Study On The Nonlinear Characteristics Of PM_2.5 Time Series During A Typical Haze Based On Fractal And Complex Networks Theory

With the rapid development of the nonlinear science, the fractal theory and complex network theory have been widely used in dealing with the various time series in nature. PM_2.5 has been given more attention as an important indicator of air pollution. However, the evolution of PM_2.5 pollution has obvious nonlinear characteristics. because of traditional time series analysis method which can not accurate, clear and comprehensive describe the dynamic characteristics of PM_2.5 pollution evolution.The present paper is aimed to study the temporal scaling properties of the hourly PM_2.5 average concentration series in a typical haze period（from 29 November to 8 December, 2013） in Chengdu City, Sichuan. The research topic is of great significance to the city because such temporal scaling properties can help to identify and determine the nonlinear dynamical mechanism of the PM_2.5 evolutionary process. We focus on the PM_2.5 series of a haze dynamic detection based on the fractal and complex networks, We mainly analyse the statistical characterization of PM_2.5 series in time domain and network topology. Then we study the nexus between the dynamics of PM_2.5 series during a haze and the topological structure of networks.First, we analysis the weather of Chengdu during the haze, it found that the city was in a calm weather. Further, we investigate the space source of PM_2.5 by using the backward trajectory model, which can help to simulate the air mass trajectory more easily and efficiently. The analysis indicates that the contributions of the regional transmission（<100km） to the receptor sites in the city are supposed to be over 90%, whereas those of long range transmission（>100km） to receptor sites in Chengdu can be found no more than just 10%. Thus, we believe that the dynamic evolutionary regularity of PM_2.5 may mainly controlled by the evolution of local atmosphere system.Second, we research the normality、nonstability and tendency of PM_2.5 series during the haze by taking relevant statistical parameters and statistical methods. It is found the PM_2.5 sequences don’t accord with normal distribution, but it performed nonlinear characteristics as fat-tailed distributions. At the same time, we found that there are upward trends in all monitoring stations.Thirdly, the law of change and the structure character of PM_2.5 series are investigated by the DFA approach. We study the structure character of the PM_2.5 series during the haze, and point out that the PM_2.5 series have persistence of state and the statistical properties of fractal distribution. Make further efforts, we investigate empirically the multifractality of the PM_2.5 series by making use of MFDFA, and compare their fractal structure character and depict their multifractality. Then the sources of multifractal characteristic are analyzed,through shuffling procedure and phase randomization procedure,it show that the persistence of large and small fluctuations has a greater impact on multifractality of PM_2.5 series than fat-tailed distributions.Fourthly, we have made an analysis of topological structures of PM_2.5 time series with the visibility graph method, which perform different dynamics, then use the basic network statistics to describe their topological structures. We find that the accumulative degree distribution of PM_2.5 time series are characterized by power-law distribution, it suggest that the PM_2.5 sequences are fractal time series. Moreover, we find those PM_2.5 time series which exhibit the small-world property.Finally, we study the nexus between the dynamics of PM_2.5 series during a haze and the topological structure of networks. With the condition of which is mainly controlled by internal force, it can be conclude that the dynamic evolutionary regularity of PM_2.5 is mainly affected by the long-range correlation mechanism, and the topology of complex network is small-world property.