A fuzzy Bayesian approach to flood frequency estimation with imprecise historical information

Estimating flood probabilities relies heavily on historical records, which often contain vague or imprecise descriptions. Traditional methods struggle to integrate such linguistic data into statistical models. While systematic data is well-suited for probabilistic analysis, historical sources like narratives and flood accounts introduce uncertainty that is not easily quantified. Prior research has shown that Bayesian approaches can model stochastic uncertainty, but they typically assume precise data inputs. This gap motivated the development of a framework that can handle both stochastic and imprecision-based uncertainty. No prior work had resolved how to incorporate fuzzy logic into Bayesian flood frequency analysis. Existing methods either ignore historical imprecision or oversimplify it. This paper introduces a novel approach that bridges this divide. The method allows for the use of vague historical information in probabilistic flood modeling. By doing so, it may improve flood risk estimation in regions with limited systematic data.

The aim of this study is to develop a framework that integrates fuzzy logic and Bayesian inference for flood frequency estimation. The specific problem addressed is how to model flood probabilities when historical information is imprecise or qualitative. The motivation stems from the need to better utilize historical records in flood risk analysis. Traditional methods either discard imprecise data or treat it as precise, leading to potential inaccuracies. This study proposes a new way to handle linguistic uncertainty in historical flood data. The approach is designed to better reflect the real-world variability in flood records. By incorporating fuzzy logic, the method can account for the vagueness in historical descriptions. This may lead to more accurate and reliable flood frequency estimates.

The study uses a fuzzy Bayesian approach to estimate flood probabilities. The method begins by analyzing historical sources to extract linguistic descriptions of flood events. These descriptions are then converted into membership functions that represent the uncertainty in the data. The membership functions are either integrated into the prior distribution or the likelihood function of a Bayesian model. This allows the model to account for both stochastic and imprecision-based uncertainty. The framework is tested using three case studies with different hydrological conditions and historical data types. The first case study uses flood records from the Rhine at Basel, the second from the Werra at Meiningen, and the third from the Tisza at Szeged. Each case study is analyzed using the fuzzy Bayesian framework to assess its performance in handling imprecise historical information.

The fuzzy Bayesian framework significantly reduces the range of Bayesian credibility bounds for 100-year flood estimates. In the Rhine case study, the range between the 5% and 95% credibility bounds was reduced by 45%. For the Werra case study, the reduction was even greater at 61%. These results suggest that incorporating imprecise historical information can lead to more precise flood frequency estimates. The framework was tested on three distinct case studies with varying hydromorphological conditions and historical data sources. The results show that the method is robust across different floodplain and river types. The case studies demonstrate the framework's flexibility in handling different types of historical information. The method's ability to reduce uncertainty is a key finding from the analysis. The results support the claim that fuzzy Bayesian inference is a viable approach for flood frequency analysis.

The fuzzy Bayesian inference framework provides a flexible method for flood frequency estimation that accounts for the imprecise nature of historical flood data. The authors propose that this approach better reflects the uncertainty inherent in linguistic historical records. The framework is found to reduce the range of Bayesian credibility bounds for flood estimates. This suggests that incorporating imprecise historical information may improve flood risk analysis. The method is demonstrated to be viable across different hydromorphological conditions and historical data types. The authors suggest that the framework is a useful addition to existing flood frequency estimation methods. The results indicate that the fuzzy Bayesian approach may offer advantages over non-fuzzy methods in handling historical uncertainty. The authors conclude that this method fits the imprecise nature of historical flood information as found in written documentation.