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Air pollution has become a major issue and caused widespread environmentaland health problems. Aerosols or particulate matters are an important componentof the atmosphere and can transport under complex meteorological conditions.Based on the data of $PM_{2.5}$ observations, we develop a network approach tostudy and quantify their spreading and diffusion patterns. We calculatecross-correlation functions of time lag between sites within different season.The probability distribution of correlation changes with season. It is foundthat the probability distributions in four seasons can be scaled into onescaling function with averages and standard deviations of correlation. Thisseasonal scaling behavior indicates there is the same mechanism behindcorrelations of $PM_{2.5}$ concentration in different seasons. Further, fromweighted and directional degrees of complex network, different properties of$PM_{2.5}$ concentration are studied. The weighted degrees reveal the strongestcorrelations of $PM_{2.5}$ concentration in winter and in the North Chinaplain. These directional degrees show net influences of $PM_{2.5}$ along Gobiand inner Mongolia, the North China plain, Central China, and Yangtze RiverDelta.

Correlation and scaling behaviors of $PM_{2.5}$ concentration in China