The MAC field campaign was conducted in November–December 2015 over coastal Antarctica and the Weddell Sea with the aim to offer detailed measurements of the microphysical and aerosol properties of the coastal Antarctic atmosphere. MAC included an extensive suite of airborne and ground-based instruments, a detailed description of which can be found in O'Shea et al. (2017). Here we only offer a brief recap of the instrumentation used in this study.

Cloud particle size distributions were derived using the images from a 2D Stereo (2DS; SPEC Inc., USA; Lawson et al., 2006) probe with a nominal size range from 10 to 1280 µm (10 µm pixel resolution). Shattering effects at the probes' inlet were corrected by applying “anti-shatter” tips (Korolev et al., 2011) and inter-arrival time (IAT) post analysis (Crosier et al., 2011). The 2DS is a single particle instrument, measuring all particles that pass through its sample volume, which depends on particle size and the data integration period. For example, at 300 µm, one count measured over a 1 s averaging window equals a concentration of 0.27 L-1; the uncertainty due to counting statistics is 100 %. Total uncertainty is even higher but cannot be quantified.

Aerosol particle measurements of sizes from 0.25 to 32 µm were made using the GRIMM optical particle counter (GRIMM model 1.109), while a cloud aerosol spectrometer (CAS; Baumgardner et al., 2001; Glen and Brooks, 2013) measured particles between 0.6 and 50 µm. Following the methodology of Young et al. (2019) and O'Shea et al. (2017), we only consider GRIMM measurements of particles with diameter smaller than 1.6 µm in our analysis to avoid including data subject to inlet losses at larger particle sizes. Finally, the aircraft also included instrumentation to measure temperature, turbulence, humidity, radiation and surface temperature (King et al., 2008).

For our investigations, we focus on the MAC case examined in Young et al. (2019) for which they showed that the H-M process, as currently parameterized in WRF, cannot explain the observed ICNCs. Young et al. (2019) utilized measurements from two MAC flights, M218 and M219, combined in one case study; both flights were conducted on 27 November 2015 over the Weddell Sea (Fig. 1): M218 between 15:18 and 16:42 UTC and M219 between 20:27 and 22:30 UTC. On that day, a low pressure system persisted over the eastern Weddell Sea resulting in a southeasterly flow reaching the aircraft with air mass back trajectories from around the low pressure system, towards the Antarctic Peninsula and southern Patagonia (O'Shea et al., 2017).

The temperature and microphysical conditions encountered during these flights are representative of the MAC campaign (see Table 1 in O'Shea et al., 2017, and Fig. S6 in Young et al., 2019). Cloud measurements were collected mainly within the lowest 1.1 km above sea level (a.s.l.) during both flights and within a temperature range of ∼-9 to -3 ∘C. The sampled stratocumulus clouds were dominated by supercooled liquid drops, while ice formation occurred in isolated ice patches characterized by substantially enhanced ICNCs: the mean (max) ICNCs in these cloud regions were 1.16 (9.03) L-1 and 3.33 (87.31) L-1 for M218 and M219, respectively. The mean concentration of aerosols with sizes between 0.5 and 1.6 µm was 0.56 and 0.41 scm-3 (cm-3 at standard temperature and pressure) for the two flights. Such low aerosol conditions and concurrently high ICNC concentrations within this temperature range are frequently found in the western Antarctic Peninsula (Lachlan-Cope et al., 2016). Moreover, similar cloud droplet concentrations (Ndrop) were measured during both flights (Young et al., 2019): the mean Ndrop was 82.7 cm-3 for M218 and 100.4 cm-3 for M219, which are comparable with previous observations from the Antarctic Peninsula (Lachlan-Cope et al., 2016).

This study is conducted with the WRF model (Skamarock et al., 2008) version 4.0.1 by applying the same model setup as in Young et al. (2019). Two domains with a respective horizontal resolution of 5 and 1 km are used, in which the inner one is two-way nested to the parent domain (Fig. 1). The polar stereographic projection is applied. The outer domain is centered at 74.2∘ N, 30∘ E and includes 201 × 201 grid points, while the second domain consists of 326 × 406 grids. Both domains have a high vertical resolution with 70 eta levels, 25 of which correspond to the lowest 2 km of the atmosphere. The model top is set to 50 hPa. The simulation period spans from 26 to 28 November 2014, 00:00 UTC, allowing for a 24 h spin up period before the day of interest (27 November). The model time step is set to 30 (6) s for the outer (inner) domain, while output data are produced every 30 min.

Input data for the initial, lateral and boundary conditions for the simulations are obtained from the European Centre for Medium-Range Weather Forecasting reanalysis (Dee et al., 2011), as recommended by Bromwich et al. (2013). For both shortwave and longwave radiation components, the RRTMG radiation scheme (Rapid Radiative Transfer Model for general circulation models) is applied. The Mellor–Yamada–Nakanishi–Niino (MYNN; Nakanishi and Niino, 2006) level-2.5 closure planetary boundary layer (PBL) and surface options are also implemented in combination with the Noah Land Surface Model (Noah LSM; Chen and Dudhia, 2001) which includes a simplified thermodynamic sea ice model. Given the short run length, time-varying sea ice concentrations are not utilized. Young et al. (2019) used the Polar WRF V3.6.1 to represent fractional sea ice, a capability not available in standard WRF V3.6. However, this option has been made available in the more recent V4.0.1 that we use in this study. Following Young et al. (2019), the sea ice albedo is set to 0.82 with a default thickness of 3 m, and snow accumulation depth on sea ice is allowed to vary between 0.001 and 1.0 m.

A so-called “cumulus parameterization” for shallow-convection subgrid processes is not activated in both domains to ensure all cloud processes are represented by the grid-scale microphysics scheme. Note that 5 km is a general upper limit for a convection-resolving resolution (Klemp, 2006; Prein et al., 2015). Cloud microphysics are parameterized following Morrison et al. (2005), hereafter M05. M05 performs well in reproducing Antarctic clouds, resulting in improved representation of the liquid phase and thus the cloud radiative effects being compared to less advanced microphysical schemes (Listowski and Lachlan-Cope, 2017; Hines et al., 2019). This bulk microphysics scheme predicts mixing ratios and number concentrations for cloud ice, rain, snow and graupel species. While the mass mixing ratio of cloud water is a prognostic variable, Ndrop is a constant parameter. The default value of the scheme is 200 cm-3; here Ndrop is set to 92 cm-3, which is the mean value of M218 and M219 flight measurements (see Sect. 2.2).

A detailed description of the ice formation processes in M05 and the implemented BR parameterizations is offered in Appendix A and B, respectively. We assume that collisions that include at least one large particle (thus ice–snow, ice–graupel and graupel–snow, snow–snow, and graupel–graupel) result in ice multiplication; contributions from collisions between small ice particles (cloud ice) are neglected. In addition to the control (CNTRL) simulation, which corresponds to the default setup of M05 and accounts only for H-M, we perform seven sensitivity simulations with varying descriptions of FBR. We also perform an additional simulation as in CNTRL except with no H-M and thus no SIP at all, which is referred to as NOSIP in the text.

In two sensitivity simulations with active breakup, we assume, as in Hoarau et al. (2018), a constant number of fragments generated per collision. This number is constrained by in situ measurements from the Arctic (Schwarzenboeck et al., 2009) which indicated that one-branch ice crystals are more common in polar clouds, resulting in the ejection of a single fragment after collision with another ice particle. However, this analysis (Schwarzenboeck et al., 2009) included only dendritic crystals with a size larger than 300 µm. Based on these results, we perform two simulations: FRAG1 assumes all collision types generate one fragment without any size restrictions, while FRAG1siz allows for ice multiplication only if the particle that undergoes fragmentation is larger than 300 µm. Note that because cloud ice with a characteristic diameter larger than 250 µm is converted to snow in the M05 scheme, collisions that include cloud ice are assumed to not result in any multiplication in FRAG1siz.

The standard temperature-dependent formula of Takahashi et al. (1995) for FBR, applied in Sullivan et al. (2018b), is tested here in the TAKAH simulation. However, Takahashi et al. (1995) used 2 cm hail balls in their experiments, which is an unrealistic setup. For this reason, we perform an additional simulation, TAKAHsc, in which this relationship is further scaled with size (see Appendix B).

Finally, the Phillips parameterization is implemented in three simulations with varying rimed fractions (Ψ) for the cloud ice or snow particles that undergo fragmentation; Ψ is not predicted in most bulk microphysics schemes, including M05, and thus it is prescribed as a constant. Note that FBR is a function of Ψ only for the ice crystals or snowflakes that undergo breakup but not for graupel (Appendix B). Graupel is assumed to have Ψ≥0.5, while the other ice types are characterized by a lower rimed fraction. 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). These simulations are referred to as PHIL0.2, PHIL0.3 and PHIL0.4 in the text, in which the number indicates the assumed values of Ψ for cloud ice and snow.

In Fig. 2a, the modeled total ice number concentrations (cloud ice + snow + graupel; Nisg) derived for the region encompassing the two MAC flights (Fig. 1) are compared with measurements derived from the 2D Stereo (2DS) probe (see Sect. 2.1 for details). ICNCs in Fig. 2 are interpolated to match the time resolution of the temperature measurements. Then cloud ice statistics are calculated for Nisg>0.005 L-1, an indicator for the presence of an ice patch (O'Shea et al., 2017; Young et al., 2019). Moreover, since 2DS cannot resolve the shape (thus cloud phase) of particles smaller than 80 µm, only modeled ice particles with sizes larger than this threshold are considered in Fig. 2, like in Young et al. (2019). While mean and maximum statistics are discussed below, additional statistical metrics (e.g., median and interquartile range) are shown in Fig. S1 (Sect. S1).

The mean observed Nisg for the whole MAC campaign generally fluctuates between 0.5 and 4.5 L-1. The variation in Nisg with temperature is somewhat larger for our case study (27 November) as maximum mean concentration goes up to ∼ 6.4 L-1 at T=-6.5 ∘C. Consistently lower concentrations are observed for temperatures ≤ -7 ∘C, but the temperature statistics are poor for this temperature range as very few observations are available (Fig. 2a). The CNTRL simulation consistently underestimates the mean observations, producing mean Nisg∼0.1 L-1 over the examined temperature range (Fig. 2a). NOSIP produces similar results to CNTRL, suggesting that the H-M process included in default M05 (CNTRL) is hardly effective at all.

PHIL0.2 and PHIL0.3 also produce similar mean ICNCs to CNTRL (Fig. 2a, b), suggesting that lightly to moderately rimed ice particles do not contribute to ice multiplication through collisional breakup. However, the higher rimed fraction in PHIL0.4 results in very good agreement with mean observations (Fig. 2a). FRAG1siz produces very weak ice multiplication that cannot explain observed ICNCs, but when the size restrictions are ignored (FRAG1), the model usually overestimates mean values, particularly at temperatures ≤ 7 ∘C for which no good measurement statistics are available (see discussion above). A similar behavior is shown by TAKAHsc, while TAKAH is the simulation that produces the most unrealistically high mean ICNCs (Fig. 2a).

Overall, CNTRL, PHIL0.2 and PHIL0.3 cannot reproduce the observed spectrum (Fig. 2b) and substantially underestimate the frequency of ICNCs larger than 2 L-1. FRAG1siz gives a wider representation of the size range in better agreement with observations; however, it cannot reproduce ICNCs larger than 30 L-1. PHIL0.4, FRAG1 and TAKAHsc can successfully reproduce the observed range of values (Fig. 2b), but the relative frequency remains substantially more underestimated in PHIL0.4. In contrast, TAKAH often overestimates the relative frequency of ICNC values larger than 10 L-1 (Fig. 2b). Maximum ICNCs in TAKAH are 2952 L-1, which is about 34 times larger that the observed maximum value: 88 L-1. The maximum ICNC in PHIL0.4 is 161 L-1, which agrees to within a factor of 2 with observations, while it is slightly larger for FRAG1 and TAKAHsc: 188 and 181 L-1, respectively. On the other hand, maximum concentrations are substantially underestimated in CNTRL (5.8 L-1), PHIL0.2 (2 L-1) and PHIL0.3 (3.5 L-1).

Vertical distributions of cloud ice (Ni), graupel (Ng), snow (Ns) and total ICNC (Nisg) number concentrations are examined in Fig. 3a–d for all simulations except TAKAH, which produces unrealistically large concentrations. The observed ICNCs are also shown in Fig. 3a and c. For consistency with M05, which converts all cloud ice particles with characteristic diameters larger than 250 µm to snow, the same threshold is adopted for splitting the observational dataset in these two ice categories. Graupel concentrations cannot be distinguished in the measurements (hence no “Nov 27” profile in Fig. 3b); however, the model simulations that are in better agreement with observations (Fig. 2) suggest that these are negligible compared to cloud ice and/or snow concentrations. Graupel concentrations in Fig. 3b are shown for the whole size spectrum. In contrast, cloud ice (Fig. 3a), snow (Fig. 3c) and total ICNCs (Fig. 3d) include only particles with a size larger than 80 µm for consistency with the observations shown in the same panel.

PHIL0.2 and PHIL0.3 produce similar Ni (Fig. 3a) to CNTRL but reduced Ng (Fig. 3b) values and reduced Ns (Fig. 3c); these mean Ni and Ns profiles are orders of magnitude lower than the observed values. Ni (Fig. 3a) and total ICNCs (Fig. 3d) are enhanced in FRAG1siz compared to CNTRL but remain a substantially lower than the observed values. PHIL0.4 produces Ni close to the observations (Fig. 3a), while Ns (Fig. 3c) and thus total ICNCs (Fig. 3d) are somewhat underestimated. FRAG1 and TAKAHsc are in better agreement with Ns observations (Fig. 3c), especially at heights below 750 m a.s.l; this is also reflected in total ICNCs (Fig. 3d). Activating BR generally results in a reduction of Ng (Fig. 3b). This decrease can be larger than 1 order of magnitude in some of the best performing simulations compared to CNTRL; however, we cannot assess which of these graupel profiles better represents reality. Nevertheless, we can overall conclude that PHIL0.4, FRAG1 and TAKAHsc result in improved agreement of the vertical distribution of total ICNCs with observations compared to the rest of the simulations (Fig. 3d), including the default setup of M05. Moreover, cloud ice concentrations (Fig. 3a) are comparable to snow concentrations (Fig. 3c) in these three simulations, in agreement with observations. In contrast, simulations with deactivated or negligible BR result in substantially larger number of snow than cloud ice particles. This indicates that BR shifts the ice particle spectra to smaller sizes, which results in a more realistic representation of the ice microphysical characteristics.

The simulated liquid water content (LWC) is compared with CAS observations in Fig. 4. All simulations, except TAKAH, produce similar or slightly overestimated mean LWC at temperatures ≤-3.5 ∘C; at -3 ∘C, the mean observed values are higher (Fig. 4a). An overestimation of LWC in these runs is more evident in Fig. 4b; the observed spectrum does not include values larger than 0.5 g m-2, while the simulated spectra are wider. An exception to this is the TAKAH simulation which underestimates mean LWCs and glaciates clouds at temperatures below -7 ∘C (Fig. 4a), while it produces a narrower LWC spectrum compared to the one observed (Fig. 4b). Apart from TAKAH, the remaining simulations produce similar liquid water properties with minor improvements in the runs with reduced LWC values, e.g., in FRAG1 (Fig. 4b).

To examine how deviations in ICNCs affect climate, mean radiative fluxes at the surface and at the top of the atmosphere (TOA) for all model simulations are presented in Table 1. Note that mass mixing ratio fields for all cloud species are provided from the microphysics to the radiation scheme, but no information on droplet and ice effective radius is exchanged.

Increasing BR multiplication has a pronounced impact on shortwave radiation as it results in decreasing sunlight reflection and thus increasing downward surface radiation (SWDSFC). Upward surface radiation (SWUSFC) is a function of SWD and thus exhibits similar behavior. This is due to the fact that increased BR efficiency (Fig. 2) results in decreased liquid water path (LWP) and cloud albedo. The difference between CNTRL and the simulations that improve ICNC representation (PHIL0.4, FRAG1 and TAKAHsc) fluctuates between 12.5 and 24.4 W m-2 for SWDSFC and 6.9 and 13.7 W m-2 for SWUSFC (Table 1).

Cloud longwave radiative effects are mainly determined by cloud liquid properties since liquid water is more opaque to longwave radiation than ice particles. However, no substantial differences in mean LWP are indicated for CNTRL (40.1 g m-2), PHIL0.2 (45.6 g m-2), PHIL0.3 (46.2 g m-2), PHIL0.4 (32.5 g m-2) and FRAG1siz (38.6 g m-2) since LWP values fall within the black body emission range (Stephens, 1978). Optically thinner clouds are produced in TAKAHsc (20.7 g m-2) and especially in FRAG1 (21.1 g m-2) and TAKAH (3.2 g m-2) runs. Note that most simulations, including CNTRL, produce wider LWC spectra than those observed by overestimating cloud liquid (Fig. 4b). Generally, decreasing liquid content is in better agreement with observations (see Sect. 4.1), suggesting that including the BR process in M05 likely shifts the simulated LWPs towards more realistic values. However, excessive ice multiplication, as in TAKAH, results in unrealistic liquid properties (Fig. 4a) and thus errors in surface radiation.

Pronounced reduction in LWDSFC is only found for the simulations FRAG1, TAKAH and TAKAHsc, which have a mean LWP well below 30 g m-2, the lowest limit of the black body emission range (Stephens, 1978). In all other simulations, the reduction in cloud liquid due to BR is not large enough to alter the cloud emissivity significantly. The upward longwave component (LWUSFC) remains almost unaffected in all simulations (≤0.6 W m-2). Young et al. (2019) showed that underestimation of ICNCs results in significant positive and negative biases in the surface cloud radiative forcing (CRF) over the coastal areas; our results agree with their findings as CRF biases vary between -68 and +87 W m-2 for the most realistic simulations (Fig. S2, Sect. S2). Furthermore, the difference between CNTRL and the realistic simulations in upward radiation flux at TOA (Table 1) is also more pronounced for the shortwave component (SWUTOA), fluctuating between 4 and 8.6 W m-2, and less significant for LWUTOA (1.3 and 2.7 W m-2). Ultimately, both surface and TOA radiation results indicate that a correct representation of SIP in the atmospheric models is critical for the projection of the energy budget and thus for the future Antarctic climate.

To investigate the interactions between BR and H-M, we compare simulations in which the H-M efficiency is either enhanced or turned off. Young et al. (2019) remove all liquid thresholds from the H-M description, allowing for the process to become active over the whole droplet spectrum. However, this change resulted in very weak ICNC enhancement in their simulations. Here we further remove all graupel and/or snow thresholds from the H-M description (Appendix A) following the methodology of Atlas et al. (2020), which implies that there are no size restrictions for the initiation of the process. This modification is applied to the CNTRL, PHIL0.3 and PHIL0.4 setups, resulting in three additional sensitivity tests: CNTRL_NOTHRES, PHIL0.3_NOTHRES and PHIL0.4_NOTHRES, respectively. Furthermore, in addition to NOSIP which corresponds to the CNTRL setup but without H-M, another two simulations are performed with BR active but H-M completely deactivated: PHIL0.3_NOHM and PHIL0.4_NOHM.

Mean ICNCs in CNTRL_NOTHRES are enhanced by on average a factor of 3 compared to CNTRL (Fig. 5a). However, this simulation underestimates concentrations at temperatures larger than -7 ∘C; the mean observed value at this range is 2 L-1, while the simulated mean is 0.3 L-1. Good agreement between CNTRL_NOTHRES and observations is only achieved at temperatures <-7 ∘C, in which statistical metrics for the two MAC cases are poor (see Sect. 4.1). While PHIL0.3 did not result in any substantial multiplication, mean ICNCs in PHIL0.3_NOTHRES are about 5 times larger. A similar enhancement is observed in PHIL0.4_NOTHRES compared to PHIL0.4, but it becomes substantially larger at colder temperatures. However, while the 95th percentiles for CNTRL_NOTHRES and PHIL0.3_NOTHRES are similar and more comparable to observations, PHIL0.4_NOTHRES produces values larger than 10 L-1 at all temperatures considered (Fig. 5b).

Excluding the temperature range (<-7 ∘C) that does not include a substantial number of measurements to evaluate model results, mean ICNC observations generally lay between PHIL0.3_NOTHRES and PHIL0.4_NOTHRES in this set of simulations, while CNTRL_NOTHRES produces somewhat lower values (Fig. 5a). However, this setup overestimates H-M efficiency as it does not include any size limitations, which is not consistent with current knowledge on the H-M mechanism derived from laboratory studies (Hallet and Mossop, 1974; Choularton et al., 1980). Nevertheless, the adapted thresholds are ad hoc and unsuitable for the examined conditions (Atlas et al., 2020); these should be refined to get a more a realistic H-M effect in polar clouds.

Deactivating H-M completely does not substantially impact the results. This further confirms the fact that the prescribed ad hoc thresholds prevent the initiation of the process in the studied conditions. Furthermore, it indicates that the BR mechanism can explain the observed ICNCs independently of whether H-M is active or not.

None of the utilized primary ice nucleation parameterizations are likely representative of the pristine conditions encountered over the high-latitude Southern Ocean; thus, it is likely that primary ice formation is overestimated in this case. To examine how the uncertainty in parameterizations for primary ice affects SIP efficiency, we perform two sets of simulations by dividing or multiplying the efficiency of all primary ice production mechanisms (immersion freezing, contact freezing, and deposition and/or condensation-freezing nucleation) by a factor of 10. Specifically, the first set with diminished ice nucleation includes CNTRL_INP0.1, PHIL0.3_INP0.1 and PHIL0.4_INP0.1, while the second set with enhanced nucleation consists of CNTRL_INP10, PHIL0.3_INP10 and PHIL0.4_INP10.

Decreasing primary ice production by a factor of 10 results in a substantial decrease in ICNCs: about 25 %–40 % fewer values (depending on the BR setup) exceed the 0.005 L-1 threshold and are included in the presented statistics (Fig. 6) compared to the simulations with the standard primary ice formation setup. BR multiplication is again evident only in the simulation with a high Ψ (Fig. 6). The ICNC enhancement in PHIL0.4_INP0.1 compared to CNTRL_INP0.1 is about on average 7 times larger (Fig. 6a). While these results are in good agreement with observations in the temperature range with poor measurement statistics (see discussion above), PHIL0.4_INP0.1 underestimates mean observations at temperatures >-7 ∘C (Fig. 6a). Moreover, the 95th percentile in this simulation remains substantially lower compared to observed values at all temperatures (Fig. 6b). These results indicate that an initial ICNC concentration of 0.1 L-1 is essential to initiate significant multiplication that can reproduce the observed values.

Increasing primary ice production by an order of magnitude in CNTRL_INP10 still results in underestimated ice concentrations than those observed, providing additional evidence for the significant role of SIP in these conditions. The increased concentration of primary ice crystals enhances BR efficiency in PHIL0.3_INP10 compared to PHIL0.3; however, the produced mean concentrations still are lower than the observed. The difference in mean ICNCs between PHIL0.4_INP10 and PHIL0.4 is on average about a factor of 2; thus, PHIL0.4_INP10 is also close to the observations, especially those from the whole MAC campaign (Fig. 6a). Nisg95 is also larger in PHIL0.4_INP10 compared to PHIL0.4 and in better agreement with observations (Fig. 6b).

In summary, the above results indicate that BR is not sufficient to explain observations when the available primary ice concentrations are substantially lower than 0.1 L-1, which is the mean primary ICNC produced in the NOSIP simulation (Fig. 2a). Yet, INPs over the Southern Ocean are often substantially lower (McCluskey et al., 2018; Schmale et al., 2019; Welti et al., 2020). Ice seeding from clouds above the boundary layer was suggested by Young et al. (2019) as a key contributor to the primary ICNC levels for the studied case (see their Supplement). Another process that can enhance primary ice nucleation is aerosol transport from the Antarctic continent, where terrestrial INPs are expected to be higher (Vergara-Temprado et al., 2018). Moreover, a combination of BR and the H-M mechanism, whose efficiency is substantially restricted in the current version of M05 (see Sect. 4.3), might also explain the observed number concentrations; this was also the case for Arctic stratocumulus conditions in Sotiropoulou et al. (2020). Understanding these interactions between different processes in the Antarctic region would likely provide insights into the conditions that favor the development of isolated ice patches with substantially high ICNCs within predominantly supercooled liquid clouds. In higher INP conditions, which are likely less representative of the coastal Antarctic climate, the activation of BR parameterization still results in improved model performance.