Characterizing hail-prone environments using convection-permitting reanalysis and overshooting top detections over south-central Europe

. The challenges associated with reliably observing and simulating hazardous hailstorms call for new approaches that combine information from different available sources, such as remote sensing instruments, observations, or numerical modeling, to improve understanding of where and when severe hail most often occurs. In this work, a proxy for hail frequency is developed by combining overshooting cloud top (OT) detections from the Meteosat Second Generation (MSG) weather satellite with convection-permitting SPHERA reanalysis predictors describing hail-favorable environmental conditions. Atmospheric 5 properties associated with ground-based reports from the European Severe Weather Database (ESWD) are considered to define specific criteria for data filtering. Five convection-related parameters from reanalysis data quantifying key ingredients for hail-storm occurrence enter the filter, namely: most unstable convective available potential energy (CAPE), K index, surface lifted index, deep-layer shear, and freezing level height. A hail frequency estimate over the extended summer season (April-October) in south-central Europe is presented for a test period of 5 years (2016-2020). OT-derived hail frequency peaks at around 15 10 UTC in June-July over the pre-Alpine regions and the northern Adriatic sea. The hail proxy statistically matches with ∼ 62 % of confirmed ESWD reports, which is roughly 22% more than the previous estimate over Europe coupling deterministic satellite detections with coarser global reanalysis ambient conditions. The separation of hail events according to their severity highlights enhanced appropriateness of the method for large-hail-producing hailstorms


Overshooting top detections
The remote detection of OTs automated by Bedka et al. (2010) has been previously used to characterize OTs climatological distribution in North America (Bedka et al., 2010), Europe (Bedka, 2011), and Australia (Bedka et al., 2018).The OT detection algorithm relies on the comparison between clusters of cold pixels likely related to strong updrafts with a tropopause tempera-170 ture, as well as with pixels consistent with the temperature of the anvil of the thunderstorm, as detected with IR satellite scans.
A large temperature difference (> 6 K) helps to separate actually occurred ::: true : OTs from other non-convective clouds (e.g., cirrus) as this difference is indicative of updraft penetration through the anvil of at least 1-2 km (Griffin et al., 2016).Recently, the automatic OT detection algorithm has been substantially improved by considering a probabilistic approach (Bedka and Khlopenkov, 2016;Khlopenkov et al., 2021) instead of the binary yes/no decisions based on predefined fixed temperature thresholds.The statistical combination of tropopause-relative IR brightness temperature, the prominence of a candidate OT relative to the surrounding anvil, and the spatial uniformity and size of the area covered by the anvil delivers a 3-km gridded probabilistic OT estimate across the domain.The validation of this methodology (Khlopenkov et al., 2021;Cooney et al., 2021) revealed important improvements compared to the original detection algorithm of Bedka et al. (2010).The present study considers IR imagery from geostationary MSG Spinning Enhanced Visible and InfraRed Imager (SEVIRI) (Schmetz et al., 2002) between 2016 to 2020 at a continuous temporal resolution of 15 minutes over south-central Europe.
Only OTs detected with the Khlopenkov et al. ( 2021) algorithm having a probability >50% are considered, similar to Punge et al. (2023).This statistical constraint was derived by the comparison of OT detections with radar echo tops (Cooney et al., 2021) that :: and : demonstrated enhanced reliability being indicative of colder and more prominent anvil-relative tops.The spatial distribution of the 991,042 OTs detected over 872 days is shown on a 10-km regular grid in Fig. 3b.A generally higher number of OTs over land is observed, especially around the Alps, Apennines, and Dinaric Alps mountainous ranges.The main OT hotspot over the study domain extends throughout the northern Po valley region adjacent to the Alps, which is bounded to the north by the most prominent minimum located in proximity of the Alpine crest (i.e., along the northern Italian border with south-eastern France, southern Switzerland, and western Austria, Fig. 3a).
The meteorological parameters selected to describe ambient conditions favorable to hailstorm development and to identify potential hail-related OTs rely on statistical relationships between hail observations and proximal atmospheric soundings (e.g., Kunz, 2007;Prein and Holland, 2018;Kunz et al., 2020;Allen et al., 2020;Jelić et al., 2020).These parameters represent the key dynamical and thermodynamical ingredients necessary for hailstorm formation: atmospheric instability and low-level moisture, storm organization, and freezing level altitude.
Finally, the amount of moisture available below the freezing level has an influence on the hydrometeor density in the updraft, and hence potentially on the growth rate of the hailstones (Johnson and Sugden, 2014;Allen et al., 2015).On the one hand, too low a freezing level may limit the amount of supercooled water in the updraft necessary for hail growth (Prein and Holland, 2018).On the other hand, thunderstorms with a high freezing level (H 0 ) are less likely to produce hail on the ground owing to enhanced melting during hailfall (Dessens et al., 2015).This causes, for example, the lower hail probability observed near the tropics where the surface atmospheric layers are generally warmer and the tropopause higher (Prein and Holland, 2018).
While CAPE, SLI, and H 0 are direct outputs of SPHERA, DLS and K index are computed from temperature and wind profiles.Every parameter is available at hourly frequency at the native horizontal resolution of 0.02°(i.e., ∼2.2 km).However, local rapidly evolving deep convective processes are characterized by a low intrisic ::::::: intrinsic predictability and this may affect the representativity of the local indices considered.Hence, SPHERA fields are remapped to a common grid of 10 km to avoid possibly "noisy" estimates and to reduce data representativity issues.

OT-reanalysis filter design
Recent findings suggest links between convective storm severity and specific characteristics of the OT detections, such as their spatial extension (Marion et al., 2019) or the temperature gradient between the OT and the tropopause (Khlopenkov et al., 2021).However, some OTs with intense updrafts reaching the tropopause and penetrating the lower stratosphere may be associated with convective environments not necessarily supportive of severe weather phenomena such as hail.The necessary discrimination between hail-and non-hail-producing OTs can be attained by additionally considering convection-related environmental conditions estimated with reanalysis (Punge et al., 2017;Bedka et al., 2018;Punge et al., 2023).
SPHERA predictors are extracted around each OT detection in a spatio-temporal neighborhood of 0.63°x 0.63°(approximately 70 km x 70 km) over the three hours preceding an OT and the hour at which the OT is issued.This relatively large spatial matching window is required owing to the extremely localized and rapidly-evolving nature of hailstorms in order to limit double-penalty issues due to the difficulties of the models to predict the exact localization of convective processes (Ebert, 2008;Marsigli et al., 2021).Additionally, to take into account pre-convective conditions from SPHERA, a temporal window before the OT event is considered.Within this spatio-temporal neighborhood, the maximum (for CAPE, K index, and DLS) or minimum (for SLI and H 0 ) values of these parameters are extracted.
The filter to select potential hail-related OTs is then constructed by employing confirmed ESWD hail reports.The environmental parameters are selected in the vicinity of the reports by considering the same spatio-temporal neighborhood used for the OTs (i.e., 0.63°x 0.63°spatial window, 0-3 hours temporal window), and the thresholds are defined as percentiles p th of the distributions of the parameters (following the approach of Punge et al., 2017).Conversely to the latter study ::::::::::::::: , where thresholds based on the 2nd or 98th percentiles were prescribed, here the slightly more stringent 5th percentile (for CAPE, K index, and DLS) or 95th percentile (for SLI and H 0 ) is selected.This is justified by the higher spatio-temporal resolution of SPHERA reanalysis (2.2 km -1 h), which, compared to ERA-Interim (80 :: 79 km -6 h) considered by Punge et al.  is detected for increasing hail sizes.Indeed, moving from the purple to the red lines in Fig. 4, increased instability (greater CAPE and K index and lower SLI), enhanced organization (greater DLS), and higher freezing levels are noted.This suggests the ability of the numerical proxies to identify hail-related ambient conditions.The shaded areas in Fig. 4 indicate the tail of the CDFs (corresponding to the 5th or 95th percentile portions) where the filter is active.

Reanalysis parameters contribution to OT filtering
The :::: Table :: 1 :::::: reports ::: the thresholds obtained, the numbers of OTs and the relative fractions filtered by the full filter (applying the five conditions together :::::::: parameter :::::::: conditions ::::::: together ::::::::: (hereafter ::::::: referred :: to :: as ::: full :::: filter) and for each parameterare listed in Table 1.Singular parameter contributions to the filter vary from 7.0 to 11.2%.Since the same OTs are sometimes filtered by more than one variable, the fraction of removed OTs with the full filter is lower than the sum of the singular filters and reaches 27.0%.The fraction of days when instability-index filters (SLI, CAPE, and K index) are active amount to ∼ 70 % and beyond.
This suggests their dominant contribution in the OT selection compared to DLS, which filters in roughly half of the days, or to H 0 , being active in less than one third of the days.The resulting full filter is active in almost the totality (95%) of days with at least one detected OT.To understand the impacts of the different parameters in the OT filtering, their spatio-temporal contributions are investigated.
Figure 5 shows the spatially-distributed filtered fractions of OTs for the single-parameters filters (Fig. 5a-e) and for the full filter (Fig. 5f).Instability parameters (Fig. 5a-c) filter mainly over :::::: certain ::::: areas :: of : the sea (especially in the southern and western Mediterranean) and the Alpine crest, particularly along the Italian-Swiss border.The largest contribution over the sea is given by K index, while over land CAPE and SLI are more active.This is presumably owing to the explicit inclusion of the water vapor content in the atmospheric column in the K index, that weights more over the sea.H 0 (Fig. 5d) filters most OTs over lower latitudes (>60% in Tunisia and Algeria) and high-elevation terrains, especially over the whole Alpine crest, where almost 100% of all OTs are filtered out.This enhanced removal is attributable to the generally colder atmospheric profiles found over the Alps (compared to lower-elevation regions) where the simulated topography reaches elevations as high as 3950 m in SPHERA reanalysis (Fig. 3a), and the freezing level usually exceeds the imposed threshold of 4098 m.However, as seen by the spatial distributions of ESWD reports (Fig. 2a) and OTs (Fig. 3b), the Alpine crest is the least populated region of the domain in terms of hail reports and prominent OTs.This is attributed to the difficulties for deep-organized convective systems to develop in extremely complex terrains, in agreement with a recent climatology of lightning flashes and associated conditions for convective initiation over the Alpine area (Manzato et al., 2022b).Hence, it is believed that the limitation imposed by choice of the ::::: chosen : H 0 threshold is not detrimental to the analysis presented here (a possible proposal for a more sophisticated H 0 -filtering could be topography-dependent).
The DLS filter (Fig. 5e) shows less prominent spatial peaks than other parameters, but enhanced activity in the northern part of the domain (i.e., southern Germany and northern Austria) and in the south-eastern Mediterranean sea.
The combination of the five individual filters (Fig. 5f) delivers maximum filtering (∼100%) along the northern Italian border where the main mountain peaks of the Alps are located, and substantially high (∼60%) but locally variable filtering over the western and southern Mediterranean sea, southern Germany and eastern Austria.In contrast, the regions with the lowest OT removal (<20%) are the Po valley in northern Italy, the northern Adriatic and Thyrrenean seas, and the associated Italian and Croatian coastlines.hours of the day (with less than 10% removal around 14-16 UTC) and during JJA (June July August).No evident differences among the three parameters are detected.
The H 0 contribution (Fig. 6d-j :: d-l) is roughly opposite to that of the instability.The largest removal is found in the afternoon (∼12% at 16-18 UTC) and in late summer, especially in August (about 20%).This seasonal variation is likely linked to the warming of the lower troposphere peaking in August in this region, owing to the annual cycle of solar insolation, producing an upward shift of the freezing level.On the other hand, the daily cycle in H 0 filter cannot be generally related to the diurnal cycle of boundary layer warming.In fact, at altitudes of ∼4 km above sea level (a.s.l.), temperature changes are mainly driven by horizontal advective processes, rather than by vertical sensible heat fluxes, which are little affected by low-level daily variability.The largest fraction of H 0 -driven OT removal is found over the main Alpine crest (Fig. 5d), where the atmospheric boundary layer could extend over 4 km a.s.l., despite being very shallow, implying a possible diurnal impact on the H 0 variation.
The DLS filter (Fig. 6e-k ::: e-m) shows the least diurnal and seasonal variations, with slightly higher OT removal rates around 10 UTC (∼12%) and in April (∼15%).The reduced variability in DLS filtering compared to all the other parameters is most likely attributed to its kinetic (rather than thermodynamic) nature, and to its direct relationship with synoptic-scale forcings.
Indeed, during the considered warm season of the year, the typical synoptic conditions found in the study region are dominated by a persistent anticyclonic ridge.This large-scale forcing produces a general less variable and lower wind magnitude difference between the surface and at ∼6 km altitude compared to its cold season counterpart, which is characterized by more dynamism (e.g., stronger jet streams), and associated with the DLS climatological maximum (Taszarek et al., 2018).The resulting full filter on the daily term (Fig. 6f) shows maximum removal of more than 30% in the morning and evening (4-7 and 20-23 UTC respectively) and to a minimum of ∼23% around 13-15 UTC.Considering the seasonal cycle (Fig. 6l : n), the parameters combination shows enhanced filtering in spring (April with almost 80% and May with almost 40%) followed by August with a removal above 30%.Hail-favoring conditions are most likely to be estabilished in July and June, where minimum OTs removal of ∼13% and ∼22% are issued, respectively.This tendency is in good accordance with the observed hailstorms distribution over the years considered (Fig. 2e), and with more robust 28-year ESWD-based hail climatology (Púčik et al., 2019).
4 Hail frequency and ambient conditions

Spatio-temporal characterization
Figure 7a shows the spatial distribution of the 723,142 OTs retained after applying the filtering described in the previous section over the five extended warm seasons considered.Compared to the original distribution (Fig. 3b), a decrease in the number of OTs over the main Alpine crest is evident, associated with the maximum removal rate in that area (Fig. 5f).Fewer OTs are also detected over land at lower latitudes (Algeria and Tunisia), over the Mediterranean sea, throughout the Apennines, and in north-eastern continental areas (Austria, Slovenia, Croatia, and Bosnia).The main hotspot of OT frequency in the region along the southern pre-Alps and northern Po valley is well preserved after filtering.Further, the resulting contrast with the minimum OT frequency found over the main Alpine crest is more pronounced than before filtering.This suggests the identification of preferential areas for hail formation, which show good agreement with findings from Punge et al. ( 2017) and recent radar-based 345 hail climatology (Nisi et al., 2020).
Hail frequency in a certain area is usually estimated as the number of hail days per year rather than counting every single hailstorm (Punge and Kunz, 2016).In this case, a potential hail day (PHD) is defined as a day when at least one hail-related OT is detected per reference area of 10 x 10 km 2 .The sensitivity tests performed by increasing the number of OTs defining a PHD showed stable and mutually consistent spatial structures (only from > 10 OTs per day the distributions started to lose 350 too much detail).The resulting average PHD distribution is reported in Fig. 7b after spatial smoothing with a Gaussian filter.
This is done to minimize potential uncertainties arising from spatio-temporal shifts between the OT proxy and the occurrence of hail on the ground, and to homogenize the gridded distribution.The result suggests a maximum hailstorm frequency of ≥ 7 PHDs per year in proximity of the southern Alpine slopes and ∼ 0 PHDs over the Alpine crest.The intra-annual variations in hail frequency are estimated on a monthly basis in terms of the geographical distribution of PHDs per month (Fig. 8), and with histograms of hail-related OTs over the whole domain separately for land and sea areas (Fig. 9).Hail frequency is found to be almost zero in early spring, but increasing from April to May, when the cooler temperatures over land and sea surface lead to lower low-level moisture, which limits the development of deep moist convection.
Hail likelihood rapidly increases in June and July over continental areas, with a well-defined peak around the Alpine region.
Particularly in July, besides the widespread maximum over the southern pre-Alps in northern Italy, circumscribed hotspots over central Switzerland and south-western Germany are detected, in accordance with Nisi et al. (2016).Starting from August and extending to September, a significant reduction in hail-filtered OT rate over land is evident (Fig. 8e-f and 9a), coupled with a gradual increase in thunderstorm development over the warm waters of the Tyrrhenian and Adriatic seas (Fig. 9b).Finally, in October (Fig. 8g) a further shift of hailstorm activity towards lower latitudes of the southern Mediterranean sea is detected, while maintaining the hail hotspot over the Thyrrenian sea.This is linked to the increased cooling of the continental surface and the growing likelihood of mid-latitude cyclone formation in this region resulting from the maintenance of warm sea surface temperatures (e.g., Flaounas et al., 2022) :::::::::::::::::::::: (e.g., Flaounas et al., 2022).
to include additional hail-related observations to expand the sample of ambient conditions, such as hailpad records.However, hailpad networks cover only a smaller part of the selected region, which prevents a substantial enlargement of the validated OT data sample.Therefore, ESWD still represents the best available dataset for ground-truth hail occurrence.

Hailstorm environmental signatures
To better understand under which conditions hail reports are correctly identified or missed by the OT-based approach, the associated environmental conditions described with the CP reanalysis predictors are investigated.Parameter distributions are analyzed separately for hit or missed reports.Further, to take into account the role of hail severity, only the subset of 2,249 ESWD reports with information on the maximum hailstone size is considered (in the following referred to as ESWD-S), and results are reported separating between small (< 3 cm) and large hail (⩾ 3 cm).For some hailstorms more than one report is issued, which share the same ambient conditions at a specific temporal stage of the storm.For this reason, duplicate values of the parameter distributions that at the same hour present exactly the same values of all five SPHERA parameters are discarded : , ::: and :::: only ::::: those ::::::::: associated :::: with ::: the ::::: report ::::::::: presenting ::: the :::::: largest ::::::::: maximum :::::::: hailstone :::: size ::: are :::: kept.This is necessary to avoid artificial deviations owing to repetitions of the samples in the resulting distributions.Finally, the satellite-measured cloud-top thermal characteristics in presence of ESWD-S reports are analyzed to further detail hailstorm ambient features.
The cumulative density functions of SPHERA parameters in the presence of ESWD-S reports, separated into four categories based on matching and hail severity conditions, are presented in Fig. 12. 66% reports are successfully detected by the filterbased proxy, the majority of which (69%) pertains to large hail, while missed cases are similarly associated with small (46%) and large hail (54%).By increasing the hailstone size, the distributions tend to shift towards values with enhanced potential for severe convection (i.e., larger CAPE, K index, and DLS, and smaller SLI) and higher H 0 .The most evident separation for all parameters (including DLS, but to a lesser extent) emerges for the missed-small hail class (Fig. 12 -dashed red lines), showing cumulative density curves systematically shifted towards less unstable, less sheared and warmer environments.Interestingly, only 4% of hit ESWD-S reports show at least one parameter falling in its filtered data range (i.e., shadowed areas in Fig. 12), while the fraction decisively increases to 42% for missed reports.
To investigate the inter-relationships between ambient descriptors, hailstorm severity and matching conditions, the parameters spaces for the four hail reports classes are considered in the form of bi-variate histograms.Figure 13 shows the joint distributions of H 0 and K index for the four hailstorm classes.A joint increase of freezing level height with atmospheric instability and low-level moisture content is noted, suggesting a positive linear relationship between H 0 and K index.The distributions for hits (13a-b) are compact and do not present relevant differences among hail sizes.On the other hand, misses counterparts (13c-d) extend over wider ranges and show evident shifts between small and large hail (with H 0 and K index medians greater by roughly 300 m and 2.3°C, respectively).This suggests that missed-large hail events are characterized by generally warm vertical atmospheric profiles (with ∼ 20% freezing level heights above the imposed threshold), while missed-small hail tends to form in lower-instability and colder ambient conditions.
More dispersion characterizes the joint H 0 -DLS distributions (Fig. 14).In all four classes, DLS covers a broad spectrum with interquartile ranges (IQRs) of ∼10 m s −1 , confirming the difficulty in separating events by their hailstone sizes through the vertical wind shear (Kunz et al., 2020).The difference of roughly 7 m s −1 in median DLS values from misses-small hail (14.39 m s −1 ) to hits-large hail (21.24 m s −1 ) suggests the increase in hail severity with storm organization.
Significant spread characterizes also the CAPE-DLS spaces describing the relationship between atmospheric instability and storm organization (Fig. 15).Also in this case, the most different conditions emerge for the missed-small hail class, characterized by generally pronounced low-CAPE (median 1,286 J kg −1 ) and low-DLS environments.

505
A factor playing a central role in the identification of an OT from satellite scans data is the thermal characteristic of the cloud top where the OT can be found.Previous research showed how OTs linked to deep convective clouds can be detected as cold pixels in infrared satellite imagery scans (e.g., Morel and Senesi, 2002;Mikuš and Mahović, 2013).These cold spots are associated with small and sharp infrared brightness temperature (IRBT) minima that are near to or colder than the tropopause temperature associated with the anvil cirrus cloud.Hence, a critical variable included in the Khlopenkov et al. (2021) algorithm for automatic OT detection is the temperature difference ∆T between infrared brightness and tropopause temperatures.A large ∆T (> 6 K) indicates a penetration of the updraft through the anvil of at least 1-2 km (Griffin et al., 2016).The investigation of the cloud-top thermal conditions in the presence of actually occurred ::: true hailstorms could help understand why these have been correctly identified or not with the OT filter approach.For this reason, the minimum IRBT and ∆T distributions in the for the filter defined in Table 1.
presence of ESWD-S reports are considered (for any OT probability of occurrence and not only for >50% as imposed up to 515 now).The distributions are separated among hit and missed reports for small, large, and very large hail occurrences (Fig. 16).
Sharp IRBT minima distributions characterize hit reports of all hailstone size (Fig. 16a), with mean values of ∼211 K and rarely exceeding higher temperatures than 224 K.The relative ∆T minima (Fig. 16c) show almost no positive values, meaning that IRBT is almost always warmer ::::: colder : than the tropopause temperature.Further, the central values of all ∆T populations are below -4 K, as expected from severe thunderstorms producing prominent OTs ::::::::::::::::::::: (e.g., Scarino et al., 2023).Missed reports 520 (Fig. 16b) present more blunted and higher IRBT minima distributions, extending to temperatures as high as 239 K.The associated mean values suggest a more pronounced separation among hail severity classes, especially in case of very large hail (∼5 K colder than for small hail).∆T minima (Fig. 16d) confirms and strengthens these results: the majority (i.e., 54%) of missed ESWD reports are associated with positive ∆T , reaching values as large as +15 K.These conditions indicate tropopause temperatures substantially lower than those of the detected OT, suggesting not prominent IR signaturesthat can be expected to 525 be detected.The enhanced separation in ∆T distributions between small and very large hail, the latter being on average more than 3 K colder, indicates the difficulty for large hailstones to form in these environments.
A method for hailstorm identification obtained by combining convection-permitting SPHERA reanalysis environmental predictors, satellite MSG OT detections, and crowdsourced ESWD hail reports has been presented.The analysis over 2016-2020 during the extended summer season (April-October) allows to assess the appropriateness of the hail proxy over south-central 530 Europe, and to investigate the environmental conditions associated with hail.The proxy is based on a filter to identify convective updrafts potentially linked to the formation of hailstones in a thunderstorm by considering the surrounding environment.Five numerical predictors, quantifying key ingredients for hail development (i.e., most unstable CAPE, K index, SLI, DLS, and freezing level height), are employed to separate OT detections.Single predictors give different spatio-temporal contributions in the identification of hail-related conditions, and their joint use enables to single out satellite-detected updrafts where hail is 535 possible.Indeed, the resulting hail proxy shows a maximum hail potential over northern Italy pre-Alpine areas in June and July peaking at 15 UTC.A hail-related OT is found in the vicinity of 61.5% of ESWD reports, exceeding roughly 22% more than the previous OT-filter estimate over Europe (Punge et al., 2017), and suggesting an improved appropriateness of the new method .
Enhanced suitability of the proxy is observed in case of severe hailstorms: the majority (69%) of correctly identified reports are linked to hailstones exceeding 3 cm diameters.Furthermore, the analysis of the ambient conditions for different hail severity 540 classes suggests the tendency for large (small) hail to form in environments with higher (lower) instability and wind shear, and within warmer (colder) atmospheric vertical profiles, as expected.However, considerable spread in the associated parameters distributions is found, especially for the missed-small hail class, which also shows the most distinct environmental signature.
Moderate hail frequency is detected in southern Germany, which is considered a main European hotspot for hail hazard (Punge et al., 2014(Punge et al., , 2017;;Fluck et al., 2021); this may be caused by the limited temporal extent of the analysis.The northern Adriatic sea represents the primary marine hotspot for hailstorms, particularly enhanced along the Croatian coastline during nighttime in late summer (August-September), similar to Jelić et al. (2020).The most favorable conditions for hail are found along the Italian pre-Alps, but the potential for hailstorm formation is met throughout north-central Italy.This agrees with several hail climatologies on the national (Baldi et al., 2014), or regional level over north-western (Davini et al., 2012) and north-eastern Italy (Giaiotti et al., 2003;Sartori, 2012;Manzato et al., 2022a).On the seasonal scale, the detected intra-annual variability well agrees with the recent Italian ERA5-and-ESWD-based hail characterization of Torralba et al. (2023Torralba et al. ( ) over 1979Torralba et al. ( -2020. .Good temporal matching is also found with the ESWD reports statistics during 1990-2018 over Europe (Púčik et al., 2019).

Figure 2 .
Figure 2. ESWD hail reports in April-October over 2016-2020.The reports are classified by distinguishing among three classes: reports with no information on hail size (in gray), small hail (maximum diameter <3 cm, in orange), and large hail (maximum diameter ⩾ 3 cm in red).a) spatial distribution, b) temporal accuracy distribution, c) maximum hailstone diameter distribution, d) number of reports per hour of the day (UTC), e) number of reports per month, and f) number of reports per year.

Figure 3 .
Figure 3. a) The spatial domain and model orography of SPHERA reanalysis.b) Number of overshooting tops detected per grid cell (on a 10-km regular grid) during April-October in 2016-2020.

(
2017) is expected to significantly enhance the representation of the atmospheric conditions described by the indices (e.g., in the form of sharper peaks in the parameter distributions owing to clearer distinction of the modeled dynamical features).The ESWD-based cumulative density functions (CDFs) of the predictors are reported in Fig.4.To investigate the relationship between each parameter and hailstorm severity, the CDFs are shown for the distribution of the entire hail reports set, and separated between small, large, and very large hail.A general shift of the predictors towards severe-convective environments

Figure 4 .
Figure 4. Cumulative density functions of the five parameters selected from SPHERA in the presence of ESWD hail reports.Hail reports are divided into different classes: all reports (blue lines), small hail (<3 cm, purple lines), large hail (⩾3 cm, green lines), and very large hail (⩾5 cm, red lines).The blue dashed vertical lines indicate the thresholds selected for defining the OT hail filter reported in Table 1.The shadowed portion of the distributions indicates the range of values where the filter is effective.a) DLS, b) H0, c) K index, d) SLI, and e) CAPE.

Figure 7 .
Figure 7. a) Same as Fig. 3b, but for OTs retained after the hail-specific filter.b) The resulting average number of potential hail days (PHDs) per year over 2016-2020 estimated from the hail-related OTs distribution in a) after spatial smoothing with a Gaussian filter.

Figure 9 .
Figure 9. Distributions of hail-related OTs per month separately over land (panel a) and sea (panel b).

Fig
Fig. ::: 11. : Hail is found to be generally more frequent over land during daytime (from 8 to 19:45 UTC, Fig. 10 ::: Fig. ::: 11a) and over the sea during nighttime (from 20 to 7:45 UTC, Fig. 10 :::: Fig. :: 11b).Hail likelihood during daytime is highest over southern pre-Alpine areas and significantly pronounced over high-elevation terrains, especially in the eastern continental part of the domain (Austria, Slovenia, and the Balkans) and over the central-southern Italian peninsula.During nighttime, the north Adriatic prominent (to a lesser extent) nocturnal potential hail signals, which are mostly underestimated by ESWD-based estimates (Fig. 2d) likely owing to the reduced observational activity during nighttime ::: (Fig. Same as Fig. 7b, but separating between a) Daytime (i.e., 8-19:45 UTC) and b) Nighttime (i.e., 20-7:45 UTC).Hourly fraction of hail-related OTs separating land (in red)from sea surface (in blue) and aggregating over the whole spatial domain.

Figure 11
Figure11shows the diurnal cycle of hail-related OT activity separated between land and sea areas.Over land, very infrequent OT detections are revealed during the night and early morning, with a rapid increase starting from 10 UTC and peaking at 15 UTC (i.e., 17 CEST).This reflects the maximum diurnal heating of the near-surface troposphere, which reduces convective inhibition and increases the likelihood for atmospheric instability conditions.During the afternoon, a slightly more gradual decrease is detected.Over the sea, OTs are more likely to form during the night and early morning (from 23 to 9 UTC) compared to land, with a local maximum at 3 UTC.This is most likely linked to the north-eastern Adriatic hotspot of nocturnal hailstorm generation detected in Fig.10b.Afterwards, a gradual decrease in marine OT activity is detected after around 12 UTC, when OT frequency slightly fluctuates during the afternoon and increases during the evening.These findings are in good agreement with the spatio-temporal distribution of the European OT characterization(over   2004-2009)ofBedka (2011) ::: B1).4.2 Matching:::: Hail ::::: proxy ::::::::: matching with ESWD hail reports

Figure 12 .
Figure 12.Cumulative density functions of the five parameters selected from SPHERA in ::the : presence of ESWD-S hail reports.The same criteria described in Sect. 3 apply to spatio-temporally aggregate the parameters in the vicinity of hail reports.Reports are divided into small hail (< 3 cm, dashed lines) and large hail (⩾ 3 cm, solid lines) when hit (in blue) or missed (in red) by the hail-specific OT dataset.The black dashed vertical lines indicate the thresholds identified for filtering (Table1).The shadowed portion of the distributions show when the filter is active.a) DLS, b) H0, c) K index, d) SLI, and e) CAPE.

Figure 13 .
Figure 13.Bi-variate histogram distributions of H0 vs K index in presence of ESWD-S hail reports for the separation considered in Fig. 12: a) hits-large hail, b) hits-small hail, c) misses-large hail, and d) misses-small hail.The blue dashed vertical and horizontal lines represent the median (p50) and the interquartile (IQR) range values (p25 and p75) of the distributions.The black dotted lines report the thresholds used

Figure 15 .
Figure 15.Same as Fig. 13, but for CAPE and DLS.

Figure 16 .
Figure 16.Normalized distributions of minimum IRBT (a b) and ∆T (c d) in presence of hit (a c) and missed (b d) hail reports.The histogram bars quantify the normalized frequency of OTs in the presence of the ESWD-S subset for small (light blue), large (purple), and very large hail (red).Indicated are the mean values (x) for each distribution.The kernel-density estimated probability density functions are shown with dashed curves in respective colors, additionally, the density functions for the whole ESWD set (including also those reports without maximum hailstone size information) are displayed with black dashed curves.

Table 1 .
Variables and thresholds used in the OT filter, relative number and fraction of OTs filtered, and number of days with active OT filtering (with fractions expressed out of the 872 days when at least one OT is detected).

Table 2 .
Comparison between OT detections and ESWD reports (with quality level QC1 or superior) considering the two spatio-temporal matching of 25 km / ±1 h and 75 km / ±3 h, both for the original "Orig OT" and the hail-filtered "Filt OT" datasets, only over land.The fractions of ESWD reports matching OT detections (Hit ESWD rep.row), and the fractions of OTs hitting at least one ESWD report (OTs hitting ESWD row) are reported. ::