A Bayesian hierarchical approach to regional frequency analysis

Abstract

[1] Regional frequency analysis (RFA) has a long history in hydrology, and numerous distinct approaches have been proposed over the years 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 gaged and ungaged sites and, importantly, rigorously quantifying the associated predictive uncertainty. A case study based on the annual maxima of daily rainfall demonstrates the applicability of this hierarchical approach. Although numerous avenues for improvement can already be identified (among which is 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.

Comparison of Flood Frequency Analysis Methods for Ungauged Catchments in France

“…To deal with the difficulty estimating the shape parameter, a Bayesian local-regional approach was employed [14,45]. The main objective was to enrich the local information with regional information to constrain the fitting process.…”

“…This can be achieved by merging local and regional data [10] or by identifying regional distributions describing the behaviour of all inner catchments [11][12][13]. Regional information can also be used to inform the fitting of at-site distribution [14]. These approaches remain purely statistical.…”

Local and regional flood frequency analysis based on hierarchical Bayesian model: application to annual maximum streamflow for the Huaihe River basin

“…drainage area, elevation) are considered as covariates in space. Of a variety of choices, the index flood method has been widely 5 applied because of its easy implementation and robustness (Renard, 2011). The index flood approach uses the mean or median of at-site hydrological variable data (Kjeldsen et al, 2002;Kjeldsen and Jones, 2006), and uses it to normalize the data series of each site.…”

Use of the spatial extremogram to form a homogeneous region centered on a target site for the regional frequency analysis of extreme storm surges

“…However, these applications were limited by the problem of the inter-site dependence issue and its impact on the variance of local and regional quantiles and on the statistical homogeneity. Recent developments go a step further and involve a procedure to consider the spatial dependence structure using copulas [11,12] and to form physically homogenous regions. Weiss [12] proposed a criterion (related to the spatial propagation of storms) to form physically homogeneous regions.…”