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Investigating the time dynamics of monthly rainfall time series observed in northern Lebanon by means of the detrended fluctuation analysis and the Fisher-Shannon method

Abstract

We investigate the time dynamics of monthly rainfall series intermittently recorded on seven climatic stations in northern Lebanon from 1939 to 2010 using the detrending fluctuation analysis (DFA) and the Fisher-Shannon (FS) method. The DFA is employed to study the scaling properties of the series, while the FS method to analyze their order/organization structure. The obtained results indicate that most all the stations show a significant persistent behavior, suggesting that the dynamics of the rainfall series is governed by positive feedback mechanisms. Furthermore, we found that the Fisher Information Measure (the Shannon entropy power) seems to decrease (increase) with the height of the rain gauge; this indicates that the rainfall series appear less organized and less regular for higher-located stations. Such findings could be useful for a better comprehension of the climatic regimes governing northern Lebanon.

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References

  1. Angulo, J.C., J. Antolín, and K.D. Sen (2008), Fisher-Shannon plane and statistical complexity of atoms, Phys. Lett. A 372,5, 670–674, DOI: 10.1016/j.physleta.2007.07.077.

    Article  Google Scholar 

  2. Chen, Z., P.Ch. Ivanov, K. Hu, and H.E. Stanley (2002), Effect of nonstationarities on detrended fluctuation analysis, Phys. Rev. E 65,4, 041107, DOI: 10.1103/PhysRevE.65.041107.

    Article  Google Scholar 

  3. Devroye, L.A. (1987), Course in Density Estimation, Birkhäuser, Boston.

    Google Scholar 

  4. Esquivel, R.O., J.C. Angulo, J. Antolín, J.S. Dehesa, S. López-Rosa, and N. Flores-Gallegos (2010), Analysis of complexity measures and information planes of selected molecules in position and momentum spaces, Phys. Chem. Chem. Phys. 12,26, 7108–7116, DOI: 10.1039/B927055H.

    Article  Google Scholar 

  5. Fisher, R.A. (1925), Theory of statistical estimation, Math. Proc. Cambridge Philos. Soc. 22,5, 700–725, DOI: 10.1017/S0305004100009580.

    Article  Google Scholar 

  6. Fraedrich, K., and C. Larnder (1993), Scaling regimes of composite rainfall time series, Tellus A 45,4, 289–298, DOI: 10.1034/j.1600-0870.1993.t01-3-00004.x.

    Article  Google Scholar 

  7. Frieden, B.R. (1990), Fisher information, disorder, and the equilibrium distributions of physics, Phys. Rev. A 41,8, 4265–4276, DOI: 10.1103/PhysRevA.41.4265.

    Article  Google Scholar 

  8. García-Marín, A.P., F.J. Jiménez-Hornero, and J.L. Ayuso-Muñoz (2008), Universal multifractal description of an hourly rainfall time series from a location in southern Spain, Atmósfera 21,4, 347–355.

    Google Scholar 

  9. Gysi, H. (1998), Orographic influence on the distribution of accumulated rainfall with different wind directions, Atmos. Res. 47-48, 615–633, DOI: 10.1016/S0169-8095(97)00089-6.

    Article  Google Scholar 

  10. Havlin, S., S.V. Buldyrev, A. Bunde, A.L. Goldberger, P.Ch. Ivanov, C.-K. Peng, and H.E. Stanley (1999), Scaling in nature: from DNA through heartbeats to weather, Physica A 273,1–2, 46–69, DOI: 10.1016/S0378-4371(99)00340-4.

    Article  Google Scholar 

  11. Hu, K., P.Ch. Ivanov, Z. Chen, P. Carpena, and H.E. Stanley (2001), Effect of trends on detrended fluctuation analysis, Phys. Rev. E 64,1, 011114, DOI: 10.1103/PhysRevE.64.011114.

    Article  Google Scholar 

  12. Janicki, A., and A. Weron (1994), Simulation and Chaotic Behavior of α-stable Stochastic Processes, Marcel Dekker, New York.

    Google Scholar 

  13. Lovallo, M., and L. Telesca (2011), Complexity measures and information planes of x-ray astrophysical sources, J. Stat. Mech. March 2011, P03029, DOI: 10.1088/1742-5468/2011/03/P03029.

    Google Scholar 

  14. Martin, M.T., F. Pennini, and A. Plastino (1999), Fisher’s information and the analysis of complex signals, Phys. Lett. A 256,2–3, 173–180, DOI: 10.1016/S0375-9601(99)00211-X.

    Article  Google Scholar 

  15. Martin, M.T., J. Perez, and A. Plastino (2001), Fisher information and nonlinear dynamics, Physica A 291,1–4, 523–532, DOI: 10.1016/S0378-4371(00)00531-8.

    Article  Google Scholar 

  16. Peng, C.-K., S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, and A.L. Goldberger (1994), Mosaic organization of DNA nucleotides, Phys. Rev. E 49,2, 1685–1689, DOI: 10.1103/PhysRevE.49.1685.

    Article  Google Scholar 

  17. Raykar, V.C., and R. Duraiswami (2006), Fast optimal bandwidth selection for kernel density estimation. In: J. Ghosh, D. Lambert, D. Skillicorn, and J. Srivastava (eds.), Proc. 6th SIAM Int. Conf. on Data Mining, April 2006, Bethesda, USA, 524–528.

    Google Scholar 

  18. Romera, E., and J.S. Dehesa (2004), The Fisher-Shannon information plane, an electron correlation tool, J. Chem. Phys. 120,19, 8906–8912, DOI: 10.1063/1.1697374.

    Article  Google Scholar 

  19. Shaban, A. (2009), Indicators and aspects of hydrological drought in Lebanon, Water Resour. Manag. 23,10, 1875–1891, DOI: 10.1007/s11269-008-9358-1.

    Article  Google Scholar 

  20. Shaban, A. (2011), Analyzing climatic and hydrologic trends in Lebanon, J. Environ. Sci. Eng. 5,483-492.

    Google Scholar 

  21. Shannon, C.E. (1948), A mathematical theory of communication, Bell Syst. Tech. J. 27,379–423, 623–656.

    Article  Google Scholar 

  22. Svensson, C., J. Olsson, and R. Berndtsson (1996), Multifractal properties of daily rainfall in two different climates, Water Resour. Res. 32,8, 2463–2472, DOI: 10.1029/96WR01099.

    Article  Google Scholar 

  23. Telesca, L. (2007), Cycles, scaling and crossover phenomenon in length of the day (LOD) time series, Physica A 379,2, 459–464, DOI: 10.1016/j.physa.2007.02.064.

    Article  Google Scholar 

  24. Telesca, L., and K. Hattori (2007), Non-uniform scaling behavior in ultra-lowfrequency (ULF) earthquake-related geomagnetic signals, Physica A 384,2, 522–528, DOI: 10.1016/j.physa.2007.05.040.

    Article  Google Scholar 

  25. Telesca, L., and M. Lovallo (2009), Non-uniform scaling features in central Italy seismicity: A non-linear approach in investigating seismic patterns and detection of possible earthquake precursors, Geophys. Res. Lett. 36,1, L01308, DOI: 10.1029/2008GL036247.

    Article  Google Scholar 

  26. Telesca, L., and M. Lovallo (2011), Analysis of the time dynamics in wind records by means of multifractal detrended fluctuation analysis and the Fisher-Shannon information plane, J. Stat. Mech. P07001, DOI: 10.1088/1742-5468/2011/07/P07001.

    Google Scholar 

  27. Telesca, L., M. Lovallo, A. Ramirez-Rojas, and F. Angulo-Brown (2009), A nonlinear strategy to reveal seismic precursory signatures in earthquake-related self-potential signals, Physica A 388,10, 2036–2040, DOI: 10.1016/j.physa.2009.01.035.

    Article  Google Scholar 

  28. Telesca, L., M. Lovallo, and R. Carniel (2010), Time-dependent Fisher Information Measure of volcanic tremor before 5 April 2003 paroxysm at Stromboli volcano, Italy, J. Volcanol. Geoterm. Res. 195,1, 78–82, DOI: 10.1016/j.jvolgeores.2010.06.010.

    Article  Google Scholar 

  29. Telesca, L., M. Lovallo, H.-L. Hsu, and C.-C. Chen (2011), Analysis of dynamics in magnetotelluric data by using the Fisher-Shannon method, Physica A 390,7, 1350–1355, DOI: 10.1016/j.physa.2010.12.005.

    Article  Google Scholar 

  30. Troudi, M., A.M. Alimi, and S. Saoudi (2008), Analytical plug-in method for kernel density estimator applied to genetic neutrality study, EURASIP J. Adv. Sig. Process., Article ID739082, DOI: 10.1155/2008/739082.

    Google Scholar 

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Correspondence to Luciano Telesca.

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Lovallo, M., Shaban, A., Darwich, T. et al. Investigating the time dynamics of monthly rainfall time series observed in northern Lebanon by means of the detrended fluctuation analysis and the Fisher-Shannon method. Acta Geophys. 61, 1538–1555 (2013). https://doi.org/10.2478/s11600-012-0094-9

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Key words

  • detrended fluctuation analysis
  • Fisher-Shannon method
  • rainfall
  • Lebanon
  • climate