Frequency Analysis and Uncertainty Assessment of Annual Maximum Flood Series Using Bayesian MCMC Method

Abstract

The calculation of flood quantiles and its uncertainty estimation are important subjects of hydraulic engineering planning and water resources management. In this study, the Bayesian theory is used to implement frequency analysis and uncertainty assessment of annual maximum flood series, the Generalized Extreme Value (GEV) distribution is considered as the flood frequency distribution line type, and the Markov chain Monte Carlo (MCMC) method based on Metropolis-Hastings algorithm is used to evaluate the GEV distribution parameters, then the posterior distributions of flood flow quantiles are used to calculate the point estimations and interval estimations of flood design values under different return periods. The results show that the fitting effect of the Bayesian MCMC method is the same as the maximum likelihood estimation (MLE), but the Bayesian MCMC more superior when the uncertainties were considered. Compared with the traditional methods of flood frequency analysis, the proposed Bayesian MCMC method provides not only the design flood estimated values, but also the confidence intervals of the estimated values. In addition, the lengths between upper confidence limits and estimated values are greater than the lower confidence limits and estimated values, this asymmetry is more realistic than the traditional methods such as the delta method, thus improve the reliability of flood frequency analysis.