The equivalent frequency regional composition (EFRC) method is an important and commonly used tool to determine the design flood regional composition at various sub-catchments in natural conditions. One of the cases in the EFRC method assumes that the exceedance probabilities of design flood volume at upstream and downstream sites are equal, and the corresponding flood volume at intermediate catchment equals the gap between the volumes of upstream and downstream floods. However, the relationship between the exceedance probability of upstream and downstream flood volumes P and that of corresponding intermediate flood volume C has not been clarified, and whether P> C or P C has not been theoretically proven. In this study, based on the normal, extreme value type I and Logistic distributions, the relationship between C and P is deduced via theoretical derivations, and based on the Pearson type III, two-parameter lognormal and generalized extreme value distributions, the relationship between C and P is investigated using Monte Carlo experiments. The results show that C is larger than P in the context of the design flood, whereas P is larger than C in the context of low-flow runoff. Thus, the issue of exceedance probability corresponding flood is further theoretically clarified using the EFRC method.

中文翻译：

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水文等效频率区域组合法对应洪水量超标概率的理论推导

等效频率区域成分 (EFRC) 方法是确定自然条件下各个子流域的设计洪水区域成分的重要且常用的工具。EFRC 方法中的一种情况假设上下游站点设计洪水量的超标概率相等，而相应的中间流域洪水量等于上下游洪水量之间的差距。但上下游洪水量P的超标概率与相应中间洪水量C的超标概率之间的关系尚未阐明，P>C还是PC尚未得到理论上的证明。在本研究中，基于正态、极值类型 I 和 Logistic 分布，通过理论推导推导出C和P之间的关系，并基于Pearson III型、双参数对数正态分布和广义极值分布，利用蒙特卡罗实验研究了C和P之间的关系。结果表明，在设计洪水的情况下，C 大于 P，而在低流量径流的情况下，P 大于 C。因此，使用EFRC方法从理论上进一步阐明了超标概率对应洪水的问题。