2.1 Data coverage and vertical distribution

The MOZAIC RH data set used for this analysis spans the period from 1995 to 2010 and is constrained to cruise altitude conditions, i.e. pressure below 350 hPa (above approx. 8 km altitude), and to ambient temperatures below 233 K to exclude potential sensor contamination by supercooled liquid water droplets. The aerial boundaries of the analysed data set are 40 to 60^∘ N and cover the eastern North American (105 to 65^∘ W), North Atlantic (65 to 5^∘ W) and European (5^∘ W to 30^∘ E) regions. Figure 1 illustrates the global coverage of water vapour observations by MOZAIC for the years 1995 to 2010. Inserted boxes mark the eastern North American, North Atlantic and European regions. The annual data coverage for each analysed regional box varies between 30 and 65 flight hours of MOZAIC aircraft per season (3 months), which corresponds to 27 000 to 60 000 data points of 4 s duration each per season per year. All investigated regions are characterized by continuous data coverage over the investigated period with no data gaps. Data are available through the open-access IAGOS data portal at https://doi.org/10.25326/20.

Figure 1Global coverage of water vapour observations by MOZAIC for the period 1995 to 2010 shown as decadal logarithm of the fraction of measurements in a certain grid box. Red boxes indicate the target areas for our analyses.

Since MOZAIC data are collected at constant pressure cruise levels of passenger aircraft which may cross from the upper troposphere (UT) through the tropopause layer (TPL) into the lowermost stratosphere (LMS) and back, the data vertical coordinates are reported relative to the tropopause pressure level.

The pressure levels of the thermal tropopause (p_therm.TPH) and the dynamical 2 PVU tropopause (p_dyn.TPH) were derived from ERA-Interim (ERA-I; Dee et al., 2011) which uses 60 model layers with the top of the atmosphere located at 0.1 hPa. For our analysis, the 6-hourly outputs from ERA-I (0.75^∘ × 0.75^∘) were interpolated onto a 1^∘ × 1^∘ horizontal grid and on 60 vertical levels of constant pressure and potential temperature (Kunz et al., 2014; Berkes et al., 2017). Additionally, the variables of the PV and the pressure of the thermal tropopause based on the WMO criteria were calculated (WMO, 1957; Reichler et al., 2003). The ERA-Interim data were then linearly interpolated with respect to longitude, latitude, pressure and time onto each flight track with a 4 s resolution, as described by Kunz et al. (2014). Interpolated tropopause pressure levels were finally used to determine the position of the aircraft relative to the thermal tropopause or to the 2 PVU isosurface and thus to distinguish whether the aircraft sampled air masses of UT, TPL or LMS origin with respect to the chosen tropopause definition.

In order to reach both a sufficiently large data set for robust statistical analyses and good vertical resolution, the ExUTLS is subdivided into seven layers of 30 hPa thickness each, with three layers located below the thermal tropopause height and three layers above. Thouret et al. (2006) used a similar definition but with reference to the dynamical tropopause at 2 PVU; i.e. they defined the tropopause as a mixing zone 30 hPa thick across the 2 PVU potential vorticity surface.

The seven layers of 30 hPa thickness each are centred at p_therm.TPH=0 hPa for the tropopause layer (TPL) itself and then at p_therm.TPH ± 30 hPa, p_therm.TPH ± 60 hPa and finally p_therm.TPH ± 90 hPa. From this vertical spacing, the separation of air masses is achieved by applying the following criteria (formulated for the thermal tropopause only).

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  LMS: $p<p_{\text{therm.TPH}}-\mathrm{15}$ hPa, which is limited by the maximum cruise altitude with p ≈ 190 hPa.

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  TPL: $p=p_{\text{therm.TPH}}\pm \mathrm{15}$ hPa.

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  UT: $p>p_{\text{therm.TPH}}+\mathrm{15}$ hPa, limited to lower altitudes by p < 350 hPa.

The bulk of our analyses refers to the classic thermal tropopause according to WMO criteria (WMO, 1957) with the exception of the occurrence of ISSRs above the tropopause, for which we present the analyses for both tropopause definitions and compare the results to learn more about the processes influencing the formation of ISSRs (see Sect. 3.3).

Since each data set from one single flight provides only a one-dimensional snapshot of the state of the atmosphere along the flight track and each aircraft cruises at a slightly different pressure level, the entire MOZAIC data are merged to season files of 3-month durations, allowing the analysis of vertical distributions of atmospheric state parameters on a robust statistical basis. For each season file, the statistical distribution (average and standard deviation, median, and percentiles) of investigated properties (temperature, O₃ VMR, H₂O VMR, RH_ice and ISSR fraction) is calculated with respect to the above-defined UT, TP and LMS vertical layers. From these seasonal averages or percentiles, respective 15-year mean values and standard deviations are determined.

In our study, we use statistical analyses in the following manner: when assessing results from laboratory studies and calibration experiments based on reproducible observations, we apply the 2σ criterion for the 95 % confidence level; when interpreting results from atmospheric observations which are taken from fast-flying airborne platforms that cover 15 years of observations, including their interannual and lateral variabilities, we report the mean values and respective 1σ standard deviations and state the statistical significance or insignificance, accordingly.

2.2 RH and O₃ instrumentation

The relative humidity measurements of MOZAIC and now IAGOS use a thin-film HUMICAP^® capacitive sensor (Vaisala) which is mounted inside an aeronautic Rosemount inlet attached to the aircraft's hull. The MOZAIC capacitive hygrometers (MCHs) are calibrated in the laboratory against a Lyman-α resonance fluorescence hygrometer (Kley and Stone, 1978) with respect to RH over liquid water (Helten et al., 1998; Smit et al., 2014). The conversion to RH_ice uses the equations by Sonntag (1994). The MCH reports RH data with an average uncertainty of 4 % RH (span 1 % to 6 % RH) in the middle troposphere at 4 to 8 km altitude during ascent and descent and 5 % RH (span 2 % to 8 % RH) at the tropopause and lowermost stratosphere at 10 to 12 km cruising altitude (Smit et al., 2014). The H₂O VMR was finally calculated from the simultaneously measured RH_ice and temperature data and from the pressure recordings of the aircraft avionic system.

The deployed sensor has been carefully compared to high-precision water vapour instruments in dedicated research aircraft studies (Helten et al., 1999; Neis et al., 2015a, b) which demonstrates a remarkably good agreement between the MCH and reference instruments with Pearson's R²=0.92 and a slope of m=1.02 from linear regression analyses. The authors report an MCH uncertainty of 5 % RH, which is in close agreement with the uncertainty determined from error propagation analysis (Smit et al., 2014).

Kunz et al. (2008), who performed a statistical analysis of water vapour measurements from the SPURT campaigns between 2001 and 2003 with a Lyman-α photo-fragment fluorescence hygrometer (Zöger et al., 1999; Meyer et al., 2015) and MOZAIC water vapour data from the same period, determined a limit of detection (LOD) of 10 ppmv for the MOZAIC sensor. Applying the same 2σ criterion (95 % confidence level), we obtain a MCH LOD of RH_ice,LOD=10 %, which again signifies a minimum detectable H₂O VMR of approx. 10 ppmv at typical mid-latitude upper tropospheric conditions (T=218 K, p=250 hPa) (see also Neis et al., 2015a, for a detailed discussion). As discussed by Smit et al. (2014), the uncertainty of the temperature measurement of the MCH sensor is included in the determination of the MCH RH_ice uncertainty so that the precision of H₂O VMR data deduced from MCH RH_ice data can be determined directly from the uncertainty of RH_ice measurements. Overall, the 5 % RH uncertainty leads to a decreasing precision of H₂O VMR deeper in the stratosphere and implies a limited use of the MOZAIC H₂O sensor in the stratosphere dominated by low RH_ice and thus an increasingly large uncertainty (Kunz et al., 2008).

The Pt100 temperature sensor of the MCH is characterized by an overall uncertainty of the ambient air temperature of ± 0.5 K, which includes the data processing (Berkes et al., 2017). The temperature range encountered during the MOZAIC observations in the ExUTLS ranges from 200 to 245 K at mid-latitudes (see Fig. 9 in Berkes et al., 2017, for details).

Since the launch of MOZAIC, the programme has also provided O₃ VMR data in addition to H₂O and RH_ice observations. On board the MOZAIC and now IAGOS aircraft, ozone is measured by means of a UV absorption instrument which is characterized by an instrumental noise of ± 2 ppbv and an integration time of 4 s (Nédélec et al., 2015). We used the collocated measurement of O₃ and RH_ice for the characterization of ice-supersaturated air masses with respect to a potential stratospheric influence.

2.3 RH data processing

The processing of the MCH data had been subjected to a calibration error from 2000 CE onwards. This error in the data analysis caused a bias of data towards higher RH_ice values and shifted the peak value of the RH_ice probability distribution function (PDF) for in-cloud observations to approx. 130 % RH_ice, which is far above the physically expected value of 100 % RH_ice. Earlier MCH data for the period 1995 to 1999, however, are not affected. The publications by Lamquin et al. (2012) (Fig. 5 of that publication) and Penner et al. (2018) (Fig. 6 of that publication) illustrate the shift of the erroneous MOZAIC data towards higher RH_ice values very clearly.

Figure 2Raw signal of the MOZAIC humidity sensor on board one MOZAIC aircraft as a function of the sensor temperature inside the aeronautic housing obtained at cruise altitude (z=9–12 km). Green line: zero signal from pre-flight calibration (PFC); blue line: superposition of zero signal from PFC and contribution of 5 ppmv water vapour; red line: zero signal from in-flight calibration (IFC).

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The calibration error was corrected in a recent reanalysis, and the PDFs of RH_ice are now consistent for the full MOZAIC period and physically reasonable with the PDF showing a second maximum at 100 % RH_ice, as expected for in-cloud segments (Smit et al., 2014).

Besides the calibration error, another limitation of the MOZAIC RH data set stemming from MCH sensor drifts required correction. In its standard operation mode, MCH sensors were replaced every 3 to 6 months. During their deployment periods, the sensors occasionally showed drifts of the sensor output signal caused by a shift of the sensor offset voltage, which results in erroneous RH_ice values. To overcome this measurement artefact, the so-called in-flight calibration method (IFC) was developed by Smit et al. (2008), which references the offset voltage of the sensor to signals from flight segments in dry stratospheric air masses where the expected RH_ice signal is below the MCH LOD, and thus the true MCH signal is considered zero RH.

The method is illustrated in Fig. 2; the MCH sensors leave the calibration facility with a baseline for dry conditions (green curve), the theoretical signal expected from the stratospheric H₂O background of 5 ppmv is then added, and this new baseline (blue curve) is the reference line for the offset determination. In the operational mode of the IFC method, the lower bound values of the MCH signal during an operational period of typically 15 consecutive flights are determined as the observations below the 1st percentile value (P01) of the data collected during the respective flight sequence. In the case of a sensor offset drift during MCH operation, the lower envelope from the P01 values is similar to the baseline for dry conditions at calibration plus the 5 ppmv stratospheric H₂O background value but shifted by a voltage offset. The difference between the lower envelope and the baseline from calibration determines the sensor offset voltage which is then subtracted from the raw signal. Details of the method are described by Smit et al. (2008).

2.4 RH data validation

The IFC method was applied to the full reanalysis data set from 1995 to 2010. Figure 3a illustrates the effect of the IFC method for the averaged RH_ice PDF for the entire MOZAIC data set, irrespective of the geographical regions where the data were collected. The average PDF and variability presented is calculated from annual PDFs. Solid lines refer to the MOZAIC average PDFs without the IFC method (white) and with the IFC method applied (blue). Grey areas (without IFC) and dashed and dotted blue lines (with IFC applied) represent the ± 1σ and ± 2σ ranges. Figure 3b shows a zoom into the PDF for the range with RH_ice > 100 %. In addition to panel (a), the red area marks the difference between the averaged PDFs with and without IFC applied.

Figure 3Averaged probability density functions of RH_ice for the entire MOZAIC period from 1995 to 2010 (a) and the zoomed in region of ice supersaturation (b). Data stem from the reanalysis (Smit et al., 2014) without (w/o: white line, grey areas) and with (w/t: blue lines) the in-flight calibration method applied to the data. The red-shaded area indicates the difference between IFC applied (w/t IFC) and not applied (w/o IFC), and vertical lines indicate the threshold RH_ice values for the homogeneous nucleation of ice at T= 205 K and T= 215 K (Koop et al., 2000).

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Figure 4Distribution of RH_ice for the entire MOZAIC period from 1995 to 2010 with IFC applied as a function of ambient temperature with the colour indicating the probability of occurrence. The lines represent water saturation (solid line; Sonntag, 1994) and the threshold RH_ice for homogeneous ice nucleation (dotted line; Koop et al., 2000; Kärcher and Lohmann, 2002).

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Figure 5Averaged probability density functions of RH_ice for the entire MOZAIC period from 1995 to 2010 with the in-flight calibration method applied (blue lines) and respective RH_ice PDF from 250 research aircraft flights collected in the Jülich in situ airborne database (Krämer et al., 2016).

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The overall features of the RH_ice PDF with an overall maximum value at dry stratospheric air mass values with RH_ice being close to the LOD of approx. 10 % and a second local maximum at RH_ice ≈ 100 % for observations inside cirrus clouds remain unaffected, whereas the deviation between the average PDFs becomes relevant for RH_ice values above 130 %. Here, the IFC leads to an average reduction of < 5 % RH_ice for an occurrence probability of 10⁻³ and approx. 7.5 % RH_ice for an occurrence probability of 10⁻⁴. More relevant, the 2σ variability of the observed ice supersaturations at 10⁻⁴ occurrence probability reduces from max. 180 % RH_ice (without IFC applied) to max. 155 % RH_ice (with IFC applied). The latter value with the IFC applied fits into the range of the homogeneous freezing thresholds at typical extratropical tropopause conditions of RH_ice,hom = 158.25 % at 205 K to RH_ice,hom = 154.15 % at 215 K (Koop et al., 2000), as sampled by MOZAIC. Respective values without the IFC applied, however, exceed the homogeneous nucleation threshold significantly. Unphysical negative values of RH_ice connected to observations below the LOD of 10 % RH_ice vanish within the range of uncertainty when applying the IFC method.

Figure 4 illustrates the distribution of RH_ice observations from the entire MOZAIC data set shown in Fig. 1 as a function of ambient temperature, colour coded by the probability of occurrence, i.e. the fraction of data points for a specific combination of temperature and RH_ice with respect to the entire ensemble. About 98 % of RH_ice observations remain inside the physical boundaries set by the water saturation line and the line for homogeneous ice nucleation. The remaining 2 % are considered outliers associated with aircraft manoeuvres. Overall, ice-supersaturated air masses are characterized by H₂O VMR ≥ 25 ppmv (1st percentile value; see Fig. 10 for details), which is in good agreement with observations of H₂O VMR > 15ppmv (Krämer et al., 2020) and 20 ppmv (Diao et al., 2014), both reported from research aircraft observations at mid-latitudes for T > 200 K (see also Sect. 3.3 for more details).

Besides the validation of MOZAIC RH_ice distributions with respect to the homogeneous nucleation thresholds from Koop et al. (2000), the data were compared to the distribution of RH_ice from observations on board of research aircraft by high-precision water vapour instruments such as Lyman-α photo-fragment fluorescence hygrometers (Zöger et al., 1999; Sitnikov et al., 2007), tunable diode laser absorption spectrometers (May and Webster, 1993; Krämer et al., 2009; Buchholz et al., 2013) and frost point hygrometers (see Meyer et al., 2015, for details). In total, 250 research flights from 32 field campaigns conducted between 1999 and 2017 globally were analysed. To ensure comparability to the MOZAIC data set, the temperature range was restricted to 205 to 235 K, which corresponds to the MOZAIC observation range with the upper temperature limit set by the homogeneous freezing threshold.

The result of this comparison is shown in Fig. 5. The MOZAIC RH_ice PDF is plotted similar to Fig. 3, whereas the RH_ice PDF from the research aircraft campaigns is shown as a red line calculated for RH_ice bin widths of 10 %. Both probability distribution functions show excellent agreement within the uncertainty ranges particularly for the regime of ice supersaturation (panel b). The differences for RH_ice near 100 % are caused by the preferred sampling of ice clouds during the field campaigns (higher probability of ice clouds at RH_ice ≈ 100 %) and by the frequent sampling of contrails at subsaturated conditions (RH_ice < 100 %).

RH_ice observations from the CARIBIC passenger aircraft exhibit similar features as the observations shown here from MOZAIC and from research aircraft with maximum probability of occurrence at RH_ice = 100 % and maximum RH_ice values of approx. 150 % (Dyroff et al., 2014). In that respect, all observation platforms provide consistent information on the distribution of ice supersaturation in the extratropical tropopause.

With the IFC method applied to the full MOZAIC RH_ice data, this data set is successfully validated against RH_ice observations by high-precision instruments and against physically justified bounding values. In summary, this data set is now considered of the highest possible quality achievable by the type of sensor applied and for the type of routine observations performed.

3.1 Annual cycles of water vapour and RH_ice distributions at the tropopause

The annual cycles of the vertical distributions of water vapour volume mixing ratio (H₂O VMR) and RH_ice were analysed for the three target regions of eastern North America (ENA), the North Atlantic (NAtl) and Europe (EU) based on 15-year averages of monthly mean profiles relative to the thermal tropopause. For all investigated regions, the annual cycles of H₂O VMR vertical distributions are shown in Fig. 6. For the lowest layer of the lowermost stratosphere, bounded from below by the thermal tropopause layer, the patterns are similar for the three regions, characterized by low H₂O VMR values in winter and spring months and a maximum H₂O VMR during summer. For all regions, the influence of upper tropospheric air masses reaches approx. 1.0–2.0 km above the tropopause with the strongest influence in summer.

Figure 6The 15-year averaged annual cycles of H₂O VMR vertical distributions of H₂O VMR for latitudes 40 to 60^∘ N and for the regions of (from a to c) eastern North America (105 to 65^∘ W), the North Atlantic (65 to 5^∘ W) and Europe (5^∘ W to 30^∘ E).

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Below the tropopause layer, however, we find different behaviours for the studied regions. It appears that over the North Atlantic and over Europe, which is strongly influenced by the North Atlantic synoptic weather systems due to the prevailing westerly winds, the annual cycles of H₂O VMR in the uppermost tropospheric and tropopause layers are coupled, while for the eastern North American region the upper free tropospheric layers seem to exhibit higher specific humidity in winter than respective air masses over the ocean. At the tropopause level, however, the differences vanish, and the annual cycles converge.

A similar behaviour of the annual cycle of H₂O VMR was reported by Zahn et al. (2014) from zonal-averaged H₂O VMR observations by the CARIBIC system. In contrast to MOZAIC, the CARIBIC H₂O sensor provides reliable data also for the lower stratosphere where the MOZAIC RH sensor loses its sensitivity, but, due to its limited regional coverage, the CARIBIC data set cannot provide regional-scale resolution. In that respect, these data sets complement each other with CARIBIC observations backing up the MOZAIC H₂O VMR reported for the atmospheric layers just above the thermal tropopause and MOZAIC providing regional-scale resolution of seasonal patterns which would not be possible otherwise.

Potential transport pathways of water vapour into the lowermost stratosphere are not in the scope of this study and cannot be deduced from the analysis shown in Fig. 6, but they are discussed in depth elsewhere (see e.g. Gettelman et al., 2011; Zahn et al., 2014; and references given therein). In summary, the seasonal variation of H₂O in the first 1–2 km above the tropopause is controlled by shallow, fast, two-way cross-tropopause mixing which is active throughout the year and is responsible for the extratropical tropopause mixing layer, or ExTL (Hoor et al., 2004), localized deep convection events which occur mainly in the summer period over continents (Anderson et al., 2012; Schwartz et al., 2013) and the hemisphere-scale effect of the Asian summer monsoon (Santee et al., 2017; Rolf et al., 2018).

Strong cases of the deep convection events have been reported particularly in the central United States with unusually wet conditions in the lowermost stratosphere being associated with these events (Anderson et al., 2017). Our long-term data do not point at a significantly higher humidity over the eastern North American region in summer compared to the North Atlantic and to Europe. However, it has to be noted that our observations are within the northern half of the continental United States and the southern half of Canada (see Fig. 1 for the aerial coverage of MOZAIC observations), whereas the deep convection events with strong overshooting are reported for regions further south over the Great Plains. This regional difference may explain the differing observations.

3.2 Annual cycles of RH_ice and ISSR distributions at the tropopause

Our study is focusing on the vertical distribution, seasonality and regional variability of RH_ice and ice-supersaturated regions in particular which are linked to the water vapour content of the investigated atmospheric layers. Therefore, we discussed the observed water vapour distribution patterns in the preceding section. To shift the focus to RH_ice, Fig. 7 represents an analysis similar to that shown in Fig. 6 but for relative humidity with respect to ice. In contrast to the differing annual cycles of water vapour distributions at the tropopause as discussed above, we find similar patterns for RH_ice over all target regions: a tropopause layer characterized by mean RH_ice of 60 % almost independent of the season, a very humid layer just below the tropopause with mean RH_ice reaching 80 % and weak seasonality, and a stronger seasonality of RH_ice approx. 1 km below the tropopause and further down into the upper free troposphere with dryer air during the summer season and very humid conditions particularly during winter and spring. Similar average values of RH_ice of 60 %–70 % for the uppermost troposphere without significant seasonality are reported from CARIBIC observations (Dyroff et al., 2014; Zahn et al., 2014).

Figure 7The 15-year averaged annual cycles of RH_ice for latitudes 40 to 60^∘ N and for the regions of (from a to c) eastern North America (105 to 65^∘ W), the North Atlantic (65 to 5^∘ W) and Europe (5^∘ W to 30^∘ E).

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Figure 8Vertical distribution of mean temperature, H₂O mixing ratio, RH_ice and fraction of ice-supersaturated regions (ISSR) for seven pressure layers around the thermal tropopause. Layer thickness is 30 hPa, and layers are spaced equally relative to the tropopause pressure level. Dotted lines indicate the MCH 2σ limit of detection of RH_ice,LOD = 12 % and the resulting minimum detectable H₂O VMR of approx. 10 ppmv.

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Grouping the data set shown in Fig. 7 into seasonal clusters of layers of 30 hPa thickness around the tropopause allows the robust statistical analysis of the vertical distributions of temperature, H₂O VMR, average RH_ice and the fraction of ice-supersaturated regions. The applied concept of the vertical spacing is described in Sect. 2.1. The seasonal variation of the vertical distributions of the selected properties is compiled in Fig. 8.

Tables 1 and 2 present the mean fractions (Table 1) and associated standard deviations normalized to the respective mean values (Table 2) for ISSR occurrence, separated for regions and seasons, and in the last set of columns averaged over all regions. As is already indicated in Fig. 7, the variation of RH_ice with altitude and season is similar for the three target regions.

Table 1ISSR frequency of occurrence: seasonal mean values are reported in percentages; the vertical distance to the thermal tropopause is reported as Δp = p_layer−p_therm.TPH.

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Table 2ISSR frequency of occurrence: normalized standard deviations of seasonal mean values are reported in percentages, and the vertical distance to the thermal tropopause is reported as Δp = p_layer−p_therm.TPH.

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For all regions, the highest RH_ice values and also the highest fraction of ISSR occurrence are observed for the two upper tropospheric layers closest to the tropopause layer, whereas for the third layer situated deepest inside the UT, RH_ice values and ISSR fractions are considerably lower. Only in the spring season (MAM) over the North Atlantic does the lowest third layer reach values similar to the RH_ice values and ISSR fractions of the two layers above. Focusing on the UT layers, the relative standard deviations of the ISSR fractions are highest for the lowest layer investigated here, at least for winter and spring seasons for which the largest ISSR fractions are found.

3.3 Physico-chemical signature of ice-supersaturated regions in the vicinity of the tropopause

As discussed in detail by Spichtinger and Leschner (2016), ice-supersaturated air masses have mostly faced a decrease in temperature or an increase in water vapour mixing ratio, i.e. specific humidity, during their lifetime. Thus, these air parcels are generally known as both colder and of higher absolute humidity than the surrounding subsaturated air masses (Gierens et al., 1999; Spichtinger et al., 2003b); for instance, research aircraft observations from 87^∘ N to 6^∘ S showed that 73 % of the ISSRs have both lower temperature and higher H₂O VMR than their horizontally adjacent subsaturated air, whereas 27 % of the ISSRs show higher temperature and higher H₂O VMR than their surroundings (Diao et al., 2014). This conclusion is valid for both ISSRs in the uppermost troposphere and the rarer cases of ISSRs above the tropopause.

Figure 9Vertical distribution of temperature T (a), H₂O VMR (b), and O₃ VMR (c) relative to the 2 PVU dynamical tropopause and to the thermal tropopause. Vertical distributions relative to the thermal tropopause are presented as percentiles (1, 25, 50, 75 and 99) by blue lines, and those relative to the 2 PVU tropopause conditions are represented by red-shaded areas.

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In order to study the formation history of ISSRs and involved processes, we analysed the occurrence frequency and physico-chemical signature of ISSRs around the tropopause layer and referred our analyses to both the thermal and the dynamical tropopause. We want to recall the tropopause definitions given in Sect. 2.1. The thermal tropopause according to WMO criteria (WMO, 1957) is usually seen as an effective transport barrier hampering troposphere–stratosphere exchange, whereas the dynamical tropopause is commonly used for separating tropospheric and stratospheric air masses in studies on troposphere–stratosphere transport since it represents the lower bound of the ExTL. These complementary views on the tropopause have been developed from extensive CO–O₃ analyses, which showed that the 2 PVU surface approximately separates the troposphere from the stratosphere with the ExTL as a transition layer of about 2 km thickness above it and centred on the thermal tropopause (Hoor et al., 2004; Pan et al., 2010; Gettelman et al., 2011). These tracer studies in the extratropics showed that on average the dynamical tropopause is situated slightly below the thermal tropopause and that the gradients of CO and O₃ are much sharper across the thermal tropopause compared to the dynamical tropopause (Hoor et al., 2004; Pan et al., 2010).

Similar features are observed for the gradients of temperature T, H₂O VMR and O₃ VMR, as shown in Fig. 9 for the North Atlantic region. Similar to the tracer gradients, the temperature gradient is also sharper across the thermal tropopause compared to the dynamical tropopause. In addition, the results confirm the good agreement between the ERA-Interim thermal tropopause height indicated by Δp_TPH=0 hPa, the lowest temperatures detected at Δp_TPH=0 hPa (panel a, blue lines) and the chemical tropopause indicated by O₃ VMR = 120 ppbv at Δp_TPH=0 hPa (panel c, blue lines) and thus the consistency of the used data set. Furthermore, the analysis of the pressure difference between the thermal and dynamical tropopauses reveal an offset of approx. 25 hPa (15–35 hPa) which translates into an altitude difference of approx. 750 m (Neis, 2017).

Our analysis of ISSR occurrence in the vicinity of the ExTL is confined to the North Atlantic region, for which we have the highest data density available with respect to vertical resolution. As described generally in Sect. 2.1, the entire data set of individual RH_ice observations over the North Atlantic region was divided into yearly subsets of seasons: DJF, MAM, JJA and SON. For each year, season and altitude layer relative to the thermal and dynamical tropopauses, the average frequency of occurrence of observations with RH_ice > 100 % was determined. The probability of ISSR occurrence per altitude layer with respect to the entire period of 15 years was then calculated from this record of seasonally averaged ISSR frequencies of occurrence. The results are compiled in Table 3 for both tropopause definitions used here. Please note that the ISSR fractions compiled for the thermal tropopause correspond to the values listed in Table 1 but without distinction for seasons.

Table 3Mean and standard deviation of seasonal fraction of ice-supersaturated regions (ISSRs) for the seven vertical layers distributed around the thermal and dynamical tropopause.

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Figure 10Vertical distribution of temperature, H₂O VMR and ozone VMR for ISSRs relative to the thermal tropopause height (a, c, e) and 2 PVU dynamical tropopause height (b, d, f). ISSR conditions are presented as percentiles (1, 25, 50, 75 and 99) by blue lines and non-ISSR conditions by red-shaded areas. Blue cross-hatched areas highlight the deviation of median values between ISSR and non-ISSR conditions.

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Figure 11Vertical distribution of the troposphericity parameter m for ISSR and non-ISSR air masses with respect to the thermal (a) and dynamical (b) tropopause.

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With reference to the thermal (dynamical) tropopause, the mean ISSR occurrence probability is 31 % (38 %) in the upper troposphere below the tropopause layer (UT1–3). The observed increases in mean ISSR occurrence probabilities towards the tropopause layer are, however, below statistical significance, and the average values for the respective pressure layers differ for the two tropopause definitions. Our finding that the ISSR occurrence probability is increasing towards the tropopause agrees with results from a previous research aircraft study using the CO–O₃ tracer correlation approach, in which the majority (69 %) of clear-sky ISSRs was found within the ExTL, while the rest were located below the transition layer (Diao et al., 2015).

Since the thermal tropopause is located at a higher altitude than the dynamical tropopause, the pressure layers below the thermal tropopause include parts of the ExTL, which explains the lower ISSR fractions for UT1–3 below the thermal tropopause compared to UT1–3 below the dynamical tropopause. Sorting the data according to their vertical distance to the respective tropopause also results in different data ensembles for the respective pressure layers because of the strong horizontal variability of RH_ice along the flight trajectories. This strong horizontal variability explains the different absolute values of ISSR occurrence with respect to the tropopause definitions. For both tropopause definitions, the standard deviation of observed ISSR fractions is largest for the lowest UT layer of the analysed atmospheric region and decreases with increasing altitude.

When crossing the thermal tropopause, the ISSR fraction drops sharply to values of 1.5 % for the lowest layer above the thermal tropopause and to statistically insignificant fractions when reaching further up into the stratosphere. In the case of the dynamical tropopause, we find a significantly higher ISSR fraction of 8.4 % for the lowest stratosphere layer and again insignificant fractions further above. This strong contrast in the ISSR occurrence probability for the lowest stratosphere layers with reference to the two tropopause definitions coincides with the behaviour of other tracers in the ExTL (see Fig. 9 for details).

In order to learn more about the history of ice-supersaturated air parcels, we further analysed the ozone content of an ISSR compared to the subsaturated air around it for air parcels below and above the thermal and dynamical tropopauses and combined the results with the distributions of temperature and H₂O VMR. The thermodynamic and chemical properties of the ISSR and the comparison between the ISSR (blue lines) and ice-subsaturated air masses (red-shaded areas and red lines) are presented in Fig. 10 with reference to both tropopause definitions. In general, ISSRs are colder than their subsaturated counterparts. The difference is low in the UT with a value of 1–2 K, which compares well to the value of 2 K at 215 hPa obtained from MLS satellite measurements (Spichtinger et al., 2003b), and it increases to a more than 6 K difference in the stratosphere above the thermal tropopause and approx. 4 K above the dynamical tropopause. The temperature difference of 3–4 K between colder tropospheric ISSRs and the surrounding subsaturated air masses reported by Gierens et al. (1999) is comparable to the temperature difference in the 30 hPa thick tropopause layer we find in our analysis.

Figure 10 also indicates a similar behaviour of the vertical distribution of H₂O VMR for ice-supersaturated and ice-subsaturated regions with exponentially decreasing absolute humidity up to the tropopause layer. Above both tropopause layers, H₂O VMR further decreases in the case of non-ISSR conditions. For ISSR conditions, however, H₂O VMR remains constant with height throughout the layer just above the tropopause. Doubling of H₂O VMR for tropopause ISSR conditions compared to non-ISSR conditions is close to the results reported from MLS observations (Spichtinger et al., 2003b). In contrast, Gierens et al. (1999) found an increase of only 50 % for H₂O VMR inside ISSRs compared to non-ISSRs. In turn, this value compares well with our observations in the uppermost troposphere.

The vertical distribution of the ozone VMR behaves in a similar way to the temperature for ice-supersaturated and ice-subsaturated regions with small differences in the ozone VMR of less than 15 ppbv in the troposphere. Already for the tropopause layer and even more pronounced for the first layer above the thermal tropopause, however, the difference increases to 60 ppmv ozone VMR and beyond.

Quantitative conclusions on air mass characteristics and history are drawn from the vertical distributions of thermodynamic and chemical properties shown in Fig. 10. The underlying concept of troposphericity (Cirisan et al., 2013) quantifies the tropospheric nature or fingerprint, of an air mass on the basis of the observed O₃ VMR. In the context of our study, we refer to troposphericity for consistency with the literature.

Using the O₃ VMR as a stratospheric air mass tracer, and, adapting the approach of Cirisan et al. (2013), we define the troposphericity parameter m for an ensemble of data characterized by median (med) and 99th percentile (P99) values as

and we apply the median value of the lowest layer analysed here as background tropospheric value so that (O₃)_tropo = 42 ppbv. Petetin et al. (2018) reported a median O₃ VMR of 49 ppbv for the Central European mountain station Sonnblick (3106 $\mathrm{m}\mathrm{a}.\mathrm{s}.\mathrm{l}$) in the Austrian Alps and a value of 50 ppbv for the high Alpine station Jungfraujoch (3580 $\mathrm{m}\mathrm{a}.\mathrm{s}.\mathrm{l}.$), whereas Cirisan et al. (2013) use a value of 33.5 ppbv from ERA-Interim air mass trajectory analyses as the tropospheric background ozone value in the upper troposphere at mid-latitudes.

Applying this definition of the troposphericity parameter m to MOZAIC and IAGOS observations over Central Europe (Petetin et al., 2018) at 4000 m altitude with (O₃)_med = 50 ppbv and (O₃)_P99 = 82 ppbv yields m=0.80, and for observations at 1500 m altitude with (O₃)_med = 42 ppbv and (O₃)_P99 = 83 ppbv we find m=1.00.

For MOZAIC and IAGOS observations in the ExUTLS, Cohen et al. (2018) report, e.g. for springtime lowermost stratosphere conditions, values of (O₃)_med = 400 ppbv and (O₃)_P95 = 600 ppbv, resulting in m=0.36, and, for tropopause layer conditions, values of (O₃)_med = 110 ppbv and (O₃)_P95 = 200 ppbv and m=0.57; note that P95 refers here to the 95th percentile value of the analysed data ensemble, as taken from Cohen et al. (2018). Deeper into the stratosphere beyond the reach of MOZAIC and IAGOS aircraft, the value of m approaches m=0.0. Thus, similar to the troposphericity parameter defined by Cirisan et al. (2013) from trajectory analyses, a value of m=0 indicates that an air parcel contains only stratospheric air, while m=1 is fully tropospheric. Defining the troposphericity as described here, we connect the troposphericity of an air mass to the observed variability of the O₃ VMR.

The analysis of troposphericity of the seven investigated layers with respect to the 99th percentile and median O₃ VMR values is presented in Fig. 11. With respect to the thermal and to the dynamical tropopause, the layers up to the tropopause layer are characterized by similar values of m>0.80 for ISSR and m>0.75 for non-ISSR air masses. The first layer above the thermal tropopause, however, shows a clear difference between ISSR (m=0.67) and non-ISSR (m=0.44) with respect to the thermal tropopause but similar values of m=0.67–0.69 for ISSR and non-ISSR with respect to the dynamical tropopause.

Recalling the structure of the ExTL with the 2 PVU dynamical tropopause at its lower bound separating the stratosphere from the troposphere and centred on the thermal tropopause, we find that on top of the ExTL non-ISSR air masses show a clear stratospheric signature, while ISSR air masses are still strongly influenced by mixing and carry a significant tropospheric fingerprint compared to the non-ISSR air masses. Above the dynamical tropopause and thus inside the ExTL, the influence of mixing increases gradually for both ISSR and non-ISSR air masses, and the difference in troposphericity is much less pronounced than near the top of the ExTL.

3.4 ISSR fraction and cirrus cloud occurrence

Ice supersaturation in the atmosphere is a prerequisite for the formation of cirrus clouds, and the degree of super-saturation, mostly driven by atmospheric dynamics, determines the mechanism by which ice particles form (e.g. Kärcher et al., 2014; Krämer et al., 2016; Heymsfield et al., 2017). On the other hand, RH_ice probability distribution functions inside cirrus clouds are characterized by most probable values at or slightly above ice-saturation at RH_ice = 100 % (Krämer et al., 2009; Diao et al., 2014, 2015; Petzold et al., 2017), which means that cirrus clouds exist to a considerable fraction also in ice-subsaturated air masses depending on their state of life. Finally, ice supersaturation can also occur in cloud-free air masses, but the fraction of ice-supersaturated air in clear sky conditions is largely unknown. However, these cloud-free ISSRs are of high importance for the formation of persistent contrails and thus for the climate impact of aviation (Irvine and Shine, 2015; Kärcher, 2018).

Figure 12Annual cycles of ISSR occurrence shown as occurrence probability for RH_ice > 100 % for the eastern North American, North Atlantic and European regions. The considered years are 1995 to 2010, with shaded areas representing probabilities for the average value (thick lines) ± 1σ and the dashed lines representing average fractions for RH_ice > = 95 % and 105 %. Calculations were conducted for the two UT layers positioned closest to the thermal tropopause.

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Figure 13(a) Seasonal cycle of ISSR occurrence probability, i.e. p(RH_ice > 100 %), averaged over Europe for the years 1995 to 2010 for the two UT layers positioned closest to the thermal tropopause. The symbols represent the annual cycle of the Lindenberg sounding (2000–2001) from Spichtinger et al. (2003a). (b) seasonal cycle of ISSR occurrence probability, as p(RH_ice > 100 %), averaged over the northern mid-latitudes from eastern North America to Europe for the period 1995 to 2010. The symbols represent high cloud fractions from the satellite cloud climatology by Stubenrauch et al. (2010) for northern mid-latitudes and the years 2003 to 2008 for AIRS-LMD (Atmospheric Infrared Sounder analysed at the Laboratoire de Météorologie Dynamique in Paris), 1987 to 1995 for TOVS-Path B (TIROS-N Operational Vertical Sounder Path-B cloud retrieval) and 2006 to 2007 for CALIPSO.

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Motivated by the high importance of ISSRs for cirrus formation and existence and also for the formation and persistence of contrails, we converted the vertically resolved observations of ISSR fractions into an annual cycle of ISSR occurrence for the three target regions. The seasonal-mean occurrence probabilities were analysed for RH_ice values of 95, 100 and 105 %, based on the sensor precision of 5 % RH_ice. The resulting annual cycles for the top two UT layers, situated just below the thermal tropopause layer are shown in Fig. 12. The range bound by the probabilities of occurrence for RH_ice > 95 % and 105 % defines the uncertainty of our analysis. Additionally, we analysed the interannual variability of ISSR occurrence from the standard deviation of the mean ISSR occurrence probability for RH_ice > 100 %. The respective variability range is shown as blue-shaded areas in Fig. 12.

For all regions, ISSR occurrence probabilities are highest in winter and spring and lowest in summer, while the absolute values particularly in summer are considerably different. The probability for finding ice-supersaturated air masses during summer is 20 % over the eastern North American regions but 30 % over the North Atlantic with Europe showing values in the range in between.

To the present, there is only very limited in situ information available about the occurrence probability of ice-supersaturated air masses in the upper troposphere in general and about their seasonality in particular. One source for in situ information stems from radiosonde observations conducted by the German Weather Service over the Lindenberg observatory in Germany (Spichtinger et al., 2003a).

Figure 13a shows the average annual cycles of ISSR occurrence frequency from 15 years of MOZAIC observations over Europe and from 15 months of radiosonde observations over Lindenberg published by Spichtinger et al. (2003a). The 15-month cycle from the radio soundings is covered by the 15 years of climatology of ISSR occurrence from MOZAIC, but it contributes only a snapshot compared to the time series of 15 years. Based on the 15 months of observation, the authors report a mean frequency of occurrence of ice-supersaturation layers over Lindenberg of 28 %, whereas the annual cycle of ISSR occurrence from our 15 years of MOZAIC observations over Europe yields a mean value of 29.5 % with a range from 35 % (RH_ice > 95 %) to 23 % (RH_ice ≥ 105 %).

Another source of data but for the occurrence frequency of cirrus clouds originates from long-term analyses of satellite observations (Stubenrauch et al., 2010, 2013). In their 6-year climatological study, Stubenrauch et al. (2010) report cirrus cloud coverage fractions for northern mid-latitudes of 35 % in January and 27 % in July from the Atmospheric Infrared Sounder analysed at the Laboratoire de Météorologie Dynamique in Paris (AIRS-LMD; 2003 to 2008), and respective fractions of 34 % and 21 % from the TIROS-N Operational Vertical Sounder Path-B cloud retrieval (TOVS-Path B; 1987 to 1995), and 42 % and 40 % from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO; 2006 to 2007). The compilation of our annual cycle of ISSR occurrence and the respective observations from space-borne sensors is shown in Fig. 13b. The agreement of the observations of ISSR occurrence from the very different sources is remarkably good with the exception of CALIPSO observations which provide higher values. According to Stubenrauch et al. (2010), the high cloud fraction of CALIPSO is about 10 % larger than respective values of CALIPSO for clouds excluding subvisible cirrus. Therefore, the difference between high cloud fractions from CALIPSO and from the other instruments shown in Fig. 13 can be attributed to instrument sensitivities.

The good agreement between MOZAIC in situ observations of ISSR occurrence with the high cloud fraction from satellite instruments encourages further detailed studies on this matter. First analyses of simultaneous observations of RH_ice and N_ice, which are now possible within the ongoing IAGOS programme, already indicate a strong correlation of high RH_ice values with its occurrence inside cirrus clouds (Petzold et al., 2017).

3.5 Trend analysis

Finally, we analysed the 15-year records of the validated MOZAIC RH_ice observations and the resulting fraction of ISSR observations for the three regions of eastern North America, the North Atlantic and Europe for potential trends. The bases of our analyses were the seasonally averaged observations in the uppermost tropospheric layer (UT) with respect to the thermal tropopause and the respective average seasonal cycles depicted in Fig. 12. The resulting time series are shown in Fig. 14. The seasonality of ISSR occurrence is clearly visible for each region but with considerable interannual variability. Similar to Fig. 12, the shaded regions represent the average fractions for 95 % < RH_ice < 105 % and indicate thus the uncertainty resulting from the instrument precision of RH_ice = 5 %. For none of the regions do we find significant trends in ISSR occurrence. Therefore, the distribution of RH_ice in the uppermost troposphere close to the tropopause layer and the resulting occurrence of ice supersaturation seem to be stable over the investigated time period from 1995 to 2010.

Figure 14Time series of ISSR fraction (probability of occurrence) for latitudes 40 to 60^∘ N and for the regions of (from a to c) eastern North America (105 to 65^∘ W), the North Atlantic (65 to 5^∘ W) and Europe (5^∘ W to 30^∘ E) for the top UT layer, situated just below the tropopause layer. Solid lines represent probabilities for the average value for RH_ice = 100 %, the shaded areas represent average fractions for 95 % < RH_ice < 105 % and long-term average values for RH_ice = 100 % are added in the panels.

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Figure 15Time series of the North Atlantic Oscillation (NAO) index (a) and de-seasonalized time series of ISSR fraction (probability of occurrence) for latitudes of 40 to 60^∘ N and for the regions of (from b to d) eastern North America (105 to 65^∘ W), the North Atlantic (65 to 5^∘ W) and Europe (5^∘ W to 30^∘ E).

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Figure 16Correlation analysis with respect to the correlation of signs between NAO index and deviation of ISSR occurrence from the long-term average (Δ ISSR) for the target regions. Numbers indicate the results from the correlation analysis with respect to number of samples n, Pearson's R and significance level p.

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In order to get a clearer understanding of the reasons for the interannual variability, we further analysed the de-seasonalized time series of the ISSR fractions by calculating the difference between each seasonal value of the ISSR fraction and the 15-year seasonal average (see Fig. 12).

The de-seasonalized time-series thus show positive and negative deviations from the long-term seasonal average values. The resulting time series are presented in Fig. 15. As for the time series of ISSR occurrence, we performed a trend analysis and added the obtained trend lines to Fig. 15. Respective decadal slopes are −1.95 ± 1.77 % for eastern North America, −3.21 ± 1.78 % for the North Atlantic and −2.39 ± 2.29 % for Europe, and the indicated uncertainties of the determined slopes refer to 1 standard deviation. Thus none of the slopes differ significantly from zero, and, similar to the time series of ISSR occurrence, we do not observe significant trends for the seasonal deviation of ISSR occurrence from the long-term average for the three target regions.

One potential weather phenomenon driving the deviation of seasonal ISSR occurrence from the long-term average in the investigated region is the North Atlantic Oscillation (NAO). The NAO index describes the deviation of the pressure difference between the Iceland low and the Azores high pressure systems from the long-term average value. As an example, a positive value of the NAO index indicates that Δp (Iceland L to Azores H) is larger than on average. This larger pressure difference causes stronger westerly winds and thereby more active storm tracks over the North Atlantic. Under such conditions, we would expect a higher probability of ice supersaturation in the uppermost troposphere due to more frequent warm conveyor belts that can induce the formation of ISSRs in the upper troposphere (Spichtinger et al., 2005). Such a positive correlation between NAO and cirrus cloud cover is reported from an analysis of cirrus cloud cover data from the International Satellite Cloud Climatology Project and relative humidity data from ECMWF/ERA40 by Eleftheratos et al. (2007).

To investigate this potential link, we added the seasonally averaged NAO index to Fig. 15 (panel a). Since there is no immediate evidence given for a link between the NAO index and the deviation of ISSR occurrence from the long-term average (Δ ISSR), we further searched for a potential link of signs in the sense that positive and negative NAO index values are associated with positive and negative deviations of ISSR occurrence from the long-term average, respectively. The results of this cross-correlation analysis are presented in Fig. 16.

For the eastern North American and European regions, the correlation between NAO index and Δ ISSR is not statistically significant. For the North Atlantic, however, the results of the cross-correlation analysis indicate statistical significance at a level of 99 %. The obtained correlation of signs is in line with the observation that the occurrence of ice supersaturation is well correlated with the storm track activity (Spichtinger et al., 2003b; Gettelman et al., 2006; Lamquin et al., 2012).