Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets

An understanding of subtidal coastal sea level fluctuations is important both because they impact the effect of tsunamis and other destructive events on human developments and because many physical and biological processes within coastal ecosystems are very sensitive to these fluctuations. We analyze a time series of subtidal fluctuations at Crescent City, California, during 1980–91 using the maximal overlap discrete wavelet transform (MODWT). Our analysis shows that these fluctuations have seasonally dependent variability over scales of 32 day and less. We show how this nonstationary behavior can be succinctly characterized in terms of the MODWT, and we indicate how this characterization can be used to improve forecasting schemes for inundation during tsunamis and storm surges. Because the standard tools in time series analysis are best suited for stationary processes and because our case study demonstrates that MODWT analysis is useful for characterizing certain nonstationary processes, we provide pseudo-code and enough background information so that data analysts in other disciplines can readily apply MODWT analysis to their time series.