Effect of Uncertainty in Historical Data on Flood Frequency Analysis Using Bayesian Method

Abstract

The purpose of this paper was to investigate the effect of the uncertainty of historical flood information on flood frequency analyses using a Bayesian approach. The uncertainty of the magnitude was described using variations in lower or upper bound values, but the return period was not changed. Two types of hydrologic data—synthetic data generated from the Pearson type three distribution population and observed peak discharge data from the Yichang hydrologic station located below the Three Gorges Dam on the Yangtze River, China—were used. For the measured and the synthetic data, when the magnitudes were underestimated and the errors increased, the accuracy of the historical flood samples decreased, the estimated values of the parameters and design floods decreased using the Bayesian and probability weighted methods, and the values using the Bayesian method were more sensitive to errors and more quickly decreased relative to the probability weighted method. In contrast, overestimated magnitudes did not improve the representativeness of the historical flood samples but merely appended their values with an increase in errors, and the estimated values were hardly affected by changes in the errors using the Bayesian approach. At the same time, the estimated values continued to increase using the probability weighted method and did not accord with the variations in the errors for the flood frequency analysis. In practice, when the return period could be set with a specific value using several historical or paleoflood events, accurately quantifying the peak values of historical floods with known information was difficult, and we overestimated their magnitudes within a specified interval using the existing approaches and available information to estimate their bounds. The estimated values of the parameters and design floods and their uncertainty were less affected when using the Bayesian approach.