2.1 Measurements during the WISE campaign 2017

In autumn 2017 the airborne research mission Wave-driven ISentropic Exchange (WISE) took place from Oberpfaffenhofen, Germany, and Shannon, Ireland, with the German HALO (High Altitude LOng Range) research aircraft. The main goals of the mission were to examine mixing processes in the UTLS in association with Rossby wave breaking and to study the impact of the Asian Summer Monsoon circulation on the budget of radiatively active species in the lower stratosphere. One specific target was to study the relation between the lower stratospheric static stability and cross-tropopause exchange in the extratropics.

During WISE, HALO was equipped with a unique set of instruments for in situ and remote sensing measurements. In this study we use in situ measurements of CO and N₂O, and potential temperature Θ. CO and N₂O have been measured with the University of Mainz Airborne Quantum Cascade Laser Spectrometer (UMAQS). The instrument is based on direct absorption spectroscopy using a continuous-wave quantum cascade laser with a sweep rate of 2 kHz (Müller et al., 2015). For the WISE campaign the total drift-corrected uncertainty was determined to be 0.94 ppb_v for CO and 0.18 ppb_v for N₂O. Basic state parameters such as temperature, pressure, the three-dimensional wind vector, and others were measured with Basic HALO Measurement and Sensor System (BAHAMAS). The system is part of the basic aircraft and consists of a data acquisition system and a suite of sensors for basic meteorological and aerodynamic measurements. The system also contains interfaces into several aircraft systems like the inertial reference unit or the air data computer in order to monitor aircraft state parameters (Krautstrunk and Giez, 2012). The nose boom of HALO is part of this system and carries the air data probe for pressure and air flow measurements which are needed for determination of the wind vector. Additional BAHAMAS installations are six total air temperature (TAT) housings on the aircraft nose which can be used for temperature measurements and as inlets for sensors inside the nose. Two of these housings contain an open wire PT100 resistance thermometer for atmospheric temperature measurements, thus providing redundancy for this important parameter. The basic frequency for all atmospheric units is 100 Hz; data are usually processed on a 10 Hz basis. The accuracy of the pressure measurement is 0.3 hPa while the accuracy of the static temperature measurement is 0.5 K. We also use remote sensing measurements from the Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA), which provides profile information of temperature and static stability, in addition to numerous trace gases (not used in this study). GLORIA is an airborne infrared limb imager combining a two-dimensional infrared detector with a Fourier transform spectrometer (Friedl-Vallon et al., 2014; Riese et al., 2014). The viewing direction is to the right of flight direction and depending on flight altitude and flight direction GLORIA observes the atmosphere between about 5 km and flight altitude with a vertical sampling of about 150 m at a tangent altitude of 10 km. The vertical resolution of retrieved temperature profiles and static stability is of the order of 300 m. The horizontal sampling along the flight track is up to 2 km (Kaufmann et al., 2015; Ungermann et al., 2015).

In total the WISE campaign comprised more than 140 flight hours during 15 research flights between 12 September 2017 and 21 October 2017. All flights except the first two started in Shannon, Ireland, and covered the North Atlantic between Greenland, Newfoundland, the Azores, and Europe as well as continental western and northern Europe. HALO was mostly flying in the UTLS up to ceiling altitudes of about 15 km, which corresponds to maximum potential temperature values of about 405 K and minimum pressure values of 130 hPa. The goal of research flight 07 (RF07) on 28 September 2017 was to study the abundance of trace species in the extratropical tropopause region. In particular, in accordance with the major goals of the WISE mission, the focus of this flight was on whether the trace species show specific signs of recent STE in regions of enhanced values of static stability in the lower stratosphere. Furthermore, the design of this flight was chosen such that the predictions of the idealized simulations of Kunkel et al. (2016) could be supported by observations. Thus, the flight was planned in the ridge of a synoptic-scale baroclinic wave which evolved during the previous days over the North Atlantic at the edge of a larger scale trough. A detailed description of the synoptic situation and the flight path will be given in Sect. 3.1.

2.2 ECMWF forecast data

We use forecast data from the European Centre for Medium-Range Weather Forecasts (ECMWF) to support the analysis of the airborne measurements and to provide more background information about the synoptic situation. We choose to use forecast data from ECMWF because they are available hourly at a very fine horizontal resolution. The forecast starts at 28 September 2017 00:00 UTC and we use the first 36 hourly steps until 29 September 2017 12:00 UTC. These data are used for analysis along the flight path where the full resolution is used corresponding to regular longitude–latitude grid spacing of about 0.07^∘. Moreover, we use a slightly degraded data set with a horizontal grid spacing of 0.125^∘ in the horizontal for a trajectory analysis. The forecast data have 137 vertical hybrid pressure-sigma levels up to 0.01 hPa with a vertical spacing of roughly 300 m in the UTLS.

2.3 Idealized baroclinic life cycle experiments

We complement our analysis of the airborne measurements using results from idealized baroclinic life cycle experiments. We continue the work of Kunkel et al. (2016) using the same setup of the COSMO (COnsortium for Small-scale MOdelling; Steppeler et al., 2003) model but extend the analysis with a more specific focus to analyze STE. For this we included additional artificial tracers to mark air masses which are initially located either in the troposphere or in the stratosphere, separated by the dynamic tropopause for which we use the isosurface of 2 pvu (1 pvu $={\mathrm{10}}^{-\mathrm{6}}$ K m² kg⁻¹ s⁻¹). Moreover, we included a tracer which is passively advected and which carries the information of the initial value of potential vorticity. With this tracer it is possible to determine how much PV in each model box has changed by diabatic processes since model start (Kunkel et al., 2014). Evaluating the difference between the current PV and the advected initial PV at the dynamic tropopause therefore allows regions of TST and STT to be detected.

We then repeated simulations from Kunkel et al. (2016) which included parameterizations for large-scale and convective clouds, radiation, and turbulence which have been labeled with BRTC (bulk microphysics, radiation, turbulence, and convection) by these authors. The model grid has a regular horizontal grid spacing of 0.4^∘ in longitude and latitude and a vertical grid spacing of 110 m in the UTLS. Since the meteorological situation during RF07 was dominated by a wave-breaking event strongly resembling life cycle 1 (LC1), we will focus our discussion in Sect. 4 to results from LC1 experiments (Thorncroft et al., 1993), but we note that we also conducted simulations of life cycle 2 (LC2). Moreover, the LC2 experiments qualitatively gave the same results as the LC1 experiments. More information about the model setup and physics is given in Appendix A.

2.4 Trajectory calculations with LAGRANTO

The Lagrangian analysis tool (LAGRANTO; Sprenger and Wernli, 2015) allows calculating trajectories using the kinematic wind from four-dimensional meteorological data. It is possible to use both ECMWF and COSMO data as input for the trajectory calculations. The first trajectory analysis is based on ECMWF forecast data, which provides wind fields every hour. Trajectories have been initialized along the flight path with the goal of obtaining a more comprehensive picture of the temporal evolution of the meteorological parameters of the measured air masses. We will give more details on the trajectory start points and the analysis in Sect. 3.3.

For the second trajectory analysis we use COSMO wind fields. COSMO output is available every hour on a horizontal grid with spacing of 0.4^∘ and a vertical spacing of about 110 m in the UTLS, thus providing a high-resolution input grid for the trajectory calculations. Based on the COSMO model output the goal of the trajectory calculations is to identify regions of cross-tropopause transport in the baroclinic life cycle experiments and whether exchange trajectories are evident in the ridge of the baroclinic wave. More details will be given in Sect. 4.

In general, we identify the exchange of air masses between the stratosphere and troposphere by the evolution of PV along a trajectory. If the PV of an air parcel increases from values below 2 pvu to values above this threshold, we mark this trajectory as a TST trajectory and vice versa for STT.

Finally, note that in this study discussion around static stability is usually associated with the first lapse rate tropopause, while discussion about STE is linked to the dynamic tropopause. Thus, both definitions will be considered in the analysis; however, if only the term tropopause is used, then we refer to the dynamic tropopause with a value of 2 pvu throughout the paper.

3.1 Synoptic situation and flight plan of WISE RF07

WISE RF07 targeted a fast-evolving baroclinic wave which emerged at the southern tip of a large-scale trough in the central North Atlantic in the early hours of 27 September 2017. While the large-scale trough traveled relatively slowly over the North Atlantic, the small-scale wave evolved rather fast, with the formation of a warm sector and well defined upper tropospheric fronts within 24 h as indicated by the PV at 330 K at 15:00 UTC on 28 September 2017 (Fig. 1a).

Figure 1Synoptic situation during WISE RF7 over the western North Atlantic at 15:00 UTC on 28 September 2017. (a) Potential vorticity on the isentropic surface of 330 K with high cloud cover (isoline showing a value of 0.9). (b) Meridional cross section of potential vorticity along −7.72^∘ E longitude and (c) zonal cross section along 54.66^∘ N latitude. The cross sections also show isolines of potential temperature (black dashed; 330, 335, 340 K), of horizontal wind velocity (light blue dashed; 45, 55 m s⁻¹), the Richardson number (red dashed–dotted; 1), static stability (yellow dashed–dotted; $\mathrm{5.5}\times {\mathrm{10}}^{-\mathrm{4}}$ s⁻²), and cloud ice content (blue dotted; $\mathrm{5}\times {\mathrm{10}}^{-\mathrm{6}}$ kg kg⁻¹). The cross sections are along the meridian and the circle of latitude of the red diamond shown in panel (a). This point also marks the location where the picture in Fig. 2b is taken.

The flight focused on the rapidly evolving ridge, which was expected to be strongly affected by diabatic processes and the vertical transport of boundary layer air in the region of the warm conveyor belt (WCB) ahead of the surface cold front. This system was expected to be situated close to Ireland in the afternoon hours of 28 September 2017. Take-off of WISE RF07 was at 13:15 UTC with a total flight time of 7 h 47 min. The flight strategy was twofold: first, staggered flight levels at FL400 (northeastward), FL380 (southwestward), FL360 (northeastward), FL340 (southwestward), FL420 (northeastward), and FL450 (southwestward) through the ridge of the baroclinic wave and second a survey of the stratospheric air with large PV values above the occlusion of the baroclinic wave west of Ireland (see also flight path in Figs. 1a and 2a). The intention of the first part in the northernmost part of the ridge of the baroclinic wave was to conduct co-located measurements of atmospheric state parameters and trace species across the local tropopause. The staggered flight level allowed these quantities to be measured in situ at different altitudes below, at, and above the level of the tropopause. From the highest flight levels (FL420 and FL450) in cloud-free conditions, two-dimensional distributions of temperature and trace species along the flight track were remotely measured with GLORIA. Our analysis focuses on the first part of the RF07, in particular on the first flight leg in the southwestward direction at FL380 (see Fig. 2a).

Figure 2(a) Three-dimensional flight track of WISE RF07, highlighting the flight legs important for this study. The arrows point in the direction of the flight on the respective levels. The dashed lines on the surface map show the angle of view of the photo shown in panel (b). (b) Photo taken on board HALO at 15:03 UTC during WISE RF07 showing Kelvin–Helmholtz cloud billows on top of a cirrus cloud deck.

A large part of the first leg of FL380 in the southwesterly direction was just above a widespread cirrus cloud deck associated with the upper tropospheric outflow of the WCB of the low pressure system. The high cloud cover in Fig. 1a shows the location of this cloud deck. The WCB also manifests itself in the low values of PV in the upper troposphere in the region where the ice clouds reach up to the tropopause (Fig. 1b, c). PV values are close to 0 pvu or even slightly below, which is common in such a situation due to a decreasing heating rate above the level of maximum heating (e.g., Chagnon et al., 2013; Joos and Wernli, 2012).

In the lower stratosphere the PV shows enhanced variability above the WCB outflow region (Fig. 1b, c). There are also high values of static stability evident, with values reaching as high as $\mathrm{10}\times {\mathrm{10}}^{-\mathrm{4}}$ s⁻². However, these high values emerge rather as wave-like patches and not as a layer. In between the high values the static stability has rather tropospheric background values (see also Fig. 3). More so, this region also exhibits low values of the Richardson number, indicative of Kelvin–Helmholtz instability and thus turbulence. Such a co-located enhancement of static stability and presence of turbulence was also evident in the life cycle experiments of Kunkel et al. (2016) and has recently been reported by Kaluza et al. (2019) based on a composite analysis of baroclinic waves over the North Atlantic.

Figure 3(a) Static stability along the flight path between 14:00 and 16:00 UTC (color-shaded) along with potential temperature (black solid), cloud ice water content (blue dashed), the altitude of the dynamic tropopause (gray solid), and the Richardson number smaller than 1 (gray dotted) based on ECMWF forecast data. Black dotted line shows the altitude of HALO. (b) Static stability at GLORIA tangent points between 17:20 and 18:20 UTC. Black line shows the flight altitude with black crosses marking points of measurement. Thick gray lines show 2 and 4 pvu, thin gray line the 350 K isentrope based on ECMWF forecast data. Gray dotted points mark the location of the first lapse rate tropopause. (c) ECMWF forecast data sampled at GLORIA tangent points.

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Another indication of turbulence in the region above the cloud deck stems directly from observations of Kelvin–Helmholtz cloud billows close to the flight path (Fig. 2b). A photo was taken at 15:03 UTC in a northwestern direction (Fig. 2a, diamond in Fig. 1a, b). The billows are indicative of a KHI which is thought to favor mixing of adjacent atmospheric layers and thus affects the vertical gradient of trace species. Notably, since the KHI emerges in the vicinity of the tropopause, it could potentially lead to STE. Commonly, a critical Richardson number of 0.25 identifies a KHI. However, in a non-convective situation such small Richardson numbers rely on large vertical shear of the horizontal wind. In turn, models based on a discretized grid with a grid spacing of a few hundred meters or more in the vertical can often not resolve the vertical shear sufficiently. In the region of the observed cloud billows we find Richardson numbers in the ECMWF model of about 1. We therefore use a Richardson number equal to 1 as a proxy for KHI in the UTLS for our analysis.

Figure 4Time series of measured N₂O (blue) and potential temperature Θ (red solid) as well as modeled potential temperature Θ_M (red dashed), Richardson number Ri (gray dashed), and altitudes of the dynamic (2 pvu, black dashed) and the first lapse rate (lrt1, black dotted) tropopause between 14:15 and 15:15 UTC during WISE RF07. Black solid line shows the altitude of the aircraft, the gray areas indicate the time periods discussed in the text.

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Now we focus on the flight leg from northeast to southwest at FL380 between 14:20 and 15:20 UTC. HALO came from FL400 which was then deeper in the stratosphere with potential temperatures above 350 K. At FL380 HALO was initially flying in the lowermost stratosphere, then gradually approaching and finally crossing the dynamic tropopause, which was slightly tilted according to the ECMWF analysis (Fig. 3a). This is in remarkable agreement with measurements of N₂O, which increases to tropospheric values at FL380 (Fig. 4), as is discussed further below. On this leg the aircraft crossed the lower part of the structures with alternating large and low values of static stability. This structure is potentially linked to a propagating inertia-gravity wave which commonly emerges during baroclinic wave developments (e.g., O'Sullivan and Dunkerton, 1995). Furthermore, in the region with low values of static stability an area with low Richardson numbers is evident which extends into the region of the maximum of static stability at around 15:00 UTC.

Before we analyze the time period between 14:00 and 15:00 UTC more specifically in Sect. 3.2, we want to point out one model deficiency. Although the ECMWF forecast predicted the atmospheric state very well, there is evidence that extreme values of state parameters are missed or at least underestimated, with potential consequences for the representation of mixing in the UTLS. We already mentioned that we think that the Richardson numbers from the ECMWF forecast might have values that are too large in regions around the tropopause where the vertical shear of the horizontal wind is large. However, this is difficult to verify from airborne measurements, since all two-dimensional information on the temperature and wind is missing along the flight path. We can overcome this issue at least partly by using temperature retrievals from GLORIA and comparing static stability (the numerator of the Richardson number calculation) from the model and from measurements (Fig. 3b, c). For this we use the last northeastward leg on FL420, i.e., ∼ 13 km and 169 hPa, between 17:20 and 18:20 UTC, when HALO was flying above the maximum values of static stability. Static stability from GLORIA measurements exhibits larger values than that from the ECMWF model as well as a smaller vertical extension of the entire wave structure. Thus, the model forecast underestimates the strength of the inversion, most potentially related to deficiencies in representing the gravity wave in this region due to the still relatively coarse grid spacing in the UTLS. Since the gravity wave also affects the three-dimensional wind, it could be assumed that the vertical shear of the horizontal wind might not be sufficiently represented in the model and thus the gradient Richardson number.

In summary, the synoptic situation during WISE RF07 strongly resembles the situation of the idealized baroclinic wave of Kunkel et al. (2016). Consequently, it is now possible to investigate a prediction from an idealized model study with airborne measurements and seek signs of turbulent motions in the measurement data.

3.2 Airborne in situ measurements and evidence of mixing around the tropopause – WISE RF07

We start our analysis by focusing on the time period between 14:20 and 14:54 UTC (gray areas in Fig. 4) and will first concentrate on the in situ measurements of nitrous oxide N₂O and potential temperature Θ along with several parameters from the ECMWF forecast interpolated on the flight track. Based on N₂O and Θ we further subdivided the time period of interest into three shorter periods (gray scales in Fig. 4). During the first period from 14:20 to 14:46 UTC, N₂O volume mixing ratios below 331.31±0.45 ppb_v indicate that HALO was flying in an air mass of stratospheric origin. This value represents the airborne measured tropospheric mean of N₂O during the WISE campaign and is calculated following Müller et al. (2015). HALO was flying at a constant pressure level while slowly approaching the dynamic as well as the first lapse rate tropopause. In the second time period between 14:36 and 14:48 UTC the distance between tropopause and flight level decreased to a few hundred meters or less according to the PV analysis. Notably, this part of the flight close to the tropopause in the ExTL shows low Richardson numbers. Around 14:40 UTC the time series of both N₂O and Θ show strong wave-like structures with periods of about 2 min. The horizontal wavelength can be roughly estimated to be about 25 km, using a mean ground speed of 210 m s⁻¹ of HALO during this part of the flight and assuming that the wave has been crossed perpendicular to the wave crests. The amplitude of the wave is about 2.5 K and the wave spans the potential temperature range between 335 and 340 K. Interestingly, this wave structure is hardly evident in the modeled Θ_M, indicating that the model might have issues representing these scales accurately. The model shows signs of gravity wave activity, however, not directly at the flight altitude but slightly above (not shown). The ECMWF forecast model with a horizontal grid spacing of about 8 km can barely resolve this wave pattern with this fine-scale structure due to the grid spacing of the model. The last period between 14:48 and 14:54 UTC shows strong variability in both N₂O and Θ without any clear wave signal but large variability of Θ and N₂O. This increase in variability could be regarded as a first indicator of increased atmospheric turbulence.

Figure 5Trace gas analysis of the first southwestward leg on FL380, i.e., 205 hPa of WISE RF07. (a) Vertical profile of carbon monoxide for the entire flight (blue dots) and color-coded for the leg on FL380. (b) Vertical profile of CO for the time period 14:20–15:00 UTC, color-coded with time since 14:00 UTC. (c) CO–N₂O correlation for the time period 14:20–15:00 UTC, color-coded with potential temperature. (d–f) Vertical profiles of CO for time periods 14:20–14:36, 14:36–14:48, and 14:48–14:54 UTC, color-coded with time. (g–i) CO–N₂O correlations for the time periods 14:20–14:36, 14:36–14:48, and 14:48–14:54 UTC, color-coded with potential temperature.

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If turbulence occurred in a region of strong tracer gradients at or upwind of where the measurements were taken, it should have affected the composition of trace gases. Both CO and N₂O exhibit vertical gradients in the lower stratosphere (Fig. 5a for CO). We first focus on CO since it has a much stronger gradient at the tropopause due to its shorter lifetime compared to N₂O. HALO was initially in the stratosphere with low values of CO and at the end of the time period close to the troposphere with larger values of CO (Fig. 5b). The gradual transition between the more stratospheric to more tropospheric CO values occurs at potential temperatures between 335 and 340 K. This Θ interval also shows low Richardson numbers in the ECMWF model (Figs. 4, 3a). Moreover, the color code in Fig. 5b reveals the consecutive alternation between low potential temperature/large CO values and high potential temperature/low CO values, indicating the impact of the small-scale wave on the tracer and potential temperature. To identify mixing of tracers, we analyzed the N₂O–CO relationship, which provides information on irreversible tracer exchange similar to CO–O₃ (e.g., Fischer et al., 2000). In general, at the tropopause the CO–N₂O correlation shows almost tropospheric mixing ratios of CO (∼90 ppb_v) and N₂O (∼331 ppb_v) at potential temperature levels typical for the extratropical tropopause in the current case (∼335 K). Above the tropopause both N₂O and CO mixing ratios decrease with increasing potential temperature. However, the CO–N₂O correlation of the time period between 14:20 and 14:54 UTC does not show such a clear relationship of decreasing N₂O and CO and simultaneously increasing potential temperature (Fig. 5c). If the time period is instead divided into three shorter time periods following the gray shading in Fig. 4, then only the first period shows a relationship between N₂O, CO, and potential temperature as one would expect from the large-scale vertical profiles of these quantities (Fig. 5d, g). However, for the other two time periods the tracer–tracer relation with respect to potential temperature changes. For the time between 14:36 and 14:48 UTC the vertical profile of CO shows a wave-like transition (Fig. 5e), while the correlation shows isentropic mixing on different isentropes as indicated by mixing lines connecting tropospheric and stratospheric values between 335 and 340 K (Fig. 5h). In the last time period the relation between N₂O, CO, and potential temperature seems to almost entirely break down, reflecting the initial thought of increased variability in the tracer mixing ratio and potential temperature (Fig. 5f, i). Thus, based on the trace gas analysis, we think that turbulence increasingly affected the second and third time periods to a substantial degree in contrast to the first time period. This could ultimately lead to exchange of trace constituents across the tropopause in a narrow range of potential temperature levels.

Figure 6Power spectral densities of measured potential temperature from HALO for selected time periods: (a) 14:20–15:00 UTC and (b) 18:19–19:18 UTC. Black solid lines are introduced for better comparability, red solid line shows a line with a slope of $k=-\mathrm{3}$, blue solid line shows a line with a slope of $k=-\mathrm{5}/\mathrm{3}$.

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We further analyze the occurrence of turbulence with the help of power spectral densities of potential temperature. Power spectral densities of trace species or state parameters allows the estimation of how much energy is present at a particular spatial scale (Vallis, 2017). On board HALO the frequency of measurements is about 10 Hz for the state parameters such as temperature and wind, while it is about 2–3 Hz for CO and N₂O. Along with an average ground speed of about 210 m s⁻¹ and with the 10 Hz measurements of the state parameters this potentially allows us to identify atmospheric structures down to about 100 m. The shape of these power spectral densities allows the contribution of individual scale ranges to the total energy spectrum to be assessed and indicates the type of turbulence that affects the considered domain (Vallis, 2017). The power spectral density from the flight leg on FL380 (Fig. 6a) reveals a slope close to $k=-\mathrm{5}/\mathrm{3}$. This slope often characterizes three-dimensional isotropic turbulence, i.e., dynamic processes on or below the mesoscale affect the flow (e.g., Tung and Orlando, 2003; F. Zhang et al., 2015). At a later leg in the same direction of the flight on flight level FL420 between 17:20 and 18:20 UTC the power spectral density follows a slope of $k=-\mathrm{3}$ (Fig. 6b). This slope indicates a dominance of geostrophic turbulence and thus larger synoptic scales affecting the flow. To summarize, the slope of $k=-\mathrm{5}/\mathrm{3}$ close to the tropopause suggests that mesoscale processes, e.g., those related to gravity waves, might be substantial to explain the dynamics in the tropopause region.

3.3 Trajectory-based history of measured air masses during WISE RF07

The analyses of trace gas distributions, tracer–tracer correlations, and power spectral densities suggest that mixing is evident in the region between 335 and 340 K. In particular, the N₂O mixing ratios reveal that tropospheric and stratospheric air masses participate in the mixing process. Our next goal is to elucidate the recent history of the measured air masses. For this we calculated kinematic trajectories backward and forward in time which start each second along the flight path for the time period between 14:24 and 14:54 UTC based on ECMWF forecast data available between 28 September 2017 at 00:00 UTC and 29 September 2017 at 12:00 UTC. More specifically, the trajectories start at the horizontal location of the airplane as well as at adjacent locations $\pm \mathrm{0.07}{}^{\circ }$ in longitudinal and latitudinal directions to cover some of the uncertainty due to the gridded representation of the meteorological input variables and to increase the number of trajectories for statistical purposes. Moreover, trajectories start at each full isentropic level between 334 and 341 K and not only at the flight altitude of HALO. This allows us to study the fate of the entire region, which is subject to mixing according to the measurement.

Since we are interested in STE and mixing, we first search for those air masses which cross the tropopause around the time of the measurement and which encounter a KHI. For this we filter all trajectories to find those trajectories which cross the dynamic tropopause and which encounter Richardson numbers smaller than 1 at any point in time during the period of the trajectory calculation. We note, however, that our STE criterion is rather weak, since we only require that the PV of the trajectories is below the PV threshold for the dynamic tropopause at the start of the analysis (28 September 2017 01:00 UTC) and above the threshold at the end (29 September 2017 11:00 UTC). Thus, for further discussion we omit the terminology of TST and STT trajectories as coherent ensembles of trajectories which cross the tropopause only once from the troposphere (stratosphere) to the stratosphere (troposphere) (Stohl et al., 2003; Wernli and Davies, 1997). We think instead of trajectories which show the potential of mixing around the tropopause by encountering low Richardson numbers and having PV values changing between tropospheric and stratospheric values, which nevertheless lead to a subsequent exchange across the tropopause. As mentioned above, we consider low Richardson numbers of the order of 1 as good proxies for KHI. We further study the three time periods of interest from the earlier analysis separately (Fig. 4).

Figure 7Trajectories crossing the 2 pvu isosurface and encountering a dynamic instability which cross the flight track between 14:36 and 14:48 UTC while HALO was flying on FL380. Trajectories start on 28 September 2017 at 01:00 UTC and end on 29 September 2017 at 11:00 UTC. The four panels show the following quantities along the trajectories: (a) pressure (in hPa), (b) potential vorticity (in pvu), (c) time since 15:00 UTC (in h), and (d) Richardson number. In total each panel shows 12 375 individual trajectories.

Interestingly, we find trajectories indicating upward transport which show the same behavior in dynamic and thermodynamic quantities in each of the three time periods between 14:20 and 14:54 UTC. These trajectories always follow a wave-like flow from the North Atlantic towards the British Isles before they turn anticyclonically towards central Europe (Fig. 7). Minimum pressure is evident over the North Atlantic when the trajectories pass through the large-scale trough. Over Ireland and the British Islands the trajectories rise again while encountering the region of the KHI with minimum Richardson numbers. Starting from this region the trajectories strongly decelerate (see Fig. 7c) in a region of alternating horizontal divergence (not shown explicitly).

Figure 8Time series of dynamic and thermodynamic quantities of mixing trajectories crossing the dynamic tropopause and experiencing a KHI. The time axis is relative to 28 September 2017 at 15:00 UTC. The eight panels show the following variables along the trajectories: (a) potential vorticity (in pvu), (b) static stability (in 10⁻⁴ s⁻²), (c) pressure (in hPa), (d) potential temperature (in K), (e) relative vorticity (in 10⁻⁵ s⁻¹), (f) vertical wind (in m s⁻¹), (g) Richardson number, and (h) turbulence index after Ellrod et al. (1992) (in 10⁻⁶ s⁻¹). Note that the time period shown here is shorter than the total time period used for the trajectory analysis.

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The analysis of the PV along the potential TST trajectories shows that these trajectories oscillate around the dynamic tropopause rather than cross the tropopause as a coherent ensemble once and then reside in the lower stratosphere. This is somewhat evident in Fig. 8a, where only those trajectories are shown which at the physical start time of the trajectories have PV values initially smaller and at the last physical time step have PV values larger than the respective dynamic tropopause PV value (here 2 pvu). The trajectories show no straight traverse from the troposphere into the stratosphere. However, several points shall be noted for the time close to the measurement briefly before 15:00 UTC. The static stability shows a maximum which is not evident in PV but is accompanied by a strong decrease in relative vorticity towards anticyclonic flow (Fig. 8b, e). The maximum in static stability follows a period where the trajectories encounter alternating vertical wind, which is a sign of flow through small-scale waves. At the end of this time period signs of turbulent motions increase. Initially, the turbulence index increases due to vertical wind shear as well as stretching and shearing deformation (Ellrod et al., 1992). Later low values of the Richardson number emerge which are indicative for KHI. The appearance of turbulence is further associated with a slight increase in potential temperature which is on the order of 1–2 K, thus the process can be regarded as quasi-isentropic.

The major difference between the three time periods between 14:20 and 14:54 UTC is the number of occurrences of these characteristic mixing trajectories, relative to the dynamic tropopause. During the first part between 14:20 and 14:36 UTC, we find only about 1.7 % out of 69 048 trajectories crossing the tropopause and having low Richardson numbers. This number increases to 23.9 % out of 51 768 in the second part and to 21.9 % out of 25 920 in the last part from 14:48 to 14:54 UTC. Notably, this result does not depend on the choice of our PV value for the dynamic tropopause. This indicates that a rather thick layer around the tropopause up to 3.5 pvu is affected by this mixing process, in particular between 14:36 and 14:48 UTC according to the trajectory analysis. Moreover, there is also a tendency of air masses from above to be mixed downward. For this we select trajectories which initially have a PV value above and finally below the desired dynamic tropopause value. Although they are most evident in the second and third part, such trajectories are in general much less common than those with an increasing PV value over the considered time period. In line with this is that the stratospheric influence on the measured air masses substantially decreases from the first to the third time period. While about two-thirds of the trajectories originate in regions above 5 pvu in the first part, only about a quarter does in the second part and less than 0.5 % in the third part.

Consequently, the trajectory analysis shows that different air masses of tropospheric and stratospheric origin come together in the second and third part of the considered time period. This is in line with the measured trace gas concentrations of N₂O and CO. However, based on the trajectory analysis it is difficult to estimate whether STE and in particular TST occurs in a way that air parcels cross the dynamic tropopause only once from the troposphere into the stratosphere and stay there afterwards. We also performed longer trajectory calculations which, however, also provide no further evidence of TST trajectories which then reside in the stratosphere over a longer time period. We instead find trajectories which, based on PV, alternate back and forth between troposphere and stratosphere and which encounter low Richardson numbers along their paths. One potential reason for why no TST trajectories which stay in the stratosphere are found is that the model fails to correctly resolve the process. In contrast, assuming that the model performed well, it could simply mean that in this specific case the mixing occurred only across the tropopause with no substantial STE taking place. Independently of which is the case, this process changes the gradients of the trace gases in this region which in turn is of importance for radiative transfer calculations (e.g., Riese et al., 2012).