Divergent European hail projections from machine learning and physically based models under global warming

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Using 11-year pan-European convection-permitting climate simulations for the present and a + 3°C pseudo-global-warming climate, we compare an online hail-growth diagnostic (HAILCAST) with an offline machine learning model (XGBoost) trained on ERA5 hail environments. We show that, under current conditions, both approaches produce comparable hail frequencies across most of Europe. However, XGBoost predicts widespread hail suppression in a warmer climate, mainly driven by increasing freezing level heights, from conditions beyond the training distribution. HAILCAST instead simulates how enhanced storm updrafts can sustain hail growth despite a warmer atmosphere, projecting regional increases over central-eastern Europe and larger hailstones. Our findings show that data-driven approaches alone should be used with caution under global warming, underscoring the need for physically based hail representations in convection-permitting climate models to robustly assess future convective hazards. Earth and environmental sciences/Climate sciences Earth and environmental sciences/Natural hazards Figures Figure 1 Figure 2 Figure 3 Introduction Severe convective storms are among the most damaging weather hazards worldwide, with hail responsible for the largest share of related economic losses 1 . In Europe, single events can exceed one billion euros in damages, affecting infrastructure, agriculture, and ecosystems 2 – 4 . Understanding how hail formation and frequency may change under global warming is therefore essential but remains challenging due to the complex interplay of thermodynamic, dynamic and microphysical processes 5 . As a result, a wide range of observational and modelling approaches has been developed to characterise hail occurrence and its spatial and temporal variability. These studies rely on four main approaches: (1) direct observations from hail pads and severe weather reports 4 , 6 – 10 ; (2) radar 11 – 13 and satellite observation 14 – 16 ; (3) empirical and statistical relationships between environmental conditions and hail occurrence 17 – 22 ; and (4) physically based hail-grow models 12 , 23 – 25 . Each method carries important limitations. Direct observations are sparse and regionally biased because hailstorms are short-lived and highly localised, while remote-sensing technologies cannot determine whether hail reaches the ground. Statistical proxies provide spatially and temporally continuous estimates but measure hail potential rather than actual hail occurrence, while physically based diagnostics remain sensitive to model resolution and parameterisations. In this context, convection-permitting climate models (CPMs) can provide a more realistic representation of convective storms, including updrafts, downdrafts and ice-phase microphysics, as they explicitly resolve deep convection, in contrast to coarser climate models 26 – 29 . Hail-growth schemes can be included within CPMs 30 , offering physically consistent diagnostics of hail formation in both present-day and future climates 31 . On the other hand, machine learning (ML) techniques are increasingly used to identify hail-prone environments by learning, based on reanalysis and observational datasets, non-linear relationships between hail occurrence and atmospheric precursors, i.e., atmospheric conditions favourable to hail 32 – 34 . Large hail frequently forms in supercell storms, where a rotating updraft allows hailstones to cycle repeatedly within the hail-growth zone 35 , 36 . Hail development is favoured in storm environments characterised by strong atmospheric instability and deep-layer shear, enhanced low-level moisture and relatively low freezing-level height (FLH) 20 . Hail formation further requires an ice embryo, abundant supercooled water, sustained vertical velocity and sufficient time, generally ten minutes or more, for accretion 5 . Recent studies indicate an increasing frequency of severe-storm favourable conditions across northern Italy and central Europe 19 , 20 , 22 , although hail-pad observations in northern Italy show mixed trends 7 . Proxy-based studies using climate models project a rise in convective hazards under global warming, driven by enhanced instability associated with warmer and moister low-level conditions 37 , 38 , but substantial regional uncertainties remain 39 . Recent pan-European CPM studies show contrasting results. Using environmental proxies, ref. 40 project an overall decline in hail potential across Europe, whereas ref. 31 , applying a hail growth model, report a dipole pattern, with reductions over southwestern Europe and increases across central and eastern regions. Ref. 40 further highlight the emergence of “warm-type” thunderstorms, characterised by FLH above 4.5 km, that may still produce very large hailstones 41 . Across these studies, the increasing FLH emerges as a key factor: deeper warm clouds can enhance hail growth aloft but also intensify melting during descent, favouring heavy rainfall over severe hail 39 , 42 , 43 . These competing processes contribute to divergent projections and highlight the need for a clearer understanding of the physical drivers of future hail characteristics. To bridge this knowledge gap, we compare two different modelling approaches to investigate European hail occurrences under both present and pseudo-global warming (PGW) conditions: a physically based hail growth model (HAILCAST 30 ) coupled to convection permitting climate simulations and a machine learning model 44 (XGBoost 45 ) trained on ERA5 46 reanalysis data and applied to the same simulations. In particular, we address two research questions: 1. Can a machine learning model reproduce hail climatology with comparable skill to a physically based approach within a convection-permitting climate model? 2. How does the machine learning model, trained on present-day conditions, represent the impact of global warming on hail, and what do differences between the two approaches reveal about the physical processes underlying future projections? By systematically comparing data-driven and physically based hail models, we aim to clarify their strengths and limitations for assessing future hail risk. Establishing whether these methods converge or diverge under warming conditions and the reasons behind it is crucial for evaluating the reliability of ML models as computationally efficient alternatives for analysing hail in existing convection-permitting climate simulations. Hail climatology in the present climate We first assess whether the XGBoost model can reproduce the spatial distribution of severe hail (hail diameter greater than 25 mm) occurrences when applied to convection-permitting climate simulations over the 2011-2021period. The analysis focuses on summer (JJA), when hail activity peaks across Europe, and is restricted to land areas where hail impacts are most relevant. Both the HAILCAST and the XGBoost model simulate similar magnitudes and spatial patterns of hail frequency, with maxima located in the Po valley and along major orographic features, including the Alpine foothills, the Pyrenees, the Carpathian Basin, and the northern Apennines, as well as over parts of central Europe (Fig. 1 a and b). These results are consistent with previous findings on large-hail climatologies 18 – 22 and highlight the strong role of topography and land-sea contrasts in organising deep moist convection, which is explicitly solved in convection-permitting simulations. Despite the comparable magnitude of hail days, regional differences are evident (Fig. 1 c): XGBoost enhances hail occurrences across central Europe and northern Italy, while reducing it over both eastern and southern Europe compared to HAILCAST. These discrepancies reflect the differing sensitivities of the two approaches. In particular, HAILCAST simulates a hail size distribution shifted toward smaller maximum hailstones compared to hail reports 24 that may explain lower hail frequencies over central Europe. HAILCAST links hail growth directly to local updraft strength and microphysical processes within the storm 30 , enhancing hail formation where strong vertical velocities favour sustained growth (Fig. S1 a). In contrast, XGBoost relies on specific environmental conditions learned from ERA5 reanalysis, describing atmospheric instability, storm organisation, moisture availability and FLH (see Methods), which reflect mesoscale processes resolved at coarser resolution than in convection-permitting simulations, potentially contributing to regional over- or underestimation of hail occurrence across Europe. In literature, hail climatologies have been constructed and evaluated at continental, national, and local scales using diverse observational products, environmental proxies, and model-based diagnostics, each with distinct assumptions and limitations. However, no unified benchmark exists. Indeed, hail climatologies based on reanalysis-derived hail precursors 18 – 22 and regional climate models, with either parameterised convection 38 or convection-permitting resolution 12 , 47 , show regional differences, with no approach emerging as a clear reference, due to the lack of a robust and homogeneous observational dataset. The spatial differences between HAILCAST and XGBoost fall within the spread of these existing climatologies, indicating that both approaches provide a potentially reliable representation of present-day hail occurrences, considering their respective driving mechanisms and limitations. Finally, both models show a similar diurnal cycle of hail with an afternoon-evening peak (Fig. 1 d), although XGBoost produces a later peak, more in line with observational studies 48 . Future changes in hail occurrence We next assess how hail occurrences respond to a warmer climate by comparing HAILCAST and XGBoost within the PGW 49 simulation. The experiment spans 11 years (2085–2095) and corresponds to + 3°C of global warming relative to the preindustrial period. The evaluation focuses on land during JJA, consistent with the historical period. HAILCAST shows a distinct dipole pattern in future severe hail frequency. Increases in hail days are projected across the Alps and central to eastern Europe (Fig. 2 a), where the frequency rises by about 25% (Fig. 2 d), while southern Europe experiences overall decreases (Fig. 2 a) reaching a reduction of roughly 40% over the western Mediterranean (Fig. 2 d). This signal reflects changes in the convective environment under warming conditions, characterized by increased maximum convective available potential energy (CAPE) over central and eastern Europe and reduced CAPE over southern land regions 31 (Fig. S2a). In contrast, XGBoost projects a widespread decrease in hail occurrences across most of Europe (Fig. 2 b). The contrasting PGW responses of the two methods arise from their different underlying approaches. XGBoost is not able to reproduce the climate change signal simulated by HAILCAST since it encounters atmospheric environments that are not in the current climate training data. This divergence motivates a deeper investigation into the physical mechanisms involved, particularly the role of FLH on hail growth and melting in a warmer climate. Drivers of future hail changes Anthropogenic climate change alters both the thermodynamic and dynamic environments in which hailstorms develop, potentially increasing the conditions conducive to deep convection across Europe 39 , primarily through enhanced low-level moisture and convective instability. However, future hail activity will be strongly shaped by rising FLH, which controls the phase and intensity of surface precipitation 43 . As FLH increases, deeper warm-cloud layers may promote both enhanced melting of hail, favouring heavy rainfall over large hail 39 , 42 , 43 , but also the formation of warm-type thunderstorms capable of producing very large hailstones that still reaches the surface 40 , 41 . These thermodynamic shifts interact with changes in storm dynamics, including deep-layer shear and mid-tropospheric updrafts in the hail growth zone, to reshape hailstorm characteristics. The compensating effects of future dynamical changes, particularly intensified CAPE (Fig. S1 a), wind shear (Fig. S2b, c) and storm-relative helicity (Fig. S2d, e) over central-eastern Europe, are coherently simulated by the convection-permitting COSMO model, providing conditions under which HAILCAST diagnoses hail despite a higher FLH of approximately 400–600 m across Europe (Fig. S3a). A key signature of this response is evident in the HAILCAST output: hail diameter increases systematically with FLH anomaly in both historical and PGW simulations (Fig. 3 a) and larger hail diameters are more frequent in the future scenario (Fig. 3 b), consistent with the hailstorm track analysis reported by ref. 50 . This indicates that, in deep warm-cloud environments, storms with sufficiently strong and persistent updrafts can sustain intense hail growth aloft and produce larger hailstones at the surface. In this respect, XGBoost similarly ingests hail-favourable environments simulated by the COSMO model under global warming; however, it is trained on present-day relationships and cannot account for changes in the physical mechanisms governing hail in a warmer climate. To quantify the influence of individual atmospheric predictors on XGBoost’s hail projection, a sensitivity experiment was performed by modifying each precursor in the PGW simulation by ± 10% toward its present-climate mean while preserving the variability of the future state. Among all predictors, FLH showed the strongest impact: reducing FLH by 10% and reapplying the XGBoost model produced hail frequency patterns closer to HAILCAST projections (Fig. 2 c), particularly, a similar ~ 25% increase over central-eastern Europe (Fig. 2 d). Adjustments to other variables resulted in negligible changes, except for a moderate sensitivity to the Total Totals (TT) Index (Fig. S4), which links instability and low-level moisture. Pearson correlation coefficients between total hail days distribution in HAILCAST and in the XGBoost sensitivity experiments, under the PGW scenario (Table 1 ), further confirm that the decreasing signal in the ML hail projection is primarily driven by higher FLH and, to a lesser extent, by increased atmospheric stability (TT index). Together, these results underscore the limits of a purely data-driven framework in representing storm-scale dynamics and adapting to future atmospheric environments outside its training range. Large-scale circulation patterns also modulate hail occurrence in Europe and analysing them provide additional insight into why the two modelling frameworks respond differently. To address this, we assessed 500-hPa geopotential height (Z500) anomalies associated with hail days diagnosed by XGBoost and HAILCAST (see supplementary information). Composite Z500 anomalies show that XGBoost-diagnosed hail days are associated with well-known 51 coherent synoptic-scale patterns favourable for severe convection, whereas HAILCAST hail days exhibit much weaker large-scale structure (Fig. S5). This indicates that the ML model primarily responds to synoptic environments, while HAILCAST is dominated by local storm-scale processes. These patterns remain largely unchanged in the PGW future climate, with only a modest strengthening in the XGBoost-based anomalies (Fig. S6). Table 1 Sensitivity of XGBoost hail projections to predictor perturbations. Pearson correlation coefficients (r) between HAILCAST PGW hail frequencies and XGBoost PGW sensitivity experiments in which each predictor is independently shifted by ± 10% toward its historical mean. The orange and blue cells indicate shifts toward more and less hail-favourable environments, respectively. All correlations are statistically significant (p-value equal to zero). FLH TT CIN RH850 RH500 No shift CAPE WS06 WS03 SRH06 SRH03 Td2 Shift % -10 + 10 -10 + 10 + 10 0 -10 -10 -10 -10 -10 -10 r 0.49 0.44 0.38 0.37 0.36 0.36 0.35 0.35 0.35 0.36 0.36 0.36 Discussion Regional contrasts and substantial uncertainties remain in projecting how hail will respond to anthropogenic climate change. While both the machine learning model (XGBoost) and the physically based hail-growth scheme (HAILCAST) provide plausible representations of present-day hail climatology over Europe, they significantly diverge in their future projections. Changes in thermodynamic and dynamical processes exert distinct influences in the two modelling frameworks, offering insights into the physical drivers of the contrasting future hail responses. In XGBoost, the large increase in FLH results in widespread suppression of simulated hail, revealing a key limitation of data-driven models when applied outside their historical training distribution. In contrast, HAILCAST simulates how enhanced storm dynamics and updraft strength can sustain hail growth aloft, enabling large hailstones to survive descent despite higher FLH. This allows a more physically consistent characterisation of how storm-scale dynamics may evolve under different climatic conditions. Further work is required to assess the robustness and generality of these findings across a broader range of modelling frameworks. Extending the analysis to ensembles of convection-permitting climate simulations, beyond a single PGW realisation, and exploring alternative machine learning architectures or predictor sets would help evaluate the sensitivity of projected hail changes to large-scale dynamical variability and to shifts in dynamical and thermodynamic conditions. Such efforts are essential to increase reliability in hail projections and to capture additional aspects of hail formation under global warming. Ultimately, our findings highlight that combining complementary tools is crucial to improve confidence in regional hail projections and advancing our understanding of the processes shaping convective hazards under climate change. Methods To investigate how hail occurrence in Europe responds to a warming climate, we compare a physically based hail-growth model with a data-driven machine learning approach, both applied to the same convection-permitting climate simulations. This dual approach allows a direct comparison between physical and statistical representations of hail, providing insight into their respective sensitivities to key atmospheric environments. Convection-permitting climate simulations We analyse two pan-European convection-permitting climate simulations performed with the non-hydrostatic COSMO model at 2.2 km grid spacing, in the configuration as described in ref 12 , 31 . The historical experiment spans 11 years (2011–2021) and is driven by ERA5 reanalysis 46 . The future simulation applies a pseudo-global warming (PGW) perturbation of + 3°C compared to preindustrial to the ERA5 boundary conditions, following the method of ref. 49 , thereby isolating the thermodynamic response to warming while retaining a similar synoptic variability as in the historical simulation. Further details on the model setup are provided in ref. 12 for the historical period and in ref. 31 for the PGW experiment. Both simulations use an outer nest (~ 12 km resolution) and an inner convection-permitting nest (~ 2.2 km) in which hail processes are represented through a one-dimensional hail-growth model (HAILCAST 30 ). HAILCAST computes the maximum hail diameter at the surface every 5 minutes based on the simulated vertical profiles of temperature, humidity and wind. The HAILCAST configuration was validated against observations, demonstrating good skill in reproducing the spatial distribution, seasonal cycle and diurnal cycle of hail occurrence over Europe 12 . The hail outputs are aggregated to hourly resolution by retaining the maximum hail diameter within each hour. A hail day is then defined at each model grid point as any 24-h period (00:00–23:00 UTC) in which HAILCAST produces at least one hailstone exceeding 25 mm in diameter. This size category corresponds to hailstones large enough to cause damage to infrastructure 18 , 52 . Machine learning algorithm: XGBoost To complement the physically based hail diagnostics, we apply a machine learning (ML) algorithm based on gradient-boosted decision trees (XGBoost 45 ) to the hourly output of the same convection-permitting climate simulations used for the HAILCAST analysis. The ML model employed here is the global XGBoost configuration (XGBGlobal) described and validated in ref. 44 . XGBGlobal is trained on ERA5 reanalysis 46 predictors matched to a compilation of more than 120,000 hail reports from the U.S.A, Europe and Australia, using an event maximum hail-size threshold of 25 mm consistent with the definition of large hail events in HAILCAST. The training dataset includes observations from NOAA over the United States, the Australian Bureau of Meteorology, and the European Severe Storm Laboratory 53 . The algorithm uses eleven atmospheric predictors associated with hail-supporting environments, including maximum convective available potential energy (CAPE), convective inhibition (CIN), freezing level height (FLH), Total Totals index (TT), 0–6 km wind shear (WS06), 0–3 km wind shear (WS03), 0–6 km storm relative helicity (SRH06), 0–3 km storm relative helicity (SRH03), 2 m dew-point temperature (Td2), relative humidity at 850 hPa (RH850) and relative humidity at 500 hPa (RH500). Ref. 44 show that XGBGlobal well reproduces observed hail climatology and outperforms the previous proxy-based statistical model of ref. 18 . Ref. 44 trained XGBoost on daily data, but we decided to apply the model with hourly predictors, which results in hourly hail probabilities (0–1), and a hail hour is diagnosed when the probability exceeds 0.5. To obtain a consistent metric with HAILCAST, a hail day is defined at each grid point as any 24-h period (00:00–23:00 UTC) containing at least one hour with a predicted probability ≥ 0.5. Data and Code availability A selection of output fields from the COSMO simulations used in this study are publicly available in the ETH research collection via https://doi.org/10.3929/ethz-b-000701925 for the historical experiment and via https://doi.org/10.3929/ethz-b-000747355 for the PGW experiment. Additional model outputs are available upon request from the authors. Hail outputs derived from XGBoost and HAILCAST and used in this study are publicly available on Zenodo at: https://doi.org/10.5281/zenodo.18243342 . All Python scripts used to generate the figures presented in this manuscript are publicly available at: https://github.com/marcochericoni95/hail_xgboost_hailcast_ncc . The XGBoost model is publicly available at: https://github.com/borusseee/XGBoost_hail . Declarations Acknowledgments This paper and related research have been conducted during and with the support of the Italian inter-university PhD course in Sustainable Development and Climate change (link:www.phd-sdc.it) and developed within the framework of the project “Dipartimento di Eccellenza 2023-2027”, funded by the Italian Ministry of Education, University and Research at IUSS Pavia. This work presented here contains analyses carried out on the High-Performance Computing DataCenter at IUSS, co-funded by Regione Lombardia through the funding programme established by Regional Decree No. 3776 of November 3, 2020. This study is carried out within the ICSC Italian Research Center on High-Performance Computing, Big Data and Quantum Computing and received funding from the European Union Next-GenerationEU (National Recovery and Resilience Plan-NRRP, Mission 4, Component 2, Investment 1.4-D.D: 3138 16/12/2021, CN00000013). We particularly thank Boris Blanc who developed the XGBoost hail prediction model. Author contributions M.C., G.F., A.A., I.T. and A.P. conceived the idea of the manuscript. M.C. performed the analysis and wrote the manuscript with inputs from all the authors. Competing interest The authors declare no competing interests. References Steve Bowen, Brian Kerschner & Jin Zheng Ng. Natural Catastrophe and Climate Report 2024 . (2025). Schmid, T., Portmann, R., Villiger, L., Schröer, K. & Bresch, D. N. An open-source radar-based hail damage model for buildings and cars. Natural Hazards and Earth System Sciences 24, 847–872 (2024). Portmann, R., Schmid, T., Villiger, L., Bresch, D. N. & Calanca, P. Modelling crop hail damage footprints with single-polarization radar: the roles of spatial resolution, hail intensity, and cropland density. Natural Hazards and Earth System Sciences 24, 2541–2558 (2024). Púčik, T. et al. Large Hail Incidence and Its Economic and Societal Impacts across Europe. Mon. Weather Rev. 147, 3901–3916 (2019). Allen, J. T. et al. Understanding Hail in the Earth System. Reviews of Geophysics 58, (2020). Hulton, F. & Schultz, D. M. Climatology of large hail in Europe: characteristics of the European Severe Weather Database. Natural Hazards and Earth System Sciences 24, 1079–1098 (2024). Manzato, A., Cicogna, A., Centore, M., Battistutta, P. & Trevisan, M. Hailstone Characteristics in Northeast Italy from 29 Years of Hailpad Data. J. Appl. Meteorol. Climatol. 61, 1779–1795 (2022). Barras, H. et al. Experiences with >50,000 Crowdsourced Hail Reports in Switzerland. Bull. Am. Meteorol. Soc. 100, 1429–1440 (2019). Kopp, J., Manzato, A., Hering, A., Germann, U. & Martius, O. How observations from automatic hail sensors in Switzerland shed light on local hailfall duration and compare with hailpad measurements. Atmos. Meas. Tech. 16, 3487–3503 (2023). Das, S. & Allen, J. T. Bayesian estimation of the likelihood of extreme hail sizes over the United States. npj Natural Hazards 1, 47 (2024). Ryzhkov, A. V., Kumjian, M. R., Ganson, S. M. & Khain, A. P. Polarimetric Radar Characteristics of Melting Hail. Part I: Theoretical Simulations Using Spectral Microphysical Modeling. J. Appl. Meteorol. Climatol. 52, 2849–2870 (2013). Cui, R. et al. A European Hail and Lightning Climatology From an 11-Year Kilometer‐Scale Regional Climate Simulation. Journal of Geophysical Research: Atmospheres 130, (2025). Nisi, L., Martius, O., Hering, A., Kunz, M. & Germann, U. Spatial and temporal distribution of hailstorms in the Alpine region: a long-term, high resolution, radar‐based analysis. Quarterly Journal of the Royal Meteorological Society 142, 1590–1604 (2016). Punge, H. J., Bedka, K. M., Kunz, M. & Reinbold, A. Hail frequency estimation across Europe based on a combination of overshooting top detections and the ERA-INTERIM reanalysis. Atmos. Res. 198, 34–43 (2017). Bedka, K. M., Allen, J. T., Punge, H. J., Kunz, M. & Simanovic, D. A Long-Term Overshooting Convective Cloud-Top Detection Database over Australia Derived from MTSAT Japanese Advanced Meteorological Imager Observations. J. Appl. Meteorol. Climatol. 57, 937–951 (2018). Giordani, A. et al. Characterizing hail-prone environments using convection-permitting reanalysis and overshooting top detections over south-central Europe. Natural Hazards and Earth System Sciences 24, 2331–2357 (2024). Allen, J. T., Tippett, M. K. & Sobel, A. H. An empirical model relating U.S. monthly hail occurrence to large-scale meteorological environment. J. Adv. Model. Earth Syst. 7, 226–243 (2015). Prein, A. F. & Holland, G. J. Global estimates of damaging hail hazard. Weather Clim. Extrem. 22, 10–23 (2018). Rädler, A. T., Groenemeijer, P., Faust, E. & Sausen, R. Detecting Severe Weather Trends Using an Additive Regressive Convective Hazard Model (AR-CHaMo). J. Appl. Meteorol. Climatol. 57, 569–587 (2018). Battaglioli, F. et al. Modeled Multidecadal Trends of Lightning and (Very) Large Hail in Europe and North America (1950–2021). J. Appl. Meteorol. Climatol. 62, 1627–1653 (2023). Mohr, S., Kunz, M. & Geyer, B. Hail potential in Europe based on a regional climate model hindcast. Geophys. Res. Lett. 42, (2015). Battaglioli, F., Taszarek, M., Groenemeijer, P., Púčik, T. & Rädler, A. Contrasting trends in very large hail events and related economic losses across the globe. Nat. Geosci. 19, 52–58 (2026). Brennan, K. P., Sprenger, M., Walser, A., Arpagaus, M. & Wernli, H. An object-based and Lagrangian view on an intense hailstorm day in Switzerland as represented in COSMO-1E ensemble hindcast simulations. Weather and Climate Dynamics 6, 645–668 (2025). Cui, R. et al. Exploring hail and lightning diagnostics over the Alpine-Adriatic region in a km-scale climate model. Weather and Climate Dynamics 4, 905–926 (2023). Malečić, B. et al. Simulating Hail and Lightning Over the Alpine Adriatic Region—A Model Intercomparison Study. Journal of Geophysical Research: Atmospheres 128, (2023). Fosser, G. et al. Convection-permitting climate models offer more certain extreme rainfall projections. NPJ Clim. Atmos. Sci. 7, 51 (2024). Coppola, E. et al. A first-of-its-kind multi-model convection permitting ensemble for investigating convective phenomena over Europe and the Mediterranean. Clim. Dyn. 55, 3–34 (2020). Prein, A. F. et al. A review on regional convection-permitting climate modeling: Demonstrations, prospects, and challenges. Reviews of Geophysics 53, 323–361 (2015). Fosser, G., Khodayar, S. & Berg, P. Benefit of convection permitting climate model simulations in the representation of convective precipitation. Clim. Dyn. 44, 45–60 (2015). Adams-Selin, R. D. & Ziegler, C. L. Forecasting Hail Using a One-Dimensional Hail Growth Model within WRF. Mon. Weather Rev. 144, 4919–4939 (2016). Thurnherr, I., Cui, R., Velasquez, P., Wernli, H. & Schär, C. The Effect of 3° C Global Warming on Hail Over Europe. Geophys. Res. Lett. 52, (2025). Torralba, V. et al. Modelling hail hazard over Italy with ERA5 large-scale variables. Weather Clim. Extrem. 39, 100535 (2023). Czernecki, B. et al. Application of machine learning to large hail prediction - The importance of radar reflectivity, lightning occurrence and convective parameters derived from ERA5. Atmos. Res. 227, 249–262 (2019). Burke, A., Snook, N., Gagne II, D. J., McCorkle, S. & McGovern, A. Calibration of Machine Learning–Based Probabilistic Hail Predictions for Operational Forecasting. Weather Forecast. 35, 149–168 (2020). Davies-Jones, R. A review of supercell and tornado dynamics. Atmos. Res. 158–159, 274–291 (2015). Feldmann, M., Hering, A., Gabella, M. & Berne, A. Hailstorms and rainstorms versus supercells—a regional analysis of convective storm types in the Alpine region. NPJ Clim. Atmos. Sci. 6, 19 (2023). Púčik, T. et al. Future Changes in European Severe Convection Environments in a Regional Climate Model Ensemble. J. Clim. 30, 6771–6794 (2017). Rädler, A. T., Groenemeijer, P. H., Faust, E., Sausen, R. & Púčik, T. Frequency of severe thunderstorms across Europe expected to increase in the 21st century due to rising instability. NPJ Clim. Atmos. Sci. 2, 30 (2019). Raupach, T. H. et al. The effects of climate change on hailstorms. Nat. Rev. Earth Environ. 2, 213–226 (2021). Kahraman, A., Kendon, E. J., Fowler, H. J. & Short, C. J. Future changes in severe hail across Europe, including regional emergence of warm-type thunderstorms. Nat. Commun. 16, 8438 (2025). Brimelow, J. C., Burrows, W. R. & Hanesiak, J. M. The changing hail threat over North America in response to anthropogenic climate change. Nat. Clim. Chang. 7, 516–522 (2017). Mahoney, K., Alexander, M. A., Thompson, G., Barsugli, J. J. & Scott, J. D. Changes in hail and flood risk in high-resolution simulations over Colorado’s mountains. Nat. Clim. Chang. 2, 125–131 (2012). Prein, A. F. & Heymsfield, A. J. Increased melting level height impacts surface precipitation phase and intensity. Nat. Clim. Chang. 10, 771–776 (2020). Blanc, B., Prein, A. F., Jeggle, K., Aellen, N. & Lohmann, U. Improving our Understanding of Large Hail Hazards Using Machine Learning. Artificial Intelligence for the Earth Systems . Chen, T. & Guestrin, C. XGBoost. in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 785–794 (ACM, New York, NY, USA, 2016). doi: 10.1145/2939672.2939785 . Hersbach, H. et al. The ERA5 global reanalysis. Quarterly Journal of the Royal Meteorological Society 146, 1999–2049 (2020). Kahraman, A., Kendon, E. J. & Fowler, H. J. Climatology of severe hail potential in Europe based on a convection-permitting simulation. Clim. Dyn. https://doi.org/10.1007/s00382-024-07227-w (2024) doi:10.1007/s00382-024-07227-w. Nisi, L. et al. Hailstorms in the Alpine region: Diurnal cycle, 4D-characteristics, and the nowcasting potential of lightning properties. Quarterly Journal of the Royal Meteorological Society 146, 4170–4194 (2020). Brogli, R., Heim, C., Mensch, J., Sørland, S. L. & Schär, C. The pseudo-global-warming (PGW) approach: methodology, software package PGW4ERA5 v1.1, validation, and sensitivity analyses. Geosci. Model Dev. 16, 907–926 (2023). Brennan, K. P., Thurnherr, I., Sprenger, M. & Wernli, H. Insights from hailstorm track analysis in European climate change simulations. Natural Hazards and Earth System Sciences 25, 3693–3712 (2025). Feldmann, M., Domeisen, D. I. V. & Martius, O. A pan-European analysis of large-scale drivers of severe convective outbreaks. Weather and Climate Dynamics 6, 1089–1106 (2025). Hohl, R., Schiesser, H.-H. & Aller, D. Hailfall: the relationship between radar-derived hail kinetic energy and hail damage to buildings. Atmos. Res. 63, 177–207 (2002). Dotzek, N., Groenemeijer, P., Feuerstein, B. & Holzer, A. M. Overview of ESSL’s severe convective storms research using the European Severe Weather Database ESWD. Atmos. Res. 93, 575–586 (2009). Additional Declarations No competing interests reported. Supplementary Files SupplementaryinformationhailNCC.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 14 Mar, 2026 Reviews received at journal 13 Mar, 2026 Reviewers agreed at journal 04 Mar, 2026 Reviews received at journal 20 Feb, 2026 Reviewers agreed at journal 16 Feb, 2026 Reviewers agreed at journal 12 Feb, 2026 Reviewers invited by journal 10 Feb, 2026 Editor assigned by journal 03 Feb, 2026 Submission checks completed at journal 02 Feb, 2026 First submitted to journal 29 Jan, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8731533","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":590779502,"identity":"a55b4b26-6782-4526-9d6b-9400e23cc3d5","order_by":0,"name":"Marco Chericoni","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVRIiWNgGAWjYBCDBAYGxgYgLSEH4RuQoMUYqoWwngQYI7GBkDW67WcffvjAYJfHL3248cPHHRbp/dMOP/zAUPAHpxazM+nGkjMYkosl+xKbJWeekcidcTvNWAKfw8wOpLEx8zAcSNxwhrGNmbdNIneDdA4bXr+YnX8G0bIfqiXdgKCWGzBbeCBaEojQ8oxZcoZBcuKMM4xAv7RJGIL9kmBgjMdhaYwfPlTYJfb3sD/88LGtTp5/djIwDP/I4dQCARiuSCCgYRSMglEwCkYBfgAAvmdJyyOj/HYAAAAASUVORK5CYII=","orcid":"","institution":"CMCC Foundation - Euro-Mediterranean Center on Climate Change","correspondingAuthor":true,"prefix":"","firstName":"Marco","middleName":"","lastName":"Chericoni","suffix":""},{"id":590779503,"identity":"30eec5f9-01e2-44b2-b50d-bf775b7f4c7c","order_by":1,"name":"Giorgia Fosser","email":"","orcid":"","institution":"University School for Advanced Studies IUSS","correspondingAuthor":false,"prefix":"","firstName":"Giorgia","middleName":"","lastName":"Fosser","suffix":""},{"id":590779504,"identity":"4a75b0a7-7dca-4196-a44a-03b014a1443e","order_by":2,"name":"Alessandro Anav","email":"","orcid":"","institution":"ENEA - National Agency for New Technologies, Energy and Sustainable Economic Development","correspondingAuthor":false,"prefix":"","firstName":"Alessandro","middleName":"","lastName":"Anav","suffix":""},{"id":590779505,"identity":"c045f3b6-360d-403c-89f2-75f4f8aef60a","order_by":3,"name":"Iris Thurnherr","email":"","orcid":"","institution":"ETH Zurich","correspondingAuthor":false,"prefix":"","firstName":"Iris","middleName":"","lastName":"Thurnherr","suffix":""},{"id":590779506,"identity":"08a4f602-6ba4-4e36-9c67-90a4ac094415","order_by":4,"name":"Andreas F. Prein","email":"","orcid":"","institution":"ETH Zurich","correspondingAuthor":false,"prefix":"","firstName":"Andreas","middleName":"F.","lastName":"Prein","suffix":""}],"badges":[],"createdAt":"2026-01-29 12:26:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8731533/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8731533/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103056291,"identity":"d349d65a-dcb7-45ff-a0ed-f85480e6eae3","added_by":"auto","created_at":"2026-02-20 09:04:06","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":701234,"visible":true,"origin":"","legend":"\u003cp\u003eSevere hail days in the present climate from CPM simulation. Total number of severe hail days (hail diameter ≥ 25 mm), during summer (JJA), for the historical period 2011-2021, simulated with (a) the HAILCAST model and (b) the XGBoost model. Panel (c) shows the difference between XGBoost and HAILCAST. The maps are shown at a spatial resolution of 2.2 km with a 1.5 σ Gaussian smoothing applied spatially. (d) Diurnal cycle of hail occurrence in the historical simulation, with solid lines for HAILCAST and dashed lines for XGBoost.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8731533/v1/837c47a43e35f0f8099a51f7.png"},{"id":102787002,"identity":"a240eb8d-8c9e-4d8d-bb53-92e005e993ce","added_by":"auto","created_at":"2026-02-16 16:20:08","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":680366,"visible":true,"origin":"","legend":"\u003cp\u003eFuture changes in severe hail days under PGW condition from CPM simulation. Climate change signal (PGW minus historical) of severe hail days (hail diameter ≥ 25 mm), during summer (JJA), simulated by HAILCAST (a) and XGBoost (b). (c) Climate change signal of XGBoost after reducing FLH by 10% in the PGW simulation. (d) Relative changes (%) in hail days between PGW and historical climates for four subregions (west MED, central MED, west EU, central EU), comparing HAILCAST (blue), XGBoost (orange), and XGBoost with reduced FLH (green).\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8731533/v1/889dd2dada1bee8dc7f4c94d.png"},{"id":102962608,"identity":"ea78df44-439f-4608-8306-59b17f8fb0c3","added_by":"auto","created_at":"2026-02-19 04:10:06","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":145145,"visible":true,"origin":"","legend":"\u003cp\u003eHail diameters from HAILCAST. (a) Hailstone diameter as a function of FLH anomalies during hail events (\u0026gt; 25 mm) in the historical (blue) and PGW (orange) simulations, with boxplots shown for 500-m anomaly bins. FLH anomalies are computed as the difference between the FLH during HAILCAST-diagnosed hail days and the JJA climatological mean. (b) Probability density functions of hail diameter for the historical (blue) and PGW (orange) climates, together with their difference (PGW minus historical; black).\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8731533/v1/0fa5b4ca77fc131453587be4.png"},{"id":103056601,"identity":"c328dfaa-fb92-4ebc-bffd-8287314e04cc","added_by":"auto","created_at":"2026-02-20 09:22:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2189490,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8731533/v1/bf3b2c3c-1ecd-4237-bd36-95120233d39c.pdf"},{"id":102787005,"identity":"552801ad-99d9-427b-9cb9-c92093e04536","added_by":"auto","created_at":"2026-02-16 16:20:08","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":5214659,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryinformationhailNCC.docx","url":"https://assets-eu.researchsquare.com/files/rs-8731533/v1/d01dac91279ab80930bd142c.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Divergent European hail projections from machine learning and physically based models under global warming","fulltext":[{"header":"Introduction","content":"\u003cp\u003eSevere convective storms are among the most damaging weather hazards worldwide, with hail responsible for the largest share of related economic losses\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. In Europe, single events can exceed one billion euros in damages, affecting infrastructure, agriculture, and ecosystems\u003csup\u003e\u003cspan additionalcitationids=\"CR3\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Understanding how hail formation and frequency may change under global warming is therefore essential but remains challenging due to the complex interplay of thermodynamic, dynamic and microphysical processes\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. As a result, a wide range of observational and modelling approaches has been developed to characterise hail occurrence and its spatial and temporal variability. These studies rely on four main approaches: (1) direct observations from hail pads and severe weather reports\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan additionalcitationids=\"CR7 CR8 CR9\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e; (2) radar\u003csup\u003e\u003cspan additionalcitationids=\"CR12\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e and satellite observation\u003csup\u003e\u003cspan additionalcitationids=\"CR15\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e; (3) empirical and statistical relationships between environmental conditions and hail occurrence\u003csup\u003e\u003cspan additionalcitationids=\"CR18 CR19 CR20 CR21\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e; and (4) physically based hail-grow models\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan additionalcitationids=\"CR24\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. Each method carries important limitations. Direct observations are sparse and regionally biased because hailstorms are short-lived and highly localised, while remote-sensing technologies cannot determine whether hail reaches the ground. Statistical proxies provide spatially and temporally continuous estimates but measure hail potential rather than actual hail occurrence, while physically based diagnostics remain sensitive to model resolution and parameterisations. In this context, convection-permitting climate models (CPMs) can provide a more realistic representation of convective storms, including updrafts, downdrafts and ice-phase microphysics, as they explicitly resolve deep convection, in contrast to coarser climate models\u003csup\u003e\u003cspan additionalcitationids=\"CR27 CR28\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. Hail-growth schemes can be included within CPMs\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e, offering physically consistent diagnostics of hail formation in both present-day and future climates\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. On the other hand, machine learning (ML) techniques are increasingly used to identify hail-prone environments by learning, based on reanalysis and observational datasets, non-linear relationships between hail occurrence and atmospheric precursors, i.e., atmospheric conditions favourable to hail\u003csup\u003e\u003cspan additionalcitationids=\"CR33\" citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. Large hail frequently forms in supercell storms, where a rotating updraft allows hailstones to cycle repeatedly within the hail-growth zone\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. Hail development is favoured in storm environments characterised by strong atmospheric instability and deep-layer shear, enhanced low-level moisture and relatively low freezing-level height (FLH)\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. Hail formation further requires an ice embryo, abundant supercooled water, sustained vertical velocity and sufficient time, generally ten minutes or more, for accretion\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eRecent studies indicate an increasing frequency of severe-storm favourable conditions across northern Italy and central Europe\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e,\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e, although hail-pad observations in northern Italy show mixed trends\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. Proxy-based studies using climate models project a rise in convective hazards under global warming, driven by enhanced instability associated with warmer and moister low-level conditions\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e,\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e, but substantial regional uncertainties remain\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. Recent pan-European CPM studies show contrasting results. Using environmental proxies, ref.\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e project an overall decline in hail potential across Europe, whereas ref.\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e, applying a hail growth model, report a dipole pattern, with reductions over southwestern Europe and increases across central and eastern regions. Ref.\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e further highlight the emergence of \u0026ldquo;warm-type\u0026rdquo; thunderstorms, characterised by FLH above 4.5 km, that may still produce very large hailstones\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. Across these studies, the increasing FLH emerges as a key factor: deeper warm clouds can enhance hail growth aloft but also intensify melting during descent, favouring heavy rainfall over severe hail\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e,\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e,\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. These competing processes contribute to divergent projections and highlight the need for a clearer understanding of the physical drivers of future hail characteristics.\u003c/p\u003e \u003cp\u003eTo bridge this knowledge gap, we compare two different modelling approaches to investigate European hail occurrences under both present and pseudo-global warming (PGW) conditions: a physically based hail growth model (HAILCAST\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e) coupled to convection permitting climate simulations and a machine learning model\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e (XGBoost\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e) trained on ERA5\u003csup\u003e46\u003c/sup\u003e reanalysis data and applied to the same simulations. In particular, we address two research questions:\u003c/p\u003e \u003cp\u003e1. Can a machine learning model reproduce hail climatology with comparable skill to a physically based approach within a convection-permitting climate model?\u003c/p\u003e \u003cp\u003e2. How does the machine learning model, trained on present-day conditions, represent the impact of global warming on hail, and what do differences between the two approaches reveal about the physical processes underlying future projections?\u003c/p\u003e \u003cp\u003eBy systematically comparing data-driven and physically based hail models, we aim to clarify their strengths and limitations for assessing future hail risk. Establishing whether these methods converge or diverge under warming conditions and the reasons behind it is crucial for evaluating the reliability of ML models as computationally efficient alternatives for analysing hail in existing convection-permitting climate simulations.\u003c/p\u003e\n\u003ch3\u003eHail climatology in the present climate\u003c/h3\u003e\n\u003cp\u003eWe first assess whether the XGBoost model can reproduce the spatial distribution of severe hail (hail diameter greater than 25 mm) occurrences when applied to convection-permitting climate simulations over the 2011-2021period. The analysis focuses on summer (JJA), when hail activity peaks across Europe, and is restricted to land areas where hail impacts are most relevant. Both the HAILCAST and the XGBoost model simulate similar magnitudes and spatial patterns of hail frequency, with maxima located in the Po valley and along major orographic features, including the Alpine foothills, the Pyrenees, the Carpathian Basin, and the northern Apennines, as well as over parts of central Europe (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea and b). These results are consistent with previous findings on large-hail climatologies\u003csup\u003e\u003cspan additionalcitationids=\"CR19 CR20 CR21\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e and highlight the strong role of topography and land-sea contrasts in organising deep moist convection, which is explicitly solved in convection-permitting simulations. Despite the comparable magnitude of hail days, regional differences are evident (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec): XGBoost enhances hail occurrences across central Europe and northern Italy, while reducing it over both eastern and southern Europe compared to HAILCAST. These discrepancies reflect the differing sensitivities of the two approaches. In particular, HAILCAST simulates a hail size distribution shifted toward smaller maximum hailstones compared to hail reports\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e that may explain lower hail frequencies over central Europe. HAILCAST links hail growth directly to local updraft strength and microphysical processes within the storm\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e, enhancing hail formation where strong vertical velocities favour sustained growth (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003ea). In contrast, XGBoost relies on specific environmental conditions learned from ERA5 reanalysis, describing atmospheric instability, storm organisation, moisture availability and FLH (see Methods), which reflect mesoscale processes resolved at coarser resolution than in convection-permitting simulations, potentially contributing to regional over- or underestimation of hail occurrence across Europe. In literature, hail climatologies have been constructed and evaluated at continental, national, and local scales using diverse observational products, environmental proxies, and model-based diagnostics, each with distinct assumptions and limitations. However, no unified benchmark exists. Indeed, hail climatologies based on reanalysis-derived hail precursors\u003csup\u003e\u003cspan additionalcitationids=\"CR19 CR20 CR21\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e and regional climate models, with either parameterised convection\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e or convection-permitting resolution\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e, show regional differences, with no approach emerging as a clear reference, due to the lack of a robust and homogeneous observational dataset. The spatial differences between HAILCAST and XGBoost fall within the spread of these existing climatologies, indicating that both approaches provide a potentially reliable representation of present-day hail occurrences, considering their respective driving mechanisms and limitations. Finally, both models show a similar diurnal cycle of hail with an afternoon-evening peak (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed), although XGBoost produces a later peak, more in line with observational studies\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eFuture changes in hail occurrence\u003c/h2\u003e \u003cp\u003eWe next assess how hail occurrences respond to a warmer climate by comparing HAILCAST and XGBoost within the PGW\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e simulation. The experiment spans 11 years (2085\u0026ndash;2095) and corresponds to +\u0026thinsp;3\u0026deg;C of global warming relative to the preindustrial period. The evaluation focuses on land during JJA, consistent with the historical period. HAILCAST shows a distinct dipole pattern in future severe hail frequency. Increases in hail days are projected across the Alps and central to eastern Europe (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea), where the frequency rises by about 25% (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed), while southern Europe experiences overall decreases (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea) reaching a reduction of roughly 40% over the western Mediterranean (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed). This signal reflects changes in the convective environment under warming conditions, characterized by increased maximum convective available potential energy (CAPE) over central and eastern Europe and reduced CAPE over southern land regions\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e (Fig. S2a). In contrast, XGBoost projects a widespread decrease in hail occurrences across most of Europe (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb). The contrasting PGW responses of the two methods arise from their different underlying approaches. XGBoost is not able to reproduce the climate change signal simulated by HAILCAST since it encounters atmospheric environments that are not in the current climate training data. This divergence motivates a deeper investigation into the physical mechanisms involved, particularly the role of FLH on hail growth and melting in a warmer climate.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eDrivers of future hail changes\u003c/h3\u003e\n\u003cp\u003eAnthropogenic climate change alters both the thermodynamic and dynamic environments in which hailstorms develop, potentially increasing the conditions conducive to deep convection across Europe\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e, primarily through enhanced low-level moisture and convective instability. However, future hail activity will be strongly shaped by rising FLH, which controls the phase and intensity of surface precipitation\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. As FLH increases, deeper warm-cloud layers may promote both enhanced melting of hail, favouring heavy rainfall over large hail\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e,\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e,\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e, but also the formation of warm-type thunderstorms capable of producing very large hailstones that still reaches the surface\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e,\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. These thermodynamic shifts interact with changes in storm dynamics, including deep-layer shear and mid-tropospheric updrafts in the hail growth zone, to reshape hailstorm characteristics. The compensating effects of future dynamical changes, particularly intensified CAPE (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003ea), wind shear (Fig. S2b, c) and storm-relative helicity (Fig. S2d, e) over central-eastern Europe, are coherently simulated by the convection-permitting COSMO model, providing conditions under which HAILCAST diagnoses hail despite a higher FLH of approximately 400\u0026ndash;600 m across Europe (Fig. S3a). A key signature of this response is evident in the HAILCAST output: hail diameter increases systematically with FLH anomaly in both historical and PGW simulations (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea) and larger hail diameters are more frequent in the future scenario (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb), consistent with the hailstorm track analysis reported by ref.\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. This indicates that, in deep warm-cloud environments, storms with sufficiently strong and persistent updrafts can sustain intense hail growth aloft and produce larger hailstones at the surface. In this respect, XGBoost similarly ingests hail-favourable environments simulated by the COSMO model under global warming; however, it is trained on present-day relationships and cannot account for changes in the physical mechanisms governing hail in a warmer climate.\u003c/p\u003e \u003cp\u003eTo quantify the influence of individual atmospheric predictors on XGBoost\u0026rsquo;s hail projection, a sensitivity experiment was performed by modifying each precursor in the PGW simulation by \u0026plusmn;\u0026thinsp;10% toward its present-climate mean while preserving the variability of the future state. Among all predictors, FLH showed the strongest impact: reducing FLH by 10% and reapplying the XGBoost model produced hail frequency patterns closer to HAILCAST projections (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec), particularly, a similar\u0026thinsp;~\u0026thinsp;25% increase over central-eastern Europe (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed). Adjustments to other variables resulted in negligible changes, except for a moderate sensitivity to the Total Totals (TT) Index (Fig. S4), which links instability and low-level moisture. Pearson correlation coefficients between total hail days distribution in HAILCAST and in the XGBoost sensitivity experiments, under the PGW scenario (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), further confirm that the decreasing signal in the ML hail projection is primarily driven by higher FLH and, to a lesser extent, by increased atmospheric stability (TT index). Together, these results underscore the limits of a purely data-driven framework in representing storm-scale dynamics and adapting to future atmospheric environments outside its training range.\u003c/p\u003e \u003cp\u003eLarge-scale circulation patterns also modulate hail occurrence in Europe and analysing them provide additional insight into why the two modelling frameworks respond differently. To address this, we assessed 500-hPa geopotential height (Z500) anomalies associated with hail days diagnosed by XGBoost and HAILCAST (see supplementary information). Composite Z500 anomalies show that XGBoost-diagnosed hail days are associated with well-known\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e coherent synoptic-scale patterns favourable for severe convection, whereas HAILCAST hail days exhibit much weaker large-scale structure (Fig. S5). This indicates that the ML model primarily responds to synoptic environments, while HAILCAST is dominated by local storm-scale processes. These patterns remain largely unchanged in the PGW future climate, with only a modest strengthening in the XGBoost-based anomalies (Fig. S6).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cb\u003eSensitivity of XGBoost hail projections to predictor perturbations.\u003c/b\u003e Pearson correlation coefficients (r) between HAILCAST PGW hail frequencies and XGBoost PGW sensitivity experiments in which each predictor is independently shifted by \u0026plusmn;\u0026thinsp;10% toward its historical mean. The orange and blue cells indicate shifts toward more and less hail-favourable environments, respectively. All correlations are statistically significant (p-value equal to zero).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"13\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFLH\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTT\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCIN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRH850\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eRH500\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNo shift\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eCAPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eWS06\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eWS03\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eSRH06\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eSRH03\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eTd2\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShift %\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e+\u0026thinsp;10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e+\u0026thinsp;10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e-10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003er\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eRegional contrasts and substantial uncertainties remain in projecting how hail will respond to anthropogenic climate change. While both the machine learning model (XGBoost) and the physically based hail-growth scheme (HAILCAST) provide plausible representations of present-day hail climatology over Europe, they significantly diverge in their future projections.\u003c/p\u003e \u003cp\u003eChanges in thermodynamic and dynamical processes exert distinct influences in the two modelling frameworks, offering insights into the physical drivers of the contrasting future hail responses. In XGBoost, the large increase in FLH results in widespread suppression of simulated hail, revealing a key limitation of data-driven models when applied outside their historical training distribution. In contrast, HAILCAST simulates how enhanced storm dynamics and updraft strength can sustain hail growth aloft, enabling large hailstones to survive descent despite higher FLH. This allows a more physically consistent characterisation of how storm-scale dynamics may evolve under different climatic conditions.\u003c/p\u003e \u003cp\u003eFurther work is required to assess the robustness and generality of these findings across a broader range of modelling frameworks. Extending the analysis to ensembles of convection-permitting climate simulations, beyond a single PGW realisation, and exploring alternative machine learning architectures or predictor sets would help evaluate the sensitivity of projected hail changes to large-scale dynamical variability and to shifts in dynamical and thermodynamic conditions. Such efforts are essential to increase reliability in hail projections and to capture additional aspects of hail formation under global warming.\u003c/p\u003e \u003cp\u003eUltimately, our findings highlight that combining complementary tools is crucial to improve confidence in regional hail projections and advancing our understanding of the processes shaping convective hazards under climate change.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eTo investigate how hail occurrence in Europe responds to a warming climate, we compare a physically based hail-growth model with a data-driven machine learning approach, both applied to the same convection-permitting climate simulations. This dual approach allows a direct comparison between physical and statistical representations of hail, providing insight into their respective sensitivities to key atmospheric environments.\u003c/p\u003e\n\u003ch3\u003eConvection-permitting climate simulations\u003c/h3\u003e\n\u003cp\u003eWe analyse two pan-European convection-permitting climate simulations performed with the non-hydrostatic COSMO model at 2.2 km grid spacing, in the configuration as described in ref\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. The historical experiment spans 11 years (2011\u0026ndash;2021) and is driven by ERA5 reanalysis\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e. The future simulation applies a pseudo-global warming (PGW) perturbation of +\u0026thinsp;3\u0026deg;C compared to preindustrial to the ERA5 boundary conditions, following the method of ref.\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e, thereby isolating the thermodynamic response to warming while retaining a similar synoptic variability as in the historical simulation. Further details on the model setup are provided in ref.\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e for the historical period and in ref.\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e for the PGW experiment. Both simulations use an outer nest (~\u0026thinsp;12 km resolution) and an inner convection-permitting nest (~\u0026thinsp;2.2 km) in which hail processes are represented through a one-dimensional hail-growth model (HAILCAST\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e). HAILCAST computes the maximum hail diameter at the surface every 5 minutes based on the simulated vertical profiles of temperature, humidity and wind. The HAILCAST configuration was validated against observations, demonstrating good skill in reproducing the spatial distribution, seasonal cycle and diurnal cycle of hail occurrence over Europe\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe hail outputs are aggregated to hourly resolution by retaining the maximum hail diameter within each hour. A hail day is then defined at each model grid point as any 24-h period (00:00\u0026ndash;23:00 UTC) in which HAILCAST produces at least one hailstone exceeding 25 mm in diameter. This size category corresponds to hailstones large enough to cause damage to infrastructure\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eMachine learning algorithm: XGBoost\u003c/h2\u003e \u003cp\u003eTo complement the physically based hail diagnostics, we apply a machine learning (ML) algorithm based on gradient-boosted decision trees (XGBoost\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e) to the hourly output of the same convection-permitting climate simulations used for the HAILCAST analysis. The ML model employed here is the global XGBoost configuration (XGBGlobal) described and validated in ref.\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. XGBGlobal is trained on ERA5 reanalysis\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e predictors matched to a compilation of more than 120,000 hail reports from the U.S.A, Europe and Australia, using an event maximum hail-size threshold of 25 mm consistent with the definition of large hail events in HAILCAST. The training dataset includes observations from NOAA over the United States, the Australian Bureau of Meteorology, and the European Severe Storm Laboratory\u003csup\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e. The algorithm uses eleven atmospheric predictors associated with hail-supporting environments, including maximum convective available potential energy (CAPE), convective inhibition (CIN), freezing level height (FLH), Total Totals index (TT), 0\u0026ndash;6 km wind shear (WS06), 0\u0026ndash;3 km wind shear (WS03), 0\u0026ndash;6 km storm relative helicity (SRH06), 0\u0026ndash;3 km storm relative helicity (SRH03), 2 m dew-point temperature (Td2), relative humidity at 850 hPa (RH850) and relative humidity at 500 hPa (RH500). Ref.\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e show that XGBGlobal well reproduces observed hail climatology and outperforms the previous proxy-based statistical model of ref.\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Ref.\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e trained XGBoost on daily data, but we decided to apply the model with hourly predictors, which results in hourly hail probabilities (0\u0026ndash;1), and a hail hour is diagnosed when the probability exceeds 0.5. To obtain a consistent metric with HAILCAST, a hail day is defined at each grid point as any 24-h period (00:00\u0026ndash;23:00 UTC) containing at least one hour with a predicted probability\u0026thinsp;\u0026ge;\u0026thinsp;0.5.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eData and Code availability\u003c/h3\u003e\n\u003cp\u003eA selection of output fields from the COSMO simulations used in this study are publicly available in the ETH research collection via \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3929/ethz-b-000701925\u003c/span\u003e\u003cspan address=\"10.3929/ethz-b-000701925\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e for the historical experiment and via \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3929/ethz-b-000747355\u003c/span\u003e\u003cspan address=\"10.3929/ethz-b-000747355\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e for the PGW experiment. Additional model outputs are available upon request from the authors.\u003c/p\u003e \u003cp\u003eHail outputs derived from XGBoost and HAILCAST and used in this study are publicly available on Zenodo at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.5281/zenodo.18243342\u003c/span\u003e\u003cspan address=\"10.5281/zenodo.18243342\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eAll Python scripts used to generate the figures presented in this manuscript are publicly available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/marcochericoni95/hail_xgboost_hailcast_ncc\u003c/span\u003e\u003cspan address=\"https://github.com/marcochericoni95/hail_xgboost_hailcast_ncc\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe XGBoost model is publicly available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/borusseee/XGBoost_hail\u003c/span\u003e\u003cspan address=\"https://github.com/borusseee/XGBoost_hail\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAcknowledgments\u003c/p\u003e\n\u003cp\u003eThis paper and related research have been conducted during and with the support of the Italian inter-university PhD course in Sustainable Development and Climate change (link:www.phd-sdc.it) and developed within the framework of the project \u0026ldquo;Dipartimento di Eccellenza 2023-2027\u0026rdquo;, funded by the Italian Ministry of Education, University and Research at IUSS Pavia.\u003c/p\u003e\n\u003cp\u003eThis work presented here contains analyses carried out on the High-Performance Computing DataCenter at IUSS, co-funded by Regione Lombardia through the funding programme established by Regional Decree No. 3776 of November 3, 2020.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis study is carried out within the ICSC Italian Research Center on High-Performance Computing, Big Data and Quantum Computing and received funding from the European Union Next-GenerationEU (National Recovery and Resilience Plan-NRRP, Mission 4, Component 2, Investment 1.4-D.D: 3138 16/12/2021, CN00000013).\u003c/p\u003e\n\u003cp\u003eWe particularly thank Boris Blanc who developed the XGBoost hail prediction model.\u003c/p\u003e\n\u003cp\u003eAuthor contributions\u003c/p\u003e\n\u003cp\u003eM.C., G.F., A.A., I.T. and A.P. conceived the idea of the manuscript. M.C. performed the analysis and wrote the manuscript with inputs from all the authors.\u003c/p\u003e\n\u003cp\u003eCompeting interest\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eSteve Bowen, Brian Kerschner \u0026amp; Jin Zheng Ng. \u003cem\u003eNatural Catastrophe and Climate Report 2024\u003c/em\u003e. (2025).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSchmid, T., Portmann, R., Villiger, L., Schr\u0026ouml;er, K. \u0026amp; Bresch, D. N. An open-source radar-based hail damage model for buildings and cars. \u003cem\u003eNatural Hazards and Earth System Sciences\u003c/em\u003e 24, 847\u0026ndash;872 (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePortmann, R., Schmid, T., Villiger, L., Bresch, D. N. \u0026amp; Calanca, P. Modelling crop hail damage footprints with single-polarization radar: the roles of spatial resolution, hail intensity, and cropland density. \u003cem\u003eNatural Hazards and Earth System Sciences\u003c/em\u003e 24, 2541\u0026ndash;2558 (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eP\u0026uacute;čik, T. \u003cem\u003eet al.\u003c/em\u003e Large Hail Incidence and Its Economic and Societal Impacts across Europe. \u003cem\u003eMon. Weather Rev.\u003c/em\u003e 147, 3901\u0026ndash;3916 (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAllen, J. T. \u003cem\u003eet al.\u003c/em\u003e Understanding Hail in the Earth System. \u003cem\u003eReviews of Geophysics\u003c/em\u003e 58, (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHulton, F. \u0026amp; Schultz, D. M. Climatology of large hail in Europe: characteristics of the European Severe Weather Database. \u003cem\u003eNatural Hazards and Earth System Sciences\u003c/em\u003e 24, 1079\u0026ndash;1098 (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eManzato, A., Cicogna, A., Centore, M., Battistutta, P. \u0026amp; Trevisan, M. Hailstone Characteristics in Northeast Italy from 29 Years of Hailpad Data. \u003cem\u003eJ. Appl. Meteorol. Climatol.\u003c/em\u003e 61, 1779\u0026ndash;1795 (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBarras, H. \u003cem\u003eet al.\u003c/em\u003e Experiences with \u0026gt;50,000 Crowdsourced Hail Reports in Switzerland. \u003cem\u003eBull. Am. Meteorol. Soc.\u003c/em\u003e 100, 1429\u0026ndash;1440 (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKopp, J., Manzato, A., Hering, A., Germann, U. \u0026amp; Martius, O. How observations from automatic hail sensors in Switzerland shed light on local hailfall duration and compare with hailpad measurements. \u003cem\u003eAtmos. Meas. Tech.\u003c/em\u003e 16, 3487\u0026ndash;3503 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDas, S. \u0026amp; Allen, J. T. Bayesian estimation of the likelihood of extreme hail sizes over the United States. \u003cem\u003enpj Natural Hazards\u003c/em\u003e 1, 47 (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRyzhkov, A. V., Kumjian, M. R., Ganson, S. M. \u0026amp; Khain, A. P. Polarimetric Radar Characteristics of Melting Hail. Part I: Theoretical Simulations Using Spectral Microphysical Modeling. \u003cem\u003eJ. Appl. Meteorol. Climatol.\u003c/em\u003e 52, 2849\u0026ndash;2870 (2013).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCui, R. \u003cem\u003eet al.\u003c/em\u003e A European Hail and Lightning Climatology From an 11-Year Kilometer‐Scale Regional Climate Simulation. \u003cem\u003eJournal of Geophysical Research: Atmospheres\u003c/em\u003e 130, (2025).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNisi, L., Martius, O., Hering, A., Kunz, M. \u0026amp; Germann, U. Spatial and temporal distribution of hailstorms in the Alpine region: a long-term, high resolution, radar‐based analysis. \u003cem\u003eQuarterly Journal of the Royal Meteorological Society\u003c/em\u003e 142, 1590\u0026ndash;1604 (2016).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePunge, H. J., Bedka, K. M., Kunz, M. \u0026amp; Reinbold, A. Hail frequency estimation across Europe based on a combination of overshooting top detections and the ERA-INTERIM reanalysis. \u003cem\u003eAtmos. Res.\u003c/em\u003e 198, 34\u0026ndash;43 (2017).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBedka, K. M., Allen, J. T., Punge, H. J., Kunz, M. \u0026amp; Simanovic, D. A Long-Term Overshooting Convective Cloud-Top Detection Database over Australia Derived from MTSAT Japanese Advanced Meteorological Imager Observations. \u003cem\u003eJ. Appl. Meteorol. Climatol.\u003c/em\u003e 57, 937\u0026ndash;951 (2018).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGiordani, A. \u003cem\u003eet al.\u003c/em\u003e Characterizing hail-prone environments using convection-permitting reanalysis and overshooting top detections over south-central Europe. \u003cem\u003eNatural Hazards and Earth System Sciences\u003c/em\u003e 24, 2331\u0026ndash;2357 (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAllen, J. T., Tippett, M. K. \u0026amp; Sobel, A. H. An empirical model relating U.S. monthly hail occurrence to large-scale meteorological environment. \u003cem\u003eJ. Adv. Model. Earth Syst.\u003c/em\u003e 7, 226\u0026ndash;243 (2015).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePrein, A. F. \u0026amp; Holland, G. J. Global estimates of damaging hail hazard. \u003cem\u003eWeather Clim. Extrem.\u003c/em\u003e 22, 10\u0026ndash;23 (2018).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eR\u0026auml;dler, A. T., Groenemeijer, P., Faust, E. \u0026amp; Sausen, R. Detecting Severe Weather Trends Using an Additive Regressive Convective Hazard Model (AR-CHaMo). \u003cem\u003eJ. Appl. Meteorol. Climatol.\u003c/em\u003e 57, 569\u0026ndash;587 (2018).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBattaglioli, F. \u003cem\u003eet al.\u003c/em\u003e Modeled Multidecadal Trends of Lightning and (Very) Large Hail in Europe and North America (1950\u0026ndash;2021). \u003cem\u003eJ. Appl. Meteorol. Climatol.\u003c/em\u003e 62, 1627\u0026ndash;1653 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMohr, S., Kunz, M. \u0026amp; Geyer, B. Hail potential in Europe based on a regional climate model hindcast. \u003cem\u003eGeophys. Res. Lett.\u003c/em\u003e 42, (2015).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBattaglioli, F., Taszarek, M., Groenemeijer, P., P\u0026uacute;čik, T. \u0026amp; R\u0026auml;dler, A. Contrasting trends in very large hail events and related economic losses across the globe. \u003cem\u003eNat. Geosci.\u003c/em\u003e 19, 52\u0026ndash;58 (2026).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBrennan, K. P., Sprenger, M., Walser, A., Arpagaus, M. \u0026amp; Wernli, H. An object-based and Lagrangian view on an intense hailstorm day in Switzerland as represented in COSMO-1E ensemble hindcast simulations. \u003cem\u003eWeather and Climate Dynamics\u003c/em\u003e 6, 645\u0026ndash;668 (2025).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCui, R. \u003cem\u003eet al.\u003c/em\u003e Exploring hail and lightning diagnostics over the Alpine-Adriatic region in a km-scale climate model. \u003cem\u003eWeather and Climate Dynamics\u003c/em\u003e 4, 905\u0026ndash;926 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMalečić, B. \u003cem\u003eet al.\u003c/em\u003e Simulating Hail and Lightning Over the Alpine Adriatic Region\u0026mdash;A Model Intercomparison Study. \u003cem\u003eJournal of Geophysical Research: Atmospheres\u003c/em\u003e 128, (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFosser, G. \u003cem\u003eet al.\u003c/em\u003e Convection-permitting climate models offer more certain extreme rainfall projections. \u003cem\u003eNPJ Clim. Atmos. Sci.\u003c/em\u003e 7, 51 (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCoppola, E. \u003cem\u003eet al.\u003c/em\u003e A first-of-its-kind multi-model convection permitting ensemble for investigating convective phenomena over Europe and the Mediterranean. \u003cem\u003eClim. Dyn.\u003c/em\u003e 55, 3\u0026ndash;34 (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePrein, A. F. \u003cem\u003eet al.\u003c/em\u003e A review on regional convection-permitting climate modeling: Demonstrations, prospects, and challenges. \u003cem\u003eReviews of Geophysics\u003c/em\u003e 53, 323\u0026ndash;361 (2015).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFosser, G., Khodayar, S. \u0026amp; Berg, P. Benefit of convection permitting climate model simulations in the representation of convective precipitation. \u003cem\u003eClim. Dyn.\u003c/em\u003e 44, 45\u0026ndash;60 (2015).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAdams-Selin, R. D. \u0026amp; Ziegler, C. L. Forecasting Hail Using a One-Dimensional Hail Growth Model within WRF. \u003cem\u003eMon. Weather Rev.\u003c/em\u003e 144, 4919\u0026ndash;4939 (2016).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eThurnherr, I., Cui, R., Velasquez, P., Wernli, H. \u0026amp; Sch\u0026auml;r, C. The Effect of 3\u0026deg; C Global Warming on Hail Over Europe. \u003cem\u003eGeophys. Res. Lett.\u003c/em\u003e 52, (2025).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTorralba, V. \u003cem\u003eet al.\u003c/em\u003e Modelling hail hazard over Italy with ERA5 large-scale variables. \u003cem\u003eWeather Clim. Extrem.\u003c/em\u003e 39, 100535 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCzernecki, B. \u003cem\u003eet al.\u003c/em\u003e Application of machine learning to large hail prediction - The importance of radar reflectivity, lightning occurrence and convective parameters derived from ERA5. \u003cem\u003eAtmos. Res.\u003c/em\u003e 227, 249\u0026ndash;262 (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBurke, A., Snook, N., Gagne II, D. J., McCorkle, S. \u0026amp; McGovern, A. Calibration of Machine Learning\u0026ndash;Based Probabilistic Hail Predictions for Operational Forecasting. \u003cem\u003eWeather Forecast.\u003c/em\u003e 35, 149\u0026ndash;168 (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDavies-Jones, R. A review of supercell and tornado dynamics. \u003cem\u003eAtmos. Res.\u003c/em\u003e 158\u0026ndash;159, 274\u0026ndash;291 (2015).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFeldmann, M., Hering, A., Gabella, M. \u0026amp; Berne, A. Hailstorms and rainstorms versus supercells\u0026mdash;a regional analysis of convective storm types in the Alpine region. \u003cem\u003eNPJ Clim. Atmos. Sci.\u003c/em\u003e 6, 19 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eP\u0026uacute;čik, T. \u003cem\u003eet al.\u003c/em\u003e Future Changes in European Severe Convection Environments in a Regional Climate Model Ensemble. \u003cem\u003eJ. Clim.\u003c/em\u003e 30, 6771\u0026ndash;6794 (2017).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eR\u0026auml;dler, A. T., Groenemeijer, P. H., Faust, E., Sausen, R. \u0026amp; P\u0026uacute;čik, T. Frequency of severe thunderstorms across Europe expected to increase in the 21st century due to rising instability. \u003cem\u003eNPJ Clim. Atmos. Sci.\u003c/em\u003e 2, 30 (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRaupach, T. H. \u003cem\u003eet al.\u003c/em\u003e The effects of climate change on hailstorms. \u003cem\u003eNat. Rev. Earth Environ.\u003c/em\u003e 2, 213\u0026ndash;226 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKahraman, A., Kendon, E. J., Fowler, H. J. \u0026amp; Short, C. J. Future changes in severe hail across Europe, including regional emergence of warm-type thunderstorms. \u003cem\u003eNat. Commun.\u003c/em\u003e 16, 8438 (2025).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBrimelow, J. C., Burrows, W. R. \u0026amp; Hanesiak, J. M. The changing hail threat over North America in response to anthropogenic climate change. \u003cem\u003eNat. Clim. Chang.\u003c/em\u003e 7, 516\u0026ndash;522 (2017).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMahoney, K., Alexander, M. A., Thompson, G., Barsugli, J. J. \u0026amp; Scott, J. D. Changes in hail and flood risk in high-resolution simulations over Colorado\u0026rsquo;s mountains. \u003cem\u003eNat. Clim. Chang.\u003c/em\u003e 2, 125\u0026ndash;131 (2012).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePrein, A. F. \u0026amp; Heymsfield, A. J. Increased melting level height impacts surface precipitation phase and intensity. \u003cem\u003eNat. Clim. Chang.\u003c/em\u003e 10, 771\u0026ndash;776 (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBlanc, B., Prein, A. F., Jeggle, K., Aellen, N. \u0026amp; Lohmann, U. Improving our Understanding of Large Hail Hazards Using Machine Learning. \u003cem\u003eArtificial Intelligence for the Earth Systems\u003c/em\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen, T. \u0026amp; Guestrin, C. XGBoost. in \u003cem\u003eProceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining\u003c/em\u003e 785\u0026ndash;794 (ACM, New York, NY, USA, 2016). doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1145/2939672.2939785\u003c/span\u003e\u003cspan address=\"10.1145/2939672.2939785\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHersbach, H. \u003cem\u003eet al.\u003c/em\u003e The ERA5 global reanalysis. \u003cem\u003eQuarterly Journal of the Royal Meteorological Society\u003c/em\u003e 146, 1999\u0026ndash;2049 (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKahraman, A., Kendon, E. J. \u0026amp; Fowler, H. J. Climatology of severe hail potential in Europe based on a convection-permitting simulation. \u003cem\u003eClim. Dyn.\u003c/em\u003e \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00382-024-07227-w\u003c/span\u003e\u003cspan address=\"10.1007/s00382-024-07227-w\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024) doi:10.1007/s00382-024-07227-w.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNisi, L. \u003cem\u003eet al.\u003c/em\u003e Hailstorms in the Alpine region: Diurnal cycle, 4D-characteristics, and the nowcasting potential of lightning properties. \u003cem\u003eQuarterly Journal of the Royal Meteorological Society\u003c/em\u003e 146, 4170\u0026ndash;4194 (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBrogli, R., Heim, C., Mensch, J., S\u0026oslash;rland, S. L. \u0026amp; Sch\u0026auml;r, C. The pseudo-global-warming (PGW) approach: methodology, software package PGW4ERA5 v1.1, validation, and sensitivity analyses. \u003cem\u003eGeosci. Model Dev.\u003c/em\u003e 16, 907\u0026ndash;926 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBrennan, K. P., Thurnherr, I., Sprenger, M. \u0026amp; Wernli, H. Insights from hailstorm track analysis in European climate change simulations. \u003cem\u003eNatural Hazards and Earth System Sciences\u003c/em\u003e 25, 3693\u0026ndash;3712 (2025).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFeldmann, M., Domeisen, D. I. V. \u0026amp; Martius, O. A pan-European analysis of large-scale drivers of severe convective outbreaks. \u003cem\u003eWeather and Climate Dynamics\u003c/em\u003e 6, 1089\u0026ndash;1106 (2025).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHohl, R., Schiesser, H.-H. \u0026amp; Aller, D. Hailfall: the relationship between radar-derived hail kinetic energy and hail damage to buildings. \u003cem\u003eAtmos. Res.\u003c/em\u003e 63, 177\u0026ndash;207 (2002).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDotzek, N., Groenemeijer, P., Feuerstein, B. \u0026amp; Holzer, A. M. Overview of ESSL\u0026rsquo;s severe convective storms research using the European Severe Weather Database ESWD. \u003cem\u003eAtmos. Res.\u003c/em\u003e 93, 575\u0026ndash;586 (2009).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-natural-hazards","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [npj Natural Hazards](https://www.nature.com/npjnathazards/)","snPcode":"44304","submissionUrl":"https://submission.springernature.com/new-submission/44304/3","title":"npj Natural Hazards","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8731533/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8731533/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eReliable fine-scale hail projections are urgently needed for robust risk assessments, yet future trends remain uncertain and contradictory across methods. Using 11-year pan-European convection-permitting climate simulations for the present and a\u0026thinsp;+\u0026thinsp;3\u0026deg;C pseudo-global-warming climate, we compare an online hail-growth diagnostic (HAILCAST) with an offline machine learning model (XGBoost) trained on ERA5 hail environments. We show that, under current conditions, both approaches produce comparable hail frequencies across most of Europe. However, XGBoost predicts widespread hail suppression in a warmer climate, mainly driven by increasing freezing level heights, from conditions beyond the training distribution. HAILCAST instead simulates how enhanced storm updrafts can sustain hail growth despite a warmer atmosphere, projecting regional increases over central-eastern Europe and larger hailstones. Our findings show that data-driven approaches alone should be used with caution under global warming, underscoring the need for physically based hail representations in convection-permitting climate models to robustly assess future convective hazards.\u003c/p\u003e","manuscriptTitle":"Divergent European hail projections from machine learning and physically based models under global warming","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-16 16:20:03","doi":"10.21203/rs.3.rs-8731533/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-14T13:42:31+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-13T08:50:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"72567324002307922062806467389290605566","date":"2026-03-04T08:23:11+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-20T15:23:48+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"245786365671421903301108332778739637694","date":"2026-02-16T11:57:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"111245970519804949300400970627803294816","date":"2026-02-12T11:06:55+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-10T16:05:20+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-03T05:35:05+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-02-03T04:09:50+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Natural Hazards","date":"2026-01-29T11:40:57+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-natural-hazards","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [npj Natural Hazards](https://www.nature.com/npjnathazards/)","snPcode":"44304","submissionUrl":"https://submission.springernature.com/new-submission/44304/3","title":"npj Natural Hazards","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"78a112cf-5687-447a-9b31-387631d62876","owner":[],"postedDate":"February 16th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":62867320,"name":"Earth and environmental sciences/Climate sciences"},{"id":62867321,"name":"Earth and environmental sciences/Natural hazards"}],"tags":[],"updatedAt":"2026-04-28T01:54:58+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-16 16:20:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8731533","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8731533","identity":"rs-8731533","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}