Meteor Radar Quasi Two-Day Wave Observations over 10 Years at Collm (51.3 ◦ N, 13.0 ◦ E)

. The quasi two-day wave (QTDW) at 82 - 97 km altitude over Collm (51 ◦ N, 13 ◦ E) has been observed using a VHF meteor radar. The long-term mean amplitudes calculated using data between September 2004 and August 2014 show a strong summer maximum and a much weaker winter maximum. In summer, the meridional amplitude is slightly larger than the zonal one with about 15 m s − 1 at 91 km height. Phase differences are slightly greater than 90 ◦ on an average. The periods 5 of the summer QTDW vary between 43 and 52 h during strong bursts, while in winter the periods tend to be more diffuse. On average, the summer QTDW is ampliﬁed after a maximum of zonal wind shear which is connected with the summer mesospheric jet and there is a possible correlation of the summer mean amplitudes with the backgound wind shear. QTDW amplitudes exhibit considerable inter-annual variability, however, a relationship between the 11-year solar cycle and the QTDW is 10 not found.


Introduction
The quasi two-day wave (QTDW) is one of the most striking dynamical features in the mesosphere and lower thermosphere. The QTDW was first reported by Muller (1972) using a meteor wind radar at Sheffield, UK. He found significant oscillations with periods near 51 h from UK radar data. Even 15 earlier, QTDWs have been discovered over Mogadishu (Babadshanov et al., 1973) near the equator.
The QTDW at mid-latitudes is characterized by a clear maximum in summer, with one or several bursts of a few weeks each. At high latitudes the wave shows a different behavior compared to mid-latitudes, e.g. with maxima during winter (Muller and Nelson, 1978;Nozawa et al., 2003).
Regarding possible forcing mechanisms, Salby (1981a, b) suggested the QTDW to be a manifes-25 tation of a Rossby gravity normal mode in an isothermal windless atmosphere with wave number 3, however, this mechanism could not explain its burst-like behavior. Applying a one-dimensional stability analysis Plumb (1983) introduced baroclinic instability as an excitation mechanism. Pfister (1985) supported this theory by using a two-dimensional quasi-geostrophic model and found a QTDW with wave numbers 2-4 and maxima at middle and high latitudes. However, this result did not 30 resemble all the characteristics of the observed wave. Hence, Salby and Callaghan (2001) combined both mechanisms in numerical experiments and found a QTDW excitation in the winter hemisphere by planetary wave activity. Crossing the equator to the summer hemisphere the QTDW is then enhanced by baroclinic instability connected with the easterly mesospheric wind jet (Wu et al., 1996).
A hemispheric asymmetry has been observed (e.g., Tsuda et al., 1988;Tunbridge et al., 2011) with 35 stronger amplitudes in the southern hemisphere (SH) compared to northern hemisphere (NH). The meridional component tends to be slightly larger than the zonal one at mid-latitudes (Pancheva et al., 2004) or of similar magnitude (Jacobi et al., 2001). The period of approximately 2 days varies between 43-56 h in the NH (Pancheva et al., 2004;Huang et al., 2013a). Generally, periods can be divided into three groups as suggested by Malinga and Ruohoniemi (2007), see also Pancheva et al. 40 (2004) and Tunbridge et al. (2011). The dominating one has periods close to 48 h with wave numbers 2 and 3. The second group has much shorter periods of about 42-43 h. Different wave numbers are reported such as 2, 3 and 4. The last group covers periods longer than 48 h and peaks at 52 h with wave numbers 2 and 3 . In the SH these three groups could not be observed and periods are close to 48 h with wave number 3 (Wu et al., 1996;Walterscheid et al., 2015). Craig and Elford (1981) 45 explored phase locking relative to the sun and suggested nonlinear interactions with diurnal tides. This is also supported by recent studies (e.g., Huang et al., 2013a;Moudden and Forbes, 2014;Walterscheid et al., 2015). A possible correlation of QTDW amplitudes with the 11-year solar cycle has been found by Jacobi et al. (1997), who explained this finding by a stronger mesospheric wind shear during solar maximum.

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In the following we present analyses of the QTDW from a meteor radar (MR) at Collm (51 • N, 13 • E) which has been started in 2004. Earlier, the low-frequency (LF) spaced receiver method has been applied at Collm since the late 1950s until 2007. This was based on the reflection of commercial LF radio waves in the lower ionospheric E region. This led to regular daily gaps due to increased absorption during daylight hours. These gaps are especially long in summer. The measurements had 55 been used earlier to obtain a QTDW climatology over Collm (Jacobi et al., 1997). However, the limitations of the LF method may give rise to potential artifacts, namely uncertainties of the amplitude, and possible effects on the analyzed phases resulting from the data gaps. Therefore, here the 2 MR winds are analyzed and can be used to evaluate the earlier results because meteor winds are observed continuously throughout the day. Possible MR data gaps owing to small meteor count rates 60 especially at the uppermost and lowermost heights are shorter and more regularly distributed than the LF data gaps. Collm MR wind data from 2004 to 2013 have already been analyzed with respect to the climatology of a 2-day oscillation by Lilienthal and Jacobi (2014), but their analyses is based on a fixed period of 48 h. This may lead to different amplitudes and phases. In the present study, the actual periods of the QTDW over Collm are calculated in order to improve the results of Lilienthal 65 and Jacobi (2014). Compared with Jacobi et al. (1997), further information about the mid-latitude QTDW can be obtained with greater accuracy than the earlier LF measurements, in particular because the amplitude and phase uncertainties due to daytime data gaps of LF measurements will be avoided. Background shear obtained from the prevailing winds observed by the radar is used as a proxy for baroclinic instability.

Measurements and Data Analysis
A commercial VHF MR, distributed under the brand name SKiYMET (All-Sky Interferometric Meteor Radar, Hocking et al., 2001) is operated at Collm Observatory (51 • N, 13 • E) since late summer 2004 to measure mesopause region winds, replacing the earlier LF drift measurements (e.g., Jacobi et al., 1997). The MR operates at 36.2 MHz and has a pulse repetition frequency of 2144 Hz which 75 is effectively reduced to 536 Hz due to a 4-point coherent integration. The peak power is 6 kW. The transmitting antenna is a 3-element Yagi with a sampling resolution of 1.87 ms and an angular and range resolution of about 2 • and 2 km, respectively. The receiving interferometer consists of five 2-element Yagi antennas arranged as an asymmetric cross. This allows to calculate azimuth and elevation angle from phase comparisons of the individual receiver antenna pairs. Together with range 80 measurements the meteor trail position is detected. The radar uses the Doppler shift of the reflected VHF radio wave from ionized meteor trails in order to measure the radial velocity along the line of sight of the radio wave. The radar and data collection procedure is described by Hocking et al. (2001).
The meteor trail reflection heights vary between 75 and 110 km with a maximum around 90 km (e.g., 85 Stober et al., 2008). To analyze the wind field, the received meteors and corresponding radial winds are binned in six height gates centered at 82 km (80.5-83.5 km), 85 km (83.5-86.5 km), 88 km (86.5-89.5 km), 91 km (89.5-92.5 km), 94 km (92.5-96.0 km) and 98 km (96.0-100.5 km). With regard to the uppermost height gate, Jacobi (2012) showed that, owing to the vertical distribution of meteor count rates, nominal and mean heights are not necessarily the same and that the uppermost gate has 90 a nominal height of 98 km which refers to a mean height of about 97 km. The radar measurements deliver half-hourly mean horizontal wind values that are calculated by a least squares fit of the horizontal half-hourly wind components to the individual radial wind under the assumption that vertical 3 winds are small (Hocking et al., 2001). An outlier rejection is added. The climatology of background winds and tides as measured by the Collm radar is presented in Jacobi (2012).

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The periods of the QTDW are obtained from Lomb-Scargle periodogram analyses that are based on 11 days of meridional half-hourly wind data each. This method is chosen due to unevenly spaced data that mainly result from too few meteors during some half-hourly time intervals, especially at the upper and lower height gates during the afternoon. The period of maximum amplitude between 40 and 60 h was defined as the most probable period of the QTDW for the respective 11-day time 100 interval. This period range is chosen in accordance with the results of Huang et al. (2013a) who did not observe longer or shorter periods. Note that there are cases with more than one maximum in the selected period interval, and the lower ones are disregarded here even if they should be close to 48 hours. The periodograms are calculated for the meridional component because the meridional QTDW amplitudes are observed to be larger than the zonal ones (Pancheva et al., 2004;Lilienthal 105 and Jacobi, 2014). This is also justified because for large amplitudes the period difference is generally small, and < 2 h in about 75% of all cases with large amplitudes. Hence, the underestimation of zonal amplitudes is small and, as will be described in Sect. 3.1, the zonal amplitude is smaller than the meridional one even when using QTDW periods that are based on a periodogram analysis for the zonal component. An example periodogram analysis for the meridional coponent is shown in Fig. 1,   110 using data of a time interval centered on 25 July 2010. In this case, the amplitude maximum between 40 and 60 h is found at a period slightly larger than 40 h which represents the QTDW period for this date.
To obtain amplitudes and phases of the QTDW a least-squares fit has been applied to the zonal and meridional horizontal half-hourly winds, which includes the prevailing wind, tidal oscillations of 24, 115 12 and 8 h, and the individual period of the QTDW as obtained from the periodogram analysis of the meridional wind. Each individual fit is again based on 11 days of half-hourly mean winds and the results are attributed to the center of this data window. Note that, if shorter data windows were used, the resulting amplitudes would be reduced. In particular, this is the case if there are 2-day bursts within the 11-day window which are not coherent. This has been discussed by Jacobi et al. (1997) 120 who used both 11-and 5-day windows for their analysis. Choosing too small window thus would include more irregular fluctuations, while the chosen 11-day window usually covers several cycles within a QTDW burst. For the example presented in Fig. 1 the resulting amplitude of the QTDW is 27.6 m s −1 at a period of 40.5 h. After analyzing the QTDW parameters in an 11-day window, the window was shifted by one day. The least-squares fit was performed for both the zonal and the

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The vertical zonal wind shear, which has been calculated from the difference of the respective prevailing wind components at 94 and 88 km, is added as a blue line. On a long-time average, the QTDW amplitudes start to increase when the shear reaches its maximum. In Sect. 3.1, we show that wind shear, taken here as a proxy for baroclinic instability, may act as a source of the QTDW. However, this relation is not observed in winter where the QTDW is assumed to appear due to instabilities of 145 the polar night jet (e.g., Venne and Stanford, 1982;Hartmann, 1983;Sandford et al., 2008;Baumgaertner et al., 2008).
Generally, the meridional amplitude in Fig. 2 is larger than the zonal one. One may argue that this is due to the fact that we define the period of the QTDW as the period of maximum meridional amplitude (see Fig. 1). This ensures strong meridional amplitudes at the chosen period but may result in 150 smaller zonal amplitudes if the maximum zonal value is found at another period. To prove that the larger meridional component is not attributed to the analysis method we performed the same analysis but determined the period of the QTDW from the zonal component (not shown here). As a result, the meridional QTDW amplitude is still larger than the zonal one.
The lower panel of Fig. 2 combines the mean seasonal cycles of all six height gates in a contour 155 plot where the respective heights of the gates are indicated by horizontal lines. The seasonal cycle is similar at different height gates except for the uppermost one. The summer amplitudes maximize at about 88 km height which is close to the value reported by Chshyolkova et al. (2005). The winter maximum is strongest at higher altitudes in late winter where 10 m s −1 can be exceeded, so that at the upper height gates, the amplitude difference between summer and winter decreases. In other years, QTDW activity is split into two or more bursts (e.g., 2005, 2006, 2009). The largest amplitudes are usually found between June and August, however, in some years (e.g., 2006, 2009, 2014) significant amplitudes are also observed in May. The running spectrum for 2006 is a typical example for a strong summer QTDW with two main bursts where the periods vary between more In the following we concentrate on the more intense summer QTDW, referring to the months of May to August. In order to investigate the distribution of periods with respect to the amplitudes, two maxima are not statistically significant but, together with the primary maximum, they correspond to the three maxima presented by Malinga and Ruohoniemi (2007).
In the following we show summer QTDW data for amplitudes of at least 15 m s −1 . Fig. 5 shows the 200 relative amplitude differences ∆v (see Jacobi, 2012) between zonal and meridional QTDW ampli-6 tudes at 91 km altitude, given by: where the index z refers to the zonal and the index m to the meridional component of the QTDW.
Hence, positive (negative) ∆v denote larger zonal (meridional) amplitudes and the value denotes 205 the percentage of amplitude differences from the mean amplitude. The mean and median of summer relative amplitude differences amount to −46.8% and −39.0%, respectively. The 5% and 95% percentiles are P 5 = −114.5% and P 95 = 2.6%, respectively. Thus, the meridional component tends to be larger than the zonal one. Note, that the meridional amplitude also tends to be slightly larger due to the fact that the periods of the QTDW were chosen from the maximum meridional amplitude.

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However, this effect is small. If we calculate the relative amplitude differences using the periods at maximum zonal amplitude we obtain P 5 = −75.5% and P 95 = 17.1% which qualitatively leads to the same conclusion that the meridional amplitude is larger.
The phase differences between zonal and meridional QTDW components at 91 km altitude are shown  Vertical wavelengths λ z were calculated for each 11-day interval when the amplitudes at 91 km altitude are larger than 15 m s −1 by: where P is the period and dT /dz is the vertical gradient of the phase T . For this analysis, the same period has to be used for each height gate to obtain consistent phases. Therefore, for wavelength calculation, we repeated the QTDW analysis for each height gate with the period found for 91 km. The vertical phase gradients were calculated by applying linear fits of phase over height. The histogram 235 in Fig. 8 shows all wavelengths smaller than 400 km. Indeed, we obtain a few very large ("infinite") wavelengths that are not presented, when the phase does not significantly change with altitude, i.e.
when the wave does not propagate vertically. This is true in about 12% of all cases considered. For the values smaller than 400 km a Lognormal probability density function is applied. This fit is accepted by several statistical hypothesis tests such as a Kolmogorov-Smirnov, Anderson-Darling and 240 a Chi-squared test. The mode of the fitted Lognormal function is 77 km whereas the median and mean of the data set < 400 km are much larger with 106 km and 127 km, respectively. Plumb (1983) introduced the idea that the origin of the QTDW is baroclinic instability of the easterly jet in the summer mesosphere. A necessary condition for that is that the northward gradient of 245 quasi-geostrophic potential vorticity q y must change sign somewhere in the flow domain to enable instability (Charney and Stern, 1962). This condition is given in the summer mesospheric jet in an altitude of about 70 km. Here, the vertical zonal wind profile has a minimum or, in other words, the easterly winds maximize. In order to investigate possible baroclinic instability by analyzing MR measurements from higher altitudes, a proxy needs to be determined because the wind maximum is 250 outside the measurement range. We analyze the vertical wind shear of the zonal wind above the jet as a measure for its strength and hence for baroclinic instability.

Connection with Background Wind Shear
We apply superposed epoch analyses in two ways: First, the key events are defined from the time series of the amplitude. Therefore, the time series is filtered using a Lanczos low-pass filter with 30 weights and a cut-off period of 20 days. When the low-pass filtered amplitudes show a maximum These results are consistent with the conclusion of Plumb et al. (1987): The QTDW is propagating eastward, opposite to the wind direction in the jet. With increasing amplitude, it tends to act against its origin (Pendlebury, 2012;Ern et al., 2013) and diminishes the wind shear. When the wind shear is too weak for amplification the amplitude decreases again. However, considering the large error 270 bars in our data we can only speak about tendencies. The effect is not clear enough to prove the 8 hypothesis of baroclinic instability as a forcing mechanism. Furthermore, the results shown here at 85 km altitude become less significant for higher altitudes.

Inter-Annual Variability
A correlation of QTDW amplitudes to the 11-year solar cycle was found in Low Frequency Mea-275 surements by Jacobi et al. (1997) and recently by Huang et al. (2013b) using satellite measurements.
Both report larger amplitudes during solar maximum. Due to the deep solar minimum in 2008 and 2009 an analysis of the inter-annual variability of the QTDW is of special interest. Figure 10 presents the F10.7 solar radio flux (black) and vertical zonal wind shear at 85 km (pink) in the upper part.
The lower part shows the the total amplitudes at the four height gates between 85 and 94 km altitude. correlations turn out to be insignificant. This is in accordance with the general view that the winter QTDW is a result of instability of the polar night jet and that the QTDW is originating from the lower atmosphere instead of being determined by the mesospheric circulation.
As presented in the periodograms in Fig. 3, the appearance of the QTDW is not uniform in each year. This is why one might expect a seasonal mean not necessarily to be representative enough to 305 describe the QTDW. Thus, we also compare different ways to describe seasonal mean QTDW activity during a season such as (1) the maximum total amplitude during a season, (2) the mean of the squared total amplitudes during a season as an estimate for energy and (3) the mean of amplitudes minus a threshold value of 6 m s −1 , while negative values are set to zero. This latter value is taken from the "noise floor" visible in Fig. 2 during the equinoxes.

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As a result, the estimates (2) and (3) behave behave very similar to the seasonal mean values concerning magnitudes and sign of the correlation coefficients for correlations with solar radio flux and vertical shear of the zonal wind.
Using the maximum as an estimate, the correlation with solar radio flux in summer turns out to be slightly positive for most altitudes with R ≈ 0.2 in the lower height gates. However, this is still no 315 clear correlation and thus the results more or less correspond with those obtained for other estimates.
The same holds for summer, where positive values for zonal and negative values for meridional amplitudes dominate. The correlation between wind shear and seasonal maxima is mostly weaker than obtained for seasonal means by about 0.2.
To conclude, differences obtained with the four methods are not very large. Thus, the obtained rela-320 tion between QTDW amplitudes and wind shear is robust and independent from the chosen method.

Discussion and Conclusion
The QTDW is analysed from Collm VHF meteor radar data. The considered time series begins after the installation of the radar in 2004 when it replaced earlier LF measurements (Jacobi et al., 1997) and reaches until 2014.

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On a 10-year average, the QTDW has amplitudes of about 15 m s −1 in summer when analyzed on an 11-day basis, and single bursts can reach values of 40 m s −1 . These values are comparable to those obtained by Guharay et al. (2013) but they presented MR measurements at low latitudes. In winter, a secondary maximum with amplitudes of 5 to 10 m s −1 is observed. These observations combined with the fact that, e.g., Muller and Nelson (1978) and Nozawa et al. (2003) report a strong winter 330 QTDW at high latitudes indicate that the influence of the winter QTDW becomes stronger with increasing latitude. The periods of the QTDW tend to be longer in winter than in summer. Some years show a typical signature of periods during summer bursts that change in length from long to short and back to long while shorter periods are generally associated with larger amplitudes. Similar features were observed by Jacobi et al. (1997) and by long-term measurements at Saskatoon, Canada, 335 by Chshyolkova et al. (2005). Tsuda et al. (1988) and Williams and Avery (1992), however, observed shortening periods during the respective bursts, while Pendlebury (2012) found continuously increasing periods during a burst.
Phase differences between the zonal and meridional component turn out to be slightly larger than 90 • which indicates that the wave is nearly but not exactly circularly polarized. This value is a bit 340 larger than the one reported by Jacobi et al. (1997). The zonal and meridional amplitudes are of comparable size at 82 km altitude but they change with height in a way that the meridional ones tend to be larger by about 50%. This coincides with the results of, e.g., Pancheva et al. (2004) and Gurubaran et al. (2001) but it could not be seen in the earlier LF measurements (Jacobi et al., 1997(Jacobi et al., , 2001).

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Vertical wavelengths were calculated from the vertical phase gradients. The mode of a fitted Lognormal distribution is 77 km, while the median wavelength is 106 km. These values are comparable to those obtained by Thayaparan et al. (1997). Smaller values below 80 km are reported, e.g., by Gurubaran et al. (2001), Guharay et al. (2013) or Huang et al. (2013b). Even larger values are found by Craig and Elford (1981) or Harris (1994), but these were obtained in the southern hemispehere.

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What all studies have in common is the fact that very large, almost "infinite" values were occasionally obtained, which is also the case over Collm. This indicates that the wave does not propagate vertically in these cases.
Furthermore, we find a connection between vertical zonal wind shear and QTDW amplitudes by applying superposed epoch analyses. They show a maximum of amplitudes about 10 days after a 355 maximum of zonal wind shear at 85 km altitude. Also, a maximum of zonal wind shear is found about 10 to 15 days before the amplitude maximizes at 85 km. In the long-term mean annual cycle, zonal wind shear has a maximum when the QTDW starts to amplify. Also, in an inter-annual view, the correlation between zonal wind shear and amplitudes of the QTDW is high in summer but not in winter where the QTDW is assumed to be amplified by instability of the polar night jet (e.g., Venne 360 and Stanford, 1982;Hartmann, 1983;Sandford et al., 2008;Baumgaertner et al., 2008). Since shear is taken here as a proxy for baroclinic instability we conclude that the QTDW over Collm is at least to a certain degree forced by instability of the summer mesospheric jet as reported by Ern et al. (2013) using satellite measurements, too. Also, Huang et al. (2013b) observed increasing QTDW amplitudes above regions of negative quasi-geostrophic potential vorticity.

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Between QTDW amplitudes and the 11-year solar cycle a positive correlation is found in winter.
In summer it is weaker and correlation coefficients tend to be negative. However, the correlation is not that clear. This can be explained by considering the results of Jacobi et al. (2011). They found a positive correlation of zonal wind shear and solar cycle except during solar minimum when correlation turns out to be negative. This may also hold for the QTDW due to the possible amplification 370 by baroclinic instability. As the strong solar minimum in 2009 is centred in the analysed time series, longer observations are necessary to draw further conclusions.