Revisiting multifractality of high‐resolution temporal rainfall using a wavelet‐based formalism
Revisiting multifractality of high‐resolution temporal rainfall using a wavelet‐based formalism
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DOI：
10.1029/2005wr004489
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发表时间：
2005-12
影响因子：
5.4
通讯作者：
V. Venugopal;S. Roux;E. Foufoula‐Georgiou;A. Arneodo
中科院分区：
文献类型：
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作者：
V. Venugopal;S. Roux;E. Foufoula‐Georgiou;A. Arneodo
我们使用基于小波的方法重新检查了时间降雨的尺度结构，正如我们所证明的那样，与更传统的多重分形方法（例如盒计数和结构函数技术）相比，该方法具有重要的优势。特别是，我们探索了两种基于连续小波变换（CWT）和小波变换模极大值（WTMM）的方法：配分函数方法和更新且更有效的幅度累积分析方法。我们还报告了两点幅度相关分析的结果，该分析能够推断乘性是否存在作为缩放的基本机制。这些方法对于小样本、小范围缩放信号以及高频波动叠加在低频分量上的信号（地球物理信号的所有常见属性）的诊断能力都得到了仔细记录。将这些方法应用于几个中西部对流风暴，在几个小时内每 5 秒采样一次，提供了新的见解。他们揭示了在 5 分钟尺度和风暴脉冲持续时间（所分析的风暴大约为 1-2 小时）之间的降雨量波动中存在非常间歇性的多重分形结构（广泛的奇点）。两点幅度统计分析表明，这种结构与乘法级联机制一致，但本质上是局部的；也就是说，它仅适用于每个风暴脉冲，但不适用于整个风暴持续时间。
We reexamine the scaling structure of temporal rainfall using wavelet‐based methodologies which, as we demonstrate, offer important advantages compared to the more traditional multifractal approaches such as box counting and structure function techniques. In particular, we explore two methods based on the Continuous Wavelet Transform (CWT) and the Wavelet Transform Modulus Maxima (WTMM): the partition function method and the newer and more efficient magnitude cumulant analysis method. We also report the results of a two‐point magnitude correlation analysis which is able to infer the presence or absence of multiplicativity as the underlying mechanism of scaling. The diagnostic power of these methodologies for small samples, signals with short ranges of scaling, and signals for which high‐frequency fluctuations are superimposed on a low‐frequency component (all common attributes of geophysical signals) is carefully documented. Application of these methodologies to several midwestern convective storms sampled every 5 s over several hours provides new insights. They reveal the presence of a very intermittent multifractal structure (a wide spectrum of singularities) in rainfall fluctuations between the scales of 5 min and the storm pulse duration (of the order of 1–2 hours for the analyzed storms). The two‐point magnitude statistical analysis suggests that this structure is consistent with a multiplicative cascading mechanism which however is local in nature; that is, it applies only within each storm pulse but not over the whole storm duration.