基于混沌理论的兰州市近10a空气污染指数时间序列分析

Chaotic analysis of air pollution index time series of Lanzhou City in recent 10 years

选择中国最具代表性的重污染城市兰州市作为研究对象,利用兰州市近10 a的空气污染指数日报数据进行时间序列分析。通过相空间重构,应用互信息法、Cao方法确定出重构参数时延和嵌入维,并运用小数据量法和G-P法分别计算了该序列的关联维、最大Lyapunov指数以及Kolmogorov熵等特征量。结果表明:兰州市近10 a空气污染指数时间序列中存在明显的混沌特性,是非线性混沌动力系统演化的结果,说明大气污染系统是混沌研究对象之一,运用混沌理论分析空气污染的动力学特征及变化规律是可行的。根据关联维的计算结果(D2=3.491 3),可以得知,特殊地形、气象条件、大气污染排放及能源消耗结构等4个因子是造成兰州市空气污染变化的主要因素。最大Lyapunov指数以及Kolmogorov熵的计算结果也为进一步研究兰州市空气污染的复杂性、演化规律及污染物预测奠定基础。

Lanzhou City is one of the most heavily air-polluted cities in China. In recent years,numerous researchers have lavished much attention on Lanzhou’s atmospheric environmental quality and air pollution. The dynamic analysis of pollution indexes,however,is rarely reported in the literature. In order to establish reasonable preventive countermeasures,it is important to understand the pollutant characteristics and the mechanisms of the pollution indexes’ temporal evolution. So,the objectives of this work were：（1） to prove the presence of chaos in air pollution index [（API] hereafter） time series;（2） to reflect the temporal evolution law of atmospheric pollutants and to identify dynamic variables to effectively interpret the changes of API time series in Lanzhou City. The time series of [API] during the past 10 years （from 2000 to 2010） in Lanzhou,northwest China,which is published on the website of Chinese Ministry of Environmental Protection （http：//www.zhb.gov.cn/）,were analyzed. In order to make full use of the abundant evolvement information contained in the API time series,the mutual information and CAO method were used to select the time delay and embedding dimension,and by reconstructing the multi-dimensional phase space,the characteristic quantities including the Lyapunov exponent,the correlation dimension and the Kolmogorov entropy,which could be taken as the chaotic features of the system,were calculated respectively. As a result,the correlation dimensions were fractioned,and the maximum Lyapunov exponent （λ1〉0）,which sufficiently shows that the time series of air pollution index over the past 10 years has fractal characteristics and chaotic characteristics. In the meanwhile,three or even four main dynamic variables （special valley basin topography,weather conditions,pollutant emissions and energy consumption structure） were discussed here that could effectively interpret the changes of air pollution index time series and their causes based on the calculated result of correlation dimension（D2=3.491 3）. These findings might provide a scientific basis for probing further into the regional complexity and evolution laws of the time series of air pollution index. At the same time,the identification of the chaotic characteristics also makes a base for non-linear forecast of the air pollution of Lanzhou City. And it has reference significance for improving the environment and promoting economy development of Lanzhou City.