2.1 IAGOS

The European research infrastructure IAGOS (Petzold et al., 2015) provides long-term in situ measurements in the UTLS region. The IAGOS-CORE component, successor of the MOZAIC part, comprises the implementation and operation of autonomous instruments installed on long-range aircraft of internationally operating airlines for continuous, global-scale and daily measurements of reactive gases and long-lived greenhouse gases (e.g. CO, CO₂, CH₄ and water vapour), important chemically active trace gases (e.g. O₃), as well as aerosol, dust and cloud particles (Bundke et al., 2015; Filges et al., 2015).

Especially in the UTLS region, these measurements are very valuable, as most flight tracks are situated in heights between 9 to 13 km, depending on the actual weather conditions, seasons and geographic region.

Starting in August 1994, more than 60 000 flights (May 2019) have been performed, including data from the IAGOS predecessor MOZAIC (August 1994 to December 2014) and data from the IAGOS project starting in July 2011 until present. It is obvious that the global data distribution is not uniform in every region. The subset covering the North Atlantic flight corridor shows the highest coverage of flights. Therefore, in our study, we focus on this region (40 to 60^∘ N, −65 to 5^∘ E) (Fig. 1). For the evaluation of the reanalysis data, we use the geographic position of the airplane (lat/long), the time, data quality flags, ambient pressure and temperature (Berkes et al., 2017), relative humidity and water vapour volume mixing ratio. In this study, we use the data collected during January 2000 to December 2009. For further information regarding the IAGOS project, the reader is referred to the project's website (https://www.iagos.org/, last access: 15 January 2020) and the references therein.

Figure 1Number of IAGOS measurements per grid box (2^∘ in longitudinal and 0.57^∘ in latitudinal directions) during 1 January 2000 to 31 December 2009.

2.2 ERA-Interim

For this study, the ERA-Interim reanalysis data set from ECMWF is used (Dee et al., 2011). The spectral resolution of the underlying IFS model from 2006 is T255, which calculates to a horizontal resolution of about 80 km in the midlatitudes. The vertical dimension is separated into 60 levels, reaching from the surface up to a pressure level of 0.1 hPa.

For the comparison with the IAGOS measurements, the 6-hourly ERA-Interim data were previously converted on a 1^∘ horizontal grid and interpolated on pressure levels (Kunz et al., 2014). Then, the fields of temperature, pressure and specific humidity are projected on the aircraft's flight path by linear spatial and temporal interpolation. Finally, the data are available with a temporal resolution of 4 s along the flight track (Berkes et al., 2017).

The relative humidity with respect to ice was calculated using the approximation by Murphy and Koop (2005). As mentioned already in the introduction, the ERA-Interim data set was obtained by using the IFS model including the so-called Tompkins scheme (Tompkins et al., 2007), which allows for the supersaturation with respect to ice in cloud-free regions. However, inside cirrus clouds, the occurring supersaturation is adjusted down to 100 %. In the following, we use “ERA” to label the ERA-Interim data.

2.3 Methodology

Aircraft-based measurements of atmospheric state variables and chemical composition usually refer to the aircraft flight altitude or pressure level, respectively. In the present work, the humidity data will be separated relative to the tropopause height in order to study the humidity in the tropopause region. We use the dynamical tropopause, which is defined by a sharp gradient in the potential vorticity (PV). The value used here to define the tropopause is PV = 2 PVU (1 PVU $={\mathrm{10}}^{\mathrm{6}}\mathrm{K}{\mathrm{m}}^{\mathrm{2}}{\mathrm{kg}}^{-\mathrm{1}}{\mathrm{s}}^{-\mathrm{1}}$, standard potential vorticity unit) (Holton, 2005). A former study (Neis, 2017) showed that the choice of the tropopause definition can have an important impact on the interpretation of the results. However, in this study, we want to compare two data sets. Therefore, the definition of the tropopause plays only a minor role. The vertical data will be distributed into three main layers: upper troposphere (UT), tropopause layer (TP) and lower stratosphere (LS) in accordance with Thouret et al. (2006). Furthermore, UT and LS are each separated into three subclasses. The width of the sublayers considers the average difference between ozone and thermal tropopause of 780 m (30 hPa at this altitude) (Bethan et al., 1996). The resulting seven 30 hPa thick bins separate the aircraft pressure relative to the tropopause pressure and are summarized in Table 1.

Table 1The data set is distributed into three main layers: the upper troposphere, tropopause layer and lowermost stratosphere. The outer layers are additionally subdivided into three sublayers. The distribution criterion is the pressure difference between aircraft pressure p_ac and the tropopause pressure p_tph with the range of ±15 hPa. Additionally, for every flight layer, the number of IAGOS measurements between 2000 and 2009 is presented.

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Before the distribution of the data, several filters are applied. First, the measured data must lie within the geographic region from 40 to 60^∘ N and −65 to 5^∘ E. All data must be collected at a height above 350 hPa and within a temperature range between 233 and 200 K, corresponding to the threshold of homogeneous freezing (Heymsfield and Sabin, 1989) and calibration limit of the humidity sensor (Neis, 2017), respectively. Additionally, the relative humidity with respect to liquid water must be below 100 % and several measurement quality flags must be fulfilled. The abovementioned criteria are applied to both data sets and are the starting point of the comparison.

3.1 Temperature

According to Eq. (1), the relative humidity depends on temperature and available water vapour. In a first step, a comparison between the temperature measurements and the reanalyses data for all seven height layers is conducted. Figure 2 shows the vertical profile of the temperature for IAGOS and ERA in the form of a box-and-whisker plot. The boxes are bounded by the 25th and 75th percentiles, while the median is marked with a vertical black line. The whiskers are defined as 1.5 ⋅ IQ, with IQ the interquartile range, equal to the distance between the 25th and 75th percentiles. Outliers, values exceeding the whiskers, are marked as black circles. As expected by definition, the tropopause layer shows the coldest mean temperatures, with 216.1 and 216.5 K for IAGOS and ERA, respectively. The warmest mean and median temperatures are visible for the lowest layer (UT3), with about 226 K in both cases. Overall, the comparison between IAGOS and ERA shows a very good agreement as far as the statistical values are concerned (see Table 2). This is supported by the equally sized boxes in Fig. 2, pointing to a similar variability of the data set.

Figure 2Vertical profile of temperature (K) for IAGOS (blue) and ERA (red).

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Table 2Median, mean and standard deviation of temperature (K) for IAGOS and ERA data. The comparison shows very good agreement.

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3.2 Water vapour

The vertical structure of the water vapour volume mixing ratio is presented in Fig. 3. Here, a clear dependence of the distribution with height is visible. The lowest mean and median values of the water vapour volume mixing ratio are observed, as expected, in the uppermost layer (LS3). In contrast, the lowermost level (UT3) shows the largest mean values of the water vapour mixing ratio. The comparison between IAGOS and ERA shows a good overall agreement (see Table 3). For the upper layers, in both data sets starting from the tropopause level (TL) up to LS3, the variability, i.e. the size of the boxes, is significantly lower compared to the tropospheric layers (UT1 to UT3). Overall, it can be stated that the variability is increasing with decreasing height. It is notable that the outliers in all layers of IAGOS reach clearly higher mixing ratios than ERA. This has significant effects on the relative humidity with respect to ice, as will be shown later. In summary, the reanalysis data are in good agreement with the vertical distribution of the IAGOS data. However, IAGOS shows a larger variability and stronger extreme values.

Figure 3Vertical profile of H₂O volume mixing ratio (ppmv) for IAGOS (blue) and ERA (red).

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Table 3Same as Table 2 but for water vapour volume mixing ratio (VMR).

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Dyroff et al. (2015) reported a moist bias comparing CARIBIC measurements with ECMWF analyses and forecasts. Since ERA-Interim is based on ECMWF analyses, one would expect also a moist bias in the lower stratosphere. In contrast to the capacitive sensor used for IAGOS, CARIBIC uses a combination of a frost point hygrometer and a photo-acoustic hygrometer, which shows a better precision and uncertainty for very low water vapour volume mixing ratios. Therefore, the uncertainties in volume mixing ratios of H₂O are large in the lower stratosphere and may explain the more wet stratospheric values compared to CARIBIC. For more information, also see Petzold et al. (2019).

3.3 Relative humidity with respect to ice

Since cloud formation is governed by the relative humidity rather than the water vapour mixing ratio, the relative humidity with respect to ice RH_i is now investigated. As mentioned in the introduction, RH_i depends on both temperature and available water vapour. Hence, relative humidity is a convolution of both variables. In Fig. 4, the vertical structure of RH_i is depicted. The overall results show two different regimes. In the troposphere, up to the tropopause layer, the statistics cover the whole range of possible saturation values. Overall, 50 % of the data, indicated by the boxes, of each layer from UT3 to TL are situated between 50 % and 100 % RH_i. The highest median values are found in the UT1 layer for both data sets (see also Table 4). In the tropopause layer, still a significant amount of the data is exceeding values of RH_i>100 %, both in the in situ data as well as in the ERA data set. However, the whisker in Fig. 4 indicates that ERA has less data points with a higher supersaturation compared to IAGOS. In the stratospheric layers, the median of the RH_i values is decreasing strongly. However, ice supersaturation is still possible, especially in the lowest stratospheric layer (LS1) (Müller et al., 2015). The statistics of ISSRs in higher levels provided by the ERA data set show clearly less occurrence of this feature. Since ISSRs are an important factor for the formation and lifetime of contrail cirrus (Kärcher, 2018), a good model representation of the abundance of ice supersaturation in this region is important for an adequate description of the Earth's radiative budget.

Figure 4Vertical profile of relative humidity with respect to ice (RH_i) (%) for IAGOS (blue) and ERA (red).

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Table 4Same as Table 2 but for RH_i (%).

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It is obvious that ERA and IAGOS show good agreement for situations below ice supersaturation. However, in this study, we focus on the situation where ice supersaturation exists. For a more distinct look at the occurrence of ISSR, we illustrate the statistic evaluation with cumulative probability in Fig. 5. Each layer is depicted with its own colour. It is clearly visible that ERA and IAGOS behave differently for RH_i>100 %, especially for the tropospheric layers. The ERA distributions of the latter layers snap off as soon as they reach ice supersaturation. As mentioned before, the IFS model allows the existence of ice supersaturation but only in cloud-free conditions. As soon as ice clouds are present in the model's grid cell, the supersaturation is adjusted to RH_i=100 %. Unfortunately, the IAGOS data set of the investigated timeframe cannot distinguish between cloudy and non-cloudy areas. ¹ Nevertheless, also in ice clouds, ice supersaturation is present (Krämer et al., 2016). Therefore, the behaviour of the cumulative distributions for ERA, especially in the layers from UT3 to TL, might be due to an untimely formation of ice clouds in the underlying IFS model, which adjusts the ice supersaturation too early.

Figure 5Cumulative distribution of RH_i for every height level in the IAGOS (a) and ERA (b) data sets. The vertical blue line denotes saturation with respect to ice.

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Another way to compare the representation of the water vapour is the fraction of ISSRs. Figure 6 presents the vertical profile of the ISSR fraction. The ISSR fraction in this study is defined as the number of data points within a layer with RH_i≥100 % divided by the total number of data points in that layer above the defined North Atlantic region. It is clearly visible that the measurements by IAGOS show a higher fraction of ISSR. Only for the two uppermost layers, the fractions of both data sets are of comparable magnitude. Here, the very dry conditions produce supersaturation only in very few cases. The largest difference between measurement and reanalysis data occurs in the tropopause layer and the flanking UT1 layer, where a high percentage of ice clouds can be expected. IAGOS shows in the latter layer an ISSR fraction of up to 40 %. Since ISSRs are a prerequisite for the formation of in situ cirrus clouds, a misrepresentation of the feature can lead to great deviations in the local radiative budget and can build up to large errors in the local dynamics. However, sensitivity studies were conducted in order to see if ERA can reproduce the ISSR fraction of IAGOS using a lower threshold than RH_i=100 %. For each layer, a different ${{\mathrm{RH}}_{\mathrm{i}}}_{\mathrm{ERA}}$ threshold for the ERA data set leads to the best agreement with IAGOS. The best comparison between IAGOS and ERA in the lower stratosphere is found when ice supersaturation in ERA is defined as ${{\mathrm{RH}}_{\mathrm{i}}}_{\mathrm{ERA}}\ge \mathrm{85}$ % (dotted red line in Fig. 6). For the tropopause layer, the best agreement is found for ${{\mathrm{RH}}_{\mathrm{i}}}_{\mathrm{ERA}}\ge \mathrm{90}$ % in ERA (dash-dotted line), while the upper troposphere shows an almost perfect match for ${{\mathrm{RH}}_{\mathrm{i}}}_{\mathrm{ERA}}\ge \mathrm{95}$ % in ERA (dashed line). This shows that the agreement between measurement and reanalysis is decreasing with increasing height. One reason might be the data assimilation of measurements into the reanalysis data set. The operational radiosondes using capacitive sensors (usually RS80 and RS92 with Humicap sensor by Vaisala) show large deviations for temperatures below −40 ^∘C or very low absolute humidities (Spichtinger et al., 2003a). Therefore, the response time is increasing in the upper troposphere to the tropopause layer due to the decreasing temperature. Further up in the stratosphere, temperatures are increasing again (Fig. 2). However, the absolute humidities are decreasing with height (Fig. 3), leading to an increased response time.

Figure 6Vertical profile of the fraction of ice supersaturated regions for IAGOS (blue) and ERA (red). Different definitions of ice supersaturation in ERA are shown in light red. The dotted line represents the fraction of ${{\mathrm{RH}}_{\mathrm{i}}}_{\mathrm{ERA}}\ge \mathrm{85}$ % , the dashed–dotted line depicts the fraction of ${{\mathrm{RH}}_{\mathrm{i}}}_{\mathrm{ERA}}\ge \mathrm{90}$ %, and the dashed line stands for the ${{\mathrm{RH}}_{\mathrm{i}}}_{\mathrm{ERA}}\ge \mathrm{95}$ %.

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Figure 7Time series of the monthly fraction of ice supersaturated regions for IAGOS (blue) and ERA (red) for the lower stratosphere (LS1 to LS3), the tropopause layer TL and the upper troposphere (UT1 to UT3). The dashed red line represents the ERA data set with the fraction of RH_i≥85 % for the lower stratosphere, RH_i≥90 % for the tropopause layer and RH_i≥95 % for the upper troposphere. Note the different scale for the lower stratosphere.

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In contrast to the total fraction over the complete period from 2000 to 2009, Fig. 7 shows a time series of the monthly ISSR fraction. For this comparison, the three stratospheric (tropospheric) layers were combined to one layer defined as “lower stratosphere” (“upper troposphere”). The dotted lines in Fig. 7 indicate the fraction of data points for ${{\mathrm{RH}}_{\mathrm{i}}}_{\mathrm{ERA}}\ge \mathrm{85}$ % in the lower stratosphere, for ${{\mathrm{RH}}_{\mathrm{i}}}_{\mathrm{ERA}}\ge \mathrm{90}$ % in the tropopause layer and for ${{\mathrm{RH}}_{\mathrm{i}}}_{\mathrm{ERA}}\ge \mathrm{95}$ % in the upper troposphere, respectively. Note that the variation of the ISSR fraction is not only affected by meteorology but also due to different data coverage. For instance, at the end of 2001, only few data points are available, which explains the prominent spikes in the lower stratosphere and upper troposphere. Comparing the time series with Fig. 6, it is again visible that ERA is underestimating the fraction of ISSR compared to the measurements from IAGOS. Using a different definition of ice supersaturation by reducing the threshold in ERA (85 %, 90 % and 95 %) improves the agreement between ERA and IAGOS in each layer. However, the different thresholds can also lead to overestimation of the ISSR fraction. While in the lower stratosphere, a threshold of ${{\mathrm{RH}}_{\mathrm{i}}}_{\mathrm{ERA}}\ge \mathrm{85}$ % shows a overall good agreement, in 2005, this threshold would lead to an overestimation of the ISSR fraction of up to 300 % (December 2005). It is also noteworthy that, although Fig. 6 shows an almost perfect agreement between IAGOS and the modified threshold of 95 % in the upper troposphere, large deviations between IAGOS and ERA can be found as well, for example, in 2004.

As a side note, the reader is referred to the companion study by Petzold et al. (2019), where also a trend analysis using the IAGOS data was conducted, which led to the conclusion that no significant trends in ISSR occurrence can be observed. However, they do find a correlation between the North Atlantic Oscillation (NAO) and ISSR occurrence.

4.1 Statistic investigation of ISSR pathlengths

It is obvious that the smallest possible pathlength of the ERA data set is limited by the model's spatial resolution. However, by calculating a moving average of the IAGOS data close to the ERA resolution, a comparison is possible. Additionally, we want to answer the question of which resolution is necessary in order to receive a helpful representation of the horizontal scales of ISSRs. A comprehensive representation of ISSRs in atmospheric models enables further investigations on the linkage between small-scale variability and large-scale features.

Figure 9Probability of ISSR pathlengths with logarithmic binning (a) and cumulative probability (b). The original IAGOS data are shown in black, while ERA is presented in red. Other colours denote different running means of the original IAGOS data set to mimic different spatial data resolution.

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For a reasonable comparison of ISSR pathlengths between IAGOS and ERA, we only evaluate ISSRs on a constant flight level. This means that an ISSR path is omitted if the pressure level of the plane is changed by more than 50 Pa. Figure 9 shows the histograms for the pathlengths of IAGOS and ERA, and running means of 2, 5, 10, 25, 50 and 100 km of the IAGOS data. On the right side, a cumulative distribution is shown. As it is expected from the different underlying resolutions of both data sets, IAGOS (black lines in Fig. 9) shows a much greater number of small pathlengths compared to ERA (red lines). On the other side, ERA shows a greater number of very large pathlengths larger than 100 km. This is especially impressive by looking at the cumulative distribution. Here, the different character of both data sets is most prominent. Comparing the median values given in Table 5 of the original IAGOS data and ERA reveals the big difference. While 50 % of the ISSR pathlengths in IAGOS are smaller than 3 km, the same threshold for the ERA data set is located at 156 km. It has to be noted that due to the lower spatial resolution of the ERA data set, only 6283 ISSRs are found compared to 81 295 for IAGOS.

Table 5Median and mean values and number of ISSR pathlengths for IAGOS, ERA-Interim and several running means of the original IAGOS data set.

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Previous studies also investigated pathlengths of ISSRs. Diao et al. (2014), hereafter D14, investigated ISSR from very-high-resolution measurements (1 Hz ≈230 m) using data from several flight campaigns. They report a mean ISSR pathlength of 3.5 km, while the median value is about 0.7 km, with a total number of 1542 ISSRs. These values are about 1 order of magnitude lower compared to our investigations. However, these data include measurements from 87^∘ N to 67^∘ S and therefore include tropical conditions.

Spichtinger and Leschner (2016), hereafter SL16, used MOZAIC data from 1995 to 1999 with an original resolution of about 14 km and artificially decreased the resolution to 100 km. They report a mean pathlength of 122 km and a median value of 55 km for the original data, which are close to our results of IAGOS with a running mean of 10 km. The coarse resolution of SL16 has a mean pathlength of 247 km and a median value of 149 km. These values are between our results for the running means of 50 km and 100 km of the IAGOS data. Additionally, the SL16 coarse data are in very good agreement with the mean and median of the ERA-Interim data.

The comparison of the mean and median values with D14 and SL16 showed that the results differ due to the underlying resolution of the measurement data. For every scale, a different conclusion can be drawn. Therefore, the question arises as to which resolution is feasible to describe the ice supersaturation in a sufficient realistic way for a certain scale. Already with a resolution of 2 km, the number of small ISSRs is decreasing strongly. The median value increases to 7 km, compared to the original resolution. Decreasing the spatial resolution further leads to a decrease in the number of found ISSRs and an increase of the mean and median ISSR pathlengths. At a resolution of 10 km, the cumulative distribution exhibits a different character compared to the original data. When reaching a running mean of 100 km, which is around the spatial resolution of the ERA data set, the numbers of found ISSRs and median pathlength are on the same order of magnitude as the reanalysis data. When comparing the results of the 100 km running mean of IAGOS with the ERA data set, it is also noteworthy that the behaviour for ERA is clearly different for pathlengths smaller than 100 km. ERA shows a significantly higher probability for very small ISSRs (<10 km) than the running mean with 100 km. However, the increase in probability to pathlengths of up to 100 km is flatter in ERA. Again, as a reminder, this is the scale of the spatial resolution of ERA.

It is clear that the ISSR with pathlengths smaller than 100 km is not represented in the ERA model in the same way that the running mean of IAGOS shows it. At first, this discrepancy may look small. However, as mentioned before, small ISSRs also can have a profound effect as a formation region of cirrus clouds. The impact of these smaller ISSRs on the larger scale by changing the dynamics around the tropopause is not clear yet.

4.2 Seasonal cycle and height dependence of ISSR pathlengths

The previous results showed the overall statistics of ISSR in the North Atlantic region. Fortunately, the data set allows for a more sophisticated investigation of ISSR properties such as seasonal cycle or height dependence. Therefore, the seasonal cycle for the lower stratosphere, tropopause and upper troposphere is presented in Fig. 10 for IAGOS and ERA. For the sake of clarity, we combine the three upper levels to “lower stratosphere” and the three lower layers to “upper troposphere”. Starting with spring (MAM), the cumulative distribution shows that for IAGOS in the lower stratosphere and the tropopause region a higher fraction of short ISSRs is present than in the upper troposphere. Up to 75 % of the ISSRs in the lower stratosphere and the tropopause region are smaller than 10 km. The upper troposphere shows the highest fraction of pathlengths between 10 and 100 km. In the lower stratosphere, pathlengths larger than 100 km are more common on a percentage basis compared to the tropopause and upper troposphere layers.

Figure 10Seasonal cycle of ISSRs for lower stratosphere (blue), tropopause (black) and upper troposphere (red). Dashed lines show results for ERA. Panels (a) and (b) represent spring and summer months; (c) and (d) represent fall and winter months, respectively.

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A clearly different result is visible during the summer months (JJA) in the lower stratosphere. Overall, 60 % of the ISSRs are smaller than 2 km and over 80 % smaller than 10 km. The special conditions for the stratosphere in summer are also visible in the statistical values shown in Table 6. While the mean pathlength in the stratosphere for spring is around 55 km, this value decreases to 35.8 km in summer, before an increase to approximately 70 km in fall and winter is observed. It has to be noted that the number of ISSRs in the stratosphere during summer is over 2 times higher compared to the other seasons.

Table 6Number (N), mean and median of ISSR pathlengths L (km) for the upper troposphere, tropopause and lower stratosphere for the MAM, JJA, SON and DJF seasons.

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It is not clear what kind of process is responsible for the large amount of small ISSRs during summer in the lower stratosphere. In principle, relative humidity with respect to ice can be altered by a change of temperature, pressure or specific humidity. Processes behind these changes can be especially adiabatic expansion or mixing of different air masses. SL16 investigated the origin of small-scale ISSRs and concluded that most of the variation of RH_i is due to adiabatic processes, i.e. cooling by expansion. This means that the transport of air masses from different altitudes creates small-scale variations of RH_i in the region from the upper troposphere to the lower stratosphere. However, a deeper investigation of this question requires three-dimensional data and trajectory analysis, which are not in the scope of the present study but should be conducted in the future.

The results for fall (SON) and winter (DJF) are very similar. The tropopause region shows the highest percentage of ISSRs with a pathlength smaller than 10 km. Pathlengths between 10 and 100 km show the highest fraction in the upper troposphere, while the highest percentage of ISSRs with sizes larger than 100 km can be found in the lower stratosphere.

The results for ERA (dotted lines) in spring, and also for the other seasons, are clearly different. As mentioned above, short ISSRs are underestimated by ERA due to the spatial resolution, which is visible for all seasons. The different resolution leads also to other relations of the pathlengths between different height levels. For instance, the highest fraction of ISSR in spring with a pathlength between 10 and 100 km is found in the lower stratosphere. This behaviour is reversed compared to the IAGOS data set, where the upper troposphere showed the highest fraction. The same observation can be made in winter as well. Not surprisingly, ERA misses also the high fraction of short ISSRs in the stratosphere during the summer season.

In general, the mean pathlength of an ISSR in the IAGOS data set is significantly larger in the stratosphere compared to the upper troposphere and tropopause layer, except for the summer season, which is also shown in Fig. 11. Comparing the mean pathlengths for every season in the IAGOS data makes clear that the strongest seasonal cycle is present in the lower stratosphere, with the lowest mean pathlength in summer and the highest values in fall and winter. This might be due to the enhanced storm track activity during fall and winter, where the mass flux (including water vapour) from the troposphere to the stratosphere is largest (Reutter et al., 2015). Further investigations are needed to answer this question.

The two lower layers also show a seasonal cycle, however with a smaller amplitude and shorter absolute mean values. While the upper troposphere also shows the shortest mean pathlength in the summer, the minimum in the tropopause is found during winter. Note that, due to the large number of very small pathlengths in all seasons and all levels and the logarithmic binning of the results, the median values show only a small interseasonal fluctuation. Figure 11 also shows the seasonal cycle of the mean and median pathlengths for the ERA data set. As expected, due to the large resolution of the data set, also the mean and median values are significantly larger compared to IAGOS. More importantly, the seasonal cycle of ERA is shifted, especially for the tropopause and lower stratosphere. The maximum mean pathlength in the tropopause can be found in summer for IAGOS, where, in the ERA data, the minimum pathlength is found. The same holds true for the lower stratosphere, where the minimum for IAGOS is also found in summer, where ERA exhibits the maximum. Additionally, the relative amplitude of the seasonal cycle is smaller compared to IAGOS, most prominent in the lower stratosphere. Here, also the spread of the data, indicated by the size of the boxes, shows a large fluctuation in the IAGOS data set, which is not captured by ERA.

Figure 11Box-and-whisker plot of the seasonal cycle of pathlengths of ISSR for different atmospheric layers in IAGOS (a–c) and ERA (d–f). For each box, the squares denote the mean pathlength and black lines the median pathlength, respectively.

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SL16 also investigated the seasonal cycle of ISSRs. All ISSRs of the extratropics (latitude ≥30^∘) were separated into “troposphere”, “stratosphere” and “in between” using the ozone mixing ratio. This chemical definition of the tropopause is close to the thermal definition. However, in our study, we use the dynamical definition of the tropopause. This has to be kept in mind for the interpretation of the comparison. As mentioned above, the data used in SL16 showed a coarser resolution of about 1 min (which converts to about 14 km depending on the true air speed of the plane) in contrast to the much higher 4 s (about 1 km) resolution in this study. They focused on the large-scale aspects of ISSRs, and therefore the original data were analysed with a coarse resolution (realized with a running mean of the original data) of about 100 km. The coarser resolution makes a quantitative comparison difficult, since already 60 %–80 % of the ISSRs in our study are smaller than 10 km, i.e. below the spatial resolution of the original data in SL16. The maximum of the mean pathlength in SL16 for the stratosphere is found in winter, while the minimum is found in fall. This is in contrast to the finding in the present study, where, on the one hand, in winter also the maximum pathlengths are found, but the minimum is found in summer. Additionally, during fall, about the same mean pathlength can be found as in winter. The comparison of the seasonal cycle for the tropopause layer between SL16 and the present study also reveals a shift. The maximum mean pathlength in SL16 is found in fall, where our study detects the maximum in summer. The seasonal cycle in the tropospheric layer in SL16 and the present study is in good agreement.

It seems that the difference in the seasonal cycle between SL16 and our study can be, to a large fraction, attributed to the spatial resolution of the data. Figure 11 shows also the seasonal cycle for ERA, where the agreement with SL16 is better. Also, as mentioned in the discussion of Table 5, the agreement between ERA, the running mean of 50 and 100 km, as well as the results of SL16, is very good. Therefore, it is important to have the awareness that the spatial resolution can strongly influence the results of ISSR pathlengths.

4.3 Seasonal cycle and height dependence of the distances between ISSRs

Finally, we present the seasonal cycle of the distance between two neighbouring ISSRs. Figure 12 shows the cumulative distributions of the distance between ISSRs for IAGOS and ERA, while in Table 7 the statistical overview for IAGOS is given. Here, a clear seasonal cycle is visible in all three layers, in contrast to the pathlengths of ISSR. For all layers, the maximum of the mean distance is found in fall, with the largest value of 79.1 km in the lower stratosphere and the smallest distance in the upper troposphere with 55 km. The shortest mean distances are found in winter for all layers with values from 35.3 km in the upper troposphere to 40.3 km in the lower stratosphere.

Table 7Mean and median of the distance D (km) between ISSRs in the IAGOS data set for the upper troposphere, tropopause and lower stratosphere for the MAM, JJA, SON and DJF seasons.

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A shorter mean or median distance implies that ISSRs are closer to each other (D14). Therefore, in winter, the conditions favour ISSRs with smaller distances. This also suggests that in the upper troposphere and the tropopause region, where the interseasonal mean pathlength of ISSR does not change strongly, the structure of ISSR is more heterogeneous than in other seasons. For the lower stratosphere, one has to keep in mind that the mean pathlength in winter is, together with fall, significantly larger than in spring or summer. Therefore, not only is the distance between ISSRs shortest, but also the pathlength is largest.

In D14, the authors presented a mean distance between ISSRs of about 47 km, while the median distance is approximately 1 km. These values are in good agreement with our findings. However, as mentioned before, D14 used global data without the distinction between geographical region or height. SL16 also investigated the distance between ISSRs. The mean and median values are significantly larger than in the present study, which is, again, due to the different spatial resolution. Also, as for the ISSR pathlength, the seasonal cycle is shifted compared to the higher resolution in our work.

The results for ERA (dotted lines in Fig. 12) show again a clearly different picture. The comparison of the height dependence between IAGOS and ERA reveals a reversed and even enhanced dependence as it is shown by the distance of the vertical layers within the ERA data set. For instance, in winter, the reversed dependence with height is most prominent. Between 1 and 100 km, the lower stratosphere shows the highest fraction of distances, followed by the tropopause layer and the upper troposphere. In ERA, this dependence is the opposite, with the highest fraction in the upper troposphere and the lowest fraction in the lower stratosphere.

Figure 12Seasonal cycle of the distance between ISSRs for lower stratosphere (blue), tropopause (black) and upper troposphere (red). Dashed lines show results for ERA. Panels (a) and (b) represent spring and summer months; (c) and (d) represent fall and winter months, respectively.

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