A. I. Semenov and N. N. Shefov
Institute of Atmospheric Physics, Moscow, Russia
The hydroxyl emission is one of the most energetically important in the upper atmosphere. It manifests the recombination process of atomic oxygen. An essential feature of this emission is the possibility of reliably registering its spectral and aeronomical parameters, which characterize not only the processes of hydroxyl radical excitation, but also properties and state of the atmosphere where it is generated. Such parameters are: the intensity Iv'v'' (in Rayleigh) of particular molecular bands (v',v''), the equilibrium Te and nonequilibrium Tne rotational temperatures, which describe a distribution of the OH excited molecules over the rotational states (J, N), the vibrational temperature TV, which characterizes a distribution of the OH molecules over the vibrational states v and the related photochemical processes. All these parameters correspond to the height zm of the maximum of the emitting layer, which has the emission measure Qm (photons cm -3 s -1 ), and the layer thickness W, which is determined at the Qm/2 level. According to the above definition the total intensity of the hydroxyl emission, which characterizes the rates of energy transformation and loss, is
Studies of the hydroxyl emission have been carried out during the past 45 years, though rather irregularly (in time and planetary distribution) from the point of view of data accumulation on various emission parameters. The latter fact creates difficulties in searches for particular types of variations. Nevertheless, these data are obviously needed, because the observed temporal and spatial variations manifest a whole spectrum of photochemical and dynamical processes in the atmosphere.
The detailed photochemistry of formation of the hydroxyl emission in the atmosphere is rather complicated and depends on a large number of geophysical conditions. However, ozone, atomic oxygen, atomic hydrogen, and the solar UV radiation are the principal components, which determine generation of the emission. Temporal and spatial behavior of the above parameters in the mesopause region may be studied on the basis of the hydroxyl emission data, so we have tried to systematize the observational results, accumulated for many years. It should be emphasized that the data available cover only the nighttime periods. There are only episodical measurements for the daytime, which are not enough for any kind of systematization.
Considering the problem of creation of the model of emission behavior one has to keep in mind a very broad spectrum of variations, which contains both regular and irregular components. The values of the regular variations can be calculated for a fixed time and place, whereas the irregular variations may begin at a moment determined by occasional events, but their behavior after the beginning is of a regular character.
There have been numerous attempts to systematize various particular types of measurements (the intensity I, and the rotational Tr and vibrational TV temperatures) to get some general ideas concerning the hydroxyl emission behavior [Fishkova, 1983; Semenov and Shefov, 1979; Shefov, 1969, 1971, 1976; Shefov and Piterskaya, 1984; Toroshelidze, 1991].
Insofar as all the variations are in fact a modulation of some average value of the hydroxyl emission characteristics, the following form of representation of the Tr, TV, and zm parameters of the hydroxyl emission was accepted as a first approximation:
The first approximation for the emission intensity is
where f0 are some global mean values for the given solar and geophysical conditions, in particular, geographic latitude is j= 45 o N; geographic longitude is l 40 o E; local time is the local solar midnight, t = 0 ; season is the equinox, day of the year is td = 80, solar activity is F10.7 = 130 ; geomagnetic activity is Kp = 0 ; the year is 1972.5.
Thus, due to a limited amount of data at the present stage it is suggested that the OH emission behavior in the northern and southern hemispheres is the same, and the longitudinal variations are governed only by the local time.
The Dfi values describe variations of different types: First, the regular variations are as follows: Dfd (c, j) are the diurnal variations during the night, c and j being the solar zenith angle and latitude, respectively; Dfte(t) are the terminator variations in the morning and evening hours, t being the local time; DfL (tLA) are the lunar variations during a synodical month (29.53 days), tLA being the lunar phase; Dfs (td) are the seasonal variations, td being the day of the year; Dfqbo(tqbo) are the quasi-biennial variations with a period of 22-32 months, tqbo being the year of the beginning of the quasi-biennial cycle; Df5.5(t5.5) are the 5.5-year variations, t5.5 being the year of the beginning of the cycle; DfF (F10.7) are the solar cycle variations, F10.7 being the solar radio emission flux (the 22-year variations are accounted for by the F10.7 index); Dftr(ttr) is the long-term trend, ttr being the year of the beginning of the trend count; Dfj (j) are the latitudinal variations; Dfor (V, L) are the orography variations, V and L being the wind velocity in the troposphere and the distance to the mountain, respectively;
Second, the irregular variations are as follows: Df27 (t27) are the 27-day variations, induced by variations of the solar activity and UV radiation, t27 being the date of the beginning of the nearest Carrington cycle; Dfsw (tsw) are the variations after stratospheric warmings, tsw being the date of the warming beginning; Dfgm (tgm, Kp, F) are the variations after geomagnetic disturbances, tgm, Kp and F being the date of the beginning of a geomagnetic storm, the planetary geomagnetic index, and the geomagnetic latitude, respectively; Dfmf (tmf) are the variations after meteor flux intrusion, tmf being the date of the intrusion beginning; Dfgw (tw) are the variations due to the internal gravity waves, tw being the wave period.
It is widely known that the hydroxyl emission, generated in the mesopause region (~87 km), is due to the rotational-vibrational transitions ( v' = 9 1, v'' = (v' - 1) 0) of the ground electronic state X2P. Its total intensity is a sum of the intensity Iv'v'' of the bands situated in the 0.5-5.0 m m spectral region. Among them the sequence Dv = 2 in the 1.4-2.2 m m spectral range has the highest intensity (in photons) [Shefov and Piterskaya, 1984].
On average the distribution of the population of the vibrational levels may be described by the Boltzmann distribution with the vibrational temperature TV 10,000 K, though there are indications of the existence of two pieces of the distribution at v = 1 5 and v = 6 9, for which T6789 T12345 [Fishkova, 1981, 1983; Shefov, 1976; Turnbull and Lowe, 1983]. Thus, the total emission intensity (in photons) is
where Av'v'' are the transition probabilities and Nv' are the populations of the v' vibrational levels. The latest values of Av'v'' are given by Nelson et al.  and Turnbull and Lowe . Table 1 shows for each (v',v'') band the average values of Av'v'', based on the data of Nelson et al. . It should be emphasized here that the use of the data of nonsimultaneous measurements of some OH bands, presented by Krassovsky et al.  but not reduced to some standard conditions, was a defect of many papers on calculation of the transition probabilities, so further specification of the Av'v'' values is needed. Vibrational level energies Gv (in cm-1 ) are determined by the relation
where k is the Boltzmann constant; Nef is the effective number (cm-2 ) of the OH excited molecules; A (Tv) (~48 s-1 for TV = 10,000 K) is the effective transition probability. The approximation has the form
where T' = TV/10,000.
From that the intensity (in photons) of a particular OH bands is
where the sum over the vibrational states is
and its approximation looks like
The total energy of the hydroxyl emission is equal to:
where lv'v'' is the wavelength of the OH bands. The effective wavelength (in m m) is
The OH rotational (equilibrium) temperature Tr is determined by the distribution of the first four- to five lines of the P branch of the rotational structure of the band [Shefov, 1961]. Information on transition probabilities for various lines of the branch may be found in the work by Krassovsky et al. . The measured value of Tr is the weighted mean of the atmospheric temperatures T inside the emitting layer. This value practically corresponds to the altitude of the layer maximum emission measure Qm. However, there is a dependence of Tr on the v number [Fishkova, 1983; Lowe et al., 1991; Shefov, 1961, 1972, 1976; Shefov and Piterskaya, 1984], which is due to some differences in the altitudes zmv of the layers corresponding to different v [Baker and Stair, 1988; Potapov et al., 1983]. The average empirical dependence has the form
Later on, all the data on Tr were reduced to the value of v = 5, for which DTrv = 0. Unfortunately, there is no information on possible variations of this value for various solar and geophysical conditions.
The nonequilibrium rotational temperature Tnr (~1100 K) was recently revealed on the basis of the intensity distribution of the lines of the P branch of the (7.3) 882.4 nm band with the rotational numbers N' = 6-12 [Perminov and Semenov, 1992]. A nonequilibrium and, as a consequence, such high values of the rotational temperature are due to incompleteness of the processes of vibrational relaxation for high N in the upper part of the emitting layer. In satellite measurements the transitions for N' 33 were reported [Dodd et al., 1993], as well as pure rotational transitions in the 10-25 m m spectral range, which occur between high rotational levels [Dodd et al., 1994].
Diurnal variations of Tnr are synchronous to the variations of the vibrational temperature and exhibit changes in altitude of the upper part of the OH emitting layer. On the basis of a small amount of data at the Zvenigorod observatory ( j = 57 o N is the latitude of the observed region of the emitting layer) the variations at night near equinoxes are described by the relation
The lunar-tide variations in the plane of the lunar orbit are
where tL is the lunar time.
The shape of the emission vertical profile until recently has been studied only by rocket methods. The measurements by the UARS satellite were started in 1991 [Lowe and LeBlanc, 1993], but the results have not yet been published. Currently 44 rocket measurements conducted from 1956 to 1992 are known [Baker and Stair, 1988; Shefov and Toroshelidze, 1975], out of which only about 30-35 flights can be analyzed. In these data the most uncertain parameter is the shape of the vertical profile. Theoretical studies point to an asymmetry of the profile, in which the upper part (above the height of maximum zm ) is thicker than the lower part (below zm ) [Moreels et al., 1977].
In that case the shape of the vertical profile of the emission measure may be presented in the form
where Qm =[ss e-s/G (s)](I/sW), W corresponds to the layer thickness at the Qm/2 level, s and s are parameters, G (s) is the Gamma function. Then
The asymmetry index P of the profile, which characterizes the portion on the thickness of the upper part of the layer, is determined by the relations:
However, rocket measurements, because of difficulties in taking into account correct orientation of the rocket and also, apparently due to a significant inhomogeneity of the emitting layer, which is created by various disturbances, point to a practically symmetric vertical distribution with thickness W. This was demonstrated by several examples of the most successful measurements [Shefov, 1978a]. Special studies on board the UARS satellite point to a presence of the asymmetry ( P 0.65 ) [Lowe and LeBlanc, 1993]. Nevertheless, while registering the vertical profile of the emitting layer intensity, which is observed along the tangent line along the limb, solution of the inverse problem of reconstruction of the shape of the emitting layer lower part presents some difficulties, because it requires a preliminary knowledge of the required function [Shefov, 1978a]. At the given stage of the analysis, a comparison of the simultaneously measured values of zm and W for various flights has shown the presence of a correlation between them and a distinct splitting into two subgroups of the vibrational levels: 1-5 and 6-9. Their average for v = 4
and for v = 8
The zm altitude dependence on v is also revealed:
That is why while analyzing the data of measurements to obtain various types of variations, all the data were reduced to v = 5. Thus,
If we assume the Gaussian shape of the vertical profile of the emission measure, then
To determine the above considered variations, a statistical systematization of the measurements of the rotational (equilibrium) and vibrational temperatures at the Zvenigorod observatory and other stations was performed [Agashe et al., 1989; Fishkova, 1955, 1978, 1981, 1983; Kropotkina, 1976; Kropotkina and Shefov, 1977; Kvifte, 1967; Matveeva and Semenov, 1985; Megrelishvili and Fishkova, 1986; Myrab et al., 1983; Perminov et al., 1993; Potapov et al., 1983; Scheer and Reisen, 1990; Semenov and Shefov, 1979; Shefov, 1967, 1968, 1969, 1971, 1972, 1973, 1974a, 1974b, 1975, 1976, 1978b; Shefov and Piterskaya, 1984; Shefov and Toroshelidze, 1975; Takahashi et al., 1990; Taranova and Toroshelidze, 1970; Toroshelidze, 1968, 1975, 1991; Turnbull and Lowe, 1991; Yarin, 1970] and also of the height of the emitting layer by rocket and satellite data [Baker and Stair, 1988; Lowe and LeBlanc, 1993; Lowe and Lytle, 1973, Moreels et al., 1977; Shefov and Toroshelidze, 1975]. Due to obvious reasons the entire huge list of the publications cannot be cited here. In spite of the amount of data available not all the types of variations can be studied in detail. This is particularly true for the data on the altitude of the emitting layer and vibrational temperature. So in determination of variations in cases where there were not enough data available, a knowledge of the behavior of other parameters was useful, because variations of various parameters were interrelated. On the basis of the performed systematization the following characteristics of the hydroxyl emission for the above indicated solar and geophysical conditions were obtained: Tr0 = 195 K; I0 = 0.95 MR, Qm0 = 1.1 106 photon cm -3 s -1 ; TV0 = 10,000 K; E0 = 1 erg cm -2 s -1 ; zm0 = 87 km; W0 = 9 km; A = 48 s -1 ; l = 1.9 m m.
Different types of variations of the considered parameters are presented in Figures 1, 2, 3, and 4. In the figures showing variations of Tr, I, and TV the points are the averaged values of these parameters, and in the figure showing zm the points are individual values. During recent years, it has become evident that the variations of the vibrational temperature TV (as well as of the nonequilibrium rotational temperature Tnr ) exhibit variations of the atmospheric density n inside the emitting layer when the zm altitude is changing [Perminov and Semenov, 1992; Perminov et al., 1993; Shefov, 1978a]. The emission intensity I and the rotational temperature Tr are also changing when the altitude of emission layer is changing. Thus, empirical approximations of the OH emission behavior for the conditions of rocket measurements [Baker and Stair, 1988; Shefov and Toroshelidze, 1975] and comparison with the data of the rocket measurements of zm reduced to the value of v=5, provide some control of correctness of the obtained relations. These results are also presented in Figures 2, 3, and 4. The regression lines look like
where n (in cm -3 ) is a function of zm.
It should be noted that the character of the variations between the hydroxyl emission parameters obtained in rocket measurements for a broad range of solar and geophysical conditions agrees well with the results of measurements at various stations [Agashe et al., 1989; Fishkova, 1955, 1981, 1983; Scheer and Reisen, 1990; Shefov, 1975; Shefov and Toroshelidze, 1975; Takahashi et al., 1990; Toroshelidze, 1991]. It follows from the above presented relations that for regular nighttime variations
The empirical relations for various types of hydroxyl emission variations are presented below.
1. Variations in the nighttime period of the day are given by
where t is the local mean solar time, and d is the solar inclination angle.
The mean behavior at night is based on the data of some publications e.g., [Agashe et al., 1989; Baker and Stair, 1988; Fishkova, 1955, 1981, 1983; Moreels et al., 1977; Myrab et al., 1983; Potapov et al., 1983; Scheer and Reisen, 1990; Shefov, 1971, 1972; Shefov and Toroshelidze, 1975; Takahashi et al., 1990; Toroshelidze, 1975, 1991; Turnbull and Lowe, 1991]. There is no doubt that variations of the hydroxyl emission parameters during the night influence the phase shifts of the thermal semidiurnal tide because of variations of the emitting layer height [Petitdidier and Teitelbaum, 1977; Takahashi et al., 1984] and also the disturbances initiated by propagation of the internal gravity waves (IGW).
Special measurements of the OH emission variations during the evening and morning twilights at c = 98-108o were carried out [Lowe and Lytle, 1973; Moreels et al., 1977; Scheer and Reisen, 1990; Taranova and Toroshelidze, 1970; Toroshelidze, 1968, 1991; Turnbull and Lowe, 1991]. Apparently, the observed maxima are related to the effect of terminator motion [Toroshelidze, 1991]. Some features of the variations can be studied on the basis of measurements at summer nights at the latitudes where c 112o [Shefov, 1971]. For these conditions the periodic (the 4 h and 2 h harmonics) temperature variations were revealed [Taranova and Toroshelidze, 1970; Toroshelidze, 1975, 1991]. At j 45 o N on average in the evening
where tc is the mean solar time (hours) for c = 98o. That means that the given atmospheric region is at the distance of about 900 km from the terminator.
In the morning time
However, the data available are not sufficient to describe the behavior of the hydroxyl emission parameters at the 80-100 o solar zenith angles; therefore the above presented formulas are not valid in this region of tc.
2. Lunar variations are given by
The lunar-tide variations during a day have small amplitudes and are not identified reliably. A representative evaluation was obtained by Scheer and Reisen  on the basis of the data for a durable observation period. The data on the heights of the emitting layer are absent. Here tL is the lunar time in hours. According to Chapman and Lindzen  tL = t - x, where x = -0.6173393 + 0.8127167 D ; D = [( YYYY-1901) 365.25] + 364.5 + td. The square brackets in the formula mean the integer part of a number. YYYY is the year.
Variations with lunar age, that is with the synodical month equal to 29.53 days, has higher amplitude than those during a lunar day.
The data for DTrLa, DILa, and DTVLa were obtained at the 57o N latitude [Shefov, 1974a, 1974b] and the data on DzmLa were obtained on average at latitudes of 30-40o N, and all the data have been reduced to the plane of the lunar orbit. An approximate evaluation of the lunar age with an accuracy up to several tenths of a day may be made by the formula [Meyes, 1988]:
The square brackets here denote the integer part of a number.
The latitude q and longitude L of the measurement point (relative to the direct line connecting the Earth and Moon centers) of the tide-distorted atmosphere is determined by Chapman and Lindzen  and Kropotkina and Shefov :
where tL and dL are the hourly angle and inclination of the Moon.
The latitudinal distribution of the amplitude of a tidal disturbance of the atmosphere is determined by the relation AL = (1/2)(3 cos2 q -1). In the equatorial system of reference the distribution has the form
The nature of such oscillations in the upper atmosphere is related to the existence in the lower atmosphere of planetary waves [Reshetov, 1973] with periods of about 15 days and 30 days, which are due to parametric excitation of the atmospheric circulation.
3. Seasonal variations are given by
The seasonal variations, as well as the diurnal ones, have the highest amplitude among other types of variations [Shefov, 1969]. Their amplitude increases with an increase of latitude. This effect in the initial papers [Kvifte, 1967; Shefov and Yarin, 1962] was explained by the Tr increase with latitude. The character of variations of the Dzms altitude agrees with the data of satellite observations [Hernandez et al., 1995].
4. Quasi-biennial oscillations (QBO) are given by
According to the middle atmosphere data the quasi-biennial oscillations have the maximum amplitude in the equatorial zone. The data in the mesopause region were obtained at the Zvenigorod observatory [Shefov, 1973] at j = 57 o N and at the Abastumani observatory [Fishkova, 1983] at j = 43 o N. The available data on zm are not sufficient for description of such variations. There is a correlation between the intensity and the zonal wind velocity: V(W E)
The tqbo moments are, for example, 1960.0 and 1981.1. The moments of cycle beginnings may be found in the work by Reid . Variations of the period of these variations during 1956-1986 in the limits of 22-23 months were obtained by Fedorov et al. . Fedorov et al.  noted that there is a pronounced correlation of the B period with the F10.7 solar activity index. An analysis of the experimental data has shown that the best negative correlation ( -0.76 ) is reached under introduction of the temporal shift q between the data, that is, B(t) = 34.5 - F10.7 (t - q)/22. Within the limits of the interval of years available it is approximately true: q = 2-0.4 cos (2 p /W)(t-1960), where W 30-35 years.
5. The 5.5-year variations are given by
These variations occur practically in phase with the 11-year solar activity cycle [Fishkova, 1983; Megrelishvili and Fishkova, 1986; Shefov and Piterskaya, 1984] and so are not well studied. The data on TV were evaluated on the basis of the correlation between the annual mean values of Tr and TV. The moments are t5.5 = 1959.0, 1970.0, 1981.0, and 1992.0.
6. Variations with solar activity level, that is, with the about 11-year period are considered next. We have for the annual mean parameters
The annual mean values of the F10.7 solar radio emission flux with a shift of 0.42 year provide the best correlation (about 0.98) [Semenov and Shefov, 1979; Shefov and Piterskaya, 1984]. The correlations were mentioned by Fishkova , Shefov , Shefov and Piterskaya , and Wiens and Weill .
7. The long-term trend is given by
where t' = (t - 1972.5)/100
The values of the trend were taken relative to 1972.5, because the annual mean value of F10.7 for this year was about 130, which corresponds to the smoothed mean (with the running interval of 22 years) value for the 19-22 solar cycles. The trends are based on the data of Fishkova , Semenov and Fishkova , Shefov , and Shefov and Piterskaya . It is worth noting that a decrease of the Tr temperature during the solar cycle against the background of the long-term trend is distinctly manifested by an increase of observation frequency of the noctilucent clouds [Gadsden, 1990; Thomas et al., 1989]. The nature of the trend is apparently of a complicated character and manifests both anthropogenic impacts and long-term changes of the solar activity.
8. We next consider latitudinal variations. For the values averaged over a night
The conclusions of Kvifte  and Shefov and Yarin  on the Tr increase with latitude j are based on the data obtained in winter time. Thus, they manifest the latitudinal dependence of the amplitude of the seasonal variations, but not the behavior of the annual mean values of Tr. The latitudinal variations of DTVj were based on correlation with Dzmj.
9. Disturbed variations after geomagnetic storms are given by
where t = tgm - (51- F)/5.4
where t = tgm - [(52 - F)/9]
where t = tgm - (52 - F)/9 ; Dzmgm = (3- Kp)/12.
The most detailed data were obtained at the Zvenigorod observatory ( F = 51 o N), and the variations are followed down to the equator using the data of several stations [Shefov, 1969; Shefov and Piterskaya, 1984]. A correlation with the ionospheric absorption was revealed [Rapoport, 1983; Shefov, 1978b]. The character of emission behavior points to propagation equatorward from the auroral zone after magnetic storms of composition waves, which transport an additional quantity of water vapor and nitric oxide. The rocket data on zm allow us only to estimate variations of the emission layer height depending on the Kp index at latitudes of about 40-45o N 5-6 days after a geomagnetic disturbance.
10. The 27-day variations are given by
This type of variation is related to the Carrington cycles of solar rotation and is evident in the 27-day cycles of solar activity, which lead to UV radiation variations. For this reason the moment of the initial disturbance in the cycle is not constant, but persists on average only during several rotations of the Sun. The variations were considered by Shefov  and Yarin . There are insufficient rocket data to obtain a picture of Dzm27 behavior.
11. Relation to stratospheric warmings is given by
where t' = tsw - 5
The temporal shift of the response of the hydroxyl emission depends on a location of the warming relatively to the place of measurement. According to some measurements not only temperature increase, but a decrease as well was observed [Fishkova, 1978, 1983; Kropotkina, 1976; Matveeva and Semenov, 1985; Shefov, 1973, 1975]. There are not enough rocket data to reveal a Dzmsw behavior.
12. The orographic variations are given by
This spatial variations of the emission parameters is related to the processes of IGW generation in the vicinity of mountains under interaction with them of the air flow, which has a prevailing wind velocity V600 at the 600 mbar isobaric level. The data for the Caucasus Mountains were presented by Sukhodoev et al. . The amplitude of the maximum disturbance, its distance from the ridge (its position is schematically denoted by the solid triangle in Figure 1) and spatial dimensions correlate to the wind velocity and are variable depending on the wind azimuth.
13. Variations after intrusion of the meteor fluxes and at the presence of noctilucent clouds are given by
The data are based on the observations at the Zvenigorod observatory in summer time. The results indicate to an intensification of the OH emission after meteor flux intrusions (MF in Figures 1, 2, and 4) and during appearance of noctilucent clouds (NC in Figures 1 and 2) [Shefov, 1968]. The mean altitude of the latter is about 82 km [Bronshten and Grishin, 1970]. Distribution of meteor fluxes during a year is presented in Abalakin .
14. The variations due to IGW propagation: is given by
where tw is the wave period (in minutes). Here
This type of variation can not be forecasted during a night, because it is initiated by passage through the mesopause of the IGW generated mainly by meteorological sources in the lower atmosphere [Krassovsky et al., 1977; Semenov and Shefov, 1989]. The location of the sources relative to the place of measurements, and thus the wave period tw, as well as the moments of IGW generation are of an occasional character.
The h parameters, which determine the ratio of relative amplitudes of variations of the intensity and temperature of the OH emission induced by IGW passage through the emitting layer, are different for the upper and lower vibrational levels v [Shagaev, 1978]. On the basis of these data
The delay time q (in minutes) of intensity variations relative to temperature variations also depends on v and the season:
The delay times for other vibrational levels have not been sufficiently studied. Assuming a linear dependence on v we have:
While developing the above presented empirical global model of temporal and spatial variations of the OH emissions, attention was primarily paid to obtaining the mean variations and their numerical characteristics. Maximum possible reduction of the measured parameters to the indicated standard solar and geophysical parameters has been made. Only in this case are theoretical calculations corresponding to particular situations possible. The presented set of variations is a first attempt of this kind, and it will doubtless be specified on the basis of specially aimed measurements. All this will influence in a significant way the creation of models of the minor atmospheric constituents, which participate in the photochemical processes of hydroxyl emission generation and whose content can not be practically determined by any other method.
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