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A Bayesian hierarchical approach to regional frequency analysis

Abstract : Regional Frequency Analysis (RFA) has a long history in Hydrology, and numerous distinct approaches have been proposed over the year to perform the estimation of some hydrologic quantity at a regional level. However, most of these approaches still rely on strong hypotheses that may limit their application and complicate the quantification of predictive uncertainty. The objective of this paper is to propose a general Bayesian hierarchical framework to implement RFA schemes that avoid these difficulties. The proposed framework is based on a two-level hierarchical model. The first level of the hierarchy describes the joint distribution of observations. An arbitrary marginal distribution, whose parameters may vary in space, is assumed for at-site series. The joint distribution is then derived by means of an elliptical copula, therefore providing an explicit description of the spatial dependence between data. The second level of the hierarchy describes the spatial variability of parameters using a regression model that links the parameter values with covariates describing site characteristics. Regression errors are modeled with a Gaussian spatial field which may exhibit spatial dependence. This framework enables performing prediction at both gauged and ungauged sites and, importantly, rigorously quantifying the associated predictive uncertainty. A case study based on annual maxima of daily rainfall demonstrates the applicability of this hierarchical approach. Although numerous avenues for improvement can already be identified (amongst which the inclusion of temporal covariates to model time variability), the proposed model constitutes a general framework for implementing flexible RFA schemes and quantifying the associated predictive uncertainty.
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Submitted on : Wednesday, January 25, 2012 - 3:23:50 PM
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Benjamin Renard. A Bayesian hierarchical approach to regional frequency analysis. Water Resources Research, American Geophysical Union, 2011, 47, p. W11513 - p. ⟨10.1029/2010WR010089⟩. ⟨hal-00662931⟩

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