Modeling geophysical complexity: A case for geometric determinism

Hydrology and Earth System Sciences

Volumn 11, Issue 2, 2007, Pages 721-724

  Puente, C E ^a   Sivakumar, B ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b GRIFFITH UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEXITY; DATA SET; FRACTAL ANALYSIS; GEOMETRY; GEOPHYSICS; HYDROLOGY; NUMERICAL MODEL; STOCHASTICITY;

EID: 33846371109     PISSN: 10275606     EISSN: 16077938     Source Type: Journal    
DOI: 10.5194/hess-11-721-2007     Document Type: Article

References (28)

1. Barnsley, M. F.: Fractals Everywhere, Academic Press, San Diego, USA, 1988.
2. Lovejoy, S. and Schertzer, D.: Multifracials, universality classes and satellite and radar measurements of cloud and rain fields, J. Geophys. Res. 95, 2021-2034, 1990.
3. Maragos, P.: Pattern spectrum and multiscale shape representation, IEEE Trans. Pattern Anal. Machine Intell., 11(7), 701-716, 1989.
4. Meneveau, C. and Sreenivasan, K. R.: Simple multifractal cascade model for fully developed turbulence, Phys. Rev. Lett., 59, 1424-1427, 1987.
5. Obregón, N., Sivakumar, B., and Puente, C. E.: A deterministic geometric representation of temporal rainfall: sensitivity analysis for a storm in Boston, J. Hydrol., 269(3-4), 224-235, 2002.
6. Osborne, A. R. and Provenzale, A.: Finite correlation dimension for stochastic systems with power-law spectra, Physica D, 35, 357-381, 1989.
7. Packard, N. H., Crutchfield, J. P., Farmer, J. D., and Shaw, R. S.: Geometry from a time series, Phys. Rev. Lett., 45(9), 712-716, 1980.
8. Puente, C. E.: Multinomial multifractals, fractal interpolators, and the Gaussian distribution, Phys. Lett. A, 161, 441-447, 1992.
9. Puente, C. E.: Deterministic fractal geometry and probability, Int. J. Bifurcations Chaos, 4(6), 1613-1629, 1994a.
10. Puente, C. E.: A fractal-multifractal approach to geostatistics. In Geostatistics for the Next Century, R. Dimitrakopoulos (Editor), Kluwer Academic Publishers, Dordrecht, 476-487, 1994b.
11. Puente, C. E.: A universe of projections: may Plato be right?, Chaos, Soliton. Fract., 19(2), 241-253, 2004.
12. Puente, C. E. and Obregón, N.: A deterministic geometric representation of temporal rainfall: Results for a storm in Boston, Water Resour. Res., 32(9), 2825-2839, 1996.
13. Puente, C. E. and N. Obregón: A geometric Platonic approach to multifractality and turbulence, Fractals, 7(4), 403-420, 1999.
14. Puente, C. E., Obregón., N., and Sivakumar, B.: Chaos and stochasticity in determinastically generated multifractal measures, Fractals, 10(1), 91-102, 2002.
15. Puente, C. E., Robayo, O., Diaz, M. C., and Sivakumar, B.: A fractal-multifractal approach to groundwater contamination. 1. Modeling conservative tracers at the Borden site, Stoch. Env. Res. Risk Asses., 15(5), 357-371, 2001a.
16. Puente, C. E., Robayo, O., and Sivakumar, B.: Afractal-multifractal approach to groundwater contamination. 2. Predicting conservative tracers at the Borden site, Stoch. Env. Res. Risk Asses., 15(5), 372-383, 2001b.
17. Puente, C. E. and Sivakumar, B.: A deterministic width function model- Nonlinear Proc. Geophys., 10(6), 525-529, 2003.
18. Rodriguez-Iturbe, I., De Power, F. B., Sharifi, M. B., and Georgakakos, K. P.: Chaos in rainfall, Water Resour. Res., 25(7), 1667-1675, 1989.
19. Schertzer, D., Tchiguirinskaia, I., Lovejoy, S., Hubert, P., Bendjoudi, H., and Larcheveque, M.: Which chaos in the rainfall-runoff process? Discussion of "Evidence of chaos in the rainfall-runoff process?", Hydrol. Sci. J., 47(1), 139-147, 2002.
20. Sivakumar, B.: Chaos theory in hydrology: important issues and interpretations. J. Hydrol., 227(1-4), 1-20, 2000.
21. Sivakumar, B.: Chaos theory in geophysics: Past, present and future, Chaos Soliton. Fract., 19(2), 441-462, 2004.
22. Sivakumar, B., Sorooshian, S., Gupta, H. V., and Gao, X.: A chaotic approach to rainfall disaggregation, Water Resour. Res., 37(1), 61-72, 2001.
23. Sivakumar, B., Berndtsson, R., Olsson, J., Jinno, K.: Reply to "Which chaos in the rainfall-runoff process?", Hydrol. Sci. J., 47(1), 149-158, 2002a.
24. Sivakumar, B., Persson, M., Berndtsson, R., and Uvo, C. B.: Is correlation dimension a reliable indicator of low-dimensional chaos in short hydrological time series?, Water Resour. Res., 38(2), 1011, doi:10.1029/ 2001WR000333, 2002b.
25. Takens, F.: Detecting strange attractors in turbulence, in: Dynamical Systems and Turbulence, edited by: Rand, D. A. and Young, L. S., Lecture Notes in Mathematics 898, Springer-Verlag, Berlin, Germany, 366-381, 1981.
26. Tsonis, A. A., Elsner, J. B., and Georgakakos, K. P.: Estimating the dimension of weather and climate attractors: important issues about the procedure and interpretation, J. Atmos. Sci., 50, 2549-2555, 1993.
27. Veneziano, D., Moglen, G. E., Furcolo, P., and Iacobellis, V.: Stochastic model of the width function, Water Resour. Res., 36(4), 1143-1158, 2000.
28. Wainwright, J. and Mulligan, M. (Eds.): Environmental Modeling - Finding Simplicity in Complexity, John Wiley & Sons, United Kingdom, 2004.