Stochastic methodology to select the best technique to incorporate historical information in flood frequency analyses for dam safety assessment

Dam design and safety assessment analyses require flood quantile estimates for high return periods up to 10000 years. However, systematic flood series are usually short with around 20-40 years, leading to high uncertainties. Historical information about floods is generally recognised as useful for estimating the magnitude of flood quantiles with return periods in excess of 100 years. Therefore, incorporating historical information in flood frequency analyses can reduce uncertainties and improve reliability of flood quantiles for high return periods. However, several techniques for incorporating historical information in flood frequency analyses have been proposed.

This study presents a methodology to select the best technique to fit a flood frequency curve considering historical information. The methodology is based on a stochastic analysis that quantifies the accuracy and uncertainty for each technique. Monte Carlo simulations are used to generate synthetic flood series. Varying lengths of both historical and systematic periods are considered. The floods that exceed a given perception threshold are considered statistically as historical floods, regardless they occur in the systematic or historical period. A varying number of historical floods are also considered.

Five streamflow gauging stations located in Spain are considered, where both systematic data and historical information are available. The analysis aims to find the best technique in each location in terms of flood quantile reliability and uncertainty reduction. It has been found that accuracy and uncertainty reduction in flood quantile estimates for each technique depend on the statistical properties of flood series.

The results show that the maximum likelihood estimator (MLE) and weighted moments (WM) techniques are the best option in regions with a milder climate, where skewness in flood series is smaller. However, in regions with more extreme climates, where skewness of flood series increases, the biased partial probability weighted moments (BPPWM) and the unbiased partial probability weighted moments (UPPWM) techniques obtain the best results.

Incorporating historical information about floods before the systematic period can improve the accuracy of flood quantile estimates, as well as reduce estimate uncertainties. The improvement is higher for shorter systematic periods and a greater number of historical floods available. In addition, historical information about floods can be crucial in arid regions where the greatest floods with low probability of occurrence are not usually recorded in the systematic period. The proposed methodology can be useful for reducing the uncertainty in design flood estimates for designing spillways and assessing hydrological dam safety.

Acknowledgments: This research has been supported by the project SAFERDAMS (PID2019-107027RB-I00) funded by the Spanish Ministry of Science and Innovation.