We have developed additive regression convective hazard models (AR-CHaMo) for predicting the occurrence of large (≥ 2 cm), very large hail (≥ 5 cm) and lightning. The models were trained using hail reports, lightning observations and parameters calculated from the ERA5 reanalysis across three different regions: Europe, the United States and Australia. The AR-CHaMo models take convective initiation explicitly into account meaning that the probability of (very) large hail is computed as the product of the probability of a thunderstorm occurring and the conditional probability of (very) large hail given a storm. AR-CHaMo outputs the probability of (very) large hail and lightning as a function of environmental predictors from the ERA5 reanalysis. While developing AR-CHaMo, we showed that a commonly used parameter such as the Convective Available Potential Energy (CAPE) should not be used as a proxy for hail worldwide as it may not fully address the fundamental physical mechanisms behind hail formation, especially across sub-tropical regions. We found the amount of CAPE released above the -10° C isotherm to outperform CAPE and to be the only instability-related parameter that can perform well regardless of the geographical region. These findings were possible thanks to the large number of (experimental) parameters,172, that were computed from ERA5 and tested within the logistic models. The AR-CHaMo models were used for two main purposes: firstly to reconstruct the long-term climatology and the associated trends in Europe, the U.S. and globally, and secondly for medium-range forecasting. The reconstruction of the long-term climatology between 1950 and 2021 across Europe and the U.S. allowed us to map the regional hotspots of (very) large hail. In the U.S., large and very large hail are most common in the Great Plains with a maximum between north-western Kansas, north-eastern Colorado and south-western Nebraska while in Europe the hotspots are northern Italy, south-western France and eastern Spain. Between 1950 and 2021, the frequency of (very) large hail has increased across most of Europe while trends are comparatively smaller in the U.S. The strongest increase is found in northern Italy where hail ≥ 5 cm is now (2012–2021) modelled to be three times more frequent than it was in the 1950s. The extension of the analysis to global scale for the period 1992–2022 showed that the positive trends detected in southern Europe are not only stronger than those in the U.S. but the strongest on a global scale. Such positive trends are driven by a local increase in low-level moisture, and consequently higher buoyancy, rather than by changes in tropospheric flow patterns. On a global scale, very large hail is most frequent across the Great Plains of the U.S., the tri-border region between Argentina, Paraguay and Brazil, and to lesser extent in South Africa. Local hotspots exist in Australia and parts of Asia but, overall, hail ≥ 5 cm is much less frequent there. During the past 30 years, very large hail is modelled to have decreased across most of the southern hemisphere especially across South America and equatorial Africa while areas of positive trends are limited to Europe and parts of the U.S. The trends of AR-CHaMo were compared to those in hail loss events across Central Europe, the U.S. and Australia. Although the number of hail loss events has increased in each of these regions, the drivers of these trends might differ. In Europe, trends in hail loss events show similarities to increases in the modelled frequency of very large hail. In the U.S., the number of hail loss events increases stronger than the modelled frequency of hail ≥ 5 cm, and in Australia the trends even show opposite signs. Increases in hail loss events are mainly driven by non-meteorological factors, namely socio-economic factors as well as more exposure with higher vulnerabilities. However, the similarities of the trend curves in Europe indicate that, here, meteorological factors might play a more important role than across the U.S. and Australia. A second application of the AR-CHaMo models involved forecasting. When applied to the ECMWF reforecasts for the period 2008–2019, AR-CHaMo proved to be skillful in predicting large hail up to 108 hours in advance. In addition, the comparison with existing composite metrics for hail forecasting showed that AR-CHaMo outperforms the product of CAPE and Deep Layer Shear (CAPESHEAR, at all lead times) and the Significant Hail Parameter (SHP, at short to medium lead times). In conclusion, the AR-CHaMo models were applied to the deterministic runs from the ECMWF IFS, GFS and ICON-EU models to yield daily probabilistic forecasts of lightning, hail ≥ 2 cm and hail ≥ 5 cm on a pan European scale. Forecasts are publicly available on the website stormforecast.eu and provide the first open- access probabilistic tool for (very) large hail forecasting. It is aimed that this tool will help forecasters in the prediction of these hazards across the whole of Europe.
