The ICON-LEM simulations which we performed cover a circular domain with approximately 100 km diameter, centred in Ny-Ålesund (Svalbard; 78.9° N, 11.9° E), and run with approximately 600 m resolution. The general setup follows the papers by and , and a thorough evaluation of the model performance is provided in those studies. While the general performance of the model was found to be very good, there were some shortcomings. In , it is shown that the cloud occurrence matches the observations well but that the occurrence of liquid containing clouds is underestimated by around 30 %.

The simulations are run for every day starting at 00:00 UTC and cover 24 h, although the first 3 h are excluded in the analysis to avoid the spin-up. The initial and boundary conditions for each ICON-LEM limited-area simulation are provided by an ICON-NWP simulation with 2.4 km resolution. This ICON-NWP simulation covers a larger domain and is forced by the operational German Weather Service global ICON-NWP runs. The turbulence is parameterized by a 3D Smagorinsky scheme . The two-moment scheme from , with an added hail class , is used for the microphysics (referred to as SB). We use the cloud condensation nuclei (CCN) activation with maritime aerosols, as well as the heterogeneous ice nucleation from , with the maritime aerosol concentrations. The output is given in the form of the vertical column above the grid cell containing Ny-Ålesund (meteogram) for every 9 s on 150 levels. This output includes the following hydrometeor mass mixing ratios and number concentrations: cloud droplets, rain, ice, snow, graupel, and hail.

For the analysis, a subset of the data, which only includes low-level clouds, was created. This was done by first selecting all grid boxes which are cloudy using a threshold for the hydrometeor concentration of 10-8 kg kg-1 same as in, above which a grid box is defined as cloudy. For a cloud to be classified as low-level, the cloud top height must be below 2.5 km same as in. Additionally, precipitating hydrometeors are not differentiated from non-precipitating ones. Therefore, a cloud with rain, graupel, hail, or snow that reaches the ground will have a cloud base height at the ground. Further, if there is a cloud with a cloud top height higher than 2.5 km above the low cloud, we only use these cases if the higher cloud's bottom height is at least 500 m higher than the low cloud's top height.

The frozen and liquid hydrometeors are grouped in the analysis to focus on phase transitions. The frozen mass mixing ratios (“frozen mass”, kg kg-1) are the sum of cloud ice, graupel, hail, and snow, and the liquid mass mixing ratios (“liquid mass”, kg kg-1) are the sum of cloud droplets and rain. Generally, the liquid and frozen mass mixing ratios lie between 10-8 and 10-3 kg kg-1. The occurrence of low-level clouds and their composition vary between seasons . Therefore, two sets of data are used. One covers the polar night (PN, November 2021–February 2022), and one covers the polar day (PD, May–August 2021). In total, for the PN, there are around 26.3 d worth of low-level clouds, and for the PD, there are around 37.9 d. For the selection of the MPCs, only cloudy pixels where both the liquid and frozen mass are above 10-8 kg kg-1 are chosen. Of the total 23.8 d worth of MPCs, 14.1 d occur during PN, and 9.7 d occur during PD.

In the analysis, the influence of the temperature, vertical velocity, and ice or water saturation on different microphysical processes is discussed. These variables were chosen as the microphysical processes are directly connected to them. As PN and PD differ strongly in parts, a short overview of the thermodynamic conditions for the selected cloudy grid points is provided here. Figure a–c show the distributions of the temperature, vertical velocity, and ice saturation for the PN and PD. The PN temperature ranges from -32 to 2 °C, with the mean at -14 °C. In contrast, the much warmer PD varies less (-22 to 8 °C) and has a mean value of -2 °C. The vertical velocity is narrowly arranged around 0 m s-1 for both PN and PD, and both the PD and PN show low variation (standard deviation: 0.35 m s-1 for PD, 0.29 m s-1 for PN). Extremes, which happen very rarely, are found more in the upwards motion, with the overall maximum at 6.43 m s-1. The saturation with respect to ice does not reach values as high during the PD compared to during the PN.

Of the total 26.3 d of low-level clouds during the PN, almost all of them contained periods with frozen hydrometeors (25.4 d), and slightly more than half contained liquid hydrometeors (15.5 d, 58 %). For the 37.9 d of low-level clouds during the PD, almost all of them contained liquid (96 %), while only 31 % contained ice. This is connected to the fact that liquid occurs at higher temperatures, which are more prevalent during the polar day (Fig. a). Another aspect to note is that, similarly to and as theorized by , we found that higher upward vertical velocities are connected to higher saturation and, with that, also to higher hydrometeor masses (not shown). This already hints at potential correlations between certain processes and the vertical wind and saturation which are presented in the results.

To extract the process rates, this study uses a “microphysical parameterization wrapper”. The goal is to provide a simple diagnostic tool with spatial and temporal flexibility. Therefore, we chose to run the two-moment SB scheme and the saturation adjustment (for condensation and evaporation) independently from the model. A meteogram (single column) or 3D output file from a previous simulation can be used as input for the wrapper. The model output is provided as input to the microphysical scheme at each time step and on the same vertical grid as used in the model. It computes a single time step, writes out the rates, and continues with the following time step. This approach allows the use of previous simulations from which the meteogram or 3D output of the required variables exists. A flowchart is shown in Fig. .

This approach has the clear advantage of being very fast compared to rerunning a full simulation, and one can focus on single processes. Further, outputting an entire domain of microphysical-process rates is extremely space-consuming in most cases and can be avoided by just using a spatial and/or temporal selection. Additionally, it is possible to explore potential sensitivities of microphysical processes by applying changes inside of the wrapper and using it as a test suite. As this tool is simplified and only captures a part of the model, the advantages come with some limitations. One must keep in mind that any transportation (advection and precipitation) of hydrometeors cannot be included as the model itself is not run. In this study, we are only interested in the microphysical processes. Therefore, this is not an issue.

The mass change due to a process is computed by taking the difference between the mass before and after the process and is called (ΔQproc). Here, a time step (Δt) of 3 s is used for the time integration. Therefore, the process rate ΔQprocΔt is given as the hydrometeor mass mixing ratio change over 3 s and is denoted as the “tendency” (kg kg-1 3 s-1) in the following sections. A minimum threshold for the tendency of ΔQprocΔt>10-18 kg kg-1 3s-1 is set to avoid including numerical noise. This threshold is much lower than the threshold for the hydrometeor mass (10-8 kg kg-1) as the microphysical-process tendencies changing the mass can be very small. As mentioned before, the hydrometeors are summed up into a liquid and frozen mass. The same is done with the processes, meaning, for example, that deposition is the sum of deposition onto ice particles, snow, graupel, and hail. In this study, only processes that cause phase changes are included as we are interested in processes that contribute to the phase-partitioning. For example, frozen collisions are not evaluated as all frozen hydrometeors are summed up to a single class and compensate for each other. Many of the processes evaluated in this study have self-explanatory names. Nevertheless, a brief process summary is given here and in Table  to prevent misunderstandings.

Deposition and sublimation. These two processes include either the decrease or increase in water vapour due to phase changes between frozen water and water vapour. They are computed using the same process and are split into negative (sublimation) and positive (deposition) contributions to the frozen mass.

Homogeneous and heterogeneous ice nucleation. These processes describe, as one part, the homogeneous nucleation of liquid aerosols, although it is rarely cold enough (T < 30 °C) in the clouds used in this study to happen. The heterogeneous nucleation describes nucleation via immersion freezing and deposition nucleation. The parameterization follows that of . As homogeneous cloud droplet freezing did not occur for the low-level clouds, it is neglected here.

CCN activation. This process describes the activation of cloud condensation nuclei following the parameterization of .

Frozen evaporation and melting. These processes refer to the melting of frozen hydrometeors, which can entail evaporation, but both are treated separately, leading to a process called evaporation for the frozen hydrometeors as well.

Riming. This process describes the accumulation of liquid mass on a frozen hydrometeor by decreasing the liquid mass and increasing the frozen mass. In SB in ICON, this also includes the Hallett–Mossop secondary ice production. If T > 0 °C, enhanced melting after riming will take place, making the frozen mass increase due to riming less as not all liquid will freeze onto the frozen hydrometeors.

Condensation and evaporation. These processes include either the decrease or increase in water vapour due to phase changes from cloud droplets and raindrops to vapour. They are the positive (condensation) and negative (evaporation) contributions of the saturation adjustment to the liquid mass. The saturation adjustment is run once before and once after the other microphysical processes (see Fig. ).

Rain freezing. This process includes only the freezing of raindrops and not of cloud droplets. As both are summed up, though, this causes a decrease in the total liquid mass, while the total frozen mass increases.

An additional process which is not directly implemented in SB but that is analysed in this study is the WBF process. As evaporation and deposition are needed simultaneously for the WBF process, it is possible to use their rates to compute the WBF rate. The saturation adjustment, which provides the evaporation rate, is computed twice at each time step in contrast to all other microphysical processes. During WBF events, the second call to the saturation adjustment happens in an atmosphere that has been deprived of moisture due to deposition on ice and hence causes additional evaporation.

We used a simple but straightforward approach to understand which processes dominate the phase-partitioning in low-level clouds. For each process, the mean value over all cases was computed. The mean values can vary, for instance, with temperature, as shown in the next section; thus, the percentage of occurrence is used as a second metric. The outcome of this is shown for all processes in Fig. , split into polar night (Fig. a, c) and polar day (Fig. b, d), as well as into MPCs (Fig. a, b) and pure frozen or liquid clouds (Fig. c, d). The further a process is towards the upper-right corner, the more relevant it is considered to be. As mentioned earlier, only processes which contribute to phase changes are included here. Further, we used the minimum of deposition and evaporation to compute the WBF tendency for the MPC cases.

What becomes very clear from Fig.  is that there is a hierarchy in how relevant a process is. In all cases, evaporation seems to be strongest followed by deposition. Here, a striking difference between MPCs and single-phase clouds becomes visible. While, in liquid clouds, it seems like the majority of the clouds are in the decaying phase, shown by the frequent evaporation (above 79 %) in contrast to condensation (below 21 %), this is not necessarily true for the MPCs. As Fig. a and b show, deposition is stronger in MPCs in contrast to the pure ice clouds, indicating that the MPCs are generally transitioning from liquid to ice. The transition from liquid to ice via the vapour phase can be quantified using the WBF tendency, which shows a frequency of around 42 % and varies little between the PN and PD. At the same time, the pure-ice clouds seem to be in a more stable state, although the higher frequency of sublimation indicates a slight decay for the ice clouds as well. The finding that all cloud types seem to be in the process of decay, where processes acting as sinks are dominant, is potentially a local feature as only the single column of Ny-Ålesund is used here. This feature indicates that the microphysical processes may also have a strong location dependency. For instance, in Ny-Ålesund, the air over the fjord is more moist than over the land , which may cause more evaporation over land if a cloud is advected there.

Another aspect to consider is that the microphysical process show different behaviours during the PN and PD. Processes involving the ice phase show a decreased mean tendency during the PD in contrast to during the PN. Additionally, one can see that riming seems to be more frequent during the PN (30 %) than during the PD (21 %), while rain freezing is less frequent during the PN (PN: 32.0 % and PD: 38.64 %). Such differences between the PN and PD are likely to be connected to the dependency of the processes on the temperature regime, as discussed later. Ice and liquid formation via nucleation and activation tend to occur quite seldom, as one can see from the CCN activation (CCN act. in Fig. ) and the homogeneous and heterogeneous nucleation (Hom. het. nuc. in Fig. ). Using the mass change as a metric for nucleation can be misleading as the number of hydrometeors produced can say more about the impact of the nucleation process than the mass change.

Evaluating this single column shows that microphysical processes vary strongly in terms of their importance and depend on the location studied. It is evident that the microphysical sinks found for liquid clouds are much weaker for mixed-phase and ice clouds. In particular, for the MPCs, it became clear that the WBF process acts strongly upon the liquid mass, and it is, therefore, worth further investigating its behaviour.

The Wegener–Bergeron–Findeisen process can be a reason why models have too little supercooled liquid, impacting the representation of MPCs. As shown in , it is also the case in ICON-LEM that the number of liquid-containing clouds is underestimated. In the previous section, we have shown that the WBF process occurs very frequently in MPCs and could be a reason for the glaciation of these clouds. Therefore, this section aims to quantify and further explore the WBF process. The first investigated aspect is whether the evaporation rate increases due to the WBF process. This does not necessarily have to be the case as evaporation could just occur more frequently but does not need to be stronger. To evaluate this aspect, the sub-selection of MPCs was evaluated where evaporation was occurring (75 % of MPC cases). This set was split into two sets. The WBF set consists of cases where deposition occurs simultaneously and where it is, therefore, sub-saturated with respect to water and saturated with respect to ice. This makes up 42 % of the MPC cases. The other set consists of cases where no deposition occurs (33 % of MPC cases). In Fig. a, the distribution of the evaporation tendency for both evaporation sets is shown, and one can clearly see that they differ strongly. For the WBF cases, the evaporation tendency is generally much larger than when no WBF is occurring. It should be kept in mind that this is a logarithmic scale, where 2 orders of magnitude make a large difference in the amount of liquid evaporating.

Continuing with the impact on the total frozen and liquid mass, there, too, the question is whether the impact of the WBF process is significant or not. In Fig. b and c, one can see the distributions of frozen and liquid masses when deposition and no evaporation are occurring (no WBF, 25 % of MPC cases) and when deposition and evaporation are occurring simultaneously (WBF, 42 % of MPC cases). Here, too, there are clear differences between the distributions, showing a shift towards higher frozen masses when WBF occurs. At the same time, the liquid mass distribution shifts towards lower values when WBF occurs. In Fig. c, the tail of the liquid mass, which is visible for the cases where WBF occurs, is due to rain, which often occurs in subsaturated layers as it falls. Combined, this demonstrates the decrease in liquid mass, while there is an increase in frozen mass when the WBF process occurs. For both Fig. b and c, we found the difference in the distributions to be statistically significant (Kruskal–Wallis test). This is also visible in the difference in mean values for both processes. When both processes occur at the same time, the average deposition rate experiences a 4-fold increase (9.8×10-9 to 3.9×10-8 kg kg-1), while the average evaporation rate also increases by around 1 order of magnitude (2×10-8 to 1.3×10-7 kg kg-1). This shows that a significant amount of water transitions from liquid to vapour and then to the frozen phase via the WBF process.

The difference in rate change could be connected to the microphysics implementation, where the saturation adjustment is called twice in contrast to the deposition, which is called only once, and to the physics of the WBF process. Considering the typical thermodynamic situation characterizing WBF, the atmosphere is subsaturated with respect to water and supersaturated with respect to ice. This causes evaporation to occur during the first call of the saturation adjustment, providing more moisture to be deposited into ice as a result of the microphysics scheme. Then, during the second call of the saturation adjustment, the atmosphere tends to return to the state it was in before deposition happened. Because of this, intuitively, evaporation would be higher than deposition. Additionally, if deposition and evaporation tendencies were to be the same, there would be a net release of latent heat, causing the equilibrium to shift towards additional evaporation. Unfortunately, it is not possible at this stage to quantify this effect in the ICON model. However, the developed microphysical wrapper can be further used to evaluate the relative contributions of the various components of the evaporation and deposition processes and to assess the sensitivity of various process rates to the thermodynamic and microphysical conditions of the clouds in the model.

Several other interesting findings appeared when we looked into the question of where and under what circumstances the WBF process occurs. There, we looked into the temperature distribution of the WBF process and found that the WBF process seems to correlate more strongly with deposition than with evaporation (Fig. ). Additionally, one can see that the distributions look different between the PN and PD (Fig. a and b, respectively). While, during the PN, the WBF process most frequently occurs between -6 and -13 °C, during the PD, two maxima are visible: one around -3 °C and one around -10 °C. As deposition should decrease with increasing temperature (shown later), the peak at higher temperatures was not expected. The higher cloud occurrence between -5 and 0 °C could suggest that this cloud occurrence maximum causes the higher process occurrences in this range. When normalizing with respect to the cloud occurrence, we still found a slight increase in deposition and WBF around -3 °C (not shown). Therefore, we investigated whether other processes could be influencing the WBF and deposition frequency. Indeed, it seems like riming and rain freezing play a role in the deposition and WBF rate increase during the PD at higher temperatures (Fig. b). We hypothesize that the increase is due to the fact that both riming and rain freezing increase the ice mass, creating more frozen mass on which vapour may deposit. This would explain the increase in the deposition rate above -5 °C causing the WBF process to set in.

Another aspect which we evaluated was whether the deposition rate or the evaporation rate is the limiting factor for the WBF rate as the WBF rate is based on the minimum rate of both. To explore this, we used the supercooled liquid fraction SLF; to categorize the clouds. An SLF of 1 indicates a pure-liquid cloud, and an SLF of 0 indicates a pure-ice cloud. A mixed-phase cloud would lie between 0 and 1. Using the SLF, we found that there seem to be two WBF regimes: one for clouds with a high liquid amount and one for clouds with a low liquid content. In cases where the liquid mass dominates, deposition is the limiting factor for the WBF process, while, for low liquid mass, evaporation limits the WBF rate. This is understandable if one considers that, if there is less ice available, the deposition rate will be lower, and if there is less liquid available, there will be less mass available to evaporate (see Fig.  for a visualization).

Looking at the WBF process and the difference in terms of processes between the PN and PD indicates that thermodynamic conditions influence the microphysical processes. To understand more about these dependencies, the microphysical-process behaviours with regard to temperature, vertical velocity, and saturation (ice, liquid water) were evaluated. It is worth mentioning here that sublimation and deposition cannot occur at the same time as they are calculated by the same process. The same is true for evaporation and condensation. Other processes can occur at the same time.

Starting with the temperature dependency, it can be seen that deposition occurs relatively consistently at all temperatures below 0 °C (Fig. f), while the mean mass change decreases (Fig. a). Sublimation shows a similar behaviour (Fig. a and f in the Appendix), although deposition shows a slight maximum between around -10 and -20 °C, where sublimation has a minimum. Another process showing a decreasing tendency with temperature is rain freezing, which occurs more often for higher temperatures, but the amount of frozen mass decreases with temperature (Fig. e and j). Rain freezing, as expected, is more efficient at lower temperatures but has less total impact the colder it is. Interestingly, a bi-modal distribution is visible in Fig. d and i for riming in terms of both the tendency and the occurrence. One maximum lies below approximately -20 °C, where there are altogether few cases, and one lies above -10 °C. This is possibly connected to the maximum saturation difference between ice and liquid water as the cloud droplet mean mass has a local minimum of around -18 °C. This hypothesis would be supported by the maximum in terms of deposition in regions where riming is lowest.

Of the processes affecting the liquid mass, evaporation dominates throughout all temperature ranges where liquid occurs. Both the occurrence and the tendency of evaporation increase with increasing temperatures (Fig. b and g). Of all processes, evaporation shows the largest tendency spread. This potentially indicates that evaporation may be more strongly influenced by other factors at negative temperatures in contrast to other processes which depend more clearly on the temperature. Combining evaporation and deposition, the WBF process occurrence has a clear maximum between -10 and -5 °C (Fig. h). At the same time, WBF seems to have the highest tendency for values below -20 °C, although, here again, caution is required due to the number of cases (Fig. c).

Further processes, shown in the Appendix, include condensation, which has a relatively constant tendency and increases in occurrence with temperature, and CCN activation, which occurs rarely and has an occurrence with temperature similar to that of condensation (Fig. ). Melting and evaporation due to melting are only active above 0 °C and decrease accordingly with increasing temperatures as less and less frozen mass is available (Fig. ). Homogeneous and heterogeneous ice nucleation occur very rarely, and more cases would be required to properly describe their thermodynamic dependencies (Fig. ).

The next variable to look at is the vertical velocity. This section only focuses on processes where a signal can be seen. One process is riming, which increases in occurrence with upward velocity. This can mainly be seen during the PN as riming is much more frequent there (Fig. b). The riming tendency may suggest an increase with upwards velocity, as shown in Fig. a, although the fact that only 1 % of the cases are above 1.2 m s-1 makes this slightly speculative. If one discards the lowest and highest 1 % of the vertical wind speed then a decrease in sublimation with upward velocity and an increase towards higher downward velocity can be seen (Fig. a, white areas). For sublimation, no difference in the behaviour between polar night and day is found. For deposition, one would expect the opposite behaviour; however, as is visible in Fig. b), in combining the PD and PN, such behaviour is not completely obvious.

Interestingly, for deposition, a difference in behaviour with vertical velocity can be seen between the PN and PD. The deposition frequency clearly increases with upward velocity for the PN (Fig. d). This behaviour is not so clear for the PD (Fig. c), where deposition seems to be common for downward motions. Additionally, the deposition rate during the PD does not show a strong dependence on the vertical velocity (not shown), although previous observations show a decrease in ice mass with downward motion , suggesting potentially less deposition. To add to the discussion, the WBF occurrence with vertical velocity shows a similar signal as the deposition for the PN and PD (Fig. b–d). Even though WBF is computed from the evaporation and deposition, the evaporation occurrence does not seem to vary strongly with the velocity (Fig. ). In addition, we found that condensation consistently increases for the PN and PD towards upwards velocities, as one would expect (Fig. ). As theorized by , the WBF process is, to a certain extent, expected for downward velocities, which can explain some of the behaviour of the deposition tendency during the PD. At the same time, it is expected that, for upward velocities, saturation with respect to ice and water will set in, causing condensation to increase and therefore preventing the WBF process. Further, found a more prevalent WBF process in downdrafts in low continental stratus clouds using ICON-LEM with the SB microphysics scheme, albeit with different aerosol concentrations. Such a relationship between the vertical velocity and the WBF process, we only found partially.

Reasons for the behaviours of the WBF process and deposition could be the lower number of frozen cases during PD or the differences in temperature range. Another reason could be differences in the vertical structure of the boundary layer and potentially increased moisture in the lower layers due to the fjord by Ny-Ålesund. One must keep in mind that the vertical wind is very narrowly distributed around 0 m s-1, and only a few absolute high values exist. To study this further, other types of clouds that have stronger vertical velocities by nature are more suitable. For the liquid mass, similarities exist between evaporation and sublimation as both show a decrease with upward velocity (Fig. a and b). Condensation resembles the deposition more strongly and increases with upward motion (Fig. c and d). The CCN activation is, by definition, dependent on the vertical velocity. Therefore, the increase with higher upward velocity, which we found, is as expected.

The last thermodynamic variable is the saturation with respect to ice and water. Processes that change the frozen mass are evaluated against the saturation with respect to ice. Here, riming stood out again. It can be seen in Fig. c and d that riming increases with saturation in both occurrence and mean tendency. This fits the increase in riming found for higher upward velocities as the saturation of rising air can increase. Some processes depend, by definition, on the saturation, for instance, deposition or sublimation and condensation or evaporation. The signal found for these processes indicated evaporation and sublimation below saturation and condensation and deposition above saturation, which was, therefore, expected (not shown). What was noticeable, though, was that the tendency of condensation showed a higher mean in combination with a much smaller spread in comparison to evaporation. It was generally an interesting finding that some processes, such as condensation and rain freezing, showed much less spread in their tendency than other processes with respect to all thermodynamic variables evaluated here.