基于Kendall重现期的华南中小流域洪水峰量联合分布研究

Joint Distribution of Flood Peaks in Medium and Small Watersheds of South China Based on Kendall’s Return Period

[目的]对山区中小流域洪水峰量联合分布进行研究,以期为山区洪水防治提供理论参考.[方法]基于Archimedean Copula函数与Kendall测度分析3个山区中小流域的洪峰洪量联合分布的3种重现水平.由择优构建的Gumbel Copula及Kendall测度计算了洪水峰量联合分布的“或”、“且”和Kendall重现期及其设计洪水分位数.[结果]①洪峰和洪量之间具有高相关性,Kendall轶相关系数达0.76以上;②3个流域洪水峰量同频遭遇风险概率很大,均超过81%;③在工程经济安全两方面,对比设定的重现期显示,介于“或”重现期和“且”重现期之间的Kendall重现期更准确地反映洪水峰量联合分布的风险率;④按两变量“或”重现期洪水峰量和同频率推算的洪水设计值偏高.[结论]以Kendall重现期推算的洪水峰量设计值,可为山区中小流域防洪工程安全提供新的选择.

[Objective]The joint distribution of flood peaks in small and medium watersheds in mountainous areas of South China was examined to provide a theoretical reference for flood control in mountainous areas.[Methods]Based on the Archimedean Copula function and the Kendall measure,three kinds of recurrence levels of the combined distribution of flood peaks in selected watersheds of three mountainous areas were analyzed.The“OR”,“AND”and Kendall return periods and their design flood quantiles for the joint distribution of flood peaks were calculated based on the Gumbel Copula funtion and Kendall measures.[Results]①There was a high correlation between flood peak and flood volume(Kendall correlation coefficient>0.76);②The probability of flood peaks in three basins was very high,all exceeding 81%;③In terms of engineering economic security,the comparison of the set-up period showed that the Kendall return period between the“OR”and the“AND”return periods more accurately reflects the risk ratio of the joint distribution of flood peaks;④The flood design value calculated by the two-variable“OR”return period and the same frequency were higher.[Conclusion]The design value of peak flood volume calculated from Kendall recurrence period can provide new safety insights for flood control projects in small and medium-sized mountain basins.