Estimated generalized dimensions of river networks

Journal of Hydrology

Volumn 322, Issue 1-4, 2006, Pages 181-191

  De Bartolo, Samuele G ^a   Veltri, Massimo ^a   Primavera, Leonardo ^a  

^a UNIVERSITY OF CALABRIA   (Italy)

Author keywords

Drainage networks; Fractal dimensions; Multifractal analysis; Rivers

Indexed keywords

CORRELATION METHODS; DRAINAGE; FRACTALS; MAPS; NUMERICAL ANALYSIS; PARAMETER ESTIMATION;

DRAINAGE NETWORKS; FRACTAL DIMENSIONS; MULTIFRACTAL ANALYSIS; RIVER NETWORKS;

RIVERS;

CORRELATION METHODS; DRAINAGE; FRACTALS; MAPS; NUMERICAL ANALYSIS; PARAMETER ESTIMATION; RIVERS;

HYDROLOGY; MAP; REMOTE SENSING; THEORETICAL STUDY;

EURASIA; EUROPE; ITALY; SOUTHERN EUROPE;

HORTONIA;

EID: 33646472434     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2005.02.033     Document Type: Article

References (60)

1. Aharony A. Measuring multifractals. Physica D 38 (1989) 1-4
2. Amritkar R.E., and Gupte N. In: Hao B.-l. (Ed). Multifractals, in Experimental Study and Characterization of Chaos (1990), World Scientific, New York pp. 227-361
3. Badii R., and Politi A. Statistical description of chaotic attractors: the dimension function. Journal of Statistical Physics 40 (1985) 725-750
4. Beauvais A.A., and Montgomery D.R. Are channel networks statistical self-similar?. Geology 25 (1997) 1063-1066
5. Beck C., and Schlögl F. Thermodynamics of Chaotic Systems: An Introduction (1993), Cambridge University Press, Cambridge
6. Block A., Bloh W., and von Schellnhuber H.J. Efficient box-counting determination of generalized fractal dimensions. Physical Review A 42 4 (1990) 1869-1874
7. Chhabra A., and Jensen R.V. Direct determination of the f(α) singularity spectrum. Physical Review Letters 62 (1989) 1327-1330
8. Claps P., and Oliveto G. Reexamining the determination of the fractal dimension of river networks. Water Resources Research 32 (1996) 3123-3135
9. De Bartolo S.G., Maiolo M., Veltri M., and Veltri P. Sulla caratterizzazione multifrattale delle reti fluviali. Idrotecnica 6 (1995) 329-340
10. De Bartolo S.G., Gabriele S., and Gaudio R. Analisi sperimentale sulla natura multifrattale delle reti fluviali. XXVI Convegno di Idraulica e Costruzioni Idrauliche, IV, Catania (1998) pp. 53-64
11. De Bartolo S.G., Gabriele S., and Gaudio R. Multifractal behaviour of river networks. Hydrology and Earth System Sciences 4 1 (2000) 105-112
12. De Bartolo, S.G., Ambrosio, L., Primavera, L., Veltri, M., 2003. Descrittori frattali e caratteri morfometrici nella risposta idrologica, La difesa idraulica del territorio 2003, Trieste 10-12 settembre (in press).
13. De Bartolo S.G., Gaudio R., and Gabriele S. Multifractal analysis of river networks: a sand-box approach. Water Resources Research 40 (2004) W02201 (doi:10.1029/2003WR002760)
14. Falconer K.J. Fractal Geometry: Mathematical Foundations and Applications (1990), Wiley, Chichester
15. Feder J. Fractals (1988), Plenum Press, New York
16. Feeny B.F. Fast multifractal analysis by recursive box covering. International Journal of Bifurcation and Chaos 10 9 (2000) 2277-2287
17. Fernandez E., Bolea J.A., Ortega G., and Louis E. Are neourons multifractals?. Journal of Neuroscience Methods 89 (1999) 151-157
18. Fiorentino M., Oliveto G., and Rossi A. Alcuni aspetti del controllo energetico ed idrologico sulla geometria delle reti e delle sezioni fluviali. Parte prima: controllo idrologico, Atti del XXVIII Convegno di Idraulica e Costruzioni Idrauliche, Potenza, Editoriale Bios Cosenza vol. 1 (2002) pp. 71-78
19. Füchslin R.M., Shen Y., and Meier P.F. An efficient algorithm to determine fractal dimensions of points sets. Physics Letters A 285 (2001) 69-75
20. Gaudio R., De Bartolo S.G., Primavera L., Veltri M., and Gabriele S. Procedures in multifractal analysis of river networks: a state of the art review. The Basis of Civilization-Water Science? Proceedings of UNESCO/IAHS/IWHA symposium held in Rome, December 2003, IAHS Publication 286 (2004) pp. 228-237
21. Grassberger P. Generalized dimensions of strange attractors. Physics Letters 97A 6 (1983) 227-230
22. Grassberger P., and Procaccia I. Characterization of strange attractors. Physical Review Letters 50 3 (1983) 346-349
23. Halsey T.C., Jensen M.H., Kadanoff L.P., Procaccia I., and Shraiman B.I. Fractal measures and their singularities: the characterization of strange sets. Physical Review A 33 2 (1986) 1141-1151
24. Helmlinger K.R., Kumar P., and Foufoula-Georgiou E. On the use of digital elevation model data for hortonian and fractal analyses of channel networks. Water Resources Research 29 (1993) 2599-2613
25. Hentschel H.G.E., and Procaccia I. The infinite number of generalized dimensions of fractals and strange attractors. Physica D 8 (1983) 435-444
26. Horton R.E. Drainage basin characteristics. Transactions of the American Geophysical Union (AGU) 13 (1932) 350-370
27. Horton R.E. Erosional development of streams and their drainage basins; hydrophysical approach to quantitative geomorphology. Geological Society American Bulletin 56 (1945) 275-370
28. Hou X.-J., Gilmore R., Mindlin G., and Solari H. An efficient algorithm for fast O(N*ln(N)) box-counting. Physics Letters A 151 1,2 (1990) 43-46
29. Ijjasz-Vasquez E.J., Rodriguez-Iturbe I., and Bras R.L. On the multifractal characterization of river basins. Geomorphology 5 (1992) 297-310
30. Jelinek H., and Fernandez E. Neurons and fractals: how reliable and useful are calculations of fractal dimensions. Journal of Neuroscience Methods 81 (1998) 9-19
31. La Barbera P., and Rosso R. Fractal geometry of river networks (abstract). Eos Transactions AGU 68 44 (1987) 1276
32. La Barbera P., and Rosso R. On the fractal dimension of stream networks. Water Resources Research 25 4 (1989) 735-741
33. Liebovitch L.S., and e Toth T. A fast algorithm to determine fractal dimensions by box-counting. Physics Letters A 141 8,9 (1989) 386-390
34. Mandelbrot B.B. Fractals: Form, Chance and Dimension (1977), W.H. Freeman and Co, San Francisco, CA
35. Mandelbrot B.B. Negative fractal dimension and multifractals. Physica A 163 (1990) 306-315
36. Mandelbrot B.B. Multifractal power law distributions: negative and critical dimensions and other 'anomalies', explained by a simple example. Journal of Statistics Physics 110 (2003) 3-6
37. Meakin P. Fractals, Scaling and Growth Far from Equilibrium (1998), Cambridge University Press, Cambridge
38. Meisel L.V., and Johnson M. Multifractal analysis of imprecise data: Badii-Politi and correlation integral approach. Physical Review E 50 5 (1994) 4214-4219
39. Meisel L.V., Johnson M., and Cote P.J. Box-counting multifractal analysis. Physical Review A 45 10 (1992) 6989-6996
40. Molteno T.C.A. Fast O(N) box-counting algorithm for estimating dimensions. Physical Review E 48 5 (1993) R3263-R3266
41. Nikora V.I., and Sapozhnikov V.B. River network fractal geometry and its computer simulation. Water Resources Research 29 (1993) 3565-3575
42. Oiwa N.N., and Fiedler-Ferrara N. A moving-box algorithm to estimate generalized dimensions and f(α) spectrum. Physica D 124 (1998) 210-224
43. Pastor-Satorras R., and Riedi R.H. Numerical estimates of the generalized dimensions of the Hénon attractor for negative q. Journal of Physics A: Mathematical and General 29 (1996) L391-L398
44. Pawelzik K., and Schuster H.G. Generalized dimensions and entropies from a measured time series. Physical Review A 35 1 (1987) 481-484
45. Renyi A. On a new axiomatic theory of probability. Acta Mathematica Hungarica 6 (1955) 285-335
46. Renyi A. Probability Theory (1970), North-Holland Publishing Company, Budapest
47. Rinaldo A., Marani A., and Rigon R. Geomorphological dispersion. Water Resources Research 27 4 (1991) 513-525
48. Rinaldo A., Rodriguez-Iturbe I., Rigon R., Bras R.L., Ijjasz-Vasquez E.J., and Marani A. Minimum energy and fractal structures of drainage networks. Water Resources Research 28 (1992) 2183-2195
49. Rodriguez-Iturbe I., and Rinaldo A. Fractal River Basins: Chance and Self-Organization (1997), Cambridge University Press, Cambridge
50. Schuster H.G. Deterministic Chaos. second ed. (1989), VCH
51. Strahler A.N. Hypsometric (area-altitude) analysis of erosional topography. Geological Society American Bulletin 63 (1952) 1117-1142
52. Strahler A.N. Quantitative geomorphology of drainage basins and channel networks. In: Chow V.T. (Ed). Handbook of Applied Hydrology (1964), McGraw-Hill, New York (section 4)
53. Tarboton D.G., Bras R.L., and Rodriguez-Iturbe I. The fractal nature of river networks. Water Resources Research 24 (1988) 1317-1322
54. Tarboton D.G., Bras R.L., and Rodriguez-Iturbe I. Comment on 'On the fractal dimension of stream networks' by P. La Barbera and R. Rosso. Water Resources Research 26 (1990) 2243-2244
55. Theiler J. Efficient algorithm for estimating the correlation dimension from a set of discrete points. Physical Review A 36 9 (1987) 4456-4462
56. Veltri, M., Gabriele, S., De Bartolo, S.G., Gaudio, R., Primavera, L., 2004. Algoritmi multifrattali e loro utilizzo per la definizione di modelli di piena, I Workshop MODECI, Modelli matematici per la simulazione di Catastrofi Idrogeologiche, Rende 30-31 Marzo, (in print).
57. Veneziano D., Moglen G.E., and Bras R.L. Multifractal analysis: pitfalls of standard procedures and alternatives. Physical Review E 52 2 (1995) 1387-1398
58. Witten T.A., and Sander L.M. Diffusion limited aggregation: a kinetic critical phenomena. Physical Review Letters 47 (1981) 1400-1403
59. Yamaguti M., and Prado C. A direct calculation of the spectrum of singularities f(α) of multifractals. Physics Letters A 206 (1995) 318-322
60. Yamaguti M., and Prado C. Smart covering for a box-counting algorithm. Physical Review E 55 6 (1997) 7726-7732