Secondary ice production (SIP) has long been acknowledged as a fundamental cloud microphysical process (e.g., Cantrell and Heymsfield, 2005; Field et al., 2017). Along with the other leading processes in cold clouds, such as primary ice formation via activation of ice nucleating particles (INPs), particle vapor growth, aggregation, riming, and sedimentation, SIP is likely to commonly play a critical role in the formation of size distributions and habits of ice particles (e.g., Ackerman et al., 2015; Ladino et al., 2017). Through the modulation of ice particle concentration, SIP can thereby impact precipitation formation, rate of glaciation of mixed-phase clouds, the longevity of ice clouds, cloud electrification, and radiative properties of clouds. On the global scale, SIP may significantly impact the hydrological cycle and climate in general. However, the commonality and precise mechanisms of SIP have remained persistently poorly established. Understanding of mechanisms of SIP is of great importance for developing a parameterization of the ice initiation processes in weather prediction and climate models.

The significance of SIP was recognized only after the beginning of regular airborne studies of cloud microstructure in different geographical regions (e.g., Koenig, 1963, 1965; Hobbs, 1969; Mossop, 1970, 1985; Mossop et al., 1972; Ono, 1972; Hallett et al., 1978; Hobbs and Rangno, 1985, 1990; Beard, 1992; and many others). A systematically observed difference of up to 5 orders of magnitude between concentrations of INPs and measured ice concentration urged provision of an explanation of the physical processes underlying this discrepancy. One of the explanations suggested an enhancement of the concentration of ice particles via a mechanism unrelated to the primary ice formation. Several possible mechanisms were proposed to explain such so-called secondary production of ice crystals.

Historically, the first proposed mechanism to explain SIP focused on droplet fragmentation during freezing (e.g., Langham and Mason, 1958; Mason and Maybank, 1960; Kachurin and Bekryaev, 1960). During the freezing of a cloud droplet, isolated pockets of liquid water may become trapped inside an ice shell. The expansion of water during subsequent freezing results in an increase of pressure inside the ice shell. If the pressure exceeds a critical point, then the ice shell may break into fragments to relieve the internal pressure. Newly formed ice fragments may serve as INPs and result in an enhancement of ice concentration.

Subsequent laboratory studies demonstrated that fragmentation of freezing drops depends on many factors such as droplet temperature before freezing, environmental temperature, droplet size, concentration of CO2 and other gases dissolved in water, the crystalline nature of the ice shell (i.e., monocrystalline or polycrystalline), drop rotation during freezing, and the type of INPs employed for droplet freezing and the manner of droplet suspension in the laboratory (Muchnik and Rudko, 1961; Evans and Hutchinson, 1963; Stott and Hutchinson, 1965; Dye and Hobbs, 1966, 1968; Johnson and Hallett, 1968; Brownscombe and Thorndike, 1968; Hobbs and Alkezweeny, 1968; Takahashi and Yamashita, 1969, 1970; Pitter and Pruppacher, 1973; Takahashi, 1975, 1976; Wildeman et al., 2017; Lauber et al., 2018). A review of the laboratory studies of droplet freezing showed a large diversity of reported results, and conditions required for droplet shattering during freezing remain not well understood.

Splintering during ice particle riming is another mechanism that can potentially explain apparent SIP (Macklin, 1960; Latham and Mason, 1961). Hallett and Mossop (1974) and Mossop and Hallett (1974) observed splinter formation during riming in a cloud chamber with liquid water content of ∼1 g m-3 and droplet concentration 500 cm-3. They found that splinter production is active in the air temperature range from -3 to -8 ∘C, and its rate has a pronounced maximum at an air temperature of -5 ∘C and drop impact velocity of 2.5 m s-1. At these conditions, one splinter was produced per 250 droplets of diameter D>24 µm. The phenomenon of splinter production during riming is usually referred to as the Hallett–Mossop (HM) mechanism. Several studies have aimed at understanding the physical mechanism responsible for the splinter production (e.g., Choularton et al., 1978, 1980; Emersic and Connolly, 2017). However, despite these efforts, the physical mechanism underlying this phenomenon is still under debate.

The collision of ice particles may result in their mechanical fragmentation and the production of secondary ice. This hypothesis was stimulated by observations of ice particle fragments collected during airborne studies (e.g., Hobbs and Farber, 1972; Takahashi, 1993) and ground-based ones (Jiusto and Weickmann, 1973). Collisional fragmentation of ice particles was explored in the laboratory by Vardiman (1978) and Takahashi et al. (1995). However, the obtained results do not allow an unambiguous conclusion about ice–ice collisional fragmentation and its contribution to SIP.

When an ice crystal collides with a supercooled drop, it will experience thermal shock due to the release of latent heat of the freezing drop. This will cause a differential expansion of the ice crystal and may result in its fragmentation. This phenomenon was observed during laboratory studies by Dye and Hobbs (1968) and Hobbs and Farber (1972). Due to the current lack of laboratory studies, the efficiency of ice particle fragmentation due to thermal shock and its effect on SIP remains inconclusive.

Ice particle fragmentation and formation of secondary ice may occur during sublimation in subsaturated areas near cloud edges or underneath the cloud base. The phenomenon of fragmentation during sublimation was studied by Oraltay and Hallett (1989), Dong et al. (1994), and Bacon et al. (1998). However, it remains unclear whether small fragments formed in the subsaturated environment can re-enter supersaturated cloud and act as SIP particles. This appears to be a significant limitation on the efficacy of sublimation breakup as a SIP mechanism.

Gagin (1972) proposed a mechanism for SIP due to the activation of INPs in high-transient-supersaturation areas around freezing drops. After nucleation, the freezing drop temperature rises to 0 ∘C. If the surrounding air is colder than 0 ∘C, the surface of the freezing drop acts as a source of water vapor to a colder environment. The resulting water vapor diffuses radially outward. Depending on the air humidity, it may create at some distance from the droplet a region with supersaturated air. Rosinski et al. (1975) and Gagin and Nozyce (1984) studied nucleation of INPs around suspended freezing drops with 1–2 mm diameter. However, simply due to limited laboratory studies, the effect of INP activation around freezing drops on SIP remains insufficiently quantified.

The hypothesis that ice concentration measurements are subject to artifacts induced by airborne instruments has been discussed over a long period of time. Larger ice particles may bounce off a forward probe's tips or inlet and shatter into smaller fragments. After rebounding, the shattered fragments may travel into the sample area and cause multiple artificial counts of small ice (e.g., Gardiner and Hallett, 1985; Gayet et al., 1996; Heymsfield, 2007; McFarquhar et al., 2007; Jensen et al., 2009; Field et al., 2003). The following introduction of antishattering K tips (A. V. Korolev et al., 2013) along with the interarrival time algorithm (Field et al., 2006) allowed for a significant mitigation of the effect of shattering and an improvement in the ice particle measurements. As was shown by Korolev et al. (2011), A. Korolev et al. (2013), and Lawson (2011), a measured concentration of ice particles smaller than 200 µm can be enhanced due to the shattering effect by up to 2 orders of magnitude.

The latter finding brings up a question that some early airborne studies that pointed out the discrepancy between concentrations of ice particles and INPs might be contaminated by shattering artifacts, which resulted in an enhancement of the measured concentration of small ice. However, numerous recent in situ measurements, which applied the antishattering techniques, are in general consistent with the early SIP observations, and they also showed that in many clouds, ice particle concentrations are still much higher than the INP concentration (e.g., Crosier et al., 2011, 2014; Crawford et al., 2012; Stith et al., 2014; R. P. Lawson et al., 2015; P. Lawson et al., 2017; Lloyd et al.,  2015; Lasher-Trapp et al., 2016; Keppas et al., 2017; Ladino et al., 2017; and others).

Another source of artifacts in measurements of high concentration of ice by optical array probes (OAPs) is related to fragmentation of particle images when particles pass through the sample volume close to the edge of the depth of field (DoF) (Korolev, 2007a). A few 1- to 2-pixel images resulting from fragmentation of large out-of-focus images have an enhanced artificial contribution to particle concentration due to their very small sample volumes. This problem is recognized by many research groups. One solution to this is the exclusion of the first two or three size bins compromised by the ambiguity of the DoF definition and contamination by image fragments. Due to the extent that particles from the first two or three size bins (<30–80 µm depending on the OAP type) may significantly contribute to the total ice concentration, a limitation is imposed on the measurements of total concentration of ice particles in SIP cloud regions.

Most observations of an enhanced concentration of ice particles have been attributed to the HM process. The list of these studies extends over 30 publications, so we name only a few of them here (e.g., Ono, 1971, 1972; Harris-Hobbs and Cooper, 1987; Bower et al., 1996; and others). In these studies, the conclusions about the HM process were obtained based on the observed association with graupel and columnar ice crystals. Fewer studies attributed observations of high ice concentration to drop shattering (e.g., Koenig 1963, 1965; Braham, 1964; Rangno, 2008; Lawson et al., 2017). Ice–ice collisional fragmentation was identified as a source of SIP in natural clouds by Hobbs and Farber (1972), Takahashi (1993), and Schwarzenboeck et al. (2009). As can be seen, the identification of SIP gravitates towards the HM process, whereas mechanisms such as activation of INPs in transient supersaturation around freezing drops, ice fragmentation due to thermal shock, or sublimation were not even considered. In this regard, the question that arises is as follows: could these observations reflect an actual occurrence of different types of SIP?

The present study is focused on revisiting the role of different SIP mechanisms and identifying conditions favorable for SIP. Cloud regions with ongoing ice multiplication were identified with the help of a new technique based on the identification of small faceted ice crystals smaller than 60–100 µm measured by a cloud particle imager (CPI). The newly developed technique was applied to the data set collected in mature tropical mesoscale convective systems (MCSs) and in midlatitude frontal clouds. The roles of six possible mechanisms to generate the SIP particles are assessed using additional observations: fragmentation of freezing drops, splintering during the HM process, ice–ice collisional breakup, ice fragmentation during thermal shock, fragmentation during ice sublimation, and INP nucleation in transient supersaturation. The variety of environmental conditions associated with SIP will be considered based on six specific cases that sampled tropical MCSs (four cases) and midlatitude frontal clouds (two cases).

Measurements were conducted from the National Research Council (NRC) Convair 580 research aircraft during two field campaigns: High Ice Water Content (HIWC) and the Buffalo Area Icing and Radar Study 2/Weather Radar Validation Experiment (BAIRS2/WERVEX).

The HIWC flight operations were conducted out of Cayenne (French Guiana) in May 2015. A total of 14 Convair 580 research flights were conducted in the frame of the HIWC campaign with the average flight endurance of approximately 4 h. Most of the flights were performed in oceanic MCSs in altitudes ranging from 6500 to 7200 m and temperatures from 0 to -15 ∘C. The observations of MCSs were performed during their mature stages, when the area of clouds with longwave brightness temperatures colder than -50 ∘C from GOES-13 approached or surpassed its maximum. At that stage, most of the volume of the MCS above the freezing level was nearly glaciated, with embedded mixed-phase regions mainly associated with vertical updrafts (Korolev et al., 2018). However, the studied MCS during the observations remained dynamically active, with updrafts peaking at 15–20 m s-1.

The BAIRS2/WERVEX flight operations were conducted over southern Ontario and upstate New York from January to March 2017. A total of five research flights were conducted in precipitating frontal cloud systems. In the framework of this study, the analysis will be focused on two flights performed on 7 February and 24 March 2017 in the range of altitudes from 1500 to 3000 m and temperature ranges from +5 to -10 ∘C.

The NRC Convair 580 was equipped with state-of-the-art cloud microphysical and thermodynamic instrumentation. Size distributions of aerosol particles were measured by a DMT Ultra-High Sensitivity Aerosol Spectrometer (UHSAS) (Cai et al., 2008). Measurements of ice particle number concentration and ice water content (IWC) were extracted from composite particle size distributions measured by optical array 2-D imaging probes (OAPs), a PMS 2DC (Knollenberg, 1981), a SPEC two-dimensional stereo (2DS; Lawson et al., 2006), and a DMT precipitation imaging probe (PIP; Baumgardner et al., 2001). Cloud droplet size distributions were measured by a PMS forward scattering spectrometer probe (FSSP; Knollenberg, 1981) and a DMT cloud droplet probe (CDP; Lance et al., 2010). Cloud particle images were measured with the SPEC CPI (Lawson et al., 2001). Bulk liquid water content (LWC) and total water content (TWC) were measured with a SkyPhysTech Nevzorov probe (Korolev et al., 1998) and a SEA isokinetic probe (IKP) (Davison et al., 2011). A Rosemount icing detector was used for detection of liquid water at T<-5 ∘C (Mazin et al., 2001). The extinction coefficient was measured with the ECCC cloud extinction probe (Korolev et al., 2014). Vertical velocity was measured by Rosemount 858 (Williams and Marcotte, 2000) and Aventech AIMMS20 (Beswick et al., 2008). The Convair 580 was also equipped with NRC airborne W-band and X-band radars (NAWX) with Doppler capability (Wolde and Pazmany, 2005). The UHSAS and IKP were employed only during the HIWC project and were not used during BAIRS2/WERVEX.

In order to mitigate the effect of shattering artifacts on ice particle measurements (Korolev et al., 2011), all cloud particle probes were equipped with anti-shattering K tips (A. Korolev et al., 2013). The remaining shattering artifacts were filtered out during data post-processing with the help of the modified interarrival time algorithm (Korolev and Field, 2015).

The collected cloud microphysical data were processed with the help of the ECCC D2G software. This software allowed composite visualization and analysis of cloud microphysical, thermodynamic, radar, and aircraft data probes.

Knowledge about the initial size and number concentration of secondary ice is of great importance for the parameterization of SIP processes in atmospheric models, including weather prediction and climate models, particularly when using multi-moment microphysics schemes. The number and size of SIP particles determine the rate of water vapor depletion, release of latent heat, cloud dynamics, and glaciation time. Because of their slow fall velocity, small SIP particles will stay longer in the environment of their origin. Small fragments will also spread faster over clouds being transported by turbulent diffusion or vertical updrafts. On the contrary, large SIP fragments will precipitate down and have a shorter residence time in the cloud. Besides that, small ice fragments have a higher probability to be monocrystalline and therefore regrow into pristine faceted ice crystals, whereas large ice fragments most likely keep an irregular shape during the subsequent growth by water vapor deposition. The size of the fragments also plays an important role in charge separation and cloud electrification in general (e.g., Jayaratne et al., 1983). Altogether, the size distribution of primary SIP particles has a great significance for precipitation production, radiation properties, and lifetime of clouds.

In this section, we will estimate typical initial sizes of the SIP particles. Identification of initial sizes of secondary ice from the CPI imagery may be problematic because of the limited pixel resolution and ambiguity of distinguishing secondary ice fragments from natural cloud particles. In order to address this issue, we will use an indirect assessment of the initial sizes of secondary ice.

Figure 17 shows images of ice particles sampled in frontal clouds at temperatures ranging from -1 to -1.5 ∘C. All small faceted ice crystals in this cloud region appear to be thin plates (red frames in Fig. 17a). The thickness of the plates (h) is estimated as varying in the range from 10 to 20 µm. Since the smallest size of drops in this region is Dmin≈40µm>h, then the origin of these plates cannot be attributed to the deposition growth on frozen droplets.

The plates in Fig. 17a have plane parallel basal surfaces without steps. None of these thin plates have a visually identifiable center of initial growth. Such a shape is suggestive that the secondary ice particles, on which these plates were formed, were monocrystalline and their initial sizes (Lmin0) were smaller than the thickness of the plates, i.e., Lmax0<h. In this case, the secondary ice particles were completely embedded inside the plates and became part of the crystallographic lattice. So, there will be no additional refraction of transmitted light and the plates will appear uniform as in Fig. 17a. Therefore, the smallest initial size of the secondary ice particles is estimated as Lmin0≤10 µm.

Secondary ice particles representing a large end of their initial sizes are shown in Fig. 17, which presents images of fragments of shattered frozen drops. Most of these images were collected in SIP regions indicated by grey areas in Fig. 17. The maximum size of droplet fragments Fig. 17 is limited by Lmax0≈400 µm. In general, Lmax0 is determined by the maximum size of ice particles that participate in SIP. Thus, for the case of freezing raindrops, Lmax0 can be extended to a few millimeters.

The obtained estimates suggest that at the moment of initiation, secondary ice particles are represented by a cascade of sizes ranging from 10 µm (or smaller) to a few hundred microns (or larger). This estimate of initial sizes of SIP particles is consistent with the videos by Wildeman et al. (2017) and Lauber et al. (2018), which showed a variety of fragments with different sizes formed during shattering of freezing drops.

The shapes of secondary ice particles that develop during τcorr may shed light on the environmental conditions associated with the SIP initiation.

A quick look at the ice particle images in Figs. 6, 7, 14, 15, and 17 shows that the aspect ratio (R=h/a) of small ice crystals (hexagonal prisms) may noticeably vary within the same SIP cloud region.

Figure 19 shows small faceted ice crystals sampled in different SIP cloud regions (Fig. 5) with narrow temperature ranges from -5.5∘C<Ta<-5∘C. As seen from Fig. 19, despite the minor changes of Ta, the habits of small ice crystals varied from plates to long columns, and the aspect ratio changed in the range of 0.3<R<6.

Based on laboratory studies, R depends on the air temperature (Ta) and supersaturation over ice (Si) of the environment where the ice crystals were grown (e.g., Mason, 1971; Kobayashi, 1961; Bailey and Hallett, 2009). Therefore, it is expected that ice crystals that were formed in the same cloud volume and were exposed to the same Ta and Si should have the same R. Thus, the following question arises: why do ice crystals with different habits form in the same cloud volume?

There are several possibilities as to how R may vary. The environment with Ta>-4 ∘C and Sw>0 corresponds to the plate growth condition. Therefore, the plates shown in the upper row in Fig. 19 could be formed a few hundred meters below at Ta>-4 ∘C and then be brought up to the level of observation with a convective updraft. The internal structure of some plates in the upper row (i.e., image nos. 8, 9, 11, 14, and 15) is indicative of the changing Ta and Si that ice crystals may experience during ascent.

As seen in Fig. 19, most of the ice crystals are solid columns and thick plates. Following laboratory studies (Mason, 1971; Kobayashi, 1961; Bailey and Hallett, 2009), such ice habits form at Ta≈-5 ∘C in the environment supersaturated with respect to ice (Si>0) but undersaturated with respect to water (Sw<0). Therefore, the cloudy air in the SIP region, despite any presence of liquid drops, was undersaturated with respect to water. Such conditions may occur during the repartitioning of water between ice and liquid phases, when the WBF process is active (Korolev and Mazin, 2003; Pinsky et al., 2018).

Ice crystals with R∼1 may be formed as a result frozen droplets developing facets and turning into isometric hexagonal prisms (e.g., Gonda and Yamazaki 1978, 1984; Magono et al., 1979; Takahashi and Mori, 2006). Long columns with 3<R<6, shown in the two bottom rows in Fig. 19, correspond to the growth condition with Sw≥0 and Ta∼-5 ∘C (Mason, 1971; Kobayashi, 1961; Bailey and Hallett, 2009).

Accordingly, the shape of secondary ice crystals during the early stage of their evolution may vary from plates to solid columns. At a later stage, ice particles metamorphosize in shape in accordance to their evolving Ta(t) and Si(t). Thus, Figs. 9 and 10 show that columns tend to be the dominant shape of the aged secondary ice particles after ascending from 5600 m (-5 ∘C) to 7200 m (-15 ∘C). The aspect ratio and size of the aged columns vary in the ranges of 2<R<4 and 150µm<Lmax<450µm, respectively.

The purpose of this section is to identify how secondary ice particles may evolve after their formation. Understanding of possible scenarios of secondary ice evolution is important for the interpretation of the obtained results and developing cloud simulations. The interactions between secondary ice and environment are specifically important for small ice splinters (Lmax<10 µm) due to different types of instability related to this size range. Below, we consider four possible scenarios of how secondary ice particles may evolve after their production.

This section revisits the discussion of the SIP mechanisms, which might be responsible for the enhanced concentration of small ice particles.

One of the most striking findings of this study is the persistent observation of SIP immediately above the melting layer. This phenomenon was observed in clouds in different geographical regions and clouds with different dynamics. So, the following question arises: what are the conditions that make the cloud environment above the melting layer favorable for SIP?

One possible explanation is the formation of large drops (D∼60–300 µm) due to the recirculation of ice and liquid through the melting layer. Thus, ice particles turn into drops after falling through the melting layer. Then, these drops are brought back above the melting layer by convective or turbulent updrafts.

The recirculation hypothesis is supported by the observation of distortion of the bright band altitude in the convective cloud regions. An example of such distortion is presented in Fig. 23. Figure 23 shows a zoomed segment of the time series in Fig. 5, which includes reflectivity (Fig. 23c) and Doppler velocity (Fig. 23d) measured by onboard X-band radar when traversing a convective cell in the tropical MCS (09:40–09:45 UTC). Comparison of Fig. 23b and c shows a peak-to-peak correlation between the vertical wind velocity and elevation of the bright band in the convective cell. In a few points, the bright band moves up to ∼600–700 m above the level of the bright band in undisturbed cloud regions (indicated by the dashed line in Fig. 23c, d). Such distortion of the bright band is explained by moving melted drops by vertical updrafts to higher levels. A spatial coincidence of the SIP area (Fig. 23a), convective updraft (Fig. 23b), and the region with the elevated bright band (Fig. 23c) is supportive of the droplet recirculation hypothesis.

In order for a drop to ascend through the melting layer, the velocity of the updraft (uz) should exceed the drop fall velocity (ufall). Figures 5f and 13f show examples of when the vertical velocity above the melting layer in the tropical MCS reached uz≈8 m s-1 and in frontal clouds uz≈3 m s-1, respectively. Such updraft velocity is sufficient to move drops with D=100–200 µm (ufall=0.3–1 m s-1 at P=500 mbar) through the melting layer (ΔZ=500 m) during a reasonable time of a few tens of seconds to a few minutes.

The vertical travel distance of the liquid drops formed in the melting layer depends on the sustainability and endurance of the convective updraft, its vertical velocity, and droplet size. Smaller droplets have higher chances to travel deeper in the cloud compared to large ones. This is consistent with the observation of occurrence of droplets with D=80 and 100 µm, as shown in Figs. 5b and 8b, which were measured in the same MCS at two different altitudes (5600 and 7000 m), respectively. Rapid decrease of the concentration of large drops with temperature (and therefore altitude) in tropical MCSs is also seen in Fig. 11.

Another explanation of the formation of drizzle size drops is related to the collision–coalescence process. However, the observed LWC and number concentration of cloud droplets with D<40 µm in a mature tropical MCS during HIWC typically varied in the ranges of 0.01<LWC<0.1 g m-3 and 5<Ndr<40 cm-3, respectively, and were always associated with a mixed phase dominated by ice (0.5<IWC<3 g m-3) (e.g., Figs. 5d, g and 8d, g). High IWC and low Ndr and LWC will hinder the collision–coalescence process due to riming and WBF processes, which result in depletion of droplets. However, the collision–coalescence process cannot be ruled out in midlatitude frontal clouds as in Fig. 13.

After arriving in the supercooled environment above the melting layer, drops collide with aged ice particles, and some of these drops may form ice shells during freezing and shatter. This may result in initiation of SIP. Images of large drops frozen on the surface of aged ice particles observed above the melting layer are shown in Fig. 24. Most of the drops have deformed shapes with bulges. Formation of bulges may be accompanied by production of ice splinters by jetting or bubble bursting (Lauber et al., 2018).

In laboratory studies, Takahashi (1975) and Lauber et al. (2018) concluded that large drops have higher occurrence of shattering compared to small ones. Therefore, despite their lower concentration, shattering of fewer large drops may play the role of a trigger in initiating SIP. As follows from Tables 1 and 2, the concentration of small ice particles has the highest correlation with the droplets from the size range of 40–60 µm. Therefore, it is expected that the droplets from this size range have the highest contribution to SIP through maintenance of a chain reaction, as shown in Fig. 25a. The conceptual model summarizing the effect of the melting layer of SIP is presented in Fig. 25b.

In the frame of this study, we explored the microphysics of SIP cloud regions in tropical MCSs at the mature stage of their development and midlatitude frontal cloud systems within the temperature range of -15∘C<Ta<0∘C. SIP cloud regions were identified based on the presence of numerous small faceted ice crystals with Lmax<100 µm. The concentration of such small crystals peaked at 500–1000 L-1. Such particles cannot be a result of the recirculation of pre-existing aged ice. Based on the estimate that the age of such small crystals is limited by τcorr∼60–120 s, it was deduced that such ice crystals are still associated with the environment of their origin. This approximation was employed to assess the environmental conditions associated with SIP. As discussed below, our method has a number of limitations. However, it allowed obtaining the following conclusions: 1.

Most SIP cases were associated with a.

the presence of liquid droplets in the SIP region or somewhere in the vicinity;

We hypothesize that the initiation of SIP above the melting layer is related to the circulation of liquid drops through the melting layer. Liquid drops formed via melting ice particles are advected by the convective updrafts above the melting layer, where they collide with aged ice, freeze, and shatter. The ice splinters generated by shattering initialize the chain reaction of SIP.

In many cases, concentrations of frozen drops and their fragments exceeding expected concentrations of INPs by orders of magnitude were observed in SIP regions. This discrepancy implies that something other than heterogenous drop freezing must be contributing to SIP. The roles of mechanisms such as HM rime splintering, ice–ice collisional breakup, thermal shock fragmentation, and INP activation around freezing drops cannot be confidently linked to SIP based on the collected data, for reasons explained at length. Thus, we conclude by process of elimination that the mechanism of droplet shattering during freezing is very likely a critical contributing factor to SIP in these cases.

The conclusions obtained in this study are based on the interpretation of observations which were obtained along needle-like penetrations of large cloud systems at some time of their evolution. The fact that initial and boundary conditions of the studied cloud systems are poorly known, and the trajectories of cloud volumes and cloud particles are not identifiable, brings a certain ambiguity into the interpretation of the obtained observations. So, in many ways, the conclusions in this work bear a qualitative character, and the emphasis of this study is on the observational part. The obtained results are expected to contribute to our understanding of SIP, and they may be used by cloud modeling studies for evaluation of secondary ice production in the numerical simulations of clouds (e.g., Qu et al., 2018), for instance, by evaluating where such small particles appear in high concentrations in simulations.

In microphysics schemes that predict the number concentration of ice crystals, i.e., spectral (bin) and multi-moment bulk schemes (e.g., Khain et al., 2004; Milbrandt and Yau, 2005), SIP is most commonly modeled exclusively with a simple parameterization of the HM process. If riming of graupel is occurring in the temperature range between -3 and -8 ∘C, an ice splinter production rate is computed for this process, with a maximum at -5 ∘C, decreasing linearly to zero at the ends of the temperature range. Assumptions of the crystal number concentration tendency and the size of the new crystals are made, based broadly on the published results of Hallett and Mossop (1974). Parameterizations that exist for other mechanisms of secondary ice production have been less widely included in modeling efforts to explain apparent SIP in observed cloud systems, but when INPs are treated rigorously in a prognostic manner, such mechanisms are generally found to be too weak to explain observed ice even when considered additively, including drop shattering and ice–ice collisions (e.g., Fridlind et al., 2007; Fu et al., 2019). It is perhaps unsurprising that such additional mechanisms are not more widely adopted if they provide only weak ice generation and still unsatisfactory results compared with observations, in addition to being highly uncertain due to a paucity of robust laboratory data. Ultimately, it may be important in atmospheric models for some purposes to improve the representation of both primary and secondary ice production in microphysics parameterization schemes based on more recent observations and the hypothesized processes. It will be a topic of future research to apply the observations presented to develop new parameterizations of SIP. However, parameterizations based on field observations will necessarily remain to some degree speculative without a strong foundation of laboratory measurements that can provide clear and repeatable evidence of specific mechanism strengths.

The obtained results bring up a more general question about the limitations of airborne techniques in the identification of major mechanisms and their efficiencies in SIP. Airborne observations deal mostly with the results of SIP in the form of different stages of aged secondary ice. However, attempts to quantify or parameterize the secondary ice production from in situ observations are limited because the initial and boundary conditions are mostly unknown. One of the fundamental limitations of airborne techniques is that they do not allow for monitoring and identifying the process of secondary ice directly. In this regard, the pursuit of SIP research lends itself well to laboratory experiments and should be emphasized in this area.