A generalized probability distribution of annual discharge derived from correlation dimension analysis in six main basins of China

• Published in: Stochastic environmental research and risk assessment Vol. 34; no. 12; pp. 2071 - 2082
• Main Authors: Wang, Guangsheng, Chen, Xi, Lu, Chengpeng, Shi, Junchao, Zhu, Jinfeng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2020; Springer Nature B.V
• Subjects: Aquatic Pollution; Basins; Chaos theory; Chemistry and Earth Sciences; Climatic conditions; Computational Intelligence; Computer Science; Correlation analysis; Discharge; Distribution functions; Earth and Environmental Science; Earth Sciences; Empirical analysis; Environment; Hydrology; Math. Appl. in Environmental Science; Original Paper; Physics; Probability distribution; Probability Theory and Stochastic Processes; Stations; Statistics for Engineering; Subtropical zones; Waste Water Technology; Water Management; Water Pollution Control; Watersheds; China; Pearson III function; Correlation dimension analysis; Annual discharge; Probability distribution; Main river in China
• ISSN: 1436-3240; 1436-3259
• DOI: 10.1007/s00477-020-01859-0

The probability distributions of hydrological series are primarily determined according to the best fitting of empirical probability from observation data. The fitted distribution functions are variable in different watersheds, and thus difficult to be applied to estimate probability of any discharge occurrence at other stations. In this study, chaotic characteristics of annual discharge series are analyzed by using correlation dimension analysis at 12 hydrological stations in the six main rivers in China. It is found that the correlation integral of annual discharge series represents the probability distribution of difference between any two annual discharges. The derived probability function can be perfectly fitted by the Pearson III function. Although the six basins have distinctively different climate conditions from the northern cold temperature zone to the southern subtropical zone, the correlation dimension of chaotic characteristics for annual discharges are similar at the 12 hydrological stations. The mean of difference between any two annual discharges, the maximum and minimum of annual discharge are found to be high correlation with the mean of annual discharge. Moreover, the derived probability distributions at 12 hydrological stations can be normalized by a universal distribution function, and the derived probability is high correlation with the probability distribution of annual discharge. This universal probability distribution can be easily applied to obtain probability distributions of annual discharge series over any stations.