Height and critical frequency variations of the sporadic-E layer at midlatitudes

ARTICLE IN PRESS Journal of Atmospheric and Solar-Terrestrial Physics 70 (2008) 1904– 1910

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Height and critical frequency variations of the sporadic-E layer at midlatitudes P. Sˇauli a,, A. Bourdillon b a b

Department of Aeronomy, Institute of Atmospheric Physics, ASCR, Bocni II/1401, 14131 Praha 4, Czech Republic IETR - Universite´ de Rennes 1, UMR CNRS 6164, Campus de Beaulieu, 35042 Rennes, France

a r t i c l e i n f o

abstract

Article history: Accepted 23 March 2008 Available online 16 April 2008

The present study concerns variations in height and critical frequency of sporadic E layer over a wide period range of hours to several days, covering tidal and planetary oscillation domain. Besides periodicities in the tidal and planetary range that are known to occur within time series of critical frequencies (foEs) of sporadic-E layer [Pancheva, D., Haldoupis, C., Meek, C.E., Manson, A.H., Mitchell, N.J., 2003. Evidence of a role for modulated atmospheric tides in the dependence of sporadic E layers on planetary waves. Journal of Geophysical Research 108, Art. No. 1176; Haldoupis, C., Pancheva, D., Michell, N.J., 2004. A study of tidal and planetary wave periodicities present in midlatitude sporadic E layers. Journal of Geophysical Research 109, Art. No. A02302] among others, we evidence the existence of the 4-day planetary wave well developed in the height of sporadic E time serie (hEs). Moreover it is shown that the central-period of the diurnal tidal component of hEs is not exactly 24 h but it varies between 22 and 26 h at the planetary wave period. At a first glance, this is surprising since the origin of the diurnal tide is a forced oscillation with a 24 h period due to the Earth rotation and the periodic heating of the atmosphere by the Sun. Our interpretation is based on the perturbation of the height of the Es layer imposed by the planetary wave. In this mechanism the Es layer is moved up and down by the planetary wave producing a Doppler effect and resulting in a shift of the central-period around 24 h. With this interpretation, the excursion of the central-period is related to the vertical velocity perturbation of the Es layer due to the planetary wave. For a central period varying between 22 and 26 h the peturbation velocities are 0.026 and 0:022 m=s, respectively. & 2008 Elsevier Ltd. All rights reserved.

Keywords: Sporadic E Planetary waves Tidal waves Mid-latitude ionosphere Wavelet transform

1. Introduction The sporadic E layers are thin layers of plasma forming mostly in the altitude range 90–130 km. Es characteristics have been studied over many years (e.g. see review by Whitehead (1989)). It is believed that vertical wind shears in the neutral velocity play a major role in the formation of Es layers thus these layers are controlled by the complex neutral dynamics in the mesosphere and lower

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E-mail addresses: [email protected] (P. Sˇauli), [email protected] (A. Bourdillon). 1364-6826/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2008.03.016

thermosphere. Our analysis concerns variations in height and critical frequency of sporadic E layer over a wide period range of hours to several days, covering range of tidal and planetary oscillation domain. The importance of meteorological influences on the overall ionospheric variability has been reported by Forbes et al. (2000). Work (Lasˇtovicˇka, 2006) reviewed effects of atmospheric waves (planetary, tidal, acoustic-gravity and infrasonic) on the ionosphere. Propagation conditions of planetary-scale disturbances from the lower atmosphere into the upper atmosphere has been analyzed in detail in the paper (Charney and Drazin, 1961). In this paper we show the variability in tidal and planetary oscillations within time series of height of sporadic E (hEs) and corresponding

ARTICLE IN PRESS P. Sˇauli, A. Bourdillon / Journal of Atmospheric and Solar-Terrestrial Physics 70 (2008) 1904–1910

critical frequency (foEs) measured during summer campaign 27 July–1 September 2004 by Digital Portable Sounder (DPS4) with a 5 min repetition time at midlatitude station Pruhonice. The aim of the present work is to study dynamic processes and links between the data series describing processes in the ionospheric plasma at heights of E layer. Besides periodicities in the tidal and planetary range that are known to occur within time series of critical frequencies of sporadic-E layer (Pancheva et al., 2003; Haldoupis et al., 2004) among others, we evidence the existence of the 4-day planetary wave (PW) well developed in the time series of hEs and foEs. Moreover it is shown that the central-period of the diurnal tidal component of hEs is not exactly 24 h but it oscillates between 22 and 26 h. At a first glance, this is surprising since the origin of the diurnal tide is a forced oscillation with a 24 h period due to the Earth rotation and the periodic heating of the atmosphere by the Sun. Nonlinear interactions between tidal waves and planetary waves are known to exist in the lower atmosphere (Teitelbaum and Vial, 1991). Nonlinearities result in amplitude modulation of the wave thus they cannot be invoked to interpret oscillation in the period of the diurnal component. To explain the variations of the period the diurnal component we propose that the height of the Es layer is slightly perturbed by the planetary wave. In this mechanism the Es layer is moved up and down at the planetary wave frequency producing a Doppler shift and a variation of the central-period around 24 h. With this interpretation, the excursion of the central-period is related to the vertical velocity perturbation of the Es layer due to the planetary wave. For a central period varying between 22 and 26 h the perturbation velocities are 0.026 and0:022 m=s, respectively. 1.1. Sporadic-E layer formation The sporadic E behavior was reviewed in the paper (Whitehead, 1989) and more recently (Mathews, 1998). In the E region, vertical plasma transport is caused by the neutral particle motion (wind systems—zonal and meridional components) with respect to the present magnetic field V n  B. The wind shear theory, proposed by Whitehead (1989) and his earlier works, shows, that vertical wind shears with proper polarity can cause, by the combined action of ion–neutral collisional coupling and geomagnetic Lorentz forcing, the long-lived metallic ions to move vertically and converge into dense plasma layers. Further studies of Mathews (1998) shows that behavior of the midlatitude sporadic E layer can be sufficiently explained using modified wind shear theory, that includes small electric field: 0 ¼ eðvi  B þ EÞ  Mnðvi  V n Þ

(1)

w ¼ ðU cos I sin I þ rV cos IÞ=ð1 þ r 2 Þ

(2)

r ¼ n=o

(3)

Here, E is electric field, vi ¼ ðu; v; wÞ is ion velocity, V n ¼ ðU; V; OÞ is neutral velocity, B ¼ Bo ðcos I; 0; sin IÞ is magnetic field vector, I stands for magnetic field inclination, r is

1905

ratio of ion–neutral collision frequency Z and ion gyrofrequency o. Vector components of vi , V n and B are in southward, eastward and vertical directions. In general, vertical winds are neglected since they are not contributing significantly to the vertical plasma transport. Below 125 km the parameter r 2 b1, collisions between ions and neutrals are very frequent, vertical plasma drift is collision-dominated and plasma motion is controlled mainly by the zonal wind (Eq. (2)), with a downward (upward) drift caused by a westward (eastward) wind. The plasma convergence is most effective in the presence of a vertical wind shear with a westward wind above and an eastward, or smaller westward, wind below. In the heights above 130 km, the parameter ro1 (Eq. (3)) as collisions decreases and plasma is controlled by the magnetic field. The meridional component in Eq. (2) is dominant component of the vertical plasma transport. In the upper E region (Northern Hemisphere), the significant convergence of the plasma occurs in the presence of meridional wind shear, that means northward wind above and southward, or smaller northward, wind below. Various processes in the lower-lying layers of the atmosphere, particularly in the troposphere, can affect the ionosphere basically through two channels: (i) electrical and electromagnetic phenomena, and (ii) upward propagating waves in the neutral atmosphere.

1.2. Tidal and planetary wave modulation Various tropospheric, stratospheric and mesospheric processes and periodic solar heating and cooling excite waves in the neutral atmosphere. Upward propagating waves in the neutral atmosphere and their modifications, interactions and modulations affect the ionosphere, when and if they reach it. Those waves are planetary waves, tidal waves, gravity waves, and infrasonic waves. Paper (Kazimirovsky et al., 2003) reviews impacts of the upward propagating gravity, tidal and planetary waves on the ionosphere. Atmospheric tidal waves are global oscillations of the neutral atmosphere at periods which are subharmonics of a solar or lunar day, either eastward or westward propagating. The largest components are westward propagating with the apparent motion of the sun or moon. The characteristic oscillation periods are 6, 8, 12, 24 h. Solar tides (thermal tides) in the atmosphere are excited by the periodic heating of the neutral atmosphere due to Earth rotation (Forbes, 1994, and references therein). The diurnal and semidiurnal tides are known to be important in the process of midlatitude sporadic E formation due to their vertical wind shear forcing of the long-living metallic ions in the lower thermosphere (Whitehead, 1989; Mathews, 1998). Paper (Haldoupis et al., 2004) reports diurnal and semidiurnal tidal modulation of the sporadic E layer critical frequency foEs. In the spectrum of foEs, they found as well weaker terdiurnal oscillation. The tidal oscillation in foEs undergo a strong amplitude modulation with periods comparable to the dominant planetary wave periodicities present in the data. Planetary waves (periods of about 2–30 days) are very predominantly of tropospheric origin and can

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penetrate directly to heights slightly above 100 km. Typical planetary wave periods are broad spectral peaks around 2, 5, 10 and 16 days (very broad spectral peak), but the planetary wave spectrum is very variable and on individual days it can be much different. They roughly correspond to eigenfrequencies of the atmosphere, which slightly differ for various modes attaining values of 1.2, 5, 8 and 12 days (these periods are Doppler shifted by the prevailing wind). All planetary wave periods are quasiperiods with the exact period varying within a period range. Amplitudes of planetary waves are unstable, as well; planetary waves typically occur in bursts of a couple of waves (Forbes, 1994). The planetary wave type oscillations have been observed in the lower and middle atmosphere but also in the ionosphere, including the ionospheric F2 layer. Periodic oscillation corresponding to planetary wave period range were observed in the lower ionosphere (Lasˇtovicˇka et al., 1994; Kingsley et al., 1978; Salby and Roper, 1980), in the ionospheric E region in h’E variability (Cavalieri, 1976), sporadic-E layer critical frequency (Pancheva et al., 2003; Haldoupis et al., 2004, 2006), in sporadic-E radar backscatter (Tsunoda et al., 1998; Voiculescu and Haldoupis, 1999) and also in the F region (Lasˇtovicˇka et al., 2006, 2003) among others. Influence of planetary waves on the state of ionosphere in the height of E layer is of particular importance for our paper. As suggested by Tsunoda et al. (1998) and further (Pancheva et al., 2003) planetary waves may play important role in the formation of sporadic E layer. The work of Tsunoda et al. (1998) reports quasi-periodic radar echoes from midlatitude sporadic E varying sinusoidally with period of 5 days. They proposed the planetary wave modulation based on presence of such oscillation in the neutral wind measurements. Further they proposed that the occurrence of the quasiperiodic echoes was affected by a contribution of the wind to the dynamo electric field and by direction of the neutral wind. Work (Pancheva et al., 2003) reports simultaneous occurrence of the 7-day oscillation within data series of foEs measured at 8 midlatitude ionosonde stations and the 7 days period of westward propagating planetary wave in the mesosphere-lower thermosphere. This work proposes the indirect influence of planetary waves through the action of the diurnal and semidiurnal tides strongly modulated by the same planetary waves, via nonlinear interaction process at altitudes below 100 km. Occurrence of planetary wave oscillation with periods 2, 5, 10 and 16 days are reported in the paper (Haldoupis et al., 2004).

1.3. Non-linear wave-wave interaction—review Upward propagating tides and planetary waves seen in the neutral atmosphere are coupled into the ionosphere via modification of the turbulent mixing, changes of E region conductivity, modulation of temperature and wind structure in the thermosphere, and generation of the electric fields. Atmospheric waves further interacts that results in wave modulation (Teitelbaum and Vial, 1991). The interaction of tidal and planetary waves has been studied on the wind data in mesosphere and lower-

thermosphere (Beard et al., 1999; Pancheva et al., 2000). The observed amplitude modulation of the tidal oscillation is explained in terms of nonlinear coupling of the tidal wave motion with the simultaneously observed planetary waves. The suggested mechanism of nonlinear interaction of primary waves generates secondary waves that beat with the tide and modulate the tide amplitude with a period equal to that of the planetary wave. The planetary waves are not necessary to be present at the studied region since their nonlinear interaction may occurs in the lower atmospheric regions (Beard et al., 1999). In the paper (Haldoupis et al., 2004) authors suggest possibility of the ionospheric measurements of sporadic E layer for study of planetary and tidal wave characteristics and their climatology in the lower thermosphere. Nonlinear interaction leads to the phase relationship known as quadratic coupling and as a result the amplitude of the wind is modulated (like in AM radio systems) and sidebands appear in the spectrum. With nonlinear interactions there is no way to explain the modulation of the central-period of the 24 h diurnal tide we observed in hEs time series. Our interpretation introduces a Doppler shift produced by a perturbation in the vertical velocity of the Es layer.

2. Campaign: parameters—measurements and data 2.1. Es Campaign 2004 The campaign of the rapid sounding observation of the occurrence of the sporadic-E layer was conducted at Pruhonice observatory (Czech republic, 49.9N, 14.5E). Data were collected via a standard vertical incidence ionospheric sounding campaign using Digital Portable Sounder with four receiving antennas (DPS4). The measurement was run during summer when the probability of SporadicE occurrence is very high, in the period from 27 July till 1 September 2004. The period is characterized by low geomagnetic activity. Only the first day on 27 July, the Kp index reached maximum value of 8, and it was the last day of the disturbance. During following days of campaign, the geomagnetic activity was low and only occasionally the Kp index reached value of 4, almost at the end of the campaign. The ionograms were measured with short repetition time of 5 min with standard resolution and then scaled manually to avoid possible errors due to automatic scaling. The DPS4 measurement allows us to precisely determine the angle of arrival and polarization of the wave in the receiver, therefore in the analysis only the vertically reflected ordinary trace is taken into account. The quality of the data is very high, however three gaps occurred due to technical problems in the sounder. Since the sporadic E is not permanently present in the ionosphere short periods of the absence of the Es layer occurred in the time series. However, since all the signal processing tools require equal data spacing, the gaps were filled as follows. From all the campaigns data, the mean and median values for the each daytime were computed and then used to replace the missing measurements. The same approach has been used for both critical

ARTICLE IN PRESS P. Sˇauli, A. Bourdillon / Journal of Atmospheric and Solar-Terrestrial Physics 70 (2008) 1904–1910

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Diurnal variation of Es height

Diurnal variation of Es critical frequency 10

190

9

180 170

8

160 Height (km)

7 6 5 4

150 140 130 120

3

110

2

100 90

1 0

4

8

12 Time (h)

16

20

0

24

4

8

12 Time (h)

16

20

24

Fig. 1. Diurnal variations critical frequency foEs and corresponding height hmEs. Left and right panel, respectively.

frequency and height of sporadic E layer. Fig. 1 shows the diurnal variation of foEs and hmEs together with their mean and median values. The variability in the data is represented by the dispersion of the data around the mean and median values.

The analyzed time series consist of the fluctuations of the critical frequency foEs and corresponding height hmEs of the sporadic E layer derived from ionograms or filled by the mean value of the particular time. The data under analysis are represented by Xðt; zÞ;

t 2 ½T 1 ; T 2 

(4)

Here, we have z ¼ ffoEs; hmEsg, T 1 ¼ 27 July; 00h00, T 2 ¼ 1 September; 23h55 UT and the time sampling period is T s ¼ 5 min. 3. Wavelet based analysis 3.1. Scalograms Fig. 2 presents scalograms (also called wavelet power spectra), i.e., plots of jT X ðo; t; zÞj with respects to time t and period P ¼ 2p=o ¼ 2pa=o0 . For a thorough introduction to wavelet transforms, the reader is referred e.g., to Mallat (1998). Because we choose to use complex motherwavelet wavelets (Morlet), the coefficients T X ðo; t; zÞ are complex numbers and fjT X ðo; t; zÞj; fðo; t; zÞg denote their modulus and phase. 3.2. Application of the continuous wavelet transform First, the continuous wavelet transform (CWT) has been blindly applied on the time series foEs and hmEs in the period ranges corresponding to gravity waves spectrum, tidal and planetary modes. Figs. 2 and 3 of the

5 10 Period (Hour)

2.2. Data

Pruhonice 27 July – 1 September

15 20 25 30 35 0

5

10

15

20

25

30

35

Time (Day) Fig. 2. Wavelet power spectrum of critical frequency foEs in the period range 1–35 h.

power spectra reveal the periodicity of the 12 and 24 h wave that has been reported and discussed in works of Haldoupis et al. (2004, 2006), Mathews (1998), Pancheva et al. (2003) and others. However, the modulation of the dominant periodicity 12 and 24 h is significantly different in the case of foEs and hmEs. As seen in Fig. 2 the oscillation with the dominant period around 12 h is attenuated between 12th and 25th day of the campaign. The modulation of foEs oscillation with period around 8 h has been reported by Pancheva et al. (2003). There is no such evidence of the period shift from 12 to 8 h in the wavelet power spectrum of hmEs as seen in Fig. 3. In addition, the period of 8 h seems to be completely missing in the wavelet power spectrum of the hmEs. Figs. 4 and 5 present wavelet power spectrum in the period range corresponding to planetary waves. The difference between the two spectra is very large. The most

ARTICLE IN PRESS P. Sˇauli, A. Bourdillon / Journal of Atmospheric and Solar-Terrestrial Physics 70 (2008) 1904–1910

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Pruhonice 27 July – 1 September

Pruhonice 27 July – 1 September 2

5

4 Period (Day)

Period (Hour)

10 15 20

6 8

25 10 30 12 35 0

5

10

15

20

25

30

35

0

5

10

Time (Day)

15

20

25

30

35

Time (Day)

Fig. 3. Wavelet power spectrum of height hmEs in the period range 1–35 h.

Fig. 5. Wavelet power spectrum of height hmEs in the period range 1–14 days.

Pruhonice 27 July – 1 September

Pruhonice 27 July – 1 September 20

2

21 22

4 Period (Hour)

Period (Day)

23 6 8

24 25 26 27

10 28 29

12

30 0

5

10

15

20

25

30

35

0

5

10

15

20

25

30

35

Time (Day)

Time (Day) Fig. 4. Wavelet power spectrum of critical frequency foEs in the period range 1–14 days.

Fig. 6. Wavelet power spectrum of height foEs in the period range 20–30 h. Blue line indicates position of the maximum.

pronounced oscillation within foEs has period 4 days and is located at the beginning of the campaign 27 July till 15 August in case of foEs and 10 August in case of hmEs. Fig. 4 shows well developed 7-day oscillation at the second half of the campaign in the time serie foEs which is completely missing in the wavelet power spectrum of the hmEs in Fig. 5. The presence of the 7-day oscillation in variation of foEs has been reported in extent by Pancheva et al. (2003). Figs. 6 and 7 present zooms performed on the scalograms in the interval 20–30 h for foEs and hmEs, respectively. The dotted lines indicate the position of the maximum power. In Fig. 7 the central period of the diurnal tide of hmEs is not exactly 24 h but it oscillates between 22 and 26 h with a quasi-period near 4–5 days. The time serie for foEs shows a weaker variation of the central-period between 23 and 25 h only between the 15th and the 30th day of the measurement campaign. Though in this example the behavior of the central-period of the diurnal tide for foEs and hmEs are similar, the Sporadic E layer

height is more sensitive to the 4–5 days planetary wave than the critical frequency. 4. Discussion Our midlatitude observations of the Sporadic E layer show the effects of tides and planetary waves on time series of foEs and hmEs. The dominant tidal periods in foEs scalogram are the terdiurnal mode at 8 h, the semidiurnal mode at 12 h and the diurnal mode at 24 h. The terdiurnal mode seems to be completely missing in the wavelet power spectrum of hmEs. The tidal modes are modulated in amplitude by long period planetary waves, as already observed by Pancheva et al. (2003). In the period range corresponding to planetary waves the most pronounced oscillation within foEs has period 4 days and is located at the beginning of the campaign 27 July till 15 August in case of foEs and 10 August in case of hmEs. Fig. 4 shows well developed 7-day oscillation during the second half of

ARTICLE IN PRESS P. Sˇauli, A. Bourdillon / Journal of Atmospheric and Solar-Terrestrial Physics 70 (2008) 1904–1910

now assume that in presence of a planetary wave the vertical velocity of the Es layer is affected by a small ~ The pulsation is now oi ¼ kðv þ wÞ. ~ Using perturbation w. the model described by Eq. (5) it is found that the period of the wave is then given by

Pruhonice 27 July – 1 September 20 21 22

Period (Hour)

23

~ T ¼ 24=ð1 þ 0:96wÞ

24

26 27 28 29 30 5

10

15

20

25

30

(6)

~ is expressed In Eq. (6), the perturbation of the velocity w ~ ¼ in km/h. In our observations, when T ¼ 22 h then w ~ ¼ 0:022 m=s. Using 0:026 m=s and when T ¼ 26 h then w ~ ¼ Eq. (2), a magnetic Dip angle I ¼ 60 , r ¼ 10 and w 0:026 m=s we deduce the amplitude of the eastward velocity of the planetary wave V ¼ 0:52 m=s. This estimate of the amplitude of the planetary wave is linearly dependent on r, the ratio of collision frequency to gyropulsation of ions, so it is dependent on the height of the Es layer. For heights greater than 130 km the northward velocity should be taken into account.

25

0

1909

35

Time (Day) Fig. 7. Wavelet power spectrum of height hmEs in the period range 20–30 h. Blue line indicates position of the maximum power.

5. Conclusion the campaign in the time serie foEs which is completely missing in the wavelet power spectrum of hmEs in Fig. 5. Oscillation in foEs due to the 7-day planetary wave have been reported by Pancheva et al. (2003). It seems that the influence of planetary waves on hmEs had not yet been considered in details for now. The diurnal tide is a forced oscillation due to the Earth rotation and to the periodic heating of the atmosphere by the Sun with a 24 h period. The oscillation of the centralperiod of the diurnal tide between 22 and 26 h observed in our hmEs time serie was thus unexpected and we will now discuss a possible mechanism able to produce a variation of the central-period. It is well established that the wind shear mechanism plays a major role in sporadic E layer formation (Whitehead, 1961, 1989). According to this theory the sporadic E layer is created by the vertical compression of metal ions in a shear of the horizontal wind (Wright et al., 1967). Wind shears are provided by tidal waves producing a descending layer. On a short time scale of a few hours, or less, the wind pattern is often modified by gravity waves that may interact with the tide (Nygre´n et al., 1990) but, here, we are mainly interested by interaction between tides and long period planetary waves. Harris and Taur (1972) have proposed a model of the prevailing wind and tides based on the analysis of rocket trails by Woodrum et al. (1969). In their model the diurnal component of the eastward velocity of the tide is given by V Tide ¼ 23 sinðð2pt=24Þ þ ð2pz=25Þ  fÞ

(5)

where the altitude is z ¼ ðheight  95Þ in km, the vertical wavelength is 25 km, t is the time in hour, the initial phase angle is f ¼ 151 and the velocity is in m/s. The phase angle is thus a function of time t and altitude z. In a frame moving downward at the vertical phase velocity of the tide, the sporadic E layer ‘‘sees’’ a constant phase value. On the ground, the pulsation of the Es layer characteristic parameters is given by oi ¼ kv, where k is the tidal wavevector and v is the vertical velocity of the Es layer. In this case the period is exactly equal to 24 h. We

In this paper the variability in tidal and planetary oscillations within time series of height of sporadic E (hEs) and corresponding critical frequency (foEs), measured during summer campaign 27 July–1 September 2004 by Digital Portable Sounder (DPS4) with a 5 min repetition time at midlatitude station Pruhonice, was studied using wavelet analysis. The dominant tidal periods in foEs scalogram are the terdiurnal mode at 8 h, the semidiurnal mode at 12 h and the diurnal mode at 24 h. The terdiurnal mode seems to be completely missing in the wavelet power spectrum of hmEs. The tidal modes are modulated in amplitude by long period planetary waves, as already reported in other studies. In the period range corresponding to planetary waves the most pronounced oscillation within foEs has period 4 days and is located at the beginning of the campaign 27 July till 15 August in case of foEs and 10 August in case of hmEs. This 4-day wave could be a Doppler shifted version of the well known 5day planetary wave. The data also shows a well developed 7-day oscillation at the second half of the campaign in the time serie foEs which is completely missing in the wavelet power spectrum of hmEs. An important finding of this study is that the centralperiod of the diurnal tidal component of hEs and foEs is not exactly 24 h but it oscillates between 22 and 26 h at the planetary wave period. At a first glance, this is surprising since the origin of the diurnal tide is a forced oscillation with a 24 h period due to the Earth rotation and to the periodic heating of the atmosphere by the Sun. To explain this observation we proposed that the height of the Es layer is slightly perturbed by the planetary wave. In this mechanism, the Es layer is moved up and down at the planetary wave frequency, producing a Doppler shift and a variation of the central-period around 24 h. The oscillation of the central-period is thus related to the perturbation of the vertical velocity. We estimated the perturbation velocity to vary between 0.026 m/s (T ¼ 22 h) and 0:022 m=s (T ¼ 26 h) and the eastward amplitude of the 4-day planetary to be 0.52 m/s.

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