The Wavelet Empirical Orthogonal Function and Its Application Analysis of Internal Tides

Joe Wang Institute of Oceanography, National Taiwan University, Taipei, Taiwan

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Ching-Sheng Chern Institute of Oceanography, National Taiwan University, Taipei, Taiwan

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Antony K. Liu Oceans and Ice Branch, NASA Goddard Space Flight Center, Greenbelt, Maryland

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Abstract

Two powerful tools, wavelet transformation (WT) and conventional empirical orthogonal function (EOF) analysis, were combined tentatively. The combination of these two techniques might be called wavelet EOF (WEOF), and has potential 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 arrayed observations. WEOF inherits the advantages of both WT and EOF. This paper presents some basic formulations of WEOF and postulates a method to correlate empirical and dynamical modes. Monte Carlo simulations have been used to assess the practicality of the theory. Moreover, the method is applied to a real-time series of water temperature profile measured in a submarine canyon. The results of WEOF analysis reveal some unique properties of local internal tides, including the inequality of frequency composition between the surface and internal tides and the intensity of the mode-two terdiurnal component, likely induced by nonlinear interactions between first mode waves. The material only illustrates a few of the many possible applications. Based on these demonstrations, however, WEOF has proven useful in the analysis of nonstationary time series associated with spatially modal structures.

Corresponding author address: Dr. Joe Wang, Institute of Oceanography, National Taiwan University, P.O. Box 23-13, Taipei, Taiwan.

Abstract

Two powerful tools, wavelet transformation (WT) and conventional empirical orthogonal function (EOF) analysis, were combined tentatively. The combination of these two techniques might be called wavelet EOF (WEOF), and has potential 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 arrayed observations. WEOF inherits the advantages of both WT and EOF. This paper presents some basic formulations of WEOF and postulates a method to correlate empirical and dynamical modes. Monte Carlo simulations have been used to assess the practicality of the theory. Moreover, the method is applied to a real-time series of water temperature profile measured in a submarine canyon. The results of WEOF analysis reveal some unique properties of local internal tides, including the inequality of frequency composition between the surface and internal tides and the intensity of the mode-two terdiurnal component, likely induced by nonlinear interactions between first mode waves. The material only illustrates a few of the many possible applications. Based on these demonstrations, however, WEOF has proven useful in the analysis of nonstationary time series associated with spatially modal structures.

Corresponding author address: Dr. Joe Wang, Institute of Oceanography, National Taiwan University, P.O. Box 23-13, Taipei, Taiwan.

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