The Two-Dimensional Stereoscopic probe (2D-S), manufactured by Stratton Park Engineering Company Inc. (SPEC), was the principal cloud instrument used for determining ice crystal size distributions during M-Phase. The 2D-S is an optical array probe (OAP) capable of providing information on the concentration, size and phase of cloud particles. The instrument comprises two identical orthogonal channels consisting of two laser beams that cross in the middle of the probe's sample volume (total of ∼ 16 L s⁻¹ at an airspeed of 100 m s⁻¹) and illuminate horizontally- and vertically-oriented 128-photodiode arrays. Shadows are produced on the arrays by particles of diameter (Dp) in the size range 10 to 1280 µm passing through either or both laser beams; images of these particles, with an effective pixel resolution of 10 µm, are built up over sequential time steps (Lawson et al., 2006). Note, particles were excluded from the analysis if their entire shadow was not contained within the photodiode array edges, thus reducing the effective sample volume for larger particles not meeting this requirement.

Raw data from the 2D-S probe was processed using the Optical Array Shadow Imaging Software (OASIS), developed by the National Centre for Atmospheric Science (NCAS) and Droplet Measurement Technologies (DMT) (Crosier et al., 2011). A threshold number of 10 µm pixels is set in the OASIS software, defining the minimum particle size accepted for further analysis. Dp describes a particle's maximum dimension length, therefore in this study, particles consisting of 20 pixels (i.e. a particle with Dp as small as 50 µm comprising 4 × 5 pixels) or less were initially excluded, given previously reported large uncertainties determining both the size (up to 50 %) and concentration (up to 100 %) of particles with Dp < 50 µm (Baumgardner and Korolev, 1997; Baumgardner et al., 2017). However, initial analysis of 2D-S particle size distributions for M-Phase revealed systematically high concentrations of ice between sizes of 50 and 100 µm across all flights, including those that captured strong evidence of recently active SIP processes (e.g. C328 and C329) and those showing negligible evidence of ice multiplication (e.g. C330 and C331) (Fig. A1 in Appendix A); this is consistent with results from early 2D-S testing by Lawson et al. (2006), in which measurements of particles of size less than 100 µm were found likely to be contaminated with out-of-focus liquid droplets erroneously identified as ice crystals. Therefore, for this work, further filtering of the 2D-S data was carried out, with only particles of Dp > 100 µm considered in the analysis; Baumgardner et al. (2017) reported reduced uncertainties of ∼ 20 % and ∼ 50 % for the size and concentration of ice crystals larger than 100 µm, decreasing further as particle size increases.

Further processing of the 2D-S data using the OASIS software included a correction for out-of-focus particles (Korolev, 2007) and application of an inter-arrival time algorithm, which removes particles with very short inter-arrival times indicative of ice crystal fragments potentially formed by shattering on the instrument (Field et al., 2006). Furthermore, following Crosier et al. (2011), discrimination was made between irregular and spherical particles based on geometric analysis of their circularity, C, according to Eq. (1): 1C=P24πA, where P is the particle perimeter and A is its area. Particle circularities were grouped into three categories: low irregular (LI), medium irregular (MI), and high irregular (HI). Particles with C < 1.2 are classified as LI; visual inspection of the corresponding 2D-S imagery confirmed that they were almost exclusively liquid droplets. Circularities greater than 1.4 are assigned to the HI category; from analysis of the particle imagery we concluded they were predominantly ice crystals. MI particles are defined as those with circularities between 1.2 and 1.4. Interpreting the phase of MI particles was a more complex task as the bulk of the images resembled aspherical ice crystals, often indicative of newly frozen drops; however, many poorly imaged liquid droplets were also likely defined as MI instead of LI. Moreover, the mean ratio of HI to MI particles during M-Phase was ∼ 10; therefore, even if, on average, some fraction of MI particles were ice crystals, the ice number concentration in the MI category would be substantially less than 10 % of the HI particle concentration. Thus, for this study, we assume the HI category alone is an accurate proxy for all ice crystals measured by the 2D-S probe. It should be noted that by (a) assuming all observed ice crystals were categorised as HI, and (b) excluding all particles with Dp < 100 µm, the ice crystal number concentrations reported in this study are likely to be slight underestimations of the true values.

In the past, measurements from aircraft-mounted cloud instruments have been subject to shattering artefacts as ice crystals collide with the probe tips (Heymsfield, 2007). For this flight campaign, the instrument was fitted with Korolev anti-shatter tips, or K-tips, designed to reduce particle-shattering artefacts by minimising inlet surface area and any inefficient heating that may cause ice to accumulate on the probe exterior (Korolev et al., 2013).

We use high time resolution 2D-S data (1 Hz); longer data averaging periods (e.g. 5 or 10 s) have previously been shown to provide a more statistically significant measurement (McFarquhar et al., 2007), but 1 Hz data enables us to better characterise fine-scale cloud structure and capture the expected large spatial variability in mixed-phase cloud ice and water contents (Huang et al., 2021; Wang et al., 2023). At an airspeed of 100 m s⁻¹, the minimum detectable ice concentration for each channel of the 2D-S is ∼ 0.12 L⁻¹ in a 1 s interval. Additionally, particle images can be captured at rates of up to 74 frames per second (Finney et al., 2024); therefore, the high sampling rate and spatial resolution of imagery measurable by the 2D-S enables the identification of cloud regions containing high concentrations of small ice crystals where SIP processes are most likely to be active (Lawson et al., 2006).

Larger ice crystals, including graupel and other precipitation-sized particles were identified in this study using the High Volume Precipitation Spectrometer Version 3 (HVPS-3, SPEC Inc.). The HVPS is a single array, two-dimensional shadow probe that functions similarly to the 2D-S, but its optics are configured to capture particle images at 150 µm resolution in the size range 150 µm < Dp < 19.2 mm. At an airspeed of 100 m s⁻¹, the sample volume is 310 L s⁻¹ (note, as with the 2D-S probe, sample volume is particle-size dependent), resulting in a minimal detectable ice concentration of ∼ 0.003 L⁻¹ at 1 Hz time resolution. Previous studies have found that ice fragments with Dp < 600 µm can be readily generated from larger crystals breaking up on impact with the HVPS probe arms, leading to the erroneous inclusion of small ice shattering artefacts in ice concentration measurements (Korolev and Isaac, 2005; Glienke and Mei, 2020; Wang et al., 2023); therefore, only particles observed by the HVPS with Dp > 600 µm were considered for this work.

Total ice concentrations were determined as the sum of HI particles observed by the 2D-S (100 < Dp < 1280 µm) and all particles measured by the HVPS outside of the particle size overlap with the 2D-S (Dp > 1280 µm); particles observed by the HVPS with Dp between 600 and 1280 µm were included if the number concentration was below the 2D-S detection limit (∼ 0.12 L⁻¹).

High-resolution images of cloud hydrometeors were captured with the 3 View-Cloud Particle Imager (3V-CPI, SPEC Inc.), providing detailed information on in-cloud liquid-ice phase partitioning and enabling more refined ice crystal habit discrimination between active SIP and neighbouring aged, background ice regions. The 3V-CPI instrument comprises a 2D-S probe integrated with a Cloud Particle Imager (CPI, SPEC Inc.). The CPI is capable of imaging and counting liquid or ice particles (15 µm < Dp < 2500 µm) at a pixel resolution of 2.3 µm, with a sample volume of ∼ 0.37 L at an airspeed of 100 m s⁻¹ (Finney et al., 2024). Hydrometeors passing down its sample tube are captured via a three-laser system. Firstly, the 2D-S, operating as in the stand-alone instrument (Sect. 2.1.1), illuminates the particles that pass down the inlet tube on-axis through the sample volumes of its two orthogonal (continuous) laser beams, located in the laser crossover region, and the scattered light is projected onto two separate diode-array detectors. When a signal is recorded simultaneously by both detectors, an imaging laser is triggered, which illuminates the particles in the CPI sample area and the instrument's imaging optics focus this light onto a high-resolution 256 grey-scale fast CCD camera to record an image of the liquid droplet or ice crystal.

Analysis of the 2D-S shadowgraphs, alongside the higher resolution CPI imagery, enables detailed characterisation of ice crystal shapes and habits, thus assisting with understanding ice crystal generation and growth processes; this is critical for identifying active SIP mechanisms (Korolev and Leisner, 2020).

In Sect. 3.1, we showed that peak ice crystal number concentrations during M-Phase, exceeding expected INP concentrations at the same temperature by more than four orders of magnitude, were observed in the active temperature range for the H–M process. These well-glaciated cloud regions were found predominantly in the convective CAO regime, which was characterised by a high frequency of moderate updrafts and a strong supply of large, supercooled liquid droplets; such conditions have been determined by previous airborne studies to be conducive to the H–M process in shallow, mixed-phase clouds (Hou et al., 2021; Huang et al., 2021).

Figures 5 to 11 focus on flights C328 and C329, which took place on 31 October and 1 November 2022, respectively. Both flights sampled convective cloud regions of CAOs (C328 sampled the stratiform-to-convective regime transition) at relatively warm temperatures, within the active H–M range, and measured the highest Nice during the campaign (Fig. 5). The ice particle size distribution (PSD) during C328 peaked between -9 and -11 °C across a narrow diameter range between 150 and 300 µm (Fig. 5a); high concentrations of small ice particles were frequently observed at temperatures a few degrees below the H–M range during the campaign and are likely related to secondary ice particles formed at lower in-cloud altitudes that have mixed upwards in convective updrafts to the point of observation. A broader size distribution peak was observed during C329, between 200 and 500 µm (Fig. 5b), at slightly warmer in-cloud temperatures (∼ -6 to -9 °C). The larger ice crystals observed during C329 may have been generated in an older SIP cell elsewhere in the cloud, before growing and evolving whilst travelling to the measurement point via advection or turbulent mixing, or by precipitating down from a higher altitude. Results from early laboratory-based work (Ryan et al., 1976) and more recent innovative cloud seeding experiments (Fuchs et al., 2025) investigating depositional ice crystal growth rates in mixed-phase clouds indicate that at temperatures within the active H–M range, assuming linear growth over time, newly generated ice columns will grow to lengths exceeding 200 µm in around 5 min (at ∼ -5 °C) to 15 min (at ∼ -8 °C). This growth time is comparable with the convective overturning timescale in these CAO clouds; at an updraft speed of ∼ 1 m s⁻¹, air would mix over a cloud depth of ∼ 1 km in around 15 min. Therefore, some of the ice crystals observed near cloud top during C329, for example, may have formed closer to cloud base under slightly different environmental conditions, limiting how confidently we can directly link all ice production to the conditions at the point of observation.

Time series of selected cloud microphysical properties (10 s averages) measured during flight C328 are shown in Fig. 6; 10 s averages are shown here to reduce the noise present in the 1 Hz data, so that in-cloud features are more clearly visible. Stratiform cloud was sampled from approximately 15:24 to 16:15 UTC; however, this was initially non-continuous, partially broken cloud (until ∼ 15:51 UTC), likely not part of the main north-westerly CAO flow, as evidenced by the satellite imagery in Fig. 2a. Cloud droplet number concentrations and LWC values measured during the sawtooth profiles conducted between 15:51 and 16:15 UTC were relatively consistent, peaking at ∼ 30–50 cm⁻³ and ∼ 0.2–0.4 g m⁻³, respectively, upon each entry into the shallow stratus cloud layer (Fig. 6). After the regime transition into broken convective cloud (16:15 to 16:35 UTC), cloud droplet concentrations decreased and glaciation levels increased significantly, with mean μ3 values reaching ∼ 0.7 in each sampled cumulus cloud segment (Fig. 6d).

Periods of active, or recently active, SIP processes (red-shaded regions in Fig. 6) were inferred from episodes of elevated ice concentrations that coincided with clear evidence of ice crystal fragmentation or splintering from manual inspection of 2D-S and CPI imagery. Neighbouring regions of lower “background” ice concentrations, where the ice particle imagery contained minimal evidence of SIP activity, are shaded in blue; although SIP does not appear to be active in these regions, measured background ice concentrations were still well above the NINP at the relevant local cloud temperature and therefore likely contain some amount of aged secondary ice, originating elsewhere in the cloud, or primary particles that have sedimented down from near cloud top. Alternatively, background ice concentrations that exceed expected NINP could be driven by some degree of spatial inhomogeneity in the INP population within the same air mass of a particular CAO event; however, it's important to note that throughout the entire campaign, NINP at any given in-cloud temperature varies by less than an order of magnitude across all upwind and below/above-cloud filter measurement legs during CAO flights (Fig. 3). As such, it is highly unlikely that spatial variability in aerosol source, and thus NINP, rather than ice multiplication processes, was the primary driver of Nice variability of up to 2–3 orders of magnitude during SIP periods (Fig. 6).

During C328, Nice across SIP regions varied from 2.0 L⁻¹ (5th percentile) to 324.9 L⁻¹ (95th percentile), with a mean of 110.7 L⁻¹. In contrast, ice particle concentrations measured across adjacent background regions were ∼ 1–2 orders of magnitude lower. As Nice was above the corresponding NINP at all temperatures (where INP measurements were above the detection limit) during C328 (Fig. 5a), secondary ice was likely mixed throughout the full sampled cloud region; our aim here was to establish the in-cloud properties (e.g. temperature, cloud droplet concentration or ice mass fraction) characterising the identified SIP periods (Fig. 6) in order to understand why ice multiplication had more recently initiated here versus nearby background regions.

SIP period 1 (hereafter, SIP 1), between 16:27:00 and 16:29:45 UTC, is marked in Fig. 6 and spanned the full vertical extent of a sampled cumulus cloud segment with cloud base and cloud top heights of ∼ 1100 and ∼ 2075 m, respectively; the corresponding cloud base and top temperatures were ∼ -4.5 and ∼ -12.2 °C, respectively. SIP 1 contained the highest measured ice concentrations across all SIP periods sampled during M-Phase, with a mean value of 154.3 L⁻¹ (1 Hz data); 40 % of the ice particles detected during this period had a diameter of less than 200 µm, suggesting ice multiplication processes were recently active. The mean in-cloud temperature during SIP 1 was -8.5 °C (∼ 40 % of measured temperatures were within the H–M zone) and conditions were mixed-phase (μ3‾ = 0.66), with a strong supply of supercooled liquid droplets of diameter greater than 24 µm (N‾droplets>24µm = 8.5 cm⁻³); therefore, the environmental conditions were favourable for the H–M process to occur.

Figure 7a shows a sequence of CPI images of cloud particles (liquid droplets and ice crystals) from SIP 1. Ice particles observed within this cloud segment were predominantly small, faceted columns of length between 100 and 200 µm (red frames). The local in-cloud temperature during SIP 1 was within the range for columnar growth (∼ -4 to -10 °C), therefore these small ice crystals likely originated via SIP processes nearby, before growing by vapour deposition whilst in transit to the measurement location. Aged ice particles observed during this period were mainly longer columns or needles (300 µm < Dp < 600 µm) (pink frames), some of which had undergone visible riming (green frames). This riming was facilitated by the high concentrations of supercooled liquid droplets present during SIP 1 (N‾droplets = 17.2 cm⁻³), with those of diameter greater than 24 µm comprising nearly half of all droplets observed throughout this period (Fig. 7c); a few larger, drizzle-sized drops with Dp > 100 µm were captured by the CPI probe and are shown in Fig. 7a. The 2D-S imagery (Fig. 7b) captured during SIP 1 shows rapid transitions in ice crystal morphology between large, heavily rimed particles or graupel and regions dominated by small columns or splinters (red frame), consistent with the activation of the H–M process.

A small subset of the CPI images of droplets from SIP 1 have distorted shapes with bulges (black frames) indicating they had frozen or were undergoing freezing at the time of observation (Korolev et al., 2020). Some of these images have small spicule-like regions protruding from the frozen droplet surface, indicative of jetting following the build-up of internal pressure and subsequent cracking of the droplet's freezing outer shell (Lauber et al., 2018); sharp fragments of shattered frozen drops are also highlighted in Fig. 7a (black frames). Examples of frozen droplets, some with adjacent shattered fragments, were also captured by the 2D-S (Fig. 7b; black frame).

In summary, the cloud microphysical properties, environmental conditions and ice crystal habits observed during SIP 1 are consistent with those expected for active rime splintering; however, it is possible that other mechanisms, such as the fragmentation of freezing droplets, were acting concurrently to help amplify in-cloud ice concentrations and produce the large ice enhancements observed within this cumulus cloud segment.

Figure 8 presents average composite size distributions of ice particles measured by the 2D-S and HVPS probes in SIP 1, an additional SIP period (SIP 2) and across both background ice periods during flight C328; all are marked in Fig. 6. SIP 1 was dominated by ice particles of size between 200 and 250 µm, corresponding to the small columnar crystals shown in Fig. 7, possibly originating from the H–M process as previously discussed. In contrast, SIP 2 (N‾ice = 32.3 L⁻¹) was mainly populated by larger ice crystals (300 µm < Dp < 500 µm), with a maximum particle size of ∼ 6 mm. The CPI images captured during SIP 2 (Fig. C2 in Appendix C) show predominantly plate-like crystals (red frames), both hexagonal and sectored. The mean measured in-cloud temperature during SIP 2 was -9.5 °C, generally warmer than plate-growth conditions (-12 to -18 °C), therefore these ice particles may have formed at higher in-cloud altitudes before sedimenting or mixing down to the measurement point. The background ice size distribution has a small peak around 300 µm (Fig. 8), as with SIP 2, likely indicative of contributions from both primary ice and a small amount of aged secondary ice particles, similar to those populating SIP 2.

SIP 2 occurred in a cumulus segment adjacent to SIP 1, with similar in-cloud temperatures; however, unlike in SIP 1, SIP 2 contained little evidence that the H–M process was active, with few observations of small columnar ice, or larger rimed crystals (Fig. C2), and very low supercooled liquid droplet concentrations (Fig. 6c). Given most of the observed ice crystals likely formed a considerable distance away from the measurement location, before growing over time to their observed final state, it is difficult to surmise the mechanisms responsible for their origins; although, there are several examples of distorted droplets, jetting and fragments of shattered drops in the CPI imagery (Fig. C2), indicative of some contribution from frozen droplet fragmentation. SIP 2 is likely an example of an old ice multiplication cell, within which SIP activity has accelerated liquid depletion via the WBF process and riming, quickly generating an almost fully glaciated (maximum μ3 value of 0.91) and precipitating cloud region.

Figure 9 shows time series of selected cloud microphysical properties measured during flight C329; all sampled cloud segments were part of the convective CAO regime. Ice multiplication activity was detected more frequently here than during any other M-Phase flight, with 35 % of in-cloud measurements made within identified SIP periods. The mean ice particle concentration measured across SIP regions during C329 was 36.2 L⁻¹, varying from 1.5 L⁻¹ (5th percentile) up to 101.6 L⁻¹ (95th percentile).

SIP periods 3 (SIP 3) and 4 (SIP 4) were sampled from 13:26:45 to 13:29:18 UTC and 14:11:25 to 14:13:03 UTC, respectively, and are marked in Fig. 9a. Measured in-cloud temperatures during both periods were well within the active range for the H–M process, ranging from -7.4 to -3.2 °C during the descending sawtooth leg in SIP 3, and across the SLR in SIP 4 the mean temperature was -6.2 °C.

Maximum measured 1 Hz ice concentrations were 95.2 L⁻¹ in SIP 3 and 145.5 L⁻¹ in SIP 4, with 12 % and 24 % of ice crystals observed during SIP 3 and SIP 4, respectively, having a diameter of less than 200 µm, indicating ice multiplication processes were likely active. This is reflected in the size distributions presented in Fig. 11, peaking between ice particle diameters of 250 and 350 µm for both SIP periods. The PSD for all background ice regions peaks at larger sizes of between 400 and 500 µm, indicative of more significant particle ageing relative to the neighbouring SIP regions.

The levels of glaciation of both cloud regions sampled during SIP 3 and SIP 4 were substantially different; the mean μ3 during SIP 3 (0.83) was more than double that during SIP 4 (0.37), reflected by much higher supercooled liquid droplet concentrations in SIP 4 (N‾droplets = 23.9 cm⁻³) compared to SIP 3 (N‾droplets = 9.3 cm⁻³). In several previous in-situ observational studies, a strong liquid water presence has been considered a pre-requisite for the initiation of SIP processes (Lawson et al., 2017; Huang et al., 2022; Waitz et al., 2022); however, as discussed in Korolev et al. (2020), a lack of liquid droplets observed within a region of apparent SIP activity, such as SIP 3, may be explained by their evaporation due to the WBF process as well as significant riming prior to the cloud region arriving at the measurement point. Indeed, the CPI images presented in Fig. 10a indicate that riming was prevalent in SIP 3, with several examples of heavily rimed columns or plates (green frames); examples of droplets freezing on contact with large ice particles are also shown (black frames). The CPI imagery from SIP 3 also contains an abundance of small columns, some hollow (red frames), with Dp between 60 and 200 µm; this, in addition to the well-mixed regions of splinters, small columns and heavily rimed graupel particles shown in the 2D-S imagery (Fig. 10b) suggests the H–M process was active during SIP 3. Furthermore, the maximum ice particle size in SIP 3, measured with the HVPS probe, was ∼ 7 mm, compared to ∼ 3 mm in SIP 4 (Fig. 11), implying that the cloud segment sampled during SIP 3 was a more mature convective cell, within which the H–M process is known to operate particularly efficiently (Yang et al., 2020).

The CPI and 2D-S images captured during SIP 4 (Fig. C3 in Appendix C) are similarly consistent with the H–M process being active and primarily responsible for the high ice concentration measurements; large, well-rimed columns, liquid droplets with Dp > 24 µm and small columns were all present within this cumulus cloud segment. Additionally, as SIP 4 was sampled during a constant altitude, SLR flight leg, we can look at how in-cloud turbulence may have affected ice multiplication; the mean vertical wind speed measured during SIP 4 was +0.94 ± 0.09 m s⁻¹, with a maximum value of +3.29 m s⁻¹, indicating updraft conditions dominated. It is well-documented that convective updrafts help provide favourable conditions for SIP processes by creating a more saturated environment for cloud droplet generation and growth (Hou et al., 2021; Qu et al., 2022; Wang et al., 2023).

The importance of large, supercooled liquid droplets in initiating SIP, and the H–M process in particular, is further emphasised by the cloud droplet size distributions shown in Fig. 12. Concentrations of droplets with diameter greater than ∼ 30 µm were substantially higher when averaged across SIP periods compared to neighbouring background ice regions during both flights C328 and C329 (Fig. 12). Interestingly, although there was clearly a strong presence of small liquid droplets (Dp < 12 µm) across SIP regions, consistent with the early experiments of Mossop (1978), their concentrations were generally higher across background ice regions. This suggests that certain mechanistic hypotheses for the H–M process may place too much importance on the role played by small droplets, such as that proposed by Choularton et al. (1980) regarding the symmetrical freezing and shattering of large droplets that impact regions of graupel particles where rime spires comprising small droplets have grown.

In this section, we explore the extent to which ice multiplication via the H–M process alone can account for the ice crystal enhancements measured during M-Phase. A splinter production rate (see Sect. 2.6) was estimated for each of the stratiform and convective cloud segments sampled throughout the campaign which had in-cloud temperatures falling within the H–M range, following Willis and Hallett (1991). As described in Sect. 2.6, our estimated rate of production of new ice crystals due to rime splintering, based on the assumption of gravitational collection of droplets by graupel particles, depends on in-situ measurements of graupel number concentration (ice crystals larger than 300 µm), graupel diameter and the concentration of liquid droplets with Dp > 24 µm; note, unlike the other commonly implemented splinter production rate formula derived by Harris-Hobbs and Cooper (1987), small liquid droplets (Dp < 12 µm) are not considered here. The Harris-Hobbs and Cooper (1987) calculation, used by Crosier et al. (2011) and Taylor et al. (2016), is based on the previously discussed theory of symmetrical droplet freezing and shattering, requiring the prior accretion of small droplets (Choularton et al., 1980; Griggs and Choularton, 1983). The formula adopted here (Eq. 4) assumes a much greater role played by large droplets, as described by Hallett et al. (1978); moreover, as shown in Fig. 12, concentrations of small liquid droplets were higher within background ice regions compared to SIP regions during M-Phase, thus calculating a splinter production rate that scales with increasing small droplet concentrations would not be consistent with the observations.

Rime splintering rates were calculated at 1 Hz resolution and averaged over the full cloud segment sampling duration. Figure 13 shows the calculated splinter production rate dNicedt as a function of mean measured ice concentration (Nice) for each individual cloud segment. For all relevant M-Phase clouds, the estimated splinter production rate can be expressed according to the power law relationship: dNicedt=1.2×10-4Nice1.4 (Table 4). By integrating this relationship and assuming that all ice multiplication can be attributed to the H–M process, an increase in Nice from 1 to 100 L⁻¹ (i.e. dNice) within a particular cloud region would take just over 4 h (i.e. dt) (Table 4). However, taking into consideration the overall relative uncertainty (±86 %) in the splinter production rate calculation (Sect. 2.6), an ice concentration increase of this magnitude due solely to the H–M process may occur over timescales as short as just over 2 h, or as long as ∼ 31 h (Table 4). This difference, of more than an order of magnitude, emphasises the need for improved rime splintering parameter constraints (Eq. 4) and real-time microphysical profiling to reduce uncertainty in future campaigns, enabling development of more robust and reliable SIP parameterisations for numerical modelling work.

Our range of estimated rime splintering timescales can be considered physically realistic for marine stratocumulus CAO clouds given their typical lifetime over the North Atlantic is known to vary from several hours to more than a day (Zhang et al., 2023). Broken cumulus cloud fields downstream of the regime transition are generally more short-lived, typically dissipating less than a few hours after forming (Murray-Watson et al., 2023); therefore, in the convective regime, only our fastest splinter production rate estimate for M-Phase can be deemed physically realistic. However, when sampled cumulus cloud segments are considered in isolation, we estimate that the H–M process can drive ice crystal enhancements on the order of 100 L⁻¹ in a more reasonable time of around 3 h (and as fast as ∼ 1.5 h) (Table 4).

Note, as discussed in Sect. 2.1.1, particles of Dp < 100 µm were excluded from our analysis given the likelihood that they would be heavily contaminated with out-of-focus liquid droplets. However, if in-situ measurements are made within a few minutes of the onset of SIP, we would expect to measure high concentrations of particles smaller than 100 µm, following previously reported ice crystal depositional growth rates within the H–M process temperature range (Fuchs et al., 2025). Therefore, as an upper-bound estimate, if we assume that all HI particles detected with the 2D-S of size less than 100 µm were ice crystals, Nice will increase on average by ∼ 45 % in stratiform and ∼ 10 % in convective cloud regions (Fig. D1a in Appendix D); subsequent glaciation timescales by rime splintering are estimated to increase to ∼ 7 h (all clouds), ∼ 4 h (convective), and ∼ 19 h (stratiform), i.e. around a factor of two. However, the bimodal PSDs (and 2D-S imagery) shown in Fig A1 strongly indicate that a large fraction of particles < 100 µm were likely not ice crystals, but instead out-of-focus droplets (Sect. 2.1.1), thus our dNicedt–Nice relationships and glaciation timescales presented in Table 4 can still be considered reasonable approximations of conditions during M-Phase. Ultimately, these glaciation timescale estimates act as order-of-magnitude feasibility tests for the H–M process dominating in marine CAO clouds; however, given the large uncertainty (±86 %) in calculated splinter production rates, strong contributions from other SIP mechanisms cannot be entirely ruled out.

During M-Phase, sampled cumulus clouds were often weakly convective, with measured updraft speeds most commonly falling between 0 and 1 m s⁻¹ (Fig. 4f); at 0.5 m s⁻¹, it would take approximately one hour for air to mix over the full vertical extent of a 2 km deep cloud region. As this convective overturning timescale is considerably faster than our best estimates for glaciation timescales due to the H–M process alone (Table 4), we would expect to observe peak ice particle concentrations across the full sampled cloud depth, rather than at specific temperatures which may be more conducive to the H–M process. Indeed, this is consistent with measurements during both case studies presented in Fig. 5; Nice values exceeding ∼ 100 and ∼ 50 L⁻¹ were observed across most in-cloud temperatures (∼ -5 to -10 °C) during flights C328 and C329, respectively.

Another way to quantitatively evaluate our estimated splinter production rates for M-Phase is by comparing them to the actual rate of ice formation required to maintain high concentrations of small ice particles, characteristic of SIP periods (Figs. 8 and 11), based on previously reported depositional growth rates of ice crystals at temperatures within the H–M range (Ryan et al., 1976; Fuchs et al., 2025). To this end, if we consider an ice concentration of 10 L⁻¹ and assume this is composed entirely of particles between 100 and 200 µm, then further assume a steady-state size distribution within this particle size range and an approximate ice crystal growth rate of 0.5 µm s⁻¹ (derived at ∼ -5 °C by Fuchs et al., 2025), an ice particle formation rate of around 0.05 L⁻¹ s⁻¹ would be required to maintain equilibrium between ice crystals growing into and out of the 100 to 200 µm size range. This ice formation rate is about an order of magnitude higher than the corresponding splinter production rate determined here for an ice concentration of 10 L⁻¹ (Fig. 13), suggesting that the H–M process can only quantitatively account for ∼ 10 % of observed ice crystals. However, the splinter production rates shown in Fig. 13 should be viewed as conservative estimates given they represent averages across full cloud segments; rime splintering rates depend on graupel and large liquid droplet concentrations (Eqs. 3 and 4), both inhomogeneous properties within clouds, producing strong in-cloud spatial variability in splinter production rates. Therefore, we also present the maximum splinter production rate as a function of maximum Nice for each cloud segment in Fig. D1b in Appendix D; this suggests that the H–M process may account for ∼ 50 % of ice crystal formation within regions where ice concentrations are highest and thus where SIP is likely to be most active. As discussed previously, it is likely that other SIP mechanisms (e.g. frozen droplet fragmentation) were acting concurrently within the H–M zone, which would further account for the discrepancy between our estimated rime splintering and ice formation rates.

Figure 13 also shows splinter production rates estimated by Mossop (1985c) and Järvinen et al. (2022), following the same approach as used in this study, for wintertime cumulus clouds over Australia, and summertime CAO clouds over the Southern Ocean during the SOCRATES campaign, respectively. Mossop (1985c) determined that rime splintering could generate ice crystal enhancements on the order of 100 L⁻¹ in ∼ 45 min, implying that the H–M process was active and dominating over other SIP mechanisms. In contrast, Järvinen et al. (2022) concluded that the splinter production rate estimated for marine CAO clouds over the Southern Ocean was too slow to explain the observed level of ice multiplication; estimated cloud glaciation timescales of approximately 200 h far exceeded the typical lifetime of Southern Ocean stratocumulus clouds. Other mechanisms such as ice-ice collisions and frozen droplet shattering were therefore considered to be contributing significantly to SIP.

It is reassuring to note that the range of splinter production rates calculated by Harris-Hobbs and Cooper (1987) for mixed-phase cumulus clouds at several locations across the United States (∼ 10⁻⁴ to 10⁰ L⁻¹ s⁻¹), using their alternative formula that incorporates small liquid droplets (Dp < 12 µm), is comparable to our results for M-Phase (Fig. 13); both studies sampled cumulus clouds of similar microphysical characteristics. Mean concentrations of large, supercooled liquid droplets (Dp > 24 µm) during two of the three aircraft campaigns discussed in Harris-Hobbs and Cooper (1987) (3.7 and 5.6 cm⁻³ in California and Montana, respectively) were strikingly similar to those observed within cumulus clouds during M-Phase (4.8 cm⁻³). Large droplet concentrations were much higher during the other campaign (16 L⁻¹ in Florida); however, this difference is compensated for to some extent by the graupel concentrations that were on average an order of magnitude greater during M-Phase. Finally, although updraft speeds were a factor of 2–3 greater in the Harris-Hobbs and Cooper (1987) study than measured during M-Phase, the role of turbulence in initiating and sustaining rime splintering remains uncertain, with some evidence suggesting that weak-to-moderate rather than strong updrafts are more favourable for ice multiplication (Hallett et al., 1978; Sullivan et al., 2017).

Overall, we estimate significant differences between glaciation timescales in the stratiform and convective regimes during M-Phase (Table 4), implying that numerical models incorporating a single parameterisation scheme for the H–M process across all cloud types may misrepresent the spatial and temporal distribution of mixed-phase cloud glaciation, with liquid-phase conditions likely overestimated in the convective regime. To address this, we recommend the application of regime-aware SIP parameterisations into larger scale cloud microphysics schemes, where SIP activation depends not only on temperature thresholds and droplet size distributions but also on dynamical context, such as updraft strength and cloud morphology. Improving the representation of SIP variability across CAO regimes in climate and NWP models is critical for properly capturing the transition from liquid- to ice-dominated, optically thinner states, thereby reducing biases in simulated cloud radiative fluxes and the onset of light precipitation in high-latitude maritime environments.

In Sect. 3.1, we showed that a secondary peak in SIP activity was observed at colder in-cloud temperatures during M-Phase, consistent with results from laboratory studies indicating that the collisional breakup of large, fragile ice particles is most efficient at around -16 °C (Vardiman, 1978; Takahashi et al., 1995; Grzegorczyk et al., 2023); fragile dendritic branches, particularly susceptible to fragmentation upon collision, are known to grow preferentially by vapour deposition at this temperature (Ryan et al., 1976; Takahashi et al., 1995).

Flight C326 took place on 28 October 2022 and utilised sawtooth profiles throughout, initially sampling stratiform cloud during the outbound leg over the Labrador Sea, which broke up into convective elements for the return leg. Cloud top temperatures as low as ∼ -19 °C were reached, corresponding to a maximum theoretical Nice from primary ice production (i.e. NINP) of ∼ 1 L⁻¹ (Fig. 14); very similar Nice and NINP were observed at ∼ -19 °C (Fig. 14) suggesting primary ice production via immersion freezing, rather than SIP, was dominant at cloud top. The highest ice particle concentrations during flight C326 were measured between -15 and -18 °C, reaching 37.4 L⁻¹, which exceeded the associated NINP by around 1–2 orders of magnitude (Fig. 14); Takahashi et al. (1995) observed a clear peak in the number of ice crystals ejected following collisions at ∼ -16 °C, sharply decaying at colder temperatures towards -20 °C, which is consistent with the comparable Nice and NINP observed at cloud top during flight C326. Järvinen et al. (2022) reported similar ice crystal enhancements within this temperature range in Southern Ocean stratocumulus clouds. This ice enhancement is considerably smaller than that observed within the H–M temperature zone during M-Phase (Sect. 3.2.1); however, previous airborne studies in shallow stratiform clouds have observed Nice exceeding several hundred per litre where cloud tops extend past temperatures lower than ∼ -15 °C (Rangno and Hobbs, 2001; Yang et al., 2014). Therefore, ice multiplication within this colder temperature region may have the potential to substantially modify cloud albedo; thus, improving our understanding of the active SIP mechanism is important for future modelling studies to fully capture the radiative effects of CAO clouds.

During C326, sampled cloud regions with temperatures between -15 and -18 °C were heavily populated with large ice crystals of Dp between 400 and 800 µm (Fig. 14). The ice breakup mechanism has been found to readily initiate in similar cloud regions where ice particles with a broad range of sizes are well-mixed, as fragmentation upon impact between ice crystals is most efficient when the difference in their terminal fall velocities is large, maximising the kinetic energy of the collision (Hoarau et al., 2018; Korolev and Leisner, 2020).

Figure 15 shows time series of selected cloud microphysical properties measured during flight C326. SIP periods 5 (SIP 5) and 6 (SIP 6) were observed from 17:55:40 to 17:56:08 UTC and 19:34:40 and 19:35:10 UTC, respectively, and are marked in Fig. 15. Mean measured temperatures during SIP 5 and SIP 6 were -13.9 and -17.0 °C, respectively; both SIP periods were observed in cloud segments which spanned the temperature range consistent with efficient ice-ice collisional breakup, according to the previously mentioned laboratory experiments (Vardiman, 1978; Takahashi et al., 1995; Grzegorczyk et al., 2023), with cloud top temperatures in both cases reaching ∼ -18 °C.

The maximum ice particle concentration (1 Hz data) measured in SIP 5 was 16.6 L⁻¹ and the corresponding PSD (Fig. 16) peaked between particle sizes of 350 and 550 µm, with a maximum Dp of ∼ 5 mm. This broad size distribution suggests that ice crystals of varying stages of growth were collocated during SIP 5, thus meeting the requirement for ice breakup that colliding particles have greatly varying vertical velocities (Korolev and Leisner, 2020).

During SIP 6, measured ice particle concentrations reached 32.2 L⁻¹ and the corresponding size distribution peaked at larger crystal diameters than during SIP 5 (500 µm < Dp < 800 µm), consistent with original assumptions by Vardiman (1978) that small ice particles do not have elaborate enough geometry or sufficiently large terminal velocity to fragment upon collision. During SIP 6, the observed PSD was narrower overall than in SIP 5, with a maximum ice crystal size of ∼ 3 mm. The relative lack of growth experienced by particles observed during SIP 6, compared to SIP 5, suggests that ice multiplication by ice-ice collisions occurred more recently in SIP 6. Furthermore, SIP 6 was sampled closer to cloud top than SIP 5; ice crystals observed during SIP 5 may have also formed near cloud top before growing while mixing or precipitating down to the point of observation, as evidenced by the images of large, branched crystals shown in Fig. 17.

Mean μ3 values for both SIP 5 (0.43) and SIP 6 (0.34) were considerably lower than those discussed previously for SIP 1 to SIP 4. These less glaciated cloud regions, reflecting a strong supercooled liquid water presence, are consistent with previous studies in which ice-ice collisional breakup was found to favour heavy riming conditions at temperatures well-below the active H–M zone (Karalis et al., 2022); fragile dendritic branches have been observed to grow particularly efficiently on heavily rimed particles (Pruppacher and Klett, 1997). Figure 17 presents CPI and 2D-S images of ice particles sampled in two cloud segments during flight C326, both with cloud top temperatures of ∼ -18 °C. Large, heavily rimed ice crystals with fragile protuberances or branches were frequently observed (red frames), alongside aggregates (green frames) and large irregular crystals with plate-like extensions (pink frames) (Fig. 17a); collisions between such particles with differing, often brittle, surface properties are most likely to cause ice breakup, producing high concentrations of small, irregular ice fragments (black frames).

Ultimately, the in-situ evidence presented here supporting active ice-ice collisional breakup during M-Phase can contribute towards constraining new physics-based model parameterisations, such as the scheme developed by Phillips et al. (2017) described in Sect. 1, that require information on the temperatures, ice mass fractions and ice particle sizes and morphologies most conducive to initiating the ice breakup process in shallow, marine CAO clouds.