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

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Abstract

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.

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Code Availability

The code generated during the current study are available from the corresponding author on reasonable request.

Data Availability

The datasets used in this study were compiled and supplied by the U.S. Geological Survey. They are available from the corresponding author on reasonable request.

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The authors declare that no funds, grants, or other supports were received during the preparation of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Turku, Turku, FIN-20014, Finland

    Heikki Ruskeepää

  2. Center for Humans & Machines - Max Planck Institute for Human Development, 14195, Berlin, Germany

    Leonardo Nascimento Ferreira

  3. Department of Water Engineering, University of Tabriz, Tabriz, Iran

    Mohammad Ali Ghorbani & Vahid Karimi

  4. Department of Civil Engineering, Istanbul Technical University, Istanbul, Turkey

    Ercan Kahya

  5. Tashkent Institute of Architecture and Civil Engineering, Tashkent, Uzbekistan

    Ercan Kahya

  6. Department of Soil, Water and Ecosystem Sciences, University of Florida, IFAS/RCREC, Ona, FL, USA

    Golmar Golmohammadi

  7. Big Data Institute, University of Oxford, Oxford, OX3 7LF, UK

    Leonardo Nascimento Ferreira

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  1. Heikki Ruskeepää
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Contributions

Heikki Ruskeepää: Resources, Computer code, Visualization, Writing - Original Draft. Leonardo Nascimento Ferreira: Conceptualization, Methodology, Writing - Original Draft. Mohammad Ali Ghorbani: Supervision, Conceptualization, Methodology. Ercan Kahya: Investigation, Writing - Original Draft, Formal analysis. Golmar Golmohammadi: Investigation, Conceptualization, Resources. Vahid Karimi: Formal analysis and Investigation, Methodology, Writing - review and editing.

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Correspondence to Leonardo Nascimento Ferreira or Mohammad Ali Ghorbani.

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Ruskeepää, H., Ferreira, L.N., Ghorbani, M.A. et al. Nonlinear and periodic dynamics of chaotic hydro-thermal process of Skokomish river. Stoch Environ Res Risk Assess 37, 2739–2756 (2023). https://doi.org/10.1007/s00477-023-02416-1

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