The revised method for retrieving daytime distributions of atomic oxygen and odd-hydrogens in the mesopause region from satellite observations

Atomic oxygen (O) and atomic hydrogen (H) in the mesopause region are critical species, governing chemistry, airglow, and energy budget. However, they cannot be directly measured by satellite remote sensing techniques and so inference techniques, by airglow observations, are used. In this work, we retrieved daytime O and H distributions at ~ 77 km–100 km from the data of observations by the SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) instrument at the TIMED (Thermosphere Ionosphere Mesosphere Energetics and Dynamics) satellite in 2003–2015. The retrieval approach considered the reaction H + O3 → O2 + OH in the ozone balance equation. Moreover, we revised all quenching and spontaneous emission coefficients according to latest published data. We then calculated daytime distributions of OH and HO2 at these altitudes with the use of their conditions of photochemical equilibrium.


Introduction
Physicochemical processes involving trace gases play an important role in the formation of the structure and evolution of the atmosphere; for example, as one of the main sources of air heating due to exothermic chemical reactions. Moreover, their space-time distributions are sensitive indicators of the main atmospheric processes and changes. However, quite a number of gases are not measured directly, so indirect methods to retrieve their distribution based on verified physicochemical models are widely used. The simplest model follows from the photochemical equilibrium assumption of a certain component with a relatively short lifetime (see, e.g., Kulikov et al. 2018a and references therein).
At the altitudes of the mesosphere-lower thermosphere (MLT), the components of the families of odd oxygen (O x : O, O( 1 D), O 3 ) and hydrogen (HO x : H, OH, HO 2 ) are most important. The processes with their participation (1) provide the total chemical heating rate of this region and influence the radiative cooling in the CO 2 15-μm band (e.g., Rodgers et al. 1992), and (2) lead to the appearance of airglow layers of OH, O, and O 2 excited states and involve in the formation of the ionosphere layers. In contrast, the spatio-temporal evolution of O x -HO x components is influenced by all types of atmospheric transport and is sensitive to temperature, variations in solar radiation, changes of anthropogenic gases, etc. Thus, these components are important indicators and tracers of the main atmospheric processes, including those occurring in the lower atmosphere. Under these conditions, while regular ground-based or satellite measurements of most O x -HO x components are still limited, the development and application of indirect methods of retrieval remains, in essence, the only way to monitor them.
For several decades the O and H distributions in the MLT region were inferred from the data of daytime and night-time rocket and satellite measurements of the ozone and the emission intensities of OH(ν), O( 1 S), and O 2 (a 1 Δ g ) (e.g., Good 1976;Pendleton et al. 1983;McDade et al. 1985;McDade and Llewellyn 1988;Evans et al. 1988;Thomas 1990;Llewellyn et al. 1993;Llewellyn and McDade 1996;Mlynczak et al. 2007Mlynczak et al. , 2013aMlynczak et al. , 2013bMlynczak et al. , 2014Mlynczak et al. , 2018Smith et al. 2010;Xu et al. 2012;Siskind et al. 2008Siskind et al. , 2015. The retrieval approach is based on the assumption of the ozone photochemical/chemical equilibrium and corresponding airglow model, which connect the local values of O and H with measurement data. The nighttime ozone equilibrium is well satisfied above a certain boundary, which varies within the range of 77-86 km depending on the season, latitude, and year (Belikovich et al. 2018;Kulikov et al. 2018bKulikov et al. , 2019. The daytime ozone equilibrium is fulfilled through the entire MLT region (Kulikov et al. 2017). Moreover, daytime OH and HO 2 are also close to their chemically equilibrium values with an accuracy better than 3% (Kulikov et al. 2006). Thus, the ternary photochemical equilibrium condition of OH, HO 2 , and O 3 is a useful system of algebraic equations that can be applied to retrieve daytime distributions of all O x -HO x components (Kulikov et al. 2006(Kulikov et al. , 2009 and to evaluate the quality of their simultaneous observations (Kulikov et al. 2018a).
The daytime balance of O 3 concentration at MLT altitudes is primarily determined by reactions R1-R3 (hereafter, R1-R12 denotes the reactions from Table 1). Nevertheless, the common approach for O and H retrieval (e.g., Pendleton et al. 1983;Evans et al. 1988;Mlynczak et al. 2007Mlynczak et al. , 2013aMlynczak et al. , 2013bMlynczak et al. , 2014Mlynczak et al. , 2018Smith et al. 2010;Siskind et al. 2015) omits R3. In particular, this is applied for processing the simultaneous data of temperature, O 3 (at 9.6 μm), and the total volume emission rate of OH(9-7) and OH(8-6) transitions at 2.0 μm measured by the SABER instrument onboard the TIMED satellite (Mlynczak et al. 2013a(Mlynczak et al. , 2013b(Mlynczak et al. , 2014(Mlynczak et al. , 2018. As a result, there is a large (since 2002 up to now) database of daytime O and H retrieval. However, 3D modeling shows that omitting R3 in the daytime ozone balance leads to noticeable (up to 50-70%) systematic underestimations of the O concentration below 92 km (Kulikov et al. 2017). Moreover, in the OH* model used by Mlynczak et al. (2013aMlynczak et al. ( , 2013bMlynczak et al. ( , 2014Mlynczak et al. ( , 2018 some quenching and spontaneous emission parameters were collected almost arbitrarily for O and H retrieval, with references that used unpublished sources (as private communication) and very old sources, which were already revised. Hence, we decided to revise all quenching and spontaneous emission coefficients according with latest published data. We show that this approach does not result in unrealistic values of retrieved chemical constituents. Certainly, more non-emissive observations are necessary in the future in order to validate the quality of this new approach.
The main goals of this paper are to: (1) illustrate that the revised procedure, which is based on a more complete theoretical framework, does not result in unrealistic values of atomic oxygen and atomic hydrogen; and (2) show the new method for retrieving OH and HO 2 from satellite data. In the next section, we describe Table 1 Reactions/processes and their constants/coefficients List of reactions with corresponding reaction rates (for three-body reactions [cm 6 molecule −2 s −1 ], for two-body reactions [cm 3 molecule −1 s −1 ]) used in our paper; and other processes (quenching [cm 3 molecule −1 s −1 ], spontaneous emission [s −1 ]) with corresponding coefficients used in our procedure (this work) and in the old procedure (Mlynczak et al. 2018 (1995) calculations and methodology. In section Results, discussion, and conclusion, we discuss the obtained results, which are followed by concluding remarks in the last section.

Calculations and methodology
We consider daytime conditions throughout the entire manuscript. If only reactions R1 and R2 are included in the daytime OBE (ozone balance equation), the condition of its equilibrium directly connects the local O concentration with the measured O 3 , temperature, and air concentration (M): where k 1 -k 10 denotes the reaction rates for the corresponding reactions R1-R10 in Table 1. In the official SABER product, this equation is used to determine the daytime O distribution in the pressure range 0.1-0.0001 hPa (~ 65-105 km) (Mlynczak et al. 2013a(Mlynczak et al. , 2018.
The measured volume emission of the vibrationally excited hydroxyl with vibrational numbers v = 9 and v = 8 in a single spectral channel centered at 2.06 μm: where VER 2μm is the measured volume emission of the vibrationally excited hydroxyl with vibrational numbers v = 9 and v = 8 in a single spectral channel centered at 2.06 μm, and V 97 , V 86 are the volume emissions for transitions of vibrationally excited hydroxyl from vibrational level nine to vibrational level seven and from vibrational level eight to vibrational level six, respectively. Each particular volume emission can be presented as the product of spontaneous emission coefficient (E 97 , E 86 ) and concentration at the corresponding vibrational level: The photochemical equilibrium is assumed in order to derive the excited hydroxyl number densities for a given vibrational level. In this case, one can calculate this number density as the ratio of the production to the loss term: where f v are the nascent distributions for vibrational level v; B v , C v , and D v are the total quenching coefficients for molecular oxygen, atomic oxygen, and molecular nitrogen, respectively, for corresponding vibrational level v; E v are the total spontaneous emission coefficients for corresponding vibrational level v; and B 98 , D 98 , and E 98 are the quenching ratios for quenching by O 2 , N 2 , and spontaneous emission coefficients, respectively, for the transitions from vibrational level 9 to vibrational level 8 (see Table 1). Please note, that in Eq. (4.2) we consider transition from vibrational level 9 to vibrational level 8 due to quenching by atomic oxygen (coefficient C 98 ≠ 0), but in old retrieving procedures it is omitted; i.e., C 98 = 0 (Mlinczak et al. 2013a). Substituting (4.1) into (4.2), both, (4.1) and (4.2) into (3), and finally (3) into (2), we obtain: In the old procedure the daytime H profiles are then retrieved from the expression for volume emission (5) (Mlynczak et al. 2013a(Mlynczak et al. , 2014. In this work, we used version 2.0 of the SABER data product (Level2A) for atomic oxygen, ozone, atomic hydrogen, temperature, and volume emission 2.06 μm for daytime profiles within the 0.018-0.00032 hPa pressure (p) interval (approximately 77-100 km) in 2003-2015. These data in the official database correspond to Mlynczak et al. (2013aMlynczak et al. ( , 2014. Recently, Mlynczak et al. (2018) considered new rates of collisional quenching of OH(υ) by O, O 2 , and revised population yield from R3. Therefore, some parameters of A(O,M,T) function were updated. Moreover, following Kaufmann et al. (2014), who presumed that the atomic oxygen from SABER is too large, as well as Smith et al. (2013), who suggested that the daytime ozone of SABER is too large, in work of Mlynczak et al. (2018) the ozone and atomic oxygen were reduced by 25%. (5) In order to obtain something equivalent to the Mlynczak et al. (2018) dataset, we repeated all filtering presented by Mlynczak et al. (2013a, Sect. 1.1). Then, following Mlynczak et al. (2018), we reduced daytime O 3 and O SABER data by 25% and calculated atomic hydrogen profiles with the use of Eq. (5) and the parameters of A(O,M,T) from the work of Mlynczak et al. (2018). Hence, we obtained reference profiles of atomic oxygen (O´) and atomic hydrogen (H´) calculated with the reduced ozone balance equation and old procedure.
Then, we consider reaction R3 in the daytime OBE: The result of O and H retrieval depends on the local value of the ozone photodissociation rate (k 2 ), which, in turn, is a function of the solar flux of UV radiation, zenith angle, and altitude. To avoid parameter disagreement between SABER team retrieval procedures and our own, we precalculated the local values of k 2 by the inverse solution of Eq. (1) for each local (in time and space) SABER dataset: Thus, we use the same values of k 2 as in Mlynczak et al. (2013aMlynczak et al. ( , 2014. Then, we solved the system of two nonlinear equations (Eqs. 5 and 7) for O and H by the bisection method.
Local daytime concentrations of OH and HO 2 were found from the condition of the photochemical equilibrium of these components, assuming that the photo dissociation of water vapor in mesopause is a minor source for OH production (Kulikov et al. 2018a;Belikovich et al. 2019): Note, the hydroxyl by R3 is formed in vibrationally excited states from fifth to ninth vibrational levels (Adler-Golden 1997). The rates of reactions R4 and R7 involving OH, which are considered in the hydroxyl/hydroperoxy radicals equilibrium (Eqs. 8 and 9), depend on the vibrational number of OH* and can differ by orders of magnitude between vibrational states (e.g., Clarmann et al. 2010). Nevertheless, in first approximation this dependence can be neglected, because, as Clarmann et al. (2010) found, the effect of considering the vibrational excitation in R7: (1) on odd-oxygens sink is negligible, (2) on the hydroxyl sink is less than 4%, and (3) on source of hydroperoxy radicals is less than 2.5%. The effect of consideration of vibrational excitation in the R4: (1) on odd-oxygens is less than 3%, and (2) on the hydroxyl sink less than 10%. Moreover, at the daytime conditions, which are the subject of our work, all of those effects are several times smaller (Clarmann et al. 2010). Certainly, in the future the precision of retrieval can be improved by employing an OH* quenching/de-excitation model. The systematic uncertainty of retrieved data is mainly defined by systematic uncertainties in O 3 , the rates of chemical reactions, and the parameters of A(O,M,T) function (Mlynczak et al. 2013a(Mlynczak et al. , 2014. We reproduced the analysis presented in Mlynczak et al. (2013a) (see Section 5) and Mlynczak et al. (2014) (see Section 3.1) and calculated the individual sensitivity of retrieved characteristic to the perturbation of each factor. The total uncertainty is obtained by calculating the rootsum-square of all uncertainties. As a result, we found that total uncertainties of O, H, OH, and HO 2 are varied in the ranges of 25-30%, 25-33%, 20-50%, and 25-50%, respectively, mainly depending on altitude. Due to averaging, the random error of presented data is negligible.
In addition to minor chemical constituents calculated with full OBE (Eq. 7) and revised procedure, we calculated O´, H´, OH´, and HO 2´ with reduced OBE (Eq. 1), and all parameters according to the old procedure. Note: we do not calculate O´ or H´ with our method, but use those from the SABER database and corrected following Mlynczak et al. (2018), as previously discussed. Both datasets of each retrieved characteristic were averaged over longitude, daytime, and season from 2003 to 2015. In each case, the time averaging in a certain latitude bin was carried out in the following manner. All data were binned by hours of the solar local time. We found the averages depending on the local time and then over all the bins. We then calculated relative deviations for each characteristic X (i.e., O, H, OH, HO 2 ) as follows: Here, for the lucidity of our work we explicitly enumerate all differences between our revised and old procedures of retrieving: (1) the revised procedure considers the reaction of atomic hydrogen with ozone; (2) the old procedure calculates O and H from linear Eqs. (1) and (5), respectively, but the new one simultaneously solves the system of two nonlinear equations (Eqs. 5 and 7); (3) the new procedure takes into account the quenching of vibrationally excited hydroxyl by atomic oxygen from levels nine to eight, but the old procedure omits this; (4) the revised procedure considers quenching by molecular nitrogen as a single-step process (i.e., v → v-1), with coefficients according to Makhlouf et al. (1995) when the (10) old procedure does not correctly consider these coefficients for a "sudden death" process (i.e., v → 0); (5) we updated quenching rates for molecular oxygen, molecular nitrogen, atomic oxygen, and spontaneous emission coefficients from recently published sources (i.e., Adler-Golden 1997; Makhlouf et al. 1995;Caridade et al. 2013;and Xu et al. 2012, respectively), while in the old procedure they sometimes come from unclear sources.
In the next section, we show and discuss the results of our calculations. The absolute values of O on seasonally averaged timescales do not exceed 8•10 11 cm −3 , with a peak at 93-96 km depending on season and latitude. These well-known distributions were retrieved with the old procedure (e.g., Russel et al. 2005;Mlynczak et al. 2013a) and by other techniques (e.g., Hedin et al. 2009;Strelnikov et al. 2019). It can be seen that the new retrieval procedure leads to enhancement of atomic oxygen throughout the region. RD O is remarkable in all seasons-in particular, the altitude-latitude regions, where RD O > 10%, covers more than half of the presented distributions. The absolute maximum of RD O (~ 60-80%) is placed at altitudes of 82-84 km at middle and high latitudes in December-February of the southern hemisphere and in June-August of the northern hemisphere. In March-May and September-November, RD O does not exceed 35-40% in either hemisphere. It is impossible in frame of this short research latter identify all reasons of changes due to application of new procedure because it is essentially differ by large number of points from the old one. Nevertheless, here we can briefly state that the RD O in Fig. 1 shows the enhancement of O at all latitudes for all seasons by using the new procedure because of including the reaction of ozone with atomic hydrogen as additional loss term. The impact of this revision is noticeable primarily in the altitude range lower than 90 km, because concentration of ozone decrease with altitude at 75-100 km at daytime condition, but atomic hydrogen concentration rises. If, in a thought experiment, a new term proportional to the concentrations of atomic hydrogen and ozone is added to the numerator of Eq. 1, the maximum change will occur in the region below 90 km where the product has a maximum.

Results, discussion, and conclusion
The lower panel of Fig. 1 compares four global annually mean O profiles 2009. The first two are the results of data averaging derived from SABER data by new and old procedures, the second two are obtained from datasets calculated by CMAM-Ext and WACCM-x models.
One can see the WACCM-x' profile is generally in good agreement with the derived data in the most part of the altitude' range, whereas CMAM-Ext underestimates the content of this component. Figure 2 illustrates the distributions of atomic hydrogen and RD H depending on the season. The concentrations of H exhibit a maximum at 80-90 km at high latitudes in spring and summer of either hemisphere with values up to 10 9 cm −3 . It can be seen that, above 93-95 km only, the relative deviation is not significant: RD H does not exceed ~ ±20% . Below, RD H increases monotonically with decreasing altitude in all seasons and at all latitudes and reaches up to ~ 160% at 77 km. We can conclude that, mainly, the new retrieval procedure enhances essentially the atomic hydrogen as in the case of O. Nevertheless, structurally, the latitude-altitude dependence of RD H differs remarkably from RD O distribution. Most of changes for this component also occur below 90 km. Our preliminary analysis shows that essential H enhancement at these altitudes is due to changes of quenching and spontaneous emission coefficients in OH* model. Detailed consideration of specific reasons of O and H changes will be carried out in a separate extended work.
The lower panel of Fig. 2 presents four global annually mean H profiles 2009 derived from SABER data by new and old procedures, and calculated by CMAM-Ext and WACCM-x models. In general, there are notable disagreements between all profiles. One can point only that new retrieval procedure and both models give close peak values (~ 3·10 8 cm −3 ), whereas the old retrieval procedure underestimates it twice. Figure 3 depicts height-latitude sections of hydroxyl and corresponding relative deviations (RD OH ) for different seasons. It can be seen that the relative deviation varies in a wide range of (− 80%, + 130%). The maxima of OH values (up to ~ (2-3)·10 7 cm −3 ) are placed at high summer latitudes and near the equator around ~ 80 km, while the maxima of OH´ values are larger (up to ~ (7-8)·10 7 cm −3 ) and are placed near the equator at 79-83 km in all seasons. Significant decrease of RD OH appears in mid-latitude and equatorial regions with a vertical extended structure between 80 and 90 km in altitude. In present time, we can't identify the reason of this structure. In particular, OH´ concentration at 77-85 km can be close to or exceed the H´ concentration at these altitudes, which is impossible due to the following reason. Roughly speaking, the principal daytime source for both H and OH at these altitudes and above is water vapor photodissociation but the photochemical lifetime of OH is much smaller than those of H (Brasseur and Solomon 2005). Thus, the H concentration should be essentially larger than the OH concentration.  Kulikov et al. Earth, Planets and Space (2022) Figure 4 shows the distributions of HO 2 and corresponding relative deviations ( RD HO 2 ) depending on the season. As expected, the distribution of HO 2 repeats mainly seasonal-latitudinal variations of OH and have lower values than hydroxyl concentrations in the mesopause region (Brasseur and Solomon 2005). Comparing RD OH in Fig. 3 and RD HO2 in Fig. 4, there seem to be many points in common, such as the overall distribution is larger at lower altitudes in both cases, and the values are slightly larger at the pole regions. A notable Fig. 3 Distributions of OH and RD OH . Daytime mean seasonally averaged distributions of OH [cm −3 ] (1st column) and RD OH (2nd column) for winter (1st row), spring (2nd row), summer (3rd row), and fall (4th row) difference between the two is the large decrease in altitude of 80-85 km in the tropical and mid-latitude regions seen in RD OH . Above 90-95 km, the concentrations of HO 2´ exceed the values of HO 2 with the relative deviation maximum up to − 45%. Below, there is the opposite situation and RD HO 2 increases with decreasing altitude and reaches up to ~ + 135% at 77 km.
Thus, we have demonstrated that the new retrieval procedure leads to, mainly, enhancement of the values of O, H, OH, and HO 2 below 90-95 km up to ~ (2-2.5) times. In order to make a final choice between two procedures more non-emissive observations (e.g., following by Richter et al. (2021)) are necessary in future.