In autumn 2017, the WISE (Wave-driven ISentropic Exchange) campaign was conducted using the German HALO (High Altitude and Long Range) research aircraft, with flight operations based in Oberpfaffenhofen, Germany, and Shannon, Ireland. In this study we focus on research flight 05 on 23 September 2017 between 08:09 and 17:04 UTC, further denoted as RF05. The goal of this flight was to investigate the dynamical and chemical structure of the atmosphere in the vicinity of the tropopause over the North Atlantic between Ireland and a subtropical intrusion extending far north of Iceland.

During the WISE campaign, HALO was equipped with a comprehensive suite of instruments for in situ and remote sensing. Our analysis is mainly based on in-situ measurement of CO and N2O from UMAQS University of Mainz Airborne Quantum Cascade Laser Spectrometer, . For the WISE campaign, the total drift-corrected uncertainty was determined to be 0.94 ppbv for CO and 0.18 ppbv for N2O . Additionally, we use meteorological parameters measured with BAHAMAS Basic HALO Measurement and Sensor System,.

As a reference for the zonal and meridional wind components and to provide the meteorological context for our analysis, we use ERA5, the fifth-generation atmospheric reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) . ERA5 is based on four-dimensional variational (4D-Var) data assimilation using cycle Cy41r2 of the ECMWF Integrated Forecasting System (IFS). The reanalysis is available on 137 model levels extending from the surface to 0.01 hPa, with a vertical grid spacing of approximately 300 m in the UTLS. For our analysis, the model-level data were additionally interpolated onto height, pressure, and isentropic coordinates. We use two ERA5-based datasets: (i) meteorological fields extracted along the HALO flight track, which are analysed in Sect.  , and (ii) four-dimensional meteorological fields with hourly temporal resolution on a 0.25°×0.25° latitude–longitude grid, which are used in Sect. .

Next, we use ECMWF IFS operational forecast data as a high resolution complement of the ERA5 reanalysis. The data are based on IFS cycle 43r3 and are provided on a regular 0.1° latitude-longitude grid with hourly temporal resolution. This dataset is particularly suitable for this study because the IFS version used to produce this forecast is closely related to the version employed for the production of ERA5. The operational IFS employs a Tco1279 spectral truncation and an associated O1280 octahedral grid, resulting in a horizontal grid spacing of approximately Δx≈ 9 km. It incorporates 137 vertical levels, corresponding to the same vertical resolution used in both ERA5 and forecasts. The operational forecast therefore shares a similar dynamical core and physical parameterizations with ERA5, allowing the impact of increased horizontal resolution on the representation of shear and GWs to be investigated. We use the operational forecast from 23 September 2017 00:00 UTC, with hourly resolution for the first 24 h of this forecast.

In addition, we use forecast data of this case from , who employed version 2.6.2 of the ICOsahedral Nonhydrostatic (ICON) modeling framework over the North Atlantic Ocean. This enables us to study the representation of the same situation in a model with a different dynamical core and physics package, as well as across three different resolutions ranging from approximately the resolution of the IFS data to near convection-permitting scales. This allows us to directly assess the robustness of our findings across different model representations.

The simulation was initialized with the operational global ICON analysis at 00:00 UTC on 20 September 2017, shortly before the cyclone developed, and integrated for 96 h until 00:00 UTC on 24 September 2017, when the cyclone life cycle was in its final stage . The global ICON model simulation used an R03B07 grid (effective resolution of ∼ 13 km) with a 120 s time step and included nested regions using R03B08 (6.5 km) and R03B09 (3.3 km) grids with time steps of 60 and 30 s, respectively (Fig. ). Vertically, the ICON simulations comprise 90 levels from the surface to 23 km altitude, with a grid spacing of approximately 250–300 m in the UTLS. Figure  illustrates the ICON nested configuration and the atmospheric situation over the study region based on ERA5 at 11:00 UTC on 23 September 2017. Further details on the physics parameterization schemes used in the ICON simulations are provided in Table .

For the analysis of GWs and turbulence using model fields, we follow the approach outlined in , with some extensions. We briefly outline the most important aspects here. First, GWs manifest themselves as small–scale deviations from the background state. We therefore use a hybrid method that combines a dynamical with a statistical approach to separate the (large–scale) background from the (small–scale) deviations similar to. Note that we define the large–scale flow as the background state in this context.

We first decompose the flow into its divergent and rotational components using a Helmholtz decomposition, i.e., the dynamical approach. For the statistical component, we then apply a spectral filter using a one-dimensional zonal Fast-Fourier Transformation (FFT) over the full domain shown in Fig. . In this step, we remove contributions from wavenumbers 0 to 20, i.e. u′=udiv-udivk≤ks, where ks=20, is the wavenumber cutoff separating the respective quantities into large–scale and small–scale components. The primes (^′) denote deviations from the background state throughout the remainder of this study. Sensitivity tests with ks values of ±4 showed no significant variations in the resulting primed quantities. The deviations of the small–scale flow from large–scale background flow are shown in Fig. .

We identify GWs once based on the horizontal divergence ∇h⋅uh e.g., . Additionally, we use the absolute momentum flux 1AMF=ρ(u′w′‾)2+(v′w′‾)2 where ρ is the mean density, and u′, v′, and w′ are the zonal, meridional, and vertical velocity perturbations, respectively. The overline over the perturbation products (i.e. u′w′‾ and v′w′‾) highlights a low-pass filtering of the quadratic quantities using the same Gaussian spectral filter as in . We use the AMF as a first proxy for the momentum flux due to small-scales and as such to GWs.

A recent study by suggests that the hybrid scale-separation approach is applicable in the LMS (e.g., around 200 hPa). Moreover, and further demonstrate that using the divergent wind to separate the GW component from the background provides more reliable estimates of GW momentum flux, particularly in the upper troposphere. Thus, we emphasize that our hybrid approach for separating the flow scales is well justified in the UTLS and follows commonly used GW scale-separation methods , despite different cutoff wavenumber used among these studies. Nevertheless, the focus in this study is primarily on the LMS, where the separation between large-scale and small-scale motions is comparatively more robust and the limitations of the method are therefore reduced.

We use several other quantities to analyze whether the flow is prone to turbulence occurrence. A key diagnostics is the vertical shear: 2S2=∂u∂z2+∂v∂z2. While S2 is derived from the full wind field, it is also calculated from the wind perturbations, further denoted as S2′. Furthermore, we use the gradient Richardson number Ri and the Ellord turbulence indices, TI1 and TI2, to estimate whether the flow is turbulent . The use of multiple diagnostics is motivated by the need to capture both the dynamical and kinematic aspects of turbulence generation in the extratropical UTLS, especially in regions affected by GW-induced shear and mixing. Here, dynamical diagnostics characterize the stratification of the flow and its susceptibility to instabilities, whereas kinematic diagnostics describe flow deformation and shear processes that can promote turbulence development. Ri is calculated as follows: 3Ri=N2S2=gθ∂θ∂z∂u∂z2+∂v∂z2 i.e., the ratio of static stability (N2) to vertical wind shear (S2). It is commonly assumed that a Richardson number below a critical value is required for a Kelvin-Helmholtz instability to occur. The critical value for linear shear instability of an idealized stratified flow is often determined to be 0.25; however, for model based analyses values on the order of 1 are considered indicative of regions susceptible to Kelvin-Helmholtz instabilities e.g.,. Note that the total vertical wind shear is used to compute Ri in order to initially evaluate regions susceptible to turbulence within the baroclinic flow.

In addition to Ri, we use the Ellord-Knapp turbulence indices, TI1 and TI2, which are empirical diagnostics specifically developed to identify CAT, to better represent turbulence under complex flow conditions. The TI1 has previously been shown to be capable of detecting 70 %–84 % of CAT occurrences e.g.,. We resort this to the small–scales, ensuring that potential turbulence in the subsequent analysis reflects subgrid or small–scale contributions. We note here that Kelvin-Helmholtz instability and turbulence are not explicitly resolved in the reanalyses and forecasts even if the GWs themselves are. While these processes are represented through subgrid-scale parameterizations, our analysis uses diagnostics based on the resolved fields in ERA5, IFS and ICON. These diagnostics highlight regions with favourable conditions for turbulence occurrence. Following , the TI1 combines vertical wind shear perturbations and the total flow deformation (DEF), whereas TI2 adds additionally a convergence (CVG) term. The TI1 is calculated as 4TI1=S×DEF and the TI2 as: 5TI2=S×(DEF+CVG) where (S) is the magnitude of vertical wind shear perturbations (S2′, see Eq. ). DEF is the total flow deformation: 6DEF=∂u∂x-∂v∂y2+∂v∂x+∂u∂y21/2 and convergence is calculated according to, 7CVG=-∂u∂x+∂v∂y Here, both CVG and DEF are consistently derived from the perturbation wind components (u′, v′), and thus TI1 and TI2 are likewise based only on the corresponding prime quantities. The inclusion of CVG in TI2 offers an advantage over TI1 by capturing the small–scale flow features such as those associated with GWs or upper level frontal structures. These region often exhibit enhanced shear and convergence making TI2 more sensitive to turbulence driven by small–scale processes.

The major goal of the flight was to determine whether trace species exhibit specific signatures of irreversible mixing in regions of enhanced static stability in the lower stratosphere. We use this flight dataset and further investigate whether this irreversible mixing event occurs in regions of GW-induced shear enhancement. The flight was conducted within the ridge of a synoptic-scale baroclinic wave which developed over the North Atlantic during the preceding days, at the edge of large–scale trough.

The isentropic distribution of potential vorticity at 340 K in Fig.  illustrates the meteorological situation during WISE RF05 for ERA5 reanalysis fields. The synoptic situation over the North Atlantic Ocean on 23 September 2017 at 11:00 UTC is dominated by a strong meridional excursion of subtropical air masses far northward, extending from the Iberian Peninsula over Great Britain to Iceland. Adjacent to the tropospheric streamer two equatorward reaching stratospheric streamers are present, the one to the west being more coherent in its structure, while the one to the east shows more internal structure in terms of its isentropic PV.

The flight was conducted from Shannon, Ireland, towards Iceland, where a hexagon pattern was flown and a dive was performed before returning to Shannon (see black line in Fig. ). The PV distribution shows that the flight took place predominantly within the region where subtropical air masses at around 11–13 km were transported poleward, while some parts of the flight track also crossed the PV gradient into the lower stratosphere. The region of the strong PV gradient corresponds to the location of the jet stream and acts as a barrier between tropospheric and stratospheric air masses. On the large–scale, IFS (Fig. ) and ICON (Fig. ) forecasts show similar patterns in terms of the overall PV distribution. Moreover, smaller scale, ripple-like structures in the PV field around 20° W and 65° N (Fig. ) could indicate wave activity similar to the another case during WISE . Such small–scale structures in the PV field may already hint at the presence of GWs associated with air-mass mixing.

Next, we examine the time series of measured and ERA5 derived quantities during WISE RF05. The goal is to identify regions and periods of potential turbulence and small–scale mixing above the tropopause.

Figure  shows a comparison of in situ measured atmospheric state parameters, including chemical tracers and potential temperature (a), and instability parameters (b) from the ERA5 reanalysis data interpolated in time and space onto the flight path. The pressure altitude measured during WISE RF05 indicates that the flight path was designed to ascend with time (Fig. a), with the exception of the dive between 13:00 and 14:00 UTC. This ascent is also reflected in the decrease of N2O with time and the corresponding increase in potential temperature and ERA5 PV. In contrast, ERA5 vertical shear S2 and Richardson number Ri exhibit a more variable temporal evolution. In particular, two shear maxima are evident, reaching values up to 8×10-4s-2, which are associated with minima in Ri below 1 (Fig. b). Compared to other periods during the flight, these two time intervals stand out in terms of enhanced vertical shear and low Ri values.

We use tracer-tracer correlations and vertical trace species profiles to further examine the time periods which showed indications of turbulence occurrence. To this end, we use CO as a tracer of tropospheric air and N2O as a tracer of stratospheric air masses.

We focus on the period between 10:45 and 13:05 UTC, bounded by the two yellow-marked regions in Fig. . During this time, HALO was flying in the LMS at potential temperatures between 330 K and just below 380 K. The measurements took place above the region of the strongest vertical gradients in CO and N2O, where the vertical gradients become small again (Fig. a, b). Since a vertical gradient in N2O is generally expected over this potential temperature range, the nearly vertical profile provides a first indication of a process that mixes, or has previously mixed (i.e. homogenized), air masses within this altitude range.

In addition, the mixing ratios of both CO and N2O are well below their tropospheric background values, which is also evident from the CO–N2O correlation (Fig. c). The highlighted period of interest (marked region) is located predominantly within the stratospheric branch and partly within the transition region between troposphere and stratosphere. These regions are characterized by low CO and N2O mixing ratios, with N2O values below the well-defined tropospheric background of 331 ppbv during WISE RF05 see also.

Ultimately, irreversible mixing can be inferred from the interrelation of CO, N2O and potential temperature Θ. Due to the chemical life times, N2O mixing ratios are almost constant throughout the troposphere, while a chemical sink in the upper stratosphere produces a weak negative vertical gradient. A similar behavior is observed for CO; however, its mixing ratios are less uniform in the troposphere, and the stratospheric gradient above the tropopause is stronger due to stronger chemical removal. Nevertheless, the tracer-tracer relationship remains positive. Consequently, we expect to find a monotonic correlation between CO, N2O and Θ. As an air mass becomes increasingly stratospheric, the mixing ratios of CO and N2O decrease, whereas Θ increases. This relationship is apparent in the both the tracer-tracer correlation (Fig. c) and the vertical profiles (Fig. ). Together, they define the expected background relationship among these three quantities. Deviations from this background state can therefore only arise from non-conservative processes. Recent studies highlighted the role of GWs in such situations and the resulting irreversible mixing of trace species e.g.,.

For further analysis, we divide the correlation into three periods: (i) 10:45–11:30 UTC (Fig. d), (ii) 11:30–12:40 UTC (Fig. e), and (iii) 12:40–13:05 UTC (Fig. f). Several interesting features emerge. The first period exhibits two branches connected by a mixing line (around N2O ∼ 324 ppbv and Θ∼ 359 K). During the second period, only one branch is evident, with Θ values spread across the entire branch. This indicates no clear relationship between Θ and the tracer mixing ratios, although CO and N2O maintain a compact positive correlation. In the third period, nearly all data points are confined to a small region of correlation space, while potential temperature varies strongly within this region. These features suggest that the air masses were affected by a process that disrupted the relationship between CO, N2O, and Θ, with irreversible mixing being a likely candidate. Notably, the first and third periods exhibit signatures of recent mixing, coinciding with indications of enhanced turbulence in the ERA5 analysis (Fig. b). In contrast, the second period more closely resembles the background CO–N2O relationship. This may indicate that the air masses sampled during the first and third periods experienced more recent mixing, whereas the air mass sampled during the intervening period had been mixed earlier and had subsequently evolved toward the background tracer relationship.

An analysis of power spectral densities of w, Θ (Fig. a, b) and N2O, CO (Fig. c, d) also suggests the presence of small–scale turbulent processes. Overall, the spectra exhibit slopes of -5/3 which is often seen to support the presence of turbulent motions on the mesoscale and below e.g.,. The w spectra show a slope of -3 at smaller wavelengths but transitions to a slope closer to -5/3 for frequencies below approximately 0.8 Hz, consistent with the findings of . At higher frequencies (shorter wavelengths), the increase in power spectra towards 0.5 Hz may indicate turbulent processes at scales below the synoptic scale. Overall, the w and Θ spectra follow a slope close to -5/3, consistent with three dimensional isotropic turbulence and suggesting that dynamical processes on or below the mesoscale affect the flow. Moreover, the spectra of N2O and CO also exhibit slopes close to -5/3 at intermediate frequencies, corresponding to smaller wavelengths. For frequencies above approximately 10-2 Hz, the N2O spectra follow a -5/3 slope, suggesting that small-scale processes, potentially associated with GWs, contribute to turbulent mixing in the lower stratosphere.

The extent to which GW contribute to the mixing of these air masses is difficult to determine based solely on the observations along the flight path. Before we broaden our scope in the analysis to the synoptic scale, we first seek additional observational evidence for the presence of GWs. The high spatial resolution of the in situ measurements allows for resolving mesoscale structures associated with the jet/front system, including regions of low Ri and possible coherent GW phase structures (see Fig. ). Nevertheless, the temporal resolution of the model output (1 hourly) is too coarse to adequately resolve waves with horizontal wavelengths of approximately 100 km. In contrast, the aircraft observations provide sufficient spatial resolution to identify coherent phase and/or mixing lines in the lower stratosphere, such as those shown in Fig. .

To isolate wind perturbations associated with GWs from the background flow, the horizontal wind components (u, v) along the flight track were bandpass filtered using a fourth-order Butterworth filter . The filter was applied to remove both large–scale trends and high-frequency noise while retaining signals within a 2–10 min period range. The resulting perturbations (u′, v′) were then used to construct hodographs and to assess wave properties from the in situ measurements. The resulting perturbation time series are shown in Fig. . Note that, due to differences in sampling frequency and noise characteristics in the measurements, the flight data are filtered using a fourth-order Butterworth bandpass filter, whereas the model data are processed using the Helmholtz decomposition approach described in Sect. , in order to isolate GW related perturbations.

Linear GW theory in a uniform background flow predicts that one vertical wavelength of an inertia GW traces an elliptical perturbation hodograph as described in The hodograph rotates anticyclonically for an upward propagating wave and cyclonically for a downward propagating wave. This technique has some limitations under conditions with strong background wind shear and is therefore only applicable to a subset of the wave spectrum, particularly in the low-frequency, long-wavelength limit for more details see. These hodographs are typically derived from vertical profiles at a given time. However, due to the limited number of altitude levels available in our dataset, we instead construct a hodograph from profiles at a single flight altitude using measurements at multiple times e.g., as in.

As an example, we use the time series of u′, v′ at ∼ 12.5 km flight altitude during the period of enhanced vertical shear and low Richardson number (Fig. ). The corresponding time series of u, v are shown in Fig. a, c (see also Fig. ). Both periods contain multiple elliptical structures, although only few segments show clear evidence of anticyclonical rotation, highlighted by the red-colored line segments in Fig. b, d. A well-defined elliptical pattern is evident in Fig. b, indicating the presence of an upward-propagating GW. In contrast, although wave-like oscillations are more prominently observed during 12:45–13:05 UTC (Fig. ), a similarly coherent elliptical structure is less apparent in Fig. d.

As a first summary, we can conclude that a turbulent region has been crossed during WISE RF05. This region exhibits enhanced vertical shear, low Richardson numbers and signs of tracer mixing. Since there are also signs of GW in the respective time periods, this motivates us to go on with our analysis on how GWs might contribute to this mixing event. For this we will broaden our scope and analyze the larger synoptic situation.

We begin by analyzing the horizontal divergence field to identify location and characteristics of potential GW signatures in the LMS. We define the extratropical tropopause based on the dynamical tropopause definition with a potential vorticity value of 3.5 PVU (1 PVU = 1×10-6 K m² kg⁻¹ s⁻¹).

Figure a–c shows the horizontal divergence field at 12.5 km altitude (∼ 200 hPa) between 11:00 and 13:00 UTC. Alternating patterns of divergence and convergence, indicative of gravity wave activity, are evident near the jet streak exit region, with enhanced signatures between 60 and 72° N above the Icelandic highlands along the flight track (Fig. a). These GWs are likely generated by the interaction of the baroclinic flow with Iceland's topography. The associated GW signatures persist over the following hours around Iceland (Fig. b, c) and are also apparent in the PV field. The horizontal wavelengths of these waves are on the order of a few hundred kilometers, consistent with typical wavelengths of inertia GWs. On the larger scale, however, all time steps exhibit similar divergence patterns, with only slight changes in amplitude and orientation, reflecting a systematic evolution of the wave field.

The corresponding vertical cross section of horizontal divergence at 14.05° W, representing the approximate flight location at 11:00 UTC (marked by the dashed line) is shown in Fig. g. The GW propagates clearly upward and undergoes changes in wavelength within the LMS. While the GW appears to be rather localized above Iceland in the troposphere, it begins to propagate away from its source region in the stratosphere. At this cross section, the GW signal extends up to an altitude of about 17.5 km. Inspection at later times shows that signal remains persistent, with only minor changes in the wave signatures near 14.05° W (see also Fig. ). It is further noteworthy that, despite its lower horizontal resolution, ERA5 is able to capture the appearance of GWs in the LMS. This is consistent with findings of previous studies which analyzed GWs in ECMWF products and reanalyses e.g.,and references therein.

Horizontally propagating GWs with large horizontal wavelengths tend to dominate the horizontal derivatives of momentum fluxes, whereas upward-propagating, large-amplitude GWs can transport substantial momentum vertically across the tropopause. This transport can modify the vertical gradients of the wind components across the tropopause, thereby enhancing shear and potentially creating conditions favorable for turbulence development. In the region of the enhanced gravity wave activity, we also find large areas of increased vertical wind shear around 12.5 km altitude between 11:00 and 13:00 UTC. There are clear signs of the enhanced vertical wind shear along the jet-stream south of Iceland. The strongest shear occurs over Iceland in the region of the GW activity (Fig. d–f). Additionally, regions of enhanced vertical shear coincide with widespread reduced Ri values (blue lines in Fig. d–f), indicating an increased potential for dynamical instability.

Furthermore, the vertical distribution of vertical shear at 14.05° W (Fig. h) reveals two distinct regions of enhanced shear. Large shear values are evident in the LMS around the jet stream, roughly around 70° N. In addition, shear maxima occur further south, within the region of GW activity. Since these maxima are located further away from the jet stream, this indicates that other, potentially smaller–scale features contribute to the observed large shear values. Also, there is a clear co-location between large-scale shear and smaller scale shear perturbations (see Fig. a) and the GW patterns across the tropopause (Fig. d–f). Thus, the vertical alignment of shear perturbations with the GW phase structure remains consistent throughout the tropopause region. Overall, this case exhibits a spatiotemporal co-occurrence of GWs and enhanced vertical wind shear.

While the co-occurrence of GWs and enhanced vertical wind shear suggests a possible link, the extent to which small–scale GWs contribute to shear modification across the tropopause remains to be assessed. One possible explanation is that vertically propagating, large-amplitude GWs with short vertical (and corresponding long horizontal) wavelengths locally modulate the static stability, N2, in the LMS , which may in turn facilitate the accumulation of vertical shear in this region. This suggests that GWs may partially contribute to, or influence, the enhancement of vertical shear in the lower stratosphere. On the other hand, shear maxima occurring outside regions of GW activity are likely associated with large–scale flow components, including the jet stream and baroclinic disturbance. This motivates a more detailed investigation of the role of small–scale GWs in the development of enhanced vertical shear and, subsequently, their potential contribution to turbulence occurrence.

After demonstrating the link between GWs and vertical shear of the total wind field, we move on to a more in-depth analysis of potential turbulence occurrence. Note that turbulence occurrence is assessed with predictors derived from the resolved model quantities. For this purpose, we analyze the AMF and the vertical wind shear perturbations in the region covered by the flight track over the North Atlantic, i.e., between 50–72° N and 5–30° W (see blue box in Fig. ). We focus on the LMS and further restrict our analysis to regions with gradient Richardson numbers between 0 and 1. The shear perturbations, S2′, show how much shear is related to the small–scale wind perturbations, whereas the AMF is used to quantify momentum transport associated with GWs. Regions of GW-induced instability and turbulence are expected to coincide with enhanced momentum-flux divergence associated with GW breaking and dissipation . We also note that turbulence is a relatively rare phenomenon under typical atmospheric conditions , and only a limited number of data points are therefore expected during episodes of potential turbulence in the LMS.

With this knowledge, we create two-dimensional probability density distributions of AMF and vertical shear perturbations in the LMS for 0≤Ri≤1 (Fig. ). The majority of points exhibits relatively low vertical shear values, as indicated by the distribution and color code in the figure. However, regions with the larger vertical shear values (>3×10-4s-2) exhibit also a larger AMF. This suggests a positive correlation between S2′ and AMF in the LMS and indicates that small–scale processes may contribute to conditions favorable for turbulence occurrence. This behavior is persistent and is especially evident during time periods of interest of our analysis (see Fig. a, b for 11:00 and 13:00 UTC). Minor changes in the probability density distributions are apparent and are most likely related to the evolving flow situation. However, the distributions show remarkable similarities to those reported from idealized baroclinic wave experiments . We therefore interpret the co-occurrences of enhanced vertical shear perturbations and AMF as evidence that small–scale dynamics, and especially GWs, contribute to the generation of turbulence-favorable conditions. The fact that this relationship is also evident in the idealized experiments further suggests that this is behavior may represent a more general characteristic of baroclinic waves rather than being unique to the present case study.

In a next step, we turn to the relationship between GWs and CAT. One previously suggested consequence of dynamical instability is that associated inertia GWs may generate CAT when they break . In light of this, showed that the emission of inertia GWs, following the release of dynamic instability, instigate light–moderate occurrences of CAT around the unstable region using idealized model simulations. We follow this line of thought and use the turbulence indices, TI1 and TI2, to identify regions of potential CAT occurrence in our region of interest in the LMS over the North Atlantic (Fig. ). In contrast to the shear analysis in the previous sections, CAT develops more sporadically, forming localized pockets. suggested that these smaller scale turbulent regions persist for a few minutes around the periphery of the unstable regions. We see similar patterns in our case study. It is noteworthy that the turbulence indices remain low in the region of low gradient Richardson numbers south of Iceland, but reach their largest values over Iceland, where Ri is also small. The TI2 values are generally higher over Iceland than the TI1, which is related to the CVG term in TI2. Together with the fact that the CAT indices are largest in the regions of GW activity, this suggests that GWs play a crucial role in the turbulence formation, despite the limitation of hourly temporal resolution of the ERA5 reanalysis data. Overall, the results support a picture in which upward-propagating GWs modify the flow across the tropopause region, enhance vertical shear, and contribute to the development of dynamical instability and subsequent CAT occurrence.

We calculate the TI1 and TI2 as proxies for CAT from zonal and meridional wind perturbations (u′, v′). Since we find several regions where CAT develops simultaneously across the tropopause, we use these indices to quantify the intensity of the CAT events based on the ERA5 data. For this purpose, we categorize the CAT values into intensity levels as given in . Light-to-moderate CAT intensity is defined by the 95th percentile of the distribution of each index within the LMS. In our case, we determine the corresponding threshold values for TI1 and TI2 to 1.4×10-7 and 1.5×10-7s-1, respectively (see also Appendix  and Fig. ).

Collating all turbulence occurrence throughout the simulation, we find that most occurrences fall into this light–moderate category, but some occurrences of moderate intensity are also apparent (Fig. a). In contrast, the moderate to greater intensity CAT events are more prominent in the positive tail of the TI2 distribution than in the TI1 distribution (Fig. b). Compared to TI1, TI2 exhibits more frequent occurrences of moderate and greater than moderate CAT events (see Fig. b). This difference can likely be attributed to the additional convergence term in TI2, which may further indicate that GWs play an important role in the formation of strong CAT events.

Similar to the analysis of the vertical shear perturbations, we finally examine the relationship between the CAT indices and the AMF. Figure  shows the two-dimensional probability density distributions of TI1 and TI2 versus AMF at two time steps for data points in the LMS over the North Atlantic domain. The overall shape of the distributions is quite similar to the distribution for the vertical wind shear perturbations. In both cases, the distributions are tilted toward higher CAT index values and larger AMF, with only minor changes in time (compare panels a and b as well as c and d in Fig. ). As before, enhanced TI2 values occur more frequently than enhanced TI1 values. Based on these distributions, we suggest that small-scale dynamics, particularly GWs, not only enhance shear, which is a necessary, but not sufficient, condition for turbulence, but also contribute to the occurrence of CAT. Furthermore, these results highlight the important role of the small-scale dynamics in the transport and deposition of momentum across the tropopause, with potential consequences on the distributions of trace species in the UTLS.

In conclusion, the results obtained in from the idealized cases are also evident in the “real” world in the ERA5 perspective. As of now, the discussion centered around the role of GWs in the occurrence of strong shear in the LMS, and whether potential turbulence occur in the region of the GW-induced shear in ERA5. In the next section, the discussion shifts to a sensitivity analysis with other models.

We first investigate the sensitivity of the results to horizontal resolution using IFS forecasts with a finer spatial resolution than ERA5. At synoptic scales, the flow evolution closely resembles that derived from ERA5 and discussed in Sect. . However, slight deviations become apparent at the mesoscale as well as in the location of GW structures (Fig. ). These similarities and differences are illustrated in Fig. a, where the IFS resolves finer-scale divergence structures indicative of GW activity over Iceland. In particular, the northwestern sector exhibits more pronounced small–scale features with moderate amplitudes than in ERA5. The corresponding vertical distribution at 14.05° W reveals a GW packet propagating upward into the lower stratosphere, with a relatively large vertical wavelength (∼ 2–3 km) and short horizontal wavelength (∼ 100 km) (Fig. c). As expected, the IFS resolves finer-scale wave structures than ERA5 (see also Fig. g), indicating that the horizontal characteristics of GWs are strongly dependent on model resolution. This dependence arises not only from the changed grid spacing but also to the representation of orography, as higher horizontal resolution better resolves terrain features and can therefore generate smaller scale orographic GWs. Overall, these results suggest that horizontal resolution strongly influences the representation, spatial structure, and amplitude of resolved GW fluctuations in both reanalyses and forecasts.

Further analysis of the vertical shear (Fig. b) at the same altitude reveals enhanced shear values around 60–65° N over the Iceland, especially in the proximity of the observed GWs. The large vertical shear values are accompanied by low Richardson numbers, especially over Iceland (blue line in Fig. b indicates regions with Ri≤1). This pattern resembles the situation described in ERA5, with a co-occurrence of GWs, enhanced shear and low Ri over Iceland. Farther south, we also identify a region of enhanced shear and low Ri values but clear signatures of GWs. The potential turbulence occurrence in this region is therefore more likely associated with the large–scale flow related to the jet stream. Overall, the IFS exhibits similar patterns of vertical shear, GW activity, and turbulence-favorable regions as ERA5. However, the spatial scales of these features are notably smaller in the vicinity of the ridge. In addition, the IFS shows a clearer spatial correspondence between enhanced shear and GW signatures than ERA5.

Next, we investigate the perturbation quantities in more detail, starting with the occurrence frequency distribution of AMF and vertical shear perturbations for Richardson numbers between 0 and 1 (Fig. ). Since IFS resolves the vertical shear similarly to ERA5 and exhibits comparable patterns of GWs activity and S2, it is not surprising that the positive correlation between AMF and S2′ in the LMS remains evident. The most notable difference is that larger absolute values of shear perturbations are present in the IFS data, and the occurrence of strong shear perturbations is increased compared to ERA5 (see Fig. ). The AMF also shows slightly larger values, indicating somewhat enhanced GW activity. Thus, the higher-resolution data further support and strengthen our hypothesis that small–scale dynamics are a vital contributor to the occurrence of enhanced shear and subsequently to conditions favorable for turbulence formation in the LMS.

With the apparently stronger shear and GW activity in the IFS forecast compared to ERA5, the next question is whether this also results in an increased occurrence of potential turbulence. To address this, we analyze the occurrences of TI1 and TI2, starting with their horizontal distributions (Fig. ). As in ERA5 (see Fig. ), the overall spatial structure is similar, but the regions of enhanced TI1 and TI2 are more localized in the IFS. The two indices show only minor differences in their spatial distribution, with TI2 exhibiting slightly larger values. Interestingly, regions of low Richardson number, indicated by the blue contour, show little overlap with regions of enhanced turbulence indices.

As before, we determine the threshold value for light moderate CAT based on the 95th percentile criterion. The resulting threshold values for TI1 and TI2 are then 2.1×10-7s-1 and 2.45×10-7s-1, respectively (Fig. ). Both values are remarkably higher than the corresponding ERA5 threshold values, further highlighting that the IFS resolves clearer signatures of potential turbulence occurrence. This behavior is also evident across the entire LMS, as shown by the two-dimensional occurrence frequency distributions of TI1-AMF and TI2-AMF pairs (Fig. ). Compared to ERA5, the distributions exhibit slightly higher maximum values of TI1 and TI2. More importantly, they show a larger frequency of high turbulence-index values, suggesting an increased occurrence of potential turbulence in the LMS. Both distributions are skewed toward high AMF and high turbulence indices, further supporting the link between turbulence occurrence and GW activity.

So far, this section has focused on the role of GWs in generating strong shear in the LMS and on whether clear-air turbulence occurs within regions of GW-induced shear in ECMWF datasets, which employ a hydrostatic dynamical core together with semi-implicit and semi-Lagrangian numerical schemes. We now investigate whether these findings also hold in ICON simulations of the same case. This provides a unique opportunity to examine the event across three model domains (with and without convective parameterization) and to relate the results to our previous idealized ICON simulations .

In this section, we not only compare the ICON model, which employs a non-hydrostatic dynamical core, with the hydrostatic ECMWF models, but also investigate the impact of horizontal resolution within the ICON framework. To this end, we analyze simulations ranging from the global configuration with an effective horizontal grid spacing of 13 km to a nested configuration with an effective grid spacing of 3.3 km. Further details on the model setup and the physical parameterization schemes used in these simulations are provided in Sect. .

We begin by examining the horizontal divergence at 12.5 km altitude (Fig. ). Overall, the structure closely resembles that of the ECMWF models (reanalysis and forecast). Pronounced GW activity over the northeastern Icelandic highlands is evident in all ICON domains (Fig. a–c), with enhanced wave signatures between 60 and 72° N, particularly over and east of Iceland along the flight track. The ICON simulation with Δx≈3.3 km captures GW activity throughout the analysis domain, including moderate wave activity in the northwestern sector (Fig. c). The GWs in this instance generally exhibit larger-amplitudes, but are spatially more confined.

Notably, the ICON simulation with Δx≈6.5 km reveals prominent upward-propagating GWs with relatively small amplitudes that closely resemble those resolved by the IFS but are not clearly captured in ERA5 (see also Fig. ). Likewise, the Δx≈13 km simulation exhibits a vertical structure similar to that of the IFS, with a slightly shorter vertical wavelength of approximately 3 km and wave signatures extending up to about 17.5 km altitude (Fig. a). In contrast, the finer-resolution simulation (Fig. c) resolves larger-amplitude waves with longer vertical wavelengths that propagate upward beyond approximately 19 km altitude. It should be noted that the shallow convection scheme employed in the nested domains (Δx≈6.5 km and Δx≈3.3 km) may contribute to the emergence of additional small–scale wave signatures. All three domain clearly exhibit a more pronounced GW signatures as the horizontal resolution increases, with slight differences evident in both amplitude and spatial structure of the GWs. This highlights that the representation and occurrence of GWs, as well as associated small–scale features, depend substantially on the model grid spacing and convection processes implemented in the respective domains.

The corresponding horizontal distribution of vertical shear (Fig. d–f) shows the maximum shear values north-east from the strongest GW signatures, north of 65° N and east of 14° W. The three domains show similar structures, in particular, the region of enhanced shear south of Iceland is weaker in ICON than in the ECMWF models. The ICON simulation with the finest grid spacing shows the highest shear values, and the shear becomes more localized with pronounced banded structures in regions of strong divergent signals. This suggests a close relationship between horizontal divergence and vertical shear in the tropopause region and in the lower stratosphere (see also Fig. d–f). The enhanced small–scale divergence in the higher-resolution simulations may partly arise from differences in the representation of convective processes and associated gravity wave sources. Moreover, this overall behavior indicates that both horizontal and temporal resolution substantially influence the amplitude and representation of GW-related fluctuations in the forecast data, consistent with the findings presented in Sect. . These results highlight the need for sufficient horizontal resolution to accurately represent GWs and small–scale processes.