In this work, measurements of the spectrometer of the Munich Aerosol Cloud Scanner specMACS, during the airborne HALO–(AC)3 measurement campaign in the Arctic are applied . In particular, data from the research flight on 1 April 2022 in the Fram Strait are analyzed. The HALO flight on that day sampled the initial phase of a MCAO following a quasi-Lagrangian flight strategy , and was coordinated with the Polar 5 and Polar 6 aircraft. specMACS consists of two hyperspectral cameras sensitive to the visible and near-infrared and the shortwave infrared wavelength ranges (so-called VNIR and SWIR) and two 2D RGB polarization-resolving cameras, which are installed in a downward-looking perspective on board HALO. This work applies measurements of the SWIR spectrometer, which covers the wavelength range between 1000 and 2500 nm wavelength and has a field of view of 35.3 ° in across-track direction, and the polarization-resolving cameras, which have a maximum combined field of view of 91°×117° in along-track and across-track direction. The specMACS measurements provide high-spatial resolution information about cloud macro- and microphysical properties, with resolutions between 10 and 100 m at typical flight altitudes, depending on the retrieved quantity.

The cloud top height is derived from measurements of the polarization-resolving cameras with the stereographic retrieval by , which was validated by based on synthetic data of a field of shallow cumulus clouds with a complex 3D cloud geometry. The effective radius of liquid cloud droplets is retrieved using the multi-angle polarimetric cloudbow retrieval by . The cloud droplet effective radius is determined by fitting polarized scattering phase functions according to Mie theory to multi-angle polarization signals of the cloudbow, which is formed by single scattering on liquid cloud droplets. The retrieval was validated with synthetic data of shallow cumulus clouds with a complex 3D geometry by , who found an average difference between the retrieved and simulated effective radii of -0.2±1.6µm. Further sensitivity studies showed that the cloudbow retrieval is not affected by the presence of cloud ice in mixed-phase clouds and yields reliable results for ice fractions up to 0.8. Since the retrieval is based on polarization, it is less affected by 3D radiative effects.

Information about the cloud thermodynamic phase is obtained with two different methods. First, the ice index, as defined by and , is calculated from the radiances measured by the SWIR for all clouds. This index is based on spectral absorption differences between liquid water and ice in the near-infrared wavelength range and provides qualitative information about the cloud thermodynamic phase, which allows for an accurate phase classification. Sensitivity studies based on radiative transfer simulations showed that values below 20 correspond to a liquid water cloud, whereas values above 20 indicate a mixed-phase cloud . The ice index is a well-established method for characterizing the cloud thermodynamic phase and has already been applied, e.g., by to study clouds during MCAOs and warm air intrusions in the Arctic.

Second, a quantitative ice fraction was retrieved from the measurements of the polarization-resolving cameras using the polarimetric phase partitioning retrieval by . It is determined by fitting multi-angle polarization signals obtained from a forward operator to measurements. The ice fraction is defined as the ratio of the ice optical thickness to the total cloud optical thickness under the assumption of a homogeneously mixed cloud. Depending on the observation geometry, either the cloudbow angular range, covering scattering angles between 135 and 165 °, or the slope angular range from 60 to 110 ° scattering angle, can be used. Further information about the retrieval, a detailed discussion of the retrieval uncertainties, and a validation based on synthetic data of low-level Arctic mixed-phase clouds with a complex 3D cloud geometry can be found in . The uncertainties include measurement uncertainties, uncertainties due to retrieval assumptions, and uncertainties due to 3D radiative effects and vary across different retrieval configurations. Here, the results of the polarized retrieval for the green wavelength channel for the cloudbow angular range using the forward operator applying a parameterization of 3D cloud geometry are used, and only observations with saturated polarization signals are considered because these provide the smallest uncertainties . For the analyses in Sect. , however, data of the ice fraction derived from the more uncertain and less sensitive slope angular range had to be used, since the observation geometry did not allow for applying measurements in the cloudbow angular range.

Since the measurements of specMACS are based on passive remote sensing, they are representative for the cloud top. The spectral measurements used to determine the ice index originate from deeper cloud layers than the polarization measurements applied to retrieve the ice fraction and the effective radius of liquid cloud droplets, because the polarization signal is dominated by single scattering. For the same reason, the polarimetric retrievals are less affected by 3D radiative effects. The spectral ice index is very sensitive to cloud ice , whereas the polarimetric phase retrieval can detect very small amounts of liquid water in ice clouds . The spectral and polarimetric phase retrievals complement each other due to their different sensitivities and provide information about the cloud thermodynamic phase at two different altitudes within the clouds due to their different penetration depths.

Similar to , measurements above sea ice with sea ice concentrations larger than 80 % were excluded from the analyses to reduce additional uncertainties due to the influence of the (unknown) surface and due to the misclassification of clouds and sea ice in the marginal sea ice zone with the brightness-based cloud masks.

In addition to the specMACS observations, measurements of other instruments on board HALO and collocated in situ measurements collected by the Polar 6 aircraft were applied to characterize the observed clouds further. Information about cloud top temperature is available from the thermal imager VELOX on board HALO, which measures brightness temperatures at six different wavelength channels between 7.7 and 12µm and has a similar field of view and spatial resolution as the spectrometers of specMACS. Here, the brightness temperatures measured by the first broadband channel (covering the wavelength range between 7.7 and 12µm) were used. For measurements in the Arctic, with low water vapor content in the atmosphere, the measurements of this channel are representative for the cloud top. Measurements of the lidar backscatter ratio and aerosol depolarization by the WALES lidar and the radar reflectivity measured by the HAMP 35 GHz cloud radar on board HALO provide vertical information about the observed clouds. Furthermore, dropsonde measurements of air temperature, pressure, and relative humidity were collected.

In addition to the measurements from the various instruments on board HALO, collocated in situ observations by the Polar 6 aircraft were used. The different scattering and optical array probes installed on board Polar 6 measure the particle number size distribution, from which the cloud droplet and ice crystal number concentrations and the effective radius and diameter of liquid cloud droplets and ice crystals can be computed as described in and . The combined particle number size distributions measured by the Cloud Droplet Probe, Cloud Imagining Probe, and Precipitation Imaging Probe were integrated over size for particles smaller than 50µm diameter, assuming these particles to be liquid, to calculate the cloud droplet number concentration and over particles larger than 50µm diameter to obtain the ice crystal number concentration .

As in , the measurements and retrieval results were combined with backward airmass trajectories to assign every measurement the time the airmass has traveled southwards since passing the sea ice edge. The backward trajectories were computed from ERA5 wind fields using Lagranto .

The parcel model predicts vertical profiles of the liquid water content in a liquid water cloud resulting from the lifting of an air parcel. The cloud droplet number concentration is assumed to be vertically constant and the actual liquid water content is linearly related to the adiabatic liquid water content through the adiabaticity fad, which accounts for entrainment . According to this model, vertical profiles of the effective radius of liquid cloud droplets can be computed with 1reff=34πρw1/3(fadCw)1/3(kNd)-1/3h1/3. Here, ρw is the density of liquid water and h=z-zbase is the height above the cloud base height. k is the factor converting volume mean radii to effective radii, with k=0.8 a typical value for maritime clouds . The condensation rate Cw depends on temperature and pressure and is computed from the dropsonde measurements using the formula given by . The adiabaticity fad accounts for the reduction in the condensation rate due to entrainment. A detailed discussion of uncertainties and assumptions of the adiabatic cloud model can be found in . Here, the adiabaticity was computed with an entrainment model to further account for variations of the entrainment with height : 2fad=exp⁡(-ϵh), with ϵ=1km-1, which is a typical value for cumuliform clouds. The cloud base height of the liquid water cloud zbase was derived from dropsonde data and the cloud heights from the stereographic, respectively, cloudbow retrieval of specMACS as described below, and increases with time above open ocean as the boundary layer evolves. Regarding the dropsonde data, the cloud base height was defined as the height at which the relative humidity with respect to liquid water first exceeded 99 %. For the specMACS measurements, the minimum height of the measurements, at which an effective radius was determined with the cloudbow retrieval was used. A relation for the cloud base height as a function of time above open ocean was obtained by fitting a linear curve to the cloud base heights obtained from the dropsondes and specMACS. This relation is used to compute the effective radius for different times above open ocean. The cloud droplet number concentration Nd was derived from in situ measurements of the P6 aircraft, which performed collocated measurements with HALO on 1 April 2022, as described above. A more detailed discussion and analysis of the cloud droplet number concentration measurements is given in Sect. .

This section gives an overview of the research flight conducted by HALO on 1 April 2022, which is analyzed in detail in this work. The flight on 1 April 2022 targeted the Fram Strait region, where a MCAO was observed on that day, and was coordinated with the Polar 5 and Polar 6 aircraft. Figure  shows the MCAO index in panel (a), the MODIS satellite image in panel (b), and the backward trajectories together with the AMSR2-MODIS sea ice concentration in panel (c). The flight track is superimposed in red and contours of the mean sea level pressure and the geopotential height at 500 hPa from ERA5 data are displayed in panel (a). The MCAO index is a measure of the strength of the MCAO. It was computed from the potential skin temperature at the surface and the potential temperature at a pressure of 850 hPa using ERA5 data following : 3MCAO=θskin-θ850hPa. According to  and , the event observed on this day with average MCAO indices of around 8 K in the Fram Strait region can be classified as a moderate to strong MCAO. It appears to be a typical event for this region at that time of the year . The synoptic situation was characterized by a high-pressure system over Greenland and the Central Arctic and a low-pressure system above Scandinavia, the Barents Sea, and Russia. This led, together with a local low-pressure system south of Svalbard, to a northerly flow in the Fram Strait as indicated by the backward trajectories in panel (c). The satellite image in Fig. b shows cloud streets extending southwards from the sea ice edge. In addition, there are local effects due to the topography of Svalbard visible with several convergence lines and cloud-free regions southwest of the island. The flight pattern targeted the initial phase of the MCAO following the quasi-Lagrangian sampling approach with flight legs oriented perpendicular to and along the wind direction . This quasi-Lagrangian observation strategy allows for studying the evolution of thermodynamic and cloud properties observed during the MCAO. The temporal and spatial evolution of cloud macro- and microphysical properties during this research flight was already analyzed in . In the following, the evolution of the vertical cloud structure will be studied.

To investigate the temperature dependence and the vertical distribution of the thermodynamic phase partitioning, retrieval results of the ice index and ice fraction from specMACS were combined with measurements of the cloud top temperature from the VELOX instrument, following the method of and . As already mentioned above, the spectral and polarized phase retrievals complement each other due their different sensitivities to liquid water and ice and their different penetration depths and are therefore analyzed jointly. The measurements from VELOX and specMACS were matched to obtain corresponding cloud top temperature measurements for every ice index, respectively, ice fraction measurement. These data were then used to construct pseudo-vertical profiles of the cloud thermodynamic phase as a function of temperature. Based on the backward airmass trajectories, the measurements were sorted into different time ranges above open ocean to account for the strong airmass transformations and the related temporal and spatial evolution of the thermodynamic structure of the boundary layer during MCAOs. By applying this method to construct pseudo-vertical profiles, it is assumed that the distribution of the thermodynamic phase is horizontally homogeneous for a given height respectively temperature for a given time interval of the cloud evolution. A more detailed discussion about this assumption and further limitations is provided later in Sect. .

Figure  shows the ice index (blue) and ice fraction (orange) as a function of cloud top temperature. The individual panels correspond to different time ranges above open ocean. The measurements for every temperature bin are normalized by the total number of measurements in the respective bin. Vertical profiles of the air temperature and potential temperature measured by dropsondes during the research flight on 1 April 2022 are shown in Fig. . The dropsonde data were combined with trajectory data to assign every measurement a time above open ocean. In general, the temperature decreases with height, and an inversion marks the top of the boundary layer. The altitude of the inversion layer increases with time above open ocean as the boundary layer deepens. In addition, the temperature increases with time. A detailed study of the thermodynamic evolution of the MCAO on 1 April 2022 during HALO–(AC)3 can be found in and . During the first hour above open ocean, high diabatic heating rates exceeding 6 Kh-1 and moistening rates larger than 0.3 gkg-1h-1 were observed at the surface. The heat and moisture are increasingly mixed upward as the time above open ocean increases and the boundary layer develops.

During the first 15 min after passing the ice edge, the ice index in Fig.  is below the threshold value of 20 for all temperatures, indicating a liquid water cloud. At later times, the ice index is still almost constant with temperature except for the coldest temperatures, where it increases with decreasing temperature and crosses the threshold value from the liquid water into the mixed-phase regime. The increase in the ice index starting from the coldest temperatures indicates that ice formation occurs preferentially at the coldest temperatures. This is reasonable, as several studies based on in situ measurements have shown that the relative fraction of ice increases with decreasing temperature and the probability for freezing of supercooled liquid cloud droplets increases with decreasing temperatures . With time, the transition from the liquid water to the mixed phase shifts to warmer temperatures, and the ice indices at the coldest temperatures further increase. This could be explained by ice, which is continuously formed at the coldest temperatures at the cloud top and sediments downwards. Consequently, the relative fraction of ice increases and liquid water might additionally be depleted through riming or the WBF mechanism. However, liquid water is still present also at lower altitudes. The observations are taken during the initial phase of a MCAO and the clouds are therefore observed during the very initial phase of their evolution from entirely liquid water clouds towards mixed-phase clouds. A similar structure of mixed-phase clouds above open ocean with increasing fractions of ice clouds with increasing height due to decreasing temperatures was also reported by , based on in situ measurements during HALO–(AC)3.

The ice fraction derived with the polarimetric retrieval is mostly constant or slightly increasing with decreasing temperature, similar to the ice index. However, a strong decrease of the ice fraction with decreasing temperature can be observed at the coldest temperatures. This indicates that there is a very thin, more liquid-dominated layer at the cloud top, which is not or only partly detected by the spectral retrieval used to determine the ice index. The spectral retrieval is sensitive to deeper altitudes within the cloud than the polarized retrieval. Therefore, the ice fraction from the polarized retrieval is more strongly affected by a thin, more liquid-dominated layer at the cloud top than the ice index from the spectral retrieval if the thickness of this layer is smaller than the penetration depths of the spectral signal. In addition, the polarized retrieval is very sensitive to liquid water, whereas the spectral retrieval is more sensitive to ice. At longer times above open ocean in the last two rows of Fig. , the retrieved ice fraction becomes variable and uncertain due to increasing solar zenith angles and a decreasing number of data points.

The ice fraction in the first 15 min above open ocean is overestimated due to sea ice, which has been misclassified as clouds by the applied cloud mask. This is a well-known issue in passive remote sensing. However, it applies only to the retrieved ice fractions in the marginal sea ice zone, since the cloud mask of the polarization-resolving cameras relies on measurements in the visible wavelength range, where sea ice is bright, whereas a wavelength of 1640 nm was chosen for the cloud mask for the SWIR-derived ice indices, where sea ice is dark compared to the liquid-containing clouds. Due to the different field of views of the sensors, it was not possible to consistently use a single cloud mask. In addition, the ice fraction generally has a high bias . The threshold value between the liquid water and mixed phase indicated by the black dashed line in Fig.  only applies to the ice index. These facts have to be kept in mind, when analyzing and interpreting the observed absolute values, in particular in the first panels. This all together can explain the observed differences between the profiles of the ice index and ice fraction.

In general, the variability of the retrieved ice fractions is large. The distribution of the ice fraction shows an almost bimodal distribution, resulting in a large standard deviation. The horizontal distribution of the retrieved ice fractions (not shown) showed generally smaller ice fractions at the cloud centers and larger ice fractions towards the lower cloud sides. In addition, small-scale variability could be observed. Part of the large spread of the ice fraction, including values close to 0 and 1 in Fig. , however, has to be related to retrieval uncertainties, which have been characterized in detail in . The horizontal distribution of the retrieved ice indices also exhibited some small-scale variability, which at least partly has to be attributed to 3D radiative effects and the related uncertainties. However, the influence of 3D radiative effects on the derived pseudo-vertical profiles is small (see the additional analyses provided in the Supplement). Given the large retrieval uncertainties for both ice index and ice fraction and the uncertainty of the necessary assumptions to construct pseudo-vertical profiles, the pseudo-vertical profiles of the ice index and ice fraction will be compared to radar and lidar measurements below, providing vertical information about the observed clouds.

The brightness temperatures measured by VELOX in Fig.  partly show warmer temperatures and a larger temperature range than the measurements of the dropsondes in Fig. . This can be explained by the influence of the warm ocean surface, which can lead to an overestimation of the measured brightness temperature for optically thin clouds. A cloud mask was applied to the data to filter the measurements, but some influence persisted in the warmer parts of the profiles. The number of affected data points is, however, small. The histograms in Fig.  are normalized by the total number of measurements for every temperature bin, leading to a false impression of many affected measurements.

Similar to the profiles of the ice index and ice fraction as a function of temperature, pseudo-vertical profiles of both quantities as a function of height can be constructed. The resulting plots are not shown here, since the temperature typically decreases with height and the results of both analyses are similar (see Fig. ), but are provided in the Supplement. The ice index and ice fraction both increased with height, in agreement with the temperature dependence. At the very top, the ice fraction generally showed a strong and sharp decrease, which was also partly captured in the pseudo-vertical profiles of the ice index. However, this decrease was less pronounced for the ice index, for the same reasons as discussed above. This confirms the existence of a geometrically thin, more liquid-dominated mixed-phase layer compared to the altitudes directly below at cloud top. The layer with increased amounts of supercooled liquid water at cloud top had a geometrical thickness of about 100 to 200 m.

Additional vertical information is obtained from active remote sensing measurements. The lidar and radar measurements on board HALO were combined with backward airmass trajectories to create composites as a function of time above open ocean. To this end, the data were sorted into one-minute bins and all measurements of a certain time bin were averaged. Figure  shows the corresponding results for the lidar backscatter ratio (first row), aerosol depolarization (second row), and radar reflectivity (third row). The cloud top height in both lidar and radar data shows an increase with time, similar to the measurements of specMACS discussed in . At cloud top, the lidar backscatter ratio is high and the depolarization is close to zero, indicating spherical particles. As the lidar is particularly sensitive to small liquid cloud droplets with a high number concentration, this hints at the presence of supercooled liquid water in this layer. The radar reflectivity increases with time and from cloud top towards the surface, as the radar signal is dominated by the larger ice crystals. These sediment downwards and grow further during their descent. After about 30 to 45 min above open ocean, the radar reflectivity exceeds the threshold value of -5 dBZ for precipitation . Moreover, the high radar reflectivities at high altitudes indicate the presence of ice close to cloud top. An increasing radar reflectivity with decreasing height is not a contradiction to the observed increasing ice fraction with increasing height and decreasing temperature. The radar reflectivity is very sensitive to the size of the ice crystals, which increases with decreasing height as the larger ice crystals sediment and further grow during their descent, and is, to a lesser degree, influenced by the number concentration. In contrast, the ice fraction is a quantitative optical measure that reflects the optical thickness of both phases and depends on the sizes and number concentrations of cloud liquid water and cloud ice.

A geometrical thin layer with increased amounts of supercooled liquid water at cloud top from which ice crystals form and sediment downwards is the expected typical structure of low-level Arctic mixed-phase clouds e.g. and was also observed for mixed-phase clouds during MCAOs . Both passive and active remote sensing measurements qualitatively show this distinct structure.

In addition to the vertical distribution of the cloud thermodynamic phase, the vertical evolution of the effective radius of the liquid cloud droplets is analyzed in the following. The analyses in the previous section and in showed that the liquid water clouds, which form at the very beginning of a MCAO close to the ice edge, rapidly transform into a mixed-phase regime. However, it was not investigated how ice processes influence the cloud liquid water over time and throughout the vertical extent of the cloud. For example, the WBF mechanism or riming could impact the cloud droplet size and number concentration. To further study these effects, measured pseudo-vertical profiles of the effective radius of the liquid cloud droplets are compared to vertical profiles calculated with the parcel model introduced in Sect. , which does not include ice processes. Differences or agreement between the theoretical and measured profiles provide insights into microphysical processes in the observed mixed-phase clouds and their temporal evolution.

Pseudo-vertical profiles of the effective radius of liquid cloud droplets are obtained from the measurements following the method of and . To this end, the individual measurements of the effective radius of liquid cloud droplets are combined with the corresponding cloud top heights, yielding a combined pseudo-vertical profile. Similar to above, the data are divided into time bins along their temporal evolution. The input variables for the parcel model are computed from dropsonde measurements, in situ measurements, and measurements of specMACS as explained in Sect. . The cloud droplet number concentration, needed for the model and obtained from the in situ observations, and its temporal evolution and vertical distribution are further investigated by also combining the measurements with backward trajectories.

Figure  displays the cloud droplet number concentration as a function of time above open ocean. The color-coding denotes the height of the respective measurements. During the first 40 min above open ocean, the cloud droplet number concentration increases with time. In this time range, the clouds are decoupled from the surface, as indicated by the at least partly increasing potential temperature with height in Fig. b . Afterwards, the cloud droplet number concentration decreases with time. Decreasing number concentrations during the initial phase of MCAOs were also observed by, e.g., and can be explained with reduced supersaturation, entrainment, and aerosol scavenging through precipitation . The initial increase of the cloud droplet number concentration is missed in , potentially due to the much coarser resolution and higher uncertainties of the satellite-derived measurements in this study compared to the in situ measurements applied here, but was also observed by, e.g., .

In addition, the number concentration in Fig.  shows only small variations with height. Lower number concentrations are measured at higher altitudes, which can, for example, be explained by the influence of entrainment or by heterogeneous freezing of liquid cloud droplets. However, the vertical variations of the number concentration are small compared to the uncertainties of the measurements, such that the cloud droplet number concentration can be assumed to be approximately constant with height. A vertically constant number concentration is a required assumption for the parcel model and this was also observed in other studies such as  for stratocumulus clouds and by  for small cumulus clouds.

For the parcel model, linear fits were applied separately to times smaller and larger than 40 min to obtain a relation of the number concentration as a function of time above open ocean. The orange and red lines in Fig.  show the resulting fits. Due to the limited range of the Polar 6 aircraft, measurements of the number concentration are only available for the first 150 min above open ocean. They were extrapolated to larger times using the obtained linear fit. With this, the theoretical vertical profiles of the effective radius of liquid cloud droplets were calculated for any time above open ocean.

Figure  shows the measured pseudo-vertical profiles of the effective radius of liquid cloud droplets for different time ranges above open ocean in black and the theoretical vertical profiles according to the parcel model in red. The measurements were again normalized by the number of measurements in every altitude bin and sorted into different time ranges above open ocean based on the backward trajectories. In general, the cloud droplet size increases with increasing cloud top height, as is expected. Moreover, the effective radius increases with increasing time above open ocean from initially about 5 µm to maximum values of approximately 10 µm during the observed time range, in agreement with and .

Large deviations of the measured and calculated profiles are observed in the first row of Fig. , especially at lower altitudes. At these times, close to the sea ice edge, the clouds are decoupled from the surface, as discussed above, and the parcel model is not applicable. Cloud formation starts as soon as small fractions of open ocean exist in the marginal sea ice zone. Above sea ice, longwave radiative cooling at the surface causes a temperature inversion. The turbulence induced by the warm open ocean surface then leads to a coupling of the boundary layer and the associated clouds. In addition, the measured and calculated profiles mostly differ at the cloud base. A reason for this could be that the lowermost part of the clouds, with very small effective radii of the liquid cloud droplets, is too optically thin to be captured by the measurements, or is geometrically not visible at large viewing angles in combination with high cloud fractions. In addition, the initial growth of small liquid cloud droplets at the cloud base is fast and the cloud base height is difficult to determine, such that small uncertainties have a larger influence.

Besides that, there is generally good agreement between the profiles, indicating that the cloud ice did not significantly impact the cloud liquid water during the observed initial phase of the cold air outbreak on 1 April 2022 and that the parcel model is applicable here. The profiles calculated with the parcel model were not fitted to the measured pseudo-vertical profiles. Instead, the input variables were computed from measurements as described above. Deviations between the parcel model and the direct measurements are explained either by uncertainties of the input variables, by droplet collision and coalescence, or by ice processes, such as riming or the WBF mechanism, which are not accounted for in the parcel model. These will further be discussed in the following section.

First, the uncertainties of the input variables to the model are considered. The measurement uncertainties of the cloud droplet number concentration from in situ observations are about 10 % to 30 % , which corresponds to an uncertainty of the modeled effective radius of about 10 %. In addition, the vertical variation of the number concentration in Fig.  is about 50 %, which could explain deviations between the effective radii of up to 25 %. The cloud base height also has uncertainties, as it is derived from measurement data, but these uncertainties only shift the computed effective radius profile in the vertical direction. Other uncertainties arise from the interpolation between the condensation rates computed from the individual dropsondes and measurement uncertainties of the dropsondes due to, e.g., a broken cloud field. However, the cloud fraction was very high (see Fig. 3 in ) and the condensation rate varies only slightly with temperature and pressure in the observed temperature range.

Furthermore, an entrainment model (Eq. ) was applied to compute the effective radius. The effective radius is, in general, only slightly influenced by entrainment . Variations of the adiabaticity by 10 % in Eq. () change the calculated effective radius by less than 4 % for the observed cloud droplet sizes. Nevertheless, the agreement between the measured and calculated vertical profiles of the effective radius varied depending on the chosen value of the adiabaticity. The good agreement between the observations and the theoretical profiles for the applied entrainment model indicates that this model realistically describes entrainment in the observed clouds. However, the adiabaticity could, in principle, also be reduced by other processes than entrainment. In mixed-phase clouds, simultaneously growing liquid cloud droplets and ice crystals compete for the available water vapor. This can lead to a reduced growth of liquid cloud droplets, similar to the influence of entrainment. At least a part of the reduction of the adiabaticity could potentially be attributed to this effect. From the measurements, it is not possible to directly distinguish between the effects of entrainment and ice crystals competing with the liquid cloud droplets for the available water vapor. However, the observed clouds are still dominated by liquid water, and the ice fraction and ice index are comparably small (see Fig. ). In addition, the applied entrainment model is a realistic assumption. Thus, entrainment is likely the dominating factor here, but the influence of the ice crystals on the droplet growth introduces an additional uncertainty.

Moreover, the uncertainty of the measured effective radii from the cloudbow retrieval based on an evaluation with synthetic data is -0.2±1.6µm . These differences include the influence of 3D radiative effects. In summary, the uncertainties of the input variables used to model the effective radius and the uncertainties of the measured effective radii can explain the observed differences between the profiles.

Besides measurement uncertainties, microphysical processes, such as droplet collision and coalescence and ice processes, can lead to deviations of the observed profiles of the effective radius from the parcel model. Collision and coalescence of liquid cloud droplets are relevant if the effective radius of the droplets exceeds 14 µm . The observed liquid cloud droplets have maximum effective radii of about 10 µm, which is much smaller than this threshold. Therefore, collision and coalescence of liquid cloud droplets can be neglected in the observed clouds.

Another possible explanation for deviations between the parcel model and the observed effective radii is ice processes, such as ice formation through freezing of supercooled liquid water droplets, ice crystal growth through the WBF, and riming. Ice formation in mixed-phase clouds predominantly happens through heterogeneous freezing of supercooled liquid water droplets . Hence, the formation of ice crystals decreases the cloud droplet number concentration. The probability that a supercooled liquid water droplet will freeze increases with increasing droplet size and decreasing temperature, but it also depends strongly on the efficiency of the ice nuclei. The ice crystal number concentration, computed from in situ measurements of the particle number size distributions from particles larger than 50 µm, amounts on average to about 20 L-1 with variations between 0 and 100 L-1, which is four orders of magnitude smaller than the observed cloud droplet number concentration. Hence, the influence of the conversion of liquid water droplets into ice crystals through freezing on the effective radius can be neglected.

A second ice process that can influence the liquid cloud droplets is the WBF mechanism. The WBF mechanism, however, is active only in a distinct regime with supersaturation with respect to ice and subsaturation with respect to liquid water . Information about the supersaturation during the research flight on 1 April 2022 is available from the dropsondes released from HALO and the in situ measurements from the P6 aircraft. Figure  displays vertical profiles of the relative humidity above liquid water in panel (a) and above ice in panel (b) measured by the dropsondes. A layer with saturation above liquid water and supersaturation above ice is observed in the upper part for most times, which coincides with regions of high lidar backscatter ratio, indicating the presence of liquid cloud droplets. In this height range, liquid water droplets and ice crystals grow simultaneously. Close to the cloud top, there is usually a thin layer with supersaturation above ice only, which could be explained by entrainment of dry air. At lower altitudes, only supersaturation above ice is reached. This is the region where the WBF mechanism is active and larger radar reflectivities indicate the presence of ice.

The measured profiles of the effective radius for the time range between 90 and 135 min show some variations of the slope with height and larger deviations from the parcel model in regions where the WBF mechanism could be active. However, there are only a few dropsonde measurements, which cover only parts of the time ranges, and the in situ data provide only limited vertical information. This makes it difficult to directly relate these deviations to the WBF mechanism, and the deviations are, in general, small compared to the measurement uncertainties. Moreover, the low ice crystal number concentration measured by the in situ probes indicates that no significant ice multiplication has taken place. Thus, even if the WBF mechanism is active, the measurements suggest that its influence on the cloud droplet effective radius is small. This can be due to inhomogeneous mixing of the liquid water and ice phases, the low ice crystal number concentration, or a combination of both, which makes the WBF mechanism less effective and limits its impact on the effective radius of the liquid cloud droplets. If highly resolved measurements of the vertical profiles of the cloud droplet number concentration were available, both effects could be distinguished.

Another ice process that can explain deviations between the parcel model and the measured effective radius profiles, especially in regions where the WBF mechanism is not active, is riming. Laboratory measurements indicate that the influence of riming on the cloud droplet size distribution is small . According to the theoretically computed collision efficiencies, the liquid cloud droplets must reach a critical size for collisions with ice crystals, depending on the crystal shape . The retrieved effective radii smaller than 7.5 µm are close to the critical radius for riming. Smaller droplets can still participate in riming , and actually riming was observed during the research flight on 1 April 2022 based on radar and in situ observations . However, the collision probability is small due to the low ice crystal number concentration. Furthermore, the normalized rime masses computed from in situ and radar measurements by  show only light riming with mean values of about 0.03 on this day, which is small.

In summary, there is agreement between the measured vertical profiles of the effective radius of liquid cloud droplets and the applied entraining parcel model within the range given by the measurement uncertainties. The measurements indicate that collision and coalescence processes of liquid cloud droplets can be neglected in the observed clouds. Furthermore, they suggest that ice processes, such as heterogeneous freezing of supercooled liquid cloud droplets, riming, and the WBF mechanism, did not significantly impact the cloud liquid water during the initial phase of this MCAO. The parcel model realistically describes the evolution of the liquid cloud droplets in the observed low-level Arctic mixed-phase clouds, except when the clouds are decoupled from the surface.

Nevertheless, we discuss some limitations of the presented methods and results in the following. In general, the same limitations as in apply, including, for example, the issue of the cloud mask in the presence of sea ice, affecting the retrieved ice fractions in the marginal sea ice zone, and increased measurement uncertainties due to large solar zenith angles in the Arctic. Strictly speaking, the method by and for constructing pseudo-vertical profiles from passive imaging observations was only validated for the cloud droplet effective radius. Here, it was also applied to the cloud thermodynamic phase in Sect. , assuming that the thermodynamic phase is also a conserved quantity and horizontally homogeneous for a given temperature respectively height, similar to the effective radius, for every time interval along the cloud evolution. Therefore, the obtained pseudo-vertical profiles were compared to radar and lidar observations, which provide vertical information about the clouds and showed general agreement with the specMACS observations. In addition, the observations are in agreement with our theoretical understanding and with the literature. Nevertheless, a study similar to , based on model data, should be repeated for cloud thermodynamic phase partitioning in future work to further investigate the validity of this assumption. Updrafts in the cloud centers or the influence of entrainment at the cloud sides could, for example, lead to variations of the thermodynamic phase partitioning and deviations from the assumption of homogeneity.

For the parcel model, the assumption of vertically constant cloud droplet number concentration is not entirely correct, and there are large uncertainties in all input parameters to the calculated effective radius profiles from the model. In the future, it would be helpful to have vertical profiles measured by the in situ probes. During the research flight analyzed here, measurements were only taken at a limited number of constant flight levels. Accurate and simultaneous measurements of the effective radius of liquid cloud droplets, pressure, temperature, supersaturation, and cloud droplet number concentration in regions with ice supersaturation and liquid water subsaturation where the WBF mechanism is active would allow to further study the effect of the WBF mechanism and even quantify it. Moreover, the observed low-level Arctic mixed-phase clouds were precipitating. In principle, the parcel model is only applicable to non-precipitating clouds. However, here it was applied only to the liquid part of the clouds, whereas the precipitation was in the ice phase.

It is important to note that the definition of the ice fraction can vary significantly across different studies, depending on the measurement techniques and the specific application . These differences should be considered when comparing results from different studies. In this work, the ice fraction refers to an optical ice fraction based on the optical thickness, whereas the ice index provides qualitative information about cloud thermodynamic phase, which can be used for a phase classification.