Intradiurnal wind variations observed in the lower thermosphere over the South Pole

The first meteor radar measurements of meridional winds in the lower thermosphere (about 95 ± 5 km), along four azimuth directions: 0°, 90°E, 180° and 90°W; approximately 2° from the geographic South Pole were made during two observational campaigns: January 19, 1995-January 26, 1996, and November 21, 1996-January 27, 1997. Herein we report analyses of the measurement results, obtained during the first campaign, which cover the whole one-year period, with particular emphasis on the transient nature and seasonal behavior of the main parameters of the intradiurnal wind oscillations. To analyze the data, two complementary methods are used: the well-known periodogram (FFT) technique and the S-transform technique. The most characteristic periods of the intradiurnal oscillations are found to be rather uniformly spread between about 7 h and 12 h. All of these oscillations are westward-propagating with zonal wave number s = 1 and their usual duration is confined to several periods. During the austral winter season the oscillations with periods less than 12 h are the most intensive, while during summer season the 12-h oscillations dominate. Lamb waves and internal-gravity wave propagation, non-linear interaction of the short-period tides, excitation in situ of the short period waves may be considered as possible processes which are responsible for intradiurnal wind oscillations in the lower thermosphere over South Pole.


Introduction
Few papers exist which describe the speci®c features of the winds in the mesosphere/lower thermosphere (MLT) region in the vicinity of the rotational poles of the Earth. Among these are the pioneering works of Hernandez et al. (1992aHernandez et al. ( , b, 1993Hernandez et al. ( , 1995. Several dierent types of day-to-day and intra-diurnal (6±24 h) wind oscillations are discussed in these papers. The observational results in these works are based upon optical observations of winds and OH-emission rates near the mesopause and thus were limited in their ability to perform long-term continuous measurements, especially during periods of signi®cant sun and moon illumination of the sampling volume.
The installation of a meteor radar at the South Pole and its successful operation without interruption during two observational campaigns; January 19, 1995±January 26, 1996, and November 21, 1996±January 27, 1997, provided unique opportunities for investigation of a broad spectrum of waves in the wind ®eld in the lower thermosphere over the South Pole for dierent seasons (Forbes et al., 1995;Portnyagin et al., 1996;Portnyagin et al., 1997Portnyagin et al., , 1998Palo et al., 1998). In these papers the main features in the seasonal behavior of the dierent wind oscillations at an average height of 95 km over the South Pole with characteristic periods equal to or greater than 12 h are discussed in detail. However, oscillations with periods less than 12 h were beyond the scope of these papers. Meanwhile, the subdiurnal oscillations in the MLT region near the South Pole appears to be a common feature of this region. Analyzing the results of MLT wind measurements made from August 1, 1991to August 25, 1991, from August 1, 1992to August 13, 1992and from June 19, 1995to June 30, 1995, Hernandez et al. (1992a show the presence of an oscillation with a period close to 10 h, propagating westward and have ascribed this to a zonal wave number one Lamb wave. In addition, during these campaigns, as well as in the campaign from August 13 to August 23, 1996 (Hernandez et al., 1997) additional oscillations with periods near 12 h were detected. These quasi-12 h oscillations were tentatively identi®ed as zonal wave number one inertio-gravity modes of atmospheric oscillation (see Longuet-Higgins, 1968).
We present a view of the intradiurnal wind oscillations in the MLT region over the South Pole, which results from analyses of our meteor radar measurements, with particular emphasis on the seasonal behavior of the main parameters of these oscillations. Meanwhile, the summer-time 12-h wind oscillations are beyond our scope remit, as these oscillations are discussed in detail in another paper .
2 The meteor radar system The meteor radar system which was used to make the neutral wind measurements we present, is described by Portnyagin et al. (1997a, b) and Palo et al. (1998). The radar operates in a monostatic con®guration with four antenna, directed in the horizontal plane along the 0°, 90°E, 180°and 90°W geographical meridians. The hourly mean winds, which are assumed to be horizontal, represent Gaussian-weighted averages centered near 95 km above sea level.

Data analysis procedures
The gaps cover about 7% of full data set and are distributed more or less randomly. We have used a leastsquares ®tting procedure by a second order polynomial to ®t the gaps.
To analyze the data, two complementary methods are used: the well-known periodgram (FFT) and the S-transform technique (Stockwell et al., 1996;Fritts et al., submitted 1997). The periodgram reveals the energy presented at discrete frequencies in the data set, supposing that these oscillations are stationary during the period to be analyzed. The transient nature of the oscillations become evident when S-transform technique is used. The S-transform is closely related to the continuous wavelet transform (CWT), but its localizing function (Gaussian) does not have zero mean (Stockwell et al., 1996;Fritts et al., 1998). The advantage of this method is its direct connection with a spectral Fouriertransformation and the better temporal and frequency resolution, in comparison with the short time Fourier transform. In addition, the S-transform permits determination of the absolutely referenced phase (F) of the considered oscillation assuming it is a nonstationary process, while the CWT gives only locally referenced phase information (Stockwell et al., 1996). Knowing the phases of the considered oscillations for dierent measurement directions gives information on the longitudinal structure of these oscillations. More detail on the S-transform can be found in the Appendix.
The hourly wind data for each direction were ®rst ®ltered using a high-frequency ®lter with the cut-o period at 36 h and a low-frequency ®lter with a cut-o period at 4 h. Then for each sequential interval with duration equal to 512 h the periodgram and S-transform were calculated (with the natural exception at the beginning and the end of the whole data set). Special attention was devoted to the period from June 19 to June 30, 1995 (see later), when the length of analyzed data set was 256 h. The oscillation parameters obtained were analyzed for each measurement direction and then were averaged for all directions. The method of estimation of the signi®cance level for the estimated parameters of the wind oscillations is presented in the Appendix. A modi®ed procedure was carried out for intervals when the regular 12-h oscillation was dominating the wind ®eld (Forbes et al., 1995;Portnyagin et al., 1997). We increased a constant c in S-transform procedure (see Appendix), which is responsible for frequency resolution. It provides the possibility to determine the frequencies of other oscillations with smaller amplitudes. June 19, 1995, to June 30, 1995 observations were made using the meteor radar and collocated OH spectrometer at the South Pole. This has provided an opportunity to compare the wind measurements made from the two instruments. Some results from these simultaneous optical and radar wind measurements have already been published (Hernandez et al., 1996). As noted, despite the dierence in the measuring heights (about 87 km for the optical device and 95 km for meteor radar) the correlation coecient between two data sets is r 0X82, which was found to be statistically signi®cant to the 99% con®dence level.

From
We begin our presentation with a more detailed analysis of the meteor radar wind data for this particular period. The periodgrams for all measurement directions and for the data, averaged over four directions, are shown in Fig. 1. In this ®gure the 95% signi®cance levels are drawn separately for three successive largest peaks as Whittle's test (Whittle, 1951). We used 64 spectral peaks, which were retained after ®ltering. For the averaged spectrum it is more reasonable to show the single signi®cance level covering all of the most prominent peaks. This level corresponds to 95% signi®cance level of the largest peak. The probability, that two or more spurious peaks would be above the level is signi®cantly less than 0.05 (Whittle, 1951). It can be seen that the relative power of a given frequency oscillation is not the same for the dierent directions. Moreover, some oscillations may be considered as signi®cant for a certain direction and as a not signi®cant for another. The same dierence between dierent directions is seen in optical data, hence it is presumed to have a geophysical origin.
There are several reasons for this. They include dierences in the sampling statistics for dierent directions; frequency spectrum and background noise levels for dierent directions. In addition there are some background oscillations, perhaps as observed by Hernandez et al. (1997) and Palo et al. (1998), which may modulate the waves considered mainly in one direction and distort the spectrum.
To be sure of the signi®cance of the results we have used the estimation of the power spectrum as an average one for all directions. The averaged periodgram shows some de®nite peaks, which are consistent with those derived from optical data analysis (Hernandez et al., 1996). The oscillations with periods equal to 11.1 h 0.4 (10.9 h), 10.3 h 0.4 (10.36 h) and 9 h 0.3 (9.9 h) deserve attention. In parentheses we point out the corresponding periods, arrived at in the analysis by Hernandez et al. (1996). An additional argument in favor of geophysical signi®cance of the selected peaks is the phase behavior of the corresponding wind oscillations (see later). There are several reasons why our results give slightly dierent results from those of Hernandez et al. (1996). They include: the Hernandez results correspond to 87 km, ours to 95 km, our data includes four azimuth directions, while the Hernandez results were received from periodogram for one direction (actually his measurements were carried out along eight azimuths); the volume sample statistics are dierent for optical and radar methods; the background noise level is dierent for dierent methods and there is dierent frequency resolution for dierent methods. Results of the S-transform analysis for this campaign are shown in Fig. 2 in a dimensionless form (the wind velocities were ®rst divided by 19 m/s). It can be easily seen that the selected oscillations reveal a very de®nite transient nature and are mainly separated by their time of appearance. Such transient behavior for the wind oscillations over the South Pole with periods of 11.6 h and 10 h has been noticed earlier (Hernandez et al., 1995;Hernandez et al., 1997). Usually each oscillation is signi®cant only for several periods of its existence. The time resolution of the S-transform results is about one period of an oscillation, then the amplitude of oscillation may attain its maximum value at dierent moments for dierent directions. As in Fig. 1, the relative strength of these oscillations is rather dierent for dierent directions. From the S-transform results the signi®cant periods are found to be: 10.7 1.5 h, 9.5 1.5 h and 8.4 1.4 h, where a resolution is de®ned as minimum separation between two peaks, which are equal in strength. There is some dierence between these values and those obtained using the periodogram technique, however taking into consideration the frequency resolution of S-transform we have concluded that this dierence is not signi®cant. The peak amplitudes of these oscillations are: 14.6 m/s (6 m/s), 16.1 m/s (5.8 m/s) and 14.6 m/s (5.7 m/s), respectively (in parenthesis we note the corresponding amplitude estimated from the Other examples of the S-transform analysis are shown in Fig. 4. It can easily be seen that for dierent months (only amplitudes greater than 10 m/s are shown) the intradiurnal oscillations are very sporadic in nature. The usual duration of these oscillations is con®ned to several periods of oscillation. More detailed information about the observed wave events for the observational period since the end of February, 1995 to the end of September, 1995 (period I) is summarized in Table 1. From this Table 1, we may conclude that in spite of the rather broad spread of the periods, the tendency is toward a general decrease in the observed periods during winter months. It is important to note that all signi®cant intradiurnal oscillations, shown in Table 1, are westward propagating with zonal wave number s 1. One can see in Fig. 5, that the some tendencies exist to concentrate the wave periods into intervals 10±11 h and 8±9 h. This histogram is based on the Table 1. The period from the beginning of October to the beginning of February (period II) is characterized by a strong semidiurnal oscillation (Forbes et al., 1995;Portnyagin et al., 1997). This oscillation masks the other weaker oscillations. As a result, the determination of the parameters of intradiurnal variations during period II are not as accurate as for period I. Figure 4e, d illustrates this situation. In Fig. 4e the results of S-transform analysis of the hourly mean data for the February, 1995 are shown. It can be seen from this ®gure that the very strong semidiurnal oscillation ceases after February 10 (hour 288). Following this time the oscillation with a period of about 9 h appears with a rather strong maximum on February 22 and a weaker maximum on February 26. Special methods must be developed for correct determination of the parameters of intradiurnal oscillations other than the strong semidiurnal oscillation, observed during period II. One possibility is to use a constant greater than 2 in the S-transform procedure. Then we will lose in temporal resolution, but increase the frequency resolution. Independent of the type of analysis applied during summer period, we have detected signi®cant oscillations with periods de®nitely exceeding 12 h (13±14 h). Hernandez et al. (1992a, b) have shown that there is no resemblance between the main parameters of the oscillations at the mesopause heights near the South Pole in the wind ®eld and in the pressure, temperature and density ®elds. The most important dierence is that the typical wind oscillations are characterized by a zonal wave number s 1, while the oscillations of the   (Hernandez et al., 1992a, b). Hence, the consideration of the intradiurnal temperature and density variations, detected in the upper atmosphere over the South Pole (Collins et al., 1992;Sivjee and Waltersheid, 1994) is beyond the scope of this work.

Discussion and conclusions
In discussing the nature of oscillations close to 10 h, detected simultaneously in the upper mesosphere at the South Pole and Scott Base station (78°S) during several observational campaigns, Hernandez et al. (1992bHernandez et al. ( , 1995Hernandez et al. ( , 1996 have concluded that the most plausible explanation for this oscillation is that it is a zonal wave number one Lamb wave, with a meridional mode of number two. This conclusion was based on estimation of the vertical wavelength of this oscillation, found to be about 100 km, from the Scott Base observations and on the identi®cation of this oscillation from the South Pole measurements. It is worthwhile noting that according to Lindzen and Blake (1972), Lamb waves below about 80 km are vertically evanescent, but above 80±90 km their behavior more closely resembles a vertically propagating internal gravity wave (IGW). The existing numerical calculations of the vertical phase structure in the transition region between 80 and 100 km are highly idealized (Lindzen and Blake, 1972). Additionally experimental determinations of the vertical wavelength of about 100 km were estimated, using the data from Scott Base within a relatively narrow height interval (80±100 km). So, the determined wavelength for this oscillation may not be considered as a crucial argument in favor of its identi®cation as a Lamb wave.
From Table 1 it may be inferred that the intradiurnal oscillations with periods exceeding 12 h are not typical of the upper mesosphere/lower thermosphere over the South Pole. The most characteristic periods of the oscillations are found to be rather uniformly spread between about 7 h and 12 h. It is interesting to note that oscillations with periods close to those of dierent tidal modes are not dominant in our results. Also having in mind the fact that all of the observed oscillations have zonal wave number one, we may conclude that the pseudo-tide mechanism, proposed by Walterscheid et al. (Walterscheid et al., 1986;Sivjee et al., 1994), even if possible, is not the main mechanism which gave rise to the observed oscillations.
There is a class of solutions of the Laplace's tidal equation which may be attributable to the considered oscillations. According to Longuet-Higgins (1968) these are the westward traveling modes of type I with s 1 for the positive values of dimensionless parameter e 4X 2 R 2 agh, involving the rate of rotation X, the radius of the globe R, the acceleration of gravity g and the equivalent depth h. Lindzen and Blake (1972) have shown that for realistic distributions of temperature and dissipation Lamb-like waves do exist, that should therefore dominate the atmospheric response to various lower atmosphere excitations. The equivalent depth for these waves is 9.95 km i.e., e is about 9. Then we may determine from Longuet-Higgins's (1968) tables the following periods of Lamb-like oscillations with s 1: 10.8 h, 8.96 h and 7.5 h, which correspond to meridional indices n À s 1Y 2Y 3. These periods are close to those observed. Actually there are meridional inhomogenities in distributions of the parameters of the real atmosphere and a background wind, which are absent in the idealized model of Longuet-Higgins (1968). Additionally the atmospheric parameters are seasonally changing. This is why we cannot expect exact correspondence.
Inertia-gravity wave propagation, non-linear interaction of the short-period tides, excitation in situ of the short period waves may also be considered as possible processes which are responsible for intradiurnal wind oscillations in the lower thermosphere over the South Pole. However due to the limited number of measurement parameters, we do not have solid reasons to discuss the possible roles of these processes in the dynamics of the near-pole region.
of order expÀ8p 2 f 2 0 r 2 a1 f 2 0 r 2 the maximum of the amplitude is attained at the point f f 0 . With the same order of accuracy the amplitude of S-transform at the point f f 0 is equal to We consider only positive value of f and f 0 (assuming f 0 T 0), therefore we have obtained only half amplitude of the signal, as can be seen from Eq. (3). This is the reason for the appearance in Eq. (4) of a factor 0.25. Hence, distortion of the duration and the maximum amplitude of the signal depends on the parameter f 0 r, which determines the ratio of the length of the periodic part of the signal to its duration. Because r is a ®nite value, the duration is overestimated, while the signal amplitude is underestimated. There is no error if a signal has a sinusoidal form. For considered signal form the ratio of the actual signal maximum amplitude to the transformed one is equal to f 2 0 r 2 af 2 0 r 2 À 1 q . This factor is less then 10% for our data set.
The signi®cance criteria of spectral maxima may be constructed in accordance with Walker's signi®cance test in harmonic analysis (Davis, 1941). Let us suppose that the input signal in any moment of time t k is a stochastic value with a normal (Gaussian) distribution (0Y r). The discrete S-transform may be divided into the two sums, real S 1 and imaginary S 2 : where i is an imaginary unit. S 1 and S 2 are also normally distributed with the parameters ES 1 ES 2 0, VarS 1 j 2 2pN 2 r 2 N À1 k0 exp À n À k 2 j 2 N 2 4 5 cos 2 2pjk N Y 6 VarS 2 j 2 2pN 2 r 2 N À1 k0 exp À n À k 2 j 2 N 2 4 5 sin 2 2pjk N 7 Near the frequencies of interest to us of order 0.1 it appears that for the time steps n in the limits 20 <n <490 VarS 1 VarS 2 jÀa4N p p r 2 with an error less than 1% and Cov(S 1 , S 2 ) = 0. Let us note that the S-transform distorts the spectral content of the data namely at the beginning and the end of the data sequence. Thus, the value S 2 1 S 2 2 aVarS 1 for a given discrete frequency, determined by j, is characterized by v 2 -distribution with two degrees of freedom. Respectively, for a case of averaging over four measurement directions we have v 2 , a distribution with 8 degrees of freedom, if it is assumed that the variances for the dierent directions are equal. We assume that the variance for the time sequence h(t k ) is known before applying the S-transform. To obtain the variance we use the corresponding non®ltered data set without trend. The number of independent peaks is estimated as a ratio of the full length of the observation period to double period of the oscillation. Thus using this algorithm we can estimate the 95% signi®cance level for any frequency.