Uncertainty analysis of designed flood on Bayesian MCMC algorithm: a case study of the Panjiakou Reservoir in China

Estimation of the magnitude of designed flood is a fundamental task crucial for the determination of scale of engineering construction and for the development of flood disaster risk management projects. Due to a high level of uncertainty in observed data, selection of frequency distribution model, and estimation of model parameters, the process of designed flood has uncertainties consequently. A Bayesian flood frequency analysis method is adopted for designed flood estimation with P-III probability distribution as its flood frequency model. In the Bayesian method, the adaptive metropolis Markov Chain Monte Carlo (AM-MCMC) sampling algorithm is employed to estimate posterior distributions of parameters, upon which estimation of expectations and credible intervals of designed floods is obtained. With analyzing the drawback of likelihood function expressed with the product of probability of occurrence of each sample individual, four likelihood functions expressed on residuals are presented, and then based on Bayesian AM-MCMC method, performance of presented likelihood functions is compared with that of the classical likelihood function, with taking peak flow uncertainty analysis of Panjiakou Reservoir as a case study. The results show that expectations of flood peak quantiles estimation with likelihood functions based on residuals between observed/censored and calculated values of flood peaks are almost the same, but there are obvious differences between likelihood function based on occurrence probability of flood sample and those based on residuals with respect to expectation of quantiles estimation and also show that expectation and credible interval of quantiles estimation with Bayesian AM-MCMC method based on the whole likelihood function are more reasonable than those acquired with maximum likelihood function. Finally, some relevant flood frequency analyses issues based on Bayesian AM-MCMC algorithm which need to be further studied are also presented.