基于层次贝叶斯法的无资料地区洪水频率分析

为验证层次贝叶斯法应用于无资料地区洪水设计值估计的可行性,构建了基于GEV分布-层次贝叶斯法的区域洪水频率分析模型;建立了GEV分布参数与空间协变量的回归关系,用于站点间的信息融合以及无资料地区参数推理;采用基于Metropolis-Hastings抽样的MCMC方法对参数和超参数的后验分布进行求解,通过超参数的随机样本与协变量的回归关系估计无资料地区的洪水设计值及其置信区间。将此方法应用于淮河流域17个水文站年最大流量数据,并以其中2个站点为交叉检验站点用于无资料地区洪水频率推求,结果表明层次贝叶斯法的结果优于指标洪水法的结果,为无资料地区洪水设计值估计提供了新途径。

Flood Frequency Analysis for Ungauged Basin Based on Hierarchical Bayesian Method

For estimating flood design values for ungauged basin, a model based the GEV distribution and hierarchical Bayesian method was built in this paper. In order to infer the parameters of ungauged sites, regression function between GEV distribution parameters and spatial covariates was established, and Markov chain Monte Carlo (MCMC) method based Metropolis-Hastings sampling was used to estimate the posterior distribution of parameters and hyper-parameters. Then the design flood value for the ungauged sites and its confidence interval was obtained by the regression function between random samples from hyper-parameter distribution and covariate of the ungauged site. The model was applied to the annual maximum flow series of 17 gauged sites in the Huaihe River basin, two of them were used as the cross-validation sites for inferring flood design values. The results show that the hierarchical Bayesian method can better estimate flood quantiles than the index flood method, which provides a new approach for the estimation of flood design values in ungauged basin.