type="main" xml:id="rssc12079-abs-0001"> <title type="main">Summary</title> <p>Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. Motivated by the facts that the wavelet transform decomposes a time series into coefficients that are associated with different scales and that the variance of these coefficients (the so-called wavelet variance) decomposes the variance of the time series across scales, the paper proposes a definition for characteristic scale in terms of peaks in plots of the wavelet variance versus scale. After presenting basic theory for wavelet-based characteristic scales, a natural estimator for these scales is considered. Large sample theory for this estimator 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. Characteristic scale estimates are calculated for medium multiyear Arctic sea ice, global temperature records, coherent structures in river flows and the Madden–Julian oscillation in an atmospheric time series.
