Nonlinear and periodic dynamics of chaotic hydro-thermal process of Skokomish river

Heikki Ruskeepää, Leonardo Nascimento Ferreira*, Mohammad Ali Ghorbani*, Ercan Kahya, Golmar Golmohammadi, Vahid Karimi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This paper investigates the dynamics of the time-series of water temperature of the Skokomish River (2019–2020) at hourly time scale by employing well-known nonlinear methods of chaotic data analysis including average mutual information, false nearest neighbors, correlation exponent, and local divergence rates. The delay time and the embedding dimension were calculated as 1400 and 9, respectively. The results indicated that the thermal regime in this river is chaotic due to the correlation dimension (1.38) and the positive largest Lyapunov exponent (0.045). Furthermore, complex networks have been applied to study the periodicity of thermal time-series throughout a year. A special algorithm is then used to find the so-called communities of the nodes. The algorithm found three communities which have been called Cold, Intermediate, and Warm. The temperatures in these three communities are, respectively, in the intervals (0.8, 5.8), (5.8, 11.63), and (11.63, 15.8). This analysis indicates that highest variations in water temperature occur between warm and cold seasons, and complex networks are highly capable to analyze hydrothermal fluctuations and classify their time-series.

Original languageEnglish
Pages (from-to)2739-2756
Number of pages18
JournalStochastic Environmental Research and Risk Assessment
Issue number7
Publication statusPublished - Jul 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


  • Complex networks
  • Correlation dimension
  • Correlation exponent
  • Maximal Lyapunov exponent
  • Phase space reconstruction


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