Author(s): Weiqiang Zheng; Shuguang Liu; Guihui Zhong; Zhengzheng Zhou
Linked Author(s):
Keywords: Uncertainty analysis; Weibull distribution; Pivotal quantities; Design rainfall depths; Shanghai
Abstract: The Weibull distribution holds a prominent position in hydrology frequency analysis and climate modeling due to its versatility and applicability. However, accurately estimating intervals for hydrology design values is challenging due to the inherent uncertainty in hydrological processes. Traditional methods often rely on assumptions about prior distributions for parameters, which can be unreliable when dealing with short sequences of data. In this paper, we propose a pivotal quantity method to analyze the uncertainty for design rainfall depths in three-parameter Weibull distribution. First, three pivotal quantities are designed whose statistical characteristics can be obtained by Monte Carlo method. Then, the uncertainties of the Weibull distribution parameters are obtained using the annual maximum rainfall series in Shanghai. Next, the uncertainty analysis on design rainfall depths is conducted based on the generated parameter realizations. Finally, the proposed method is compared with conventional Bayesian method and bootstrap method. The results show that the proposed method can provide satisfying estimations for the parameters and design rainfall depths. At some rain stations in the north and middle of Shanghai, the uncertainties of design rainfall depths are pretty high. For the rainfall frequency analysis in Shanghai, compared the conventional methods, the pivotal quantity method can provide satisfying estimations for parameters and more reliable results on design rainfall depths. The overall framework offers broader applicability in hydrological fields and can be adapted to other three-parameter distributions commonly used in hydrology frequency analysis, as well as to various types of hydrological datasets.
Year: 2024