基于DFA的雷暴日时间序列分形特征分析

运用最小二乘法、非趋势波动分析(DFA)与小波变换三种方法对比分析许昌市1961—2012年52 a雷暴日时间序列的变化特性,揭示雷暴日的长程相关性及其内在规律。研究结果表明:许昌市52 a月雷暴日时间序列属于分形时间序列,存在内在的长程相关性,其雷暴日数每10 a减少1.6689天,雷暴日时间序列长程幂律相关的标度指数为0.8940,该幂律关系至少可持续17个月,并将2011年和2012年观测数据作为验证数据加以验证,结果与DFA分析结果一致;雷暴日时间序列具有2个显著的标度不变区域,存在一个突变点,反映了雷暴日系统具有复杂的物理作用机制;三种分析方法均得出许昌市雷暴日呈减少趋势的结论,最小二乘法虽然能定量计算出雷暴日每10 a的减少量,但年度尺度较大,精确度变低,而DFA和小波分析法的分析结果更加细致;但在定量描述雷暴日变化趋势上DFA法优于小波分析结果,而在分析雷暴日时序的细节分量和周期特性时小波分析更加清晰;DFA法可作为预测未来雷暴日发展趋势时长的有效方法之一。

Fractal Characteristics Analysis of Thunderstorm Time Series Based on DFA

A comparative analysis of the fluctuation characteristics of thunderstorm time series in Xuchang for 52 years from 1961 to 2012 was conducted by using three methods which are least squares method, detrended fluctuation analysis (DFA) and wavelet transform. Then the long-range correlation and inherent laws of thunderstorm days were revealed. The results show that: time series of monthly average thunderstorm days in Xuchang for 52 years belongs to fractal time series, which has an inherent long-range correlation that the thunderstorm days will be reduced by 1.6689 days every 10 years. The scaling exponent of long-range power-law-related of thunderstorm days time series is 0.8940 and it can last for at least 17 months. Using the observation data since 2011 to 2012 as validation data to verify the results, they are in agreement with DFA analysis. The thunderstorm days time series has two significant scale invariant region and a jump point which reflect complex physical mechanisms of thunderstorm days system. The same conclusion is drawn that the thunderstorm days in Xuchang tend to decrease by the three analytical methods. The least square method can calculate the decline value of thunderstorm days every 10 years quantitatively, but the year scale is too large and accuracy is low; while the results of DFA and wavelet analysis are more detailed. DFA is superior to wavelet analysis when describing the trend of thunderstorm days quantificationally, but wavelet analysis is more clear when analyzing the characteristics of detail components and cyclophysis of thunderstorm days. DFA can be used as one of the effective methods to predict duration about future trends of thunderstorm days.