Changes in the number concentration of aerosols (Na) directly affect the number concentration of cloud droplets (Nc) and, consequently, the microphysical processes related to Nc and the resulting hydrometeors, such as raindrops. First, the response of the Nc to an increase in volcanic aerosols was investigated. Figure  shows the horizontal distribution of the total columns of Na and Nc in the NO-VOLCANO simulation (a, b), in the VOLCANO (c, d) simulation, and the difference between the two simulations (e,f). As shown, the presence of volcanic aerosols significantly increases the number of cloud droplets.

Figure  shows the spatiotemporal averages of the number concentrations and mass mixing ratios of liquid hydrometeors, as well as the autoconversion and accretion rates inside and outside of the plume in the VOLCANO and NO-VOLCANO simulations. These profiles demonstrate the combined impact of volcanic aerosols and meteorological conditions on cloud microphysics. Comparing values inside the plume reveals significant differences between the VOLCANO and NO-VOLCANO simulations. However, values outside the plume remain largely unchanged. These results suggest that the changes observed within the plume are driven by volcanic aerosols. The differences between the inside and outside of the plume within the same simulation, however, are due to varying meteorological conditions and aerosol concentrations. The vertical profile of Nc in Fig. a supports the findings in Fig. f, which demonstrate that higher aerosol number concentrations result in greater cloud droplet number concentrations. Figure a shows that Nc is approximately six times higher inside the plume in the VOLCANO simulation than in the same region in the NO-VOLCANO simulation. It also indicates that the maximum value of Nc is shifted to higher levels in the VOLCANO simulation. Notable differences in the VOLCANO simulation are revealed by comparing Nc inside and outside the plume. By contrast, the NO-VOLCANO simulation shows only a modest difference in Nc across these regions. Nevertheless, even without volcanic emissions, Nc is higher inside the plume area, possibly due to the enhanced presence of sea salt aerosols in those regions or to meteorological factors like differences in humidity and stability (not shown). An analysis of the cloud water mixing ratio (qc) reveals that it increases by a factor of two within the plume in the VOLCANO simulation compared to the NO-VOLCANO simulation. In both cases, qc values are higher inside the plume than outside. Although qc is not directly influenced by the aerosol number concentration (Na), it is indirectly affected through aerosol impacts on cloud microphysical processes. As shown in Fig. c and f, our results demonstrate that the VOLCANO simulation shows a reduction in autoconversion and accretion processes compared to the NO-VOLCANO simulation. In the VOLCANO simulation, cloud droplets are smaller because available water vapor is distributed among more cloud condensation nuclei. As a result, these droplets have smaller collision cross sections and lower fall velocities, making them less likely to collide and grow. This reduction of autoconversion and accretion ultimately leads to reduced raindrop formation in the VOLCANO simulation, as shown in Fig. b. In the VOLCANO simulation, the conversion of cloud droplets to raindrops decreases, resulting in more cloud water remaining. This leads to a higher cloud water mass (qc) and a lower rainwater (qr) mass in the VOLCANO simulation compared to the NO-VOLCANO simulation as shown in Fig. d and e.

In addition to the effects of volcanic aerosols on cloud hydrometeors, our results reveal clear differences in the behavior of cloud and rain water inside and outside the plume. While Nc and qc are higher inside the plume – even in the absence of volcanic aerosols (NO-VOLCANO simulation) – both Nr and qr are significantly higher outside the plume. This indicates that the conversion of cloud droplets into raindrops is more efficient outside the plume, consistent with the higher autoconversion and accretion rates observed there (Fig. c and f). The efficiency of these processes depends on the mass concentration of the cloud and raindrops, as well as the mean particle size, which is defined as the mass divided by the number of droplets. Our results show that outside the plume, where cloud droplet numbers are relatively low but droplet sizes are large, autoconversion and accretion remain active in both VOLCANO and NO-VOLCANO simulations. By contrast, inside the plume, where cloud droplets are more numerous but smaller, these processes are suppressed. Consequently, raindrop formation is enhanced outside the plume compared to inside (Fig. b).

The Holuhraun eruption did not emit ash particles. As a result, ice crystals formed primarily through the homogeneous freezing of cloud droplets and liquid aerosols (sulfate particles), along with the heterogeneous freezing driven by background INPs. Our results indicate that the contribution of heterogeneous freezing was negligible, and that homogeneous freezing of sulfate aerosols had only a limited effect on ice formation. As shown in Fig. , the mass mixing ratio and number concentration of ice particles differ only slightly between the VOLCANO and NO-VOLCANO simulations. However, further analysis revealed that mixed–phase cloud processes are influenced by variations in volcanic aerosols (Fig. ). Since frozen hydrometeors show only slight changes in the VOLCANO simulation compared to the NO-VOLCANO simulation, the changes in mixed–phase clouds can be attributed to changes in liquid hydrometeors.

To study the development of microphysical processes in mixed-phase clouds, we examined the total riming rate – the process by which supercooled droplets collide with ice or snow particles – and the formation of graupel, which forms through riming. The efficiency of collisions between liquid and frozen hydrometeors depends strongly on droplet size; larger droplets rime more efficiently than smaller ones. Figure  shows the vertical profiles of the riming rate and graupel mass mixing ratio (qg). As shown, the riming rate and qg are approximately 1.5 to 2 times lower in the VOLCANO simulation than in the NO-VOLCANO simulation. These results align with previous studies (e.g., ). In addition to riming, graupel can also form from the freezing of raindrops. Our analysis (not shown) revealed that this process occurs more frequently inside the plume because outside the plume raindrops are smaller and freeze less. Nevertheless, our results indicate that raindrops freezing contribute much less to graupel formation than riming does (not shown). A comparison of the results inside and outside the plume revealed that the mass of graupel, as well as the riming process, is greater outside the plume. These results are consistent with our previous findings regarding the behavior of hydrometeors and processes in warm clouds (Fig. ). As previously mentioned, frozen hydrometeors do not change with volcanic aerosol loading. However, they are more abundant outside the plume (Fig. ). Therefore, because the hydrometeors involved in riming and graupel formation are more abundant outside the plume, both riming and graupel production are also enhanced outside the plume.

The reduction of the riming process means that more liquid droplets remain in the mixed–phase cloud in the VOLCANO simulation compared to the NO-VOLCANO simulation. This was confirmed by analyzing the binary liquid fraction in mixed–phase clouds. Following the method of , we calculated the liquid cloud pixel fractions. A cloudy pixel was classified as a liquid pixel if its liquid mass fraction exceeded 0.5; otherwise, it was classified as an ice pixel. The liquid cloud pixel fraction was calculated as the ratio of the number of liquid cloud pixels to the sum of all cloudy pixels. As can be seen in Fig. , liquid cloud pixel fractions are more abundant in the VOLCANO simulation than in the NO-VOLCANO simulation, and they are more abundant inside the plume than outside. This is in line with the riming rate results and indicates that, compared to NO-VOLCANO, more liquid water remained in the mixed phase in VOLCANO and did not rime.

Our results show differences in the processes and hydrometeors in the warm and mixed phase clouds in the VOLCANO and NO-VOLCANO simulations. We used the Mann-Whitney U test to calculate the p-value. Based on this approach, relative differences are considered significant if the p-value is below 0.05. Due to the large number of grid points, the data were first averaged spatially over the vertical and horizontal dimensions, with the analysis restricted to cloudy grid points within the plume region. This produced time series of domain-averaged values, with one sample per time step. The Mann–Whitney U test was then applied to these time series. Additionally, the direction of change was assessed by calculating the relative difference between their mean values. Figure  shows the resulting relative differences, with colors indicating the sign of the change and p-values below 0.05 highlighted by black frames around the boxes, for the mass mixing ratios and number concentrations of all hydrometeors over six days of simulation. The relative differences indicate that Nc, qc, and qs are larger in the VOLCANO simulations (red boxes), whereas Nr, qr, Ng, and qg are larger in the NO-VOLCANO simulations (blue boxes). These results are consistent with the findings shown in Figs.  and . On the first day, significant differences were only observed for cloud droplet number concentration (Nc), indicating an early aerosol impact on this variable. As the volcanic plume evolves, statistically significant differences emerge for cloud water (both Nc and qc), cloud rain (Nr and qr), and graupel (Ng and qg) between the VOLCANO and NO-VOLCANO simulations. Conversely, no statistically significant changes were found for cloud ice (Ni and qi) and snow (Ns and qs), suggesting these hydrometeors are less sensitive to volcanic aerosol perturbations under the simulated conditions.

Since we had already investigated the effects of volcanic aerosols on warm cloud processes by analyzing the results of the Holuhraun eruption, here we were interested in investigating the activation of mixed-mode aerosols as CCN in addition to soluble mode particles (i.e., comparing VOLCANO and VOLCANO-MIXED rather than comparing the results of VOLCANO and NO-VOLCANO simulations). However, our results show only a slight changes in the number concentration of cloud droplets between VOLCANO and VOLCANO-MIXED (not shown). In general, we found that volcanic aerosols from the La Soufrière eruption had limited impact on warm and mixed-phase clouds. One possible reason for this is the plume height. stated that most of the plumes either spread near the tropopause at 16–17 km altitude or penetrated the stratosphere at 18–20 km altitude. This causes the volcanic aerosols to be more dominant where there is less water vapor than at lower altitudes, where warm and mixed–phase processes occur. Additionally, investigating the distribution of mass mixing ratios and number concentrations of cloud hydrometeors inside and outside the plume in these four simulations revealed that ice clouds, rather than warm and mixed-phase clouds, were the dominant cloud type in the simulation domain and throughout the simulation period. Figure  shows the distributions of ice and snow; however, the results for cloud droplets, raindrops, and graupel are not shown. The distributions of ice are relatively symmetric, with close proximity between the mean and median values and minimal skewness. In contrast, the distributions of cloud water, rain, graupel (not shown) and snow exhibit pronounced skewness, characterized by a large difference between their mean and median values. These results suggest that warm and mixed–phase clouds with higher concentrations of cloud droplets, raindrops, graupel and snow were less frequent in the simulation domain, while grid points with very low values (near zero) were dominant, indicating that these clouds rarely covered the sky during the simulation. Conversely, the distribution of ice, with close median and mean values, shows that ice clouds are more evenly and widely distributed across the domain. This is consistent with the dominance of ice clouds throughout the simulation.

Analyzing the liquid fractions as a function of temperature confirms the claim that ice clouds dominated the simulation domain during the simulation period. Using a similar approach to that described for defining cloud water and ice pixels in the Holuhraun simulations, we identified these pixels in the four La Soufrière simulations and plotted the liquid fraction against temperature, as shown in Fig. . Since the VOLCANO simulation includes two types of volcanic aerosols, it was compared with others to determine if changes in aerosol concentrations and CCN activation settings impact the redistribution of liquid and ice pixels. First, the results of the VOLCANO and NO-VOLCANO simulations (Fig. a) were examined. Different from the Holuhraun case, no notable changes were observed between the results of these simulations inside the plume, and the results were close inside and outside the plume for both simulations. This indicates that neither the emission loading of aerosols nor the meteorological conditions impact the redistribution of the frequency of clouds and ice in mixed–phase clouds. Similar results were found when investigating the results of VOLCANO and VOLCANO-NO-ASH (Fig. b) and VOLCANO and VOLCANO-MIXED (Fig. c). These results confirm that mixed–phase processes are unaffected by volcanic aerosols and show that ice pixels dominate. For example, at a temperature of -7 °C, the liquid fraction is 0.2, whereas it was 0.6 in the Holuhraun case at the same temperature. This again confirms that ice clouds dominated during these simulations.

Figure  shows that the VOLCANO-MIXED simulation did not affect the mass mixing ratio or number concentration of ice and snow compared to the VOLCANO simulation. Therefore, we excluded the results of the VOLCANO-MIXED simulation from the analysis in this section.

To analyze the effects of volcanic ash on heterogeneous ice nucleation and the redistribution of available water vapor, we examined the spatiotemporal profiles of ice nucleation-related variables in the ART simulations for the VOLCANO, NO-VOLCANO, and VOLCANO-NO-ASH scenarios. Figure  illustrates these variables within the plume. Figure a shows the vertical profile of ash particle number concentration. Although the VOLCANO-NO-ASH and NO-VOLCANO simulations do not consider volcanic ash, small predefined background values are considered. Since these values are much lower (1×106 m-3) compared to the volcanic ash concentrations in the VOLCANO simulation (1.5×108 m-3), they appear negligible or close to zero.

Figure b shows the concentration of ice crystals formed heterogeneously. As can be seen, there appear to be no such crystals in the VOLCANO-NO-ASH and NO-VOLCANO simulations because the ash concentration is low in these simulations. However, the VOLCANO simulation shows three peaks: one between 10 and 12 km, and two between 14 and 18 km. Our analysis showed that supersaturation with respect to water is greater than 1 between 10 and 12 km. Therefore, we can conclude that the ice crystals formed at this altitude are the result of immersion freezing, while those formed at higher altitudes are the result of deposition nucleation.

Figure c illustrates the vertical profile of Smaxice in the three simulations. We observed a reduction in Smaxice at the altitude at which ice crystals form heterogeneously. When ash particles are activated as INPs, they consume water vapor, reducing the maximum supersaturation with respect to ice. The depletion of water vapor through INP activation redistributes the available water vapor between homogeneously and heterogeneously frozen crystals, thereby affecting the total number of ice crystals. Aqueous sulfate droplets require high supersaturation with respect to ice in order to freeze homogeneously. This is because the droplets must dilute to increase water activity and overcome the energy barrier of the phase transition from liquid to ice. Without sufficient water vapor, the droplets may lose moisture to the surrounding air, becoming highly concentrated and preventing homogeneous ice nucleation. Our results show that, when activated as INPs, ash particles reduce the available water vapor and lower the supersaturation over ice. Consequently, homogeneous freezing occurs less frequently in the VOLCANO simulation, resulting in a smaller total number of ice crystals than in scenarios without ash activation.

In addition to sufficient water vapor, the concentration of liquid aerosol particles is an important factor in homogeneous ice nucleation. Figure d shows the vertical profile of sulfate particle number concentration. As can be seen, sulfate particles are more abundant in the VOLCANO-NO-ASH simulation than in the VOLCANO simulation. This is due to coagulation processes, whereby ash and sulfate particles stick together. The result is particles that are categorized as insoluble modes or forms of internally mixed aerosols, which occur when the 5 % mass threshold of soluble coatings on insoluble particles is exceeded. Consequently, despite having identical SO2 source strengths, the number of soluble particles (i.e., sulfate aerosols) differs between the two simulations. Since the concentration of liquid aerosols is lower in the VOLCANO simulation, the number of ice crystals formed through homogeneous ice nucleation is reduced relative to the VOLCANO-NO-ASH simulation. In the NO-VOLCANO simulation, sulfate concentrations are much lower than in the other two cases because only small predefined background values were applied.

Figure e shows the diameter of liquid aerosols in the three simulations. Below an altitude of 13 km, sulfate particles are larger in the NO-VOLCANO simulation. At higher altitudes, however, sulfate particles are larger in the VOLCANO and VOLCANO-NO-ASH simulations than in the NO-VOLCANO simulation. This affects the total number of ice crystals, as shown in Fig. f.

Figure f illustrates the total number of ice crystals formed through a combination of homogeneous and heterogeneous ice nucleation. Taking into account the activation of ash particles as INPs, the resulting depletion of water vapor, and the varying concentrations and sizes of liquid aerosols – all of which play a significant role in the competition between homogeneous and heterogeneous nucleation – we ultimately found that the total number of ice crystals formed in VOLCANO is lower than in VOLCANO-NO-ASH and NO-VOLCANO at altitudes below 14 km. For instance, at 13 km, the ice crystal number concentrations are approximately 5×105 m-3 in VOLCANO, 7.5×105 m-3 in VOLCANO-NO-ASH, and 1×106 m-3 in NO-VOLCANO. However, at altitudes above 14 km, the VOLCANO simulation produces more ice crystals than NO-VOLCANO but fewer than VOLCANO-NO-ASH. For example, at 17 km, the concentrations are approximately 1×107 m-3 in NO-VOLCANO, 2.8×107 m-3 in VOLCANO, and 6×107 m-3 in VOLCANO-NO-ASH. At altitudes between 10 and 12 km, there is a local maximum in the profile of the VOLCANO simulation that was previously observed in Fig. b. This small peak indicates immersion freezing. As even the reduction of Smaxice cannot diminish its effect, at these altitudes, the VOLCANO simulation has a slightly larger number concentration of ice crystals than the other experiments. Since the values in this figure are widely dispersed, Fig. f employs a logarithmic scale.

Figure g illustrates specific humidity (qv) which is used as a mass conservation check in the ICON-ART model. After a check for a water mass conservation to ensure that the newly nucleated particles predicted by the ice nucleation scheme after are consistent with the actually available water vapor, the number of ice crystals formed in the upper troposphere above 14 km is reduced to the values shown in Fig. h.

Ultimately, considering homogeneous and heterogeneous ice nucleation, as well as mass conservation, Fig. h shows the total number of ice crystals produced in the ART model in the three simulations. As can be seen, the large number of ice crystals at altitudes above 14 km disappeared after applying the mass conservation check, and the difference between the simulation results is clearer at lower altitudes. According to the results shown in Fig. h, the total number of ice crystals is lower in the VOLCANO simulation, in which ash particles act as INPs, than in the VOLCANO-NO-ASH simulation, in which volcanic ash is not considered. However, the total number of ice crystals in these two simulations is lower than in the NO-VOLCANO simulation due to the presence of smaller liquid aerosols in those simulations compared to the NO-VOLCANO simulation.

Figure  shows the number concentration and mass mixing ratio of ice crystals simulated with ICON-ART. After ice crystals form both through homogeneous and heterogeneous nucleation (see Fig. h) and through rain or cloud droplet freezing, they grow (or shrink) through the deposition of water vapor and subsequently undergo transport by sedimentation, advection and diffusion. The vapor deposition directly influences the mass mixing ratio of the ice crystals. Although the simulations show a notable difference in ice number concentration, the difference in mass mixing ratio between the VOLCANO-NO-ASH and NO-VOLCANO simulations is minimal. This can be attributed to the effect of the deposition rate on ice crystal growth. In the VOLCANO simulation, ash particles act as INPs. They consume available water vapor and reduces the deposition rate. This limits the growth – and thus the mass mixing ratio – of ice crystals. Consequently, the deposition rate is higher in the former two cases. The small difference in the mass mixing ratio between the VOLCANO-NO-ASH and NO-VOLCANO simulations may be due to the difference in size of the liquid aerosols, which are larger in the NO-VOLCANO simulation. This promotes more efficient freezing, resulting in a greater total mass conversion to ice.

Snow particles form through the aggregation of ice crystals. Figure  illustrates the number concentration and mass mixing ratio of snow particles, as well as the number and mass aggregation rates in the simulations. The plots in the top row show the number (a) and mass (b) aggregation rates. As expected, the VOLCANO simulation has the fewest aggregated ice crystals, corresponding to the smaller quantity of ice crystals present in that scenario. Consequently, the lowest snow number concentration was observed in the VOLCANO simulation. In our simulations, the number concentration of snow particles behaves similarly to the number concentration of ice particles. This shows that more ice particles lead to more aggregation and, consequently, more snow particles. However, the mass mixing ratio of snow remains largely unchanged among the simulations. Since there are fewer snow particles in the VOLCANO simulation than in the other two simulations and the mass does not change significantly, the snow particles must be larger in the VOLCANO simulation.

As in the case of Holuhraun, we used the Mann-Whitney U test to calculate p-values and evaluate the statistical significance of the differences in hydrometeor properties across the simulations. Additionally, the direction of changes were assessed by calculating the relative difference between their mean values. Four simulations were conducted for the La Soufrière eruption. As previously discussed, we observed no notable differences between the VOLCANO and VOLCANO-MIXED simulations. The calculated p-values confirmed this observation, indicating no statistically significant differences between these two cases. Figure  shows the resulting relative differences, with colors indicating the sign of the change and p-values below 0.05 highlighted by black frames around the boxes, for the mass mixing ratio and number concentration of all hydrometeors over the four-day simulation period. Since no significant differences were found between the VOLCANO and VOLCANO-MIXED simulations, their respective p-values were excluded from the figure. The figure shows the comparison between VOLCANO and NO-VOLCANO (top panel) and VOLCANO and VOLCANO-NO-ASH (bottom panel). In the VOLCANO simulation, the presence of sulfate particles results in a higher concentration of cloud droplets compared to NO-VOLCANO. As the top panel of Fig.  shows, the difference in the number of cloud droplets between the two simulations is statistically significant for the last three days of the simulation. However, the cloud droplet mass mixing ratio shows a significant change on the last two days. An examination of the cloud vertical profiles (not shown) revealed scattered clouds at lower atmospheric levels. There are no significant differences in the number concentration or mass mixing ratio of rain between these two simulations, indicating that the warm rain process is largely unaffected by changes in aerosol number concentration. Although the number of cloud droplets increases in the VOLCANO simulation, the mass remains relatively unchanged because there is no substantial conversion of cloud water into rainwater – the water remains within the cloud category. Examining all two plots and making pairwise comparisons reveals no significant changes in the mass mixing ratio or number concentration of graupel, which may be due to the absence of mixed–phase clouds during the simulations. However, the results indicate that volcanic aerosols significantly affect the number and mass of ice particles in all simulations. Figure  illustrates that ash and sulfate both affect the number concentration and mass mixing ratio of ice. P-values demonstrate that the differences between the simulations are significant. We also observed a significant difference in snow number concentration. However, the snow mass mixing ratio behaved differently, and no notable differences were observed between the simulations.