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Modeling Geophysical Complexity: a Case for Geometric Determinism : Volume 11, Issue 2 (17/01/2007)

By Puente, C. E.

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Book Id: WPLBN0004010253
Format Type: PDF Article :
File Size: Pages 4
Reproduction Date: 2015

Title: Modeling Geophysical Complexity: a Case for Geometric Determinism : Volume 11, Issue 2 (17/01/2007)  
Author: Puente, C. E.
Volume: Vol. 11, Issue 2
Language: English
Subject: Science, Hydrology, Earth
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2007
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Sivakumar, B., & Puente, C. E. (2007). Modeling Geophysical Complexity: a Case for Geometric Determinism : Volume 11, Issue 2 (17/01/2007). Retrieved from http://ebook.worldlibrary.net/


Description
Description: Department of Land, Air & Water Resources, University of California, Davis, USA. It has been customary in the last few decades to employ stochastic models to represent complex data sets encountered in geophysics, particularly in hydrology. This article reviews a deterministic geometric procedure to data modeling, one that represents whole data sets as derived distributions of simple multifractal measures via fractal functions. It is shown how such a procedure may lead to faithful holistic representations of existing geophysical data sets that, while complementing existing representations via stochastic methods, may also provide a compact language for geophysical complexity. The implications of these ideas, both scientific and philosophical, are stressed.

Summary
Modeling geophysical complexity: a case for geometric determinism

Excerpt
Barnsley, M. F.: Fractals Everywhere, Academic Press, San Diego, USA, 1988.; Maragos, P.: Pattern spectrum and multiscale shape representation, IEEE Trans. Pattern Anal. Machine Intell., 11(7), 701–716, 1989.; Lovejoy, S. and Schertzer, D.: Multifractals, universality classes and satellite and radar measurements of cloud and rain fields, J. Geophys. Res. 95, 2021–2034, 1990.; Meneveau, C. and Sreenivasan, K. R.: Simple multifractal cascade model for fully developed turbulence, Phys. Rev. Lett., 59, 1424–1427, 1987.; 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.; Osborne, A. R. and Provenzale, A.: Finite correlation dimension for stochastic systems with power-law spectra, Physica D, 35, 357–381, 1989.; 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.; Puente, C. E.: Multinomial multifractals, fractal interpolators, and the Gaussian distribution, Phys. Lett. A, 161, 441–447, 1992.; Puente, C. E.: Deterministic fractal geometry and probability, Int. J. Bifurcations Chaos, 4(6), 1613–1629, 1994a.; 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.; Puente, C. E.: A universe of projections: may Plato be right?, Chaos, Soliton. Fract., 19(2), 241–253, 2004.; 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.; Puente, C. E. and N. Obregón: A geometric Platonic approach to multifractality and turbulence, Fractals, 7(4), 403–420, 1999.; Puente, C. E., Obregón., N., and Sivakumar, B.: Chaos and stochasticity in deterministically generated multifractal measures, Fractals, 10(1), 91–102, 2002.; 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.; Puente, C. E., Robayo, O., and Sivakumar, B.: A fractal-multifractal approach to groundwater contamination. 2. Predicting conservative tracers at the Borden site, Stoch. Env. Res. Risk Asses., 15(5), 372–383, 2001b.; Puente, C. E. and Sivakumar, B.: A deterministic width function model- Nonlinear Proc. Geophys., 10(6), 525–529, 2003.; 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.; 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.; Sivakumar, B.: Chaos theory in hydrology: important issues and interpretations. J. Hydrol., 227(1–4), 1–20, 2000.; Sivakumar, B.: Chaos theory in geophysics: Past, present and future, Chaos Soliton. Fract., 19(2), 441–462, 2004.; Sivakumar, B., Sorooshian, S., Gupta, H. V., and Gao, X.: A chaotic approach to rainfall disaggregation, Water Resour. Res., 37(1), 61–72, 2001.; 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.; 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.; Takens, F.: Detecting strange attractors in turbulence, in: Dynamical

 

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