Advances in Earth Science
), Dong WANG
Xiaosan SHANG, Dong WANG. Multi-dimensional Joint Flood Frequency Analysis Considering the Uncertainty of Historical Flood Events[J]. Advances in Earth Science, 2022, 37(4): 407-416.
The entire flood process consists of multiple characteristic variables， including the flood peak and flood volume， for different durations. There is a positive correlation between these variables， and multivariate joint analysis should be performed for flood frequency analysis. However， the multi-dimensional joint distribution has greater sampling uncertainty with increasing variables using limited measurable samples. This could improve the accuracy of the marginal distribution of each characteristic variable and the correlation parameters of the Copula function using historical flood information that predated the period of systematic gauging for extending observation records in the multi-dimensional joint frequency analysis. Based on the hierarchical Archimedean Copulas function， a multi-dimensional joint flood frequency analysis hierarchical model， considering the uncertainty of historical flood events， was constructed and decomposed into several cascaded multi-level forms of two-dimensional Copula functions. Combined with the maximum likelihood method， the parameters of the nested multi-level Copula function and the marginal distribution of the characteristic variables are effectively estimated using a genetic algorithm. The Yichang hydrological station， located in the main stream of the Yangtze River， was selected as a case study， including systematic gauge records and historical flood data. The results show that it can completely describe the entire flood process and consider the correlation between the characteristic variables of the flood process with the multi-dimensional joint flood frequency analysis hierarchical model. This could improve the representativeness of the values of the marginal distribution parameters. Meanwhile， it could effectively use historical floods and improve the representativeness of the samples， and the correlation parameters of the Copula function were more consistent with the correlation between the measured data.