Spatial modeling of extreme snow depth (1111.7091v1)

Abstract: The spatial modeling of extreme snow is important for adequate risk management in Alpine and high altitude countries. A natural approach to such modeling is through the theory of max-stable processes, an infinite-dimensional extension of multivariate extreme value theory. In this paper we describe the application of such processes in modeling the spatial dependence of extreme snow depth in Switzerland, based on data for the winters 1966--2008 at 101 stations. The models we propose rely on a climate transformation that allows us to account for the presence of climate regions and for directional effects, resulting from synoptic weather patterns. Estimation is performed through pairwise likelihood inference and the models are compared using penalized likelihood criteria. The max-stable models provide a much better fit to the joint behavior of the extremes than do independence or full dependence models.

Spatial Modeling of Extreme Snow Depth

This paper focuses on the spatial modeling of extreme snow depth in Switzerland using statistical methods grounded in the theory of max-stable processes. The paper spans data collected from 1966 to 2008 across 101 stations, which is crucial for risk management in mountainous regions subject to severe snow events. Utilizing a climate space transformation, the modeling accounts for climate regions and directional effects arising from synoptic weather patterns. The estimation process employs pairwise likelihood inference, with model comparison based on penalized likelihood criteria. Overall, max-stable models offer a superior fit for joint behavior of extremes compared to independence or full dependence models.

Key Highlights and Numerical Results

The research elucidates that extreme snow depth statistics have not been extensively explored compared to other meteorological phenomena. The application of multivariate extreme value distributions, particularly max-stable processes, provides a robust method for modeling spatial dependence of extreme snow events. For example, extremal coefficients estimated using the madogram differ noticeably from independence, indicating substantial spatial dependence in snow depth extremes.

Overall model fitting was carried out using a profiling approach, showing significant improvement in computational efficiency and optimization quality. The results reveal a marked elevation effect, demonstrating that higher altitude stations tend to show stronger dependence in snow extremes. The detailed spatial analysis also uncovers a directional effect and identifies weak dependencies between Alpine regions, attributed to different meteorological conditions influencing each slope.

Implications

From a practical standpoint, this modeling approach enables a comprehensive understanding of the spatial variation in snow depth extremes, aiding infrastructure design and risk management strategies, such as dimensioning avalanche defense structures. Theoretically, this research expands on existing max-stable process literature by integrating climate transformations to account for anisotropy and climate regions, enhancing prediction accuracy for extreme snow depths.

Theoretical Innovations and Future Directions

While the paper successfully applies max-stable processes to model snow depth data, further improvements could include integrating a more complex spatial model with covariates like temperature and wind speed, which were not leveraged sufficiently due to data limitations. Time-based covariates could be integrated to assess climate changes impacting extreme snow events, especially at differing elevations. Further exploration into spatial nonstationarity using local covariance models might refine the understanding and prediction of extreme snow events across diverse terrains. Extending these methodologies to model spatial extremes in rainfall and temperature data could offer additional insights and predictive capabilities for varied climatic conditions.

In conclusion, the research outlines a sophisticated approach to spatial modeling of snow depth extremes using max-stable processes that account for both spatial dependence and regional climatic variations. The proposed models demonstrate considerable efficacy in risk assessment and management, paving the way for future studies on enhancing spatial extreme value theory and its applications in meteorology and environmental science.