Exploring hail and lightning diagnostics over the Alpine-Adriatic region in a km-scale climate model

. The north and south of the Alps, as well as the eastern shores of the Adriatic Sea, are hot spots of severe weather events (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) convective (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) storms, including hail and lightning associated with deep convection. With advancements in computing power, it has become feasible to simulate deep convection explicitly in climate models by decreasing the horizontal grid spacing to less than 4 km. These so-called kilometer-scale or convection-resolving models improve the representation of orography and reduce uncertainties associated with the use of deep convection parameterizations. 5 In this study, we perform convection-resolving (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) km-scale simulations for eight observed cases of severe convective events

In the past decade, climate simulations at the kilometer-scale grid spacing started to emerge.The main advantages of running a model at such a high resolution are a better representation of orography and no need for a deep convection parameterization, which is often associated with large uncertainties in climate simulations (Prein et al., 2015;Leutwyler et al., 2016;Ban et al., 2021).Such km-scale simulations lead to improved representation of the diurnal cycle of precipitation, heavy precipitation, clouds, snow, and local winds (Ban et al., 2021;Pichelli et al., 2021;Hentgen et al., 2019;Lüthi et al., 2019;Belušić et al., 2018).Still, hail and lightning are commonly not resolved or diagnosed in such models because of the complicated hail growth processes and electrification mechanisms that would make the models too expensive for climate simulations.The need to understand, predict and project hail and lightning have led to the development of diagnostic tools such as the hail growth model HAILCAST (Adams-Selin and Ziegler, 2016) and the Lightning Potential Index (LPI) (Lynn and Yair, 2010).
Such diagnostics implemented in km-scale models take advantage of a more realistic representation of convection and microphysical processes and provide information on hail and lighting without a significant increase in the computational cost of simulations.Comparison with observations shows that HAILCAST diagnostic is a good indicator of the hailstone sizes at the ground (Adams-Selin et al., 2019;Malečić et al., 2022), and LPI is highly correlated with the observed lightning flashes (Yair et al., 2010) when the convection is well simulated.There are some models that include a more sophisticated treatment of hail and lightning processes.For instance, Meso-NH supports an explicit treatment of lightning, which represents the life cycle of the electric charges from generation to neutralization via lightning flashes, and a two-moment aerosol-could-microphysics scheme (Lac et al., 2018).Such simulations are far more expensive and currently not yet suited for simulations over climate time scales in large computational domains.
In this study, we use the Consortium for Small-scale Modeling (COSMO) model with HAILCAST and LPI diagnostics and available observations to explore severe convective events :::::: storms over the Alpine Adriatic region.The specific objectives of the study are: -Evaluate the performance of the COSMO model at km-scale grid spacing in simulating hail and lightning.
-Explore the hail and lightning mechanisms and associated environments under different synoptic situations.
To address the above objectives, we simulate eight cases of severe convective storms (including moderate to severe hailstorms, and one no-hail storm) over the Alpine-Adriatic region that occurred in the period from 2009 to 2018 under different synoptic conditions.
The paper is structured as follows: Section 2 describes the model configurations and diagnostics together with the available observations and validation methods.Section 3.1 presents the eight selected cases with observed severe weather over the Alpine-Adriatic region.Section 3.2 evaluates the performance of HAILCAST and LPI.Section 3.4 analyzes the results for four :::: three : selected cases to understand the drivers of such events and how they are represented in the model.And finally, Section 4 presents a summary of the results with a discussion of the potential use of HAILCAST and LPI diagnostics in future climate simulations.
2 Data and methods

Model description
The simulations are performed with the climate version of the non-hydrostatic COSMO model (Baldauf et al., 2011).More specifically, we use COSMO-crCLIM, a version of COSMO that is able to run on hybrid CPU-GPU architectures (Leutwyler et al., 2017;Schär et al., 2020).Hereafter, we refer to COSMO-crCLIM as COSMO for simplicity.The simulations are conducted following a two-step one-way nesting approach with a horizontal grid spacing of 12 km for the first nest and 2.2 km for the second nest (Fig. 1a).The simulations are driven by the ERA5 reanalysis (Hersbach et al., 2020)  From the parameterization packages, we apply a single-moment bulk microphysics scheme with prognostic cloud water, cloud ice, graupel, rain and snow (Reinhardt and Seifert, 2006), and a radiation scheme with a δ-two-stream approach (Ritter and Geleyn, 1992).For the outer 12 km domain, the Tiedtke (1989) convection scheme is turned on for shallow convection and switched off for deep and mid-level convection following Vergara-Temprado et al. (2020).For the inner 2.2 km domain, the convection parameterization scheme is switched off entirely to resolve the convection processes explicitly as far as feasible.

LPI -::
-lightning potential index The lightning potential index (LPI, J kg −1 ) is a measure of the potential for charge generation and separation that leads to lightning flashes in convective thunderstorms (Lynn and Yair, 2010;Yair et al., 2010).It considers the separation region of clouds within the main charging zone (0 to -20 °C), where the contribution of non-inductive mechanisms is the most efficient.Noninductive mechanisms refer to the rebounding collisions between cloud ice crystals and graupel particles under the presence of supercooled liquid water (Takahashi, 1978).We use the updated LPI version after Brisson et al. (2021): and q F = q g (q i q g ) 0.5 q i + q g + (q s q g ) 0.5 q s + q g (4) where q c , q r , q i , q s :: q c , ::: q r , :: q i , :: q s : and q g are the mixing ratios of cloud water, rain water, cloud ice, snow and graupel, respectively.
g (w) is a boolean function equal to 1 when vertical velocity w ≥ 0.5 m s −1 , and 0 otherwise.The dimensionless quantity ϵ : ε :: is : a :::::::::::: dimensionless :::::: number :::: that ::: has : a ::::: value ::::::: between :: 0 ::: and :: 1, :::: and : it : scales the cloud updrafts and reaches the maximum when the vertically averaged mixing ratios of liquid (q L ) and combined ice (q F ) species are equal.Thus, the LPI is non-zero when liquid water and ice species co-exist in the grid boxes with updraft velocity above 0.5 m s −1 , a threshold that identifies the growth phase of the thunderstorm.However, this chosen threshold generates many LPI signals.To overcome this issue, two Boolean functions f 1 and f 2 are included to filter out weak and noisy LPI signals caused by isolated single-grid-column updrafts (f 1 ) and to filter out false LPI signals in strong orographic gravity wave clouds (f 2 ) following Brisson et al. (2021).f 1 is TRUE if more than 50% of grid boxes in a surrounding area of 10 × 10 km 2 have an updraft larger than (or equal to) a threshold w max .
The threshold w max is somehow arbitrary (see Brisson et al. (2021)) and depends on the grid spacing used.In our application, we have set it to 2 m s −1 , which showed a reasonable distribution of LPI.However, this threshold is slightly different from 1.1 m s −1 used by in a surrounding area of 20×20 km 2 is larger than (or equal to) -1500 J kg −1 :: −2 .As for w max , this threshold is also arbitrary, but in this case, we did not do any additional test and have simply used the one recommended by Brisson et al. (2021).Thus, for more detail on these functions and choices, please see Brisson et al. (2021).LPI is calculated every 15 minutes in the COSMO 2.2 km simulations, and it is saved as an hourly maximum.

Observational datasets
Precipitation observations.The Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG, Huffman et al. ( 2019)) dataset is used to validate the simulated ::: total : precipitation.It has a spatial grid spacing of 0.1 • (≈ 10 km) and is available at half hourly time frequency.The IMERG data covers our entire analysis domain, including oceans that lack in-situ precipitation-measuring instruments.
Hailpads provide information about the number and diameters of hailstones that hit the measuring plate.The hailpad networks in Croatia include i) stations in the continental part of Croatia (590 hail stations with a mean distance of about 5.5 km between hailpads), ii) the hailpad polygon in the western part of Zagorje (150 hailpads with an equidistant spacing of 2 km), and iii) the hailpad network installed in Istra (67 hailpads) (Fig. 1c).It should be noted that hailpads :::::: hailpad observations do not report hail sizes smaller than 5 mm.
Two radar-based hail products are used to analyze hail swaths over the complex topography of the Alpine region (Fig. 1b): Probability of Hail (POH) and Maximum Expected Severe Hail Sizes (MESHS) (Nisi et al., 2016).POH is a measure of the likelihood of hail occurrence and ranges from 0% to 100%.Using crowd-sourced :::::::: insurance :::: loss reports, Nisi et al. (2016) found that when POH equals or exceeds 80%, a day can be considered as hail day.The same threshold is used by Meteoswiss Swiss Hail Climatology Project, and in the current study.On the other side, MESHS estimates the largest expected hail diameter in units of centimeters, starting at 20 mm (Nisi et al., 2016).Both products are available on a spatial grid of 1×1 km 2 and every 5 minutes and cover the area of Switzerland and the surrounding area.They rely on the third-generation C-band radars (in operation since 2009) and the fourth-generation :::: 2002 ::: and :::: were :::: later :::::::: replaced :::: with dual-polarization radars (in operation since ::::::: between :::: 2011 :::: and 2012 ) :::::::::::::: (Nisi et al., 2018).The algorithms require information on the freezing-level height (H0) provided by the MeteoSwiss weather forecasts using COSMO.POH considers the vertical distance between the highest radar reflectivity of at least 45 dBZ and H0 (Waldvogel et al., 1979;Foote et al., 2005), while MESHS considers the vertical distance between 50 dBZ and H0 (Treloar, 1998;Joe et al., 2004).The availability of the hail data differs between the analyzed cases, so we list which hail observations are considered for each of the cases in Table 1.

Diagnostic radar reflectivity.
The COSMO model provides a diagnostic forward operator to derive an estimate of radar reflectivity.This tool will be used in some diagrams to visualize the thunderstorm development.It :::::::: However, :: it should be noted that this tool does not account for all aspects that contribute to radar reflectivity, for instance, it does not generate the bright band near the melting level.For these reasons, we have not used it as a validation product.
For each case, we have estimated whether the atmospheric instability was generated by local conditions or synoptic atmospheric processes.This classification depends on the convection adjustment scale τ , which is derived using the precipitation rate P (kg m −2 s −1 ) and CAP E according to the following equation (Keil et al., 2013) : daily ::::::::: maximum : τ ::: for :::: each ::::: case, :: as :: it :::: must ::: be :::::::: calculated :::: over :: a ::::: region ::::: large :::::: enough ::: to :::::: smooth ::: the ::::::::: variability :::: from ::::::::: individual :::::: clouds.Keil et al. (2013) suggests that if τ is shorter than 12 hours, the atmospheric instability is governed by the synoptic conditions, and the event is then classified as strong synoptic forcing.A larger τ (> 12 ::: >12 hours), however, indicates that the convection is driven by high local CAPE values, in which case the event is classified as weak synoptic forcing.We should note that the threshold between weak and strong synoptic forcing varies in literature (see e.g., Zimmer et al. (2011)), and should thus not be taken strictly, especially for the cases close to it.We use the hourly domain-averaged CAPE and precipitation from ERA5 (same domain as in Fig. 2) and calculate the daily maximum τ for each case, as it must be calculated over a region large enough to smooth the variability from individual clouds.Here we just use it as an indication of prevailing conditions.
Predictability with adopted simulation strategyA central element of the simulation strategy is the use of high spatial (30 km) and high temporal (hourly) ERA5 lateral boundary conditions, with the initialization taking place at 12 UTC on the day before the event to account for the spinup of the storms.The simulation is thus guided along the reanalysis, and the predictability of our simulations is much higher than a numerical weather prediction (NWP)forecast.The strategy is ideal to test diagnostic tools that require adequate synoptic forcing.Despite the use of ERA5 lateral boundaries, there is some inherent internal variability.To test the effect of model internal variability on our results, we have conducted a small ensemble of simulations for three events by shifting the initialization by +6 and -6 hours (Section 3.3).This procedure follows previous studies of Walser et al. (2004) and Hohenegger and Schär (2007).-1 June 2013.Warm and humid air transported from the northeast towards the Alps encountered cool air from the west (Fig. 2b).The event produced heavy precipitation ::: rain : (without hail) in a very narrow band near the foothills of the Alps and caused ::::: water discharges with return periods of 10 to 30 years reported from several weather stations in central and eastern Switzerland (FEON, 2013;Grams et al., 2014).We selected this event to evaluate the ability of the model to simulate heavy precipitation ::: rain : without hail.
-18 June 2013.A low pressure system was situated over the Bay of Biscay (Fig. 2c) and brought warm and moist unstable air masses to central Europe with very large CAPE (not shown).Several localized and short-lived thunderstorm cells developed in the afternoon to the east of this system.Hailstones observed near Zurich caused massive localized damages :::::: damage : estimated at 15 million CHF according to the building insurance of the Canton of Zürich (Gebäudeversicherung Kanton Zürich, GVZ (2013)).
-25 June 2017.This event is characterized by heavy precipitation which occurred south of the Alps.A thunderstorm that hit the city of Lugano in the early morning produced 81.5 mm of precipitation ::::: rainfall : within an hour, which is expected over a long period of time less frequently than every 100 years (MeteoSwiss, 2017).It was the second hottest June since measurements began in 1864 (MeteoSwiss, 2017).Prior to this event, the high temperatures above 30 °C recorded in the Po Valley lasted for more than three days.A surface front was not present but a short-wave upper-level trough moving over Switzerland can be seen from the geopotential field at 500 hPa (Fig. 2d).
-24 July 2017.A slow-moving cut-off low passed over the northern side of the Alps.On the western side of the low, upper-level cold air advection occurred and led to an unstable environment (Fig. 2f).With the deepening of the system, low-level convergence and ascending motion initiated several thunderstorm cells to the south of the Alps, which later shifted north-eastward with the prevailing flow.
-17 May 2018.Under the influence of the upper-level low over Poland (Fig. 2g), several isolated and local thunderstorms developed in the afternoon over the eastern shores of the Adriatic Sea.Hail was observed over the northern part of Istria (Croatia) according to hailpad observations.Affected by the Bise (a north-easterly wind that blows across the Swiss plateau to the north of the Alps), local rain showers developed over Switzerland without hail and lightning.
-30 May 2018.Scattered and widespread thunderstorms were initiated near the mountainous region of central Europe :::::: eastern ::::: France :::: and ::: the ::::::: southern ::::: flank :: of ::: the :::: Alps.The slow-moving storms caused significant damage across a large area.The surface pressure distribution was relatively flat (not shown), characterized by a "fair-weather" : " : situation with weak temperature gradients over the eastern Alps.The Alpine region was affected by the southerly upper-level flow (Fig. 2h), where a trough extended over the Mediterranean and an anticyclonic curvature north of the trough axis.During the day, the southerly flow started to affect the weather in the Alpine region.A similar situation continued the next day.
3.2 Evaluation of :::: total : precipitation, hail, and lightning In this section, we assess how COSMO, with a 2.2 km grid spacing, performs in simulating ::: total : precipitation, hail, and lightning.To do so, we look into the model performance with SAL diagrams (explained in Section 2.5) shown in Fig. 3, and  the case of 18 June 2013.The inability of the model to simulate this event properly is attributed to the local processes involved.
The event is associated with weak synoptic forcing, with the largest convective timescale of all cases (Table 1).Thus, due to its more chaotic nature, this event has small predictability.We should note, however, that the SAL components of precipitation are computed against IMERG, which has a much coarser resolution than the model.Some ::::::::: Therefore, ::::: some of the biases can therefore be attributed to the rather smooth precipitation distribution (larger precipitation objects of lower intensity) shown by the observations (Fig. 4).It is also interesting to note that none of the used precipitation observations, neither IMERG nor RhiresD, captured the record-breaking hourly precipitation amount of 82 mm as observed at the rain gauge station in Lugano (southern Switzerland) on 25 June 2017.However, such a high precipitation intensity is simulated by the model, even though it is slightly misplaced.
To evaluate the hail produced by HAILCAST and COSMO ::::::: COSMO ::::::::::: HAILCAST, we first compare the model output against radar-based observations available over Switzerland and its surrounding areas (Fig. 5a-h).We first show the simulation against the POH data in terms of the hail footprint/coverage, but the comparison against MESHS data looks qualitatively similar.
To further explore the performance of the model and HAILCASTdiagnostics ::::::: COSMO ::::::::::: HAILCAST, we compare the simulated hail sizes against available hail size ::::: against :::::::: available : observations for different cases as listed in Table 1.-the larger the initial embryo, the larger the output hail size.However, the size also depend ::::::: depends on the model micro-physics, the strength of the updrafts that hail has to overcome to fall to the surface, and the initial temperature level.For example, if updrafts are weaker, larger hail fall ::: falls : down faster and do :::: does : not have enough time to grow further, while smaller hail have ::: has more time to grow but do :::: does not reach sizes above 20 mm.In a parallel study, in which the same eight cases are simulated with the WRF model (Malečić et al., 2023), larger hailstones are obtained  spectively.Note that the coverage bias does not provide any information on the overlap of simulated and modeled lightning, but this is qualitatively assessed from the spatial representation.Overall, the model using LPI diagnostics is able to capture the lightning patterns for each case, although it tends to slightly overestimate the spatial patterns of the signal (as for :::: total precipitation and hail).The largest overestimation of spatial patterns, and thus the coverage bias, is found in the case of 1 June 2013, when very little lightning was observed over the Adriatic and no lightning over the Alpine region.However, the model diagnostics produced lightning over the eastern Alps, which coincides with the area of very intense precipitation.The case of 1 June 2013 is the case without hail over the Alpine region, which was successfully reproduced by the model.Differences in representing hail and lightning can be related to different updraft thresholds used by LPI and HAILCAST, which is lower for LPI -0.5 m s −1 for LPI (Section 2.3) versus 10 m −1 for HAILCAST (Section 2.2).The smallest coverage bias is obtained for the case of 24 July 2017 and 30 May 2018, even though there is a slight shift between the observations and the model.
We should also note that both of these cases are characterized by weaker synoptic forcing and more locally driven convection, which is well reproduced by the model.The largest underestimation of the spatial coverage of lightning is found in the case of 25 June 2017.A large part of this bias is visible over the Adriatic Sea -:: -the area over which the model fails in reproducing :::: total precipitation as well.Overall and not surprisingly, we can see that the performance of both hail and lightning diagnostics strongly depends on 400 simulated :::: total precipitation, since both hail and lightning diagnostics depend on the same ingredients as precipitation.

Assessment of model internal variability
A central element of the simulation strategy is the use of ERA5 lateral boundary conditions, with the initialization taking place at 12 UTC on the day before the event to account for the spinup of the storms.The simulation is thus guided along the reanalysis, and the predictability in our simulations is much higher than in a numerical weather prediction (NWP) forecast.The 405 strategy is ideal to test :: for :::::: testing diagnostic tools that require adequate synoptic forcing.Despite the enhanced predictability due to the use of ERA5 lateral boundaries, there is some remaining internal variability.To test the effect of model internal The ensemble simulations are initialized at 06, 12, and 18 UTC on the day before the events ::::: storms : occurred.Consideration is given to the whole modeling chain with nested simulations at 12 and 2 km resolutions.
Results show that even for localized deep convective events :::::: storms, the predictability of precipitation and HAILCAST ::: hail is overall quite high (Fig. 9).However, there are significant differences in detail, due to the chaotic nature of the nonlinear flow evolution.For example, in the case of July 2009 (top two rows of Fig. 9), there are considerable differences in the length and location of the hail swaths.Likewise, in the case of 18 June 2013, precipitation is simulated over the Black Forest when initialized at 12 UTC, but not when initialized at 06 and 18 UTC.Similarly, in the case of 30 May 2018, there are pronounced differences in the precipitation fields with concomitant differences in hail.Overall, however, the internal variability is rather small and hence the simulations confirm the suitability of the selected modeling strategy for assessing the performance of the modeling approach for case studies of severe convection.Comparison :: A ::::::::: comparison : of the cases shown in Fig. 9 suggests that synoptically-driven convective events :::::: storms have a higher predictability.

Analysis of the driving mechanisms for three specific cases
To further investigate the environmental conditions and the mechanisms that are favourable for the development of thunderstorms over the Alpine-Adriatic region, we present a more detailed analysis of three specific cases, which affected different areas under different synoptic situations.
The resulting convective cells moved northeastward (Fig. 10f) and weakened in the middle of the night.At 00 UTC on 24 July 2009, CIN was completely depleted (not shown).A comparison of the model simulation against observations at Payerne station reveals that COSMO reproduces this environment very well (Fig. 10b).This relatively good simulation of the storm environment leads to a good overall performance of the model in simulating ::: total : precipitation, hail and lightning during that event.
Further analysis of the case based on the model output reveals that the southwesterly flow transported warm and moist air from the Mediterranean with an abundant water content of 35 kg m −2 (Fig. 10c).This warm and moist air, together with extremely large 0-6 km bulk wind shear defined as the difference in horizontal velocity between 6 km and the surface (exceeding 40 m s −1 in some areas; for :::::::: hundreds :: of ::::::::: kilometers : over Switzerland (Fig. 10f).The system extended for hundreds of kilometers and caused long hail 3.4.2The case of 25 June 2017 -A record-breaking precipitation event in Lugano The case of 25 June 2017 is associated with ::: the record-breaking precipitation rate in Lugano during the measurement period (see Section 3.2 above).We choose :::: chose : this event for detailed analysis since interesting conditions triggered the event as explained below.The COSMO model shows a good performance in simulating :::: total precipitation, hail and lightning over the Alpine region.However, at the same time, it underestimates ::: total : precipitation and lightning over the Adriatic Sea.As for the previous case, we first look at the structure and evolution of the pre-storm environments using radiosonde profiles, but this time at the Milano station (since it is closer to the event) in the north-western section of the Po Valley in Italy (Fig. 11a-b).
A comparison of the simulated profile at the Milano station (Fig. 11b) with the observed and above-discussed profile (Fig. 11a) reveals a good performance of the model in capturing the vertical profile and thus the triggering mechanisms of the event.The model reproduced the "capping" : " : layer on the day before the event occurred and the deepening of the moist and warm air several hours before the event occurred.
Analysis of the model output shows a warm and moist layer over the Po Valley with simulated total water content larger than 45 kg m −2 (Fig. 11c-d).Given the southeasterly flow, a :: As :::::: shown :: in ::: 3.4.3The case of 8 July 2017 -thunderstorms near the Jura mountain The case of 8 July 2017 is characterized by multiple thunderstorms over the Alps.Overall, the precipitation structure for this case is well reproduced, while the intensity is slightly underestimated with a large location error, which is most likely due to the southerly shift or the underestimation of the precipitation system :::: total ::::::::::: precipitation.We again start with a look into the thermodynamic environment with the help of sounding observations at Payerne (Switzerland :::::: Stuttgart ::::::::: (Germany) near the location of hail occurrence (Fig. 12a-b :: a,b).At 00 UTC, the profile shows a dry layer below 950 ::: 800 hPa capped by :: and : a moist layer or most probably by ::::::: probably ::::::::: associated :::: with : a cloud at around 800 ::: 850 hPa, which is topped ::: and :::::: capped : by a dry layer above of 650 ::: 700 hPa :: to :::::: 500 hPa : (Fig. 12a).The observed CIN amounted to -130 J kg −1 and CAPE to only 70 J kg −1 , which is not a favourable environment for thunderstorm development.In the morning hours, the stable layer was eroded away due to the strong upper-level westerly flow (see Fig. 2) ::::::: warming :: of ::: the ::::::::::: near-surface :: air :: in ::: the ::::::: morning ::::: hours, making the conditions more favourable for the development of convection.At 12 UTC, a deep and well-mixed boundary layer was observed up to 800 hPa, nearly following the dry adiabatic profile.Comparison with the model (Fig. 12b) reveals that the model captures the vertical profile, even though temperature and dew-point temperature do not come as close as in observations at around 800 hPa level.
Fig. 12d shows a band of very low relative humidity at the 500 hPa level, consistent with a stratospheric intrusion embedded in the strong upper-level westerly flow (Fig. 2e).This band is near the Stuttgart sounding, but slightly to the south of it.There is also a pronounced upper-level cut-off low over Spain.
Overall, the COSMO model together with HAILCAST and LPI diagnostics performed well in simulating :::: total precipitation, hail and lightning.In particular, the case-study simulations captured the main characteristics of the cases considered, such as the large-scale precipitation distributions, or the occurrence of elongated hail swaths versus localized hail events controlled by topography (Fig. 4-8).The best performance was obtained for the cases with strong synoptic forcing.This is to some extent associated with the chaotic nature of the underlying dynamics and the lower predictability of these kinds of :::::::: localized events.
The two events associated :::: cases : with the strongest synoptic forcing (1 June 2013 and 17 May 2018) are events ::::::::: associated with heavy precipitation (especially 1 June 2013), but with no or very little hail and lightning.Even though the model overestimated the precipitation intensity for these two events ::::: cases, it produced no or very little hail, which is in accordance with the observations.Overall, we see that the performance in the simulation of hail and lightning is consistent with the model performance for precipitation ::::::::: convection.Comparison of the model with radar-based hail estimates revealed that COSMO integrated with HAILCAST tends to underestimate the frequency of large hailstones, and fails to produce extra-large hailstones (larger than 40 mm).However, when compared to crowd-sourced and hailpad observations, it ::::::: COSMO : shows a good ::: hail :::: size distribution.
It is possible that some of the biases could be addressed by tuning the diagnostic computations of hail and lightning.
The ability of COSMO to simulate severe convective events ::::: storms : associated with hail and lightning enables further exploration of the mechanisms that drive such events.By investigating three specific cases that are :::: cases ::: that ::::: were selected according to their impacts over different severe weather :: in ::::::: different ::::::: synoptic :::::::: situations ::::: over hot spots of the Alpine-Adriatic region, we identified several storm environments that contribute to heavy precipitation , :::::::: associated :::: with : hail and lightning.These mechanisms include a capping layer that serves to accumulate humidity and energy below this layer (23 July 2009, 25 June 2017), a "back building process" : " : that contributes to convective cells that remain quasi-stationary near elevated terrains ::::: terrain : (25 June 2017), dry air above a warm and moist surface that leads to higher instability and stronger downdrafts (8 July 2017), and an upper-level trough that promotes ascent (25 June 2017).The results show that, although the simulations are not designed to simulate the detailed structure, amplitude and location of the events in terms of :::: total precipitation, hail and lightning, COSMO is generally able to credibly replicate key processes of severe thunderstorms and create the related favourable environments for storm development.
Our findings show that HAILCAST and LPI integrated with COSMO are promising tools to diagnose hail and lightning over the Alpine Adriatic region (as also shown by (Malečić et al., 2023)).However, a couple of shortcomings are revealed: (i) Comparison of the model to available hail observations reveals that COSMO HAILCAST fails to reproduce extra-large hailstones.The most likely cause for the lack of large hailstones is the underestimation of strong updrafts in COSMO.Such an underestimation is plausible, as with a computational resolution of 2 km, simulations of heavy convection exhibit signs of bulk converge, but not yet structural convergence (Panosetti et al., 2018).In other words, the horizontal scales of the thunderstorm are overestimated, and peak updrafts are underestimated.In this context, wind shear is important as it influences the convective dynamics and the generation of rotating thunderstorms with strong updrafts.(ii) The spatial extent of hail footprints are overestimated :::: large :::::::: hailstones :: is ::::::::::::: underestimated in COSMO HAILCAST compared to the radar-based observations.This could be due to :: We :::::: should :::: note : the fact that MESHS only provides the estimation of hailstones larger than 20 mm, while POH only provides the probability of hail.(iii) The output of HAILCAST is sensitive to the initial hail embryo ::: size : (e.g., the maximum hail diameter always comes from the largest hail embryo) as shown by Adams-Selin and Ziegler (2016); Adams-Selin et al. ( 2019).(iv) For the LPI, the threshold of vertical velocity is ::::: should ::: be resolution dependent (Brisson et al., 2021), ::: and thus a comprehensive analysis against observations is required before application.The LPI provides the potential of lightning, not the exact number of lightning flashes, which makes it difficult to evaluate against observations.Thus our analysis was only focused on the coverage or footprints of the lightning.

Figure 1 .
Figure 1.COSMO model topography, analysis domains, and observational coverage.(a) Computational domains for the simulations with 12 and 2.2 km grid spacings :::::: spacing.The innermost box denotes the analysis domain.(b) COSMO 2.2 km analysis domain (thick solid line), LINET lightning observations (thin line), radar-based hail observations (dashed line).Black dots represent the four :::: three sounding stations used in this study: Payerne, Milano and Stuttgart.(c) Available hailpad measurements over Croatia (black dots).A dense hailpad polygon (150 hailpads aligned with a distance of around 2 km between hailpads) is located in the northwestern part of Croatia.The red-shaded area indicates the region used to evaluate hail simulated by COSMO ::::::::: HAILCAST.

Figure 2 .
Figure2.Synoptic overview of the eight case studies :::: cases : considered in this paper.Panels show geopotential height at 500 hPa (m, black contours), temperature at 850 hPa (°C, shaded), : and wind barbs at 500 hPa obtained from ERA5 reanalysis at 12 UTC on the day when the respective case was observed.

Figure 3 .
Figure 3. SAL diagrams ::::::diagram of daily accumulated ::: total : precipitation in COSMO simulations compared to IMERG observations over the analysis domain for all eight analyzed cases.The S, A, L components evaluate the differences in structure, amplitude, and location of the events, respectively.Values near zero signal a perfect match with observations.

Figure 4 .
Figure 4. Daily accumulated :::: total precipitation (mm d −1 ) for all eight cases obtained from observations (first and third rows) and COSMO simulations (second and fourth rows).The IMERG observations cover the entire analysis domain, while high-resolution RhiresD gridded rain gauge observations (shown in the upper right corners) cover Switzerland only.

Figure 5 .
Figure 5. Observed and simulated daily hail footprints for all eight cases analyzed in this study.COSMO hail footprint is shown in blue shading and compared against different observations over different regions.(a)-(h) COSMO against radar-based POH observations, shown in orange shading for the radar-covered area.A grid point with POH larger than 80% is considered a grid point with hail.(i)-(k) COSMO against crowd-sourced reports collected within Switzerland, indicated with purple dots and classified according to various categories of hail sizes.Note that after 2018, there was a change in the definition of hail sizes.(l)-(n) COSMO against hailpad measurements.Available hailpads are indicated with black dots and hailpads recording hail during the events are indicated in red for the three cases where hail occurred in Croatia.

Figure 8 .
Figure 8. Foot prints of daily LINET lightning flashes (>0, orange) and COSMO LPI (>0 J kg −1 , blue) for all eight cases.The number in the upper-right corner of each panel displays a coverage bias, defined as the ratio of grid points with lightning in model and observations.Values larger and smaller than 1 indicate model overestimation and underestimation of spatial coverage, respectively.

Figure 10 .
Figure 10.Detailed characteristics of the case 23 July 2009.Thermodynamic skew-T log-P :::: log-p : diagrams of (a) sounding observations and (b) COSMO extracted profiles at Payerne station at 00 (solid) and 12 UTC (dashed).Red and green lines represent the temperature and dew-point temperature profiles, respectively.Corresponding wind hodographs, shown in the bottom left corner, are obtained for 12 UTC on 23 July 2009.:::::: COSMO :::::::: simulated (c) COSMO simulated total water content and vertically integrated water flux vectors, (d) 0-6 km bulk wind shear, (e) temperature at 700 hPa, and (f) simulated reflectivity and wind barbs at 1 km above ground level at 12 UTC on 23 July 2009.The red box A1 indicates the zoomed subdomain shown in (f).

Figure 11 .
Figure 11.Similar as :: As :: in Fig. 10, but for the case of 25 June 2017.(a) Sounding observations and (b) COSMO extracted profiles at Milano station at 12 UTC on 24 June 2017 (solid lines) and 00 UTC on 25 June 2017 (dashed lines).(c) COSMO simulated total water content and vertically integrated water flux vectors, (d) 2 m temperature at 03 UTC on 25 June 2017, and (e) footprints of LPI and HAILCAST obtained between 03 and 04 UTC are shaded in yellow and purple, respectively.The red box B3 in (c) indicates the zoomed subdomain shown in (de).(f)-(h) Vertical cross-sections of potential temperature (gray contours), equivalent potential temperature (red contours), specific humidity (blue shaded), and simulated reflectivity (colour shaded) along the red transect B1-B2 at 02, 04 and 06 UTC on 25 June 2017.

Figure 12 .
Figure 12.As in Fig. 10, but for the case of 8 July 2017.(a) Sounding observations and (b) COSMO extracted profiles at Stuttgart at 00 (solid lines) and 12 UTC (dashed lines).(c) COSMO simulated total water content, (d) relative humidity at 500 hPa, (e) temperature at 925 hPa, and (f) vertical velocity at 850 hPa at 12 UTC on 8 July 2017.The red box C3 in (c) indicates the zoomed subdomain shown in (e), and the box C4 in (d) indicates the zoomed subdomain shown in (f).(g)-(i) Vertical cross-sections of humidity, temperature (red isolines) and simulated radar reflectivity along the red transect C1-C2 in (d).
Brisson et al. (2021)with a grid spacing of 2.8 km.

Table 1 .
List of eight selected cases and their characteristics.The convection adjustment time τ is calculated according to the equation 2.5 and indicates cases with stronger (small τ ) or weaker (large τ ) synoptic forcing. ::