Photochemical modeling of molecular and atomic oxygen based on multiple nightglow emissions measured in situ during the Energy Transfer in the Oxygen Nightglow rocket campaign

Electronically excited states of molecular and atomic oxygen (six O2 and two O) were implemented in the proposed Multiple Airglow Chemistry (MAC) model as minor species coupled with each other as well as with the ground states of O2 and O to represent the photochemistry in the upper mesosphere and lower thermosphere (MLT) region. The MAC model combines chemical processes of wellknown photochemical models related to identified O2 and O species and some additional processes. Concentrations of excited O2 and O species were retrieved using the MAC model on the basis of the multiple nightglow emissions measured in situ during the Energy Transfer in the Oxygen Nightglow (ETON) rocket campaign. The proposed retrieval procedure to obtain the concentrations of these minor species in the MLT region is implemented by avoiding a priori data sets. Unknown and poorly constrained reaction rates were tuned, and the reaction rates of the well-known models were updated with the MAC model by comparing in situ and evaluated emission profiles as well as in situ and retrieved O concentration profiles. As a result, precursors of O2 and O species responsible for the transitions considered in the MAC model are identified and validated.


Introduction
Airglow is a permanent global atmospheric phenomenon that can hardly be seen without appropriate instruments. Ångström (1869) used such instruments and observed the green line emission at 557.7 nm in the nightglow (airglow at night) from the Earth's surface in 1868 for the first time. The origin of airglow was considered to be the same as the ori-gin of aurora, a sporadic arc-like atmospheric phenomenon that has fascinated numerous spectators for many thousands of years. Table 1 provides an overview of relatively strong airglow emissions detected in the upper mesosphere and lower thermosphere (MLT) in situ and remotely. The Energy Transfer in the Oxygen Nightglow (ETON) rocket campaign, conducted in March 1982 and discussed in Sect. 2, was conceptualized to obtain in situ profiles of airglow volume emission rates (VERs) and other atmospheric parameters like atomic oxygen (O) in the ground state (O( 3 P )) to verify and validate photochemical models describing airglow.
O( 3 P ) is a chemically active MLT trace gas and a critical component for the energy budget of the MLT region. O( 3 P ) is also required to retrieve carbon dioxide (CO 2 ) concentrations as well as profiles of kinetic temperature and pressure Rezac et al., 2015). In addition, O( 3 P ) is also a major component of the neutral bath gas in the upper thermosphere, significantly contributing to the nighttime ionosphere (Shematovich et al., 2011;Wei et al., 2014).
The transition O( 1 S − 1 D) from the second excited O state (O( 1 S)) to the first one (O( 1 D)) is detected as the 557.7 nm green line emission. The Chapman excitation scheme and the Barth excitation transfer scheme were proposed in 1931 and 1962, respectively, to explain the origin of the green line emission in the MLT. The Chapman excitation scheme considers a collision of two O( 3 P ) atoms and a third body represented by O( 3 P ) to produce O( 1 S) (Chapman, 1931(Chapman, , 1937. The Barth excitation transfer scheme considers (1) a collision of two O( 3 P ) atoms and a third body represented by an abundant molecule, e.g., molecular nitrogen (N 2 ) and oxy- Table 1. Relevant optical transitions of terrestrial airglow in the Earth's atmosphere. Emissions (see the column labeled "Emission") observed in the wavelength range shown in the λ column are denoted by abbreviations (see the column labeled "Ident."). Typical intensity values of an integrated (limb) emission rate profile are given for nightglow (see the "Int." column before the comma) and, if available, dayglow (see the "Int."column after the comma). The altitudes of the corresponding emission rate peaks are shown in the column labeled "Alt.". Atomic oxygen emissions are denoted by abbreviations as follows. GrL -the green line emission at 557.7 nm, ReL -the red line emissions at 630.0 and 636.4 nm, UVL and UVL * -the ultraviolet line emissions at 297.2 and 295.8 nm, respectively. Molecular oxygen emissions are denoted by abbreviations as follows. IRAtm -the infrared atmospheric band emission at 1270 nm, Atm -the atmospheric band emission at 761.9 nm, Nox -the atmospheric band emission at 1908 nm, HzI -the Herzberg I band emissions, BG -the Broida-Gaydon band emissions, Chathe Chamberlain band emissions, HzIII -the Herzberg III band emissions, HzII -the Herzberg II band emissions, cbK -the new system band emissions measured using the Keck I/II instrument (Slanger et al., 2004a), RJ -the Richards-Johnson band emissions. References are marked with upper indices as follows: sc - Slanger and Copeland (2003), mc -McConkey et al. (1966), na -Nagy et al. (2008), md -McDade (1998), kh -Khomich et al. (2008.

Emission
Ident. λ (nm) Int., night, day Alt.(km)    (O 2 ), to produce O 2 in an unidentified excited state (O * 2 ) as well as (2) an energy transfer from O * 2 to O( 3 P ) so that O( 1 S) is produced (Bates, 1979). Comparing both excitation schemes, Bates (1979) interpreted the Chapman excitation process to consist of four steps as follows: (1) two O( 3 P ) atoms collide, (2) creating a common surface of potential energy of, presumably, an electronically excited O 2 molecule in the upper Herzberg state (Greer et al., 1987); (3) after its collision with a third O( 3 P ) atom (4) one vibrationally excited O 2 molecule and one O( 1 S) atom are created. One of the differences between the Chapman and Barth excitation schemes is the kind of third body, which is an O( 3 P ) atom or an abundant molecule in the MLT, respectively. The energy transfer considered in the Barth scheme includes O * 2 acting as the O( 1 S) precursor, but the Chapman scheme does not include it. Photochemical models proposed to implement the Chapman and Barth schemes are hereafter referred to as the first (one-step) and the second (two-step) type, respectively.
Airglow emissions are very complex atmospheric phenomena so that photochemical models are often proposed to derive unknown or poorly constrained reaction rates, which can be backed up by reaction rates determined in the laboratory with the use of the Stern-Volmer method. The Stern-Volmer method is applied to analyze concentrationdependent kinetics in a homogeneous system, to which a quencher was added (Lakowicz, 2006). According to the Stern-Volmer method, excited and quenching chemical species are considered in a system of a few photochemical reactions so that steady-state methods can be applied to describe emissions. Then measurements of the lifetimes or concentrations of emitting species enable the determination of the true pseudo-first-order decay required to calculate the rate coefficient of the considered quenching reaction. However, the same values of the pseudo-first-order decay rate are possible for both the dynamic quenching and the static quenching at the given temperature (Lakowicz, 2006). Dynamic quenching reduces the apparent fluorescent lifetime, while static quenching rather reduces the apparent concentration of fluorescent species during inelastic collisions (Lakowicz, 2006). Unfortunately, the reactive collisions responsible for static quenching are not so well understood compared to the products of dynamic quenching and can introduce difficulties calculating the rate coefficient of the considered quenching reaction.
If no more than one emission, e.g., VER{O( 1 S − 1 D)} in McDade et al. (1986), is considered in the model of the second type then the resulting steady-state chemical balance equation (hereafter referred to as the continuity equation) is of the third degree with respect to [O( 3 P )], and the respective solutions can be easily interpreted. As for the O 2 McDade et al. (1986) and modified by Lednyts'kyy et al. (2015) according to Gobbi et al. (1992) and Semenov (1997). Odd oxygen processes related to O 2 (b) were described with the well-known quadratic equation of McDade et al. (1986). Odd oxygen processes related to O( 1 S) were described by two models. The first model excluded two processes, R g1.2 and R g2.1 , and resulted in the well-known cubic Eq. (2) of McDade et al. (1986). The second model included two processes, R g1.2 and R g2.1 , and resulted in the extended cubic Eq. (3) of Lednyts'kyy et al. (2015). The processes marked with a character P were not considered in proposing the MAC model but were used in the first step (prior) retrieval of [O( 3 P )]. Odd oxygen processes related to O( 1 S) represent the two-step Barth transfer scheme (see reactions R v1.1-2 , R v2.1 and the resulting reaction R g3.0 ) accompanied by quenching. The symbolic representation of the reaction rates shown above the arrows in the second column of this table was adopted from Khomich et al. (2008) and used in Sect. 3.1. The symbolic representation shown in the third column of this table was used by Lednyts'kyy et al. (2015). For instance, the reaction rate β O (Khomich et al., 2008) corresponds to γ SP 3P (Lednyts'kyy and von Savigny, 2016), β O 2 (Khomich et al., 2008) corresponds to γ SP O 2 (Lednyts'kyy and von Savigny, 2016), A 558 (Khomich et al., 2008) corresponds to γ A 557n7 (Lednyts'kyy and von Savigny, 2016) and A 558 + (A 297 + A 296 ) (Khomich et al., 2008) corresponds to γ A 1S3Pe (Lednyts'kyy and von Savigny, 2016). Processes marked with a character P were used at the prior retrieval steps applied to calculate [O( 1 S)] (see Sect. A1.1) and [O( 3 P )] (see Sect. 3.1 and 3.5).
Odd oxygen processes related to O 2 (b) Symbol Odd oxygen processes related to O( 1 S) Symbol  O 2 ). This transition in the atmospheric band was measured in situ in the Earth's atmosphere during the ETON campaign to retrieve VER{O 2 (b − X)}. The model of the second type developed by McDade et al. (1986) with the O 2 (b) precursor and O 2 (b) was proposed to explain nonlinearities detected in quenching processes simulated by using the model of the first type developed by McDade et al. (1986) with O 2 (b) only. McDade et al. (1986) used known reaction rates and tuned poorly constrained reaction rates of these quenching processes in the atmosphere so that simulated profiles match the in situ observations. The processes considered in the models of the first and second types provided in Table 2 were developed by McDade et al. (1986) to describe atmospheric airglow emissions and to verify the obtained results in the laboratory using the Stern-Volmer relationship. The total number of reactions considered in the models of López-González et al. (1992b) and McDade et al. (1986) with the O( 1 S) precursor (O * 2 ) and O( 1 S) was limited to 10, and these reactions are separated in two groups according to the Barth excitation transfer scheme. A full overview of these reactions including O 2 in an unidentified excited state (O * 2 ) is not provided in this short overview except for two reactions. Specifically, López-González et al. (1992b) considered the reaction O( 1 S) + O( 3 P ) → products, which McDade et al. (1986) did not consider. But McDade et al. (1986) considered the reaction O 2 * + N 2 → products, which López-González et al. (1992b) did not consider. Possible reasons to limit the list of all possible reactions in these models are as follows: (1) the Barth excitation transfer scheme can be represented by the most important (e.g., 10) reactions, (2) the system of a few reactions can be easily represented by a low degree polynomial equation regarding [O( 3 P )], (3) additional reactions would introduce difficulties to derive their rates, which are sometimes treated as ratios of reaction rates and tuned as empirical coefficients, and (4) the choice of approaches applied to derive empirical coefficients is limited depending on the considered reactions, e.g., compare approaches applied by McDade et al. (1986) and López-González et al. (1992b).
These reasons limit the applicability of the mentioned methods used to analyze laboratory results and atmospheric measurements, which are usually studied without propagation in time. The computational simulation of a chemical kinetics system enables the study of the time evolution of chemical species using the ordinary differential equation (ODE) system matrix and initial conditions; see, e.g., Sandu and Sander (2006) for an overview of zero-dimensional box models developed to integrate ODEs numerically in time. Unfortunately, computer modeling depends on the a priori data sets used to initialize a box model. In situ atmospheric measurements may be influenced by gravity waves and atmospheric tides at particular moments in time, which hinders the use of box models on the basis of such measurements. The current article studies MLT photochemistry on the basis of the in situ ETON measurements using steady-state continuity equations, i.e., without propagation in time and without a priori data sets.
The ETON multiple airglow emissions described in Sect. 2 can be applied simultaneously in the model proposed in this study to decrease uncertainties when tuning unknown and poorly constrained reaction rates with the use of the verification and validation procedures. Torr et al. (1985) appear to be the first to consider multiple emissions in a model with several O 2 states based on observational data from the shuttle Spacelab 1. In fact, these data sets were extremely scattered in time and place and might have stopped Torr et al. (1985) from combining identified O 2 states in one model. Instead, they considered a number of photochemical models with some excited O 2 states in each model so that all discussed excited O 2 states appeared to be uncoupled with each other. Note that Torr et al. (1985) also considered O 2 (c) to be the O( 1 S) precursor, as suggested by Greer et al. (1981), and applied the O( 1 S) quenching with O 2 (a) according to Bates (1981) and Kenner and Ogryzlo (1982).
In summary, the current investigation was conducted to study the following topics regarding the new photochemical model proposed here: (1) processes of O( 1 S) formation and quenching (see Sect. 3.1), (2)  The O( 3 P ) retrieval scheme was proposed to be solved in subsequent steps as described in Appendix A on the basis of multiple airglow emission profiles as discussed by Lednyts'kyy and von Savigny (2016) and Lednyts'kyy et al. (2018). Note that a priori data are not required to initiate calculations with the MAC model. Concentrations of O 2 in higher excited states are calculated in earlier steps of the retrieval procedure and are used to calculate concentrations of O 2 in lower excited states in the following steps. It should be noted that a limited number of multiple airglow emissions available from the ETON measurements or other sources can also be applied to retrieve [O( 3 P )] values at some of the mentioned retrieval steps; see Sects. 2 and 5 for details.

Data sets applied in the Multiple Airglow Chemistry (MAC) model
In situ measurements obtained during the Energy Transfer in the Oxygen Nightglow (ETON) campaign and simulations using the most recent version of the MSIS (Mass Spectrometer Incoherent Scatter) semi-empirical model are the focus of this section. Volume emission rates (VERs) of the nightglow emissions measured in situ during the ETON campaign and the corresponding statistical errors provided by Greer et al. (1986) were used in this study. The ETON campaign is comprised of measurements obtained during coordinated launches of seven sounding rockets at South Uist (∼ 57 • 16 N, ∼ 7 • 19 W) in Scotland in the westerly direction on 23 March 1982 from ∼ 21:27 to ∼ 23:55 UT (Greer et al., , 1987. All VER profiles considered in the MAC model were measured during flights of two ETON rockets. The infrared atmospheric band emission at 1.27 µm was measured with a photometer aboard only one ETON rocket: the P227H rocket launched at ∼ 22:11 UT. The Herzberg I and atmospheric band emissions at 320 and 761.9 nm, respectively, were also measured by the P227H rocket. The P229H rocket was launched at ∼ 22:58 UT right after the P227H rocket and provided measurements of the Herzberg I, Chamberlain and atmospheric band emissions at 330, 370 and 761.9 nm, respectively, as well as the oxygen green line emission at 557.7 nm. It should be noted that the Chamberlain band emissions were measured by the P229H rocket only. The absolute accuracy of ±20 % in VER peak values for the infrared at-mospheric band emissions and better than ±10 % in other wavelength ranges  introduces uncertainties in the [O( 3 P )] retrievals.
In situ measurements of atomic oxygen (O) concentrations ( [O]) in the ground state [O( 3 P )] were carried out by the P232H and P234H rockets launched at ∼ 21:49 and ∼ 23 :55 UT, respectively. [O( 3 P )] values were determined directly using the resonance fluorescence and absorption technique at ∼ 130 nm  and were interpolated for the launch time of the other ETON rockets. The statistical (and the systematic) error was less than about ±10 % (and about ±30 %) at about 100 km (where peak [O( 3 P )] values were measured) and increased up to ±50 % (and about ±20 %) at other altitudes (where low [O( 3 P )] values were measured) .
The most recent version of the MSIS model, NRLMSISE-00 (Naval Research Laboratory MSIS Extended, 2000; see Picone et al., 2002), was used to obtain the following input parameters required to run the MAC model: temperature (T ), molecular nitrogen concentrations ([N 2 ]) and [O 2 ]. Because the highest number of O 2 and O transitions were sounded by the P229H rocket, the time of in situ measurements obtained by the P229H rocket at ∼ 97 km over South Uist in Scotland was specified for the NRLMSISE-00 model. It should be mentioned that McDade et al. (1986) developed the wellknown cubic equation deriving empirical coefficients using the MSIS-83 model (Hedin, 1983) that is no longer available.
The input parameters required to run the established models and the proposed MAC model are profiles of T , [N 2 ], [O 2 ] and VER values. The following abbreviations of in situ VER profiles are used in this study: VER{O 2 (A − X)} (Herzberg I band, HzI), VER{O 2 (A − a)} (Chamberlain band, Cha), VER{O 2 (b − X)} (atmospheric band, Atm), VER{O( 1 S − 1 D)} (green line, GrL) and VER{O 2 (a − X)} (infrared atmospheric band, IRAtm). Some of the O 2 transitions listed in Table 1 correspond to these VER profiles. Note that the other listed O 2 transitions were also considered in the proposed MAC model; see Sect. 3.3 for details. It is worth mentioning that all of these O 2 transitions were measured remotely using the instrument SCIA-MACHY (SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY) aboard the satellite ENVISAT (ENVIronmental SATellite) launched by the European Space Agency (Burrows et al., 1995;Bovensmann et al., 1999).
It should be mentioned that Lednyts'kyy and von Savigny (2016) tuned unknown or poorly constrained reaction rates considered in the MAC model on the basis of the data sets obtained during the ETON campaign. The corresponding reaction rates are shown in Tables 8, 9, 10 and 11. Then, the MAC model was applied by Lednyts'kyy et al. (2019) on the basis of data sets obtained during the following three campaigns: the WADIS-2 (WAve propagation and DISsipation in the middle atmosphere), WAVE2000 (WAVes in airglow structures Experiment, 2000) and WAVE2004. The WADIS-2 rocket provided all data sets required to retrieve [O( 3 P )] values. Data sets measured in situ with rockets launched during the WAVE2000 and WAVE2004 campaigns were combined with the collocated data sets measured remotely. Convincing retrieval results enabled the validation of tuned reaction rates and calculations carried out with the MAC model. The established photochemical models of McDade et al. (1986), Gobbi et al. (1992) and Semenov (1997) related to the oxygen green line emission are described briefly in this section; see Lednyts'kyy et al. (2015) for details. McDade et al. (1986) considered the processes provided in Table 2 that resulted in two photochemical models according to the two-step Barth excitation transfer scheme implemented in each model and involving precursors of O 2 (b) and O( 1 S), respectively. McDade et al. (1986) also implemented one model according to the one-step excitation scheme and related to O 2 (b), but excluding the O 2 (b) precursor. Both models related to O 2 (b) were used to retrieve [O( 3 P )] on the basis of the volume emission rates (VERs) of the atmospheric band emissions. All processes of the O 2 (b) model involving the O 2 (b) precursor are provided in the upper part of and R P u4.0 ) are absent in the model implemented without the O 2 (b) precursor. The model implemented without the O 2 (b) precursor exhibits nonlinearities in quenching processes, but the model implemented with the O 2 (b) precursor (O 2 * * ) does not result in such nonlinearities . Note that McDade et al. (1986) described the green line emission considering the O( 1 S) precursor according to the Barth excitation transfer scheme. In fact, the well-known quadratic equation resulting from the model with the O 2 (b) precursor and the well-known cubic equation resulting from the model with the O( 1 S) precursor were concluded by McDade et al. (1986) to be favorable compared to models based on the onestep (Chapman) excitation scheme. It is worth mentioning that Grygalashvyly et al. (2019) proposed a model combining the Chapman and Barth excitation schemes, which were implemented in both O 2 (b) models of McDade et al. (1986) separately. Applying self-consistent data sets (see Sect. 2) and fitting retrieved data sets, Grygalashvyly et al. (2019) applied the methods of McDade et al. (1986) to derive new values of empirical coefficients, which were initially derived by McDade et al. (1986) for the well-known quadratic equation. The newly derived coefficients were preferred by Grygalashvyly et al. (2019) to be applied in their model.
The well-known cubic equation of McDade et al. (1986) provided below in the full form was used here to retrieve [O( 3 P )] on the basis of VER of the green line emission (VER 558 , also referred to as VER{O( 1 S − 1 D)}).

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O. Lednyts'kyy and C. von Savigny: O 2 and O modeling on the basis of ETON in situ emissions The cubic equation in the full form is as follows: where R ≈ 4 represents the mean [N 2 ]/ [O 2 ] ratio valid in the altitude range 80-120 km according to McDade et al. (1986). All reaction rates shown in Eq. (1) correspond to the ones provided in the lower part of Table 2. Ratios of some of these reaction rate values were derived by McDade et al. (1986) (see the empirical coefficients in Eq. (2) of Murtagh et al., 1990) on the basis of the ETON in situ measurements as well as simulated temperature, [N 2 ] and [O 2 ] profiles. The well-known cubic equation and the derived empirical coefficients in particular were verified by Murtagh et al. (1990), who provided the well-known cubic equation in the short form as follows: where the rate coefficient of the R g1.2 reaction provided in Table 2 is 3 κ 5 = 4 × 10 −12 exp(−865/T ) molec −1 cm 3 s −1 , the Einstein coefficients of the reactions R g3.0 and R g(3-4).0 are A 558 = 1.18 s −1 and A1 S = 1.35 s −1 , and the rate βκ 1 of the three-body recombination reaction R P v1.1-2 is the product of κ 1 = 4.7 × 10 −33 (300/T ) 2 molec −2 cm 6 s −1 and an empirical β value. The R P v1.1-2 reaction refers to the first step of the Barth excitation transfer scheme describing the production of O The values of the empirical coefficients C(0), C(1) and C(2) are equal to 0, 211 and 15, respectively, and these values are used in this study for retrievals using the wellknown cubic equation according to Murtagh et al. (1990). Note that these empirical coefficients were derived by Mc-Dade et al. (1986) using semi-empirical models, including MSIS-83 (Hedin, 1983), that are no longer available. The NRLMSISE-00 model mentioned in Sect. 2 is used in this study to simulate temperature, [N 2 ] and [O 2 ] profiles. Mc-Dade et al. (1986) used various available models that resulted in other values of temperature, [N 2 ] and [O 2 ] profiles and different values of the empirical coefficients. The lowest obtained values of C(0), C(1) and C(2) from all obtained ones, which are related to the O( 1 S) precursor, were found by Mc-Dade et al. (1986) to be equal to 13 ± 4, 183 ± 10 and 9 ± 3, respectively, and their highest values were found to be 23±9, 224 ± 20 and 17 ± 3, respectively. Gobbi et al. (1992) suggested that processes of the enhanced O( 1 S) quenching with O( 3 P ) and N 2 should also be considered in the well-known Eq. (2). The extended cubic equation provided by Gobbi et al. (1992) is as follows: where the rate coefficients corresponding to the reactions R g1.1 , R g2.1 and R g1.2 are 1 κ 5 = 2 × 10 −14 molec −1 cm 3 s −1 , 2 κ 5 = 5 × 10 −17 molec −1 cm 3 s −1 and 3 κ 5 = 4.9 × 10 −12 exp(−885/T ) molec −1 cm 3 s −1 , respectively. The other coefficients are shown and described for Eq. (2). The photochemical model resulting in the extended cubic equation is hereafter referred to as the G model in short according to the surname of the first author in Gobbi et al. (1992), who proposed this model.
The O( 1 S) quenching with N 2 is not effective according to Atkinson and Welge (1972) because the 2 κ 5 value is 5 orders lower than the 3 κ 5 value of the O( 1 S) quenching with O 2 . Therefore, the O( 1 S) quenching with N 2 was neglected ( 2 κ 5 = 0) by Semenov (1997), who considered a relatively high 1 κ 5 value of 5 × 10 −11 exp(−305/T ) molec −1 cm 3 s −1 compared to the 1 κ 5 value of 2×10 −14 molec −1 cm 3 s −1 used by Gobbi et al. (1992). The low 1 κ 5 value was obtained theoretically by Krauss and Neumann (1975) and approved experimentally by Kenner and Ogryzlo (1982). However, Johnston and Broadfoot (1993) and a number of other scientists including Khomich et al. (2008) used the high 1 κ 5 value. Semenov (1997) developed the photochemical model that resulted in the cubic equation as follows: where α O 2 = βκ 1 and α O = δβ * O ; see the notation of process rates provided in Table 2. The notation of other process rates shows that Eq. (4) can be transformed into Eq. (3) by using The O( 1 S) quenching with O 2 (a) is very effective according to Bates (1981) and Kenner and Ogryzlo (1982), but the direct inclusion of O 2 (a) in Eq. (3) would increase its order so that the number of the obtained solutions would be very complicated to interpret. Therefore, the high 1 κ 5 value of the O( 1 S) quenching with O( 3 P ) was adopted by Lednyts'kyy et al. (2015) in order to implicitly include the O( 1 S) quenching with O 2 (a) and to keep the order of the polynomial in Eq. (3). In this context it is worth mentioning that -according to Garcia and Solomon (1985) -O( 1 S) quenching reactions are not completely established. The direct correspondence of Eq. (4) (with defined empirical coefficients C(0), C(1) and C(2)) and Eq. (3) enabled the specification of how the relationship between values of [O( 3 P )] and VER 558 can be used to solve both Eqs. (4) and (3) by applying the analytical method of Semenov (1997).
The well-known cubic Eq. (2) represents the reduced form of the extended Eq. (3). Indeed, the reaction rates 1 κ 5 and 2 κ 5 are not equal to zero in the extended Eq. (3) to represent the O( 1 S) quenching with O 2 , O( 3 P ) and N 2 . If they are equal to zero then the extended Eq. (3) becomes identical to the well-known Eq. (2). The other values of reaction rates and empirical coefficients were proposed by Lednyts'kyy et al. (2015) to be the same in both Eqs. (2) and (3) Gobbi et al. (1992) used in situ measurements obtained during the solar minimum phase at the transition from solar cycle 21 to cycle 22, but the ETON in situ measurements were obtained during the solar maximum phase of the 21st solar cycle. It is worth mentioning that Gobbi et al. (1992) used Eq. (3) instead of Eq. (2) with the same empirical coefficients derived by McDade et al. (1986). Lednyts'kyy et al. (2015) adjusted the values of these empirical coefficients for the present study based on solar activity. This was done to reflect differences in ultraviolet irradiance and optical depth values during phases of the solar maximum and minimum. Indeed, Dudok de Wit et al. (2009) andMeier (1991) reported that the irradiance in the extreme ultraviolet wavelength range 30-121 nm affects thermospheric O( 3 P ), O 2 , N 2 , N and N 2 O ionization. Colegrove et al. (1965) emphasized that O( 3 P ) is generated in the lower thermosphere and transported downwards to the mesosphere. Equation (2) of Murtagh et al. (1990) was extended by Lednyts'kyy et al. (2015) with the empirical coefficient C(0) = 0 because the first term on the right-hand side of Eq. (1) is not equal to zero so that C(0) should be introduced. However, the influence of C(0) on solutions of Eq. (2) is negligible compared to C(1) [O( 3 P )] or C(2) [O 2 ] so that the exact C(0) value is not important. The NRLMSISE-00 model was applied by adjusting the empirical coefficients C(0), C(1) and C(2) instead of the MSIS-83 model applied by McDade et al. (1986).
In summary, polynomial equations of the second and third order with respect to [O( 3 P )] ) are used to retrieve [O( 3 P )]; see Figs. 4a and 5a in Sect. 3.5. The extended cubic Eq. (3) was solved for this study using the analytical method of Semenov (1997), also de-scribed by Khomich et al. (2008). As for the well-known cubic Eq. (2), it was solved for this study using the program available at https://idlastro.gsfc.nasa.gov/ftp/contrib/ freudenreich/cuberoot.pro (last access: 1 March 2019) within the Astronomy User's Library distributed by the National Aeronautics and Space Administration. Note that values of reaction rates and empirical coefficients provided by Lednyts'kyy et al. (2015) were used according to the extended cubic Eq. (3) for O( 3 P ) retrievals in this study. As for the well-known cubic Eq. (2) used for O( 3 P ) retrievals in this study, the values of the reaction rates and empirical coefficients used are the ones provided by Murtagh et al. (1990).
Photochemical models based on identified O 2 states and their coupling with each other are described in Sect. 3.2.

Models with identified excited O 2 states
A short review regarding approaches for developing photochemical models was provided in Sect. 1. The established photochemical models described in the following sections include O 2 (b, a, X) in the first model (see Sect. 3.2.1) and O 2 (c, b, X) in the second model (see Sect. 3.2.2).

The modified kinetic model of O 2 and O 3 photolysis products
A photochemical model taking O 2 (b, a, X) states and O( 1 D, 3 P ) states into account was developed by Mlynczak et al. (1993) with the use of the basic daytime O 2 (a) kinetic model employed by Thomas (1990). The model of Mlynczak et al. (1993) was extended by Sharp et al. (2014) by including the three-body recombination reaction producing O 2 (a) during nighttime; see the R a1.1-2 reactions provided in Table 3. The model of Sharp et al. (2014) also included processes related to laser excitation, but these processes are not relevant for the present study and are excluded. All other processes of the model proposed by Sharp et al. (2014) are shown in Table 3. The modified kinetic model with these processes is hereafter referred to as the M model in short according to the surname of the first author in Mlynczak et al. (1993). Processes marked with a character E and shown in Table 3 were excluded from the resulting M model because they were not found in the latest version of the 2015 database of the Jet Propulsion Laboratory (Burkholder et al., 2015).
The M model was verified on the basis of a few emission lines (with high signal-to-noise ratios) from possible band emissions measured remotely. Some of these strongest O 2 nightglow emissions are provided in Table 1. One of them is the infrared atmospheric band represented by the vibrational transition 0 − 0 of the forbidden electronic transition a 1 g , . Note that processes of the M model were used to develop the MAC model on the basis of VER profiles from the ETON campaign including VER values of O 2 (a −X){0−0} (VER{O 2 (a −X)}).  O 2 and O 3 photolysis occur in sunlight conditions. The processes marked with a character E are not considered in the MAC model shown in Tables 6 and 7 because they were not listed in the online version of the JPL 2015-year database (Burkholder et al., 2015) and were replaced by other relevant up-to-date processes.
Odd oxygen processes related to O 2 Hickey et al. (1997). The first implementation of O 2 (c) as the O( 1 S) precursor seems to have been carried out by Torr et al. (1985) on the basis of multiple emissions simultaneously measured from the Spacelab 1 shuttle. The O( 1 S) precursor was also assumed to be O 2 (c) by Greer et al. (1981), describing in situ measurements of the ETON campaign, and Hickey et al. (1997). Huang and George (2014) tuned some rates of quenching reactions on the basis of measurements of the green line emissions at 557.7 nm and the atmospheric band emissions at 864.5 nm. The vibrational transition 0 − 1 of the electronic transition b 1 + g , ν = 0 − X 3 − g , ν = 1 at 864.5 nm can be observed from the Earth's surface and it is denoted at 762.2 nm in the atmospheric band (Meinel, 1950). Prof. Huang provided rate coefficients in the model of Huang and George (2014) All processes of the model of Huang and George (2014) are hereafter referred to as processes of the H model with the capital H for the surname of the first author in Huang and George (2014).
It should be noted that both can be observed remotely from space, e.g., using the SCIAMACHY instrument mentioned in Sect. 2, because radiation was measured using the SCIA-MACHY instrument simultaneously in the wavelength range from 240 to 1750 nm (Bovensmann et al., 1999). Makhlouf et al. (1998) proposed a photochemical model considering electronic-vibrational kinetics according to the Barth excitation transfer scheme. They suggested O 2 (c, ν ≥ 3) instead of O * 2 as the O( 1 S) precursor based on the conclusions of Krasnopolsky (1981). The results of Makhlouf et al. (1998) were obtained for O 2 (c, ν = 0. . .16) regarding the oxygen green line emission by simulating gravity-wavedriven fluctuations like Huang and George (2014) did. Nevertheless, the rate values of the O 2 (c, ν = 0, 1) quenching used by Makhlouf et al. (1998) differ from those used by Huang and George (2014), implying that these rate values derived by tuning the H model depend on the data sets used. It should be mentioned that tuning results for the M model also depended on the data sets used; see Sect. 3.2.1.

Processes of the MAC model
The processes from the G model (see Sect. 3.1), the M model (see Sect. 3.2.1) and the H model (see Sect. 3.2.2) were adopted in the proposed MAC model. Rate values of the processes considered in these models were updated using the JPL 2015 database (Burkholder et al., 2015) and the database of the National Institute of Standards and Technology (NIST) available at https://www.nist. gov/pml/productsservices/physical-reference-data (last access: 1 March 2019) as well as other high-ranking sources listed in Huestis (2002) and Jones et al. (2006).
The following processes were adopted in the MAC model from the M model of Mlynczak et al. (1993) and Sharp et al.
(2014) (see Table 3 in Sect. 3.2.1): 3. the infrared atmospheric band emission (R a1.1-2 , R a2.2-4 , R a3.0 , R a4.0 ), and 4. the red line emission (R r2.1,3 , R E r2.2 ). It should be noted that the processes R E b2.1 and R E r2.2 were replaced by processes with other products according to Burkholder et al. (2015). These replaced processes and the other processes of the M model were adopted in the proposed MAC model and are referred to as M processes.
These processes were all adopted in the proposed MAC model and are referred to as H processes.
The following processes were adopted in the MAC model from the G model of Gobbi et al. (1992) (see Table 2 in Sect. 3.1): 1. the green line emission (R g1.1-2 , R g2.1 , R g3.0 , R g(3-4).0 ) and 2. the O( 1 S) precursor responsible for the green line emission (R P v1.1-2 , R P v2.1 , R P v3.1-3 , R P v4.0 ). It should be noted that the G-model processes R P v1.1-2 , R P v2.1 , R P v3.1-3 and R P v4.0 were replaced by corresponding processes of the H model, which were adopted in the proposed MAC model. All processes of the G model are referred to as G processes.
In addition to the G, M and H processes, complementary processes (C processes) were proposed to couple O 2 ( 5 , A, A , c, b, a, X) with each other and O( 1 S, 1 D, 3 P ) by taking the hypotheses of Huestis (2002) and Slanger et al. (2004b) into account. The C processes were also discussed by Lednyts'kyy and von Savigny (2016) and Lednyts'kyy et al. (2018). Huestis (2002) suggested that the de-excitation of O 2 states with higher energy to O 2 states with lower energy only occurs in a cascade that was described by Slanger et al. (2004b) as the integrity of identity of the O 2 electronic states. This enables the assumption that the O( 1 S) precursor can be represented by one O 2 state or a group of O 2 states according to the hypothesis of the integrity of identity of the O 2 electronic states. Although the Barth excitation transfer scheme was formulated with O * 2 considered to be one unidentified O 2 state, a group of many unidentified O 2 states coupled in a cascade of de-excitation reactions is also possible.
The hypothesis of Huestis (2002) was refuted by Slanger et al. (2004b) on the basis of laboratory measurements discussed by Huestis (2002) and Slanger et al. (2004b) and summarized by Pejaković et al. (2007). Slanger and Copeland (2003) stated that energetically nearly resonant intermolecular processes are responsible for conversions of higher to lower excited O 2 electronic states. Specifically, Slanger et al. (2004b) suggested that the de-excitation of the O 2 states does not occur in a cascade-like process. They emphasized the presence of a cycle of de-excitation and excitation of O 2 ( 5 ) and the Herzberg O 2 states in high vibrational levels. These O 2 states transform back and forth into each other through collisions. Finally, the O 2 ( 5 )-O 2 (A, A , c) group is removed by conversion to very high vibrational of O 2 (b, a, X) states. In fact, the removal of the O 2 ( 5 )-O 2 (A, A ) group through collisions was suggested by Slanger et al. (2004b) and implicitly implemented in the MAC model by increasing the association rates of O 2 (b, a, X) in the three-body recombination reactions. This was done implicitly because reactions including O 2 ( 5 ) are not well known, e.g., compare Krasnopolsky (2011) and Krasnopolsky (1986). It should be noted that O 2 ( 5 ) has a shorter lifetime and a higher energy compared to the other states O 2 (A, A , c, b, a, X) as was also mentioned by Huestis (2002) and Slanger et al. (2004b). It should be noted that 5 is an electronically excited O 2 state with higher energy than O 2 in the Herzberg states. This, in contrast to the hypothesis of Huestis (2002), makes it more complicated to operate with the O( 1 S) precursor as a group of many unidentified O 2 states.
The C processes related to the Herzberg states A 3 + u and A 3 u (hereafter referred to as O 2 (A, A )) are not considered in the G, M and H models. These C processes are related to the following: These C processes are shown in Tables 6 and 7, and they were considered and discussed by Lednyts'kyy and von Savigny (2016). The corresponding reaction rates are shown in Tables 9, 10 and 11.
Unknown or poorly constrained reaction rates of these complementary processes might be compromised by boundary effects if they were measured in the laboratory. Therefore, an appropriate photochemical model including many chemical species obtained on the basis of multiple emissions measured in situ in the Earth's atmosphere may be a valuable complement to laboratory experiments. In fact, unknown or poorly constrained reaction rates were tuned according to the verification and validation procedures discussed in Sect. 3.5 and applied on the basis of the ETON in situ measurements. The advantage of the ETON campaign compared to other rocket campaigns is that multiple emissions and [O( 3 P )] were measured almost simultaneously. This enables a comparison of the in situ and retrieved [O( 3 P )] using each particular emission profile described in Sect. 2.  Odd oxygen processes related to O 2 (A) and O 2 (A )

Tuning rate values of quenching processes implemented in the MAC model
All processes of the MAC model are provided in Sect. 3.3. These processes were separated into four groups: those considered in the G, M and H models as well as those considered complementary processes completing the MAC model and denoted as C processes. Unknown or poorly constrained reaction rate values of the C processes were tuned by comparing (1) retrieved and evaluated concentrations of excited chemical species, (2) Tables 8, 9, 10 and 11.
As mentioned in Sect. 2, unknown or poorly constrained reactions in the MAC model were tuned on the basis of the ETON in situ measurements and applied to data sets measured during the WADIS-2, WAVE2000 and WAVE2004 campaigns; see Lednyts'kyy et al. (2019) for details. Dr. Fytterer and Dr. Sinnhuber from the Karlsruhe Institute of Technology suggested the rate values of the reactions R b2.1 , R b4.1 , R b6.0 , R r1.2 and R r2.3 for the data sets of the WAVE2004 campaign. The other reaction rates were adjusted on the basis of the described verification and validation procedures. Particularly, the R a2.2 reaction rate was also adjusted within the range provided by Burkholder et al. (2015), who gave the upper limit of this reaction. Rate values of the reactions R t10.1 , R d9.1 and R c2.1 regarding O( 1 S) production were adjusted by taking the studies of Krasnopolsky (2011), Huang and George (2014), Steadman and Thrush (1994), and Torr et al. (1985) into account. The adjustment of the rate values of the three-body recombination reactions is described in Sect. 4.1. Table 6. The processes shown here comprise the MAC model together with the processes shown in Table 5 and the processes shown in Table 7.
Odd oxygen processes related to O 2 The tuning of the rate coefficients was carried out by changing the values of dimensionless scaling factors (cTDu, cTCu, cTBu, cTAu, cDCu, cDBu, cDAu, cCBa, cCBm, cCAa, cCAm, cBAa, cBAm and cAXa shown in Tables 8, 9, 10 and 11), which are multiplied with the corresponding rate coefficients and describe the strength of the coupling among O 2 states as follows: 3. cCBa is for coupling of O 2 (c) and The values of these scaling factors were altered to determine their influence on [O current ] calculating differences with respect to [O reference ] retrieved without adjusting these scaling factors. The differences were calculated according to Eq. (5) and used in the sensitivity analysis; see the third column of Tables 8, 9, 10 and 11 for a summary. For instance, perturbations in cTDu values do not cause changes in retrieved and evaluated MAC output parameters. Therefore, the tested interval is shown as cTDu ∈ [1 × 10 −30 , 1 × 10 30 ] in Table 8, and cTDu is set to an arbitrary value of cTDu = 1 × 10 −2 .
The concentrations of various chemical species were retrieved using sequentially applied continuity equations in the steady state, i.e., polynomial equations of the second or the third order. An overview of all retrieval steps of the MAC model is provided in Appendix A devoted to the description of all algorithmic steps; see also Table 12 for a short overview. The input VER profiles shown in Table 12 correspond to O 2 transitions shown in Table 1. In fact, all reactions relevant for the particular chemical species were used in the retrievals, and the retrieved concentration profiles are marked by character R, e.g., R- [O 2 (A)]. Additionally, concentrations of the same chemical species were evaluated by dividing the R-VER profiles, which correspond to the particular chemical species, by the respective transition probability. The evaluated concentration profiles are marked by character E, e.g., E- [O 2 (A)]. As for the evaluated VER profiles, which are marked by character E as E-VER profiles (e.g., E-VER{O 2 (A − X)}), they are obtained by multiplying the retrieved concentrations of the same chemical species by the respective transition probability.
The results of calculations carried out using the MAC model are verified by a visual comparison of retrieved and evaluated profiles, i.e., the respective emission and concentration values. Note that the prior step 1 shown in Table 12 and briefly described in Sect. A1 is omitted for the ETON campaign because such input parameters as [O 3 ] and [H] are not known a priori. Instead, the short list of the input parameters required to run the MAC model is applied: T , [N 2 ], [O 2 ] from the NRLMSISE-00 model and VER profiles from the ETON campaign. For instance, the quadratic continuity equation is solved to retrieve R- [O 2 (A)] on the basis of R-VER{O 2 (A − X)} using all relevant processes of the MAC model. This retrieval step is shown as step 2.1 in Table 12 and step 2. Note that values of the in situ R-VER{O( 1 S − 1 D)} profile are less than zero randomly below 92 km due to the measurement noise. Therefore, the in situ R-VER{O( 1 S − 1 D)} profile is approximated by the asymmetrical Gaussian distribution described by Semenov (1997) and Khomich et al. (2008) to obtain the shown A-VER{O( 1 S − 1 D)} profile and to retrieve the corresponding [O( 1 S)] profile.
The retrieved and evaluated VER profiles indicated by the dashed lines and the symbols, respectively, shown in Fig. 3a are compared with each other by sight to verify calculations carried out with the MAC model involving O 2 (A) and O 2 (A ). The retrieved and evaluated VER profiles belonging to each pair regarding the considered excited O 2 state seem to be in perfect agreement with each other by sight. Next, the retrieved and evaluated concentration profiles shown in Fig. 3b by the dashed lines and the symbols, respectively, are also compared with each other for each retrieval step. These profiles also seem to be in perfect agreement with each other by sight. The excellent agreement of the retrieved and evaluated products (VER or concentration profile) enables the conclusion that all calculations carried out using the MAC model are consistent with each other and coherent with measurements.
Before we discuss results of the [O( 3 P )] retrievals obtained with the proposed MAC model, a short overview of the previously used photochemical models is given to estimate our current situation and to argue whether the proposed MAC model is needed. The published photochemical models based on the processes provided in Table 2 Table 1, and the sequence of the retrieval steps is provided in Table 12. Values of temperature, [N 2 ] and [O 2 ] were obtained by using the NRLMSISE-00 model (see Sect. 2) for the time and place of the P229H rocket. in this finding. Empirical coefficients were derived for these previously used photochemical models phenomenologically, i.e., in relation to reaction rates in which an unidentified O * 2 is involved. Therefore, [O( 3 P )] retrievals on a new photochemical basis are required. Note that processes of the previously used photochemical models were also used to propose the MAC model, which is applied as follows.  Llewellyn and Solheim (1978) analyzed emissions in the IRAtm and Meinel bands and proposed the rate of the reaction OH(ν ≥ 1) + O( 3 P ) → H + O 2 (a), which they suggested to implement in a photochemical model to retrieve [O( 3 P )]. The reaction R h2.1 implemented in the MAC model and shown in Table 7 is similar to that considered by Llewellyn and Solheim (1978) where OH * describes the hydroxyl radical in all possible levels ν . It should be mentioned that it would be possible to retrieve [O( 3 P )] if the vibrational population of OH(ν ) were known. Wayne (1994) presented an excellent overview of reactions involving O 2 (a) and assumed that the reaction emphasized by Llewellyn and Solheim (1978) only produces about one-half of the VER{O 2 (a −X)} intensity needed. Wayne (1994) suggested that the reaction OH(ν ≥ 3)+O 2 → OH+O 2 (a) can be neglected due to its negligible contribution, which was experimentally confirmed. Hislop and Wayne (1977) emphasized two sources of the emission line at λ 1270 = 1270 nm. The first source is the O 2 (a − X){0 − 0} transition at λ 1270 that enables the determination of VER{O 2 (a − X)} profiles. The second source is the HO 2 { 2 A (001)− 2 A (000)} electronic transition at λ HO 2 = 1265±10 nm, which is very close to λ 1270 . 2 A denotes the ground state of HO 2 , 2 A its first excited state, and the three numbers in parentheses the various levels of the vibrational excitation. Additionally, Hislop and Wayne (1977) mentioned the reaction HO 2 { 2 A (001)}+ O 2 → HO 2 + O 2 (a), which negligibly produces O 2 (a). It is possible to process OH * emissions in future versions of the MAC model applied to measurements obtained during the ETON campaign, but emissions related to the excited HO 2 (HO 2 * ) were measured neither during the ETON campaign nor other rocket campaigns known to the authors of this article. Unfortunately, it would not be enough to extend future versions of the MAC model with processes considering vibrational levels of OH * because of the HO 2 * contribution. Sharma et al. (2015) proposed a new mechanism responsible for the deactivation of OH * as follows: Sharma et al. (2015) emphasized that this mechanism is represented by two reactions producing a transient HO 2 * complex at first, which is de-excited, resulting in the products shown in the proposed mechanism on the right. Contributions of processes involving both OH * and HO 2 to the production of O 2 (a) need to be considered in order to retrieve [O( 3 P )] using VER{O 2 (a − X)}. This enables the conclusion that the disagreement of the reference [O( 3 P )] profiles with the current [O( 3 P )] profiles retrieved at step 3.2 using the MAC model will remain if only the currently known in situ measurements are applied.
In summary, the MAC model was carefully applied to retrieve [O( 3 P )] on the basis of a limited number of VER profiles: (1) including or neglecting VER{O 2 (A − X)} and S) production is negligible. Therefore, O 2 (c) can be considered the major O( 1 S) precursor. It follows also that the triplet Herzberg states (A 3 + u , A 3 u ) are more strongly coupled with the triplet ground state (X 3 − g ) than with the singlet states (c 1 − u , b 1 + g , a 1 g ) because the O 2 (X) production is considered to be invariable. (2) using all VER profiles or a VER{O 2 (b − X)} profile only. This is possible because calculations carried out using the MAC model are separated by steps, and the concentrations of various O 2 states are considered at each of the retrieval steps listed in Table 12. profiles are compared with the unperturbed (hereafter referred to as reference) [O( 3 P )] profiles by estimating differences between them as follows:

Influence of perturbations in model parameters on
where the [O reference ] profiles are shown in Fig. 4. To keep the results obtained according to Eq. (5) positive, perturbations in T were chosen to be +5 % of T , but perturbations in [N 2 ] and [O 2 ] by −5 % of the respective ([N 2 ]+ [O 2 ]) values. Perturbations in VER profiles were introduced by positive values of the respective error values. Specifically, the absolute accuracy of VER{O 2 (a−X)} (infrared atmospheric band, IRAtm) values was assumed to be ±20 %, and the absolute accuracy of the other VER values was assumed to be ±10 % according to Greer et al. (1986); see Sect. 2 for details.
Both the perturbed and reference [O( 3 P )] profiles were retrieved using the MAC model with one MAC input parameter perturbed at a time according to the description provided at the beginning of this section. For instance, values of one VER profile only were perturbed at the particular retrieval step; see Table 12 for an overview of all steps of the consequent retrieval procedure. Figure 6 shows values (units: atoms cm −3 ), illustrating the influence of the perturbed input parameters on [O( 3 P )] profiles. Because the number of VER profiles used in the [O( 3 P )] retrieval increases with each step, the number of profiles of [O( 3 P )] differences also increases from panel (a) to panel (e) of this figure. Note that a VER profile, which was considered to have a significant impact at one of the retrieval steps performed previously to calculate the corresponding concentration profile, was taken only implicitly into account at the current retrieval step, at which these concentrations are considered instead of the corresponding VER profile. A comparison of difference values shown in various panels indicates that perturbations in the VER and T profiles introduced simultaneously will cause the highest impact on [O( 3 P )] profiles.

Discussion of the obtained results
In situ measurements obtained during the ETON campaign enable the estimation of the efficiency of [O( 3 P )] retrievals carried out using the well-known photochemical models and the proposed MAC model; see Sect. 3.5. For instance, Led-  Table 12 on the basis of the following perturbed input parameters: volume emission rates (VERs), temperature (T ), [N 2 ] and [O 2 ]. Additionally, [O( 3 P )] profiles were retrieved on the basis of the unperturbed input parameters and denoted as reference [O( 3 P )] profiles shown in Fig. 4. Finally, differences between the reference and perturbed [O( 3 P )] profiles were estimated and are shown in five panels using the colors of the perturbed input parameters in the legend, which is shown in panel (f). The units of the differences shown in panels (a)-(c) are the same as those of panels (d)-(f). VER values were perturbed by values of the absolute error: +20 % for the VER{O 2 (a − X)} profile and +10 % for the other VER profiles. Data sets of T , [N 2 ] and [O 2 ] were obtained using the NRLMSISE-00 model and perturbed by 5 %: +5 % for the T values and −5 % for the sum of the [N 2 ] and [O 2 Brus (1977). The atlas of terrestrial nightglow emission lines in the range 314-1043 nm, including the emission lines of these O 2 states, is provided in Table 3 as a compressed form of the electronic supplement of Cosby et al. (2006). Vibrational states of these triplet states and the O 2 (c) singlet state are also very close to each other, but the spin flip energy is required for transitions from these triplet states to the O 2 (c) singlet state. Secondly, the probability of transitions from  (Hollas, 2004). Therefore, we conclude that transitions from O 2 It should be kept in mind during the interpretation of the obtained results that the uncertainties of the ETON data sets are 10-20 % in VER peak values; see Sect. 2. Varying the MAC input data within these uncertainty ranges significantly influences the magnitude of products obtained with the MAC model. For example, the retrieved [O( 3 P )] peak values increase by up to 40 % if VER values are increased by 10 % due to the VER uncertainty; compare Figs. 6 and 3. Additionally, uncertainty in the in situ [O( 3 P )] profile values of less than about 40 % in [O( 3 P )] peak values is very high, implying that novel in situ data sets obtained with more accurate measurement techniques should be measured in the future. In fact, the ETON in situ measurements were used to tune unknown or poorly constrained rate values of the complementary processes, and the importance of precise in situ measurements is tremendous. Nevertheless, rate values of the processes implemented in the MAC model are considered to be validated through a comparison of the in situ and retrieved [O( 3 P )] profiles. In the following three sections we discuss the tuning based on the ETON data set.

Discussion of the obtained results regarding tuned rate values for implemented three-body recombination processes
The MAC model was proposed on the basis of the hypothesis of Huestis (2002) and Slanger et al. (2004b), who stressed that association rates of excited O 2 states in the three-body recombinations must be modified because O 2 molecules in various excited states collide with each other and other molecules so that an excitation transfer takes place. However, Huestis (2002) and Slanger et al. (2004b) did not provide modified association rates. This was also emphasized by Krasnopolsky (2011), who applied the two-step Barth excitation transfer scheme for each of the ETON VER profiles separately. Thus, Krasnopolsky (2011) substantially limited (compared to Krasnopolsky, 1986) the number of considered chemical reactions related to O 2 ( 5 ). Because the lifetime of O 2 ( 5 ) is less than ∼ 0.4 µs (Slanger and Copeland, 2003), it is impossible to determine a number of reaction rates involving O 2 ( 5 ) in the laboratory. For this reason reactions involving O 2 ( 5 ) cannot be adequately included in chemical-dynamic time-dependent atmospheric models. Nevertheless, the association rate values of O 2 states were tuned with the use of the hypothesis of Slanger et al. (2004b) to apply them in the MAC model as follows. Firstly, the theoretically known association rates (Bates, 1988a) were considered. Then, they were used to obtain the new association rate values of O 2 (b, a, X); see the respective yielding factors bY , aY and xY in Tables 9 and 10. Specifically, values of the known association rates were increased using the association rate (pY ) of O 2 ( 5 ). For instance, the association rate of O 2 (b) was increased by an arbitrary value of 7 % of the pY value to determine a new value of bY . In a similar way, the association rates of O 2 (a) and O 2 (X) were increased by arbitrary values of 68 % and 25 % of the pY value to determine new values of aY and xY , respectively. It should be noted that Bates (1988a) provided the association rates for O 2 ( 5 , A, A , c, b, a, X) by applying the concept of a hard sphere to the reaction rates in the threebody recombinations (O( 3 P ) + O( 3 P ) + {N 2 , O 2 }) as was done by Bates (1951), Wraight (1982) and Smith (1984). It is remarkable that N 2 was used as the third body in laboratory studies and that the reaction rate of the three-body recombination updated by Smith and Robertson (2008) is lower than that one provided by Campbell and Gray (1973) above 200 K and higher below 200 K. Nevertheless, Campbell and Gray (1973) and Smith and Robertson (2008) assumed the obtained reaction rate (χ Px N 2 ) to be equal to the one (χ Px O 2 ) considering O 2 to be the third body because of the hardsphere concept used. Unfortunately, neither χ Px O 2 nor χ Px N 2 is provided in the established studies on chemical kinetics, e.g., the Jet Propulsion Laboratory databases (Burkholder et al., 2015). It is worth mentioning that Bates (1979) interpreted the Chapman excitation process as follows: two colliding O( 3 P ) atoms create an electronically excited O 2 molecule, which is presumably in the upper Herzberg state (Greer et al., 1987); see Sect. 1 for details. This altogether implies that an interaction of O 2 in the ground or excited states with one or more O( 3 P ) atoms is a complicated process worthy of further investigation, and the hard-sphere concept should be used with caution.
There are two main adjustments done in the MAC model with respect to the three-body recombinations. The first one is related to the increased association rates of O 2 (b, a, X) taking collisions of higher excited O 2 molecules with O 2 ( 5 ) into account and being implicitly considered in the MAC model. The second one is related to the increase in χ Px O 2 compared to χ Px N 2 of the reactions R x1.2 and R x1.1 , respectively. This adjustment was done because the hardsphere concept used is probably misleading and because other O( 3 P ) loss processes were required to be implicitly implemented in the MAC model according to the verification and validation procedures. The origin of the required O( 3 P ) loss processes is currently not definitely known because both photochemical and dynamical phenomena might contribute to the total O( 3 P ) loss. Note that the O 2 photodissociation into O( 3 P ) atoms has its maximum at ∼ 120 km according to Solomon and Qian (2005), and Colegrove et al. (1965) invoked eddy diffusion to describe the O( 3 P ) loss by transport from the lower thermosphere downwards.
Two cases are considered in terms of adjusting the rate values of the R x1.1-2 reactions in the MAC model. In the first case the χ Px O 2 rate value is multiplied by ∼ 3.56 × 10 4 , and the χ Px N2 rate value is left to be equal to the one given by Smith and Robertson (2008). The first case is used as the standard case of using the R x1.1-2 reactions in the MAC model. In the second optional case both rate values (χ Px O 2  It should be noted that the [O( 3 P )] values retrieved at steps 2.1, 2.2, 2.3, 3.1, 3.2 and 4.1 significantly depend on perturbations in VER values. It follows from the discussion of Fig. 6 that the dependence of [O( 3 P )] values on VER values applied directly at the current step, e.g., VER{O( 1 S − 1 D)} at step 4.1, at which VER values belong to the MAC input parameters, is lower than the dependence of [O( 3 P )] values on VER values applied directly, e.g., VER{O 2 (a−X)}, at the previous steps. As for the last retrieval step 5.1, concentrations of chemical species are applied at this step to retrieve [O( 3 P )].
In summary, the verification and validation procedures based on the comparison of the in situ O( 3 P ) profile with several O( 3 P ) profiles retrieved at steps 2.1, 2.2, 2.3, 3.1, 3.2, 4.1 and 5.1 support the complementary reactions considered in the continuity equations; see Appendix A. This implies that additional O( 3 P ) loss processes implicitly considered by the R x1.1-2 reactions are supported by calculations carried out with the MAC model; see also the next section.

Discussion of the causes responsible for additional O( 3 P ) loss processes
This section deals with additional O( 3 P ) loss processes implicitly considered in the MAC model by the R x1.1-2 reactions according to the description provided in the previous section. Steady-state chemical balance equations (also referred to as continuity equations) implemented in the MAC model include the production and loss terms of various chemical species. The mentioned additional O( 3 P ) loss processes concluded using results obtained at the last [O( 3 P )] retrieval step 5.1 were validated on the basis of all results obtained with the MAC model at each of the retrieval steps. Unfortunately, there are not enough data to quantify contributions of the diffusive velocities (molecular and turbulent ones) and the Eulerian mean velocity in the considered continuity equations to the transport of various chemical species. For instance, the molecular diffusive velocity may contribute to the additional O( 3 P ) loss processes. The maximum of the O 2 photodissociation into O( 3 P ) atoms is at ∼ 120 km (Solomon and Qian, 2005). Shematovich et al. (2011) and Wei et al. (2014) discussed the ionized O( 3 P ) drag to outer space. This drag might play a relatively negligible role in normal solar activity and atmospheric conditions due to a low-rate production of the ionized O( 3 P ) from inelastic collisions involving O( 3 P ) atoms. Colegrove et al. (1965) discussed the downward O( 3 P ) transport from the lower thermosphere. The total downward O( 3 P ) transport was explained by Colegrove et al. (1965) to occur due to high values of the diffusive transport velocity. Note that Grygalashvyly et al. (2012) and Qian et al. (2009) also derived relatively high values of the diffusive transport velocity in the MLT region compared to those of Swenson et al. (2018).
The molecular diffusion velocity was emphasized in Brasseur and Solomon (2005) on page 138 to occur because of elastic collisions between particles and taking into account the effect of thermal diffusion, whereas reactive collisions were neglected. The issue regarding reactive collisions was discussed in Sect. 1 with respect to difficulties calculating the respective rate coefficients. In fact, it is even difficult to address the static and combined quenching processes in the laboratory, where dynamic quenching processes are often studied with the use of the Stern-Volmer method (Lakowicz, 2006). For instance, a tetraoxygen molecule, the chemistry of which is not well known because it has only recently been discovered by Cacace et al. (2001), may be produced from reactive collisions involving O( 3 P ). It can be concluded that these reactive collisions are not considered in the steady-state continuity equations applied in the MAC model, but they should be taken into account. Therefore, a temporary solution was introduced to implicitly implement possible O( 3 P ) loss processes discussed in the previous section , i.e., simply increasing the rate value of the three-body recombination reaction with O 2 as a third body. We start the discussion regarding the O( 1 S) precursor with two main findings and finish by considering arguments published previously.
Firstly, the MAC model is based mainly on the two-step Barth excitation transfer scheme that requires the consideration of the O( 1 S) precursor; see Sects. 1 and Appendix A. The nature of the oxygen green line emission was investigated by many atmospheric scientists on the basis of in situ airglow measurements by tuning the reaction rates including the O( 1 S) precursor as an unidentified O * 2 state and the comparison of these rates with the ones measured in a groundbased laboratory. It can be assumed that the deduced O * 2 corresponds to an excited O 2 in a specific state or a group of O 2 states according to Huestis (2002). However, the hypothesis of Huestis (2002) was refuted by Slanger et al. (2004b).
Secondly, the Barth excitation transfer scheme was sequentially implemented in the MAC model considering O 2 (A), O 2 (A ) and O 2 (c) as multiple O( 1 S) precursors according to Slanger et al. (2004b). It should be noted that O 2 (A), O 2 (A ) and O 2 (X) are triplet states, and O 2 (c) is a singlet state. The verification and validation results shown in Sect. 3.5 enable the separation of MAC processes in two groups related to O 2 ( 5 , A, A , c, b, a, X) and O( 1 S, 1 D, 3 P ) as well as O 2 ( 5 , c, b, a, X) and O( 1 S, 1 D, 3 P ). This conclusion reflects the importance of the ETON rocket campaign  for identifying the O( 1 S) precursor. O 2 (c) was proposed by Solheim and Llewellyn (1979), Llewellyn et al. (1980), and Krasnopolsky (1981) to be the O( 1 S) precursor on the basis of the electron-impact excitation spectrum of O 2 determined by Trajmar et al. (1972) and Stern-Volmer relations. As far as the results of Trajmar et al. (1972) are also valid for O 2 ( 5 ), Krasnopolsky (1986) and Krasnopolsky (2011) proposed O 2 ( 5 ) to be a possible O( 1 S) precursor. Nevertheless, O 2 (A) was concluded by Krasnopolsky (2011) to be the most probable O( 1 S) precursor according to the experimental measurements of Stott and Thrush (1989) and Steadman and Thrush (1994). Stott and Thrush (1989) is allowed by symmetry. The validity of this argument was tested in the MAC model by implementing O 2 (A , c) quenching to O 2 (X) using the reactions R d9.1 and R c2.1 . Steadman and Thrush (1994) suggested that if O 2 (c) is considered to be the O( 1 S) precursor, then it is probably at the vibrational state ν = 8 because of the favorable Franck-Condon factors for transitions to vibrational states of the electronic O 2 ground state O 2 (X). Krasnopolsky (1981) also considered O 2 (c) to be the O( 1 S) precursor on the basis of observations in the atmospheres of Venus and Mars, where O 2 (c) is in the vibrational ground state ν = 0. Krasnopolsky (1981) concluded that the activation energy of 2.1 kcal mol −1 is required for quenched O 2 (c, ν = 0) molecules to produce O( 1 S). Altitude profiles of the fractional O 2 (c) vibrational populations with ν = 3-10 are characterized by various peak altitude values in the altitude range 80-120 km, where they were derived by Llewellyn and McDade (1984) from a model using reaction rate values given by Kenner and Ogryzlo (1983). The [O 2 (c, ν = 6)] peak is at 94 km, and the [O 2 (c, ν = 8)] peak is at 103 km according to the results of atmospheric modeling shown in Fig. 5 in Llewellyn and McDade (1984). These results enable the determination of the peak of [O 2 (c, ν = 7)] at about 97 km, where the green line emission peak is; see Table 1. Additionally, the modeling results obtained by López-González et al. (1992a) and shown in their Fig. 6c indicate that the [O 2 (c, ν = 6)] peak is at about 97 km. Stott and Thrush (1989) compared results obtained with laboratory experiments and atmospheric models (their Fig. 10) and found that the maximum of the relative vibrational O 2 (A) population is at O 2 (A, ν = 2, 3) in laboratory experiments and at O 2 (A, ν = 5) in model results. It follows that the maximum of the relative vibrational O 2 (c) population found in laboratory experiments might differ from the respective model results published in, e.g., Llewellyn and McDade (1984) and López-González et al. (1992a).
In summary, the exact role of the vibrational excitation of O 2 (c) as a precursor of O( 1 S) is still not well understood and should be investigated in future studies.

Conclusions
Photochemical processes in the altitude range 80-105 km were modeled considering seven states of molecular oxygen, O 2 ( 5 , A, A , c, b, a, X), and three states of atomic oxygen, O( 1 S, 1 D, 3 P ). The Multiple Airglow Chemistry (MAC) model was proposed to explain the excitation mechanisms responsible for observed airglow. Processes of the photochemical models discussed in Sect. 3.1, 3.2.1 and 3.2.2 were combined with suggested complementary processes to complete the list of processes implemented in the MAC model. Additional processes were proposed to couple the mentioned O 2 states and to implement the O 2 ( 5 )-O 2 (A, A , c) group in the MAC model according to the hypothesis of Slanger et al. (2004b). In situ VER profiles obtained during the ETON campaign were applied to determine unknown or poorly constrained reaction rates and update known ones considered in the MAC model; see Sects. 3.4, 4.1 and 4.2. Note that in situ VER profiles obtained during the WADIS-2, WAVE2000 and WAVE2004 campaigns were applied to validate these reaction rates used in calculations carried out with the MAC model; see Lednyts'kyy et al. (2019). We would like to emphasize that the agreement between [O( 3 P )] profiles obtained at various retrieval steps and the corresponding in situ [O( 3 P )] profiles for these three campaigns is perceived as significantly better than that for the ETON campaign. The proposed algorithm enabled the calculation of the concentrations of such coupled minor species as O 2 (A, A , c, b, a) and O( 1 S, 1 D, 3 P ) for the first time.
The hypothesis of the integrity of identity of the O 2 electronic states of Huestis (2002) was refuted by Slanger et al. (2004b) Convincing verification and validation results should be accepted critically because the tuned rate values were obtained on the basis of the in situ measurements with uncertainties provided by Greer et al. (1986)  The following four key findings required to develop the MAC model were proposed for the first time to the best of our knowledge. Firstly, the algorithm was proposed without using a priori data applied to initiate calculations with the MAC model. Instead, sequent retrieval steps were applied to solve the system of continuity equations by starting calculations from higher excited species and providing the concentrations of excited species for the following retrieval steps. Each polynomial equation was solved separately to obtain the concentrations of chemical species required for the next polynomial equations, which were sequentially introduced and solved to retrieve [O( 3 P )] profiles; see Table 12 for the retrieval steps applied using the MAC model. Secondly, the participation of O 2 ( 5 ) in chemical reactions was implicitly implemented by adjusting the association rates of O 2 (b, a, X) (Bates, 1951)  The proposed algorithm used to solve the system of continuity equations also enabled the introduction of perturbations in tuned rate values, and their impact on the MAC output parameters was studied. The results of the sensitivity analysis enable the neglect of unimportant processes coupling O 2 states; see the third column of Tables 8, 9, 10 and 11. For instance, transitions from the triplet O 2 (A, A ) states to the singlet O 2 (c, b, a) states were found not to be intense and less probable than transitions from these excited triplet and singlet states to the triplet O 2 (X) ground state. This might be explained by the energy required for the spin flip during transitions between one triplet and one singlet states.
The following conclusions can be drawn from the results of the sensitivity analysis. Firstly, the triplet O 2 (A, A ) states can be neglected in the MAC model because of their strong coupling with the ground triplet O 2 (X) state. Then, the following correspondences regarding the selection rules for chemical reactions were established. Collisional deactivation implemented in the MAC model was found to be (1) strong between O 2 (c 1 − u ) and O 2 (b 1 + g ), (2)   Decisions and processes are denoted by rhombs and rectangles, respectively. Connectors are denoted by empty circles. The flowchart is read following lines with arrows from one flowchart symbol to another. The prior retrieval procedure is described by the text shown in blue. If the prior retrieval procedure can be omitted (as is the case for the ETON campaign), then the corresponding decision "not important" (shown in violet) near a rhomb is to be taken, which is denoted by "optionally" (shown in violet in a rectangle) and is relevant for the optional calculation result (shown in blue in a rectangle). The optional procedure carried out to calculate [O 2 (A)] and [O 2 (A )] is described by the text shown in green. If emissions in the Herzberg I and Chamberlain bands are not available (see "no" shown in violet near the respective rhombs) or optional (see "not important" shown in violet near the respective rhombs), then this optional procedure can be omitted at steps 2.3 and 3.1; see [O 2  A1 The first retrieval step  [O 2 ] were obtained using the NRLMSISE-00 model. Nevertheless, measurements obtained remotely and in situ during the WAVE2004 campaign represent data sets required at the prior retrieval step applied by Lednyts'kyy et al. (2019).
The processes shown in Tables 2 (see Sect. 3.1) and A1 were used for calculations carried out at this step. Processes marked with a character P in these tables were not used as complementary processes in the MAC model. The resulting concentration values obtained at the prior retrieval step are also marked with the character P. The production and loss terms were calculated according to the processes shown in Tables 2 and A1 as follows: [O 2 ], [O 2 ], [CO 2 ]}+R r3.0 . The prior calculation results in [O( 1 D)] profile values as follows: P- [O( 1 [O 3

A2 The second retrieval step
The second retrieval step was performed within four substeps to calculate [O 2 (b)] values.

A2.1 Substep 1: calculation of [O 2 (A)]
The Herzberg I band emission measured at 320 nm was used to retrieve VER{O 2 (A − X)} values and then to retrieve The production and loss terms were calculated considering the processes shown in Tables 5 and 6 as follows: Complementary processes were used in the production and loss terms denoted with a character C. Therefore, R- [O 2 (A)] is also marked with the character C instead of the character R as follows: R- [O 2  [O 2 (A)] values were retrieved and then evaluated to compare and verify these calculations. VER{O 2 (A − X)} values were also evaluated to compare them with retrieved values in order to verify the MAC calculations; see Sect. A2.4. Table A1. Processes of the prior retrieval, continued from those shown in Table 2.
Odd oxygen processes related to O( 1 S) Odd oxygen processes related to absorption and catalytic ozone destruction Odd hydrogen processes  [O 2 (A )] values were retrieved and then evaluated to compare and verify these calculations. VER{O 2 (A − a)} values were also evaluated to compare them with the retrieved values in order to verify the MAC calculations; see Sect. A2.4.

A2.3 Substep 3: calculation of [O 2 (b)]
The atmospheric band emission measured at 761.9 nm was used to retrieve VER{O 2 (b − X)} values and then to retrieve [O( 3 P )] values according to the continuity equation for [O 2 (b)], i.e., the cubic equation with respect to [O( 3 P )]. Note that [O 2 (A)] and [O 2 (A )] values calculated at the previous steps were used in the [O( 3 P )] retrieval at this step. However, if the MAC model excluding O 2 (A) and O 2 (A ) is used then [O 2 (A)] and [O 2 (A )] profile values are set to zero because these concentrations were not calculated at the previous steps. This is justified because the hypothesis of Slanger et al. (2004b) was adopted to propose the MAC model. Note that the MAC calculations were verified and validated; see Sect. 3.5 for details. Then, [O 2 (b)] values were retrieved (R- [O 2 (b)]) on the basis of [O( 3 P )] values by using the continuity equation considering all relevant processes of the MAC model. The continuity equation for [O 2 (b)] including terms of the [O 2 (b)] production (P {O 2 (b)}) and its loss (L{O 2 (b)}) is as follows: d [O 2 The production and loss terms were calculated considering the processes shown in Tables 5 and 6.
The production term was calculated as follows: The loss term was calculated as follows: [O 3 ]}+R b2.1 [O 3 ]) corresponds to the complementary processes relevant here. Note that [O 2 (b)] values were calculated taking M, H and C processes into account as follows: R- [O 2 In the case when atmospheric band emissions are not given, [O 2 (b)] values can be calculated on the basis of already known [O( 3 P )] values. [O 2 (b)] values were also evaluated (E- [O 2 (b)]) on the basis of retrieved VER{O 2 (b−X)} values (R-VER{O 2 (b−X)}) using the corresponding transition probability: E- [O 2 Finally, VER{O 2 (b − X)} values were evaluated (E-VER{O 2 (b − X)}) on the basis of R- [O 2 (b)] values and the respective transition probability: values were retrieved and then evaluated to compare and verify these calculations. VER{O 2 (b − X)} values were also evaluated to compare them with the retrieved values in order to verify the MAC calculations; see Sect. A2.4. Step 2.3 described in Sect. A2.3 was carried out with the MAC model to retrieve R- [O 2 (b)] and [O( 3 P )] values on the basis of R-VER{O 2 (b − X)} values. E- [O 2 (b)] values were also evaluated to compare them with R- [O 2 (b)] values. Additionally, E-VER{O 2 (b − X)} values were also evaluated to compare them with R-VER{O 2 (b − X)} values.

A3 The third retrieval step
The third retrieval step was performed in three substeps to calculate [O 2 (c) Tables 5 and 6. The production term was calculated as follows: The loss term was calculated as follows: [O 2 (c)] values were calculated taking M, H and C processes into account as follows: R- [O 2 (c) The infrared atmospheric band emission measured at 1.27 µm was used to retrieve VER{O 2 (a − X)} values and then to retrieve   [O 2 ].
The loss term was calculated as follows: [O 2 (a)] values were retrieved and then evaluated to compare and verify these calculations. VER{O 2 (a − X)} values were also evaluated to compare them with the retrieved values in order to verify the MAC calculations; see Sect. A3.3.

A3.3 Substep 3: consistency tests in the calculation of
The consistency tests in the calculations performed with the MAC model are based on the comparison of the retrieved and evaluated values.
Step 3.1 described in Sect. A3.1 was carried out to retrieve R- [O 2 (c)] and [O( 3 P )] values. The corresponding calculations carried out at step 3.1 could not be tested for consistency because [O 2 (c)] was calculated on the basis of concentrations available from the previous steps, whereas VER profiles were not employed for the [O 2 (c)] calculations directly. Indeed, emissions in the Herzberg II band were not measured, whereas emissions in the new system from Keck I/II and the Richards-Johnson system have a low signal-to-noise ratio. Therefore, only calculations carried out at step 3.2 are tested for consistency.
Step 3.2 described in Sect. A3.2 was carried out to retrieve R- [O 2 (a)] and [O( 3 P )] values on the basis of R-VER{O 2 (a − X)} values and the concentrations of available excited chemical species. E- [O 2 (a)] values were also evaluated to compare them with R- [O 2 (a)] values. Addition-ally, E-VER{O 2 (a − X)} values were also evaluated to compare them with R-VER{O 2 (a − X)} values.

A4 The fourth retrieval step
The fourth retrieval step was performed in two substeps to calculate [O( 1 S)] values. [O( 1 S)] values were retrieved and then evaluated to compare and verify these calculations. VER{O( 1 S − 1 D)} values were also evaluated to compare them with the retrieved values in order to verify the MAC calculations; see Sect. A4.2.
A4.2 Substep 2: consistency tests in the calculation of The consistency tests in the calculations by using the MAC model are based on the comparison of the retrieved and evaluated values.

A5 The fifth retrieval step
The fifth retrieval step was performed to calculate [O x  The production and loss terms were calculated considering the processes shown in Tables 5, 6 and 7.
The calculation of the production term was based on the considered M, H and C processes as follows:  [O 3 ] involving all relevant chemical species [O 3 ] values were retrieved (R- [O 3 ]) on the basis of the concentrations of atmospheric minor species obtained in the previous steps according to the continuity equation for [O 3 ] considering all relevant processes of the MAC model. The continuity equation for [O 3 ] including terms of the [O 3 ] production (P {O 3 }) and loss (L{O 3 }) is as follows: d [O 3 ]/dt = P {O 3 } − L{O 3 } = 0.

A5.3 Substep 3: calculation of
The production and loss terms were calculated considering the processes shown in Tables 5, 6 and 7.
The calculation of the production term was based on the considered M, H and C processes as follows: The calculation of the loss term was based on the considered M, H and C processes as follows: L{O 3 } = L{O 3 -M} + L{O 3 -H} + L{O 3 -C} = [O 3 ] × D 3 , where L{O 3 -M} = R s2.3 , L{O 3 -H} is absent, L{O 3 -C} = R x2.1 [O( 3 P )]+R b4.1 [O 2 (b)