PM2.5Variation Trend Research Based On Multifractal Analysis

Because the time that PM2.5got into the public is very short, PM2.5is a new topic in the academic circles, especially the statistical data of PM2.5and the related factors are too little. So far it is very difficult to overall understand the objective laws of PM2.5. According to this hotspot issue of PM2.5, atmospheric pollutants problem has been studied based on multifractal so as to understand the PM2.5variation trend.The main contents of this paper are as follows:(1) Deal with rearrangement and phase randomization to the PM2.5time series of different cities, which can find the multifractal behavior in time series, namely long-range correlations and the fat-tails probability distributions. Their contribution rate in multifractal causes has been studied herein. The empirical study found the multifractal strength of rearrangement PM2.5sequences is weaker than the original PM2.5time series. Multifractal strength of substitution sequence is weaker than that of PM2.5rearrangement sequence. The data multifractal is mainly due to long-range correlations for small and large fluctuations, but the fat-tailed probability distributions also contribute to the multifractal behavior of PM2.5time series at some level. The results show that both long-range correlations and the fat-tailed probability distributions lead to multifractal characteristics.(2) Use principal analysis to know that the change of PM10concentration can influence the change of PM2.5concentration. Then the relationship between PM2.5and PM10in different cities are to be known by joint multifractal. So it has been found that the relationship between PM2.5and PM10in different cities are consistent. Specifically, PM2.5concentration is always in low level when PM10concentration has different levels. No matter how changes the concentration of PM10, relatively speaking, the PM2.5concentration fluctuation of London is even stronger than Xi’an.(3) Based on asymmetric multifractal detrended cross-correlation analysis method to further explore the cross-correlation between PM2.5and PM10time series in different cities respectively. Then we found H12+(q) and H12-(q) aren’t fixed constants in different cities. So the asymmetric cross-correlation of the PM2.5and PM10time series are multifractal in different cities. The asymmetric cross-correlation between PM2.5and PM10of Xi’an in four quarters has been discussed separately when PM10time series have different trends. Then we found in the first quarter and the second quarter, the asymmetric of cross-correlation between PM2.5and PM10are less persistent for large fluctuations of PM10than for small ones. By contrast, in the third quarter and the fourth quarter, the asymmetric of cross-correlation between PM2.5and PM10are more persistent for large fluctuations than for small ones. In addition, for q=2,｜△H12(2)｜of the first quarter is the largest and the asymmetric is the strongest;｜△H12(2)｜of the fourth quarter is the smallest and the asymmetric is the weakest.