The wavelet empirical orthogonal function and its application to the analysis of internal tides

Two powerful tools, wavelet transformation (WT) and conventional empirical orthogonal function (EOF) analysis, were combined tentatively. The combinat ion of these two techniques might be called wavelet EOF (WEOF), and has pot ential for analyzing complicated signals associated with modal structures. The WT is versatile in handling transient or nonstationary time series, and EOF is capable of detecting statistically coherent modal structures from a rrayed observations. WEOF inherits the advantages of both WT and EOF This p aper presents some basic formulations of WEOF and postulates a method to co rrelate empirical and dynamical modes. Monte Carlo simulations have been us ed to assess the practicality of the theory. Moreover, the method is applie d to a real-time series of water temperature profile measured in a submarin e canyon. The results of WEOF analysis reveal some unique properties of loc al internal tides. including the inequality of frequency composition betwee n the surface and internal rides and the intensity of the mode-two terdiurn al component, likely induced by nonlinear interactions between first mode w aves. The material only illustrates a few of the many possible applications . Based on these demonstrations, however, WEOF has proven useful in the ana lysis of nonstationary time series associated with spatially modal structur es.