Boundary of nighttime ozone chemical equilibrium in the mesopause region: long-1 term evolution determined using 20-year satellite observations

. The assumption of nighttime ozone chemical equilibrium (NOCE) is widely employed for


Introduction
The mesopause (80-100 km) is an interesting region of the Earth's atmosphere possessing quite a number of unique phenomena and processes which can be considered as sensitive indicators/predictors of global climate change and anthropogenic influences on atmospheric composition (e.g., Thomas et al., 1989).Here, the summer temperature at middle and high latitudes reaches its lowest values (down to 100K (Schmidlin, 1992)).The temperatures below 150K lead to water vapour condensation and formation of the highest altitude clouds in the Earth's atmosphere, the so-called Polar Mesospheric Clouds or Noctilucent Clouds consisting primarily of water ice (Thomas, 1991).In turn, the temperature of the winter mesopause is essentially higher, so there is a strong negative temperature gradient between the summer and winter hemispheres.At these altitudes, atmospheric waves of various spatiotemporal scales are observed, in particular, internal gravity waves coming from the lower atmosphere.Destruction of gravity waves leads to strong turbulence that affects the atmospheric circulation and ultimately manifests itself in the mentioned temperature structure of this region.
Many layer phenomena in the mesopause are related to the photochemistry of the О x -НO x components (O, O 3 , H, OH, and HO 2 ).There is a narrow (in height) transition region where photochemistry behaviour transforms rapidly from "deep" diurnal oscillations, when the difference between daytime and nighttime values of the О x -НO x components can reach several orders of magnitude, to weak photochemical oscillations.As a result, above this region, O and H accumulate to form the corresponding layers.This layer formation manifests itself in the appearance of a secondary ozone maximum and airglow layers of OH and O excited states.Thus, О x -НO x photochemistry in the mesopause is responsible for the presence of important (first of all, from a practical point of view) indicators observed in the visible and infrared ranges, which are widely used for ground-based and satellite monitoring of climate changes and wave activity.Moreover, О x -НO x photochemistry provides the total chemical heating rate of this region, influences the radiative cooling and other useful airglows (for example, by O 2 excited states), is involved in the plasma-chemical reactions and formation of layers of the ionosphere.The mentioned transformation of О x -НO x behaviour with height may occur via the nonlinear response of О x -НO x photochemistry to the diurnal variations of solar radiation in the form of subharmonic (with periods of 2, 3, 4, and more days) or chaotic oscillations (e.g., Sonnemann and Fichtelmann, 1997;Feigin et al., 1998).This unique phenomenon was predicted many years ago (Sonnemann and Fichtelmann, 1987) and investigated theoretically by models taking into account different transport processes (Sonnemann and Feigin, 1999;Sonnemann et al., 1999;Sonnemann and Grygalashvyly, 2005;Kulikov and Feigin, 2005;Kulikov, 2007;Kulikov et al., 2020).It was revealed, in particular, that the nonlinear response is controlled by vertical eddy diffusion (Sonnemann and Feigin, 1999;Sonnemann et al., 1999), so that 2-day oscillations can only survive at real diffusion coefficients, but the eddy diffusion in zonal direction leads to the appearance of the so-called reaction-diffusion waves in the form of propagating phase fronts of 2-day oscillations (Kulikov and Feigin, 2005;Kulikov et al., 2020).Recently, the satellite data processing revealed the first evidence of the existence of 2-day photochemical oscillations in the real mesopause (Kulikov et al., 2021).
While regular remote sensing measurements of most O x -HO x components are still limited, the indirect methods based on the physicochemical assumptions are useful tools for monitoring these trace gases.In many papers, O and H distributions were retrieved from the daytime and nighttime rocket and satellite measurements of the ozone and the volume emission rates of OH(ν), O( 1 S), and O 2 (a 1 Δ 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., , 2018;;Smith et al., 2010;Xu et al., 2012;Siskind et al., 2008Siskind et al., , 2015)).The retrieval technique is based on the assumption of ozone photochemical/chemical equilibrium and physicochemical model of the corresponding airglow, which describe the relationship between local O and H values and measurement data.
The daytime photochemical ozone equilibrium is a good approximation everywhere in the mesospherelower thermosphere (MLT) region (Kulikov et al., 2017) due to ozone photodissociation, whereas the applicability of the assumption of nighttime ozone chemical equilibrium (NOCE) is limited: there is an altitude boundary above which NOCE is satisfied to an accuracy better than 10%.Below this boundary, the ozone equilibrium is disturbed essentially and cannot be used.Good (1976) supposed that NOCE is fulfilled above 60 km, whereas other papers apply the NOCE starting from 80 km, independent of latitude and season.However, studies of NOCE within the framework of the 3D chemical-transport models (Belikovich et al., 2018;Kulikov et al., 2018a) revealed that the NOCE boundary varies within the range of 81-87 km, depending on latitude and season.In view of the practical need to determine the local altitude position of this boundary, Kulikov et al. (2018a) presented a simple criterion determining the equilibrium boundary using only the data provided by the SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) instrument onboard the TIMED (Thermosphere Ionosphere Mesosphere Energetics and Dynamics).Making use of this criterion, Kulikov et al. (2019) retrieved the annual evolution of the NOCE boundary from the SABER data.It was revealed that a two-month averaged NOCE boundary essentially depends on season and latitude and can rise up to ~ 86 km.
Moreover, the analysis of the NOCE boundary in [2003][2004][2005] showed that this characteristic was sensitive to unusual dynamics of stratospheric polar vortex during the 2004 Arctic winter, which was named a remarkable winter in the 50-year record of meteorological analyses (Manney et al., 2005).Moreover, Belikovich et al. (2018) found by 3D simulation that the excited OH layer repeats well spatiotemporal variability of the NOCE boundary.These results allowed us to speculate that the NOCE boundary can be considered as an important indicator of mesopause processes.
The main goals of this paper are (1) to investigate the relationship between the NOCE boundary according to the mentioned criterion and O and H variability with the use of the 3D chemical transport model, and (2) to retrieve and analyze the spatiotemporal evolution of the NOCE boundary in 2002-2021 from the SABER/TIMED data set.In the next section, we present the used model.In Section 3, we briefly describe the criterion of determining the NOCE boundary local height and study how this height is related to the features of O and H distributions from the 3D model.Section 4 explains the methodology of determining the NOCE boundary from satellite data.Section 5 presents the main results obtained from SABER/TIMED data discussed in Section 6.

3D model
We use the 3D chemical transport model of the middle atmosphere developed by the Leibniz Institute of Atmospheric Physics (Sonnemann et al., 1998;Körner and Sonnemann, 2001;Grygalashvyly et al., 2009;Hartogh et al., 2004Hartogh et al., , 2011)).The three-dimensional fields of temperature and winds were adopted by Kulikov et al. (2018b) from the Canadian Middle Atmosphere Model (Scinocca et al., 2008) for the year 2000 with an updated frequency of 6 hours.To exclude unrealistic jumps in the evolution of calculated chemical characteristics, linear smoothing between two subsequent updates of these parameters is applied.The model takes into account 3D advective transport and vertical diffusive transport (both, turbulent and molecular).The Walcek-scheme (Walcek, 2000) and the implicit Thomas algorithm (Morton and Mayers, 1994)  O, CHO, CO, CO 2 ), 54 two-and three-body reactions, and 15 photo-dissociation reactions.The model uses pre-calculated dependences of dissociation rates on altitude and solar zenith angle (Kremp et al., 1999).The chemistry is calculated by the Shimazaki scheme (Shimazaki, 1985) for the integration time of 9 sec.

The NOCE criterion
The nighttime ozone chemistry at the mesopause heights is determined mainly by two reactions R1-R2 (e.g., Allen et al., 1984), see Table 1.The secondary ozone loss via the O + O 3 → 2O 2 reaction becomes important above ~ 95 km (Smith et al., 2009).Kulikov et al. (2023) verified with simulated and measured data that this reaction does not influence the NOCE boundary determination and may be skipped.Thus, the ozone equilibrium concentration ( ) corresponding to the instantaneous balance between the production and loss terms is as follows: where M is air concentration, and are the corresponding rate constants of the reactions (see Table 1).
As mentioned above, the NOCE criterion was developed in Kulikov et al. (2018a).The main idea is that the local values of and are close ( ), when , where is the ozone lifetime and is the local time scale of : , . (3) As shown in Kulikov et al. (2018a), can be determined from a simplified photochemical model describing the O x -HO x evolution in the mesopause region (Feigin et al., 1998), so the criterion of the NOCE validity can be written in the form: where k i are the corresponding reaction constants from Table 1.Calculations with the global 3D chemistry-transport model of the middle atmosphere showed (Kulikov et al. 2018a) that the criterion defines well the boundary of the area where .Kulikov et al. (2023) presented the theory of chemical equilibrium of a certain trace gas .Strictly mathematically, the cascade of sufficient conditions for was derived considering its lifetime, equilibrium concentration, and time dependences of these characteristics.In case of the nighttime ozone, it was proved that is the main condition for NOCE validity and the criterion limits a possible difference between and to not more than ~10%.
Moreover, Kulikov et al. (2023) slightly corrected the expression for the criterion (4): . (5) One more important condition for at the time moment is: where is the time of the beginning of the night.The ozone equilibrium concentration jumps at sunset due to the shutdown of photodissociation.Thus, the condition (6) shows that it takes time for the ozone concentration to reach a new equilibrium.Kulikov et al. (2023) revealed that, at the solar zenith angle χ > 95°, the condition ( 6) is fulfilled almost in all cases and the condition (5) becomes the main criterion for dividing deep and weak oscillations whose height position depends on latitude and season.In particular, in summer the middle latitude transition is higher than in winter.Figures 1-3 show also the magenta lines pointing the NOCE boundary in accordance with the criterion (5) ( ).One can see that the NOCE criterion almost perfectly reproduces the features of the transition zone.Thus, our criterion is not only a useful technical characteristic to retrieve O from satellite data, but it also points to an important dynamical process in the О x -НO x photochemistry.

NOCE boundary from satellite data
We use version 2.0 of the SABER data product (Level2A) for the simultaneously measured profiles In 2015, because of slight changes in the satellite geometry, there appeared additional months.This is especially noticeable above ~66ºS,N and manifests itself by extension of the variation range of at these latitudes in 2015-2021.Second, the variation range of , annual cycle and spectrum of harmonic oscillations depends essentially on the latitude.Near the equator, varies in the 81-83 km range mainly and there are two main harmonics with periods of 1/2 and 1 year in the spectrum.At low latitudes, the variation range of narrows down to a minimum (~82-83 km at 16.7-20.05°S,N),which is accompanied with the appearance of a wide spectrum of harmonics with periods of 1/5, 1/4, 1/3, 1/2, and 1 year.At middle latitudes, the range of variation monotonically increases up to ~81.5-85.5 km with latitude and the harmonic with a period of 1 year becomes the main mode in the spectrum of oscillations.
At both, low and middle latitudes, there is no signal from quasi-biennial oscillations but one can see a remarkable amplitude of a harmonic with a period of ~10 years, which can be associated with a manifestation of 11-year solar cycle.It is interesting that the mentioned features are typical for both hemispheres.At high latitudes, varies in the range of 79-86.5 km.At these latitudes, one can see the main difference between the northern and southern hemispheres: the sharp falls and rises of the northern boundary of NOCE by several km (up to 3-4 km) appearing in January-March 2004, 2006, 2009, 2010, 2012, 2013, 2018and 2019 that are absent at southern latitudes.
The analysis of Figures 5-6 demonstrates the following redistribution in the annual cycle with increasing latitude from equator to polar latitudes.Near the equator, the annual cycle has two maxima in June -July and in December -January.The first one is more pronounced.That is why there are two main harmonics with periods of 1/2 and 1 year in the spectrum.At low latitudes, one maximum (summer) does not change, while the other approaches the first one.As a result, the spectrum of harmonics is wide.At middle latitudes, the maxima gradually merge so that the 1 year-harmonic becomes the main one.-February 2004-February , 2006-February , 2009-February , 2010-February , 2012-February , 2013-February , 2018-February and 2019, , which are absent at southern latitudes.One can see from Figure 5 that, on the average, is lower than by 0.5-1 km, depending on latitude.One can see from Figure 6 that the spectra of harmonic oscillations are similar to the spectra except for the absence of a signal of the 11-year solar cycle.As in the case of , we found with the use of multiple linear regression the slow (up to ~-10 m/year) and statistically insignificant linear trend of as a function of latitude.Moreover, the regression analysis of latitude-averaged also revealed a statistically insignificant trend.

Discussion
The NOCE boundary is an important technical characteristic for correct application of the NOCE approximation to retrieve the nighttime distributions of minor chemical species of MLT.Kulikov et al.
(2019) repeated the O and H retrieval by Mlynczak et al. (2018) from the SABER data for the year 2004.
It was revealed that the application of the NOCE condition below the boundary obtained according to the criterion could lead to a great (up to 5-8 times) systematic underestimation of O concentration below 86 km, whereas it was insignificant for H retrieval.The results presented in Figures 4, 5 and 11 demonstrate that, except for high northern latitudes, there is a stable annual cycle of the NOCE boundary.The monthly mean boundary can rise up to geometrical altitudes of 82-83 km (~(5.2-6.2)•10 - hPa) at low latitudes and up to 84-85 km (~(3.7-4.4)•10 - hPa) at middle and high latitudes.Thus, the SABER O data below these altitudes/pressures may be essentially incorrect and the retrieval approaches without using the NOCE condition (e.g., Panka et al., 2018) should be more appropriate.
Note that the NOCE condition was used not only for O and H derivation from satellite data.This assumption is a useful approach helping (i) to study hydroxyl emission in the MLT region with simulated and measured data, in particular, OH* mechanisms, morphology and variability caused, for example, by atmospheric tides and gravity wave activity (e.g., Marsh et al., 2006;Nikoukar et al., 2007;Xu et al., 2010Xu et al., , 2012;;Kowalewski et al., 2014;Sonnemann et al., 2015); (ii) to analyze the MLT response to sudden stratospheric warmings (SSWs) (e.g., Smith et al., 2009); (iii) to derive exothermic heating rates of MLT (e.g., Mlynczak et al., 2013b); (iv) to analytically simulate the mesospheric OH* layer response to gravity waves (e.g., Swenson and Gardner, 1998); and (v) to derive the analytical dependence of excited hydroxyl layer number density and peak altitude on atomic oxygen and temperature (e.g., Grygalashvyly et al., 2014;Grygalashvyly, 2015).Perhaps some results require revision or reanalysis taking the NOCE boundary into account.For example, Smith et al. (2009) used the NOCE condition to analyze the ozone perturbation in the MLT, in particular, during the SSW at the beginning of 2009 (the central day was January 24).Our preliminary results of processing the SABER and simulated data in January 2009 show that the NOCE boundary above 70ºN may jump from ~80 km to ~90-95 km due to a short-time abrupt temperature fall above 80 km during this SSW.Thus, one can assume that the NOCE condition is not a good approximation for the description of ozone variations directly in the process of SSWs.This case will be studied in a separate work.Note also that after the SSW of January 2009 there began a long-time (several tens of days) event of elevated (up to ~80-85 km) stratopause (see, e.g., Figure 1 in Smith et al. (2009)), which led to the corresponding increase of temperature above 80 km.The occurrence of this event and its duration are in a good correlation with sharp lowering of the NOCE boundary at high northern latitudes (see Figures 4 and 11).Moreover, all abrupt changes of the NOCE boundary at these latitudes in January-March of other years (2004, 2006, 2010, 2012, 2013, 2018, and 2019) can be also associated with the elevated stratopause events in these years (see García-Comas et al. (2020) and references there). According Neglecting the second term in the first equation as a secondary one, this system can be solved analytically, so that the nighttime evolution times of O and H are: , where is the time of the beginning of the night, is the ratio at the beginning of the night.Note that is much larger than (see Table 1).Based on the daytime O and H distributions in the mesopause region obtained in Kulikov et al. (2022), we calculated the ratio of the summer to the winter O/H (see Figure 14).During the summer, at middle latitudes is remarkably less than in winter in both, northern and southern hemispheres, whereas the air concentration and the rate of reaction R4 (see Table 1) increase due to a decrease in temperature.As a result, the summer and are essentially shorter than their winter values, which explains the summer rise of the transition zone and the NOCE boundary.
Finally, let us briefly discuss other qualitative indicators of the NOCE boundary, which could be found in the SABER database.As mentioned above, Kulikov et al. (2019) showed that the nighttime O SABER profiles are correct above the NOCE boundary, whereas the H profiles hold within the whole pressure interval.Kulikov et al. (2021) demonstrated that, in the altitude range of 80-85 km, many H profiles have a sharp jump in concentration when it increases from ~ 10 7 cm -3 to ~ 10 8 cm -3 .Our analysis with the criterion (9) shows that the altitude of these jumps can be used as a rough indicator of the NOCE boundary.

Conclusions
The NOCE criterion is not only a useful technical characteristic for the retrieval of O from satellite data, but it also reproduces the transition zone position which separates deep and weak diurnal oscillations of O and H at low and middle latitudes.At middle latitudes, the summer boundary of NOCE is remarkably (by several kilometers) higher than the winter one, which is accompanied with the same variation of the transition zone.This effect is explained by the markedly lower values of the O and H nighttime evolution times in summer than in winter by virtue of the lower values of the ratio at the beginning of the night and air concentration increase.
The NOCE boundary according to the criterion is sensitive to sporadic abrupt changes in the dynamics of the middle atmosphere.
The NOCE boundary at low and middle latitudes expressed in pressure altitudes contains a clear signal of 11-year solar cycle and can be considered as a sensitive indicator of solar activity.

Reaction
Figures 1-3 demonstrate model examples of O and H time-height variations above different points over three months.In order to focus attention on diurnal oscillations, the concentrations are normalized by mean daily values, which were calculated as a function of altitude.These daily average O and H values were different for each altitude.One can see in all panels of these figures "deep" diurnal oscillations that occur below 81-87 km.Due to the shutdown of sources at night and high rates of the main НO x and O sinks nonlinearly dependent on air concentration (Konovalov and Feigin, 2000), the variables change during each night within the range of several orders of magnitude with low values of time evolution.Above 83-88 km, the situation differs essentially from the previous case.One can see relatively weak diurnal oscillations.These regimes of O and H behaviour are consistent, i.e. deep H diurnal oscillations correspond to the same dynamics in O, and so on.There exists a few-km thick layer (transition zone) Figure 4 demonstrates the time evolution of the pressure altitude in 2002-2021 in all latitude bins.Figures 5 (left column) show the mean (for 2002-2021) annual cycle of at four specific latitudes and Figures 6 (left column) present the Fourier spectra at these latitudes obtained from the data

Figure 7 (
Figure 7 (left) demonstrates a contour map of the space-time evolution of the average annual pressure altitude in 2002-2021.Figure 8 presents the time evolution of this characteristic at different latitudes.Based on the Fourier spectra presented in Figures 6 (left column), we can suppose that, at low and middle latitudes, the interannual variation of is caused by the 11-year solar cycle mainly.Figure 9 (left) presents the correlation coefficient of with index (solar radio flux at 10.7 cm, see the red curve in Figure 10) as a function of latitude.One can see good anticorrelation (with a coefficient from -0.72 to -0.92) between ~55ºS and ~55ºN.At high latitudes, the absolute value of the correlation coefficient decreases sharply down to ~0.58 in the south and to ~0.1 in the north.The blue curve in Figure

Figure 11
Figure 11 demonstrates the time evolution of the geometrical altitude in 2002-2021 in all latitude bins.Figures 5 (right column) show the mean (for 2002-2021) annual cycle of at four specific latitudes and Figures 6 (right column) present the Fourier spectra at these latitudes obtained from the data in Figure 11.Comparison with Figures 4 and 5-6 (left columns) shows that repeats many qualitative features of the space-time evolution of pressure altitude .In particular, in the direction from the equator to the poles, the variation range of first decreases down to 1 km at 16º-25ºS,N and then expands to several km at middle and high latitudes.One can see the same redistribution of the annual cycle with latitude, similarly to the pressure altitude case.Near the equator, the annual cycle possesses two maxima occurring in June -July and in December -January.At low latitudes, one maximum continues in summer, whereas the other shifts to spring.At middle latitudes, the maxima gradually coalesce forming a single summer maximum.At high northern latitudes, there are the same local sharp variations of the NOCE boundary in January-February 2004-February  , 2006-February  , 2009-February  , 2010-February  , 2012-February  , 2013-February , 2018 and and

Figure 7 (
Figure 7(right) demonstrates a contour map of space-time evolution of the annually average geometrical altitude in 2002-2021.Figure 12 presents the time evolution of this characteristic at different latitudes.One can see that there is no clear evidence of 11-year solar cycle manifestation at all latitudes.This is confirmed by the calculation of the correlation coefficient of with index as a function of latitude (see Figure 9 (right)).Moreover, the latitude-averaged (in the range of 55ºS-55ºN) has a correlation coefficient equal to ~-0.55.
to the used chemical-transport model, the NOCE boundary reproduces well the transition zone dividing deep and weak diurnal oscillations of O and H (see Figures1-3).We verified this feature with the annual run of SD-WACCM-X model for the year 2017 provided by the NCAR High Altitude Observatory (https://doi.org/10.26024/5b58-nc53).Despite the low time resolution of the downloaded data (3-hour averaging), we obtained the results (see Figure13) similar to Figures1-3.Note also that both models give the same consistence between the altitudes of the NOCE boundary and the mentioned transition zone at high latitudes in spring and autumn.The space-time evolution of the NOCE boundary expressed in terms of pressure altitudes contains a clear signal of the 11-year solar cycle in the 55ºS-55ºN range, which is suppressed mainly at high latitudes.The weak correlation of with index at high southern latitudes may be caused by the mentioned data gaps specified by the satellite sensing geometry.The same reason and distortions by SSWs evidently determine no correlation at high northern latitudes.Thus, at low and middle latitudes can be considered as a sensitive indicator of solar activity.Below, we present a simple and short explanation for this.Let us consider the NOCE criterion (9) at the pressure level : shows that this function can be approximately rewritten as .So, one can see that is strongly dependent on .Moreover, it anticorrelates with .Gan et al. (2017) andZhao et al. (2020)  analyzed the simulated and measured data and revealed a clear correlation between the MLT temperature above 80 km and the 10.7-cm solar radio flux.Moreover, the dependence of the correlation coefficient of with index on latitude in the 55ºS-55ºN range given in Figure9in the paper by of Zhao et al. (2020) is consistent with our Figure9(left panel), taking into account the sign of the correlation.Thus, we can conclude that the found anticorrelation of the NOCE boundary with solar activity is caused by the strong connection with temperature, which, in turn, is in a good correlation with the index.A detailed analysis of the reasons why the solar cycle weakly manifests itself in the spatio-temporal variability of is not so simple and is beyond the scope of this work.

Figure 5
Figure5illustrates an interesting peculiarity.At middle latitudes, the summer and are remarkably (by several kilometers) higher than the winter ones, while the opposite relationship could be expected.Due to more effective daytime HO x photoproduction at these altitudes, the summer H values at the beginning of the night are higher than the ones in winter.So, the summer ozone lifetimes should be shorter and the NOCE condition is more favourable than in winter.Nevertheless, the same ratio between the summer and winter NOCE boundaries at middle latitudes was revealed in Belikovich et al. (2018) andKulikov et al. (2018a), where the boundary of this equilibrium was determined by direct comparison of and concentrations from results of 3D chemical-transport models.Based on the results of Section 3, we can assume that the discussed effect is connected with the height position of the transition zone, which demonstrates the same variation (see Figures1-3).Kulikov et al. (2023) derived the equations describing pure chemical O and H nighttime evolution:

Figure 1 .
Figure 1.O and H time-height variations above different points in January 2000 calculated by 3D chemical transport model of middle atmosphere.Concentrations are normalized by mean daily values, correspondingly, calculated as a function of altitude.Dark bars mark daytime, light bars mark nighttime.Black lines point the NOCE boundary altitude in accordance to criterion (5) ().

Figure 2 .
Figure 2. The same as in Fig. 1, but in April 2000.Black lines point NOCE boundary altitude according to criterion (5) ().

Figure 3 .
Figure 3.The same as in Fig. 1, but in July 2000.Black lines point the NOCE boundary altitude according to criterion (5) ().

Figure 4 .Figure 5 .
Figure 4. Time evolution of monthly mean pressure altitude at different latitudes.

Figure 6 .
Figure 6.Fourier spectra of monthly mean pressure altitude and geometrical altitude at four specific latitudes.In each spectrum, the amplitudes of harmonics were normalized to the corresponding zero harmonic.

Figure 8 .
Figure 8.Time evolution of annually mean pressure altitude at different latitudes.

Figure 9 .Figure 10 .
Figure 9. Correlation coefficient of index with pressure altitude (left) and geometrical altitude (right) as a function of latitude.

Figure 11 .
Figure 11.Time evolution of monthly mean geometrical altitude at different latitudes.

Figure 12 .
Figure 12.Time evolution of annually mean geometrical altitude at different latitudes.

Figure 13 .
Figure 13.O and H time-height variations above different points in January 2017 calculated by SD-WACCM-X model.Concentrations are normalized by mean daily values, correspondingly.Dark bars mark daytime, light bars mark nighttime.Black lines point the NOCE boundary altitude according to criterion (5) ().

Figure 14 .
Figure 14.Logarithm of the ratio of and distributions obtained with the use of daytime seasonally mean distributions of O and H averaged in 2003-2015.was determined from the SABER data measured in December, January, and February.was determined from the SABER data measured in June, July, and August.
are used for advective and diffusive transport, respectively.The model grid