Spatial Prediction of Extreme Value Return Levels

• Activity Number: 19
• Type: Topic Contributed
• Date/Time: Sunday, August 7, 2005 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Daniel Cooley*+ and Philippe Naveau and Douglas Nychka
• Companies: University of Colorado at Boulder and University of Colorado at Boulder and National Center for Atmospheric Research
• Keywords: extremes ; generalized pareto ; bayesian hierarchical ; precipitation ; climate

Abstract

Quantification of extreme values is important for planning purposes. To aid with the understanding of flooding along Colorado's Front Range, we develop a map of extreme precipitation return levels for the region. To perform this task, we rely on the theory of extreme values. Specifically, we use the generalized Pareto distribution (GPD) to model precipitation above a high threshold at 56 weather stations throughout the region. Using a Bayesian hierarchical model, we pool the data from all stations, which helps to overcome the lack of data in an extreme-value analysis. In the hierarchy, the spatial structure is modeled via the stations' GPD parameters. This strategy yields parameter and return-level estimates with more spatial consistency. The parameter estimates also take into account the available covariates on the spatial field. Model inference is obtained using a straightforward MCMC method, which also produces measures of uncertainty at each station. We then use a spatial interpolation process to produce the map of return levels along with a map of uncertainty measures.