The study domain surrounds Switzerland (43.5 to 48.5∘ N and 4 to 12∘ E) and contains most of the Alps. Figure  shows the geographic distribution of all satellite tracks that go through the chosen domain. In order to evaluate the frequency of seeder–feeder situations four variables were created: frac_cov (–) The fraction of sky covered with a specific combination of cloud top and cloud base temperatures. icebase (m) The height (altitude above sea level) of the lowest cloud grid point with T<-35∘C (lowest base of a cirrus cloud). Δzim (m) The distance between the lowest cirrus cloud base and the highest top of the cloud below (in the following called mixed-phase cloud). reff (µm) The effective radius of ice crystals at the lowest cirrus cloud base. All variables were derived from a cloud mask, where DARDAR categories 1, 2, 3 and 4 (ice, ice plus supercooled, liquid (warm and supercooled)) were combined to simply signify the presence of cloud layers. This cloud mask was found to be noisy and was therefore filtered (using a median filter over the surrounding 7×7 point plane, in altitude and horizontally along the track). For icebase, Δzim and reff the cloud mask were combined with a temperature mask to differentiate between mixed-phase and cirrus clouds. In this study, cirrus clouds are defined as clouds at temperatures lower than -35 ∘C, and mixed-phase clouds are defined as all clouds with temperatures warmer than -35 ∘C. Depending on their size, liquid cloud droplets supercool to -35 to -40 ∘C before freezing homogeneously (e.g. ). However, in tests preceding this study, a threshold of -38 instead of -35 ∘C proved to have no evident impact on the results. Note that clouds termed “mixed-phase” could in principle be in the liquid or ice phases in reality, depending on their history and the presence of ice-nucleating particles (see Fig. a). Similarly, in this study, we denote all ice clouds at temperatures colder than -35 ∘C as cirrus clouds, which could be isolated ice clouds or the upper parts of mixed-phase clouds.

The combined cloud and temperature masks were applied to the altitude and effective ice crystal variable in the DARDAR data to find the values at the lowest cirrus cloud base (for icebase, reff and Δzim) and at the highest mixed-phase cloud top (for Δzim). Prior to this, the effective ice crystal radius was also filtered for consistency. As a filter for the effective radius, the vertical median with an extent of four pixels up and four pixels down from the one in question was applied, using only those pixels where the unfiltered cloud mask detected a cloud. For Δzim, the altitude of the highest mixed-phase cloud top was subtracted from the altitude of the lowest cirrus cloud base. Finally, the dataset was saved on a grid with a resolution of 0.005∘×0.005∘ with no quality loss compared to the original DARDAR data. During regridding, areas containing no satellite tracks were set to missing data to be able to derive the total number of observations later on.

Figure shows the average frequency of Δzim, the distance between the cirrus and mixed-phase cloud, within the DARDAR dataset (as described in Sect. “Analysis method”, any cloud at temperatures >-35 ∘C is termed “mixed-phase” in this study). It can be understood as the average distribution of Δzim within a unit area. Overall, 69 % of all measurements do not show a cirrus–mixed-phase cloud distance at all. In those cases, either clouds of only one category were present or none at all (30 % of the measurements are cloud free). In total, 31 % of the measurements contain both a cirrus and a mixed-phase cloud simultaneously. This is the percentage of cases in which a seeding of the lower cloud by ice crystals falling from the ice cloud above is possible. Tailoring this result to the sedimentation of ice crystals from a cirrus cloud, when only the measurements that detect a cirrus cloud are taken into account, in 75 % of these measurements also a mixed-phase cloud below them is detected.

In 44 % of the cases with a detected cirrus cloud (18 % in total), Δzim is smaller than 100m. This may either be the case when the cirrus and the mixed-phase cloud are truly separated by a small distance, or when the two differently classified layers are actually part of the same cloud. From the construction of the classification algorithm, the latter would be the case when the -35 ∘C isotherm intersects the cloud. This case is illustrated in Fig. b. In contrast to and , our algorithm does not require a cloud-free layer in between the mixed-phase and the cirrus cloud, so we also observe a potential for in-cloud seeding. However, clouds connected by sedimenting ice would also be seen as a cirrus cloud with a very small or no distance to the next mixed-phase cloud in our analysis. observed ice virga between the seeder and the feeder cloud and also mentioned this as a cause of misclassification in their study. Of course, in cases where the -35 ∘C isotherm lies within the cirrus cloud, there could be another mixed-phase cloud underneath. The distance to this second cloud does not appear in our analysis.

The other half of the cases (Δzim>100 m) represents the classical external seeder–feeder situation, with a cirrus cloud clearly separated from a mixed-phase cloud below (see Fig. a). The Δzim are distributed equally between 2000 and 6000 m, increase for smaller and decrease for larger Δzim. The smaller frequencies at Δzim<2000 m are due to the few possibilities for both cirrus and mixed-phase cloud to be located close to the -35 ∘C isotherm. Because the cirrus cloud frequency decreases for large heights, the Δzim occurrence frequency decreases as well for Δzim>6000 m. Generally speaking, Δzim increases with increasing upper cloud height (see Fig. ).

In this distribution and in the following analysis, the effect of vertical wind shear of the horizontal wind cannot be taken into account, because the satellite retrieval only obtains instantaneous profiles, without any information on their temporal development. In the time that ice crystals need to sediment distances of a few kilometres, undoubtedly the clouds in question move relative to each other when wind shear is present. However, this movement can go in both ways, either removing or creating a multi-layer cloud situation. On average, these two effects are expected to cancel out, so that the results with and without considering wind shear should be similar.

Our results for multi-layer cloud occurrence frequency, 13 % (Δzim>100 m), are smaller than the ones given in the following literature. In their analysis of CALIPSO and CloudSat data, estimated the global occurrence of multiple layers to be 24 %. derived an estimate of 42 % from a radiosonde dataset. Of course the domain around Switzerland in this study is not expected to reproduce the global average, but Fig. 17a in and Fig. 5 in show average frequencies for Switzerland that are similar to the global average frequency. Using CloudSat and CALIPSO data as well, found an average multi-layer cloud fraction of about 25 % for the midlatitudes of Switzerland. The layers derived from radiosonde data by are much thinner than the ones found with remote sensing, possibly because large sedimenting particles cause multiple thin layers to be identified as one large layer by the radar . One might therefore expect that the results from this current satellite study are closer to the ones from and . Most importantly, the present study only looks at multiple layer occurrence between cirrus and mixed-phase clouds, which is lower than the total multi-layer occurrence frequency. As a proxy for the multiple layer occurrence between cirrus and mixed-phase clouds in , one might use the relative occurrence frequency of low with high clouds and middle with high clouds from (about 70 % and 10 %), relative to their overall multi-layer occurrence frequency of 24 %. Their resulting absolute high with low or mid-cloud layer occurrence frequency is then approximately 20 %. The result for two cloud cases in this study of 13 % is smaller than the value derived by , although they used even more restrictive conditions for their classification of multiple layers, requiring almost 1 km of cloud-free space in between them. As mentioned before, the in-cloud seeder–feeder situations provide no information on the occurrence of mixed-phase layers below, hiding possible two-cloud cases. Cirrus clouds in the tropical tropopause layer and clouds close to the surface are known to be missed by the radar and lidar on CloudSat and CALIPSO , but these are not relevant for this study.

A geographical difference in cloud cover could be expected from the differing impacts that weather regimes have on different European regions in general . The study domain contains locations with a large range of surface altitudes (see Fig. ). One could imagine the Δzim to be smaller in the Alps than over the Swiss Plateau, simply because of a thinner troposphere over orography. Also the orographic forcing would be expected to increase cloud cover. For an analysis of topographical influence, we split the dataset by surface altitudes above or below 1km and analyse the distribution of Δzim, shown in Table . The difference in the fraction of distances larger than 100m between locations with a topography higher or lower than 1km is less than 1%. The distribution of total Δzim between mountainous terrain and flat land reproduces the distribution of measurements (about 30 % are taken over orography higher than 1000m and about 70 % over terrain lower than 1000m; not shown). Contrary to what we expected, we find no topographical effect in the distribution of Δzim (see also Fig. ).

Table also contains the results of the seasonal analysis of Δzim. Winter measurements have more multi-layer clouds according to our definition than summer measurements. The relative increase of the fractions of Δzim is similar for the smaller (Δzim<100 m) and the larger distances (Δzim>100 m). In particular, winter nights have the highest fraction of multiple layer cloud measurements. Multiple cloud layers are about 23 % more frequent in winter nights than in summer nights, mostly due to an increase in Δzim larger than 100 m. Other than the increase in Δzim during the night in winter, there are no substantial differences in frequencies between day and night within a seasonal category.

The simplest explanation for the increased frequency of multi-layer clouds in winter measurements is simply an increased cloud cover in winter. To see whether this is a robust finding, it was tested with the CALIPSO – GCM Oriented Cloud Calipso Product (GOCCP) dataset . With a comparison of frac_cov from DARDAR vs. CALIPSO cloud cover data (Fig. ), the two datasets were found to mostly agree. Therefore, the CALIPSO dataset can be used to validate the hypothesis of an increased cloud cover in winter. Indeed, in CALIPSO, total winter cloud cover is higher over almost the whole domain (Fig. c). The increase of cloud cover in winter is strongest for low and high clouds (low clouds: pressure >680 hPa, height <3.2 km, high clouds: pressure <400 hPa, height >6.5 km in the CALIPSO data; not shown). This confirms the finding that in winter we see an increase in both small and large Δzim. In addition, icebase is lower in winter (not shown), in particular for Δzim<100 m, which also increases the number of Δzim.

The DARDAR dataset provides the mean effective ice crystal radius, which we use in our sublimation calculations. In Fig. , the size distribution is displayed by the ice crystals' occurrence height, namely the lowest cirrus cloud base heights (icebase). The ice crystal size range, between 25 and 60 µm in radius, agrees with the one found in another DARDAR study by . It is also within the range from 1 to 100 µm that find for cirrus clouds in aircraft campaigns.

There is a visible trend for smaller ice crystals at higher altitudes. This again agrees with and , who find that ice crystal size decreases with decreasing temperature. An interesting feature in Fig. a is that while the shape of the distribution is rather symmetrical around this trend, large ice crystals abruptly stop appearing at heights larger than about 9.5 km. This hints at two modes within the size distribution. These have been found in earlier studies and have lately been linked to the different origins of cirrus clouds by , , , , and . Liquid origin clouds form from supercooled water droplets which are uplifted to the cirrus temperature range. They freeze either heterogeneously at warmer temperatures or predominantly homogeneously at temperatures around -35 ∘C. In the cirrus temperature range, cirrus clouds can also form by homogeneous nucleation of solution droplets or heterogeneous nucleation on ice-nucleating particles. These cirrus clouds are termed “in situ origin cirrus clouds”. The two types mostly differ in their ice water content and the ice crystal size, with both being larger for liquid origin cirrus clouds .

We split the dataset into one part with Δzim>100 m and one with Δzim<100 m as a proxy for the two cloud origins: in situ origin cirrus have large distances to the next underlying mixed-phase cloud, while liquid origin cirrus appear close to the -35 ∘C isotherm. This separation indeed produces two different modes, as can be seen in Fig. b and c. Figure b corresponds to liquid origin cirrus clouds. It displays larger ice crystals, from ≈35 to ≈90 µm at cirrus cloud base heights from 4500 to 9500 m, with an abrupt decrease in occurrence frequency at cirrus cloud base heights higher than 9500 m. The decrease at the maximum cirrus cloud base height is associated with Δzim<100 m (see Fig. ). The in situ cirrus clouds in Fig. c display smaller crystals, from ≈30 to ≈60 µm, over a larger cirrus cloud height range, from roughly 6 to 13 km. Here, the trend of smaller ice crystals at larger cirrus cloud heights is obvious. Figure  confirms the distinction between liquid origin and in situ cirrus clouds as proposed, e.g. by . It also confirms the finding from that liquid origin cirrus clouds are composed of larger ice crystals.

There are a few caveats to this result. First, by the construction of the classification algorithm, in situ cirrus clouds are sampled for the ice crystal radius at their base, while liquid origin clouds are sampled in the interior. However, this difference is expected to have the opposite effect of what we observed (larger ice crystals for liquid origin clouds). At the cloud bases, the ice crystals are expected to be larger than in their core , simply because of larger particles sedimenting further down within a cloud. Secondly, the classification scheme only has liquid origin clouds in the Δzim<100 m part, while liquid origin clouds that have been uplifted entirely to heights above the -35 ∘C isotherm are present in the second, in situ origin cirrus part of the dataset (Δzim>100 m), if such a lifting occurs. This erroneous classification has already been noted by . However, Fig. c displays only one mode, missing any signal of the mode present in the Δzim<100 m part of the dataset (see Fig. b). This suggests that the influence of the liquid origin on the microphysical properties of the cirrus clouds is lost once the clouds are lifted, for example, because the large ice crystals sediment out, or that lifting of entire clouds above the -35 ∘C isotherm hardly ever occurs. , who investigated the frequency of the formation pathways in a trajectory-based analysis, noted that ice crystal sedimentation and cloud turbulence could “potentially alter the local cirrus characteristics and “confuse” the simple categorization”. However, the distinctively different ice crystal size distributions for the two modes in Fig. b and c suggest that liquid origin clouds are not altered by sedimentation so much that they are confused for in situ clouds. Instead, the data suggest that liquid origin clouds are hardly ever lifted entirely above the -35 ∘C isotherm, which is likely because of their large vertical extent.

In a broader context, the results in Fig.  show that satellite data, in particular the DARDAR dataset, are valid means to explore the classification of cirrus clouds into liquid and in situ origin further, as it has been called for by .

Note that the ice crystal radii, the cirrus cloud base heights and the Δzim values span a wide range of values (see Figs.  and ). Therefore, sublimation calculations needed to be applied to each instance individually, as detailed in the next section.

For the evaluation of the survival chance, only cases with Δzim>100 m were taken into account. Distances smaller than 100 m represent the in-cloud seeder–feeder mechanism, where ice crystals fall through saturated or supersaturated cloudy air only before interacting with other hydrometeors. Comparing Fig. a and b, one can see the effect of temperature and relative humidity: ice crystals only reach the lower cloud if RHi>90 %. Only those starting at temperatures warmer than -65 ∘C seed. At lower temperatures, the ice crystals sublimate, even if the air was supersaturated at the start of the sedimentation. Note that due to data storage constraints, we can only show the impact of the temperature and relative humidity at the starting cirrus cloud base height on the falling ice crystals. But height-resolved ERA5 data of temperature and relative humidity were used for the calculations. These starting values can be seen as proxies for the values during sedimentation, but for large sedimentation distances of up to about 5 km, the starting values are not representative. conducted a sensitivity study with relative humidities varying by ±5 %, but this variation is rather small. In this, their resulting seeding fraction does not change substantially. However, the relative humidity variations over the distances travelled by ice crystals in our calculations can exceed 5 % substantially.

Figure c shows that ice crystals do not survive the fall from cirrus cloud base heights above 11 km. We attribute this to smaller ice crystals at these colder temperatures and to the fact that high cirrus cloud bases correspond to large distances to lower-lying mixed-phase clouds that ice crystals are less likely to survive. This also explains why ice crystals starting their sedimentation at colder temperatures sublimate more often before reaching a lower cloud than those sedimenting from warmer cloud bases, as the temperature limit of -65 ∘C corresponds to the height limit of 11 km (see Fig. ). Both and identified the ice crystal size as important determinant for ice crystal survival. Here, we find that ice crystals with radii smaller than 30 µm usually do not survive the sedimentation. On the other hand, also larger ice crystal sizes, above 50 µm, do not guarantee a successful seeding. Note that we only evaluate the mean ice crystal size is used in this study so that the large spread which occurs in ice crystal size distributions is not represented.

For the analysis of both environmental parameters and DARDAR variables on ice crystal survival, the results assuming ice crystals to be plates and bullet rosettes are similar to those presented in here. One marked difference is that crystals starting in a subsaturated environment with respect to ice sublimate and do not seed when assuming them to be plates or bullet rosettes (see Fig. ).

A comparison to literature data is difficult because the assumptions vary greatly between studies. compute sublimation heights for ice particles with an initial radius of 160 µm, at fixed relative humidities with respect to ice between 30 % and 90 %. Their spherical ice particles sublimated at distances of 1 to 4 km from the starting altitude of about 9 km. The relative humidities that we find at the starting altitudes are similar to their range, as are our survival distances. did not provide information on the distances between the cloud layers they studied. Preliminary work by contained the result of two exemplary sublimation calculations assuming constant temperature and relative humidity in the subsaturated layer. The result is in line with the results presented in Fig. , where about 42 %, 47 % or 64 % of cases with Δzim=500 m lead to successful seeding (for rosettes, plates and spheres, respectively).

The fraction of Δzim with successful seeding is shown in Fig.  for plates, spherical ice crystals and bullet rosettes. For Δzim>5 km, there is a only a slight chance for ice crystals to survive the fall between the cirrus and the underlying mixed-phase cloud. For Δzim=2 km the survival rate of spherical ice crystals increases to 20 %. Survival chances increase linearly, until 81 % of the spherical ice crystals cause seeding at a falling distance of 200 m. Plate-like ice crystals experience a larger drag force and therefore fall slower than spheres. As they have more time to sublimate during their slower fall, they are less likely to survive at any of the distances. This was also found by and is even more pronounced for bullet rosettes. Combining this with the respective Δzim frequencies, Fig.  also displays the fraction of successful seedings in our measurements. In 14 % of the measurements, we see a seeder–feeder situation where plate-like ice crystals do not sublimate but can seed the lower-lying cloud after sedimentation (11 % for rosettes and 19 % for spheres).

A surprising result for all ice crystal shapes is that the survival fraction for Δzim<100 m is smaller than 1. As explained before, there is no subsaturated layer in this continuous cloud, so the sedimenting ice crystals should not sublimate at all. The reason for the discrepancy most likely lies in the usage of two independent datasets in the classification of cloud layers and the calculation of ice crystal survival: the distance between the two layers and the cloud heights are taken from the DARDAR dataset, while the relative humidity was taken from ERA5. For example, the temperature profile in ERA5 over Switzerland is about 5 ∘C colder than the one in the DARDAR data, which also originates from ECMWF. A reason for this discrepancy could not be found, and it is not thought to change our findings significantly, but the discrepancy between the datasets should be investigated further. One might correct for this by simply setting the survival fraction to 1 within the Δzim<100 m bin, i.e. within the cloud. However, we chose to leave the inconsistency as an estimate of the uncertainty associated with the seeding fractions given for larger distances.

In general, as stated before, the ice crystal radius and hence the survival fraction shown in Fig.  are conservative estimates. In particular, with the new DARDAR dataset (v3) , survival fractions are expected to be higher than shown here for DARDAR v2, since the effective ice crystal radii are larger in the former (see Sect. ). In their sublimation calculations, use larger ice crystal radii of 100 µm for cirrus clouds as well. Additionally, there is the possibility of seeding by pre-activated particles even after the macroscopic ice crystal has sublimated, as described in . Some ice in pores or shielded pockets of these particles could survive the subsaturated air in between cloud layers and initiate new ice crystal formation once the particle reaches the supersaturated air in the lower cloud layer.

With the results presented here, one can comment on the method used in to filter out ice clouds that were seeded. They simply reclassified any cloud with an ice cloud less than 2 km above as a liquid cloud. Given that Fig.  shows that only 10 % to 20 % of ice crystals survive Δzim=2 km, it is likely that find too many seeded clouds. Finally, comparing to observations, the case of a survival of Δzim=5 km, as the one case evaluated in , is rather unlikely according to our data.