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Ice multiplication from ice-ice collisions in the high Arctic: sensitivity to ice habit, rimed fraction and the spectral representation of the colliding particles

Abstract. Atmospheric models often fail to correctly reproduce the microphysical structure of Arctic mixed-phase clouds and underpredict ice water content, even when simulations are constrained by the observed levels of ice nucleating particles. In this study we investigate whether ice multiplication from ice-ice collisions, a process missing in most models, can account for the observed cloud ice in a stratocumulus cloud observed during the Arctic Summer Cloud Study campaign. Our results indicate that including ice-ice collisions can improve the modeled cloud water properties, but the degree of influence depends on other poorly constrained microphysical aspects that include ice habit, rimed fraction and cloud ice-to-snow autoconversion rate. Simulations with dendrites are less sensitive to variations in the assumed rimed fraction of the particle that undergoes break-up, compared to those with planar ice. Activating cloud ice-to-snow autoconversion decreases the sensitivity of the break-up process to both the assumed ice habit and rimed fraction. Finally, adapting a relatively small value for the threshold diameter at which cloud ice is converted to snow enhances break-up efficiency and improves the macrophysical representation of the cloud.


However, despite their significant climatic impact, Arctic mixed-phase clouds remain a great source of 35 uncertainty in climate models (Stocker et al., 2013;Taylor et al., 2019). To accurately predict the radiative effects of mixed-phase clouds in models, an adequate description of their microphysical structure, such as the amount and distribution of both liquid water and ice, is required . Both ice nucleation and liquid drop formation require seed particles to be present known as ice nucleating particles (INPs) and cloud condensation nuclei CCN), respectively. However, the observed 40 ice crystal number concentrations (ICNCs) are often much higher than the observed INP concentrations in the Arctic (Fridlind et al., 2007;Gayet et al., 2009;Lloyd et al., 2015), where INPs are generally sparse (Wex et al., 2019). Moreover, model simulations constrained by INP measurements frequently underpredict the observed amount of ice (Fridlind and Ackerman, 2019).
Secondary Ice Processes (SIP) have been suggested as the reason why ice crystal concentrations 45 exceed INP levels (Field et al., 2017;Fridlind and Ackerman, 2019). SIP involve the production of new ice crystals in the presence of pre-existing ice, without requiring the presence of an INP. The most wellknown mechanism is rime-splintering (Hallet and Mossop, 1974), which refers to the ejection of ice splinters when ice particles collide with supercooled liquid drops. Rime-splintering is active only in a limited temperature range, between -8 o C and -3 o C, and requires the presence of liquid droplets both 50 smaller than 13 µm and larger than 25 µm (Hallett and Mossop, 1974;Choularton et al., 1980). Moreover, recent studies have shown that rime-splintering alone cannot explain the observed ICNCs in polar clouds even within the optimal temperature range (Young et al., 2019;Sotiropoulou et al., 2020a,b). Ice fragments may also be generated when a relatively large drop freezes and shatters (Lauber et al., 2018;Phillips et al., 2018); drop-shattering, however, has been found insignificant in polar 55 conditions (Fu et al., 2019;Sotiropoulou et al., 2020a). Finally, ice multiplication can occur from mechanical break-up due to ice-ice collisions (Vardiman et al., 1978;Takahashi et al., 1995). Despite that breakup has been observed in in-situ measurements of Arctic clouds (Rangno and Hobbs, 2001; spacing of 25 m. The integration time step is variable (~ 1-3 sec), calculated continuously to satisfy the 145 Courant-Friedrichs-Lewy criterion for the Leapfrog method. While this approach prevents numerical instabilities, its dynamic nature does not allow sensitivity simulations to be performed with exactly the same timestep. Lateral boundary conditions are periodic, while a sponge layer in the top 400 m of the domain dampens vertically-propagating gravity waves generated during the simulations. To accelerate the development of turbulent motions, the initial ice-liquid potential temperature profiles are randomly 150 perturbed in the first 20 vertical grid levels with an amplitude less than 3×10 -4 K.
Surface pressure and temperature are set to 1026.3 hPa and -3.2 o C, respectively, constrained by surface sensors deployed on the ice-pack. The surface moisture is set to the saturation value, which reflects summer ice conditions. The surface albedo is assumed to be 0.85, which is representative of a multi-year ice pack. In MIMICA, subsidence is treated as a linear function of height: w LS = -D LS . z,155 where D LS is set 1.5×10 -6 s -1 and z is the height in meters. Finally, the prescribed number of CCN is set to 30 cm -3 over the whole domain, which represents mean accumulation mode aerosol concentrations observed during the stratocumulus period (cf. Igel et al., 2017). The duration of all simulations is 24 hours, where the first 4 hours constitute the spin-up period.  Ickes et al. (in prep.) recently implemented several primary ice production (PIP) schemes in MIMICA. Here, we utilize the empirical ice nucleation active site density parameterization for 165 immersion freezing, which is based on Connolly et al. (2009) and was further developed by Niemand et al. (2012) for Saharan dust particles. This formulation was used by Ickes et al. (2017) to describe the freezing behavior of different dust particle types, including microline (Appendix A). Microcline is a feldspar type that is known to be an efficient INP (Atkison et al., 2013). As no aerosol composition (or INP) measurements are available for the ASCOS campaign, we will use this INP type as a proxy for an 170 aerosol constituent that can produce primary ice at the relatively warm sub-zero temperatures (-7 o C to -10 o C) of the initial observed cloud profile (Fig. 1a). At these temperatures it is reasonable to assume that most of the PIP occurs through immersion freezing (Andronache, 2017), i.e. that an aerosol must be both CCN active and contain ice-nucleating material to initiate ice production. Thus, we will simply assume that a specified fraction of the CCN population contains some efficient ice-nucleating material, 175 here represented as feldspar, and match this fraction so that the model simulates reasonable values of LWP, IWP and ICNC (Appendix A, Text S1). Based on this procedure, we specify that the CCN population contains 5% microline, a value that results in realistic primary ICNCs (Wex et al., 2019), but in an underestimate of the IWP and an overestimate of the LWP (Text S1, Fig. S1). Note that even though we assume this relatively high fraction of ice-nucleating material (Text S1, Fig. S1), MIMICA still underestimates the IWP; we hypothetize that secondary ice production may be the reason for this bias.

Ice multiplication from ice-ice collisions
The observed in-cloud temperatures are generally below the rime-splintering temperature range, 185 except for the somewhat warmer temperatures near cloud base (Fig. 1a). Moreover, drop-shattering has been found ineffective for Arctic conditions (Fu et al., 2019;Sotiropoulou et al., 2020a). Our simulations further support the inefficiency of both these processes, as the concentration of large raindrops is too low (below 0.1 cm -3 ) to initiate them (Fig. S1c). Hence we focus solely on ice multiplication from ice-ice collisions. 190 We implement the parameterization developed by Phillips et al. (2017a) in MIMICA and allow for ice multiplication from cloud ice-cloud ice, cloud ice-graupel, cloud ice-snow, snow-graupel, snowsnow and graupel-graupel collisions (Appendix B). The generated fragments are considered "small ice" crystals and are added to the cloud ice category in the model. The Phillips parameterization explicitly considers the effect of ice type, ice habit and rimed fractions of the colliding particles on fragment 195 generation (Appendix B). The sensitivity of the model performance to these parameters is examined through sensitivity simulations.

Sensitivity simulations
A detailed description of the sensitivity tests is provided in this section, while a summary is 200 offered in Table 2.

The role of ice habit
Cloud ice observed within the examined temperature range can either be shaped as a dendrite or a plate, depending on the supersaturation with respect to ice (Pruppacher and Klett, 1997). However, as 205 the mean vapor density excess in the simulated cloud layer varies between 0.03 and 0.22 g m -3 , it is not clear which shape should theoretically dominate (Pruppacher and Klett, 1997). Moreover, observations often indicate variable shapes within the same temperature conditions (Mioche et al., 2017). The formulations for ice multiplication due to break-up are substantially different for these two ice habits (Appendix B). Generally, the number of fragments (F BR ) generated from break-up of a dendrite is lower 210 than that generated by a plate, assuming that the two particles have the same mass and size (Appendix B).
ΜΙΜΙCA allows for variable treatment of the ice habit for the cloud ice category. These variations correspond to different characteristic parameters in the (m = a m D b m ) and fallspeed-diameter (v = a v D b v ) relationships, whose values (Table 1) are adopted from Pruppacher and Klett (1997) and the two simulations CNTRLDEN and CNTRLPLA are performed. 'CNTRL' refers to simulations that account only for PIP, while the suffixes 'DEN' and 'PLA' indicate dendritic and planar cloud ice shape, respectively. 220

The role of rimed fraction
F BR is parameterized as a function of the rimed fraction (Ψ) of the ice crystal or snowflake that undergoes break-up; fragment generation from break-up of graupel does not depend on Ψ (see Appendix B). This parameter is not explicitly predicted in most bulk microphysics schemes, but can substantially affect the multiplication efficiency of the break-up process (Sotiropoulou et al., 2020a). 225 For this reason, we will consider values of Ψ for cloud ice and snow between 0.2 (lightly rimed) and 0.4 (heavily rimed) (Phillips et al., 2017a, b); graupel particles are considered to have Ψ ≥ 0.5. Both Sotiropoulou et al. (2020a) and(2020b) found that ice multiplication in polar clouds at temperatures above -8 o C is initiated only when a highly rimed fraction of cloud ice and snow is assumed. Their conclusions however may not be valid for our case, as the temperature and microphysical conditions are 230 substantially different.
The effect of varying Ψ is examined for the two ice habits that prevail in the observed temperature range (Section 3.2.2). The performed simulations are referred to as BRDEN0.2, BRDEN0.3, BRDEN0.4, and BRPLA0.2, BRPLA0.3, BRPLA0.4, for dendrites and plates respectively (see Table 2). 'BR' indicates that collisional break-up is active, while the number 0.2-0.4 corresponds to 235 the assumed value of Ψ.

The impact of the representation of the ice particle spectrum
The MIMICA LES has previously been used to study ice-ice collisions in Sotiropoulou et al. (2020a), however, they used a parcel-model-based parameterization of the process, instead of implementing a 240 break-up parameterization as a part of the MIMICA microphysics scheme. Sotiropoulou et al. argued that the efficiency of the process is likely underestimated in bulk microphysics schemes, where the dynamics of the ice particle spectrum is poorly represented and fixed particle properties are assumed typically for three ice types (cloud ice, graupel, snow), which is rather unrealistic. Their argument might be particularly true for the studied case where no snow is produced in the simulations with dendrites 245 (Fig. S1d).The MIMICA microphysics scheme allows for snow formation only through aggregation of cloud ice particles. However, these are particularly few in the CNTRLDEN simulation and thus collisions between them are negligible. Other microphysics schemes (Morrison et al., 2005;Morrison and Gettelman, 2008) typically include an ice-to-snow autoconversion parameterization, which means that cloud ice particles become snowflakes once their size exceeds a specified critical diameter (D c ). 250 To test the impact of a broader ice particle spectrum on the multiplication effect of break-up, we implement a description for ice-to-snow autoconversion in MIMICA (Appendix C). Eidhammer et al. https://doi.org/10.5194/acp-2020-786 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License.

Sensitivity to ice habit
The impact of the assumed ice habit is investigated using the two simulations that account only for PIP (CNTRLDEN and CNTRLPLA) and two of the simulations that include break-up: BRDEN0.2 270 and BRPLA0.2. Time series of LWP and IWP are shown in Fig. 2, while the domain-averaged ice particle concentrations for the three ice categories are shown in Fig. 3. Median and interquartile statistics are summarized in Table 3, while the ICNC enhancement from break-up is shown in the Supplementary Information (Text S2, Fig. S2).
Small differences are observed in the integrated cloud water quantities between CNTRLDEN 275 and CNTRLPLA, as both produce median LWP values ~143 g m -2 and median IWP values of 1.8-1.9 g m -2 . Hence, both simulations overestimate cloud liquid ( Fig. 3a-b) and underestimate ice ( Fig. 2c-d).
Specifically, the median observed LWP (73.8 g m -2 ) is overestimated by almost a factor of two, while IWP (7 g m -2 ) is underestimated by more than a factor of 3.5 (Table 3), which is larger than the uncertainty in the observations. Activating break-up results in improved simulated water properties, 280 independently of the assumed ice habit. LWP decreases by 32 g m -2 (37 g m -2 ) in BRDEN0.2 (BRPLA0.2) compared to CNTRLDEN (CNTRLPLA) at the end of the simulation. Ηowever, in both BR simulations, the LWP remains above the observed interquartile range ( Fig. 2a-b): the median LWP is 105 and 119 g m -2 in BRDEN0.2 and BRPLA0.2. The simulated IWP is also improved when breakup is considered, as it remains within the observed interquartile range for most of the simulation time 285 (Fig. 3d). Statistical metrics of IWP are shifted to larger values in BRDEN0.2 compared to BRPLA0.2 (Table 3), suggesting a better agreement of BRDEN0.2 with observations. https://doi.org/10.5194/acp-2020-786 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License.
Planar ice is expected to generate more fragments per collision compared to plates if the diameter of the particles and the collisional kinetic energy are the same (see equations 6-7 in Appendix B). However, BRDEN0.2 eventually produces about the same or slightly more ice compared to 290 BRPLA0.2 ( Fig. 2c-d). Figure 4a shows that the cloud ice number (Ni) enhancement due to break-up of dendrites is more consistent compared to planar ice (Fig. 3b, Table 3). Ni for planar ice displays large fluctuations; large Ni enhancements are followed by substantial decreases (Fig. 3b). This variability indicates that precipitation processes (i.e. the precipitation sink) are more effective in the simulations with plates, which is linked to the larger characteristic mass and terminal velocity specified for this ice 295 habit, compared to dendrites of similar size ( Table 1). The larger lifetime of dendritic Ni in BRDEN0.2 within the cloud layer leads to more frequent collisions with liquid drops and thus enhanced graupel formation ( Fig. 3c), compared to BRPLA0.2 (Fig. 3d). Fragment generation in BRDEN0.2 further enhances cloud ice aggregation compared to CNTRLDEN as indicated by the fact that snow formation is only favored in the former (Fig. 3e). This is not always the case for BRPLA0.2 where enhanced 300 removal of Ni, as discussed above, suppresses ice-ice collisions and thus snow formation compared to CNTRLPLA (Fig. 3f).
Despite the different feedbacks between ice multiplication and precipitation in BRDEN0.2 and BRPLA0.2, ICNC enhancement rarely exceeds a factor of 2 when compared to the CNTRLDEN and CNTRLPLA simulations (Text S2, Fig. S2). However, this weak enhancement found for the ASCOS 305 case can still bridge the gap between observed and modeled ice water content, especially when a dendritic ice habit is assumed. The median IWP enhancement is approximately 2.7 and 3.3 in the BR simulations with dendrites and plates, respectively. Moreover, including break-up reduces the bias in LWP, although this parameter remains overestimated by the model, independently of the chosen ice habit. Stevens et al. (2018) showed that simulations with interactive aerosols produce less LWP during 310 the examined case, compared to simulations with a fixed background CCN concentration. Thus deviations between the simulated and observed LWP could also be attributed to the simplified aerosol treatment, rather than to uncertainties in the representation of the break-up process.

Sensitivity to rimed fraction 315
Since the rimed fraction of cloud ice/snow particles is not explicitly predicted in MIMICA, we investigate the sensitivity of the simulated LWP and IWP to the prescribed Ψ value (Fig. 4). To better understand the differences between the simulations, fragment generation rates (P BR ) for the different collision types are shown in Fig. 5 (see Appendix B for detailed formulas). P BR results are only presented for cloud ice-graupel, graupel-snow and snow-snow collisions since we find negligible 320 contributions from cloud ice-cloud ice, cloud ice-snow and graupel-graupel collisions.
All sensitivity simulations with dendrites produce similar LWP values (Fig. 4a), constantly remaining above the observed interquartile range. Small differences are also found in IWP (Fig. 4c).
The median LWP fluctuates between 104.8-110.9 g m -2 and IWP between 5-6.3 g m -2 among the three sensitivity simulations (Table 3), suggesting that cloud liquid remains overestimated while ice 325 properties are in agreement with the observed range. The total fragment generation from all collisions remains constantly below 1.4 L -1 s -1 with small differences between the three simulations with varying Ψ The effect of Ψ is more evident in the simulations with planar shape (Fig. 4b,d). BRPLA0.2 is the only simulation that sustains a cloud layer throughout the simulated period (Fig. 4b), since total P BR remains below 2.2 L -1 s -1 throughout the simulation time ( Fig. 5b,d,f) and ICNC enhancement never exceeds a factor of 3 (Fig. S2). The cloud dissipates in BRPLA0.3 and BRPLA0.4 after 17 and 7 hours, 335 respectively (Fig. 4b). The cloud in BRPLA0.4 rapidly dissipates owing to excessive multiplication, with the total P BR reaching a maximum of 73.6 L -1 s -1 (Fig. 5b,d,f). However, the cloud reforms after 15 hours; LWP increases again to values larger than 100 g m -2 by the end of the simulated period (Fig. 4b), while IWP remains at substantially underestimated levels compared to observations (Fig. 4d). The total fragment generation is more moderate in BRPLA0.3 than in BRPLA0.4 reaching a maximum rate of 340 14.6 L -1 s -1 after 14.5 hours (Fig. 5b,d,f), causing a gradual cloud glaciation. ICNCs in BRPLA0.3 are enhanced by up to a factor of 80, compared to CNTRLPLA, while in BRPLA0.4 the ICNC enhancement can be up to three orders of magnitude (Fig. S2). Our findings are in agreement with Loewe et al. (2018) who showed a prescribed ICNC value of 10 L -1 can lead to cloud dissipation for the specific case study. However, collisional break-up of moderately to highly rimed plates is likely not the 345 reason that lead to cloud dissipation after 31 August 9 UTC in reality (see Section 2.2). In the next section we will show that the excessive multiplication in these two simulations is due to limited snow formation in this model set-up.
Variations in ice habit do not result in significant changes in cloud properties when a low Ψ (~0.2) is assumed (see Section 4.1). However, the assumed ice habit significantly impacts cloud 350 conditions for moderate or high Ψ values. Furthermore, in the simulations with dendrites, statistics of cloud water properties show low sensitivity to variations in Ψ (Table 3). In contrast, errors in Ψ could substantially change the results for planar ice, as it exerts significant control on cloud life-cycle.

Sensitivity to the representation of the ice particle spectrum 355
Implementing cloud ice-to-snow autoconversion in MIMICA is expected to alter the representation of the ice particle spectrum and thus impact the efficiency of the break-up process (see Section 3.3.3). The simulation with a relatively low critical diameter for autoconversion, set to 125 µm, https://doi.org/10.5194/acp-2020-786 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License.
is examined in subsection 4.3.1. The simulations with the cloud ice/snow separation diameter set to 500 µm is discussed in subsection 4.3.2. 360

Cloud ice-to-snow autoconversion with critical diameter 125 µm
CNTRLDENauto1 produces somewhat larger IWP than CNTRLDEN (Fig. 6c) and falls within the observed range after 18 hours of simulation, however, LWP values remain overestimated (Fig. 6a). 365 These small increases (decreases) in IWP (LWP) in simulations with autoconversion are associated with larger ICNCs; the maximum concentration is about two times larger in CNTRLDENauto1 (Fig. S3) compared to CNTRLDEN (Fig. S2). This is due to the fact that conversion of cloud ice to snow increases snow formation but at the same time results in fewer graupel particles (not shown), likely due to decreasing efficiency of cloud-ice and liquid droplet collisions. As graupel particles have larger 370 terminal velocities than snow (see Section 3.3.1), the net result of decreasing (increasing) graupel (snow) formation is less precipitation and thus enhanced ICNCs within the cloud layer. Nevertheless, limiting the ice precipitation sink in CNTRLDENauto1 still results in underestimated (overestimated) IWP (LWP) statistics (Table 3); the median IWP and LWP is 4 g m -2 and 130 g m -2 , respectively.
In simulations with break-up, BRDEN0.2auto1 and BRDEN0.4auto1, IWP increases in better 375 agreement with reality ( Fig. 6b, Table 3). While median LWP remains overestimated compared to observations (Table 3), these are the only simulations so far that result in LWP values (Fig. 6a) that eventually match the observed range (at least within the last 9 hours of simulation). This result is more clearly seen in Fig. 7: while CNTRLDEN and CNTRDENauto1 fail to reproduce the observed relative frequency of the LWP-IWP fields, the frequency distributions of BRDEN0.2auto1 and BRDEN0.4auto1 380 are shifted towards more realistic values. Also note that while BRDEN0.4auto1 produces statistical metrics closer to the observations (Table 3), BRDEN0.2auto1 gives a better representation of the LWP/IWP variability (Fig. 7).
Including snow autoconversion in simulations with planar ice that account only for PIP also results in enhanced ICNCs (Fig. S3) due to decreasing graupel formation and thus decreasing 385 precipitation (see discussion above). This explains the IWP enhancement in CNTRLPLAauto1 compared to CNTRLPLA (Fig 6d, Table 3). Yet, median IWP remains underestimated more than a factor of two in this simulation (3.1 g m -2 ) compared to observations (7 g m -2 ), while LWP statistics are substantially overestimated (Table 3). Moreover, autoconversion does not improve substantially the simulated LWP-ΙWP relationship compared to ASCOS measurements (Fig. 8). Activating break-up for 390 this set-up improves modeled cloud ice properties, as BRPLA0.2auto1 and BRPLA0.4auto1 produce median IWP at 6.1 g m -2 and 6.4 g m -2 . The LWP bias is also improved, with median values 89.6 g m -2 and 77.8 g m -2 in BRPLA0.2auto1 and BRPLA0.4auto1, respectively. Furthermore, these simulations produce more realistic distributions of the LWP-ΙWP fields compared to set-ups that do not account for https://doi.org/10.5194/acp-2020-786 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License. break-up (Fig. 8). From all simulations presented so far, BRPLA0.4auto1 is the one that produces the 395 most realistic interquartile range for cloud liquid properties (Table 3).

Cloud ice-to-snow autoconversion with critical diameter 500 µm
Adapting a larger cloud ice/snow separation diameter results in enhanced (reduced) liquid (ice) water properties (Fig. 9). This is because lower cloud ice concentrations are converted to snow, which 400 enhances graupel formation (not shown) through cloud ice -droplet collisions and thus ice precipitation (see discussion above). In particular, ICNCs in CNTRLDENauto2 and CNTRPPLAauto2 do no exceed 1.3 L -1 (Fig. S4), which is about 38% smaller than the maximum values found in CNTRLDENauto1 and CNTRLPLAauto1 (Fig. S3). Moreover, water paths in these simulations are very similar to CNTRLDEN and CNTRLPLA (Fig. 9, Table 3). 405 Activating break-up for this set-up results in median IWP=5.4 g m -2 in both BRDEN0.2auto2 and BRDEN0.4auto2, while the median LWP values are 103.8 and 106.9 g m -2 , respectively. These are lower (larger) than the median IWP (LWP) results produced in the corresponding runs with D c =125 µm (Table 3). In particular, BRDEN0.2auto2 and BRDEN0.4auto2 produce more similar results as the simulations that do not account for autoconversion (BRDEN0.2 and BRDEN0.4 in Fig. 2 and Table 3). 410 Simulations with plates respond in a similar manner to variations in separation diameter as those with dendrites (Fig. 9b,d). CNTRLPLAauto2, BRPLA0.4auto2 and BRPLA0.2auto produce increased (reduced) liquid (ice) water properties compared to CNTRLPLAauto1, BRPLA0.2auto1 and BRPLA0.4auto1, respectively (Table 3). However, while CNTRLPLAauto2 and BRPLA0.2auto2 produce similar results as the corresponding simulations with inactive autocoversion (CNTRLPLA, 415 BRPLA0.2), this is not the case for BRPLA0.4auto2. While BRPLA0.4 results in cloud glaciation, BRPLA0.4auto2 sustains the cloud layer throughout the simulation. This indicates that activating cloud ice-to-snow autoconversion can moderate secondary ice production and prevent cloud dissipation, independently of the assumptions in separation diameter.
The large differences in the cloud life-cycle produced by BRPLA0.4 and 420 BRPLA0.4auto1/BRPLA0.4auto2 occur because small ice fragments accumulate within the cloud layer in the former simulation (Fig. 6b), continuously feeding the break-up process. In contrast, active autoconversion eventually converts the new ice fragments into snow, allowing for their faster depletion through precipitation. In other words, as precipitation processes are more effective for snow than for cloud ice, snow formation prevents accumulation of cloud ice particles and thus decreases the frequency 425 of ice particle collisions (Figs 5b,d,f and 10b,d,f). This snow precipitation feedback inhibits the explosive multiplication (Yano and Phillips, 2011;2016) observed in the simulations that do not allow for cloud ice depletion through the autoconversion process.
The better agreement with observed LWP and IWP for the simulations with a separation diameter of 125 µm compared to those with 500 µm is due to changes in a number of ice processes that impact each other. Increasing graupel formation with increasing D c (see discussion above) results in more frequent snow-graupel collisions; P BRsg is on average about 3 to 5 times larger in simulations with D c = 500 µm compared to those with a similar set-up but D c = 125 µm (Fig. 10c-d). For the same reason, cloud ice-graupel collisions also become more frequent with increasing D c , but the fragment generation rate of this collision type is generally small (Fig. 10a-b). Meanwhile, the increased snow 435 formation through decreasing D c results in more efficient snow-snow collisions (Fig. 10e-f). This collision type results in larger fragmentation rates when D c is set to 125 µm, eventually exceeding 1 L -1 s -1 (2 L -1 s -1 ) in simulations with plates (dendrites); these are on average about 7-8 (8.5-10) times larger than the corresponding rates in simulations with D c = 500 µm. Thus while changes in D c impact all collision types, the changes in snow-snow collision efficiency are mainly responsible for the 440 differentiations in cloud water properties observed between the two simulation set-ups (Figs. 6,9).
In summary, while it was concluded in the previous subsection that the assumed ice habit for highly-rimed ice particles can result in completely different cloud conditions (Fig. 4), this sensitivity is substantially smaller when ice-to-snow autoconversion is active (Fig. 6, 9). At the same time, while the assumed Ψ played a significant role in the simulations with plates presented in Fig. 4b, its impact is 445 substantially decreased when autoconversion is allowed (Fig. 6,9b). Finally, the mean ICNC enhancement due to break-up in all these simulations remains weak, rarely exceeding a factor of 2-3 ( Fig. S3-4). Yet, despite the weak ice enhancement, activation of break-up can still substantially impact the simulated macrophysical properties of the cloud (Figs. 7-8), provided that cloud ice-to-snow autoconversion at a relatively low D c is adopted. 450

Discussion
Ice formation processes in Arctic clouds are sources of great uncertainty in atmospheric models, often resulting in underestimation of the cloud ice content. In this study we attempt to quantify the impact of ice multiplication through collisional break-up for summertime high-Arctic conditions and 455 examine the sensitivity of the efficiency of this process to a number of uncertain parameters, such as the ice habit, ice type and rimed fraction of the colliding particles.
Uncertainties in ice habit are in general not important as long as a low rimed fraction (~0.2) is assumed. However, while changes in the rimed fraction have a small impact on the simulations with dendrites, break-up of moderately to highly rimed particles can result in explosive multiplication in the 460 simulations with plates, if cloud ice-to-snow autconversion is not accounted for in the model. This is because the freshly formed small fragments can stay long and accumulate in the cloud ice category, continuously feeding the multiplication process as they grow, until the cloud glaciates. If a substantial amount of the new planar fragments would be converted to snow, then this ice type has a shorter lifetime within the cloud layer. As a result, the continuous feeding of break-up is balanced by 465 precipitation processes, which prevents cloud dissipation. https://doi.org/10.5194/acp-2020-786 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License.
Activation of cloud ice-to-snow autoconversion generally decreases the sensitivity of the simulation results to both the assumed ice habit and the rimed fraction. This result indicates that if the autoconversion process allows for sufficient snow formation, there is no great need to accurately constrain these two parameters in the description of break-up; note that there are limited observations of 470 rimed fraction and ice habits in the Arctic, which are highly variable parameters (Mioche et al., 2017).
The break-up efficiency can be largely affected by the separation diameter prescribed in the autconversion process; this is the threshold diameter at which cloud ice is converted to snow. This parameter has little physical basis (Eidhammer et al., 2014) and cannot be measured directly, thus it is generally tuned in atmospheric models. 475 Our simulations suggest that decreasing the separation diameter for cloud ice and snow promotes snow formation and thus snow-snow collisions, which is a very efficient collision type. As a result, adapting a relatively small threshold improves the representation of cloud water properties and especially cloud liquid content, which is substantially overestimated in all other simulation set-ups.
However apart from ice-to-snow autoconversion, other factors can also contribute to decreasing liquid 480 properties, such as the prognostic treatment of aerosols (Stevens et al., 2018). Thus, while with the current model setup with fixed background aerosol concentrations, a low separation diameter results in more realistic cloud properties, it is uncertain whether the same tuning would work for other models with a more advanced aerosol treatment.
Nevertheless, ICNC enhancement in the most realistic simulations rarely exceeds a factor of 2-3. 485 This suggests a lower efficiency of the break-up process in the examined temperature range, compared to warmer polar conditions studied by Sotiropoulou et al. (2020a,b). In their studies they focused on the Hallet-Mossop temperature range characterized by lower INP concentrations that do not exceed 0.1 L -1 and found a 10-20 fold enhancement in ICNCs due to break-up compared to the available INPs.
However in sensitivity tests of primary ice nucleation, they showed that increasing INPs result in 490 decreasing secondary ice production.
In the present study, relatively high INP conditions are adapted. Primary ICNCs increase with time as cloud cools through radiative cooling, reaching a maximum of 1 L -1 towards the end of the simulation; these concentrations are even larger in simulations with active cloud ice-to-snow autoconversion. While primary ice formation in our set-up is likely overestimated (Fridlind et al., 2007;495 Wex et al., 2019), our results support the conclusions of Sotiropoulou et al. (2020a,b) and further suggest that as primary ice nucleation becomes more and more enhanced at colder temperatures, ice multiplication from ice-ice collisions will likely become less significant. It is interesting that while laboratory experiments from Takahashi et al. (1995), based on collisions of two hailstones, suggest increasing ice multiplication with decreasing temperature from -3 o C to -15 o C, our findings indicate that 500 this might not happen in the real atmosphere due to increasing availability of INPs.

Conclusions
In this study, ice multiplication from ice-ice collisions is implemented in the MIMICA LES, following Phillips et al. (2017a,b), to investigate the role of this process for ice-liquid partitioning in a 505 summertime Arctic low-level cloud deck observed during ASCOS. The sensitivity of the simulated results to the prescribed ice habit, rimed fraction and the ice particle spectrum of the colliding particles (i.e. by including ice-to-snow autoconversion) is investigated. Our findings can be summarized as follows:

510
• For the simulated temperature range (-12.5 to -7 o C), ice multiplication from collisional break-up is generally weak, enhancing ICNCs by on average no more than a factor of 2-3 in simulations that are most consistent with observations. This enhancement can result in a 2-3 fold increase in median IWP and deplete median LWP by 30-40%, compared to simulations that do not account for this process. Simulation set-ups that produce very large ICNC enhancements, up to 2-3 orders of 515 magnitude, result in cloud glaciation.
• Ice multiplication from break-up of dendrites is not very sensitive to assumptions regarding the rimed fraction. Break-up of lightly rimed planar ice also results in similar cloud water as simulations with dendrites. In contrast, break-up of highly rimed plates can lead to cloud glaciation, if cloud iceto-snow autoconversion is not accounted for in the microphysics scheme. 520 • Activating cloud ice-to-snow autoconversion results in substantially reduced sensitivity to the assumed ice habit as well as the rimed faction. Decreasing the critical diameter in the autoconvertion process, and thus allowing for more snow to form, enhances break-up efficiency.
This model set-up substantially improves the simulated distribution of the LWP-IWP fields compared to observations. 525 While ice enhancement due to ice-ice collisions in Arctic clouds is weaker within the examined temperature range compared to warmer sub-zero temperatures and lower INP conditions (Sotiropoulou et al. 2020a,b), including this process in models can still have a significant impact on the cloud macrophysical state. However, processes that govern the ice particle spectral representation, such as 530 cloud ice-to-snow autoconversion in bulk microphysics schemes, substantially affect the simulated collisional break-up. In particular, uncertainties in the separation diameter between cloud ice and snow can have a larger effect on the break-up efficiency than poorly constrained parameters that are directly included in the description of the process (i.e. ice habit or rimed fraction). Hence, to capture the effects of ice multiplication from ice-ice collisions, it is important to better understand the cloud ice-to-snow 535 autoconversion process and to evaluate the separation parameter through model-observation comparisons for the range of atmospherically-relevant conditions. https://doi.org/10.5194/acp-2020-786 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License.
Code and data availability: ASCOS data are available at https://bolin.su.se/data/ascos/ . The modified LES code is available upon request 540 Competing interests: The authors declare that they have no conflict of interest.

APPENDIX A: PRIMARY ICE PRODUCTION
The immersion freezing parameterization is based on the concept of ice nucleation active site density.
The formulation of Niemand et al. (2012) is used, adapted for microline dust particles (Ickes et al., 2017). It is utilized here as the only primary ice production mechanism. In this scheme, the number of 560 nucleated ice particles (N INP, m -3 ) is given as function of !!" and temperature T ( o C) : X is the percentage of !!" (m -3 ) that acts as efficient INP, e.g. 50%, 10%, 5% (see Text S1 in Supporting Information) and n s (m -2 ) the ice nucleation active site density of the INP species assumed (here microcline). r =46.5 . 10 -9 m is the mean radius of the nucleating particles for ASCOS (Ickes et al., in prep.). The temperature dependency is determined by the coefficients 565 α=0.73°C -1 and b=9.63.

APPENDIX B: ICE MUTIPLICATION FROM ICE-ICE COLLISIONS
Three types of ice particles are considered in MIMICA: small (cloud) ice, snow, and graupel. Ice multiplication is allowed after cloud ice-cloud ice cloud ice-snow, cloud ice-graupel, graupel-snow, 570 snow-snow and graupel-graupel collisions. Collisions between cloud ice-cloud ice, cloud ice-snow, graupel-snow and snow-snow are already included in the model to represent aggregation. The rate of number ( !!" ) and mass ( !!" ) concentration of particle 1 that is collected by particle 2 during these https://doi.org/10.5194/acp-2020-786 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License. collisions is given: where subsrcript 'n' and 'm' denote number-and mass-weighted parameters, respectively. N and Q 580 refer to number and mass concentration of the particle, while D and v represent its diameter and terminal velocity. a is the shape parameter of the size distribution for each particle, set to 2 for cloud ice (independently of the ice habit, 1 for snow and 0 for graupel, while b v is a coefficient in the fallspeeddiameter relationship (see Section 3.3.1). E col is the collection efficiency, given as a function of temperature (K): E col= exp [0.09(T-273.15)]. For self-collection, thus collisions between same ice types, 585 the above equations take the form: !! (4).

590
The above equations are further used to determine collisions that result in ice multiplication, by replacing the collection efficiency with the term E * =1-E col . This means that the collisions that do not result in aggregation are those that contribute to SIP. Since aggregation after cloud-ice-graupel and graupel-graupel collisions does not occur, we assume that 100% of these collisions result in multiplication: E * =1. 595 The Phillips et al. (2017a) parameterization allows for varying treatment of !" depending on the ice crystal type and habit: are the masses of the colliding particles and Δu n12 is the difference in their terminal velocities. A correction is further applied in Δu n12 to account for underestimates when !! ≈ !! , following Mizuno et al. (1990) and Reisner et al. (1998): 605 A represents the number density of the breakable asperities in the region of contact. C is the asperityfragility coefficient, which is a function of a correction term (ψ) for the effects of sublimation based on the field observations by Vardiman (1978). Exponent γ is a function of rimed fraction for collisions that 610 include cloud ice and snow. Particularly, for planar ice or snow, with rimed fraction Ψ < 0.5, that undergoes fracturing after collisions with other ice particles: For fragmentation of dendrites, A and C are somewhat different : 615 For graupel-graupel collisions, an explicit temperature dependency is included in the equation,while γ is contant: The parameterization was developed based on particles with diameters 500 µm < D < 5 mm, however Phillips et al. (2017a) suggest that it can be used for particle sizes outside the recommended range as long as the input variables to the scheme are set to the nearest limit of the range. Moreover, an upper limit for the number of fragments produced per collision is imposed, set to !" !"# = 100 (Phillips et al., 625 2017a), for all collision types. The production rate of fragments is estimated using Eq. (1) or (3) and one of the proposed formulations for F BR above, e.g. !"!" = !!" !" . Whenever mass transfer also https://doi.org/10.5194/acp-2020-786 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License.
occurs, e.g. if assume that fragments ejected from snow-gruapel collisions are added to the cloud ice category, we assume that this is only 0.1% of colliding mass (Eq. (2) or (4)) that undergoes break-up (Phillips et al. 2017a). 630

APPENDIX C: CLOUD ICE -TO -SNOW AUTOCONVERSION
For cloud ice-to-snow autoconversion, we use the formula adapted in Wang and Chang (1993) for cloud ice-to-graupel and graupel-to-hail autoconversion: and D c is the critical diameter that separates the two ice cateogries. N i and Q i are the number and mass cloud ice concentrations, respectively.          Table 2).   Table 2).
Cloud ice-to-snow autoconversion is active in panels (c-e). Collisional break-up is included only in panels (d-e) with the cloud ice/snow rimed fraction set to (d) Table 2).
The set-up in each panel is similar to Fig. 7, except that in all simulations a planar cloud ice habit is assumed.   Fig. 6 but for simulations that include cloud ice-to-snow autoconversion with separation diameter 500 µm (see Table 2). https://doi.org/10.5194/acp-2020-786 Preprint. Discussion started: 2 October 2020 c Author(s) 2020. CC BY 4.0 License. Figure 10: Timeseries of domain-averaged fragment generation rate (L -1 s -1 ) from (a, b) cloud ice-1120 graupel (P BRig ), (c, d) snow-graupel (P BRsg ) and (e, f) snow-snow collisions (P BRss ), for simulations with active cloud ice-to-snow autoconversion and collisional break-up (see Table 2). The cloud ice habit is set to (a, c) dendrites and (b, d) plates. Red (blue) lines represent simulations with a prescribed rimed fraction set to 0.2 (0.4). Darker (lighter) colors correspond to simulation with a cloud ice/snow separation diameter set to 125 µm (500 µm).