Analysis of Geophysical Time Series Using Discrete Wavelet Transforms: An Overview

Discrete wavelet transforms (DWTs) are mathematical tools that are useful for analyzing geophysical time series. The basic idea is to transform a time series into coefficients describing how the series varies over particular scales. One version of the DWT is the maximal overlap DWT (MODWT). The MODWT leads to two basic decompositions. The first is a scale-based analysis of variance known as the wavelet variance, and the second is a multiresolution analysis that reexpresses a time series as the sum of several new series, each of which is associated with a particular scale. Both decompositions are illustrated through examples involving Arctic sea ice and an Antarctic ice core. A second version of the DWT is the orthonormal DWT (ODWT), which can be extracted from the MODWT by subsampling. The relative strengths and weaknesses of the MODWT, the ODWT and the continuous wavelet transform are discussed.