High-resolution neutral air density measurements with the ionization gauges “TOTAL” (which stands for total number density, used in 1980–1992; ; ) and “CONE” (“Combined sensor for Neutrals and Electrons”, which have been used since 1992; ) yield absolute densities of the atmosphere in the height range 70–110 km . These instruments have an effective altitude resolution of ∼ 0.3 m for a typical rocket velocity of 1000 m s-1. CONE is sensitive to relatively small density fluctuations of as low as 0.05 %. These relative density fluctuations are used as a tracer (scalar) for turbulence. Its power spectral densities (PSDs) can be calculated by using either Fourier or wavelet analysis techniques . Next, a one-dimensional model spectrum for a turbulence tracer is fitted to the measured PSD yielding the turbulent energy dissipation rate, ε. The best known and most frequently used spectral models which have been adapted to neutral air density fluctuations are those by , , and . The last of these is better suited for tracers that have different viscosity to diffusivity ratio than the background media. For detailed description of the instruments, the analysis technique, and an overview of measurements conducted so far, the reader is referred to .

The radar turbulence measurement techniques are based on the assumption that the broadening of the Doppler spectrum is mainly caused by velocity fluctuations around a mean Doppler shift in the observational volume. If wind fluctuations are caused by a turbulent medium, this measured spectral width in velocity units can be uniquely related to the turbulent energy dissipation rate in the volume, ε see, e.g.,. demonstrated that backscattering from PMSEs is a coherent scattering from turbulent structures and that observed spectral width in velocity units is a measure of energy dissipation rate independent of radar frequency. In this work we analyze PMSE measurements with two radars, the MAARSY (Middle Atmosphere ALOMAR Radar System) and the EISCAT (European Incoherent SCATter Scientific Association) radar near Tromsø.

The main parameters of radars used in this study are summarized in Table . Particular experiment configurations used for turbulence measurements are compiled in Table .

The WADIS-1 payload was launched into both PMSEs observed with the MAARSY and NLCs monitored with the ALOMAR RMR lidar on 27 June at 23:52:30 UTC. The EISCAT VHF radar in Tromsø was also continuously detecting PMSEs during the entire night of the WADIS-1 launch. The EISCAT UHF radar observed PMSEs during the launch window, but these were only sporadic and very weak. Also, Na lidar observed a large sporadic Na layer several hours around the WADIS-1 launch.

Figure  shows a height–time intensity plot of radar volume reflectivity observed by the vertical beam of MAARSY. The volume reflectivity was converted directly from the absolute value of the received signal power as described in . The vertical magenta line marks the WADIS-1 launch time when MAARSY was detecting a double-layered structure. Figure  shows the signal-to-noise ratio detected by the MAARSY beams along the expected rocket trajectory shortly before launch time, indicating an extension of the double-layer structure towards the direction of the planned rocket flight.

Figure  shows NLC observations by the RMR lidar. The vertical dashed line marks the WADIS-1 launch and one can see that the NLC was co-located with the lower PMSE layer, which is a common feature see e.g.,.

Figure  also shows EISCAT measurements in terms of radar reflectivity. One can see a prominent PMSE signature in the VHF data. Also, a double-layered structure similar to that observed by MAARSY is seen in the VHF display. The strong persistent signature in the UHF data appearing above 90 km heights is a sporadic E layer, i.e. a layer of enhanced electron density, which is also seen in the VHF measurements. The UHF PMSE is so weak that it cannot be identified on this volume reflectivity plot without special treatment. Yellow contours in the UHF plot mark regions where the VHF radar observed PMSEs. The gap in the UHF data is because of some technical issues that briefly interrupted the radar operation during that night. Around the time of the WADIS-1 launch (23:52:30 UTC) both MAARSY and the EISCAT radars produced high-quality measurements, which we discuss in detail in the Sect. .

The persistent PMSE observations with the MAARSY and the EISCAT radars indicate that turbulence was occurring over an extended horizontal area in the mesopause region. We note, however, that PMSEs also occur during periods of fossil turbulence such that the PMSE spectral width also needs to be evaluated in order to draw firm conclusions concerning the spatial extent of turbulence.

The rocket WADIS-1 was launched as vertically as possible based on launch safety requirements. The geometry of the measurements is sketched in Fig. .

The upleg and downleg measurements at a height of ∼ 80 km are separated horizontally by about 30 km.

As stated above, one of the telescopes of the twin ALOMAR lidar system, i.e. of both RMR and Na lidars, was pointing to the direction of the anticipated rocket trajectory to achieve the best possible common-volume measurements. In the next section we discuss the measured parameters starting with the background state of the atmosphere.

The background wind field was continuously monitored with the SAURA-MF radar . The zonal and meridional wind measurements around the WADIS-1 launch time are shown in Fig. . SAURA measurements reveal that between 80 and 90 km altitude mean horizontal wind was stably directed to the southwest several hours around the WADIS-1 launch time. The zonal wind shows a quite stable field, whereas the meridional component reveals a fluctuating behavior with prominent shears at ∼ 80 and 90 km.

Temperatures were continuously measured both by ALOMAR RMR and Na Weber lidars. The Na lidar additionally measured winds with relatively high temporal and spatial (vertical) resolution. The joint measurements by both lidars are shown in Fig. .

Also, as mentioned above, the RMR lidar was continuously observing NLCs throughout the entire night of the WADIS-1 launch, meaning that low temperatures below the frost point persisted in the corresponding altitude range of 80–90 km during that time.

The temperature was also measured in situ, applying the ionization gauge CONE. The corresponding temperature profiles are shown in Fig.  for up- and downleg in red and blue, respectively. The two temperature profiles measured with the Na and RMR lidars at the time of the rocket launch are shown in yellow and green, respectively. The black line shows temperature from the NRLMSISE-00 reference atmosphere . Pronounced wave signatures are seen in all temperature profiles above ∼ 80 km. The difference of ∼ 30 K at heights of 85–90 km between temperatures measured on the up- and downleg can be attributed to gravity waves with a horizontal wavelength on the order of 60 km (twice the distance between the up- and downleg). Notably, between 90 and 95 km height the temperature reveals a very similar structure and very similar values in all profiles. This may be seen as an indication for a reduction of GW activity due to wave breakdown at heights of 80 to 90 km; for a detailed discussion of this hypothesis see below.

It can be seen in Fig.  that the temperature profiles often exhibit near-adiabatic lapse rates. The in situ turbulence detection technique based on neutral density fluctuations measurements with CONE can be insensitive to turbulent layers where temperature gradient is adiabatic e.g.,. However, the plasma density fluctuations reveal positive vertical gradients in these regions and therefore can be used as a tracer for turbulence. The results of plasma density measurements during upleg of the WADIS-1 rocket flight are shown in Fig. . The high-resolution electron density measurements with the LP are shown by red line. It is seen that inside the NLC or lower PMSE layer the electron density profile exhibits a bite-out. This is a well-known and common feature see, e.g.,and references therein. Since the electron density in such a case is drastically affected by ice charging process, it cannot be considered as a passive tracer for turbulence, which prevents turbulence analysis from the electron density data inside PMSE layers. Note that beside the bite-out region, the LP yielded high-quality plasma density measurements. The ion density measurements were not sensitive enough to resolve full spectrum of turbulence needed for ε derivation.

To summarize, the snapshot of the background temperature field in the mesopause region reveals a wealth of wave signatures in both vertical and horizontal extent. The relatively stable wind field between 80 and 90 km height suggests a dynamically stable atmosphere at these altitudes. Taken together this suggests that turbulence generation at these heights may be attributed to GW breakdown processes. In the next sections we investigate the corresponding variation in the turbulent energy dissipation rate to see whether these are consistent with our hypothesis.

Profiles of measured turbulence energy dissipation rates, ε, are compiled in Fig. . The blue and green lines show ε values derived from the in situ measurements using and spectral models, respectively. It is seen that both models yield very close values and generally agree very well. The left and right panels show upleg and downleg measurements, respectively. The lines in magenta show energy dissipation rates derived from the vertical beam measurements with MAARSY during the time of the rocket ascent. The dark-red profile represents the results of turbulence estimates from the EISCAT VHF radar measurements, also during the time of the WADIS-1 launch. The solid gray and black lines show ε climatologies derived from the same in situ technique for winter and summer , respectively. The black dashed line shows low limit estimate for turbulence energy dissipation rate derived as εmin=ν×ωB2, where ν is the kinematic viscosity of neutral air and ωB is the Brunt–Väisälä frequency see, e.g.,.

Between 82 and 90 km height both radars (MAARSY and EISCAT) and the sounding rocket detected two major turbulent layers, marked in Fig.  by the shaded areas. This is consistent with the PMSE display observed by MAARSY. The upper layer is located between 85 and 90 km and the lower between 82 and 85 km height. Here the rocket upleg measurements are noteworthy, which show turbulence layers between 82 and 70 km altitude, something rather unusual for summer conditions. Note that both the MAARSY and the EISCAT radar are only capable of measuring turbulence inside the PMSE layers that is between ∼ 80 and 90 km.

To better compare the in situ and radar turbulence measurements, we plotted mean energy dissipation rates derived between 80 and 90 km heights from the rocket-borne and radar measurements which are shown by vertical dashed lines. Note that the mean values compare well. The rocket upleg data were measured spatially close to the vertical MAARSY beam and the derived dissipation rates reveal close values: 〈εuplegHeisenberg〉=74 mW kg-1, 〈εuplegTatarskii〉=73 mW kg-1, 〈εMAARSY〉=58 mW kg-1, where 〈…〉 denotes spatial averaging over the height range 80–90 km. The downleg rocket measurements reveal larger energy dissipation rates and the derived mean values are closer to those of the EISCAT radar, which was located ∼ 100 km east of the rocket launch site. The corresponding mean values are 〈εdownlegHeisenberg〉=492 mW kg-1, 〈εdownlegTatarskii〉=307 mW kg-1, and 〈εEISCAT〉=769 mW kg-1. Also, within the upper turbulent region the in situ downleg measurements show two pronounced sub-layers with very high ε values. The lower one is found between 85.5 and 85.8 km that is only 300 m thick and reveals energy dissipation rates of up to ∼ 7 mW kg-1. The upper one appears between 87.2 and 87.8 km and shows ε≈1 mW kg-1.

This indicates that the high ε values, derived from the EISCAT measurements in this study or, for example, by are likely realistic. Another important remark regarding these measurements is that the mean ε values differ from high-resolution instantaneous measurements by orders of magnitude. The latter must be kept in mind when comparing means and especially climatologies by and with other measurements in the context of case studies.

Another characteristic feature seen in the in situ turbulence measurements is the large vertical gradients in the ε profiles. Thus, for instance the downleg data between 85.0 and 85.5 km reveals an increase by 5 orders of magnitude in the turbulence dissipation rate value. Also, intermittency, i.e., the rapid change in ε values on very short (down to 100 m) vertical scales, and discontinuities in the ε profiles are clearly seen in the in situ measurements. Such pronounced gradients and intermittency in the ε profiles were previously observed by the same instrument e.g., and also appear in direct numerical simulations see, e.g., and seem to be an immanence of atmospheric turbulence.

Radars do not detect such very strong gradients, most probably because of the large measurement volume and the additional time averaging needed to achieve a reasonable signal-to-noise ratio (SNR). For example, the EISCAT VHF radar beam reveals 300 m vertical and 2300 m horizontal extent at 85 km height e.g.,. The maximum vertical gradient of the ε values observed by the EISCAT VHF during WADIS-1 campaign was 33 mW kg-1 km-1, whereas the maximum ε gradient revealed by the in situ measurements is ∼ 44 mW kg-1 km-1. Though the ε gradient value derived from the EISCAT observations is slightly lower than those from the rocket-borne measurements, the values are still remarkably close to each other. This further supports the reliability of the EISCAT turbulence measurements. Unfortunately, the EISCAT measurements are only available on a campaign basis, which makes it difficult to get a large data set of concurrent measurements with MAARSY. However, the 5 h of the EISCAT measurements yield important geophysical information, discussed in Sect. .

The MAARSY beam geometry at those heights was set up for ∼ 10 km horizontal extent, and the maximum ε gradient value observed during WADIS-1 campaign was only 3 mW kg-1 km-1. On the other hand, MAARSY yields continuous observations and therefore allows investigations of temporal evolution of mesospheric turbulence, which are discussed below.

To summarize, even though the MAARSY turbulence measurements are somewhat limited in magnitude of ε values, their vertical mean agrees reasonably with the mean over the same height range derived by the reliable in situ technique.

Figure  shows histograms of all measured single ε values for 5 h of the EISCAT and MAARSY measurements during the WADIS-1 launch night (red and green, respectively), as well as in situ measurements (blue).

First of all, due to their high sensitivity, the rocket-borne ε measurements reveal a much broader distribution than those derived from the radar measurements. In situ measured turbulence energy dissipation rates span over five decades, whereas radar measurements only vary by 3.5 and 4 orders of magnitude for MAARSY and EISCAT, respectively. Also, the in situ data reveal two subsets separated at ε=10 mW kg-1. The subset with high energy dissipation rates results from the strong turbulent sub-layers observed on the downleg.

The solid lines in Fig.  show the probability density functions (PDFs) for normal distributions of log10(ε), fitted to the respective histograms. Interestingly, the widths of these PDFs for both radar data sets are equal to the third decimal digit, σ=0.489 in log10 space. The subset of in situ data with higher ε values (i.e., 101–104 mW kg-1) has broader width of σ=0.750 in log space. The mean values in log10 space for these distributions of single ε points in the range 80–90 km are highest for the EISCAT and smallest for the in situ measurements. The dynamic range of the ε values, i.e., [max⁡(ε)-min⁡(ε)], is also larger for EISCAT than for MAARSY data. The in situ data reveal a larger range of the observed turbulence energy dissipation rates, and if we fit a single PDF to the entire range of the measured dissipation rates, i.e. from 10-1 to 104 mW kg-1, it reveals σ(log⁡10(ε))≈1 (discussed below and shown in Fig. ).

Next, we look how vertical mean values derived from the radar measurements are distributed by their magnitude. The same sort of distributions as in Fig. , but for vertical mean of the radar measurements between 80 and 90 km are shown in Fig. . The PDFs of the vertical means are closer to the in situ data and the σ values are equal to the first decimal digit, σ=0.5. Also, the entire distribution lies closer to the in situ data.

Now, we take larger data sets, which are available for us for the in situ and MAARSY measurements and compare the same statistics in Fig. . The statistics of all the rocket-borne turbulence measurements in summer in the altitude range between 80 and 90 km are shown in Fig.  in black. It yields a mean of ε≈10 mW kg-1 and σ≈1 in log10 space . The highest ε values in the total statistics only slightly exceed those derived from the WADIS-1 flight data. However, the entire ε range is broader by 2 orders of magnitude and thereby spans over seven decades of ε values. The blue line in Fig.  shows PDFs fitted to the entire (not split) set of the WADIS-1 rocket-borne measurements.

The histogram of all MAARSY turbulence measurements during the PMSE season of the year 2013 is shown in Fig.  in green. The histogram represents distribution of the vertical mean ε values obtained by MAARSY between 80 and 90 km height. The solid line shows the corresponding PDF and the dashed line shows PDFs derived for distribution of single ε values similar to those, shown in Fig. , but for the entire PMSE season 2013 (the corresponding histogram is not shown here). It is apparent that the rocket-borne and the MAARSY mean-based ε distributions reveal close mean values (i.e., peak of the probability) of about 10 mW kg-1. The width of the distributions, σ, is 1.5 orders of magnitude larger for the in situ measurements than for mean MAARSY observations. It is seen from the MAARSY measurements statistics that distribution of the vertical mean ε values is centered at values almost 1 order of magnitude smaller and thereby agrees better with the in situ statistics, than that of the single ε points (Fig. , dashed line).

To summarize, the comparison of statistical distributions of ε values derived using different approaches in the altitude range 80–90 km shows that probability to measure mean value of the energy dissipation rate by MAARSY is close to those by the in situ results. Further, in Sect.  we will show that this vertical mean ε value reflects wave activity at different timescales, which is otherwise not seen.

Another interesting feature apparent in the in situ measurements is the wavelike behavior of the ε profiles. It is especially seen in the downleg data (Fig. , right panel). It is intuitive to suggest that this might be a signature of gravity waves that could, for example, modulate the turbulence field.

In situ measurements of the background density and/or temperature can be used to derive vertical wavelengths of the gravity waves in the same measurement volume, getting insight into the observed oscillating feature. Since the turbulence field in the MLT is essentially intermittent, and therefore the in situ measured energy dissipation rate profiles have many singularities, we apply the Lomb–Scargle spectral analysis technique to infer wavelengths of the observed modulation. The Lomb–Scargle scalograms of the two in situ measured ε profiles are shown in Fig.  as green lines. For consistency, we use the same technique to infer GW parameters from the relative fluctuations of density and temperature which are shown in Fig.  as blue and red lines, respectively. The upper panel of Fig.  shows upleg data and the lower panel is for downleg measurements.

Both up- and downleg data reveal most pronounced spectral peaks inferred from density and temperature fluctuations at ∼ 3.2 km. The upleg turbulence measurements also reveal a strong signature at this scale, but not the downleg ε measurements. The upleg data also reveal an obvious and pronounced maximum at 5 km scale in both density and temperature fluctuations as well as in the spectral morphology of the turbulence energy dissipation rates. The downleg data reveal a wealth of wavelengths larger than the 5 km apparent in the upleg measurements, which are merged and cannot be discriminated. The wavelength range from about 2 to 10 km is characteristic for gravity waves propagating to the MLT region e.g., and suggests a modulation of the turbulence dissipation field by gravity waves.

Both upleg and downleg ε profiles also reveal clear signatures at smaller scales, i.e. ∼ 2.1, ∼ 1.5, and ∼ 1 km (see Fig. ). At the same time, only the downleg measurements of temperature and density fluctuations clearly show the presence of peaks at the ∼ 2.1 and ∼ 1.5 km wavelengths. The smallest scale of the strong wavelike modulation of both ε profiles at ∼ 1 km is not so clearly present in the in situ temperature and density profiles.

To summarize, the spatial variation in the in situ measured turbulence energy dissipation rates shows wavelike modulations typical for the MLT-GW range of wavelengths and thereby suggests that the morphologies of these two dynamical processes are ultimately coupled. If the observed oscillating behavior of the ε profiles is indeed a signature of gravity waves, we should be able to find similar signatures in other turbulence measurements, e.g., in MAARSY data.

In Sect.  we showed that the vertical mean over the altitude range 80–90 km of radar ε measurements appears to be a suitable measure of the overall turbulence activity for a given time. In this section we investigate how this mean varies in time. Figure  shows variation in the vertical mean of the MAARSY turbulence measurements, with full time resolution shown by the blue line. Similarly, the green line represents the full time resolution of the mean of the EISCAT turbulence measurements. Bold red and black lines were derived as running means of the blue and green profiles for MAARSY and EISCAT, respectively.

Figure  shows quite prominent wavelike features with smaller modulations at about 1 h periods modulated by an about 24 h wave. The short-period (∼ h) ε variations have amplitudes of up to ∼ 1 order of magnitude, whereas 24 h modulation introduces change of up to ∼ 2 orders of magnitude in the energy dissipation value.

The general trend of the 5 h of EISCAT measurements during the WADIS-1 launch night falls quite well on the MAARSY data, suggesting that both radars might reveal similar time variability.

Since the MAARSY-based measured vertical mean of turbulence energy dissipation rate is available for the entire season, we constructed a continuous and smooth time series that can be analyzed applying, for example, the Fourier analysis technique. The resulting power spectrum is shown in Fig. . The 24 h period inferred from the time-series plot (Fig. ) is clearly seen as a peak in the spectrum, and its significance can be judged by the naked eye. Also, a 12 h peak is apparent in the spectrum in Fig. .

By applying different filters and looking at the spectrum of the shown in Fig.  time series, but over the entire season, one can also find some short-period wave signatures, which are not pronounced in the spectrum of the full-resolution data shown in Fig. . Thus, one can isolate, for example, 1.6 and 0.9 h peaks in the spectrum which are also apparent in the time-series plot (Fig. ).