is almost 4 orders of magnitude smaller than k23, and the NO concentrations remained about 3 orders of magnitude smaller than the O3 measured during the campaign.

The impact of the methylglyoxal (CH3C(O)C(O)H) photolysis was also investigated by using the CH3C(O)C(O)H∗ measurements provided by the miniDOAS instrument. The CH3C(O)C(O)H∗ measured is the sum of CH3C(O)C(O)H and a fraction of other substituted dicarbonyls (mainly 2,3-butanedione, C3H6O2), with similar visible absorption spectra. For the calculation, CH3C(O)C(O)H was assumed to be half of CH3C(O)C(O)H∗ as recommended by Zarzana et al. (2017) and Kluge et al. (2020). The RO2∗ calculated by including CH3C(O)C(O)H photolysis systematically overestimated the measurements. As the adequacy of the recommended factor of 0.5 varies with the actual air mass composition, CH3C(O)C(O)H was not included in the calculations.

Figure 9 shows the fractional contribution of the destruction rate (DRO2∗) calculated for a 1:1 mixture of HO2 and CH3O2 using the reactions included in Eq. (6) as a function of altitude. The data are classified into three groups according to the rate of destruction of RO2∗ mixing ratio: DRO2∗<0.01 pptv s-1 (a), 0.01<DRO2∗<0.9 pptv s-1 (b), and DRO2∗>0.9 pptv s-1 (c) to show the lowest, most common, and highest ranges, respectively, encountered during the EMeRGe campaign. For 90 % of the measurements, 0.01<DRO2∗<0.9 pptv s-1 applies, while the rest of the data are equally distributed in the other two DRO2∗ ranges. The data in each group are always binned over 500 m when available.

As can be seen in Fig. 9, the ±1σ standard deviation of the obtained bins is very high. In spite of this, the HO2–CH3O2 and HO2–HO2 reactions seem to dominate the radical destruction processes in the air masses probed. Their combined contribution is >70 % in all the cases except in the 1000 m bin of DRO2∗>0.9 pptv s-1. Other significant radical losses occur through the HONO and HNO3 formation. The contribution of the CH3O2+ CH3O2 reaction to the total RO2∗ destruction rate is <5 %.

Since Eq. (6) is quadratic in [RO2∗], it can be solved for RO2∗c, where “c” stands for calculated, as 9RO2∗c=--LRO2∗-LRO2∗2-4-2kRO2∗PRO2∗22-2kRO2g∗, where kRO2∗=k16a1-δ2+k15δ1-δ+k14δ2,LRO2∗=δk23NO+k24O3ρ,PRO2g∗=2j1O3β+j3HONO1-ρ+2j8HCHO+2j9[CH3CHO]+2j10a+j10b[CH3C(O)CH3]+2j11CHOCHO, and where kRO2∗ is a weighed rate coefficient of RO2∗ self-reactions for a 1:1 mixture of HO2 and CH3O2, LRO2∗ comprises the formation of HONO and HNO3, and PRO2g∗ is the gross production of RO2∗.

The second solution of the quadratic equation gives negative values for RO2∗c; therefore, it is assumed to have no physical meaning. A more detailed derivation of Eqs. (6) and (9) are given in the Supplement.

Figure 10 shows the measured RO2∗ (hereinafter referred to as RO2m∗) mixing ratio versus the calculated RO2c∗ mixing ratio using Eq. (9). RO2m∗ and RO2c∗ are the measured and calculated RO2∗ respectively for δ=1 (i.e. RO2∗=HO2) and δ=0.5 (i.e. HO2=RO2). The eCL values corresponding to δ=1 and δ=0.5 used for the RO2m∗ retrievals were determined in laboratory experiments, as reported by George et al. (2020). The small circles represent 1 min RO2m∗, whereas the large circles are the mean of the RO2m∗ binned over 10 pptv RO2c∗ intervals. The RO2∗ data are colour-coded with the onboard NO measurements. The linear regression slopes are around 0.7 (R2=0.96), indicating an overall 25 %–30 % overestimation of the RO2m∗. The y-axis intercept is below the instrumental detection limit for most measurement conditions.

Figure 11 shows the vertical profiles of RO2m∗ and RO2c∗ mixing ratios calculated for δ=0.5, averaged for the EMeRGe flights over Europe in 500 m altitude bins. RO2c∗ seems to overestimate RO2m∗ for altitudes above 4000 m. As mentioned in Sect. 4.1, the vertical profiles are a composite from averaging flights with legs carried out at different longitudes and latitudes. Therefore, the differences between RO2m∗ and RO2c∗ have been studied in more detail with respect to the composition of the individual air masses (see the RO2m∗ and RO2c∗ mixing ratios as a function of latitude and altitude in Fig. S4 in the Supplement).

Figure 12 shows the data for δ=0.5 colour-coded with NO; NOx; the sum of HCHO, CH3CHO, CHOCHO, CH3OH, and CH3C(O)CH3 (from now on referred to as ΣVOCs), as a surrogate for the amount of OVOCs acting as RO2∗ precursors; and the ΣVOCs to NO ratio. The largest differences between RO2m∗ and RO2c∗ are observed for the bins around 50 pptv. The RO2c∗ values overestimate the RO2m∗ mostly for RO2m∗<25 pptv observed above ≈4000 m. These air masses are characterised by NO <50 pptv, ∑VOCs typically below 4 ppbv, high ΣVOCs / NO ratios (>50), and low insolation conditions (i.e. jO(1D)<2×10-5 s-1) (see Fig. S5 in the Supplement). Under these insolation conditions, the radical production rate is expected to be low, and the RO2∗–RO2∗ reactions are expected to dominate the RO2∗ loss processes. As OH and H2O2 were not measured during the EMeRGe campaign in Europe, Eq. (9) does not include the loss Reactions (R17) and (R18), which might be significant under such conditions (Tan et al., 2001) and explain the overestimation of RO2m∗. This is also the case for the overestimations observed below 40 pptv RO2m∗ at other altitudes, where NO <50 pptv but the ΣVOCs / NO ratios remain low. The overestimation may therefore be independent of the ΣVOCs / NO ratios. For NO ≤50 pptv, NO2≤100 pptv, RO2∗≤40 pptv, and HCHO ≤1 ppbv, the rate of Reaction (R17), which forms H2O and O2 from OH and HO2, is about 4 times faster than the rate of the OH oxidation reaction of the dominant OVOCs (Reaction R12) considered in this study or the rate of formation of HONO (Reaction R19).

RO2m∗ is both underestimated and overestimated for ∑VOCs mixing ratios greater than 7 ppbv. The composition of these air masses is very different, as reflected by the ΣVOCs / NO ratios. This implies that Eq. (9) does not capture the peroxy radical yields adequately from the measured VOCs and OVOC in these cases. The differences between RO2m∗ and RO2c∗ may be explained in part by (a) changes in OH yields due to additional VOC oxidation processes, which are not in Eq. (9); (b) RO2∗ production from the photolysis of carbonyls, which were not measured; (c) RO2∗ production from the ozonolysis of alkenes or unidentified biogenic terpene emissions; and/or (d) overestimation of the loss processes.

In addition, Eq. (9) does not consider the loss of RO2 through the organic nitrate formation (Reaction R25b), which results in an underestimation of radical loss in the presence of RO2 with organic groups larger than CH3. Tan et al. (2019) reported that changing the yields for organic nitrate formation channel in Reaction (R25) from 5 % to 20 % has a small but notable influence on their experimental budget analysis. Similarly, the RO2 loss through organic nitrate formation, which is not included in Eq. (9), might explain the RO2m∗ overestimations for ∑VOC <2 ppb, ∑VOCs / NO <20, and for NO >200 pptv.

Although considered small, the spatial and temporal differences in the in situ measurements of the key trace gases (O3, NO, H2O, CO, CH4, VOCs) as compared to those of the remote sensing observations (NO2 and HONO) used in Eq. (9) may also contribute to the overall spread observed in Fig. 12. Although the temporal evolution and the amount of the trace gases measured using in situ and remote sensing instruments agree reasonably well, as shown for HCHO in Fig. 13, the remote sensing instruments have, in general, larger air sampling volumes compared to that of in situ instruments. This may occasionally lead to significant differences depending on the location of the pollutant layers with respect to HALO. In addition, PTR-MS measurements of HCHO might include interferences from molecular fragments of other compounds in the sample air (Inomata et al., 2008). Further details about the accuracy and comparability of the onboard instrumentation during the campaign can be found elsewhere (Schumann, 2020).

In summary, apart from the inaccuracies in the reaction rate coefficients, the differences between RO2m∗ and RO2c∗ might be caused by a combined effect of the limitations of the analytical expression to simulate complex non-linear chemistry and the measurement uncertainties arising from the spatial heterogeneity of the plume for the remote sensing instruments. Consequently, the quantification of limiting factors in Eq. (9) require the analysis of the pollution events encountered along the flights individually.

The ratio of RO2m∗ to RO2c∗ (RO2m∗ / RO2c∗) has been used to assess the applicability of Eq. (9) for the calculation of RO2∗ in the air masses probed. In Fig. 14, the data are colour-coded with respect to RO2m∗ / RO2c∗, H2O, ΣVOCs, and NOx. The air masses probed at altitudes above 2000 m are close to the PSS assumptions used to develop Eq. (9), and consequently, the RO2m∗ / RO2c∗ ratio remains ≤1. In contrast, RO2m∗ / RO2c∗ is at its highest value below 2000 m, reaching up to 3. At these altitudes, most of the flights in Europe were carried out in pollution plumes, in which both the amounts of NOx and RO2∗ precursors are high. The analytical expression does not capture the RO2∗ variations resulting from fast non-linear photochemistry present in these pollution plumes. This is the case for the measurements made between 42 and 46∘ N in the outflow of the Po Valley and Rome. ∑VOCs >7 ppbv and NOx mixing ratios >500 pptv indicate high radical precursor loading and relatively fresh emissions. The RO2m∗ / RO2c∗ is also >2 in the measurements over the English Channel (between 50 and 52∘ N) with ∑VOCs and NOx mixing ratios >7 ppbv and 1000 pptv, respectively.

The applicability of Eq. (9) for calculating the in-flight measurements of RO2∗ along the track of the E-EU-03 flight on 11 July 2017 was studied in more detail. The E-EU-03 flight investigated the outflow of selected MPCs in Italy (i.e. Po Valley and Rome). Consequently, the flight track was routed along the western coast of Italy and included vertical profiling over the Tyrrhenian Sea upwind of Rome (see Fig. S6 in the Supplement). As indicated by jO(1D), in Fig. 15, cloudless conditions dominated throughout the flight track. The RO2c∗ values agree reasonably well with RO2m∗ throughout this period except in the pollution plume measured from 12:05 to 12:25 UTC. In this plume, CO, NO, NO2, HONO, NOy, and HCHO were 100 ppbv, 180 pptv, 150 pptv, 120 pptv, 1 ppbv and 2 ppbv, respectively. The RO2m∗ values are approximately 20 % underestimated by RO2c∗ during this period. Backward trajectories calculated using FLEXTRA (Stohl et al., 1995; Stohl and Seibert, 1998) indicate the transport of pollution through the Mediterranean mixed with dust plumes originating from Tunisia. The NO mixing ratios observed indicate the proximity to emission sources.

The measurements of VOCs used in Eq. (9) may not be representative of the actual complex VOC composition in the plume measured from 12:05 to 12:25 UTC. Consequently, the RO2 to HO2 ratio, the branching ratios, and effective rate coefficients for RO2∗–RO2∗ reactions might not be well represented in Eq. (9). Taking CH3O2 as a surrogate for all RO2 might lead to uncertainties in the RO2∗ calculations in the presence of OVOCs with larger organic chains. On the experimental side, changes in the HO2 to RO2 ratio affect the accuracy of the PeRCEAS retrieval of the total sum of radicals. As noted in Sect. 3, in this study RO2∗= HO2+0.65×RO2, and the eCL is determined for a 1:1 mixture of HO2:CH3O2 (i.e. δ=0.5 is used for the RO2∗ retrieval). However, the HO2 to CH3O2 ratio is not expected to remain constant in all the air masses probed. For a 3:1 ratio of HO2:RO2, the RO2m∗ would decrease by 10 %. Similarly, a HO2:RO2 ratio of 1:3 would lead to an increase of 10 % in the reported RO2m∗. This uncertainty is well below the in-flight uncertainty of the PeRCEAS instrument indicated by the error bars in Fig. 14 (George et al., 2020) and cannot account for the overall underestimation. However, it might reduce the differences observed between RO2m∗ and RO2c∗ in particular cases. A complete explanation of the variability of RO2∗ in the pollution plumes measured within the campaign in Europe is beyond the scope of this analysis and requires an investigation by high-resolution chemical models.