During the three summer seasons of the years 1998, 2000 and 2001 mid-latitude mesosphere summer echoes (MSE) were observed with the OSWIN VHF radar. The radar is located at Kühlungsborn (54.1°N, 11.8°E). Based on nearly continuous operation of the radar a large data set with altogether more than 200 hours of MSE observations with signal-to-noise ratios greater than 0 dB has been obtained. We present and discuss the results of the three years observation. Mid-latitude mesosphere summer echoes occur much more seldom than their corresponding polar mesosphere summer echoes (PMSE) in polar regions. Both phenomena are characterized by very strong radar returns with a high aspect sensitivity and a restriction to the summer mesosphere. But beside these analogies their main differences will be discussed also. MSE occur in a shorter time interval in the summer months and normally only during daytime. They are still observable although the low temperatures and the sufficient degree of saturation necessary for the existence of ice particles cannot be reached at all times. Furthermore we show MSE distribution, scattering characteristics, aspect sensitivity, and turbulence characteristics as functions of height.
 Strong radar echoes at frequencies near 50 MHz from upper mesospheric heights are a well known phenomenon for several years. They are typical especially for the polar mesosphere during summer condition which is characterized by the lowest temperatures observed in the Earth's atmosphere. These radar echoes are an important possibility to investigate the structure and dynamics of this part of the atmosphere.
 Radar waves in the VHF range are backscattered by irregularities of the refraction index of half the radar wavelength mainly caused by electron density fluctuations. Such small irregularities should normally be destroyed at mesospheric heights by viscous forces. Therefore, Kelley et al.  and Cho et al. [1992a] suggested that large aerosol or small ice particles should prevent the destruction of these irregularities by an effective reduction of the electron diffusivity. The good correlation between PMSE and noctilucent clouds (NLC) as found in simultaneous and common volume observations [von Zahn and Bremer, 1999] confirms the existence of ice particles during PMSE. The creation of the small-scale irregularities in the electron density is however an unsolved question. Some ideas can be found in Cho and Röttger .
 In this paper we present results of MSE observations during the summer months of 1998, 2000 and 2001 at Kühlungsborn (54.1°N, 11.8°E). Nearly continuous measurements provided large data sets and hence the chance to study the main properties of MSE on good statistical conditions.
 The MSE observations were performed with the VHF radar system OSWIN (Ostsee Wind Radar) at Kühlungsborn. The essential radar parameters used for MSE measurements are listed in Table 1.
Table 1. System Parameters
36 kW (72 kW in 2001)
144 Yagi array
Effective antenna area
Half-power beam width
16 bit complementary code
Pulse repetition frequency
Length of time series
∼15 sec (∼22 sec in 1998)
Complete time resolution
 The system is capable of unattended continuous operation. It works at a frequency of 53.5 MHz with a peak power of 36 kW (72 kW in 2001) provided by six transmitting modules. The antenna array consists of 12 × 12 four-element Yagi antennas with 0.7 λ spacing, where λ is the radar wavelength. The whole antenna array of 144 Yagis associated with a half-power beam width of 6° was used for transmission. For receiving, this array was divided into six discrete blocks of 6 × 4 Yagis to organize individual signal recordings for the spaced antenna (SA) method. The effective pulse width of 2 μs used in the experiments corresponds to a range resolution of 300 m. To operate at the maximum duty cycle a pulse coding has been applied using a 16-bit complementary code.
 During the three summers the radar system was operating in the spaced antenna as well as in the Doppler beam swinging (DBS) mode alternately with a complete time resolution of 2–3 min. However, in this paper we focus on the results of the spaced antenna mode. The length of time series is about 15 sec in 2000 and 2001 and about 22 sec in 1998.
 The operation of the OSWIN radar in the spaced antenna mode provides separated receiving signals of the six antenna subarrays. On the one hand it is possible to recombine these signals phase compatible to gain the receiving signal from the whole antenna. By this way we get the maximum signal-to-noise ratio (SNR) for detection of MSE. We used this enhancement for the investigations of the seasonal and diurnal variations as well as the height distribution of the backscattered echo power. On the other hand the signals from the antenna subarrays are applied for studies of the aspect sensitivity and turbulence characteristics using spaced antenna conveniences. Both receiving antenna configurations (whole antenna and a subarray only) have been used for the investigation of the scattering characteristics of the MSE.
 For the description of the seasonal and diurnal variation of MSE in the sections 3.1 and 3.2 and of the height distribution in section 3.3 we estimated PMSE occurrence rates. These occurrence rates have been derived on the basis of data blocks separated by about 2–3 min. For each of these values it was tested whether at least for one of the height channels between 78.5 km and 92 km its SNR value is greater than a threshold value SNRmin. Afterwards, the mean hourly or daily occurrence rates were calculated from the hourly or daily number of samples with SNR > SNRmin to the corresponding total numbers of data blocks with radar measurements.
 As marked in Table 1, all MSE observations were carried out with nearly the same radar set-up, except in 2001 the radiated power is doubled comparing with the years 1998 and 2000. Therefore, for the derivation of consistent occurrence rates, we had to use different threshold values. We utilized SNRmin = 0 dB for the years 1998 and 2000 and SNRmin = 3 dB for the year 2001 since the radiated power is 3 dB larger than the years before. Using this difference in SNRmin, we are able to compare the occurrence rates for all years investigated at mid-latitudes. They are also comparable to the PMSE occurrence rates derived from measurements at polar latitude at Andenes (69.3°N, 16.0°E) for the years 1999 until 2001 because the used VHF radar system ALWIN (ALOMAR Wind Radar) has nearly identical parameters as the OSWIN radar at Kühlungsborn (including the antenna system and 36 kW peak power). Still it should be noted here that absolute values like backscatter cross section or radar reflectivity have to be used for comparisons, if the parameters of the different radars are not nearly identical. In such a case absolute radar calibrations would be necessary.
 For the investigations of scattering and turbulence parameters presented in sections 3.4 to 3.6 we did not use different threshold values SNRmin since no comparison of the results of different years or different stations is made. Here, we only have to avoid that the noise do not strongly influence the behaviour of the backscattered radar signal. Therefore, only signals received with the antenna subarrays at SNRmin > 0 dB have been analysed.
3.1. Seasonal Variation
 In general, MSE are observed at Kühlungsborn between the beginning of June and the middle of August. From the observations in 1998, 2000, and 2001 the mean starting day of MSE events is 3 June and the mean last day is 14 August. These dates are marked by the thin vertical dashed lines in Figure 1. The vertical bars in the upper part of Figure 1 characterize the mean daily occurrence rates estimated from the three years of observation. Strong day-to-day variations with values between 0% and 23% are shown. The dashed curve has been estimated by a polynomial fit through the daily values of the MSE occurrence rates. As already discussed in the introduction a good correlation between PMSE and NLC has been found at polar latitudes. At mid-latitudes, however, the occurrence of NLC is markedly smaller than the occurrence of MSE. In lidar observations at Juliusruh (54.6°N, 13.4°E) and Kühlungsborn [von Cossart et al., 1996; Alpers, private communication, 2002] NLC have been detected very rarely (no more than three events per year). The first observation has been made at 3 June and the last at 9 July during the summer seasons between 1995 and 2001. This NLC period characterized by the horizontal box in the lower part of Figure 1 is obviously shorter than the mean MSE season.
 For all NLC observations at Kühlungsborn during the years 1998, 2000, and 2001, MSE were observed at the day before and after the NLC occurrence. It has to be mentioned here, however, that no simultaneous observations of MSE and NLC were possible until now since the lidar observations are performed only during night and MSE are normally detected only during daytime.
 As mentioned in the introduction large aerosol or ice particles play an important role for the existence of PMSE. Therefore the degree of saturation S = pH2O/pS has been calculated for the altitude of the maximum MSE occurrence at 85 km (see section 3.3). In this equation pH2O is the partial pressure of water vapor and pS is the saturation pressure of water vapor which can be calculated from the temperature T by a formula derived by Marti and Mauersberger 
 For calculating Equation 1 temperature data from potassium lidar (K-lidar) observations at Kühlungsborn [Latteck et al., 1999] have been used, which are shown in the lower panel of Figure 1 by the solid curve.
 The partial pressure of water vapor pH2O = p · w has been derived from the atmospheric pressure p of the CIRA86-model data [Fleming et al., 1990] and from model values of the water vapor mixing ratio w from calculations by Körner and Sonnemann  and Sonnemann (private communication, 2002) for summer conditions at a height of 85 km and a latitude of 55°N. The seasonal variation of w is characterized by smaller values at the beginning of the MSE season (w = 1.6 ppmv), a maximum near the end of July (w = 2.6 ppmv) and a small decrease toward the end of the MSE season (w = 2.5 ppmv). Using these pH2O data and the pS values of Equation 1 the degree of saturation S has been estimated (dash-dotted curve in the lower part of Figure 1). The estimated values of S are remarkably smaller than one, the lowest value necessary for the existence of ice particles in the mesosphere. The consequences of this result will be discussed in more detail in section 4.
3.2. Diurnal Variation
 The mean diurnal variation of the occurrence rate of MSE is separately shown for the three years of observation in Figure 2 (solid curves). In general, MSE are only observed during daytime with a maximum near noon (9–13%). During night-time no MSE occur, except in connection with the very strong geomagnetic disturbance on 15 July 2000 MSE events have also been detected at night. Additionally, in Figure 2 the diurnal variation of electron density (dashed curves) is shown for an altitude of 85 km at mid-latitudes after the IRI-95 model (http://nssdc.gsfc.nasa.gov/space/model/models/iri.html). The comparison of MSE occurrence rates with the electron densities leads to the conclusion that MSE can only be observed if the electron density is greater than a value of about 500 el./cm3. Therefore, MSE can only occur during night-time if an additional ionization is created by precipitating high energetic particle fluxes in connection with geomagnetic storms.
3.3. Height Distribution
 MSE are observed more or less regularly in the summer mesosphere, but their occurrence rate strongly depends on the altitude. Figure 3 represents the height distribution of three-year-mean MSE occurrence for SNR > SNRmin with SNRmin = 0 dB for the years 1998 and 2000 and SNRmin = 3 dB for 2001 as also used in Figures 1 and 2.
 It is shown that MSE layers normally occur in an altitude range between 80 km and 90 km with a maximum incidence near 85 km. The average occurrence falls rapidly away the peak, which means that more than 90% of MSE occur between 82 and 88 km.
3.4. Scattering or Reflection?
 As remarked in the introduction the reason of mesospheric summer echoes is only partly understood. Especially the creation of small scale irregularities in the electron density is an unsolved problem until now. Therefore, the question whether the MSE are caused by atmospheric scattering or reflection processes will be discussed here in more detail. The following explanation could help to find the physical processes which create the irregularities necessary for the MSE and PMSE.
 For isotropic volume scattering Balsley and Gage  give a linear dependence of the received radar echo power Ps on the effective antenna area AE by the radar equation
where α is an efficiency factor for the antenna transmission lines, Pt the peak transmitter power, r the distance to the center of the scattering volume, Δr the range gate width, and η the radar reflectivity.
 The power received by reflection from a single discontinuity is given by the equation
where ρ is the amplitude reflection coefficient of the discontinuity, which is a function of the radar wavelength and the vertical refractive index gradient [e.g., Gage et al., 1981].
 Although for special instances these equations have to be varied as described by different authors, in any case the signal power depends linearly on the antenna area for a perfect scattering process, and quadratically on the antenna area for a plain specular reflection process. If we observe mesosphere echoes at the same location simultaneously with different antenna arrays, i. e. different effective antenna areas AE, and assuming that all other parameters of equation 2 and equation 3, respectively, are the same, we can estimate whether volume scattering or specular partial reflection is responsible for the echoes [Zecha et al., 2001].
 For spaced antenna operation the antenna array is divided into six subarrays formed by 6 × 4 Yagis for receiving with each subarray separately. This give us the opportunity to obtain several receiving antenna arrays. We used the whole antenna with 144 Yagis (antenna area A144 = 1900 m2) for transmission and for reception in the first case, but a subarray with 24 Yagis (antenna area A24 = 320 m2) for reception in the second case. This leads to effective antenna areas of AE1 = = 1900 m2 and AE2 = = 780 m2 in first and second case, respectively. Hence, we get the area ratio AE1/AE2 = 2.45. If both antenna configurations have the same efficiency otherwise, we expect this ratio corresponding to a power ratio of 3.9 dB for a plain scattering process with linear dependency (Ps1/Ps2 = AE1/AE2) and to a power ratio of 7.8 dB for a plain reflection process, since the latter depends quadratically on the antenna area (Pr1/Pr2 = (AE1/AE2)2).
 The relation of the signal powers P144 and P24 detected by the complete 144 Yagi receiving antenna and a subarray of 24 Yagi are calculated, respectively. To avoid a bias due to very weak signals we have only plotted data points if the signal-to-noise ratio exceeds 0 dB for the small antenna.
 It can be seen clearly in the histogram shown in Figure 4 that the ratios are mostly distributed between the two extrema with a tendency towards to the lower limit of Ps1/Ps2 = 3.9 dB than to the upper limit of Pr1/Pr2 = 7.8 dB. The median value is about 5.6 dB. Please note the logarithmic scale. This result indicates that MSE seem to be caused by a mixture of pure scatterring and reflection processes where the scattering features slightly dominate. This pointed out that the irregularities necessary for the creation of PMSE cannot be caused by atmospheric turbulence only. Other processes as discussed by Cho and Röttger  may play an important role.
Figure 5 shows the individual values P144/P24 in dependence on height plotted as crosses. The solid line connects the median values for each height channel. It is clearly evident that, in general, the scattering character gains more and more with increasing height.
3.5. Aspect Sensitivity
 The aspect sensitivity of the radar signals is closely connected with the investigations of the reflection and scattering properties discussed in the preceding section 3.4. Especially for radar reflections but also for anisotropic scattering an aspect sensitivity is expected [Röttger, 1989] with the strongest radar echoes from the vertical direction and a pronounced dependency on the zenith angle. This aspect sensitivity can be calculated using the echo power from different incidence angles at DBS mode operation. It can also be determined from results of the Full Correlation Analysis (FCA), which is described in detail by Briggs . Here we follow the calculation method derived by Hocking et al. . It is assumed that the scatters are oblate spheroids with a Gaussian decrease in refraction index from the center toward the edge. The aspect sensitivity can be estimated using the characteristics of the spatial correlation ellipse of the FCA model and the half-width of the radar beam. We have calculated the half-angular width ΘS of the backscatter polar diagram. Small values of ΘS indicate large values of aspect sensitivity, while large ΘS values indicate less aspect sensitivity and a more isotropic scatter.
 Like PMSE, mid-latitude mesosphere summer echoes show a substantial aspect sensitivity. The crosses in Figure 6 indicate all available values of ΘS. They are mainly distributed between 1.5 and 4 degree. The solid line indicates the median values for each height channel. It shows that the aspect sensitivity is very strong especially at the lower part of the MSE layers and it decreases with increasing height.
3.6. Turbulence Parameter
 The temporal characteristics of the scatters can be specified by a fading time which is closely related to the total spectral width σtot of the radar echoes. This measured spectral width contains contributions due to turbulent processes in the atmosphere (σfluct), representing the mean square fluctuating velocity within the illuminated radar volume, and it contains contaminations by non-turbulent contributions (σbroad) due to the reception of wind components by the radar with a finite beam width, which leads to a spectral broadening [Hocking, 1983]: σtot2 = σfluct2 + σbroad2. As shown by [Czechowsky and Rüster, 1997] the dominating non-turbulent process is the so-called beam broadening due to the different impacts of the horizontal wind on different positions inside the finite radar volume. This effect can be eliminated if the horizontal wind speed and the half-power beam width of the effective radar beam are known [Hocking, 1983]. The real values of the resulting spectral width σfluct due to turbulent processes are shown in the Figure 7 for the observations with a signal-to-noise ratio greater than 0 dB. The solid line connects the medians for each height channel. It shows that, in general, the turbulent character tends slightly upwards with increasing height.
 There are some remarkable differences in the seasonal and diurnal variations between PMSE and MSE. The occurrence rate of MSE is obviously smaller than those of PMSE. On individual days the MSE occurrence rate can be up to 50% (see, e. g., the daily data during summer 1998 in Latteck et al. ). During the mean seasonal variation estimated from all three years of observation in Figure 1 the maximum daily values are reaching up to 23% of occurrence rate, but otherwise there are also days without any MSE. Therefore, the mean occurrence rate (dashed curve in the upper part of Figure 1) reaches its maximum value in the first part of July with only 7.5%. This value is markedly smaller than mean PMSE values observed during 1999–2001 at Andenes with occurrence rates of more than 90% [Bremer et al., 2003]. The reason of this strong difference are the small values of the degree of saturation S in the lower part of Figure 1 derived from K-lidar temperatures at Kühlungsborn and model values of the water vapor mixing ratio described above in section 3.1. The S values in Figure 1 are clearly smaller than one even at its maximum during the second half of June.
 To get S values equal or greater than one, as it is necessary for the existence of ice particles in the mesosphere, it is essential to assume either generally higher values of the water vapor or lower temperatures. The condition of S = 1 is shown in dependence on the temperature T and the water vapor content w for 55°N and summer solstice conditions in Figure 8.
 For the lowest mean temperature of Figure 1 with 157 K the water vapor mixing ratio should be in the range of about 70 ppmv. This value of w is absolutely unrealistic according to all model calculations [Körner and Sonnemann, 2001] and experimental observations [Seele and Hartogh, 1999; von Cossart et al., 1999] known until now. For periods outside the temperature minimum even higher values of w are necessary to get S = 1. Therefore MSE observations cannot be explained by changes of atmospheric water vapor content.
 The more realistic possibility includes the assumption of lower temperatures caused by atmospheric waves (gravity waves and/or tides). Wave induced temperature changes of about 10 K up to almost 20 K are necessary during the first part of the MSE season near the maximum of the S curve from beginning of June until about 10 July. Such temperature changes have often been observed by K-lidar measurements at Kühlungsborn [Oldag, 2001], unfortunately not simultaneously with MSE observations because until now lidar measurements have only been carried out during night-time as already remarked above. During the first part of the MSE season the existence of ice particles is supported by the seldom observed NLC (see horizontal box in the lower part in Figure 1). In June 1992 and July 1994 Chilson et al.  found by simultaneous radar and lidar observations at 52°N MSE and NLC structures which were closely related to temperature changes induced by gravity waves. During the second part of the MSE season from 10 July until its end near the middle of August no NLC were detected by lidar observations at Kühlungsborn and Juliusruh. But nevertheless, MSE have been detected also during this time interval. To get S values greater than one during this period atmospheric waves have to be assumed with amplitudes of more than 20 K or even 35 K. Therefore, it seems to be very questionable that such strong waves are the only explanation of MSE. Another possibility could be that instead of ice also other particles may be important (large water cluster ions or sulphur aerosols as proposed by Mills et al. ). This point is an unsolved problem until now and needs further investigations.
 The diurnal variation of MSE is different from those of PMSE. Whereas the diurnal variation at Andenes is characterized by a typical semidiurnal variation with maxima near noon and midnight, the variation of MSE is dominated by a diurnal variation with a maximum near noon and a minimum during night-time. As demonstrated by Hoffmann et al. , Klostermeyer  and Bremer et al.  the PMSE variation is caused, in general, by dynamical effects and ionization changes due to variations of the Lyman α radiation (maximum effect near noon) as well as precipitating high energetic particle fluxes (maximum effect near midnight). Extremly strong particle effects may however destroy PMSE as found by Rapp et al. . The diurnal MSE variation is mainly caused by the ionization due to solar wave radiation (ionization of nitric oxide (NO) by solar Lyman α radiation, Brasseur and Solomon ). The maximum ionization is produced near noon in agreement with the MSE variation, whereas the undisturbed ionization during night-time is too small for MSE creation. Only during strong geomagnetic storms the ionization level is high enough to cause MSE also during night due to precipitating high energetic particle fluxes.
 For polar latitudes a threshold of about 500 el./cm3 necessary to create MSE has also been estimated by Goldberg et al.  and Rapp et al.  from PMSE observations and simultaneous electron density measurements as well as different electron density models. As discussed in Rapp et al.  in detail such a lower limit of the electron density is to be expected if the radar cross section per unit volume is proportional to the power spectral density of the electron density fluctuations. If these electron density fluctuations are proportional to the electron density the backscattered radar signals should become smaller with decreasing electron density. At the threshold value of about 500 el./cm3 the radar signals are too small to be detected with the used radars, for very powerful radars this level may, however, be slightly smaller.
 As demonstrated by the ratio of the backscattered power observed with different receiving antennas (P144/P24) in Figures 4 and 5, the MSE are caused by a mixture of scattering and reflection features with a slightly enhanced amount of the scattered components. Similar investigations of PMSE at Andenes [Zecha et al., 2001] yielded comparable results, however the scattered part of PMSE is slightly more enhanced. With increasing height the scattered part of MSE increases (Figure 5). This behaviour is also described by the aspect sensitivity values Θs in Figure 6. Qualitative the same result got Huaman and Balsley  for the aspect sensitivity of PMSE observations using old radar observations at Poker Flat and Singer and Latteck  for PMSE data of Andenes. Also the turbulent parameter σfluct in Figure 7 increases with height. This result is in agreement with investigations reported by Balsley et al.  and Rüster and Reid .
 Therefore, all three parameters investigated in sections 3.4 to 3.6, P144/P24, Θs, and σfluct support an increasing turbulent and isotropic structure of the atmosphere with increasing height during summer between about 80 and 90 km. Rocket observations of the atmospheric turbulence at Andenes by Lübken et al.  confirm this result at least qualitatively. After their measurements during eight rocket flights the probability of enhanced turbulence is higher at the upper boundary of PMSE or even above than at lower heights.
5. Summary and Conclusions
 Based on three years of radar observations at Kühlungsborn (54.1°N, 11.8°E) the following characteristic features of mesospheric summer echoes (MSE) have been detected:
MSE are observed from beginning of June until the middle of August. The daily occurrence rates vary between 0 and about 50%, the mean occurrence rate has its maximum in the first part of July with about 7.5% and is therefore remarkable smaller than typical occurrence rates of PMSE (90% and more) detected by a VHF radar at Andenes with nearly the same technical parameters including the antenna system as the radar at Kühlungsborn. Low temperatures induced by atmospheric waves (gravity waves and/or tides) play an important role for the existence of large aerosols or ice particles which are necessary to explain MSE.
At undisturbed conditions MSE can only be observed during daytime for electron densities of more than about 500 el./cm3. During a very strong geomagnetic storm MSE have also been detected during night-time.
MSE are observed between an altitude range of about 80–90 km with a maximum near 85 km. This result is in general agreement with PMSE.
As found from simultaneous observation with different receiving antennas MSE have more scattering than reflection characteristics. The dominance of scattering processes increases with height.
Similar to PMSE mid-latitude mesosphere summer echoes are markedly aspect sensitive. This feature is strongest at the lower part of MSE and becomes smaller with increasing height.
The turbulence characteristics (turbulent part of the spectral width) during MSE appearance in general tends slightly stronger with increasing height.
 Therefore, all parameters describing the MSE scattering process support an increasing turbulent and isotropic structure at altitude within the interval of 80 to 90 km.