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

Springer Science and Business Media LLC - Tập 37 - Trang 2739-2756 - 2023
Heikki Ruskeepää1, Leonardo Nascimento Ferreira2,3, Mohammad Ali Ghorbani4, Ercan Kahya5,6, Golmar Golmohammadi7, Vahid Karimi4
1Department of Mathematics and Statistics, University of Turku, Turku, Finland
2Center for Humans & Machines - Max Planck Institute for Human Development, Berlin, Germany
3Big Data Institute, University of Oxford, Oxford, UK
4Department of Water Engineering, University of Tabriz, Tabriz, Iran
5Department of Civil Engineering, Istanbul Technical University, İstanbul, Turkey
6Tashkent Institute of Architecture and Civil Engineering, Tashkent, Uzbekistan
7Department of Soil, Water and Ecosystem Sciences, University of Florida, IFAS/RCREC, Ona, USA

Tóm tắt

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.

Tài liệu tham khảo

Abarbanel H, Parlitz U (2006) Nonlinear analysis of time series data.Handb Time Ser Anal WILEY-VCH1–37 Abarbanel HDI (2001) Challenges in modeling nonlinear systems: a worked example. Nonlinear dynamics and statistics. Springer, pp 3–29 Abarbanel HDI (1996) Reconstruction of Phase Space. Analysis of observed chaotic data. Springer, pp 13–23 Azra MN, Aaqillah-Amr MA, Ikhwanuddin M et al (2020) Effects of climate‐induced water temperature changes on the life history of brachyuran crabs. Rev Aquac 12:1211–1216 Barabási AL, Pósfai M (2016) Network Science. Cambridge University Press Bärlocher F (2007) Molecular approaches applied to aquatic hyphomycetes. Fungal Biol Rev 21:19–24 Benyahya L, Caissie D, St-Hilaire A et al (2007) A review of statistical water temperature models. Can Water Resour J 32:179–192 Caissie D (2006) The thermal regime of rivers: a review. Freshw Biol 51:1389–1406 Canning DJ, Randlette L, Haskins WA (1988) Skokomish River comprehensive flood control management plan. Washingt Dep Ecol Rep 87:24 Clauset A, Newman MEJ, Moore C (2004) Finding community structure in very large networks. Phys Rev E 70:66111 Delafrouz H, Ghaheri A, Ghorbani MA (2018) A novel hybrid neural network based on phase space reconstruction technique for daily river flow prediction. Soft Comput 22:2205–2215 Di C, Wang T, Istanbulluoglu E et al (2019) Deterministic chaotic dynamics in soil moisture across Nebraska. J Hydrol 578:124048 Dugdale SJ, Hannah DM, Malcolm IA (2017) River temperature modelling: a review of process-based approaches and future directions. Earth Sci Rev 175:97–113 Elshorbagy A, Simonovic SP, Panu US (2002a) Noise reduction in chaotic hydrologic time series: facts and doubts. J Hydrol 256:147–165 Elshorbagy A, Simonovic SP, Panu US (2002b) Estimation of missing streamflow data using principles of chaos theory. J Hydrol 255:123–133. https://doi.org/10.1016/S0022-1694(01)00513-3 Ferreira LN, Ferreira NCR, Macau EEN, Donner RV (2021) The effect of time series distance functions on functional climate networks. Eur Phys J Spec Top 230:2973–2998 Ferreira LN, Zhao L (2014) Detecting time series periodicity using complex networks. In: 2014 Brazilian Conference on intelligent systems. IEEE, pp 402–407 Fraser AM, Swinney HL (1986) Independent coordinates for strange attractors from mutual information. Phys Rev A 33:1134–1140. https://doi.org/10.1103/PhysRevA.33.1134 Galka A (2000) Topics in nonlinear time series analysis: with implications for EEG analysis. World Scientific Garcia S, Luengo J, Sáez JA et al (2012) A survey of discretization techniques: taxonomy and empirical analysis in supervised learning. IEEE Trans Knowl Data Eng 25:734–750 Ghorbani MA, Karimi V, Ruskeepää H et al (2021) Application of complex networks for monthly rainfall dynamics over central Vietnam. Stoch Environ Res Risk Assess 35:535–548. https://doi.org/10.1007/s00477-020-01962-2 Ghorbani MA, Kisi O, Aalinezhad M (2010) A probe into the chaotic nature of daily streamflow time series by correlation dimension and largest Lyapunov methods. Appl Math Model 34:4050–4057 Henry B, Lovell N, Camacho F (2001) Nonlinear dynamics time series analysis. Nonlinear Biomed signal Process Dyn Anal Model 2:1–39 Jackson FL, Malcolm IA, Hannah DM (2016) A novel approach for designing large-scale river temperature monitoring networks. Hydrol Res 47:569–590 Jayawardena AW, Gurung AB (2000) Noise reduction and prediction of hydrometeorological time series: dynamical systems approach vs. stochastic approach. J Hydrol 228:242–264 Jayawardena AW, Lai F (1994) Analysis and prediction of chaos in rainfall and stream flow time series. J Hydrol 153:23–52 Kantz H (1994) A robust method to estimate the maximal Lyapunov exponent of a time series. Phys Lett A 185:77–87 Kantz H, Schreiber T (2004) Nonlinear time series analysis. Cambridge university press Karvonen A, Rintamäki P, Jokela J, Valtonen ET (2010) Increasing water temperature and disease risks in aquatic systems: climate change increases the risk of some, but not all, diseases. Int J Parasitol 40:1483–1488 Kennel MB, Abarbanel HDI (2002) False neighbors and false strands: a reliable minimum embedding dimension algorithm. Phys Rev E 66:26209 Kennel MB, Brown R, Abarbanel HDI (1992) Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 45:3403–3411. https://doi.org/10.1103/PhysRevA.45.3403 Khatibi R, Ghorbani MA, Aalami MT et al (2011) Dynamics of hourly sea level at Hillarys Boat Harbour, Western Australia: A chaos theory perspective. In: Ocean Dynamics. pp 1797–1807 Khatibi R, Sivakumar B, Ghorbani MA et al (2012) Investigating chaos in river stage and discharge time series. J Hydrol 414–415:108–117. https://doi.org/10.1016/j.jhydrol.2011.10.026 Kim S, Noh H, Kang N et al (2014) Noise reduction analysis of radar rainfall using chaotic dynamics and filtering techniques Lee M, Kim HS, Kwak J et al (2021) Chaotic features of decomposed Time Series from Tidal River Water Level. Appl Sci 12:199 Li J, Kong K, Cui C, Zhang Z (2020) Rainfall Data Reconstruction Based on Chaotic Characteristics of Meteorological Factors. In: IOP Conference Series: Earth and Environmental Science. IOP Publishing, p 12027 Markarian RK (1980) A study of the relationship between aquatic insect growth and water temperature in a small stream. Hydrobiologia 75:81–95 Marwan N, Donges JF, Zou Y et al (2009) Complex network approach for recurrence analysis of time series. Phys Lett A 373:4246–4254 Ng WW, Panu US, Lennox WC (2007) Chaos based Analytical techniques for daily extreme hydrological observations. J Hydrol 342:17–41. https://doi.org/10.1016/j.jhydrol.2007.04.023 Patra RW, Chapman JC, Lim RP et al (2015) Interactions between water temperature and contaminant toxicity to freshwater fish. Environ Toxicol Chem 34:1809–1817 Porporato A, Ridolfi L (1997) Nonlinear analysis of river flow time sequences. Water Resour Res 33:1353–1367. https://doi.org/10.1029/96WR03535 Ren K, Huang Q, Huang S et al (2021) Identifying complex networks and operating scenarios for cascade water reservoirs for mitigating drought and flood impacts. J Hydrol 594:125946 Ruskeepää H (2014) Analysis of chaotic data with Mathematica. https://library.wolfram.com/infocenter/ID/8775/ Shang P, Na X, Kamae S (2009) Chaotic analysis of time series in the sediment transport phenomenon. Chaos Solitons Fractals 41:368–379 Silva TC, Zhao L (2016) Machine learning in Complex Networks. Springer International Publishing Sitzenfrei R, Wang Q, Kapelan Z, Savić D (2020) Using Complex Network Analysis for optimization of water distribution networks. Water Resour Res 56. https://doi.org/10.1029/2020WR027929. :e2020WR027929 Sivakumar B (2016) Chaos in Hydrology: bridging determinism and stochasticity. Springer Netherlands Sivakumar B (2009) Nonlinear dynamics and chaos in hydrologic systems: latest developments and a look forward. Stoch Environ Res Risk Assess 23:1027–1036. https://doi.org/10.1007/s00477-008-0265-z Sivakumar B, Jayawardena AW, Li WK (2007) Hydrologic complexity and classification: a simple data reconstruction approach. Hydrol Process 21:2713–2728. https://doi.org/10.1002/hyp.6362 Sivakumar B, Persson M, Berndtsson R, Uvo CB (2002) Is correlation dimension a reliable indicator of low-dimensional chaos in short hydrological time series? Water Resour Res 38:3–8. https://doi.org/10.1029/2001WR000333 Smith K (1975) WATER TEMPERATURE VARIATIONS WITHIN A MAJOR RIVER SYSTEM. Hydrol Res 6:155–169. https://doi.org/10.2166/nh.1975.0011 Sprott JC, Sprott JC (2003) Chaos and time-series analysis. Oxford university press Oxford Stover SC, Montgomery DR (2001) Channel change and flooding, skokomish river, Washington. J Hydrol 243:272–286 Takens F (1981) Detecting strange attractors in turbulence. In: Rand D, Young L-S (eds) Dynamical Systems and Turbulence, Warwick 1980: Proceedings of a Symposium Held at the University of Warwick 1979/80. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 366–381 Tao H, Sulaiman SO, Yaseen ZM et al (2018) What is the potential of integrating Phase Space Reconstruction with SVM-FFA Data-Intelligence Model? Application of Rainfall forecasting over Regional Scale. Water Resour Manag 32:3935–3959. https://doi.org/10.1007/s11269-018-2028-z USGS (2020) National Water Information System: Web Interface: U.S. Geological Survey database. https://waterdata.usgs.gov/wa/nwis/uv?site_no=12056500 Vaheddoost B, Kocak K (2019) Temporal dynamics of monthly evaporation in Lake Urmia. Theor Appl Climatol 137:2451–2462. https://doi.org/10.1007/s00704-018-2747-3 Vega-Oliveros DA, Cotacallapa M, Ferreira LN et al (2019) From spatio-temporal data to chronological networks: An application to wildfire analysis. In: Proceedings of the 34th ACM/SIGAPP Symposium on Applied Computing. pp 675–682 Vignesh R, Jothiprakash V, Sivakumar B (2015) Streamflow variability and classification using false nearest neighbor method. J Hydrol 531:706–715. https://doi.org/10.1016/j.jhydrol.2015.10.056 Wang M, Tian L (2016) From time series to complex networks: the phase space coarse graining. Phys A Stat Mech its Appl 461:456–468. https://doi.org/10.1016/j.physa.2016.06.028 Wang S, Huang GH, Baetz BW, Ancell BC (2017) Towards robust quantification and reduction of uncertainty in hydrologic predictions: integration of particle Markov chain Monte Carlo and factorial polynomial chaos expansion. J Hydrol 548:484–497. https://doi.org/10.1016/j.jhydrol.2017.03.027 Webb BW, Nobilis F (2007) Long-term changes in river temperature and the influence of climatic and hydrological factors. Hydrol Sci J 52:74–85. https://doi.org/10.1623/hysj.52.1.74 Wichert GA, Lin P (1996) A Species Tolerance Index for Maximum Water temperature. Water Qual Res J 31:875–893. https://doi.org/10.2166/wqrj.1996.048