DISCUSSION of “Evidence of chaos in the rainfall-runoff process” Which chaos in the rainfall-runoff process?;Quel chaos dans le processus pluie-débit?

Hydrological Sciences Journal

Volumn 47, Issue 1, 2002, Pages 139-148

  Schertzer, Daniel ^a,b   Tchiguirinskaia, Ioulia ^c   Lovejoy, Shaun ^d   Hubert, Pierre ^e   Bendjoudi, Hocine ^c   LarchevÊque, Michele ^a  

^a SORBONNE UNIVERSITÉ   (France)

^b MÉTÉO FRANCE   (France)

^c UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^d MCGILL UNIVERSITY   (Canada)

^e PSL RESEARCH UNIVERSITY   (France)

Author keywords

(multi ) fractals; Chaotic dynamics; Correlation dimension; Nonlinear analysis; Rainfall runoff models; Stochastic processes; Time series analysis

Indexed keywords

EID: 84998728905     PISSN: 02626667     EISSN: 21503435     Source Type: Journal    
DOI: 10.1080/02626660209492913     Document Type: Article

References (28)

1. Essex, C., 1991. “ Correlation dimension and data sample size. ”. In Non-Linear Variability in Geophysics, Scaling and Fractals Edited by:Schertzer, D., and Lovejoy, S., Dordrecht, The Netherlands:Kluwer.
2. Grassberger, P., 1983. Generalized dimensions of strange attractors. Phys. Rev. Lett. A, 97:227
3. Grassberger, P., 1986. Are there really climate attractors?. Nature, 322:609–612.
4. Grassberger, P, and Procaccia, I., 1983. Characterization of strange attractors. Phys. Rev. Lett., 50 (5):346–349.
5. Hubert, P., Tessier, Y., Ladoy, Ph., Lovejoy, S., Schertzer, D., Carbonnel, J. P., Violette, S., Desurosne, I., and Schmitt, F., 1993. Multifractals and extreme rainfall events. Geophys. Res. Lett., 20 (10):931–934.
6. Kahane, J. P., 1995. “ Definition of stable laws, infinitely divisible laws, and Lévy processes. ”. In Lévy Flights and Related Phenomena in Physics Edited by:Shlesinger, M., Zaslavsky, G., and Frisch, U., 99–109. Berlin, Germany:Springer-Verlag.
7. Lovejoy, S., and Schertzer, D., 1995. “ Multifractals and rain. ”. In New Uncertainty Concepts in Hydrology and Water Resources Edited by:Kundzewicz, Z. W., 62–103. Cambridge, UK:Cambridge University Press.
8. Lovejoy, S., and Schertzer, D., 1998. “ Stochastic chaos, scale invariance, multifractals and our turbulent atmosphere. ”. In ECO-TEC:Architecture of the In-between, Storefront Book Series Edited by:Marras, A., 80–99. Princeton, USA:copublished with Princeton Architectural Press.
9. Lorenz, E. N., 1963. Deterministic nonperiodic flow. J. Atmos. Sci., 20:130–141.
10. Nerenberg, M. A.H., and Essex, C., 1990. Correlation dimension and systematic geometric effects. Phys. Rev. Lett., A42 (12):7065–7074.
11. Nicolis, C., and Nicolis, G., 1984. Is there a climate attractor?. Nature, 311:529–533.
12. Osborne, A. R., and Provenzale, A., 1989. Finite correlation dimension for stochastic systems with power-law spectra. Physica D, 35:357–381.
13. Packard, N. H., Crutchfield, J. P., Farmer, J. D., and Shaw, R. S., 1980. Geometry from a time series. Phys. Rev. Lett., 45 (9):712–716.
14. Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1986. Numerical Recipes, The Art of Scientific Computing. Cambridge, UK:Cambridge University Press.
15. Ruelle, D., 1989. Chaotic Evolution and Strange Attractors. Cambridge, UK:Cambridge University Press.
16. Sauer, T., Yorke, J., and Casdagli, M., 1991. Embedology. J. Statist. Phys., 65:579
17. Schertzer, D., and Lovejoy, S., eds. 1991. Non-Linear Variability in Geophysics, Scaling and Fractals. Dordrecht, The Netherlands:Kluwer.
18. Schertzer, D., Lovejoy, S., Schmitt, F., Chigirinskaya, Y., and Marsan, D., 1997. Multifractal cascade dynamics and turbulent intermittency. Fractals, 5 (3):427–471.
19. Schertzer, D., Larchevěque, M., Duan, J., Yanovsky, V. V., and Lovejoy, S., 2001. Fractional Fokker-Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises. J. Math. Phys., 41:12
20. Sivakumar, B., 2000. Chaos theory in hydrology:important issues and interpretations. J. Hydrol., 227 (1, E4):1–20.
21. Sivakumar, B., Liong, S. Y., Liaw, C. Y., and Phoon, K. K., 1999a. Singapore rainfall behaviour:chaotic?. J. Hydrol. Engng ASCE, 4 (1):38–48.
22. Sivakumar, B., Phoon, K. K., Liong, S. Y., and Liaw, C. Y., 1999b. A systematic approach to noise reduction in chaotic hydrological time series. J. Hydrol., 219 (3/4):103–135.
23. Sivakumar, B., Berndtsson, R., Olsson, J., and Jinno, K., 2001. Evidence of chaos in the rainfall-runoff process. Hydrol. Sci. J., 46 (1):131–146.
24. Takens, F., 1980. “ Detecting strange attractors in turbulence. ”. In Dynamical Systems and Turbulence. Lecture Notes in Mathematics 898 Edited by:Rand, D. A., and Young, L. S., 366–381. Berlin, Germany:Springer-Verlag.
25. Theiler, J., 1986. Spurious dimensions from correlation algorithms applied to a limited time-series data. Phys. Rev. Lett. A, 34:2427
26. Theiler, J., 1991. Some comments on the correlation dimension of a 1/f-alpha noise. Phys. Rev. Lett. A, 155:480
27. Van Kampen, N. G., 1981. Stochastic Processes in Physics and Chemistry. Amsterdam, The Netherlands:North-Holland Physics Publishing.
28. Wiener, N., 1938. The homogeneous chaos. Am. J. Math, 60:887–936.