The currently most widely accepted theory of polar mesosphere summer echoes (PMSE) assumes that the echoes originate from turbulence-induced scatter in combination with a large Schmidt number caused by the presence of charged ice particles. We test this theory with calibrated observations with the European Incoherent Scatter (EISCAT) Svalbard Radar (ESR) at 500 MHz (Bragg wavelength 30 cm) and the Sounding System (SOUSY) Svalbard Radar (SSR) at 53.5 MHz (Bragg wavelength 2.8 m), which are collocated near Longyearbyen on Svalbard (78°N, 16°E). Our observations in June 2006 yield volume reflectivities ranging from values of 2.5 × 10−19 m−1 to 1 × 10−17 m−1 for the case of the ESR echoes and from 5 × 10−16 m−1 to 6.3 × 10−12 m−1 for the SSR echoes. In the frame of the above-mentioned theory the expected reflectivity ratio should be equal to or larger than the ratio of the frequencies to the third power (i.e., larger than (500 MHz/53.5 MHz)3 = 816). Our experimental results show that 94% of the observations satisfy this expectation. The remaining 6%, which show too small ratios, can be tentatively attributed to calibration uncertainties and an incomplete filling of the scattering volume of the SSR, which is significantly larger than that of the ESR. Hence our observations are largely consistent with the predictions of the above-mentioned theory even though we note that it cannot prove it, which would require additional observations at different frequencies. However, this consistency is used as sufficient motivation to apply the assumed theory to the observations in order to derive Schmidt numbers and radii of the charged aerosol particles. Corresponding results are in excellent agreement with expectations from microphysical models and independent satellite and lidar observations, thereby corroborating our initial assumptions.
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 The polar mesosphere in summer is host to a number of fascinating geophysical phenomena that are primarily caused by its extraordinary thermal structure. Owing to the gravity wave driven mean meridional circulation with upwelling and adiabatically expanding air masses above the summer polar regions, mean minimum temperatures of ∼130 K are attained at the mesopause at around 88 km [e.g., Lübken, 1999]. These extremely low temperatures marginally allow ice particles to form and grow at altitudes between ∼80 km and 90 km from where they are observed both optically (then called noctilucent clouds or polar mesospheric clouds, NLC/PMC) and using radars, i.e., as so-called polar mesospheric summer echoes or PMSE (see, e.g., Thomas  and Rapp and Lübken  for reviews regarding NLC and PMSE, respectively). In recent years, these high atmospheric ice clouds are of considerable scientific interest since it was suspected that the mesopause environment should change due to anthropogenic activity and solar forcing which in turn should give rise to changes in the properties of mesospheric ice clouds [e.g., Roble and Dickinson, 1989; Thomas et al., 1989; Garcia, 1989]. While it is currently being controversially discussed whether we already observe such long-term changes [von Zahn, 2003; Thomas et al., 2003; DeLand et al., 2007], there appears to be an unambiguous and pronounced solar cycle signal in the occurrence frequency of mesospheric ice clouds in both satellite data sets and ground-based observations [DeLand et al., 2003; Shettle et al., 2009; Kirkwood and Stebel, 2003; Kirkwood et al., 2008]. That is, occurrence frequencies of mesospheric ice clouds appear to be anticorrelated with solar cycle indicators like the solar Ly-α flux. However, even this prominent signal can currently not be explained within the available models and theories [e.g., Sonnemann and Grygalashvyly, 2005]. This questions our current understanding of the main drivers of these clouds and their basic microphysics. Hence, it appears that even though NLC and PMSE have been studied for decades, and even though there is a clear scientific interest in these phenomena, there is a wealth of fundamental questions that await to be answered and additional observations of the microphysical properties of mesospheric ice clouds and their environment are needed.
 An excellent way for a continuous monitoring of the mesopause region, including mesospheric ice clouds, involves radar measurements which are not hampered by tropospheric weather conditions (such as ground-based optical measurements) and which can give information with excellent time and altitude resolution. However, the interpretation of any radar measurement, including of course observations of PMSE, requires a rigorous understanding of the scattering process. While there is consensus in the community that ice particles play a dominant role for the creation of the scattering structures leading to PMSE, there is still some controversy regarding the details of the physical processes involved. The theory with largest acceptance in the community was originally put forward by Kelley et al.  and was then further developed by Cho et al. , Hill et al.  and Rapp and Lübken  based on the multipolar diffusion theory by Hill . This approach basically combines neutral air turbulence with reduced electron diffusivity owing to the effect of ice particles which become charged by electron attachment. Subsequently these charged heavy particles influence the remaining free electrons (from which the radar waves are scattered) by Coulomb interaction [see also Lie-Svendsen et al., 2003]. Importantly, this theory is in accord with almost all currently available experimental results [Rapp and Lübken, 2004; Rapp et al., 2008; Nicolls et al., 2009]. Note further that alternative theories invoking plasma instabilities due to large electric fields [e.g., D'Angelo, 2005] or metal coatings on the ice particles [Bellan, 2008] have been seriously questioned based on independent observations and theoretical arguments [Shimogawa and Holzworth, 2009; Rapp and Lübken, 2009]. In addition, earlier theoretical attempts and/or objections against a turbulence-based theory have previously been ruled out based on available experimental facts and/or theoretical arguments as discussed in detail by Cho and Röttger , Rapp and Lübken , and Rapp et al. . This discussion will not be repeated here but the reader is referred to the references above.
 In any case, an excellent experimental possibility to test a potential theory is to perform PMSE observations at different frequencies and hence different spatial scales in the D-region plasma, i.e., the radar Bragg wavelengths (= half the radar wavelengths for monostatic radars). Since the turbulence-based theory mentioned above predicts a distinct spatial-scale dependence, this offers the unique possibility for a direct experimental test. As of today, PMSE have been observed in a wide frequency range from the MF to the UHF band (see Rapp and Lübken  for a review), however, very few observations have been carried out using calibrated signals and more than one frequency at the same time and same place. Examples are the studies by Röttger  who presented a preliminary comparison of measurements with the EISCAT Svalbard Radar (ESR) at 500 MHz and with the SOUSY Svalbard Radar (SSR) at 53.5 MHz (corresponding to Bragg wavelengths of 30 cm and 2.8 m, respectively) and the study by Rapp et al.  who compared measurements with the EISCAT VHF and UHF radars in Tromsø (at frequencies of 224 MHz and 930 MHz and Bragg wavelengths of 67 cm and 16 cm, respectively) and the ALWIN radar at Andenes (53.5 MHz, i.e., Bragg wavelength = 2.8 m) and found excellent agreement between the above-mentioned theory invoking turbulence in combination with a large Schmidt number and observations.
 However, in spite of these few previous case studies one has to note that the statistics of such observations is so far extremely scarce. As for the case of measurements involving the EISCAT UHF radar, one has to note that the reason for this poor statistics is indeed of geophysical origin since PMSE at such very large frequencies and small Bragg wavelengths is very weak. Hence, only a handful of observations has been reported in the literature so far [Turunen et al., 1988; Collis et al., 1988; Röttger et al., 1990; Cho and Kelley, 1992; La Hoz et al., 2006; Belova et al., 2007; Rapp et al., 2008; Naesheim et al., 2008]. Concerning the ESR, on the other hand, the frequency is only half as large (500 MHz) and PMSE are correspondingly expected to occur much more frequently. This is the reason why a dedicated PMSE campaign involving the ESR and the SSR on Svalbard was carried out in summer 2006. In the current paper we start with a short description of the ESR and SSR and the measurement program carried out during that period (section 2). We then describe our observations at two Bragg wavelengths and derive corresponding occurrence rates, spectral parameters including turbulence estimates, and volume reflectivities (section 3). In section 4 we then demonstrate that the measurements are in very good agreement with the above-mentioned PMSE theory and we then proceed to apply this theory to the observations to derive microphysical parameters of the involved ice clouds. Corresponding results are further compared to independent measurements with the Solar Occultation For Ice Experiment (SOFIE) on board the Aeronomy of Ice in the Mesosphere (AIM) spacecraft as well as with the ALOMAR RMR lidar. Finally, our conclusions are presented in section 5.
2. Experimental Details
 The measurements described in this manuscript were obtained with the EISCAT Svalbard Radar (ESR) and the SOUSY Svalbard Radar (SSR) both located near Longyearbyen (78.2°N, 15.8°E) on the north polar island of Spitsbergen which is part of the archipelago Svalbard; details about these radars are given by Wannberg et al.  and Röttger , respectively. Previous studies of PMSE using these radars are described by Hall and Röttger  and Röttger  for the case of the ESR and, for example, by Lübken et al.  and Zecha and Röttger  for the case of the SSR. Technical and physical parameters relevant to our study are summarized in Table 1. The measurements we report here were obtained in June 2006. During this period, the SSR was run continuously, whereas the ESR was run for 1–4 h during 18 days around noon. A detailed list with the exact times of ESR operation and the hours during which PMSE were observed is presented in Table 2. From these measurements, signal power values, vertical velocities, and spectral widths were determined from 6 s long time series in the case of the ESR, and 10 s long time series in the case of the SSR. Note that no incoherent integrations were carried out until this point. We note that unlike in the study of Zecha and Röttger , the SSR was constantly pointed vertically; that is, no Doppler beam swinging experiments were performed such that no horizontal wind information is available from the PMSE observations itself. In addition, both radars were calibrated and power values were converted to absolute volume reflectivities for quantitative comparison to each other and to theory. Corresponding results are described in section 3.
For easier comparison to the earlier study by Röttger , experiment parameters from this previous study are also listed in brackets.
Antenna gain (dBi)
Half-power beam width (°)
Peak power (MW)
complementary, no phase flip
complementary, with phase flip
Number of code bauds
System efficiency (assumed)
Baud length (μs)
Range resolution (m)
Number of coherent integration
4 × 2 (number × code pairs)
16 × 2 × 2 (number × code pairs × phase flip)
System temperature (K)
Table 2. Observing Times With the ESR During the PMSE Campaign 2006a
Month and Year
PMSE Time (UT)
All times are given in UT. Local solar time (LST) and UT are related by LST = UT + 68 min. At this time of the year, solar noon is at 1052 UT.
0900–1100 and 1200–1300
0900–1000 and 1200–1300
0900–1000 and 1200–1300
1000–1100 and 1200–1300
3.1. PMSE Occurrence Rates at Svalbard Observed at Bragg Wavelengths of 2.8 m and 30 cm
Figure 1 shows two typical examples of simultaneous PMSE observations with the ESR and SSR on 18 and 20 June 2006, respectively. In the two cases shown in Figure 1, both radars show prominent echoes in approximately the same altitude range, where, however, the SSR echoes generally extend over a larger altitude range than the ESR echoes.
 In a first step, these observations were used to infer occurrence rates as a function of altitude. For the case of the ESR data set, this analysis was carried out on single power profiles, where echoes which extended more than three standard deviations above the mean noise level (equivalent to an SNR threshold of +0.5 dB) were identified as PMSE. We note that any choice of a threshold for PMSE is somewhat arbitrary. In this case, our choice was mainly driven by the detectability of the rather weak echoes observed by the ESR and revealed to be the optimum compromise between the requirement to miss as few as possible real PMSE but also to suppress as many as possible false detections. In addition, in order to avoid false PMSE detections in the ESR data due to possible contamination by occasionally detectable incoherent scatter, we also investigated the corresponding spectral widths. These are expected to be much larger in the case of incoherent scatter at this frequency and in the 80–90 km altitude range as compared to the coherent scatter of PMSE [e.g., Röttger and La Hoz, 1990]. For the case of the SSR data set, we adopted the methodology used by Zecha and Röttger  who defined a SNR threshold of −10 dB for PMSE detection for similar observing conditions.
 Resulting altitude profiles of the occurrence rates for both frequencies are shown in Figure 2. The occurrence rates for the ESR are much smaller than those for the SSR. Furthermore, ESR PMSE occurred in a considerably narrower altitude range, i.e., between 81 and 88 km, whereas SSR PMSE was observed in the entire altitude range between 80 and 92 km.
 Since ESR observations were restricted to hours from 0900–1300 UT, we further compared the SSR PMSE occurrence rate observed in the same period to the SSR PMSE occurrence rate for all observations. This comparison shows that the SSR PMSE occurrence rate is actually significantly larger during the 0900–1300 UT period than during the entire day. This is in line with the diurnal pattern of PMSE occurrence at Svalbard described by Zecha and Röttger , who found a maximum PMSE occurrence around local noon based on measurements during the years 1999–2001 and 2003–2004. According to Zecha and Röttger  this maximum can be explained by the diurnal variation of solar UV and particle precipitation and corresponding enhanced electron densities at PMSE altitudes during the same period.
 We also note in passing the apparent two maxima structure of these profiles which is likely related to the influence of long-period gravity waves on the layering of the ice particles. The interested reader is referred to Hoffmann et al. [2005, 2008] for a detailed discussion of this mechanism including additional references. In addition, Zecha and Röttger  provide a detailed statistical analysis of the multilayer occurrence in PMSE observed by the SSR in previous years.
3.2. Spectral Widths and Turbulence Parameters
 We next turn to a comparison of spectral widths observed at both frequencies and discuss potential implications for underlying mesospheric turbulence. Spectral widths were determined as the half power half width of corresponding Doppler spectra assuming a Gaussian spectral shape. In order to compare the ESR and SSR observations, both data sets were projected onto a joint time grid with 1 min resolution. That is, 10 (6) spectra of 6 s (10 s) long ESR (SSR) time series were first corrected for their Doppler velocity and then incoherently averaged over 10 (6) spectra. In order to demonstrate the excellent quality of the Doppler spectra obtained from the ESR measurements we show a sequence of 4 min of such spectra at four consecutive range gates in Figure 3. Quite evidently, the spectra are reasonably well described by a Gaussian spectral shape. This was also verified quantitatively by fitting the magnitudes of the corresponding auto correlation functions (which according to the Wiener-Khinchine theorem are just the Fourier transforms of the power spectra) with an expression ACF = ACF0 · exp(−(t/τ)n) where t is the lag time, τ is the decay time (which is inversely related to the spectral width), and n is an exponent describing the shape of the spectrum [e.g., Rapp et al., 2007; Strelnikova and Rapp, 2009]. That is, n = 1 corresponds to a Lorentzian spectrum as expected for pure incoherent scatter from the D region, and n = 2 corresponds to a Gaussian spectrum. Indeed, this analysis yielded an average n of 1.9, i.e., close to n = 2. However, we also note that occasionally, some spectra appear to show multiple peaks that could actually be indicative of inhomogeneities within the radar beam. This issue will be considered in more detail in a future study.
 In Figure 4 we compare mean profiles (along with corresponding standard deviations) of spectral widths from observations with the SSR (black line with grey shading and red lines) and the ESR (blue line with error bars). First of all, we note that there is one common feature of all profiles, namely that the mean spectral widths increase with increasing altitude which is in agreement with many previous PMSE observations [e.g., Czechowsky et al., 1988]. Besides this general agreement, however, we stress two additional points: when comparing SSR and ESR observations at times when both radars observed PMSE (blue and red lines), it is striking that the resulting profiles show on average larger values for the SSR below about 85 km while the values agree nicely above that altitude when the profiles show mean values of up to ∼3 m/s.
 When comparing spectral widths from two different radars with two very different beam widths (see Table 1), one has to consider the fact that the observed spectral width σobs is actually the sum of different terms, i.e.,
where σturb is the contribution from turbulent velocity fluctuations in the medium, σbeam is the contribution from beam broadening, σshear is the contribution from shear broadening, and finally σwave is the contribution from high-frequency gravity waves [Hocking, 1985; Murphy et al., 1994; Nastrom and Eaton, 1997]. According to Hocking , beam broadening may be quantified as σbeam = · ϑ · V where ϑ is the 3 dB full beam width of the transmitted radar beam (in radian) and V is the horizontal wind speed. Expressions for shear broadening are given, for example, by Nastrom and Eaton . However, the latter is almost 2 orders of magnitude smaller than beam broadening for the vertical measurements considered here. Hence, shear broadening will not be considered any further. Finally, the broadening contribution owing to high-frequency gravity waves was derived by Nastrom and Eaton  and may be written as σwave2 = σw2 · f(Z, D, T, ωG, k, m). Here, σw2 is the observed variance of the vertical wind, Z and D are the depth and width of the observing volume at given height (i.e., 300 m and 7400 m at 85 km in the case of the SSR), T is the sampling time (i.e., 10 s for the SSR), ωG is the circular frequency of the high-frequency gravity wave, and k and m are its horizontal and vertical wave numbers (see equations (A12)–(A15) of Nastrom and Eaton  for more details).
 In order to quantify σbeam, we considered actual wind measurements with the collocated Nippon/Norway Svalbard Meteor 31 MHz Radar (NSMR). Details regarding this meteor radar system as well as corresponding scientific results are given, for example, by Hall et al. [2002, 2003]. The wind data are provided as half-hourly mean values only such that we did not attempt to correct individual spectral width observations with the ESR and SSR. Instead, we derived a mean profile of horizontal wind velocities during the time that the ESR observed PMSE. The latter is shown in Figure 5 (top).
 Further on, we considered whether or not high-frequency gravity waves were present at the times of our PMSE observations and could have contributed to broadening the spectra. Indeed, it turns out that the times at which the ESR registered PMSE are characterized by the prevalent occurrence of gravity waves with typical periods of about 10 min. One typical example is presented in Figure 6 showing the vertical wind variation on 18 June 2006, as derived from PMSE observations with the ESR and SSR. From all such ESR observations we derived the variance of the vertical wind over the period of the PMSE observations. The latter is shown in Figure 5 (middle). In order to proceed further and estimate the broadening contribution owing to these high-frequency waves, we further need information on the horizontal and vertical wavelengths. While these two parameters are not directly available from our observations, we may constrain reasonable estimates based on published climatologies of high-frequency gravity waves as derived from airglow observations. Nielsen et al.  have recently published a corresponding climatology for 76°S and found prevalent periods of about 10 min as in our own observations with corresponding horizontal wavelengths of about 20 km. Importantly, these values are in reasonable agreement with several independent observations at other locations (see the overview of previous observations as summarized in Table 1 of Hecht ). While this certainly does not prove that the waves present during our PMSE observations had exactly the same properties, we may still use a horizontal wavelength of about 20 km in order to estimate the order of magnitude effect of wave broadening on our own spectral observations. Finally, we used the dispersion relation for high-frequency gravity waves [e.g., Fritts and Alexander, 2003, equation (30)] to derive a corresponding vertical wavelength.
 The overall result of this exercise is presented in Figure 5 (bottom). Here, we show the altitudes profiles of all relevant terms in equation (1). Note that altitude profiles of σbeam2 and σwave2 are only shown for the case of the SSR, since corresponding values for the ESR are minute and only make a negligible contribution to σESR2. Hence, we use the latter as our best estimate of σturb2. Figure 5 reveals that the broadening contribution from wave broadening to the spectrum recorded with the SSR exceeds that one from beam broadening at basically all altitudes. Even more important, we see that the sum of σESR2 ≈ σturb2, σwave2, and σbeam2 closely reproduces the altitude profile of σSSR2. Hence, we tentatively conclude that the observed difference in ESR and SSR spectral widths below 85 km is likely caused by the combined effect of wave and beam broadening (with some remaining uncertainty caused by the need to estimate part of the wave parameters based on climatologies and not direct observations).
 The other striking feature that we would like to stress here is the fact that spectral widths observed with the SSR in the presence of PMSE in the ESR are significantly larger at altitudes above 85 km as compared to the cases when PMSE was only observed by the SSR. This can be clearly seen in Figure 4b in which histograms of spectral widths from altitudes of 85–88 km are compared for cases where PMSE was observed by the SSR only (in green) and simultaneously by the SSR and ESR (red and blue). Since the histograms of the simultaneous ESR and SSR measurements agree nicely indicating that the increased spectral widths are due to an increased level of turbulent velocity fluctuations (and not increased broadening effects owing to large horizontal winds and/or high-frequency gravity waves), this implies that the upper PMSE layer observed with the ESR (see also Figure 2) occurs in the presence of enhanced mesospheric turbulence.
 Finally, we convert the observed spectral widths from the ESR, which are only marginally contaminated by artificial broadening effects (see above), to turbulent energy dissipation rates following Hocking  and Röttger et al. ,
where ε is the turbulent energy dissipation rate, λ is the wavelength of the radar (e.g., 0.6 m for the ESR), σ is the half power half width of the Doppler spectrum (in m/s) and N is the buoyancy frequency which we take from the MSIS climatology [Picone et al., 2002]. Note that we have chosen MSIS rather than a climatology based on actual observations on Svalbard since corresponding data sets either do not cover the relevant time of the year or the relevant height range [Lübken and Müllemann, 2003; Höffner and Lübken, 2007]. Histograms of ε for altitudes below and above 85 km are presented in Figure 7. Importantly, the spectral resolution of the ESR measurements (i.e., 0.167 Hz or 0.05 m/s) and the contribution to the spectral width by beam and wave broadening (i.e., 0.26 m/s on average) cause corresponding minimum detectable energy dissipation rates of significantly less than 1 mW/kg and hence do not significantly influence the here presented values. Figure 7 clearly shows that energy dissipation rates follow a very asymmetric distribution with a long tail toward large values as expected for intermittent processes like turbulence. Above 85 km most values fall into a range from 5 to 200 mW/kg whereas values are significantly smaller (5–50 mW/kg) below that altitude. We note that these values are in general agreement with the few independent estimates of turbulent energy dissipation rates based on direct rocket soundings during polar summer [Lübken et al., 2002; Strelnikov et al., 2006].
3.3. Volume Reflectivities
 For a further quantitative comparison of our measurements with the ESR at a Bragg wavelength of 30 cm and the SSR at a Bragg wavelength of 2.8 m, we next converted the measurements to absolute volume reflectivities, i.e., scattering cross sections per unit volume. In the case of the ESR, this was done on the basis of a noise calibration; that is, a well-known calibration noise source was switched on during each pulse reception interval and fed into the receiver system [see Wannberg et al., 1997, Figure 5]. By normalization of the received echo power to that of the calibration noise source, measured power values were converted into values in absolute units of Watts. Making additional use of the radar equation and using the radar system parameters given in Table 1 volume reflectivities were finally derived. From previous comparison of pure incoherent scatter echoes (where the volume reflectivity is directly proportional to electron density) with ionosonde data this technique is known to yield volume reflectivities within an accuracy of ∼10% [Kirkwood et al., 1986]. Note that the latter estimate includes the variation of transmitted ESR power which is routinely measured and logged during ESR operation.
 In the case of the SSR, a delay line calibration was performed and verified against an additional noise calibration as described in detail by Latteck et al. . For the delay line calibration, the transmitter output itself is fed into the receiver input using a directional coupler and delaying the transmitted pulse by 100 μs (corresponding to a range of 15 km) using an ultrasonic delay line. Since the transmitted power can be measured within an accuracy of less than 1% (i.e., better than 100 W at a transmitter output of a few kilowatts) this allows to express any received signal in absolute units within an accuracy of a few percent. Making again use of the radar equation and using the radar system parameters given in Table 1 volume reflectivities are derived. Unlike in the case of the ESR, a statement on the accuracy of this calibration procedure is more difficult, since independent measurements of the volume reflectivity are not available. However, based on the accuracy with which the delay line calibration can be carried out (accuracy of a few percent, see above) and also based on the variation of transmitted power which was regularly measured during the radar experiments described here we estimate the accuracy of this calibration to be on the order of a few tens of percent.
 We note that there could be additional systematic errors originating from the radar system parameters as summarized in Table 1 and as needed for the calculation of volume reflectivities. Where not measured directly, stated quantities were derived on a “best effort” basis (e.g., the SSR antenna gain had to be calculated).
 As the final result of this exercise, histograms of the volume reflectivities η obtained from PMSE observations with the ESR and SSR in June 2006 are presented in Figure 8. The η values obtained from the ESR and SSR observations fall within the range from 2.5 × 10−19 m−1 to 1 × 10−17 m−1 and from 5 × 10−16 m−1 to 6.3 × 10−12 m−1, respectively. This means that SSR η values at a Bragg wavelength of 2.8 m are on average more than 3 orders of magnitude larger than ESR η values at a Bragg wavelength of 30 cm. A more detailed comparison of the volume reflectivities at these two frequencies along with an in depth discussion in terms of our theoretical understanding of PMSE is presented in section 4.
4.1. Comparison With Theory: Turbulence With Enhanced Schmidt Number
 We now turn to a detailed comparison of volume reflectivities observed at the two radar frequencies (and Bragg wavelengths). In an initial attempt we have tested whether there is any direct and obvious correlation between η at the two Bragg wavelengths of 2.8 and 30 cm. For this direct comparison, the measurements were put on an identical time grid of 1 min. Subsequently, times and altitudes were identified during which PMSE occurred simultaneously in both radar observations. A scatterplot of corresponding reflectivities is presented in Figure 9. At first glance, there is no obvious correlation between the data.
 The question, however, is what we may expect to find based on the above-mentioned PMSE theory according to which PMSE is caused by a combination of neutral air turbulence and an enhanced Schmidt number (reduced diffusivity) of electron density fluctuations (= fluctuations of the radio refractive index). For looking into this, we follow the formulation of Rapp et al.  which is based on the classical formulation for pure turbulent scatter by Hocking  and using the results of Batchelor  for the case of tracers with Schmidt numbers larger than 1. According to this work, the theoretical expression for the radar volume reflectivity for the case of the turbulent scatter aided by an enhanced Schmidt number is given by
where ε is the turbulent energy dissipation rate, ν is the kinematic viscosity, N is the buoyancy frequency, k = 4π/λ is the Bragg wave number of the radar, is the Kolmogorow microscale, re is the classical electron radius, and Sc = ν/De is the Schmidt number introduced in section 1. is the reduced potential refractive index gradient, i.e., which depends on the electron number density ne, the buoyancy frequency, and the density scale height Hn. Finally, fα, q, Ri and Prt are all “constants” (i.e., they are constant for a given event) derived from either theory or by comparison with observations (see Appendix A of Rapp et al.  for more details).
 In Figure 10 we have plotted various theoretical curves η(k) for different combinations of the electron density and electron density gradient and the Schmidt number Sc. In addition, the two vertical bars indicate the Bragg wave numbers of the SSR (k = 2.24 m−1) and the ESR (k = 20.93 m−1). Figure 10 shows two interesting things: if the Schmidt number is large, then the ratio between η(SSR) and η(ESR) should be a constant value; that is, the curves of log(η(k)) are parallel to each other. Going back to equation (3) we see that in this case η(k) k−3; that is, for large Sc, both η values fall into the viscous-convective subrange such that the ratio η(SSR)/η(ESR) is given by (kESR/kSSR)3 = (500 MHz/53.5 MHz)3 = 816. If, however, the Schmidt number is not very large, then η(SSR) would fall into a part of η(k) where the latter is dominated by the k−3 dependence whereas η(ESR) would already fall into the part where η(k) is dominated by the exponential term. In consequence, the ratio η(SSR)/η(ESR) should be larger than the minimum value of (kESR/kSSR)3 = (500 MHz/53.5 MHz)3 = 816 in those cases (indicated by the red line in Figure 9).
 In order to investigate this further, we next show histograms of the ratio η(SSR)/η(ESR) in Figure 11. Figure 11 demonstrates that the ratios vary between ∼400 and 100,000. Importantly, however, more than 94% are larger than a value of 816, i.e., the ratio of the radar frequencies to the third power (see above). This means that the large majority of our data is consistent with the expectations based on the here considered theory. The remaining 6% which lie to the left of 816 can likely be explained by the uncertainty of the calibrations (see above) as well as by the fact that the radar volume of the ESR is significantly smaller (beam width 1.2°; see Table 1) than the radar volume of the SSR (beam width 5°; see Table 1). This means that an incomplete filling of the latter by scatterers will result in an underestimate of the “real” volume reflectivity. Importantly, we can find independent support for this explanation by means of a similar analysis of PMSE observations with the EISCAT VHF and UHF radars in Tromsø. From measurements conducted in the years 2004, 2005 and 2006 we could identify a total of 296 1 min samples of simultaneous PMSE observations with these two radars operating at 224 MHz and 930 MHz (Bragg wavelengths of 67 cm and 16 cm, respectively). Importantly, unlike in the case of the SSR and ESR, the beam widths and hence observing volumes of these two radars are near identical such that one would expect to find an even larger percentage in agreement with theory, provided that the latter is correct. Indeed, this analysis yielded the result that 99% of derived volume reflectivity ratios were larger than the corresponding ratio of the radar frequencies to the third power. A detailed description of the latter analysis of the EISCAT VHF and UHF measurements will be published in the near future (M. Rapp et al., manuscript in preparation, 2010). We note, however, that we can certainly not exclude that some other, yet unidentified physical process, is responsible for the above-described discrepancy for 6% of the presented data.
 We note that the here demonstrated consistency between theoretical expectations and observations allows us to disregard any theory which predicts a wave number dependence which is less steep than k−3. However, it certainly does not allow us to disregard other potential theories with functional dependencies steeper than k−3. In order to distinguish such different possible functional dependencies, observations at more than two frequencies would be required. Hence, our analysis can certainly not prove that the assumed turbulence theory is correct. Nevertheless, we consider the consistency demonstrated above as sufficient motivation to proceed further and derive microphysical parameters from our data which may then be compared to independent observations in order to further corroborate or falsify our assumptions.
4.2. Microphysical Properties Derived From Signal Ratios
 We now proceed and apply the turbulence with large Schmidt number theory to the observations in order to derive microphysical parameters from the radar measurements. Using equation (3) we see that the ratio η(SSR)/η(ESR) can be written as
Note that this equation only contains two remaining unknowns, i.e., the Schmidt number Sc and the Kolmogorow microscale ηK, while all other, partly largely uncertain, factors contributing to the expression for the volume reflectivity in equation (3) have canceled. The ηK can be easily calculated using the energy dissipation rates estimated from the ESR spectral widths (see section 3.2) and an estimate of the kinematic viscosity using Sutherland's formula and densities and temperatures from the MSIS climatology [Picone et al., 2002]. As a result, we may solve equation (4) for the Schmidt number Sc and obtain
Taking further into account that the Schmidt number can be expressed in terms of the properties of the charged ice particles, corresponding ice particle radii can be derived from the following relation:
 All simultaneous measurements with the SSR and ESR were analyzed for Sc and rA resulting finally in histograms of the Schmidt number and ice particle radii shown in Figure 12. Figure 12 shows that Schmidt numbers vary between a few hundred and ∼32,000 with corresponding radii between 10 and 70 nm. Interestingly, we note that the Schmidt number distribution appears to show two distinct peaks. We will show below, that these two peaks correspond to different particle populations below and above ∼85 km altitude.
 Note that similarly large Schmidt numbers with maximum values of 4000 have recently been independently reported based on direct in situ observations of the spectral content of small-scale fluctuations in the neutral gas and in charged particles under PMSE conditions [Strelnikov et al., 2009]. Importantly, independent observations on the same sounding rocket proved the presence of large ice particles [Megner et al., 2009] and allowed determination of corresponding particle radii in the range of 20–30 nm [Rapp et al., 2009], i.e., in good agreement with equation (6).
 In order to further assess the accuracy of the derived ice particle radii, in Figure 13 (top) we have plotted contour lines of particle radii as a function of turbulent energy dissipation rates ε and ratios η(SSR)/η(ESR) according to equations (6) and (5). In the same plot we have marked combinations of these two quantities derived from our simultaneous SSR and ESR PMSE observations. This comparison confirms that our measurements correspond to particle radii between ∼10–70 nm. Furthermore, it also shows that this method to derive particle radii becomes more and more inaccurate as it approaches the theoretical lower limit of η(SSR)/η(ESR) corresponding to the largest particle radii. The reason for this behavior can be easily understood by going back to Figure 10: As the ratio η(SSR)/η(ESR) approaches its smallest possible theoretical value of 816, a further increase of the particle radius and hence the Schmidt number will hardly lead to any further change in η(SSR)/η(ESR) because for large Schmidt number it is asymptotically given by ratio of the Bragg wave numbers to the third power. As a next step, Figure 13 (bottom) shows relative errors of the radii assuming relative errors in ε and η(SSR)/η(ESR) of 10% and 50%, respectively. We note that the 10% error estimate for the accuracy of ε only reflects the uncertainty of deriving the spectral width from measured Doppler spectra and does not take into account possible systematic problems with Equation 7 as suggested on the basis of the direct numerical simulations presented by Gibson-Wilde et al. . These authors showed that for the case of a simulated Kelvin-Helmholtz instability ε derived on the basis of equation (7) and using a constant background buoyancy frequency resulted in an underestimate of the real energy dissipation rate by a factor of five which would lead to a corresponding systematic shift of derived particle radii to smaller values. Whether or not this factor does apply to our observations is difficult to judge since no information is available to us about the type of instability which led to the observed turbulence events. Furthermore, we note that the only so far available direct comparison of ε measurements based on the spectral width method with a well established in situ technique showed overall very good quantitative agreement [Engler et al., 2005, Figure 9] such that our choice to only consider random errors and ignore potential systematic errors appears to be justified.
 Note further that also other potential systematic effects like an incomplete filling of the radar beam in the case of the SSR, or a systematic overestimate or underestimate of the SSR antenna gain cannot be excluded and would bias the results shown above to one direction. However, since we are so far incapable of quantifying these effects, they will not be considered any further.
 In any case, using the above-stated assumptions, Figure 13 (bottom) reveals that derived particle radii have typical uncertainties of 30% and less except for those cases where η(SSR)/η(ESR) is close to its theoretical lower limit as already mentioned above. We also note that smaller radii (<20 nm) have even much smaller uncertainties of less than 15%.
 In order to further judge whether these distributions are geophysically reasonable or not we have finally compared our results to independent observations of ice particle radii in mesospheric ice clouds. A survey of available measurements quickly shows that there is currently only one instrument which has sufficient sensitivity to detect ice particles with radii down to as small values as 10 nm. This is the Solar Occultation For Ice Experiment (SOFIE) on board the Aeronomy of Ice in the Mesosphere (AIM) spacecraft [Gordley et al., 2009]. SOFIE measures vertical profiles of limb path atmospheric transmission within 16 spectral bands between 0.29 and 5.32 μm wavelength. SOFIE observes about 15 sunsets in the Southern Hemisphere and 15 sunrises in the Northern Hemisphere each day. Measurement latitude coverage ranges from about 65° to 80° north or south. SOFIE measurements are used to retrieve extinctions of mesospheric ice clouds at eleven wavelengths from 0.330 to 5.01 μm. In addition to temperature and the abundance of gaseous species, mesospheric ice clouds are measured by monitoring the attenuation of solar radiation using broadband radiometers. The SOFIE field of view is about 1.5 km vertical and about 4.3 km horizontal. Detectors are sampled at 20 Hz which corresponds to ∼145 m vertical spacing. The sample volume length, as defined by the line-of-sight entrance and exit of a spherical shell with vertical thickness of the FOV, is ∼290 km. Details of the method to derive microphysical parameters including effective radii (which are independent of the assumption of a specific particle size distribution) from SOFIE observations have recently been presented by Hervig et al. . Here, we compare estimates of effective radii obtained during the entire northern summer season 2007 (data version V1.022) to our own results.
 Finally, we also compare the radar results to observations with the ALOMAR Rayleigh/Mie/Raman (RMR) lidar located at 69°N from June 2006. The ALOMAR RMR lidar measures relative density profiles and particle (aerosol) properties in the stratosphere and mesosphere and has been described in detail by von Zahn et al. . A recent review of corresponding results including a detailed description of the method to derive ice particle parameters from observations at three wavelengths is presented by Baumgarten et al. . For the current purpose, suitable three-wavelength lidar data were integrated for 14 min and then analyzed for particle number densities, mean radii and widths of a Gaussian particle size distribution. For comparison to SOFIE and radar data, these parameters were then converted to effective radii as described by Hervig et al. .
 Before going into the details, a few caveats should be mentioned: first we note that we compare measurements from different years and also from different latitudes: while our radar measurements were done in June 2006, the AIM satellite was only launched on 25 April 2007 so that the 2007 summer season is the first available data set. Concerning latitudinal coverage, we note that the bulk of the SOFIE observations is from 68°N and the lidar observations are from 69°N and not from 78°N as in the case of our radar measurements. Furthermore, SOFIE observations were taken between 2200 and 2300 LST and lidar data were gathered between 2300 and 0300 LST, whereas the radar observations were taken between 1000 and 1400 LST such that potential tidal differences in particle properties might occur. Based on the multiyear lidar statistics of Fiedler et al.  this effect is, however, expected to be small since both local time intervals correspond to comparable values in the observed semidiurnal variation of brightness values (see their Figure 3). Then one must realize that SOFIE observations are proportional to the cube of particle radius (i.e., absorption in the Rayleigh regime) whereas the Schmidt number depends quadratically on the particle radius because a hard sphere collision model is here assumed. Finally, one must also note that there are certainly many occasions where PMSE (and hence mesospheric ice particles) was only observed with the SSR and not with the ESR. Hence, our data set of combined SSR/ESR observations represents in itself a biased data set; that is, it is not representative of an average state of the atmosphere but rather of a situation which allows PMSE to occur at the rather large frequency of 500 MHz. As described in detail above, these favorable conditions depend on the turbulence activity, the background ionization, and the size of the ice particles involved.
 Having all these caveats in mind, we now compare radii derived from our radar observations to radii derived from the SOFIE occultations and ALOMAR RMR lidar observations at three wavelengths in Figure 14. For this comparison, we have divided the data again into a subset for altitudes from 81 to 85 km and from 85 to 88 km. Focusing first on the radar results, we see that radii above 85 km are on average significantly smaller (median value of ∼20 nm) than below 85 km (median value of ∼35 nm) which is in line with our current microphysical understanding of these ice clouds which assumes that the particles nucleate at the mesopause and then grow and sediment to lower altitudes [e.g., Rapp and Thomas, 2006]. Coming now to the comparison to the SOFIE data, we note that the overall agreement between radar and optical measurements is actually very good: Above 85 km, the agreement is actually remarkably good with both data sets peaking at around 15 nm and showing a tail down to values of about 40 nm. Below 85 km, both satellite, radar, and lidar data show a rather broad distribution with median values of 28 nm in the case of the SOFIE measurements, 30 nm in the case of the lidar data, and 35 nm in the case of the radar observations. Taking into account the very different statistics of the three data sets (see caption of Figure 14) as well as the known fact that ice particle radii tend to increase toward the pole [Karlsson and Rapp, 2006] this difference can likely be explained by different latitudes at which radar (78°N) and satellite observations (68°N) were taken. In summary, taking all the caveats mentioned above into account, we consider this an excellent agreement and very strong support that the radii retrieved from the radar observations are meaningful.
 Finally, we present full altitude profiles of ice particle radii for one given event together with the mean of all observations in Figure 15. These results demonstrate that both in a given event as well as in the statistical average, the radii show an increase with decreasing altitude as suggested by independent observations [e.g., von Savigny et al., 2005; Hervig et al., 2009; Rapp et al., 2009] and our current microphysical understanding [e.g., Rapp and Thomas, 2006].
 In the current paper we have presented simultaneous and common volume measurements of PMSE using two calibrated radars at well separated frequencies (53.5 and 500 MHz) and hence Bragg wavelengths (2.8 m and 30 cm). These are the SOUSY Svalbard Radar (SSR) and the EISCAT Svalbard Radar (ESR) which are collocated near Longyearbyen on Svalbard (78°N, 16°E). A statistical comparison of occurrence rates shows that PMSE observed at a Bragg wavelengths of 30 cm occurs much rarer than PMSE at the ‘standard’ Bragg wavelength of 2.8 m, where most PMSE observations are obtained worldwide. That is, PMSE at 30 cm was observed during only 16% of the observation time, whereas PMSE at 2.8 m occurred during 94.5% of the same period in June 2006. In addition, the latter echoes occurred over a significantly larger altitude range, i.e., from 80 to 92 km as compared to 81 to 88 km for the case of the 30 cm echoes. As an additional remarkable feature, we note that the 30 cm echoes occurred in two well separated regions from 81 to 85 km and from 85 to 88 km. Interestingly, we were able to show that spectral widths (and hence turbulence activity) were significantly larger in the cases where 30 cm echoes were observed above 85 km as compared to cases when PMSE was only observed at 2.8 m. This implies that enhanced turbulence plays an important role for the occurrence of this layer of 30 cm echoes at altitudes above 85 km. Finally, converting spectral widths observed with the narrow-beam ESR resulted in distributions of turbulent energy dissipation rates with values between 5 and 200 mW/kg which is in line with previous estimates from rocket borne in situ soundings. Remarkably, the statistical distribution of this parameter shows an asymmetric distribution with a very long tail to large energy dissipation rates as expected for intermittent processes like turbulence.
 Turning next to a quantitative comparison of the observed signal strengths, the latter were converted to absolute volume reflectivities η (scattering cross sections per unit volume) making use of a noise calibration in the case of the ESR and a delay line and noise calibration in the case of the SSR. This resulted in η distributions ranging from values of 2.5 × 10−19 m−1 to 1 × 10−17 m−1 for the case of the 30 cm ESR echoes and from 5 × 10−16 m−1 to 6.3 × 10−12 m−1 for the case of the 2.8 m SSR echoes. We stress that this enormous dynamical range of the observations caused by the very large geophysical variability of PMSE demands that a quantitative comparison of volume reflectivities with different radars must be carried out on the basis of simultaneous and common volume observations. Given a variability of up to 4 orders of magnitude, comparisons of volume reflectivities from different times and locations are not suited for a comparison to theory.
 We next compared observed ratios of the volume reflectivity at 2.8 m to the volume reflectivity at 30 cm and were able to show that 94% of the observations showed ratios that were larger than a theoretically lower limit predicted by the turbulence with large Schmidt number theory. The remaining 6% which show too small ratios can be tentatively attributed to an incomplete filling of the scattering volume of the SSR which is significantly larger than that of the ESR as well as the uncertainty of the radar calibrations. This implies that our observations are largely consistent with the above-mentioned theory, even though we have to caution that the 6% which show too small reflectivity ratios could potentially indicate some yet unidentified physical process. This question will be addressed in a future study in which we will investigate all available simultaneous PMSE observations with the EISCAT VHF and UHF radars in Tromsø. These have the advantage of almost identical observations volumes as well as identical calibration routines (Rapp et al., manuscript in preparation, 2010).
 We note that the here demonstrated overall consistency between theoretical expectations and observations allows us to disregard any theory which predicts a wave number dependence which is less steep than k−3. However, it certainly does not allow us to disregard other potential theories with functional dependencies steeper than k−3. In order to distinguish such different possible functional dependencies, observations at more than two frequencies would be required. Hence, our analysis can certainly not prove that the assumed turbulence theory is correct but it provides sufficient motivation to proceed further and derive microphysical parameters from our data which may then be compared to independent observations in order to further corroborate or falsify our assumptions.
 In the frame of the turbulence with large Schmidt number theory the ratio of volume reflectivities at two Bragg wavelengths only depends on two unknown parameters, i.e., the turbulent energy dissipation rate and the Schmidt number which is itself a unique function of the radius of the charged ice particle leading to the required electron diffusivity reduction. Since turbulent energy dissipation rates can be derived from the spectral information of the ESR measurements, this ratio can be used to infer particle radii. Applying this method to our data set we derive ice particle radii between 10 and 70 nm with typical uncertainties of less than 30% (up to 50% for the largest radii). Dividing our data set in two samples above and below 85 km shows that inferred radii are on average smaller above (median value of ∼20 nm) and larger below 85 km (median value of ∼35 nm). This is in full accord with expectations from microphysical models which predict particle nucleation close to the mesopause around 90 km and subsequent growth and sedimentation to lower altitudes. Finally, we compared our data set to independent observations from the Solar Occultation For Ice Experiment (SOFIE) on board the Aeronomy of Ice in the Mesosphere (AIM) spacecraft and the ALOMAR RMR lidar and find overall excellent agreement. This confirms that calibrated radar measurements of PMSE at two well separated Bragg wavelengths (frequencies) are a well suited tool for studying the microphysics of mesospheric ice clouds and related questions such as solar induced variations as well as long-term trends.
 For the future, corresponding observations should be carried out together with multiwavelength lidar observations at the same location in order to allow a direct consistency check regarding inferred particle sizes [e.g., Baumgarten et al., 2008]. A first such attempt is planned for summer 2010 making use of observations with the EISCAT VHF and UHF Radars in Tromsø and the ALOMAR Rayleigh/Mie/Raman lidar.
 This project was supported by DFG in the frame of the CAWSES priority program under grants RA 1400/2-1 and RA 1400/2-2. We greatly appreciate the contribution by A. Serafimovich and N. Engler of their assistance with the radar observations in June 2006 and J. Trautner for repeated dedicated technical support of the SSR. Many thanks also go to A. Westman and the entire ESR team on Svalbard for excellent support. EISCAT is an international association supported by research organizations in China (CRIRP), Finland (SA), France (CNRS, until end 2006), Germany (DFG, formerly MPG), Japan (NIPR and STEL), Norway (NFR), Sweden (VR), and the United Kingdom (PPARC).