99 / 2024-01-19 22:51:41

Interval estimation on design rainfall based on Weibull distribution: Using rainfall records in Shanghai

interval estimation,Weibull distribution,pivotal quantities,design rainfall,joint confidence space,Shanghai

The Weibull distribution is one of the most popular widely used distributions in hydrology frequency analysis and climate modeling. Interval estimation for the hydrology design value is of great importance due to the complex uncertainty regularity in hydrological process. However, conventional interval estimation methods in frequency analysis require several assumptions on prior distributions for parameters and performs poorly in case of short sequence lengths. In this paper, we propose an interval estimation method on design rainfall based on three-parameter Weibull distribution. First, three statistical magnitudes are constructed to provide the statistical inference for the parameters. The statistical characteristics of these magnitudes are independent with the parameters. Then, the joint confidence space for the three parameters and the confidence interval for each parameter are obtained based on the frequency distributions of the statistical magnitudes. Finally, the interval estimation on design rainfall is simulated based on the joint frequency distribution of parameters, where the uncertainty analysis on design rainfall is carried out. An example with precipitation station records in Shanghai is illustrated to show the process. The proposed method can support the statistical inference on parameters and design rainfall. The assumptions on prior distributions of both parameters and design values are avoided in the proposed method, which provides more reliable results. Also, the influence of sequence length is considered in the interval estimation on parameters. Although the proposed method is carried out based on Weibull distribution and practiced on design rainfall, it is also applicative in some other three-parameter distributions which are frequently recommended in hydrology frequency analysis, and applicative in other hydrology sequences.