High resolution observations of small scale gravity waves and turbulence features in the OH airglow layer

A new version of the Fast Airglow Imager (FAIM) for the detection of atmospheric waves in the OH airglow layer has been set up at the German Remote Sensing Data Center (DFD) of the German Aerospace Center (DLR) at Oberpfaffenhofen (48.09 ° N, 11.28 ° E), Germany. The spatial resolution of the instrument is 17 m in zenith direction with a field of view (FOV) of 11.1 km x 9.0 km at the OH layer height of ca. 87 km. Since November 2015, the system has been in 10 operation in two different setups (zenith angles 46 ° and 0 °) with a temporal resolution of 2.5 to 2.8 s. In a first case study we present observations of two small wave-like features that might be attributed to gravity wave instabilities. In order to spectrally analyse harmonic structures even on small spatial scales down to 550 m horizontal wavelength, we made use of the Maximum Entropy Method (MEM) since this method exhibits an excellent wavelength resolution. MEM further allows analysing relatively short data series, which considerably helps to reduce problems such as 15 stationarity of the underlying data series from a statistical point of view. We present an observation of the subsequent decay of well-organized wave fronts into eddies, which we tentatively interpret in terms of an indication for the onset of turbulence. Another remarkable event which demonstrates the technical capabilities of the instrument was observed during the night of 4th to 5th April 2016. It reveals the disintegration of a rather homogenous brightness variation into several filaments moving 20 in different directions and with different speeds. It resembles the formation of a vortex with a horizontal axis of rotation Atmos. Meas. Tech. Discuss., doi:10.5194/amt-2016-292, 2016 Manuscript under review for journal Atmos. Meas. Tech. Published: 12 September 2016 c © Author(s) 2016. CC-BY 3.0 License.

leading to formation of Kelvin-Helmholtz instabilities (KHI), whereas convective instabilities are induced when the temperature lapse rate gets superadiabatic (Fritts and Alexander, 2003).
Turbulent processes are characterized to cover several magnitudes of the length scale. The complete range of turbulence can be divided into three parts: within the largest regime, the so-called buoyancy subrange, energy is still carried by waves and the buoyancy force is dominating viscosity. Distortions on scales below the buoyancy subrange let the transported energy 50 cascade to smaller and even smaller structures (inertial subrange) where energy is still conserved within the eddies until it is dissipated into the atmosphere due to viscous damping (viscous subrange) (e.g. Lübken et al., 1987). It must be noted that the scale limits between the three subranges are strongly dependent on the altitude. Within the abovementioned region of the OH* peak concentration at an altitude of about 87 km, the inertial subrange of turbulence is on a scale of a few hundreds of metres, starting just below 1 km and reaches the viscous subrange at about 30 m (Hocking, 1985). 55 Signatures of atmospheric gravity waves have already been extracted from time series of OH rotational temperatures which can be derived from airglow emission spectra (e.g. Scheer, 1987;Takahashi et al., 1999;Schmidt et al., 2013;Wüst et al., 2016).
In order to deduce horizontal information of atmospheric waves, infrared camera systems have come up as a highly promising remote sensing technique (see e.g. Peterson and Kieffaber, 1973;Herse et al., 1989;Moreels et al., 2008) as they 60 allow obtaining images of atmospheric waves. Gravity wave activity at airglow altitude of the entire night sky can be imaged using all sky lenses (Taylor et al., 1997;Smith et al., 2009 and many others). Another application for airglow imagers is the investigation of small scale gravity wave structures, such as acoustic-gravity waves (e.g. Nakamura et al., 1999) or instability features (Hecht et al., 2014). A high spatio-temporal resolution is required for this purpose, which is achieved at the expense of the aperture angles of the imager. However, theoretical calculations especially in the spatial regime below 1 km are hardly 65 supported by experimental observations yet, since a better spatial resolution than 500 m is needed to image structures on these scales (Hecht et al., 2014).
As it has been reported by (Hannawald et al., 2016), the infrared imaging system FAIM (Fast Airglow Imager) is currently being operated by the German Aerospace Center (DLR) in order to continuously observe gravity waves in the OH airglow each night with a temporal resolution of 0.5 s. Obtaining a mean spatial resolution of 200 m, small scale gravity wave 70 Atmos. Meas. Tech. Discuss., doi:10.5194/amt-2016-292, 2016  In order to investigate even smaller scale gravity wave signatures and turbulent features within the inertial subrange at mesopause heights a further developed FAIM system, FAIM 3, with a considerably improved spatial resolution is presented in this paper.

Instrumentation
FAIM 3 is the second version of the already mentioned Fast Airglow Imagers established at DLR (Hannawald et al., 2016). 80 It is based on the SWIR camera CHEETAH CL developed by Xenics nv. Its 640 x 512 pixels InGaAs sensor array with a pixel size of 20 µm x 20 µm is sensitive to the spectral range from 0.9 to 1.7 µm. The raw signal is converted into a 14 bit digital stream, which is sent to a frame grabber via CameraLink. The sensor is thermoelectrically cooled down to an operational temperature of 233 K. The dissipated heat is carried away by a closed circuit water cooling system. A schematic drawing of the entire setup is shown in Figure 1. 85 All measurements presented here are performed at DLR at Oberpfaffenhofen (48.09 ° N, 11.28 ° E), Southern Germany. A 100 mm SWIR lens by Edmund Optics ® is used. Its aperture angles have been determined to be 7.3 ° in horizontal direction and 5.9 ° in vertical direction. In the first measurement configuration the camera was mounted on a fixed stage with a zenith angle of 46 °. Simple geometric considerations reveal that, using the above mentioned lens, the observed area corresponds to a trapezium-shaped region of the airglow layer, with the height of the trapezium being 18.6 km and a width of 15.2 km to 90 16.9 km (see (Hannawald et al., 2016) for details of the calculation). We note that the curvature of the Earth has been neglected within these considerations. Thus, horizontally an area of about 299 km² is observed with a mean spatial resolution of 30 m. The camera is adjusted to an azimuth angle of 214 °. In order to record a sufficiently strong airglow signal the integration time of the camera is set to 2.5 s. The instrument in this configuration has been in operation from 18th to 30th Atmos. Meas. Tech. Discuss., doi:10.5194/amt-2016-292, 2016 Manuscript under review for journal Atmos. Meas. Tech. Published: 12 September 2016 c Author(s) 2016. CC-BY 3.0 License.
November 2015, corresponding to 12 measured nights. The data of the first shown case study was measured with this 95 configuration.
In a second measurement configuration the FAIM 3 zenith angle is adjusted to 0 °. Still using the 100 mm lens, a 11.1 km x 9.0 km rectangular area of the airglow layer is acquired. This leads to a mean spatial resolution of 17 m. The integration time has to be raised to 2.8 s since the airglow intensity decreases with decreasing zenith angle due to the van-Rhijn effect (van Rhijn, 1921). 100 A flat field correction is applied in order to remove the fixed pattern noise and the vignetting of the acquired images.
As outlined above the section of the sky observed by the FAIM 3 instrument in zenith position is limited to an area of about 100 km². In order to better judge on the overall dynamical situation we operated the FAIM 3 zenith measurements simultaneously with the FAIM 4 instrument where FAIM 4 was allowed to sense the overall sky. The temporal resolution of FAIM 4 in this case was 1.5 s while the horizontal resolution is roughly 400 m within the image centre. 105

Data Analysis
The horizontal wavelengths of gravity waves in an image can for example be estimated by analysing the data series of the pixel intensities along a cross section perpendicular to the wave fronts. The distortion resulting from the abovementioned trapezium-shaped FOV projected onto rectangular images has to be corrected prior to analysis, so that an equidistant metric scale is provided. The images are mirrored and rotated into the proper azimuthal direction, so that they can be rendered true 110 to scale onto a map (see Figure 2). This correction is performed using the same algorithm as described in (Hannawald et al., 2016). As a typical example, Figure  In the image a wavelike structure reveals as more or less periodic brightness variations. This brightness variation clearly appears in the series of pixel intensities along a direction perpendicular to the wave fronts in the image, as it is shown in 115 the Maximum Entropy Method (MEM) turned out to be a powerful technique to estimate the spectral density of the data sets (Ulrych and Bishop, 1975), even if the data series is so short. As an example, Figure 4 shows the MEM spectrum of the data 120 series shown in Figure 3.
The MEM provides an approach for estimating the spectral density of a time series with a high frequency resolution (e.g. Bittner et al., 1994). While other methods like the wavelet analysis try to fit a predefined function to the data, the MEM does not claim any assumptions about the theoretical shape of the signal but to be a stationary Gaussian process. According to (Jaynes, 1963) the most probable of all possible spectra describing a dataset is the one which makes the least assumptions 125 about the information the data contain. This corresponds to the state of maximum entropy. The MEM derives the most probable spectrum of a time series by fitting an autoregressive model (AR) of order N to the data. The AR coefficients are determined using Burg's algorithm, which calculates them based on forward and backward predictions of the data. The major issue of the MEM is to find the right order N of the underlying AR process. If the order is chosen too small several frequency peaks may not be resolved, whereas an overestimated order will lead to further splitting of the peaks into spurious 130 subpeaks due to noise approximation (e.g. Wüst and Bittner, 2006).

Results
During the night from 18th to 19th November 2015 observations were performed at a zenith angle of 46 °, leading to a spatial resolution of approximately 30 m. In order to demonstrate the performance of the instrument, one interesting gravity wave event, registered between 22:59:25 and 23:04:33 UTC, is presented. The relevant period is shown in parts by a series 135 of six images in Figure 2a -f and in its entirety in Video 1 in the supplemental material. First order difference images (that means the temporal derivation of the original signal, here Δt = 7.5 s) are shown here to help better visualize wave structures.
The difference of two images acts as a high pass filter, suppressing long-period oscillations and highlighting the regions with varying intensity between the two images. However, the original data is used, of course, for spectral analysis in order to retrieve the correct spatial content. It is interesting to note that obviously a smaller scale wave packet is propagating from the 140 left corner of the FOV (West) to the right corner (East). The packet, which is marked by white circles in Figures 2a -e, moves in the same direction as a second, larger wave structure but its wave fronts are tilted against each other horizontally Atmos. Meas. Tech. Discuss., doi:10.5194/amt-2016-292, 2016 Manuscript under review for journal Atmos. Meas. Tech. decompose into some disordered features as time proceeds and is no longer visible in Figure 2f. This is best recognizable at the end of Video 1, starting at 23:03:20. Figure 3 shows in black the pixel intensities along a cross section perpendicular to the wave fronts of the small wave packet in the image acquired at 23:00:42 UTC (the position of the cross section is given in Figure 2b). Visual inspection of the image series and the cross section shows that the wavelength of the wave packet is about half a kilometre. The wavelength of the larger wave structure can be visually estimated as about 1.7 km. For a more detailed 150 analysis of the smaller structure the MEM is applied to the data series of Figure 3. An order of 20 is chosen as this corresponds to one third of the number of data points, which has turned out to be a good choice for analysing short data series with less than 100 values (Bittner et al., 1994). The MEM spectrum in Figure 4 exhibits a strong peak at about 550 m.
It is clearly above the 99 % level of statistical significance and fits to the small scale wave packet discovered in the images as already mentioned above. It is interesting to note that the MEM spectrum also reveals four other significant peaks at 155 wavelengths well below 200 m, which can also be found in the signal of Figure 3. In the following we will focus on the 550 m wave structure, as it is clearly recognizable in Video 1.
It can be seen in the image series that the 550 m wave signal is visible in the examined cross section from 23:00:17 to 23:00:55 UTC. In a next step the same cross section as above is analysed for each image to derive some insight about the spatio-temporal evolution of the structure. Figure 5 shows the temporal development of the MEM spectrum. The order has 160 been raised to 36 ensuring that signatures of wavelengths below 1 km are fully resolved. A stable maximum in the spectrogram ( Figure 5)  To put the observations into a larger spatial context, the FAIM 3 data are compared to simultaneous all sky measurements taken by the FAIM 4 instrument. Since the two cameras are deployed next to each other, the FOV of FAIM 3 is embedded in 175 the centre of the FOV of FAIM 4 with a tilt of 19 °. The FAIM 4 measurements are presented in Video 3. A snapshot is given in Figure 7. Besides the normal image (Figure 7a), the difference image (time difference of 60 s) is displayed on the right side ( Figure 7b). The approximate FOV of FAIM 3 is indicated by the green boxes in Video 3 and the white boxes in Figure   7. The all sky images reveal a clear and starry sky with high gravity wave activity, which can be determined on the basis of the characteristic patchy structures. The remarkable structure observed by FAIM 3 can be found again in Video 3 as a bright 180 feature within the green box, propagating towards its lower left corner. It can be well recognized in the screenshot of Figure   7.

Discussion
The first of the two case studies presented here shows a wave packet with a horizontal wavelength of about 550 m moving in the same direction as a 1.7 km wave with the wave fronts being tilted about 45 ° against the other structure. We therefore 185 tentatively interpret the wave packet as a ripple structure; see e.g. (Peterson, 1979). Ripples are spatially limited wave structures with a short life time (Adams et al., 1988) and are caused by atmospheric instabilities (Taylor and Hapgood, 1990). As the 550 m wave packet does not form within the FOV, its lifetime cannot be estimated from our data. However, the appearance and disappearance of the 1.7 km wave is located within the FOV, which allows estimating its lifetime to about 16 min if our speculation holds. According to (Taylor and Hapgood, 1990) this feature can also be referred to as a 190 ripple structure. The fact that the spatial extent of the wave fronts perpendicular to the direction motion is much smaller than Atmos. Meas. Tech. Discuss., doi:10.5194/amt-2016-292, 2016 Manuscript under review for journal Atmos. Meas. Tech. Published: 12 September 2016 c Author(s) 2016. CC-BY 3.0 License. the extent of the wave packet in propagation direction is unusual (ratio approximately 1:6). Obviously, it cannot be described as a plane wave (of infinite extent), it may rather be trapped in a duct or the entire pattern, which appears to be a wave structure, may indeed be an instability feature itself, which is not unlikely given the small dimension with an apparent wavelength of 1.7 km. It may be consequently speculated that the 1.7 km wave itself is a possible instability feature of a 195 larger scale wave with a horizontal wavelength of several kilometres and decays into the 550 m wave packet as a subordinate instability structure. Such dynamics have already been observed on larger scales in (Hecht et al., 2014). Assuming the same scenario here, the ratio of primary to secondary wavelength is about 3.1. This number agrees quite well with earlier KHI models (Klaassen and Peltier, 1991). As described in section 1, KHIs are instabilities caused by wind shear. This could be a possible explanation for the tilt of the wave fronts. 200 At around 23:03:30 UTC the 550 m wave packet starts to collapse into some disordered features, which we tentatively assign to turbulence. Following the considerations of (Hocking, 1985), observations on that scale are already situated in the inertial subrange at airglow altitudes. Similar turbulent-looking features resulting of atmospheric instabilities have been found in the measurements of (Hecht et al., 2014) in the buoyancy regime. Related Direct Numerical Simulations (DNS) (see Fritts et al. 2014) to that data have already predicted secondary instability features below 1 km, which had not been able to observe with 205 an airglow imager so far. However, it must be stressed that these interpretations remain speculative at this stage as the focus of this paper is to demonstrate the performance of the FAIM 3 instrument in order to resolve smaller spatio-temporal scale dynamics in the mesopause altitude region. Alternatively, the periodic structures could simply be remarkably small scale gravity waves with wavelengths of 1.7 km and 550 m as well, without being results of atmospheric instability. As a possible explanation for the narrow shape of the greater wave horizontal winds could then be considered to forbid wave propagation 210 in the respective areas.
The second interesting event detected by FAIM 3 is a vortex-shaped structure, which develops out of filament-like features within a wave front and continues propagating in the initial direction before decaying into some disordered features. The of gravity wave fronts, like in (Hecht et al., 2014). The effects of KHI dynamics in the airglow layer have been modelled using DNSs and large eddy simulations in (Fritts et al. 2014). The vortex structure as well as the filament features turns out to be a typical manifestation of turbulence due to KHIs. The high gravity wave activity of the overall night sky, revealed by FAIM 4 all sky measurements at the same time, possibly contributes to atmospheric instability by influencing the lapse rate. 220 The aforementioned wave front is also visible in the all sky images. A close inspection of Video 3 shows that even with this system's coarse resolution indications for the separation of parts from the bright crest can be identified, which agrees with the turbulent looking decomposition of the wave crest found in the FAIM 3 measurements.

Summary and Conclusions
In order to observe smaller scale gravity wave events and instabilities or turbulence features in the metre regime, the 225 established airglow imaging system FAIM (Hannawald et al., 2016) has been improved with regard to spatial resolution, using an InGaAs sensor array with the fourfold number of pixels (327680)  16 min, which leads to the presumption that it might be an instability feature of a larger gravity wave with a wavelength of 235 several kilometres which cannot be seen in our small FOV. Following this hypothesis, the 550 m structure could be the resulting subsequent instability feature. Another possibility is that the 550 m wave packet could be the primary instability feature caused by a small 1.7 km gravity wave. Both cases agree with the theory of turbulence: when atmospheric instabilities lead to the breakdown of waves, their transported energy is cascaded to smaller scale structures in the inertial Atmos. Meas. Tech. Discuss., doi:10.5194/amt-2016-292, 2016 Manuscript under review for journal Atmos. Meas. Tech. Published: 12 September 2016 c Author(s) 2016. CC-BY 3.0 License.
subrange. These considerations combined with the ratio of the wavelengths, which fits to values of earlier theoretical studies 240 like (Klaassen and Peltier, 1991), suggest that the event of 18th November 2015 could be triggered by KHIs.
Zenith measurements on 5th April 2016 from 03:15:58 to 03:27:46 UTC exhibit the breakdown of a wave front into a vortex structure and the subsequent decay into disorganized features, probably due to turbulence. Characteristic dynamics of filament-like features indicate that instability could be generated by wind shear. The observations look similar to modellings of KHI development and the consecutive turbulence dynamics of waves in the airglow layer (Fritts et al., 2014). 245 Comparisons with parallel measurements of FAIM 4 obtaining all sky images reveal the high gravity wave activity all over the sky at that time, which might have contributed to increased atmospheric instability.
It has been demonstrated that FAIM 3 is able to image the dynamics of gravity waves on scales significantly below 1 km.
This can provide experimental insight into processes like turbulent breakdown of waves or generation of smaller scale wave structures due to atmospheric instabilities. FAIM 3 observations support earlier simulations of instability dynamics as 250 presented in (Fritts et al., 2014). Apart from that, FAIM 3 is an ideal addition to all sky imagers, since it provides the opportunity to closer investigate specific airglow structures with a much higher spatial resolution, as it is demonstrated in the second case study in this paper.
Operational zenith measurements with a mean spatial resolution of 17 m and a temporal resolution of 2.8 s are being performed automatically every night since 22th February 2016 at Oberpfaffenhofen, Germany. The data is archived at the 255 WDC-RSAT (World Data Centre for Remote Sensing of the Atmosphere, http://wdc.dlr.de). FAIM 3 is part of the Network for the Detection of Mesospheric Change, NDMC (http://wdc.dlr.de/ndmc).