Upper mesosphere OH temperature measurements are compared at the stations of Wuppertal (51°N, 7°E) and Hohenpeißenberg (48°N, 11°E) for 2004–2009 in order to form a combined data set which considerably improves the measurement statistics. This allows time analyses near the Nyquist frequency (2 days) which is used for a study of the quasi 2 day wave (QTDW) in summer. The well-known maximum near solstice is observed. In addition, there are two unexpected side maxima about 45–60 days before and after the center peak. A similar triplet is seen in the QTDW analysis of Microwave Limb Sounder temperature data. The triple structure is also found in a very similar form 15 years earlier in the interval 1988–1993 in early Wuppertal data. In these 15 years the time distance between the first and last triple peak has increased by about 22 days. Amplitudes of the QTDW correspond to the meridional gradient of the quasi-geostrophic potential vorticity (from MLS data) and baroclinic instabilities (bc) from radar winds (at Juliusruh, 55°N, 13°E). Parameter bc also shows a triple structure, when mean values 2003–2008 are calculated. The QTDW triplet results from the combination of atmospheric (in)stability and critical wind speed. The widening of the QTDW triple structure suggests a long-term change of mesospheric stability and wind structure. This is found, indeed, in the bc and zonal wind data. The changes likely reflect a long-term circulation change in the middle atmosphere extending up to the mesopause.
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 Temperature and winds in the mesosphere are highly variable. Most of these fluctuations stem from atmospheric waves that occur at various frequencies and often with high amplitudes. The most important wave types are gravity waves, traveling planetary waves, quasi-stationary planetary waves, and tides. There is a wealth of literature on waves observed in mesospheric winds [e.g., Manson et al., 2004, and references therein]. Temperature waves have also been reported on numerous occasions. A survey of mesospheric temperature waves has recently been given by Offermann et al. [2009, and references therein].
Sounding of the Atmosphere using Broadband Emission Radiometry
Upper Atmosphere Research Satellite
 QTDW analyses mostly found westward traveling planetary waves with zonal wave number 3. These are normal modes and have a period of about 2.1 days, which can vary substantially [Norton and Thuburn, 1996; Salby and Callaghan, 2001]. Values between 1.8 and 2.3 days have been reported. They appear to depend on season and location [Palo et al., 1999; Baumgaertner et al., 2008]. This type of wave is especially pronounced in summer. The QTDW in wind is one of the strongest dynamical features in the summer mesosphere. Maximum amplitudes occur at 80–100 km shortly after summer solstice [e.g., Jacobi et al., 1998; Pancheva et al., 2004]. Maximum temperature amplitudes on the order of 11 K have been reported (Southern Hemisphere [e.g., Limpasuvan and Wu, 2003], but mean amplitudes are much smaller (see Figure 1). QTDW are sporadic phenomena. They occur in bursts; that is, there is a large short-term variation. There is also a great interannual variability. Therefore averaging of several years is required to obtain reliable mean values in a climatological sense.
 Temperatures in the mesosphere have been measured for many years by a variety of ground based instruments [e.g., Beig et al., 2003; Offermann et al., 2004]. Several satellite instruments with improved altitude resolution are also available [e.g., von Savigny et al., 2004; Remsberg et al., 2008]. OH temperatures derived from the near infrared emissions of the hydroxyl layer in the upper mesosphere (87 km) are quite suitable for traveling planetary wave measurements because of the long vertical wavelengths of the latter (considering the OH layer thickness of 8 km). An OH measurement station has been operated since 1980 at the University of Wuppertal (51°N, 7°E). A second station was set up approximately 360 km south of Wuppertal with the same type of instrument in 2003. It is located at the Deutscher Wetter Dienst (DWD) Meteorological Observatory of Hohenpeissenberg (48°N, 11°E). The intention was to look for spatial similarities and/or differences at the two stations. The details have recently been described by Offermann et al. .
 In the present paper we give further comparisons of the two stations. It turns out that the results can be combined into one data set (“combi temperatures”) for planetary wave studies. This offers a much higher data coverage (i.e., number of nights with clear weather) and hence increased time resolution of the measurements. Consequently, high-frequency waves can be studied. As an example an analysis of the QTDW over 6 years (2004–2009) is given here. It is compared to the zonal wind field measured nearby (Juliusruh, 55°N, 13°E) and to earlier OH temperature data dating back to 1988. Earlier QTDW summer studies have been limited to relatively short time intervals (order 1 month). In the present study we analyze extended summer periods including parts of spring and autumn (about DOY 100–260). This reveals an unexpected triple structure of QTDW amplitudes.
 The paper is organized as follows: In section 2 the data of the two stations (“twin stations”) are described and compared to each other. They are combined into one data set (“combi data”). Section 3 gives the spectral analysis of the combi data and the resulting quasi 2 day waves (QTDW). The intraseasonal variations of the QTDW are described (triplet). The ground-based data are compared to corresponding results from MLS satellite temperature measurements. In section 4, the occurrence of the QTDW is discussed in the context of atmospheric stability. Geostrophic winds are derived from MLS measurements, and are compared to radar winds measured at Juliusruh. Unstable conditions are diagnosed using the meridional derivative of the quasi-geostrophic potential vorticity. Baroclinic instabilities are also estimated from the radar winds. These wind data reach back until 1990. Section 5 shows the long-term development of the QTDW amplitudes since 1988. Similarities to the development of the baroclinic instabilities and the wind field are discussed. In section 6 the results are compared to other published data, and the long-term changes are discussed in terms of the changes of summer duration in the mesosphere. Section 7 summarizes the results and suggests conclusions in the context of long-term changes of the middle atmosphere circulation.
2. OH Temperatures
 To determine upper mesosphere temperatures two similar grating spectrometers are used at the two stations (GRIPS I and II, Ground-Based Infrared P-Band Spectrometer). Emissions from three lines of the Meinel bands near 1.5 μm are measured by liquid nitrogen-cooled Germanium detectors. Homogeneous data sets (harmonic fits, see below) are available at Wuppertal since 1987 (GRIPS II) and at Hohenpeißenberg since 2004 (GRIPS I). Data accuracy has been analyzed by detailed comparison with Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) V1.07 data. Wuppertal temperatures are found to be 3.4 K higher than SABER on average. Precision of the nightly mean values is better than 2 K. Results for Hohenpeißenberg are similar such that both data sets are intercalibrated using SABER as the transfer standard. Details are given by Offermann et al. .
 The two stations are further checked for agreement by means of harmonic analyses of the seasonal temperature variations that are quite strong at these altitudes. Analysis parameters are the annual mean temperature T0 and the three amplitudes of the annual, semiannual, and terannual oscillations. The differences between the measurements and the harmonic fit (called “residues” in the following) are a measure of atmospheric wave activity, and their standard deviation σM is calculated and compared on a monthly basis. The means of the semiannual and terannual fit parameters over 5 years of simultaneous measurements at the two stations agree within 1 K, and for T0 and the annual amplitude they agree within a few tenths of a Kelvin. The difference of the standard deviations σM is 6%, only. For details see Offermann et al. .
 The close agreement of the standard deviations is mirrored by high correlation coefficients between the data measured at Wuppertal and Hohenpeißenberg. Typical coefficients are 0.8–0.9 at times of high wave activity [Offermann et al., 2010]. Wave activity around the OH layer is dominated by gravity waves and traveling planetary waves. Quasi-stationary planetary waves and tides yield a smaller contribution at the middle latitudes considered here as shown by Offermann et al.  using a combination of satellite and ground-based data. Gravity waves, however, should not contribute too much to the fluctuations of temperature measured by the GRIPS instruments. Because of their short periods they should mostly be filtered out by taking nightly means (several hours). Quasi-stationary planetary waves cannot be seen either at a fixed station if they are truly stationary. Tidal influences on summer temperatures at our latitudes appear to be relatively small [Offermann et al., 2009, 2010; Yuan et al., 2010]. Hence the GRIPS day-to-day fluctuations are essentially caused by traveling planetary waves.
 The close agreement of the fit parameters at the two stations and the substantial coherence of the fluctuations suggest combining the measurements of the two stations into one data set for the analysis of large-scale structures like planetary waves. This is justified by the relatively short distance between Wuppertal and Hohenpeißenberg, which is about 360 km (approximately southward) and hence much shorter than the horizontal wavelength of typical planetary waves. The advantage of this combination is that the two stations see the same planetary wave (in the mesosphere), but not the same weather (cloud coverage in the troposphere). In 2004–2008 the coverage of measurements (times of clear weather) at either of the two places was about 60% or less; that is, 60% of all nights (or less) yielded good data. The time coverage of the combined data, however, was about 80%. The combi data are defined as the temperature mean of the two stations if they have simultaneous data. Otherwise the single station data are used.
3. QTDW Observations
 A time coverage of 80% allows planetary wave analyses near the theoretical Nyquist limit, which is 2 days for daily measurements. The combi data were thus used to study the summer QTDW. A Fast Fourier Transform (FFT) analysis was performed for 6 years of combi temperatures available (2004–2009). Analysis windows of 16 days length were used. This length was chosen because it is half a month long, and contains 24 days, which helps the FFT analysis. Data gaps of moderate length (up to 7 days) were filled by linear interpolation. Windows with long gaps (more than 7 days) were excluded from the analysis because linear interpolation would deform the spectrum too much. The vast majority (77%) of our 16 day windows has only small gaps (0 to 4 days); that is, the influence of the gaps should be moderate. Furthermore it is the goal of the paper to study the relative variations of QTDW amplitudes during the course of the summer and over longer times. If there should be some influence of the data gaps it should be about constant and hence unimportant. An FFT on a 16 day window yields fixed frequency results at periods of 2, 2.3, 2.7, 3.2, and 4 days, etc. As said above, the typical period of the QTDW is 2.1 days, but it can vary considerably (1.8–2.3 days [e.g., Palo et al., 1999; Baumgaertner et al., 2008]). We use the 2.3 day component of our FFT here. To increase the time resolution, we shift our analysis window in steps of half a window length and thus obtain data points every 7.5 days. This analysis is performed for the summer of each year separately. Afterward, several years are grouped in a cluster, and the cluster mean is computed.
 The weather statistics of the combi data yielded a data coverage of 80.3% in 2004–2008. For comparison, the Wuppertal measurements alone had data coverage of 60.7% in the same interval, which turned out to be insufficient for spectral analysis. This is typical of most of the earlier years at Wuppertal: in years 1994–2008 the mean coverage was 60.4%. There is an exception in years 1988, 1989, 1992, and 1993. In these years, the data coverage was 75%, which allows spectral analyses. Years 1990 and 1991 could not be included in the analysis because of distorted harmonic fit curves. These were due to a larger data gap in 1990 and the Pinatubo eruption in 1991. The years 1994–2003 were excluded from the analysis because of insufficient statistics.
 The seasonal variation of the QTDW amplitudes is characterized by a strong summer maximum that typically occurs shortly after summer solstice. Wave activity is known to occur in bursts and to have a large interannual variability. Our QTDW results show strong variability, indeed, and maximum amplitudes reached about 4 K. Mean values of the two time intervals 1988–1993 and 2004–2009 are given in Figure 1. The error bars are the errors of the mean.
 The amplitude distribution of the QTDW in Figure 1 shows a broad maximum shortly after solstice, as expected [e.g., Pancheva et al., 2004; Baumgaertner et al., 2008; Richter et al., 2008]. There are, however, two unexpected additional side peaks. These are somewhat smaller and occur 45–60 days earlier or later. This “triple structure” is 1–2 K high and appears to sit on a base of about 1 K amplitude. It is a real structure as the error bars show. (These bars should be rather called “scatter bars” as they mostly do not show measurement errors but atmospheric interannual variations.) The triplet is a very characteristic feature and will therefore be discussed in more detail below. When analyzing single years the triple structure is not always easy to identify because of the high interannual and intraseasonal variability. A number of years need to be averaged to make it visible.
 In Figure 2 we compare our results with corresponding ones from the Microwave Limb Sounder (MLS) instrument on the NASA Earth Science Projects Division Earth Observing System (EOS) Aura satellite. These are from a spectral analysis of MLS temperatures at 51°N in a latitude band 5° wide. Data are for a westward traveling zonal wave No.3 (W3). The altitude range covered by the MLS instrument is ∼10–97 km and the altitude used here is 86 km. MLS uses microwave emissions in the range 118 GHz to 2.5 THz and is in a Sun-synchronous orbit. The range of latitude measured by the satellite is approximately 82°N to 82°S. The spatial resolution is approximately 500 km horizontally and 3 km vertically, decreasing to about 10 km near the mesopause. A more detailed description of Aura and MLS is provided by Waters et al. . Here we use the temperature from the level 2 version 2.2 data product. The data were screened as recommended by the data quality document of Livesey et al. . The least squares fitting method of Wu et al.  was used, which was applied to identify the 2 day wave in Upper Atmosphere Research Satellite (UARS) MLS measurements. In our application of the method here, a sinusoidal function at a period of 2.3 days was least squares fitted to the satellite data in a 6 day window at a height of 86 km. The data were sorted into a band of 5 degrees latitude centered around 51 degrees N. The window was then incremented through the time series in steps of 6 days.
 The agreement of the QTDW amplitudes derived from ground-based OH and satellite MLS temperatures is moderate. A detailed analysis shows that this is because the amplitudes depend on altitude, latitude, and on the width of the latitude band analyzed. Wave maxima furthermore do not always occur at the same altitude and latitude in different years. This makes the results appear intermittent.
 To obtain robust results, one needs to average the measurements of several years. We therefore show mean values of the MLS data for years 2005–2009 in Figure 2a. QTDW amplitudes are shown for the W3 planetary wave with 2.3 days period at 51°N. The analysis interval is 5° wide in latitude. The MLS data are compared to corresponding Wuppertal OH data in Figure 2b. This curve looks somewhat different from that in Figure 1 because the years that have been averaged are different. Years 2005–2009 have been used in Figure 2 for comparison with MLS. Adding or omitting 1 year can make a visible difference in these curves due to the high interannual variability. The basic structure of the OH temperature curve in Figure 2b is, however, the same as in Figure 1. There is a major amplitude maximum shortly after solstice and two somewhat smaller peaks in early and late summer. The same structure is also seen in the MLS data in the upper panel. The corresponding maxima are connected by vertical red lines to guide the eye. The three peaks are somewhat different in magnitude and shape. The center peak is much broader and the early summer peak somewhat higher than in the OH data. The late summer peak, on the contrary, is substantially smaller. It is, nevertheless, about significant as the error bars show. (These are standard errors of the mean.) The major result of Figure 2 is that the triple structure of QTDW amplitude development during the course of summer is essentially seen in either of the two data sets that stem from quite different measurements and analysis techniques. It will be discussed in section 4 that wave excitation is possible if the atmospheric instability is strong and at the same time the zonal wind meets the phase velocity of the wave. Times of favorable wind speeds for wave W3 can be taken from Figure 5 and are shown in Figure 2a as a horizontal bar. Minimum values of the atmospheric instability (parameter bc; see section 4) are indicated in Figure 2 at DOY 151 and DOY 211 by vertical dashed lines (blue). They are taken from Figure 11 and will be explained below.
 Further westward traveling QTDW modes have also been analyzed from MLS data, with wave numbers 2 (W2) and 4 (W4). Their mean amplitudes in summers 2005–2009 are shown in Figure 3 for comparison. They are almost as high as for W3, but their distribution during the summer is different: while W3 is present over large parts of the summer, W4 is more restricted to late summer, and W2 appears to be concentrated in the center of the summer. Times of favorable wind speeds as taken from Figure 5 are again shown in Figures 3a and 3b by horizontal bars. As in Figure 2, also here the higher amplitudes mostly-but not always-correspond to the favorable wind speeds. This is discussed in detail below. The dashed vertical lines (blue) in Figure 3 again denote the bc minima in Figure 11.
 The OH measurements “see” all QTDW modes W2, W3, and W4 superimposed. This does not, however, mean that the curve in Figure 2b should be the sum of the other curves in Figure 2 and 3. The reason is that the waves W2–4 can have various phase shifts that lead to constructive or destructive interferences. Only this much can be concluded that the three peaks in Figure 2b appear to stem mostly from W3. W4 appears to contribute some to the late summer peak of Figure 2b, and so does W2 to the midsummer peak. These correspondences are, however, not very pronounced.
 We have checked the response of our analysis method with respect to the periods assumed in the fit procedure. We have assumed wave periods between 2 and 3 days at increments of 0.25 days and fitted wave modes W2, 3, and 4 to the MLS data of 2005–2009. The results in a 15 day window around the midsummer peak are shown in Figure 4. Wave mode W3 has maximum response at 2–2.3 days period with decreasing values at longer periods. Mode W4 behaves similarly. Mode W2, however, has some increasing response at longer periods. (As mentioned a period of 2.3 days has been used for all three wave modes in the present paper to allow comparison with the FFT analysis.) We have performed a similar analysis in a 15 day window around the early summer peak. The results look similar to Figure 4. In the area of the late summer peak the amplitudes of the wave modes W 2, 3, and 4 are fairly small. The corresponding spectra therefore are dubious.
4. Atmospheric Instability and Critical Zonal Winds
where β = 2Ω cos Φ/a, Φ = latitude, Ω = Earth angular velocity, a = Earth radius; f is the Coriolis parameter; σ = −(RT/p) d(lnΘ)/dp is a static stability parameter with R = gas constant, and Θ = potential temperature. In order to evaluate equation (1) for summer 2005, measurements of the MLS/Aura instrument were used (version 2.2 data [Schwartz et al., 2008]). Assuming geostrophic balance quasi-geostrophic zonal wind speeds were derived from the data for 52°N and 56°N. The average of the zonal means at these two latitudes are shown in Figure 5 for the altitude of 0.046 hPa (about 70.5 km, black squares). They are compared to winds measured by a MF radar at 70.5 km altitude (red dots). These measurements were taken at the station of Juliusruh (55°N, 13°E) relatively near to Wuppertal. Details are given by, e.g., Keuer et al. . Mean values of radar winds of years 2004–2009 are shown in the upper mesosphere in Figure 6. Here, the mean winds were separated from fluctuations caused by gravity waves, tides and transient planetary waves with periods up to about 20 days by least square fits of 10 day composite days shifted by 5 days for each individual year (for details see, e.g., Singer et al.  and Hoffmann et al. ).
 The wind field in summer shows a westward jet at altitudes below about 85 km, and an eastward jet above this altitude. The times of wind turn around are shown as zero-wind lines in Figure 6. These lines are not vertical in the picture, but somewhat inclined with altitude above about 87 km, and strongly inclined at around 85 km.
 The altitude range at about 70 km is close to the lower limit for MF radars due to the reduced signal-to-noise ratios. Nevertheless, the agreement of the quasi-geostrophic winds and the radar winds in Figure 5 is fairly good and appears to be typical of such data [e.g., Labitzke et al., 1987; Oberheide et al., 2002]. The error bars shown are standard errors of the derived quasi-geostrophic zonal winds and of the least square fits of the MF winds. We use the quasi-geostrophic MLS winds to estimate the quasi-geostrophic potential vorticity gradient Qy. The radar winds are used to estimate the baroclinic instability below. Most of these data are used for relative comparisons in the following and therefore do not need high absolute accuracy.
 Examples of Qy values determined from MLS winds are shown in Figure 7 for the month July 2005. Time resolution is 5 days. The picture shows that instability occurs in localized altitude/latitude areas on a given day. It also shows that our analysis latitude and altitude (51°N. 0.046 hPa) is at the fringes of the unstable areas. This may explain part of the high variability of our QTDW amplitudes.
 If a critical wind line cuts into an instability area there is potential for strong flow/wave interaction and hence wave excitation [e.g., Burks and Leovy, 1986; Limpasuvan et al., 2000]. The phase speed of a westward traveling wave W3 with wave number 3 at 2.3 days period is a little larger than 40 m/s. This critical wind speed is indicated in Figure 5 by a dashed horizontal line. Respective lines for waves W4 and W2 are also given.
 The time development of the radar winds at 79 km altitude is also shown in Figure 5 for comparison with the 70.5 km data (blue triangles). This altitude is chosen because it is at the upper boundary of atmospheric instability (see Figure 7). The time regime favorable for wave excitation can thus be plotted in Figure 5. It is the time (on a horizontal critical wind line) between the blue and red curves (including error bars). This is because above the blue curve the atmosphere is no longer unstable. The red curve gives approximately the lowest (strongest negative) winds in this part of the atmosphere (see Figure 6). These favorable intervals are shown by heavy horizontal bars for the QTDW modes W2, W3, and W4 in Figure 5. A given wave mode will find on its corresponding bar its critical wind speed at some altitude between 70.5 km and 79 km. The atmosphere is unstable approximately between the blue and the red curves as is seen for July in Figure 7, and it is assumed here that this is approximately true for the rest of the summer. There are, however, two exceptions by the times of the vertical dashed lines, which are discussed below.
 The horizontal bars of favorable wind speed have also been plotted in Figure 2a and Figures 3a and 3b. They coincide with periods of high wave amplitudes relatively well. This implies that excitation of a given wave mode occurs at different altitude levels at different times.
 The three peaks of our amplitude triplet (OH measurements, Figure 2b) typically occur at DOY 130–140 in early summer, at DOY 180–200 in midsummer, and at DOY 230–240 in late summer. These time intervals are shown in Figure 5 by hatched areas. Comparison with the horizontal bars suggests that the midsummer peak should mostly be influenced by the W3 mode, and somewhat by the W2 mode. The early and late summer peaks, however, should in addition to W3 also see some contribution from the W4 mode at the “outer wings” of the wind profiles in Figure 5. (The horizontal bar of favorable wind for W3 is from DOY 153–229. An extension (blue) of this bar to earlier times at DOY 136 has been added in Figure 5 because during this time wind variances were strong (10–15 m/s) and can contribute to wave excitation.)
 The two exceptions from the general instability mentioned are near DOY 151 and DOY 211. These are two essential reductions in instability as is shown below in Figure 11. This means that around these times the atmosphere tends to become stable, and wave excitation is reduced. The times when this occurs are given in Figure 5 by vertical dashed (blue) lines. Respective lines have also been added in Figures 2 and 3.
 The time development of instability during the whole summer of year 2005 is shown in Figure 8. Negative values of dQ/dy are plotted (as −Qy, red dots) such that high values indicate high atmospheric instability. Mean values of 52°N and 56°N are given. Data are for 0.046 hPa altitude (about 70.5 km). Units used are 10−11 1/ms. At high instability (high −Qy) one could expect high QTDW amplitudes. Therefore such amplitudes derived from the OH combi data in 2005 are plotted in Figure 8 for comparison. Their time resolution is 7.5 days; that of −Qy is 5 days. For easier comparison the −Qy data have been interpolated to the times of the OH measurements. There are quite a number of (nearly) coincident peaks in the two data sets (at least in the core of summer). They are indicated by vertical ovals. Correlation coefficient of the two data sets is r = 0.57 at 98% significance. Hence there is substantial support for the concept that QTDW are excited in instable atmospheric regions. A close correlation cannot, of course, be expected as a high instability value alone is not a sufficient condition for wave excitation.
 Some typical error bars are shown in Figure 8. They cannot be used to compare the two curves as these have different units. They are rather meant to show the internal consistency of either of these curves. For estimation of the error of the QTDW amplitude on a given day, random noise was added to the spectrum measured, and the spectral analysis was repeated. This was performed ten times, and the standard deviation of the results was used as an error estimate in Figure 8. Errors of Qy were estimated by calculating Qy differences at five adjacent altitudes and two latitudes. The standard deviations of these differences are given in Figure 8. They are upper limits for the measurement uncertainty as they still may contain “real” atmospheric variations. This influence is noticeable in the second half of summer 2005 when instability is large. In this part of Figure 8 error bars could therefore not be given.
N is the buoyancy frequency, f is the Coriolis parameter, and ρ is the density. The BCL term can be estimated from the vertical wind profiles measured at Juliusruh. These zonal winds are available at 1.5–2 km altitude resolution and 5 days time resolution, and reach back to 1990. Hence information on atmospheric stability may be obtained much further back than satellite data can do. As the barotropic part (next to last term in equation (1)) is not available from a single station this information is only an approximation of the atmospheric instability. The BCL parameter is, nevertheless, quite useful as is shown below.
 To obtain an instability situation BCL should be positive. Hence we may expect large QTDW amplitudes if there are large positive BCL values. We are interested here in the relative variations of the QTDWs and hence of BCL during the course of the year. For our estimation, we assume (as approximations) f2/N2 to be constant and ρ = ρ0 exp(−z/H) with a scale height H = 6.3 km. Hence we obtain the instability term
We perform the analysis at 74 km altitude because here the signal/noise ratio of the wind measurements is better than at the lowest altitudes available (70 km). First we compare the two instability parameters −dQ/dy (equation (1)) and bc (equation (3)) by means of data of year 2005 in Figure 9. Qy values (red dots) are means of 52°N and 56°N, and are given in units of 10−11 1/ms. Bc data (black squares, in relative units) are from 55°N. The time resolution of either data set is 5 days. Hence two peaks may be considered to show the same event if they occur within about 5 days. There is an approximate correspondence between the two data sets as almost each peak in the one curve finds its counterpart in the other (see the vertical ovals). We therefore use bc as an approximate indicator of instability below even though the barotropic contribution is lacking.
 A comparison of bc values and QTDW amplitudes (from OH measurements) is shown in Figure 10 for year 2007. The bc values are lower limits, only. This is because bc depends on the altitude resolution of the radar wind measurements. The basic principle of the MF radar used at Juliusruh has been changed in 2003 [e.g., Keuer et al., 2007]. Comparison of the earlier and the later data shows that the altitude resolution of the more recent data was reduced, and so are the bc values obtained. Hence the bc values before 2003 cannot be compared to those after 2003. With regard to this all bc values are given in relative units.
 Year 2007 was chosen for Figure 10 because its QTDW amplitudes are highly structured, as is shown by the triple structure in midsummer. This structure is mirrored in the bc values: most QTDW maxima meet a corresponding maximum in this parameter as indicated by the vertical dashed lines in Figure 10. The minima behave similarly. The correspondence is, however, not perfect neither for the maxima nor for the minima. This is seen for instance at and after DOY 240, and is typical also of the other years (2004–2008). In general it is found that in the earliest and the latest parts of summer, i.e., at and before DOY 120 as well as at and after DOY 240 the correspondence is marginal. The interval in between is called here the “core of summer” and is indicated in Figure 10 by a horizontal bar near the abscissa. We have analyzed the maxima in either parameter in this core interval in all 6 years. We score a coincidence if a maximum of QTDW amplitude occurs within 5 days of a bc maximum. This time difference appears acceptable considering the time resolutions of 7.5 days and 5 days for the QTDW amplitudes and the bc data, respectively. For the QTDW maxima we find bc counterparts in 83% of all (23) cases of QTDW maxima in 2004–2008. The “core of summer” identified this way is almost identical with the time interval of favorable wind speeds shown in Figure 5 (heavy horizontal bars). These two analysis results were obtained independently of each other.
 An interesting correspondence of bc and the QTDW amplitudes is also seen if mean values of several years are compared. Figure 11 shows 6 year mean values of QTDW (2004–2009) as compared to bc averages (2003–2008, at 74 km altitude). Averaging over several years is needed because of strong interannual variations (compare Figures 9 and 10). The triple structure of the QTDWs appears to be present in a similar form in the bc means, too. A closer correlation is not to be expected as the barotropic part of the instability is missing. If this result should substantiate in future years it is remarkable because the two curves result from measurements that are taken at different altitudes and are quite independent of each other.
5. Long-Term Development
 The triple structure in Figure 1 is very pronounced and has a characteristic form. This makes us suppose that it might be possible to determine long-term variations which would be indicative of changes of the dynamic stability of the mesosphere. We have therefore separately analyzed our OH data in the two time intervals 1988–1993 and 2004–2009, and show the results in Figure 12. (The years 1994–2003 could not be used because of bad statistics.) The mean intraseasonal variations of the 6 years of the later interval (2004–2009) are shown in Figure 12a (from Figure 11), those of the 4 years of the earlier interval (1988–1993) in Figure 12b. The amplitudes of the QTDW are found to be quite similar in the two intervals, and so is the form of the summer variation. This also applies to the comparison with Figure 1. There are, however, two important differences. (1) The center peaks of the triplets are somewhat narrower than that in Figure 1, and so are the late summer peaks. (2) The second, more important difference is that the time structure is somewhat different in Figure 1, and Figures 12a and 12b. The reason is indicated in Figure 12 by the upward directed red arrows. They connect the most pronounced amplitude maxima and minima in Figures 12a and 12b. These extrema are quite characteristic, and there is little doubt about their correspondence. It is now important to note that the time difference between the first and last summer maximum is larger in the more recent time interval (Figure 12a, 2004–2009) than in the time interval 15.5 years earlier (Figure 12b, 1988–1993). Hence, the length of the summer season as indicated by QTDW peaks appears to have increased during this time span. This is discussed in more detail in section 6. Summation of these slightly shifted peaks yields the broader peaks of Figure 1.
Figure 12 shows a long-term change in wave activity. Given the correspondence between QTDW amplitudes and atmospheric instability (bc) on the one the hand and the favorable zonal wind speeds on the other some long-term changes of these parameters are suggested, too. We have therefore calculated bc for the measurements available at Juliusruh, in the years 1990–2002. These are shown in Figure 13 (at about 75 km altitude). The picture compares mean bc values from the time interval 1990–1995 to the interval 1997–2002. The first interval covers 6 years, the second one only 5 years as the year 2000 could not be used because of data gaps. The data have been smoothed by a 5 day running mean. The error bars give the error of the mean. A comparison with the more recent data in 2003–2009 is not possible because of the change in radar in 2003 mentioned above. The curves in Figure 13 indicate some long-term bc changes, indeed, with some increases of the later seasonal curve in early summer. These are significant as shown by the error bars.
 Mean zonal wind speeds in the two intervals 1990–1995 and 1997–2002 are shown in Figure 14 (radar winds at Juliusruh, 73 km). Significant differences between the two intervals are seen, the more recent winds being generally faster than the earlier ones. The phase speeds of wave modes W3 and W4 are indicated by horizontal dashed lines at 40 m/s and 30 m/s, respectively. In the first half of summer these lines meet the winds of the more recent interval at some earlier time than the winds of the earlier interval. In the second half of summer it is the other way round. This is indicated by horizontal (blue) arrows in Figure 14. Hence the time interval when the wind is faster than 30 m/s increases by 16.2 days, and by 15.4 days for the 40 m/s speed. This is discussed below.
 Amplitudes of the QTDW in the mesosphere exhibit a triple structure during the course of summer. Figure 1 shows that this structure is statistically significant; that is, the error bars of adjacent pairs of minima and maxima do not overlap. Corresponding pictures are also seen in Figure 2a, 2b, 12a, and 12b. Figures 1, 2a, 2b, 12a, and 12b show in total 20 adjacent pairs of extrema. Only four of these have some overlap of error bars, which is mostly marginal. The triple structure shows considerable interannual variation, and hence many years need to be averaged to show it reliably. In Figures 2a, 2b, 12a, and 12b, with a case of overlap, only 5 to 6 years were available for averaging. The picture with the largest number of years is Figure 1 (10 years). It exhibits the triple structure clearest and most convincingly.
 A westward traveling planetary wave of wave number 3 appears to be the major contribution to the QTDW triplet of period 2.3 days analyzed here. It has a phase velocity of about −40 m/s. Vertical propagation of such a wave is inhibited if the zonal wind speed is smaller (more negative) than this. Figure 6 shows that this is the case in large part of the upper mesosphere and of summer. Hence the question arises where our QTDW originate from, especially in the center peak of the triplet when the easterly winds are very strong (Figure 5). Here the wave origin cannot be at lower altitudes in the middle atmosphere. We have also performed QTDW analyses of the MLS data at lower altitudes (in 2005) and found that amplitudes are very small below about 70 km (not shown here). From this and from the instability and phase velocity analysis given we therefore conclude that the waves most likely have been excited in situ [see also Riggin et al., 2004; Day and Mitchell, 2010].
 Excitation of QTDWs is favored by two conditions: (1) the atmosphere must be dynamically unstable and (2) the zonal wind should have the critical speed (i.e., equal to the wave phase speed). This has been summarized in Figure 5. This picture is for year 2005; it is, however, also typical of the other years. The picture shows-together with Figures 2 and 3–that relatively long periods of favorable wind speeds and hence wave activity exist. They are, however, interrupted by times of decreased atmospheric instability as shown by our bc analysis.
 We have estimated the baroclinic instability by means of the zonal winds measured at Juliusruh (1990–2008). The baroclinic instability parameter bc (equation (3)) compares well with the general atmospheric instability given by the meridional gradient of the quasi-geostrophic potential vorticity (equation (1), year 2005). The parameter bc also compares favorably with the QTDW amplitudes in recent years. A close correspondence of the maxima of the two parameters (coincidences in 83% of all cases in years 2004–2008) is obtained. This is, to our knowledge, the first multiyear analysis of the baroclinic instability and QTDW amplitudes. Baumgaertner et al.  used the baroclinicity for comparison in their 1 year analysis. It should be noticed that a close linear correlation between atmospheric instability and QTDW amplitudes cannot be expected as the processes involved are highly nonlinear. Comparison of mean QTDW amplitudes in 2004–2009 and bc values in 2004–2008 shows that the triple structure seen in the seasonal variation of the waves appears to be also present in a similar form in the instability parameter bc (Figure 11).
 The minima of bc values around DOY 151 and DOY 211 coincide with reduced wave amplitudes by these times or shortly afterward. It is especially interesting to see in Figure 2a that the two steepest decays of wave amplitudes occurring at all follow immediately after the minima of instability bc. (Time resolution of the QTDW amplitudes in Figure 2a is 6 days; that of the bc data in Figure 11 is 5 days.) Figure 11 thus suggests a QTDW dissipation time of a few days.
 Comparison of Figure 2b with Figure 2a indicates that all peaks of the QTDW triplet in Figure 2b see major contributions from wave mode W3. The center peak can also be influenced by W2 as is indicated by Figure 3b. Figure 3a suggests that the late summer peak in Figure 2b sees essential contributions from W4 with wind speeds being favorable for this mode by this time. Hence the triple structure of our QTDWs (OH data) appears to result from the interplay of atmospheric instability and critical wind speeds.
 We have also analyzed MLS data (2005–2009) at other latitudes (30°N–57°N) and altitudes (60–95 km) with similar results as shown here. A detailed discussion is, however, beyond the scope of the present paper.
 As the triple structure of the QTDW summer record is a striking feature, the question arises whether it can be found in earlier data records. SABER temperature data reach back until 2002, and are therefore not very helpful. MLS data are available since the UARS launch in 1991. They have been used for QTDW analyses on several occasions. A triple structure has, however, obviously not been seen earlier than 2005. The standardized OH measurements at Wuppertal are available since 1988, and the data set 1988/1993 appears to be the earliest temperature data available for QTDW analyses in the upper mesosphere. It was measured early enough to allow a long-term analysis by comparison with the interval 2004–2009.
 These two data sets have been linked to each other by the red arrows in Figure 12. Individual maxima or minima in Figure 12a have shifted during this 15.5 year time span with respect to Figure 12b. The direction of these shifts is not uniform. It is to earlier times of the year in the first part of the summer, and to later times in the later part of summer. This applies as well to the pronounced maxima as to the pronounced minima. (The divide appears to be near DOY 210.) In consequence the duration of the wave activity period in summer appears to have become longer. The distance between the first and the last amplitude peak in Figure 12b is 90 days, and in Figure 12a it is 112.5 days. This is an increase of 22.5 days in 15.5 years, i.e., an increase rate of 1.45 d/y. The time resolution of our analysis (7.5 days) determines the accuracy of this estimation. Hence it is 22.5 ± 7.5 days, and the increase rate is 1.5d/y ± 0.5 d/y.
 The “duration of summer” and its changes have been described for the mesosphere and stratosphere by Offermann et al. , for instance by analysis of the shape of the seasonal temperature variation. For the upper mesosphere these authors obtain an increase of summer length since 1988 at a change rate of 1.16 d/y. This is surprisingly similar to the rate given here for the period of QTDW activity. These changes may be related to a change of the upper mesosphere summer jet analyzed by Keuer et al. . We have extended these analyses by including the recent years of wind measurements (Figure 6). We find that the lower boundary of this eastward jet; that is, the zero wind line in Figure 6 (at about 85 km, DOY 200) has decreased in altitude at a rate of about 0.3 km/y, i.e., by almost 6 km during 19 years of observations. As the zero wind lines at higher altitudes in Figure 6 are not vertical but somewhat inclined this means an increase of the eastward wind regime at a given altitude. As the OH measurements are taken at a fixed altitude (87 km) it is consistent that they show an increase of the summer duration. This obviously corresponds to a widening of the QTDW regime.
 Long-term changes of baroclinic instability parameter bc and of zonal wind speed u in the middle mesosphere have also been analyzed, and the results are shown in Figures 13 and 14. Two intervals 1990–1995 and 1997–2002 have been considered. Because of the similarity in behavior with the QTDW amplitudes, changes of parameter bc were expected. Some long-term changes (increases) appear to be present, indeed. Also the zonal wind shows a change, i.e., a long-term increase of absolute wind speed. As a consequence of this the favorable (critical) velocity for a given wave mode is met at an earlier time in the first half of summer, and at a later time in its second half. This is indicated in Figure 14 for QTDW modes W3 and W4. As the picture shows the total change is about 15–16 days for these two modes. (This number is somewhat altitude dependent, but is similar at other heights.) Figures 2, 3, and 5 show that such changes should lead to shifts of the favorable time intervals for the wave modes. Especially one would expect the early wave peaks to shift toward earlier times, and the late summer peaks to later times. This is exactly what is seen in Figure 12. The increase of time distance of 22.5 days in 15.5 years compares to 15–16 days in 7 years in Figure 14, which is the same order of magnitude. Changes in the time structure of the QTDW triplet as well as the zonal wind speeds and apparently the baroclinic parameter bc thus fit well together and are similar to the increases of the summer duration analyzed by Offermann et al. . The latter increases have been interpreted as being indicative of a long-term change of middle atmosphere dynamics/general circulation. Our changes in QTDW activity support this.
7. Summary and Conclusions
 Study of the quasi 2 day wave (QTDW) at a given OH ground station requires one measurement per day according to the Nyquist theorem. This is difficult to fulfill at medium latitudes with frequent cloud coverage. Furthermore an extended series of measurement years is needed to obtain robust mean results because the QTDW shows large volatility (intraseasonal and interannual variations). A homogeneous data set of upper mesosphere temperatures derived from OH emission measurements is available since 1988 at the station of Wuppertal (51°N, 7°E). Weather at this station allows a mean data coverage of about 60%; that is, data are obtained during 60% of the time available. This is not sufficient for QTDW analyses. In the measurement record mentioned there is only one period (1988–1993) with better coverage (75%) which can be used.
 A similar OH instrument is operated at the station of Hohenpeißenberg (48°N, 11°E) since autumn 2003. Comparison of the temperatures obtained simultaneously at the two places shows a very good agreement. Hence the two data sets are combined into one (“combi temperatures”) for analyses of large-scale phenomena. The combi data have an improved data coverage of about 80%. A QTDW analysis is therefore possible, and the 6 year period 2004–2009 yields fairly robust results.
 The QTDW analysis (at 87 km) during summer shows high amplitudes as expected. There are, however, three maxima instead of one (“triple structure”). The error bars allow this conclusion even though they are relatively large because of the interannual variations The combi data results are compared to a QTDW analysis (W3 mode) of MLS measurements (2005–2009, 86 km), and a triplet is also obtained in this case. In addition two other modes are analyzed (W2, W4). Maximum amplitudes occur at times when critical wind speeds prevail. Altogether these modes suggest a triplet structure, too, with W3 as the main contributor. Our results appear to be the first multiyear QTDW analysis in temperature.
 Atmospheric instability has been estimated by means of the meridional gradients of the quasi-geostrophic potential vorticity derived from MLS data in 2005 (near 70 km) and by a baroclinic instability parameter bc based on zonal winds measured by a nearby wind radar (at 74 km, Juliusruh, 55°N, 13°E, 2003–2008). As these instabilities should be linked to the occurrence of atmospheric waves we have compared our QTDW structures to them. A close correspondence of the peaks in the QTDW amplitudes and in the instabilities is obtained in a “core” period of summer (DOY 125–235).
 Mean values of parameter bc in years 2003–2008 appear to show a triple structure, too, with maxima by the times of the QTDW peaks. Hence we see triplets in three data sets that are from quite different measurements and at different altitudes. Two of the data sets are from local measurements (OH temperatures, radar winds), one is from global measurements (MLS).
 The detailed QTDW time structure during the course of summer appears to result from the interplay of atmospheric instability and zonal winds favorable of wave modes W2, W3, and W4.
 A long-term trend is indicated when the combi data results 2004–2009 are compared to those from Wuppertal in 1988–1993. The triple structure is also found in the early data, but the three peaks are closer together than in the later data. This long-term trend, i.e., the widening of the triplet during the recent 15 years, is believed to be related to the increase of summer duration in the mesosphere that has recently been suggested.
 The QTDWs show that the stability of the summer mesosphere has changed. A trend is seen in QTDW amplitudes as well as in zonal winds and baroclinic instability. This suggests that long-term circulation changes presently discussed for the middle atmosphere extend in some form to the uppermost part of the mesosphere.
 Future analyses are needed to substantiate the triple structure in the temperature and baroclinic data. Numerous satellite data are available. Their analysis has, however, mostly been restricted to relatively short time intervals. More full summer analyses are needed. Determination of the long-term changes of the triple structures, however, appears to rest on the ground-based measurements as satellite data do not reach far enough back.
 J.O. was supported by Deutsche Forschungsgemeinschaft (DFG), grant OB 299/2–3. The analysis of EOS/MLS data was supported by NASA contract NNH05CC70. D.O. thanks J. Wintel for many helpful discussions.