The numerical model used in this study is the Global Environmental Multiscale (GEM) model (Côté et al., 1998; Girard et al., 2014). GEM is used for operational numerical weather prediction (NWP) in Environment and Climate Change Canada (ECCC) as well as research in ECCC and Canadian universities. The dynamical core of GEM is formulated based on the non-hydrostatic fully compressible primitive equations with a terrain-following hybrid vertical grid. As such, it can be run at cloud-resolving (sub-km grid spacing) scales. It can be run on global or limited-area domains and is capable of one-way nesting. In this study, four cascade domains with horizontal grid-spacings of 10, 2.5, 1.0 and 0.25 km and sizes of 3600 × 2600, 1800 × 1800, 1024 × 1024 and 512 × 512 km² are used respectively. The high-resolution simulation with a grid spacing of 0.25 km provides enhanced capability to resolve small-scale phenomena such as convective updrafts and the recirculation of raindrops by these updrafts near the melting layer. Accurately resolving these physical processes is crucial for better representing SIP mechanisms, including HM, FFD and CB processes (Korolev et al., 2024). For ICICLE Flight 9, the simulation is initiated at 12:00 UTC on 7 February 2019 and runs for 12 h. All four nesting domains are centred on 44.5° N and 88.75° W (Fig. 1). For ICICLE Flight 20, the simulation is initiated at 06:00 UTC on 23 February 2019 and runs for 12 h, with all four nesting domains centred on 42.7° N and 89.9° W (Fig. 1). 84 unevenly spaced hybrid vertical levels are used for 10 km simulations and 62 levels are used for all other simulations.

In the GEM simulations of this study, all grid-scale cloud microphysical processes were represented by the Predicted Particle Properties (P3) bulk microphysics parameterization scheme. The original version of the P3 scheme is described in detail in Morrison and Milbrandt (2015). Since its inception, there have been several advances which have been described in various publications.

The liquid-phase component of P3 uses a standard two-category, two-moment approach whereby all liquid-phase hydrometeors are partitioned into “cloud” (non-sedimenting droplets) and “rain”, each of whose PSDs are represented by complete gamma functions and each has the mass and number mixing ratios as prognostic (and advected) variables. Droplet activation is parameterized following the approach of Morrison and Grabowski (2007, 2008), which assumes a constant background aerosol concentration of 300 cm⁻³ with a mean particle size of 0.05 micrometers (µm), composed of ammonium sulfate. Work is currently underway to include prognostic aerosols.

P3 has a unique approach to represent ice-phase hydrometeors. In the traditional approach, as used in nearly all bulk and bin microphysics schemes, particles are partitioned into predefined categories (e.g. “ice”, “snow”, “graupel”, etc.) with prescribed physical properties (e.g. density, fall speed parameters, etc.). In contrast, P3 has a user-specified number of freely evolving generic ice-phase categories, each of whose physical properties evolve continuously in time and space. Because of this, each ice category in P3 can represent any type of ice-phase hydrometeor, although, as in any bulk scheme, ice categories in P3 remain constrained by assumed PSD parameters type and the number of prognostic moments. Also, there is no artificial “conversion” between ice-phase categories, which is an inherent weakness in traditional schemes. Similar to the liquid categories, the PSD of each ice category in P3 is represented by a complete gamma function but has an optional triple-moment approach (Milbrandt et al., 2021). The generalization to the multi-category version of P3 is described in Milbrandt and Morrison (2016). The incorporation of an optional prognostic liquid fraction, which allows for mixed-phase particles and improves the simulation of processes such as melting and refreezing, is described in Cholette et al. (2019, 2024).

All simulations in this study use the configuration with triple-moment ice, prognostic liquid fraction, and four ice-phase categories. The decision to use four ice categories was made to maximize the representation of the multi-modal ice particle size distribution during conditions of high SIP rate where large pre-existing ice particles coexist with small ice splinters. Ice splinters generated by various SIP processes are assumed to have a diameter of 10 µm. These small ice particles are incorporated into one of the four ice categories corresponding to the closest particle size. Qu et al. (2022) showed that three ice categories in the P3 scheme are sufficient to effectively capture the size distribution when SIP is active; Milbrandt et al. (2025) showed a similar “convergence” with three categories for the simulation of hail. Nevertheless, four categories were used in this study since the additional category should, in principle, model the total ice phase slightly better without significantly increasing computational cost.

In the “official” P3 scheme, ice is initiated via homogeneous freezing of cloud droplets, immersion/contact freezing of cloud droplets and rain drops (temperature-dependent following Bigg (1953) with parameters from Barklie and Gokhale (1959)), heterogeneous nucleation through condensation freezing of cloud droplets and rain drops, and deposition nucleation (Cooper, 1986), and rime splintering (Hallett and Mossop, 1974). Deposition nucleation is specifically restricted to temperatures at or below 258.15 K and requires ice supersaturation of at least 5 %.

This study focuses on assessing the impact of including three SIP processes in the NWP simulations: the HM rime splintering process, the FFD process and the CB process. As discussed, additional SIP processes are currently known; however, due to limited understanding of each, including HM, FFD and CB, this study examines only these relatively better-characterized processes. Future studies will aim to incorporate more SIP processes.

On 9 February 2019, the Great Lakes region experienced a significant winter storm fuelled by a low-pressure system that intensified as it stalled over Lake Huron (Fig. 2a and b). This system resulted in prolonged snowfall across the region. In the area west of Lake Michigan, including Wisconsin and northern Illinois, cold temperatures and snowy conditions prevailed due to the influence of a passing low-pressure system. A comparison between the visible radiances (Fig. 2a) and infrared brightness temperatures (Fig. 2b) from GOES-16 satellite imagery reveals scattered convective cells. These isolated convective updrafts, though sparse, were capable of producing brief bursts of snow or freezing rain.

Figure 3 shows the combined zenith and nadir pointing X-band radar reflectivity along with in situ observations of IWC, ice number concentration (Ni, excluding particles smaller than 40 µm in diameter), LWC, air temperature (T), and the aircraft's altitude (H). The bright band at approximately 2.5 km is clearly visible before 20:00 UTC, but it disappears after 20:30 UTC. A temperature inversion is present near an altitude of 2 km, although the maximum temperature at this altitude remains below freezing after 20:00 UTC. Based on in situ observations there are many regions of mixed-phase clouds, particularly between 19:50 and 20:40 UTC and around 21:00 UTC, which provide potential favourable conditions for SIP.

Figure 4 displays the simulated brightness temperature at 10.3 µm for the 2.5 km resolution domain (northern border limited at 50° N due to GOES-16 data availability) using the RTTOV (Radiative Transfer for TOVS) fast radiative transfer model (Saunders et al., 2018) for the F9-BASE simulation (Fig. 4a). This is compared with the GOES-16 observation at 20:30 UTC on 9 February 2019 (Fig. 4b). The F9-BASE simulation effectively reproduces the large-scale sea-level pressure pattern (shown by yellow lines). The simulated brightness temperature at 10.3 µm closely matches the GOES-16 observations. However, a positive bias (indicating warmer values) is evident compared to the satellite data. Investigations into the cause of this bias are currently underway. Additionally, the simulation slightly underestimates cloud coverage over the southern part of Lake Michigan and in the southeastern corner of the simulation domain.

Figures 5 and 6 present the simulation profiles for the region within 10 km on each side of the aircraft track. The profiles display averaged values, except for Fig. 5c, which shows 99 percentile of ice water content, the maximum vertical wind speeds (Fig. 5d), and the median radar reflectivity (Zmedian, Fig. 6c). Significant variations in mean IWC among different simulations can be seen in Fig. 5a. The F9-BASE simulation for ICICLE Flight 9 produces the lowest IWC, with slightly higher values observed in F9-HMgr-FFDh. In contrast, F9-HMgc-FFDh and F9-HMgc-FFDl-CB exhibit notable increases in IWC.The F9-HMr-FFDh simulation exhibits extremely high IWC near the surface. All SIP simulations produced a significant enhancement in the 99th percentiles of IWC at various altitudes compared to the F9-BASE simulation. The extremely high IWC observed below 1.8 km in the F9-HMr-FFDh simulation (below the temperature inversion at ∼ 2 km altitude, as shown in Fig. 5e) aligns with the elevated Ni in the same altitude range (purple dash-dotted lines in Fig. 5c). This IWC enhancement is strongly associated with increased freezing efficiency of liquid water (LWC and rain water content – RWC), as shown in Fig. 6a and b, and enhanced vapor deposition growth due to the higher Ni, leading to a larger ice surface area for deposition. These findings suggest that SIP processes may contribute to the formation and persistence of HIWC condition.

For Zmedian (Fig. 6c), the F9-BASE and F9-HMgr-FFDh simulations produce the highest values, despite having the lowest IWC. Due to the relatively low Ni in these simulations, the ice particles in F9-BASE and F9-HMgr-FFD are larger compared to those in the other three SIP simulations. F9-HMgc-FFDh and F9-HMgc-FFDl-CB generate the lowest Zmedian across most altitudes below 5 km, while F9-HMr-FFDh shows even lower Zmedian below approximately 0.9 km. This reduction in Zmedian is due to the extremely high Ni in F9-HMr-FFDh, which significantly reduces the size of the ice particles. By 20:30 UTC, the clouds near the flight track had already glaciated, so no bright band could be seen in Fig. 6c.

Although all three two-process SIP simulations use the same FFDh parameterization, differences in how the HM process is modeled result in markedly different outcomes. Figure 6d and e illustrate the HM and FFD rates at the simulation time step of 20:30 UTC. At this time, there is no SIP activity within 10 km of the flight track for F9-HMgr-FFDh. Similar to F9-HMgr-FFDh, F9-HMr-FFDh calculates the number of ice splinters based on collected rain mass, but without the requirement that the ice must be graupel. By omitting this graupel condition, F9-HMr-FFDh produces a high HM rate (Fig. 6d, purple dash-dotted line), which subsequently triggers the FFD process, leading to an even higher FFD rate near 1 km altitude. On the other hand, F9-HMgc-FFDh generates a lower HM rate near both 3.5 and 1 km altitudes (Fig. 6d, red lines). Consequently, the FFD rate is also very low near 3.8 km, with no FFD activity below 2 km near the flight track at this time step. These results indicate that under freezing conditions with an abundant supply of supercooled rain, the initiation of the FFD process is highly dependent on the rate of the HM process, or potentially any SIP processes which could provide sufficient amount of small ice particles.

Including the CB process in the experiment led to an explosive increase in FFD rates near the surface (not shown). To mitigate this, we applied the FFDl (lower rate) parameterization, as proposed by Lachapelle et al. (2025). Results from the three-process experiment (F9-HMgc-FFDl-CB) were similar to those of F9-HMgc-FFDh in terms of Ni, IWC, LWC, and Zmedian. The CB process (types I, II, and III) produced positive SIP rates at multiple altitudes, including levels below 2 km (Fig. 6f, g), potentially further activating the FFD process. The use of the FFDl parameterization effectively suppressed near-surface FFD rates, resulting in values that were substantially lower and more realistic.In the simulations for Flight 9, condensation freezing/deposition ice nucleation likely initiated ice particle formation at altitudes above 4.5 km (T< -15 °C, as implemented in P3 scheme). As these ice crystals descend, they tend to aggregate, leading to decreased Ni values (typically less than 10² m⁻³) (see Fig. 7b, blue dashed line from the F9-BASE simulation). In addition, the immersion/contact freezing process could also introduce low number of Ni at higher T (T< -4 °C). Ice particles produced via heterogeneous nucleation can subsequently trigger the HM or CB processes. However, since Ni generated by heterogeneous nucleation remains low at lower altitudes, where supercooled liquid drops are abundant, the likelihood of activating significant FFD rates is limited. In contrast, the HM and CB processes can produce Ni values at least an order of magnitude higher than those from heterogeneous nucleation alone, substantially increasing the potential for interactions between ice splinters and supercooled raindrops.

To further assess the simulation results, in situ aircraft data were used for comparisons. Figure 7 compares the distributions of simulated IWC and Ni within 10 km of the flight track and within the flight altitude range of 0.5 to 3.8 km, with the observations shown by black lines. In the simulation results presented here, quantities from all four ice categories are summed and for the simulated Ni, ice particles smaller than 40 µm are excluded.

For IWC, the F9-BASE simulation significantly underestimates the frequency of clouds with IWC > 0.1 g m⁻³. The F9-HMgr-FFDh simulation (yellow dotted line) shows some improvement, especially for IWC > 0.5 g m⁻³, though most frequencies remain underestimated. While both F9-HMgr-FFDh and F9-HMgr-FFDl-CB considerably improve the estimated IWC frequency, they still underestimate conditions of high IWC. Conversely, F9-HMr-FFDh overestimates the frequency of high IWC above 0.8 g m⁻³.

For Ni, both the F9-BASE and F9-HMgr-FFDh simulations produce very low values, while F9-HMr-FFDh (purple line) significantly overestimates Ni. The F9-HMgc-FFDh and F9-HMgr-FFDl-CB simulations (red line and green dashed line respectively) provide the closest estimates of Ni, although the peak values remain slightly lower than observed. Based on this, the subsequent discussion on SIP simulations focuses exclusively on F9-HMgc-FFDh and F9-HMgc-FFDl.

Figure 8 presents the two-dimensional histograms of Ni (x-axis) as a function of T (y-axis). In the F9-BASE simulation (Fig. 8a), the majority of Ni values are low, ranging between 10¹ and 10² m⁻³, predominantly at temperatures above -10 °C. Because SIP processes are not included in this simulation and the cloud top remains warmer than -40 °C (the threshold for homogeneous nucleation), ice particles primarily originate from heterogeneous ice nucleation. In the P3 scheme, the parameterization by Cooper (1986) is applied for temperatures below -15 °C and ice supersaturation greater than 5 % to estimate Ni due to condensation freezing and deposition ice nucleation. Since this scheme tends to overestimate Ni at lower temperatures, Ni values due to condensation freezing/deposition ice nucleation are capped at 1 × 105 m⁻³. Therefore, one of the sources of ice particles observed at temperatures warmer than -10 °C might have originally formed at colder temperatures below -15 °C, governed by the estimated Ni which is represented by the line of small red circles. As these primary ice particles descend, they aggregate, resulting in the low Ni values at temperatures warmer than -10 °C. Another source of ice could be from the immersion/contact freezing of cloud droplets or rain drops (T < -4 °C).

The two simulations that include SIP processes, F9-HMgc-FFDh and F9-HMgc-FFDl (Fig. 8b and c respectively), still exhibit similar cluster (highlighted by large red circles) as in the F9-BASE run, representing ice particles resulting from heterogeneous nucleation. Additionally, a second distinct cluster appears (highlighted by large green circles in Fig. 8b and c), displaying higher Ni values at slightly warmer temperatures (i.e., lower altitudes). This pattern contrasts with the expected reduction of Ni at lower altitude due to aggregation, suggesting a strong influence of SIP on enhancing Ni.

Finally, the observed distribution shown in Fig. 8d is very similar to those in the two SIP simulations, but with even higher Ni values near T = -5 °C (between 10³ to 10⁵ m⁻³). This pattern further underscores the pronounced impact of SIP on increasing ice particle concentrations.

Comparing the simulated and observed Z values shows that both F9-HMgc-FFDh and F9-HMgr-FFDl-CB simulations resulted in a closer match to the observation data (Fig. 9). The F9-BASE simulation produces Zmedian values 5 to 10 dBZ higher than observed below 5 km. In contrast, F9-HMgc-FFDh and F9-HMgr-FFDl-CB show slight underestimations below 2.5 km and small overestimations between 2.5 and 5 km. There may be artifacts related to ground clutters which cause enhanced Z at altitudes twice the aircraft height, as indicated in Fig. 3a. The values of Zmedian shown in Fig. 9e suggest that the simulations might underestimate above 5 km. This underestimation will be further discussed in Sect. 5.2.

Figure 10 shows the averaged values of IWC and Ni for the F9-BASE (Fig. 10a, d), F9-HMgc-FFDh (Fig. 10b, e) and F9-HMgr-FFDl-CB (Fig. 10c, f) simulations between altitudes of 0.5 and 3.8 km. Comparing Fig. 10a and b/c, there are noticeable local enhancements of IWC, particularly in the western part of the simulation domain (indicated by the white circles), where larger amounts of LWC and RWC are available (not shown). A similar pattern is observed for Ni (Fig. 10d, e, f). Despite this being a winter case, some of these updrafts reach speeds up to approximately 7 m s⁻¹, as shown in Fig. 5d. Thus, convective updrafts may play a crucial role in creating favourable conditions for SIP even under winter conditions.

Active SIP processes not only enhance IWC and Ni but also accelerate the freezing of existing liquid water, as shown in Fig. 6a and b. This can potentially lead to a significant reduction in the area of freezing rain near the surface. Figure 11 presents the RWC and IWC near the surface at the lowest model layer (approximately 20 m above surface) for the F9-BASE (first column), F9-HMgc-FFDh (middle column) and F9-HMgr-FFDl-CB (third column) simulations. The black contours indicate areas where supercooled rain is present near the surface. Comparing Fig. 11a and b/c, the area of freezing rain is reduced by approximately 50 % in both the F9-HMgc-FFDh and F9-HMgr-FFDl-CB cases relative to F9-BASE (highlighted by black contours). At the same time, IWC in the western part of the simulation domain increases from approximately 0.1 g m⁻³ in F9-BASE to about 1.0 g m⁻³ in the F9-HMgc-FFDh and F9-HMgr-FFDl-CB cases (as indicated by the white circles in Fig. 11d, e, and f).

The reduction in the freezing rain area in the SIP simulations aligns more closely with observations. As shown in Fig. 3, the aircraft descended to low altitudes during two simulated missed approaches shortly before and after 20:30 UTC (indicated by the yellow and turquoise arrows respectively). These simulated missed approaches were intentional, pre-planned manoeuvres that replicate a missed landing, allowing the aircraft to collect in-situ observations near the surface. During the first simulated missed approach (Point 1 in Fig. 3, marked by the yellow arrow), in situ observations indicated the presence of both IWC (Fig. 3b) and LWC (Fig. 3d). This simulated missed approach corresponds to the yellow-highlighted flight path in Fig. 11. All simulations predict the coexistence of liquid and ice, consistent with the observations. In the second simulated missed approach (Point 2 in Fig. 3, marked by the turquoise arrow), high IWC values between 0.7 and 1.0 g m⁻³ were observed with no liquid water present, as shown in Fig. 3. This second simulated missed approach corresponds to the turquoise-highlighted flight path in Fig. 11. In the F9-BASE simulation, both supercooled rain and IWC were predicted, and the IWC value is very low (< 0.1 g m⁻³). The F9-HMgc-FFDh and F9-HMgc-FFDl-CB simulations, on the other hand, produced conditions with no RWC and high IWC, which closely matches the observations. The improved simulation of freezing rain conditions in this study is consistent with the findings of Cholette et al. (2024) in which the freezing rain areas are significantly reduced comparing to the simulation without SIP, despite only using the HM process in their study.

On 23 February 2019, a significant winter storm impacted the Great Lakes region, including Wisconsin, and northern Illinois, bringing heavy snowfall, high winds, and blizzard conditions. Satellite data from GOES-16 (Fig. 12) indicated widespread overcast conditions, with thick clouds dominating the region. The cloud cover consisted of mostly stratiform clouds, typical of large-scale winter systems.

ICICLE Flight 20 was conducted on 23 February, in the area west of Lake Michigan. The flight encountered an extensive cloud system spanning over more than 300 km, within which HIWC conditions were frequently observed. Figure 13 presents the observed X-band radar reflectivity, in situ data, and flight altitude. A consistent bright band was detected throughout the flight. A temperature inversion was also observed as the aircraft passed through the bright band. Below the bright band, the aircraft primarily detected liquid water, often supercooled (Fig. 13e), with no ice present. Above the bright band, observations indicated mostly ice, often with IWC exceeding 0.5 g m⁻³, and little to no liquid water, particularly between 13:45 and 16:00 UTC. One exception is between 12:25 and 13:45 UTC. As a result, mixed-phase conditions were less frequent in this case compared to the previous Flight 9.

Figure 14 shows the simulated brightness temperature at 10.3 µm for the F20-BASE simulations (Fig. 14a), along with the observed brightness temperature from GOES-16 on 23 February 2019 at 14:30 UTC (Fig. 14b). The F20-BASE simulation effectively reproduces the large-scale sea-level pressure pattern (shown by yellow lines). The simulated brightness temperature at 10.3 µm closely matches the GOES-16 observations, exhibiting a warm bias, although it slightly underestimates cloud coverage.

The simulated profiles within 10 km of the aircraft track indicate that the impact of SIP (across all four SIP simulations) on IWC and Ni is minimal (Fig. 15a, c). The F20-HMgc-FFDh and F9-HMgc-FFDl-CB simulations show the maximum IWC increases of approximately 10 % at altitudes of 3 and 3.7 km, respectively, compared to the F20-BASE simulation. The increase in Ni is about 2–3 times, which is significantly smaller than the Flight 9 case, where increases reached 2–3 orders of magnitude. Additionally, both F20-HMgc-FFDh and F9-HMgc-FFDl-CB generate lower LWC and RWC above 2.5 km (Fig. 16a, b). Due to the higher Ni, the values of Zmedian in both F20-HMgc-FFDh and F9-HMgc-FFDl-CB simulations are about 3 dBZ lower than in the F20-BASE simulation between 2 and 4 km altitude. No SIP activity is detected in any of the simulations at 14:30 UTC (Figs. 16d to 15g) within 10 km of distance to the flight track, except for F9-HMgc-FFDl-CB, which exhibits very low rates of both FFD and CB type I. Note that there are regions with SIP activities at this time step, but they are away from the selected regions for statistics. The simulated case on 23 February 2019 appears more stratiform, with maximum vertical updraft velocities typically below 4 m s⁻¹. This condition likely contributes to the less frequent occurrence of mixed-phase conditions near the bright band, whereas precipitation size drops driven by updrafts through the melting layer could play a crucial role in enhancing SIP activity, as suggested by Korolev et al. (2024).

Although SIP activity during ICICLE Flight 20 is minimal in the simulation, a large area of HIWC conditions is observed. Unlike localised convective cases during the ICICLE Flight 9 or tropical cases (Huang et al., 2022; Qu et al., 2022; Korolev et al., 2024), the results from ICICLE Flight 20 suggest that HIWC conditions can develop without significant contributions from SIP processes, particularly in stratiform and long-lasting cloud systems.

All simulations, including F20-BASE, show reasonably good agreement with the observations for IWC and Ni, as illustrated in Fig. 17. Unlike the ICICLE Flight 9 case, the F20-BASE simulation does not significantly underestimate the frequency of HIWC conditions. For the Ni distribution, while F20-HMgc-FFDh and F20-HMgc-FFDl-CB provide the closest matches to the observations, the F20-BASE simulation also produces a fairly accurate estimate.

One possible reason for the fairly accurate Ni values in the F20-BASE simulation is that in this stratiform case Ni is likely governed by the heterogeneous nucleation process, with SIP playing a relatively less important role. In the F20-BASE simulation, most Ni values between -15 and -25 °C (T of the maximal flight altitude for Flight 20 at ∼ 6.4 km) are higher than the parameterized Ni due to condensation freezing/deposition ice nucleation (lower half of the small red cycles in Fig. 18a) within the same temperature range, but lower than the parameterized Ni for colder temperatures (upper half of the small red cycles in Fig. 18a). Ice particles formed at temperatures below -25 °C through condensation freezing/deposition ice nucleation may gradually fall to warmer, lower-altitude regions, thereby contributing to higher Ni compared to the parameterized Ni. Another possible source of the enhanced Ni is immersion and contact freezing. Additionally, simulated results from F20-BASE (Fig. 18a) show a gradual decrease in Ni with increasing temperature, underscoring the effect of ice particle aggregation.

In the case of Flight 20, the cloud top extends above the homogeneous freezing threshold at -40 °C, allowing for the possibility that homogeneous ice nucleation could also influence Ni at lower altitudes as these ice particles descend. However, as shown in Fig. 18a, the Ni values above the -40 °C level are not substantially higher than most Ni values seen between -20 and -30 °C (ranging from 10³ to 10⁵ m⁻³). As ice particles formed through homogeneous freezing descend into warmer temperatures, aggregation processes are expected to further decrease Ni, resulting in concentrations lower than those shown between -20 and -30 °C in Fig. 18a, where most values range from 10³ to 10⁵ m⁻³. This pattern indicates that, at temperatures warmer than -25 °C, the ice particle concentrations are more likely dominated by heterogeneous nucleation rather than by the effects of homogeneous nucleation.

Compared to F20-BASE (Fig. 18a), F20-HMgc-FFDh (Fig. 18b) and F20-HMgc-FFDl-CB (Fig. 18c) have more frequent occurrences of higher Ni values for temperatures above -10 °C, indicating the influence of SIP. However, these impacts remain moderate.

In the observed Ni frequency distribution (Fig. 18d), two distinct clusters are apparent. One cluster (indicated by the large red circle) aligns closely with the parameterized Ni line, suggesting the influence of condensation freezing/deposition ice nucleation. The second cluster, which exhibits higher Ni values below -20 °C, may indicate the influence of immersion and contact freezing, as well as the presence of falling ice particles originating from higher altitudes, regions that were not directly observed due to the flight's altitude limitations. The higher Ni values may also result from the effects of SIP. However, Ni gradually decreases with increasing temperature. Unlike the F20-HMgc-FFDh (Fig. 18b) and F20-HMgc-FFDl-CB (Fig. 18c) cases, there is no distinct “protruding” cluster (green circles in Fig. 18b, c) that would indicate a sudden Ni increase at lower altitudes due to SIP. Thus, ice formation in warmer regions (lower altitudes) in Fig. 18c is likely dominated by heterogeneous nucleation, although the influence of SIP cannot be ruled out.

Observed Ni values at T > -20 °C (Fig. 18c, Ni > 1 × 10⁴ m⁻³) are frequently higher than those in the simulations (Fig. 18a, b and c, where Ni mostly ranges between 1 × 10³ and 1 × 10⁴ m⁻³). This discrepancy warrants further investigation into the uncertainties associated with the parameterized heterogeneous nucleation at colder temperatures (T < -20 °C), the ice–ice collection efficiency and SIP.

For the 2D histogram of Z and the Zmedian profiles shown in Fig. 19, there is good agreement in Zmedian between the observation and the F20-BASE, F20-HMgc-FFDh and F20-HMgc-FFDl-CB simulations between 2 and 4 km altitude. However, all three simulations underestimate Zmedian above 4 km.

Several factors may contribute to the underestimation of Zmedian at higher altitudes, including uncertainties in the initial conditions of the simulation and the exclusion of certain SIP processes. One additional key source of uncertainty is related to the parameterized collection efficiency amongst ice particles. Among the available parameterizations, the range varies by nearly two orders of magnitude between the highest (Lin et al., 1983) and lowest (Ferrier et al., 1995) estimates (Khain and Pinsky, 2018). The current study employs the parameterization from Cotton et al. (1986), which represents a mid-range approach.

Figure 20 shows the averaged IWC and Ni between 2.6 and 6.4 km for the F20-BASE, F20-HMgc-FFDh and F20-HMgc-FFDl-CB simulations. Although the overall differences among the three simulations are relatively small, minor variations in IWC and Ni are noticeable, particularly in localized areas in the western part of the domain. These localized enhancements in IWC and Ni in the two SIP simulations correspond to the locations of updrafts, albeit weaker in this case. The impact on domain-averaged IWC and Ni remains small. Although Fig. 16d to g show no SIP activity (except very low rates from F20-HMgc-FFDl-CB) at this specific time step within 10 km of distance to the flight track, the local enhancements of IWC and Ni in close regions to the flight track are the results of SIP processes from earlier time steps.