Complexity measurement of precipitation series in urban areas based on particle swarm optimized multiscale entropy

Entropy theory is commonly applied to study the complexity of hydrological systems. In view of the subjectivity and uncertainty of parameter selection in entropy theory research, this paper combines a particle swarm optimization (PSO) algorithm with entropy theory to improve the traditional parameter selection method and the accuracy and reliability of the complexity measurement results. We combined PSO and multiscale entropy (MSE) to analyze the complexity of monthly precipitation series from 11 stations in Harbin, Heilongjiang Province, China, and the complexity results were classified into three levels. Harbin, Shuangcheng, Yilan, and Fangzheng are level I areas; Wuchang, Tonghe, Yanshou, and Binxian are level II areas; and Bayan, Mulan, and Shangzhi are level III areas. We selected the mountainous area ratio, water area ratio, GDP, and grain production as indicators that influence the complexity of local precipitation. The results showed that the correlation between the precipitation complexity and terrain was obvious, the impact of the water area ratio on the precipitation complexity was small, and the GDP and grain production were mostly negatively correlated with precipitation. These results reveal the spatiotemporal characteristics of the precipitation complexity and the factors that potentially influence the complexity. This study provides a reference model for other complexity measures in the field of regional water resource systems and related studies.