In this work, we use experimental in situ data gathered during three airborne field campaigns:

ACLOUD – Arctic CLoud Observations Using airborne measurements during polar Day, May/June 2017 based in Svalbard (Spitsbergen, Norway) with the AWI Polar6 aircraft (∼165 flight hours),

An overview of the microphysical conditions as well as the instrumentation during those campaigns can be found in and for ACLOUD, for SOCRATES and for IMPACTS. The sampling during these three campaigns includes a wide variety of different cloud conditions: warm clouds, supercooled liquid clouds, ice clouds and MPCs. The clouds sampled ranged in altitude from boundary-layer clouds below 200 m to mid-level clouds between 4000 m and 6000 m a.s.l. Temperatures ranged from -20 to +5 ∘C during ACLOUD, -35 to +5 ∘C during SOCRATES and -32 to +9 ∘C during IMPACTS. The sampled ice particles covered a wide range of different particle shapes and habits (columns, plates, needles, bullet rosettes, dendrites and irregulars, including rough, rimed and pristine particles) as well as sizes in the range of D=20–700 µm.

The instrumentation on the three aircraft included cloud particle probes such as the SID-3 (Small Ice Detector Mk. 3), CDP (Cloud Droplet Probe, DMT, Longmont, USA), CIP (Cloud Imaging Probe, DMT, Longmont, USA) and PIP (Precipitation Imaging Probe, DMT, Longmont, USA) during ACLOUD, 2DS, 2DC (Two-dimensional Stereo Probe, Two-dimensional Cloud Probe, SPEC Inc., Boulder, USA) and CDP during SOCRATES and 2DS, CDP and CPI (Cloud Particle Imager, SPECinc, Boulder, CO, USA) during IMPACTS.

For SOCRATES, vertical Doppler velocity was measured by the HCR (HIAPER Cloud Radar, ), which has a transmit frequency of 94.40 GHz (W-band), temporal resolution of 10 Hz, vertical range resolution of 20–180 m and a typical radial velocity uncertainty of 0.2 m s-1 at a Doppler velocity of w=2 m s-1). The velocity data are corrected for aircraft motion and aliasing-bias.

The ambient temperature was measured with a heated temperature sensor (Harco 149 Model 100009-1 Deiced TAT) that has a general accuracy of 0.3 ∘C.

The vertical velocity was measured using a radome air-motion system .

Relative humidity was measured by the VCSEL (Vertical-Cavity Surface-Emitting Laser) hygrometer with an uncertainty ranging from 6 % to 10 % .

During ACLOUD, the temperature was measured using an open-wire Pt100 in an unheated Rosemount housing at the tip of the nose boom with a frequency of 100 Hz and an estimated accuracy of ±0.1 ∘C. The vertical wind was measured using a Rosemount 858 five-hole probe with a relative accuracy of the vertical wind speed of ±0.05m s-1 for straight and level flight sections.

During IMPACTS, atmospheric state measurements were performed using the Rosemount total air temperature (TAT) probe and the Edgetech three-stage chilled mirror hygrometer with 1 Hz temporal resolution . For each particle observed by PHIPS, the corresponding temperature, humidity and velocity data as well as liquid water content (LWC) were determined as the average over t=ts±0.5 s around the time of acquisition ts where each PHIPS particle was sampled.

Due to the variability of the microphysical conditions and sampled particles, the data gathered during these three campaigns provide a suitable and representative dataset for a comprehensive characterization of riming in mixed-phase clouds. All data cited in this work can be found in the corresponding databases for the three campaigns: for ACLOUD, for SOCRATES, for IMPACTS.

PHIPS is designed to investigate the microphysical and light-scattering properties of cloud particles. It produces microscopic stereo images while simultaneously measuring the corresponding angular scattering function for the angular range from 18 to 170∘ for single cloud particles. More in-depth information and a detailed characterization of the PHIPS setup and instrument properties can be found in and . From the stereo images, single-particle microphysical features such as, e.g., area equivalent diameter or aspect ratio can be obtained. The image analysis algorithm is explained in depth in . Based on the single-particle angular scattering function, the thermodynamic phase and the scattering equivalent diameter can be derived, as explained in .

For ACLOUD and SOCRATES, the instrument settings were set to measure single cloud particles in a size range of 50 and 20µm≤D≤700µm for droplets and ice particles, respectively. The image acquisition rate of the microscopic system was limited to 3 Hz in these campaigns, while singe-particle scattering data could be acquired up to a maximum rate of 3.5 kHz. The magnification settings of the cameras corresponded to an optical resolution of approximately 3.3 µm. Since PHIPS characterizes individual particles, it has a narrow sensitive area (Asens). As discussed in , Asens is size dependent (e.g., Asens=0.5 mm2 for ice particles with D=200µm). Assuming a relative flight speed of vs=150 m s-1, this corresponds to a sampling volume of Vsens=Asens⋅vs=0.08 L s-1. During IMPACTS, the scientific focus was on larger ice crystals so the trigger threshold and the magnification were increased to trigger only particles larger than D≥100 µm for droplets and D≥40 µm for ice. The magnification settings of the cameras corresponded to an optical resolution of approximately 4 µm and the maximum camera acquisition rate was varied between 3 and 10 Hz, which corresponds to a maximum spatial resolution of roughly one stereo image per 15 m.

All PHIPS stereo images from the ACLOUD and SOCRATES datasets were visually classified into seven habit classes: (i) plate-like particles (single plates, sectored plates, skeleton plates and side planes); (ii) columnar particles (solid columns, hollow columns and sheaths); (iii) needles; (iv) frozen droplets; (v) bullet rosettes; (vi) graupel; and (vii) irregular particles. In addition to the habits, the particles were assigned the attributes rimed or unrimed. The temperature-dependent frequency of occurrence distributions of the different particle habits is shown in the Supplement (Fig. S1). An overview of the riming fraction and riming type (normal, epitaxial, see Sect. ) per habit is shown in Fig. S2.

In the next classification step, a subset of the well-classified particles was again visually classified further with regard to their riming features. The second classification step was performed only for particles larger than 100 µm sampled at a temperature of T≥-17 ∘C. Smaller particles were almost exclusively small irregulars whose riming state could not be classified with certainty due to the limited optical resolution and almost no riming was observed at lower temperatures (see Fig. a). The CDP LWC ranged from 0 to 0.5  m-3 and vertical HCR Doppler velocity from -4 to +2 m s-1 (negative velocity corresponds to downward direction, positive to upward direction).

Particles were classified with regard to their surface riming degree (SRD) as (i) unrimed (SRD = 0 %, no visible riming on any of the two stereo-micrographs); (ii) slightly rimed (SRD < 25 %, a few scattered rime particles on the crystal's surface); (iii) moderately rimed (25 % ≤ SRD ≤ 50 %, up to half of the particle's surface is covered by rime); (iv) heavily rimed (50 % < SRD < 100 %, most of the particle's surface is covered by rime); as well as (v) graupel (SRD = 100 %, the whole particle surface is covered by multiple layers of rime, so that the structure of the underlying particle is no longer recognizable). Exemplary PHIPS particles from these classes are shown in Figs.  and . This classification approach is similar to the definition of riming degree used in previous studies such as, e.g., . Also, the attributes (i) one-sided riming and (ii) epitaxial riming (which will be explained in detail in Sect. ) were assigned. As each particle is imaged from two different viewing angles (120∘ apart), whether or not a particle has rime only on one side can also be assessed for opaque particles (see examples in Fig. ).

The remaining dataset includes 3957 particles from ACLOUD and 1413 from SOCRATES. Examples of particles classified in the different categories are shown in the following section. Manual classification was not applied for the complete IMPACTS dataset due to the large number of ice particle images (over 250 000 images were acquired). Therefore, only the set of images used for the case study presented in Sect.  was manually inspected.

In the following, riming fraction refers to the relative amount of rimed particles compared to total amount of classified ice particles (rime + unrimed). Figure a shows the correlation of riming fraction and ambient temperature (R2=0.94). The corresponding fit parameters for all histograms are shown in Table . Most riming was observed in a temperature range of -10 ∘C ≤T≤0 ∘C with the maximum around T≃-7 ∘C where up to 55 % of all ice particles were rimed. The high riming fraction around -17 ∘C is due to a very high rimed fraction in this temperature bin during a single cloud segment of RF09 of SOCRATES. It is based on a low number of total particles (n=213) and is therefore not assumed to be a generalizable feature.

For the following analysis, apart from Fig. a, only particles sampled at T≥-17 ∘C are considered. Figure b shows riming statistics as a function of an ice particle's area equivalent diameter retrieved from the stereo-microscopic images. It can be seen that the percentage of rimed particles increases with particle size (R2=0.96). The riming fraction increases from below 5 % for particles smaller than Dim,A≤150 µm to over 35 % for particles larger than Dim,A≥400 µm. Above that, the riming fraction is only weakly dependent on particle size. The smallest ice particle where riming was observed was a column with an area equivalent diameter of Dim,A=116.1 µm and maximum dimension of Dim,max=193.7 µm (shown in Fig. S7). This is a larger riming onset size compared with that of, e.g., and , who reported a critical minimum diameter of D≥60 µm for riming on columns collected via glass slides and analyzed by optical microscopy.

The correlation of riming fraction and cloud LWC measured by the CDP is shown in Fig. c (R2=0.86). The riming fraction increases from 25 % in cloud segments with low LWC below 0.05 g m-3 to 60 % for LWC ≥ 0.5 g m-3. Rime particles had a size around roughly Dmax≃20 and 50 µm as shown in Fig. a, b for two exemplary ice crystals that were among the crystals with the smallest and largest rime particles based on visual inspection. This is in agreement with results presented by and , who reported sizes of rime particles between 10 and 60 µm. Since there is no automated method available to determine the size of the rime particles based on the PHIPS images, the size of rime particles is not further investigated in this work. A comparison with the CDP mean droplet diameter showed a slight relation with a maximum riming fraction at Ddrop, mean=20 µm (see Fig. S3f). Figure c, d shows drizzle-rimed ice (ice lollies). Such contact freezing of relatively large droplets compared to the size of ice particle was reported by . We also see this in our dataset, but there are only very few cases. Due to the low number, no relationship with the sampled PHIPS drizzle droplet concentration was found and no detailed statistical analysis was conducted.

Figure d, e shows the correlation (R2=0.7) with the Doppler radial velocity measured by the HCR, which is the sum of vertical air velocity and particle fall speed, corrected by the vertical motion of the aircraft. HCR data are only available for the SOCRATES campaign. Since the HCR has a dead zone of 145 m around the aircraft in which data are not usable, there are no data available at the location of the aircraft. Hence, each data point corresponds to the measured HCR Doppler velocity of the first valid gate closest to the aircraft. The HCR was typically rotated to point in zenith direction when flying beneath clouds or ascending through boundary-layer clouds and in nadir at other times. The sign was adjusted based on HCR orientation so that negative velocity always corresponds to downward direction, positive to upward direction. The analysis was divided into stratiform and convective cloud segments based on the flag given in . For stratiform cases, events for which the melting layer was close to the position of the aircraft were omitted, since events where in situ probes and the first gate were not “on the same side” of the melting layer would lead to potentially biased velocities due to the discontinuity at the melting layer . It can be seen that there is a clear trend of increasing riming fraction toward more positive (upward) Doppler velocities. Furthermore, on average, the riming fraction is much higher in convective (52 %) than in stratiform clouds (34 %). This can be explained by updrafts and in-cloud turbulence, which increases the time and trajectory that the particles remain in the cloud as well as the relative velocity of ice particles against droplets and thus increases the probability that they collide to form riming. Furthermore, both the ice particles and the droplets can grow larger in updrafts due to the increased time they spend in the cloud as well as the typically higher supersaturation values affiliated with updrafts. The measurement of ambient vertical velocity around the aircraft shows a slight trend toward both higher positive and negative values (see Fig. S3h). This could indicate a relationship with turbulent air motion, as riming is expected to be more likely if particles remain longer in the cloud, having a longer total travel path and hence a higher chance of collecting droplets. However, at the same time, a lot of one-sided rimed plates were observed during the campaigns (see Fig. ), which would be unlikely if all riming would necessarily be correlated with turbulent air motion. This confirms observations of fallen snow by and . Note that the ambient vertical velocity measured at the aircraft is the combination of small-scale turbulence and large-scale vertical motion which cannot be easily disentangled. Roughly 15 % of all plates at high temperatures T>-10 ∘C are rimed on one side (see Fig. S6a and the corresponding discussion in the Supplement) and almost none at lower temperatures. No significant relationships (R2 below 0.5) or only very minor dependency of riming fraction and CDP droplet number concentration, CDP mean droplet diameter, ambient vertical velocity, relative cloud height and relative humidity were found. The corresponding plots are shown in Fig. S3.

All rimed ice particles were manually classified concerning their riming degree, i.e., their estimated SRD. This classification was carried out manually based on visual inspection of the particle's individual stereo images. Exemplary particles are shown in Fig. .

Figure  shows the relative distribution of SRD with three ambient and microphysical parameters: temperature (Fig. a), ice particle area equivalent diameter (Fig. b) and vertical Doppler velocity (Fig. c, d). A relationship is seen between temperature and SRD. At lower temperatures ice particles are more heavily rimed. At temperatures of T≤-15 ∘C, more than 80 % of all rimed particles are heavily rimed or graupel, whereas most slightly rimed particles are found at high temperatures between -5 and 0 ∘C.

A positive trend is also visible between SRD and ice particle size: Most small particles around Dim,A≤250 µm show only slight riming whereas heavy riming is mostly found on larger particles. These typically large heavily rimed and graupel particles relate to an increased negative (downward) Doppler velocity (Fig. c, d) as they are almost spherical and hence more densely packed compared to aspherical ice particles. This is in agreement with Doppler radar studies presented by . This effect is weaker for convective clouds (Fig. d) than for stratiform clouds (Fig. c). A possible explanation is that the increased fall speed due to the increase SRD is canceled out with updrafts of the air parcels that cause the increased SRD in the first place. Comparisons with LWC and the other previously discussed parameters (plots shown in the Supplement) show no apparent relationship. Since the classification of SRD is only based on visual inspection, no further numerical analysis was conducted and no fit parameters are presented.

In Fig. , we show the relative occurrence of normally and epitaxially rimed particles during the ACLOUD and SOCRATES campaigns as related to ambient microphysical parameters. The corresponding fit parameters for all histograms are shown in Table . Again, only particles sampled at a temperature of T≥-17 ∘C with a diameter of D≥100 µm that were distinctively classified according to the aforementioned manual classification are included.

Figure a shows that there is a tendency to find more epitaxial riming at higher temperatures near T=0 ∘C, where up to almost 40 % of all rimed particles show epitaxial riming (R2=0.93). Between -5 and -10 ∘C, the fraction of epitaxial riming slightly decreases from 40 % to 30 %. Below T<-10 ∘C, the percentage of epitaxial riming decreases below 20 %, although it should be noted that the statistics for this temperature region are weak. This temperature dependency is in accordance with the aforementioned studies showing that the rime particles tend to freeze as single crystals along the c axis of the underlying particle.

Figure b shows a slight relation of the occurrence of epitaxial particles with the size of the underlying particle. For small particles below D≤150 µm, the fraction of epitaxially rimed particles is 20 %. This increases to up to 40 % for ice particles larger than D≥300 µm. For larger particles, the fraction of epitaxially rimed crystals is only weakly dependent on particle size. The relation of particle size with the presence of epitaxial riming can be explained by the fact that epitaxial riming is caused by vapor deposition during the aging process of rimed particles, which naturally also causes the particle to grow on their main surfaces.

Figure c, d shows a trend of increasing fraction of epitaxially rimed particles with positive (upward) Doppler velocity, indicating a relationship with updrafts. We see no substantial difference between the stratiform and convective cases. Again, comparisons with LWC and the other previously discussed parameters show no significant relationship (plots shown in the Supplement).

Next, we present a case study of an MPC sampled during the IMPACTS campaign. We investigate the assumption that the ice particles with epitaxial riming are the result of aging of rimed particles and discuss the formation process.

Figure  shows microphysical data collected on 1 February during the 2020 IMPACTS campaign. The MPC segment discussed in this case study was probed from 12:42:30 to 12:49:00 UTC (Δt=06:30 min, which corresponds to Δs=58.5 km) at an altitude of approximately 4300 m and a temperature of about -12 ∘C around 36∘ N/73∘ W, roughly 300 km off the US east coast. The vertical wind velocity was at a constant value around ± 0 m s-1. The relative humidity with respect to water averaged about 93 %. The LWC measured with the CDP averaged around 0.1 g m-3 and the total water content (TWC) measured with the 2DS was around 0.5 g m-3. The number-weighed mean particle diameter was around 20 µm for droplets and between 200 and 800 µm for ice particles based on the measurements of CDP and 2DS, respectively.

The trigger threshold of PHIPS was set in a way that the instrument started to trigger on droplets with diameters larger than D>100 µm. In this segment, in total, 1589 particles were triggered and 575 stereo images were acquired. Examples of micrographs of particles from this flight segment are shown in Fig. . Of the 575 stereo images, 259 (45 %) were not classified since they were identified as potential shattering fragments smaller than D=100 µm. Shattering artifacts can be identified from the PHIPS stereo images that have a field of view of approx. 2.19 mm × 1.65 mm by looking for satellite particles. Shattering fragments do not always appear as “satellites” but can be found as single fragments within the image frame. Such individual shattering fragments can be typically identified as having sharp edges and a shape that does not appear to resemble that of a typical vapor grown crystal (i.e., a lack of hexagonal symmetry of the crystal facets). If such particles were identified during the manual image inspection, they were also categorized as shattering cases. Of the remaining ice particles (320), most are classified as columnar particles (173) and needles (33). These particles show a wide spectrum of riming degree, ranging from unrimed (43) to slightly (44), moderately (42) and heavily rimed particles (124). We see different “types” of riming: most are epitaxially rimed (87), while 56 show normal riming. Furthermore, we see numerous particles with evidence of both normal and epitaxial riming on the same particle (20), which we refer to as mixed riming in the following. Apart from that, we see the presence of three large drizzle droplets with diameters of 200–300 µm as well as rimed dendrites (30) and graupel (48) particles. Overall, 35 particles were classified as irregulars. Similar particle shapes are observed on the CPI imagery (not shown here).

The lower panel of Fig.  shows four exemplary ice particles that were sampled within a 45 s window (12:47:07–12:47:52 UTC, corresponding to a distance of 6.7 km) that is indicated by the shaded green area in Fig. . The particles that were sampled within this period show columnar particles during different stages of the riming process: an unrimed (a), a normally rimed (b), a mixed rimed (c) and epitaxially rimed column (d). Since we observe normal and epitaxial riming not only within the same segment in close spatial vicinity, but also on the same singular particles, we argue that normal riming and epitaxial riming are, as hypothesized, interlinked. As proposed by , we argue that epitaxial riming is the result of the aging (deposition growth) of normally rimed particles as sketched in the upper panel of Fig. : An unrimed ice particle (a) accretes a supercooled droplet and forms the initial primary “normal” riming (b). Ambient water vapor is deposited on the rime matching the lattice structure of the underlying particle and thus forming the faceted surface. More droplets are accreted such that normal and epitaxial riming can be observed on the same particle (c). The process is repeated and the particle grows further until, eventually, the whole surface is covered by epitaxial rime (d).