2.1 GLORIA observations

GLORIA is a cryogenic limb-imaging spectrometer deployed on board high-altitude aircraft (Friedl-Vallon et al., 2014; Riese et al., 2014). Measurements are performed in limb mode (Fig. 1) to the right-hand side of the flight track. Using 128 vertical × 48 horizontal pixels of a HgCdTe detector, GLORIA passively observes the thermal radiation of the atmosphere in the spectral range from 780 to 1400 cm⁻¹. The pointing of GLORIA is stabilized using a gimballed frame, aided by an inertial navigation system. During each interferometer sweep, GLORIA records data cubes of interferograms with all pixels simultaneously. Thereby, the detector rows correspond with limb-viewing geometries with tangent altitudes typically between ∼5 km and flight level. In post-flight data processing, spectra of the detector rows within each data cube are binned to reduce uncertainties. The spectra are quantitatively calibrated using in-flight blackbody measurements (Kleinert et al., 2014).

GLORIA can be operated with different spectral sampling rates. Thereby, a higher spectral sampling results in a lower along-track sampling. Here, we use measurements in high-spectral-resolution mode (“chemistry mode”) with a spectral sampling of 0.0625 cm⁻¹. The resulting apodized spectral resolution of 0.121 cm⁻¹ (full width at half maximum) is particularly useful for resolving weak and narrow spectral signatures of minor species. In this measurement mode, one data cube resulting in one vertical sequence of calibrated spectra is recorded within 13 s. This corresponds with a net along-track sampling of ∼3 km.

Figure 1Illustration of GLORIA observation geometries (blue lines) with the carrier HALO moving away from the reader. Limb observations are characterized by their tangent points, where the line of sight is closest to the earth surface (red lines). Low tangent points are situated further away from the observer than high tangent points. The regions around the tangent points contribute the major part of the information derived in atmospheric parameter retrievals. Upward viewing observations have no tangent points along the line of sight and contribute limited information on the scenario above the flight track.

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The retrieval of atmospheric parameters from the high-spectral-resolution mode observations during PGS and their validation are reported by Johansson et al. (2018). Prior to the retrieval, the binned spectra are cloud-filtered according to the cloud index method by Spang et al. (2004). A variable threshold value is applied, increasing linearly from 3.0 for the lowest limb views to 1.8 at flight altitude. For the retrievals, the radiative transfer model KOPRA (Karlsruhe Optimized and Precise Radiation transfer Algorithm; Stiller et al., 2002) is used in combination with the inversion algorithm KOPRAFIT (Höpfner et al., 2001). Temperature is retrieved using 2×2 rotational–vibrational transitions of CO₂ in the micro-windows from 810.5 to 812.9 cm⁻¹ and 956.0 to 958.2 cm⁻¹. These micro-windows show a sufficient transparency at low altitudes. The spectral transitions used are suited well for a temperature retrieval, since they are sufficiently strong, clearly separable from other signatures, and characterized by different opacities and different temperature dependences. In the temperature retrieval, IFS high-resolution (HRES) operational analyses spectrally truncated at wavenumber 213 and at 137 vertical hybrid levels are used as initial guess and a priori information. The operational ECMWF data were interpolated directly to the GLORIA tangent points. The data are available every 6 h and are hereafter referred to as “HRES”. All retrievals are based on geometric altitude levels. Associated pressures are interpolated from the HRES data. GLORIA's potential temperature is calculated from the retrieved temperature and the HRES pressure field.

Ozone volume mixing ratio is retrieved using several rotational–vibrational transitions in the micro-windows from 780.6 to 781.7 cm⁻¹ and 787.0 to 787.6 cm⁻¹. The ozone initial guess and a priori profile is taken from Remedios et al. (2007). The natural logarithm of water vapour volume mixing ratio is retrieved using a single rotational transition in the microwindow from 795.7 to 796.1 cm⁻¹ and then converted to volume mixing ratio. For initial guess and a priori a vertically constant profile is applied; the value is the logarithm of 10.0 ppmv. In all cases, narrow micro-windows are chosen to minimize spectral interference with pressure-broadened signatures of other gases at lower altitudes. Typical vertical resolutions between 300 and 900 m are achieved between flight altitude and the lowest tangent point. Finally, the retrieved profiles are combined to 2-D vertical cross sections of the respective target parameters along the flight track.

2.2 ECMWF IFS forecasts

The IFS model is a global, hydrostatic, semi-implicit, semi-Lagrangian NWP model. The IFS cycle 41r1 was operational from 12 May 2015 until 8 March 2016 and utilized a linear grid with a spectral truncation at wavenumber 1279 (T_L1279), which corresponds to a horizontal resolution of approximately 16 km. In the vertical, 137 levels (L137) ranged from the model top at a pressure level of 0.01 hPa down to the surface. The vertical resolution in the vicinity of the extra-tropical tropopause is less than 400 m and increases with decreasing altitude. The IFS cycle 41r1 was replaced by cycle 41r2 on 8 March 2016. The horizontal resolutions of all the different operational applications using the IFS were upgraded (Hólm et al., 2016). The deterministic high-resolution analyses and forecasts are computed on a cubic octahedral grid with a resolution of approximately 9 km while the spectral truncation remained at wavenumber 1279 (T_L1279) (Malardel and Wedi, 2016). A large contribution to the gain in effective resolution of the IFS cycle 41r2 results from the reduced numerical filtering and the preparation of the physiographic data at the surface.

IFS cycle 41r2 was running in a pre-operational, experimental suite in January 2016. Here, 1-hourly short-term forecasts of the 00:00 UTC run at 09:00, 10:00, and 11:00 UTC are used. These data were interpolated to a regular ${\mathrm{0.25}}^{\circ }\times {\mathrm{0.25}}^{\circ }$ latitude–longitude grid and will be compared to the GLORIA observations. The IFS data are retrieved as fully resolved fields, containing all 1279 spectral coefficients. Background temperature fields are computed as a moving average within a horizontal window of 3^∘ in the meridional direction and 4^∘ in the zonal direction (∼330 km × 330 km). The difference between the fully resolved IFS temperature field (or the GLORIA temperature field) and the IFS background temperature field yields perturbations, which accentuate mesoscale temperature variations, e.g. due to mountain waves.

Studies using the same IFS cycle are reported in the literature: Ehard et al. (2018) documented the high fidelity of the IFS fields representing the mean stratospheric temperature over Sodankylä, Finland (67.5^∘ N, 26.5^∘ E), in December 2015 and the gravity activity at this location in the winter of 2015–2016. Dörnbrack et al. (2017) compared the mesoscale structure of mountain-wave-induced polar stratospheric clouds with the simulated temperatures of the IFS and found a remarkable agreement with the space-borne measurements.

2.3 GLORIA observational filters

There are two ways to compare the GLORIA data resulting from radiance integrated along extended limb views (Fig. 1) with the numerical IFS fields. First, the time-dependent 3-D IFS data are linearly interpolated in space to the GLORIA tangent points which are provided as function of latitude, longitude, altitude, and time. This procedure does not take into account the horizontal smoothing characteristics intrinsic to the GLORIA observations. As a second approach, the observational filters of the GLORIA observations are characterized. In effect, we calculate exemplary 2-D averaging kernels (Ungermann et al., 2011) providing the horizontal and vertical smoothing characteristic along GLORIA's viewing direction (i.e. perpendicular to the flight track). These averaging kernels are then used to smooth the IFS data for comparison. While the first approach is straightforward, the second one requires the following calculation of the 2-D averaging kernels.

According to Rodgers (2000), the averaging kernel matrix $\mathbf{A}\in {\mathbb{R}}^{n\times n}$ is the product of the gain matrix $\mathbf{G}\in {\mathbb{R}}^{n\times m}$ and the Jacobi matrix $\mathbf{K}\in {\mathbb{R}}^{m\times n}$. Thereby n is the number of retrieval grid levels (i.e. altitudes) and m the number of elements of the measurement vector (i.e. spectral grid points within the micro-windows used, for all vertical viewing angles of the measurement). By multiplying A with the delta between an estimate of the true atmospheric state x (e.g. model data or in situ profile) and the a priori profile x_a used for the retrieval, the atmospheric state projected by the retrieval $\widehat{\mathit{x}}$ (i.e. smoothed model or in situ profile) can be calculated as follows (measurement errors neglected):

This approach is often used for comparing in situ observations or model data of high vertical resolution with a retrieval result with a lower vertical resolution. However, this approach involves a single profile representing the true atmospheric state and assumes homogenous conditions along the viewing direction.

According to Ungermann et al. (2011), a number of profiles representing the true state along the viewing direction can be involved in cases where this condition is not fulfilled. A modified averaging kernel matrix $\stackrel{\mathrm{̃}}{\mathbf{A}}\in {\mathbb{R}}^{n\times (n\cdot o)}$ can be used to replace A in Eq. (1), with o representing the number of profiles used to sample the variation along the additional dimension along the viewing direction. The 2-D averaging kernel matrix $\stackrel{\mathrm{̃}}{\mathbf{A}}$ is calculated as the product of G and a modified Jacobi matrix $\stackrel{\mathrm{̃}}{\mathbf{K}}\in {\mathbb{R}}^{m\times (n\cdot o)}$ including the additional horizontal dimension. The individual Jacobi matrix elements are calculated for all elements of the measurement vector and with reference to all discretized retrieval grid levels (vertical domain) and locations along the viewing direction (horizontal domain). We calculate $\stackrel{\mathrm{̃}}{\mathbf{K}}$ using the 3-D inhomogeneous radiative transfer routine of KOPRA (von Clarmann et al., 2009). The calculations of the elements of $\stackrel{\mathrm{̃}}{\mathbf{K}}$ are extensive, since the retrieval micro-windows used in the GLORIA high-spectral-resolution mode include many spectral grid points. Together with the large number of viewing angles of a single GLORIA data cube (i.e. up to 128, depending on quality and cloud filtering), large sizes result for $\stackrel{\mathrm{̃}}{\mathbf{K}}$.

Figure 2GLORIA observational filters including the horizontal domain along the line of sight. The plots show rows of the 2-D averaging kernels $\stackrel{\mathrm{̃}}{\mathbf{A}}$ for the logarithm of water vapour (a, c, e) and temperature (b, d, f) corresponding with the retrieval grid levels indicated at the top of the panels. Black dots in all panels: retrieval grid tangent points of the GLORIA retrieval.

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Our aim is to apply the horizontal smoothing procedure for water vapour and temperature and only for two subsections of the flight (i.e. the two passages of the tropopause fold). Therefore, we calculate $\stackrel{\mathrm{̃}}{\mathbf{K}}$ and $\stackrel{\mathrm{̃}}{\mathbf{A}}$ for each target parameter only for a single observation characteristic for the respective flight passage. The resulting observational filters $\stackrel{\mathrm{̃}}{\mathbf{A}}$ for water vapour and temperature are then applied to sample the IFS data of the entire passage. A horizontal discretization of 25 km is chosen to calculate the elements of $\stackrel{\mathrm{̃}}{\mathbf{K}}$ along the horizontal dimension, i.e. along the viewing direction. Since the calculation of $\stackrel{\mathrm{̃}}{\mathbf{K}}$ takes into account the entire light paths of the limb views up to the top of the atmosphere, the discretized elements of $\stackrel{\mathrm{̃}}{\mathbf{K}}$ are calculated within 1500 km along the viewing direction. The resulting contributions of $\stackrel{\mathrm{̃}}{\mathbf{A}}$ far beyond the tangent points are, however, negligible. Therefore, elements of $\stackrel{\mathrm{̃}}{\mathbf{A}}$ beyond 600 km are omitted in IFS data sampling.

In the case of temperature, $\stackrel{\mathrm{̃}}{\mathbf{A}}$ is used together with x (including the o model profiles along the viewing direction) and x_a (including o times the a priori profile) to calculate a single smoothed IFS profile $\widehat{\mathit{x}}$ for the comparison with a single corresponding GLORIA profile. In the case of water vapour, $\stackrel{\mathrm{̃}}{\mathbf{A}}$ is calculated with respect to the natural logarithm of the volume mixing ratio. Since the 3-D inhomogeneous radiative transfer routine of KOPRA provides the Jacobi matrix elements corresponding with volume mixing ratio and not the logarithm, the matrix elements of $\stackrel{\mathrm{̃}}{\mathbf{K}}$ are post-differentiated with respect to the logarithm of volume mixing ratio. The logarithms of x and x_a are then used in the smoothing procedure of the IFS data.

Figure 2 shows exemplary rows of $\stackrel{\mathrm{̃}}{\mathbf{A}}$ for water vapour and temperature for the first tropopause fold passage (figuratively: n⋅o horizontal profiles out of a single row of $\stackrel{\mathrm{̃}}{\mathbf{A}}$, stacked above each other). The individual panels show how a single-state element of the retrieval result (i.e. target parameter at altitude level indicated at the top of a panel) responds to an atmospheric grid point along the viewing direction (characterized by geometric altitude and horizontal distance) in the true state (Ungermann, 2011; Ungermann et al., 2011). Thereby, “constructive” contributions (in red) correspond with atmospheric grid points where a higher (lower) value in the true state results in a higher (lower) value in the retrieval result. However, “destructive” contributions (in blue) correspond with atmospheric grid points where a higher (lower) value in the true state, counter-intuitively, results in a lower (higher) value in the retrieval result. In this manner, the response of the retrieval and its weighting functions in the vertical and horizontal domain along the viewing direction are characterized.

In Fig. 2, $\stackrel{\mathrm{̃}}{\mathbf{A}}$ is calculated for the measurement at a geolocation at 725 km along flight path (compare Fig. 8). Thereby, the latitude of the uppermost tangent points is ∼42.46^∘ N (compare Fig. 6). For the second passage (not shown), $\stackrel{\mathrm{̃}}{\mathbf{A}}$ was calculated for the measurement at a geolocation at 2852 km along flight path, with the uppermost tangent points at ∼42.33^∘ N. In the case of water vapour (Fig. 2a, c, and e), the plots show the response of the logarithm of water vapour at the indicated retrieval grid level to variations in the logarithm of water vapour in the true state (i.e. interpolated IFS data) along the viewing direction. In the case of temperature, the response of retrieved temperature at the indicated level to variations of temperature in the true state along the viewing direction is shown in the same manner (Fig. 2b, d, and f).

Figure 2a and b show the situation at a retrieval grid level of 12.25 km, which approximately coincides with the flight altitude (∼12.40 km) during the measurement. In the case of the logarithm of water vapour (Fig. 2a), the retrieval result is dominated by constructive contributions within an arched lobe peaking ∼50–100 km away from the observer. Further significant constructive contributions originate from locations closer to the observer position, and also a long tailing towards higher altitudes further away is noted. Another significant destructive lobe is found above the dominating constructive lobe. Here, the presence of more water vapour in the true state diminishes the retrieval result at the indicated level. For temperature (Fig. 2b), the result is similar to the logarithm of water vapour. Here, the constructive lobe peaks slightly closer to the observer position at a distance of ∼25–75 km.

The response at the retrieval grid level of 10 km is shown in Fig. 2c and d. For both the logarithm of water vapour and temperature, the arched constructive lobes are centred approximately at the corresponding retrieval grid tangent point. However, the main maxima are shifted by about 50 km towards the observer and a few hundreds of metres to higher altitudes. Behind the tangent point, the constructive lobes extend further to higher altitudes in both cases. Furthermore, a weak destructive lobe is found on top of the dominating constructive lobe in both cases. Overall, the bulk response is found in a region roughly within about ±100 km around the tangent point (i.e. shifted slightly to the observer in the case of temperature).

The responses at 8 km shown in Fig. 2e and f show a similar pattern. In the case of the logarithm of water vapour (Fig. 2e), again a constructive main lobe and a weak destructive lobe are found. Their maxima are aligned more symmetrically around the corresponding tangent point when compared to Fig. 2c and d. In the case of temperature (Fig. 2f), both the constructive main lobe and the weaker destructive lobe develop to be stronger at the observer-facing side of the tangent point, with the extrema shifted by ∼50 km to the observer. Again, the bulk response originates from a region within about ±100 km around the tangent point (i.e. in the case of temperature shifted slightly to the observer).

Overall, the results in Fig. 2 show that the retrieval results at certain altitudes are affected significantly by regions around and above the tangent points as a consequence of the viewing geometry and the retrieval algorithm. This is of particular importance for comparisons with highly resolved model data including local fine structures (see Fig. 6b). In the following, we use exemplary observational filters $\stackrel{\mathrm{̃}}{\mathbf{A}}$ both for water vapour and temperature, calculated for the respective tropopause fold passages for detailed comparisons with the IFS.

2.4 In situ observations

The temperature data retrieved from the GLORIA observations are compared with static air temperature at flight altitude provided by HALO's Basic Halo Measurement and Sensor System (BAHAMAS, Krautstrunk and Giez, 2012). The static air temperature data are characterized by a total uncertainty of 0.5 K and are available with a temporal resolution of 1 s. Furthermore, vertical profiles of temperature and water vapour retrieved from the GLORIA measurements are compared with the radiosonde profile of the 12:00 Z (11:00 UTC) launch from LIRE Pratica Di Mare (station number 16245) on the flight day (available at http://weather.uwyo.edu/upperair/sounding.html, last access: 10 October 2018). Typical radiosonde measurement uncertainties are 0.4 to 1 K for temperature, around 24 % for water vapour below −50 ^∘C, and between 5 % and 14 % at higher temperatures (Nash, 2015). However, low stratospheric water vapour mixing ratios are not resolved by the radiosonde data.

Figure 3Horizontal and vertical profiles of the HALO flight PGS06 on 12 January 2016: (a) flight legs (black line) and tangent points of GLORIA observations, colour-coded with tangent altitude in kilometres; (b) flight track (black line) and topography (black). Green arrows indicate flight direction. Contours: Horizontal wind (m s⁻¹, blue lines) and potential temperature Θ (K, ΔΘ=10 K, solid lines and ΔΘ=2 K, dashed lines up to Θ=360 K) at 13^∘ E from ECMWF IFS, valid at 10:00 UTC. Waypoints A, B, C, D, and E are mentioned in the text.

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4.1 Flight level data

Figure 7a shows GLORIA water vapour (red) and the pressure at flight altitude (black). The grey lines mark the constant 10 ppmv values of the initial guess and a priori profile used for GLORIA's water vapour retrieval. Regions highlighted in yellow indicate where the GLORIA tangent points passed the radiosonde launch site ±50 km. Right at waypoint A, GLORIA measured dry stratospheric air of about 3–5 ppmv at the cyclonic shear side of the PFJ. Further southward, water vapour mixing ratios increased gradually as HALO approached the tropopause layer. Water vapour varied at upper tropospheric mixing ratios between >6 and 22 ppmv up to waypoint B. Thereby, the strongly oscillating signature of the observed water vapour might be related to the wave-induced up- and downdrafts along GLORIA's viewing paths (see Fig. 5a, b). At a distance of ∼800 km, HALO had to lower the flight level by ∼10 hPa temporarily for safety reasons (see dip in pressure in Fig. 7a). Here, an unexpected feature is observed. While the water vapour mixing ratio of ∼9 ppmv before the descent would be assumed to increase, the opposite is found: the water vapour mixing ratios drop back to stratospheric values of about 5 ppmv at minimum and rise again to ∼9 ppmv as HALO climbed back to 180 hPa (FL410). Bramberger et al. (2018) explain this flight sequence in detail and GLORIA's water vapour observations can be interpreted by the abruptly changing sign of the vertical wind induced by the mountain waves along HALO's flight track. Thus, GLORIA measured descending dry stratospheric air related to the mountain waves at this location. The subsequent ascent of HALO to FL430 (∼160 hPa) after waypoint B brought the observed water vapour mixing ratios back to stratospheric levels. The amplitude of the water vapour oscillations along the northbound leg are much smaller since HALO was flying entirely inside stratospheric air masses.

Figure 7Comparison of GLORIA data with in situ data along flight track and radiosonde data. (a) GLORIA water vapour and initial guess and a priori data along flight track. (b) GLORIA temperature data, HRES initial guess and a priori data, and BAHAMAS in situ data along flight track. Flight altitude in (a) and (b) is shown in black and refers to the right y axis. Windows highlighted in yellow correspond with the passages of the radiosonde launch site. (c, d) GLORIA water vapour profiles and constant 10 ppmv initial guess and a priori profiles during first and second passage of the radiosonde launch site together with the radiosonde profile. (e, f) GLORIA temperature profiles and HRES initial guess and a priori profiles during first and second passage of the radiosonde launch site together with the radiosonde profile.

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Figure 7b shows the comparison of GLORIA temperature data (red) with the BAHAMAS temperature data (blue) along the flight track. The ECMWF HRES temperature data used as initial guess and a priori information for the GLORIA temperature retrieval are superimposed as a grey line. The smooth HRES profile follows the BAHAMAS data, roughly indicating that the HRES data represent the large-scale meridional temperature variations very well. Likewise, GLORIA's retrieval results follow the in situ observations very closely. However, the GLORIA measurements reveal stronger temperature variations and more scattering than the HRES profile. In some flight sections (e.g. 900 to 1400 km and 3300 to 3700 km), the GLORIA results clearly resemble the BAHAMAS data more closely than the much smoother HRES data.

However, there are moderate deviations between the GLORIA and the BAHAMAS data which can be explained by the different regions sampled, since the horizontal focus of the GLORIA observations at flight altitude is located about 50 km away from the carrier. For example, the negative offset of GLORIA temperature by 1–2 K compared to BAHAMAS directly south of waypoint A could be produced by zonal temperature gradients induced by the mountain waves whose phases are nearly aligned parallel to the flight track; see Fig. 5c and d. Moreover, a strong anti-correlation is seen between the GLORIA and BAHAMAS data during the first crossing of the radiosonde launch site. There, the BAHAMAS temperature drops by more than 5 K within several tens of kilometres, while the GLORIA temperatures rise by 2–3 K at the same time. This anti-correlation can be explained by the mentioned phase orientation of the mountain-wave-induced temperature perturbations. While HALO streaked along a strong local temperature minimum, the GLORIA temperatures observed remotely were dominated by a wave-induced, local temperature maximum located west of the flight track.

4.2 Radiosonde sounding

Figure 7c–f compare the GLORIA profiles with the LIRE radiosonde sounding at 11:00 UTC during the first and second HALO passages of the launch site. All GLORIA profiles from the two segments marked in yellow in Fig. 7a and b are considered for the comparison. In the case of water vapour (Fig. 7c and d), the constant 10 ppmv initial guess and a priori profile is also shown. As background reference for temperature, the initial guess and a priori HRES profiles are added again (Fig. 7e and f). While the geographical match of GLORIA tangent points covering the launch site was better during the first passage (Fig. 7c, e), the time period of the second passage suits the sounding better (Fig. 7d, f; GLORIA data measured shortly after 11:00 UTC). However, during the second passage, GLORIA was pointing away from the launch site, and a v-shaped gap is found in the tangent point distribution due to a slight azimuth turn of HALO and a data gap. The vertical resolution of the GLORIA profiles as derived from the traces of the usual 1-D averaging kernels of the profiles are shown on the right-hand-side panels of Fig. 7c–f. They amount to 300 to 600 m below flight altitude. Further down, the vertical resolution deteriorates towards about 900 m. Above the flight level, the vertical resolution decreases rapidly due to the sampling characteristics of the airborne limb observations.

Below the flight level and above 11 km altitude, both the GLORIA and radiosonde data show typical dry stratospheric water vapour mixing ratios, which increased markedly to tropospheric values below 10 km (Fig. 7c, d) as HALO was located south of the tropopause break; see Fig. 3b. The sounding indicates H₂O mixing ratios of around ∼100 ppmv down to 7 km whereas the GLORIA profiles measure larger values up to 800 ppmv. During the first passage, all the GLORIA profiles show qualitatively the same altitude dependence (Fig. 7c). Both GLORIA and the sounding detected the strong decrease in water vapour associated with the stratospheric intrusion at about 6 km altitude. During the second passage, however, two different GLORIA profiles are found (Fig. 7d). While one branch (red) follows the radiosonde data closely, the second branch (green) remains at very low stratospheric water vapour levels at all altitudes. The absence of a smooth transition between the two branches can be explained by a data gap and slight azimuth turn of HALO. As a consequence of both, GLORIA's viewing direction changed, and horizontally separated air masses with different humidity were sampled. Unlike the GLORIA measurements, the sounding data indicate another dry stratospheric intrusion as a water vapour minimum at around 5 km altitude.

The comparison of the GLORIA temperature profiles with the radiosonde data are shown in Fig. 7e and f. The temperature sounding shows a vertical profile where the tropopause is characterized by a pronounced inversion at about 12 km, the tropopause inversion layer (TIL). GLORIA observations reproduce the TIL as well as the upper tropospheric lapse rate very well during the first passage on the southbound leg. During the second passage, as for the water vapour profiles, two profile branches are visible in the GLORIA data: one set of profiles (red) follows closely the sounding below 12 km altitude and shows a sharp TIL. The other one (green) associated with the dry air masses exhibits a lower lapse rate and temperatures lower by 10 K at 8 km. This suggests that dry descending stratospheric air within the tropopause fold is responsible for this finding. Furthermore, at the height of the H₂O minimum, the radiosonde sounding detected shallow layers of stably stratified air (Fig. 7e, f). The coincidence of local inversions with low water vapour values is in agreement with the conceptual picture of stratospheric intrusions into the troposphere, as mentioned in the Introduction. Unfortunately, no GLORIA data exist at these lower levels.

Figure 8GLORIA observations of water vapour mixing ratio (a), absolute temperature (b), and ozone mixing ratio (e) along two passages of the tropopause fold. IFS water vapour mixing ratio (c) and temperature (d) interpolated to the GLORIA tangent points. IFS horizontal wind V_H (m s⁻¹, dashed lines, ΔV_H=10 m s⁻¹) is superimposed on (b) and (d), GLORIA potential temperature Θ (K, solid and dashed lines, ΔΘ=4 K) on (e). Bold solid lines in all panels mark HALO's flight levels. Waypoints mentioned in the text are denoted by A, B, C, and D.

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5.1 Overview

Figure 8a, b, and e overview the water vapour, temperature, and ozone distributions observed by GLORIA between waypoints A and D. The tropopause fold can be identified by extruding dry and ozone-rich air extending down and southward from the stratosphere into the troposphere. The tongue-like extensions of stratospheric air are located between 300 and 800 km during the southbound as well as between 2700 and 3300 km during the northbound leg (Fig. 8a, e). Within the tropopause fold, narrow bands of dry filaments with enhanced ozone values suggest advective processes as the main driver of their formation. Both at the upper north and lower south edges of the tropopause fold, gentle horizontal H₂O gradients point to diffusive processes levelling the troposphere–stratosphere contrast out. Temperature observations across the tropopause fold confirm the expected reversal of the meridional temperature gradient from the lower troposphere to the upper troposphere, which is responsible for closing the jet stream in the lower stratosphere (Fig. 8b). South of the tropopause fold at the anticyclonic side of the PFJ, GLORIA observed a rather gradual, diffusive transition of high tropospheric to very low stratospheric H₂O values between 300 and 180 hPa. At certain places, high H₂O values seem to be injected into stratospheric altitudes. Interestingly, the low ozone values in this part of the flight suggest that the air is mainly transported upwards; there are only a few segments where ozone mixing ratios are enhanced, indicating mixing processes between the stratosphere and troposphere. We refer to this layer as the extratropical transition layer (ExTL), Gettelmann et al. (2011), as it marks the crossover from tropospheric to stratospheric air. Moreover, the presence of rather cold stratospheric spots with T<215 K (maybe wave-induced) and clouds (blocked areas in Fig. 8a, b, and e) point to non-adiabatic processes such as radiative cooling and cloud formation.

The corresponding IFS cross sections of water vapour and temperature taken at 10:00 UTC and interpolated to the GLORIA tangent points already reveal a remarkable agreement with the GLORIA observations (Fig. 8c, d). The tropopause fold is identified at the same position as in the GLORIA observations and its vertical and horizontal extents are similar to the observations. However, the H₂O values inside the fold are higher and the observed separated dry filaments are missing in the IFS data. Although the structure of the tropospheric water vapour distribution is well represented by the IFS, there are notable deviations from the GLORIA observations. In particular, the IFS simulates much smaller vertical H₂O gradients in the transition zone from tropospheric to stratospheric air near the tropopause. Furthermore, higher water vapour mixing ratios reach up to higher altitudes and the very dry stratospheric air sensed by GLORIA north of PFJ is only partly reproduced. The comparison of GLORIA's temperature with the IFS field shows a remarkable agreement (Fig. 8b, d). Again, local deviations occur. For example, the observed temperature maximum around flight altitude at a distance of about 700 km and the cold spots south of the tropopause fold are reproduced moderately by the IFS.

Figure 9GLORIA observations of water vapour mixing ratio (a–b) and of ozone mixing ratio (e–f) for the southbound leg (a, c, e) and the northbound leg (b, d, f), respectively. Superimposed on panels (a), (b), (e), and (f) is potential temperature Θ (K, solid and dashed grey lines, ΔΘ=4 K), derived from GLORIA temperature observations and HRES background pressure. Panels (c) and (d): IFS water vapour mixing ratio sampled using GLORIA observational filters. Horizontal wind V_H (m s⁻¹, solid and dashed grey lines, ΔV_H=5 m s⁻¹) is superimposed on (c) and (d). Bold solid lines in all panels mark HALO's flight levels.

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5.2 Mesoscale fine structure

The IFS data used to compare with the GLORIA observations as shown in Fig. 8 were interpolated directly to the tangent points. However, in the presence of horizontal H₂O and temperature gradients and mesoscale fine structures along GLORIA's line-of-sight view, the horizontal smoothing characteristics of GLORIA may affect the comparison significantly. Therefore, we apply the observational filter in the following to sample the IFS data as outlined in Sect. 2.3. Figure 9a and b display close-ups of the retrieved water vapour distributions along the tropopause fold during the south- and northbound legs, respectively. In the same way, Fig. 9e and f show the ozone distributions.

Essentially, Fig. 9 juxtaposes snapshots of a tropopause fold at two different stages of its evolution which are separated by about 2.5 h and sampled in different viewing directions. GLORIA water vapour and ozone measurements show remarkably well-resolved signatures of stratosphere–troposphere exchange: tongues of dry and ozone-rich stratospheric air intrude deeply into the troposphere (Fig. 9a, e). The observed distribution of the potential temperature reveals descending isentropes in agreement with the conceptual view of the processes inside the tropopause fold. Simultaneously, moist tropospheric air with low ozone values is entrained into the stratosphere. This happens in the vicinity of and above the core of the PFJ above about 280 hPa where the isentropic surfaces are folded and indicate mixing processes (Fig. 9a, e); see Sect. 5.4. In contrast, the sharper horizontal H₂O gradients at the southern and lower side of the tropopause fold are indicative of advective processes extruding dry stratospheric air down. During the second passage, essentially the same overall structure of the tropopause fold was observed (Fig. 9b, f). However, the intruding filaments of low H₂O and high ozone are much fainter inside the fold. Furthermore, the water vapour distribution in the jet stream region appears notably smoother. Again, a sharp contrast towards tropospheric water vapour is found in the lower compartment of the fold at the anticyclonic side. (Fig. 9b). The GLORIA observations as presented in Fig. 9a, b, e, and f are the first combined temperature and trace gas observations resolving a horizontally and vertically extended active mixing region belonging to a tropopause fold.

Figure 10Temperature perturbations ΔT (K, colour coded) and Θ (K, solid and dashed grey lines, ΔΘ=4 K) as derived from GLORIA's temperature measurements (a, b), IFS vertical wind (m s⁻¹, colour-coded) and V_H (m s⁻¹, solid and dashed grey lines, ΔV_H=5 m s⁻¹) at GLORIA tangent points (c, d), and IFS temperature perturbations ΔT (K, colour-coded) sampled using GLORIA observational filters (e, f) for the southbound leg (a, c, e) and the northbound leg (b, d, f), respectively. Bold solid lines in all panels mark HALO's flight levels.

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Figure 9c and d juxtapose the IFS water vapour fields using the respective observational filters $\stackrel{\mathrm{̃}}{\mathbf{A}}$ at 09:00 and 11:00 UTC, respectively. The application of the observational filters improves the agreement with GLORIA observations significantly (see Appendix A). Overall, the IFS water vapour distributions agree remarkably with the GLORIA observations. The tropopause fold is wrapped around the jet stream and is found at the same position as in the observation, and its overall shape compares well to the GLORIA measurements. However, the IFS fields appear to be too moist in the stratosphere and the very low H₂O values as observed by GLORIA were not reproduced. Furthermore, a smoother transition from tropospheric towards stratospheric mixing ratios is found in the IFS data. In spite of the rather high spatial resolution of the global IFS data, the filamentary structure inside the tropopause fold is not resolved.

5.3 Mountain-wave-induced temperature perturbations

Figure 10a and b display the observed temperature perturbations (versus IFS background temperatures; see Sect. 2.2) and the potential temperature along the south- and northbound legs, respectively. During the first passage of the tropopause fold, the GLORIA observations show large temperature perturbations exceeding ±3 K, whereas their values are slightly lower and mostly do not exceed ±2 K during the second passage on the northbound leg. Below about 300 hPa, the temperature perturbations reflect the large-scale meridional temperature gradient discussed above in relation to Fig. 8b: warm anomalies are located to the south, cold anomalies to the north. Above that level, the meridional gradient of absolute temperature reverses sign (Fig. 8b) and this is generally reflected here by warm temperature anomalies in the north and cold ones to the south (Fig. 10a and b). Moreover, there are alternating patterns of positive and negative temperature perturbations above about 300 hPa which indicate the presence of mountain waves. On the southbound leg, their phase lines extend from 45 to about 41^∘ N, whereas on the northbound leg they are restricted to the segment from 40 to 42^∘ N when HALO approached the Italian peninsula from the south again (Fig. 5).

As mentioned above, HALO flew nearly parallel to the phase lines of the vertically propagating mountain waves. This was confirmed by the IFS phase line orientations as documented in Fig. 5 and also by recent high-resolution numerical simulations presented in Fig. 11 in Bramberger et al. (2018). Therefore, the observed tilt of the phase lines and their changing vertical wavelength are related to the different propagation conditions in terms of wind and stability along the flight track. In particular, the temperature perturbations along the southbound leg show nearly horizontal orientation inside the core of the PFJ at around 42^∘ N. In this segment the largest temperature fluctuations were observed and they are related to the sudden and dramatic change of temperature and meridional wind at flight level which resulted in the stall event and the subsequent forced descent of HALO (Bramberger et al., 2018).

The vertical wind of the IFS short-term forecasts provides indication of the secondary circulation around the core of the PFJ. While the vertical velocity along the northbound leg (Fig. 10d) reveals nearly undisturbed upwelling south and downwelling north of the PFJ as expected, the vertical flow field is heavily disturbed along the southbound leg (Fig. 10c). There again, stacked alternating positive and negative values indicate the presence of mountain waves.

In the IFS data, the temperature perturbations mainly reflect the large-scale meridional temperature gradient (Fig. 10e and f). As shown in Appendix A, particularly for temperature, the application of the observational filter strongly improves the agreement with the GLORIA observations. Their amplitudes are, however, generally weaker than in the GLORIA observations. Exceptionally, the vertical structure of the temperature fluctuations north of the stall event around 500 km is well represented, indicating that the IFS captured the vertically propagating mountain waves at least partially. Overall, the IFS temperature perturbations reproduce the major structures found in the GLORIA data well. Temperature amplitudes are typically weaker by ∼1 K, and less fine structures are identified.

Figure 11Tracer–tracer correlations of GLORIA's water vapour and ozone profiles during both tropopause fold passages as function of the observed potential temperatures. All observational data along south- and northbound passages are included in the 2-D and 3-D illustrations in panels (a) and (b). Panels (c) and (d) display the southbound and northbound passage observations separately. Panels (e) and (f) show GLORIA water vapour (as in Fig. 9a and b), with data points characterized by ozone >65 ppbv and water vapour >12 ppmv marked by white diamonds (cf. dashed black lines in panels (a), (c), and (d); colour-coded points in panel (b); and Gettelmann et al., 2011, their Sect. 4.3). Θ (K, solid and dashed grey lines, ΔΘ=4 K) as derived from GLORIA's temperature and IFS horizontal wind V_H (m s⁻¹, bold magenta lines) are superimposed in panels (e) and (f).

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5.4 Mixing in the vicinity of the tropopause fold

Figure 11a–d show the tracer–tracer correlations of GLORIA observations between 40 and 45^∘ N as functions of potential temperature in different views. These plots include simultaneous GLORIA observations of water vapour, ozone, and potential temperature covering an altitude range of about 6 km below HALO's flight level. As expected, higher ozone values are correlated with low H₂O values and characterize the stratospheric tracer distribution along the vertical axis. Conversely, low ozone and high H₂O values represent the tropospheric tracer distribution along the horizontal axis (Fig. 11a, c and d). In general, the potential temperature follows the altitude dependence, i.e. lower Θ values are associated with high H₂O values and low O₃ values, and vice versa. Maximum water vapour values appear at the intermediate range of 310 K $<\mathrm{\Theta }<\mathrm{330}$ K, marking high tropospheric mixing ratios sampled south of the tropopause fold (compare Fig. 11b with high mixing ratios and isentropes south of the tropopause fold in Fig. 11e and f). Low H₂O values in Fig. 11a–d around Θ=310 and 320 K correspond to the stratospheric water vapour mixing ratios within the lower compartment of the tropopause fold, while the slightly enhanced H₂O values (up to ∼50 ppmv) below Θ=310 K mark the upper troposphere at the north of the tropopause fold (cf. Fig. 11b, e, and f).

Classically, the tracer relationship is used to define the provenance of the sampled air masses. Gettelman et al. (2011) used H₂O mixing ratios of less than about 12 ppmv as a threshold for stratospheric air and ozone values of less than about 65 ppbv as a threshold for tropospheric air. The respective thresholds are added in Fig. 11a, c, and d. This means that data points which are close to both tracer axes of the diagrams in Fig. 11a–d indicate an atmospheric state with no mixing and belonging either to the stratosphere or the troposphere (e.g. Plumb, 2007; Gettelman et al., 2011). Data outside these regions are called mixed regions of the ExTL. Typical aircraft observations of stratosphere–troposphere mixing along vertically stacked flight legs appear in such diagrams as so-called mixing lines connecting both reservoirs; see Fig. 11 in Gettelman et al. (2011). Here, the close-up image of the GLORIA observations along the individual legs reveals a widespread mixing area without individual mixing lines. These observations indicate active stratosphere–troposphere exchange in the vicinity of the tropopause fold. Between 330 and 350 K in particular, we find enhanced water vapour values, which are accompanied by notably enhanced ozone volume mixing ratios above 200 ppbv (Fig. 11b, c, and d). However, slightly enhanced ozone values up to 200 ppbv, which are accompanied by enhanced H₂O well above 20 ppmv, are found, particularly below 330 K. The change in the shape of the mixing region with potential temperature is visualized in Fig. 11b by colour-coding only data points falling into the 2-D mixing area.

To illustrate the locations of the mixing regions, data points indicative for the ExTL mixing region (water vapour >12 ppmv and ozone >65 ppmv) are flagged in the vertical cross section displayed in Fig. 11e and f. Particularly, the data points with Θ values between 330 and 350 K, sticking out most of all in the correlations (data points with ozone up to 400 ppbv and more at water vapour well above 12 ppmv), show compact distributions above the PFJ core which are tilted towards the fold. This suggests that the secondary circulation around the core of the PFJ (see Fig. 10c and d) entrains moist air from the troposphere at the anticyclonic side and mixes it into the stratosphere. Vice versa, the flagged data points characterized by lower Θ values below the PFJ core in Fig. 11e indicate mixing of stratospheric air masses into the troposphere due to advection and filamentation, probably intensified by the PFJ secondary circulation. Here, and also in the ExTL mixing region south of the tropopause fold, only weaker enhancements of ozone up to ∼200 ppbv are found for the data points attributed to the mixing zone. In Fig. 11f, the dense mixing region in the lower compartment of the fold is missing, probably due to the data gap between 42 and 43^∘ N. Figure 11b reveals how the mixing region changes, like on a spiral stair, from a predominantly tropospheric correlation (low ozone, strongly variable water vapour) below 330 K to a predominantly stratospheric correlation (low water vapour, more variable ozone). Thereby, the 330 K isentrope roughly separates the regions of stratosphere-to-troposphere and troposphere-to-stratosphere exchange.

The ExTL mixing zone during the first passage of the tropopause fold is notably disturbed by the mountain wave (see Fig. 11e). The wave-induced temperature anomaly (Fig. 10a) results in a distortion and spreading of the isentropic bands in the mixing zone between 41.5 and 43^∘ N above 270 hPa. This coincides with the clear air turbulence mixing region in the vicinity of the jet stream core (Shapiro, 1980) and suggests that ongoing mixing processes are altered. Moreover, the temperature anomaly results in a steepening and overturning of isentropes. The consequence is a region of convective instability, which further supports turbulence and mixing. When compared to the mixing zone associated with a tropopause fold near the subtropical jet stream in July 2006 analysed by Ungermann et al. (2013), a larger mixing region stretching deeper into the jet stream core is observed here. The large extent of the observed mixing zone thus might be a consequence of the interaction with the mountain wave.

Another interesting detail is found when Figs. 10c and 11e are compared: the separated narrow moist filament attributed to the mixing zone between ∼43.5^∘ N (250 hPa) and ∼42.5^∘ N (320 hPa) (Fig. 11e) coincides with the position and alignment of a region of wave-induced wind shear (Fig. 10c). While advection within the tropopause fold probably is the main driver for the formation of the filaments, the wave-induced wind shear is likely to enhance mixing processes here. Further complex patterns of the data points at the lower southern side of the PFJ attributed to the mixing zone are interpreted as being produced by the complex dynamics and mixing processes around the PFJ.