22 April 2015 ESSC Brown Bag/Climate Dynamics Seminar
11:15 am, 529 Walker

A Powerful and Improved Approach to Significance Testing in Wavelet Analysis: The Cumulative Areawise Test and Its Applications to Geophysical Time Series

Justin Schulte
Department of Meteorology
Penn StateUniversity

A cumulative areawise test was developed to eliminate the binary decision from which an existing geometric test suffers. A set of experiments determined that the test has greater statistical power than the geometric test in most cases, especially when the signal-to-noise ratio is high. For low signal-to-noise ratios, differences in the ability of both tests to detect true positives is small. The number of false positives identified by both tests were found to be similar if the significance levels of both tests were set to 0.05. On the other hand, if the cumulative areawise test significance level was set to 0.01, the cumulative areawise test not only detected fewer false positives but also detected more true positives than the geometric test performed on 5% pointwise significance patches, contiguous regions of pointwise significance. The new testing procedure was applied to the time series of the Atlantic Multi-decadal Oscillation (AMO), North Atlantic Oscillation (NAO), Pacific Decadal Oscillation (PDO), as well as, to the Niño 3.4 index. The testing procedure determined that the NAO is consistent with a red-noise process and that the PDO and AMO exhibited enhanced multi-decadal variability that could not be distinguished from a red-noise background. On the other hand, numerous significant results were found in the 2-7 year period band for the Niño 3.4 index.