Theoretical derivation for the exceedance probability of corresponding flood volume of the equivalent frequency regional composition method in hydrology

Abstract

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. HIGHLIGHTS The relationship between the intermediate exceedance probability and the design exceedance frequency in the equivalent frequency regional composition method depends on the design exceedance frequency and the distribution of flood volume.; The relationship is investigated via theoretical derivations and Monte Carlo experiments.; The intermediate exceedance probability is larger than the design exceedance frequency in the context of design flood.; The design exceedance frequency is larger than the intermediate exceedance probability in the context of low flow.;

Keywords

• design flood
• equivalent frequency regional composition method
• flood distributions
• flood regional composition
• monte carlo experiments