To determine the potential for contrail formation in the air masses meeting the above thresholds, air mass thermodynamic properties are analysed by applying the Schmidt–Appleman criterion (SAC). The SAC at aircraft pressure level p depends on the gradient G of the mixing line (see Fig. 1) (Schumann, 1996): 1G=EIH2OcppεQ1-η, where p is the ambient air pressure, cp is the isobaric heat capacity of air (1004 J kg-1 K-1), and ε is the ratio of molar masses of water and dry air (0.622). For the calculation of G, the emission index of water vapour EIH2O and fuel heat capacity Q from burning conventional jet fuel (kerosene) are considered: EIH2O=1.25 kg (kg fuel)-1 and Q=43.2 MJ (kg fuel)-1, assuming an overall propulsion efficiency η=0.31. G (unit: Pa K-1) represents the gradient of the trajectory of aircraft exhaust air isobaric mixing with the surrounding ambient air – the blue line in Fig. 1, where the dependence of the water vapour partial pressure on temperature in the isobaric mixture of an aircraft plume and ambient air is illustrated (adapted from Fig. 3 in Schumann, 1996). The sampled air masses are assumed to be released from aircraft engines and have undergone the isobaric mixing process while detraining into ambient air. Tamb and RHice at an assumed measuring position (the red dot in Fig. 1), therefore, mark the ending point of an individual air parcel's mixing line. If the mixing line touched or crossed the ice–liquid saturation curve, for example, the blue, dashed black, or cyan lines in Fig. 1, the measured cloud particle could have been very probably involved in the formation of contrails during its evolution. Cirrus cloud particles sampled at thermodynamic positions not fulfilling SAC are considered irrelevant to contrail formation and are treated as natural cirrus.

To better discriminate between contrail and natural cirrus, we define another criterion by dividing the altitude range of the dataset fulfilling SAC into the most frequent aircraft cruising altitude (CA) range and the altitudes beyond. To determine the CA pressure range, we surveyed the 15 years of IAGOS-MOZAIC pressure measurements over the North Atlantic and Europe regions aboard passenger aircraft. The occurrence probabilities of flight levels per 10 hPa bin are shown in Fig. 2. The most frequently visited atmospheric pressure levels are from 200 to 270 K. However, ice cloud properties at lower altitudes with pressure greater than 245 hPa show distinct behaviour from those at higher altitudes below 245 hPa and seem closer to those observed at positions not fulfilling SAC, implying that they could be natural cirrus or extensively aged contrail cirrus. Hence, the pressure altitude range of 200–245 hPa is adopted as the CA range for further analysis.

The principle of the aircraft exhaust plume detection assumes that a simultaneous enhancement of multiple products emitted from aviation fuel combustion, here total aerosol particles and reactive nitrogen NOy measured by the instruments AMETYST and AENEAS (Sect. 2.1), serves as a clear marker for air masses influenced by aircraft exhaust (Schumann et al., 2002). In this work, the total aerosol particle number concentration and the mixing ratio of NOy, which can be considered a passive tracer in aircraft plumes up to a plume age of 18 h, are used to detect aircraft exhaust plumes along the flights from the concurrent increased particle number concentrations and NOy mixing ratios in comparison to atmospheric background values (Mahnke et al., 2022). The plume detection algorithm is restricted to a minimum NOy excess of around 0.1 ppbv above the atmospheric background, which corresponds to a maximum plume age of approximately 2–5 h, depending on the diffusion speed of aircraft exhaust and NOy emission index according to aircraft type.

The plume detection algorithm is applied to 10 ML-CIRRUS flights, for which both NOy and aerosol measurements are available. Only the air masses containing ice particles detected at Tamb<235 K are considered as contrail cirrus. Different from the passive tracer NOy, cirrus particles are subjected to gravity waves and turbulence. As a result, at some point the contrail ice particles may become spatially separated from the plume, and/or the plume may become spatially associated with particles formed in natural cirrus clouds. Therefore, the plume detection algorithm may miss contrail cirrus particles. The contrails that can be found with the help of the plume detection algorithm can be viewed as a subset of the contrails because as long as the plume is detected and contains cirrus ice particles, these ice crystals are highly likely to stem from contrails. The final in-cloud sampling time with aircraft exhaust plume encounter, as identified by the plume detection algorithm, is approximately 0.99 h, around 3200 cloud samples (max. ∼ 1 km length of sampled in-cloud space) at 1 Hz sampling frequency. The sizes in flight hours of each sub-datasets after applying the SAC, CA, and plume detection criteria are listed in Table S2. We use the plume subset to show that the microphysical properties of these contrails are comparable to those from the larger dataset (determined with SAC + CA) that also includes contrail ice particles spatially separated from the plume. This comparison increases our confidence in the method to identify contrails via the SAC and CA criteria.

Our attempt at SAC calculation divides the ML-CIRRUS cirrus dataset discussed in the previous section into two categories: the dataset of cloud particles sampled under conditions fulfilling SAC (SAC+, ∼ 11.2 h) and the complementary dataset not fulfilling SAC (SAC-, ∼ 3.5 h); see Fig. 1d for details. As discussed in Sect. 2.3.1 and shown in Fig. 1, a cloud sample fulfilling SAC is considered very possibly involved in the formation of contrails during its evolution, and the one measured at thermodynamic positions failing SAC is considered irrelevant to contrail formation and is regarded as natural cirrus.

Note, however, that natural cirrus could also be included in the SAC+ group, meaning that SAC alone is not a sufficient criterion to identify contrail cirrus, while cirrus detected in the SAC- group can be unambiguously attributed to natural cirrus. Despite the limited differentiation between contrail and natural cirrus using SAC alone, we will first discuss the differences in the microphysical properties between the SAC+ and SAC- datasets. The sharpening of the separation of the full ensemble into aviation-influenced cirrus and natural cirrus by adding another criterion of the most frequent cruising altitude range will then be discussed in Sect. 3.2.2.

Figure 4a and b display the Nice–Rice relations for the SAC+ and SAC- datasets, respectively, with the occurrence frequency normalized to the total number of measurements in each dataset. Small ice crystals in higher concentrations are mainly found in the SAC+ group. In the SAC+ dataset, the median Nice=0.04 cm-3 doubles the median value of the SAC- dataset. Conversely, the median Rice of the SAC+ group (20.6 µm) is only half of the value (42.4 µm) of the SAC- counterpart. Nice in the SAC+ dataset reaches values as high as 20 cm-3 for Rice smaller than 30 µm, while Nice in the SAC- dataset is mostly below 1 cm-3, with most particles larger than 30 µm. The highest occurrence frequencies in the SAC+ and SAC- datasets (enclosed by the 50th percentile contours) dwell on the lower and upper sides of the 10 ppmv IWC isoline, respectively.

Besides the fact that in the SAC+ dataset both natural and contrail cirrus can be found, the SAC- group only contains natural cirrus. The two groups largely correspond to cirrus formed from different mechanisms, namely in situ- and liquid-origin cirrus. Most in situ-origin (IWC <10 ppmv) and some liquid-origin cirrus (IWC >10 ppmv) are found in the SAC+ group; conversely, most of the liquid-origin cirrus and a small part of the in situ-origin cirrus are in the SAC- counterpart. Contrail cirrus belongs to the in situ-origin cirrus type, since it appears in the temperature range Tamb<235 K, either without pre-existing cirrus (contrail cirrus) or superimposed on existing cirrus (embedded contrails). As embedded contrails, they could also appear as the liquid-origin cirrus.

The contrast between the SAC+ and SAC- groups is illustrated in Fig. 4c, showing the differences between Fig. 4a and b. The reddish area indicates that ice crystals measured in the environments satisfying SAC are prone to contrail cirrus, whereas the bluish area, in contrast, shows ice crystals that are linked to natural cirrus.

The other pronounced differences between the SAC+ and SAC- groups are the most frequently appearing RHice and the respective temperature ranges, as shown in the lower panel of Fig. 4. The highest occurrence frequencies of RHice in the SAC+ group concentrate at slight ice subsaturation at ∼ 90 % RHice in the Tamb range of 207–218 K. The slight ice-subsaturation feature is associated with younger contrails with high Nice and small Rice, as can been seen from Fig. S2b (see Supplement), where the Nice–Rice relation is shown colour-coded with RHice for the SAC+ group in the CA range (see Sect. 2.3.2). In the SAC- dataset, the highest frequencies of RHice cluster around 100 % at 10 K warmer temperatures and spread over the Nice–Rice parameter space (Fig. S2c). The warm temperature range, which is already shown in Fig. 3, reflects the fact that colder temperatures are needed to fulfil SAC because the water saturation pressure at warmer temperatures is almost always so high that the amount of water in the ambient air together with the additional water from aircraft exhaust is insufficient to reach supersaturation with respect to water to form droplets.

In spite of the clear differences in ice particle properties and ambient RHice conditions resulted from applying SAC (Fig. 4f), ambiguities remain to characterize contrail cirrus and distinguish it from natural cirrus because the natural cirrus of in situ-origin that has formed at rather low temperatures can show the characteristics of medium Nice (0.1 cm-3), low IWC, and small Rice as well and would thus be misclassified as contrail cirrus. Additionally, even high Nice accompanied by small Rice can appear in natural cirrus as a result of in situ homogeneously freezing in high updraughts (Krämer et al., 2016).

Here, the SAC+ dataset shown in Fig. 4a and d is split into one group inside the most frequent cruising altitude (CA) range and the other one outside the CA range using the CA pressure boundaries defined in Sect. 2.3.2. The ice cloud properties and RHice occurrence frequencies related to ambient temperature inside and outside the CA range are presented and discussed below.

The Nice–Rice relation of the cirrus fulfilling the SAC and detected inside the CA range is shown in Fig. 5a, while the cirrus outside the CA range is depicted in Fig. 5c. Comparing the Nice–Rice relation showing all SAC+ cirrus (Fig. 4a) to that inside and outside the CA range, it becomes clear that the entire group of liquid-origin cirrus (Rice>30 µm and IWC >10 ppmv) and a part of the in situ-origin cirrus (Rice<30 µm and IWC <10 ppmv) occur outside the CA range; i.e., the cirrus outside the CA range represents a mixture of contrail cirrus, in situ-origin cirrus, and liquid-origin cirrus, later referred to as a cirrus mixture. Inside the CA range, almost only in situ-origin cirrus is present. The mean Rice and Nice of cirrus particles inside the CA range (Fig. 5a) are approximately 17 µm and 0.21 cm-3, corresponding to previous field observations of pure contrail cirrus older than 30 min (Schröder et al., 2000; Voigt et al., 2017; Schumann et al., 2017; Chauvigné et al., 2018).

The classification that the cirrus fulfilling SAC and inside the CA range is pure contrail cirrus is confirmed by the validated contrail cirrus, which fulfils SAC and is identified by applying the aircraft plume detection algorithm (Mahnke et al., 2022) described in Sect. 2.3.3. Since the aerosol and NOy measurements for both flights on 22 March 2014 were missing and aircraft plumes detected at Tamb>235 K are screened out, the valid sampling time encountered aircraft exhaust plumes is approximately 0.9 h, around 3200 cloud samples at 1 Hz sampling frequency, among which 1270 cloud samples are located in the CA range. As adding the CA constraint to the SAC fulfilled plume dataset does not improve the validation significantly (See Sect. S4 in the Supplement for detailed analysis), the following discussion is based on the plume dataset with only the SAC applied.

The Nice–Rice relation for the validated contrail cirrus is displayed in Fig. 5e. The shape of the overall Nice–Rice occurrence frequency distribution for the validated contrail cirrus shows similarity to the pure contrail cirrus differentiated by combining SAC and the CA range (Fig. 5a), especially when looking at the particle population that contains 50 % of the most frequently appearing ice crystals. The median Rice and Nice of the pure contrail cirrus are also close to those of the validated cirrus. In conclusion, combining SAC and the CA range has effectively exposed the differences in the microphysical properties of pure contrail cirrus (SAC+; inside the CA range, Fig. 5a), a cirrus mixture (SAC+; outside the CA range, Fig. 5c), and mostly liquid-origin natural cirrus (SAC-; outside the CA range, Fig. 4b).

In addition, we also inspected the frequency distributions of ice particle sizes in diameter, which are not integrated like mass mean radius and will give further insights into the differences among the cirrus categories and, in addition, confirm the differentiation using the SAC–CA method.

Figure 6a shows the normalized occurrence frequencies of ice particle sizes in the contrail cirrus (in situ-origin), cirrus mixture (contrail cirrus and in situ- and liquid-origin natural cirrus), and mostly liquid-origin natural cirrus. Three size modes of ice particle sizes can be identified from the frequency distributions of the contrail cirrus and natural cirrus: ice particles in the first size mode – Dp=3–17 µm (marked by the short red arrow) – appear more frequently inside the CA range and are attributed to pure contrail cirrus. The next size mode – Dp=3–200 µm (the long red arrow) – is present in contrail cirrus as well as in natural cirrus and is attributed to aged contrails or in situ-origin natural cirrus. The mode Dp=50–400 µm (the black arrow) originates from liquid-origin cirrus. The maximum sizes represent the largest ice particle size of the particle population including 90 % data. Large ice crystals up to about 200–300 µm do appear in contrail cirrus but with a low frequency (see the blue curve in Fig. 6a and also Kübbeler et al., 2011; Voigt et al., 2010). Also, note that 17 µm marks the instrument switches from NIXE-CAS-DPOL to NIXE-CIPg. This might cause the jump of occurrence frequencies instead of a smooth transition.

The histograms in Fig. 6a show that the contrail (red line) and liquid-origin natural (black line) cirrus are most probably distinguishable in the small ice particle diameter range (Dp<17 µm) and the larger size range (Dp>80 µm). Ice crystals between Dp=17–45 µm occur frequently in the contrail cirrus but also in the natural cirrus, which makes it difficult to discriminate between the contrail and natural cirrus in this size range. The signature of a larger number of small ice crystals in natural cirrus occurs in the early phase of homogeneous ice nucleation in faster updraughts. However, such events are transient in time and space and are, therefore, not often found in in situ measurements (Krämer et al., 2020). The contrail cirrus considered here does not contain such homogeneous freezing events. Therefore, ice crystals in the diameter range Dp=3–17 µm with relatively high occurrence frequencies and the large particles of maximum size of about 200 µm can be attributed to contrail cirrus, as already noted above. On the contrary, the natural cirrus has the second highest frequency peak in the ice crystals larger than 54 µm, with the maximum diameter being about 400 µm. This means that the observed contrail cirrus was formed in situ with the special feature of frequently appearing small ice crystals; the natural cirrus, however, as introduced before, is a mixture of in situ-origin and liquid-origin cirrus. It is to be noted here that adding an extra constraint of the CA range to the SAC+ group has greatly minimized the interference of the natural cirrus as well as possibly undistinguishable, deeply aged contrail cirrus of much larger sizes.

The cirrus mixture is interpreted above as a mixture of aged contrail cirrus, mainly in situ-origin cirrus with a small portion of middle-sized liquid-origin cirrus. This is confirmed by the frequency distribution of ice particle sizes shown in Fig. 6a (blue line), where the majority (80 % of the total frequencies) of particle diameters are between 17 and 66 µm, and the maximum size is near 300 µm. From this analysis, it is impossible to judge whether the in situ-origin cirrus is aged contrails, which show the same properties as natural cirrus, or whether these cirrus clouds have formed naturally.

Figure 6b shows that the occurrence frequency distribution of ice particle sizes in the contrail cirrus identified using the SAC–CA combination is very similar to that of the validated contrail cirrus aided by the plume detection scheme. In the reference case of the plume-marked contrail cirrus, there are even more smaller ice particles than in the SAC–CA-determined contrail cirrus. Furthermore, the large ice particles occur with very low frequencies not only in the plume-marked contrail cirrus but also in the contrail cirrus constrained by SAC and the CA range. This adds confidence in the discrimination between contrail cirrus and natural cirrus with the SAC–CA combination.

The RHice–Tamb distribution for the contrail cirrus (SAC+, inside the CA range) is shown in Fig. 5b, while Fig. 5d depicts that for the cirrus mixture (SAC+, outside the CA range). In comparison to Fig. 4e, where the frequencies of RHice in the natural cirrus (SAC-) centre around 100 % at temperatures above 225 K (also reported in regional and global research flight measurements by Krämer et al. (2020), Patnaude et al. (2021), Diao et al. (2014, 2017), and RHice observations on board passenger aircraft by Spichtinger et al. (2004), the RHice inside the contrail cirrus (Fig. 5b) distributes most frequently around 90 % and appears almost exclusively in the temperature range Tamb=207–218 K. As mentioned in Sect. 3.2.1, this subsaturation feature is associated with high Nice and small Rice inside the CA range (Fig. 5a), namely the contrail cirrus, as discussed in previous subsections and shown in the Nice–Rice relations colour-coded with RHice in Fig. S2 (see Supplement). Compared to the RHice distribution in the contrail cirrus (Fig. 5b) and natural cirrus (Fig. 4e), the RHice frequencies in the cirrus mixture (in Fig. 5d) are more broadly distributed around 100 % RHice between 204 and 229 K, yet with slightly higher frequencies between 80 and 100 % at Tamb=207–218 K, similar to the contrail cirrus. The high RHice values up to 140 % in the cirrus mixture are closely related to the in situ-origin cirrus (Nice<0.1 cm-3 and Rice<30 µm) and liquid-origin cirrus (IWC >10 ppmv, Rice>50 µm), as seen from Fig. S2d.

Figure 5f shows that RHice in the validated contrail cirrus falls mostly below ice saturation in the temperature range of 208–218 K, consistent with the ice-subsaturation feature in the pure contrail cirrus (Fig. 5b). We consider the agreement as verification of the method for separating contrail cirrus from natural cirrus using only SAC and the CA range.