The cloud-tracking toolbox of is used to track individual clouds in time-resolved observations with geostationary sensors. The algorithm identifies objects in 2 consecutive time steps and uses particle image velocimetry to create a velocity field between them in multiple overlapping windows of different sizes. This process determines the displacement that best matches objects in a pair of consecutive binary 2D images by means of cross-correlation. Matches between the objects from one time step to the next are created by considering the distance of the centroids of the identified objects and their overlapping area. The best match within set thresholds is kept if the difference in area does not exceed a factor of 4. This areal threshold ensures realistic growth (decay) rates for non-merging (non-splitting) clouds and is based on our observations of small clouds – particularly the growth of one-pixel and two-pixel clouds. In the case of a splitting event (one object is matched to multiple objects), one match is chosen arbitrarily. In the case of a merging event (multiple objects are matched to one object), the best match is kept. In the case of a tie, again, one match is chosen arbitrarily. This process is repeated for all consecutive time steps to form a trajectory of a tracked object.

This method has so far been applied to the binary cloud mask inferred from observations of MSG-SEVIRI and the Advanced Baseline Imager (ABI; ) aboard NASA's Geostationary Operational Environmental Satellites – R Series (GOES-R ABI) . Cloud physical properties (CPP) can be derived from those observations only during the daytime, as visible reflectances are needed for the retrieval. The CPP generally include Ttop, cloud top height (htop), cloud top pressure (ptop), COT, reff, and L. Nd is derived using COT and reff . This work uses CPP derived from MSG-SEVIRI observations and provided in the CLAAS-2 data set with a temporal resolution of 15 min. These CPP are matched to the trajectories of tracked clouds to obtain mean and median values per time step and for the lifetime of individual clouds.

For a first application of the C×C approach, we want to focus on low-level liquid clouds and mid-level mixed-phase clouds as observed by MSG-SEVIRI over Europe, the Mediterranean, and northern Africa. As outlined in , the data set of all tracked clouds is filtered to obtain sub-samples that correspond to the targeted cloud types. Firstly, a cloud has to show a cloud top height that relates to the targeted cloud type. Secondly, a cloud has to form and dissolve in clear air to provide assurance that well-defined development can be observed. Finally, a cloud has to occur entirely during the daytime so that CPP data are available throughout its lifetime.

Ground-based lidar measurements provide great potential for inferring height-resolved CCN and INP concentrations . However, adaptation of the ground-based approach to spaceborne lidar observations is not straightforward, as the required extinction-to-number-concentration conversion factors show strong regional variation . The Optical Modelling of CALIPSO Microphysics (OMCAM; ) algorithm provides an alternative approach for inferring CCN concentrations from spaceborne Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO; ) lidar observations that is consistent within the wider CALIPSO retrieval. Figure  presents a flow chart of the OMCAM algorithm. In short, quality-assured CALIPSO Level 2 aerosol profiles are used to obtain aerosol-type specific extinction coefficients (upper panel in Fig. ) that constrain light-scattering calculations based on the normalized size distribution and complex refractive indices (middle panel in Fig. ) for different aerosol types in the CALIPSO aerosol model . The scaled size distribution relating to the modelled extinction coefficient that best reproduced the measurement is then integrated from a lower size limit at which the different aerosol types are likely to be relevant for cloud properties to obtain the number concentration of reservoir particles (lower panels in Fig. ). The latter are then used as input to commonly used parametrizations to infer CCN and INP number concentrations, nCCN and nINP respectively. For more details on the OMCAM retrieval and its uncertainties, readers are referred to .

Thorough validation of OMCAM-derived nCCN generally finds values that are within a factor of 1.5 to 2.0 of independent airborne and ground-based in situ observations , which is far less than their natural variability. OMCAM-derived data have been used to compile a global height-resolved nCCN climatology from 15 years of CALIPSO observations that can be used complementary to model-derived nCCN as a benchmark for cloud-resolved climate modelling.

For this work, OMCAM was expanded analogous to and to estimate the concentration of INP reservoir particles which are subsequently used as input to INP parametrizations to obtain nINP (lower-right panel in Fig. ). This capability allows us to extend the scope of the C×C approach towards studying aerosol effects on ice-containing clouds. In contrast to nCCN, independent in situ measurements of nINP are sparse. This is why the validation of OMCAM-derived values is still a matter of ongoing research. Nevertheless, initial findings based on comparison to airborne in situ measurements indicate that CALIPSO-derived nINP have a quality comparable to those inferred from ground-based lidar measurements .

The intercept points between individual cloud trajectories and the CALIPSO ground track are obtained with the TrackMatcher tool (; https://github.com/LIM-AeroCloud/TrackMatcher.jl.git, last access: 18 March 2024). The purpose of TrackMatcher is the identification of intercept points between two lines on a latitude–longitude grid and the collocation of the respective data fields along those tracks. In the context of the C×C approach, this enables us to match cloud properties along a cloud trajectory from geostationary satellite observations (Sect. ) to the surrounding cloud-relevant aerosol concentrations from polar-orbiting lidar observations (Sect. ). The algorithm allows us to find intersections in any pair of tracks that provide information on time (t), latitude (φ), longitude (λ), and height (h). The main steps of the algorithm are to (i) load track data related to two platforms, (ii) interpolate the individual tracks using a piecewise cubic Hermite interpolating polynomial, (iii) find intersections by minimizing the norm between the different track point coordinate pairs, and (iv) extract auxiliary information at or around the intercept point as set by the operator. For applying the C×C approach, the auxiliary formation extracted from the CALIPSO Level 2 aerosol profile product consists of height profiles of the OMCAM input parameters, i.e. backscatter and extinction coefficients, particle linear depolarization ratio, vertical feature mask, and cloud–aerosol discrimination (CAD) score. In addition, the accepted time difference between the two tracks can be chosen to best suit the application. In this study, we did not limit the time difference for finding matches between a cloud track and the CALIPSO satellite, but most cases fell within a range between 0 and ± 90 min. This time difference is well below the timescale for which major changes in an aerosol field could be expected .

An example for matching a cloud trajectory with a CALIPSO measurement is presented in Fig. . CALIPSO Level 2 data are available in 5 km intervals along the ground track, while the example trajectory consists of four time steps. When a match is made, CALIPSO profiles are filtered for quality-assured data at the height levels of the paired cloud following the criteria summarized in Table 1 of . Aerosol data might be absent or dismissed in cases of low aerosol load (low signal-to-noise ratio), retrievals with low confidence scores, or cloud presence. In Fig. , the cloud changes from purely liquid (time steps 1 and 2) to mixed-phase (time step 3) to purely ice (time step 4). Aerosol information is available in the vicinity of the matching point and can be used to infer mean CCN or INP concentrations surrounding the tracked cloud. Further details on this procedure are provided below.

Our cloud tracking (Sect. ) is generally performed on a binary cloud mask in which pixels are differentiated as either cloud or cloud-free. In passive observations, cloudy pixels do not unambiguously refer to a specific cloud type . Instead, the column information observed at the top of the atmosphere might actually be the product of contributions of very different clouds, such as low-level water clouds and high-level ice clouds. While these contributions will not be discernible in a cloud mask, they will propagate into the inferred cloud physical properties. Clouds that are found to intercept a CALIPSO overpass (Sect. ) therefore have to undergo quality assurance before they can be considered for further analysis.

This quality screening is performed in two steps. Clouds are initially sorted according to their phase and subsequently investigated for realistic development of their physical properties. The phase categorization sorts clouds as

liquid-water if (i) the phase of all pixels is liquid or (ii) the median cloud top temperature is warmer than -5 °C;

The objective of our C×C approach is to investigate liquid-water clouds for their response to changes in CCN concentrations and in mixed-phase and heterogeneously frozen ice clouds for their response to changes in INP concentrations. To obtain meaningful results, however, we need to exclude those clouds that appear to evolve non-physically, i.e. that show a large variation in their properties from time step to time step or throughout their lifetime. We have therefore identified four objective criteria for assessing realistic cloud development based on cloud top temperature, area, and phase. A cloud is flagged if it shows

unrealistic development of Ttop from start to end (the norm of the difference between median Ttop at cloud beginning and end exceeds 30 K);

These criteria apply to the entire trajectory. A cloud is kept for by-eye inspection if one of criteria 1 to 4 is met. It is dismissed (considered as unrealistic) if multiple criteria are met. The latter also applies if criterion 2 or 4 is met multiple times. While this rigorous screening of tracked clouds implies a high level of data reduction, it ensures that only cases in which the observations show a cloud that develops in a physically meaningful way along its trajectory (i.e. that are not affected by any of the limitations of passive remote sensing) will be considered in the subsequent investigation of aerosol–cloud interactions. In other words, we can only obtain robust findings from the bottom-up database if the highest level of scrutiny is applied in the identification of trustworthy aerosol–cloud cases.

Figure  presents the development of two tracked clouds to illustrate the quality assurance methodology. The example cloud on 14 August 2014 shows a development that we consider as realistic. The cloud was tracked from its formation at 13:15 UTC until it dissolved at 16:45 UTC. Median, minimum, and maximum Ttop values all vary within a reasonable range throughout all 15 min time steps. The cloud is partly or fully glaciated at temperatures where this is not unlikely. The change in cloud size is indicative of plausible growth and decay rather than merging and splitting. Overall, this case represents a heterogeneously frozen ice cloud that can be used in studies of the effect of surrounding INP concentrations on cloud properties and development. In contrast, the example cloud on 24 March 2014 raises some of the flags listed above. Over the length of its existence from 08:45 to 11:30 UTC, median Ttop shows multiple time-step-by-time-step changes of more than 15 K (criterion 3). This indicates the coinciding presence of low and high clouds within the cloud area or even on a pixel basis, and it would already lead us to dismiss that cloud as unrealistic. The spread in Ttop per time step exceeds 35 K for 10 out of 12 time steps (criterion 4) provides another indication that clouds at different height levels contribute to the column signal detected in the passive observation. Finally, the areal growth from time step 2 to time step 3 exceeds a doubling (criterion 2), and the norm of the difference in Ttop at the first and last time steps is very close to 30 K (criterion 1).

The consideration for realistic cloud development puts another constraint on the selection of cases that can actually be used in the formation of our bottom-up database. Overall, the initial matching of trajectories to CALIPSO overpasses, followed by the demand for valid aerosol observations at cloud level and the subsequent requirement for realistic cloud development, reduces the database from an order of 1 million tracked clouds to an order of a few hundred cases for consideration in our C×C approach. We have opted for the exceptionally high level of scrutiny despite the resulting poor data yield to provide assurance that findings later inferred from the bottom-up database are physically meaningful. In future, the length of the available time series of around 15 years, the possibility to extend the CCN and INP retrievals to newer spaceborne lidar missions, the option for expanding the study area, and the application to further geostationary sensors provide ample opportunities for extending the number of cases without compromising their quality.

For testing the new C×C approach, we have selected a region that covers Europe and northern Africa. Figure  shows that our study region extends from the Atlantic coast to eastern Ukraine and from southern Sweden to the southern tip of Tunisia and the Sinai Peninsula. All four cloud categories listed in Sect.  are found in the study region. In addition, the region covers the pathways of mineral dust transport to Europe. This is of particular interest to our work, as mineral dust particles are very efficient INPs and are most likely to cause detectable changes in cloud phase.

The data obtained from matching the information related to tracked cloud properties and cloud-relevant aerosol properties are presented based on the case study of 18 March 2014 shown in Fig. . A liquid-water cloud could be tracked for four time steps between 11:00 and 11:45 UTC. Its first time step shows a median Ttop of about 14 °C which corresponds to a htop of about 500 m. The median reff for this initial time step is 12.5 µm. Over the next three time steps, Ttop decreases to 2 °C as htop increases to 2.2 km. At the same time, reff decreases slightly to 12 µm. Throughout its lifetime, the cloud consisted of 18 pixels of which none revealed the presence of ice. The CALIPSO lidar overpass matched with this trajectory occurred at 11:37 UTC between the third and fourth time step of cloud lifetime. Around the overpass, CALIPSO measurements reveal the presence of aerosols and clouds with upper-level clouds attenuating the lidar signal before it can reach the surface (Fig. b). The OMCAM retrieval gives an estimated nCCN of around 2000 cm-3 between the surface and 2.5 km height – well within the height range of the observed cloud.

Pixel-wise, cloud properties are matched to the aerosol field within an along-track distance of thirteen 5 km CALIPSO intervals and five 60 m height bins around the pixel's htop. Valid data in CCN concentration within such a box is averaged to obtain a median nCCN that can be related to the cloud properties. In the example in Fig. , 14 cloud pixels show values of htop that allow us to assign a median nCCN to their cloud properties, while 4 pixels reveal values of htop that fell within a height range for which no CCN information could be retrieved. Consequently, the case of 18 March 2014 contributes 14 pairs of matched aerosol–cloud information to the statistical analysis presented below.

To summarize, the C×C approach allows us to decompose clouds at three stages:

The pixel stage considers individual cloud pixels and the CALIPSO aerosol with 13 profiles by 5 height bins around the pixel's htop. This is referred to as pixel-wise information in this paper.

For a first application of the C×C approach, we want to focus on (i) liquid clouds which have been extensively studied with other methods and (ii) ice-containing clouds for which our new approach will enable us to assess the impact of INP concentrations on cloud phase and development. The tracking of clouds in CLAAS-2 data (Sect. ) within the region of interest (Fig. ) for 2014 gives a total of 8 924 639 trajectories of clouds with well-defined start and end points, i.e. forming and dissolving in clear air. The matching procedure outlined in Sect.  implies rigorous screening of that data set to trajectories that coincide with a CALIPSO observation during both day and night. This constraint reduces the number of data to 4393 tracked and matched clouds that could potentially be used for further investigation. Out of those, 964 daytime trajectories of liquid clouds are found to be vertically co-located with CCN layers (Sect. ). Further quality assurance regarding realistic cloud development (Sect. ) finally gives 399 trajectories for further analysis. In the case of ice-containing clouds, 844 daytime trajectories could be matched to vertically co-located INP layers of which 95 clouds remained after quality assurance (Sect. ). Following the phase categorization in Sect. , the ice-containing clouds can be further separated into 42 clouds that are homogeneously frozen, 8 clouds that are heterogeneously frozen, and 45 mixed-phase clouds. The data set of liquid clouds also contains 37 trajectories of supercooled clouds for which neither the median Ttop per time step exceeds 0 °C nor cloud ice is detected. These supercooled liquid clouds provide a reference in studying the impact of nINP on the ice-containing clouds.

Figure  gives an overview of the cloud trajectories that could be matched to aerosol information from CALIPSO measurements over Europe and northern Africa for the year 2014. We will start with a description of the matched data sets before presenting the first results of applying the C×C approach for studying liquid-water and ice-containing clouds.

The data set of matched cases for the year 2014 within the study region in Fig.  consists of 399 trajectories of liquid clouds and 95 trajectories of ice-containing clouds. Both cloud types are rather small and short-lived. They span lifetimes from 3 to 47 (3 to 20 for ice-containing clouds) time steps of 15 min with a median of 4 time steps. The histogram of trajectory length in Fig.  shows that the majority of clouds exist for less than 2 h. The size of the liquid clouds per time step ranges from 1 to 341 pixels with a median of 5 pixels (not shown). Clouds consisting of 10 pixels or fewer make up 70 % of the data set. The ice-containing clouds considered here are smaller than the liquid clouds with sizes ranging from 1 to 53 pixels, a median of 4 pixels, and 90 % of clouds consisting of 15 pixels or fewer (not shown).

Figure  gives an overview of the distribution of htop and Ttop of the liquid and ice-containing clouds that could be matched with information of the surrounding aerosol field. Most liquid clouds persist below 1.0 km. The median htop is 0.6 km, while the occurrence of few pixels with large htop increases the mean to 0.9 ± 1.1 km. The majority of cloud pixels (95 %) show positive values of Ttop with a mean of 21.0 ± 12.4 °C and a median of 20.9 °C. These comparably high temperatures are related to the fact that a large number of tracked clouds are located over northern Africa (see Fig. ). Cloud pixels with negative Ttop in the liquid data set refer to supercooled clouds, which can be used as a reference in the investigation of the effect of nINP on ice-containing clouds. When data are aggregated to represent the median values of entire trajectories, htop slightly increases to 1.3 ± 1.5 km with a median of 0.8 km, while Ttop decreases correspondingly to 17.4 ± 15.0  °C with a median of 16.9 °C. The overview of the ice-containing clouds in Fig. b shows that those clouds generally occur at larger heights and lower temperature than the liquid clouds. One group of ice-containing clouds occurs at Ttop<-38 °C and htop>8 km, which is in line with the regime of homogeneous freezing. The other group with Ttop>-38 °C covers the regime of heterogeneous freezing (i.e. INPs are needed to form cloud ice; ) and represents the temperature range at which supercooled, mixed-phase, and ice clouds can be observed. We expect that the latter clouds would be most susceptible to changes in aerosol concentrations. They make up 2673 pixels (53 clouds) with htop ranging from 0.4 to 9.7 km (0.8 to 9.2 km) and a median of 5.8 km (5.7 km). When considering all ice-containing clouds, the pixel-wise (whole-trajectory) mean values are htop=6.8±2.4 km (7.5±2.5 km) and Ttop=-23.6±18.5 °C (-30.0±18.8 °C), with median value of 6.6 km (7.2 km) and -17.2 °C (-25.2 °C).

The pixel-wise and whole-trajectory histograms of COT and reff for both liquid and ice-containing clouds are presented in Fig. . Because retrievals of cloud microphysical properties require data at visible wavelengths, this information is available only during the daytime. Hence, and as a result of measurement restrictions such as weak signal-to-noise ratio, not all tracked pixels provide meaningful data. The majority of liquid clouds are optically thin with medians of 0.92 and 0.74 and means of 2.38 ± 5.23 and 2.47 ± 3.83 for the pixel- and trajectory-based analysis respectively. About 75 % of all cases are below the mean value. For ice-containing clouds, these values increase to pixel- and trajectory based medians of 4.88 and 1.85 and means of 8.26 ± 10.77 and 3.94 ± 4.86 respectively. An even larger difference is revealed in the size of the cloud particles. For liquid clouds, the median reff is 7.8 µm for both the pixel- and trajectory-based analysis with means of 10.1 ± 5.0 µm and 9.8 ± 4.0 µm respectively. Only 15 % of cases show median values larger than 12 µm, which indicates the likely presence of precipitation . The presence of ice in clouds increases the inferred values of reff to pixel- and trajectory-based means of 20.9 ± 7.5 µm and 22.0 ± 5.7 µm and medians of 23.2 and 24.4 µm respectively.

The histogram of nCCN for the 399 matched liquid clouds in Fig.  shows that the C×C approach is capable of covering a wide range of CCN conditions. While values range from 17 to 25 721 cm-3 with a median of 872 cm-3, the majority of cases (about 90 %) are in a realistic range below 3000 cm-3. In the analysis of our data set, we will use nCCN to discriminate between clean and polluted conditions. This is done in two steps. Firstly, the upper and lower 5 % of cases are dismissed from the data set, as they are likely to represent unrealistic values that result from propagating unreliable measurements through the analysis chain. For the present data set, this means that nCCN<154 cm-3 and nCCN>4409 cm-3, and the related cloud data are omitted from further analysis. While the exclusion of unrealistic values of nCCN does not affect the data set presented here, it will become more crucial as the volume of the bottom-up data set increases. Secondly, the remaining 90% of cases is split into three ranges that represent clean (lower quantile), moderate (middle quantile), and polluted conditions (upper quantile). The resulting ranges contain about 4800 matched data points each and are 154 cm-3≤nCCN<610 cm-3, 610 cm-3≤nCCN<1210 cm-3, and 1210 cm-3≤nCCN<4409 cm-3.

Figure  presents the histogram of nINP related to the 95 ice-containing clouds. The majority of clouds (81 %) occur in aerosol fields that relate to values of nINP between 10-3 and 10 L-1 which are realistically found at atmospheric conditions . About 3 % of inferred values fall outside the presented range of 7 orders of magnitude (2 % lower and 1 % higher). These values are likely the result of unreliable CALIPSO retrievals or originate from extrapolating the applied INP parametrizations to temperatures at which they are no longer applicable . As in the case of nCCN, unrealistic nINP are excluded by dismissing the lowest and highest 5 % of values and related cloud data from further data analysis. As mentioned earlier, the detailed evaluation of the number concentration of reservoir particles and nINP with independent in situ measurements analogous to , , and is ongoing and will be the focus of a future publication.

Now that we have obtained a data set of matched cloud and aerosol observations, we can start to investigate cloud properties for different ranges of nCCN. Figure  shows that the mean nCCN in the three quantiles mentioned before are 403 ± 110, 875 ± 189, and 2123 ± 733 cm-3. If the values of reff that have been matched to the aerosol observation are grouped according to those three nCCN ranges, we can see a clear decrease in reff and an increase in Nd from clean to polluted aerosol conditions that is in line with the Twomey effect. While reff=11.78±6.6 µm (median of 9.0 µm) and Nd=68±166 cm-3 (median of 42 cm-3) for the lower third of nCCN observations, values decrease to 9.99 ± 4.72 µm (median of 8.0 µm) and 75±100 cm-3 (median of 53 cm-3) for the middle third and even further to 9.34 ± 3.86 µm (median of 7.8 µm) and 95±199 cm-3 (median of 60 cm-3) for the upper third (see Fig. ).

This allows a first quantification of the change in reff and Nd related to a change in nCCN rather than aerosol proxies such as AOT or AI generally used in ACI studies based on satellite data . An overview of the inferred sensitivities of reff and Nd to changes in nCCN is provided in Table . We find a Δreff/ΔnCCN in the range from -0.81 to -3.78 nm cm-3 depending on the considered quantiles and the use of median or mean values of the distributions in Fig. . In the same way, Nd is found to increase between 1.17 and 2.30 per increase of 100 cm-3 in nCCN. The larger sensitivities found when derived over just the lower two quantiles (columns 4 and 6 in Table ) corroborate that reff and Nd are most susceptible to changes in CCN concentration for low baseline values and that the effect becomes saturated with a further increase in nCCN .

For better comparison to studies based on passive CCN proxies, Table  also provides sensitivities for logarithmic changes. The analysis of the C×C data set gives values of Δln⁡reff/Δln⁡nCCN between -0.09 and -0.21 while Δln⁡Nd/Δln⁡nCCN is found to vary in the range from 0.13 to 0.30. The latter values are at the lower end of earlier findings of 0.3 to 0.8 based on column CCN proxies . There are likely two factors at play. Firstly, our study is the first one to derive sensitivities based on inferred CCN concentrations at cloud level. On the one hand, this ensures that we only consider cases in which the observed aerosols can actually interact with the observed clouds. On the other hand, cloud-layer nCCN is likely to give a weaker aerosol signal than a column proxy, potentially reducing the deduced sensitivity. Secondly, the isolated clouds considered in the current data set might not be as sensitive to changes in aerosol concentration as e.g. widespread stratocumulus clouds , or their lifetime might be too short to reveal the full impact of the aerosol perturbation . Future research based on a larger C×C data set will reveal if the lower sensitivity can be corroborated and if the regional variation of sensitivity of cloud parameters to changes in nCCN can also be resolved with our new approach.

Applying the same analysis to COT (mean and median of around 2 and 1 respectively), cloud lifetime (mean and median of 8 and 5 time steps respectively), and cloud top height (mean and median of 800 m and 600 m respectively) does not reveal any change in those parameters with changing aerosol concentration (not shown). For L, we find a decrease in the mean from 25 ± 47 g m-2 for clean conditions to 16 ± 37 g m-2 for polluted conditions. However, median values show comparable values around 5 g m-2 for all three intervals of aerosol concentration in line with optically thin clouds. While these findings are not in line with the assumption that increased nCCN increases cloud lifetime, albedo (COT), htop, and L, we consider the results as still preliminary. The C×C approach will need to be applied to a longer time series and over a larger region to extend the data set for ACI studies from which more robust conclusions regarding the adjustments can be drawn. This will be the focus of follow-up work.

Furthermore, the use of CALIPSO observations allows us to allocate nCCN to a specific aerosol type. In the data set presented here, mineral dust and polluted continental make up the most of the CCN population. Therefore, a specific aerosol-type investigation of the connection between nCCN and reff will also be left for follow-up studies with a larger C×C data set.

The capability of the C×C data set to provide information on nINP and the development of the phase of a tracked cloud (Sect. ) opens new avenues for also studying the effect of aerosols on ice-containing clouds. However, the related constraints for quality-assured cloud development and the lower abundance of successful INP retrievals from CALIPSO observations lead to a data set that is much smaller than the one for studying effects of changes in nCCN on the properties of warm liquid-water clouds. Keeping this in mind, the current C×C data set for 1 year of data can only provide an outlook of its potential for spaceborne ACI studies.

The impact of nINP on different cloud types in the regime of heterogeneous ice nucleation is illustrated in Fig. . We consider all clouds in Fig.  as supercooled if their whole-trajectory Ttop and their Ttop per time step never exceeded 0 °C and if all pixels were classified as liquid. These conditions are fulfilled by 42 clouds. Mixed-phase clouds have to show a combination of pixels that are classified as liquid and ice (see Fig.  for an example). This is the case for 45 clouds. Heterogeneously frozen clouds feature only pixels that are classified as ice and have to show values of Ttop larger than -38 °C, which is the case for 8 clouds. Supercooled clouds show a mean Ttop of -11.7±15.7 °C and a median of -6.2 °C. Mixed-phase clouds are colder with a mean Ttop of -14.0±7.5 °C and a median of -11.2 °C), while heterogeneously frozen clouds show the lowest mean Ttop of -17.1±3.7 °C and median of -16.9 °C. These clouds occur in an aerosol environment with mean nINP values of 0.04±0.11, 0.23±0.31, and 2.64±1.79 L-1 and medians of 0.02, 0.05, and 2.92 L-1 respectively.

The parametrizations used to infer nINP from the CALIPSO observations are strongly dependent on temperature. For mineral dust, they generally show an increase in nINP by about 1 order of magnitude per 5 °C decrease . The INP data set presented here consists primarily of CALIPSO observations in which the detected aerosols are classified as mineral dust. Hence, we would expect a similar relationship between the inferred Ttop and nINP of different cloud types if there was no change in the number of reservoir particles that could become INP-active, i.e. if there was no increase in aerosol concentration. Instead, we find that mean nINP changes by about 1 order of magnitude already for a 3 °C decrease in mean Ttop. This indicates that the increase in nINP observed in the presence of mixed-phase clouds compared to supercooled clouds and of heterogeneously frozen clouds compared to mixed-phase clouds is not purely related to the decreasing Ttop of the different cloud types but also to an increase in the concentration of aerosols that can act as INPs. In return, we can reason that the increased aerosol concentration facilitates earlier cloud glaciation as clouds surrounded by the largest abundance of INPs are fully glaciated, while those with medium and low nINP are mixed-phase and liquid-phase respectively. This is in agreement with studies in which dust concentrations from aerosol reanalysis fields are used as a proxy for the presence of INPs . Those studies address the issue by resolving the occurrence of ice-containing clouds within different ranges of Ttop for different ranges of background aerosol concentrations, while our approach directly relates nINP at cloud level to the occurrence of ice in the matched clouds. However, resolving a consistent picture through an entirely different data analysis concept increases our overall confidence in applying the C×C to both liquid-water and ice-containing clouds.

As in the case of liquid clouds, a larger data set is needed to obtain more robust constraints on the effect of aerosol concentrations on the properties of ice-containing clouds. This would facilitate e.g. assessing if variation in nINP can also be found for supercooled, mixed-phase, and heterogeneously frozen clouds with comparable Ttop, which would be a more direct indication of the effect of aerosol concentration on cloud phase.