A. N. Fakhrutdinova and R. A. Ishmuratov
Kazan State University, Kazan, Tatarstan, Russia
Theoretical and experimental studies demonstrate that the terrestrial atmosphere is a complicated dynamical system in which waves of various scales (internal gravity, tidal, and planetary) are present. The interest in studies of atmospheric wave processes, in particular, of day-to-day wave variations (WV) with periods from several days to several weeks (usually called long-period WV), is due to their important role in the thermodynamic regime and interactions between various atmospheric layers. This interaction is manifested in the global redistribution of energy, mass, and momentum, which is carried out by atmospheric waves in the process of their generation, propagation, and attenuation. Studies of the vertical structure of the long-period (day-to-day) WV in the intermediate region (the upper mesosphere and lower thermosphere (MLT)) are of special interest. The dynamical impact of the neutral atmosphere on the state of the lower ionosphere in this altitude region becomes comparable to the influence of aeronomical and radioactive factors; therefore an allowance for dynamical processes, the long-period WV in particular, is needed to create adequate ionospheric models.
Many experimental works study long-term WV in the MLT region. However, comprehensive study of the vertical WV structure requires further development. For example, the series of data on wind velocities in the MLT region which have been obtained during recent years in Eastern Europe (Kuhlungsborne, 54o N, 12o E) do not have sufficient duration to reveal the vertical and seasonal structure of the long-period WV and their interannual variability. Long-term observations of the dynamical regime in the 80- to 110-km region, conducted at Kazan University (56o N, 49o E) by the radio meteor method since 1986, allow us to provide a comprehensive study of the vertical structure and seasonal and interannual variability of the long-period WV of both the zonal and meridional winds in the upper mesosphere and lower thermosphere.
To study long-term day-to-day variations of the wind, meteor radar observations during 1986-1988 were analyzed. The technical characteristics of the meteor radar and the methods of determination of wind parameters on the basis of angular measurements were described in detail by Fakhrutdinova and Ishmuratov  and Sidorov et al. . Briefly, we show basic momenta.
The facility location is 56o N, 49o E; the operating frequency is 32 MHz; the pulse power of the transmitter is ~150 kW; the doubled transmitting antenna is of the "wave channel" type; the receiving antennas are five three-element antennas of the wave channel type. All the antennas are automatically installed in four mutually orthogonal azimuths in accordance with the observational program; the height resolution is ~1 km; and the horizontal dimensions of the atmospheric region sounded are 400 400 km under a circular survey.
Briefly, the radio meteor data processing is as follows. All of the meteor zone from 80 km to 110 km was split into 10 height layers with a thickness of 3 km. Then an averaging over two adjoining intervals was performed to get smoother and more statistically stable data. The zonal u and meridional v components of the hourly mean wind velocity were evaluated for each height layer. As a result of this processing, temporal series of the hourly mean values of the wind velocity at 10 heights for the entire observation cycle are observed. These data are analyzed using harmonic analysis [Portnyagin and Shprenger, 1978] to determine the prevailing wind and the tidal harmonics. For a more detailed study of the day-to-day variations of the parameters, the harmonic expansion procedure is carried out as follows.
The temporal series of the hourly mean wind values at the interval is represented by the Fourier series:
where Tk are equal to 24, 12, and 8 hours. The operation of evaluation of the parameters for each of the components consists of a mathematical filter, a running mean with averaging interval T and frequency characteristic
To minimize the effect of the side lobes of the frequency characteristics of the filter (2), a temporal "window" with Gaussian weights was used. The half-power bandwidth of a filter with such a temporal window is about 1.2/T. Calculations show that statistically stable nonshifted evaluations of all the parameters of (1) are obtained with an interval of about 2.5 days. In that case, the passband width of frequency characteristics in temporal representation is 2.1 days, and it provides studies of the day-to-day variations with a period longer than 2 days. One should bear in mind that for harmonics with periods of about 2 days the spectral estimates would be underestimated because of the averaging effect in the interval (for a period longer than 4 days the underestimation is less than 10%). Taking into account the temporal window, the parameters sought are determined by the least squares method using additional weight multipliers p 1/s, where s is the standard errors of the V(t) values. For detailed analysis of the day-to-day variations, harmonic decomposition was performed with a running averaging interval of 1 day, which allows us to study wave variations with a period longer than 2 days.
Temporal series of the zonal and meridional winds were obtained from the daily perturbations using this method, as well as the amplitudes and phases of the diurnal, semidiurnal, and 8-hour tides at 10 height levels for the entire observational period.
Together with the day-to-day variations of the wind with periods from several days to several weeks (related to the planetary waves), atmospheric motions are subjected to seasonal variations, which are due to the seasonal reversal of the circulation. To study the day-to-day WV, a low-frequency filtration of the temporal series from the seasonal harmonics is needed. To determine parameters of the harmonics of seasonal wind variations, a Fourier expansion of the series at the 365-day interval was used. The results demonstrate that besides the dominating annual and semiannual oscillations, which characterize the principal global circulation processes and were considered in detail by Fakhrutdinova and Ishmuratov , some periodic structure with a pronounced increase of harmonic amplitudes in the period range 40-60 days is seen in the distribution of the seasonal harmonic amplitudes. For example, in 1987 at an altitude of ~80 km the amplitude of the seventh harmonics (period of 52 days) reaches 7 m s -1 (for the zonal component) which exceeds the values of other harmonics (except the first annual harmonics). What is the source of the wind variations in the upper mesosphere and lower thermosphere with periods of 1-3 months? Such periodicities are also observed in the strato-mesosphere [Labitzke, 1980]. These wind variations in the 40- to 60-day range may be the result of propagation from the lower atmosphere of planetary waves with periods of about 50 days. Their existence in the lower atmosphere of equatorial latitudes and the possibility of penetration into the midlatitude mesosphere were suggested by Krivolutsky .
To study the long-term WV of the wind with a period from several days to several weeks, the temporal series of the prevailing wind were filtered from the first-ninth harmonics of the seasonal behavior (365-40 days). The temporal series obtained as a result of the high-frequency and low-frequency filtrations are continuous wavelike perturbations of the wind with various temporal scales in the 2- to 40-day range. To perform further analysis of the day-to-day wave variations, spectral analysis is used. Calculation of the autospectra was performed in two ways. The classical Blackman-Tewkey method [Jenkins and Watts, 1968] with a correlation "window" with a changeable cutoff interval was used to study general spectral features. The Blackman-Tewkey method has a low-frequency resolution; however, this method is most convenient while studying energy relations of various spectral frequency regions but not individual spectral peaks. For more detailed analysis of individual spectral peaks, one version of the periodogram analysis [Vitman and Yanovskaya, 1980], which makes it possible to estimate both the amplitude and phase of spectral harmonics, was applied. To make the comparison analysis of the seasonal and interannual variations of the WV structure more convenient, the values of the calculated spectra for each season or year were normalized to the united average variance of 50 m 2 s -2. (Such united normalizing makes it possible to come from the spectral density of power S(f) to the amplitude A of corresponding harmonics. In fact, the spectral density S(f) is ~ A2/2. For transition to the amplitude it is enough to multiply 100 times the value of the spectral peak in the diagram and to calculate a square root. The value obtained may be interpreted as a harmonic amplitude (in m s -1 ).)
Figures 1 and 2 show the power spectra, obtained by the Blackman-Tewkey method, of the wind WV for the winter (December, January, and February) and summer (June, July, and August) seasons separately for the u and v components for 1986-1988. The spectral curves for each layer in Figures 1 and 2 are presented with a coordinate shift, the reference system zeroes being marked by the horizontal ticks on the vertical axis. The spectra obtained demonstrate a pronounced periodic structure of the long-term day-to-day WV with a prevalence of definite period groups. As altitude increases, the majority of the spectral maxima decrease, but some spectral values increase. The net effect is a shift of the main spectral maxima and a pronounced vertical profile of the WV.
The WV vertical structure has typical seasonal features. In winter (Figure 1) the dependence on altitude of the dissipative processes prevailing in both zonal u and meridional v winds is more obvious than that in summer. At altitudes of about 80 km, the main energy of the zonal wind WV is concentrated in the lower-frequency region in the 30- to 10-day range (in Figure 1c the main spectral maximum for the 1987/1988 winter and 80- to 84-km levels overlaps the spectral curves for the levels above 84 km). The WV with the 30- to 10-day period weaken with an increase of altitude, and above 90 km the main spectral energy is concentrated in a higher-frequency region. The 1986/1987 winter presents an exception, when contrary to the above an increase of WV in the 24- to 18-day range in the zonal wind field was observed. However, calculation of spectra in the lower-frequency region of the periods (calculated on the basis of the initial temporal series before the filtration out of the interannual harmonics) for the same 1986/1987 winter has shown that the lower-frequency ~50-day periodicity which dominates in this season at heights of 80-84 km also demonstrates a tendency to attenuate with height.
Similar vertical behavior may be detected in the meridional wind v field, some features being observed for particular winter seasons. In the winter of 1986/1987, at 80-96 km the spectra of the meridional and zonal winds differ only slightly. Above 96-102 km the main maximum of the spectrum has considerably smaller power for the meridional wind than for the zonal wind. In the winter of 1987/1988 the spectra of the meridional and zonal winds are also slightly different from each other.
The periodogram analysis carried out provides a better representation of the formation mechanism of the observed WV vertical structure and the spectrum transformation with height. The method of periodogram analysis is based on an a priori presentation of the temporal series in the form of a superposition of the final number of harmonics with some amplitude and phase values [Vitman and Yanovskaya, 1980]. Spectral estimation is provided by detection of the amplitude and phase values of each composite harmonic.
The periodogram analysis carried out has shown that the WV have a complicated periodic structure. The amplitude of each spectral peak may be increased, preserved, and decreased with height, and the height dependencies may differ even for the spectral peaks with close periods. The vertical phase profiles for almost all spectral peaks have a quasi-linear character with a small negative inclination, which may be interpreted as wave disturbances propagating upward. They may be, for example, the tropospheric planetary waves or wave disturbances related to sudden stratospheric warmings. The values of the vertical phase gradient oscillate from 0-0.5o km -1 to 2.5-3o km -1 and have no pronounced dependence on the wave period. During some WV in winter, phase jumps or sharp changes of the vertical phase gradient accompanied by a strong attenuation of WV amplitude at these heights may be observed.
Briefly summarizing the results obtained, one can state the following. According to current ideas [Danilov et al., 1987] the planetary waves generated in the lower atmosphere propagate upward and are filtered by the altitude dependent zonal wind system. This leads to the formation of a certain spectral structure of the wave motions which we observe at a height of about 80 km. We see further that at altitudes from 80 km to 110 km this spectral structure is changed significantly with height, this fact manifesting considerable changes of the atmospheric physical characteristics at these heights.
Let us consider now the spectra of the day-to-day WVs in summer (Figure 2). On the whole, the WV intensity is less in summer than in winter, in the meteor zone (80-110 km) the variance of the wind day-to-day variations being on the average about 65-70% of its summer value. This fact confirms the theoretical conclusions that the westward winds in the summer stratosphere should prevent vertical propagation of the planetary waves [Dickinson, 1968]. However, one can see from Figure 2 that the westward wind system does not present an absolute barrier, and part of the waves penetrate up to lower thermospheric heights. The long-period WV which reach these heights demonstrate a vertical structure different from the WV vertical structure in winter.
Let us consider the 1986 summer season (Figure 2a). The main spectral energy for the zonal wind u at 80- to 84-km heights lies in the 3- to 4-day range. With an increase of altitude, the spectral shape changes slightly, but on the whole the WV intensity decreases insignificantly, unlike strong WV weakening in winter (1985/1986). A similarity of the meridional wind v spectra for the lower and upper height regions with the main maxima in the ranges of ~16 and 5-6 days should also be noted. The behavior of these maxima is somewhat different: the maximum with a period of ~16 days first weakens with a height increase and then intensifies, but the maximum in the 5- to 6-day range monotonously intensifies with altitude. An extra maximum with a period of ~7 days appears at the upper levels of the meteor zone. Similar features of the vertical structure may be observed in the summer of 1988 (Figure 2c). In this summer season the spectral maxima in the zonal and meridional wind fields are observed in the 26- to 28-day and 8- to 10-day intervals. In the summer of 1987, the WV spectrum of the zonal wind u differs from the spectra for 1986 and 1988. The difference is that the main maximum is shifted to T 6 days. The maximum of the WV with T 6 days attenuates with height. In the meridional wind field the summer of 1987 differs, first of all, by a decrease of the total WV intensity. It is worth noting that during this season pronounced variations with periods of about 2 days were observed and their intensity dominated the entire range of WV periods. A monotonous increase of wave amplitude with height is a typical feature in the behavior of the 2-day-period wave.
One can see in Figure 2c that in the summer of 1988 the intensity WV with periods close to the 27-day period of solar rotation prevail in the long-period variation spectra of the zonal and meridional wind. The existence of a solar control of the wave disturbances of the dynamical state of the upper mesosphere and lower thermosphere has been recognized by many investigators (see, for example, Fakhrutdinova and Berdunov  and Volland ). However, Danilov et al.  noted that such WV of the meteorological parameters and variations of solar radiation are two separate processes having no mutual relation. To answer this question, a mutual spectral correlation analysis of the zonal and meridional wind variations and the variations of solar radio emission intensity at the 2800-MHz frequency, measured in the summer of 1988 [Solar Data, 1988], was performed. The analysis showed the presence of a significant coherency (correlation) for variations with periods of about 27 days. The coherency reaches 0.7 (that exceeded the 80% confidence level) for both the zonal and meridional winds. The coherency is much less than the 80% confidence level for WV with periods of 10 and 8 days, which are also pronounced in the autocorrelation spectra of wind variations.
For a more generalized representation of the vertical-seasonal variations, it is convenient to consider the variance of the wind long-period day-to-day variations s2, which characterizes the total WV intensity in the period range of 2-40 days. Figure 3 shows the vertical profiles of the variance s2 for the winter and summer seasons and the annual mean for the period 1986-1988; the variance of variations of the zonal wind u and meridional wind v are shown by solid and open circles, respectively. Figure 3 shows that the winter and summer vertical profiles of WV variance (intensity) differ significantly. This fact was noted above from the analysis of height transformations of the WV spectra. For the winter season (except the 1987/1988 winter, which will be considered below) there is a strong weakening of WV intensity with height. In winter the intensity weakens up to 95- to 105-km heights, and above about 105 km an increase of WV amplitude due to the atmospheric density decrease exponentially throughout the atmosphere begins.
For summer seasons (except the summer of 1987 for the zonal component) a strong weakening of the WV occurred, apparently in the strato-mesosphere; so at altitudes of about 80 km their intensity is insignificant (from 40 to 80 m 2 s -2 ). At 80-110 km a weak attenuation with height is observed up to 85-95 km, the WV amplitude increasing above this region (Figure 3b, summer). In some cases a weakening of the WV intensity does not occur (the meridional component in summer 1987 and zonal component in summer 1988). Nonlinear wave interaction both between themselves and with the background flow, which leads to wave destruction and energy redistribution along the chain (the long-period WV-Internal gravity wave (IGW) turbulence), is a possible mechanism for the weakening of the WV which is better pronounced in winter than in summer. Thus the results obtained confirm, as was noted, that destruction of the long-period WV and IGW occurs up to altitudes of about 105 km and 95 km in winter and summer, respectively.
Let us consider now the differences in wave activity behavior of the zonal and meridional winds between the winter and summer seasons of 1986, 1987, and 1988. In the zonal wind field one can note the following. The WV intensity during the winter of 1986/1987 at altitudes of about 80 km is significantly lower than that during the 1985/1986 and 1987/1988 winters, whereas at altitudes above ~90 km the 1986/1987 intensity is higher (Figure 3, winter, solid circles). One can see in the corresponding spectra (Figure 1, the u component) that the above excess is due to the amplitude increase of WV with 18- to 28-day periods. The opposite picture is observed for summer seasons: at heights of ~80 km the 1987 WV intensity is higher than that in 1986 and 1988 (Figure 3, summer, solid circles). The WV intensity in the meridional wind field both in summer and in winter is less than that in the same seasons of 1986 and 1988. Thus the interannual variability mentioned above demonstrates a certain repeatability: the WV intensity behavior in 1988 repeats general features of the intensity behavior in 1986. The new analysis with attraction of the data obtained from observations in winter 1988/1989 and summer 1989 confirmed the repeatability (periodicity) detected: the WV intensity and its vertical dependence in 1989 are close to the intensity in 1987. This biennial periodicity is pronounced especially clearly for the meridional wind. For the averaged height of the meteor zone (~95 km) the variances of the day-to-day variations of the meridional wind in winter and in summer of 1986-1989 are shown in Table 1.
We consider possible causes of such behavior of the wave activity intensity. It is known that the prevailing circulation in the middle atmosphere demonstrates cyclic variations with a period of ~2 years: quasi-biennial oscillations (QBO). In 1986-1988, Fakhrutdinova and Ishmuratov  observed upward quasi-biennial oscillations of the circulation with amplitudes of up to 6 m s -1 and phase velocities of ~3 km/month in the lower thermosphere of middle latitudes. The QBO westerly phase was observed at about 80 km in the summer of 1987 and above ~95 km in the winter of 1986/1987. Kats  showed that a relation between the phase of the QBO cycle and the wave activity exists in the low-latitude stratosphere. The above results demonstrate that such a relationship may also exist in the midlatitude lower thermosphere. Further studies should answer the following questions: is the detected interannual variability of the WV intensity related to the QBO of the prevailing circulation, and how stable is the periodicity? It is also worth noting here that the existence of the interannual differences of the wave activity comparable with the seasonal variations demonstrates the ability of long-term wind observations to reveal vertical-seasonal variations of the long-period wave processes in the MLT region.
Comparison of the spectra presented above (Figures 1a and 1b and Figures 2a and 2b) shows that the periodic structures of the zonal and meridional wind WV demonstrate not only some similarity, but significant differences as well, a fact that is a signature of differences in propagation of wave disturbances of the zonal and meridional winds both in winter and in summer. This anisotropy of the long-period WV is noted not only in spectral structure, but is also seen in the vertical profiles of the wind variance characterizing total WV intensity (Figure 3). In some height intervals, the variation intensity of the meridional wind is less than the zonal one; in other height intervals, on the contrary the variation intensity of the meridional wind is higher than that of the zonal one. The ratio of WV variance of meridional and zonal components may vary from 0.3-0.4 to 1.5-1.7. On the whole in a year, the WV intensity of the zonal component is higher than that of the meridional component, the difference tending to decrease with height (Figure 3, year).
We present some preliminary results of investigation of the relation between the long-period day-to-day WV of the neutral wind in the lower thermosphere and the state of the ionosphere. The values of the foF2 critical frequency of reflection from the ionospheric F region obtained by vertical sounding at IZMIRAN (Moscow) in 1986-1988 [Cosmic Data, 1986-1988] were used as the ionospheric parameter. The temporal series of the daily mean values of foF2 were normalized and filtered from the seasonal harmonics. For each year of observations a mutual spectral correlation analysis of the variations of foF2 and neutral wind in the 80- to 110-km region was performed. The analysis has shown the existence of joint periodicities in the fields of both zonal and meridional winds, confirming a meteorological impact on the state of the ionospheric F region. This fact confirms the results obtained before (see, for example, Forbes and Leveroni ). The coherency spectra demonstrate definite periodic structure: there are frequency intervals with a high coherence value of 0.6-0.7 (above the 80% confidence level) and frequency intervals where the coherence is practically absent (or close to zero). There intervals may vary (be shifted along the frequency axis) depending on season and year of observations and wind component. On the average in 1986-1988 the highest coherence values (with a confidence level above 80%) are observed in the frequency intervals with periods of 11-16, 7-9, and 5-6 days. Mutual analysis of variations of foF2 and solar activity (the intensity of solar radio emission at a frequency of 2800 MHz) has shown that in this range of periods the coherence of variations of foF2 and wind exceeds the coherence of variations of foF2 and solar radiation. Solar radiation variations were found to govern the long-period variations of foF2 in the period range ~26-30 days.
The long interval of radio meteor observations of the wind (with altitude measurements) in the lower thermosphere conducted at Kazan University from 1986 to 1989 reveals the following:
1. The interannual and seasonal variations of the vertical structure of the long-period day-to-day wave variations of the zonal and meridional winds in the upper mesosphere and lower thermosphere in the period range 2-40 days are found for the first time in Eastern Europe from a long homogeneous series of wind measurements. The results obtained indicate a strong variability with height of the spectral structure of long-term WV.
2. The WV vertical structure shows seasonal variations. In winter the dissipation processes are weaker for both zonal and meridional winds. The variations with periods of 14-30 days are subjected to stronger weakening with height. Attenuation of the WV energy is observed up to 95-105 km. In summer the long-period variations also show vertical variability of the spectral structure. The weakening of the WV energy with height (less pronounced than in winter) is observed up to 85-95 km. On the whole, the WV intensity in the meteor zone at 80-110 km in summer is 65-70% of the WV intensity in winter.
3. The WV spectra of the zonal and meridional components show differences in the vertical and spectral structure. There is anisotropy in the long-period wave variations, their WV intensity in the zonal wind field exceeding, on the whole, the intensity in the meridional wind field.
4. Interannual variability of the WV intensity is found. From data of four sequent observational years (1986-1989) it is detected that the interannual variations are of a periodic character with a quasi-biennial period. The interannual variations have considerable differences for the zonal and meridional winds. In the zonal wind field the interannual variations also demonstrate differences between the height regions above and below 95 km.
5. Coherence of the neutral wind long-period WV in the 80- to 110-km region and variations of the foF2 parameter of the ionospheric F region at planetary wave periods are found, confirming the meteorological impact of dynamical processes in the neutral lower thermosphere on the ionosphere.
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