变参数PDS/GP模型及其在洪水频率分析中的应用

PDS/GP model with variable parameters and its application for flood frequency analysis

传统的洪水频率分析模型一般假定研究区域是完全均质的,未能考虑分布函数参数会随协变量而变化,忽略了水文序列时空上的异质性。本文将广义Pareto(GP)分布函数的参数作为随机变量,利用自动阈值法确定独立样本的超定量系列(PDS),并将线性矩法和核回归法相结合估计含协变量的模型参数,从而构建了可考虑水文序列时空分布异质性的变参数PDS/GP模型。丹江口水库实例研究表明:定参数模型的尺度参数估计值和设计洪水预测值均在变参数PDS/GP模型的估计区间内,这说明本文提出的变参数PDS/GP模型能够更好地反映参数变化对模型不确定性的影响。而且,变参数PDS/GP模型的估计区间随重现期的增大而变宽,表明频率分析外延存在较大的不确定性,有必要考虑丹江口水库水文序列时空分布的异质性。

Flood frequency analysis is traditionally based on the assumption that the region is homogenousand the parameters are constant. Taking parameters of generalized Pareto distribution（GP） as random vari-ables,the PDS/GP model which can reflect the spatial and temporal heterogeneity of hydrological series isconstructed in this paper. The PDS of independent samples is firstly determined by an automatic thresholdselection method. Then the linear moment（LM） with covariate is derived and the estimators are given bykernel regression technology. The case study in Danjiangkou Reservoir shows that the estimation intervals ofscale parameter and design floods include those values calculated by the static model. It is obvious that thePDS/GP model with variable parameters does well in uncertainty analysis of random variable on prediction.Furthermore,it indicates that the estimation interval range becomes larger as the return period increases,which reflects the uncertainty of extrapolation of the frequency distribution. And it is necessary to considerthe spatial and temporal heterogeneity of hydrological series in Danjiangkou Reservoir.