使用Wavelength评估特征尺度
Assessing Characteristic Scales Using Wavelets
摘要：
特征尺度是地球物理学中的一个概念，但至今没有一个被广泛接受的精确定义。小波变换将时间序列分解为与不同尺度相关联的系数。这些系数的方差可以用于分解不同尺度上的时间序列的方差。特征尺度的实际定义可以用小波方差与尺度的曲线图中的峰值来表示。本文介绍了基于离散小波变换的特征尺度的基本理论，提出了这些尺度的自然估计，并提供了一个大样本理论，这种估计，允许建设的置信区间为一个真正的未知特征尺度。计算机实验证明了有限样本量的大样本理论的有效性。给出了全球温度记录、河流中的相干结构、大气时间序列中的Madden-Julian振荡和一种类型的北极海冰断面的特征尺度估计的例子。
英文摘要：
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The variance of these coefficients can be used to decompose the variance of the time series across different scales. A practical definition for characteristic scale can be formulated in terms of peaks in plots of the wavelet variance versus scale. This paper presents basic theory for characteristic scales based upon the discrete wavelet transform, proposes a natural estimator for these scales and provides a large sample theory for this estimator that permits the construction of confidence intervals for a true unknown characteristic scale. Computer experiments are presented that demonstrate the efficacy of the large sample theory for finite sample sizes. Examples of characteristic scale estimation are given for global temperature records, coherent structures in river flows, the Madden-Julian oscillation in an atmospheric time series and transects of one type of Arctic sea ice.
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