PHIPS-HALO: the airborne particle habit imaging and polar
scattering probe – Part 3: Single Particle Phase Discrimination and
Particle Size Distribution based on Angular Scattering Function

Abstract. A major challenge for for in-situ observations in mixed phase clouds remains the phase discrimination and sizing of cloud hydrometeors. In this work, we present a new method to determine the phase of individual cloud hydrometeors based on their angular light scattering behaviour employed by the PHIPS airborne cloud probe. The phase discrimination algorithm is based on the difference of distinct features in the angular scattering function of spherical and aspherical particles. The algorithm is calibrated and validated using a large data set gathered during two in-situ aircraft campaigns in the Arctic and outhern Ocean. Comparison of the algorithm with manually classified particles showed that we can confidently discriminate between spherical and aspherical particles with a 98 % accuracy. Furthermore, we present a method to derive particle size distributions based on single particle angular scattering data for particles in a size range from 100 μm 



Introduction
Mixed-phase clouds, consisting of both supercooled liquid droplets and ice particles, play a major role in the life cycle of clouds and the radiative balance of the earth (e.g. Korolev et al. (2017)). Despite their widespread occurrence, mixed-phase cloud processes are still rather poorly understood and represent a great source of uncertainty for climate predictions (e.g. McCoy 15 et al. (2016)). As a consequence, more in-situ observations are needed to better understand mixed-phase cloud processes and improve climate models. Microphysical properties and life cycle of mixed-phase clouds are strongly dependent on the phase separation of liquid and ice phase (e.g. Korolev et al. (2017)). Furthermore, the radiative properties of cloud particles depend on their phase, shape and size. Despite the importance of mixed-phase cloud phase composition, a major uncertainty remains in the correct phase discrimination of cloud hydrometeors.
Particle Imager (CPI, SPECinc, Boulder, USA), have a finer resolution and are able to discriminate particles down to 35 µm McFarquhar et al. (2013). Still, the phase discrimination between droplets and quasi-spherical or small irregular ice particles based on their images can be challenging, as shown in Fig. 1.
The SID family of instruments has the disadvantage, however, that they do not measure the phase of each single particle but only for a sub-sample. Therefore, a large sampling statistics is required to derive ice concentrations in mixed-phase clouds that are dominated by droplets. The Cloud and Aerosol Spectrometer with Polarization (CAS-POL, DMT, Longmont, USA, Glen and Brooks (2013)) is an instrument that measures the light scattered by single cloud particles and aerosols in a size range 15 of 0.6 µm ≤ D ≤ 50 µm in the forward and backward directions. Based on the polarization ratio of the backscattered light, the sphericity of the cloud particles can be determined (Sassen (1991); Nichman et al. (2016)). However, recent studies have suggested, that particle phase discrimination of polarization-based measurements can misclassify up to 80% of the ice particles as droplets in the presence of small, quasi-spherical ice ).
Hence, in the size range D ≤ 100 µm, methods for reliable particle phase discrimination, are still needed. The Particle 20 Habit Imaging and Polar Scattering probe (PHIPS) is a unique instrument designed to investigate the microphysical and light scattering properties of cloud particles. It produces microscopic stereo-images whilst simultaneously measuring the corresponding angular scattering function from 18 • to 170 • for single particles in a size range from 50 µm ≤ D ≤ 700 µm and 20 µm ≤ D ≤ 700 µm for droplets and ice particles, respectively. More information and a detailed characterization of the PHIPS setup and instrument properties can be found in depth in Abdelmonem et al. (2016) and Schnaiter et al. (2018). 25 In this work, we will present a method to discriminate the phase of single cloud particles based on their angular scattering function. An algorithm was developed using experimental in-situ data from two aircraft campaigns targeting mixed-phase clouds. We present a method to use single-particle angular light scattering measurements to produce size distributions for spherical and aspherical particles separately.
This work is structured in the following: in section 2, the aircraft campaigns during which the experimental data sets used 30 in this work, are introduced. Next, in section 3 the methodology and calibration of the phase discrimination algorithm are explained. In section 4, the particle sizing will be introduced and several methods for shattering correction will be discussed.
Finally, in section 5, the described methods will be used in three case studies. The results will be compared to measurements by other cloud particle probes during the same campaigns. Figure 1. Stereo micrograph of a droplet (a) and a quasi-spherical ice particle (b) taken by the PHIPS probe. In the stereo micrograph, the two views of the particle have an angular distance of 120°. The instrument concurrently recorded the angular light scattering functions of the imaged particles as displayed in (c). The theoretical scattering function calculated for a droplet with a diameter of 200 µm by Mie theory is shown for comparison in (c).

Experimental Data Sets
In this work, we use experimental in-situ data gathered during two airborne field campaigns to develop and test a single-particle phase discrimination algorithm for the PHIPS probe. The two data sets refer to the two respective campaigns: 1. ACLOUD -Arctic CLoud Observations Using airborne measurements during polar Day, May/June 2017 based in Svalbard (Spitsbergen, Norway) and The sampling during both campaigns includes a wide variety of different cloud conditions: warm clouds, supercooled liquid 10 clouds, ice clouds and mixed-phase clouds. Clouds were sampled in an altitude range from boundary layer clouds below 200 m to mid-level clouds between 4000 m and 6000 m. Temperatures ranged from -15 to +5 • C during ACLOUD and -35 to +5 • C during SOCRATES. The sampled ice particles covered a range of different particle shapes and habits (columns, plates, needles, bullet rosettes, dendrites and irregulars, including rough, rimed and pristine particles) as well as sizes. More details can be found in the supplementary material (S1). The instrumentation on the two aircrafts included cloud particles probes 15 such as the SID-3, CDP (Cloud Droplet Probe, DMT, Longmont, USA), CIP and PIP (Precipitation Imaging Probe, DMT, Longmont, USA) during ACLOUD and 2DC, 2DS and CDP during SOCRATES. Due to the variability of the meteorological conditions and sampled particles, the data gathered during these two campaigns makes a suitable and representative data set to develop the phase discrimination and particle size distribution algorithms that are presented in this work.

Single-Particle Phase Discrimination Algorithm
The angular scattering properties of spherical particles can be analytically calculated using Mie theory. The angular scattering 5 properties of usually aspherical ice particles, however, are much more complex, which significantly alters their scattering properties compared to spherical particles Schnaiter et al. (2018); Sun and Shine (1994)). Hence, it is possible to differentiate between the angular scattering functions (ASF) of spherical and aspherical particles by looking into differences in the angular light scattering behaviour in the angular regions where spherical particles exhibit unique features, like the minimum around 90 • and the rainbow around 140 • . In this section, we introduce four scattering features and develop 10 an algorithm that is able to classify each particle based on the combined information from multiple features of the ASF (see  The basic concept of the development procedure for the single-particle phase discrimination algorithm will be explained in this section and is shown in Fig. 3. In the first step, ASFs calculated by Mie theory (BHMIE, Bohren and Huffmann) for spherical particles using the refractive index for water (n refr = 1.332) are compared to modelled ASFs of aspherical ice 15 crystals (Baum et al. (2011) and Yang et al. (2013)). Based on the differences in the ASFs, typical features are determined 4 https://doi.org/10.5194/amt-2020-297 Preprint. Discussion started: 29 September 2020 c Author(s) 2020. CC BY 4.0 License. that are characteristic for spherical or aspherical particles (see Fig. 2). The algorithm is then calibrated and validated using PHIPS data from the two field campaigns that were introduced in the previous section. This data set consists of about 23.000 representative single cloud particles of various phase, habit and size for which stereo micrographs as well as the corresponding ASFs are available. Those particles are manually classified as spherical or aspherical based on their appearance in the stereo micrographs. The calibration of the phase discrimination algorithm is then based on the ACLOUD data set only. This way, 5 a classification probability for every feature is determined. The different features are then weighed and combined to a final discrimination probability for every single particle. Lastly, the data from the SOCRATES campaign is used to validate the discrimination algorithm and to determine the discrimination accuracy. One approach to discriminate between spherical and aspherical particles is to compare a particle's ASF with theoretical Mie calculation. To estimate the deviation of the observed ASF from the calculated Mie scattering, we evaluate the integrated difference between measurement and calculation (shaded area between the curves in Fig. 2). We define the ratio between the measured intensity I exp and the Mie calculation I Mie for a spherical reference particle with a diameter of 100 µm 15 for every nephelometer angle θ i . Similar to the actual PHIPS measurement, the calculated theoretical Mie scattering is integrated over the field of view of the polar nephelometer channels. For a spherical particle, this ratio is approximately q const.
(see Supp. S2). Since we do not know the diameter of the measured particle without applying a size calibration, q is normalized by the median over all channelsq and the influence of the approximately constant factor can be neglected. This also has the advantage, that we do not need to calibrate the conversion factor from counts to power unit (W ) of the photomultiplier array 20 which can change for different campaigns, gain settings and changes in laser power. Thus, the discrimination algorithm works for different campaigns and settings without further calibration.
Furthermore, as the deviation in 'both directions' from the calculated Mie intensity have to be weighted equally, i.e. q i = 2 and q i = 1 2 should be equivalent. Therefore, we make the transformation q i → log(q i /q). The resulting 'feature parameter' is then finally defined as the integral over all angles θ i : To demonstrate that this feature is representing a distinctive difference between spherical and aspherical particles, the dis-5 tribution of the feature parameter value f 1 of representative, manually classified spherical and aspherical particles from the experimental in-situ aircraft measurement campaigns introduced in section 3.3, are shown in Fig. 4a. It can be seen that, roughly, if a given particle has a feature value of e.g. f 1 < 4.5, it is likely spherical , if f 1 > 5, it has a high probability of being an aspherical particle. Phase discrimination based on this feature alone would already allow a reasonable discrimination, but there also exist spherical particles with e.g. f 1 > 5 that would be misclassified by using this approach. Hence, multiple features 10 are taken into account to increase the discrimination accuracy.

f 2 + f 3 : Down and Up-Slope
When looking at Fig. 2, the most distinctive differences between the ASF of spherical and aspherical particles are the minimum around 90 • and the rainbow maximum around 140 • for spherical particles, whereas aspherical particles often show a flatter angular scattering behaviour. One way to extract those features is to evaluate the 'exponential slope' 15 f 2 = log(I(θ 2 )) − log(I(θ 1 )) in the region before and after the minimum around 90 • . This results in two features: the negative slope before the minimum and the positive slope between minimum and rainbow around 140 • . In general, steeper slopes mean that a given particle is likely to be spherical. The first 'slope feature' (f 2 ) is the 'Down Slope', which is simply the linear slope from θ 1 = 42 • to θ 2 = 74 • .
The first three scattering channels (Θ = 18 • , 26 • ,34 • ) are not taken into account here, because they have a larger possibility to 20 be saturated for larger particles. The slopes are determined by applying a linear fit to the logarithmic intensities in the channels between θ 1 and θ 2 .
The second slope feature (f 3 ), the 'Up Slope', is calculated as the (logarithmic) slope from the minimum around 90 • to the maximum of the rainbow peak. Since the scattering intensity can be very low and, therefore, comparable to the magnitude of the background noise (especially for small particles), hence the 'lower end' is averaged over multiple channels from θ = 25 74 • to 106 • . The upper end of the slope is not fixed either, but rather chosen dynamically as the angular position of the rainbow peak can vary within four scattering channels between θ = 130 • and 154 • . Thus, we define the slope feature f 3 as with the corresponding angle of the rainbow maximum θ 2 and the minimum θ 1 = 90 • . This way, even small particles and elongated particles with a shifted rainbow peak (see Supp. S4) can be classified correctly.

f 4 : Ratio around the 90 • Minimum
Another possible way to depict the depth of the 90 • minimum is to directly compare the intensities in the vicinity around θ = 90 • with channels that are farther away (see Fig. 2). Hence, the 'Mid Ratio' feature is defined as With the distinct shape of the ASF of droplets around the 90 • minimum one could argue that an intensity threshold might be 5 enough to discriminate between spherical and aspherical particles (e.g. classifying every particle with I(θ = 90 • ) smaller than a certain threshold I thresh as spherical). However, looking at absolute values would prove impractical as the ASF scales with particle size: a very small aspherical particle could still fulfil I(θ = 90 • ) < I thresh as well as a rather large spherical particle I(θ = 90 • ) > I thresh , respectively. Hence, the discrimination features presented here are all based on relative values, slopes and ratios instead of discrete thresholds. Further, all discrimination features are based on the scattering signal of multiple channels 10 instead of only one channel to minimize the impact of noise. This allows the discrimination algorithm to be used for multiple campaigns (even with differing settings or minor hardware changes or malfunction) without additional calibration (see section 3.4).

Simulations of the feature parameters
To prove that the defined set of discrimination features reliably discriminates between spherical and aspherical particles, we 15 calculate the feature parameter values f i based on theoretical ASF. For droplets, we use Mie theory for spherical particles with diameters from 100 µm ≤ D ≤ 700 µm. For ice, we use modelled ASF of ice crystals of different habits and roughness using the databases from Baum et al. (2011) and Yang et al. (2013) in the size range from 20 µm ≤ D ≤ 700 µm. The distribution of feature parameters is shown in Fig. 5. It can be seen, that the resulting values differ significantly for droplets and ice. This shows, that the aforementioned features are in fact fit to discriminate the ASF of spherical and aspherical particles. From 20 now on, we will assume that particles that appear spherical in terms of their angular light scattering behavior are droplets and particles that appear aspherical in their ASF are ice. Note that this includes also deformed droplets (as discussed in the supplementary material S4) as well as quasi-spherical ice as shown in Fig. 1.

Calibration
Next, the discrimination features were applied to experimental data sets of real cloud particles. We used in-situ data of represen-25 tative, manually classified single particles to validate the calculated features. This experimental data was then used to calibrate the algorithm (i.e. the classification probability functions P i (f i ) for every feature), in order to have a numerical function that calculates a classification probability for every feature of a given particle, and later a combined probability that can be used to discriminate every single particle based on its phase.
The experimental data sets used for the calibration and verification of the discrimination algorithm are described in detail in 30 section 2. As it is the goal to develop an algorithm that is suitable without any further calibration for upcoming campaigns, the . Left: normalized histograms of the discrimination features, f1, f2, f3 and f4, of all manually classified particles (blue: droplets, red: ice) from the ACLOUD campaign that were used for the calibration of the discrimination algorithm. The histograms can be nicely fitted by normal distributions (solid lines). Right: corresponding probability for a given particle with a given feature parameter value to be classified as ice or droplet, including sigmoidal fits.
8 https://doi.org/10.5194/amt-2020-297 Preprint. Discussion started: 29 September 2020 c Author(s) 2020. CC BY 4.0 License. Figure 5. Normalized histograms of the discrimination features, fi, evaluated for theoretical ASFs. Simulated ASFs were calculated using Mie theory in case of droplets (blue) and by selecting typical ice particle habits (red) from the light scattering databases by Baum et al. (2011) and Yang et al. (2013). Normal distribution fits to the data are depicted by solid lines in the graphs.
calibration and verification data sets are entirely disjunct: the ACLOUD data set is used for calibration, the verification is done using the SOCRATES data set. The ACLOUD and SOCRATES campaigns comprise 14 and 15 research flights, during which, in total about 41.000 and 235.000 single particles were detected by PHIPS, respectively. More details about sizes and habits of the manually classified particles used for the calibration can be found in the supplementary material (S1). Because the imaging component of PHIPS has a limited temporal resolution, this results in about 22.000 and 32.000 events with matching stereo 5 micrographs for the ACLOUD and SOCRATES flights, respectively. Based on these stereo micrographs, all imaged particles were manually classified as ice or droplets. To ensure a representative data set, only clearly distinguishable particles were taken into account, whereas images that show multiple particles and particles that are only partly imaged, out of focus or not 9 https://doi.org/10.5194/amt-2020-297 Preprint. Discussion started: 29 September 2020 c Author(s) 2020. CC BY 4.0 License.
clearly distinguishable, were ignored. Hence, the resulting data set used for the calibration (based on the ACLOUD campaign) includes 1.853 droplets and 7.885 ice crystals. The data set used for the validation and determination of the discrimination accuracy (see section 3.4) contains of 2.284 droplets and 9.936 ice crystals from the SOCRATES campaign. The chosen data sets consist of representative cloud particles which cover a wide range of different particle shapes and habits (columns, plates, needles, bullet rosettes, dendrites and irregulars, including rough, rimed and pristine particles) as well as sizes D = 20 -700 µm 5 and D = 100 -700 µm for ice and droplets, respectively.
The left panels of Fig. 4 show, similar to the simulations, the relative amount n(f i ) of particles that share a certain feature parameter value X. To account for the different amount of ice and droplets in the data set (N ice ≈ 3 · N droplet ), the number frequencies n droplet/ice are normalized by the total amount of droplets and ice particles. The plots show that the distribution of the four aforementioned feature parameters are clearly distinct for droplets and ice and thus represent features that can be used 10 to discriminate droplets from ice. Further, it can be seen that these normalized occurrences n(f i ) are normally distributed.
However, Fig. 4 also shows that the ice and droplets modes are not always clearly separable for every feature and for every particle. Therefore, instead of using a sharp threshold, a classification probability that a particle is classified as ice (or with 1 − P i (f i ) as a droplet) based on the ratio between n droplet (f i ) and n ice (f i ) for each 15 feature (see right panels of Fig. 4), is defined. Assuming that the n i (f i ) follow normal distributions with comparable widths, P i (f i ) can be approximated and fitted by a sigmoid function. Following that, the probability functions P i (f i ) are determined by using a sigmoidal fit for every feature based on the empiric data. These probabilities, P i , for each feature are combined to with empiric weights w i that are determined using recursive, linear optimization. Coincidentally, the optimum weight is to 20 weigh all four features equally, i.e. w 1 = w 2 = w 3 = w 4 = 1 and thus P combined = mean(P i ). Finally, this results in a classification probability for every given particle with a set of calculated feature parameter values {f 1 , f 2 , f 3 , f 4 }, which is then classified based on P combined as a droplet (P ≤ 50%) or ice particle (P > 50%). Details on the fit parameters for P i can be found in App. A and B.

25
Discrimination algorithms often run in danger of "overtraining" or creating a "lookup table", resulting in seemingly very good discrimination accuracies that, in reality, are just recreating the "training data" used for calibrating the system but fail to classify new, "unknown" data sets. In order to avoid this, the "training" and "test" data set are not only disjunct, but from entirely different field campaigns. Furthermore, this proves that the algorithm is able to function independently for different campaigns without further calibration.

30
The confusion matrices (Fawcett (2006)) for the discrimination algorithm for the two campaigns is shown in Fig. 6. For the SOCRATES data set, 99.7% of ice particles could be correctly classified as ice and only 29 out of 9.936 were misclassified as droplets. 95.8% droplets were classified correctly and 95 out of 2.284 were misclassified as ice. In total, out of all particles, 99.0% were classified correctly. Respectively, if a particle is classified as ice (droplet) by the algorithm, the expected error (i.e. the probability that the initial particle was actually a droplet) amounts to 0.9% (1.3%). Also, 100% of the theoretical particles used in section 3.2 (which were not used for the calibration) were classified correctly. More details about the discrimination accuracy and misclassified particles can be found in the SI.
5 Figure 6. Confusion matrices that visualize the classification accuracy of the ice discrimination algorithm. The discrimination algorithm was applied to all manually classified particles from both the ACLOUD (left) and SOCRATES (right) data sets. In both cases the combined probability P combined from the ACLOUD calibration was used to calculate the classification probability of each individual particle.
Note that during ACLOUD, one channel (θ = 34 • ) was malfunctioning and is hence excluded from the analysis. During SOCRATES, the θ = 90 • channel was observed be affected by the background noise in case of droplets and was thus excluded.
However, due to the design of the discrimination features (i.e. averaging over multiple channels) the implications on the discrimination are reduced and the same parameterization still works well for the SOCRATES data set.

10
Since only a sub-sample of the PHIPS particle events produce a stereo micrograph (i.e. maximum imaging rate of 3 Hz in ACLOUD and SOCRATES), particle size distributions that are based on the analysis of the images can only be calculated with a limited statistics. Furthermore, particle sizing might be biased for particles with sizes smaller than 30 µm, due to the limited optical resolution of the PHIPS imaging system ). Hence, in the following section, particle sizing based on the single particle ASFs is introduced. The calibration based on the stereo micrographs is done following a similar approach as the phase discrimination in the previous section.
In order to calculate a particle number size distribution (PSD) per volume from the single particle sizing data, as shown in Fig. 8, the volume sampling rate of the instrument has to be known. This sampling rate is simply the product between the speed of the aircraft and the sensitive area A sens of the trigger optics. The size of the sensitive area A sens is determined using optical 5 engineering software. This is presented in section 4.2.
4.1 Particle Sizing Figure 7. Calibration of the PHIPS integrated light scattering intensity measurement, expressed by the partial scattering cross section σ partial scatt , against the geometric diameter D geom p deduced from the concurrent stereo micrographs. Stereo micrographs from the SOCRATES data set were manually classified for droplets (left) and ice particles (right).
The individual detector channels of the PHIPS nephelometer measure scattered light intensity I(θ) of individual cloud particles that can be converted to a differential scattering cross section, σ diff scatt (θ),

10
with I inc and d laser the power and diameter of the incident laser beam, respectively. Note that I(θ) in Eq. (8) has to be corrected for possible background intensity due to stray light in the instrument as well as dark photon counts of the photomultiplier array.

15
For spherical particles, σ partial scatt is approximately proportional to their geometrical cross section π · D 2 p /4, with D p the particle diameter. This is demonstrated in the supplementary material using Mie calculations (S2). Assuming that this is valid not only for spherical droplets but also for aspherical ice particles, the scattering cross section equivalent particle diameter D scatt p can be deduced from the PHIPS intensity measurement I(θ) In Eq. 10, a is a calibration coefficient that describes the incident laser properties, the detection characteristics of the polar nephelometer (e.g. the photomultiplier gain settings) as well as the angular light scattering properties of the particle, and c BG 5 the integrated background intensity. As already discussed in the previous section, ice and droplets have vastly differing angular scattering characteristics, i.e. scattering cross sections σ diff scatt (θ). Hence, different a coefficients are needed and the calibration is done separately for ice and droplets. The coefficient a is calibrated based on the geometric cross section equivalent diameter D geom p derived from the stereo micrographs. A correction for the slight size overestimation of the CTA 2 for small particles due to the lower magnification is applied (see Schnaiter et al. (2018)). More details on PHIPS image analysis routines can be found  stereo micrographs (average of CTA1 and CTA2, solid line) for droplets (blue) and ice particles (red). The data is from all flights recorded during SOCRATES. Only stereo micrographs that showed only one, completely imaged particle were taken into account. The same particles were used for both size distributions.
Similar to the calibration of the phase discrimination algorithm, manually classified imaged particles were used as a calibration data set. The data is binned with respect to the particle's geometrical area equivalent diameter. The bin edges are the same as used for the final PSD data product. Those are 20,40,60,80,100,125,150,200,250,300,350,400, 500, 600 and fitted through all data points since the data points are distributed over fewer size bins. The background intensity c BG is determined as the integrated intensity from forced triggers averaged over time periods when no particles were present. c BG is the same for droplets and ice. The calibration is performed for each campaign separately, assuming that the instrument parameters remain unchanged over the duration of one campaign. The resulting calibration of the scattering equivalent diameter for the 5 SOCRATES campaign is shown in Fig. 7a and Fig. 7b for droplets and ice, respectively. The corresponding fit parameters are a ice = 1.4167 and a droplet = 1.4441. The background measurement value is c BG = 238.12.
Using this calibration Fig. 8 shows the comparison of the particle size distributions averaged over all flights of SOCRATES for both ice (red) and droplets (blue). It can be seen that the size distribution based on the images (solid lines) agrees well with the size distribution based on the angular light scattering functions (dotted lines). Due to the the facts that the scattering laser of PHIPS has Gaussian intensity profiles and the field of view of the trigger optics shows gradual detection boundaries, A sens is expected to be size dependent with a larger sensing area for larger particle sizes. Moreover, as (aspherical) ice particles usually have different differential scattering cross sections compared to (spherical) droplets, especially in side scattering directions where the trigger optics is located, A sens is expected to be dependent also on 15 the phase of the cloud particles. Therefore, we simulated the size dependence of A sens for spherical and aspherical particles 14 https://doi.org/10.5194/amt-2020-297 Preprint. Discussion started: 29 September 2020 c Author(s) 2020. CC BY 4.0 License. separately using the optical engineering software FRED (Photon Engineering, LLC, USA), which combines light propagation by optical raytracing simulations with 3D computer aided design (CAD) visualization.
For the FRED simulations, the actual PHIPS trigger optics and 3D laser intensity distribution were reconstructed in the 3D CAD environment of the software resulting in the actual intensity field the particle is exposed to when penetrating the sensitive area of the instrument. Particles were step-wise positioned at different x,y and z position across the trigger field of 5 view and depth of field to get a map of the scattered light intensity that reaches the sensitive area of trigger detector. Similar to the actual measurement, a threshold value for the simulated detector intensity was used that would trigger the system and, therefore, defines A sens . This threshold was deduced by mapping the sensitive area of the instrument in the laboratory using a piezo-driven droplet dispenser which generates single 80 µm diameter water droplets . Equating A sens from the laboratory mapping with A sens for the corresponding 80 µm FRED simulation then defined the threshold value that 10 has to be used for all FRED simulations to calculate the size dependence A sens .
The FRED simulations were performed for spherical particles with the refractive index of supercooled liquid water (n = 1.3362 + i1.82 × 10 −9 ) and the three sizes 80 µm, 300 µm and 600 µm. The resulting A sens are shown in Fig. 9 in grey color.
Additionally, to validate the method, A sens was also estimated using Mie Theory to calculate the differential scattering cross section for the trigger direction and multiplying the results with the actual intensity field as defined by the FRED simulations.

15
Although Mie calculations are faster to conduct, these calculations have the disadvantage that they assume a dimensionless particle, which induces uncertainties at the boundaries of the trigger field of view. Yet, the FRED simulations compare reasonably well with the results of the Mie calculations.
Ice particles were simulated roughened spheres whose surface light scattering was defined by the ABg Model (Pfisterer (2014)). A refractive index of n = 1.3118 + i2.54 × 10 −9 , Warren (1984)) was used for the ice simulations. The roughened ice 20 sphere approach was chosen here to avoid computationally expensive orientation averaging, which was necessary in case of using a non-spherical particle habit. The FRED simulations for ice particles were conducted for the five particle sizes 80 µm, 150 µm, 300 µm, 450 µm and 600 µm. As can be seen in Fig. 9, the A sens values for ice are significantly larger than those for water droplets of the same diameter. An exponential function was fitted to the FRED results to get A sens as a function of particle diameter. These functional dependencies are then used to calculate the volume sampling rate that is required to convert 25 the single particle data to particle size distributions.

Correction for Shattering Artefacts
One major source of uncertainty for wing mounted probes is shattering of ice particles on the instrument's outer mechanical structures or breakup of particles in the instrument inlet. An example of the shattering of a large particle and breaking up of aggregates in the inlet flow field can be found in the supplementary material (S5). Shattering can lead to a significant 30 overcounting of ice particles (e.g. up to a factor of 5 using a fast forward scattering spectrometer probe (FSSP), Field et al. (2003)) and a bias in the particle size distribution towards smaller sizes. Here, we characterized the frequency of shattering events in the SOCRATES data set and present a method to detect shattering events within the PHIPS data sets. Even though the geometry of PHIPS was designed to minimize disturbances and turbulences in the instrument (e.g. sharp edges at the front of the inlet and an expanding diameter of the flow tube towards the detection volume (see Abdelmonem et al. (2016)), shattering can still be an issue, especially in clouds where large cloud particles and aggregates with D > 1 mm are present.
Since the field of view of the camera telescope assembly (CTA) is much larger (typically 1.5 × 1 mm) compared to the sensitive trigger area (see previous section), the stereo micrographs can be used to detect shattering events. However, as only a subset of detected particles is imaged, a shattering correction based on inspection of the stereo micrographs is not a practical 5 and reliable solution. Still, manual examination of the stereo micrographs can be helpful to determine whether or not a a cloud segment was affected by shattering in individual cases.

Interarrival Time Analysis
The most common method to detect shattering that is based on the analysis of particle interarrival times Field et al. (2003). If two (or more) particles are detected in very short succession, those particles are identified as shattering fragments and removed. 10 Fig. 10 shows a histogram of interarrival times (τ ) of ice particles (left) and droplets (right) measured during two flights of SOCRATES. For ice, it is apparent, that the otherwise approximately log-normal distributed interarrival times show a second, lower mode below τ ≤ 0.5 ms (equivalent to spatial separation of ≤ 10 cm, assuming a relative air speed of v = 200 ms −1 ) that is likely caused by shattering. For droplets, the second mode is not visible, since droplets tend to less fragment when entering the instrument inlet.

15
Whereas the interarrival time analysis method is used in multiple optical array probes (2DS, 2DC, Field et al. (2003)), the application is limited for single-particle instruments, like PHIPS, due to their small sensitive area. Near the detection volume, the inlet has a diameter of 32 mm, whereas the sensitive area measures only about 0.7 mm (depending on phase and size, as discussed in 4.2), which means that the probability to detect two (or more) fragments of the same shattering event is very low. Furthermore, the instrument has a dead time of t = 12 µs after each trigger event . Shattering fragments 20 that pass during this time, are not detected. As shown in Fig.10, only a small percentage of the particles whose images were manually classified as shattering (red), could be identified as shattering using the interarrival time analysis method. Hence it can be concluded, that interarrival time analysis alone is not fit as a reliable shattering flag, either. Nevertheless, all particles with a low interarrival time τ ≤ 0.5 ms are removed and excluded from the analysis. In the next section, a shattering flag is introduced, that flags segments which are affected by particle shattering, so they can be excluded from further analysis.

Shattering Flag based on the Presence of large Particles
It is known, that a particles shattering probability is strongly size dependent. Large particles and aggregates are much more prone to shattering compared to small particles. To overcome the limitation of the interarrival time method to eliminate shattered particles, we introduce a shattering flag based on the presence of large particles. Fig. 11a shows the total number concentration of particles in the size overlap region of PHIPS and 2DS (200 µm ≤ D ≤ 500 µm) for all SOCRATES flights. The data is 30 averaged over 30s segments. Only segments with N 2DS, overlap ≥ 0.5 L −1 are taken into account. The colour-code indicates the fraction of 2DS particles in the size range of D max ≥ 200 µm that are larger than 800 µm. The diagonal lines mark the median ratio between N PHIPS /N 2DS of each colour. Fig. 11b shows the correlation of the difference between PHIPS and 2DS in the Comparison of the interarrival times of all particles (blue) and only particles whose images were manually classified as shattering events (red). The red vertical line marks the τ ≤ 0.5 ms threshold. overlap region and the ratio of large particles. It can be seen, that the two probes agree very well in segments with only a few large particles.
In segments that consist of more than 10% large particles, PHIPS and 2DS tend to disagree and PHIPS can overestimate particle concentrations up to a factor > 10. This can be explained by the shattering of large particles on the instrument inlet tip or wall or disaggregation of large aggregates due to shear forces in the inlet flow. Therefore, said marker for the presence of 5 large particles will be used as a shattering flag to mark cloud segments that are potentially affected by shattering. In segments where the 2DS did not detect any particles or was not measuring, for any reason, 2DC data is used instead. That means, cloud segments with more than 10% large particles are removed for future analysis. For the SOCRATES data set, 44% of all 1s segments are flagged as shattering. This means that about half of all 30s segments in mixed-phase clouds and approximately 75% of pure ice clouds are removed. Droplet dominated cloud segments are not affected by this shattering flag.

Case Studies
In this section, the above presented methods are applied for three representative case studies from the SOCRATES campaign in altitudes below 2000m, one purely liquid cloud and two mixed-phase clouds. The results are then compared to the measurements of other instruments from the same flights.  The trigger threshold of PHIPS was set in a way that the instrument started to trigger on droplets with diameters larger than 50 µm. This remained unchanged over the whole campaign. The stereo micrographs from this flight segment (Fig.12c)   The PSD has a maximum at around 15 µm and the maximum particle sizes are found at 300 µm. All the PSDs agree well with each other. Information on the phase on the largest particles can be acquired from the PHIPS ASF measurements. The phase discrimination algorithm classified every particle in the presented segment as droplet, which is in agreement with the stereo micrographs. This shows, that this cloud, despite the low temperature and the particle sizes up to 300 µm, consists purely of 5 supercooled liquid droplets.

Case Study 2 -Heterogeneous Mixed-Phase Cloud
Low-level mixed-phase clouds were investigated during SOCRATES research flight RF07 on January 31st, 2018. During that flight, the G-V sampled clouds south-east from Hobart, including an overpass over Macquarie island. The aircraft flew at cruising altitude towards the most southward point, where it descended down to lower altitude, probing multiple thin and persistent supercooled and mixed-phase clouds on its way back to Hobart. Fig. 13a shows a cloud segment at around -58 • N, 162 • E, shortly after the turnaround at the most southward point. The cloud was probed in an altitude of 1,800 m at a temperature of about -10 • C. The vertical wind velocity was slightly below zero and the relative humidity with respect to ice averaged about 107%. The maximum of the CDP LWC was 0.5 g L −1 and the 5 maximum of the 2DS TWC was 2 g L −1 . Fig. 13b shows the PSDs between 04:16:40 and 04:21:00 UTC. The PSD has a maximum at 15 µm and the maximum particle sizes are found at 700 µm. All the probes agree well. Based on the PHIPS phase information, the whole segment can be divided in two sub-segments. Until 04:19:30 PHIPS detects only supercooled liquid droplets, after that only ice particles. This is backed up by PHIPS' representative stereo micrographs from the two sub-segments. In the first sub-segment, Fig. 13c 10 shows supercooled drizzle droplets with diameters from 50-200 µm similar to the pure liquid case. During the second subsegment Fig. 13d shows irregular and columnar ice crystals with sizes from 100-500 µm, some of which appear to be rimed or faceted. This coincides with the high reflectivity area measured by the HCR (lower panel in Fig. 13a) and the decrease in LWC measured by the CDP . No ice particles were present on stereo micrographs taken during the first sub-segment and no droplets during the second, respectively. Fig. 14a shows a low-level mixed-phase cloud of SOCRATES research flight RF08 on February 4th, 2018. Due to a low pressure system south of Tasmania, cold air was expected advecting north from the Antarctic. During this flight, the aircraft flew straight southwards from Hobart. After turning back at the most southward point, the flight path back to Hobart was alternating between a "saw-tooth" pattern (going up and down through the clouds) and a "staircase" pattern (10 minutes above 20 the cloud, then 10 minutes inside the cloud and 10 minutes below, as explained previously).

Case Study 3 -Ice dominated Mixed-Phase Cloud
The presented case study shows one segment during the ascend of the final saw-tooth leg around -51 • N, 147 • E in a thin mixed-phase cloud in the Hallet-Mossop temperature regime (Hallet and Mossop (1974)). The cloud was approximately 700 m thick and the temperature within the cloud ranged between -5 • C at cloud base at 700 m and 0 • C at the cloud top at 1400 m.
The vertical wind velocity was fluctuating around zero and the relative humidity with respect to ice was between 80 and 100%.

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The maximum of the CDP LWC was 0.5 g L −1 and the 2DS TWC was 3 g L −1 . Fig. 14b shows the PSDs between 05:13:10 and 05:15:35 UTC. The PSD has a maximum at 15 µm and the maximum particle sizes are found at up to 800 µm. Again, all three probes agree well. Contrary to the previous case, the stereo micrographs in Fig. 14c+d are almost exclusively ice crystals. The sizes range from 20 µm to 500 µm. Observed ice crystal habits throughout the cloud were mostly needles with some hollow columns and small irregulars -all with different degrees of surface roughness 30 and riming. Also, a few supercooled droplets were present. The presence of supercooled droplets is also confirmed by the scattering measurements. This shows, that our method is also able to detect and correctly classify single large supercooled drizzle droplets in mixed-phase clouds which are otherwise dominated by ice in that size range.

Conclusions
A major challenge in the observations of mixed-phase clouds remains the phase discrimination of cloud droplets and ice crystals. Especially, in the size range of D <100 µm, reliable phase discrimination of cloud particles has been proven difficult.
Here, we present a new method to derive the phase of single cloud particles using their angular light scattering information.
ASFs of single cloud particles were measured with the airborne PHIPS probe. We identified four features in the particle light 5 scattering function that were used for estimating the probability for the particle to be spherical or aspherical. The method was calibrated with a data set of 9.738 manually classified cloud particles and tested against a data set of 12.220 manually classified particles from two different aircraft campaigns. This yields a confidence rate above 98%. Further, we have shown that the phase discrimination algorithm is functioning independently of the experimental data set used for the calibration, so no further calibration is needed for upcoming future campaigns.

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Additionally, we presented a method to derive PSDs based on single particle scattering data for particles in a size range from 100 µm ≤ D ≤ 700 µm and 20 µm ≤ D ≤ 700 µm for droplets and ice particles, respectively. The newly developed data analysis 21 https://doi.org/10.5194/amt-2020-297 Preprint. Discussion started: 29 September 2020 c Author(s) 2020. CC BY 4.0 License. algorithms were applied to three case studies that did not show the presence of large (>1 mm) ice crystals. Comparison of the PSDs from other instruments showed a good agreement. The presented case studies show, that PHIPS can provide unique and detailed insight about the phase composition of clouds, where phase discrimination based solely on particle size or aspect ratio could potentially be difficult, such as e.g. in mixed-phase cloud conditions where large droplets and small ice crystals coexist.
With these methods available, PHIPS can provide additional information on the microphysical properties of mixed-phase 5 clouds in situations, where the data is not affected by shattering. We have also shown that phase discrimination based on single-particle angular light scattering behaviour is a robust method, which could be implemented in future cloud research instrumentation.
Code availability. The code used for the phase discrimination and particle sizing algorithms in this paper is written in MATLAB and is available upon request from the authors.    Since the Gaussian distributions are of similar width σ, the corresponding discrimination probabilities (Fig. 4, lower panels), defined as can be approximated by a sigmoid function of the form 10 The corresponding fit parameters are shown in Tab. A2. In section 3.3 we have argued, that one feature alone is not sufficient to reliably classify all cloud particles, due to the particles that lie in the overlap between the two peaks in Fig. 4. Now the question is, how dependent the four features are and whether 27 https://doi.org/10.5194/amt-2020-297 Preprint. Discussion started: 29 September 2020 c Author(s) 2020. CC BY 4.0 License.
or not a particle, that cannot be confidently (or is even falsely) classified by e.g. f 3 , i.e. that lies in the overlap of the feature space, can be confidently classified by the other feature parameters or if it lies in the overlap for the other features as well. Figure B1a shows the correlation of the classification confidence based on only one feature parameters f 3 and of the combined result for all 4 features for all manual classified ice particles of the ACLOUD campaign. It can be seen, that lots of particles that cannot be classified with high confidence by the first feature (P (f 3 ) < 66%) are classified with high confidence  lines mark the confidence limits. P (f ) > 66% corresponds to particles, that are classified correctly with high confidence, 33 < P (f ) ≤ 66% means the classification is uncertain and particles with P (f ) ≤ 33% are classified falsely as droplets with high confidence. b) shows the corresponding statistics of the plot in a confusion matrix. The squares correspond to the dashed lines in a).