Statistics of multifractal processes using the maximum entropy method

Geophysical Research Letters

Volumn 38, Issue 17, 2011, Pages

  Nieves, V ^a   Wang, J ^a   Bras, R L ^b  

^a University of California at Irvine   (United States)

^b Georgia Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENTROPY; FRACTALS; INFERENCE ENGINES; WAVELET ANALYSIS;

DIFFERENT SCALE; GEOMETRIC MEAN; INFERENCE ALGORITHM; MAXIMUM ENTROPY METHODS; MAXIMUM ENTROPY PRINCIPLE; MULTIFRACTAL PROCESS; MULTISCALING; SCALING PROPERTIES;

PROBABILITY DISTRIBUTIONS;

ALGORITHM; MAXIMUM ENTROPY ANALYSIS; PROBABILITY; STATISTICAL ANALYSIS; TOPOGRAPHIC MAPPING; TOPOGRAPHY; WAVELET ANALYSIS;

EID: 80052770938     PISSN: 00948276     EISSN: None     Source Type: Journal    
DOI: 10.1029/2011GL048716     Document Type: Article

References (33)

1. Arneodo, A. (1996), Wavelet Analysis of Fractals: From the Mathematical Concepts to Experimental Reality, Oxford Univ. Press, Oxford, U. K.
2. Arneodo, A., G. Grasseau, and M. Holschneider (1988), Wavelet transform of multifractals, Phys. Rev. Lett, 61, 2281-2284.
3. Daubechies, I. (1992), Ten Lectures on Wavelets, CBMS-NSF Reg. Conf. Ser. Appl. Math., vol. 61, Soc. for Ind. and Applied Math., Philadelphia, Pa.
4. Dewar, R. C. (2005), Maximum entropy production and the fluctuation theorem, J. Phys. A, 38, L371-L381. (Pubitemid 40669834)
5. Dewar, R. C. (2009), Maximum entropy production as an inference algorithm that translates physical assumptions into macroscopic predictions: Don't shoot the messenger, Entropy, 11, 931-944.
6. Fiorentino, M., P. Claps, and V. P. Singh (1993), An entropy-based morphological analysis of river basin network, Water Resour. Res., 29, 1215-1224. (Pubitemid 23382387)
7. Frisch, U. (1995), Turbulence: The Legacy of A. N. Kolmogorov, Cambridge Univ. Press, Cambridge, U K.
8. Gregory, P. C. (2005), Bayesian Logical Data Analysis for the Physical Sciences, Cambridge Univ. Press, Cambridge, U. K.
9. Gupta, V. K., and E. C. Waymire (1993), A statistical analysis of mesoscale rainfall as a random cascade, J. Appl. Meteorol, 32, 251-267. (Pubitemid 23381911)
10. Jaynes, E. T. (1957), Information theory and statistical mechanics, Phys. Rev., 108(2), 171-190.
11. Jaynes, E. T. (2003), Probability Theory: The Logic of Science, Cambridge Univ. Press, Cambridge, U. K.
12. Kapur, J. N. (1989), Maximum Entropy Models in Science and Engineering, J. Wiley, New York.
13. Kleidon, A., and K. Fraedrich (2004), Biotic Entropy Production and Global Atmosphere-Biosphere Interaction, Springer, New York.
14. Lashermes, B., E. Foufoula-Georgiou, and W. E. Dietrich (2007), Channel network extraction from high resolution topography using wavelets, Geophys. Res. Lett, 34, L23S04, doi:10.1029/2007GL031140. (Pubitemid 351247044)
15. Lienhard, J. H. (1964), A statistical mechanics prediction of the dimension-less unit hydrograph, J. Geophys. Res., 69, 5231-5238.
16. Mallat, S. (1999), A Wavelet Tour of Signal Processing, Academic, San Diego, Calif.
17. Mandelbrot, B. B. (1983), The Fractal Geometry of Nature, W. H. Freeman, San Francisco, Calif.
18. Mishra, A. K., and P. Coulibaly (2009), Developments in hydrometric network design: A review, Rev. Geophys., 47, RG2001, doi:10.1029/2007RG000243.
19. Newman, W., and D. Turcotte (1990), Cascade model for fluvial geomor-phology, Geophys. J. Int., 100, 433-439.
20. Nieves, V., and A. Turiel (2009), Analysis of ocean turbulence using adaptive CVE on altimetry maps, J. Mar. Syst, 77, 482-494.
21. Nieves, V., J. Wang, R. L. Bras, and E. Wood (2010), Maximum entropy distributions of scale-invariant processes, Phys. Rev. Lett, 105, 118701, doi:10.1103/PhysRevLett.105.118701.
22. Paltridge, G. W. (1975), Global dynamics and climate-A system of minimum entropy exchange, Q. J. R. Meteorol. Soc, 101, 475-484.
23. Pottier, C, A. Turiel, and V. Garçon (2008), Inferring missing data in satellite chlorophyll maps using turbulent cascading, Remote Sens. Environ., 112, 4242-4260.
24. Rinaldo, A., I. Rodriguez-Iturbe, R. Rigon, E. Ijjasz-Vasquez, and R. L. Bras (1993), Self-organized fractal river networks, Phys. Rev. Lett., 70, 822-825.
25. Rodriguez-Iturbe, I., and A. Rinaldo (1997), Fractal River Basins: Chance and Self-Organization, Cambridge Univ. Press, Cambridge, U. K.
26. Rodriguez-Iturbe, I., E. J. Ijjasz-Vasquez, R. L. Bras, and D. G. Tarboton (1992), Power-law distributions of mass and energy in river basins, Water Resour. Res., 28, 1089-1093.
27. Schertzer, D., and S. Lovejoy (1996), Resolution Dependence and Multi-fractal in Remote Sensing and Geographical Information System, McGill Univ. Press, Montreal, Quebec, Canada.
28. Tarboton, D. G., R. L. Bras, and I. Rodriguez-Iturbe (1989), Scaling and elevation in river networks, Water Resour. Res., 25, 2037-2051. (Pubitemid 20400991)
29. Turiel, A., and N. Parga (2000), Multifractal wavelet filter of natural images, Phys. Rev. Lett, 85, 3325-3328.
30. Veneziano, D., and J. D. Niemann (2000), Self-similarity and multifractal-ity of fluvial erosion topography 1. mathematical conditions and physical origin, Water Resour. Res., 36, 1923-1936. (Pubitemid 30651205)
31. Vergassola, M., and U. Frisch (1991), Wavelet transforms of self-similar processes, Physica D, 54, 58-64.
32. Wang, J., G. D. Salvucci, and R. L. Bras (2004), An extremum principle of evaporation, Water Resour. Res., 40, W09303, doi:10.1029/2004WR003087. (Pubitemid 39385268)
33. Wang, J., R. L. Bras, M. Lerdau, and G. D. Salvucci (2007), A maximum hypothesis of transpiration, J. Geophys. Res., 112, G03010, doi:10.1029/ 2006JG000255. (Pubitemid 350120710)