Abstract
Turbidity data obtained by field observations off the Tenryu River mouth were analyzed using the Hilbert-Huang Transform (HHT) in order to investigate the characteristic variations in time and in the frequency domain. The Empirical Mode Decomposition (EMD) decomposed the original data into only eight intrinsic mode functions (IMFs) and a residue in the first step of the HHT. In the second step, the Hilbert transform was applied to the IMFs to calculate the Hilbert spectrum, which is the time-frequency distribution of the instantaneous frequency and energy. The changes in instantaneous frequencies showed correspondence to high turbidity events in the Hilbert spectrum. The investigation of instantaneous frequency variations can be used to understand transitions in the state of the turbidity. The comparison between the Fourier spectrum and the Hilbert spectrum integrated in time showed that the Hilbert spectrum makes it possible to detect and quantify the cycle of locally repeated events.
Highlights
Field observations typically include many phenomena in time and space operating at a variety of scales
In the HILBERT-HUANG TRANSFORM (HHT), the Hilbert transform (HT) is applied to the intrinsic mode functions (IMF) and instantaneous variables such as instantaneous amplitude (IA) and instantaneous frequency (IF) are obtained
The empirical mode decomposition (EMD) could decompose the turbidity data obtained through field observation into a small number of IMFs and a residue, whereas the Fourier transform needs a large number of harmonic functions to represent the data
Summary
Field observations typically include many phenomena in time and space operating at a variety of scales. It is difficult to analyze the characteristics of the temporal variation in turbidity using traditional methods such as Fourier transform (FT) analysis. The HHT has been applied in many research fields, for example, mechanical engineering (Chen et al, 2007), earthquake engineering (Dong et al, 2008), structural engineering (Quek et al, 2005), fluid dynamics (Ding et al, 2007), molecular dynamics (Phillips et al, 2003), and financial analysis (Huang et al, 2003), as a useful method for the analysis of non-stationary and/or nonlinear data. Analysis of turbidity data inherently contains many difficulties because there is high intermittency, often with much similarity to spiky noises, and HHT may be a suitable method to apply. Water Resources Engineering, Lund University, Box 118, 221 00 Lund, Sweden 3 Architecture and Civil Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho, Toyohashi, Aichi, 441-8580, Japan 4 Architecture and Civil Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho, Toyohashi, Aichi, 441-8580, Japan
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