Geometry of river networks. I. Scaling, fluctuations, and deviations

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 63, Issue 1, 2001, Pages

  Dodds, Peter Sheridan ^a   Rothman, Daniel H ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FRESH WATER;

ECOSYSTEM; THEORETICAL MODEL;

ECOSYSTEM; FRESH WATER; MODELS, THEORETICAL;

EID: 18644386664     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.016115     Document Type: Article

References (68)

1. R. Albert, H. Jeong, and A.-L. Barabasi, Nature (London) 406, 378 (2000).
2. D. J. Watts and S. J. Strogatz, Nature (London) 393, 440 (1998).
3. M. Zamir, J. Theor. Biol. 197, 517 (1999).
4. S. N. Coppersmith, C.-h. Liu, S. Majumdar, O. Narayan, and T. A. Witten, Phys. Rev. E 53, 4673 (1996).
5. C. Cherniak, M. Changizi, and D. W. Kang, Phys. Rev. E 59, 6001 (1999).
6. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1983).
7. I. Rodríguez-Iturbe and A. Rinaldo, Fractal River Basins: Chance and Self-Organization (Cambridge University Press, Cambridge, 1997).
8. A. Rinaldo, I. Rodríguez-Iturbe, and R. Rigon, Annu. Rev. Earth Planet Sci. 26, 289 (1998).
9. P. Ball, The Self-Made Tapestry (Oxford University Press, Oxford, 1998).
10. P. S. Dodds and D. H. Rothman, Annu. Rev. Earth Planet Sci. 28, 571 (2000).
11. J. T. Hack, U.S. Geol. Surv. Prof. Pap., 294-B, 45 (1957).
12. A. Maritan, A. Rinaldo, R. Rigon, A. Giacometti, and I. Rodríguez-Iturbe, Phys. Rev. E 53, 1510 (1996).
13. R. Rigon, I. Rodríguez-Iturbe, A. Maritan, A. Giacometti, D. G. Tarboton, and A. Rinaldo, Water Resour. Res. 32, 3367 (1996).
14. H. Jaeger, S. Nagel, and R. Behringer, Rev. Mod. Phys. 68, 1259 (1996).
15. L. Kadanoff, Rev. Mod. Phys. 71, 435 (1999).
16. T. R. Smith and F. P. Bretherton, Water Resour. Res. 3, 1506 (1972).
17. S. Kramer and M. Marder, Phys. Rev. Lett. 68, 205 (1992).
18. N. Izumi and G. Parker, J. Fluid Mech. 283, 341 (1995).
19. K. Sinclair and R. C. Ball, Phys. Rev. Lett. 76, 3360 (1996).
20. J. R. Banavar, F. Colaiori, A. Flammini, A. Giacometti, A. Maritan, and A. Rinaldo, Phys. Rev. Lett. 78, 4522 (1997).
21. E. Somfai and L. M. Sander, Phys. Rev. E 56, R5 (1997).
22. R. Pastor-Satorras and D. H. Rothman, Phys. Rev. Lett. 80, 4349 (1998).
23. R. Pastor-Satorras and D. H. Rothman, J. Stat. Phys. 93, 477 (1998).
24. M. Cieplak, A. Giacometti, A. Maritan, A. Rinaldo, I. Rodríguez-Iturbe, and J. R. Banavar, J. Stat. Phys. 91, 1 (1998).
25. A. Giacometti (unpublished).
26. H. Takayasu and H. Inaoka, Phys. Rev. Lett. 68, 966 (1992).
27. R. L. Leheny, Phys. Rev. E 52, 5610 (1995).
28. G. Caldarelli, A. Giacometti, A. Maritan, I. Rodríguez-Iturbe, and A. Rinaldo, Phys. Rev. E 55, 4865 (1997).
29. C. P. Stark, Nature (London) 352, 405 (1991).
30. T. Sun, P. Meakin, and T. Jøssang, Phys. Rev. E 49, 4865 (1994).
31. T. Sun, P. Meakin, and T. Jøssang, Phys. Rev. E 51, 5353 (1995).
32. L. B. Leopold and W. B. Langbein, U.S. Geol. Surv. Prof. Pap. 500-A, 1 (1962).
33. A. E. Scheidegger, Bull. Int. Assoc. Sci. Hydrol. 12, 15 (1967).
34. S. S. Manna and B. Subramanian, Phys. Rev. Lett. 76, 3460 (1996).
35. A. Maritan, F. Colaiori, A. Flammini, M. Cieplak, and J. R. Banavar, Science 272, 984 (1996).
36. P. S. Dodds and D. H. Rothman, following paper, Phys. Rev. E 63, 016116 (2000).
37. P. S. Dodds and D. H. Rothman, third paper, Phys. Rev. E 63, 016117 (2000).
38. R. E. Horton, Bull. Geol. Soc. Am. 56, 275 (1945).
39. P. S. Dodds and D. H. Rothman, Phys. Rev. E 59, 4865 (1999).
40. E. Tokunaga, Geophys. Bull. Hokkaido Univ. 15, 1 (1966).
41. E. Tokunaga, Geogr. Rep., Tokyo Metrop. Univ. 13, 1 (1978).
42. E. Tokunaga, Trans. Jpn. Geomorphol. Union. 5, 71 (1984).
43. D. M. Gray, J. Geophys. Res. 66, 1215 (1961).
44. J. E. Mueller, Geol. Soc. Am. Bull. 83, 3471 (1972).
45. M. P. Mosley and R. S. Parker, Geol. Soc. Am. Bull. 84, 3123 (1973).
46. J. E. Mueller, Geol. Soc. Am. Bull. 84, 3127 (1973).
47. D. R. Montgomery and W. E. Dietrich, Science 255, 826 (1992).
48. R. Rigon, I. Rodríguez-Iturbe, and A. Rinalod, Water Resour. Res. 34, 3181 (1998).
49. The topography used to extract areas and stream lengths is a composite of United States Geological Survey 3-arcsec digital elevation models available on the Internet at www.usgs.gov. These datasets provide grids of elevation data with horizontal resolution on the order of 90 m. The Kansas river was analyzed directly from the data, while the Mississippi basin was studied on a coarse-grained version with a horizontal resolution of approximately 1000 m.
50. D. G. Tarboton, R. L. Bras, and I. Rodríguez-Iturbe, Water Resour. Res. 26, 2243 (1990).
51. H. Takayasu, I. Nishikawa, and H. Tasaki, Phys. Rev. A 37, 3110 (1988).
52. P. Meakin, J. Feder, and T. Jøssang, Physica A 176, 409 (1991).
53. G. Huber, Physica A 170, 463 (1991).
54. D. Dhar and S. N. Majumdar, J. Phys. A 23, 4333 (1990).
55. D. Dhar, Physica A 186, 82 (1992).
56. D. Dhar, Physica A 263, 4 (1999).
57. W. Feller, An Introduction to Probability Theory and Its Applicatioins, 3rd ed. (Wiley, New York, 1968), Vol. I.
58. W. Feller, An Introduction to Probability Theory and Its Applications, 2nd ed. (Wiley, New York, 1971), Vol II.
59. The data for the Nile and Congo were obtained from the United States Geological Survey’s 30-arcsec Hydrol K dataset, which may be accessed on the Internet at edcftp.cr.usgs.gov. Note that these Hydrol K datasets have undergone the extra processing of projection onto a uniform grid.
60. The dataset used for the Amazon has a horizontal resolution of approximately 1000 m and comes from 30-arcsec terrain data provided by the National Imagery and Mapping Agency available on the Internet at www.nima.mil.
61. W. Dietrich and D. Montgomery, in Scale Dependence and Scale Invariance in Hydrology, edited by G. Sposito (Cambridge University Press, Cambridge, 1998), pp. 30–60.
62. W. E. Dietrich and T. Dunne, in Channel Network Hydrology, edited by K. Beven and M. Kirkby (Wiley, New York, 1993), Chap. 7, pp. 175–219.
63. A. N. Strahler, EOS Trans. AGU 38, 913 (1957).
64. S. A. Schumm, Bull. Geol. Soc. Am. 67, 597 (1956).
65. S. Peckham and V. Gupta, Water Resour. Res. 35, 2763 (1999).
66. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C 2nd ed. (Cambridge University Press, Cambridge, 1992).
67. E. L. Lehman, Nonparametrics: Statistical Methods Based on Ranks (Holden-Day, San Francisco, 1975).
68. P. Sprent, Applied Nonparametric Statistical Methods, 2nd ed. (Chapman and Hall, New York, 1993).