The simulations were performed using two models. MIMICA (the MISU/MIT Cloud-Aerosol model) is an LES model that has been successfully used for simulating Arctic mixed-phase clouds (e.g. Ovchinnikov et al., 2014; Savre and Ekman, 2015; Igel et al., 2017; Stevens et al., 2018; Christiansen et al., 2020). The model solves the equations for a non-hydrostatic, anelastic atmospheric system; a full description of the model can be found in Savre et al. (2014). A two-moment bulk microphysics scheme (Seifert and Beheng, 2001) is used to calculate the prognostic variables (i.e. mass mixing ratio and number concentration) of five different hydrometeor types considered, namely cloud droplets, raindrops, cloud ice, graupel and snow. All hydrometeor categories have mass distributions in the form of regular gamma functions. Autoconversion and self-collection of liquid particles are also calculated, as described in Seifert and Beheng (2001). A pseudo-analytic method is used to model the supersaturation, with the integration of condensation/evaporation at the model time step of ∼2 s (Morrison and Grabowski, 2008). The terminal fall speed of the hydrometeors is calculated using a simple power law of the diameter of the particle, which determines the wet deposition (Pruppacher and Klett, 1997). To represent an aerosol population of different particle sizes and chemical compositions, MIMICA includes a two-moment aerosol module (Ekman et al., 2006). All aerosol modes are described with lognormal distributions. In the model, aerosols can act as cloud condensation nuclei, following the kappa–Köhler theory (Petters and Kreidenweis, 2007), but not as ice nuclei. The number concentration of ice crystals is prescribed and kept quasi-constant during the simulations (Ovchinnikov et al., 2011, 2014). This parameterization mimics immersion freezing, i.e. ice can only form if there is supercooled water present. Aggregation of ice crystals is permitted in the model. The radiative transfer is calculated, following a four-stream radiative transfer solver (Fu and Liou, 1993), which includes six bands for shortwave and 12 bands for longwave radiation.

The second model used is the Regional Atmospheric Modeling System (RAMS; Cotton et al., 2003), which has also been successfully used in studies of Arctic mixed-phase clouds (e.g. Avramov and Harrington, 2010; Ovchinnikov et al., 2014). RAMS is a flexible model that is most commonly used for cloud-resolving and large-eddy simulations. It uses a two-moment bin-emulating bulk microphysics scheme to predict the mass and number mixing ratios of liquid and ice hydrometeor species (Meyers et al., 1997; Saleeby and van den Heever, 2013). In this study, six species are used, namely, cloud droplets, raindrops, cloud ice, snow, graupel and hail. RAMS typically uses two cloud ice species, but only one was used in this study as was done in MIMICA. Collision–coalescence of liquid drops is done through the use of lookup tables that are generated by solving the stochastic collection equation (Feingold et al., 1997). Condensation depends explicitly on the hydrometeor properties and allows for supersaturation at the end of the time step of 1.5 s (Walko et al., 2000). The terminal fall speed of the hydrometeors is calculated based on piecewise power laws (Mitchell, 1996). RAMS also includes a user-defined number of lognormal aerosol distributions. Aerosol particles act as CCN and are activated using additional lookup tables generated from an offline parcel model based on kappa–Köhler theory (Saleeby and van den Heever, 2013). Aggregation of ice crystals is permitted. Radiative transfer is calculated following Harrington (1997).

The Arctic Summer Cloud Ocean Study (ASCOS) campaign took place in the summer of 2008 on board the Swedish icebreaker Oden, and included a 3-week ice drift with enhanced meteorology measurements when Oden was anchored to a large ice floe slightly north of 87∘ N. A full description of the expedition can be found in Tjernström et al. (2014). This campaign has, so far, been one of the most extensive studies in the central Arctic, focusing on the atmosphere, clouds and aerosol properties and their linkages to the microbiological life in the upper ocean. To investigate a case with a quasi-steady-state cloud regime, the simulations are based on a period that was characterized by a persistent, low-level SMP cloud observed from 18:00 universal coordinated time (UTC) on 30 August to 12:00 UTC on 31 August 2008. The period represents one of the last days of the ice drift episode, which took place from 12 August to 2 September 2008. During this period, the number concentration of accumulation mode particles was relatively low (Leck and Svensson, 2015). Therefore, a change in the aerosol population could be particularly important for inducing cloud perturbations that may affect the surface energy budget.

During the ice drift, radiosondes were launched from the ice surface every 6 h and provided profiles of thermodynamic properties (e.g. pressure, temperature and relative humidity) and wind speeds (see Fig. 1). The one from 05:35 UTC on 31 August 2008 was representative of the conditions observed during the stratocumulus period and was used to initialize the simulations. Cloud properties and thermodynamic characteristics of the atmosphere were monitored with surface-based remote sensing instruments (Shupe et al., 2013). The cloud base and cloud top were nearly constant during the cloud lifetime (500 and 1000 m, respectively). Retrievals of liquid water path (LWP) were made from the 23 and 30 GHz microwave radiometer measurements (Sedlar and Shupe, 2014). The combination of different sensors was used to estimate the ice water path (IWP; Shupe et al., 2008). The observed LWP uncertainty was around ∼25 g m-2, while the uncertainty in the IWP was about a factor of 2 (Shupe et al., 2008; Birch et al., 2012). A CCN counter that was situated on Oden, at 25 m above the sea surface, measured a mean CCN concentration of about 25 cm-3 at a supersaturation of 0.2 % during the period of the ice drift (Martin et al., 2011; Leck and Svensson, 2015). The ship and the inlets were facing the wind so that local pollution from the ship was avoided. Furthermore, a pollution controller was used to prevent direct contamination from the ship, and the main pumps were turned off whenever the conditions for a clean environment were not completely satisfied (details on the pollution control system can be found in Leck et al., 2001, and in Tjernström et al., 2014). Since the surface boundary layer typically was decoupled from the turbulent layer associated with a cloud (Tjernström et al., 2012), it is, however, not certain if the CCN concentrations measured at the ship were representative for the cloud layer (see also the observed vertical profiles of particle concentrations in Igel et al., 2017; Fig. 1).

We performed simulations with different prescribed aerosol size distributions to investigate the influence of Aitken mode particles on cloud properties and the dependence of this influence on the background concentration of accumulation mode aerosols. For both models, there is no sink or source of aerosols within the model domain during the simulations. We conduct two sets of simulations with two different background concentrations of the Aitken mode particles (20 and 200 cm-3). Each set contains five cases with different levels of accumulation mode particles (0, 3, 5, 10 and 20 cm-3), i.e. 10 simulations in total. All particle concentrations are assumed to be constant with height. The simulations are named using a combination of two numbers, where the first number refers to the accumulation mode and the second to the Aitken mode number concentration (e.g. the case with 0 cm-3 of accumulation and 20 cm-3 of Aitken mode particles is referred to as the AC0_AK20 simulation). The concentrations are chosen to cover a range typical for aerosol size distributions in the summertime high Arctic (Heintzenberg and Leck, 2012; Leck and Svensson, 2015). If we assume that the accumulation mode contributes most to atmospheric CCN, then the simulation with 20 cm-3 of accumulation mode aerosols agrees the best with the observations in terms of the CCN concentrations measured on board the ship (Sect. 2.2). In this study, the simulation AC20_AK20 is defined as the baseline simulation.

A full description of meteorological conditions during the ASCOS campaign is available in Tjernström et al. (2012). During the ASCOS ice-drift period, observations were done over a surface dominated by pack ice, and the surface conditions are, thus, set to represent sea ice in both models. The values used for the surface temperature and surface pressure are 269.8 K and 1026.3 hPa, respectively. The observed turbulent fluxes were usually smaller than 5 W m-2, with peaks in the probability distributions around zero. Accordingly, the prescribed sensible and latent heat fluxes are set to zero (see also Stevens et al., 2018). The surface roughness is set to 0.0004 and the surface albedo to 0.844 (see Sedlar et al., 2011). In both models, the large-scale divergence is set to 1.5×10-6 s-1 at all model levels, which is the value required to obtain a stable cloud layer (see Stevens et al., 2018). There is no large-scale advection in the models. The aerosol population in both modes is represented by lognormal functions, with the distribution parameters based on the ASCOS campaign measurements (Igel et al., 2017). Modal diameters of 32 and 93 nm and standard deviations of 1.1 and 1.5 are used for the Aitken and accumulation modes, respectively. The simulations are initialized with the prescribed cloud droplet number concentration equal to 30 cm-3 and the cloud water mixing ratios derived from the observations, i.e. a cloud is present at the beginning of all simulations. All microphysical processes are active at the beginning of the simulations in both models. The prescribed ice crystal concentration is 0.2 L-1 (see Stevens et al., 2018). The model domain is 3D and covers a region of 6×6×1.7 km3. In the horizontal direction, there is a fixed grid distance of 62.5 m in both models. In the vertical direction, the grid in MIMICA is variable with the highest resolution (7.5 m) at the surface and in the cloud layer. In RAMS, the vertical grid spacing is kept constant at 10 m. The different default configurations of vertical grid spacing in the two models could potentially generate discrepancies in the simulated cloud properties. However, we performed an additional baseline simulation with a fixed vertical resolution of 10 m with MIMICA and found no significant differences in the simulated results compared to the default version. The simulation period is 12 h. The first 2 h are assumed to be a spin-up period and are therefore excluded from the figures and analysis. After the spin-up period, the cloud layer is stable in the baseline simulations.

In clean environments, the source of Aitken mode aerosols is typically new particle formation (NPF) and subsequent growth. In the high Arctic, however, different sources of Aitken mode aerosols have been proposed. Some studies associate the Aitken mode with the NPF events and subsequent growth by dimethyl sulfide (DMS) oxidation products (e.g. Wiedensohler et al., 1996). Other studies suggest that the Aitken mode particles in this region are made up of marine gels produced by phytoplankton and sea ice algae at the sea–surface interface (Leck and Bigg, 2005b). Different mechanisms imply different chemical compositions and, thereby, different hygroscopic properties that aerosol particles might have in the high Arctic. To study the impact of aerosol hygroscopicity, we performed additional simulations with different values of the hygroscopicity parameter kappa, κ (Petters and Kreidenweis, 2007). The default κ value used to describe the hygroscopic properties of both aerosol modes is set to 0.4 (Leck and Svensson, 2015). As some previous studies (e.g. Christiansen et al., 2020) have shown that a change in hygroscopicity of the accumulation mode aerosols has almost no influence on the cloud properties, we only examined the sensitivity of the κ value of the Aitken mode particles. Simulations AC3_AK20 and AC3_AK200 were performed with two additional κ values equal to [0.1, 1.1], which cover a typical range of hygroscopicity of compounds expected to be present in high Arctic Aitken mode particles (Leck and Svensson, 2015). The lower limit of the hygroscopicity parameter tested (κ=0.1) would be representative of e.g. many organic compounds (e.g. Leck and Svensson, 2015), while the upper limit prescribed (κ=1.1) would correspond to a water-soluble inorganic salt like ammonium sulfate (Petters and Kreidenweis, 2007).

We also examined how the influence of Aitken mode particles on cloud microphysical properties depends on the amount of ice present in the cloud. Additional versions of the simulations AC3_AK20 and AC3_AK200 were performed with prescribed values of the ice crystal concentrations set to 0 and 1 L-1. These values were chosen somewhat arbitrarily but should generally represent a range describing an ice-free and an ice-rich cloud in the high Arctic. Note that the RAMS microphysical scheme includes hail, and the one in MIMICA does not. However, the riming process in RAMS is inefficient for the examined conditions, and pure ice crystals dominate the simulated ice water budget. The hail contribution to total surface precipitation is also 2 orders of magnitude lower than the rain contribution in RAMS.

We first compare our baseline simulations (AC20_AK20) with time series of observed LWP and IWP (Fig. 2).

RAMS produces LWP values that fall within the observed range, whereas MIMICA simulates a LWP that is 12 %–25 % higher than the 75th percentile of the observed range (Fig. 2a). In general, the use of prescribed aerosol particle concentrations should result in a higher LWP than if the simulations were performed with interactive aerosol particle concentrations (e.g. Stevens et al., 2018). It may be that MIMICA is more sensitive than RAMS in this regard. Furthermore, RAMS simulates weaker radiative cooling rates than MIMICA, which should produce a lower LWP in RAMS compared to MIMICA (see Sect. 3.2). The simulated IWP in both models is close to the 25th percentile of the observed range (Fig. 2b). In MIMICA, the IWP overlaps with the 25th percentile value in the second half of the simulation, while in RAMS it is 17 %–33 % lower than the 25th percentile. Overall, the results show that both models simulate reasonable LWP and IWP compared to the observational data; however, it is hard to conclude which model performs better due to the large uncertainty of and variability in the retrieved cloud variables (see also Sect. 2.2).

Simulated cloud droplet, rain and total ice mixing ratios for the baseline simulation are shown for the two models in Fig. 3. In both models, the cloud base (cloud top) height is the altitude above (below) which the cloud droplet mixing ratio exceeds the value 1×10-6 kg kg-1. The cloud droplet mixing ratio increases towards the top of the cloud in both models, but MIMICA produces slightly higher values in the upper part of the cloud layer (Fig. 3a and b), consistent with the higher LWP values (Fig. 2a). There is also a difference in the cloud top height evolution. In MIMICA, the cloud top height increases with time, whereas it remains constant in RAMS. Rain mixing ratios are similar for the two models (Fig. 3c and d), but RAMS produces slightly more rain below the cloud. For the baseline simulations, the sum of the autoconversion rate and the collection rate of cloud droplets by raindrops is 2 orders of magnitude higher in RAMS than in MIMICA, which contributes to the higher rain mass mixing ratios in the RAMS sub-cloud layer. Both models also simulate similar values of total ice mixing ratios, although MIMICA produces a few stronger vertical bands after 6 h of simulation (Fig. 3e and f). This type of pronounced band is a result of strong collection rates of raindrops by graupel, which appear at different times due to different temporal distributions of updrafts and downdrafts (Fig. A8). To better understand the cloud dynamics, we have also examined the cloud diagnostics (i.e. mass transfer rates between gas and condensed phases) for cloud droplet water, rainwater and ice crystals (Fig. 4). In MIMICA, cloud droplet water has the highest condensation rate at the top of the cloud, whereas in RAMS it is homogenously distributed within the cloud layer (Fig. 4a and b). The reason is most likely the higher entrainment rates at cloud top in MIMICA (not shown) that bring more water vapour into the cloud from the moist air that is present across the humidity inversion, which caps the cloud-topped boundary layer (Fig. 1c). Higher entrainment rates are also consistent with the higher cloud top cooling rates present in MIMICA. Below the cloud base, there is first a thin layer of cloud droplet evaporation in both models. In RAMS, there is also a sub-cloud condensation layer, which is produced by weak sub-cloud convection (not shown). Even though the condensation in this layer is infrequent, the associated mean rates are of the same order of magnitude as the condensation rates within the main cloud layer. The pockets of condensation and evaporation present in the main cloud layer are well correlated with the updrafts and downdrafts, and they tend to cancel each other out in the mean (not shown). This is why the average condensation rate in the main cloud is of the same order of magnitude as the one in the sub-cloud layer in RAMS. However, if we consider the domain median instead of the mean, then the condensation rates are higher within the main cloud layer, and they are zero below the evaporation layer also in RAMS (not shown). In both models, the condensational growth of raindrops is limited to the upper part of the cloud layer, while the maximum evaporation rates are found around the cloud base (Fig. 4c and d). This typically happens when the environment is subsaturated for liquid water but supersaturated for ice, which results in the evaporation of raindrops and growth of ice crystals. Ice crystals grow throughout the whole cloud layer, with the highest deposition rates around cloud base (Fig. 4e and f), which corresponds well to the highest rain evaporation rates that are clearly seen in MIMICA (Fig. 4c). The ice crystal deposition and sublimation rates are higher in RAMS than in MIMICA, since the two models partition the total ice deposition differently among ice hydrometeor categories (not shown). Overall, the comparison shows that the simulated cloud microphysical properties are within the same order of magnitude for the two models, i.e. both models simulate the same cloud mechanisms, leading to cloud dynamics that are similar in many aspects. However, there are still some notable differences that arise from the different model configurations.

The cloud droplet mixing ratio for all simulations is shown in Fig. 5. In both models, the cloud thickens and the cloud base altitude changes less with time when the number of accumulation mode aerosols increases. In general, MIMICA simulates a thicker cloud than RAMS. In both models, the cloud base altitude changes at the beginning of the simulation, and it is especially pronounced in the cases with low accumulation mode particle concentrations. However, the turbulence (Fig. A6) is strong enough in MIMICA to develop and maintain a stable cloud during the whole simulation for all cases. This is not the case for RAMS, where the cloud dissipates in the simulations with 0 cm-3 of accumulation mode particles (i.e. the AC0_AK20 and AC0_AK200 simulations). As one of the main generators of cloud turbulence is radiative cooling at the top of the cloud, we have compared the cooling rates between the two models. They are about 2 to 3 times greater in MIMICA than in RAMS (Figs. 6 and A2) and are more similar in MIMICA to values obtained from radiative transfer calculations based on observational data (Brooks et al., 2017). For the baseline case, both models simulate a relatively thick cloud (LWP > 40 g m-2), which indicates that the differences in the cloud top cooling rates between MIMICA and RAMS do not arise from the difference in simulated LWP (see Garrett and Zhao, 2006). Moreover, the cooling rates in RAMS are smaller already at the beginning of the simulations when the liquid water contents are very similar in the two models. A plausible explanation could instead be a less efficient radiative cooling parameterization in RAMS than in MIMICA. To further investigate the influence of the radiation parametrization on the model results, we performed additional simulations with simplified radiative transfer schemes in both MIMICA and RAMS and simulation with a prescribed higher cloud top cooling rate in RAMS (Appendix A; Fig. A1). These simulations show that the radiation parameterization significantly modifies the simulated liquid water content and could be the cause of the observed differences between the models.

Both models suggest that Aitken mode particles are important as CCN in summertime high Arctic SMP clouds if accumulation mode concentrations are low. Guided by these analyses, we have revisited the observed aerosol size distributions from four high Arctic expeditions, including the ASCOS campaign (Leck et al., 1996, 2001, 2004; Tjernstöm et al., 2014). We first examined the representativeness of the size distributions that we have applied in our simulations, i.e. how frequently these types of distributions occur in the observations. Figure 16 shows two classes of size distributions, namely one with Aitken (AIT) mode concentrations lower than 25 cm-3 (AIT < 25 cm-3; blue line) and one with Aitken mode concentrations between 100 < AIT < 200 cm-3 (orange line). The cases with accumulation mode number concentrations equal to 20 cm-3 (i.e. the maximum accumulation mode concentration prescribed in the simulations) have the occurrence probability of 5 % and 17 % (of total minutes of observations) for the class 100 < AIT < 200 cm-3 and AIT < 25 cm-3, respectively. This means that, in conditions with low accumulation mode concentrations (i.e. lower than 20 cm-3), there is a higher probability for the Aitken mode particle concentration to also be low in number (i.e. lower than ∼25 cm-3). However, it also happens that Aitken mode concentrations are much higher (> ∼ 100 cm-3). In other words, the prescribed size distributions that we have applied in our simulations are reasonable.

Probability density functions (PDFs) of observed Hoppel diameters (Hoppel et al., 1986; Fig. 17), calculated as detailed in Heintzenberg and Leck (2012), show that the PDFs for all four expeditions peak around 60 nm, i.e. this should be the most common activation diameter. However, the smallest observed Hoppel diameters are around 40 nm, supporting our conclusions that small Aitken mode particles may be activated in the summertime high Arctic under certain conditions. The observational statistics agree well with the calculations of the critical dry diameters obtained from the simulated ss values (Sect. 4).

Our study focuses on the summertime, ice-covered, high (> 80∘ N) Arctic region. However, it is reasonable to assume that the results are also valid for low-level mixed-phase clouds in other regions with low (< 10–20 cm-3) accumulation mode aerosol concentrations. The activation diameters derived in Sect. 4 support recent findings for the region south of the ice edge during summertime, which show that particles smaller than the accumulation mode potentially can act as CCN (i.e. smaller than 50 nm in diameter; Willis et al., 2016; Kecorius et al., 2019; Koike et al., 2019). Several studies have investigated the seasonality of aerosol particle size distributions in the Arctic (e.g. Tunved et al., 2013; Freud et al., 2017; Koike et al., 2019). They show that number concentrations of accumulation mode particles are lowest during the summer and autumn months and that they can reach values below < 10–20 cm-3 at several locations in the Arctic. However, extremely low accumulation mode number concentrations (occasionally below 1 cm-3) have only been found in the high Arctic (Bigg et al., 1996; Mauritsen et al., 2011; Heintzenberg et al., 2015; Leck and Svensson, 2015). During summertime, conditions in the Arctic are generally favourable for NPF (Tunved et al., 2013; Croft et al., 2016; Nguyen et al., 2016), and local marine sources are active (Leck and Bigg, 2005a; Heintzenberg and Leck, 2012; Karl et al., 2013; Heintzenberg et al., 2015), supporting the presence of high concentrations of small particles. It is thus likely that Aitken mode particles are most important during the summer months (high concentrations of Aitken mode aerosols) and over remote areas covered by ice or snow (low accumulation mode aerosol concentrations).

Note that the simulated influence of Aitken mode particles can also be dependent on details in the simulation setup. In this study, there are no sources or sinks of aerosols during the simulation time, the aerosols are only passively advected within the model domains (see Sect. 2.3). If aerosol sinks were included, the influence of Aitken mode particles would most likely be even more pronounced since accumulation mode aerosols are more efficient as CCN and should be removed faster from the cloud than the Aitken mode particles. Furthermore, the dependence of the Aitken mode influence on the cloud ice amount is investigated here based on different, prescribed ice crystal concentrations (see Sect. 2.3). The results most likely depend on whether the ice crystal concentrations are prognostic or prescribed and if secondary ice processes are considered in the calculations of the ice crystal number concentration (Sotiropoulou et al., 2020).