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Singular spectrum analysis and Fisher–Shannon analysis of spring flow time series: An application to Anjar Spring, Lebanon

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  • Telesca, Luciano
  • Lovallo, Michele
  • Shaban, Amin
  • Darwich, Talal
  • Amacha, Nabil

Abstract

In this study, the time dynamics of water flow from Anjar Spring was investigated, which is one of the major issuing springs in the central part of Lebanon. Likewise, many water sources in Lebanon, this spring has no continuous records for the discharge, and this would prevent the application of standard time series analysis tools. Furthermore, the highly nonstationary character of the series implies that suited methodologies can be employed to get insight into its dynamical features. Therefore, the Singular Spectrum Analysis (SSA) and Fisher–Shannon (FS) method, which are useful methods to disclose dynamical features in noisy nonstationary time series with gaps, are jointly applied to analyze the Anjar Spring water flow series. The SSA revealed that the series can be considered as the superposition of meteo-climatic periodic components, low-frequency trend and noise-like high-frequency fluctuations. The FS method allowed to extract and to identify among all the SSA reconstructed components the long-term trend of the series. The long-term trend is characterized by higher Fisher Information Measure (FIM) and lower Shannon entropy, and thus, represents the main informative component of the whole series. Generally water discharge time series presents very complex time structure, therefore the joint application of the SSA and the FS method would be very useful in disclosing the main informative part of such kind of data series in the view of existing climatic variability and/or anthropogenic challenges.

Suggested Citation

  • Telesca, Luciano & Lovallo, Michele & Shaban, Amin & Darwich, Talal & Amacha, Nabil, 2013. "Singular spectrum analysis and Fisher–Shannon analysis of spring flow time series: An application to Anjar Spring, Lebanon," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3789-3797.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:17:p:3789-3797
    DOI: 10.1016/j.physa.2013.04.021
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    References listed on IDEAS

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    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
    2. Telesca, Luciano & Lovallo, Michele & Hsu, Han-Lun & Chen, Chien-Chih, 2011. "Analysis of dynamics in magnetotelluric data by using the Fisher–Shannon method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(7), pages 1350-1355.
    3. Martin, M.T. & Perez, J. & Plastino, A., 2001. "Fisher information and nonlinear dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 291(1), pages 523-532.
    4. Telesca, Luciano & Lovallo, Michele & Ramirez-Rojas, Alejandro & Angulo-Brown, Fernando, 2009. "A nonlinear strategy to reveal seismic precursory signatures in earthquake-related self-potential signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(10), pages 2036-2040.
    5. Hassani, Hossein, 2007. "Singular Spectrum Analysis: Methodology and Comparison," MPRA Paper 4991, University Library of Munich, Germany.
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    1. Lai, Lin & Guo, Kun, 2017. "The performance of one belt and one road exchange rate: Based on improved singular spectrum analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 299-308.

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