Corresponding author: R. Latteck, Leibniz‒Institute of Atmospheric Physics, Rostock University, Schlossstraße 6, 18225 Kühlungsborn, Germany. (email@example.com)
 Polar mesosphere summer echoes (PMSE) are strong enhancements of received signal power at very high radar frequencies occurring at altitudes between about 80 and 95km at polar latitudes during summer. PMSE are caused by inhomogeneities in the electron density of the radar Bragg scale within the plasma of the cold summer mesopause region in the presence of negatively charged ice particles. Thus, the occurrence of PMSE contains information about mesospheric temperature and water vapor content but also depends on the ionization due to solar electromagnetic radiation and precipitating high energetic particles. Continuous and homogeneous observations of PMSE have been done on the North-Norwegian Island Andøya (69.3°N, 16.0°E) from 1994 until 2008 using the ALOMAR SOUSY and the ALWIN radar at 53.5MHz. In 2009, the Leibniz-Institute of Atmospheric Physics in Kühlungsborn, Germany started the installation of the Middle Atmosphere ALOMAR Radar System (MAARSY) at the same location. The observation of mesospheric echoes could be continued in spring 2010 starting with an initial stage of expansion of MAARSY and is carried out with the completed installation of the radar since May 2011. Since both the ALWIN radar and MAARSY are calibrated, the received echo strength of PMSE from 14 years of mesospheric observations (1999–2012) could be converted into absolute signal power. This data series could be extended to the years 1994 until 1997 on the basis of signal-to-noise ratio values derived during the years between 1994 and 2008. The PMSE occurrence rate is positively correlated with the geomagnetic Ap index (significance level χ=85−95%), however, is not correlated with the solar Lyman α radiation. Using different regression analysis methods, the PMSE occurrence rates show a significant positive trend during the time interval from 1994 until 2012 (χ=95−99%).
 The phenomenon of strong echoes from the mesopause region during summer is well known from radar observations at frequencies between ∼2MHz and ∼1GHz at polar and middle latitudes for more than 30 years. These so-called Polar Mesosphere Summer Echoes (PMSE) are caused by inhomogeneities in the electron density of a size comparable to the radar Bragg scale (about 3m at 50MHz radar frequency) in the presence of negatively charged aerosol particles. At mesospheric heights, irregularities in the electron density distribution in the order of about 3m are smoothed out by molecular diffusion under normal condition [Lübken et al., 2002]. Small-scale structures of, e.g., charged ice particles created by turbulent advection lead to similar structures in the distribution of free electrons and positive ions due to multipolar coupling between all charged species [Rapp et al., 2008]. These small-scale structures in the electron gas may well exist a considerable time after molecular diffusion has already destroyed any structures in the neutral gas distribution [Rapp and Lübken, 2003]. First, mesospheric summer echoes were observed at the end of the 1970s at midlatitudes above the Harz mountains of Germany [Czechowsky et al., 1979] before the first echoes of this type were seen at polar latitudes above Poker Flat [Ecklund and Balsley, 1981]. A detailed review about the early observations of PMSE can be found in Cho and Röttger , and an overview on the understanding of this phenomenon has been published by Rapp and Lübken .
 This paper gives an overview about the long-term observations of PMSE obtained with three very high frequency (VHF) radars at the Norwegian Island Andøya (69.3°N, 16.0°E) from 1994 until 2012. PMSE occurrence rates recently published by Latteck and Bremer  were merged with results from earlier investigations by Bremer et al. , and the resulting 17 years long data set was analyzed in dependence on solar and geomagnetic activity as well as analyzed for long-term trends.
2 Observation of Polar Mesosphere Summer Echoes at Andøya From 1994 Until 2012
2.1 Radars Used for PMSE Observations
 The observation of PMSE at Andøya started in the early 1990s using the mobile sounding system (SOUSY) radar [Czechowsky et al., 1984]. Continuous observation of PMSE started in 1994 using the Arctic Lidar Observatory for Middle Atmosphere Research (ALOMAR) SOUSY radar [Singer et al., 1995]. The latter was replaced in 1998 by the ALOMAR Wind (ALWIN) radar [Latteck et al., 1999] which allowed unattended and remote-controlled operation. After 10 years of nearly continuous operation, the ALWIN radar was switched off in September 2008 to be replaced by MAARSY [Latteck et al., 2010; Latteck et al., 2012a], the more powerful and flexible Middle Atmosphere ALOMAR Radar System. Parts of the ALWIN antenna array and the container housing the transmitter and receiving units were moved approximately 100m westward of the old radar site to be used for PMSE observation during the construction of the MAARSY antenna array in 2009. This interims solution called ALWIN64 [Latteck et al., 2010; Latteck et al., 2012a] used six of the newly designed MAARSY antennas for transmission and 64 of the old ALWIN Yagi antennas for reception. The successive installation of MAARSY started in September 2009 upon completion of the new antenna array and the radar started continuous operation using 217 transceiver modules in a first stage in spring 2010 [Latteck et al., 2012b]. A second stage of expansion to 343 transceiver modules was brought into service in November 2010 [Latteck et al., 2012b], and the system was finally upgraded to 433 transceiver modules in May 2011 [Latteck et al., 2012a].
 In this paper we use data from 18 years of continuous PMSE observation at Andøya starting in summer 1994 until 1997 and from 1999 up to now, using the ALOMAR SOUSY radar, ALWIN, ALWIN64, and MAARSY. All radars were run at 53.5MHz but most of the other technical parameters as, e.g., the peak power, the gains for the transmitting and receiving antennas, the antenna beam width and the loss factor as well as operation parameters for PMSE observation as, e.g., the used effective pulse width and the number of used code elements or the number of coherent integrations were different. Table 1lists the most important radar parameters and experiment configurations as used for PMSE observations during the various periods of operation. All observations were made using vertically pointing radar beams with comparable effective beam widths. Since the half power half width of the combined transmitter-receiver polar diagrams varies by a factor of less than 2 (except for the ALWIN64 observations, which were not included to the long-term studies) and the pulse volumes vary by a factor of 3, the observed PMSE strengths are likely not biased by scattering volumes incompletely filled with irregularities.
Table 1. Basic Radar Parameters [Singer et al., 1995; Latteck et al., 1999; Latteck et al., 2010; Latteck et al., 2012a] Relevant for Volume Reflectivity Determination and Experiment Configurations as Used for PMSE Observations
Peak power Pt
Number of transmitting antennas
Transmitting antenna gain Gt
Number of receiving antennas
Receiving antenna gain Gr
Effective beam width (HPHW) θ1/2
Effective pulse width τ
→Effective pulse volume @ 82km
System losses e
2.2 Adaption of Results From Different Radar Observations
 In order to derive occurrence rates of PMSE obtained with different radars, the received signals need to be absolute values to apply common thresholds. Radar volume reflectivity is a system independent, absolute parameter in contrast to, e.g., relative signal strength or signal-to-noise ratio (SNR). It can be derived from the received signal power taking into account all the individual radar characteristics and experiment configurations. Radar volume reflectivity η is defined as the power which would be scattered if all power were scattered isotropically with a power density equal to that of the backscattered radiation, per unit volume and per unit incident power density [Hocking and Röttger, 1997]. It can be expressed as
where r is the range to the scatterers, Gtand Grare the one-way gain of the transmitting and receiving antenna, respectively, θ1/2is the two-way half power half width (HPHW) of the antenna beam, λ is the radar wavelength, e is the system efficiency containing mainly the losses of the antenna feeding system, Pt is the transmitted peak power, Pr is the received signal power, c is the speed of light, and τis the effective pulse width [Hocking and Röttger, 1997]. The factor 2ln(2) is a correction term related to the nonuniform antenna gain over the half-power beam width [Probert-Jones, 1962; Skolnik, 1990] applicable for azimuthally symmetric Gaussian beams [Hocking, 1985]. All system-dependent parameters of equation (1) can be combined into a system factor csys as shown in Table 1 for the different periods and radar configurations. Hence, the radar reflectivity ηdepends only on the range to the scatterers r and the absolute value of the received signal power Pr
 The correct determination of Prrequires the calibration of the receiving path of the radar system as, e.g., described in Latteck et al. .
 ALWIN, ALWIN64, and MAARSY were calibrated regularly, and the PMSE data were stored as received signal power in arbitrary units. Therefore, it was possible to convert the received signal power to radar volume reflectivity and compare the results from 1999 to 2012 directly by using a common threshold [Latteck and Bremer, 2013]. The PMSE data obtained with the ALOMAR SOUSY radar from 1994 to 1997 were stored as SNR values only. Since variations in the operational parameters as, e.g., the transmitted peak power, the effective pulse width, or the number of coherent integrations change, the sensitivity of the radar Bremer et al.  had to use different thresholds of SNRmin to make the results comparable obtained with ALOMAR SOUSY and ALWIN between 1994 and 2008.
 Figure 1 shows the annual distribution of PMSE volume reflectivity observed with ALWIN, ALWIN64, and MAARSY on Andøya between 1999 and 2012 depicted as SNR (left panel) and volume reflectivity (right panel). The left borders of the distributions illustrate the differences in sensitivity of the operational modes of the radars, most convincingly shown by the solid blue line representing the ALWIN64 observations in 2009. The differences in echo detection sensitivity are also represented in the absolute values of the peaks of the distribution of the various years. This parameter is also predominantly affected by the annual variation of PMSE occurrence caused by geophysical variations, as can clearly be seen by comparing, e.g., the dashed curves representing ALWIN results only.
 A qualitative comparison of PMSE occurrence rates from various years of observation using different radars or operation modi requires a comparable parameter as, e.g., radar volume reflectivity and a definition of the event. A PMSE was defined as a radar signal power enhancement above the detection limit, but for a minimum duration of 20min in one range gate as described in Latteck et al. . The remaining signal power values were converted to volume reflectivity using equation (2), and occurrence rates were calculated for PMSE greater than a minimum value of ηmin=10−15m−1[Latteck and Bremer, 2013]. The left plot in Figure 2 illustrates the results as daily values (black stars) of the individual years and a polynomial fit (red line) through the corresponding daily averages. The characteristic of the derived mean seasonal variation of PMSE as shown in Figure 2 is similar to the results shown in Figure 1 in Bremer et al. . Therefore, it was natural to combine both series of occurrence rates in order to extend the whole data set.
 Seasonal mean values of PMSE occurrence for the time period from 1 June until 31 July and the height range between 78.5 and 92km (gray-shaded areas in Figure 2) were calculated for every year. These mean values have been included in our analyses as we are mainly interested in the estimation of mean long-term variations of PMSE. The use of such seasonal mean values suppresses the short-term variability in the polar mesopause region often caused by different atmospheric waves. One important wave is the 5 day wave detected in PMSE measurements [Zecha and Röttger, 2009], in noctilucent cloud observations [Kirkwood and Stebel, 2003], and in polar mesospheric cloud observations onboard satellites [Merkel et al., 2008; von Savigny et al., 2007].
 The top panel of Figure 3 shows both the resulting occurrence rate series OR(η≥10−15)(OR−15) from Latteck and Bremer  and the occurrence rate series OR(SNR>SNRmin)(ORSNR) from Bremer et al. . In spite of the different methods used, both data series show a highly significant correlation (r=0.94 with significance level χ≥ 99%) for the common years 1999 until 2008 as shown in the bottom panel of Figure 3. Using the derived linear regression equation
for all years with ORSNR data (1994–2008) the corresponding values have been estimated. These data are shown in Figure 4(red) together with the experimental OR−15 values (black). As to be seen, the agreement of both data sets is very reasonable with a correlation coefficient r=0.94 in the common interval 1999–2008. Therefore, the experimental OR−15data series can be extended to the years 1994–1997 by the estimated values. The final OR−15′data series used in the following investigations consists therefore of the experimental OR−15 values for the years 1999–2012 and the estimated data for the years 1994–1997.
2.3 Long-Term Changes in PMSE Occurrence Rates
 The extended occurrence rate series OR−15′containing data from 1994 to 2012 without the years 1998 (no radar observations) and 2009 (omitted due to markedly reduced echo detection sensibility of the ALWIN64 observations). These data are presented in the lower part of Figure 5 together with a positive linear trend with a statistical significance of 95%. The significance level has been derived by the Student's t test [Taubenheim, 1969]. In the upper two parts of this figure, the solar Lyman α flux (blue) and the global geomagnetic activity index Ap(red) are shown for the same time interval. Both data sets are presented by their mean values and their error limits calculated from the 61 daily mean values of the time interval from 1 June until 31 July of each year. The error values ϵhave been calculated for a significance level of 99% from the following formula [Taubenheim, 1969]
 Here N is the number of days investigated, STD the standard deviation, and t99(N−1) the Student's t parameter for a 99% significance level. Whereas the error limits of the solar Lyman αradiation are very small, the error bars of the geomagnetic activity are markedly larger. The strong error values of Apin 2000 and 2004 are mainly caused by geomagnetic storm events (15 July 2000: Ap=164, 25 July 2004: Ap=154, and 27 July 2004: Ap=186). As to be seen by a rough comparison between OR−15′and the corresponding Apand Lyman αmean values, there seems to be a connection between these data series. Near solar minima (1996 and 2000), there are also minimal PMSE occurrence rates, whereas near solar maximum (2000), the PMSE occurrence rate is in general enhanced. Only the marked PMSE minimum at 2002 looks unusual. As explained in detail by Bremer et al. , this PMSE minimum can be explained by enhanced mesospheric temperatures at polar latitudes due to an interhemispheric coupling.
 The individual connection between the PMSE occurrence rate and the solar and geomagnetic indices can be seen in Figure 6 in more detail. In the upper part of this figure, the OR−15′ values are shown in dependence on the solar Lyman αradiation together with the corresponding linear regression line. There is a slightly positive connection between both parameters. However, the significance level χ of the derived correlation coefficient (r=0.23) is with χ=70%very small.
 The correlation of the OR−15′ values with the global geomagnetic activity index Ap, shown in the middle part of Figure 6, is markedly more pronounced with a correlation coefficient r=0.53. The corresponding significance level with χ=95%demonstrates the close connection between the PMSE and the geomagnetic activity.
 For PMSE trend estimations, it is necessary to remove the solar and geomagnetically induced parts with a suitable regression analysis. At first, we fit the OR−15′ data series by the method of least squares with the following twofold regression equation
 Subsequently, we calculated the differences between the extended occurrence rate series OR−15′ and the adjusted occurrence rates ORmodof equation (5)
 These residual PMSE values ΔOR′are shown in the lower part of Figure 6 in dependence on time. The PMSE occurrence rate has a marked positive trend with a high significance level of about 99%.
 The PMSE trend can, however, also be estimated by another regression analysis again by the method of least squares but using the following threefold equation
 Here the partial regression coefficient d [%/year] is the trend value of the PMSE occurrence rate and can be compared with the ΔOR′trend from the twofold regression analysis (equations (5) and (6)).
 A third method for the derivation of PMSE trends is similar as the first method described in equations (5) and (6) but using only the influence of Ap and neglecting the Lyman αradiation. The reason for this approach can be seen in Table 2. Here the partial regression coefficients b=OR−15′(Lyα).Ap and c=OR−15′(Ap).Lyαare presented together with the corresponding partial correlation coefficients r(b) and r(c) for three different methods. For the twofold and threefold regression methods, the partial correlation coefficients r(b) are near zero, thus demonstrating that the solar Lyman αinfluence can be neglected for the explanation of the variability of PMSE occurrence rates. Therefore, the above mentioned third trend analysis has been carried out similar as described in equations (5) and (6) but only with Ap and without Lyman α. The significance levels of the correlation coefficients r(c) shown in Table 2are near 95% for the method OR−15′(Ap) and slightly below for the twofold and threefold regression analyses due to the reduced degrees of freedoms in these analyses. The PMSE trends deduced from all methods used are compiled in Table 3. The first trend has been derived from the original OR−15′ data without elimination of the influence of Apand Lyman α(shown in the lower part of Figure 5). The second trend has been estimated after elimination of the geomagnetically caused variation (OR−15′(Ap)). The third trend (OR−15′(Lyα,Ap) was derived after elimination of the solar and geomagnetically induced parts due to equations (5) and (6). The resulting trend can be seen in the lower part of Figure 6. The last trend value follows from the threefold regression analysis (OR−15′(Lyα,Ap,time)) due to equation (7). The trend values in Table 3 are in all cases positive with 0.57 %/year, only the trend with the original occurrence rates is slightly smaller with 0.51 %/year. The significance levels χ are between 95% and 99% using the Student's t test [Taubenheim, 1969]. In general, the significance level is higher if the geomagnetically caused parts alone or together with the Lyman αcaused parts have been removed. The reason for the slightly reduced significance level for the threefold regression analysis is the reduced number of freedom in this analysis. Summarizing, we can state that the detected trends in the analyzed PMSE occurrence rate data series are in each case significantly positive.
Table 2. Partial Regression Coefficients b=OR(Lyα). Ap and c=OR(Ap). Lyα and Corresponding Partial Correlation Coefficients r(b) and r(c) With Significance Levels (sig.) Concerning the Solar and Geomagnetic Influence on PMSE Occurrence Rates in Different Trend Analyses (NS: Not Significant)
OR(Ly α, Ap)
OR(Ly α, Ap, Time)
Table 3. Trend Values of PMSE Occurrence Rate by Use of Different Analysis Methods (OR: Trends For Original OR Values, OR(Ap): Trend After Elimination of Ap Influence, OR(Ly α, Ap): Trend After Elimination of Ly α and Ap Influence; OR(Ly α, Ap, Time): Trends Due to Threefold Regression)
OR(Ly α, Ap)
OR(Ly α, Ap, Time)
 The present study was conducted to update earlier investigations [Bremer et al., 2006; Bremer et al., 2009] with data series obtained at the same location but with the more powerful and flexible Middle Atmosphere ALOMAR Radar System (MAARSY). All available raw data obtained during 1999 and 2012 obtained with the ALWIN radar and MAARSY were analyzed on the bases of radar volume reflectivity using a common threshold to ensure and simplify the comparability of results obtained with these different radar systems. Since the PMSE data obtained with the ALOMAR SOUSY radar from 1994 to 1997 were stored as SNR values only, the thereon-based occurrence rates needed to be adjusted to the occurrence rate series based on volume reflectivity. This was possible since 10 years of PMSE data obtained with the absolute calibrated ALWIN radar were available in both data formats.
 The resulting PMSE occurrence frequency series OR−15′containing 17 years of observations has been used to investigate the dependency of PMSE occurrence on solar and geomagnetic activity. The simple linear correlation with Lyman αas shown in the upper panel of Figure 6 is slightly positive indicating a small dependency of PMSE occurrence on solar activity. However, the estimated significance level is small with χ=70%. This confirms the results by Bremer et al.  who already analyzed data from the same location but from 1994 to 2008. Latteck and Bremer  also showed results of the dependency of PMSE occurrence rates based on radar volume reflectivity on solar Lyman α radiation using, however, various thresholds ηmin=10−15, ηmin=10−14m−1 and ηmin=10−13m−1. They found that the correlation of the PMSE occurrence is small positive and in one case even slightly negative. As the PMSE occurrence rate depends on Lyman α and Ap and these two parameters are positively correlated with each other, we have to use not the simple linear correlation coefficient OR−15′(Lyα) but the partial regression coefficient b=OR−15′(Lyα).Ap and the corresponding correlation coefficient r(b). As presented in Table 2, this partial correlation coefficient is near zero, thus indicating that the PMSE occurrence rate is not significantly dependent on the solar Lyman α radiation. An increasing solar Lyman αradiation should cause an increasing electron concentration in the mesosphere and lower thermosphere due to an increasing ionization of nitric oxide [Hargreaves, 1979] and therefore increase the PMSE occurrence rate. On the other hand, enhanced solar radiation should reduce the mesospheric water vapor content due to an increasing photodissociation as well as enhance mesospheric temperature, thus supporting the sublimation of ice particles. The last two processes reduce the influence of the increasing electron density and could therefore be responsible that there is no significant correlation between PMSE occurrence rate and solar Lyman αradiation. If we used another solar activity index as the solar radio flux F10.7, we got the same result in all our analyses.
 The correlation of the PMSE occurrence rate with the geomagnetic activity is more pronounced as shown in the middle part of Figure 6 if the linear correlation OR−15′(Ap) is considered. Similar results have also been found by Bremer et al.  and Latteck and Bremer . Using the more representative partial regression coefficient c=OR(Ap).Lyα and the corresponding correlation coefficients r(c)=0.49−0.62 from Table 2, the PMSE occurrence rate positively depends on the geomagnetic activity with a significance level between 85% and 95%. As the geomagnetic activity is an indicator of precipitating energetic particles, these particle fluxes should increase the mesospheric electron concentrations and therefore increase the PMSE occurrence rate. Effects of photodissociation on the mesospheric water vapor cannot be expected. Moreover, there are some indications that also the influence of precipitating particle fluxes on the mesospheric temperature is only small [Zeller and Bremer, 2009].
 Using four different analysis methods, consistent PMSE long-term trends have been derived with significance levels between 95% and 99%. These data presented in Table 3demonstrate a significant positive trend of the PMSE occurrence rate. Qualitatively similar positive PMSE trends have also been detected by Bremer et al.  and Latteck and Bremer . Due to the smaller length of their data series, the derived significance levels were, however, smaller. This positive PMSE trend could be caused by an increasing trend of the mesospheric water vapor and/or a decreasing temperature trend. From microwave measurements at Andøya, Hartogh et al.  detected decreasing summer water vapor mixing ratios between 1996 and 2006. These measurements are, however, restricted to an altitude up to about 80km. Nevertheless, this result is a strong indication that the positive PMSE trend may be caused by a negative temperature trend and probably not by an increasing water vapor trend.
4 Summary and Conclusion
 Polar mesospheric summer echoes from 17 years of continuous VHF radar observations at Andøya (69°N) have been investigated for solar and geomagnetic control as well as for possible long-term changes. The investigation is based on occurrence rates derived from radar volume reflectivity of the received echoes considering the differences in technical performance and experimental operation of the radars used at the site during the long period of observation. Results from earlier investigations by Bremer et al. [2006, 2009] for the time period from 1994 to 2008 based on occurrence rates derived from SNR and adapted minimum thresholds regarding to the technical parameters of the used radars were adjusted to the occurrence rate series based on volume reflectivity.
 PMSE occurrence at Andøya (69°N) is positively correlated with geomagnetic activity; the solar Lyman αradiation, however, has no significant influence. The geomagnetic activity is an indicator of fluxes of precipitating high energetic particles which are connected with the ionization level in the polar mesopause region, thus directly influencing the PMSE. While an increasing solar Lyman α radiation enhances the mesospheric ionization, such an increase simultaneously reduces mesospheric water vapor and enhances mesospheric temperature. These three processes compensate each other and lead to the neglecting influence of Lyman α on PMSE. By means of different regression analysis methods, the PMSE occurrence frequencies show a positive trend with a high significance level χ>90%. This is consistent with results found by Bremer et al.  and confirms also the conclusions by Latteck and Bremer  that a long period of observations is needed to derive reliable trends from this kind of observations.
 Future activities have to be directed to the direct integration of PMSE data from earlier years obtained with the ALOMAR SOUSY radar between 1994 and 1997 by using volume reflectivity. Even since these data are stored as SNR values, they can be converted to volume reflectivity if detailed calibration data are available.