VAHCOLI, a new concept for lidars: technical setup, science applications, and ﬁrst measurements

. A new concept for a cluster of compact lidar systems named VAHCOLI (Vertical And Horizontal COverage by LIdars) is presented which allows to measure temperatures, winds, and aerosols in the middle atmosphere ( ∼ 10-110 km) with high temporal and vertical resolution of minutes and some tens of meters, respectively, simultaneously covering horizontal scales from few hundred meters to several hundred kilometers (’four-dimensional coverage’). The individual lidars (’units’) being used in VAHCOLI are based on a diode-pumped alexandrite laser currently designed to detect potassium ( λ =770 nm), as 5 well as on sophisticated laser spectroscopy measuring all relevant frequencies (seeder laser, power laser, backscattered light) with high temporal resolution (2 ms) and high spectral resolution applying Doppler-free spectroscopy. The frequency of the lasers and the narrow-band ﬁlter in the receiving system are stabilized to typically 10–100 kHz which is a factor of roughly 10 − 5 smaller than the Doppler-broadened Rayleigh signal. Narrow-band ﬁltering allows to measure Rayleigh and/or resonance scattering separately from the aerosol (Mie) signal, all during night and day. Lidars used for VAHCOLI are compact (volume: 10 ∼ 1 m 3 ) and are multi-purpose systems employing contemporary electronical, optical, and mechanical components. The units are designed to autonomously operate under harsh ﬁeld conditions at remote locations. An error analysis with parameters of the anticipated system demonstrates that temperatures and line-of-sight winds can be measured from the lower stratosphere to the upper mesosphere with an accuracy of ± (0.1–5) K and ± (0.1–10) m/s, respectively, increasing with altitude. We demonstrate that some crucial dynamical processes in the middle atmosphere, such as gravity waves and stratiﬁed turbulence, can be 15 covered by VAHCOLI with sufﬁcient temporal/vertical/horizontal sampling and resolution. The four-dimensional capabilities of VAHCOLI allow to perform time-dependent analysis of the ﬂow ﬁeld, for example employing Helmholtz decomposition, and to carry out statistical tests regarding intermittency, helicity etc. First test measurements under ﬁeld conditions with a prototype lidar being built for VAHCOLI were performed in January 2020. The lidar operated successfully during a six week period (night and day) without any adjustment. These observations covered a height range of ∼ 5–100 km and demonstrate the 20 capability and applicability of this unit for the VAHCOLI concept.


Introduction
Lidars (light detection and ranging) have been applied in atmospheric research since many years. Here we concentrate on the middle atmosphere, namely on the altitude range 10-120 km. Different techniques have been used to measure, e. g., tempera-a fast tuning of the power laser to a wide range of frequencies from one pulse to the other. We currently use a maximum tuning rate of 1000 MHz per milli-second, which can be increased if required. An example of controlling and measuring the power laser frequency is shown in Fig. 4. The seeder laser (and thereby the power laser) is tuned across the confocal etalon Fig. 4 where the frequency range of the tuning (=100 MHz) was chosen such that it covers the spectral width of the confocal etalon.
The frequency sampling covers frequencies with a difference of 2 MHz. As can be seen in Fig. 4 the advanced ramp-and-fire 130 technique ensures that the frequencies of the power laser pulses are indeed very close to the nominal frequencies, ν i (within less than 100 kHz), namely within the width of each red line in Fig. 4. The intensity distribution as a function of ν i is given by the convolution of the spectral width of the confocal etalon and the spectral width of the power laser (the spectral width of the seeder laser is only ∼100 kHz and can be ignored in this context). Fig. 4 demonstrates that the frequency control of the power laser by the seeder laser works very successfully, namely within less than approximately 100 kHz. 135 The temporal stability of the laser frequency control is demonstrated in Fig. 5 where measurements of the frequencies of the Fig. 5 seeder laser and the confocal etalon are shown. More precisely, in the upper panel the difference between the nominal seeder laser frequency and the actual true frequency is shown, where the latter is determined by comparison with high precision Doppler-free spectroscopy. Data points are shown for ∼3 min with a temporal resolution of 1/10 s. The mean offset between nominal and true frequencies is only 21.44 kHz with a RMS variation of 170 kHz. The same procedure is repeated for the 140 confocal etalon (lower panel in Fig. 5), i. e., the seeder laser is directed into the confocal etalon, and nominal and 'true' frequencies (from the seeder laser) are compared to each other. The mean uncertainty of the confocal etalon frequency is 187.92 kHz which corresponds to an uncertainty in wind measurements of 0.072 m/s. In fact, the final contribution of this uncertainty to the wind error is even smaller since the offset (in this case 187.92 kHz) is measured and later considered in the data reduction procedure. 145 Finally, the spectrum received from the atmosphere is compared with the spectral characteristic of the instrument including laser line width, spectral filters etc. For Rayleigh and Mie scattering it is not necessary to know the absolute frequency of the laser light and the absolute frequency position of the etalon's transmission functions. It is only important to know the frequency of the pulsed laser relative to the frequency of the spectral filters which is achieved by the procedure described above. On the other hand, resonance scattering requires frequency measurements on an absolute frequency scale which is 150 achieved by applying Doppler-free polarization spectroscopy to an atomic absorption line of potassium, which in turn is used to control the output of the seeder laser and the spectral filters with an accuracy of a few kHz (see above).

Laser specifications
A VAHCOLI-unit requires a compact, efficient, and high performance laser designed for atmospheric applications. For Doppler-Mie the laser should preferentially have an exceptionally small line-width. For Doppler-resonance the laser must be tunable to 155 an atomic absorption line. We have developed a highly efficient, narrow-band diode-pumped alexandrite ring laser in cooperation with the Fraunhofer Institut for Laser Technology in Aachen (Höffner et al., 2018;Strotkamp et al., 2019). The laser head includes various subsystems such as Q-switch driver, cavity-control, power measurement, and a beam expansion telescope all 5 https://doi.org/10.5194/amt-2021-33 Preprint. Discussion started: 10 February 2021 c Author(s) 2021. CC BY 4.0 License. of which are placed in a sealed housing for touch free operation over long periods. The laser head is pumped via a fiber cable connected to a separate diode array acting as an optical pump. The beam profile of the laser is nearly perfect with very little 160 aberration (M 2 =1.1). The spectral width is ∼3.3 MHz with a pulse length of ∼780 ns. In Q-switch mode, the variation of the output power from pulse to pulse is only 0.2%. A first test of the robustness of the laser was performed when it was transported from Aachen to Kühlungsborn in early 2020. After a transport of nearly 700 km in a standard truck the laser performed without any degradation (see section 3). Thereafter, the entire lidar was aligned and operated successfully during a six week period without any further adjustment.

Telescope and receiver
The field-of-view (fov) of the telescope is currently 33 µrad which corresponds to a diameter of 3.3 m at a distance of 100 km.
The accuracy to keep the laser beam inside the field of view of the telescope is better than 10 cm at 100 km which corresponds to a position accuracy of better than 1 µrad. This is achieved as follows: the photons being scattered by 180 degree from the atmosphere follow the optical path of the outgoing laser-beam but in retrograd direction. The light from the atmosphere is 170 separated from the outgoing laser pulse using its polarization characteristics. This implies that outgoing and incoming light paths are automatically co-aligned and no active control of the outgoing laser beam on a pulse-to-pulse basis is needed. Slow drifts of the laser beam relative to the optical axis of the telescope caused by, for example, temperature drifts are compensated for by a control loop (maximizing the atmospheric signal) with a time constant of few minutes. The current plan is to have 5 telescopes with different viewing directions which are fed subsequently (switching within 1 ms) by one laser. Only one receiver 175 system (and one transmitter) will be needed.
The prime mirrow (diameter = 50 cm) and related optics are integrated into a system which is manufactured by large scale 3D printing. Complex thermal balancing considerations ensure that the telescope (optics and walls) are stabilized to the outside temperature by maintaining an active airflow through the cube. This prevents convection and turbulence and also keeps dust, snow, and sea salt away from the optics. On the other hand, the mechanical structures supporting the primary and secondary 180 mirrors are stabilized to the temperature inside the main housing. This eliminates the need to realign the telescope when ambient temperatures are changing, for example, from day to night. In summary, the mechanical design and thermal balancing allow to operate the lidar under harsh conditions at a wide range of ambient temperatures during day and night.
The most important components of the receiver are the spectral filters in combination with other optical systems such as the seeder laser and the Doppler free spectroscopy (see Fig. 3). All components fit into a compact, optically tight, dust free, and 185 lightweight housing of 15 x 15 x 80 cm which is manufactured by 3D printing together with all mechanical mounts for the optical components (∼75 in total). Avalanche Photodiodes (APD) are used for counting photons.

Data acquisition and lidar control
After a laser pulse has been released, it takes 1 ms until photons scattered at a distance of 150 km arrive at the detector. This implies that the maximum possible pulse repetition frequency is k max =1000 laser pulses per second (we use 500 per second), 190 assuming that only one laser pulse is in the air at any given time. Photons from a single pulse scattered from a height range δz 6 https://doi.org/10.5194/amt-2021-33 Preprint. Discussion started: 10 February 2021 c Author(s) 2021. CC BY 4.0 License. arrive at the detector in a time interval of ∆t = 2·δz/c. During arrival the number of photons N ph from the height range δz create a count rate R sgl at the detector of R sgl =N ph /∆t =N ph /(2·δz/c). Here and in the following we ignore any impact by the dead-time of the detector. The time between two pulses is given by dt=1/k where k is the pulse repetition frequency. Therefore the effective number of photons counted per time interval is reduced relative to R sgl by a factor of ∆t/dt = (2·δz/c) · k. For 195 example, for δz=200 m and k=500/s the reduction factor is 1/1500. In other words, the number of photons, N ph , counted per integration time δt and height interval δz is related to the count rate (R) and the pulse repetition rate (k) via For technical reasons the count rate of typical detectors (PMT, APD) is limited to approximately R max =10 7 Hz. As mentioned before, the maximum pulse repetition rate is given by the uppermost altitude (z max ) wanted, k max =1000/s for 200 z max =150 km. Higher pulse repetition frequencies may be chosen if the maximum altitude is reduced. According to equation 1 this leads to a larger number of photons at a given altitude. The receiver relies on high speed single photon data acquisition system with compression for fast analysis. Each pulse is stored with 1 m altitude resolution and with further information regarding, for example, pulse energy as well as frequency and FWHM of the laser pulse. Each VAHCOLI-unit is connected to the internet and, if necessary, can be controlled and operated in real time. This includes the frequency control of the seeder and 205 power lasers as well as the filter system (see above). The entire receiver system (actually the entire lidar) is based on a single standard PC with integrated commercially available electronics. Data from the lidar are automatically downloaded to a remote server.  Chanin et al., 1989;She and Yu, 1994;Baumgarten, 2010). In our first measurements presented in section 3 we concentrated on measuring winds by detecting the spectral shift of the narrow band aerosol signal.

Measuring
Resonance scattering on metal atoms (K, Fe, Na) has frequently been applied to derive number densities and temperatures 225 in the altitude range of roughly 80 to 120 km by measuring the Doppler width of the backscattered light (see, for example, Fricke and von Zahn, 1985;von Zahn et al., 1988;Alpers et al., 1990;She et al., 1990;Clemesha, 1995;Chu et al., 2011;Höffner and Lautenbach, 2009). Different from these lidars, VAHCOLI can observe winds and temperatures from resonance scattering in the presence of aerosols, namely NLC. The resonance scattering application of VAHCOLI is based on our experience with a potassium lidar being operated at several locations, for example on the research vessel Polarstern or in Spitsbergen 230 (Höffner and von Zahn, 1995;Lübken et al., 2004;Höffner and Lübken, 2007). The technique has been improved substantially for a VAHCOLI-unit by applying high temporal and high spectral resolution detection of Doppler broadening (temperatures) and Doppler shift (line-of-sight winds). See section 2.1.1 for more details.

Aerosol parameters and winds
VAHCOLI is designed to also measure the presence of aerosols, more precisely background aerosols, polar stratospheric clouds 235 (PSC), and noctilucent clouds (NLC). Precise and fast measurements of the spectrum of the filters allows to position the narrow spectral filter (few MHz) exactly at the position of the Mie peak related to aerosol backscattering, as is shown in Fig. 2. Since the Mie spectrum in the stratosphere is also very narrow (typically 0.1 MHz, see above) only the backscattered signal from aerosols is detected, whereas nearly all of the Rayleigh scattering is blocked (this implies that the solar background signal is negligible which is known as 'solar blind'). Therefore, Mie scattering is detected irrespective of the Rayleigh signal (and vice 240 versa). The precise measurement of spectra allows to derive line-of-sight winds from the Doppler shift of the Mie peak (see section 3). In the future, we envisage multi-color observations of PSC and NLC to deduce particle characteristics such as size and number densities (see, for example, von Cossart et al., 1999;Alpers et al., 2000;Baumgarten et al., 2010).

Metal densities
Resonance scattering on metal atoms in the upper mesosphere/lower thermosphere is applied to derive metal number density 245 profiles. We have used this technique mainly to observe potassium (λ=770 nm) and iron (λ=386 nm), but other metals have also been measured (see, e.g., von Zahn et al., 1988;Gerding et al., 2000;Chu et al., 2011).

Other
Several secondary parameters are typically derived from the prime observables such as the potential (E pot ) and kinetic energy (E kin ), momentum flux, and wave action densities. Note that the latter requires to measure the background mean winds in order to consider the Doppler shifting effect on gravity waves. A Helmholtz decomposition of the flow, i. e., its divergent and 255 rotational component, can be applied to better unterstand the physical processes involved. Lidars typically measure relative number densities, n(z), which allows to determine E pot from i. e., from number density instead of temperature fluctuations. This allows to reach to higher altitudes and avoids uncertainties due to the start temperature.

260
Since VAHCOLI measures the dynamical and thermal components of the flow field, the heat flux due to fluctuations caused by gravity waves can also be derived. Statistical quantities are derived from fluctuations, for example longitudinal and transversal structure functions.

Lidar operation
After manufacturing, installation, and testing in the laboratory, the lidar can be transported to the location of interest where it 265 is assembled for operation under field campaign conditions. The lidar is designed as a sealed and automated system, i. e., it is controlled remotely and can therefore run for long periods without any manual operation. This includes to stop measurements on short notice and very quickly (from one pulse to another) if required by, for example, air safety regulations or by bad weather conditions. Information regarding air safety is currently provided by an internal camera, and weather conditions are monitored by an external weather station. Further constraints provided by external sources, e. g., a weather radar or air traffic control, can 270 easily be incorporated into the lidar operation. If conditions are favorable again, the lidar switches on automatically within less than one minute.

First measurements
In the following we show results from the very first atmospheric measurements by a prototype of a VAHCOLI-unit ('first light') performed in the period 17 to 19 January 2020. Some specifications of this lidar are summarized in Table 1. In Fig. 6 we show Tab. 1

Fig. 6
275 raw count rates observed on 19 January 2020 as detected by the detectors D R−R and D Mie (see Fig. 3). The goal of these measurements was to perform a first test of the entire lidar, i. e., laser, frequency control and analysis, telescope, detection system, Doppler free spectroscopy, lidar operation etc., under realistic conditions including rain, low temperatures, and storm, without touching the system for several days. Note that the FOV of the telescope was only 33µrad which allowed measurements even during full daylight. According to the description of the lidar presented in section 2.1.2 the confocal etalon is stabilized to 280 a certain frequency, ν cf , and the power laser is normally tuned by typically ±1000 MHz relative to this frequency. In the first 9 https://doi.org/10.5194/amt-2021-33 Preprint. Discussion started: 10 February 2021 c Author(s) 2021. CC BY 4.0 License.
measurements presented here we concentrated on wind measurements (Doppler-Mie) and have therefore used a much smaller frequency range for tuning, namely only ±50 MHz. In the case shown in Figure 6, the etalon's central frequency, ν cf , was chosen such that it coincides with the mean resonance frequency of potassium to allow for a detection of the potassium layer.
The etalon transmits backscattered light from the atmosphere within a frequency range of ν cf ±∆ν cf where ∆ν cf =FWHM/2 285 and FWHM∼7.5 MHz (blue line in Fig. 6). Note that the spectral width of the Mie peak is only ∼0.1 MHz which can be neglected in this context. Furthermore, ∆ν cf is much smaller than the spectral width of the Doppler broadened Rayleigh signal, i. e., only a very small fraction of the backscattered light from the atmosphere passes through the etalon, the rest is reflected and detected by a separate detector (red line in Fig. 6).
At altitudes below the potassium layer the total signal is due to backscattering from molecules (Rayleigh scattering) and a 290 small contribution from Mie scattering from aerosols at altitudes below ∼30 km. When the frequency of the Mie peak is outside the frequency range of the confocal etalon, ν cf ±∆ν cf , the backscattered light from the atmosphere detected at D Mie stems from Rayleigh scattering only, whereas D R−R detects Rayleigh (and resonance) scattering plus a small contribution from Mie scattering. The signal at D R−R is much larger compared to D Mie since most of the signal is reflected by the narrow band confocal etalon (see Fig. 2 and 3). When the power laser frequency is within ν cf ±∆ν cf , however, the signal at D Mie includes 295 Mie scattering which varies when scanning the power laser, whereas the contribution from Rayleigh scattering is basically constant within ν cf ±∆ν cf because the Rayleigh peak is very flat within ν cf ±∆ν cf . The signal at D Mie can therefore be used to measure Mie scattering only, which is subsequently used to subtract the Mie signal from the Rayleigh signal. Furthermore, the signal at D Mie is used to derive the Doppler shift of the Mie peak due to winds. In Figure 6 we show signals from the detectors D R−R and D Mie . The exponential decrease of the Rayleigh signal and some very small 'bumps' due to aerosol 300 scattering are clearly visible. After subtracting the Mie contribution the signal can be used to determine a temperature profile (not shown). Note that temperatures can also be derived from the spectral width of the Rayleigh signal (not done in this first test). The Mie signal caused by stratospheric aerosols is roughly 0.1% -10% of the Rayleigh signal and disappears above roughly 30 km.
In Fig. 7 we show line-of-sight winds derived from the Doppler shift of the Mie peak observed on 19 January with a height Fig. 7 305 resolution of 200 m, integrated for a period of 20 minutes (18:10:00-18:30:00 LT). As can be seen from this Figure, the central frequency of the spectra changes with height, which is used to calculate line-of-sight winds. Note that the wind uncertainties shown in the right panel of Fig. 7  The agreement between observations and ECMWF winds is very good considering the constraints regarding temporal/spatial coverage and sampling, and the fact that this was the very first test of the entire lidar using some preliminary optics. The results shown in Figure 7 demonstrate that the initial optical alignment of the lidar, including laser-beam adjustment relative to the telescope, was stable under harsh conditions and no re-alignment was required. The performance of the lidar during this first light measurements was significantly lower compared to expected future capabilities because the telescope and the detection 320 system were not yet optimized. As will be explained in more detail in section 6 the efficiency of VAHCOLI-units will be improved further in the near term future.

Expected performance
The following calculations of sensitivities and uncertainties are based on our experience with a potassium lidar which was 325 housed in a container and operated in various remote locations such as on the research vessel Polarstern or in Spitsbergen Höffner and Lübken, 2007). In Fig. 8 we show expected count rates (R) as a function of altitude Fig. 8 which in this case reaches the maximum possible value of R=1×10 7 Hz at 20 km. We have assumed a laser power of 6 mJ (next generation of this laser) and an efficiency of the detector system of 30%. For a typical time and height interval of δt=5 min and δz=200 m, respectively, and a pulse repetition frequency of k=500/s this gives the number of photons as function of altitude 330 according to equation 1, also shown in Fig. 8. For example, for R=1×10 7 Hz (at 20 km) the number of photons (at 20 km) in a time and height interval of of 5 min and 200 m, respectively, is N ph =2×10 6 . We have also indicated a typical dark count rate of 20 Hz in Figure 8 which is realistic for state-of-the-art detectors. The green line in Figure 8 gives the temperature uncertainties according to equation 5 (see later). The blue lines indicate the errors to measure winds from the shift of the Rayleigh spectrum (above 20 km) and from the shift of the Mie peak (below appr. 30 km). Hereby we have assumed that at 30 km the Mie 335 signal is 0.5% of the Rayleigh signal increasing to 10% at 10 km. These values are consistent with typical observations of Mie scattering from stratospheric aerosols but may vary substantially throughout the season and from one location to another (Langenbach et al., 2019).
The calculation of the wind error is based on our experience that it takes approximately 100,000 photons to measure a wind with an accuracy of 1.35 m/s. Within limits (background noise etc.) the accuracy is proportional to the square-root of the 340 number of photons. As can be seen in Figure 8, winds can be measured with high precision, i. e., better than 1 m/s below 40 km and 10 m/s below 70 km, respectively. Due to the small line width, Mie scattering is particularly suitable for measuring winds.
In Figure 8 we also indicate the number of photons expected from an NLC layer assuming a backscatter coefficient at the peak of β=30·10 −10 /(m · sr) (see, for example, Fiedler et al., 2009). We also show typical backscattered signal from a potassium layer with a maximum number density of 50 atoms/cm 3 .

Error analysis for Rayleigh temperatures
As is explained above, the lidars being built for VAHCOLI can measure the Rayleigh signal without contamination due to aerosols. We consider altitudes sufficiently below the uppermost height where uncertainties due to the start temperature are negligible. Starting from an altitude bin centered at z 1 with a temperature T 1 and number density n 1 , the following equation gives the temperature error in the next height bin (at z 2 ) due to uncertainties in density measurements ∆n 1 and ∆n 2 at level z 1 350 and z 2 , respectively: where n 2 is the number density in the altitude bin centered at z 2 , and H p is the pressure scale height. This equation can be further simplified by assuming that H p ≈ H n within a height interval of δz= z 2 − z 1 (which is typically a few hundred meters only) and that the uncertainties in n i are determined by Poisson statistics of counting N i photons, i. e.
Since N 1 ≈ N 2 within the height interval δz we finally get: The number of photons counted per time and altitude interval, N (z), decreases with altitude according to where N ref is the number of photons counted at the reference altitude z ref , and H n is the number density scale height. In Fig. 9 altitude profiles of temperature errors according to equation 5 are shown assuming a number of photons at the reference Fig. 9 level (20 km) of N ref =2×10 6 (see above) and N ref =2×10 5 , respectively. Since count rates are normally suppressed at lower altitudes (to avoid a saturation of detectors) they may be increased at higher altitudes, for example by reducing the attenuation in the receiver. Using telescopes with appropriate diameters is another method to focus on certain altitude ranges. In Fig. 9 we 365 have assumed an enhancement of N due to 'cascading' by a factor of 100 (for N ref =2×10 6 ) at altitudes above 50 km which leads to a reduction of ∆T by a factor of 10. In total, typical temperature errors are smaller than 5 K up to the upper mesosphere.
Another method to increase the effective count rate is to increase the height range (δz) and/or the integration time (δt). In Fig.   10 the effect of increasing δt and/or δz on temperature errors is shown. More precisely, temperature errors (∆T ) are shown as Fig. 10 a For example, increasing δz·δt by a factor of 60 (e. g., by increasing the integration time from 5 min to 1 hour and the height interval from 200 m to 1 km) decreases the temperature error at 50 km from ∆T=5.3 K (g=1) to ∆T=0.7 K (g=60).

Multi-beam operation and horizontal coverage
The flexibility of VAHCOLI allows to place the lidars at distances which are optimized according to the science objectives (see

General
Dynamical processes on medium spatial scales (up to several hundred km) are important for the atmospheric energy and 395 momentum budgets which are directly relevant for climate models on regional and global scales (see, e. g. Becker, 2003;Shepherd, 2014). More specifically this concerns the question how energy and momentum are transferred from large to small scales (or vice versa?) and how the horizontal/vertical transport of energy, momentum, and constituents are described correctly.
A prominent example of dynamical impact on the background atmosphere is the summer mesopause region at high latitudes where temperatures deviate by up to 100 K from a state which is controlled by radiation only. This strong deviation is primarily 400 caused by gravity waves which deposit energy and momentum and lead to a 'residual circulation' and related upwelling and cooling. Major aspects of this dynamical control of the atmosphere are only poorly understood due to the complexity of the problem, both from the experimental and theoretical point of view. In models, the impact of these processes is typically considered by parameterizations. If, or if not, these parameterizations adequately describe the real atmosphere can best be verified by comparing models with observations which are capable of fully characterizing the atmospheric variability at these 405 medium scales. Temporal and spatial variability is observed in the atmosphere at a large range of scales which reflect various processes and their (mostly) non-linear interactions. Since these fluctuations vary in time and space it is necessary to measure spatial and temporal variations of, e. g., winds and temperatures simultaneously to achieve a complete picture.
The ultimate aim of VAHCOLI is to characterize the three-dimensional and time-dependent morphology of atmospheric flow, including gravity waves. This allows to disentangle temporal from spatial variability of the main flow and associated 410 fluxes and to test frequently assumed simplifications in modeling (and some observations) regarding homogeneity, isotropy, and stationarity. In this paper we concentrate on medium scales, i. e., horizontal distances of one to few hundred kilometers, and vertical distances of 100 m to several kilometers.
It is often assumed that atmospheric processes on medium scales are stationary which is very unlikely to be true in general since energy and momentum are continuously removed from the flow. If, or if not, this assumption is perhaps valid within 415 certain limits or within certain scales may be verified by comparing with suitable observations spanning a sufficient range of temporal and spatial scales. Other assumptions include isotropy and homogeneity, for example regarding fluctuations in zonal and meridional direction. Again, such similarities are rather unlikely because normally the background flow is systematically different in zonal compared to meridional directions.
There are several rather fundamental questions in atmospheric dynamics where VAHCOLI can contribute to a better un-420 derstanding. For example, are the governing processes of fluctuations at spatial scales larger than the buoyancy scale (L b , see below) determined by saturation of breaking gravity waves or by un-isotropic large scale turbulence being damped vertically by buoyancy, or by a combination of both? Which type of instability is most relevant in a specific situation, velocity shears (Kelvin-Helmholtz instabilities) or convective instabilities ? Another fundamental aspect of atmospheric variability regards the question if spectra are separable, i. e., if they can be expressed in the form Separability is frequently assumed to be valid but there is no fundamental reason why this should be the case (Fritts and Alexander, 2003). VAHCOLI aims at contributing to a better understanding of these fundamental aspects with observations of winds and temperatures with substantial temporal and spatial resolution and coverage.
In atmospheric science the variability of winds and temperatures is frequently characterized by a spectral index ξ in the 430 expression k ξ (k = wavenumber). For example, zonal winds (u) as a function of horizontal wavenumber (k h ) in the range from few to several hundred kilometers follow a quasi-universal law u(k h ) ∼ k −5/3 h (Nastrom and Gage, 1985). Keeping the temporal and spatial variability of the atmosphere in mind it may require several days of averaging to actually observe such a behavior (Weinstock, 1996). Furthermore, measuring ξ alone may not be sufficient to characterize the underlying physical ior in a specific situation, although the fundamental concepts are very different. In any case, the spectral representation should include as many observables as possible (zonal/meridional/vertical winds, temperatures, kinetic/potential energies, wave action density, momentum flux, etc.) in terms of vertical/horizontal wavenumbers and frequencies.
A powerful tool to describe atmospheric flows is to apply a Helmholtz decomposition, namely to separate the kinetic energy of the flow into divergent and rotational components: This sometimes allows to distinguish different physical processes from each other (see below). Obviously, this requires 3d-observations of the flow. Furthermore, since this separation may vary in time, a time-resolved measurement of the entire horizontal wind vector is required, as is planned for VAHCOLI. 445 Lidars have frequently been applied to measure gravity waves, both in case studies and also deducing climatologies (see Hauchecorne and Chanin, 1980;Liu and Gardner, 2005;Rauthe et al., 2008;Kaifler et al., 2015;Chu et al., 2018;Baumgarten et al., 2017;Strelnikova et al., 2021, for some examples). More recently, lidars have been applied to simultaneously detect GW in temperatures and winds in the middle atmosphere and to apply hodograph methods which allows to derive potential and kinetic energy and to separate upward and downward propagation (Baumgarten et al., 2015;Strelnikova et al., 2020). Note that back-450 ground winds are needed to determine Doppler shifting which is essential, for example, to unambiguously separate upward and downward progression of gravity waves, where the latter could for example be due to secondary wave generation (Kaifler et al., 2017;Becker and Vadas, 2018). Sometimes only certain parts of the GW field are measured and dispersion and polarization relations are applied (plus further assumptions regarding isotropy and/or stationarity) to derive quantitative results (Ern et al., 2004;Pautet et al., 2015).

455
To exploit the capabilities of VAHCOLI of studying gravity waves, we concentrate on waves with medium frequencies, i. e.,ω ≫f∼10 −4 /s at mid latitudes (ω = intrinsic frequency, f = Coriolis parameter). Corresponding periods are smaller than roughly 17 h and, of course, larger than the Brunt-Väisälä (BV) period of several minutes. Since E div /E rot =ω 2 /f 2 ≫1 this implies that the divergent part of the GW flow is much larger compared to the rotational component.
The dispersion relation for gravity waves (assuming that λ z ≪4π·H) is where N is the Brunt-Väisälä frequency, and ϕ is the angle between the phase propagation direction and the horizontal direction (see Dörnbrack et al., 2017, for a recent summary on lidar applications for atmospheric GW detection). For intrinsic periods significantly larger than the Brunt-Väisälä period (but still smaller than f), we haveω/N ≪ 1, i.e., ϕ ∼90 • , i. e., the gravity waves, both in winds and temperatures (Baumgarten et al., 2015).
A graphic representation of the dispersion relation is shown in Fig. 12. Several investigations have studied the specifics of Fig. 12 GW which normally propagate from low to high altitudes including the question which part of these GW can be observed by satellites (see, for example, Preusse et al., 2008;Alexander et al., 2010). We do not include radiosondes and balloons here due to their sporadic nature and limited height coverage. Satellites can only observe GW with typical horizontal/vertical 470 wavelengths larger than appr. 50-100 km and 3-5 km, and periods larger than typically 1-2 hours. However, the effect of high frequency waves on the circulation is crucial since the vertical flux of horizontal pseudo-momentum is given by F P = u ′ w ′ ·ρ·(1−f 2 /ω 2 ) which is largest for mid and high frequency gravity waves, e. g., whenω ≫ f (Fritts and Alexander, 2003).
As can be seen from Figure 12 VAHCOLI covers an important part of the gravity wave spectrum which is not accessible by satellites, in particular waves with small horizontal wavelengths and small periods (large frequencies). As mentioned before, 475 the phase of these waves preferentially propagates vertically, e. g., the energy propagates obliquely.
The aim of VAHOCLI is to characterize the three-dimensional time-dependent morphology of gravity waves. A comprehensive characterization of gravity wave propagation requires to measure the three-dimensional vector of phase propagation, i.
e., the vertical and the horizontal components. Horizontal fluxes of gravity wave momentum are typically ignored (compared to vertical) in middle atmosphere modeling where it is often assumed that the effect of gravity waves takes place directly 480 above the source and instantaneously. It is known from model studies, however, that GW can propagate over large horizontal distances before depositing momentum and energy (Alexander, 1996;Ehard et al., 2017;Stephan et al., 2020). Furthermore, a background varying with time can change the propagation of GW (e. g., by refraction) and can drastically modify the deposition of momentum and its effect on the background flow (Senf and Achatz, 2011). Simulations of GW propagation show that the horizontal distance between wave packets usually increases with altitude (see, for example, Alexander and Barnet,485 2007). This is favorable for VAHCOLI since the horizontal distance between obliquely pointing beams also increases with altitude (see Figure 11). Furthermore, it is known that the spatial and temporal distribution of gravity wave sources influences their effect on middle atmosphere dynamics (Šácha et al., 2016). A more fundamental question addresses the role of non-linear interactions of gravity waves compared to a quasi-linear superposition. This leads to rather different concepts regarding gravity wave parametrization (Lindzen, 1981;Gavrilov, 1990;Fritts and Lu, 1993;Medvedev and Klaassen, 1995;Hines, 1997;490 Becker and Schmitz, 2002). It could well be that the applicability of one concept or the other depends on the temporal/spatial scales under consideration. In order to measure and study the effects outlined above it is obviously necessary to observe gravity waves in all directions over a longer period of several hours or even days, and with sufficient horizontal coverage. Such instrumental capabilities are envisaged for VAHCOLI.

495
The concept of stratified turbulence (ST) has recently been developed to explain the energy cascading in stratified flows at mesoscales as an alternative to classical linear or non-linear breakdown of gravity waves. This transfer is relevant for the momentum and energy budgets which affect the Lorenz cycle and thereby (regional) climate modeling. Lindborg (2006)  developed an energy cascade theory for these scales in a strongly stratified fluid which involves horizontal and vertical length scales as well as kinetic and potential energy. The theory of ST has recently been applied to wind measurements by radars in 500 the mesopause region (Chau et al., 2020).
ST resembles the well-known energy spectra (horizontal kinetic energy and potential energy) characterized by k −5/3 h (Nastrom and Gage, 1985). This theory invokes strong non-linearities (in contrast to 2D-turbulence and to weakly nonlinear interacting gravity waves) and the cascading of energy from large to small scales (see, for example Billant and Chomaz, 2001;Lindborg, 2006;Brethouwer et al., 2007;Lindborg, 2007, and references therein). It covers horizontal scales smaller  Table 2. A more detailed Tab. 2 representation of spatial and temporal scales as well as velocities associated with stratified turbulence is shown in Fig. 13 for Fig. 13 a large range of ǫ-values. Note that most quantities depend on season, latitude, and altitude (regarding ǫ see, for example, Lübken, 1997). Some dimensionless numbers are frequently used to characterize the relevance of physical processes. For 520 example, the horizontal Froude number, which is the ratio of inertial to buoyancy forces, must be small to allow for ST to exist: . Indeed F r h is very small for the examples shown in Table 2.
Another relevant parameter is the buoyancy Reynolds number, Re b = ǫ/(ν · N 2 ), which should be large both for ST and for the Kelvin-Helmholtz instability regime (ν = kinematic viscosity). In the height range from the lower stratosphere to the upper mesosphere, and turbulence intensities of ǫ=10 mW/kg and ǫ=100 mW/kg this parameter varies between Re b =2.5×10 5 to 525 Re b =25 and Re b =2.5×10 6 to Re b =250, respectively, i. e., Re b is indeed much larger than unity. Regarding the application of VAHCOLI we note that the requirements to cover ST scales, namely a vertical/horizontal resolution of 200m/2km, a horizontal coverage of up to 200 km, and temporal and velocity resolutions of 10-20 min and 0.5-1 m/s, respectively, are well within the instrumental capabilities of VAHCOLI. The temporal development of the flow is important to judge various forcings, energy injection, the conversion of E pot and E kin , and the transition to stationary conditions (see, e.g., Lindborg, 2006).

530
There are several aspects of ST theory which are particularly relevant for a comparison with observations by VAHCOLI.
For addressing the question, if energy is cascading from large to small scales ('forward') or the other way around ('inverse') it is helpful to consider not only the horizontal kinetic energy spectra (typically from aircraft observations) but also the ver-tical spectra of horizontal kinetic and potential energy, typically from balloon borne observations (Li and Lindborg, 2018;Alisse and Sidi, 2000;Hertzog et al., 2002). Note that a fundamental scale invariance of the Boussinesq equations in the limit 535 of strong stratification implies an equi-partitioning of potential and kinetic energy (Billant and Chomaz, 2001). Regarding spectra, the ST theory (invoking downscale energy flow) predicts that vorticity Φ(k) and divergence Ψ(k) spectra should be of similar magnitude, Φ(k) ≈ Ψ(k), whereas for spectra dominated by gravity waves one would expect Φ(k) ≪ Ψ(k), and for stratified turbulence dominated by vortical coherent structures one expects Φ(k) ≫ Ψ(k). Furthermore, it is helpful to measure spectra of longitudinal and transversal velocity structure functions simultaneously (Lindborg, 2007).

540
In summary, the expected horizontal and vertical coverage of the flow field by VAHCOLI will allow to study details of the relationship between rotational and divergent components of mesoscale dynamics including the important question, how energy is transfered from large to small scales. The instrumental capabilities of VAHCOLI will cover spatial and temporal scales being highly relevant for mesoscales. Apart from the Helmholtz decomposition there are other important quantities, such as the helicity, H=v · rot(v), which may be helpful to separate vortical coherent structures from GW and to characterize 545 the flow and its potential impact on the background atmosphere (Marino et al., 2013). Again, such a comprehensive analysis requires a 3d-characterization of the flow field, as is envisaged for VAHCOLI.

Other dynamical parameters
There are several dynamical processes in the atmosphere which take place at spatial or temporal scales which are normally outside the range of VAHCOLI, at least for the time being. For example, the smallest scales of inertial range turbulence are on the 550 order of L η = (ν 3 /ǫ) 1/4 . Measuring fluctuations at L η scales offers a unique chance to unambiguously determine ǫ (Lübken, 1992). However, L η varies by several orders of magnitude from the troposphere to the upper mesosphere and is in the range of centimeters to several meters only. It will be challenging to detect fluctuations at these scales by, for example, placing several VAHCOLI-units very close to each other. On the other hand, measuring the longitudinal and transversal structure functions of winds and temperatures at somewhat larger scales also allows to derive reasonable estimates of ǫ. Furthermore, we envisage 555 to measure the spectral broadening of the stratospheric aerosol signal to an extent that allows to deduce turbulent velocities.
Note that typical turbulent velocities are on the order of 1 m/s (see Table 2) which corresponds to a spectral broadening of the Mie peak of 2.5 MHz. This is much larger than the Doppler broadening of the Mie peak due to Brownian motions (roughly 0.1 MHz).
Trace constituents may sometimes be used as passive tracers for transport and mixing. This mainly concerns vertical and 560 horizontal advection and mixing of stratospheric aerosols and noctilucent clouds, but also the transport of metal atoms. Care needs to be taken when interpreting such measurements since these constituents may not be passive tracers, i. e., they may experience modifications, for example, by variable background temperatures. In the future we envisage to measure small scale turbulence (see above) and to improve the spatial resolution of aerosol observations to an extend that the eddy correlation technique to measure turbulent transport should be applicable.

565
On the other side of the spectrum of scales, tides are global scale phenomena with horizontal wavelengths of several hundred kilometers. Certainly, the relevant periods and vertical wavelengths are within the scope of standard MLT lidars (see Baumgarten et al., 2018, for a recent example). Regarding horizontal wavelengths, one could consider placing several VAHCOLI-units at very large distances.
Dynamical phenomena are frequently characterized by calculating statistical quantities, such as the variance and higher mo-570 ments (skewness, kurtosis, etc.) as well as intermittency. Due to the operational advantages of VAHCOLI (low cost, unattended operation, low infrastructure demands, long-term stability etc.) there is an opportunity to extend such an analysis to bi-or multi-variate distributions, for example, correlating wind components at various places with each other, or with temperatures.

NLC, PSC, background aerosols, and metal densities
Ice layers in the summer mesosphere at middle and polar latitudes are known as NLC ('noctilucent clouds') (Gadsden and Schröder,575 1989). They exhibit a large range of temporal/spatial variability which can even be observed by naked eye or by camera. Most of these variations are presumably related to gravity waves, tides, and associated instability processes (see Baumgarten and Fritts, 2014, for a more recent example). NLC are studied in great detail by modern lidars which sometimes detect temporal fluctuations on time scales down to seconds, or other unexpected characteristics (Hansen et al., 1989;Alpers et al., 2001;Gardner et al., 2001;Kaifler et al., 2013). NLC are frequently used in models describing dynamical phenomena such as gravity wave break-580 ing (Fritts et al., 2017). This raises the question, up to which scales NLC can be treated as passive tracers. Note that several processes act on similar temporal and spatial scales, for example, nucleation, sedimentation, and horizontal transport. Furthermore, there is an impressive amount of observations of mesospheric ice clouds available from satellites, which sometimes show unexpected temporal and/or spatial variations ('voids') (see Russell III et al., 2009, for details on a more recent satellite mission dedicated to NLC science). Understanding the physics of NLC is important, for example, to interpret long term variations of ice 585 layers and their potential relationship to climate change (Thomas, 1996;von Zahn, 2003;Lübken et al., 2018). Similar science questions occur regarding PSC, which also play a crucial role in ozone chemistry. Very thin layers of background aerosols have been observed in the stratosphere which are presumably caused by intrusion of mid-latitude air into the winter polar vortex (see, for example, Plumb et al., 1994;Langenbach et al., 2019). Several VAHCOLI-units could be placed at appropriate locations, e. g., at the edge of the polar vortex, to observe the temporal and spatial development of such intrusions.

590
For solving some of the open science questions regarding NLC, PSC, and background aerosols, it is very helpful to distinguish between temporal and spatial (horizontal) variations, and to know the status of the background atmosphere. VAHCOLI is designed to detect these aerosol fluctuations and to observe background temperatures and winds simultaneously by applying high resolution spectral filtering (see section 2.5.2).
Despite substantial progress in recent years, the physics and chemistry of metal layers still leaves many open questions, 595 for example, regarding their (meteoric) origin, their spatial and seasonal distribution, the impact of diffusion and turbulent transport, as well as the effect of gravity waves and tides on number density profiles (see Plane, 2003, for a recent review on mesospheric metals). The morphology of metal profiles offers a variety of phenomena on short spatial and temporal scales, such as sudden (sporadic) layers and their connection to ionospheric processes, or the uptake of metal densities on ice particles (see, i.e., Hansen and von Zahn, 1990;Alpers et al., 1993;Collins et al., 1996;Plane et al., 2004;Lübken and Höffner, 2004).   shown for two cases of L h , namely L h =100 km and L h =400 km, as well as for two cases of energy dissipation rates ǫ, namely ǫ=10 mW/kg and ǫ=100 mW/kg. For the kinematic viscosity a value of ν=0.01 m 2 /s was chosen which is typical for an altitude of 45 km (note that ν increases exponentially with increasing height). See text for more details.