title: A fuzzy Bayesian approach to flood frequency estimation with imprecise historical information.
abstract: This paper presents a novel framework that links imprecision (through a fuzzy approach) and stochastic uncertainty (through a Bayesian approach) in estimating flood probabilities from historical flood information and systematic flood discharge data. The method exploits the linguistic characteristics of historical source material to construct membership functions, which may be wider or narrower, depending on the vagueness of the statements. The membership functions are either included in the prior distribution or the likelihood function to obtain a fuzzy version of the flood frequency curve. The viability of the approach is demonstrated by three case studies that differ in terms of their hydromorphological conditions (from an Alpine river with bedrock profile to a flat lowland river with extensive flood plains) and historical source material (including narratives, town and county meeting protocols, flood marks and damage accounts). The case studies are presented in order of increasing fuzziness (the Rhine at Basel, Switzerland; the Werra at Meiningen, Germany; and the Tisza at Szeged, Hungary). Incorporating imprecise historical information is found to reduce the range between the 5% and 95% Bayesian credibility bounds of the 100 year floods by 45% and 61% for the Rhine and Werra case studies, respectively. The strengths and limitations of the framework are discussed relative to alternative (non-fuzzy) methods. The fuzzy Bayesian inference framework provides a flexible methodology that fits the imprecise nature of linguistic information on historical floods as available in historical written documentation.
authors.affiliation: Institute of Hydraulic Engineering and Water Resources Management Vienna University of Technology Vienna Austria; Centre for Water Resource Systems, Vienna University of Technology Vienna Austria.
authors.forename: José Luis
authors.initials: JL
authors.lastname: Salinas
authors.affiliation: Institute of Hydraulic Engineering and Water Resources Management Vienna University of Technology Vienna Austria.
authors.forename: Andrea
authors.initials: A
authors.lastname: Kiss
authors.affiliation: Institute of Hydraulic Engineering and Water Resources Management Vienna University of Technology Vienna Austria.
authors.forename: Alberto
authors.initials: A
authors.lastname: Viglione
authors.affiliation: Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology Vienna Austria.
authors.forename: Reinhard
authors.initials: R
authors.lastname: Viertl
authors.affiliation: Institute of Hydraulic Engineering and Water Resources Management Vienna University of Technology Vienna Austria; Centre for Water Resource Systems, Vienna University of Technology Vienna Austria.
authors.forename: Günter
authors.initials: G
authors.lastname: Blöschl
keywords: Bayesian; estimation; flood frequency; floods; fuzzy; historical