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

Electronically excited states of molecular and atomic oxygen (six of O2 and two of 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 is proposed combining chemical processes of the well-known 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 5 basis of the multiple in-situ nightglow emissions measured during the Energy Transfer in the Oxygen Nightglow (ETON) rocket campaign. The proposed retrieval procedure to obtain concentrations of these MLT minor species is implemented avoiding a priori data sets. Unknown and poorly constrained reaction rates were tuned and reaction rates of the well-known models were updated with the MAC model 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 transitions considered in the MAC model are identified 10 and validated by calculations with the MAC model.

statistical procedures on the basis of sampled integrated emission profiles.
In the Appendix A2, A3.2, A3.3 and A4.1, where VER profiles were employed to retrieve oxygen concentration profiles, we are going to use the term "retrieve". We are going to use the term "calculate" in the Appendix A1.1, A1.2, A1.3, A3.1 and A5, where VER profiles were not employed. To avoid confusion comparing three kinds of the MAC products, we are going to use the term "retrieve" to mark concentration profiles by a character R and summarizing calculations and evaluations in the Appendix or elsewhere in the article. Our decision is backed up by using the search engine GoogleScholar for the two following cases: (1) retrieve oxygen density rocket VER and (2) calculate oxygen density rocket VER. Both terms are used approximately equally in the literature.

Specific comment:
The Anonymous Referee #2 also suggested that Appendix A is not written clearly enough for the reader to duplicate the model. This is a necessary requirement for scientific papers and I agree with their opinion. To rectify this, I suggest adding a couple of paragraphs at the beginning of this Appendix describing how a user should approach using the MAC model and what they might use it for. As currently written, the first couple of paragraphs address details which a typical reader would initially not be familiar with. This is useful information, but only once the reader has set up the model. Thank you for your work on revising and clarifying the paper to this point. The following paragraphs were added after line 3 (3) on page 41 (41): The MAC model was implemented to study the photochemistry of excited oxygen species in the MLT. [O( 3 P )] retrievals are carried out sequentially and start with higher excited O 2 species, concentrations of which are applied at the next retrieval steps to obtain concentrations of lower excited O 2 and O species, see Ta During the first retrieval steps, the MAC calculations are carried out on the basis of multiple VER profiles of strong nightglow emissions discussed using Table 1. The obtained verification and validation results, see Section 3.5, enabled assessing the most effective group of emissions for the measurement, e.g., of [O( 3 P )]. This group is represented by emissions in the Atmospheric band, the Infrared Atmospheric band and the oxygen green line emission. Additionally, the results obtained studying the influence of perturbations in parameters of the MAC model on the retrieved [O( 3 P )] profiles, see Fig. 6 in Section 3.6 for details, enabled assessing the most effective emission line for the [O( 3 P )] retrievals. This emission line measured at 761.9 nm is represented by transitions O 2 (b − X){0 − 0} in the Atmospheric band. Figure 6 enables concluding that only profiles of temperature, atmospheric density and VER{O 2 (b − X)} are required for the [O( 3 P )] retrievals, see Section A2.3 for details. Another essential characteristic of the MAC model is that calculations discussed in Section A2.3 are carried out by using simple steady state chemical balance equations (referred to as continuity equations) represented by the polynomial equations of the second or third degree with respect to [O( 3 P )]. Solutions of such equations are easy to interpret. These findings might be of great help to the scientific community dealing with processing of remote and in situ measurements to design future [O( 3 P )] experiments.
Additionally, the following relevant change was carried out in lines 6-7 (31) on page 41 (41): Then simple steady state chemical balance equations (referred to as continuity equations). . . was changed to: Then continuity equations. . .
Additionally, the following relevant change was carried out in line 25 (16-21)  Additionally, the following relevant change was carried out in line 32 (29) on page 41 (42): E-VER{O 2 (b − X)} was changed to: E-VER{O 2 (A − X)} Comments of the Anonymous Referee #1 Feedback: In this paper the authors present a new airglow model (MAC, Multiple Airglow Chemistry model) that includes electronically excited states of molecular and atomic oxygen (six of O2 and two of O) and their ground states. The model is based on the measurements and findings of the ETON sounding rocket campaign conducted from South Uist, Scotland in March 1982 and extends this with later efforts by several authors to model the photochemistry of the MLT (Mesosphere/Lower Thermosphere) region, and updated reaction rates. Unfortunately, the in situ measurements of the atmospheric neutral temperature during the ETON campaign were not successful. Instead, the temperature (and neutral density) were taken from the NRLMSISE-00 model in the current study. A sensitivity study was conducted by the authors to investigate the influence of changes in temperature and neutral density in the retrieval of the different excited and ground states of molecular and atomic oxygen. General comments: The paper presents an extensive model to explain the excitation mechanisms responsible for the observed airglow emissions from the MLT region of the Earths atmosphere. It is a nice review of the current knowledge of airglow photochemistry, and it constrain the precursors responsible for the Atmospheric band, Infrared Atmospheric band and the Oxygen Green Line emissions. It is an important contribution to the scientific community. The authors have done a good job in revising the manuscript in accordance with the Referee Comments in the interactive discussion. The structure and language have been substantially improved and the manuscript is much easier to read.
The paper provides a comprehensive review of the many papers and model in the area of nightglow emissions and attempts to produce an all inclusive model that relates the concentration of atomic oxygen to the volume emission rates. I believe that this paper makes a significant contribution to the field and should be published.

List of corrections regarding specific comments of the Anonymous Referee #2
The authors of the manuscript are grateful to the Anonymous Referee #2 for the specific comments. The manuscript was revised and has been hopefully improved to make it easier to follow. Changes provided in this response are indicated by numbers of lines and pages by black (red) font to find these changesin the previous (current) version of the manuscript.
Specific comment to page 32, line 22: page 34 line 22: It is here correctly stated that the accuracy of the ETON profiles is in the order of 10-20%. The accuracy of the integrated emission intensities should however be better than this probably better that 5%. Have the authors considered this in their model comparisons? Response: VER profiles published in McDade et al. (1986), Greer et al. (1986) and Greer et al. (1987) were retrieved on the basis of Integrated Emission Rate (IER) profiles measured during the ETON campaign. Unfortunately, in these works IER profiles were not published to retrieve VER profiles again. If new VER profiles with higher accuracy values were obtained, then this could be considered in the model comparisons explicitely. We would like to emphasize that this had been implicitely considered using our appendix and Specific comment: Appendix A: I still find this section to be very heavy reading and difficult to follow. I wonder whether a reader could recreate the MAC model and all of these steps.

Response:
The response to this specific comment was worked out in the text provided above according to insightful comments of the Co-Editor.
Specific comment: I also do not really like the use of the word retrieve in the first part of the first sentences of sections A2.x with respect to the VER. I did mention that I though that calculate would be a better word in my first review. Retrieve to me tends to imply more than the division by an Einstein A coefficient (or a population scaling factor) as appropriate.

Response:
The response to this specific comment was worked out in the text provided above according to insightful comments of the Co-Editor.
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 1 Introduction Airglow is a permanent global atmospheric phenomenon that can be hardly 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 origin of aurora, a sporadic 15 arc-like atmospheric phenomenon, which fascinated numerous spectators for many thousands of years. Table 1  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, profiles of kinetic temperature and pressure (Remsberg et al., 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 being 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 15 and Barth schemes are hereafter referred to be of 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 concentration dependent kinetics in a homogeneous system, to which a quencher was added (Lakowicz, 2006). According to the Stern-Volmer method, excited and 20 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 lifetimes or concentrations of emitting species enable determining 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 25 reduces the apparent concentration of fluorescent species during inelastic collisions (Lakowicz, 2006). Unfortunately, reactive collisions responsible for the static quenching are not so well understood compared to the products of the 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 continuity equation) is of the third degree with 30 respect to [O( 3 P )], and the respective solutions can be easily interpreted. As for the O 2 (b−X) transition, McDade et al. (1986) developed photochemical models of the first and second types to describe transitions from O 2 (b) (the second electronically excited state of molecular oxygen, O 2 ) to O 2 (X) (the electronic ground state of 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 non-linearities detected in quenching processes simulated by using the model of the first type developed by McDade et al. (1986) 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 and 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.

5
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 ten, 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 a not identified excited state O * 2 is not provided in this short overview excepting two reactions. Specifically, López-González et al. (1992b) considered the reaction McDade et al. (1986) did not consider. But McDade et al. (1986) considered the reaction 10 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. ten) reactions, (2) the system of a few reactions can be easily represented by a low degree polynomial equation regarding (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 15 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 studying the time evolution of chemical species using the ordinary differential equations (ODE) system matrix and 20 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 a priori data sets used to initialize a box model.
In situ atmospheric measurements may be influenced by gravity waves and atmospheric tides at the particular moments of time that hinders the use of box models on the basis of such measurements. The current article studies the MLT photochemistry on the basis of the in situ ETON measurements using steady state continuity equations, i.e. without propagation in time, and 25 without a priori data sets.
The ETON multiple airglow emissions described in Section 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 obser-30 vational 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) as 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).

35
In summary, the current investigation was conducted to study the following topics regarding the new photochemical model proposed here: (1) processes of the O( 1 S) formation and quenching, see Section 3.1, (2) processes including identified O 2 states, see Sections 3.2.1, 3.2.2 and 3.3, and (3) the O( 1 S) precursor represented by one O 2 state or a group of them, see Section 4.3.
The O( 3 P ) retrieval scheme was proposed to be solved in subsequent steps as described in Appendix A on the basis of 5 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 be also applied to retrieve [O( 3 P )] values at some of the mentioned retrieval steps, see Sections 2 and 5 10 for details.  Volume Emission Rates (VER) 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, Great Britain, in westerly direction on 23rd March 1982 from ∼21:27 UT 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 Atmo-20 spheric 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. 25 The absolute accuracy of ±20% in VER peak values for the Infrared Atmospheric band emissions and better than ±10% in other wavelength ranges       .
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 well-known cubic equation 5 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, 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 10 correspond to these VER profiles. Note that the other listed O 2 transitions were also considered in the proposed MAC model, see Section 3.3 for details. It is worth mentioning that all of these O 2 transitions were measured remotely using the instrument SCIAMACHY (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 con- The established photochemical models of McDade et al. (1986), Gobbi et al. (1992) and Semenov (1997) Table 1. Relevant optical transitions of terrestrial airglow in the Earth's atmosphere. Emissions (see column "Emission") observed in the wavelength range shown in column "λ" are denoted by abbreviations (see column "Ident."). Typical intensity values of an integrated (limb) emission rate profile are given for nightglow (see column "Int." before the comma) and, if available, dayglow (see column "Int." after the comma). Altitudes of the corresponding emission rate peaks are shown in column "Alt.". Atomic oxygen emissions are denoted by abbreviations as follows: GrL is for 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 is for the InfraRed Atmospheric band emission at 1270 nm, Atm -the Atmospheric band emission at 761.9 nm, Noxthe Atmospheric band emission at 1908 nm, HzI -the Herzberg I band emissions, BG -the Broida-Gaydon band emissions, Cha -the Chamberlain band emissions, HzIII -the Herzberg III band emissions, HzII -the Herzberg II band emissions, cbK -the New system band emissions measured by 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 is for 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)    McDade et al. (1986) to be favorable compared to models based on the one-step (Chapman) excitation scheme. It is worth 5 mentioning that Grygalashvyly et al. (2018) 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 Section 2) and fitting retrieved data sets, Grygalashvyly et al. (2018) applied 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. (2018) to be applied in their model. on the basis of VER of the green line emission (VER 558 also referred to as VER{O( 1 S − 1 D)}).
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 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 , the rate βκ 1 of the three-15 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 * 2 , the O( 1 S) precursor. The rates β * O , β * N2 , β * O2 of the R P v3.1−3 reactions describe the O * 2 quenching. The R P v2.1 reaction with the rate value δβ * O , where δ is an empirical value, refers to the second step of the Barth excitation transfer scheme resulting in O( 1 S) + O 2 . 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 20 in this study for retrievals using the well-known cubic equation according to Murtagh et al. (1990). Note that these empirical coefficients were derived by McDade et al. (1986) using semi-empirical models, including MSIS-83 (Hedin, 1983) profiles and different values of the empirical coefficients. The lowest obtained values of C(0), C(1) and C(2) from all obtained 25 ones, which are related to the O( 1 S) precursor, were found by McDade 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.

R #
Odd oxygen processes related to O2(b) Symbol and described for Eq. (2). The photochemical model resulting in the extended cubic equation is hereafter referred to as the Gmodel 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 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 15 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.  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 30 worth being mentioned 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 5 NRLMSISE-00 model was applied 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 the third orders with respect to [O( 3 P )] ) are used to retrieve [O( 3 P )], see left panels in Figs. 4 and 5 in Section 3.5. The extended cubic Eq. (3) was solved for this study using the analytical method of Semenov (1997) also described by Khomich et al. (2008). As for the well-known cubic Eq. (2), it was 10 solved for this study using the program available at https://idlastro.gsfc.nasa.gov/ftp/contrib/freudenreich/cuberoot.pro 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). 15 Photochemical models based on identified O 2 states and their coupling with each other are described in the following Section 3.2.

Models with identified excited O 2 states
A short review regarding approaches developing photochemical models was provided in Section 1. The established photochemical models described in the following sections include O 2 (b, a, X) in the first model, see Section 3.2.1, and O 2 (c, b, X) 20 in the second model, see Section 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 night time, see the 25 R a1.1−2 reactions provided in Table 3. The model of Sharp et al. (2014) also included processes related to the 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 30 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 Atmo- Table 3. Processes of the model of Mlynczak et al. (1993) modified by Sharp et al. (2014) are hereafter referred to as the M-model, see Section 3.2.1. Processes of O2 and O3 photolysis occur at 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.

R #
Odd oxygen processes related to O2(b), O2(a) and O( 1 D) spheric band represented by the vibrational transition 0−0 of the forbidden electronic transition . Note that processes of the M-model were used to develop the MAC model on the basis of VER profiles O 3 altitude profiles obtained by using the modified kinetic model of Mlynczak et al. (1993) and the YM2011 model.  Hickey et al. (1997). The first implementation of O 2 (c) as the O( 1 S) precursor seems to be 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 Σ + g , ν = 0 − X 3 Σ − g , ν = 1 at 864.5 nm can be observed from the Earth's surface and it is denoted as transition 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). 10 It should be noted that both can be observed remotely from space, e.g. using the SCIAMACHY instrument mentioned in Section 2 because radiation was measured using the SCIAMACHY instrument simultaneously in the wavelength range from 240 to 1750 nm (Bovensmann et al., 1999).

Processes of the MAC model
The processes from the G-model (see Section 3.1), the M-model (see Section 3.2.1) and the H-model (see Section 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 as well as other high ranking sources listed in Huestis 25 (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 Section 3.2.1):   (Hickey et al., 1997;Huang and George, 2014) hereafter referred to as the H-model, see Section 3.2.2. The MAC modell includes all processes listed here and also the processes shown in Tables 6 and 7.
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.
The following processes were adopted in the MAC model from the H-model of Huang and George (2014) and Hickey et al. (1997) (see Table 4 in Section 3.2.2): These processes were all adopted in the proposed MAC model and are referred to as H-processes. 10 The following processes were adopted in the MAC model from the G-model of Gobbi et al. (1992) (see Table 2 in Section 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 Π, A, A , c, b, a, X) with each other and O( 1 S, 1 D, 3 P ) taking the hypotheses of Huestis (2002) and Slanger et al. (2004b) into account. The C-5 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)  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)  implicitly 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 Π) are not well known, e.g., compare Krasnopolsky (2011) and Krasnopolsky (1986). It should be noted that O 2 ( 5 Π) has a shorter lifetime and a higher energy compared to the other states O 2 (A, A , c, b, a, X) as it was also mentioned by Huestis (2002) and Slanger et al. (2004b). It should be noted that 5 Π 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 25 complicated to operate with the O( 1 S) precursor as a group of many not identified O 2 states.
The C-processes related to the Herzberg states A 3 Σ + 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: 6. the O( 1 S) precursor responsible for the green line emission (R t10.1 , R d9.1 ).
These C-processes and the corresponding reaction rates are provided in Tables 5 and 8, respectively.
The C-processes related to the G-, M-and H-processes complete the coupling of O 2 ( 5 Π, c, b, a, X) with each other and 6. the green line emission (R g1.3 , R g2.2 ), 15 7. three-body recombination and ozone (R x1.1−2 , R x2.1 , R x3.1−2 ). 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 20 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 Section 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 comparing the in situ and retrieved [O( 3 P )] using each particular emission profile described in 25 Section 2.   Tables 6 and 7. R # Odd oxygen processes related to O2(A) and O2(A ) Table 6. Processes shown here comprise the MAC model together with processes shown above in Table 5 and processes shown below in Table 7. Table 7. Processes shown here comprise the MAC model together with processes shown above in Tables 5 and 6.
R # ∆H (eV) Rate value Rate unit Ref.
The tuning of the rate coefficients was carried out by changing the values of dimensionless scaling factors (cTDu, cTCu,   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 .
Step # Input-VER Input-concentration Output-concentration

Verification and validation of calculations carried out with the MAC model
The input parameters of the MAC model are described in Section 2 and include VER profiles retrieved on the basis of in situ measurements during the ETON rocket campaign    ) marked by character R, e.g. R-VER{O 2 (A − X)}.
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 Additionally, concentrations of the same chemical species were evaluated 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. 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 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 2.1 described in Section A2.1 in Appendix A. Then, the verification of calculations at step 2.1 is carried out  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) Table 1, and the sequence of the retrieval steps is provided in Table 12 were derived for these previously used photochemical models phenomenologically, i.e. in relation to reaction rates in which a not identified 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.  Table 7 is similar to that considered by Llewellyn and Solheim (1978):  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 that 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 determining VER{O 2 (a−X)} profiles. The second source is the HO 2 { 2 A (001) − 2 A (000)} electronic transition at λ HO2 =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 three numbers in parentheses -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  that the triplet Herzberg states (A 3 Σ + u , A 3 ∆u) are more strongly coupled with the triplet ground state (X 3 Σ − g ) than with the singlet states (c 1 Σ − u , b 1 Σ + g , a 1 ∆g) because the O2(X) production is considered to be invariable. Sharma et al. (2015) proposed a new mechanism responsible for the deactivation of OH * as follows: OH(ν ≥ 5)+O( 3 P ) → OH(0 ≤ ν ≤ ν −1)+O( 1 D). Sharma et al. (2015) emphasized that this meachanism is represented by two reactions producing a transient HO * 2 complex at first, which is de-excitated resulting in 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   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 in units of atoms cm −3 illustrating the influence of the perturbed input parameters on  Fig. 8 by Goodman and Brus (1977). The atlas of terrestrial nightglow emission lines in the range 314. . .1043 nm including 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  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 the considered chemical reactions related to O 2 ( 5 Π). Because the lifetime of O 2 ( 5 Π) is less than ∼0.4µs (Slanger and Copeland, 2003), it is impossible to determine a 5 number of reaction rates involving O 2 ( 5 Π) in the laboratory. For this reason reactions involving O 2 ( 5 Π) 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 It should be noted that Bates (1988a) provided the association rates for O 2 ( 5 Π, A, A , c, b, a, X) applying the concept of a 15 hard-sphere to the reaction rates in the three-body recombinations (O( 3 P )+O( 3 P )+{N 2 , O 2 }) as it 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 N2 ) to be equal to that one (χ Px O2 ) considering O 2 as the third body because of the used 20 hard-sphere concept. Unfortunately, neither χ Px O2 nor χ Px N2 is provided in the established studies on chemical kinetics, e.g. the Jet Propulsion Laboratory databases (Burkholder et al., 2015). It is worth being mentioned 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 Section 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 worth of further investigation, 25 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 Π) into account and being implicitly considered in the MAC model. The second one is related to the increase of χ Px O2 compared to χ Px N2 of the reactions R x1.2 and R x1.1 , respectively. This adjustment was done because the used hard-sphere concept is 30 probably misleading and because other O( 3 P ) loss processes were required to be implemented in the MAC model implicitly according to the verification and validation procedures. The origin of the required O( 3 P ) loss processes is currently not known definitely 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 adjusting rate values of the R x1.1−2 reactions considered in the MAC model. In the first case the χ Px O2 rate value is multiplied by ∼ 3.56 · 10 4 , and the χ Px N2 rate value is left to be equal to that 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 case used optionally both rate values (χ Px O2 and χ Px N2 ) are multiplied by 7.67 · 10 3 . The R x1.1−2 reactions are only involved in the last [O( 3 P )] retrieval step considering all chemical species. The rate values of the R x1.1−2 reactions were tuned and applied on 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 at normal solar activity and atmospheric conditions due to a low-rate production of the ionized O( 3 P ) from inelastic collisions 30 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 Section 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 5 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 implement possible O( 3 P ) loss processes discussed in the previous section implicitly, i.e. simply increasing the rate value of the three-body recombination reaction with O 2 as a third body. We start the discussion ragarding the O( 1 S) precursor with two main findings and finish with considering arguments published previously.
Firstly, the MAC model is based mainly on the two-step Barth excitation transfer scheme which requires to consider the O( 1 S) precursor, see Sections 1 and A. The nature of the oxygen green line emission was investigated by many atmospheric 20 scientists on the basis of in situ airglow measurements by tuning the reaction rates including the O( 1 S) precursor as a not identified O * 2 state and the comparison of these rates with the ones measured in a ground-based 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 implemented in the MAC model sequentially considering O 2 (A), O 2 (A ) 25 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 Section 3.5 enable separating MAC processes in two groups related to O 2 ( 5 Π, A, A , c, b, a, X) and O( 1 S, 1 D, 3 P ) as well as related to O 2 ( 5 Π, 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. 30 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 Π), Krasnopolsky (1986) and Krasnopolsky (2011) proposed O 2 ( 5 Π) 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 experimental measurements of Stott and Thrush (1989) and Steadman and Thrush (1994). Stott and Thrush (1989) excluded O 2 ( 5 Π), O 2 (A , ν = 2 − 4) and O 2 (c, ν = 0) from the list of possible O( 1 S) precursors and concluded that O 2 (A, ν ≥ 5) is the O( 1 S) precursor. Various arguments were provided by Stott and Thrush (1989) O 2 (b, a) states. The validity of this argument was tested in the MAC model implementing the O 2 (A) quenching to O 2 (b) by using the R t4.1−3 reactions, the O 2 (A) quenching to O 2 (c) by using the R t3.1−3 reactions, and the O 2 (A) quenching to O 2 (a) by using the R t6.1−3 reactions. The results of the sensitivity analysis discussed in Section 3.4 show that these reactions can be neglected in the MAC model, see Tables 5 and 8. Similarly, the O 2 (A ) quenching to O 2 (c, b, a) implemented in the reactions R d2.1−2 , 10 R d3.1−2 and R d4.1−2 can be also neglected in the MAC model. Quenching of the triplet O 2 (A, A ) states to the singlet O 2 (b, a) states requires the spin flip that is energetically not favorable, and the arguments of Stott and Thrush (1989) can be considered as refuted. Therefore, O 2 (c, ν ≥ 2) can be considered the O( 1 S) precursor. Steadman and Thrush (1994) is symmetry allowed. The validity of this argument was tested in the MAC model implementing the O 2 (A , c) quenching to O 2 (X) by using the reactions R d9.1 and R c2.1 .  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 determining 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 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, 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 5 was proposed to explain the excitation mechanisms responsible for observed airglow. Processes of the photochemical models discussed in Sections 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 Π)-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 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) and discussed in Section 2. The influence 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 5 model. Instead, sequent retrieval steps were applied to solve the system of continuity equations starting calculations from higher excited species, and providing concentrations of excited species for the following retrieval steps. Each polynomial equation was solved separately to obtain 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 retrieval steps applied using the MAC model. Secondly, participation of O 2 ( 5 Π) in chemical reactions was implemented implicitly adjusting the association rates retrieval steps are provided with the results obtained from the prior retrieval procedure and described in the appendix starting from Section A2. An overview of these sequentially applied retrieval steps is provided in Section 3.5 in Table  and rectangles, respectively. Connectors are denoted by empty circles. The flow chart is read following lines with arrows from one flow chart symbol to another. The prior retrieval procedure is described by the text shown in blue. If the prior retrieval procedure can be omitted (as it is the case for the ETON campaign), then the corresponding decision "Not important" (shown in violet) near a rhomb is to be taken that is The processes shown in Tables 2 (see Section 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: The continuity equation for [HO 2 ] including terms of the [HO 2 ] production (P {HO 2 }) and its loss (L{HO 2 }) is as follows: d[HO 2 ]/dt = P {HO 2 } − L{HO 2 } = 0. The production and loss terms were calculated according to the processes shown in Tables 2 and A1 as follows: The system of continuity equations for [OH * ] and [HO 2 ] was transformed to a system of the two following equations: P- The 2 nd retrieval step The 2 nd retrieval step was performed within four substeps to calculate [O 2 (b)] values.  Tables 5 and 6 as follows:    The production term was calculated as follows: The loss term was calculated as follows:  Additionally, E-VER{O 2 (b − X)} values were also evaluated to compare them with R-VER{O 2 (b − X)} values.  The continuity equation for [O 2 (c)] including terms of the [O 2 (c)] production (P {O 2 (c)}) and its loss (L{O 2 (c)}) is as follows: d[O 2 (c)]/dt = P {O 2 (c)} − L{O 2 (c)} = 0. The production and loss terms were calculated considering the processes shown in Tables 5 and 6. The production term was calculated as follows: P {O 2 (c)} = P {O 2 (c)-M} + P {O 2 (c)-H} + P {O 2 (c)-C}, where The loss term was calculated as follows: The production term was calculated as follows: 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 Section A3.3.     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: P {O 3 } = P {O 3 -M}+   Table A1. Processes of the prior retrieval and continued to shown in Table 2. Author contributions. Olexandr Lednyts'kyy worked out the concept of the MAC approach proposed by Torr et al. (1985), developed corresponding software, performed needed computations and prepared the manuscript of the article. Christian von Savigny contributed to planning the work activities regarding the article, discussed the results, contributed to the manuscript of the article, corrected and edited it.
Competing interests. The authors declare that they have no conflict of interests.
Acknowledgements. The authors acknowledge the financial support provided by the German Research Foundation (German: DFG) through