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Simple model for river network evolution

Robert L. Leheny

  • The James Franck Institute and The Department of Physics, The University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637

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Phys. Rev. E 52, 5610 – Published 1 November, 1995

DOI: https://doi.org/10.1103/PhysRevE.52.5610

Abstract

We simulate the evolution of a drainage basin by erosion from precipitation and avalanching on hillslopes. The avalanches create a competition in growth between neighboring basins and play the central role in driving the evolution. The simulated landscapes form drainage systems that share many qualitative features with Glock’s model for natural network evolution and maintain statistical properties that characterize real river networks. We also present results from a second model with a modified, mass conserving avalanche scheme. Although the terrains from these two models are qualitatively dissimilar, their drainage networks share the same general evolution and statistical features.

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References (59)

  1. L. B. Leopold and W. B. Langbein, U.S. Geol. Surv. Prof. Paper 500A, 1 (1962).
  2. A. E. Scheidegger, Int. Assoc. Sci. Hydro. Bull. 12, 15 (1967).
  3. P. Meakin, J. Feder and T. Jøssang, Physica A176, 409 (1991).
  4. I. Seginer, Water Resour. Res. 5, 591 (1969).
  5. J. S. Smart and V. L. Moruzzi, J. Geol. 79, 572 (1971).
  6. A. D. Howard, Geogr. Anal. 3, 29 (1971).
  7. A. D. Howard, Geol. Soc. Am. Bull. 82, 1355 (1971).
  8. D. L. Dunkerley, J. Geol. 85, 459 (1977).
  9. C. P. Stark, Nature 352, 423 (1991).
  10. A. D. Abrahams, Water Resour. Res. 20, 161 (1984).
  11. A. D. Howard, Water Resour. Res. 26, 2107 (1990).
  12. I. Rodríguez-Iturbe, A. Rinaldo, R. Rigon, R. L. Bras, A. Marani and E. Ijjasz-Vasquez, Water Resour. Res. 28, 1095 (1992).
  13. A. Rinaldo, I. Rodríguez-Iturbe, R. Rigon, E. J. Ijjasz-Vasquez and R. L. Bras, Phys. Rev. Lett. 70, 822 (1993).
  14. H. Inaoka and H. Takayasu, Phys. Rev. E 47, 899 (1993).
  15. G. R. Willgoose, R. L. Bras and I. Rodríguez-Iturbe, Am. Geophys. Union Trans. 71, 1806 (1990).
  16. G. R. Willgoose, R. L. Bras and I. Rodríguez-Iturbe, Water Resour. Res. 27, 1685 (1991).
  17. A. D. Howard, Water Resour. Res. 30, 2261 (1994).
  18. A. Czirok, E. Somfai and T. Vicsek, Phys. Rev. Lett. 71, 2154 (1993).
  19. R. L. Leheny and S. R. Nagel, Phys. Rev. Lett. 71, 1470 (1993).
  20. C. G. Chase, Geomorphology 5, 39 (1992).
  21. K. M. Gregory and C. G. Chase, Geophys. Res. 99, 20141 (1994).
  22. This procedure resembles that developed to identify networks on digital elevation maps of natural terrains; see J. F. O'Callaghan and D. M. Marks, Comput. Vision Graphics Image Process. 28, 323 (1984).
  23. W. S. Glock, Geograph. Rev. 21, 475 (1931).
  24. R. J. Small, The Study of Landforms (Cambridge University Press, New York, 1978).
  25. See, e.g., R. V. Ruhe, Am. J. Sci. 250, 46 (1952).
  26. S. A. Schumm, Geol. Soc. Am. Bull. 67, 597 (1956).
  27. M. Morasawa, Am. J. Sci. 262, 340 (1964).
  28. S. A. Schumm, M. P. Mosley, and W. E. Weaver, Experimental Fluvial Geomorphology (Wiley, New York, 1987).
  29. M. A. Carson and D. J. Petley, Trans. Inst. Brit. Geogr. 49, 71 (1970).
  30. M. A. Carson, Inst. Brit. Geogr. Spec. Publ. 3, 31 (1971).
  31. A. D. Howard, W. E. Dietrich and M. A. Seidl, Geophys. Res. 99, 13971 (1994), and reference therein.
  32. As a first approximation to such a model, we have introduced to the rules a minimum height to simulate the presence of a bedrock or a base level, below which erosion via Eq. (4) ceases. Preliminary results indicate that this assumption generates interesting changes in landscape features; R. L. Leheny and S. R. Nagel (unpublished).
  33. R. E. Horton, Geol. Soc. Am. Bull. 56, 275 (1945).
  34. A. N. Strahler, Geol. Soc. Am. Bull. 63, 1117 (1952).
  35. A. D. Abrahams, Water Resour. Res. 8, 624 (1972).
  36. Field observations, which show a threshold length for overland flow before channels form [see, for example, D. R. Montgomery and W. E. Dietrich, Science 225, 826 (1992)], suggest that subtracting R in the simulations should be unnecessary. We note, however, that this correction effects only small basins and becomes negligible for A >> R.
  37. V. I. Nikora, Water Resour. Res. 30, 133 (1994).
  38. R. Rosso, B. Bacci and P. La Barbera, Water Resour. Res. 27, 381 (1991).
  39. R. L. Shreve, J. Geol. 77, 397 (1969).
  40. R. L. Shreve, J. Geol. 74, 17 (1966).
  41. J. T. Hack, U.S. Geol. Surv. Prof. Paper 294B, 45 (1957).
  42. O. J. Mesa and V. K. Gupta, Water Resour. Res. 23, 2119 (1987).
  43. R. S. Snow, in Fractal in Geophysics, edited by C. H. Scholz and B. B. Mandelbrot (Birkhauser Verlag, Boston, 1989), p. 100.
  44. A. Robert and A. G. Roy, Water Resour. Res. 26, 839 (1990).
  45. E. J. Ijjasz-Vasquez, R. L. Bras and I. Rodríguez-Iturbe, Geophys. Res. Lett. 20, 1583 (1993).
  46. Strictly, the model's early precipitation follows rules matching the directed walk model only in the limit D << I << 1 /E; however, the initial value of alpha appears independent of D / I.
  47. Compare, for example, Fig. 6 with Fig. 3 of [19].
  48. J. E. Mueller, Geol. Soc. Am. Bull. 84, 3127 (1973).
  49. M. P. Mosley and R. S. Parker, Geol. Soc. Am. Bull. 83, 3669 (1972).
  50. M. P. Mosley and R. S. Parker, Geol. Soc. Am. Bull. 84, 3123 (1973).
  51. D. G. Tarboton, R. L. Bras and I. Rodríguez-Iturbe, Water Resour. Res. 24, 1317 (1988).
  52. A. N. Strahler, J. Geol. 62, 1 (1954).
  53. J. J. Smart, Adv. Hydrosci. 8, 305 (1972).
  54. I. Rodríguez-Iturbe, E. J. Ijjasz-Vasquez, R. L. Bras and D. G. Tarboton, Water Resour. Res. 28, 1089 (1992).
  55. To construct the distributions we use every site on the landscape. However, we find that this procedure and that used in [54] lead to identical distributions for our data, except at late times when the increased importance of second-generation branches disproportionate weight to links of large area.
  56. R. Rigon, A. Rinaldo, I. Rodríguez-Iturbe, R. L. Bras and E. Ijjasz-Vasquez, Water Resour. Res. 29, 1635 (1993).
  57. See, for example, D. G. Tarboton, R. L. Bras and I. Rodríguez-Iturbe, Hydro. Proc. 5, 81 (1991).
  58. J. J. Flint, Water Resour. Res. 10, 969 (1974).
  59. G. Dietler and Y. Zhang, Physica A 191, 213 (1992).

Outline

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Phys. Rev. E 52, 5610– Published 1 November, 1995
  • Received 28 April 1995

© 1995 American Physical Society

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