Modeling snow depth extremes in Austria

Abstract

Maps of extreme snow depths are important for structural design and general risk assessment in mountainous countries like Austria. The smooth modeling approach is commonly accepted to provide more accurate margins than max-stable processes. In contrast, max-stable models allow for risk estimation due to explicitly available spatial extremal dependencies, in particular when anisotropy is accounted for. However, the difference in return levels is unclear, when modeled smoothly or with max-stable processes. The objective of this study is twofold: first, to investigate that question and to provide snow depth return level maps for Austria; and second, to investigate spatial dependencies of extreme snow depths in Austria in detail and to find a suitable model for risk estimation. Therefore, a model selection procedure was used to define a marginal model for the GEV parameters. This model was fitted to 210 snow depth series comprising a length of 42 years using the smooth model approach and different max-stable models allowing for anisotropy. Despite relatively clear advantages for the Extremal-t max-stable process based on two scores compared to the smooth model as well as the Brown–Resnick, Geometric Gaussian and Schlather processes, the difference in 100-year snow depth return levels is too small, to decide which approach works better. Spatial dependencies of snow depth extremes between the regions north and south of the Austrian Alps are almost independent. Dependencies are stronger in the south for small distances between station pairs up to 120 km and become stronger in the north for larger distances. For risk modeling the Austrian Alps could be separated into regions north and south of the Alps. Fitting an anisotropic Extremal-t max-stable process to either side of the Alps can improve modeling of joint exceedance probabilities compared to one single model for the whole of Austria, especially for small station distances.

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Acknowledgements

The authors are grateful to ZAMG for data acquisition and supply. The computational results presented have been achieved (in part) using the HPC infrastructure LEO of the University of Innsbruck.

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Correspondence to Harald Schellander.

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Schellander, H., Hell, T. Modeling snow depth extremes in Austria. Nat Hazards 94, 1367–1389 (2018). https://doi.org/10.1007/s11069-018-3481-y

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Keywords

  • Extreme values
  • Max-stable process
  • Smooth model
  • Snow depth
  • Spatial modeling
  • Risk estimate
  • Spatial dependence