Incorporating spatial dependence in regional frequency analysis

Abstract

The efficiency of regional frequency analysis (RFA) is undermined by intersite dependence, which is usually ignored in parameter estimation. We propose a spatial index flood model where marginal generalized extreme value distributions are joined by an extreme-value copula characterized by a max-stable process for the spatial dependence. The parameters are estimated with a pairwise likelihood constructed from bivariate marginal generalized extreme value distributions. The estimators of model parameters and return levels can be more efficient than those from the traditional index flood model when the max-stable process fits the intersite dependence well. Through simulation, we compared the pairwise likelihood method with an L-moment method and an independence likelihood method under various spatial dependence models and dependence levels. The pairwise likelihood method was found to be the most efficient in mean squared error if the dependence model was correctly specified. When the dependence model was misspecified within the max-stable models, the pairwise likelihood method was still competitive relative to the other two methods. When the dependence model was not a max-stable model, the pairwise likelihood method led to serious bias in estimating the shape parameter and return levels, especially when the dependence was strong. In an illustration with annual maximum precipitation data from Switzerland, the pairwise likelihood method yielded remarkable reduction in the standard errors of return level estimates in comparison to the L-moment method.

Goodness‐of‐fit tests for copula‐based spatial models

“…This model can be interpreted as the superposition of an infinite number of normal‐shaped storms centered at location ξ i and having severity γ i . The model has found practical applications in the study of spatial extremes; see, for example, Coles (), Shang, Yan, and Zhang (), and Wang, Yan, and Zhang (). Although the model is anisotropic in general, an isotropic random field occurs if one lets Λ 12 =Λ 21 =0 and Λ 11 =Λ 22 .…”

Estimating extreme areal precipitation in Norway from a gridded dataset

“…Matalas & Langbein, 1962;Stedinger, 1983;Hosking & Wallis, 1988). To deal with the issue of inter-site correlation Wang et al (2014) incorporated spatial dependence into an index-flood model and showed significantly increased accuracy in return level estimates in Switzerland, compared to the L-moment method. In orographic regions, like Norway, RFA can be particularly challenging due to the large spatial variation of precipitation and the difficulty in defining homogenious regions (e.g.…”

Toward Optimal Fingerprinting in Detection and Attribution of Changes in Climate Extremes

“…Another example in spatial extremes modeling is regional frequency analysis. Covariates can also be incorporated into the GEV scale and shape parameters (e.g., Wang, Yan, and Zhang 2014), in which case, the CSE method can be applied to one set of parameters at a time given others in an iterative estimation procedure.…”