The DIAL WALES (Wirth et al., 2009) was developed at the German Aerospace Center (DLR) and has been operated on board the German research aircraft HALO since 2010. The instrument design is based on two identical laser systems that generate four wavelengths in the near-infrared (NIR) absorption band of water vapour between 935 and 936 nm, allowing for water vapour observations from the planetary boundary layer up to the stratosphere. WALES furthermore operates two polarization-sensitive channels at 1064 nm and at 532 nm. The latter channel comprises a high spectral resolution lidar (HSRL; Esselborn et al., 2008), enabling extinction coefficient observations and thus aerosol characterization (Groß et al., 2013). WALES and its underlying DIAL technique is briefly introduced in the following, and a more detailed description can be found in Wirth et al. (2009).

The four NIR wavelengths are separated into three online channels (strongly absorbed by water vapour) and one offline channel (weakly absorbed). The number concentration of water vapour in the probed volume is derived from the ratio of the backscattered light of the on- and offline wavelengths and then converted to specific humidity. The online channels are sensitive to different trace gas concentrations and in turn to different altitude levels. The exact wavelengths are selected such that they are optimally aligned to the moist boundary layer, the UT, and the dry LS. Note that the WALES humidity profiles are only available in cloud-free regions or regions with optically thin clouds. In optically thick clouds the extinction by cloud particles is so strong that no water vapour information can be retrieved within or below the cloud.

Due to the photon statistics of the backscattered light as well as detector and background light noise, the retrieved water vapour profiles undergo statistical variations, which are effectively reduced by temporal (i.e. horizontal) and vertical averaging. Thus, the retrieved DIAL water vapour profiles are averaged over 12 s or approximately 3 km in the horizontal. In the vertical, data are available every 15 m, although the effective vertical resolution is 300 m according to the full width of half maximum of the averaging kernel. It should be stressed that the averaging kernel of the WALES DIAL is exactly zero outside of about 2 times the effective resolution. This is in sharp contrast to most passive remote sensing techniques, where the side modes of the kernels can lead to erroneous dry or wet layers in the retrieved humidity profile. In the DIAL data retrieval, the statistical error of the observed volume is different for each flight and depends on the water vapour distribution and the background light. To remove high noise, typically occurring in dry air lying underneath moist air, for example, in the vicinity of stratospheric intrusions (Trickl et al., 2016), we filtered 5 % of the noisiest data for each individual flight. This threshold turned out to be useful but reduced the data availability in the lower- to mid-troposphere. Furthermore, Rayleigh–Doppler beam broadening, laser spectral impurity, and uncertainties in spectral databases are sources of systematic errors, which are compensated for in the retrieval algorithm. The total systematic error was found to be in the order of 5 % (Kiemle et al., 2008). The high reliability of WALES was demonstrated in various intercomparisons, for example, with Lyman-α in situ hygrometers (Kiemle et al., 2008), comparable airborne and ground-based DIAL instruments (Bhawar et al., 2011), and radiosondes with a frost point hygrometer (Trickl et al., 2016).

In this study, we use DIAL observations from six campaigns from 2013–2021 that provide almost 33 000 water vapour profiles obtained during 41 research flights. The profiles were sampled along the flight track and extend from the surface up to about 14 km altitude, corresponding to the maximum flight level of the HALO aircraft (Krautstrunk and Giez, 2012). As the focus of this study is the mid-latitude UTLS, we only consider flights that provide a significant amount of data across the tropopause. The majority (25) of these flights took place in the northern hemispheric autumn season during the North Atlantic Waveguide Downstream impact EXperiment (NAWDEX; Schäfler et al., 2018) and the Wave-driven ISentropic Exchange campaign (WISE; Kunkel et al., 2019). As part of the campaigns ElUcidating the RolE of Cloud-Circulation Coupling in ClimAte (EUREC4A; Stevens et al., 2021), the Next-generation Aircraft Remote sensing for VALidation studies (NARVAL; Klepp et al., 2014), and NARVAL2 (Stevens et al., 2019) measurements were taken during eight flights in the winter season. In addition, the Cirrus in High-Latitudes (CIRRUS-HL) mission provides observations in summer. Figure 1 depicts the parts of HALO research flights where DIAL observations were obtained. Most flights were carried out over the North Atlantic between 48 and 66∘ N, the North Sea and central to western Europe. Additionally, the subtropics (>35∘ N) and the Arctic were covered by individual flights as well.

During the WISE campaign, WALES was operated in a different setup to measure both water vapour and ozone, concurrently. For this purpose, two of the 935 nm NIR water vapour channels were replaced by two ultraviolet (UV) channels covering the 300–305 nm ozone absorption line (Fix et al., 2019). The use of two instead of four channels per trace gas leads to a reduced vertical coverage, which was optimized so that the selected NIR wavelengths cover the tropopause region. Increased statistical noise required averaging over a period of 24 s (∼ 6 km horizontally), while the effective vertical resolution remains approximately 300 m (Fix et al., 2019).

The number of observations with respect to latitude (Fig. 2a) illustrates the high data availability in the mid-latitudes, which is the region of interest in this study. This data set that covers humidity observations in a broad spectrum of synoptic situations is considered to be representative of mid-latitude weather. Figure 2b shows the distribution of the water vapour observations covering 4 orders of magnitude, ranging from 10-3 to 101 g kg-1. The bimodal shape of the histogram is composed of a broad moist part that can be assigned to the troposphere and a fraction of low humidity representing the dry conditions in the stratosphere. Each campaign exhibits an individual footprint of measured humidity, depending on the season, observation areas, and the flight level selection. For instance, the histograms for NAWDEX and WISE are remarkably similar since both campaigns took place over the North Atlantic in autumn. However, as only two NIR wavelengths were operated to measure water vapour during WISE, fewer measurements are available at high humidity levels. NARVAL shows a distinctive dry spectrum of measured humidity corresponding to the winter season, and fewer data are available for the LS, resulting from frequent low flight altitudes. The CIRRUS-HL summer campaign stands out because a large proportion of high moisture values was observed. The NARVAL2 and the EUREC4A campaign provide UTLS measurements only for one flight and, thus, compared to the other field campaigns, provide a small number of observations (see also Table 1).

ERA5 is the latest-generation reanalysis of the ECMWF based on the IFS Cycle 41r2 that was used for operational weather prediction in 2016. Atmospheric quantities are provided on a global grid with a horizontal resolution (TL639) of about 31 km and on 137 hybrid sigma-pressure model levels, ranging from the surface up to 0.01 hPa (∼ 80 km) in the vertical. The altitude range of the DIAL observations is covered by the lowermost 70 model levels. The vertical grid spacing of the model levels ranges from a few metres in the boundary layer to about 300 m at the tropopause level (Schäfler et al., 2020). ERA5 reanalyses are available with a time resolution of 1 h, which is an improvement compared to a 6-hourly resolution of its predecessor ERA-Interim (Dee et al., 2011). Further details about ERA5 are documented in Hersbach et al. (2020). For this study, model level data are retrieved on a regular 0.36∘ × 0.36∘ latitude–longitude grid. Pressure and altitude of each model level are derived following the IFS documentation (ECMWF, 2015). To be able to compare ERA5 and WALES data, the gridded model data are interpolated in space and time to the observation location. Our interpolation method uses a horizontally bilinear interpolation, followed by a linear interpolation in the vertical. Finally, a linear interpolation in time of the hourly ERA5 profiles towards the observation time is carried out. This sequence of interpolation steps has been applied similarly in other studies (e.g. Schäfler et al., 2010).

First, an example cross section of water vapour measurements of the research flight on 1 October 2017 during the WISE campaign is presented in Fig. 4. The case is selected as it possesses a good data coverage across the UTLS and as it additionally provides ozone observations (see Sect. 3.3). HALO flew meridional transects over the North Atlantic (50–60∘ N) at 13∘ W, aiming to measure a zonal jet stream and its associated predicted strong trace gas gradients. The underlying synoptic situation and the corresponding mission objectives are provided in detail by Schäfler et al. (2021). The left part of Fig. 4a (up to a distance of roughly 800 km) illustrates the water vapour distribution north of the jet stream (see magenta isopleths) where the aircraft flew above the low-located tropopause within the LS. HALO then crossed the pronounced jet stream with wind velocities of more than 90 m s-1. Near the jet core, the tTP altitude jumps from 6.5 to 14 km within a few kilometres' flight distance. The dynamical tropopause (2 PVU contour line) also displays the ascent of the tropopause and a corresponding tropopause fold that extends along inclined isentropes into the mid-troposphere. In the right part of Fig. 4a, the air mass located to the south of the jet stream exhibits high tropopause altitudes exceeding the flight level by roughly 2 km, so that measurements are restricted to tropospheric air. Along the entire cross section, the highest specific humidity is observed at the lowest levels in the UT, ranging from 10-2 g kg-1 to occasionally more than 10 g kg-1. The tropospheric air to the south of the jet stream has an increased humidity content compared to the air north of the jet stream. In the LS, specific humidity values lower than 10-2 g kg-1 are frequently observed. At a first glance, the specific humidity curtain of ERA5 (Fig. 4b) is very similar to the observations. However, the ERA5 humidity field appears to be smoother, particularly in the presence of strong horizontal water vapour gradients, for instance, near the jet stream and mesoscale filaments. Differences between observations and model, calculated by applying Eq. (3), are shown for the vertical section in Fig. 4c. Reddish regions indicate an overestimation of humidity by ERA5, while bluish areas represent an underestimation. High positive and negative values of the bias alternate below the tropopause. In the LS, a coherent region of positive values is detected between 1 and 3 km above the tTP, indicating an overestimated humidity that extends over the entire part north of the jet. At the highest altitudes, beyond 3 km above the tropopause, the moist bias is smaller. In order to study the systematic nature of the diagnosed LS moist bias and its vertical structure, a statistic of all observations in tropopause-relative coordinates is performed.

In the following it is examined to what extent the observed air masses have experienced mixing in their history and whether this is related to the vertical structure of the moist bias. For this purpose, we examine collocated ozone and water vapour observations that were collected during four WISE research flights and that provide a suitable data coverage. First, the observed ozone distribution for the same case study as introduced in Sect. 3.1 is shown in Fig. 10a. Note that the ozone and water vapour observations are given as volume mixing ratios (VMR) in the following. The distribution of ozone is opposite to that of water vapour, with the lowest concentrations (VMRO3 < 100 ppb) in the troposphere and an increase with altitude across the tropopause to VMRO3 > 500 ppb. Note the filamentary structures of increased ozone values in the LS and the ozone-rich air which is transported downward within the tropopause fold (see detailed description in Schäfler et al., 2022).

Following the approach by Schäfler et al. (2021), the collocated water vapour and ozone observations for four WISE flights are illustrated in tracer–tracer (T–T) phase space in Fig. 11, and three classes of observations are identified based on the characteristic distributions (e.g. Pan et al., 2004). First, tropospheric observations are characterized by low VMRO3 (typically < 100 ppb) and a large spread of VMRH2O. Second, high VMRO3 at low VMRH2O (<6.5 ppm or <4×10-3 g kg-1) is assigned to lower-stratospheric air. Third, a class with intermediate chemical characteristics (VMRH2O > 6.5 ppm and VMRO3 > 100 ppb) is attributed to mixed air masses that experienced mixing between the troposphere and stratosphere. Although Schäfler et al. (2021) suggested a careful selection of the threshold for individual flights, here constant values (see caption of Fig. 11) are used for all four WISE flights, which is sufficient to fundamentally identify the three air masses. Sensitivity tests with slightly varied thresholds have shown only a little impact on the distribution of the classes in geometrical space. Such a re-projection of the air mass classification from T–T space to geometrical space with a coherent distribution of the three classes is shown in Fig. 10b. Observations below the tTP are predominantly assigned to tropospheric air, while the uppermost data to the north of the jet stream are classified as stratospheric air. South of the jet stream, where the flight altitude is below the tTP, only tropospheric air is detected. In between the tropospheric and the stratospheric air, the mixed air mass is following the tropopause in a 2–3 km thick layer, which appears to be vertically deeper in the tropopause fold.

For each bin in T–T space, the average humidity bias and the mean tropopause-relative altitude are displayed in Fig. 12. The humidity bias is weak for both tropospheric and stratospheric air (Figs. 12a and 11b), ranging mostly between -0.25 and 0.25. In the mixed air class, the humidity bias is most pronounced (>0.25), particularly where the VMRH2O is below 40 ppm. In the tropospheric and stratospheric air, a stronger positive/negative bias is indicated for lower/higher VMRH2O, which is associated with the sharper humidity distribution in ERA5 (see discussion in Sect. 3.2.1). Figure 12b displays the tropopause-relative height, which is the vertical distance to the tTP, for each bin. Across the mixed air class, an increase of the tropopause-relative altitude is visible, corresponding to a decrease of VMRH2O and to an increase of VMRO3. At low VMRH2O (<10 ppm) and low VMRO3 (100–200 ppb), the transition of tropopause-relative altitudes is more abrupt, which is related to tTP variability across the jet stream, for example, as visible in the uppermost part of Fig. 10b. When comparing the tropopause-relative height with the distribution of the bias (Fig. 12a), it is noticeable that the average bias is particularly increased between 1 and 3 km, where it ranges from 0.5 (40 %) up to 1.25 (137 %). In contrast, the mean bias is weak beyond 3 km above the tTP and below the tropopause.

The average vertical profile of the moist bias for the WISE flights (Fig. 13a) is similar to the full data set (Fig. 5b) at the tTP and in the LS, i.e. a local minimum is found at the tTP (0.1; 7 %) and a pronounced maximum of 0.62 (54 %) peaking at about 1 km above the tTP. The tropospheric part of the profile, however, is almost constant in the full data set (0.2–0.25) but decreases with increasing altitude in the WISE data (0.4–0.1). Figure 13b shows the relative proportion of the individual air masses at a given tropopause-relative altitude and thus provides information about the connection between the vertical structure of the moist bias and the air mass classes. In the entire UT, the tropospheric air provides the largest contribution of more than 80 % up to 500 m below the tTP. Across the tTP, the proportion of tropospheric air rapidly decreases with altitude in accordance with a rapid growth of the fraction of mixed air. This is accompanied by an increase of the moist bias, and the altitude of the largest bias (1–2 km above the tTP) coincides with the maximum relative contribution of the mixed air class (>90 %). Above, the relative fraction of stratospheric air grows, while the moist bias reduces and reaches constant values (0.2) at ∼ 4 km above the tTP with a 65 %–85 % share of stratospheric air. Please note that contributions of mixed air below the tropopause and at altitudes >4 km above the tTP may be related to falsely detected tropopause altitudes (see discussion in Sect. 4) or situations of complex tropopause structure (e.g. as shown in the second part of Fig. 10b).