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Fractals, Wavelets, and their Applications pp 479–490Cite as

Trend, Time Series, and Wavelet Analysis of River Water Dynamics

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 92))

Abstract

Time series, trend, wavelet and statistical analysis of water quality parameters Chemical Oxygen Demand (COD), Biochemical Oxygen Demand (BOD), Dissolved Oxygen (DO) monitored for river Yamuna in India have been studied. It is observed that COD is highly correlated with BOD. For all auto regressive integrated moving average model (p,d,q) value of “d,” i.e. middle value is zero thus process is stationary. It is also observed that RMSE values are comparatively very low, thus dependent series is closed with the model predicted level. MAPE, MaxAPE, MAE, MaxAE, Normalized BIC are calculated and have low value for all parameters. Trend is calculated by using auto correlation function, partial auto correlation function, and lag. Thus the predictive model is useful at 95 % confidence limits. 1-D discrete and continuous Daubechies Wavelet analysis explains that the parameters COD, BOD, DO have the maximum value 120, 50, 8 and amplitude (a5) varies between 52 to 78, 10 to 30, 0.2 to 1.4, respectively. The scale values of Db5, i.e. d5, d4, d3, d2, and d1 range between − 20 and + 20 for all parameters. All parameters cross the prescribed limits of WHO/EPA, thus water is not fit for drinking, agriculture, and industrial use.

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Acknowledgements

Authors are thankful to University Grant Commission (UGC), Government of India for financial support (F. 41-803/2012 (SR)); Central Pollution Control Board (CPCB), Government of India for providing the research data; Guru Gobind Singh Indraprastha University, Delhi (India) for providing research facilities. First author is thankful to Sant Baba Bhag Singh Institute of Engineering and Technology for providing study leave to pursue research degree.

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Authors and Affiliations

  1. Non-Linear Dynamics Lab, Department of Mathematics, University School of Basic and Applied Sciences Guru Gobind Singh Indraprastha University, New Delhi, 110078, India

    Kulwinder Singh Parmar & Rashmi Bhardwaj

Authors
  1. Kulwinder Singh Parmar
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  2. Rashmi Bhardwaj
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Correspondence to Rashmi Bhardwaj .

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Editors and Affiliations

  1. Institut für Mathematik und Informatik, Universität Greifswald, Greifswald, Mecklenburg-Vorpomm., Germany

    Christoph Bandt

  2. Mathematical Sciences Institute, Australian National University, Canberra, Australia

    Michael Barnsley

  3. Math Department, Boston University, Boston, Massachusetts, USA

    Robert Devaney

  4. Mathematical Institute, University of St Andrews, St Andrews, Fife, United Kingdom

    Kenneth J. Falconer

  5. Department of Mathematics and Statistics, University of Hyderabad, Hyderabad, India

    V. Kannan

  6. Department of Basic Sciences & Humanities, Rajagiri School of Engineering & Technology, Kerala, India

    Vinod Kumar P.B.

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Parmar, K.S., Bhardwaj, R. (2014). Trend, Time Series, and Wavelet Analysis of River Water Dynamics. In: Bandt, C., Barnsley, M., Devaney, R., Falconer, K., Kannan, V., Kumar P.B., V. (eds) Fractals, Wavelets, and their Applications. Springer Proceedings in Mathematics & Statistics, vol 92. Springer, Cham. https://doi.org/10.1007/978-3-319-08105-2_33

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