Application of the cross wavelet transform and wavelet coherence to geophysical time series

TLDR

Many scientists use wavelet methods for time‑series analysis with free software, yet no easy tools exist for jointly analyzing two series. The study aims to apply cross wavelet transform and wavelet coherence to examine relationships between two time series, using the Arctic Oscillation index and Baltic sea ice extent as an example. The authors employ cross wavelet transform, wavelet coherence, phase‑angle statistics, and Monte Carlo significance testing against red‑noise backgrounds to analyze the two series. They show that phase‑angle statistics can confirm causal relationships and provide a software package for performing cross wavelet transform and wavelet coherence analysis (www.pol.ac.uk/home/research/waveletcoherence/). Abstract.

Abstract

Abstract. Many scientists have made use of the wavelet method in analyzing time series, often using popular free software. However, at present there are no similar easy to use wavelet packages for analyzing two time series together. We discuss the cross wavelet transform and wavelet coherence for examining relationships in time frequency space between two time series. We demonstrate how phase angle statistics can be used to gain confidence in causal relationships and test mechanistic models of physical relationships between the time series. As an example of typical data where such analyses have proven useful, we apply the methods to the Arctic Oscillation index and the Baltic maximum sea ice extent record. Monte Carlo methods are used to assess the statistical significance against red noise backgrounds. A software package has been developed that allows users to perform the cross wavelet transform and wavelet coherence (www.pol.ac.uk/home/research/waveletcoherence/).