Evidence for nonlinear coupling of planetary waves and tides in the lower thermosphere over Bulgaria

Evidence for nonlinear coupling of planetary waves and tides in the lower thermosphere over Bulgaria

Journal of Atmospheric and Solar-Terrestrial Physics 62 (2000) 115±132 Evidence for nonlinear coupling of planetary waves and tides in the lower ther...

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Journal of Atmospheric and Solar-Terrestrial Physics 62 (2000) 115±132

Evidence for nonlinear coupling of planetary waves and tides in the lower thermosphere over Bulgaria Dora Pancheva* Geophysical Institute, Bulgarian Academy of Sciences, So®a, Bulgaria Received 23 November 1998; accepted 7 June 1999

Abstract Analyses of hourly values of zonal and meridional wind near 95 km observed by meteor radar at Yambol (42.58N, 26.68E) during January 1991±June 1992 indicate the presence of planetary waves with prevailing periods of 1.5±2.5, 4±6, 9±10 and 16±18 days. About 20% of the whole power of atmospheric motions is connected with these waves, so they play an important role in the dynamics of the mesosphere-lower thermosphere (MLT) region. By dynamic spectral analysis applied to the hourly neutral wind and to the calculated hourly values of tidal amplitudes it has been demonstrated that there is considerable modulation of tidal amplitudes by planetary waves in the neutral wind, as this process is better expressed in the semidiurnal tides. The nonlinear interaction between tides and planetary waves is studied by bispectral analysis. The results of these analyses indicate again that the nonlinear interactions between semidiurnal tides and planetary waves with periods 2±20 days are stronger than those of the diurnal tides and planetary waves. A peculiar feature of dynamics in the MLT region above Bulgaria is the presence of strong oscillations with periods of 20 and 30 h, which indicate signi®cant nonlinear coupling between them. 7 2000 Elsevier Science Ltd. All rights reserved.

1. Introduction The latitudinal and vertical average behaviour of atmospheric tides as a function of season in the mesosphere and lower thermosphere (MLT) region is quite well understood (Manson et al., 1989; Vincent et al., 1989). However, the strength of the solar tides in the MLT region can be rather variable with time scales of a few days to three weeks (synoptic periods) (Avery et al., 1989; Fraser et al., 1989; Williams and Virdi, 1989; Huuskonen et al., 1991). Variability in the amplitude and phase of the solar tides can be caused by a num-

* Present address: University of Wales, Department of Physics, Aberystwyth, Ceredigion SY23 3BZ, UK. Tel.: +441970-621902; fax: +44-1970-622826. E-mail address: [email protected] (D. Pancheva).

ber of mechanisms: (1) changes in the tidal forcing; (2) propagation through changing background winds; (3) additional energy near the tidal frequencies due to local or synoptic scale disturbances; (4) nonlinear interactions between the tides, or between the tides and planetary waves (Cevolani and Kingsley, 1992; Pancheva and Mukhtarov, 1994; Mitchell et al., 1996). Some observations indicate the presence of subsidiary components close to tidal periods and this e€ect can be explained by nonlinear interactions between tides and planetary waves (Teitelbaum and Vial, 1991). The process of nonlinear coupling can generate two secondary waves whose frequencies are the sum and di€erence of the frequencies of the primary waves (tide and planetary wave). Then these two secondary waves beat with the primary tide, modulating its amplitude with the planetary wave period. Modulation of the semidiurnal tidal amplitudes with a period near 2 days is demon-

1364-6826/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 4 - 6 8 2 6 ( 9 9 ) 0 0 0 3 2 - 2

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strated by Mitchell et al. (1996). Manson et al. (1982) suggested that the 9.7-h and 16-h period waves frequently observed above Saskatoon are generated by a nonlinear interaction between the semidiurnal tide and quasi-2-day planetary wave, while RuÈster (1992) indicates that the 16-h wave, observed in the summer polar mesosphere, is produced by a nonlinear interaction between the diurnal tide and quasi-2-day wave. Cevolani and Kingsley (1992), on the basis of more than 10 years of meteor radar observations near Bologna, suggest that peaks in the 10-h±16-h band result from the nonlinear coupling between tides and planetary waves. Evidence from bispectral analysis for nonlinear interactions of planetary waves with periods in the range of 2±19 days and diurnal and semidiurnal tides at various intervals during 1990 in the Antarctic mesopause is presented by Kamalabadi et al., (1997). The typical planetary waves derived by the authors in the Antarctic MLT region are related to planetary waves observed in the stratosphere and are consistent with theoretical predictions of the periods of free Rossby modes (Salby, 1984). The horizontal and vertical structures of normal modes are strongly in¯uenced by the background wind and temperature through which they propagate (Salby, 1981). This in¯uence is a reason for the observed variability in the periods of normal modes. Williams and Avery (1992) found that oscillations with periods between 1.5 and 20 days in the middle/high-latitude mesosphere could be related to those observed in the lower altitudes. Theoretical simulations by Forbes et al. (1995) suggest that planetary wave oscillations in the two hemispheres may be coupled, possibly through a transequatorial ducting channel. Consequently, there are di€erent sources for the generation and damping of planetary waves in the atmosphere and their potential in¯uence on the MLT region, even when they may not penetrate beyond the mesosphere, is considerable. The main goal of the present paper is to study the appearance, signi®cance and variability of the ¯uctuations with periods 1.5±20 days in the neutral wind measured by a meteor radar in Yambol (Bulgaria) during the interval from January 1991±June 1992. The possible nonlinear planetary wave±tide interaction in the MLT region is investigated by bispectral analysis.

2. Data analysis and interpretation A meteor radar has operated regularly in Bulgaria (Yambol, 42.58N, 26.68E) since the end of 1989 and the measurements have been processed and analyzed in the Geophysical Institute, So®a since the end of 1990. The meteor radar provides an integrated measurement of a weighted wind pro®le over about 95 2 2 km. The

measurements were obtained by sounding simultaneously in four geographical directions; however, because of disturbances in two of them (east and north) during most of the daytime, only the measurements of the western and southern antennae were used for processing and analyzing the data. This fact is a reason for an increase of the level of noise for these measurements compared with the ®rst ones when the north and south measurements were averaged together to produce a single data set corresponding to the meridional component of the wind and, similarly, the east and west measurements produce a single zonal component. The measurements were averaged to produce one value per hour in zonal and meridional directions, so the minimum identi®able period is 2 h (Nyquist period). The main features of the monthly mean regime of the dynamics in the MLT region above Bulgaria were described by Pancheva and Mukhtarov (1994). The characteristics of the observed quasi-2-day variations and the in¯uence of winter stratospheric warming on the tidal variability were also brie¯y considered there. Using the daily values of the tidal characteristics a seasonal model of them was created by Pancheva and Mukhtarov (1996). In some of the tidal characteristics the existence of shorter period seasonal components (as, for example, 2-month period) is observed. 2.1. `Instantaneous' characteristics of the MLT region dynamics As the main goal of the present paper is to study the waves in the MLT region, ®rst the data sets of hourly values of zonal and meridional components of the measured neutral wind were analyzed. The time interval under consideration, from January 1991±June 1992 is divided into two subintervals: 1 January±23 October 1991 and 21 November 1991±16 June 1992. The data for the interval 24 October±20 November 1991 were not included in our analysis because there are many data gaps with lengths of more than 4 h. For spectral estimates we use a periodogram analysis in the form of the correloperiodogram (Kopecky and Kuklin, 1971), described in detail by Kuklin in the book of Vitinsky et al., (1986). This method allows simultaneous assessment of the amplitude, phase and the probability of presence (i.e. the signi®cance of the ¯uctuation) for every harmonic component by means of the selection of all reasonable values of the probe periods with an increment, ensuring the required precision. The advantage of this method is that we can obtain high-resolution spectral estimates in the desired period range with an arbitrarily small period step. The amplitude spectra for the period interval 4±36 hours for the zonal and meridional wind components are shown respect-

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Fig. 1. (a) Amplitude spectra obtained by correloperiodogram analysis of hourly values of zonal wind in the period interval 4±36 h; the solid line indicates the amplitude spectrum for the ®rst subinterval: 1 January±23 October 1991, while the dashed line is for the second subinterval: 21 November 1991±16 June 1992 (the abbreviation ASZW means Amplitude Spectrum of Zonal Wind); (b) The same as (a) but for the hourly values of meridional wind (the abbreviation ASMW means Amplitude Spectrum of Meridional Wind).

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ively on Fig. 1a and Fig. 1b (the solid line is for the ®rst subinterval and the dashed line for the second one). It is clearly evident that the semidiurnal tides are de®nitely stronger and more regular events than the diurnal tides. Except for these tides, the 8- and 6-h sub harmonics are also well expressed, as the terdiurnal tides demonstrate a permanent feature of the MLT region dynamics above Bulgaria. On the grounds of this result the main tidal components describing the dynamics of the MLT region over Bulgaria are: semidiurnal, diurnal, terdiurnal and quaterdiurnal tides. The prevailing wind and tidal amplitudes and phases are determined by the best-®t procedure to a 24-h segment of wind data, as the derived characteristics are assigned to the centre of the time segment. The 24-h segment was incremented in 1-h steps producing hourly estimates of prevailing wind and tidal amplitudes and phases. In this way we calculate the so-called `instantaneous' values of tidal characteristics of neutral wind. The above procedure is described in detail by Mukhtarov and Pancheva (1993). When the time series of hourly measurements of the zonal (or meridional) component of neutral wind is replaced by the time series of the sum of hourly values of prevailing zonal (or meridional) wind and hourly values of all tides, the latter time series actually represents the ®ltered data. The procedure described by Mukhtarov and Pancheva (1993) can be also considered as a linear ®lter. Its amplitude-phase characteristic is shown in Fig. 2. In the range of transparency (periods longer than 6 h) the amplitude and phase in¯uences are insigni®cant, while

the suppression of oscillations with periods shorter than 6 h increases suciently rapidly. The nonlinear distortions in the ®ltered sine functions are perfectly insigni®cant if the amplitude of the non ®ltered data is unity, the mean square deviation of the ®ltered data is smaller than 10ÿ7. Strictly speaking, the above described procedure is not a real ®lter, as it cannot work in real time; the value at the current moment depends on future values; however, it is very suitable for retrospective analysis and especially connected with the transient behaviour of the tidal characteristics. The same approach was used by Mitchell et al. (1996) investigating the short-time variability of the amplitude of the semidiurnal tides, as well as by Pancheva and Mukhtarov (1998) in studying the response of the MLT region dynamics above Bulgaria to major geomagnetic storms. 2.2. Observed oscillations and their signi®cance The amplitude spectra for zonal and meridional components of the neutral wind in the periodic interval 36±480 h (1.5±20 days) are shown in Fig. 3a and Fig. 3b, respectively. Again the spectra are obtained by the method of correloperiodogram analysis separately for the two subintervals. The horizontal solid and dashed lines represent the 90% con®dence level. Certain repetition of the well expressed ¯uctuations in both subintervals can be noticed for the zonal, as well as for the meridional, components. The most well pronounced peaks in the zonal wind component are:

Fig. 2. The amplitude-phase characteristic of the linear ®lter; the solid line describes the in¯uence of the ®lter on the amplitude K and the dashed line that on the phase F (measured in radians) of the sine function.

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Fig. 3. (a) Amplitude spectra obtained by correloperiodogram analysis of hourly values of zonal wind in the period interval 36± 480 h (1.5±20 days). The horizontal solid and dashed lines indicate the 90% con®dence level (solid line Ð result for the ®rst subinterval; dashed line Ð for the second subinterval); (b) The same as (a) but for the hourly values of meridional wind.

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about 2-, 4±5-, 9±10-, 12±13- and about 16±18-day ¯uctuations. Almost the same peaks are detected in the meridional wind component with a slight di€erence connected mainly with the 12±13-day waves, which are strong enough only in the second subinterval. The results from Fig. 1 and Fig. 3 demonstrate a big variety of waves contained in the hourly measurements of the neutral wind. In order to estimate the signi®cance of each wave component we use the statistical result that the power of some process is equal to the sum of the square of its mean value and its dispersion

(variance). As in almost all cases, in this study the square of the mean value is many times smaller than the respective variance; then, as a ®rst approximation, we can accept that the power of the process is proportional to its dispersion. In order to derive the signi®cance of the contributions of the main tides (semidiurnal and diurnal) as well as the above-mentioned planetary waves, the time series of measurements are subjected to band-pass ®ltering around each major peak. Then the variance of every ®ltered time series can be calculated. The ratio of the dispersion of

Fig. 4. (a) Filtered velocity values (10±14 h) of meridional wind component at Yambol during 1 January±23 October 1991; (b) Filtered velocity values (20±28 h) of meridional wind component at Yambol during 1 January±23 October 1991.

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each ®ltered time series to that of the original measurements provides a statistical measure of the contribution of each period band (Kamalabadi et al., 1997). In order to separate the oscillations under investigation we use a band-pass ®lter with a linear phase, described by Luzov et al. (1965), which is centred on the wanted peak and suppresses low and high frequency variations. Fig. 4a shows the 10±14-h waves (semidiurnal tide) in the meridional wind component, while Fig. 4b presents 20±28 h waves (diurnal tide) only for the ®rst subinterval. The mean variance of the

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®ltered signal for both subintervals is 139 m2/s2. Comparing this value to that of the original signal, which is 538 m2/s2, we conclude that the contribution of the semidiurnal meridional waves is 25.8% of all variations. The mean variance of the diurnal (20±28 h) meridional waves is 68 m2/s2, corresponding to 12.6% of all variations. Fig. 5a shows the ®ltered values of the 1.5±2.5-day waves and Fig. 5b those of about 9± 10-day waves in the meridional wind component. The mean variance of the 1.5±2.5-day waves in the meridional wind component is 47 m2/s2, or the contribution of

Fig. 5. (a)Filtered velocity values (1.5±2.5 days) of meridional wind component at Yambol during 1 January±23 October 1991; (b) Filtered velocity values (8±10 days) of meridional wind component at Yambol during 1 January±23 October 1991.

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these waves is about 8.7% of all variations. The 9±10day waves demonstrate a comparatively regular persistence in the observed time interval. Their variance is 42 m2/s2, corresponding to 7.8% of all variations. The longer 15±19-day ®ltered time series has dispersion 9.2 m2/s2; the contribution of these waves is only 1.7% of all variations. By analogy, the results for the zonal wind component are as follows: the contribution of (1) the 10± 14-h waves is 21.8%; (2) 20±28-h waves is 17.7%; (3) 1.5±2.5-day waves is 9.9%; (4) 9±10-day waves is about 8.4%, and (5) 15±19-day waves is 2.9% of all variations. The above results demonstrate that the observed planetary waves possess about 20% of the whole power of the motion and therefore they play an important role in the dynamics of the MLT region over Bulgaria. 2.3. Dynamic amplitude spectra The method of correloperiodogram analysis (Kopecky and Kuklin, 1971), as was mentioned before, allows simultaneous assessment of amplitude, phase and the probability of presence of every harmonic component by means of the selection of all reasonable values of the probe period with an increment, ensuring the required precision. This method is very convenient also for deriving the moving, known also as dynamic, amplitude spectra, through which the development of the wave process could be estimated. The choice for the length of the segment and the interval of sliding depends on the time-scale of the waves under investigation. The shorter-period planetary waves, such as 1.5±5 days, which also have shorter lifetimes and rapid changes in temporal characteristics of the signal, have to be studied by a smaller length of the segment. In our case we accepted the length of the segment as 20 days and the interval of sliding as 4 days. Figs. 4a and 4b de®nitely demonstrate an essential variability of semidiurnal and diurnal tides in the meridional wind component (a similar result is observed in the zonal wind component, not shown here), as a signi®cant part of this variability appears at periods identical to those of identi®ed planetary waves. In order to study the appearance and development of the planetary waves in the amplitude variation of the diurnal and semidiurnal tides, as well as to compare the relations of the observed waves with the analogous waves in the neutral wind measurements (if they exist) we apply the dynamic spectral analysis to the time series of hourly values of: (1) measured neutral wind; (2) `instantaneous' amplitudes of semidiurnal tide, and (3) `instantaneous' amplitudes of diurnal tide. Time-period distributions of the amplitude spectra give information about the non-stationary characteristics of

the process (i.e. the period content changes with time). In this study we utilize a moving spectral analysis to both zonal and meridional wind components. The time-period distributions of the amplitude spectra for the period interval 1.25±5 days for the zonal wind, `instantaneous' amplitudes of semidiurnal and diurnal zonal tides are shown in Fig. 6. The 1.5±2.5-day waves can be seen on the maps of zonal wind and amplitudes of semidiurnal tides during the summer months of July±August and very weak ones in the diurnal amplitudes. There are a few more impulses of these waves in the zonal wind, but their response in the semidiurnal and diurnal tides is weak. The correspondence between the planetary waves in the zonal wind and the semidiurnal tides is better than that between wind and diurnal tides, not only for 1.5±2.5-day waves, but also for the longer waves (for example, 3.5±4-day waves in May±June, 1991). The 4±5-day waves in summer are well developed, not only in zonal wind and semidiurnal tides, but also in the diurnal tides. In order to study the longer period waves, from 4±5 up to 20 days, we apply the moving spectral analysis; however, in this case the length of the segment is 54 days and the time increment is 12 days. The time-period distributions of the amplitude spectra are shown in Fig. 7. Again the correspondence between the planetary waves in the zonal wind and the semidiurnal tide is better expressed than that between zonal wind and diurnal tide. This is particularly valid for the 16±18-day waves in the winter of 1991 and about 16-day waves in the early summer of 1991. The correspondence of the 8±9-day waves in the zonal wind and the semidiurnal tide is better expressed in the late summer and autumn of 1991 and the winter of 1992, while that in the winter of 1991 is better displayed in the behaviour of the diurnal tide. The results for the time-period distribution of the amplitude spectra in the period interval 1.25±5 days for the meridional wind and amplitudes of semidiurnal and diurnal tides are shown in Fig. 8. Again the correspondence between the 2.5±3-day and 3.5±4-day waves in the meridional wind and the semidiurnal tide is better outlined; however, the planetary wave response of the diurnal meridional tide is stronger than that of the diurnal zonal tide. Fig. 9 is similar to Fig. 8, but for the longer time planetary waves, 4±20 days. This ®gure demonstrates a good response of the amplitudes of the semidiurnal tide to planetary waves existing in the neutral meridional wind, as the reactions to 8±10- and to 16±17-day waves are strong. The amplitudes of the diurnal tide react to 8±10-day waves also, but only in the winter of 1992. The response of semidiurnal tides to the 4±5-day waves in the neutral wind is also very strong, as even the trend in the change of prevailing period in the winter and spring of 1992 is well depicted. Some reaction of these waves is observed in

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Fig. 6. Time-period distribution of the amplitude spectra in the period interval 1.25±5 days for: the zonal wind (upper), amplitudes of semidiurnal (middle) and diurnal zonal tides (bottom). The scale column represents the amplitude spectrum measured in m/s.

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Fig. 7. The same as Fig. 6, but for the period interval 4±20 days.

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Fig. 8. The same as Fig. 6, but for the meridional wind (upper), amplitudes of semidiurnal (middle) and diurnal meridional tides (bottom).

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Fig. 9. The same as Fig. 8, but for the period interval 4±20 days.

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the diurnal tide also; however, it is considerably weaker. The last four ®gures, displaying the time-period distributions of the amplitude spectra for the hourly measurements of neutral wind and for the calculated `instantaneous' amplitudes of semidiurnal and diurnal tides, de®nitely demonstrate the correspondence between the planetary waves in the neutral wind and those in the tides. The correspondence is signi®cantly stronger between wind and semidiurnal tide than that between wind and diurnal tide. The above results clearly outline the process of the amplitude modulation of the tides, connected with the nonlinear coupling between tides and planetary waves observed in the neutral wind measurements. There are a few time intervals when a temporal evolution of the observed period can be marked. These cases also suggest a nonlinear energy cascading process. It is necessary to underline that the results from Figs. 6±9 do not show some seasonal course in the appearance of the planetary waves in the MLT region above Bulgaria during the investigated time intervals.

3. Nonlinear wave interactions According to Fig. 1 a presence of subsidiary components around the tidal periods can be clearly recognized. Such components have been found in many other investigations (Manson and Meek, 1990; Cevolani and Kingsley, 1992; RuÈster, 1992, 1994; Kamalabadi et al., 1997). Some of these oscillations can be independent harmonic components; however the others, symmetrically situated around the main tidal peak in the frequency domain, are usually a result of amplitude modulation of the tides by planetary waves. Such pairs of peaks are: 10.7 and 13.6; 11.4 and 12.6; 11.7 and 12.3 or 22.5 and 25.7 h, observed in the zonal wind spectra, and 10.1 and 14.8; 11.4 and 12.6; 11.65 and 12.35; 19.3 and 31.6, or 21.9 and 26.7 h in the meridional wind component. Teitelbaum and Vial (1991) have shown theoretically that the nonlinear interaction of a tide and a planetary wave can modulate the tidal amplitude with a period equal to the planetary wave period. This nonlinear interaction mechanism could also provide an explanation of the existence of several waves near the tidal periods. Because of the nonlinear advective terms in the general dynamical equations governing atmospheric motions a possible wave±wave or tide±wave interaction process, identifying it as a quadratic coupling cannot be examined by traditional spectral analysis. This is due to the fact that conventional spectral analysis is based mainly on the power spectrum, where the phase relations between frequency components are suppressed; it does not pro-

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vide information on possible interactions between waves as does the bispectral analysis. 3.1. Bispectral analysis If the process under consideration is non stationary, or if there is interaction among di€erent frequencies (the simplest extension is to study an interaction between pairs of frequencies), the bispectral analysis technique has to be used. The bispectrum retains phase information and it is able to identify a possible nonlinear process that might generate phase coupling. The bispectrum is de®ned (Hasselmann et al., 1963; MacDonald, 1963; Haubrich, 1965) as: …… B… f1 , f2 † ˆ R…t1 , …1† t2 † exp‰ÿj2p… f1 t1 ‡ f2 t2 †Šdt1 dt2 where: R…t1 , t2 † ˆ hX…t†X…t ‡ t1 †X…t ‡ t2 †i

…2†

is the third-order moment of the stationary stochastic process {Xi }, where <> denotes the ensemble average. The bispectrum is equivalent to the two-dimensional Fourier transform of the third-order moment sequence R(t1,t2). For a Gaussian process the bispectrum B( f1, f2)00, because the third-order moment for the Gaussian process is zero. The bispectrum gives a measure of the multiplicative interactions of the frequency components in {Xi }. It can be shown (Nikias and Raghuveer, 1987) that the bispectrum represents the contribution of the mean product of three Fourier components where one frequency equals the sum (or di€erence) of the other two. The bispectrum will be nonzero only when the resonance condition will be ful®lled, or if f3=f1+f2 and f3=f1+f2, where f denotes the phase of the components. Hinich and Clay (1968) give the estimation of the bispectrum from a ®nite record: m X ^ fi , fl † ˆ 1 B… S p S p Sp m pˆ1 i l i‡l

…3†

where the asterisk denotes the complex conjugate, Si,l are estimates of the discrete Fourier transform of {Xi }, m is the total number of data segments for each of which the Si,l are repeatedly estimated. In the present paper the bispectrum is presented by the quantity: R2 … f1 , f2 † ˆ

^ f1 , f2 † j2 m3 j B… s3

…4†

where s 2 is the variance of the time series under investigation. In this way, the bispectrum determines if

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components at harmonically related positions in the amplitude spectrum are, in fact, phase coupled. The non zero points ( f1, f2), or (T1, T2), where T is the period in a two-dimensional bispectrum period plane, produce components that are nonlinearly interacting and result in quadratic phase coupling. The interpretation of peaks in bispectral plots is explained clearly by Clark and Bergin (1997). 3.2. Results In order to study the nonlinear interactions between tides and planetary waves in the MLT region over Bulgaria we apply the bispectrum analysis to the hourly measurements of neutral wind. To investigate the possible interaction between tides, as well as between tides and the well known quasi-2-day waves, we show ®rst the result for the bispectrum estimate in the period interval 0.25±3 days. Fig. 10 displays the contour plot of the calculated bispectrum quantity for the zonal wind component in the ®rst subinterval. The non-zero points in this plane indicate quadratic phase coupling between waves with periods corresponding to the respective coordinate values of these points. The semidiurnal tides are the more active in the nonlinear process of interactions. The coupling between semidiurnal tides and diurnal tides, as well as terdiurnal tides, is indicated. A strong process of coupling is observed also between semidiurnal tides and quasi±2-

day waves. The diurnal tides interact predominantly with semidiurnal and terdiurnal tides, as well as with components with periods 20 and 22 h (they are expressed in Fig. 1a). A very strong coupling process is observed between waves with periods 20 and 30 h. These oscillations are really regular events in the zonal neutral wind and they are well outlined in Fig. 1a. Caution must be exercised in the interpretation of peaks arising at tidal periods, as the solar tides (diurnal, semidiurnal and terdiurnal) have an obvious harmonic relationship, and tidal phases will display a certain degree of phase consistency owing to their common forcing. This may well result in a non-zero bispectral estimate. However, these are the peaks that would be expected if a nonlinear interaction occurred between the tidal components, so the unambiguous detection of such an interpretation between tides using bispectral analysis is impossible (Clark and Bergin, 1997; Beard et al., 1999). Fig. 11 shows the bispectrum estimate where the longer planetary waves, with periods up to 20 days are included. Again the semidiurnal tides display stronger activity in coupling with the longer period planetary waves than the diurnal tides. The interactions are signi®cant between the semidiurnal tides and planetary waves with periods of 4±6 days, about 9 days, about 13 days and about 17±18 days. The diurnal tide almost does not interact with the longer period planetary waves, except for very weak coupling with about 5-

Fig. 10. Bispectrum estimate for the zonal wind component during 1 January±23 October 1991 for the period interval 0.25±3 days.

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and 16-day waves. The above mentioned results for the bispectrum evaluations of the zonal wind con®rm the fact that the observed amplitude modulations of zonal tides, obtained by dynamic spectra (shown in Fig. 6 and Fig. 7), result from the nonlinear interaction between tides and planetary waves. It would be better to note, also, that Fig. 11 shows an interaction process between 30 h and 5-day waves. The bispectrum assessments for the meridional wind in the period range 0.25±3 days are shown in Fig. 12. Again the semidiurnal tides are more active in the process of nonlinear interaction. The couplings between themselves and between semidiurnal and diurnal tides are the strongest ones. The interaction between semidiurnal and terdiurnal tides is also visible, but (similarly to the zonal wind component) these results could be because the tides are harmonically related and their phases tend to be ®xed. The semidiurnal tide also interacts with about 2.5±3-day waves and this was demonstrated in Fig. 8. The diurnal tide, besides coupling with the semidiurnal tide, displays a weak interaction with 2.5±3-day waves. On the same ®gure some interaction process is marked between 2.5±3-day and about 1.5-day waves. The coupling processes of the meridional tides with the longer period planetary waves are shown in Fig. 13. The diurnal tide in the meridional wind demonstrates now a stronger tendency for interaction with planetary waves than the diurnal tide in the zonal wind com-

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ponent. This result was also obtained before, on the basis of dynamic spectra (Fig. 9). Besides the interaction with the 2.5±3-day waves, the diurnal tide indicates strong coupling with 4-day and with about 10day waves. The semidiurnal tide, as usual, is more active in coupling with the planetary waves than the diurnal tide. The couplings with 4-, 9±10- and 17±18day waves are very well expressed. The bispectrum evaluations for the meridional wind con®rm the fact that the amplitude modulations of the meridional tides (shown in Figs. 8 and 9), result from the nonlinear interaction between tides and planetary waves.

4. Summary and conclusions On the basis of the hourly data set of neutral winds measured by a meteor radar and of calculated `instantaneous' values of the characteristics of tides, a number of oscillations with periods between 1.5 and 20 days are found to be present in the MLT region above Bulgaria. The most well observed oscillations in both the zonal and meridional components belong to the periodic bands: 1.5±2.5-, 4±6, 9±10- and about 16±18-day waves, as well as about 12±13-day waves mainly in the zonal wind component. Similar waves have been reported for the Antarctic mesopause during 1990 in the excellent study of Kamalabadi et al. (1997). These periods have also been observed in the stratosphere

Fig. 11. The same as Fig. 10, but for the period interval 0.25±20 days.

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Fig. 12. The same as Fig. 10, but for the meridional wind component.

Fig. 13. The same as Fig. 12, but for the period interval 0.25±20 days.

D. Pancheva / Journal of Atmospheric and Solar-Terrestrial Physics 62 (2000) 115±132

and lower mesosphere and belong to the periods of free Rossby modes. An assessment of the statistical signi®cance of the identi®ed ¯uctuations is derived. It was found that the power possessed by the planetary waves is about 20% of all variations. This result demonstrates that the observed planetary waves make signi®cant contributions to the variability of upper atmosphere dynamics and consequently play an important role in the MLT region over Bulgaria. The temporal variability of the above mentioned planetary waves in the wind and tides is investigated by dynamic spectra, and the results are shown in Figs. 6±9. Nevertheless, the planetary waves conclusively demonstrate their transient character; they have lifetimes of days to weeks when their periods are almost constant. Unfortunately, some seasonal distribution of these oscillations has not been found in the studied time interval. The results from the dynamic spectra addressing the amplitudes of the diurnal and semidiurnal tides de®nitely show the amplitude modulations of tides by planetary waves in the neutral wind. This process is stronger for the semidiurnal tides, which means that the correspondence between the planetary waves in the neutral wind and the semidiurnal tides is better than that between the wind and diurnal tides. The results from a bispectrum analysis exactly con®rm the results from the dynamic spectra, showing that the nonlinear interactions (in the form of quadratic phase coupling) between semidiurnal tides and planetary waves are stronger than those between diurnal tides and planetary waves. The meridional diurnal tide indicates higher activity toward nonlinear coupling with planetary waves than the zonal one. A peculiar feature of dynamics in the MLT region above Bulgaria is the presence of strong oscillations with periods 20 and 30 h (particularly in the zonal wind component). To clarify the origin of these oscillations a further study has to be conducted.

Acknowledgements The author thanks Pl. Mukhtarov from the Geophysical Institute for the help in making some calculations and for the valuable discussions in preparing the present paper.

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