Abstract: The different multi-fractal behaviors of relative humidity and temperature over China are studied by means of multi-fractal detrended fluctuation analysis (MF-DFA for short) method. Three multi-fractal parameters (the spectrum width Δα, the asymmetry Δα_as?as and the long range correlation index α₀) of singularity spectrum are introduced to quantify the multi-fractal behaviors. Results show that multi-fractality in humidity daily records are stronger than that of temperature’s; stations with strong multi-fractality of relative humidity and temperature lie in different regions: southwest of China for relative humidity and South China and north of the Yellow River for the latter; asymmetry of singularity of relative humidity records is weaker than that of temperature’s and their singularity spectra exhibit left-skewed; singularity spectrum of temperature records exhibit symmetry on the whole; long range correlation of relative humidity records is higher than that of temperature’s. Combination of three parameters of multi-fractal spectrum stands for a kind of long range correlations and different behaviors of them reveal different dynamics underlying relative humidity and temperature.

Key words: long range correlation, scaling exponent, multi-fractal, multi-fractal detrended fluctuation analysis

摘要： 应用多分形去趋势涨落分析(MF-DFA)方法, 研究了中国地区相对湿度和温度序列的多分形特征差异, 并对比分析了其对应的奇异谱3个参数(奇异谱宽度Δα、奇异谱不对称性Δα_as和长程相关性α₀)的特征。结果表明: 1) 相对湿度序列的多分形强度弱于温度序列; 2) 相对湿度序列多分形性强的地区与温度序列有较大差异, 前者主要位于我国西南地区, 后者主要在华南和黄河以北地区; 3) 相对湿度序列的多分形不对称性强于温度序列; 4) 相对湿度序列的奇异谱均为左偏, 温度序列则基本是对称的; 5) 相对湿度序列的长程相关性大于温度序列。奇异谱的3个特征参数的组合完整地刻画了特定的长程相关特性, 相对湿度和温度序列多分形特征的不同, 揭示了其生成动力过程的差异。

关键词: 长程相关性, 标度指数, 多分形, 多分形去趋势涨落分析