Modeling the Spatial Distribution of Hail Damage in Pine Plantations of Northern Spain as a Major Risk Factor for Forest Disease

Hail storms are able to cause severe damages to all kind of goods. While mostly economic damages of hail events are considered, damages to vegetation are more complex to quantify due to their complexity and hetereogen- ity regarding species and types. Few research exists on this topic which relies on the complexity of hail as a phenomenon itself: Due to its small-scale characteristics only few in situ measurement systems exist, making it problematic to gather long time series of reliable data. Furthermore, almost no research has been done under- taken yet on the follow-up e ects of hail damage to plants.  is work aims to contribute to this science  eld by analyzing the spatial distribution of hail damages in pine plantations in northern Spain.

For this purpose, binomial statistical learning methods (Generalized Linear Mixed Model (GLMM) and Generalized Additive Mixed Model (GAMM)) were applied to surveyed "hail damage to trees" distributed across the Basque Country. Climate variables like precipitation, temperature and Potential Incoming Solar Radia- tion (PISR), extracted from a long term climate data set with a spatial resolution of 200 m, were used as pre- dictors in the models to explore the relationship between them and the response. Age of the surveyed trees was used as a biological component in the model. Underlying grouping structures (spatial autocorrelation and ran- dom e ects) in the data were investigated and accounted for in the models. Additionally, the synoptic weather situation of hail occurence was analyzed using long term weather station data for the cities Bilbao, San Sebastian and Vitoria.

 e prime time for hail occurence was found to be between November and April.  e analysis of the weather station data revealed non-linear relationships between hail occurence and climatic variables.  e GAMM, ac- counting for the underlying spatial autocorrelation, did not converge. Hence, these results have to be treated with caution due to a violation of the independence assumption of the residuals. Di erent risk areas were carried out with the result of the northeast of the Basque Country being most susceptible of "hail damage to trees" (for both models). A considerably decrease of "hail damage to trees" susceptibility was observed along the Cantabrian Range with very low estimated probabilities of "hail damage to trees" for areas located further south.  is  nding runs contrary to the absolute occurence of hail events which is highest in areas with estimated low probabilities, inferring that most of the hail events in this region happen with a low destructive energy. A substantial increase of "hail damage to trees" probability was observed in the Generalized Additive Model (GAM) for the top third range of the predictor range of precipitation and minimum temperature with examplary odds ratios of 7.9 (0.125 m/mm2 - 0.14 m/mm2) and 3.99 (5°C - 6°C), respectively. Estimated probabilities range between 0%-50% for the GLMM and 0%-100% for the GAM.  e latter revealed high uncertainties in areas with low precipitation and/or temperature values pointing to a likely over tting of the model which is also con rmed by the large gap between the (100 repetitions, ten fold) spatial cross-validation result of the training set (0.87) and the test set (0.62).

Further research using more environmental variables explaining hail occurence (e.g. wind speed) is suggested. Also, the outcomes of this work (risk areas, estimated probabilities) need to be compared to analyses using direct hail observations (in contrast to derivated observations like in this work) in the Basque Country.