Temporal complexity of daily precipitation records from different atmospheric environments: Chaotic and Lévy stable parameters

Atmospheric Research

Volumn 101, Issue 4, 2011, Pages 879-892

  Millan H ^a   Rodriguez J ^a   Ghanbarian Alavijeh, B ^b   Biondi, R ^c   Llerena, G ^d  

^a University of Granma   (Cuba)

^b UNIVERSITY OF TEHRAN   (Iran)

^c UNIVERSITY OF PERUGIA   (Italy)

^d UNIVERSIDAD ESTATAL AMAZÓNICA   (Ecuador)

Author keywords

Chaos methods; Meteorology; Rainfall; Stable distributions

Indexed keywords

ATMOSPHERIC ENVIRONMENT; CHAOS METHOD; CHAOTIC BEHAVIORS; CHAOTIC STRUCTURE; DAILY RAINFALL; LYAPUNOV EXPONENT; RAINFALL DATA; RAINFALL DYNAMICS; RAINFALL EVENT; SCALE-FREE BEHAVIOR; SPATIAL SCALE; STABILITY INDICES; STABLE DISTRIBUTIONS; STATISTICAL RELATIONSHIP; SUB-GAUSSIANS;

CHAOS THEORY; DIFFERENTIAL EQUATIONS; LYAPUNOV FUNCTIONS; RAIN; TIME SERIES;

LYAPUNOV METHODS;

CHAOS THEORY; METEOROLOGY; NUMERICAL MODEL; PRECIPITATION ASSESSMENT; RAINFALL; SPATIAL ANALYSIS; TEMPORAL ANALYSIS; TIME SERIES ANALYSIS;

EID: 79960911334     PISSN: 01698095     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.atmosres.2011.05.021     Document Type: Article

References (58)

1. Bordi I., Sutera A. Fifty years of precipitation: some spatially remote teleconnections. Water Resour. Manage. 2001, 15:247-280.
2. Bordi I., Sutera A. Drought variability and its climatic implications. Glob. Planet. Chang. 2004, 40:115-127.
3. Bunde A., Havlin S., Koscielny-Bunde E., Schellnhuber H.-J. Long term persistence in the atmosphere: global laws and tests of climate models. Physica A 2001, 302:255-267.
4. Chaudhuri S. Predictability of chaos inherent in the occurrence of severe thunderstorms. Adv. Complex Syst. 2006, 9:77-85.
5. D'Amato N., Lebel T. On the characteristics of the rainfall events in the Sahel with a view to the analysis of climatic variability. Int. J. Climatol. 1998, 18:955-974.
6. Ditlevsen P.D. Observation of α-stable noise induced millennial climate changes from an ice-core record. Geophys. Res. Lett. 1999, 26(10):1441-1444.
7. Feller W. An Introduction to Probability Theory and Its Applications. Vol. II 1971, Wiley, New York, N.Y. 2nd ed.
8. Hayes M. Revisiting the SPI: Clarifying the process. Drought Network News (1994-2001) 2000, Vol. 12:12-14. National Drought Mitigation Center, University of Nebraska, NE.
9. Hegger R., Kantz H., Schreiber T. Practical implementation of nonlinear time series methods: the TISEAN package. Chaos 1999, 9:413-440.
10. Hense A. On the possible existence of a strange attractor for the southern oscillation. Beitr. Phys. Atmos. 1987, 60:34-47.
11. Iqbal M.J. Study of fractal properties of climatic time series from Pakistan. J. Math. 2010, 42:17-24.
12. Jayawardena A.W., Lai F. Analysis and prediction of chaos in rainfall and stream flow time series. J. Hydrol. 1994, 153:23-52.
13. Kantz H., Schreiber T. Nonlinear Time Series Analysis 2003, Cambridge University Press, Cambridge, UK.
14. Kantz H., Holstein D., Ragwitz M., Vitanov N.K. Extreme events in surface winds: predicting turbulent gusts. Experimental Chaos: 8th Experimental Chaos Conference 2004, 315-324. American Institute of Physics. S. Boccaletti (Ed.).
15. Kaplan D.T., Glass L. Direct test for determinism in a time series. Phys. Rev. Lett. 1992, 68:427-430.
16. Kaplan J., Yorke J. Chaotic behavior of multidimensional difference equations. Functional Differential Equations and Approximation of Fixed Points 1987, Springer, New York, NY. H.O. Peitgen, H.O. Walther (Eds.).
17. Kennel M.B., Brown R., Abarbanel H.D.I. Determining embedding dimension for phase space reconstruction using a geometrical construction. Phys. Rev. A. 1993, 45:3403-3411.
18. Klüpfel V., Kalthoff N., Gantner L., Kottmeier C. Evaluation of soil moisture ensemble runs to estimate precipitation variability in convection-permitting model simulations for West Africa. Atmos. Res. 2011, 10.1016/j.atmosres.2011.02.008.
19. Lovejoy S., Mandelbrot B.B. Fractal properties of rain, and a fractal model. Tellus 1985, 37A:209-232.
20. Lovejoy S., Schertzer D. Stochastic Chaos and Multifractal Geophysics. Chaos, Fractals and Models 1998, 96:38-52. Italian University Press. F.M. Guindani, G. Salvadori (Eds.).
21. Makarieva A.M., Gorshkov V.G., Li B.-L. Precipitation on land versus distance from the ocean: evidence for a forest pump of atmospheric moisture. Ecol. Comp. 2009, 6:302-307.
22. Mandelbrot B., Van Ness J.W. Fractional Brownian motion, fractional noises, and applications. SIAM Rev. 1968, 10:422-437.
23. Mandelbrot B., Wallis J.R. Noah, Joseph, and operational hydrology. Water Resour. Res. 1968, 4:909-918.
24. Marwan N., Trauth M.H., Vuille M., Kurths J. Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series methods. Clim. Dyn. 2003, 21:317-326.
25. McKee T.B., Doesken N.J., Kliest J. The relationship of drought frequency and duration to time scales. Proc. Eight Conference on Applied Climatology, Anaheim, CA 1993, 179-184. American Meteorological Society, Boston, MA.
26. Millán H., Kalauzi A., Llerena G., Sucoshañay J., Piedra D. Meteorological complexity in the Amazonian area of Ecuador: an approach based on dynamical system theory. Ecol. Comp. 2009, 6:278-285.
27. Millán H., Kalauzi A., Cukic M., Biondi R. Nonlinear dynamics of meteorological variables: multifractality and chaotic invariants in daily records from Pastaza, Ecuador. Theor. Appl. Climatol. 2010, 102:75-85.
28. Mishra A.K., Desai V.R. Drought forecasting using feed-forward recursive neural network. Ecol. Model. 2006, 198:127-138.
29. Molz F.J., Boman G. Further evidence of fractal structure in hydraulic conductivity distributions. Geophys. Res. Lett. 1995, 22:2545-2548.
30. Nagashima H., Baba H. Introduction to chaos. Physics and Mathematics of Chaotic Phenomena 1999, Institute of Physics Publishing, Ltd, Philadelphia.
31. Nolan J.P. Numerical computation of stable densities and distribution functions. Stoch. Model. 1997, 13:759-774.
32. Nolan J.P. Parameterizations and modes of stable distributions. Stat. Probl. Lett. 1998, 38:187-195.
33. Parlitz U. Identification of true and spurious Lyapunov exponents from time series. Int. J. Bifurcation Chaos 1992, 2:155.
34. Pathirana A., Hearth S., Musiake K. Scaling rainfall series with a multifractal model. Annu. J. Hydraul. Eng., JSCE 2001, 45:295-300.
35. Pathirana A., Hearth S., Yamada T. Estimating rainfall distributions at high temporal resolutions using a multifractal model. Hydrol. Earth Syst. Sci. 2003, 7:668-679.
36. Pelino V., Matera A., Colombo T., Giorgi F. Validation of precipitation events in a climate model simulation using methods from complex systems theory. Theor. Appl. Climatol. 2006, 84:213-218.
37. Perc M. User-friendly Programs for Nonlinear Time Series Analysis, Version 5 2005, available at. http://fizika.uni-mb.si/~matjaz/ejp/time.html.
38. Peters E.E. Fractal Market Analysis 1994, John Wiley and Sons, New York.
39. Peters O., Neelin J.D. Critical phenomena in atmospheric precipitation. Nat. Phys. 2006, 2:1-15. (preprint).
40. Peters O., Christopher H., Christensen K. A complexity view of rainfall. Phys. Rev. Lett. 2002, 88(1). 10.1103/PhysRevLett.88.018701.
41. Rodríguez-Iturbe I., De Power F.B., Sharifi M.B., Georgakakos K.P. Chaos in rainfall. Water Resour. Res. 1989, 25:1667-1675.
42. Rosenstein M.T., Collins J.J., De Luca C.J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 1993, 65:117-134.
43. Samorodnitsky G., Taqqu M.S. Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance 1994, Chapman and Hall, New York, NY.
44. Sano M., Sawada Y. Measurement of the Lyapunov spectrum from a chaotic time series. Phys. Rev. Lett. 1985, 55:1082.
45. Sarkar A., Barat P. Analysis of rainfall records in India: self-organized criticality and scaling. Fractals 2006, 14:1-5. (preprint).
46. Schertzer D., Lovejoy S. Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative process. J. Geophys. Res. 1987, 82:9693-9714.
47. Schertzer D., Tchiguirinskaia I., Hubert P., Bendjoudi H., Larcheveque M. Discussion of "Evidence of chaos in the rainfall-runoff process: which chaos in the rainfall-runoff process?". Hydrol. Sci. 2002, 47:139-148.
48. Shumway H., Stoffer D.S. Time Series Analysis and Its Applications 2006, Springer-Science, New York, NY.
49. Sivakumar B. Chaos theory in geophysics: past, present and future. Chaos, Solitons Fractals 2004, 19:441-462.
50. Sivakumar B., Berntsson R., Olsson J., Jinno K. Reply to "Which chaos in the rainfall-runoff process?". Hydrol. Sci. 2002, 47:149-158.
51. Sprot J.C. Maximally complex simple attractors. Chaos 2007, 17:033124.
52. Takemi T. Dependence of the precipitation intensity in mesoscale convective systems to temperature lapse rate. Atmos. Res. 2010, 96:273-285.
53. Takens F. Detecting Strange Attractors in Fluid Turbulence. Dynamical Systems and Turbulence, Lecture notes in Mathematics 1981, vol. 898:366-381. Springer-Verlag, Berlin.
54. Washington R. Quantifying chaos in the atmosphere. Prog. Phys. Geog. 2000, 24:499-514.
55. Yang Ch.-Y., Hsu K.-C.h., Chen K.-C.h. The use of the Levy-stable distribution for geophysical data analysis. Hydrogeol. J. 2009, 17:1265-1273.
56. Yano J.-I., Fraedrich K., Blender R. Tropical convective variability as 1/f noise. J. Clim. 2001, 14:3608-3616.
57. Zeng X., Pielke R.A. What does a low-dimensional weather attractor mean?. Phys. Lett. A. 1993, 175:299-304.
58. Zhou X., Persaud N., Wang H. Periodicities and scaling parameters of daily rainfall over semi-arid Botswana. Ecol. Model. 2005, 182:371-376.