As in our previous study , we used the regional weather and climate model COSMO with the identical configuration. A brief summary is provided here; full details can be found in . The model was run on a rotated latitude–longitude grid at 0.01° horizontal resolution (approximately 1.1 km at mid-latitudes) with 80 vertical hybrid layers extending up to 20 km altitude, a 6 s time step, and output every 5 min. Deep convection was explicitly resolved without parameterization. The simulation domain extends from 45.45 to 49.50° N and from 6.17 to 13.83° E, encompassing Switzerland, southern Germany, and parts of the other surrounding countries. Initial and boundary conditions were taken from hourly COSMO-7 analyses provided by MeteoSwiss.

Cloud microphysics is represented by the two-moment bulk scheme of with extensions by , predicting mass and number concentrations for cloud droplets, raindrops, cloud ice, snow, graupel and hail. Key processes for our analysis included in this scheme are riming, sedimentation, melting, and graupel–hail interactions. Raindrop freezing forming graupel or hail follows the same size-dependent thresholds as in . In both the previous and current study, the Hallett–Mossop mechanism is disabled due to its lack of reliability . Hydrometeor characteristic diameters were derived as mass-equivalent spherical diameters from the model-predicted mass and number concentrations, following the relation suggested by . 1D=6qπρn1/3×1000 where q is the species mass concentration (kgm-3), n the number concentration (m-3), and ρ the bulk density. To avoid spurious values at low concentrations, we applied species-specific thresholds prior to the conversion: cloud droplets with nc > 1 cm-3, rain nr > 1 m-3, ice ni > 1 m-3, graupel ng > 1 m-3, and hail nh > 10⁻³ m-3 ; for hail, an additional size condition D > 5 mm was applied to conform to the definition of hail .

Heterogeneous ice nucleation is parameterised using the empirical scheme of , as in our earlier work, with background ice-nucleating particle (INP) concentrations of 1–10 L-1, consistent with previous experiments (). Control (CTRL) simulations contain no seeding agents, whereas seeding simulations (SEED) include fully prognostic AgI particles that are advected with the flow, consumed during ice formation, and released back to the atmosphere via sublimation. Immersion freezing efficiency for these AgI particles is prescribed from laboratory measurements for 400 nm particles , the most likely mode for initiating freezing from AgI flares . Cloud droplet activation is parameterized following , using the “intermediate” cloud condensation nuclei (CCN) concentration of ≥ 500 cm-3 in the planetary boundary layer, decreasing with height . The activated CCN concentration depends on the updraft speed at the cloud base and is derived using lookup tables. As a result, it varies among the cases and the ensemble members .

To generate the ten ensemble members for each of the eight cases, we produced perturbed versions of the control simulation by adding small, spatially and temporally uncorrelated Gaussian noise to the model temperatures, following the approach of and among others. The perturbations are additive, drawn from a normal distribution with zero mean and a standard deviation of 0.01 K, and applied independently to every grid point throughout the vertical column. In this study, all simulations were initialised at 00:00 UTC, in contrast to our previous work where a time-lagged ensemble approach was used. This change allows us to analyse convective cells forming before 12:00 UTC, thereby enabling the selection of storms over a broader temporal spectrum. In the previous setup, such early-day cases could not be examined due to model spin-up time constraints.

In this study, we seed hail producing convective cells during their cumulus stage, the initial phase of convective storms characterized by the presence of updrafts and the absence of downdrafts. With a model output frequency of 5 min and an AgI flare burn time of about 10 min, up to three output times occurred within a single seeding event. For each of these times, we identified the grid column with the maximum updraft in the cell we want to seed during its cumulus stage and defined a fixed 5.5 km × 5.5 km box centred on that location (Fig. ). The seeding area was taken to include all three boxes from the different time steps (Fig. ). We recognize that this area is likely larger than real world flare plumes, which is a limitation of our approach. Across ensemble members, the position of the cells we seeded during the cumulus stage varied little, so the seeding area changed only slightly, with differences of no more than ± 1 grid point. Seeding was applied for 10 min to five model levels immediately below and at the cloud base at a constant rate of ∼ 0.033 cm-3s-1 . As a result of temporal accumulation within this fixed volume, the AgI concentration reached a peak value of 20 cm-3 at the end of the seeding interval.

Hailstorms can be relatively small-scale atmospheric features that are often advected with high wind speeds, posing challenges for tracking algorithms. Such rapid movement may result in a lack of spatial overlap between consecutive model output time steps . In the tracking algorithm used in this study, hailstorms are identified when specific parameters exceed predefined thresholds. The first is the maximum updraft within a grid column, which helps to distinguish convective clouds from stratiform or stratocumulus clouds . The presence of AgI particles, which is the second criterion for tracking, leads us to follow the cells based on the seeding simulations. Accordingly, the CTRL data are masked using the results of the seeding simulations. These thresholds play a significant role in determining which features are tracked and, consequently, influence the results. That is why, in this study, we devote a dedicated section to examining how these thresholds influence the mass of ice, graupel, and hail. In all other sections, the tracking thresholds are fixed at an AgI concentration of 150 L-1 and a maximum updraft velocity in the grid column exceeding 1 ms-1. While literature suggests that updrafts exceeding 10 ms-1 are generally required for sustained hail growth , we employ the tracking threshold of 1 ms-1. This choice is motivated by three factors: first, sensitivity tests show that results on hail size remain consistent regardless of the updraft threshold used (see Fig. S8 in the Supplement). Second, given our 1.1 km horizontal resolution, a threshold of 1 ms-1 is sufficient to identify the core ; third, a more restrictive threshold would drastically reduce the number of available grid points.

To build upon our previous proof-of-concept study , we extend the analysis to eight convective storm cases that occurred over Switzerland and southern Germany during the summers of 2019 and 2020. These cases were selected based on the presence of observed hail at the surface. The selected storms span a range of topographic and meteorological environments, characterized by varying CAPE and wind shear values, as well as maximum updrafts in the hail growth zone (HGZ, defined between -10 and -30 °C; ) ranging from 7.3 to 28.8 ms-1 (Table ). These storms occur in settings from moderately complex terrain to high-altitude regions under diverse synoptic conditions (Fig. S1). This variability provides a representative background that allows us to evaluate the robustness of seeding effects across diverse environmental and topographic contexts.

Specifically, seven cases occurred over moderate topography, while one case (28 July 2020) was located over high-altitude terrain. Across all cases, the ensemble simulations exhibit substantial variability in the spatial distribution of the tracked grid points, as shown in Fig. , particularly during the later stages of the convective storms. This variability reflects the sensitivity of convective storm evolution to small perturbations in the initial temperature field, which leads to divergent storm tracks among ensemble members as time progresses. In other words, the locations and extents of the convective cores that meet the tracking criteria differ significantly between members. This is consistent with the findings of , who showed that errors in convective-scale forecasts grow much faster than those in larger-scale forecasts, due to the high sensitivity of moist convection to small atmospheric changes.

In this section, we compare the modeled precipitation with the CombiPrecip dataset from and the Lightning Potential Index (LPI) e.g., with the low-frequency (VLF/LF) international lightning detection network LINET e.g.,. CombiPrecip provides hourly precipitation fields derived from a geostatistical combination of rain-gauge measurements and radar estimates. The dataset extends 100–150 km beyond the Swiss border, covering neighboring countries, which makes it well-suited for our analysis. Another advantage is its spatial resolution of 1 km, which matches that of our model output. As shown in Fig.  (left panel), despite the limited number of data points and considerable spread, it is evident that COSMO tends to underestimate precipitation. This finding is consistent with , who used a similar model setup. Furthermore, Fig.  (right panel) compares the modeled LPI with the LINET dataset. The LPI evaluates the potential for charge separation by combining updraft speeds with cloud hydrometeor data (graupel, ice crystals, snow, supercooled droplets, and raindrops), whereas LINET monitors lightning activity across most of Europe, including Switzerland and Germany. Notably, the 5 min temporal resolution of the LINET data matches the temporal resolution of our model output. Although the two datasets utilize different units, this comparison demonstrates that the observed lightning activity occurred within the same domain and during the same time periods as the simulated convective storms, albeit with spatial spread. Thus, the simulated storms and their broader environment are broadly comparable to the observed storms, despite the underestimation of precipitation.

Figure  presents the time evolution of the mean vertically integrated cloud ice. In the CTRL simulations, mean vertically integrated ice exhibits substantial variability across cases and ensemble members, as illustrated by the spread. For instance, the 95th percentile reaches 0.2 kgm-2 after 0.75 h of tracking, while the 5th percentile remains below 0.025 kgm-2 throughout the entire tracking period. The median across all 80 simulations peaks at the first hour of tracking. Differences between the SEED and CTRL simulations reveal a clear pattern during the initial 1.5 h: the majority of simulations show an increase in cloud ice in the convective clouds following seeding, with a median increase of approximately 0.03 kgm-2. Beyond 1.5 h, the median difference approaches zero, suggesting that the ice content in the seeded clouds converges with that of the CTRL simulations. After 1.2 h, 2 of the 8 cases, are no longer tracked by the tracking algorithm as they fall below the AgI or updraft threshold. Overall, this consistent increase in vertically integrated ice mass following seeding is in line with earlier findings e.g.,.

Figure  presents the vertical profiles of the mean updraft (ms-1) – based on data averaged over the first 1.2 h of the tracking period, during which all cases are tracked (Fig. ) – and the ice mass fraction in the mixed-phase layer for each of the eight convective cases for the ensemble median. The ice fraction is calculated as: Ice Mass Fraction=MiceMwater+Mice where Mice is the total ice mass (sum of all frozen hydrometeors except snow, which was excluded due to its negligible contribution relative to the other hydrometeors) and Mwater is the total liquid-water mass (cloud water and rain).

The CTRL vertical profile of the mean updraft (Fig. , top) increases from the surface to the mid-troposphere, where it reaches its maximum, and then approaches zero near 13 km at the cloud tops of the studied storms. The spread – reaching about 1.5 ms-1 in the mid-troposphere – indicates substantial variability in updraft strength among the eight cases and the ensemble members.

In the seeded simulations (Fig. , bottom), AgI consistently increases the ice fraction within the mixed-phase layer, reflecting a systematic shift of condensate from liquid to ice due to enhanced ice nucleation from AgI particles and riming. This increase ranges from 3.8 % to 18.8 %. Examination of the vertical profiles and the SEED–CTRL differences shows that, in most cases, the increase in ice fraction is accompanied by stronger mean updrafts from the 0 °C level up to approximately 10 km. Consistent with the findings of , our simulations suggest that the latent heat of fusion released during enhanced riming and ice nucleation dominates over any updraft-weakening mechanisms, producing a weak but systematic enhancement of the mean updraft in the majority of the simulations.

Figure  shows the updraft area distributions for the > 1 and > 10 ms-1 thresholds in the CTRL and SEED simulations. For the > 1 ms-1 threshold, seeding slightly alters the shape of the distribution while maintaining its bimodal structure. The median area is 640 km2 for the CTRL and 661 km2 for the SEED simulations; however, these changes are not statistically significant according to the Mann–Whitney U test (p=0.45). This non-parametric test was selected because the pooling of the data results in unpaired distributions of unequal sizes, precluding a direct one-to-one comparison. Conversely, for the > 10 ms-1 updraft threshold, seeding modifies the shape of the distribution by slightly increasing the peak and reducing the probability density for updraft areas below 70 km2. Although the median area shifts from 101 km2 (CTRL) to 96 km2 (SEED), these differences are also not statistically significant (p=0.22). Consequently, while we observe updraft invigoration in our simulations, there are no significant changes in the overall updraft area in response to seeding.

Figures  and  show vertical profiles of hydrometeor types – cloud droplets, raindrops, ice crystals, and graupel – averaged spatially and temporally (over the first 1.2 h) for both CTRL simulations and the SEED–CTRL differences. The analysis of both figures proceeds sequentially, beginning with cloud droplets, followed by raindrops, ice crystals, and graupel, starting with the CTRL results and then examining the SEED–CTRL difference.

Figure  presents scatter plots of the spatial and temporal mean of hail sizes at the surface for each case, classified according to CAPE and 0–6 km wind shear. In the CTRL panel, hail sizes span a wide range, from 8.3 to 14.9 mm. Notably, there is no clear relation between higher CAPE values and larger hail sizes. This suggests that CAPE alone is not a sufficient predictor of severe hailstorms . Relatively large hail sizes are observed even in cases with CAPE below 1000 Jkg-1, which typically corresponds to weak instability during summer months . Similarly, no consistent pattern is evident with respect to 0–6 km wind shear. The largest mean hail sizes are associated with wind shear values between ∼ 10 and 13.5 ms-1, which, according to , falls within the multicell storm category. Additionally, most cases exhibit substantial variability among ensemble members, as indicated by the marker sizes. In the SEED–CTRL panel, the response of hail to AgI cloud seeding is consistent with what we observed in Fig. . Seeding reduces the mean hail size only in one case, with CAPE of 237 Jkg-1 and wind shear of 13.4 ms-1, where a decrease of about 1 mm is found. Conversely, in all other cases, seeding increases the mean hail size by up to 5.1 mm, and no clear pattern emerges that links the seeding impact to either CAPE or wind shear. Overall, this figure reinforces our findings in the previous section, where seeding – in the majority of cases and simulations – increases hail sizes and, consequently, hail kinetic energies.

Figure  displays scatter plots of the number of grid points with hail at the surface and, similarly to Fig. , classifies the cases according to CAPE and wind shear. In the CTRL panel, the highest number of hail-producing grid points is found in the case with the largest CAPE value (296 grid points). However, as in Fig. , no consistent pattern emerges indicating that higher CAPE results in a larger spatial extent of hail. The same applies to wind shear: the cases with the most extensive hail coverage correspond to wind shear values of approximately 10 and 16.4 ms-1. In the SEED–CTRL panel, the effect of AgI cloud seeding is consistent across all cases: every case shows a decrease in the number of hail-producing grid points. The largest reduction occurs in the case with the highest CAPE, but there is no evidence that the magnitude of the reduction is systematically related to either CAPE or wind shear. Overall, these results are consistent with our earlier findings: seeding increases the mean hail size in most cases while simultaneously decreasing the spatial extent of hail.

In this chapter, we analyze the impact of the AgI and updraft thresholds applied in our tracking algorithm on the vertically integrated masses of ice, graupel, and hail. Figure S3 shows that in the CTRL panel, an increase in the threshold updraft within the grid column specified for tracking leads to an increase in the vertically integrated cloud ice mass. This relationship can be explained by two key processes. First, stronger updrafts activate more CCN, as described by the parameterization. These activated droplets are then advected into the mixed-phase region of the cloud, where they freeze and contribute to the cloud ice mass. Second, stronger updrafts loft larger droplets and keep them suspended for longer periods, allowing them to grow through condensation and collision–coalescence before freezing. Once frozen, these supercooled droplets significantly enhance the total ice content in the cloud. In the CTRL simulations, where no seeding is applied, the AgI threshold affects only the number of grid points included in the analysis and the spatial domain, which is defined based on the SEED simulations. Since AgI particles are absent in the CTRL simulations, varying the AgI threshold does not influence the vertically integrated cloud ice mass in a consistent way. Additionally, the highest values of vertically integrated cloud ice mass are found in the case with the second-lowest CAPE, indicating that there is no direct correlation between the ice content of a convective cloud and CAPE.

In the SEED–CTRL panel (Fig. ), the pattern is clear: seeding increases the vertically integrated cloud ice mass irrespectively of the chosen thresholds. The applied thresholds influence the magnitude of this change, without altering its overall direction. As for the CTRL simulations, the difference in cloud ice mass increases more when only considering grid points with higher updraft thresholds. The maximum differences are observed for the highest updraft and highest AgI concentration thresholds. This robust outcome reinforces the conclusion drawn from Fig. , where we showed that AgI particles effectively act as ice-nucleating particles. Through immersion freezing, they enhance ice production in seeded clouds regardless of the selected tracking thresholds.

Similarly to Fig. S3, the vertically integrated graupel mass increases when limited to grid cells with higher updraft thresholds (Fig. S4). This is because graupel grows by riming – supercooled liquid droplets accreting onto ice embryos – and stronger updrafts lead to enhanced CCN activation and droplet formation, thereby increasing the amount of supercooled liquid water available for riming, while also prolonging particle residence time in the mixed-phase region . In COSMO's two-moment microphysics scheme , an instantaneous saturation adjustment prevents explicit supersaturation peaks, but droplet number concentrations are nonetheless diagnosed from updraft-dependent aerosol-activation lookup tables , so stronger updrafts still produce more cloud droplets. Thus, even with saturation adjustment, stronger updrafts yield more droplets and thereby enhance graupel production through riming. Interestingly, graupel mass in our simulations does not correlate with CAPE. For example, the maximum simulated graupel mass is 10.1 gm-2, occurring at a relatively low CAPE value of 237 Jkg-1. In the SEED-CTRL plot (Fig. ), a similar pattern to Fig.  is evident. Cloud seeding consistently increases graupel mass across all scenarios. While the magnitude of this increase varies depending on the tracking threshold, the direction of change remains positive. This indicates that the effect of seeding on graupel mass is robust, as also demonstrated in Fig. .

A similar pattern is observed for hail such that stronger updrafts yield higher values of total hail mass, reaching up to 2.4 kgm-2 in the case with 511 Jkg-1 CAPE (12 July 2019) (Fig. S5). This increase can be attributed to the same mechanisms discussed in the previous paragraph for graupel – namely, enhanced supercooled liquid water content and prolonged particle residence time in the mixed-phase region. As with graupel, there is no apparent correlation between the vertically integrated hail mass and CAPE, indicating that hail mass is independent of bulk instability.

However, the SEED–CTRL panel reveals a more complex pattern (Fig. ). The impact of AgI seeding on hail mass is strongly case-dependent and varies with the chosen tracking thresholds. Only one case – 28 July 2020, with CAPE of 237 Jkg-1 – shows a consistent reduction in hail mass across all tracking thresholds. In all other cases, both the sign and magnitude of the seeding response depend on the specific tracking thresholds applied. This behaviour is consistent with the conclusions drawn before: while the increase in ice and graupel mass following seeding is robust across all cases and all thresholds, the response of hail mass is considerably weaker and far less systematic. This weakening reflects the increasing microphysical complexity associated with hail formation, including variability in residence time, riming efficiency, and competition for available liquid water.