Ice-nucleating particle versus ice crystal number concentration in altocumulus and cirrus embedded in Saharan dust: A closure study

For the first time, a closure study of the relationship between ice-nucleating particle concentration (INPC) and ice crystal number concentration (ICNC) in altocumulus and cirrus layers, solely based on ground-based active remote sensing, is presented. Such aerosol-cloud closure experiments are required (a) to better understand aerosol-cloud interaction in the case of mixed-phase clouds, (b) to explore to what extent heterogeneous ice nucleation can contribute to cirrus formation which is usually controlled by homogeneous freezing, and (c) to check the usefulness of available INPC parameterization 5 schemes, applied to lidar profiles of aerosol optical and microphysical properties up to tropopause level. The INPC-vs-ICNC closure studies were conducted in Cyprus (Limassol and Nicosia) during a six-week field campaign in March-April 2015 and during the 17-month CyCARE (Cyprus Clouds Aerosol and Rain Experiment) campaign. Focus was on altocumulus and cirrus layers which developed in pronounced Saharan dust layers at heights from 5-11 km. As a highlight, a long lasting cirrus event was studied which was linked to the development of a very strong dust-infused baroclinic storm (DIBS) over 10 Algeria. The DIBS was associated with strong convective cloud development and lifted large amounts of Saharan dust into the upper troposphere, where the dust influenced the evolution of an unusually large anvil cirrus shield and the subsequent transformation into an cirrus uncinus cloud system extending from the Eastern Mediterranean to Central Asia, and thus over more than 3500 km. Cloud top temperatures of the three discussed closure-study cases ranged from −20◦C to −57◦C. INPC was estimated from polarization/Raman lidar observations in combination with published INPC parameterization schemes, 15 whereas ICNC was retrieved from combined Doppler lidar, aerosol lidar, and cloud radar observations of the terminal velocity of falling ice crystals, radar reflectivity and lidar backscatter in combination with modeling of backscattering at 532 nm and 8.5 mm wavelength. Good to acceptable agreement between INPC (observed before and after the occurrence of the cloud layer under investigation) and ICNC values was found in the discussed three proof-of-concept closure experiments. In these

development of the ice phase in clouds. Costa et al. (2017) also made an attempt to combine aerosol and ice crystal information gained from airborne in situ observations to characterize the link between INPC and ICNC and thus the potential impact of heterogeneous ice formation on cirrus evolution.
However, it remains difficult to obtain a clear picture of the influence of aerosols on the life cycle of ice-containing clouds from airborne in situ measurements. Usually the environmental conditions (temperature, relative humidity, INPC) at which the 5 ice crystals nucleated remain unkown in the analysis of aircraft observation performed within the clouds. Most of the aircraft tracks are hundreds of meters below cloud top and thus below the coldest region of the cloud where the probability of ice nucleation is highest. After nucleation, the ice crystals grow fast to sizes of 50-100 µm within minutes (Bailey and Hallett, 2012) and immediately start falling through the cloud deck and influence the further evolution of the entire cloud system from the top to base and the virga zone (Spichtinger and Gierens, 2009a, b;Field and Heymsfield, 2003). Clear and unambiguous 10 conclusions on the specific impact of aerosol particles on the evolution of the ice phase can only be obtained by monitoring aerosol layering and embedded cloud systems at all heights simultaneously from cloud base to top.
A promising way to explore cloud evolution processes with focus on heterogeneous ice nucleation is the use of ground-based remote sensing (see, e.g., the approach presented by Simmel et al., 2015). Continuous vertical profiling of aerosol, altocumulus and cirrus layers (from the base of the virga zone up to cloud top at the same time) with lidars and radars allows us to study The first attempts to find agreement between INPC and ICNC levels in natural cloudy environments date back to the early 1960s. Auer et al. (1969) performed closure studies by comparing INPC with ICNC observation in cap clouds (at 3350 m height above sea level, a.s.l., Elk Mountain, Wyoming, in autumn 1967). Hobbs (1969)  were considered. For smaller ice particles, INPC and ICNC differed by more than two orders of magnitude. This difference was attributed to ice shattering artifacts (Korolev et al., 2011). However, ice multiplication effects caused by riming and ice-breakup processes cannot be fully excluded at these temperatures (Sullivan et al., 2017(Sullivan et al., , 2018. (of INPC and ice crystal microphysical properties), active remote sensing with several cloud radars (cloud profiling in terms of radar reflectivity, Doppler velocities related to air motion and falling ice crystals), radiosonde observations of atmospheric state parameters, and large-eddy-simulation (LES) modeling to test the hypothesis that INPC values measured above cloud top can account for the observed ICNC values. Reasonable agreement between INPC and ICNC was obtained in this way for low- 25 lying mixed-phase Artic cloud layers observed in northern Alaska in April 2008. However, a key aspect was that a second INP reservoir, located below the well-mixed cloud layer, had to be assumed in the LES modeling efforts as well. These INPs were slowly mixed upward (into the cloud) in the simulations and helped to maintain the INPC values in the model close to those observed. A similar approach, based on cloud radar observations and estimates of INPC from airborne in situ measurements of aerosol size distributions below and above a long-lasting shallow mixed-phase cloud deck over United Kingdom,was used 30 in the investigation of a long-lived altocumulus layer regarding the impact of INPC on the cloud lifetime (Westbrook and Illingworth, 2013).
In strong contrast to these Arctic and mid-latitude aerosol-cloud closure studies at clean-air and thus low aerosol concentration levels, our remote-sensing-based INPC-vs-ICNC closure approach deals with stratiform altocumulus and cirrus layers which developed in pronounced Saharan dust layers in the middle and upper troposphere over Cyprus (at Middle-East me-35 teorological conditions). Such clouds were frequently observed during our field campaigns, conducted in each of the spring seasons from 2015-2018, and thus are obviously very common in the Eastern Mediterranean. Cloud top temperatures typically ranged from −20 • C to about −60 • C. Secondary ice production (SIP), that can sensitively disturb any ice closure experiment, is assumed to have a minor impact on ICNC at these low temperatures. The Hallett-Mossop SIP process is associated with splinter ejection during riming of ice cyrstals at temperatures between −3 • C and −8 • C (Hallett and Mossop, 1974).

3 Cyprus field campaigns
The Mediterranean Basin is well recognized by IPCC (International Panel for Climate Change) (Stocker et al., 2013) as a hot spot for climate change, the impacts of which are expected to amplify further in the years to come. However, IPCC also identified aerosol-cloud-precipitation relationships as one of the unsolved problems of atmospheric research and thus their simplified representation in atmospheric circulation models as one of the most prominent reasons for the large uncertainties 10 in the present future-climate-change debate. The European Commission responded to this issue by funding the BACCHUS project. BACCHUS aimed at a better understanding of heterogeneous ice formation in tropospheric clouds around the globe and improved consideration of cloud processes in cloud-resolving and Earth system models. In the framework of this research initiative, in which about 20 European research institutes, universities, and weather services were involved, a series of shortterm intensive field observations was conducted in Cyprus in each spring of 2015-2017. The spring season coincides with Mediterranean Experiment (ChArMEx; http://charmex.lsce.ipsl.fr) (Mallet et al., 2016) is a collaborative research program federating international activities to investigate Mediterranean regional chemistry-climate interactions. The ENVI-Med regional program is a French cooperation initiative for countries in the Mediterranean Basin designed to encourage and strengthen highlevel scientific and technological cooperation in the region as well as research networking on sustainable development and understanding the environmental (ENVI) operation of the Mediterranean Basin (Med). In partnership with France, the program 5 is focused on Mediterranean rim countries.

Cyprus 2016
The follow-up Cyprus-2016 campaign included further aerosol and INP observations performed by the German INUIT (Ice Nuclei Research Unit, https://www.ice-nuclei.de/the-inuit-project/) research group. The INUIT consortium studied heterogeneous ice formation in the atmosphere within three different work packages divided into laboratory studies, field measurements, 25 and modeling. The European research infrastructure project ACTRIS-2 (Aerosols, Clouds, and Trace gases Research InfraStructure, https://www.actris.eu/) supported the field activities in Cyprus as well. Almost the same infrastructure consisting of a ground station (Agia Marina Xyliatou), an UAV airport (now at Orunda, 7 km northeast of Agia Marina Xyliatou, and 21 km west of the lidar station at Nicosia), and the NOA Polly site (Marinou et al., 2019) (Schrod et al., 2017;Mamali et al., 2018;Marinou et al., 2019). Some of these results will be discussed in Sect. 5. 3.3 CyCARE (2016-2018 As one of the central BACCHUS remote sensing initiatives the mobile Leipzig Cloudnet supersite LACROS (Leipzig Aerosol and Cloud Remote Observation System, http://lacros.rsd.tropos.de/) (Bühl et al., 2013(Bühl et al., , 2016  is part of a long-term cooperation between TROPOS and CUT established in 2012 and integrated into the Cloudnet activities coordinated by the European Union infrastructure project ACTRIS-2. The mobile Leipzig Cloudnet supersite is shown in Fig. 2 and is equipped with a multiwavelength polarization/Raman lidar Polly, wind Doppler lidar, 35 GHz Doppler cloud radar, ceilometer, disdrometer, and microwave radiometer. All tools were run continuously over the 17-month period. In addition, nearby AERONET sun photometer observations (CUT-TEPAK site) were taken. An excellent data set was collected for 10 in-depth studies of the impact of dust and aerosol pollution on cloud and rain evolution in the Eastern Mediterranean. During the intensive CyCARE field phase in April 2017, 43 Vaisala radiosondes were launched at Limassol (Dai et al., 2018). level are compared with ICNC values obtained from combined backscatter lidar, wind Doppler lidar, and cloud Doppler radar observations in the lower part of a cirrus cloud (see Fig. 3a) or in the virga zone below a mixed-phase altocumulus layer (see Fig. 3b). We assume that ice crystals nucleate at the coldest point of the cloud (at cloud top), where INPC is highest because of the rather strong INP number increase with deceasing temperature (Kanji et al., 2017). Furthermore, we assume that the freshly formed ice crystals grow fast by water vapor deposition, immediately start falling and do not collide and form aggregates so that 20 the number of ice crystals does not change during sedimentation to the lower part of the cloud and the virga zone. In Sect. 4.1, we briefly outline the methods of the INPC retrieval (Mamouri and Ansmann, 2016;Marinou et al., 2019). Section 4.2 deals with the estimation of ICNC.

INPC and ICNC from ground-based active remote sensing
The uncertainties in our closure methodology caused by the idealized assumptions may be small in the case of geometrically and optically thin ice clouds (case study 1 in Sect. 5.1) with a vertical extent of a few 100 meters and in case of shallow mixed- 25 phase altocumulus layers (case study 3 in Sect. 5.3) with the nucleation of a comparably low amount of ice cyrstals within the thin liquid-water layer at the top of the altocumulus. However, in geometrically and optically thick cirrus (as is the case in case study 2, Sect. 5.2) the assumption of an height-independent ice crystal number concentration from the top, at which ice crystals preferably nucleate, down to the virga zone is probably not well justified. Crystal-crystal collisions and subsequent aggregation processes can cause a significant decrease by a factor of 3-10 in ICNC from the upper part to the lower part of a 30 cirrus deck (Field and Heymsfield, 2003;Field et al., 2006). Based on CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations), the retrieved ICNC near cloud top was frequently five times higher than in the lower half of vertically deep cirrus clouds (Mitchell et al., 2018). Further processes such as ice nucleation within the central and lower parts of the cirrus layer as well as dilution and accumulation effects by turbulent processes and wind shear can lead to a strongly varying ICNC profile from cloud top to base (Spichtinger and Gierens, 2009a, b). Since we concentrate on clouds and heterogeneous ice nucleation at temperatures < −20 • C secondary ice nucleation (Field et al., 2017;Korolev et al., 2019) (Ansmann et al., 2008) when we made an attempt to investigate the impact of dust particles on ice formation in altocumulus which formed at the top of the Saharan dust layer over southeastern Morocco at temperatures from −10 to −18 • C. Later, when aerosol-based INP parameterization schemes became available (DeMott et al., 2010;DeMott et al., 2015;Niemand et al., 2012;Ullrich et al., 2017), a lidar-based methodology was developed . In the first step of the INPC estimation, height profiles of the dust-related extinction coefficient σ d at 10 532 nm wavelength and the non-dust extinction coefficient σ c for continental aerosol particles (anthropogenic haze, biomass burning smoke, biological decay products) are derived and then converted into number concentrations of large aerosol particles n 250,d and n 250,c (considering particles with radius >250 nm only) and particle surface area concentrations s d and s c .
These microphysical parameters together with temperature profiles are used as input for the INPC estimation by means of INPC parameterization schemes as given in Table 1. We use GDAS (Global Data Assimilation System) temperature profiles 15 of the National Weather Service's National Centers for Environmental Prediction (NCEP) in our computations. NOAA's Air Resources Laboratory (ARL, https://www.ready.noaa.gov/gdas1.php) NCEP model GDAS1 output archives contain these data (GDAS, 2019). During CyCARE we found remarkably good agreement between the GDAS1 and radiosonde temperature profiles (Dai et al., 2018). The standard deviation (root-mean-square deviation based on all 43 radiosonde profiles and respective GDAS1 profiles) was 0.87 K. 20 The complete lidar-based INPC retrieval is decribed in detail by Mamouri and Ansmann (2016). The uncertainties in the products are as follows: The dust extinction coefficients can be obtained with 15-25% relative error, the non-dust extinction Favorable INPs are insoluble particles such as mineral dust particles, biological material, volcanic ash and dust, and soot particles originating from open fires, burning and heating processes (e.g., Seifert et al., 2010Seifert et al., , 2011Seifert et al., , 2015Hoose and Möhler, 2012;Murray et al., 2012;Kanji et al., 2017). According to the INP parameterizations in Table 1, we consider immersion freezing (D10, D15, U17-I) and deposition nucleation (U17-D). In the case of immersion freezing, ice nucleates on a solid 30 particle immersed within a supercooled liquid droplet (e.g. Murray et al., 2012;Vali et al., 2015). Particles may contain insoluble and soluble components. The soluble fraction triggers the formation of supercooled liquid droplets, and the insoluble part is then responsible for heterogeneous freezing events. The D10 parameterization can be used to estimate INPC from the measured overall (dust plus non-dust) aerosol number concentration of particles with radius >250 nm. We use the D10 retrieval method also for dust and non-dust INP estimation in Sect. 5. The D15 parameterization was explicitly introduced for dust particles. Deposition nucleation describes the process when an ice embryo directly forms by water vapor deposition to an insoluble surface. The deposition nucleation parameterization (U17-D in Table 1) includes pore condensation and freezing (PCF) (Marcolli, 2014) occurring in voids and cavities of aggregated primary particles at relative humidity over water of RH w <100% and low temperatures of < −38 • CK when at least one pore is filled with water.

5
Our INPC-vs-ICNC closure study however ignores contact nucleation and pre-activation influences. Contact freezing occurs when an INP initiates freezing by colliding with a supercooled droplet (see latest research by Hoffmann et al., 2013). As outlined in detail by Marcolli (2017), pre-activation denotes the capability of particles or materials to nucleate ice at lower relative humidities or higher temperatures compared to their intrinsic ice nucleation efficiency after having experienced an ice nucleation event before. The subsequent, next ice nucleation event is then thought to occur because of ice preserved in pores 10 between the first ice nucleation event and second ice growth cycles.
There is an ongoing discussion on the applicability of the INP parameterization methods (Phillips et al., 2013;Boose et al., 2016;DeMott et al., 2017;Schrod et al., 2017;Price et al., 2018;Marinou et al., 2019). Our closure study contributes to this discussion. Because most of the INP parameterization schemes are based on laboratory studies performed at well-defined meteorological conditions (temperature, cooling rate, ice supersaturation level) and precisely known aerosol properties (aerosol 15 type, chemical composition, size distribution), the central question arises: Can these parameterisations be applied to predict INPC, e.g., in the upper troposphere up to cirrus height level, at which aged, chemically-and cloud-processed aerosol particles may prevail? Chemical reactions on the surfaces of the particles may have already significantly changed the potential of the particles to serve as ice nuclei (Archuleta et al., 2005;Möhler et al., 2008;Cziczo et al., 2009;Sullivan et al., 2010a, b;Wex et al., 2014).  (Schrod et al., 2017). These results are also discussed in Sect. 5.

ICNC retrieval
Three different ways are used in order to derive ICNC from combined lidar and radar observations. The basic methodology is described in detail in Bühl et al. (2019) and briefly in this section.

Combined observations of cloud radar reflectivity and ice extinction coefficient from backscatter lidar
Lidar return signals (backscatter) and cloud radar reflectivity show approximately a diameter (D) and (equivalent) diame-30 ter dependence on ice crystal size of D 2 and D 6 , respectively. This difference in sensitivity between both signals can be exploited in order to derive information about particle size. ICNC is estimated by comparing simulations of the ice crystal light-extinction coefficient at 532 nm and of the radar reflectivity at 8.5 mm wavelength with the respective measured extinc-tion coefficients (Polly lidar) and radar reflectivity values. The lidar extinction values are obtained from the observed cirrus backscatter coefficients after multiplication with the climatological mean cirrus extinction-to-backscatter ratio of 32 sr (Seifert et al., 2007;Giannakaki et al., 2007;Josset et al., 2012;Garnier et al., 2015;Haarig et al., 2016). In the simulations, ICNC and the crystal size distribution are input parameters. For realistic size distributions ICNC is varied until the simulations match the observations. Such a combined lidar/radar approach has been widely used before, e.g., for estimating particle properties from dominate. Again, this information is used to correct for air motions (eventually induced by gravity waves, radiative cooling and entrainment processes). In the case of stratiform mixed-phase clouds with shallow liquid-water layer at cloud top, v t is usually offset by the vertical air motion v air , which is estimated at the base of the liquid-water layer directly above the zone 20 dominated by ice crystals. In the ICNC retrieval, we take into account that values of v t from Doppler lidar and cloud radar are weighted by the particle area, or the particle mass squared, respectively. The terminal velocity of ice crystals is also a strong function of their shape and size characteristics. All this is considered and described in detail in (Bühl et al., 2019). Regarding the assumption on crystal shapes (plates, needles, complex forms), we make use of a variety of laboratory studies made under ambient temperature conditions (Fukuta and Takahashi, 1999;Furukawa and Wettlaufer, 2007;Myagkov et al., 2016). All 25 in all, the terminal velocity spectrum of falling ice crystals can be retrieved with an uncertainty of about 30-50%. From the vertical velocity information particle size and the ice-crystal size distribution is retrieved.
In the next step, ICNC is estimated by comparing simulations of the ice crystal light-extinction coefficient and of the radar reflectivity, in which ICNC is now left as the only input parameter, with the measured extinction coefficients and radar reflectivity values. ICNC is varied in the simulations until the measured extinction and reflectivity values are matched. The uncertainty 30 in the ICNC estimates would be in the order of 50% in the case of perfectly calibrated lidar and radar systems. However, realistic radar reflectivity uncertainties lead to ICNC uncertainties of a factor of 3. Such large uncertainties are still acceptable in our closure studies as we show in Sect. 5.

Observations of characteristic ice crystal terminal fall velocity (Doppler lidar) and extinction coefficient (backscatter lidar)
During the BACCHUS Cyprus-2015 campaign, we ran a Polly together with a vertically pointing Doppler lidar. A cloud radar was not available. Under these condition the entire retrieval is usually much more uncertain because of the missing Doppler spectrum information and the backscatter wavelength dependence (532 nm vs 8.5 mm). However, for the selected two case 5 studies of the Cyprus-2015 campaign discussed in Sects. 5.2 and 5.3, stable, temporally constant ice sedimentation conditions were observed so that a good retrieval of the terminal velocity and estimation of the mean ice crystal size within an uncertainty of 30-50% was possible. ICNC is again derived from comparison of observations with respective simulations of the light extinction coefficient from lidar with ICNC as input and for an assumed size distribution adjusted to the devired mean ice crystal size. The overall uncertainty factor of 3 was also assumed in this case of ICNC estimation (applied in Sects. 5.2 and 10 5.3) .
At the end of Sect. 4, it is noteworthy to mention that it is practically impossible to measure, retrieve, or estimate INPC with an overall uncertainty range of less than one order of magnitude (factor 3) (DeMott et al., 2017). This holds also for many retrieval techniques and in situ measurement approaches in the case of ICNC. But, as will be shown in the next section, these uncertainties still allow us to study aerosol-cloud interaction in detail, to quantify the aerosol impact on cloud properties (such 15 as ICNC), and to evaluate and rate the closure study as good or acceptable, or even that we failed to achieve closure between INPC and ICNC.

Field observations and closure studies
We begin with an overview of desert dust conditions over Cyprus in the spring of 2015. Figure  immersion/condensation freezing mode). Ten nighttime lidar observations (30-60-minute mean values, for the height layer from 450-550 m a.s.l.) are shown for comparison. We used the immersion freezing parameterizations D15 and D10(d) (see Table 1) for the dust fraction and D10 also for the non-dust particles as described in Sect In the following Sects. 5.1-5.3, we present and discuss three cases of cloud evolution with focus on the ICNC vs INPC 15 relationship. These three closure experiments cover the deposition nucleation as well as the immersion freezing regime. In the framework of these closure studies, we further check the quality and applicability of the different INPC parameterization schemes listed in Table 1. All clouds developed in pronounced Saharan dust layers. Case 1 (10 April 2017) deals with a rather thin and shallow cirrus layer that began to form at 8 km height at −35 • to −36 • C in a pure Saharan dust layer (not mixed with pollution). Deposition nucleation is the prevalent ice nucleation mode at these temperatures. In Sect 5.2, we then discuss  Temperatures were −35 • C to −36 • C at these heights. The particle depolarization ratio indicated ice crystal backscattering from the beginning of cirrus formation (the absence of any liquid phase) so that deposition nucleation or PCF (because this would also occur without a bulk liquid phase being detected) was obviously exclusively responsible for ice crystal nucleation.
The available INPs thus determine the maximum number of observable ice crystals.
The backward trajectories in Fig. 8 suggest that the air masses that reached Limassol at 8 km height crossed the Sahara at comparably high altitudes of 4.5-5 km height. Marinou et al. (2017) showed that dust layers over northern Africa (Algeria, Libya) reach to 6 km throughout the year, except during the main winter months (December-January) so that significant dust 5 uptake is always possible during spring months as long as the trajectories are below 6 km over northern Africa.
In Fig. 9, the main closure results are summarized. A pronounced dust layer was present from 7.2 to 9.3 km height at times before the cirrus developed (6:10-6:25 UTC) and showed 532 nm particle extinction coefficients of about 25 Mm −1 at 8 km height (see Fig. 9a). The particle depolarization ratio (not shown) was around 0.3 in the dust layer. This means that dust particles dominated and contribution from non-dust aerosol particles to the overall particle lidar backscatter return signals was 10 negligible. The radiosonde RH w indicated a moist layer which coincided with the dust layer. The air in the middle troposphere (at 5 km height) and at cirrus level (10 km) was dust free according to the trajectory analysis in Fig. 8 and our lidar observations. The dust extinction coefficients were then converted into number concentrations of large particles, n 250,d , and surface area concentration s d . At cloud level, the peak n 250,d and s d values were close to 5500 L −1 and around 85×10 −12 m 2 cm −3 , respectively (Fig. 9b). By applying the INPC parameterization schemes U17-I(d), U17-D(d), and D15 (see Table 1)  would have been the dominant ice-nucleation mode. As we will discuss below, such high numbers are in strong contradiction with the estimated ICNC that were clearly <100 L −1 as shown in Fig. 9c as well. 20 In the second part of the closure experiment, we estimated ICNC in the thin ice cloud. In  Table 2. Taking an uncertainty of a factor of 3 into account, ICNC was in the range of 4-39 L −1 .
The 35.5 GHz cloud radar (8.5 mm wavelength) provided useful reflectivity and Doppler information, caused by growing ice crystals, not before 6:52 UTC. During the initial phase (6:30-6:50 UTC) the cirrus remained invisible for the radar (see light blue profile in Fig. 9a with a peak ice extinction coefficient of 115-120 Mm −1 ). Our simulations with the cirrus information obtained from the Polly and Doppler lidar observations and by assuming a radar reflectivity value (clearly below the detection limit) reveal that ICNC was probably in the range of 2-10 L −1 before 6:50 UTC. Here, we used the approach described in 5 Sect. 4.2.1. However, we cannot fully exclude that a rather narrow ice crystal spectrum with crystal sizes of 10-20 µm was present at the beginning of the cirrus formation and ICNC was as high as 100-200 L −1 . However, such high numbers of ICNC would be in contradiction with the lidar-based INPC estimates of < 50 L −1 as discussed above and shown in Fig. 9c.
As shown in Fig. 9a (light blue curve, 6:35-6:42 UTC) the thin cirrus layer developed in the center of the dust layer. No indication for strong lifting of the Saharan air mass and rapid growth of the nucleated ice crystals and subsequent evolution 10 of fall streaks were visible within the first 20 minutes (6:30-6:50 UTC) of the evolving ice layer (see Fig. 7). It seems that the ice supersaturation level S i for the initiation of heterogeneous ice nuclation was slowly reached so that ice crystals formed, but then S i decreased again towards ice saturation (S i = 1.0) because of water vapor deposition on the nucleated ice crystals and, as a consequence, strong growth of ice crystals and the formation of a virga zone were not possible. Virga were absent during the first 20 minutes of cloud evolution. 15 Regarding the required ice supersaturation conditions, we assume that large-scale lifting and advection of moist air was responsible for the evolution of the cirrus layer at 8 km height. The radiosonde measured a relative humidity over water (RH w ) of 63% at 8.2 km height at about 6:30 UTC, obviously in clear air, i.e., before cirrus formation started. As can be seen in Fig. 9c, closure between ICNC of 13 L −1 (or from 4-39 L −1 ) in the developing cirrus layer and INPC at cloud top of 8.4-8.5 km is obtained for ice supersaturation values around 1.2-1.25 (or RH i of 120-125%) which corresponds to RH w of about 90-95% at 20 temperatures of −35 • C to −36 • C. It is interesting to note that Roberts and Hallett (1968) and Schaller and Fukuta (1979) found in laboratory studies more than 40 years ago that deposition nucleation occurs when S i exceeds 1.2. This finding is in good agreement with our observation and the applied U17-D INP parameterization. Nevertheless, according to Fig. 9c deposition nucleation can occur at any RH i >100% and S i >1.0 as already found earlier (Mangold et al., 2005;Kanji and Abbatt, 2006).
In this context, it should be mentioned (in order to avoid confusion about the apparently high INPC numbers outside the 25 clouds) that the presented INPC profiles are given for fixed, height-independent ice supersaturation levels. In reality, these high supersaturation values typically only hold for those parts of the cloud layers (e.g., from 8.2-8.5 km height in Fig. 9) in which ice nucleation takes place. Outside the clouds (and below the ice virga zone) ice subsaturation (S i <1.0) is given so that INPC=0.
As a final remark, it should also be emphasized that the unknown vertical motions have a sensitive impact on the actually active INPs and thus on the success of the INPC vs ICNC closure study. Even weak short-lived updrafts associated with cooling

The 17-March-2015 case study: long-lasting cirrus evolution in Saharan dust
The next closure study deals with cirrus formation in the upper troposphere. This case is shown in Fig. 5e and f and was measured during the Cyprus-2015 campaign (see Sect. 3.1). The ice cloud developed in the upper part of a Saharan dust layer.

5
According to the backward trajectory analysis in Fig. 11, Saharan dust was lifted from heights close to the surface up to the upper troposphere over Africa two days before arriving over Nicosia. We observed the final phase of a complex and long-lasting cloud evolution event which started on 15 March 2015 over northern Africa. The particle linear depolarization ratio measured with lidar during cloud-free periods was again around 0.3 throughout the dust layer and indicated pure desert dust conditions. The trajectory analysis in Fig. 11 further reveals that the boundary layer aerosol was advected from Turkey and crossed Europe 10 days before, whereas the dust layer from 2-6 km (see Fig. 5f Cirrus uncinus belongs to the synoptic cirrus category (Sassen, 2002). These ice clouds form in situ in the upper troposphere in response to a variety of weather disturbances. They typically form from the top down (i.e, ice crystal nucleation occurs at cloud top and subsequent sedimentation of ice crystals lead to an extended virga zone). The almost constant (non-descending) cirrus top height, observed over the whole day of 17 March 2015 with lidar, indicated an active ice cloud that continuously 30 produced new ice crystals. Usually dissoloving anvil cirrus fields descend with time (Strandgren, 2018). However, these clouds were visible in the satellite images until 18 March, about three days after the formation of the DIBS-related cloud complex over Algeria and did not descend according to our lidar observations. These long-living cirrus features were probably the result of favorable meteorological conditions (high humidity, permanent occurrence of vertical motions) (Feng et al., 2012) in combination with the high dust load in the upper tropopshere serving as an almost unlimited reservoir of INPs. Feng et al. (2012) reported that typical lifetimes of midlatitudinal anvil cirrus systems are <3 h in 50% of observed cases, the majority shows lifetimes <15 h. Here, we have an overall cirrus life time of 2-2.5 days, and thus all in all of 48-60 hours. Note, that reduced cirrus lifetimes are usually assumed when heterogeneous (instead of homogeneous) ice nucleation dominates (see, e.g., Storelvmo et al., 2018;Gruber et al., 2019). This may indeed be the case in controlled seeding experiments or, more 5 generally, in cases with a limited, depletable source of INPs.
Following the terminology of Kuebbeler et al. (2014), our closure study in Fig. 13 describes ice nucleation at pre-existing ice conditions. Strong supersaturation over ice is no longer possible at pre-existing ice conditions, i.e., in a fully developed cirrus system, so that homogeneous freezing can be excluded in our closure analysis. Homogeneous freezing needs stable conditions regarding lifting of air parcels over a long time period so that S i steadily rises and can finally reach values of 1.4-1.7. Number  Fig. 13c. The results of the ICNC and INPC data analysis for this case are also presented in Table 2.  were determined and ranged from 0.1 to about 5 L −1 . For several cloud segments with cloud top height between 5 to 6.5 km height, quite different ICNC values were derived, ranging from 0.2-2 L −1 to 4-36 L −1 . Besides the uncertainties in the remote-sensing-based INPC estimation (already considered in the shown INPC numbers in Fig. 14) ice break-up processes and crystal collision events associated with crystal aggregation formation which leads to an increase and reduction of ICNC, 5 respectively, must be kept in mind in the closure studies at these relative high ice formation temperatures ranging from about −15 to −25 • C. These problems mostly associated with high ICNC-to-INPC ratios were already reported by Auer et al. (1969) and Hobbs (1969) (see Sect. 2).

The 8-March-2015 case study: evolution of a mixed-phase altocumulus layer in polluted Saharan dust
In the first two closure studies, we discussed ice nucleation processes at relatively low temperatures of −35 • C to −57 • C and 10 found that deposition nucleation explained the ICNC observed. The third case now deals with heterogeneous ice nucleation within a stratiform mixed-phase altocumulus layer with cloud top temperatures of −20 to −23 • C. As mentioned, immersion freezing is the prevalent ice nucleation mode at these temperatures.
The altocumulus developed over Nicosia in desert dust at heights around 6 km in the late evening of 8 March 2015 (after 21:00 UTC). The case is shown in Fig. 5a and b. According to the backward trajectories in Fig. 15, the dust above 4 km height 15 originated from the Sahara, whereas the dust layer between 1 and 3.5 km was aged dust from the Middle East mixed with eastern European aerosol pollution. The dust from northern Africa was contaminated by anthropogenic fine-mode aerosol because the measured particles depolarization ratio was significantly below the pure dust value of 0.3. Small particles cause depolarization ratios of less than 0.05 20 so that depolarization ratio values around 0.2 indicate a significant contribution of continental fine-mode particles (indicated by the index c) to total particle backscattering and extinction as shown in Fig. 16. After separation of the dust and non-dust continental extinction coefficients σ d and σ c as described in detail by Mamouri and Ansmann (2014), the particle extinction profiles were used as input in the retrieval of the particle number concentrations n 250,d and n 250,c and of the particle surface area concentrations s d and s c in Fig. 17b  For the non-dust continental aerosol fraction we then applied the U17-I(c) INP parameterization (Table 1)  (with radius >100 nm) should be considered that serve as cloud condensation nuclei (Ansmann et al., 2019). The respective surface area concentration is a factor of 1.5-2 lower than the total particle surface area. It remains to be mentioned that a similar deviation of the U17-I(d) from the D15 INPC numbers as shown in Fig. 17c  Regarding the estimation of the ICNC values, we followed the strategy illustrated in Fig. 3b. The first altocumulus layer (22:29-22:31 UTC) started to form at 5.6 to 6.1 km height (dark blue profile in Fig. 17a) in the center of the upper dust layer (peaking at 5.8 km). Peak cloud extinction values (not shown) in the main altocumulus layer of 5000 Mm −1 (in the case of the light blue curve) to 8000 Mm −1 (in the case of the blue curve) occurring at heights from 6-6.2 km height, i.e., at the 25 cloud top are typical for cloud layers dominated by liquid-droplet backscattering. The depolarization ratio also dropped to low values typical for spherical droplets in this droplet-dominated layer. Virga developed (see Fig. 5a and b) and caused ice particle extinction coefficients of 100-150 Mm −1 below 5.6 km height (see Fig. 17a). Later, the second cloud layer (22:43-22:53 UTC) was found roughly at 250 m higher so that the cloud top temperature decreased by 2 • C which means that the INPC values increased by a factor of roughly 2-4 assuming that the dust particle concentrations remained almost constant. As 30 a consequence of the increased availability of INPs, also more crystals nucleated and consequently ice extinction coefficients in the virga zone increased to 150-180 Mm −1 in Fig. 17a (ice virga zone from 4.7-5.7 km height).
For completeness it should be mentioned that the primary lidar cloud parameter is the cloud backscatter coefficient. The liquid-water extinction coefficients are obtained by multiplying the strong cloud backscatter coefficients (in the cloud top region of the altocumulus layer) with the droplet lidar ratio of 18 sr (O'Connor et al., 2004). The ice crystal extinction coefficients in 35 the ice virga zone are obtained as described in the sections before by using a typical cirrus lidar ratio of 32 sr (Seifert et al., 2007;Giannakaki et al., 2007) in the conversion of the ice crystal backscatter values into the extinction coefficients. Note also, that the backscatter coefficient profiles are determined by means of the Raman lidar method (Ansmann et al., 1992) in which no lidar ratio profile is needed as input, in contrast to the widely and commonly used Fernald backscatter retrieval technique (Fernald, 1984) so that the obtained backscatter profiles are very accurate and not corrupted by strong height variations of the 5 lidar ratio (from the dust layer below the cloud dust over ice virga zone to the liquid-water layer at cloud top).
The Doppler lidar measurements of the fall speed of the ice crystals and the ice extinction values of 120 and 180 Mm −1 in the virga zone were then used to estimate the ICNC numbers in Fig. 17a for the two cloud cases following the methodology described in Sect. 4.2.3. By considering an uncertainty of a factor of 3, ICNC was between 0.3 and 7.5 L −1 . The cloud top height increased by 250 m from cloud segment 1 to cloud segment 2 in Fig. 17a. The respective decrease 15 in temperature leads to an increase in INPC by a factor of 2-3. This lifting of cloud and dust parcels is not included in the INPC profiles (estimated from the aerosol conditions before the cloud field arrived and before the lifting took place). All in all, we rate this closure experiment also as successful. As already discussed above, a better agreement cannot be expected. With increasing cloud top temperature the probability of secondary ice formation and thus of strong changes in the ICNC numbers increases. Furthermore, ice crystals nucleated via immersion freezing can grow very fast in the (almost) unlimited liquid-water 20 reservoir and then probably create ice crystal clusters with complex shape features which may intensify ice-break-up as well as collision processes. sensitively influenced the cloud evolution processes and extended the cloud lifetime. Such cloud evolution cases with largely extended cloud life time and increased regional coverage may be counted as contribution to anthropogenic climate forcing if it can be shown that the occurrence frequency and strength of these MCSs, able to lift large amount of natural INPs into the upper troposphere, increased during the last decades in a warming climate caused by man-made activity.

As mentioned, the comparison of estimated ICNC and INPC values is difficult in view of the large differences between the
(2) Our remote-sensing-based closure experiments demonstrated that dust can trigger significant ice formation in the middle 5 and upper troposphere via the heterogeneous ice nucleation. The homogeneous freezing path way was not needed to explain the evolution of the cirrus uncinus fields at −55 to −57 • C (case 2 of our closure studies).
(3) A new lidar-radar-based methodology based on new ICNC (Sourdeval et al., 2018;Mitchell et al., 2018;Bühl et al., 2019) and INPC retrieval techniques Ansmann, 2015, 2016;Marinou et al., 2019) is now available to investigate the role and impact of aerosol particles on ice formation in atmospheric clouds and on subsequent precipitation processes. UAVs are mostly used in atmospheric research at heights below 3 km, UAV-Balloon systems are under development that can 25 even reach stratospheric heights and will be able to profile particle size distribution and other aerosol properties within the entire troposphere. We also need such kind of in-situ-vs-remote-sensing studies to validate our developed remote-sensingbased ICNC retrieval method. Airborne in situ observations of ice crystal size distributions, shape properties, and ICNC in ice clouds over the remote sensing facility would be desirable for intensive ICNC comparisons.
(4) As a significant contribution to climate-change research, we need to apply the INPC-vs-ICNC closure concept to space- regimes and aerosol conditions. We moved our lidar-radar LACROS equipment after the CyCARE campaign (October 2016-March 2018 to Punta Arenas at the southern most tip of South America (long term measurements started DACAPO-PESO at the end of November 2018) to investigate aerosol cloud interaction at rather pristine conditions, with only a few episodes of siginfcant amounts of continental aerosols (smoke and dust from southern parts of South America, and long-term transport for Australia).

5
(5) As an outlook and to reduce the number of critical assumptions in our closure methodology as discussed in Sect. 4, we may include the next generation of powerful water vapor differential absorption lidars (DIALs) or Raman lidars to obtain temporally and vertically highly resolved water vapor and relative humidity profiles in cirrus and transparent altocumulus layers (Leblanc et al., 2012;Reichardt et al., 2012;Späth et al., 2016;Sakai et al., 2019) as well as information on liquid-water and ice-water content (Wang et al., 2004;Sakai et al., 2013;Reichardt, 2014) in future closure studies. We may also integrate 10 radar wind profilers in our cloud studies to obtain detailed updraft and downdraft observations in the cloud top regions Radenz et al., 2018), and even lidar techniques for quantification of mineral dust concentrations within the ice clouds (Tatarov and Sugimoto, 2005;Müller et al., 2010;Tatarov et al., 2011).

INP method Reference, equation
Nucleation mode Aerosol type Input       (see Table 1). All INPC values (HINC, lidar) are given for −30 • C.    The deposition-nucleation U17-I(d) parameterization is used on 17 March (at 9-10 km height for Si=1.1) and the immersion-freezing D15 parameterization is applied in the evening data analysis on 18 March (at 5-6 km height). Dashed white lines show the GDAS1 temperature isolines with 3-hour resolution.