An existing Bayesian flood frequency analysis method is applied to quantile estimation for Pearson type three (P-III) probability distribution. The method couples prior and sample information under the framework of Ba...An existing Bayesian flood frequency analysis method is applied to quantile estimation for Pearson type three (P-III) probability distribution. The method couples prior and sample information under the framework of Bayesian formula, and the Markov Chain Monte Carlo (MCMC) sampling approach is used to estimate posterior distributions of parameters. Different from the original sampling algorithm (i.e. the important sampling) used in the existing approach, we use the adaptive metropolis (AM) sampling technique to generate a large number of parameter sets from Bayesian parameter posterior distributions in this paper. Consequently, the sampling distributions for quantiles or the hydrological design values are constructed. The sampling distributions of quantiles are estimated as the Bayesian method can provide not only various kinds of point estimators for quantiles, e.g. the expectation estimator, but also quantitative evaluation on uncertainties of these point estimators. Therefore, the Bayesian method brings more useful information to hydrological frequency analysis. As an example, the flood extreme sample series at a gauge are used to demonstrate the procedure of application.展开更多
Estimating the design flood under nonstationary conditions is challenging. In this study, a sample reconstruction approach was developed to transform a nonstationary series into a stationary one in a future time windo...Estimating the design flood under nonstationary conditions is challenging. In this study, a sample reconstruction approach was developed to transform a nonstationary series into a stationary one in a future time window (FTW). In this approach, the first-order moment (EFTW) of an extreme flood series in the FTW was used, and two possible methods of estimating EFTW values in terms of point values and confidence intervals were developed. Three schemes were proposed to analyze the uncertainty of design flood estimation in terms of sample representativeness, uncertainty from EFTW estimation, and both factors, respectively. To investigate the performance of the sample reconstruction approach, synthesis experiments were designed based on the annual peak series of the Little Sugar Creek in the United States. The results showed that the sample reconstruction approach performed well when the high-order moment of the series did not change significantly in the specified FTW. Otherwise, its performance deteriorated. In addition, the uncertainty of design flood estimation caused by sample representativeness was greater than that caused by EFTW estimation.展开更多
基金supported by the National Basic Research Pro-gram of China ("973" Program) (Grant No. 2007CB714104)the National Natural Science Foundation of China (Grant No. 50779013)
文摘An existing Bayesian flood frequency analysis method is applied to quantile estimation for Pearson type three (P-III) probability distribution. The method couples prior and sample information under the framework of Bayesian formula, and the Markov Chain Monte Carlo (MCMC) sampling approach is used to estimate posterior distributions of parameters. Different from the original sampling algorithm (i.e. the important sampling) used in the existing approach, we use the adaptive metropolis (AM) sampling technique to generate a large number of parameter sets from Bayesian parameter posterior distributions in this paper. Consequently, the sampling distributions for quantiles or the hydrological design values are constructed. The sampling distributions of quantiles are estimated as the Bayesian method can provide not only various kinds of point estimators for quantiles, e.g. the expectation estimator, but also quantitative evaluation on uncertainties of these point estimators. Therefore, the Bayesian method brings more useful information to hydrological frequency analysis. As an example, the flood extreme sample series at a gauge are used to demonstrate the procedure of application.
基金supported by the National Key Research and Development Program of China(Grant No.2018YFC1508001)the National Natural Science Foundation of China(Grant No.51709073)the Fundamental Research Funds for the Central Universities of China(Grant No.B220202031).
文摘Estimating the design flood under nonstationary conditions is challenging. In this study, a sample reconstruction approach was developed to transform a nonstationary series into a stationary one in a future time window (FTW). In this approach, the first-order moment (EFTW) of an extreme flood series in the FTW was used, and two possible methods of estimating EFTW values in terms of point values and confidence intervals were developed. Three schemes were proposed to analyze the uncertainty of design flood estimation in terms of sample representativeness, uncertainty from EFTW estimation, and both factors, respectively. To investigate the performance of the sample reconstruction approach, synthesis experiments were designed based on the annual peak series of the Little Sugar Creek in the United States. The results showed that the sample reconstruction approach performed well when the high-order moment of the series did not change significantly in the specified FTW. Otherwise, its performance deteriorated. In addition, the uncertainty of design flood estimation caused by sample representativeness was greater than that caused by EFTW estimation.
