The quasi 2-day wave (QTDW) is one of the most striking dynamical features in the mesosphere and lower thermosphere. The QTDW was first reported by using a meteor wind radar at Sheffield, UK. He found significant oscillations with periods of approximately 51 h from UK radar data. Even earlier, QTDWs were discovered over Mogadishu 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 at mid-latitudes, e.g., with maxima during winter . The QTDW has been frequently observed by ground-based e.g., and satellite instruments . Additionally, several numerical studies simulated possible excitation processes .

Regarding possible forcing mechanisms, suggested the QTDW to be a manifestation 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 introduced baroclinic instability as an excitation mechanism. 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 resemble all the characteristics of the observed wave. Hence, 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 .

A hemispheric asymmetry has been observed e.g., with stronger amplitudes in the Southern Hemisphere (SH) compared to in the Northern Hemisphere (NH). The meridional component tends to be slightly larger than the zonal one at mid-latitudes or of similar magnitude . The period of approximately 2 days varies between 43 and 56 h in the NH . Generally, periods can be divided into three groups as suggested by ; see also and . The dominating one has periods of approximately 48 h with wave numbers 2 and 3. The second group has much shorter periods of about 42–43 h. Different wave numbers such as 2, 3 and 4 are reported. 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 . explored phase locking relative to the sun and suggested nonlinear interactions with diurnal tides. This is also supported by recent studies e.g.,. A possible correlation of QTDW amplitudes with the 11-year solar cycle has been found by , who explained this finding by a stronger mesospheric wind shear during solar maximum.

In the following we present analyses of the QTDW from a meteor radar (MR) at Collm (51∘ N, 13∘ E) which was started in 2004. Earlier, the low-frequency (LF) spaced receiver method was applied at Collm, from 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 been used earlier to obtain a QTDW climatology over Collm . 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 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 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 , but their analysis 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 . Compared with , 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.

A commercial VHF MR, distributed under the brand name SKiYMET All-Sky Interferometric Meteor Radar; 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.,. The MR operates at 36.2 MHz and has a pulse repetition frequency of 2144 Hz which 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 calculating the azimuth and elevation angle from phase comparisons of the individual receiver antenna pairs. Together with range 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 .

The meteor trail reflection heights vary between 75 and 110 km with a maximum around 90 km e.g.,. 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, 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 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 winds are small . An outlier rejection is added. The climatology of background winds and tides as measured by the Collm radar is presented in .

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 interval. This period range is chosen in accordance with the results of 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 h. The periodograms are calculated for the meridional component because the meridional QTDW amplitudes are observed to be larger than the zonal ones . 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 component is shown in Fig. , 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, 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 who used both 11- and 5-day windows for their analysis. Choosing windows that are too small would thus include more irregular fluctuations, while the chosen 11-day window usually covers several cycles within a QTDW burst. For the example presented in Fig. , 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 1 day. The least-squares fit was performed for both the zonal and the meridional wind component, and for each height gate separately. The following results are based on these data.

The upper and lower panels of Fig.  present the mean seasonal cycle of QTDW amplitudes. Here, we also present the total amplitudes as a combination of zonal and meridional components. The upper panel of Fig.  refers to an altitude of 91 km (gate 4). It shows the total amplitudes of each year in light gray, starting in September 2004 and ending in August 2014. The black lines show the 10-year average for total (straight), meridional (dashed) and zonal (dotted) amplitudes and the red line shows 45-day adjacent averages of the 10-year mean total amplitude. As previously reported in the literature, we find a strong summer and a weaker winter maximum. The first increase of the summer burst starts during May, where the year 2006 shows a strikingly strong burst. Maximum amplitudes are usually reached at the end of July and beginning of August, where the long-term average amplitudes (red curve) exceed 15 m s-1. The maxima during individual bursts (gray curves) can be even larger and in some years they reach up to 40 m s-1. The winter QTDW appears much weaker with average amplitudes between 5 and 10 m s-1.

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. , 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 the polar night jet e.g.,.

Generally, the meridional amplitude in Fig.  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. ). This ensures strong meridional amplitudes at the chosen period but may result in 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.  combines the mean seasonal cycles of all six height gates in a contour 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 . 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 gate, the amplitude difference between summer and winter decreases.

The distribution of meridional amplitudes during the years 2004–2014 as obtained from the Lomb–Scargle periodograms is shown in Fig. . As in Fig. , they refer to an altitude of 91 km. The white line denotes the period of maximum amplitude between 40 and 60 h. Note that this curve determines the period that is taken as the real QTDW period for further analyses. Having a look at the summer season it is apparent that in certain years the QTDW appears in one single burst (such as 2007, 2010 or 2012) with typical seasonal maxima at the end of July or beginning of August. 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 or less 40 and 52 h. At the onset of the summer wave in May and when it vanishes in August, the periods are longer than during the event. This feature from long periods to shorter ones and back to long ones is also seen in other years such as 2007 and 2012. In 2005 and 2009 the period is also largest at the onset of the wave burst and lowest at the maximum of the wave, but it is more variable in between.

In each winter from 2005 to 2014 slightly increased amplitudes of the QTDW can be seen. The 10-year mean winter maximum is small and the amplitudes are, on average, only about 2 times as large as during the September minimum, which is comparable to earlier observations e.g.,. The winter oscillations are irregular: they are particularly large in January 2006, 2012 and 2013. In some cases the enhancement already starts at the end of the previous year, e.g., large amplitudes in December 2011 continue in January 2012. Several studies e.g., suggest a possible relation between QTDW amplitudes and the strong major sudden stratospheric warming in January 2006. The 2012 and 2013 maxima are also found during winters of major stratospheric warmings: however, during the 2009 stratospheric warming no QTDW enhancement is seen in the measurements. In some years (e.g., 2009, 2011, 2012) amplitudes also maximize in November or December. Periods are very short in January with 44 h or less and they increase until February where they often reach 52 h or more.

In the following we concentrate on the more intense summer QTDW, referring to the months of May–August. In order to investigate the distribution of periods with respect to the amplitudes, Fig.  shows histograms of periods for different magnitudes of the amplitude where boundary periods (≤41 h or >59 h) are omitted. Dark bars denote only larger amplitudes while white bars include days of all amplitudes. The histogram refers to an altitude of 91 km during summer (May–August). As a result, intervals with large QTDW amplitudes tend to exhibit shorter periods. The median for large amplitudes (black columns) is 47.9 h but the median for all amplitudes including small ones (white) is 49.3 h. For amplitudes larger than 15 m s-1 (black columns), the lower and upper quartiles are 45.8 and 52.7 h, respectively. For larger periods, smaller amplitudes dominate. Furthermore, we find a clear maximum at 47–48 h and two secondary maxima at 42–43 h and 50–51 h. The latter two maxima are not statistically significant but, together with the primary maximum, they correspond to the three maxima presented by .

In the following we show summer QTDW data for amplitudes of at least 15 m s-1. Figure  shows the relative amplitude differences Δv see between zonal and meridional QTDW amplitudes at 91 km altitude given by Δv=2vz-vmvz+vm⋅100%, where the index z refers to the zonal and the index m to the meridional component of the QTDW. Hence, positive (negative) Δv values denote larger zonal (meridional) amplitudes and the value denotes 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 P5=-114.5 % and P95=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. However, this effect is small. If we calculate the relative amplitude differences using the periods at maximum zonal amplitude we obtain P5=-75.5 % and P95=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 in Fig. . The histogram includes the results for amplitudes larger than 15 m s-1 in black and white for summer (May–August) and the rest of the year, respectively. The small number of the latter shows that large amplitudes do mainly appear in summer. A Gaussian fit was applied to the summer histogram. As a typical feature of that distribution, mean (102.2∘), median (101.1∘) and mode (102.4∘) are all of similar value. These values are only slightly larger than 90∘ and hence the zonal and meridional components are nearly in quadrature. Other height gates have Gaussian modes that are up to 10∘ larger compared to the 91 km altitude.

Figure  (left panel) shows the means and standard deviations of the phase difference at all six height gates for amplitudes larger than 15 m s-1. The standard deviation of the uppermost gate is almost twice as large as those of the lower gates. Considering the lower gates, the means are comparable to the one at 91 km, slightly higher than 90∘. However, the standard deviation of about 30∘ is large. The right panel of Fig.  shows the profile of the mean QTDW zonal and meridional amplitudes as well as their differences. At 82 km the meridional amplitude is only slightly larger than the zonal one. For greater altitudes, the difference is increasing up to a height of 91 km and almost constant above.

Vertical wavelengths λz were calculated for each 11-day interval when the amplitudes at the 91 km altitude were larger than 15 m s-1 by λz=PdT/dz, 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 in Fig.  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 a chi-squared test. The mode of the fitted lognormal function is 77 km whereas the median and mean of the data set for < 400 km are much larger with 106 and 127 km, respectively.

The QTDW is analyzed 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 and continues until 2014.

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 , but they presented MR measurements at low latitudes. In winter, a secondary maximum with amplitudes of 5–10 m s-1 is observed. These observations combined with the fact that e.g., and report a strong winter 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 and by long-term measurements at Saskatoon, Canada, by . and , however, observed shortening periods during the respective bursts, while 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 larger than the one reported by . 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., and but it could not be seen in the earlier LF measurements .

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 . Smaller values below 80 km are reported, e.g., by , or . Even larger values are found by and but these were obtained in the Southern Hemisphere. 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 maximum of zonal wind shear at 85 km altitude. Also, a maximum of zonal wind shear is found about 10–15 days before the amplitude maximizes at 85 km. In the long-term mean annual cycle, zonal wind shear reaches 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.,. 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 , using satellite measurements too. Also, observed increasing QTDW amplitudes above regions of negative quasi-geostrophic potential vorticity.

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 . 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 by baroclinic instability. As the strong solar minimum in 2009 is centered in the analyzed time series, longer observations are necessary to draw further conclusions.