Articles | Volume 23, issue 13
Research article
14 Jul 2023
Research article |  | 14 Jul 2023

Airborne observations of peroxy radicals during the EMeRGe campaign in Europe

Midhun George, Maria Dolores Andrés Hernández, Vladyslav Nenakhov, Yangzhuoran Liu, John Philip Burrows, Birger Bohn, Eric Förster, Florian Obersteiner, Andreas Zahn, Theresa Harlaß, Helmut Ziereis, Hans Schlager, Benjamin Schreiner, Flora Kluge, Katja Bigge, and Klaus Pfeilsticker

In this study, airborne measurements of the sum of hydroperoxyl (HO2) and organic peroxy (RO2) radicals that react with nitrogen monoxide (NO) to produce nitrogen dioxide (NO2), coupled with actinometry and other key trace gases measurements, have been used to test the current understanding of the fast photochemistry in the outflow of major population centres. The measurements were made during the airborne campaign of the EMeRGe (Effect of Megacities on the transport and transformation of pollutants on the Regional to Global scales) project in Europe on board the High Altitude and Long Range Research Aircraft (HALO). The measurements of RO2 on HALO were made using the in situ instrument Peroxy Radical Chemical Enhancement and Absorption Spectrometer (PeRCEAS). RO2 is to a good approximation the sum of peroxy radicals reacting with NO to produce NO2. RO2 mixing ratios up to 120 pptv were observed in air masses of different origins and composition under different local actinometric conditions during seven HALO research flights in July 2017 over Europe.

Radical production rates were estimated using knowledge of the photolysis frequencies and the RO2 precursor concentrations measured on board, as well as the relevant rate coefficients. Generally, high RO2 concentrations were measured in air masses with high production rates. In the air masses investigated, RO2 is primarily produced by the reaction of O1D with water vapour and the photolysis of nitrous acid (HONO) and of the oxygenated volatile organic compounds (OVOCs, e.g. formaldehyde (HCHO) and glyoxal (CHOCHO)). Due to their short lifetime in most environments, the RO2 concentrations are expected to be in a photostationary steady state (PSS), i.e. a balance between production and loss rates is assumed. The RO2 production and loss rates and the suitability of PSS assumptions to estimate the RO2 mixing ratios and variability during the airborne observations are discussed. The PSS assumption for RO2 is considered robust enough to calculate RO2 mixing ratios for most conditions encountered in the air masses measured. The similarities and discrepancies between measured and PSS calculated RO2 mixing ratios are discussed. The dominant terminating processes for RO2 in the pollution plumes measured up to 2000 m are the formation of nitrous acid, nitric acid, and organic nitrates. Above 2000 m, HO2HO2 and HO2RO2 reactions dominate the RO2 removal. RO2 calculations by the PSS analytical expression inside the pollution plumes probed often underestimated the measurements. The underestimation is attributed to the limitations of the PSS equation used for the analysis. In particular, this expression does not account for the yields of RO2 from the oxidation and photolysis of volatile organic compounds, VOCs, and OVOCs other than those measured during the EMeRGe research flights in Europe. In air masses with NO mixing ratios ≤50 pptv and low VOC/NO ratios, the RO2 measured is overestimated by the analytical expression. This may be caused by the formation of H2O and O2 from OH and HO2, being about 4 times faster than the rate of the OH oxidation reaction of the dominant OVOCs considered.

1 Introduction

Hydroperoxyl (HO2) and organic peroxy (RO2, where R stands for any organic group) radicals are reactive species that play a key role in the chemistry of the troposphere. In combination with the hydroxyl (OH) radical, HO2 and RO2 take part in rapid chemical processes that control the lifetime of many key trace constituents in the troposphere. Examples of key tropospheric processes involving HO2 and RO2 are as follows:

  • the catalytic cycles which produce and destroy ozone (O3);

  • the generation of inorganic acids, which are precursors of aerosol and important chemical constituents in both summer and winter smog (e.g. sulfuric acid, H2SO4, and nitric acid, HNO3);

  • the generation of organic acids and the production of hygroscopic hydrogen peroxide (H2O2) and organic peroxides (ROOH), which enter aerosol and cloud droplets;

  • the generation of organic peroxy nitrates (RO2NO2), peroxyacetyl nitrate (CH3COO2NO2, PAN), and other summer smog constituents.

The abundance of HO2 and RO2 in the free troposphere has a non-linear and complex dependency on photochemistry, initiated by solar actinic radiation, and on the concentration of the precursors, such as carbon monoxide (CO), volatile organic compounds (VOCs), and peroxides. It also strongly depends on the amounts of nitrogen monoxide (NO) and nitrogen dioxide (NO2) due to the gas-phase reactions of NO and NO2 with the OH and organic oxy (RO) radicals formed during the radical interconversion. The main production and loss processes of HO2 and RO2 in the troposphere are summarised as follows:

  1. Production processes of HO2 and RO2:

    (R1) O 3 + h ν ( λ < 320 nm ) O ( 1 D ) + O 2 ;
    (R3)HONO+hν(λ400nm)OH+NO;(R4)H2O2+hν2OH;(R5)OH+O3HO2+O2;(R6)OH+CO+O2HO2+CO2;(R7)OH+CH4+O2CH3O2+H2O;(R8)HCHO+hν(λ<340nm)+2O22HO2+CO;(R9)CH3CHO+hν(λ<340nm)+2O2CH3O2+HO2+CO;,(R10)CH3C(O)CH3+hν(λ<340nm)+2O22CH3O2+CO;(R11)CHOCHO+hν+2O2M2HO2+2CO;(R12)VOCs+OHOH+HO2+RO2+other oxidation products;(R13)alkenes+O3OH+RO2+ other oxidation products;


  2. Loss processes of HO2 and RO2:


In addition, HO2 and RO2 participate in radical interconversion reactions such as


Reactions (R23) and (R25a) are two of the most important reactions in the troposphere as they lead to O3 formation via Reactions (R27) and (R28). The rate of Reaction (R22) in the atmosphere compared to that of Reaction (R26) is negligible.

The sum of HO2 and RO2 that react with NO to produce NO2 can be estimated by assuming that the interconversion of NO to NO2 reaches a photostationary steady state (PSS), in which production and loss of NO2 are to a good approximation equal.

The PSS assumption for [NO2] in the following mechanism (Reactions R23 to R29) leads to Eq. (1):

(R23)HO2+NOOH+NO2,(R25a, R26)RO2+NO+O2RH-1O+NO2+HO2,(R27)NO2+hν(λ<400nm)NO+O,(R28)O+O2MO3,(R29)NO+O3NO2+O2,

(1) HO 2 + RO 2 PSS = k NO + O 3 k NO + ( HO 2 + RO 2 ) j NO 2 NO 2 k NO + O 3 NO - O 3

where jNO2 is the photolysis frequency of NO2; kNO+O3 (1.9×10-14 cm3 molecules−1 s−1 at 298 K and 1 atm) is the rate coefficient of the reaction of NO with O3; and kNO+(HO2+RO2) is usually estimated for the most abundant peroxy radicals HO2 and CH3O2 by assuming a 1:1 HO2 to CH3O2 ratio and averaging the kNO+HO2 (8.2×10-12 cm3 molecules−1 s−1 at 298 K and 1 atm) and kNO+CH3O2 (7.7×10-12 cm3 molecules−1 s−1 at 298 K and 1 atm) rate coefficients for the reaction with NO. As noted by Parrish et al. (1986), the PSS assumption for NO2 requires conditions with sufficient and stable solar irradiation, ensuring stable jNO2.

The radical calculation made on the assumption of the NO2 steady state is very sensitive to the accuracy of the NO2 to NO ratio and the O3 measurements. The comparison of HO2+RO2PSS calculated using Eq. (1) with ground-based (e.g. Ridley et al., 1992; Cantrell et al., 1997; Carpenter et al., 1998; Volz-Thomas et al., 2003) as well as airborne measurements has shown in the past different degrees of agreement. The underestimations and overestimations found in air masses with different chemical compositions are not well understood. For the case of airborne measurements, the NO2 steady-state calculation generally overestimates the measured peroxy radicals (Cantrell et al., 2003a, b). The differences observed could not be attributed to systematic changes in NO, altitude, water vapour, or temperature, although these variables are often correlated. The NO to NO2 ratio calculated from NO measured using an in situ technique and NO2 measured using remote sensing (more detail about the measurement techniques is given in Table 1) used in this study is considered not to have sufficient accuracy to calculate [HO2+RO2] from the NO2 steady-state approach.

Ground-based (Mihelcic et al., 2003; Kanaya et al., 2007, 2012; Elshorbany et al., 2012; Lu et al., 2012, 2013; Tan et al., 2017, 2018; Whalley et al., 2018, 2021; Lew et al., 2020) and airborne (Crawford et al., 1999; Tan et al., 2001; Cantrell et al., 2003b) measurements have also been compared with model simulations of HO2 and RO2. The discrepancies encountered depend upon the chemical composition of the air mass and the chemical mechanisms and constraints used in the model simulations. Recently, Tan et al. (2019) and Whalley et al. (2021) reported experimental radical budget calculations using the PSS assumption for OH, HO2, and RO2 together with the published reaction rate coefficients of Reactions (R1) to (R26), which control OH, HO2, and RO2 in the lower troposphere, and the ground-based measurements of all relevant reactants and photolysis frequencies. In this study, a similar approach has been used (i.e. the sum of HO2 and RO2 is assumed to be in PSS) to calculate the amount of peroxy radicals in the air masses measured on board of the High Altitude and Long Range Research Aircraft (HALO) over Europe during the first campaign of the EMeRGe (Effect of Megacities on the transport and transformation of pollutants on the Regional to Global scales) project. The available onboard measurements of RO2 are defined as the total sum of OH, RO, and peroxy radicals (i.e. RO2= OH +RO + HO2+RO2, where RO2 are the organic peroxy radicals producing NO2 in their reaction with NO). As the amount of OH and RO is much smaller, RO2 to a good approximation is the sum of HO2 and those RO2 radicals that react with NO to produce NO2. For the calculation, RO2 is assumed to be in PSS, and an analytical expression is developed with a manageable degree of complexity to estimate the concentration and mixing ratios of RO2. The simultaneous onboard measurements of trace gases and photolysis frequencies are used to constrain the estimate of the RO2 concentration.

In contrast to other experimental deployments, the concentrations and/or mixing ratios of the majority of the key species involved in Reactions (R1) to (R26) were continuously measured on board HALO during the EMeRGe campaign. This enables the use of a large number of measurements to constrain the PSS calculation of RO2. Consequently, this data set provides an excellent opportunity to gain deeper insight into the source and sink reactions of RO2 and the applicability of the PSS assumption for the different pollution regimes and related weather conditions in the free troposphere.

2 EMeRGe field campaign in Europe

The overarching objective of the EMeRGe project is to test and improve the current understanding of the photochemical and heterogeneous processing of pollution outflows from major population centres (MPCs) and their impact on the atmosphere. Two intensive observational periods (IOPs) were carried out to investigate selected European and Asian MPC outflows. The European IOP took place from 10 to 28 July 2017 (, last access: 19 June 2023). An extensive set of in situ and remote sensing airborne measurements of trace gases and aerosol particles were made on board the HALO aircraft (see, last access: 19 June 2023) along flight tracks in the lower layers of the troposphere from northwest Europe to the Mediterranean region.

During EMeRGe in Europe, HALO made a total of 53 flight hours distributed over seven flights to investigate the chemical composition of the outflows from the target MPCs: London, Paris, Benelux, Ruhr metropolitan area, Po Valley, and urban agglomerations such as Rome, Madrid, and Barcelona. The flight tracks are shown in Fig. 1. All measurement flights started from the aircraft hangar at the DLR in Oberpfaffenhofen, southwest of Munich, Germany. To achieve the scientific goals, 60 % of the flights flew at altitudes below 3000 m. Vertical profiles of trace constituents were typically made by keeping the flight altitude constant at different flight levels upwind and downwind of the target MPCs. The flights are named E-EU-FN, where E stands for EMeRGe, EU for Europe, and FN is the two-digit flight number. More details about the EMeRGe IOP in Europe and the set of instruments deployed on board the HALO aircraft are described elsewhere (Andrés Hernández et al., 2022).

Figure 1The research flight tracks made by HALO during the EMeRGe Europe campaign on 11, 13, 17, 20, 24, 26 and 28 July 2017 (E-EU-03 to E-EU-09, respectively, colour coded). MPC target areas are colour coded by shading, and the targeted locations/regions are marked with red stars, M: Madrid, B: Barcelona, P: Paris, L: London; BNL: Benelux; Ru: Ruhr area; PV: Po Valley, R: Rome. The location of the aircraft hangar at the DLR in Oberpfaffenhofen (OP), Germany, is indicated by a yellow star.

3 PeRCEAS and other instruments on board HALO during EMeRGe

The RO2 measurements on board HALO during EMeRGe were made using the Peroxy Radical Chemical Enhancement and Absorption Spectrometer (PeRCEAS). PeRCEAS combines the peroxy radical chemical amplification (PeRCA) and cavity ring-down spectroscopy (CRDS) techniques in a dual-channel instrument. Each channel has a separate chemical reactor and detector, which operate alternatively in both background and amplification modes to account for the rapid background variations during airborne measurements. In both modes, NO is continuously added to the air sampled at the reactor, while CO is only added in the amplification mode to initiate the chain conversion of RO2 into NO2. In the amplification mode, the sum of the NO2 produced from ambient RO2 through the chain reaction, the ambient NO2, the NO2 produced from the ambient O3–NO reagent gas reaction, and the NO2 produced in the inlet from any other sources (e.g. thermal decomposition of PAN) is measured. In the background mode, the sum of the ambient NO2, the NO2 produced from the ambient O3–NO reagent gas reaction, and NO2 produced in the inlet from any other sources is measured. The RO2 is retrieved by dividing the difference in NO2 concentration (ΔNO2) between amplification and background mode by the conversion efficiency of RO2 to NO2, which is referred to as eCL (effective chain length). The PeRCEAS instrument and its specifications have been described in detail elsewhere (Horstjann et al., 2014; George et al., 2020; George, 2022).

The two chemical reactors for sampling the ambient air are part of the DUal channel Airborne peroxy radical Chemical Amplifier (DUALER) inlet installed inside a pylon located on the outside of the HALO fuselage. During the EMeRGe campaign in Europe, a reagent gas mixing ratio of 30 ppmv NO ([NO] =1.46×1014 molecules cm−3 at 296 K, 200 mbar) and of 9 % CO ([CO] =4.4×1017 molecules cm−3 at 296 K, 200 mbar) was added to the sample flow for the chemical conversion of RO2 to NO2. The DUALER inlet was operated at an internal pressure of 200 mbar to achieve stable chemical conversion. The HO2 and RO2 detection sensitivity depends on the rates of loss of HO2 and RO2 by Reactions (R19) and (R22). The latter depends on the concentration of the reagent gas NO added and the reaction rate coefficients, where k22 is larger than k19. The average eCL for a 1:1 HO2 to CH3O2 mixture under the DUALER conditions during the campaign in Europe was determined to be 50±8 from laboratory calibrations, where the error is the ±1σ standard deviation estimated from the reproducibility of the experimental determinations. Likewise, the ratio α=eCLCH3O2/eCLHO2 was determined to be 65 % for the measurement conditions (George et al., 2020). The values obtained from calibrations before and after the campaign agreed within their experimental errors.

Although the DUALER pressure is kept constant below the ambient pressure, variations in dynamical pressure >10 mbar during the flight change the residence time and induce turbulence inside the inlet (Kartal et al., 2010; George et al., 2020). These may lead to different physical losses of radicals before amplification and affect the eCL. In the measurements presented in this study, variations in dynamical pressure of this magnitude were only encountered during flight level changes of the aircraft. When used during the analysis, these data sets are either excluded or flagged (P_flag). The effect of the ambient air humidity on eCL (Mihele and Hastie, 1998; Mihele et al., 1999; Reichert et al., 2003) has been accounted for by a calibration procedure reported in George et al. (2020). The [H2O] in the DUALER inlet was lower than 1×1017 molecules cm−3 for 60 % of measurements during EMeRGe in Europe, for which the eCLwet=76 % of eCLdry. At the highest humidity observed during the campaign, i.e. [H2O]inlet=2×1017 molecules cm−3, the eCLwet is 55 % of eCLdry (see Fig. S1 in the Supplement).

In addition to the measurement of RO2 from PeRCEAS, other in situ and remote sensing measurements and basic aircraft data from HALO are used in this study. Details of the corresponding instruments are summarised in Table 1. The remote sensing instruments used on HALO during EMeRGe were the mini-differential optical absorption spectrometer (miniDOAS) and the Heidelberg airborne imaging DOAS instrument (HAIDI). The miniDOAS observes the atmosphere using six telescopes: two being optimised for the ultraviolet, two for the visible, and two for the near-infrared (nIR). Three telescopes observe in nadir-viewing mode and three in limb-viewing mode. The three limb scanning telescopes point to the starboard side perpendicular to the aircraft fuselage axis. They are rotated to compensate for roll relative to the horizon. A variant of the DOAS retrieval technique uses least square fitting of the measured and radiative transfer modelled absorption along the line of sight to retrieve the differential slant column density (dSCD) of the target gas and a scaling reference gas. The latter is the dimer of molecular oxygen (O4). As the vertical profile of the concentrations of O2 and thus O4 are known, the mixing ratios of the target gas at the flight altitude are obtained from the target gas and O4 dSCDs (for more details, see Stutz et al., 2017; Hüneke et al., 2017; Kluge et al., 2020; and Rotermund et al., 2021). The HAIDI nadir observations are used to retrieve dSCDs below the aircraft. The dSCDs from HAIDI are then converted to mixing ratios using knowledge of the aircraft altitude and the corresponding geometric air mass factor (AMF), calculated by a radiative transfer model under a well-mixed NO2 layer assumption. As a result of this assumption, the calculated mixing ratios for HAIDI target gases are lower limits and similar to the actual values while flying within and close to a well-mixed boundary layer. In spite of the differences in sampling volume and temporal and spatial resolution between the in situ and remote sensing measurement techniques, the concentrations of the gas HCHO measured by both techniques were in good agreement, and the concentrations of the NO2 (remote sensing) and NOy (in situ) were consistent (for more details, see Schumann, 2020).

Table 1List of the airborne measurements and instrumentation used in this study. PeRCA: peroxy radical chemical amplification; CRDS: cavity ring-down spectroscopy; PTR-MS: proton-transfer-reaction mass spectrometer; AT-BS: adsorption tube and bag air sampler; TD-GC-MS: thermal desorption gas chromatography and mass spectrometry; DOAS: differential optical absorption spectrometry; Univ.: University; KIT: Karlsruher Institut für Technologie; DLR: Deutsches Zentrum für Luft- und Raumfahrt; IPA: Institut für Physik der Atmosphäre; FZ: Forschungszentrum; FX: Flugexperimente; HKMS: HALO Karlsruher Mass Spectrometer; VUV: visible–UV; SR: spectroradiometer; BAHAMAS: Basic Halo Measurement and Sensor System; FAIRO: Fast Accurate aIRborne Ozone instrument; CATS: cavity ring-down spectrometer and Tedlar bag sampler.

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4 Results and discussion

4.1 Airborne RO2 measurements during EMeRGe in Europe

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.

Figure 2RO2 measured during EMeRGe-Europe: (a) as a function of longitude and latitude and (b) as a function of latitude and altitude.

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.

Figure 3Composite average vertical profiles of (a) RO2, (b) jO(1D), and (c) [H2O] observations. The measurements are binned over 500 m altitude. The error bars are the ±1σ standard deviation of each bin. Median values (red triangles), the interquartile 25 %–75 % range (shaded red area), and the number of individual measurements for each bin (in green) are additionally plotted.


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.

4.2RO2 production rates

The rate of production of RO2 from Reactions (R1) to (R13) is given by

(2) P RO 2 = 2 j O D 1 O 3 k O D 1 + H 2 O H 2 O k O D 1 + H 2 O H 2 O + k O D 1 + O 2 O 2 + k O D 1 + N 2 N 2 + j HONO HONO + 2 j H 2 O 2 H 2 O 2 + 2 i j i OVOC i + k O 3 + alkenes k O 3 alkenes k γ k ,

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:

(3) P RO 2 = 2 j O ( 1 D ) O 3 k O D 1 + H 2 O H 2 O k O D 1 + H 2 O H 2 O + k O D 1 + O 2 O 2 + k O D 1 + N 2 N 2 + j HONO HONO + 2 j HCHO HCHO + 2 j CH 3 CHO CH 3 CHO + 2 j CH 3 C ( O ) CH 3 CH 3 C ( O ) CH 3 + 2 j CHOCHO CHOCHO .

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 PRO20.4 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 PRO20.5 pptv s−1.

Figure 4(a) Composite averaged vertical distribution of measured RO2 colour-coded according to the value of PRO2; (b) the number of measurements in each altitude bin. Small circles are 1 min individual measurements binned with PRO2 values in 0.1 pptv s−1 intervals. Larger circles result from a further binning over 500 m altitude steps. All the production rates below 0.1 pptv s−1 and above 0.8 pptv s−1 are binned to 0.1 and 0.8 pptv s−1, respectively. The error bars are the standard deviation for each altitude bin.


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.

Figure 5Total PRO2 and fractional precursor contributions estimated using Eq. (3) as a function of altitude for (a) PRO2<0.07 pptv s−1, (b) 0.07 pptv s-1<PRO2<0.8 pptv s−1, and (c) PRO2>0.8 pptv s−1. Note the different scales in the number of measurements.


Figure 6Vertical distribution and variation of (a) to (c) precursor mixing ratios; (d) to (f) photolysis frequencies for the PRO2 bins as in Fig. 5. Note the different scales in the H2O concentration.


4.3 PSS estimation of the RO2 mixing ratios

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:

(4) P RO 2 = D RO 2 .

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 RO2RO2 reactions are assumed to be the dominant radical terminating processes.

(5) 2 j O ( 1 D ) O 3 k O D 1 + H 2 O H 2 O k O D 1 + H 2 O H 2 O + k O D 1 + O 2 O 2 + k O D 1 + N 2 N 2 + j HONO HONO + 2 j HCHO HCHO + 2 j CH 3 CHO CH 3 CHO + 2 j CH 3 C ( O ) CH 3 CH 3 C ( O ) CH 3 + 2 j CHOCHO CHOCHO = k RO 2 + RO 2 RO 2 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 HO2HO2, HO2RO2, and RO2RO2 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 PRO22. Generally, both [RO2] and PRO22 increase with the photolysis frequency of O3 (jO(1D)). Measurements with [RO2] <0.5×1012 molecules cm−3, PRO22<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 PRO22 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+RO2RO22 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).

Figure 7Measured [RO2] versus calculated PRO22 colour-coded for values of (a) jO(1D) and (b) latitude.


The correlation between [RO2] and PRO22 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 PRO22 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 PRO22, which is generally applicable under all conditions for these two latitude windows.

Figure 8Measured [RO2] versus PRO22 for the following latitudes: (a, c) south of 47 N and (b, d) north of 47 N. Note that (a) and (b) are colour-coded with jO(1D); (c) and (d) are colour-coded with the NOx mixing ratio. The dashed lines indicate the linear fit for visual support.


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:

(6) 2 j 1 O 3 β + j 3 HONO 1 - ρ + 2 j 8 HCHO + 2 j 9 [ CH 3 CHO ] + 2 j 10 a + j 10 b [ CH 3 C ( O ) CH 3 ] + 2 j 11 CHOCHO = δ RO 2 k 23 NO + k 24 O 3 ρ + 2 k 15 δ 1 - δ RO 2 2 + 2 k 16 a 1 - δ RO 2 2 + 2 k 14 δ RO 2 2 ,

where β is the effective yield of OH in the reaction of O(1D) with H2O given by

(7) β = k 2 a H 2 O k 2 a H 2 O + k 2 b O 2 + k 2 c N 2 .

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

(8) ρ = k 19 NO + k 20 NO 2 + k 21 HONO k 5 O 3 + k 6 CO + k 7 CH 4 + k 12 a HCHO + k 12 b CH 3 CHO + k 12 c CH 3 C O CH 3 + k 12 d CH 3 OH + k 12 e CHOCHO + k 19 NO + k 20 NO 2 + k 21 HONO .

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 δRO2k23NO+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 HO2HO2 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 %.

Figure 9RO2 destruction rate (DRO2) and fractional contributions from loss reactions in Eq. (6) as a function of altitude for (a) DRO2<0.01 pptv s−1, (b) 0.01 pptv s-1<DRO2<0.9 pptv s−1, and (c) DRO2>0.9 pptv s−1. Note the different scales in the number of measurements.


Since Eq. (6) is quadratic in [RO2], it can be solved for RO2c, where “c” stands for calculated, as

(9) RO 2 c = - - L RO 2 - L RO 2 2 - 4 - 2 k RO 2 P RO 2 2 2 - 2 k RO 2 g ,



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 RO2c; 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 10RO2m versus RO2c using Eq. (9) for (a) δ=1 and (b) δ=0.5. The data are colour-coded with the measured NO mixing ratios. The 1 min data (small circles), the mean of the binned RO2m over 10 pptv RO2c intervals (large circles), and the median of each bin (grey triangles) are shown. The error bars indicate the ±1σ standard deviation of each bin. The linear regression for the binned values (solid line) and the 1:1 relation (dashed line) are also depicted for reference.


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 11Vertical distribution of the mean RO2m and mean RO2c using Eq. (9) for δ=0.5 for the EMeRGe data set in Europe. The measurements are binned over 500 m altitude. The error bars are the ±1σ standard deviation of each bin. Median values (red and cyan triangles), the interquartile 25 %–75 % range (red and blue shaded areas), and the number of individual measurements for each bin (in green) are additionally plotted.


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 RO2RO2 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, RO240 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.

Figure 12RO2m versus RO2c using Eq. (9) for δ=0.5 colour-coded with the measured (a) NO mixing ratio; (b) NOx mixing ratio; (c) ΣVOCs mixing ratio, where ΣVOCs = HCHO + CH3CHO + (CHO)2+ CH3OH + CH3C(O)CH3; and (d) ΣVOCs / NO ratio. The 1 min data (small circles), the mean of the binned RO2m over 10 pptv RO2c intervals (large circles), and the median of each bin (triangles) are shown. The error bars represent the ±1σ standard deviation of each bin. The linear regression for the binned values (solid line) and the 1:1 relationship (dashed line) are plotted for reference.


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).

Figure 13An example of the time series of the measured HCHO mixing ratios retrieved from the remote sensing (HAIDI in blue and miniDOAS in green) and in situ (HKMS in red) instruments during the E-EU-04 flight on 14 July 2017. The shaded region shows ±1σ uncertainties of the HKMS and miniDOAS instruments. The flight altitude is depicted in black.


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.

Figure 14Plots of (a) the ratio of RO2m to RO2c (RO2m/RO2c) assuming that δ=0.5; (b) H2O; (c) VOCs; (d) NOx as a function of latitude and altitude for the EMeRGe measurements in Europe.


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 RO2RO2 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.

Figure 15Temporal variation of RO2m and RO2c, selected radical precursors, and jO(1D) along the E-EU-03 flight track: (a) RO2m and RO2c mixing ratios. The flight altitude is indicated in black. The P_flag indicates RO2 measurements affected by dynamical pressure variation in the inlet; (b) O3, CO, HCHO mixing ratios, and jO(1D); (c) NO, NO2, NOy, and HONO mixing ratios.


4.4 Comparison of results with other studies

4.4.1RO2 production rate

Cantrell et al. (2003b) proposed that the production of RO2, PRO2, is equal to the sum of two terms representing RO2RO2 reactions and the RO2–NOx reactions in the troposphere. As a result of this assumption, these authors describe the relationship between HO2, RO2, PRO2, and NOx as

(10) P RO 2 = k RR [ HO 2 + RO 2 ] 2 + k RN [ HO 2 + RO 2 ] [ NO x ] ,

where kRR and kRN refer to effective rate coefficients for RO2RO2 and RO2–NOx reactions, respectively, and are calculated as fit parameters. Solving Eq. (10) for [HO2+RO2]2 leads to

(11) [ HO 2 + RO 2 ] = A + B 2 2 - B ,

where A=PRO2kRR and where B=kRN[NOx]2kRR. For low NOx and/or high PRO2, B becomes negligible compared to A. Then [HO2+RO2] approaches A2 and is independent of NOx. For high NOx and/or low PRO2, [HO2+RO2] approaches zero.

The RO2m and RO2c values for the EMeRGe observations in Europe, binned in 0.1 pptv s−1 PRO2 intervals, were fitted according to the procedure by Cantrell et al. (2003b), and the results are shown in Fig. 16. The obtained fit parameters for Fig. 16a and b are kRR=7×10-5 and kRN=9×10-6. The RO2 calculated by Eq. (9) appears to be close to the linear function of the NOx measured. Similar to the results of the study by Cantrell et al. (2003b), a decrease in RO2 with NOx is identified for NOx>1000 pptv. RO2c does not show any decrease with increase in NOx for PRO20.7 pptv s−1. This might be explained by the underestimation of radical losses through organic nitrate formation in Eq. (9) as explained in Sect. 4.3.

Despite the low agreement of the fitted lines with the RO2m, a decrease in RO2m as a function of NOx is still observed. The disagreement between RO2m and the curves estimated using Eq. (11) implies that the simplified Eq. (10) from Cantrell et al. (2003b) is insufficient to adequately describe the chemical and physical processes occurring in the air masses probed. Part of the disagreement might arise from missing terms in the PRO2 calculated using Eq. (3) or inaccuracies related to the NO to NO2 ratio in the air mass, which are more evident at higher PRO2. As expected, the ratio of calculated [RO2c] to PRO22 has a negative linear dependence on the measured [NOx] (see Fig. 16c). The comparable relationship of RO2mPRO22 to [NOx] is not linear for NOx<100 pptv approximately (see Fig. 16d). This indicates that the simplified approach by Cantrell et al. (2003b) is not applicable to the more complex non-linear processes involved in the air masses investigated within EMeRGe.

Figure 16(a) RO2c binned into PRO2 intervals of 0.1 pptv s−1 versus binned NOx; (b) RO2m binned into PRO2 intervals of 0.1 pptv s−1 versus binned NOx; (c) ratio of [RO2]c to PRO22 versus NOx; and (d) [RO2]m to PRO22 ratio versus NOx. The data in panels (a) and (b) are assigned different colours, as a function of the radical production rate interval. The NOx observations are binned into 50 equidistant intervals on a logarithmic scale. The solid lines in panels (a) and (b) are the least square fits, obtained using Eq. (10). In panels (c) and (d), the ratios of [RO2]c to PRO22 and [RO2]m to PRO22 are binned into 50 NOx intervals equidistant on the logarithmic scale from 10 to 10 000 pptv. Error bars indicate the ±1σ standard deviation for the distribution in each bin.


4.4.2 O3 production rate

The O3 production rate (PO3) is calculated from the EMeRGe Europe data set using the reaction of RO2 with NO in a similar manner to that used in previous studies of photochemical processes in urban environments (e.g. Kleinman et al., 1995; Volz-Thomas et al., 2003; Mihelcic et al., 2003; Cantrell et al., 2003b; and references herein).

(12) P O 3 = k RO 2 + NO RO 2 [ NO ] ,

where kRO2+NO is taken as the average of kHO2+NO and kCH3O2+NO.

Figure 17 shows the mean PO3 calculated using Eq. (12) from RO2m and RO2c as a function of NO. The measured NO mixing ratios are binned into 50 bins. The bin size increases with NO to keep the points equidistant on the logarithmic scale. The calculated PO3 values for the RO2m and RO2c agree well within the standard deviation of the bins.

Figure 17Calculated O3 production rate (PO3) determined using RO2m (red dots) and RO2c (blue dots) as a function of the following: (a) NO mixing ratio and (b) NO number density. The 1 min measurements are binned into 50 bins of NO equidistant on the logarithmic scale for panel (a) from 10 to 10 000 pptv and for panel (b) from 5×107 to 3.5×1010 molecules cm−3, respectively. The shaded area shows the ±1σ standard deviation of each bin. To facilitate comparison with ground-based measurements, the black line plotted in panel (b) is the number density corresponding to 1 ppbv NO at 1000 mbar and 25 C.


Similar PO3 values have been reported for ground-based measurements in polluted areas such as Wangdu (Tan et al., 2017) and Beijing (Whalley et al., 2021) and similar ranges of peroxy radicals and NO mixing ratios. In previous work, Whalley et al. (2018) calculated PO3 to be about an order of magnitude lower than that found in this study from observations in central London for about an order of magnitude lower amount of HO2+RO2. For NO >1 ppbv, the PO3 estimated from the measurement of HO2 and RO2 or from the assumptions of an HO2 to RO2 ratio were underestimated by the models in other studies in the urban 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., 2013; Brune et al., 2016; Griffith et al., 2016). This behaviour is generally attributed to an underestimate of the concentration of RO2 with a large organic group, which likely undergoes multiple bimolecular reactions with NO before forming an HO2 radical.

During the EMeRGe campaign in Europe, the NO mixing ratios were <1 ppbv (approximately <3×1010 molecules cm−3). The ozone production rates obtained for both RO2m and RO2c are in reasonable agreement with other modelling studies in urban environments where the mixing ratio of NO is <1 ppbv (Tan et al., 2017; Whalley et al., 2021).

5 Summary and conclusions

This study exploits the airborne measurements of various atmospheric constituents on board HALO over Europe in summer 2017 to investigate radical photochemistry in the probed air masses. RO2 values are calculated by assuming a photostationary steady state (PSS) of RO2 and are compared with the actual measurements. The calculation is constrained by the simultaneous airborne measurements of radical precursors, photolysis frequencies, and reactants of RO2 such as NOx and O3. The calculated radical production rates, PRO2, do not significantly vary with altitude in the air masses investigated as the increase in the photolysis frequencies as a function of altitude is concurrent with decreases in precursor concentrations.

The significance and the importance of selected initiating and terminating processes in the RO2 chemistry are investigated by gradually increasing the complexity of the analytical expression. The agreement of the calculations with the measurements over a wide range of chemical composition and insolation conditions improves when the analytical expression is extended to account for effective radical yields from VOC oxidation and radical losses through nitrate and nitrite formation. The RO2 measured is usually overestimated when NO is <50 pptv in the air probed. This behaviour might be explained by RO2 loss processes involving reactions with OH (e.g. the reaction of HO2 with OH but possibly to a lesser extent the three-body reaction of OH with itself to make H2O2). These reactions may become significant RO2 loss processes at low NO concentrations as measured during the campaign but are excluded from the analytical expression, which is constrained by onboard measurements. Similarly, the RO2 loss through organic nitrate is also excluded from the analytical expression. These reactions may become significant RO2 loss processes in the presence of RO2 with organic groups larger than CH3. This might explain some of the RO2 overestimations by the analytical expression observed for NO >200 pptv.

The RO2 calculated under assumption of a photostationary state mostly underestimated the RO2 measured in polluted plumes of urban origin at altitudes below 2000 m. Changes in the HO2 to RO2 ratios in different plumes can account for the disagreement in particular cases. In pollution plumes with the sum of the OVOCs measured mixing ratios being higher than 7 ppbv approximately, the underestimation of the measurements can reach up to 80 %. In these plumes, the oxidation and/or photolysis of VOCs, which were not measured, and the ozonolysis of alkenes might be significant sources of RO2, limiting the accuracy of the analytical expression. More information about peroxy radical speciation and VOC partitioning is required to better describe the fast photochemistry in these pollution plumes.

However, the analytical expression developed is robust enough to simulate the radical chemistry in most of the conditions in the free troposphere encountered during EMeRGe in Europe. Speciated radical and VOC measurements in future campaigns would facilitate the estimation of radical loss reactions in air masses having NO <50 pptv and improve radical production rate estimations in pollution plumes having a high amount of VOCs, where non-linear complex chemistry is involved. Comparing RO2 measurements with RO2 calculations from the analytical expression helps to identify different chemical and physical regimes, which can be used to constrain future model studies.

The calculated O3 production rates for NO <1 ppbv are in the same order of magnitude as those previously reported for urban environments. This indicates that the selected RO2 production and loss processes and observations of the radical precursors on board are, to a good approximation, adequate for the estimation of the O3 production in the measured air masses in the free troposphere over Europe.

Data availability

The EMeRGe data are available at the HALO database (,, 2022) and can be accessed upon registration. Further data can be made available upon request to the corresponding author.


The supplement related to this article is available online at:

Author contributions

MG, VN, and YL undertook the RO2 measurements, flying as key scientists on board HALO. VN led the deployment of PeRCEAS in the HALO aircraft. MG led the analysis of the PeRCEAS measurements and prepared the manuscript with contributions from all co-authors. MDAH and JPB initiated the EMeRGe research project and consortium, acted as co-principal and principal investigators, and participated in the measurement campaigns. They developed the overarching EMeRGe scientific objectives and the required measurement portfolio, directed the EMeRGe research campaigns, and participated in the data analysis presented. AZ, BB, BS, EF, FO, FK, HS, HZ, KB, KP, and TH have contributed by providing their measurements made on board HALO during the campaign and participated in the discussion of results.

Competing interests

The contact author has declared that none of the authors has any competing interests.


Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Special issue statement

This article is part of the special issue “Effect of Megacities on the Transport and Transformation of Pollutants at Regional and Global Scales (EMeRGe) (ACP/AMT inter-journal SI)”. It is not associated with a conference.


The authors thank the DLRFX and HALO EMeRGe teams for the HALO flight organisation and implementation. Special thanks are given to Lisa Kaser, Frank Probst, Michael Großrubatscher, Stefan Grillenbeck, and Marc Puskeiler for flight coordination and planning; to Alexander Wolf and Thomas Leder, the flight engineers; and to the BAHAMAS team. The authors also thank enviscope GmbH, in particular Nicole Brehm and Rolf Maser, for the support during the integration and preparation phase of the IOP in Europe.

Midhun George, M. Dolores Andrés Hernández, Vladyslav Nenakhov, Yangzhuoran Liu, and John Phillip Burrows thank Wilke Thomssen for support during the preparation and integration phases of EMeRGe and Heiko Schellhorn for continuous technical support and retrieval of model data during the campaigns.

Financial support

The study was funded in part by the German Research Foundation (Deutsche Forschungsgemeinschaft; DFG) HALO-SPP 1294, as well as the University of Bremen and the State of Bremen, IPA, DLR, Oberpfaffenhofen, Germany. The contributions from Benjamin Schreiner, Flora Kluge, and Klaus Pfeilsticker were supported via the DFG (grant nos. PF 384/16, PF 384/17 and PF 384/19). KB was granted funding via the DFG (grant no. Pl 193/21-1) and received additional financial from the Heidelberg Graduate School for Physics. Eric Förster was supported via the DFG (grant no. NE 2150/1-1) and received additional financial support from the Karlsruhe Institute of Technology. Midhun George, Yangzhuoran Liu, Maria Dolores Andrés Hernández, and John Philip Burrows received financial support from the University of Bremen.

The article processing charges for this open-access publication were covered by the University of Bremen.

Review statement

This paper was edited by Barbara Ervens and Nga Lee Ng and reviewed by four anonymous referees.


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The CH3 produced from the oxidation of CH4 or the photolysis of VOCs further reacts with O2 to form CH3O2. The net or overall reaction is used, because the formation of CH3O2 is much faster than the CH3 formation due to the high amount of O2 present in the atmosphere.


H and CHO formed through the VOC photolysis further react with O2 to form HO2. The net or overall reaction is used, because the formation of HO2 is much faster than the H and CHO formation due to the high amount of O2 present in the atmosphere.

Short summary
The applicability of photostationary steady-state (PSS) assumptions to estimate the amount of the sum of peroxy radicals (RO2*) during the EMeRGe airborne observations from the known radical chemistry and onboard measurements of RO2* precursors, photolysis frequencies, and other trace gases such as NOx and O3 was investigated. The comparison of the calculated RO2* with the actual measurements provides an insight into the main processes controlling their concentration in the air masses measured.
Final-revised paper