Cross-wavelet analysis: A tool for detection of relationships between paleoclimate proxy records

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), nonstationarity, 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 (CO2 content approximated from plant cuticles and paleotemperature derived from delta O-18 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 (similar to 200 ppm parts per thousand) between the CO2 and delta O-18 record in the 20-50 Myr waveband, however, fluctuating phase differences prevent a statistical conclusion on causal relationship at this waveband.