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Measuring nonlinear dependence in hydrologic time series

  • H. S. KimEmail author
  • K. H. Lee
  • M. S. Kyoung
  • B. Sivakumar
  • E. T. Lee
Original Paper

Abstract

It has been a common practice to employ the correlation dimension method to investigate the presence of nonlinearity and chaos in hydrologic processes. Although the method is generally reliable, potential limitations that exist in its applications to hydrologic data cannot be dismissed altogether. As for these limitations, two issues have dominated the discussions thus far: small data size and presence of noise. Another issue that is equally important, but less discussed in the literature, is the selection of delay time (τ d ) for reconstruction of the phase-space, which is an essential first step in the correlation dimension method, or any other chaos identification and prediction method for that matter. It has also been increasingly recognized that fixing the delay time window (τ w ) rather than just the delay time itself could be more appropriate, since the delay time window is the one that is of actual interest at the end to represent the dynamics. To this effect, Kim et al. (1998a) [Phys Rev E 58(5):5676–5682] developed a procedure for fixing the delay time window and demonstrated its effectiveness on three artificial chaotic series, and followed it up with the development of the C–C method to estimate both the delay time and the delay time window. The purpose of the present study is to test this procedure on real hydrologic time series and, hence, to assess their nonlinear deterministic characteristics. Three hydrologic time series are studied: (1) daily streamflow series from St. Johns near Cocoa, FL, USA; (2) biweekly volume time series from the Great Salt Lake, UT, USA; and (3) daily rainfall series from Seoul, South Korea. The results are also compared with those obtained using the conventional autocorrelation function (ACF) method.

Keywords

Hydrologic time series Nonlinearity Chaos Correlation dimension Delay time Delay time window 

Notes

Acknowledgments

This study was supported by the 2007 SOC Project (07-GIBANGUCHUK-D03-01) through the Design Criteria Research Center of Abnormal Weather-Disaster Prevention in KICTTEP of MOCT. Bellie Sivakumar would like to thank the Korea Science and Technology Societies (for the Brainpool Fellowship) and Inha University that facilitated his stay at Inha University to collaborate on the above project.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • H. S. Kim
    • 1
    Email author
  • K. H. Lee
    • 1
  • M. S. Kyoung
    • 1
  • B. Sivakumar
    • 2
  • E. T. Lee
    • 3
  1. 1.Department of Civil EngineeringInha UniversityIncheonSouth Korea
  2. 2.Department of Land, Air and Water ResourcesUniversity of CaliforniaDavisUSA
  3. 3.Department of Civil EngineeringKyungHee UniversitySuwonSouth Korea

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