基于数据的Copula 法对极端降雨-径流的二元不确定性评估：年最大值序列（AMS）和超过阈值的峰（POT）的比较。

Department of Watershed Management, Sari Agriculture Science and Natural Resources University, P.O. Box 737, Sari, Iran.

Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, 701, Taiwan.

Environ Monit Assess. 2019 Jan 12;191(2):67. doi: 10.1007/s10661-019-7202-0.

Bivariate frequency analysis of extreme rainfall and runoff is crucial for water resource planning and management in a river basin. This study is aimed at accounting for uncertainties in bivariate analysis of extreme rainfall-runoff frequency in the Taleghan watershed, one of the major watersheds in northern Iran, using copulas. Two types of paired rainfall and runoff data, including annual maximum series (AMS) and peaks over threshold (POT) are adopted to investigate the uncertainties that arose due to the input data. The Cramer von-Mises goodness-of-fit test and Akaike information criteria (AIC) reveal that the Student's t copula is the best-fit copula for P-Q with Gaussian-Pearson III (P3) margins, while the Plackett copula is the best-fit copula for P-Q with generalized Pareto (GPAR-GPAR) margins. A nonparametric bootstrapping method for sampling from p-level curves is established to investigate the effects of univariate and bivariate models selection and uncertainties induced by input data. The results indicated that the sampling uncertainty reduces POT data compared to AMS data due to the increased sample size. However, the parameterization uncertainty of the POT data increases because of the weaker dependence structure between rainfall and runoff for the POT data. The results also reveal that the larger sampling uncertainties are associated with higher p-level curves for both AMS and POT data which are induced by lower data density in the upper tail. For the study area, the input-data uncertainty is most significant in bivariate rainfall-runoff frequency analysis and quantile estimation, while the uncertainty induced by probabilistic model selection is least significant.

双变量极值降雨和径流频率分析对于流域水资源规划和管理至关重要。本研究旨在利用 Copulas 方法考虑伊朗北部主要流域之一塔莱甘流域的极值降雨-径流频率双变量分析中的不确定性。采用两种类型的配对降雨和径流数据，包括年最大系列（AMS）和超过阈值的峰值（POT），以研究由于输入数据引起的不确定性。Cramer von-Mises 拟合优度检验和 Akaike 信息准则（AIC）表明，对于具有高斯-皮尔逊 III（P3）边缘的 P-Q，学生 t Copula 是最佳拟合 Copula，而对于具有广义 Pareto（GPAR-GPAR）边缘的 P-Q，Plackett Copula 是最佳拟合 Copula。建立了一种基于非参数 bootstrap 方法从 p-level 曲线中抽样的方法，以研究单变量和双变量模型选择的影响以及输入数据引起的不确定性。结果表明，由于样本量增加，抽样不确定性降低了 POT 数据相对于 AMS 数据。然而，由于 POT 数据中降雨和径流之间的依赖结构较弱，因此 POT 数据的参数化不确定性增加。结果还表明，对于 AMS 和 POT 数据，较大的抽样不确定性与较高的 p-level 曲线相关，这是由于上尾数据密度较低引起的。对于研究区域，输入数据不确定性在双变量降雨-径流频率分析和分位数估计中最为显著，而概率模型选择引起的不确定性则最小。