Measurements were carried out during the AIRTOSS-ICE campaign with a Learjet G35A of the Gesellschaft für Flugzieldarstellung (GFD) from Hohn, Germany. The aircraft was equipped with the University of Mainz Airborne QCL Spectrometer (UMAQS), an infrared absorption spectrometer which provided N2O and CO data with a total uncertainty of 0.39 ppbv for N2O and 1.40 ppbv for CO at a measurement frequency of 1 Hz. Details regarding the UMAQS instrument can be found in .

As a unique extension of the measurement setup the aircraft is equipped with the AIRcraft TOwed Sensor Shuttle (AIRTOSS, namesake of the campaign, in the following abbreviated as TOSS). The TOSS constitutes a second measurement platform towed by the Learjet with a vertical distance of typically between 70 and 180 m. The TOSS was released at the first level after takeoff and carries additional lightweight measurement devices, which are partly redundant to the instrumentation on the Learjet and therefore allow the calculation of vertical gradients of the measured quantities as schematically depicted in Fig. . These redundant measurements include in particular temperatures and cloud particle number concentrations as well as size distributions. The particles at the TOSS were measured by the Cloud Combination Probe and Cloud Droplet Probe (CCP–CDP) instrument in a size range between 2 and 50 µm . Particle measurements on board the Learjet were taken by a FSSP (Forward Scattering Spectrometer Probe) in a size range between 2 and 47 µm . In this study both instruments will be used as cloud indicators. Temperature and humidity measurements were taken by two capacitive hygrometers on the Learjet and TOSS, respectively (ICH sensors) . This sensor type is part of the IAGOS measurement instrumental packages and has been evaluated in , with estimates of accuracy and precision for temperature and humidity of ±0.5 K and 5 % RH_liquid.

Potential temperature at the Learjet is calculated from the temperature measurements of the ICH sensor and the static pressure from the altimeter of the Learjet. The pressure at the TOSS was not measured directly and had to be calculated under the assumption of hydrostatic equilibrium from the pressure at the Learjet and the vertical distance between the two platforms derived from GPS data. Relative humidity was derived from the H2O mixing ratios measured by the SEALDH-II instrument with an uncertainty of ±1 ppmv H2O for the condition encountered in this study . During flight level changes and turns, the airstream towards the TOSS inlets is perturbed and subject to turbulence. This leads to flow conditions outside the envelope of the normal flight operation and unknown effects on temperature and humidity measurements. In the following we therefore only use data from horizontal flight legs with well-defined flow around the sensors.

For a detailed analysis of the water vapor distribution, transport pathways, and cloud formation, simulations with the numerical weather prediction model ICON version 2.6.2 have been conducted . Two model simulations have been conducted and were initialized from the ECMWF (IFS) operational analysis at 12:00 UTC on 6 May 2013 and 00:00 UTC on 7 May 2013, respectively. Integration stops at 00:00 UTC on 8 May 2013. A global simulation on a R3B7 grid (effective grid spacing ≈ 13 km) is refined with two two-way interactive nested grids over central Europe . The two nests use R3B8 and R3B9 grids with effective grid spacings of ≈ 6.5 and ≈ 3.25 km, respectively. In the vertical, 150 model levels between the surface and 23 km altitude are used, the spacing of which follows terrain-following smooth level vertical (SLEVE) coordinates . This results in a vertical grid spacing of about 165 m (200 m) at 10 km (12 km) altitude. A time step of 12 s (6 s; 3 s) is used for the integration of the model on the three grids. Sub-grid-scale processes are described by the following parameterizations: the Tiedtke–Bechtold convection scheme (deep convection in the global domain only, ), turbulence following , sub-grid-scale orographic drag following , non-orographic gravity wave drag following , cloud processes by the double-moment scheme from , and radiation by the ecRad scheme .

Lagrangian analysis is facilitated by the computation of online trajectories during the simulation . Online trajectories are calculated based on the resolved wind field on the native grid and time step of the ICON model in the best-resolved nest at a given geolocation. Trajectories are started at model initialization at all grid points and vertical levels between 500 m and 15 km in three sub-regions: -2 to 5° E and 47 to 52° N, 3 to 12° E and 43 to 48.5° N, and 10 to 18° E and 46 to 50° N. The regions have been selected on the basis of backward offline trajectories calculated from the ICON wind fields at 15 min resolution with LAGRANTO . In total about 6.1 million online trajectories have been computed. Output of (thermo)dynamic variables as well as integrated potential vorticity (PV), potential temperature (θ), and selected moisture tendencies are available every 10 min along the trajectories. For further analysis, we have selected trajectories that pass through the area of Learjet measurements (6.5 to 7.5° E and 54.2 to 55.2° N, 8 to 12 km altitude) between 14:00 and 16:00 UTC on 7 May 2013.

The synoptic situation on the day before the flight, i.e., 6 May 2013, is characterized by southerly flow over Germany associated with a ridge and weak trough at its western flank. Until the time of measurement the ridge shifted slightly towards the east, but southerly flow still prevailed over Germany. The trough developed into a filament accompanied by streamers of stratospheric air and filaments of dry air between an approaching weak cyclonic system from the west and the eastward-shifted ridge. An associated elongated PV filament extended southwards to central Italy. In connection with the southerly flow at the western flank of the ridge high humidity is transported to the north, just adjacent to the dry filament, leading to strong humidity gradients in the upper troposphere over western Germany. Satellite images suggest that optically thin cirrus clouds form in the humid southeasterly flow at the western edge of the ridge over southern Germany and are advected to the North Sea region (see Sect. ). Convective activity in the afternoon of 6 May and the morning of 7 May over eastern Germany and eastern Europe extending northwards from the Baltics may have contributed to the moistening of the ridge, albeit likely with no direct contribution to the ExTL cirrus discussed here (see also Sect. ). However, the optically thick upper-tropospheric cirrus below the ExTL is likely partly linked to this convection (see Fig. ). Furthermore, in the early morning of 7 May some deep clouds formed over the Benelux region, likely influencing upper-tropospheric humidity westwards of the stratospheric filament.

The section of the flight path considered in this study is depicted in Fig. , with the occurrence of cirrus particles marked in orange for the TOSS platform and yellow for the Learjet. The measurements show an extended cirrus deck, with its upper edge initially localized between the two measurement platforms until the Learjet also reaches the cloud top at around 55.0° N, 7.2° E. We focus on a short section from 15:08:00 UTC, when ice particles are first measured at the TOSS, to 15:16:00 UTC, before the Learjet changes altitude to the next, higher, flight leg. This section of the flight took place on a pressure level of 250 hPa and is considered to be in the stratosphere since N2O mixing ratios never reached tropospheric values of 325.9 ppbv (Fig. a, upper panel) as also discussed in . This is consistent with PV values of 2–4 pvu indicated by ERA5 analysis at the location of the aircraft (Fig. a, second panel). The thermal tropopause, derived from the temperature profile during the descent of the Learjet as depicted in Fig. b, left panel, had an altitude of 10.35 km, which is below the level of cirrus measurements at the Learjet with an altitude of 10.4 km. Note, however, that the temperature profile was recorded several minutes after the cirrus occurrence. The third panel in Fig. a shows the potential temperature measured by the Learjet (blue) and TOSS (green) along the flight segment and an indication of observed ice particles by the gray and black circles. Over the entire considered time period, cirrus particles were measured at the TOSS at a potential temperature of up to θ = 320 K. At the beginning of this flight section the Learjet was located above the cirrus deck at a potential temperature of θ = 322 K. During the horizontal (i.e., isobaric) flight leg, the potential temperature at the position of the Learjet decreased slowly over time, while the potential temperature at the TOSS varied around θ = 320 K. At the time when cirrus particles were also measured at the Learjet, the potential temperature reached θ = 320 K as well.

The combined TOSS and Learjet measurements allow for the derivation of the vertical temperature gradient above and in the cirrus, which is shown in the bottom panel of Fig. a. Over the considered flight section, the vertical distance between the TOSS and the Learjet was constant. At 15:08:00 UTC a positive vertical gradient of potential temperature was measured, i.e., higher potential temperatures above the cirrus deck then within, as expected in the stratosphere and consistent with the vertical profile (Fig. b, right panel). However, inside the cirrus (at ≈ 15:14:00 UTC, where both platforms measured cirrus particles) the gradient of potential temperature vanishes. Hence, the measurements indicate different regimes of static stability: neutral stratification inside the cirrus and, starting at the cirrus top, high static stability above the cirrus.

Correlations of CO and N2O measurements are shown in Fig. , colored with potential temperature (a) and relative humidity with respect to ice (b). The two species show compact mixing lines typical for the ExTL, connecting typical values of mixing ratios for the troposphere with such typical for a reservoir deeper in the stratosphere for both species, thereby indicating irreversible mixing. The mixing line with lower N2O mixing ratios corresponds to the western part of the flight section at about 6.6° E, which is not influenced by the cirrus at the Learjet level, albeit showing cirrus occurrence at the TOSS (see Fig. ). Values of relative humidity with respect to ice based on measurements of H2O mixing ratios, temperature, and pressure at the Learjet do not exceed 70 % in this segment of the flight (Fig. b). However, on the mixing line with higher N2O mixing ratios, corresponding to the flight segment with cirrus occurrence at the Learjet level, relative humidity exceeds saturation (RH_ice ≥ 100 %) inside the cirrus and reaches up to RH_ice = 140 % in close vicinity to the cirrus in clear air. The highest values of relative humidity coincide with the lowest potential temperature (Fig. a) during the entire flight leg. The presence of two distinct mixing lines suggests a different air mass history in terms of the occurrence of mixing events and contributing air masses for air above and in the cirrus layer.

In summary, during AIRTOSS-ICE, observations of a cirrus cloud located in an air mass with a distinct stratospheric chemical signature were obtained. The direct measurement of stratification inside the cirrus and in the surroundings with the dual-platform approach suggests reduced stability inside and strong stratification above the cirrus. The occurrence of cirrus particles in this air mass is accompanied by high relative humidity with respect to ice.

We analyze the structure of the UTLS as represented in the ICON simulation in a 2 h window around the observations presented in Sect.  and at the geographic location of the aircraft measurement (6.5–7.5 and 54.3–55.1° E; see also Fig. ), which we will refer to as “measurement area” in the following. Exact spatiotemporal matching of ICON and aircraft is not attempted, as the finite horizontal and vertical grid spacing as well as initial condition and model uncertainty make a perfect forecast of features on the scale discussed in Sect.  extremely unlikely. Nevertheless, as we will demonstrate in the following, the model is able to capture some key features of the observed UTLS and cirrus structure. This section focuses on the UTLS structure in the simulation started at 00:00 UTC on 7 May 2013; equivalent metrics for the simulation started 12 h earlier are shown in Appendix A. The latter simulation is also discussed in Sect. .

The modeled UTLS structure (potential temperature, potential vorticity, water content, and ice content) and its evolution in the area targeted by the flight is shown in Fig. . At the altitude of the aircraft measurements (Sect. ) the model locates the transition region between tropospheric, low-PV, and weakly stratified air and stratospheric, high-PV, and strongly stratified air (Fig. a, b). The simulated vertical profile of potential temperature (Fig. a) matches the transition from tropospheric to stratospheric stability at the aircraft location as observed (Fig. ). PV in the two model levels closest to the aircraft altitude increases rapidly from below 2 to 3 pvu on average, i.e., suggesting the location of the dynamical tropopause at around the altitude of the aircraft (Fig. b). This is consistent with ICON data interpolated to the Learjet position, which shows PV values in the range of 2–3 pvu (not shown), which is slightly lower than in ERA5. However, it should be noted that a vertical displacement less than the distance between two successive model levels suffices to significantly improve the consistency of ICON and ERA5. A slightly higher position of the modeled tropopause than in observations is supported by potential temperature at the aircraft altitude being about 1.5 K colder in the model (not shown). Over the considered time period from 14:00 to 16:00 UTC the vertical PV and potential temperature gradient at around 10.5 km altitude slightly increases.

The ice mass mixing ratio profiles suggest a cirrus cloud extending up to about 10.7 km in the model (Fig. c). Near-constant mass mixing ratios are simulated between 9.0 and about 10.0 km, with an increasingly rapid drop in the four model levels above. Over the analyzed 2 h time window the mass mixing ratio of ice gradually increases (Fig. c). Ice mass mixing ratios of around 0.1 mg kg⁻¹ are found up to PV values of about 4 pvu, which suggests the presence of ExTL cirrus consistent with observations (Fig. a). Vertical profiles subsampled for model columns with and without cirrus indicate that the potential temperature gradient in upper part of the cirrus layer is smaller than in the surrounding air and above the cirrus (Fig. b). Note, however, that the modeled stratification is substantially larger than the neutral stratification observed by the Learjet–TOSS platform. Consistent with the smaller vertical potential temperature gradient, PV values in the cirrus column are smaller than in the surrounding air (Fig. c).

The total water content, i.e., the sum of specific humidity and cloud condensate, remains almost constant throughout the considered 2 h time period (Fig. d). The humidity gradient changes rapidly at about 10.6 km altitude to larger values at higher altitudes. Hence, the tropospheric humidity gradient is continuing beyond the dynamical tropopause, consistent with the Learjet observations and the presence of a mixing-influenced ExTL.

The simulation with the earlier start time has a much higher tropopause with less sharp gradients. Therefore, the cirrus layer is found predominantly at tropospheric PV values (Fig. ). Hence, the match with observation is not as good as in the simulation with the later initialization date. Nonetheless, contrasting the two simulations provides insight into the processes leading to the cirrus formation and moisture content of the lower stratosphere as well as potential model deficiencies in the representation of diabatic PV production, as discussed in more detail in Sect. .

In summary, the model simulation contains an ExTL cirrus expanding to well above the local dynamical tropopause as well as reduced stratification in the cirrus. This structure of the UTLS is qualitatively consistent with the observations, although there are some small quantitative differences, e.g., concerning tropopause altitude.

The UTLS structure as observed with the Learjet/TOSS framework and captured by the ICON model emerges due to advection and diabatic processes in the hours and days before arrival over the North Sea. To investigate these processes we analyze high-resolution air mass trajectories from the ICON model simulations.

The path as well as the temporal evolution of PV and ice mass mixing ratio for trajectories arriving in the measurement area is shown in Fig. . The different rows show different subsets of trajectories: the first two rows show trajectories passing through areas with tropospheric (557 trajectories) and stratospheric (309 trajectories) air mass composition based on the Learjet/TOSS N2O measurements, respectively. The last row shows trajectories arriving in the measurement area with PV values larger than 2 pvu and ice mass mixing ratios larger than 10⁻³ mg kg⁻¹ (1511 trajectories). The PV values in tropospheric air are predominantly smaller than 2 pvu, with a few exceptions at the lowest pressures, which may be due to inconsistencies in the location of the local tropopause in the model and observations (fraction of trajectories with PV ≥ 2 pvu ≈ 7 %). The tropospheric air mass contains a thick cirrus layer consistent with the profiles shown in Sect. , which forms in slowly ascending air masses over southeastern Germany about 12 h before arrival in the measurement area (Fig. a–c). The ice mass mixing ratio displays strong temporal variability likely induced by gravity waves associated with the passage over the small mountain ranges in central Germany. These wave motions are superimposed on the general slow ascent as already discussed in . As will be discussed later, the cirrus evolution is consistent with the indication of cirrus presence from MSG satellite data (see Sect. ).

The trajectories arriving in the area with stratospheric air mass characteristics according to the observations are located on average at slightly higher altitudes, slightly further west (Fig. d–f), and arrive in the measurement area predominantly in the later half of the considered time interval (not shown). They also contain an extensive cirrus cloud, but PV values are predominantly around 2 pvu. Again some spatiotemporal inconsistency between model simulation and observed situation may explain the presence of some trajectories with PV values below 2 pvu. The cirrus structure and the general characteristics of the vertical motions are not systematically different from the trajectories traveling through the area with observed tropospheric characteristics. Importantly, this also holds when considering the subset of trajectories with stratospheric PV values and cirrus content in the model (Fig. g–i). The major differences are a shift towards even lower pressures and the dismissal of the easternmost origin region. As the general characteristics of the evolution do not differ substantially for the last two trajectory subsets, we focus in the following analysis on the trajectories with PV ≥ 2 pvu and qi > 10⁻³ mg kg⁻¹. This offers a physically consistent picture on the emergence of the observed ExTL cirrus.

The extensive cirrus cloud seen in Fig.  emerges in the 12 h before the arrival of the trajectories in the measurement area and arises by a combination of moist ExTL air over southern Germany (see discussion of Fig.  and Sect. ) and strong lifting of up to 25 hPa, which corresponds to a vertical displacement of about 1000 m (median: ≈ 500 m) (not shown), during its northward propagation. Cirrus clouds are formed in the model by deposition nucleation as indicated by the process rates from the different ice formation parameterizations in ICON traced along the trajectories, which are zero for all processes except deposition nucleation (not shown). Deposition nucleation may be overestimated by the used parameterization as it was developed for dust outbreak cases over central Europe. Relative humidity over ice RH_ice in the cirrus layer, which is completely below the homogeneous freezing temperature, peaks at around 120 %, consistent with deposition nucleation being the dominant mode of nucleation (Fig. a). If only cirrus clouds along trajectories with substantial deposition nucleation rates are considered, the small RH_ice values are not present anymore, because air parcels acquiring ice through sedimentation are excluded (compare filled and unfilled histograms in Fig. a). This distribution of relative humidity is consistent with observed relative humidity in cirrus clouds from IAGOS measurements .

The Lagrangian diagnostics allow us to assess the change in humidity during the transport. Figure b shows the Lagrangian change in total water content from 00:00 UTC on 7 May 2013 until the arrival of the trajectories in the measurement area. The dominant feature is a loss of total moisture of air parcels with less than 4 pvu, which coincides with the vertical extent of the cirrus deck. Hence, there is no indication that the ExTL air mass located between 2 and 6 pvu gained substantial moisture in the 12 h preceding its arrival in the measurement area. If considering the parcel's initial PV for constructing the vertical profile, the same structure emerges with small variations (not shown). This suggest that vertical scrambling of air parcels and non-uniformity of Lagrangian PV change does not affect our diagnostics of moisture change. The relatively high moisture content in the source region is consistent with evidence from MSG satellite data and radiosonde data over southern Germany (as discussed in detail later; see Sect. ).

The Lagrangian diagnostics further allow us to assess when the air parcels obtained their stratospheric characteristics at least in terms of their PV. Consistent with the visual perception of the data in Fig.  only a small fraction cirrus-forming trajectories passed the dynamical tropopause in the 12 h before the arrival in the measurement area (Fig. a): of the fraction of trajectories that contain ExTL cirrus in the measurement areas, only 12.5 % transition from below to above 2 pvu values in the considered time period and only 7.7 % do so after the formation of cirrus. These trajectories that undergo troposphere-to-stratosphere exchange arrive in the measurement area with PV values only slightly larger than 2 pvu (mean: 2.24; maximum 2.89 pvu). This is consistent with the relatively small ΔPV for parcels located close to the dynamical tropopause in Fig. a). Further, this implies that the majority of trajectories form cirrus in dynamically stratospheric air and cirrus is not “mixed in” from dynamically tropospheric air.

Diabatic PV modification becomes more important for parcels deeper into the ExTL: those arriving with PV values between 3 and 4 pvu gained about 1 pvu in the preceding 12 h (Fig. a). However, due to their larger initial PV values, these trajectories did not pass the dynamical tropopause in the considered time period. Evaluation of the PV budget along trajectories indicates the strongest contribution from changes in thermal stratification by radiative processes (red line) followed by changes in thermal stratification and momentum by turbulent processes (light- and dark-green lines). Below 3 pvu some negative PV tendency due to latent heating from cloud microphysics is evident (blue line). Note that the Lagrangian PV budget is difficult to close likely due to the reconstruction of PV and vorticity gradients on the staggered vertical grid followed by interpolation to the parcel positions. In particular, the turbulent PV tendency field is relatively noisy on the native model grid spacing (Δx ≈ 3.25 km), as has been noted by previous studies . Composite profiles of the PV and PV modification terms along the trajectories are therefore more useful in discerning the key physical mechanisms (note that the results are qualitatively consistent with the statistics along the trajectories). The compact nature of the trajectory bundle contributing to the ExTL cirrus and the limited vertical and horizontal shear allow a physical meaningful analysis of composite profiles, which are shown in Fig. b–f. Composites are constructed for different times t before the arrival of trajectories in the measurement area. The PV profile indicates a narrowing of the geometric vertical extent of the ExTL, if defined as the layer between the 2 and 6 pvu isoline (Fig. b). The trajectories forming the cirrus cloud in the measurement area (red hatching) travel in the ExTL, and the ExTL coincides with the top of the extensive cirrus deck (dots). The composite analysis suggests that the narrowing of the ExTL is mainly driven by increasing PV in the upper part of the ExTL, i.e., the highest-altitude parcels. Radiative PV modification provides a consistent source of increasing PV values close to the top of the cirrus deck, consistent with the expected PV change above a cooling maximum (from longwave emission) (Fig. c). Additionally, PV modification by turbulent processes is of similar amplitude but much more localized (Fig. d, f). Therefore, the overall impact of turbulence on the PV of the considered trajectories is smaller than that of the radiative processes. The (partly) compensating negative PV tendency from turbulent mixing at t = ≈ -8 to -4 h and positive PV tendency from turbulent mixing at t > -2 h contribute additionally to a reduction in the total impact of turbulence on the PV structure. In general, contributions from turbulent stratification changes are larger than but of similar sign to those from turbulent momentum transport. However, the momentum transport terms are still substantial and are an important, albeit often not quantified, contribution to the PV budget. PV modification from cloud microphysical processes, i.e., latent heating and cooling, in the ExTL is generally small and decreases PV (Fig. e). This is consistent with the PV modification expected above a latent heating maximum associated with the cirrus formation and ice crystal growth. The largest contributions are found around t = -6 h at the lower edge of the ExTL and appear to contribute to the narrowing of the ExTL by increasing PV on the tropospheric side. Note that this time period is also associated with the strongest radiative PV modification and is well aligned with the largest ice water content along the trajectories (Fig. c, f, i).

Overall, the ICON model simulations suggest that the observed cirrus cloud formed by slantwise lifting and gravity wave activity (see Fig. ) in an already moist ExTL air mass originating over southern Germany (≈ 12 h before arrival in the measurement area). The model provides no indication of moisture transport into the ExTL from the troposphere or evidence for substantial STE. However, the model suggests that the extensive cirrus deck results in an enhanced PV gradient and therefore a narrowing of the ExTL in terms of its geometric depths. This results from cloud microphysical PV destruction at the bottom of the ExTL as well as radiative and turbulent PV production at the top of the ExTL. Note that the modeled PV structure is consistent with the observed vertical potential temperature gradients by the Learjet/TOSS, i.e., near zero ∂θ∂z in the cirrus deck and much larger ∂θ∂z across the cloud top. Further, note that the observations suggest a much sharper cloud top than can be represented on the model vertical grid. This likely makes the discussed processes even more efficient in the real atmosphere.