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.
Highlights
Numerous extreme floods around the world in the last decades [Hall et al, 2014] have resulted in a renewed interest in historical floods
Fuzzy Bayesian Inference In this paper we propose a method that transforms the descriptions found in historical records into fuzzy peak discharges, and combines them with systematic discharge measurements by Bayesian flood frequency analysis
Value of Fuzzy Historical Information The methodology proposed for transforming historical records into fuzzy numbers representing peak discharges of historical flood events, seems to be flexible in terms of being able to be adapted to diverse types of linguistic evidence and hydromorphological conditions
Summary
Numerous extreme floods around the world in the last decades [Hall et al, 2014] have resulted in a renewed interest in historical floods. Numerous formal statistical methods have been proposed that combine information on historical floods with systematic flood discharge measurements [e.g., Leese, 1973; Cohn et al, 1997; O’Connell et al, 2002; England et al, 2003; Benito and Thorndycraft, 2005] and with regional and process information [see e.g., Merz and Blo€schl, 2008a,b; Viglione et al, 2013]. Information on historical floods, usually, is stochastically uncertain and vague or imprecise. Stochastic uncertainty relates to a lack of information about the world and is usually represented by random variables. If historical records described a flood as a ‘‘large flood’’, there is nothing uncertain about this statement Rather it is a vague or imprecise statement, as ‘‘large’’ can imply a wide range of water levels. This kind of information can be useful
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