The intricate small-scale structure of noctilucent or polar mesospheric clouds (PMCs) has been attributed to the action of gravity waves very early on . To this day, the strong backscatter of the ice particles that PMC are made of represents a unique opportunity to observe dynamical processes in the upper mesosphere. High-resolution observations of PMC are obtained using both active and passive remote sensing instruments that are based on the ground or carried by satellite, aircraft, or balloon e.g.. Lidar instruments allow for high vertical resolution down to a few metres, revealing various stages in the approach to, or attainment of, gravity wave breaking and other nonlinear dynamics made visible by the PMC layer. However, a comprehensive physical interpretation of the waves and structures inside the PMC layer observed by lidar is limited by the sparseness of the horizontal sampling. Complementary spatial information can be provided by, for example, cameras, but opportunities in terms of time and location for observations from the ground are scarce, as lidars operate best in darkness, but cameras can observe PMC during twilight only. Hence, both camera and lidar instruments have to be operated at significant distance for common-volume observations, and simultaneous observations depend on suitable conditions at two places . This limitation is overcome by lifting a single payload, including a lidar instrument and cameras, to the upper stratosphere, where the sky is always dark and the view unhindered by tropospheric clouds. This was accomplished first by the Polar Mesospheric Cloud Turbulence (PMC Turbo) Balloon Mission that observed the PMC layer along the Arctic circle during a 6 d flight in July 2018 .

The effect of gravity waves and the processes associated with their breaking on the PMC layer is not fully understood to date, in part due to the wide range of scales, the often unknown state of the background atmosphere, and the microphysical evolution of PMC particles in this multiscale environment. Whether stratospheric gravity wave activity influences the occurrence of PMCs, or not, has been answered differently at different locations . Gravity wave activity based on upper mesospheric radar measurements was not found to be correlated with the occurrence of PMCs at a specific Arctic site . However, deduced from the global Cloud Imaging and Particle Size (CIPS) dataset that regions of strong gravity wave activity, for both long and short periods, suffer from reduced PMC brightness on average. This finding is supported by a number of modelling studies using microphysical models that showed that gravity waves generally act to destroy PMCs . The altitude and temperature variations induced by gravity waves or other small-scale dynamics can result in the rapid sublimation of ice particles. The asymmetry in the growth and sublimation rates ensures that particles are more likely to be destroyed than to grow large enough in size to be observable and that particles, once sufficiently reduced in diameter, are unlikely to regrow to observable sizes for a significant amount of time. The outcome may depend on the period of gravity waves modulating the environment in the vicinity of PMC. found a reduction in PMC brightness for short-period gravity waves below 6.5 h only. In three-dimensional simulations, observed the sublimation of a modelled PMC layer caused by breaking gravity waves within 30 min, leading to the formation of holes (or voids) which resemble structures observed in PMC satellite images . At timescales of minutes, the PMC layer can generally be considered a passive tracer of the dynamic processes . Lidar measurements of the changes in volume backscatter coefficient, also termed PMC brightness, are at these scales therefore predominantly due to changes in density and not changes in particle size. As visual PMCs frequently display small-scale structures attributed to gravity waves and processes associated with their breaking, high-resolution observations of the PMC layer are ideally suited to studying the statistics and pathways of energy transfer from gravity waves down to turbulent scales .

Among the millions of images acquired during the PMC Turbo mission were intriguing displays of small-scale vortex rings , Kelvin–Helmholtz instabilities , and mesospheric bores . The selection of these events was mainly based on the interpretation of the images that were post-processed to enhance small-scale structures , and they make up only the tip of an iceberg of potentially interesting observations. Colocated lidar data have, in all cases, revealed significant small-scale structures with signatures that are likely inherent to the dynamic processes studied. To foster further analysis and interpretation of this dataset and others, we here aim to provide statistics and a systematic review of such patterns. We will employ a general, easy-to-implement method for identifying features related to quick changes in the volume backscatter coefficient or PMC brightness on scales of 40 m and 20 s that represent processes related to dynamical instabilities following the breaking of gravity waves. The results can be used to select promising subsets of the PMC Turbo dataset for subsequent case studies, aid the interpretation of similar signatures in other lidar datasets, and serve as a reference for future modelling of the effect of gravity waves on PMC layers. As stated by , such observations have the potential to confirm or constrain modelling results or discover processes that are as yet unknown. In addition, we present a statistical analysis of the occurrences of such patterns with regard to ambient conditions. Gravity wave activity and layer brightness can be derived from the lidar data and thus provide the chance to relate the occurrence of small-scale structures that are related to gravity wave (GW) breaking or other nonlinear dynamics, to the strength of short-period gravity wave activity, and to the mean layer brightness. The intention is to find out whether the studied events arise during periods of intense gravity wave activity or rather during quiet times and whether this goes along with enhanced or reduced PMC brightness. This study thus also aims to complement the modelling study of with a comprehensive observational dataset. The step beyond previous analysis of observational data is rooted in the high temporal and spatial resolution of the PMC Turbo lidar dataset that facilitates the detection of turbulent-like features and instabilities that arise as an effect of breaking gravity waves. Intentionally, we focus this study on the PMC lidar dataset of PMC Turbo and will make use of the associated images in subsequent case studies identified by this work.

At a resolution of 20 m and 10 s, the BOLIDE dataset includes 1.06×106 independent measurements with sufficient signal-to-noise ratio of PMC volume backscatter coefficient. A total of 672 921 values have neighbours that allow for the calculation of both gradients ∂zβ and ∂tβ. They occur within 13 255 independent vertical profiles totalling 36.8 h. Figure a and b show normalized probability density functions of all gradients ∂tβ and ∂zβ derived from measured data. The distributions have approximately zero mean and extend to ∂zβ=6.0×10-2ln⁡(10-10 m-1 sr-1) m-1 and ∂tβ=13.4×10-2ln⁡(10-10 m-1 sr-1) s-1. Gradients of this magnitude mean that the brightest local PMC volume of 4.67×ln⁡10-10 m-1 sr-1 can potentially emerge from or fade within 4.67/0.060=78 m in the vertical or 4.67/0.134=35 s in time. The maximum gradient value is thus close to the limits given by the resolution and smoothing of the gradients.

The moments of the distributions of ∂zβ and ∂tβ are listed in Table . The standard deviations are σz=0.79×10-2ln⁡(10-10 m-1 sr-1) m-1 and σt=1.66×10-2ln⁡(10-10 m-1 sr-1) s-1, respectively. The distributions are skewed to positive values, especially ∂zβ. This indicates the steeper lower boundaries of the PMC layers or respective sublayers compared to top boundaries. The kurtosis is positive, meaning that the distributions have longer tails than the normal distribution. For comparison, we plot the Gaussian distributions with the same mean and standard deviations in Fig. a and b as dotted lines. This is an indication of intermittent behaviour.

To further characterize the distributions of ∂zβ and ∂tβ with regard to the occurrence of large gradients, we shift a threshold lσ, with σ being the standard deviation of the dataset, and l=0…5. l=2 is marked by vertical lines in Fig. a and b, as an example. For l=2, 5.3 % of the ∂zβ (∂tβ) values are found in the tail of the respective distribution (Fig. a and b), while 9.7 % of all PMC detections exhibit gradients that are within the tail of either distribution. The latter quantity is shown in Fig. c as a function of l as a solid curve. The dashed curve shows the percentage of the vertical profile that exhibits gradients within the tail of either distribution. The result that 9.7 % of all gradients that are found in the tails for l=2 are actually distributed across 96.6 % of vertical profiles means that large gradients occur frequently and that smooth and unperturbed PMC layers are rare.

The mean PGW of all the PMC observations within the BOLIDE dataset is 0.76±0.77ln⁡km2, corresponding to a PMC layer altitude variability of exp⁡(0.76)=1.46 km in the 5–62 min spectral band. The minimum value is -2.1 and corresponds to a variability of 350 m, while the maximum value is 2.26 with a variability of 3.1 km. The mean Pβ is 0.29±0.18ln⁡10-6 sr-1 and values range between 0.02 and 0.96×ln⁡10-6 sr-1. We divide the PMC profiles into four categories relative to these mean values PGW‾ and Pβ‾ in order to assess the occurrence rate of large gradients in brighter or dimmer PMC layers exposed to weak or strong gravity wave activity. The selection criteria are defined in Table . Though desirable, a finer division is not implemented because of the limited number of independent values due to the smoothing of PGW and Pβ. The fractions of gradient values per category as a function of the threshold l are shown in Fig. , where, again, all profiles are included on the left for l=0, and on the right, only those with larger gradients in either ∂tβ or ∂zβ remain. We find that dimmer layers with strong gravity wave activity (category B in Fig. ) are most common, followed by brighter layers with strong gravity wave activity (category D). As the statistics are narrowed to the largest-gradient profiles, category D layers make up the largest share. The PMC layers belonging to the most common category (B) are, however, unlikely to exhibit large gradients compared to layers of the other categories.

In the next section, we will look into the morphology of the layers that exhibit large gradients. We will first discuss the already published cases in the light of our results and then proceed to describe four general groups of PMC layer sections based on their morphology and discuss their link to the dynamical processes that led to their formation.

The PMC layer sections that contain mostly PMC profiles with gradients larger than 2σ exhibit all types of small-scale variability, including vertical, oscillatory motions of bright, thin layers, the internal structure of wider layers, multiple layers, and vertical displacements of PMC layers. Both large and small displacements are included. Although more sophisticated methods could be developed to detect those signatures, we deem the gradient analysis a suitable choice. It is an easy-to-implement and general method that is not tailored to specific patterns and is thus suitable for the detection of signatures of potentially previously unknown dynamics. We refrained from the application of wavelets, either one- or two-dimensional, to assess the small-scale variability in PMC as we did not want to make the assumption of an underlying periodicity but rather to allow for singular or irregular structures within the PMC layer at the smallest scales.

An evaluation of the statistics of the gradients, in particular Fig. c, has established that gradients larger than 2σ are widespread whenever PMC is present. This is in agreement with the visual impression from both ground-based observations and the PMC Turbo images of highly variable PMC layers at small spatial scales. divided the PMC Turbo dataset into eight major PMC events, gave an initial assessment of the relevant dynamics and likely impact, and stated the magnitude of the forcing and the occurrences of gravity wave breaking, fronts, or bores and Kelvin–Helmholtz instabilities. In Table , we complement this list with the results of our analysis, including an approximate category based on PGW and Pβ averaged over the time period listed and percentages of PMC detections and PMC profiles in the tails as shown in Fig. c. The assessment by of weak, moderate, or strong dynamics or forcing is reflected in our result for the category, in the way that mostly weak dynamics or forcing relates to categories A and C, and stronger dynamics and forcing to categories B and D. The events that stood out in the initial visual inspections of PMC Turbo images and lidar data, some of which have already been analysed for their dynamics, all show increased and, in most cases, even very large gradients. The small-scale vortex rings studied by were observed on 10 July 2018 between 02:30–02:57 UT. Their signature includes a rapid (1 min period) downward extension of comparably weak PMC backscatter by almost 1 km from the lower PMC boundary. The upper boundary, in contrast, was clearly defined and constant in altitude. This resulted in a large vertical gradient ∂zβ of 4.4×10-2ln⁡(10-10 m-1 sr-1) m-1 at the top boundary, and the variation in the lower boundary is clearly reflected in quick successions of positive and negative values of ∂tβ amounting to ±9.6×10-2ln⁡(10-10 m-1 sr-1) s-1. This case was the only occurrence of small-scale vortex rings located at the lower PMC boundary at this level of clarity during PMC Turbo. Rapid oscillations in ∂tβ at the top boundary or within the layer were also observed on 10 July 2018 at 03:17 UT and 11 July 2018 at 09:20 UT (not shown here). Also characterized by rapid changes in the temporal evolution are the Kelvin–Helmholtz instabilities that occurred on 12 July at 13:30 UT that were studied in detail by . During this event, vertical displacements affect the whole PMC layer, including multiple narrow sublayers and a sharp lower boundary. The induced absolute gradients amount to 4.5×10-2ln⁡(10-10 m-1 sr-1) m-1 and 11.3×10-2ln⁡(10-10 m-1 sr-1) s-1 and are thus among the largest observed. Similar signatures are visible in the aftermath of this specific event until 12 July 14:20 UT and also on 10 July between 18:45–19:20 UT, on 11 July between 03:55–06:00 UT (compare Fig. c), and on 11 July at 13:30 UT (not shown). Looking at the remaining dataset of PMC profiles with large gradients, the patterns can be associated with one or more of the following four groups.

1.

PMC layers with largely sinusoidal undulations in altitude. The selected examples shown in Fig.  show undulations with periods between 5 and 30 min and are thus likely induced by linear, short-period gravity waves. For the observation shown in Fig. a, corresponding PMC Turbo images have confirmed a linear gravity wave of 20 min period and ≈50 ms-1 phase speed. Also, PGW is well above its mean, putting these layers in category B or D. These types of PMC layers have sharp boundaries, often at the lower edge, and thus vertical gradients are large where the layers emerge from or fade into the background. This is seen, for example, in ∂zβ on 10 July 2018 at 19:20–20:10 UT (Fig. a). Because of the oscillatory motions of these layers, large temporal gradients are also induced, e.g. on 13 July 2018 10:25–11:05 UT (Fig. c). But a closer look reveals that those PMC layers are not smooth at smaller scales. Superposed to the larger-scale linear oscillation are small-scale perturbations at timescales of 1–2 min, which result in the detection of large gradients, e.g. around 19:40 UT on 10 July 2018 (Fig. a) and at 01:35 UT on 11 July 2018 (Fig. b). The PMC Turbo images for Fig. a, for example, show evidence for large- and small-scale vortex rings, embedded local instabilities, and multiscale breaking (their Fig. 11b). The example on 13 July 2018 (Fig. c) highlights another common feature with very narrow-spaced (100 m or less), well-defined sublayers visible 10:35–10:48 UT. The brightest sublayer, starting at 82.6 km, can be traced over several gravity wave periods until around 11:00 UT, when it appears to dissolve. As in all of the examples in Fig. , multiple layers exist, with an interlayer spacing between 100 m and 2 km.

2.

PMC layers indicating gravity wave breaking in response to gravity wave steepening. Examples of these very variable layer types are shown in Fig. . In these cases, the amplitude of an undulation increases, and the period shortens. This is followed by a reduction in PMC brightness and/or the emergence of small-scale structures. For example, around 05:33 UT on 10 July 2018 (Fig. a), a PMC layer perturbed by a large-amplitude gravity wave that is reduced to 10 min period experiences a quick descent with a peak-to-peak amplitude of almost 3 km and β values distributed over a wide range down to the detection limit, likely caused by complex instability dynamics. Interestingly, the situation seems analogous but is mirrored in time at around 05:48 UT except that here a double layer is affected. For a full interpretation of such cases, knowledge of the gravity wave propagation directions and wind speeds relative to the lidar beam path across the PMC layer and the 2-dimensional imaging of PMC structures is very helpful. This information can be deduced from the PMC Turbo images that will be available from NASA's Space Physics Data Facility (or on request). Nevertheless, this lidar observation seems to confirm theoretical results predicting that very strong gravity wave activity inducing large displacements significantly reduces PMC brightness close to or below the detection threshold . The time frame on 10 July between 17:45 and 19:00 UT is another example of a strong PMC layer modulated by a 10–30 min period gravity wave that causes a multitude of strong instabilities including cusps, linked rings, and herringbone structures see Fig. 11b inat 18:15 UT, and their discussion. The examples featured in Fig.  have the largest PGW in the PMC Turbo dataset.

3.

PMC layers that show transitions from weak or no gravity wave activity to major bore-like responses during a few minutes or tens of minutes. These types of layers suggest a rapid evolution or rapid advection of the leading edge of a nonlinear gravity wave packet. Examples are shown in Fig. . At 05:13 UT on 11 July 2018, the core of a PMC layer is both deflected upward and downward by 2 and 1 km, respectively, induced by the passage of a mesospheric bore front. The corresponding imagery reveals such a bore by showing a narrow and bright band that extends several hundreds of kilometres across the camera field of view and moves through the lidar beam at 05:13 UT (not shown). The increase in PMC brightness at the bore front revealed by the images is therefore caused by up- and downdrafts that increase the PMC layer width, hinting that, in this case, the bore altitude coincided with the PMC layer altitude. We selected the subset of data including this observation for a detailed future study that employs the PMC images and derived quantities. The successive mesospheric bores studied by also belong to this group. Their signatures include extensions of the PMC layer to lower altitudes (in fact, the lowest altitudes in the BOLIDE dataset), as demonstrated by the observations on 13 July 2018 in Fig. b and c. For a duration of few minutes only, the layer spreads to approximately double its width, while the brightness remains about constant, leading to a strong increase in integrated brightness. These bores were accompanied by various and intense leading and trailing instabilities . At the times of largest descent, tendrils associated with Kelvin–Helmholtz instabilities extrude from the PMC layer (Fig. b). Between 13:20 and 13:35 UT, localized increases in brightness indicate successions of small-scale vortex rings, as deduced from the joint analysis of images and lidar soundings. The observation and identification of small-scale vortex rings in lidar data have first been accomplished by using the BOLIDE lidar dataset.

4.

PMC layers that show the break up and/or mixing of previously multilayered, thin features. This class of events is sometimes accompanied by apparent breaking or overturning events associated with group 2. Examples are shown in Fig. . These events are ideal targets for the modelling efforts of the effect of gravity waves on PMC layers, as thin layers can be regarded as reliable tracers of small-scale variability. Layers of group 4 and group 2 make up about 20 % of the BOLIDE dataset (13 h) and conform to the irregular or non-parallel multiple layer categories defined by their category IIIb and IIIcii that accounted for about 25 % of the Arctic Lidar Observatory for Middle Atmosphere Research (ALOMAR) Rayleigh–Mie–Raman lidar dataset. All other BOLIDE data with profiles showing large gradients can be sorted into categories of short-period height variations in both the narrow and wide layers defined by their category Ib and IIbii.

Our analysis in Fig.  showed that large gradients are likely to occur during the conditions of both strong and weak gravity wave activity. Most of the examples featured here belong to categories B or D (large PGW), but PMC layers associated with low values of PGW can also show distinct small-scale variability. The case with the lowest value is on 11 July at 10:30–12:30 UT, a moderately bright layer of 1–2 km thickness that contains a variety of internal structures. Although undulations in altitude are small during this period, there are large undulations before and after that were likely induced by a gravity wave with a period larger than 60 min. In conclusion, we observed small-scale variability in the PMC layer in all conditions of weak, moderate, and strong short-period gravity wave activity, and the occurrence of truly unperturbed layers can be regarded as a rare phenomenon. We find that PMC observations with below-threshold gradients are generally associated with wide, dim layers without a discernible inner structure category IIIa of or well-defined thin layers of low brightness with distinct sinusoidal motions our category B; category I of. An example is a set of very narrow PMC layers with sinusoidal undulations of about 20 min periods, as shown in Fig. b. While there are several well-defined stacked layers in the beginning, over time the brightness decreases and gradients become smaller. This behaviour is in agreement with theoretical results showing that, under conditions of gravity wave activity, weak layers are further mixed, and ice particles are likely to sublimate, resulting in volume backscatter coefficients that are below the detection threshold. A comprehensive and general assessment of the effect of short-period gravity waves on the ice particle size and number density is likely difficult to obtain from lidar profiling data alone. Atmospheric dynamics occur in three dimensions, and knowledge of the phase speeds and orientations of the gravity waves relative to the wind speed and direction and thus the transport of ice particles is required for a comprehensive analysis. In particular, the temporal axis we show in this work transforms via the local wind speed and the lidar beam movement across the sky to a spatial axis. Our resolution of 10 s likely relates to few hundred metres in the horizontal domain. The required information can be obtained by future experiments including, for example, coincident and common volume imaging and radar observations.

We set out to systematically screen, identify, and characterize small-scale signatures that are likely caused by dynamical instabilities generated by the breaking of gravity waves and other nonlinear processes in PMC Turbo BOLIDE lidar data. The focus of this work was on the smallest scales (at 20 m and 10 s resolution), and we applied an easy-to-implement, general method to our lidar data without presupposing any specific patterns. We presented the statistics of gradients occurring in PMC backscatter data and performed a classification of PMC layers based on gradient thresholds, layer brightness, and gravity wave activity. In accordance with visual observations, we confirmed that smooth, unperturbed PMC layers are rare and that small-scale structures are very common. We found that probability density functions of PMC brightness gradients exhibit longer tails compared to a normal distribution, which is an indication of intermittency. Large gradients in the vertical and temporal/horizontal dimension occur frequently during times with both weak and strong gravity wave activity. We believe that the cases identified and presented in this work, in addition to the quantification of gradients, will be helpful for future modelling of the effects of gravity waves on PMC layers.