Cross-Wavelet Analysis: A Tool for Detection of Relationships Between Paleoclimate Proxy Records

Abstract

Cross-wavelet transform (XWT) is proposed as a data analysis technique for geological time-series. XWT permits the detection of cross-magnitude, phase differences (=lag time), non-stationarity, and coherency between signals from different paleoclimate records that may exhibit large stratigraphic uncertainties and noise levels. The approach presented herein utilizes a continuous XWT technique with Morlet-wavelet as the mother function, allows for variable scaling factors for time and scale sampling, and the automatic extraction of the most significant periodic signals. XWT and cross-spectral analysis is applied on computer generated time-series as well as two independently sampled proxy records (CO^_2 content approximated from plant cuticles and paleotemperature derived from δ¹⁸O from marine fossil carbonate) of the last 290 Ma. The influence of nonstationarities in the paleoclimate records that are introduced by stratigraphic uncertainties were a particular focus of this study. The XWT outputs of the computer-models indicate that a potential causal relationship can be distorted if different geological time-scale and/or large stratigraphic uncertainties have been used. XWT detect strong cross-amplitudes (∼ 200\ ppm•permil) between the CO^_2 and δ¹⁸O record in the 20–50 Myr waveband, however, fluctuating phase differences prevent a statistical conclusion on causal relationship at this waveband.