Optical properties based on (referred to as YG13 in the following) were used for eight different habits: solid columns, hollow columns, plates, 8-element aggregate of columns, 5-element aggregate of plates, 10-element aggregate of plates, solid bullet rosettes, and hollow bullet rosettes, all of which are based on hexagonal crystal symmetry. Droxtals were not considered for the retrieval since they do not produce a 22∘ halo . For the sake of brevity, we will refer to the aggregates of columns and plates as 8-element columns and 5- and 10-element plates. Since this parameterization provides only three different roughness levels (smooth, moderately roughened, and severely roughened), the optical properties of smooth and severely roughened ice crystals were mixed linearly to achieve a continuous distribution of roughness levels. It should be noted that in this parameterization ice crystal surface roughness is approximated by distortion of the particle geometry. For each habit separately, optical properties of smooth and rough ice crystals were mixed by scaling their extinction coefficients in the radiative transfer simulations. The resulting ice crystal properties assumed here represent a single ice crystal shape and two levels of surface roughness and follow a particle size distribution n according to 1n(D)=Dνexp⁡(-λD), with maximum crystal dimension D and ν=1 fixed. For a given effective radius reff, the optical properties provided for a range of maximum dimensions D in YG13 were integrated over the size distribution. During integration, λ was determined iteratively to match the computed effective radius with the prescribed one. The smooth crystal fraction (SCF) 2SCF=βext,smooth/βext,total, with βext,total=βext,smooth+βext,rough, ranges between 0≤SCF≤1, resulting in a rough crystal fraction (RCF) of 3RCF=1-SCF=βext,rough/βext,total.

Note that the retrieved ice crystal effective radius, shape, and SCF will depend on assumptions about the underlying particle distribution, since the bulk optical properties, e.g., the extinction coefficient βext, are obtained by integrating the single scattering properties over Eq. ().

Ice crystals in cirrus clouds are known to follow multimodal rather than monomodal size, shape, and surface roughness distributions. Therefore, matching ice crystal properties could be retrieved for mixtures of arbitrary complexity. However, this study aims at finding the simplest ice crystal model with the minimum degrees of freedom that matches the observations within the measurement uncertainty. Inspired by and , who separate the huge variety of ice crystal shapes into simple and complex crystals, we employ this two-habit approach for smooth and rough crystals to represent the “halo-producing” and “non-halo-producing” categories of ice particles. The radiative transfer simulations for compiling the LUT were performed using the US standard atmospheric profile and assuming a cirrus cloud between 10 and 11 km in height. Sensitivity studies in Appendix  show that the effect of cloud base height, geometric thickness, as well as atmospheric profile cause a bias in the 22∘ halo radiances of less than 1 %. Furthermore, to save computation time, the radiative transfer simulations were performed for a representative wavelength of each color channel of HaloCamRAW rather than integrating over the spectral response function: 618 nm for the red channel, 553 nm for the green channel, and 498 nm for the blue channel. Figure  in Appendix  shows that this causes a bias in the 22∘ halo radiances of 1.5 % for the blue channel, 2.0 % for the green channel, and 1.2 % for the red channel.

Figure  illustrates how the properties of the 22∘ (upper panel) and 46∘ (lower panel) halos, represented here by their respective halo ratio, vary with effective crystal radius reff and SCF. A halo ratio of 1 is considered the threshold for a visible halo display, indicated by the white contour. Below this value, the halo features are assumed to vanish compared to the background illumination. The key takeaway from this figure is that column-shaped crystals (solid columns, aggregates of 8-element columns, solid bullet rosettes) produce the most pronounced 22∘ halo, i.e., the largest halo ratio for a given smooth crystal fraction and effective radius. To produce a comparable 22∘ halo ratio, plate-like crystals (plates and 5- and 10-element aggregates of plates) need a much larger fraction of smooth crystals, which implies a significantly larger 46∘ halo ratio compared to columnar crystals. Ice crystals with a hollow base (hollow column, hollow bullet rosette) result in 22∘ halo ratios ranging between the values for columnar and plate-like crystals; however, they do not produce a 46∘ halo since the cavity prevents the necessary ray path.

To obtain representative results for ice crystal properties of halo-producing cirrus clouds, long-term observations are required. These are provided by the weather-proof Sun-tracking camera HaloCamRAW which was installed in September 2015 on the rooftop platform of MIM (Meteorological Institute Munich, LMU) . Between 22 September 2015 and 31 December 2016, HaloCamRAW recorded scenes with a 22∘ halo on 52 d with a temporal resolution of 10 s. The automated halo detection algorithm HaloForest, described in , was used to filter the HaloCamRAW images for 22∘ halos. Additional Sun photometer measurements are used to constrain aerosol optical thickness (AOT) and COT. As demonstrated in Appendix , additional knowledge about these two parameters is critical for retrieving information about the ice crystal microphysical properties. The aerosol optical thickness was derived from the AERONET AOT product (version 2) for the observation site on the MIM rooftop platform. The AOT during the time of the halo observation is constrained to a 2σ confidence interval around the daily average AOT estimated during clear-sky periods.

The COT introduces an ambiguity in the brightness contrast of the 22∘ halo . Constraining the COT is therefore necessary for a stable retrieval. For this retrieval the COT is derived from Sun photometer measurements using the SSARA instrument . SSARA provides direct Sun measurements with a temporal resolution of 2 s which are much more suitable for the observation of the highly variable cirrus clouds than AERONET with 15 min . The COT is derived by calculating the total optical thickness from the SSARA direct Sun measurements. The previously estimated AOT is then subtracted, and a correction factor is applied to account for the increased forward scattering of the ice crystals (cf. Appendix ). The retrieval is applied to the red channel of HaloCamRAW with a central wavelength of 618 nm (cf. Fig. ) to minimize the relative contribution of Rayleigh and aerosol scattering compared to the scattering by ice crystals.

Using additional observations of AOT requires clear-sky periods before and/or after the 22∘ halo event. Simultaneous AOT and COT observations from SSARA and AERONET (including the necessary clear-sky scenes) together with 22∘ halo observations from HaloCamRAW are available for only 8 of the 52 d, which are listed in Table . Figure  shows an example of the AOT and apparent COT derived from Sun photometer measurements on 21 April 2016. The AOT is obtained from the AERONET dataset and is represented by turquoise stars. The daily average AOT amounts to about 0.08 ± 0.04 at 618 nm. The blue dots in Fig.  indicate the apparent COT derived from SSARA direct Sun measurements, which are available from about 11:30 UTC. Figure b shows slices of the HaloCam images along the principal plane above the Sun; 22∘ halos and upper tangent arcs appear as a bright line in the center of the panel with a reddish inner, i.e., lower, edge from about 11:30 until 14:00 UTC.

The HaloCamRAW observations were geometrically and radiometrically calibrated as described in . To apply the retrieval to the HaloCamRAW data, the LUT was calculated for a wavelength of 618 nm with a surface albedo of 0.065. The remaining LUT parameters are provided in Table . To use as much information as possible from the HaloCamRAW images for the retrieval, the radiative transfer simulations for the LUT were performed for the viewing angles of all five image segments. The file size of the LUT and observations was then reduced by averaging both simulated and measured images over the five segments in the direction of the relative azimuth angle φ Fig. 3b. Thus, a separate LUT was compiled for each of the five HaloCamRAW image segments, which are evaluated separately.

Observations and LUT are compared in the scattering angle range between 18∘≤Θ≤25∘ with an angular resolution of 0.5∘. Maximizing the scattering angle range, which is used for this comparison, provides more information. On the other hand, for an increasing angular region, inhomogeneities in the cirrus optical and microphysical properties become relevant. The goal of the retrieval is to find the ice crystal properties which best match the observed radiance distributions across the scattering angle range of the 22∘ halo. Therefore, the scattering angle range was optimized to cover as much as possible of the vicinity of the 22∘ halo in addition to its peak while keeping it as small as possible to avoid inhomogeneities of the cirrus cloud.

To ensure that only samples with a clearly visible 22∘ halo are considered, the results were filtered for a halo ratio HR>1 (cf. Eq. 1 in ), and the uppermost image segment (no. 3 at φcenter=180∘; cf. Table ) was excluded. This segment might contain signatures of the upper tangent arc, which is produced by oriented ice crystal columns.

Sundogs appear in the left and right image segments (nos. 1 and 5) only for SZA<45∘ at scattering angles of Θ>29∘, which does not interfere with the 22∘ halo, as discussed in . While observations of upper tangent arcs and sundogs contain valuable information about the fraction of oriented columns and plates, they are excluded from the retrieval presented in this study, which focuses on randomly oriented crystals.

Figure  presents the retrieval results for the 3080 samples (four segments per image) of a 22∘ halo observed on 21 April 2016. The histograms display the retrieved LUT parameters based on the assumption that the representative ice crystal habit is either solid columns (a), hollow columns (b), or plates (c). The retrieved values for the SCF, effective radius, asymmetry factor g, COT, and AOT are provided as histograms with parameter boundaries and bins as defined in the LUT. The RMSE between LUT and measurement is provided in the rightmost panels of Fig. .

For solid columns (Fig. a), the SCF peaks below 50 %, and HaloCamRAW's 22∘ halo observations are represented best by a mean SCF of 35.9 % and an RCF of 64.1 % (cf. Eq. ). The ice crystal effective radii peak at 20 µm with a mean value of 24.5 µm and a mean asymmetry factor of 0.788. The majority of COT values are below 1 with a mean value of 0.53, whereas the AOT (constrained between 0.05 and 0.15 using AERONET data) yields a mean value of 0.11. In the case of hollow columns (Fig. b), the retrieved SCF ranges around 50 % with effective radii of 22.9 µm on average and a mean asymmetry factor of about 0.811. The average COT of 0.41 is slightly smaller compared to the solid column case. For ice crystal plates (Fig. c), a larger SCF of about 72.8 % (and an RCF of 27.2 %) on average is required to match the brightness contrast of the 22∘ halo measured with HaloCamRAW. The mean effective radius with 20.2 µm is slightly smaller compared to the solid column case. Assuming plates to be a dominating ice crystal habit causes a larger asymmetry factor on average of 0.879. The average COT amounts to 1.07 with a few values larger than 2. The retrieved COT in the case of plates is significantly larger compared to solid and hollow columns due to the increased forward scattering indicated by the large asymmetry factors. Increasing the asymmetry factor (i.e., the amount of forward scattering) of ice crystals in a cloud with a constant crystal concentration would result in higher radiance values measured by the same detector (cf. Appendix ). Compared with solid and hollow columns, the plate habit shows the smallest RMSE values for this dataset.

Figure  displays the results of the retrieval applied to the 8 d of 22∘ halo observations with HaloCamRAW. Panel a presents the retrieved SCF for each day and for the eight habits. By grouping the ice crystal habits into columnar (green, triangles down), hollow (pink, circles), and plate-shaped (blue, triangles up) crystals, the average SCF clusters at ∼30 %, ∼60 %, and ∼80 %, respectively. A similar clustering results for the asymmetry factor, which is smallest for columnar crystals and largest for plate-like crystals. In contrast to the differences of the retrieved mean SCFs and asymmetry factors among the habits, the retrieved mean effective radii, shown in Fig. c, seem to be almost independent of ice crystal habit and roughness. This confirms that the width of the 22∘ halo is primarily determined by ice crystal size, while shape and surface roughness play a minor role. The mean effective radius amounts to about 20 µm. Due to the skewed distribution of the retrieved effective radii (cf. Fig. ), more than 90 % of the results are smaller than 40 µm.

Figure a shows cloud top (circles) and base (dots) height represented by the mean value and standard deviation, which were derived from co-located measurements of a MIRA-35 cloud radar on the MIM rooftop platform. On 4 November 2016 cirrus clouds formed only in the south and southeast during the 22∘ halo event (cf. Table ). Thus, the zenith-pointing cloud radar did not detect the cirrus cloud observed by HaloCamRAW, and therefore no cloud height could be provided. In the other cases, the cirrus clouds had a larger horizontal extent, and the 22∘ halo was visible over a longer time period. The cloud top height varied around 10 km, except for 20 January 2016, with 6 km. The cloud base height exhibits a larger variability between 5 and 10 km. The corresponding temperatures at cloud top (circles) and cloud base (dots), indicated by mean value and standard deviation, are displayed in Fig. b. The threshold temperature for homogeneous nucleation is represented by the blue dashed line at -38∘ C. For all seven cases, the cloud top temperature was equal to or colder than -38∘ C, while the cloud base temperature varied between -10 and -50∘ C on average. It is noteworthy that the coldest and thinnest cirrus on 10 November 2015 with a cloud base temperature of about -50∘ C coincides with the smallest retrieved effective radii in Fig. . This tendency is in agreement with, e.g., and , who report the smallest ice crystals close to cloud top and at the coldest temperatures in the case of synoptic cirrus. While observing ice crystals directly at cloud top is impossible for ground-based imaging in the case of thick clouds, geometrically thin cirrus provides an opportunity to infer ice crystal properties close enough to the cloud top and ensure more homogeneous atmospheric conditions, which are conducive to a more homogeneous size and shape distribution. also found effective radii of ice crystals to decrease with increasing cloud top height and thus decreasing temperature using the airborne Research Scanning Polarimeter's (RSP's) observations together with reanalysis data from the Goddard Earth Observing System Model Forward Processing (GEOS-FP) data assimilation system.

Table  presents the retrieved SCF, effective radius, and asymmetry factor for all evaluated days, sorted by increasing mean RMSE. The retrieval revealed that ice crystal plates have the overall smallest mean RMSE and thus seem to match the HaloCamRAW observations better in the scattering angle range between 18 and 25∘ than the other seven habits of the YG13 database. The best-matching LUT elements of ice crystal plates have an SCF of (80 ± 10) %, an effective radius of (21.9 ± 17.1) µm, and an asymmetry factor of 0.880 ± 0.028. With increasing RMSE, the plates are followed by 8-element columns and solid columns. Hollow columns and bullet rosettes result in the largest mean RMSE, which is mainly due to an additional peak in the radiance distribution at scattering angles around 18∘ as shown in , Fig. 13.

In the following we assess how stable the retrieved ice crystal habit is considering the necessary assumptions regarding spectral response, aerosol type, and radiometric uncertainty. Using the representative wavelength of HaloCamRAW's red channel instead of accounting for its full spectral response introduces a small bias of less than 1.2 % (cf. Fig. ). Since the LUT was calculated for the OPAC continental average aerosol type, the retrieval results might be biased if the actual aerosol type differs. To investigate the sensitivity of the retrieval to different aerosol types, we would ideally compute new LUTs. Since computing a new LUT would require several weeks' computation time on MIM's high-performance computing cluster for each new aerosol type and the radiance at each scattering angle would basically only differ by a multiplicative factor, we repeated the retrieval with a modified LUT to estimate the effect of these approximations. The LUT was modified by multiplication by a factor for each scattering angle, which is representative of the amount and the sign of the bias introduced by the approximations. The multiplicative factor for each scattering angle in the LUT, which we refer to as “slope” in the following, was computed by the ratio between two radiance distributions simulated with DISORT: one “reference” radiance distribution using the continental average aerosol type and one “modified” radiance distribution for each of the aerosol types: continental clean, continental polluted, and urban. In addition, a slope was generated by computing the ratio between a “reference” radiance distribution accounting for HaloCamRAW's full spectral response (cf. the solid red line in Fig. ) and a “modified” radiance distribution based on HaloCamRAW's representative wavelength of 618 nm for the red channel (cf. the dashed red line in Fig. ). These slopes were computed for each of the eight ice crystal habits assuming a representative atmospheric setup: COT = 0.8, AOT = 0.1, and SCFs of 30 % for columnar crystals, 60 % for hollow column crystals, and 70 % for plate-like crystals.

Table  shows the results of the best-matching habit for each day retrieved with the modified LUT. The best-matching habit changed slightly for the different modifications of the LUT, but only within the plate-like or column-like crystal groups. The ice crystal plates remain the overall best-matching habit in the considered scattering angle range. The retrieved SCF in Table  remained mostly unaffected by using the modified LUT for the retrieval. Only for the urban aerosol case did the retrieved SCF for plates change from (80±10) % to (70±10) %, for 10-element plates from (70±10) % to (80±10) %, and for 5-element plates from (70±20) % to (60±20) %. Another uncertainty for cloud base temperatures higher than -38∘ C might be the presence of supercooled water droplets, which act similarly to rough ice crystals in diminishing the 22∘ halo, as discussed in Appendix . However, Fig.  showed that the presence of water droplets has only a small effect on the retrieved SCF.

The presence or absence of the 46∘ halo adds important information about the ice crystal shape and surface roughness. In a second step we use this information to find the ice crystal shape, which is representative for the whole scene, i.e., the scattering angle range for both the 22 and 46∘ halos. While the 22∘ halo provides the most pronounced signal and is therefore used for the quantitative retrieval of ice crystal properties, the signal of the 46∘ halo is much fainter and is subject to inhomogeneities in the cirrus. To analyze this scattering angle region, we therefore use HaloCamRAW observations averaged over each day and make use of the presence or absence of the 46∘ halo in a qualitative way to further constrain the retrieved ice crystal properties from Sect. . We focused this analysis on 6 of 8 d, for which the number of halo samples was high and the horizontal extent of the cirrus cloud was large enough to yield homogeneous conditions across both the 22 and 46∘ halo regions in the averaged image. If ice crystals in the cirrus cloud were able to form a 46∘ halo, we would expect to see it in the averaged image. Figure  displays the averaged HaloCamRAW measurements for 22 September 2015 (a) in comparison with DISORT simulations (b) using ice crystal plates, which were found to best match the observations in the region of the 22∘ halo (cf. Table ). Figure c shows the relative difference between measured and synthetic images in percent. Apparently, the averaged HaloCamRAW image does not show any 46∘ halo, whereas the optical properties of plates produce a pronounced 46∘ halo in addition to the 22∘ halo in the simulated DISORT image. This can be observed for all evaluated days and is presented here for 22 September 2015 as an example. Comparing the retrieval results for all eight habits revealed that 8-element columns best match the whole scene of the HaloCamRAW images – both in the scattering angle range of the 22 and 46∘ halos. The results using the overall best-matching habit of 8-element columns for the DISORT simulations are displayed in Fig. , which shows the averaged HaloCamRAW images (left) in comparison with synthetic images simulated with DISORT (center) and their relative difference (right). This analysis demonstrates that the scattering angle range around the 46∘ halo provides further valuable information for the retrieval of ice crystal optical properties. Figure  illustrates why the absence of the 46∘ halo indicates columnar crystals rather than plates to best match the observed cirrus. For the selected LUT elements, a 22 or 46∘ halo would be visible for HR>1, i.e., SCF–reff combinations with HR values above the white contour. In the case of ice crystal plates, the majority of SCF–reff combinations, which produce a visible 22∘ halo (upper panel), will be accompanied by a visible 46∘ halo (lower panel). In fact, for the retrieved SCF–reff combinations, plates would produce a pronounced 46∘ halo and thus do not match the observations.

As mentioned above, applying the retrieval to HaloCamRAW observations, which were averaged over a whole day, yields only qualitative results that help us confirm which ice crystal shape best matches the region of both the 22 and 46∘ halos. Since it does not allow for the retrieved cirrus and aerosol optical thickness to follow their natural temporal fluctuation, the retrieved smooth crystal fraction and ice crystal radius might become biased

For the sake of completeness, we provide here the ice crystal properties used for the DISORT simulations: Fig. b (SCF = 80 %, reff=10 µm), Fig. b (SCF = 20 %, reff=10 µm), Fig. e (SCF = 20 %, reff=10 µm), Fig. h (SCF = 20 %, reff=10 µm), Fig. k (SCF = 80 %, reff=5 µm), and Fig. n (SCF = 20 %, reff=10 µm).

This study revealed that the overall best-matching ice crystal habits are 8-element and solid columns with an SCF of (30±20) % and (40±30) % and asymmetry factors at 618 nm between 0.752 and 0.787, respectively. The optical properties of solid columns and aggregates of columns, as YG13's 8-element columns, are very similar. The main difference is that the 8-element column is an aggregate of individual solid columns with different aspect ratios and sizes. The fact that 8-element columns proved to be a slightly better match to the observations than solid columns indicates that a distribution of variable aspect ratios and sizes is more representative of the observed cirrus clouds than a “mono-disperse” ice crystal distribution of solid columns. It is noteworthy that 8-element columns, the overall best-matching ice crystal habit in this work, is the same habit as used in the MODIS Collection 6 (C6) data product for operational retrieval of ice cloud optical thickness and effective radius . While the 8-element columns used for MODIS C6 have severely roughened surfaces to achieve consistency with spectral and polarimetric satellite observations , the results of this study suggest a fraction of about 30 % smooth crystals and 70 % severely roughened crystals to account for the presence of halo displays.

Ice crystal columns and aggregates of columns were also found by , without any smooth crystals however, resulting in an asymmetry factor of about 0.75 in the mid-visible spectrum. Also, retrieved a mixture with a dominating fraction of columnar crystals to best match the MODIS and CALIPSO observations over ocean with an SCF of 10 % and an asymmetry factor of 0.778 at a wavelength of 0.65 µm. These retrievals were performed for COT<3, which is comparable to the optical thickness range observed in this work. Moreover, found columnar crystals to be the most representative ice particle shape using both total and polarized airborne reflectance measurements from AirMSPI for cirrus clouds of optical thicknesses up to 5.

Several other studies found plate-like or compact ice crystals to better represent the observations than columns, for example, , , , and . However, these studies focus on optically thick ice clouds, in particular anvil cirrus, with potentially very different formation mechanisms compared to thin halo-producing ice clouds. studied aspect ratios of natural ice crystals, which were collected during field campaigns by a cloud particle imager for temperatures between 0 and -87∘ C, and found that synoptic cirrus is dominated by columnar crystals, while anvil cirrus contains a larger fraction of plate-like crystals. All evaluated HaloCamRAW observations showed synoptic cirrus or contrail cirrus and did not contain any anvil cirrus. Columnar ice crystals were found to best match these HaloCamRAW observations, which is in agreement with the findings of .

Ice crystal plates of the YG13 database produce a pronounced 46∘ halo for the retrieved effective radii which was not visible in the HaloCamRAW observations. YG13 assumes that the ice crystal aspect ratio is coupled with crystal size and that crystal top/base faces grow more quickly than their side faces starting from a cubic shape (aspect ratio 1). For this parameterization, smaller crystals with aspect ratios closer to 1 produce more pronounced 46∘ halos compared to larger crystals. A possible explanation for why YG13 plates match the HaloCamRAW observations in the 22∘ halo region but not the 46∘ halo region could be that this parameterization does not represent the observed ice crystal shape: the observed crystals could have larger top/base faces for smaller crystal sizes. Another reason for the missing 46∘ halo could be that crystal base and top faces have defects strong enough to inhibit the ray path responsible for the formation of this halo type. These defects have been commonly observed in laboratory as well as in situ observations e.g., and are not represented in the YG13 database. While YG13's hollow column crystal shape mimics these defects by a cavity at its top and base faces, they appear to be too pronounced to match the HaloCamRAW observations since they introduce a new intensity peak at around 18∘ scattering angle, which is not visible in the observations Fig. 13. Optical properties ideally suited for this study would allow choosing of ice crystal size independent of the aspect ratio while still taking into account physical optics effects.

As shown in , long-term HaloCam observations in Munich revealed that about 25 % of the cirrus clouds produced a 22∘ halo. This fraction would be slightly larger when considering other halo types, such as sundogs and upper tangent arcs as well: a visual evaluation of the 6-week HaloCam dataset during the ACCEPT campaign resulted in about 27 % halo-producing cirrus clouds, accounting for all three halo types. The remaining ∼73 % of cirrus clouds could either be too opaque (optical thickness >5) for the 22∘ halo to be visible or contain predominantly rough or complex ice crystals.

The results of the present study focus on cirrus clouds that produce a visible 22∘ halo. Averaged over all 4400 images, the SCF for columnar, hollow, and plate-shaped crystals amounts to about ∼37 %, ∼47 %, and ∼73 %. Based on the study by , a minimum fraction of smooth crystals of 10 % in the case of columns or 40 % in the case of plates can be estimated for the halo-producing cirrus clouds if multiple scattering and scattering by aerosol are neglected. The retrieved fractions in this study taking into account aerosol and cirrus optical thickness result in an about 27 % (33 %) larger SCF for solid columns (plates).

Our finding that columnar ice crystal shapes best represent the HaloCam observations further implies that the majority of rough ice crystals mixed with a smaller fraction of smooth crystals is sufficient to produce a visible 22∘ halo. Finding predominantly rough and complex ice crystals to best match the observations is in agreement with the results of several studies based on satellite retrievals. Using multi-angle reflectance measurements, and found polycrystals and complex crystals to better represent the observations than pristine single crystals. Studies based on multi-angular polarized reflectances from POLDER also report that featureless phase functions, which correspond to roughened or complex crystals, better represent the measurements than phase functions of a single ice crystal habit . and confirmed that rough and complex crystals better match the observations than smooth single crystals for optically thin clouds (COT<3) using retrievals based on lidar observations and reflectances in the infrared spectrum.

The retrieved effective radii in this study are, to the best of the authors' knowledge, the first observational results for 22∘ halos and yield similar results for all eight ice crystal habits, with 90 % of the radii being smaller than 40 µm and having a mean value of 20 µm. Several studies e.g., investigated the size range in which ice crystals produce a 22∘ halo based on theoretical and analytical considerations for single crystals. A lower boundary for ice crystal maximum dimensions of about 10 µm was found based on an analysis of the 22 and 46∘ halos in the scattering phase functions of and . This lower boundary is in agreement with the results from laboratory studies of . Another criterion for the formation of 22 and 46∘ halos is random orientation. This occurs for compact ice crystals with maximum dimensions smaller than about 100 µm. Ambiguities might occur since aggregated ice crystals such as bullet rosettes can be oriented, while their components are randomly oriented relative to each other . Another indication of this upper size limit is the finding of , who report that air bubbles develop in larger ice crystals, which cause the 22∘ halo to fade. Furthermore, state that pristine shapes are mostly found in the laboratory for maximum dimensions smaller than about 100 µm.

Note that the term “circumscribed halo” in was incorrectly used as a collective term for the 22 and 46∘ halos. In fact, the circumscribed halo occurs at high solar elevations when upper and lower tangent arcs merge and is formed by oriented columns instead of randomly oriented hexagonal crystals.