Flood frequency analysis using multi-objective optimization based interval estimation approach

Flood frequency analysis (FFA) is a necessary tool for water resources management and water infrastructure design. Owing to the existence of variability in sample representation, distribution selection, and distribution parameter estimation, flood quantile estimation is subjected to various levels of uncertainty, which is not negligible and avoidable. Hence, alternative methods to the conventional approach of FFA are desired for quantifying the uncertainty such as in the form of prediction interval. The primary focus of the paper was to develop a novel approach to quantify and optimize the prediction interval resulted from the non-stationarity of data set, which is reflected in the distribution parameters estimated, in FFA. This paper proposed the combination of the multi-objective optimization approach and the ensemble simulation technique to determine the optimal perturbations of distribution parameters for constructing the prediction interval of flood quantiles in FFA. To demonstrate the proposed approach, annual maximum daily flow data collected from two gauge stations on the Bow River, Alberta, Canada, were used. The results suggest that the proposed method can successfully capture the uncertainty in quantile estimates qualitatively using the prediction interval, as the number of observations falling within the constructed prediction interval is approximately maximized while the prediction interval is minimized.