降雨事件中 Kolmogorov 类标度与多重分形特征的证据
Evidence of Kolmogorov like scalings and multifractality in the rainfall events
AI总结：
本文通过统计与多重分形分析，揭示印度东北部降雨具有Kolmogorov类标度、约70公里空间相关及多重分形特性，Hurst指数约0.65。
摘要：
本文利用印度东北部地区（$26.05^{\circ}N-26.95^{\circ}N$, $88.05^{\circ}E-94.95^{\circ}E$）过去20年（2001-2020年）的半小时降雨数据，对该地区降雨模式中存在的空间和时间波动进行了详细的统计分析。我们通过计算时间降雨数据的均值、波动的二阶矩、偏度和峰度来分析分布的性质，结果表明右偏分布中存在重尾，这是稀有事件存在的典型特征。我们发现降雨数据的时间分布遵循乘性对数正态概率分布。此外，我们计算了该地区降雨的空间和时间相关性，表明降雨事件在约70公里的空间方向上具有相关性。时间降雨的功率谱密度显示出随频率的幂律行为，指数约为$\sim -1.5$，接近由平均流驱动的湍流被动标量所呈现的 Kolmogorov 指数（$-1.67$）。我们的小波分析揭示了降雨模式中存在多个频率的证据，这可归因于导致降雨的不同短期和长期因素。我们还使用了 Hilbert-Huang 变换来识别降雨时间序列中波动部分对应的频率。最后，利用多重分形去趋势波动分析，我们确定了降雨模式的多重分形性质，Hurst 指数接近 $0.65$。
英文摘要：
In this paper we present a detailed statistical analysis related to the characterization of the spatial and temporal fluctuations present in the rainfall patterns of North-East region ($26.05^{\circ}N-26.95^{\circ}N$, $88.05^{\circ}E-94.95^{\circ}E$) of India using half hourly rainfall data over the last 20 years for the range 2001-2020. We analyze the nature of the distribution by computing the mean, second moment of the fluctuation, skewness and kurtosis of the temporal rainfall data that indicate the presence of heavy tail in the right skewed distribution a typical feature of the presence of rare events. We find that the temporal distribution of the rainfall data follow the multiplicative Log-Normal probability distribution. Further we compute the spatial and temporal correlation of the rainfall in this region indicate that the rainfall events are correlated in the spatial direction of about 70 Km. The Power spectral density of temporal rainfall shows power law behaviour with frequency with an exponent $\sim -1.5$ close to the Kolmogorov exponent ($-1.67$) exhibited for the turbulent passive scalar driven by the mean flow. Our wavelet analysis reveals the evidence of multiple frequencies in the rainfall pattern which can attributed to different short and long range factors responsible for the rainfall. We have also used the Hilbert Huang transformation to identify the frequencies corresponding fluctuating part of the rainfall time series. Using multifractal detrended fluctuation analysis, finally we establish the multifractal nature of the rainfall pattern with Hurst exponent close to $0.65$ .
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