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Is correlation dimension a reliable indicator of low-dimensional chaos in short hydrological time series?

Sivakumar, B; Persson, Magnus LU ; Berndtsson, Ronny LU and Bertacchi Uvo, Cintia LU (2002) In Water Resources Research 38(2).
Abstract
The reliability of the correlation dimension estimation in short hydrological time series is investigated using an inverse approach. According to this approach, first predictions are made using the phase-space reconstruction technique and the artificial neural networks. The correlation dimension is estimated next independently and is compared with the prediction results. A short hydrological series, monthly runoff series of 48 years (with a total of only 576 values) observed at the Coaracy Nunes/Araguari River watershed in northern Brazil, is studied. The correlation dimension results are in reasonably good agreement with the optimal embedding dimension obtained from the phase-space method and the optimal number of inputs from the neural... (More)
The reliability of the correlation dimension estimation in short hydrological time series is investigated using an inverse approach. According to this approach, first predictions are made using the phase-space reconstruction technique and the artificial neural networks. The correlation dimension is estimated next independently and is compared with the prediction results. A short hydrological series, monthly runoff series of 48 years (with a total of only 576 values) observed at the Coaracy Nunes/Araguari River watershed in northern Brazil, is studied. The correlation dimension results are in reasonably good agreement with the optimal embedding dimension obtained from the phase-space method and the optimal number of inputs from the neural networks. No underestimation of the correlation dimension is observed due to the small data size, rather there seems to be a slight overestimation due to the presence of noise in the data. The results indicate that the accuracy of the correlation dimension may not be judged on the basis of the length of the time series but on whether the time series is long enough to reasonably represent the dynamical changes in the system. Such an observation suggests that the correlation dimension could indeed be a reliable indicator of low-dimensional chaos even in short hydrological time series, which is certainly encouraging news for hydrologists who often have to deal with short time series. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
runoff, prediction, correlation dimension, low-dimensional chaos, reliability, data size
in
Water Resources Research
volume
38
issue
2
publisher
American Geophysical Union
external identifiers
  • wos:000176039800003
  • scopus:0036214974
ISSN
0043-1397
DOI
10.1029/2001WR000333
language
English
LU publication?
yes
id
9693659b-4e11-41ae-94b1-9c840d2a6a12 (old id 335653)
date added to LUP
2007-11-14 12:25:11
date last changed
2017-09-03 04:27:22
@article{9693659b-4e11-41ae-94b1-9c840d2a6a12,
  abstract     = {The reliability of the correlation dimension estimation in short hydrological time series is investigated using an inverse approach. According to this approach, first predictions are made using the phase-space reconstruction technique and the artificial neural networks. The correlation dimension is estimated next independently and is compared with the prediction results. A short hydrological series, monthly runoff series of 48 years (with a total of only 576 values) observed at the Coaracy Nunes/Araguari River watershed in northern Brazil, is studied. The correlation dimension results are in reasonably good agreement with the optimal embedding dimension obtained from the phase-space method and the optimal number of inputs from the neural networks. No underestimation of the correlation dimension is observed due to the small data size, rather there seems to be a slight overestimation due to the presence of noise in the data. The results indicate that the accuracy of the correlation dimension may not be judged on the basis of the length of the time series but on whether the time series is long enough to reasonably represent the dynamical changes in the system. Such an observation suggests that the correlation dimension could indeed be a reliable indicator of low-dimensional chaos even in short hydrological time series, which is certainly encouraging news for hydrologists who often have to deal with short time series.},
  author       = {Sivakumar, B and Persson, Magnus and Berndtsson, Ronny and Bertacchi Uvo, Cintia},
  issn         = {0043-1397},
  keyword      = {runoff,prediction,correlation dimension,low-dimensional chaos,reliability,data size},
  language     = {eng},
  number       = {2},
  publisher    = {American Geophysical Union},
  series       = {Water Resources Research},
  title        = {Is correlation dimension a reliable indicator of low-dimensional chaos in short hydrological time series?},
  url          = {http://dx.doi.org/10.1029/2001WR000333},
  volume       = {38},
  year         = {2002},
}