Response of the Nighttime Midlatitude Ionosphere to ... - Springer Link

ISSN 00167932, Geomagnetism and Aeronomy, 2008, Vol. 48, No. 4, pp. 511–517. © Pleiades Publishing, Ltd., 2008. Original Russian Text © A.F. Yakovets, V.V. Vodyannikov, G.I. Gordienko, Ya. F. Ashkaliev, Yu.G. Litvinov, S.B. Akasov, 2008, published in Geomagnetizm i Aeronomiya, 2008, Vol. 48, No. 4, pp. 534–541.

Response of the Nighttime Midlatitude Ionosphere to the Passage of an Atmospheric Gravity Wave A. F. Yakovets, V. V. Vodyannikov, G. I. Gordienko, Ya. F. Ashkaliev, Yu. G. Litvinov, and S. B. Akasov Institute of the Ionosphere, AlmaAta, Kazakhstan Received April 13, 2007; in final form, August 24, 2007

Abstract—Using the data of the ionospheric vertical sounding in Almaty, the response of various parameters of the nighttime F layer to the passage of an atmospheric gravity wave, generated during the large magnetic storm on July 24–25, 2004, is studied. The analysis of the phase relations between the variations in the elec tron density at the F layer maximum (NmF), the layer maximum height (hmF), and the layer halfthickness showed that they are determined by the slope of the wave phase front. It is shown that the halfthickness of the layer changes in antiphase with the variations in NmF2. The known fact that the amplitudes of variations in the critical frequencies of the F2 layer are smaller than the amplitudes of electron density variations at fixed heights is explained. PACS numbers: 94.20.Wg, 92.60.hh DOI: 10.1134/S0016793208040129

1. INTRODUCTION Internal atmospheric gravity waves (AGWs) play an important role in the thermospheric dynamics. Prop agating through the thermosphere and interacting with ionospheric plasma, AGWs cause appearance of traveling ionospheric disturbances (TIDs) registered using various radiophysical methods [Afraimovich et al., 1998; Williams, 1996]. The propagation of AGWs in the neutral atmosphere and their ionospheric man ifestation have been studied both experimentally and theoretically for many years. The results of these stud ies are presented in the series of reviews [Hocke and Schlegel, 1996; Hunsucker, 1982; Yeh and Liu, 1974]. It is very actual to study the interaction between AGWs and TIDs within the scope of the problem of the ther mosphere–ionosphere coupling. A few models, describing the main characteristics of the interaction between AGWs and TIDs, were developed based on the theoretical and experimental studies. Kirchengast [1996] modeled the impact of AGWs on the parame ters of ionospheric plasma obtained with the incoher ent scatter radar. These parameters include electron density, ion and electron temperature, and ion drift velocity along magnetic flux tubes. Millward et al. [1993] modeled the interaction bewteen AGWs and TIDs in order to compare model results with the data of vertical ionospheric sounding using the global ther mospheric–ionospheric model developed by Fuller Rowell et al. [1987]. In this model a substantial short time enhancement of the auroral electrojet, causing local heating of the atmosphere, served as a cause of AGW generation. The expansion and the following compression of the atmosphere generate largescale

AGW, which propagates equatorward and generates TIDs on its path. Millward et al. [1993] calculated the behavior of the electron content at various heights, including the F2layer maximum height. Recently, Ashkaliev et al. [2003] compared the results of numer ical simulation with those of the ionospheric vertical sounding. The behavior of the majority of TID param eters obtained experimentally demonstrated good agreement with model results. This paper continues the work [Ashkaliev et al., 2003]. This paper analyzes the response of various parameters of the nighttime F2 layer to the passage of AGWs, that originated during the large magnetic storm of July 24–25, 2004. The analysis of the phase relations between the variations in the electron density in the F2layer maximum (NmF2) and the behavior of the F2layer maximum height (hmF2) showed that the published concept [Balthazor and Moffet, 1997; Fesen et al., 1989] that variations in NmF2 and hmF2 are antiphased is not quite correct. We show that the F2layer layer halfthickness is the parameter varying in antiphase with NmF2. A quantitative picture of the physical processes responsible for the observed results is presented. 2. EQUIPMENT AND OBSERVATIONS Nighttime observations of TIDs in the ionospheric F2 layer have been performed at the Institute of Iono sphere (Almaty, 76°55 E, 43°15 N) since 1997 using a digital ionosonde combined with a “Pentium166” computer, which is used to gather, store, and process ionograms in the digital form. Information needed to

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fF, MHz 9

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8

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6 fxF

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Fig. 1. Variations in (a) the critical frequencies and (b) vir tual reflection heights at the series of sounding frequencies.

calculate various TID parameters is taken from the ionograms using a semiautomatic method. The iono spheric sounding is conducted at an interval of 5 min. The length of the measurement session changes with season and is ~8–12 h, the middle of the session coin ciding with local midnight. The values of the virtual reflection heights h'(t) of the radio signal at a series of fixed working sounding frequencies and values of the critical frequencies (foF2) are taken from ionograms. The further processing makes it possible to obtain the vertical distributions of the electron density (N(h) pro files). The ionosonde provides the accuracy of the

reading h'(t) and foF2 of approximately 2.5 km and 0.05 MHz, respectively. The choice of the nighttime for TID observations using the ionosonde was caused by at least two factors. First, nighttime TIDs are usual events observed during approximately 70% of nights [Aushev et al., 2002]. Second, largescale TIDs with large amplitudes of variations in ionospheric parame ters, substantially exceeding the accuracy of the h'(t) and foF2 reading from ionograms, are observed at midlatitudes mainly at night [Hajkowicz, 1990; Yako vets et al., 1995]. Substantial part of the obtained experimental time series was characterized by quasiperiodic variations in the ionospheric parameters; in this case the varia tion spectrum usually contained several peaks. It is more convenient to study the phase relations between the variations in various ionospheric parameters by choosing for the analysis the data of TID observations with one dominating spectral component. In particu lar, the variations registered at night on July 24–25, 2004, satisfy this condition. Figure 1 shows the varia tions in (a) the critical frequencies of the ordinary and extraordinary components (foF2 and fxF2) and (b) h'(t) for the extraordinary component at the series of sounding frequencies shown near the corresponding curves. Quasiperiodic TIDs shown in Fig. 1 can be related to the large geomagnetic storm with a sudden commencement on July 24, 2004, at 0600 UT. The storm was initiated by the arrival to the Earth’s mag netosphere of coronal mass ejections, registered on July 22, 2004, by the SOHO spacecraft after the series of Xray solar flares observed on July 22, 2004, between 0633 and 0808 UT. The maximum values of the Dst and Kp indices during July 24–25, 2004, were –150 nT and 8, respectively. It follows from Fig. 1 that the critical frequencies show quasiperiodic variations with a period of ~140 min against a background of their gradual decrease (caused by the usual diurnal behavior of the electron density in the maximum of the F2 layer). Clearly defined variations with the same period are also observed in the behavior of h'(t). It is evident that only the lower variation in the series of the h'(t) varia tions shown in Fig. 1 is present during the entire 11h observation session. Due to the changes in the critical frequency of the layer during the night, higher working frequencies were sometimes exceed the critical fre quency of the layer, and the reflections at these fre quencies disappeared. The h'(t) records presented in Fig. 1 contain features typical for the majority of the measurement sessions in which quasiperiodic varia tions in ionospheric parameters were observed. We now consider these features. The amplitude of the h'(t) variations increases with increasing sounding fre quency and, consequently, radio signal reflection height. Figure 1 also shows that the variations in h'(t) at lower heights delay relative to the variations at higher frequencies. Two conclusions follow. First, the h'(t) variations at fixed frequencies occur as a result of

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RESPONSE OF THE NIGHTTIME MIDLATITUDE IONOSPHERE

propagation of waves; second, these waves are internal gravity waves, which are characterized by opposite directions of the group and phase velocities in the ver tical plane [Hines, 1960]. It is known that the energy of AGWs is transported into the thermosphere from the lower ionospheric layers; therefore, the AGW phase front should move downward, which is observed in Fig. 1. Further processing included obtaining profiles from the N(h) ionograms using the [Titheridge, 1985] method and obtaining variations in the F2layer parameters from the profiles. Figure 2 shows the smoothed variations in the ionospheric electron con tent (N(t) for the night in question at a series of heights with the distance between the adjacent heights of 10 km. The lower curve corresponds to the height of the layer bottom (h = 190 km). The top (thick) curve corresponds to the variations in N(t) at the layer max imum at hmF2. To evaluate the HF components of the ionospheric origin and caused by noise that appears during data processing, LF filtering of the series was performed, using a running “window” of T = 30 min. The records of N(t) variations presented in Fig. 2 con tain features typical of the majority of the measure ment sessions, during which quasiperiodic variations in ionospheric parameters were observed. In the same way as the variations in the virtual heights, variations in N(t) at lower heights delay relative to the variations at higher altitudes. The mean vertical phase velocity of the wave calculated from the expression V = ∆h/τ (where ∆h is the mean over the session halfwidth of the layer and τ is the mean over the session delay in the N(t) variations in the bottom of the layer relative to the variations within the layer maximum) was found equal to 220 m/s. The average vertical wavelength for such a velocity is λz = VT = 1850 km, where T is the wave period. For the two wave periods taking place within the time interval from ~2330 to 0430 LT, one can determine the height (h = 290 km) corresponding to the maximum absolute amplitude. During the first two periods of the wave (t ~ 1930–2330 LT) the layer max imum was located near this height; therefore, it was impossible to identify this height. The sharp decrease in the amplitude of N(t) variations within the layer maximum (the thick curve) attracts attention as com pared to the amplitude variations at the fixed height

N, m−3 8 × 1011

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6 × 1011

4 × 1011

hmF

2 × 1011

300 km 250 km 200 km

0 × 100 1800 2000 2200 0000 0200 0400 0600 0800 LT, h Fig. 2. Variations in the ionospheric electron density at the series of fixed heights with the distance between the adja cent heights of 10 km and at the F2layer maximum.

nearest to the maximum. The cause of this event will be discussed below. Table 1 shows the calculated values of the absolute (AN) and relative (AN/N0) amplitudes of the wave for the height h = 290 km, corresponding to the height at which the maximum absolute amplitude is observed, and the values of the amplitudes at the layer maximum at sequent time moments corresponding to the wave peaks. The AN values were estimated after the elimina tion of significant time trends, caused by the diurnal variations in the electron density, from the N(t) varia tions. Polynomial filtering with the help of the second degree polynomial was used to eliminate the trend. At the end of night, the absolute wave amplitude at a height of 290 km and at the layer maximum decreases by approximately factors of 5 and 4, respectively. At the same time, the relative amplitude decreases only by a factor of 1.5. The main cause of the substantial decrease in the absolute amplitude is the diurnal behavior of the background ionization of the iono

Table 1. Absolute and relative amplitudes of variations in N(t) at the layer maximum and at a height of 290 km, correspond ing to the maximum absolute amplitude, and the background values of the electron density N0 at the same heights tmax, LT

AN × 1011, m−3 (h = 290 km)

AN/N0, % (h = 290 km)

AN × 1011, m−3 (hmaxF)

AN/N0, % (hmaxF)

N0 × 1011, m−3 (h = 290 km)

N0 × 1011, m−3 (hmaxF)

2000 2220 0040 0255

2.45 1.7 0.95 0.5

65 68 56 41

0.94 0.56 0.28 0.25

18 14 9.6 10.8

3.8 2.5 1.7 1.3

5.3 4.0 2.9 1.95


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Fig. 3. Variations in foF2 and hmF2 presented in the form of a hodograph. The adjacent points are separated by the 30min interval and arrows show the direction of the pro cess.

sphere, as a result of which the background ionization decreased by a factor of 3 during the night. It is conve nient to analyze the phase relations between the varia tions in the critical frequency of the layer (foF2) and the layer maximum height (hmF2) using the presenta tion of the variations in the hodograph form (Figs. 3a, 3b). Points marked by the sequence of numerals with the distance between the adjacent points equal to 30 min are shown in the hodograph. Points 1 and 22 correspond to the beginning of the session and to its end, respectively. The arrows show the direction of the course of time. The hodograph shown in Fig. 3a is cre

ated on the basis of the initial series of hmF2 and foF2. It presents the result of a superposition of quasiperi odic variations and the trend of the analyzed parame ters. It is rather difficult to obtain phase relations between the variations in hmF2 and foF2 from this rep resentation; therefore, we withdrew the trend from the time series of foF2, leaving unchanged the series of hmF2 which contained insignificant trend. This trend was left because, on one hand, it did not mask phase relations between the parameters and, on the other hand, shifting insignificantly in height the sequent ellipses, simplified the perception of the general pic ture. The hodograph presented in Fig. 3b demon strates the elliptical trajectories with the clockwise polarization. The eccentricity of the ellipses and the inclination of the main axis are determined based on the phase delay between the variations in foF2 and hmF2 and on the relation between their amplitudes. Although all cycles presented in the hodograph dem onstrate a tendency toward a decrease in foF2 with increasing hmF2, the phase difference between the variations is not exactly equal to π. Considering, e.g., the time interval between points 3 and 5, we see that after time moment 4, foF2 not reaching the minimum value, begins to grow, whereas the increase in hmF2 still continues. From this it follows that the maximum in hmF2 lags behind the minimum in foF2 in phase. This is true also for the behavior of the minimum in hmF2 relative to the maximum of foF2. In order to explain this effect and find parameter with which foF2 oscillates exactly in antiphase, we calculated the behavior of some additional parameters of the iono spheric layer. Figure 4 shows variations in the layer maximum height (hmF2), the layer bottom height (hbotF2), value of the layer halfthickness (∆hF = hmF – hbotF), and the critical frequency (foF2). The layer bottom corresponded to the height with the electron density value at the level of 0.3 NmF2. Figure 4 shows that the variations in hmF2, hbotF2, and ∆hF2 are very similar; however, there exist phase shifts between them. Variations in hbotF2 go behind the variations in hmF2. This fact is explained by the inclination of the phase front of AGWs leading to phase delays of the wave at lower altitudes relative to higher altitudes. In order to find the phase of the variations in the layer halfthickness, we present the variations in hm(t) and hbot(t) in the form: hm(t) = hm0 + Amsin(ωt – ϕ1) and hbot(t) = hbo + Abot sin(ωt – ϕ2), where hm0 and hbo are the average values of the heights of the maximum and layer bottom, respectively. Then the behavior of the layer halfthickness will be written in the form: ∆hF ( t ) = ∆h 0 + A ∆ sin ( ωt – ϕ 3 ),

(1)

where ∆h0 = hm0 – hb0 and A∆sin(ωt – ϕ3) = Amsin(ωt – ϕ1) – Abotsin(ωt – ϕ2). To find the phase relations between the variations in the considered parameters, it is convenient to represented these relations in the form of a vector diagram (Fig. 5) as radiusvectors with


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Fig. 4. Variations in the layer maximum height (hmF2), the height of the layer bottom (hbotF2), the layer halfthickness (∆hF = hmF – hbotF) and critical frequency (foF2) caused by the passage of AGW.

lengths equal to the corresponding amplitudes and with polar angles equal to the corresponding phases. The vectors rotate clockwise with an angular velocity ω. The projections of the vectors to the y axis are sinu soidal values. The diagram shows that the variations in phase in the layer maximum being ahead of the layer bottom lead to the fact that the layer halfthickness is ahead of the variations in the layer maximum, this fact being observed in the experiment (Fig. 4). Figure 4 also shows that the maximums and minimums of foF(t) are the most close in time to minimums and maximums in ∆hF(t), respectively. The vector diagram also shows that the difference in phases between the variations in the height of maximum and the height of the layer bottom determines not only the value of the phase advance of the variations in the layer halfthick ness but also the value of its variations amplitude. To quantitatively determine the phase relations between the variations in parameters shown in Fig. 4, we applied the Blackman–Tukey crossspectral analy sis [Jenkins and Watts, 1966] to the corresponding pairs of the time series. In order to exclude the effects related to the sunset, we terminated the series at t = 0400 LT. Before calculations, we used the polynomial filter in order to eliminate the trend from the foF(t) variations, and the filtered series was multiplied by (– 1) in order to exclude π from the phase difference. GEOMAGNETISM AND AERONOMY

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Thus, the phase and time delays between foF(t) and ∆hF(t) shown in Table 2 present the delay between the minimum of one series and the maximum of the other series. Table 2 contains the variation period, mutual coherency of the corresponding series, phase differ ence between them, and the corresponding time delay. y

ωt Abot

ϕ2 0

ϕ1 ϕ3

Am

A∆ x

Fig. 5. Vector diagram of the variations in the layer maxi mum height, the height of the layer bottom, and the value of the layer halfthickness. 2008

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Table 2. Time and phase delays between variations in vari ous TID parameters Parameters Period, h Coherency Delay, min hm−hbot ∆h−hm ∆h−hbot foF−∆h

2.31 2.31 2.25 2.31

0.81 0.69 0.56 0.73

5.83 11.97 19.58 1.27

∆ϕ, deg 16.2 33.1 54.2 3.5

Table 2 shows that the variations in foF(t) and ∆h(t) occur almost in antiphase. Insignificant deviation from the antiphase character (3.5°) can be explained by the statistical scatter of the calculation estimates caused by nonabsolute mutual coherency of the series. We note the substantial phase delay between ∆hF(t) and hm(t) equal to the delay between the max imums in foF(t) and minimums in hm(t). It follows from Fig. 5 that the phase relations between the con sidered parameters are determined only by the incli nation of the wave phase front. If the front is vertical (i.e., the variations in hm(t) and hbot(t) go in phase), the variations in ∆hF(t) are in phase with them, whereas the variations in foF(t) occur in antiphase with the variations in all three height parameters. 3. DISCUSSION Physical processes, which proceed in the iono sphere at the propagation of AGWs and are responsible for the behavior of the F2 layer, were studied using the Millward et al. [1993] model. When AGW generated in the polar region reaches midlatitudes, it has a wave length exceeding 2000 km. For such a wave, the motion of the neutral gas at heights of the F region pre sents a horizontal wind blowing southward along the meridian during the passage of the positive halfwave over the observation point and northward during the passage of the negative halfwave over this point. Since the ionospheric F region presents a weakly ionized plasma, it is involved into the motion due to the colli sions of neutrals with ions. The plasma in the F region is magnetized and, therefore, can move only along the magnetic flux tubes. The velocity of this motion is gov erned by the neutral wind component directed along the magnetic field. The neutral wind induced in sequence by the positive and negative halfwaves causes plasma to move along the magnetic field lines upward and downward, respectively, leading to period ical variations in the F2layer maximum height. Based on the character of the variations in the main parameters of the ionospheric F2 layer shown in Figs. 2 and 4, we can describe the qualitative picture of the electron density behavior in the F2 layer during the passage of AGW with a vertical phase front. The fact that the TID amplitude increases with height is a com mon characteristic of TID. Therefore, the value of the

horizontal velocity of the transport of neutral particles in AGW causing TID increases with height. We con sider the neutral halfwave in which particles move southward along the meridian. The motion of neutral particles causes charged particles to move upward along geomagnetic field lines to higher altitudes. And, as far as the wave amplitude is larger at higher alti tudes, the ionized plasma located there will move upward over larger distance as compared to the plasma that was initially located at a lower height. Therefore, an increase in the layer thickness and decrease in the ionization density in the layer maximum will finally be observed. The next AGW halfwave with the particles moving northwards, will lead to an opposite picture: F2 layer begins to move downward to lower heights. Its thickness will decrease, whereas the value of the ion ization density in the layer maximum will increase. The deviation of the phase front of the wave from the vertical, usually observed experimentally, does not substantially change the presented picture. This devi ation leads to an appearance of phase shifts between variations in various parameters of the layer; in this case the variations in the layer halfthickness lead the variations in the heights of the layer maximum and bottom. That is how the process of periodical redistri bution of the ionospheric plasma along the changing halfthickness of the layer proceeds if the integral con tent of the ionosphere remains below the layer maxi mum during the period of wave propagation (this con tent is close to a constant value if the changes related to the diurnal behavior are not taken into account). Note that the influence of the height gradients of the horizontal velocity of neutrals on the deformation of the F2 layer was, apparently, for the first time shown by Smertin and Namgaladze [1982], who numerically solved the continuity equation for the atomic oxygen ions and demonstrated the difference in the response of the ionosphere to propagation of AGW under the daytime and nighttime conditions. When we discussed Fig. 2, we have noted that the amplitude of the electron density at the layer maxi mum is substantially less than the amplitude of varia tions at the fixed height the closest to the maximum. The cause of this event consists in the difference in physical mechanisms determining the amplitude val ues. The amplitude of variations in N(t) at a fixed height is determined by the mean value and vertical gradient of the electron density at this height, whereas the amplitude at the layer maximum (the height of which does not stay constant but undergoes periodical variations) is determined by the amplitude of varia tions in the layer halfthickness, which, in turn, is gov erned by the vertical gradient of the AGW amplitude. Smertin and Namgaladze [1982] noted that the ampli tude of the variations in the critical frequency becomes equal to zero in the extreme case in the absence of the vertical gradient of the amplitude, when the F2 layer varies in height not changing its shape.


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The most important results obtained in the paper can be formulated as follows:

6. C. H. Fesen, G. Crowley, and R. G. Robley, “Iono spheric Effects at Low Latitudes during the March 22, 1979 Geomagnetic Storm,” J. Geophys. Res. 94, 5405–5417 (1989).

1. We demonstrated that all parameters of the nighttime F2 layer, obtained from the data of the iono spheric vertical sounding, undergo quasiperiodic variations initiated by the passage of largescale AGW generated by the large magnetic storm.

7. T. J. L. FullerRowell, D. Rees, S. Quegan, et al., “Interactions between Neutral Thermospheric Com position and the Polar Ionosphere Using a Coupled Ionosphere–Thermosphere Model,” J. Geophys. Res. 92, 7744–7775 (1987).

2. The value of the phase delays between the varia tions in the electron density at the F2layer maximum (NmF2), the layer maximum height (hmF2), and the layer halfthickness are determined by the inclination of the wave phase front.

8. L. A. Hajkowicz, “Global Study of Large Scale Travel ling Ionospheric Disturbances (TIDs) Following a StepLike Onset of Auroral Substorm in Both Hemi spheres,” Planet. Space Sci. 38, 913–923 (1990).

3. We indicated that the critical frequency of the layer or NmF2 varies in antiphase with the variations in the F2layer halfthickness. This result contradicts the existing ideas of the antiphase variations in the critical frequency and layer maximum height.

9. C. O. Hines, “Internal Atmospheric Gravity Waves at Ionospheric Heights,” Can. J. Phys. 38, 1441–1481 (1960). 10. K. Hocke and K. Schlegel, “A Review of Atmospheric Gravity Waves and Travelling Ionospheric Distur bances: 1982–1995,” Ann. Geophys. 14, 917–940 (1996). 11. R. D. Hunsucker, “Atmospheric Gravity Waves Gener ated in the HighLatitude Ionosphere: A Review,” Rev. Geophys. 20, 293–315 (1982).

ACKNOWLEDGMENTS The paper was performed within the scope of the Research Work supported by the Program of Funda mental Studies (F.03512) (The State Contract No. 8 of March 2, 2006). REFERENCES 1. E. L. Afraimovich, K. S. Palamarchouk, and N. P. Pere valova, “GPS Radio Interferometry of Traveling Iono spheric Disturbances,” J. Atmos. Sol.–Terr. Phys. 60, 1205–1223 (1998). 2. Y. A. Ashkaliev, G. I. Gordienko, Ch. Jacobi, et al., “Comparison of Travelling Ionospheric Disturbance Measurements with Thermosphere/Ionosphere Model Results,” Ann. Geophys. 21, 1031–1037 (2003).

12. G. Kirchengast, “Elucidation of the Physics of the Gravity Wave TID Relationship with the Aid of Theo retical Simulations,” J. Geophys. Res. 101, 13353– 13368 (1996). 13. G. H. Millward, R. J. Moffet, S. Quegan, and T. J. FullerRowell, “Effect of an Atmospheric Gravity Wave on the Midlatitude Ionospheric F Layer,” J. Geo phys. Res. 98, 19 173–19 179 (1993). 14. V. M. Smertin and A. A. Namgaladze, “On Different Ionospheric Responses to the Effect of Internal Graviry Waves under Day and Nighttime Conditions,” Izv. Vyssh. Uchebn. Zaved., 25, 577–579 (1982). 15. J. E. Titheridge, Ionogram Analysis with the Generalized Program (Polan. Nat. Geophys. Data Center, Boulder, 1985).

3. V. M. Aushev, Ya. F. Ashkaliev, R. H. Wiens, et al., “Spectrum of Atmospheric Gravity Waves in the Meso sphere and Thermosphere,” Geomagn. Aeron. 42 (4), 560–568 (2002) [Geomagn. Aeron. 42, 533–541 (2002)].

16. P. J. S. Williams, “Tides, Atmospheric Gravity Waves and Traveling Disturbances in the Ionosphere,” in Modern Ionospheric Science (EGS, KatlenburgLinday, 1996), pp. 136–180.

4. R. J. Balthazor and R. J. Moffet, “A Study of Atmo spheric Gravity Waves and Travelling Ionospheric Dis turbances at Equatorial Latitudes,” Ann. Geophys. 15, 1048–1056 (1997).

17. A. F. Yakovets, V. I. Drobjev, and Yu. G. Litvinov, “The Spatial Coherence of Travelling Ionospheric Distur bances at MidLatitudes,” J. Atmos. Terr. Phys. 57, 25–33 (1995).

5. G. Jenkins and D. Watts, Spectral Analysis and Its Appli cations (HoldenDay, San Francisco, 1966; Mir, Mos cow, 1972) [in Russian].

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