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Calculation of Hydrological Random Variables and Probability Distribution Based on Copula Function

Songbai Song, Xiaojun Wang


Hydrological random variables and distribution calculation are important contents for deducing design flood area composition, design flood downstream of cascade reservoirs, etc. They are of great importance for planning, design and management of water conservancy and hydropower projects downstream of reservoirs, and urban flood control risk assessment, etc. The traditional hydrological random variables and distribution are derived from the function distribution of two-dimensional variables. The marginal distribution must be of the same type, and its application is limited. According to the definition of two-dimensional random variables and probability distribution, this paper uses the Copula function and product variation to change the original principle, and strictly deduces the calculation formula of two-dimensional phase distribution according to machine variation and probability.  The distribution probability calculation formula of the sum of variables under the two commonly used marginal distributions of Gamma distribution and P-Ⅲ distribution is only one-dimensional integration of conditional Copula function, thus avoiding information distortion of data conversion by probability combination discrete summation method and overcoming the requirement of traditional multivariate distribution that the marginal distribution is of the same type. Taking the 3h flood volume composition from Shuibuya Reservoir to Geheyan Reservoir in Qingjiang River Basin as an example, the calculation method of hydrological random variables and distribution is given. The model and calculation method in this paper are expected to provide theoretical support for the composition of design flood areas and the calculation of design flood downstream of cascade reservoirs in China.

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