Probabilistic analysis of rainfall in Chongqing based on probability density evolution theory

As one of hazard actions in the field of municipal engineering and civil engineering, the probabilistic structure of rainfall is very important for the analysis of stochastic systems involved in rainfall. However, it is difficult for modeling the probabilistic structure of rainfall by a traditional probability density function, sometimes it is impossible. In this work, a new technique coming from probability density evolution theory is proposed to describe the probabilistic structure of rainfall. Based on the analytical solution for generalized density evolution equations of a virtual random process, the transiting solution of a probability density function and its approximation via a family of δ sequences are derived. This transiting solution promotes probability density evolution theory from dynamical systems to static systems. Obviously, it is applicable to the probability analysis of random data, which can be viewed as a self-mapping static system. Therefore, the probabilistic structure of rainfall in Chongqing can be obtained by this method, verified by the frequency histogram of an equal interval, a frequency histogram of equal probability and empirical cumulative distribution functions. In order to build up a simple and practical model for the complicated, a class of linear combined model based on traditional probability density functions is put forward, and linear combined models for maximum daily rainfall are obtained by try and error.