Incorporating spatial dependence in regional frequency analysis

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.