Cloud Chamber Studies on the Linear Depolarisation Ratio of Small Cirrus Ice Crystals

depolarisation ratios in the near-backscattering direction (178°) of up to 0.4 for sublimating small ice crystals (<10 μm) at a 45 temperature range between -50 °C and -70 °C (Schnaiter et al., 2012). A cloud chamber study conducted at a higher temperature range between -7 °C and -30 °C by Smith et al. (2016) showed large discrepancies between the measured linear depolarisation ratio and simulations assuming idealized pristine hexagonal shapes for larger ice crystals (20 μm < maximum dimension < 200 μm) for the near-backscattering (178°) and the backscattering (180°) directions. These discrepancies could be reduced by assuming stepped hollowness and by using a tilted facet method in the ray tracing simulations to account for ice crystal 50 complexity. This study advances previous work on the relationship between ice microphysical properties and linear depolarisation ratio by providing a more statistically robust analysis, based on a multi-year dataset from four laboratory cloud chamber campaigns. In total, 47 ice cloud simulation experiments were conducted under well-controlled conditions at cirrus temperatures between –39°C and –75°C. A key strength of this study is the ability to control ice crystal growth under specific, known temperature 55 and supersaturation conditions, enabling a direct assessment of how particle size, shape, and optical complexity influence depolarisation signals. In addition, the measurements are compared with results from conventional as well as state-of-the-art 2 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. light scattering models. Together, this approach provides new insight into the microphysical drivers of depolarisation and offers improved constraints for the interpretation of active remote sensing observations of cirrus clouds. 2 Methods 60 2.1 Optical instrumentation The linear depolarisation ratio (δ) is measured with the SIMONE (Streulichtintensitätsmessungen zum optischen Nachweis von Eispartikeln - Scattering Intensity Measurements for the Optical Detection of Ice Particles) instrument (Schnaiter et al., 2012). The instrument measures the scattered intensity in the near forward direction (2°) and in the near-backscattering di- rection (178°) from a 488 nm continuous wave laser beam propagating through the cloud chamber. The detection volume of 65 approximately 7 cm3 is defined by the overlap between the laser beam and field of view of the detector. The laser beam is linearly polarised and the polarisation axis can be rotated with a liquid crystal rotator. For this study, a polarisation parallel to the scattering plane is chosen. In the 178° direction the scattered light is split with a polarising beam splitter and the resulting co- and cross-polarised states are analysed using two photomultiplier tubes (Perkin Elmer MP-1383). The response of the two photomultiplier tubes are calibrated for each campaign using a Spectralon target with a known linear depolarisation ratio that 70 can be placed in the scattering center inside the cloud chamber. The resulting relative uncertainty in the the linear depolarisation ratio derived from the calibration cycles is ∆δ = 1.4 % (Schnaiter et al., 2012). Details about the instrument and the calibration procedure can be found in Schnaiter et al. (2012). For the RICE03 campaign, data from a different instrument with the same operation principle (SIMONE-Junior), an emission wavelength of 552 nm, a detection volume of approximately 30 cm3 and a measurement uncertainty of ∆δ = 3 % were used, which is described in Järvinen (2016). 75 The linear depolarisation ratio for incoming light with a polarisation parallel to the scattering plane δ∥ is calculated as (Mishchenko and Hovenier, 1995): δ∥ = I⊥ − I⊥,bg I∥ − I∥,bg (1) where I⊥ − I⊥,bg is the background-subtracted light intensity with a polarisation perpendicular to the scattering plane and I∥ − I∥,bg with a polarisation parallel to the scattering plane. The linear depolarisation ratio from the SIMONE instrument is 80 averaged over time intervals of 10 s. Hereafter we refer to it as δ. 2.2 Microphysical instrumentation The particle size, shape and small-scale morphological complexity are optically characterised using the Particle Phase Dis- criminator 2 Karlsruhe edition (PPD-2K) and the Small Ice Detector 3 (SID-3) (Kaye et al., 2008; Ulanowski et al., 2014; Vochezer et al., 2016; Schnaiter et al., 2016). Both instruments are optical particle counters that detect the scattered light of 85 individual particles. A sample air flow passes the measurement volume that is defined by the overlap between the laser beam with a wavelength of 532 nm from a frequency-doubled Nd:YAG laser and the field of view of the trigger optics. The design 3 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. of the trigger optics differs in both instruments. In PPD-2K a beam splitter diverts 8 % of the forward scattering light to the trigger detector. SID-3 uses two nested trigger detectors with half angles of 9.25° at an angle of 50° to the forward scattering direction. In both instruments the trigger intensity is detected with a photomultiplier tube and used to determine the size of 90 the individual particles with a maximum count rate of 11 kHz. A special feature of SID-3 and PPD-2K is that they use an intensified Photek ICCD218 camera to record the spatial intensity distribution of the forward scattered light over an annulus between approximately 5° and 26° with a resolution of 780×592 pixels (SID-3) and between 7.4° and 25.6° with a resolution of 582×592 pixels (PPD-2K). Images are taken for a subsection of the triggered particle events due to the camera’s maximum imaging rate of 30 Hz. These diffraction patterns contain information on the particle habit and morphological complexity at 95 scales of the wavelength of the used light. Both instruments were operated simultaneously. Here we use PPD-2K for getting the size information due to higher counting statistics compared to SID-3 (Vochezer et al., 2016) and SID-3 for getting information on the crystal shape and degree of morphological complexity, similar to Schnaiter et al. (2016). The ice crystal spherical equivalent diameter d is calculated from the trigger intensity I using the following equation (Vochezer et al., 2016): 100 d = a · Ib (2) where calibration coefficient a depends on the laser power and PMT gain and calibration coefficient b = 0.522 depends on the trigger geometry and must be around 0.5 because the scattered intensity is proportional to the geometric cross section of the particle. For each measurement campaign the factor a is calibrated with spherical droplets where the size is determined comparing the Mie fringes of the diffraction patterns to Mie theory (see Vochezer et al. (2016) for details). The ice crystal 105 maximum dimension is estimated to be approximately 1.0 to 2.5 times larger than the spherical equivalent diameter depending on the crystal shape and complexity (see appendix A). Besides particle size, other microphysical features can be extracted from the diffraction patterns recorded by PPD-2K and SID-3, such as particle shape and degree of crystal complexity. The degree of crystal complexity can be derived from a speckle pattern texture analysis of the diffraction patterns, and is represented by the ice crystal normalised energy feature parameter ke 110 (Schnaiter et al., 2016). ke is a measure for particle complexity with scales around the laser wavelength of the incident light, 532 nm, including surface roughness, polycrystallinity and (stepped) hollowness (Järvinen et al., 2023). The parameter ranges between about 3.8 and 7.0 and a threshold of kthr e = 4.6 was defined by Schnaiter et al. (2016) for the SID-3 measurements, where lower values correspond to pristine particles and higher values for morphologically complex particles. Similarly to Schnaiter et al. (2016), ke is only calculated for particles with trigger intensities between 10 counts and 25 counts in this work 115 to reduce the effect of particle size biases on ke, which is caused by varying mean intensity of the diffraction pattern images. In this work, the probability of coincident particle sampling is below 1 % with a maximum detected particles concentration of 42.6 cm−3 and 22.3 cm−3 measured by PPD-2K and SID-3 (Vochezer et al., 2016). The particle shape is derived from the diffraction patterns using a discrete fast Fourier transform of the polar integrated azimuth intensity profile (Vochezer et al., 2016). Maximum Fourier coefficients 2 and 4 are the result of a columnar shape (Fig. 120 1c) and maximum Fourier coefficients 3 and 6 of a hexagonal plate (Fig. 1c). If the maximum coefficient is of a non-symmetric 4 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. (a) Plate (b) Irregular (c) Column (d) Droplet 0 10 20 30 40 50 GMD in μm 1.0 1.5 2.0 2.5 3.0 3.5 4.0 = 1.26 ± 0.13 GMD < 10 m = 1.21 ± 0.08 (e) Figure 1. Example diffraction patterns of PPD-2K from the RICE01 campaign are shown for a plate (a), an irregular particle (b) a column (c) and a sphere (droplet) (d). The standard deviation σ of the logarithm of the particle diameter is shown as a function of geometric mean diameter (GM D) for log-normal fits to the particle size distributions at temperatures below -39 °C (e). order the particles are interpreted as irregulars (Fig. 1b), unless there are clear maxima in the azimuthally integrated polar profile (Mie fringes) that occur only for spherical particles (Fig. 1d). In this case they are classified as droplets. It needs to be noted that if a particle is classified as irregular it does not necessarily mean that it has an irregular shape. Irregular diffraction patterns can also come from sufficiently roughed columnar or hexagonal ice particles, which do not show their usual, distinct 125 diffraction patterns. In this work the measured single particle scattering information is converted to a particle size distribution with 50 bins in a range between about 7 μm and 70 μm depending on the campaign-specific size calibration. The particle size distributions are given at a time resolution of 10 s and are fitted with a log-normal distribution to obtain the geometric mean diameter GM D and the standard deviation σ of the logarithm of the spherical equivalent diameter. The log-normal particle size distribution is 130 defined as (Feingold and Levin (1986); Tian et al. (2010)): n(d) = n0 √2π · d · log σ · e(− log2 d GM D 2 log2 σ ) (3) where n0 is the total concentration and d is the particle diameter. Fig. 1e shows the retrieved log-normal parameters σ over GM D. Most σ are in a range between 1.1 and 1.5 with some outliers to higher values. σ has a mean value of 1.26 ± 0.13. For all curve fits with GM D < 10 μm, σ has a mean value of 1.21 ± 0.07. 135 To analyse the size of ice crystals that are smaller than the lower size limit of PPD-2K (7 μm) a Fourier transform infrared spectrometer (FTIR) was used to determine the particle size during the HALO06 campaign (Wagner et al. (2006)). The FTIR measures the spectral extinction of the ice particle ensemble at wave numbers between 6000 cm−1 and 800 cm−1. At mid- infrared wavelengths, the extinction spectra only vary slightly with particle shape unless highly irregular habits are involved. For this study, similar to Schnaiter et al. (2012), the ice particle size distribution was assumed to be log-normal and retrieved 140 5 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. from the measured extinction spectra using T-matrix calculations for a fixed aspect ratio of 0.7 (circular columns). The FTIR retrieval provides reliable results down to mean particle maximum dimensions of about 1 micron. Furthermore, a formvar replicator was operated in the cloud chamber during measurement campaigns RICE01 and RICE03 to generate replica of the ice crystals on a 35 mm transparent plastic film strip. Details can be found in Schnaiter et al. (2016). The formvar replica are analysed using a Zeiss IM35 inverted microscope with a magnification of up to 500 and an Imaging 145 Source DFK41AU02 camera with a resolution of 1280 x 960 pixels. The images of the replica allow to obtain additional information about the particle shape that cannot be derived from the diffraction patterns, such as information about hollowness, but the statistics are poorer. 2.3 Experiment procedure The expansion experiments were conducted in the Aerosol Interactions and Dynamics in the Atmosphere (AIDA) cloud cham- 150 ber at the Karlsruhe Institute of Technology (Möhler et al., 2005). Here, the data from different ice nucleation measurement campaigns at cirrus temperatures between -75 °C and -39 °C are analysed (see Table 1). The expansion experiments are con- ducted with the following procedure discussed in Schnaiter et al. (2016): 1. Preparation: The cloud chamber is cleaned by evacuation and flushing cycles and then humidified to ice-saturated con- ditions by forming a thin ice coating on the inner chamber walls. 155 2. Aerosol addition: The aerosols are added with an aerosol generator. The particle types were soot or mineral dust for heterogeneous ice nucleation experiments and sulphuric acid solution droplets for homogeneous freezing experiments. 3. Initial cloud activation: A cloud chamber expansion is started by opening the valve to the vacuum pumps. The start of pumping is indicated in Fig. 2 as reference time zero. The pressure and gas temperature in the cloud chamber decrease (Fig. 2a) and the relative humidity (RH) increases (see Fig. 2b). RH is measured with a tunable diode laser absorption 160 spectrometer (Ebert et al., 2005). When the relative humidity with respect to ice (RHice) reaches homogeneous freezing conditions or exceeds the aerosol-specific threshold for heterogeneous ice nucleation, the ice nucleation process starts, e.g. at 2 min in Fig. 2d. The nucleated ice crystals deplete the supersaturation in the gas phase, leading to a reduction in RHice. Once the particles reach sizes that are larger than the detection limit of the PPD-2K instrument particles are detected. 165 4. Sublimation: In order to remove the ice crystal morphological complexity from the initial growth period, the expansion is stopped and dry synthetic air is fed into the chamber between minute five and minute nine of the experiment, increasing the gas pressure again (Fig. 2a). This further reduces RHice to below 100 % (Fig. 2b), leading to a decrease of the ice particle size by sublimation (Fig. 2d). 5. Regrowth: The dry air flow is stopped and the evacuation of the cloud chamber is resumed, leading to a second, controlled 170 growth period at a defined RHice-level above 100 %. This can be seen between minute 10 and 15 (Fig. 2b), when the 6 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. 500 750 1000 p in hPa p 0 50 100 150 200 RH in % RHice RHwater 0.0 0.1 0.2 0.3 0.4 Linear depolarisation ratio 0 5 10 15 20 25 30 35 40 Time after start of expansion in min 0 10 20 30 Spherical equivalent diameter in m GMD 50 55 60 T in °C Tgas Twall (a) (b) (c) 10 1 100 101 dN/dlogDp in cm 3 (d) Figure 2. Example expansion experiment 06 from the RICE02 campaign. Initial growth, sublimation and two regrowth cycles can be seen. The gas pressure p, gas temperature Tgas and wall temperature Twall inside the cloud chamber (a), the relative humidity with respect to water RHwater and ice RHice (b), the linear depolarisation ratio δ from SIMONE (c) and the geometric mean diameter (GM D) derived from from PPD-2K (d) are shown as a function of time after the start of the experiment. particle size increases again due to growth at this defined supersaturation (Fig. 2d). Multiple sublimation and controlled regrowth cycles can be done in one experiment. 7 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. Table 1. Campaigns that are used for the analysis of the linear depolarisation ratio. Campaign Time SIMONE wavelength Size data from Number of experiments analysed HALO06 Jan−Feb 2011 488 nm FTIR 11 RICE01 Nov 2012 488 nm PPD-2K 9 RICE02 Apr−May 2014 488 nm PPD-2K 14 RICE03 Dec 2014 552 nm PPD-2K 13 6. Final sublimation: The expansion is stopped and due to the heat transfer from the chamber walls, whose temperatures have only slightly decreased during the expansion, the humidity in the cloud chamber falls below ice saturation, initiating 175 the ice cloud sublimation. This can be seen in Fig. 2 after minute 25. To correlate the linear depolarisation ratio to the particle size at cirrus temperatures, the following conditions are applied: – The gas temperature of the cloud chamber Tgas is below -39 °C. – The expansion was started. – The SIMONE forward scattering intensity is above a threshold value to obtain high enough counts on the photomul- 180 tipliers for an accurate retrieval of δ (106 counts for SIMONE and 104 counts for SIMONE-Junior). The SIMONE instruments use an automated neutral density filter system to avoid saturation of the photomultiplier and increase the range of detection. The counts measured with the neutral density filter are normalized to the counts without neutral density filter. – The GM D determined by a log-normal fit is at most 20 % smaller than the center of smallest bin of the PPD-2K size 185 range: 1.2 · dmin ≤ μ . The center of the smallest bin ranges between 6.4 μm and 7.9 μm depending on the campaign specific calibration and photomulitplier gain settings. – The particle concentration measured with PPD-2K is larger than a lower threshold of 0.3 cm−3 to ensure PPD-2K mea- sures enough particle events during the 10 s integration time for a log-normal fit to the particle size distribution. Only those data points of the linear depolarisation ratio and GM D are used for further analysis where the conditions above are 190 fulfilled. This leads to 24 % of data being discarded due to PPD-2K limitations. This discarded data is predominantly due to low particle concentration or small particle sizes that regularly occur in the sublimation phase of the expansion experiments and can only be detected by SIMONE and not by PPD-2K. The data is averaged over the same 10 s periods for both instruments. 2.4 Numerical simulations Transition matrix (T-matrix) (Mishchenko and Travis, 1998) and conventional geometric optics (CGOM) ray tracing Monte 195 Carlo (Macke, 2020; Macke et al., 1996b, a) methods are used to simulate the near-backscattering depolarisation ratio that is 8 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. measured with the SIMONE instrument. Here we use the T-matrix code from Leinonen (2014) to perform the T-matrix simu- lations of spheroidal particles, which are constrained to small size parameters below approximately 50 due to computational limitations. For size parameters larger than 90 we use CGOM simulations of hexagonal particles with a tilted facet method and internal scatterers to generate complex ice crystals. For size parameters between 50 and 90 numerically exact methods 200 are needed that can represent more accurate the polarimetric properties of complex particles. The size parameter is defined as x = 2πa λ with characteristic particle length a and wavelength λ of the light in the surrounding medium. A wavelength of λ = 488 nm and a refractive index of 1.31 are used. All simulations calculate the scattering matrix elements that are needed to obtain the linear depolarisation ratio. For this the assumption of randomly oriented ice particles is used. The linear depolarisation ratio for incident polarisation parallel to the 205 scattering plane δ∥ for an arbitrary scattering angle θ is defined as (Mishchenko and Hovenier, 1995): δ∥(θ) = S11(θ) − S22(θ) S11(θ) + 2S12(θ) + S22(θ) (4) where S11(θ), S12(θ) and S22(θ) are the scattering matrix elements obtained from the CGOM and T-matrix simulations for the scattering angle θ. The T-matrix method is applied to simulate δ for the light scattered by randomly oriented pristine spheroids with aspect 210 ratios ranging between 1.5 and 2.0. This range is based on the replica images that are presented later. In order to be comparable to the measurements, the T-matrix scattering matrix elements are integrated over a log-normal size distribution similar to Saito et al. (2021) with 41 particle sizes varying from 0.5 μm to 10.0 μm and a fixed σ of 1.21. This is the mean σ found in the log-normal fits to the PPD-2K particle size distributions with GM D smaller than 10 μm. The maximum dimension of the spheroids is used for the comparison to the PPD-2K spherical equivalent diameter. 215 The CGOM simulations use hexagonal ice particles and average over 2 million particle orientations. The calculated scattering matrix elements are integrated over a log-normal size distribution with 42 particle sizes between 8.4 μm to 37.3 μm and a fixed σ of 1.26. This is the mean σ of all fits to PPD-2K cirrus particle size distributions. Ice crystal complexity is represented with the tilted facet approach where a random tilt angle is applied to the ice crystal surface. A distortion parameter describes the maximum possible angle of a random tilt that is applied to the crystal surface. With a distortion of 0 no tilt is applied and 220 a distortion of 0.5 is equivalent to a random tilt of up to 45°. Additional ice crystal complexity can be simulated with the mean free path by adding internal scatterers to the simulation that randomly change the direction of the internal rays (Macke et al., 1996b). In this work, the internal scattering is non-absorbing with a single scattering albedo of 0.999, representative of air bubbles. The mean free path is the mean distance that a simulated ray propagates through the crystal in the Monte Carlo simulation before changing direction due to the simulated internal scatterer. We have no direct information about concentration, 225 size and type of internal scatterers inside the cloud chamber grown ice particles. Therefore, the mean free path is varied between 150 μm for high internal scattering and 104 μm for negligible internal scattering to find the best overlap with the measurement data. The column length is used for the comparison to the PPD-2K spherical equivalent diameter. Furthermore, we use a dataset of numerically exact Invariant-Imbedding T-matrix Method (IITM) simulations of hexagonal ice crystals published in Saito and Yang (2023). It simulates particle complexity as surface roughness. The degree of this 230 9 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. 0 10 20 30 40 50 60 GMD in m 0 200 400 600 800 1000 1200 Frequency 0 50 100 150 200 250 300 Frequency -75°C < T < -45°C GMD = 10.6 m -45°C < T < -39°C GMD = 17.4 m Figure 3. Histograms of geometric mean diamaters (GM D) derived from 10 s averaged PPD-2K particle size distributions for initial AIDA gas temperatures between -75 °C and -45 °C (blue) and between -45 °C and -39 °C (red). The vertical lines show the median values for the distributions. The median GM D of ice crystals grown at lower cirrus temperatures is 39 % smaller than of ice crystals grown at higher cirrus temperatures. surface roughness is defined by the variance (σ2) of a two-dimensional Gaussian distribution of local planar surface slopes. The scattering matrix elements are integrated over a log-normal size distribution with 31 particle sizes between 0.1 μm to 24.6 μm, using a fixed σ of 1.21 for particle sizes of up to 10 μm and a fixed σ of 1.26 for larger particle sizes. The dataset was computed using the refractive index of ice at 532 nm, which differs slightly from that at 488 nm. This difference has a marginal effect on light scattering in the backward direction. The aspect ratio ranges from 1.0 to 2.0, with decreasing maximum particle 235 size for increasing aspect ratio due to increasing computational effort. 3 Results 3.1 Microphysical properties of the cloud chamber grown cirrus PPD-2K measured particle spherical equivalent diameters of up to 70.5 μm for ice crystals nucleated and grown in the AIDA chamber at gas temperatures below -39 °C. Fig. 3 shows histograms of the GM D of ice crystals grown between AIDA initial 240 gas temperatures between -45 °C and -39 °C and between -75 °C and -45 °C, respectively. At initial gas temperatures between -45 °C and -39 °C, the median GM D was 17.4 μm (Interquartile range (IQR) = 6.7 μm). In comparison, ice crystals grown at lower cirrus temperatures between -75 °C and -45 °C had a median GM D of 10.6 μm (IQR = 3.6 μm). The GM D of ice crystals grown in the lower cirrus temperature range is 39 % smaller than of ice crystals grown in the higher cirrus temperature range. It is expected that ice crystals at higher temperatures grow to larger sizes, since at the same relative humidity the growth 245 10 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. (a) (b) 100 ± 10 μm 50 ± 5 μm (c) 50 ± 5 μm (d) 100 ± 10 μm (d) 100 ± 10 μm (e) Figure 4. Microscopic images of example formvar replica of cloud chamber grown ice crystals highlighting different ice crystal complexities. The hexagonal ice crystals in (a) show hollowness on the basal facets and occasionally have air inclusions and the ice crystal in (b) has a central dislocation. (c) and (e) show columnar and irregularly shaped ice crystals and in (d) budding rosettes can be seen. The image shows ice crystals grown during RICE03 experiment 40 at an initial gas temperature of -50 °C and a supersaturation of 16 % with respect to ice (a), during RICE01 experiment 22 at an initial gas temperature of -50 °C and a supersaturation of 4 % with respect to ice (b), during RICE03 experiment 38 at an initial gas temperature of -50 °C and a supersaturation of 12 % with respect to ice (c), during RICE03 experiment 32 at an initial gas temperature of -40 °C and a supersaturation of 10 % with respect to ice (d) and during RICE03 experiment 29 at an initial gas temperature of -40 °C and a supersaturation of 4 % with respect to ice (e). rate increases for increasing temperatures due to more available condensible water vapour (Bailey and Hallett, 2009). Ice crystals grown in the AIDA cloud chamber were limited to maximum sizes of about 70 μm due to sedimentation losses. A visual analysis of the ice crystal shapes was performed using microscope images of the formvar replica during regrowth phases when the relative humidity was kept constant. This is done for a subsample of the cloud chamber experiments (see Table 2). The aim is to identify differences in the growth characteristics on the formvar replica at different growth conditions. 250 The relative humidity with respect to ice (RHice) in the regrowth phases is varied between 105 % and 120 %. The number of columnar ice crystals and the number of hollow columnar ice crystals were manually counted per microscopic frame, which usually contained some tens of ice crystals. Out of the 11096 imaged ice crystals on 324 microscope frames. 29 % were clas- sified having columnar and 71 % of ice crystals were classified having other, mainly irregular shapes (see exemplary replicator images in Fig. 4a-e). The irregular shapes were predominantly compact crystals that sometimes showed several c-axes radiating 255 from a center point, resembling budding rosettes (e.g. Fig. 4d). The columnar growth regime at temperatures below -40 °C is consistent with previous laboratory studies, e.g. by Bailey and Hallett (2009). They reported that for relative humidities below RHice = 125 % mainly single columns grow, while for higher relative humidity (budding) rosettes are expected. In Table 2 the 11 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. Table 2. Results of the analysis of the microscope images of the formvar replica taken during regrowth phases. Only experiments are analysed where a stable relative humidity during the regrowth phase was achieved. Ntot is the total number of investigated ice particles. fcol is the fraction of identified columnar particles of the total number of particles and fhollow is the fraction of identified hollow columnar particles of all identified columnar particles. fcol (SID-3) is the fraction of columnar particles derived from the SID-3 diffraction patterns during the regrowth phases of the experiments as a comparison. Tgas in °C -40 -50 Campaign RICE01 RICE03 RICE01 RICE03 Experiment 27 29 30 32 20 38 39 40 41 Ntot 508 787 764 1516 424 1350 1113 638 406 fcol 25 % 22 % 12 % 17 % 23 % 40 % 39 % 42 % 59 % fcol (SID-3) 42 % 24 % 23 % 19 % 39 % 25 % 43 % 43 % 47 % fhollow 45 % 33 % 73 % 36 % 12 % 4 % 36 % 70 % 29 % RHice mean 120 % 105 % 107 % 111 % 105 % 109 % 108 % 112 % 120 % fraction of replica classified as columnar is shown for different relative humidity with respect to ice between 105 % and 120 % and for different gas temperatures. At -40 °C the column fraction ranges between 12 % and 25 % with no clear dependence 260 on the relative humidity with respect to ice. At -50 °C the fraction of replica classified as columnar is larger than at -40 °C, ranging from 23 % (RHice = 105 %) to 59 % (RHice = 120 %). At this temperature range the columnar fraction increases with increasing supersaturation in the regrowth phase. The higher column fraction with a mean of 41 % at -50 °C in comparison to a mean of 19 % at -40 °C agrees well with previous results of laboratory-grown ice crystals by Bailey and Hallett (2009), where at -50 °C more single crystal columns are expected in comparison to the transition region between columnar and plate-like 265 growth regimes at -40 °C. The observed transition towards columnar growth with increasing relative humidity between -40 °C and -50 °C for RHice < 130 % has also been reported. Statistically more robust information about ice crystal shapes can be derived from the SID-3 diffraction patterns using the Fourier analysis method. Of all particle images at cirrus temperatures of the investigated campaigns 0.4 % show diffraction patterns with features of spherical particles, 3.8 % show diffraction patterns with features of plates, 35 % show diffraction 270 patterns with features of columns and 61 % show diffraction patterns with features of irregular ice particles. This is in good agreement with the fractions of columnar and irregular particles identified on the microscope images of the replica taken during the regrowth phases of a subsample of the experiments (see Table 2). In Fig. 5a the fractions of the ice crystal shapes are shown for the different campaigns and temperature groups. It can be noted that the fraction of columns increases from 19 % (RICE01) and 18 % (RICE03) for initial gas temperatures between -45 °C and -39 °C to 44 % (RICE01), 36 % (RICE02) and 275 38 % (RICE03) between -75 °C and -45 °C. This characteristic was also seen in the replica analysis. Furthermore, different types of morphological complexities can be studied with the ice crystal replica. The most common type of complexity is hollowness of the basal facets (Fig. 4a) with occasional air inclusions (Fig. 4e). Table 2 shows the fraction of hollow columns to all columns. This fraction varied between 33 % (RHice = 105 %) and 73 % (RHice = 107 %), with a mean 12 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. R01 warm R03 warm R01 cold R02 cold R03 cold 0.0 0.2 0.4 0.6 0.8 1.0 SID3 shape fraction Spherical Irregular Columns Plates (a) R01 warm R03 warm R01 cold R02 cold R03 cold 4 5 6 7 8 ke value kthr e = 4.6 (b) Figure 5. Particle shape fractions that are determined from all forward scattering images taken with the SID-3 instrument during the different campaigns (a). Each campaign is divided into two different groups. Cold refers to AIDA initial gas temperatures between -75 °C and - 45 °C and warm to temperatures between -45 °C and -39 °C. In (b) ke is plotted over the different campaigns. kthr e is the threshold of 4.6 for morphologically complex ice crystals defined by Schnaiter et al. (2016). More complex ice particles are observed for the higher cirrus temperatures. of 46 % for experiments initiated at -40 °C. At initial gas temperatures of -50 °C the mean fraction of columns that are hollow 280 per experiment ranges between 4 % (RHice = 109 %) and 70 % (RHice = 112 %), with a mean of 40 %. Hollow fractions below 30 % are only observed for experiments at initial gas temperatures of -50° C. Thus, for both investigated temperatures a significant mean fraction of columns (more than 40 %) show hollowness. This is in contrast to a laboratory study by Harrington and Pokrifka (2024), who estimated a critical supersaturation of 20 % for columns to develop hollowness at the basal facets at temperatures below -40 °C. It is not always possible to visually identify hollowness on the microscope images of the formvar 285 replica. Therefore, the observed hollow fraction should be considered as a lower limit. In atmospheric cirrus observations Walden et al. (2003) found all bullets but only few columns to be hollow in microscope pictures of precipitation at cirrus temperatures at South Pole station between -73 °C and -35 °C. Schmitt and Heymsfield (2007) observed hollow ends in 52 % to 80 % of all bullet-rosette and columnar particles of formvar replica from balloon-borne mid-latitude cirrus observations between -46 °C and -33 °C. The increasing trend in the fraction of columns with hollow ends with temperature is in agreement 290 with our cloud chamber observations. Another type of crystal complexity that was observed on the replica are dislocations (Fig. 4b). They are thought to form from thermal stress in the changing growth conditions that can be present during the experiments (Baker, 2003). Due to the optical limitation of the microscope and the replication technique, it is not possible to make conclusions about sub-micron scale complexity, such as surfacet roughness, from the microscope replica analysis. For this, we use the crystal 295 complexity information derived from the SID-3 diffraction patterns. Fig. 5b shows a statistical analysis of the optical com- plexity parameter ke for the different campaigns and temperature groups. For the ice crystals grown in the higher temperature 13 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. 0 5 10 15 20 25 GMD in m 0.0 0.1 0.2 0.3 0.4 0.5 Linear depolarisation ratio -45°C < T < -39°C (a) 0 5 10 15 20 25 GMD in m 0.0 0.1 0.2 0.3 0.4 0.5 -75°C < T < -45°C Measurements RICE01 RICE02 RICE03 HALO06 (b) Figure 6. Linear depolarisation ratio measured with SIMONE as a function of geometric mean diameter (GM D) of the ice particles measured with the PPD-2K and FTIR instruments. (a) includes all measurements with initial cloud chamber temperatures between -45 °C and -39 °C and (b) between -75 °C and -45 °C. Each data point represents 10 s averaged measurement data out of multiple experiments, which consisted of multiple growth and sublimation phases with different pump speeds. range, the median ke is with 5.22 clearly higher than the threshold of 4.6 defined for morphologically complex ice crystals. In the lower cirrus temperature range median ke is with 4.54 below the threshold of complex ice crystals. One reason can be that higher growth rates at higher temperatures promote crystal complexity, as discussed in Schnaiter et al. (2016). In addition, 300 small differences can be seen in the fraction of columnar ice crystals and ke for the different measurement campaigns in the same temperature groups. For example, RICE03 has a higher median ke in comparison to RICE02 and RICE01 in both tem- perature groups. These differences can be explained by different RHice during the experiments of the different campaigns. In the next section, we analyse the depolarisation properties for each of the two temperature ranges separately. 3.2 Effects of particle size on the linear depolarisation ratio 305 In Fig. 6 the measured δ is shown as a function of GM D derived from the PPD-2K particle size distributions for the previously defined temperature ranges. Fig. 6a shows the data in the higher temperature range between -45 °C and -39 °C, where δ has a minimum of 0.08 for a GM D around 12 μm and increases for both larger and smaller GM D up to 0.3. In the lower temperature range between -75 °C and -45 °C during RICE01 and RICE02, δ has a constant low value between 0.05 and 0.10 for sizes between 8 μm and 25 μm (Fig. 6b). For smaller sizes below 8 μm observed during the HALO06 campaign, δ increases 310 sharply and reaches values up to 0.5. These are two distinct temperature-dependent depolarisation ratio - size modes. However, the data from the RICE03 campaign show a similar behaviour as for the higher temperature range in Fig. 6a. This difference is likely caused by more complex crystals during the lower cirrus temperatures of RICE03 with a median higher than the 14 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. 4 5 6 7 Mean ke value in RICE03 0.0 0.2 0.4 0.6 Linear depolarisation ratio R(9 11) m=-0.05 R(14 16) m=-0.03 R(19 21) m=0.16 (c) 4 5 6 7 Mean ke value in RICE02 0.0 0.2 0.4 0.6 R(4 6) m=0.13 R(9 11) m=-0.0 R(14 16) m=-0.02 (b) 4 5 6 7 Mean ke value in RICE01 0.0 0.2 0.4 0.6 Linear depolarisation ratio R(9 11) m=0.21 R(14 16) m=0.61 R(19 21) m=0.55 Measurements for 4 m < GMD < 6 m 9 m < GMD < 11 m 14 m < GMD < 16 m 19 m < GMD < 21 m (a) Figure 7. Linear depolarisation ratio as a function of optical particle complexity ke measured with the SID-3 instrument for the RICE01 campaign (a), for the RICE02 campaign (b) and for the RICE03 campaign (c) with linear fits to the data. Only a weak to moderate correlation is observed. threshold value of kthr e = 4.6 (see Fig. 5). A detailed comparison to previous atmospheric observations is given in Section 4. In the following section, we investigate the link between δ and the optical crystal complexity. 315 3.3 Effects of the optical crystal complexity on the linear depolarisation ratio In Fig. 7 the measured δ is shown as a function of the optical crystal complexity metric derived from SID-3 measurements for all available cirrus temperatures between −75 °C < T < −39 °C. A linear regression is added to the data and Pearson product- moment correlation coefficients R are determined. This is done separately for each campaign where SID-3 was operated. The results are separated into size groups of (5 ± 1) μm, (10 ± 1) μm, (15 ± 1) μm and (20 ± 1) μm to limit the effect of a possible 320 size dependence of ke. During the two measurement campaigns RICE02 and RICE03, |R| ≤ 0.16 indicates no or weak correlation between ke and δ. During the RICE01 measurement campaign a moderate positive correlation with 0.21 ≤ R ≤ 0.61 is found. The weaker cor- relation seen in RICE02 in comparison to RICE01 can be explained by the narrower temperature range during RICE02. Here, AIDA initial gas temperatures were constantly at -50 °C, whereas in RICE01 the initial gas temperatures were varied between 325 -50 °C and -39 °C. A wider temperature range allows a larger range of ice crystal complexity that is needed to measure the median correlation between ke and δ. RICE03 has a weaker correlation than RICE01 even with AIDA initial gas temperatures 15 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. ranging between -50 °C and -40 °C. During RICE03 no δ smaller than 0.15 were observed, which can be a possible reason for the weak correlation. The weak to moderate correlation between the optical complexity parameter ke and the depolarisation ratio δ contrasts with 330 previous studies, which have reported increasing δ with increasing surface roughness in the 5 - 20 μm size range (Smith et al., 2016; Saito and Yang, 2023). Using numerical simulations, Saito and Yang (2023) showed that δ increases with increasing surface roughness up to a threshold of σ2 ≈ 0.1, beyond which additional roughening has little to no further effect on δ. Most of the crystals in our experiments fall within the range ke > 4.6, which could indicate that their surface roughness was already above this threshold—potentially explaining the weak dependence of δ on optical complexity. Schnaiter et al. (2016) 335 found that ke > 4.6 is indicative of moderately to strongly roughened crystals, supporting this interpretation. Growing more pristine crystals with σ2 < 0.1 would require very low supersaturations and long growth times, conditions that are difficult to maintain in the AIDA cloud chamber due to sedimentation losses. Alternatively, other morphological features not captured by ke, such as crystal habits, may have varied across experiments and influenced δ, further weakening the observed correlation. This highlights the complexity of the relationship between δ and ice crystal morphology. 340 3.4 Comparison of measurements to numerical simulations The measurement data for the two temperature ranges are compared to T-matrix and conventional geometric optics numerical (CGOM) simulations at the near-backscattering direction of 178°. Fig. 8 shows δ from T-matrix numerical simulations of spheroidal particles and CGOM simulations of columns with hollow basal facets, together with the measurement data from Fig. 6. The simulation parameters are detailed in Section 2.4. The T-matrix results are only meaningful in the lower temperature 345 range (Fig. 8b), as for the warmer temperature range the ice crystals are too large. The T-matrix simulations reproduce the size- dependence of the measurement data well in the size range of about 2 μm to 9 μm. The CGOM simulations of δ use hollow columns where each basal facet is hollowed to a depth of 33.3 % of the length of the column. The schematics are shown in Fig. 8c. This type and length of hollowness is consistent with the ice crystal replica that are found on the microscope images of the formvar slides (e.g. see Fig. 4a) and with the hollowness parametrisation of Zhu et al. 350 (2023). The consideration of hollowness lowers the linear depolarisation ratios to the range of the measurement data, likely due to the presence of additional planar surfaces inside the crystal (Yang et al., 2008; Smith et al., 2016). CGOM simulations of solid columns overestimate δ and are shown in appendix B1. Different levels of ice crystal complexity are simulated by varying distortion parameters from 0, representing pristine ice crystals, to 0.5, representing highly complex morphologies. Using a mean free path around 2000 μm (B), the δ values of the higher cirrus temperature range between -45 °C and -39 °C 355 can be reproduced. Using a mean free path of about 4000 μm (A), the CGOM simulations reproduce the δ values of the lower cirrus temperature range between -75 °C and -45 °C. The implementation of ice crystal complexity with hollowness, surface roughness and internal scatterers in the CGOM ray tracing methods allows to reproduce the measured δ. The simulation results are almost identical for aspect ratios of 1.75 and 2.0, and for the wavelength of λ = 552 nm, which was used during the RICE03 campaign (see appendix B3 and B4). CGOM simulations of hollow columns using mean free path from 104 μm, indicating 360 negligible internal scattering, to 500 μm, indicating high internal scattering are shown in appendix B2. 16 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. Figure 8. Linear depolarisation ratio as a function of geometric mean diameter (GM D). The measurement data (dots) are compared to T-matrix simulations of spheroidal particles at 178° near-backscattering direction (lines) (Leinonen, 2014) and to CGOM simulations of columns with hollow basal facets (Macke, 2020). The experimental data at initial gas temperatures between -45 °C and -39 °C is shown in (a) and between -75 °C and -45 °C in (b). (c) shows the schematics of the used column shape with hollow basal facets entering 33.3 % of the column height from each prism facet. There is a good overlap between the measurement data and the simulations. CGOM simulations use the geometric optics approximation and therefore only yield reliable results for size parameters larger than about 102. Numerically exact simulations like IITM are needed for smaller sizes. Fig. 9 shows δ from IITM simulations with aspect ratios between 1.0 and 2.0. There is a sharp increase in δ with increasing particle size from δ ≈ 0 at particle sizes <1 μm to 0.2 < δ < 0.5 at particle sizes around 3 μm. For particle sizes larger than about 3 μm, δ reaches a plateau with smaller 365 variation with size. The value of δ on the plateau increases with increasing surface roughness σ2. The simulations with aspect ratios of 1.5 and 2.0 show slightly higher results for δ in comparison to simulations with an aspect ratio of 1.0. The simulated δ almost always overestimates the measurement data. Only for the pristine case (σ2 = 0) with aspect ratio 1.0, the simulations partly overlap with the measurement data. However, based on the microphysical data at least some degree of complexity on the ice crystal replica images and the optical small-scale complexity parameter is expected. Further refining the ice crystal 370 complexity model, for example by incorporating hollowness, could enhance its agreement with the measurement data. 4 Discussion Sassen and Benson (2001) observed a mean δ of 0.33±0.11 for cirrus with a mid-latitude ground-based lidar at a wavelength of 694 nm located at the facility for atmospheric remote sensing of the University of Utah. CALIPSO space-borne lidar mea- surements at 532 nm have given similar results for daytime measurements of cirrus with a global mean of δ = 0.34, whereas 375 the nighttime global average of δ = 0.24 is closer to our cloud chamber findings (Sassen and Zhu, 2009). Yet, the authors 17 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. 0 5 10 15 20 25 0.0 0.1 0.2 0.3 0.4 0.5 Linear depolarisation ratio -45°C < T < -39°C (a) IITM: AR = 1.0 0 5 10 15 20 25 0.0 0.1 0.2 0.3 0.4 0.5 -75°C < T < -45°C (b) IITM: AR = 1.0 0 5 10 15 20 25 0.0 0.1 0.2 0.3 0.4 0.5 Linear depolarisation ratio (c) IITM: AR = 1.5 0 5 10 15 20 25 0.0 0.1 0.2 0.3 0.4 0.5 (d) IITM: AR = 1.5 0 5 10 15 20 25 GMD in m 0.0 0.1 0.2 0.3 0.4 0.5 Linear depolarisation ratio (e) IITM: AR = 2.0 0 5 10 15 20 25 GMD in m 0.0 0.1 0.2 0.3 0.4 0.5 IITM: 2 = 0.0 IITM: 2 = 0.01 IITM: 2 = 0.03 IITM: 2 = 0.15 IITM: 2 = 0.5 Measurements (f) IITM: AR = 2.0 Figure 9. Comparison between the measured linear depolarisation ratio as a function of geometric mean diameter (GM D) (dots) and Invariant Imbedded T-Matrix (IITM) simulations of hexagonal particles at 178° near-backscattering direction (lines). Surface roughness variance σ2 between 0 and 0.5 are used. The results for an aspect ratio of 1.0 are shown in (a) and (b), for an aspect ratio of 1.5 in (c) and (d), and for an aspect ratio of 2.0 in (e) and (f). The experimental data at initial gas temperatures between -45 °C and -39 °C is added in (a), (c) and (e), and between -75 °C and -45 °C in (b), (d) and (f) for comparison. The IITM simulations without internal crystal complexity overestimate the measured δ for most sizes. explain the lower nighttime values as an artefact caused by background signals from Rayleigh scattering of the atmosphere. Most other lidar studies of mid-latitude cirrus reported δ in the same range between approximately 0.2 and 0.5 (e.g. Urbanek et al., 2018; Li and Groß, 2021). Polar cirrus are shown to have a lower δ between 0.1 and 0.3 compared to mid-latitude cirrus 18 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. at the same temperature from ground-based lidar observations with a wavelength of 532 nm (Del Guasta, 2001; Del Guasta 380 and Vallar, 2003) as well as from CALIPSO space-borne lidar measurements (Sassen et al., 2012). The cloud chamber grown ice particles that we observed in this study have δ between 0.08 and 0.3 at GM D below 70 μm, which is in good agreement with polar studies. One potential explanation for lower δ values in polar observations is the common occurrence of diamond dust and ice fog particles at sizes smaller than 100 μm in high latitudes, which rarely exist in mid-latitudes (e.g. Walden et al., 2003; Gultepe et al., 2017). 385 Our laboratory results are restricted to relatively small ice crystals, whereas atmospheric ice crystals in cirrus regularly reach sizes larger than 100 μm, especially at higher cirrus temperatures (Mitchell et al., 2011; Woods et al., 2018; De La Torre Castro et al., 2023). Groß et al. (2023) investigated the linear depolarisation ratio of case studies of different cirrus between -63 °C and -58 °C during the CIRRUS in Mid-Latitudes (CIRRUS-ML) campaign. In the four investigated case studies the linear depolarisation ratio also increases with increasing particle size from a median δ of 0.39 for the cloud with the smallest medium 390 effective diameter of 52.2 μm to a median δ of 0.52 for the cirrus with the largest medium effective diameter of 193.8 μm. This decrease in δ towards the smaller particle size investigated in this work is coherent with our cloud chamber observations of δ. The findings indicate that more comprehensive optical models are necessary to accurately reproduce the observed linear depolarisation ratios of morphologically complex ice crystals. Small ice crystals with sizes below 10 μm are known to cause high δ (Schnaiter et al., 2012). The cloud chamber grown ice 395 clouds with GM D below 10 μm that we observed in this study showed δ of up to 0.45. This can explain the high δ observed in lower cirrus temperatures in the atmosphere (e.g. Sassen and Zhu, 2009; Li and Groß, 2021) by the presence of small ice crystals with spherical equivalent diameters below 5 μm. In situ observations of small (1 μm<maximum dimension<10 μm) ice crystals have been made in tropical tropopause cirrus at temperatures below -40 °C (Woods et al., 2018; Lawson et al., 2019). This can be a driver of higher δ observed for cirrus at lower latitudes where deep convective systems occur with higher 400 frequencies (Futyan and Del Genio, 2007). Small ice particles in this size range also occur in contrails (Singh et al., 2024), influencing δ retrieved by lidar measurements. Laboratory studies by Smith et al. (2016) investigated δ of artificially grown ice crystals at -30 °C with similar maximum dimensions between 20 μm and 80 μm at a wavelength of 532 nm. The ice crystals were grown in a fall tube and contained a higher fraction of plate-like particles according to the replica photographs. For the columnar particles hollowness on the basal 405 facets and air inclusions were visible on the replica images, similar to our observations. The ice crystals were found to have δ measured at 180° backscattering direction between 0.25 and 0.45 and at 178° near-backscattering direction between 0.1 and 0.35, which is comparable to our measurements. This raises the question of how much lower our observed δ at 178° (δ178°) is in reference to exact backscattering δ at 180° (δ180°) (Schnaiter et al., 2012). The simulated difference between δ180° and δ178° is shown in Fig. 10a for T-matrix simulations, in Fig. 10b for CGOM 410 simulations of solid columns, in Fig. 10c for CGOM simulations of hollow columns and in Fig. 10d for IITM simulations. For T-matrix and CGOM simulations the largest difference δ180° − δ178° is below 0.04, and thus cannot explain the difference between our cloud chamber observations and atmospheric values. Only the IITM simulations show a clear bias towards lower depolarisation ratios for the 178° measurements compared to measurements at the exact backscattering direction for roughened 19 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. 2 4 6 8 0.2 0.1 0.0 0.1 0.2 180° - 178° (a) T-matrix 12.5 15.0 17.5 20.0 22.5 25.0 0.2 0.1 0.0 0.1 0.2 (b) CGOM solid columns: Mfp = 150 m, dist = 0.3 12.5 15.0 17.5 20.0 22.5 25.0 GMD in m 0.2 0.1 0.0 0.1 0.2 180° - 178° Aspect ratio for (a) - (c) 1.5 1.75 2.0 (c) CGOM hollow columns: Mfp = 2000 m, dist = 0.3 0 5 10 15 GMD in m 0.2 0.1 0.0 0.1 0.2 Surface roughness for (d) 2 = 0.0 2 = 0.03 2 = 0.1 2 = 0.25 2 = 0.5 (d) IITM with asp=1.0 Figure 10. Difference between the linear depolarisation ratio at the exact backscattering direction (δ180°) and at 178° (δ178°) for T-matrix simulations (a), CGOM simulations of solid columns with a distortion of 0.3 and a mean free path of 150 μm (b), CGOM simulations of hollow columns with a distortion of 0.3 and a mean free path of 2000 μm (c) and IITM simulations with roughness variance σ2 between 0 and 0.5 and an aspect ratio of one (d). IITM simulations show the highest possible bias up to 0.17 for GM D = 13.8 μm. crystals (Fig.10d). This bias increases with increasing particles sizes, and for roughened crystals a maximum bias of 0.17 for 415 a GM D of 13.8 μm is found. Therefore, it cannot be entirely ruled out that the slightly lower δ values observed in AIDA, compared to atmospheric lidar, are due to the deviation from exact backscattering. However, this offset does not affect the comparison with numerical models, which are also evaluated at the near-backscattering angle of 178°. The results suggest that more comprehensive optical models are required to reproduce the observed depolarisation ratios of complex ice crystals. While the IITM simulations, which included only surface roughness on solid columns, showed poor 420 agreement with measurements, the CGOM model achieved better correspondence only when multiple scales and types of com- plexity—such as hollowness and internal scatterers—were incorporated. Although the applicability of the CGOM simulations to correctly model polarimetric properties has been questioned, because changes in polarisation caused by internal scattering are omitted in the simulations, and interference effects from different rays leaving the particle are excluded (e.g. Smith et al., 20 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. 2016; Macke et al., 1995), it was still possible to reproduce observed δ values when a suitable combination of complexity 425 parameters was applied. This supports our conclusion that capturing the full range of morphological complexity is critical for accurate optical modelling. However, commonly used approaches like the tilted facet method remain limited, as they lack physical surfaces and are difficult to relate to real, observed ice crystal features (Macke et al., 1996a; Liu et al., 2013). Since many complexity features occur at scales comparable to the wavelength of light, their representation within geometric optics frameworks remains questionable. Together, these findings highlight the need for more physically realistic models that include 430 both surface and internal complexity or even more complex shapes to accurately simulate polarimetric scattering properties. 5 Summary In this study, we analysed the relationship between the linear depolarisation ratio and the simultaneously measured micro- physical properties of laboratory-generated ice crystals, specifically size, shape and optical complexity. The ice crystals were grown under controlled cirrus conditions with sizes predominantly below 70 μm. The analysis of the microphysical properties 435 of about 47 ice clouds grown in the AIDA cloud chamber shows that smaller and more pristine ice crystals tend to form at lower cirrus temperatures between -75 °C and -45 °C, while larger and more complex crystals are more common at higher cirrus temperatures between -45 °C and -39 °C. According to formvar replica photographs, the fraction of hexagonal colum- nar particles increases with decreasing temperature from 19 % at -40 °C to 41 % at -50 °C. A significant fraction of columns exhibited hollowness on the basal facets, with 46 % and 40 % at initial gas temperatures of -40 °C and -50 °C, respectively. 440 We found that particles with GM D larger than 10 μm have a linear depolarisation ratio below 0.3. This is lower than atmo- spheric lidar measurements in mid-latitude cirrus but agrees well with lidar measurements in polar regions. Two temperature- dependent modes are found. For cloud chamber temperatures of -45 °C and lower, in most cases δ stays constant for increasing size. For cloud chamber temperatures between -45 °C and -39 °C, δ increases with increasing size up to about 20 μm. δ in both temperature ranges can be well reproduced with CGOM simulations of hollow columnar ice crystals using the tilted facet 445 method and mean free paths for internal scattering to model ice crystal complexity. For ice crystals with GM D below 10 μm, the strong increase in δ up to values of 0.45 with decreasing size is in good agreement with T-matrix simulations assuming spheroidal shapes. Recent IITM simulations for small and roughened hexagonal ice crystals were tested against our observa- tions, but the comparison showed that the IITM simulations overestimate the measured δ by about 15 %. Adapting the model of ice crystal complexity further, for instance by including hollowness, may improve agreement with the measurement data. 450 We also investigated the link between the small-scale morphological complexity, measured using the optical complexity parameter ke, and δ, but no clear correlation was found. One reason can be that other morphological features, that are not constant during the experiments (like the particle shape), affect δ. It is also possible that, even at the lowest supersaturation levels generated in the cloud chamber, ice crystals already have a baseline roughness, potentially limiting the range of ke so that a correlation cannot be observed with the current laboratory setup. 455 Understanding how size and morphological complexity influence the ice cloud backscattering linear depolarisation ratio is essential for interpreting atmospheric remote sensing data from instruments such as the Cloud-Aerosol Lidar with Orthogonal 21 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. Polarization (CALIOP) of the CALIPSO mission, the Cloud-Aerosol Transportation System (CATS) lidar on the International Space Station (ISS) or the Atmospheric Lidar (ATLID) on the new Earth Cloud, Aerosol and Radiation Explorer (EarthCARE) satellite (Sassen and Benson, 2001; Pauly et al., 2019; do Carmo et al., 2021). Additionally, our measurements of the optical 460 properties of small ice crystal can be useful for testing and validating optical particle models at the limit of the geometric optics approximation. 22 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. 0 5 10 15 20 25 Spherical equivalent diameter in μm 0 10 20 30 40 50 60 70 Maximum dimension in μm Rough Droplet Solid column Hollow column Hollow bullet rosette Plate (a) 0 5 10 15 20 25 Spherical equivalent diameter in μm 0 10 20 30 40 50 60 70 Smooth (b) Figure A1. Ice crystal maximum dimensions of different habits are shown as a function of their spherical equivalent diameter for rough ice particles (a) and smooth ice particles (b). The spherical equivalent diameter is estimated by integrating the light that is scattered by an ice crystal in the direction of the solid angle of the PPD-2K trigger field of view, based on a light scattering database by Yang et al. (2013) and Mie theory for droplets (Prahl, 2024). The maximum particle size can be up to 2.5 times the spherical equivalent diameter for rough plates. Appendix A: Relation between spherical equivalent diameter and particle maximum dimension Due to different light scattering properties in the direction of the trigger field of view of the PPD-2K, the relationship between the ice particle spherical equivalent mean diameter and the maximum dimension is influenced by the ice particle shape and 465 complexity. The fraction of light scattered by water droplets of different sizes over the trigger optics solid angle is calculated with Mie theory (Prahl, 2024). It is compared to the intensity of light scattered in the direction of the trigger field of view by ice crystals based on light scattering properties from a database by Yang et al. (2013). We estimate a spherical equivalent diameter of 25 μm to be equivalent to a maximum dimension between 30 μm for a rough hollow column and up to 69 μm for a smooth plate. The maximum dimensions of ice crystals of different habits and water droplets are shown in Fig. A1a for rough 470 particles and in Fig. A1b for smooth particles. The conversion factor ranges between 1.0 and 2.5. It can be noted that the spread in size conversion between the different habits is larger for smooth particles than for rough ones. Increasing particle roughness smooths out the characteristic scattering features of the particle habits, such as the 22° halo. Thus, the habit of pristine particles has a stronger effect on the size conversion than that of complex particles. Appendix B: Additional numerical simulations 475 This section provides additional numerical simulations of the linear depolarisation ratio. T-matrix simulations of spheroids and CGOM simulations of solid and hollow hexagonal ice crystals are presented for, multiple aspect ratios and for the wavelength of 552 nm that was used in the SIMONE-Junior instrument. 23 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. 0 5 10 15 20 25 0.0 0.2 0.4 0.6 0.8 1.0 Linear depolarisation ratio (mfp = 150 m) -45°C < T < -39°C (a) 0 5 10 15 20 25 0.0 0.2 0.4 0.6 0.8 1.0 -75°C < T < -45°C (b) 0 5 10 15 20 25 GMD in m 0.0 0.2 0.4 0.6 0.8 1.0 Linear depolarisation ratio (mfp = 10000 m) (c) 0 5 10 15 20 25 GMD in m 0.0 0.2 0.4 0.6 0.8 1.0 (d) Ray tracing solid column with AR = 1.5 RT distortion = 0.0 RT distortion = 0.15 RT distortion = 0.30 RT distortion = 0.50 Measurements Figure B1. Linear depolarisation ratio from CGOM simulations at 178° near-backscattering direction as a function of geometric mean diameter (GM D) for solid columns (Macke, 2020). The aspect ratio (AR) is fixed at 1.5 and the distortion is varied between 0 and 0.5. The simulations in (a) and (b) use a mean free path of 150 μm (c) and of 104 μm for high and negligible internal scattering, respectively (d). For comparison, (a) and (c) include all measurements with initial gas temperatures between -45 °C and -39 °C and (b) and (d) between -75 °C and -45 °C as gray dots. δ simulated for solid columns overestimates the measurement data. B1 CGOM simulations of solid columns Fig. B1 shows the measurement data with CGOM simulations of solid columnar ice crystals with a fixed aspect ratio of 1.5. 480 The simulations of solid columns always overestimate our observations, independent of varying surface roughness or mean free path. An increase in the distortion parameter up to about 0.3 leads to a decrease in δ for all investigated sizes. Beyond this point, δ increases again with increasing distortion for all investigated sizes. B2 Effect of mean free path on CGOM simulations of hollow hexagonal particles Fig. B2a and Fig. B2b show CGOM simulations of hexagonal ice particles with hollow basal facets using mean free paths 485 between 104 μm (label A), indicating negligible internal scattering, and 500 μm (label E), indicating high internal scattering. 24 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. 0 5 10 15 20 25 GMD in m 0.0 0.2 0.4 0.6 0.8 Linear depolarisation ratio C A B -45°C < T < -39°C (a) 0 5 10 15 20 25 GMD in m 0.0 0.2 0.4 0.6 0.8 C A B -75°C < T < -45°C (b) Ray tracing of columns with AR = 1.5 and distortion = 0.3 Measurements Ray tracing with 488 nm Ray tracing with 552 nm A for hollow columns with mfp = 2000 m B for solid columns with mfp = 10000 m C for solid columns with mfp = 150 m Figure B2. Linear depolarisation ratio as a function of geometric mean diameter (GM D). The measurement data (dots) are compared CGOM simulations of columns with hollow basal facets (entering 33.3 % of the column height from each basal facet) using mean free paths between 104 μm (label A) and 500 μm (label E) (Macke, 2020). The experimental data at initial gas temperatures between -45 °C and -39 °C is shown in (a) and between -75 °C and -45 °C in (b). A mean free path around 2000 μm (C) reproduces δ of the higher cirrus temperature range between -45 °C and -39 °C. Using a mean free path of about 4000 μm (B), the CGOM simulations reproduce δ of the lower cirrus temperature range between -75 °C and -45 °C. A decrease in mean free path increases the linear depolarisation ratio. B3 Effect of aspect ratio in CGOM simulations 490 Fig. B3a and Fig. B3b show that changes of the aspect ratio between 1.5 and 2.0 only have a minor effect on the simulated δ for the CGOM simulations of solid and hollow columns. This is the range of aspect ratios for columns seen on the microscope images of the formvar replica sampling at the AIDA cloud chamber. A distortion parameter of 0.3 and different mean free paths are used. The difference in δ is largest with 2.5 % between an aspect ratio of 1.5 and 2.0 for hollow columns. In addition, T-matrix simulations of spheroids with aspect ratios between 1.5 and 2.0 are shown. Here, the aspect ratio has a larger effect 495 on δ with differences of up to 20 % between aspect ratios of 1.5 and 2.0. Nonetheless, all three aspect ratios reproduce the size-dependence of the measurement data well in the size range of about 2 μm to 9 μm. B4 Effect of SIMONE-Junior wavelength of 552 nm Fig. B4a and B4b show the simulated linear depolarisation ratio for solid and hollow columns at the different wavelengths of 448 nm and 552 nm, which are used in the SIMONE and SIMONE-Junior instruments, respectively. The wavelength of 500 552 nm used in SIMONE-Junior during the RICE03 measurement campaign only causes minor changes in δ, with a maximum 25 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. 0 5 10 15 20 25 GMD in m 0.0 0.2 0.4 0.6 0.8 Linear depolarisation ratio A B C -45°C < T < -39°C (a) 0 5 10 15 20 25 GMD in m 0.0 0.2 0.4 0.6 0.8 A B C -75°C < T < -45°C (b) T-matrix of spheroids and RTMC of columns with distortion = 0.3 T-matrix: AR = 1.5 T-matrix: AR = 1.75 T-matrix: AR = 2.0 Measurements Ray tracing: AR = 1.50 Ray tracing: AR = 1.75 Ray tracing: AR = 2.00 A for solid columns with mfp = 150 m B for solid columns with mfp = 10000 m C for hollow columns with mfp = 2000 m Figure B3. Linear depolarisation ratio as a function of geometric mean diameter (GM D). The measurement data (dots) are compared to T-matrix simulations of spheroidal particles at 178° near-backscattering direction (lines) (Leinonen, 2014) and to CGOM simulations of columns with a distortion of 0.3. The aspect ratio (AR) is varied between 1.5 and 2.0. Mean free paths of 150 μm (high internal scattering) and 104 μm (negligible internal scattering) are used for solid columns (see A and B), and a mean free path of 2000 μm is used for solid columns (see C). For comparison (a) includes all measurements with initial gas temperatures between -45 °C and -39 °C and (b) between -75 °C and -45 °C as gray dots. Changes in aspect ratio in the observed range between 1.5 and 2.0 only cause minor changes in δ. deviation of 1.5 % in comparison to the wavelength of 488 nm that is used by the SIMONE instrument in all other measurement campaigns. 26 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. 0 5 10 15 20 25 GMD in m 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Linear depolarisation ratio B C D E A -45°C < T < -39°C (a) 0 5 10 15 20 25 GMD in m 0.0 0.1 0.2 0.3 0.4 0.5 0.6 B C D E A -75°C < T < -45°C (b) Ray tracing hollow column with AR = 1.5 Measurements RT distortion = 0.0 RT distortion = 0.15 RT distortion = 0.30 RT distortion = 0.50 A for mfp = 10000 m B for mfp = 4000 m C for mfp = 2000 m D for mfp = 1000 m E for mfp = 500 m Figure B4. Linear depolarisation ratio from CGOM simulations at 178° near-backscattering direction as a function of geometric mean diameter (GM D) for solid and hollow columns (Macke, 2020) and for wavelengths of 488 nm and 552 nm, as they are used by the SIMONE and SIMONE-Junior instruments, respectively. The aspect ratio (AR) is fixed at 1.5 and the distortion is fixed at 0.3. Mean free paths of 150 μm (high internal scattering) and 104 μm (negligible internal scattering) are used for solid columns (see C and B) and 2000 μm for hollow columns (see A). For comparison (a) includes all measurements with initial gas temperatures between -45 °C and -39 °C and (b) between -75 °C and -45 °C as gray dots. Small changes in the used wavelength of the two instruments only cause minor changes in δ according to the CGOM simulations. 27 https://doi.org/10.5194/egusphere-2025-3515 Preprint. Discussion started: 11 August 2025 c © Author(s) 2025. CC BY 4.0 License. Data availability. All measurement data are available on RADAR4KIT: https://doi.org/10.35097/66tc7z2u0s2gf1fe Author contributions. EJ and AH conceptualised the manuscript. MSc developed the SIMONE instrument. MSc planned and led the AIDA 505 cloud chamber experiments. MSa provided the IITM simulations. RW operated and analysed the data of the FTIR. AH analysed the data and wrote the manuscript. 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