Exploring multiscale interactions between bivariate time series — A BEMD and DTW approach

The coupled relationship and mutual interaction between the global sea surface temperature (SST) and the global sea level (GSL) is one of key questions about global change. However, non-uniform distribution, nonlinearity and complex mechanism make so many uncertainties on the multiscale relationship between them. In this paper, BEMD and DTW methods are combined to investigate the multiscale interactions between these two. First, BEMD is adapted to extract multiscale characteristic and the instantaneous local variations of both time series at the same time scales. The DTW method is then applied to the decomposed components, tending to synchronize time series at different scales. The wrap functions of different scales provide information for local phase variability, which also reveal the dynamic interactions between the two time series. The result indicates that equilibrious relationship exists between SST and GSL, which supports Rahmstorf's equilibrium assumption on global sea level rise projection.