Are American rivers Tokunaga self-similar? New results on fluvial network topology and its climatic dependence

Journal of Geophysical Research: Earth Surface

Volumn 118, Issue 1, 2013, Pages 166-183

  Zanardo, S ^a   Zaliapin, I ^b   Foufoula Georgiou, E ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

^b UNIVERSITY OF NEVADA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLIMATE EFFECT; DRAINAGE NETWORK; ESTIMATION METHOD; FLUVIAL GEOMORPHOLOGY; GEOMORPHOLOGICAL RESPONSE; HYDROGEOLOGY; HYDROLOGICAL MODELING; LANDSCAPE EVOLUTION; NUMERICAL MODEL; PARAMETERIZATION; RIVER BASIN;

UNITED STATES;

EID: 84877637873     PISSN: None     EISSN: 21699011     Source Type: Journal    
DOI: 10.1029/2012JF002392     Document Type: Article

References (63)

1. Aharonson, O., A. Hayes, J. I. Lunine, R. D. Lorenz, and C. Elachi (2009), An asymmetric distribution of lakes on Titan as a possible consequence of orbital forcing, Nat. Geosci., 2, 851-854.
2. Band, L. E. (1986), Topographic partitioning of watersheds with digital elevation models, Water Resour. Res., 22, 15-24.
3. Bonnet, S., and A. Crave (2003), Landscape response to climate change: Insights from experimental modelling and implications for tectonic versus climatic uplift of topography, Geology, 31(2), 123-126.
4. Bracquemond, C., E. Cretois, and O. Gaudoin (2011), A comparative study of goodness-of-fit tests for the geometric distribution and application to discrete time reliability. http://www-ljk.imag.fr/SMS/ftp/BraCreGau02.pdf. [Online; accessed 11-May-2011].
5. Burd, G. A., E. C. Waymire, and R. D. Winn (2000), A self-similar invari-ance of critical binary Galton-Watson trees, Bernoulli, 6, 1-21.
6. Cui, G., B. Williams, and G. Kuczera (1999), A stochastic Tokunaga model for stream networks, Water Resour. Res., 35(10), 3139-3147.
7. Dodds, P. S., and D. H. Rothman (2000), Scaling, universality, and geomor-phology, Ann. Rev. Earth Planet. Sci., 28, 571-610, doi:10.1146/annurev. earth.28.1.571.
8. Efron, B., and R. J. Tibshirani (1994), An Introduction to the Bootstrap, 456, CRC, Boca Raton, Fla.
9. Elachi, C., et al. (2005), Cassini Radar views the surface of Titan, Science, 308, 970-974.
10. Erskine, R. H., T. R. Green, J. A. Ramirez, and L. H. McDonald (2007), Digital elevation accuracy and grid cell size: effects on estimated terrain attribute, Soil Sci. Soc. Am. J., 71, 1371-1380.
11. Furey, P. R., and B. M. Troutman (2008), A consistent framework for Horton regression statistics that leads to a modified Hack's law, Geomor-phol., 102(3-4), 603-614, doi:10.1016/j.geomorph.2008.06.002.
12. Gardiner, T. W., K. C. Sasowsky, and R. L. Day (1991), Automated extraction of geomorphic properties from digital elevation data, Z. Geomorphol. Suppl., 80, 57-68.
13. Gesch, D. B. (2007), The National Elevation Dataset, in Digital Elevation Model Technologies and Applications - The DEM Users Manual, 2nd ed., edited by D. Maune, chap. 499-118, Am. Soc. for Photogram. and Remote Sensing, Bethesda, Md.
14. Hack, J. T. (1957), Studies of longitudinal stream profiles in Virginia and Maryland, U.S. Geol. Surv. Prof. Pap., 294-B, 1-97.
15. Horton, R. E. (1945), Erosional development of streams and their drainage basins: Hydrophysical approach to quantitative morphology, Geol. Soc. Am. Bull., 56, 275-370.
16. Kiffney, P. M., C. M. Greene, J. E. Hall, and J. R. Davies (2006), Tributary streams create spatial discontinuities in habitat, biological productivity, and diversity in mainstream rivers, Can. J. Fish. Aquat. Sci., 63, 2518-2530, doi:10.1139/F06-138.
17. Kirkby, M. J. (1976), Tests of the random network model, and its application to basin hydrology, Earth Surf. Processes, 1, 197-212.
18. Leeder, M. R. (1993), Tectonic controls upon drainage basin development, river channel migration and alluvial architecture: Implications for hydrocarbon reservoir development and characterization, in Characterisation of Fluvial and Aeolian Hydrocarbon Reservoirs, edited by C. North and J. Prossor, Geol. Soc. London Spec. Publ., 73, 9-24.
19. Mantilla, R., B. M. Troutman, and V. K. Gupta (2010), Testing statistical self-similarity in the topology of river networks, J. Geophys. Res., 115, F03038, doi:10.1029/2009JF001609.
20. Mark, D. M. (1988), Network models in geomorphology, in Modeling Geomorphological Systems, edited by M. G. Anderson, 73-97, John Wiley, New York.
21. Masek, J. G., and D. L. Turcotte (1993), A diffusion limited aggregation model for the evolution of drainage networks, Earth Planet. Sci. Lett., 119, 379.
22. McConnell, M., and V. Gupta (2008), A proof of the Horton law of stream numbers for the Tokunaga model of river networks, Fractals, 16, 227-233.
23. Menadbe, M., S. E. Veitzer, V. K. Gupta, and M. Sivapalan (2001), Tests of peak flow scaling in simulated self-similar river networks, Adv. Water Resour., 24(9), 1037-1049.
24. Montgomery, D. R., and W. E. Dietrich (1992), Channel initiation and the problem of landscape scale, Science, 255, 826-830.
25. Montgomery, D., and E. Foufoula-Georgiou (1993), Channel network source representation for digital elevation models, Water Resour. Res., 29(12), 3925-3934.
26. Muneepeerakul, R., E. Bertuzzo, H. J. Lynch, W. F. Fagan, A. Rinaldo, and I. Rodriguez-Iturbe (2008), Neutral metacommunity models predict fish diversity patterns in Mississippi-Missouri basin, Nature, 453, 220-222, doi:10.1038/nature06813.
27. Newman, W. I., D. L. Turcotte, and A. M. Gabrielov (1997), Fractal trees with side branching, Fractals, 5, 603-614.
28. Nikulin, M. S. (1992), Gihman statistic and goodness-of-fit tests for grouped data, C. R. Math. Rep. Acad. Sci. Can., 14(4), 151-156.
29. O'Callaghan, J., and D. Mark (1984), The extraction of drainage networks from digital elevation data, Comput. Vision Graphics Image Process., 28, 328-344.
30. Orlandini, S., G. Moretti, M. Franchini, B. Aldighieri, and B. Testa (2003), Path-based methods for the determination of nondispersive drainage directions in grid-based digital elevation models, Water Resour. Res., 39(6), 1144, doi:10.1029/2002WR001639.
31. Ossadnik, P. (1992) Branch order and ramification analysis of large diffusion limited aggregation clusters, Phys. Rev. A, 45, 1058.
32. Passalacqua, P., T. Do Trung, E. Foufoula-Georgiou, G. Sapiro, and W. E. Dietrich (2010), A geometric framework for channel network extraction from lidar: Nonlinear diffusion and geodesic paths, J. Geophys. Res., 115, F01002, doi:10.1029/2009JF001254.
33. Peckham, S. (1995a), New results for self-similar trees with applications to river networks, Water Resour. Res., 31(4), 1023-1029.
34. Peckham, S. (1995b), Self-similarity in the three-dimensional geometry and dynamics of large river basins, PhD thesis, Univ. of Colo., Boulder, Colorado.
35. Peckham, S., and V. K. Gupta (1999), A reformulation of Horton's laws for large river networks in terms of statistical self-similarity, Water Resour. Res., 35(9), 2763-2777.
36. Peucker, T. K., and D. H. Douglas (1975), Detection of surface-specific points by local parallel processing of discrete terrain elevation data, Comput. Graphics Image Process., 4, 375-387.
37. Power, M. E., and W. E. Dietrich (2002), Food webs in river networks, Ecol. Res., 17, 451-471.
38. Rodriguez-Iturbe, I., and A. Rinaldo (1997), Fractal River Basins: Chance and Self-Organization, Cambridge Univ. Press, New York.
39. Rodriguez-Iturbe, I., and J. B. Valdes (1979), The geomorphologic structure of hydrologic response, Water Resour. Res., 15, 1409-1420, doi:10.1029/WR015i006p01409.
40. Schaake, J. C., Q. Duan, M. Smith, and V. Koren (2000), Criteria to select basins for hydrologic model development and testing, Preprints, 15th Conf. On Hydrology, 10-14 January 2000, Paper P1.8, Am. Meteorol. Soc., Long Beach, Calif.
41. Schaake, J., S. Cong, and Q. Duan (2006), The US MOPEX data set, IAHS-AISH Publ., 307, 9-28.
42. Sklar, L. S., W. E. Dietrich, E. Foufoula-Georgiou, B. Lashermes, and D. Bellugi (2006), Do gravel bed river size distributions record channel network structure?, Water Resour. Res., 42, W06D18, doi:10.1029/2006WR005035.
43. Stewart-Koster, B., M. J. Kennard, B. D. Harch, F. Sheldon, A. H. Arthington, and B. J. Pusey (2007), Partitioning the variation in stream fish assemblages within a spatio-temporal hierarchy, Mar. Freshwater Res., 58, 675-686.
44. Strahler, A. N. (1957), Quantitative analysis of watershed geomorphology, Trans. AGU, 38, 913-920.
45. Tarboton, D. (1996), Fractal river networks, Horton's laws and Tokunaga cyclicity, J. Hydrol., 187, 105-117.
46. Tarboton, D. G., R. L. Bras, and I. Rodriguez-Iturbe (1991), On the extraction of channel networks from digital elevation data, Hydrol. Processes, 5, 81-100.
47. Thompson, J. A., J. C. Bell, and C. A. Butler (2001), Digital elevation model resolution: Effects on terrain attribute calculation and quantitative soil-landscape modeling, Geoderma, 100, 67-89, doi:10.1016/S0016-7061(00)00081- 1.
48. Tokunaga, E. (1966), The composition of drainage network in Toyohira river basin and valuation of Horton's first law (in Japanese with English summary), Geophys. Bull. Hokkaido Univ., 15, 1-19.
49. Tokunaga, E. (1978), Consideration on the composition of drainage networks and their evolution (1978), Geograph. Rep. 13, 1-27 Tokyo Metro. Univ., Japan.
50. Tomasko, M. G., et al. (2005), Rain, winds and haze during the Huygens probe's descent to Titan's surface, Nature, 438, 765-778.
51. Troutman, B. M. (2005), Scaling of flow distance in random self-similar channel networks, Fractals, 13(4), 265-282.
52. Tucker, G. E., and R. L. Bras (1998), Hillslope processes, drainage density, and landscape morphology, Water Resour. Res., 34(10), 2751-2764.
53. Turcotte, D. L., J. D. Pelletier, and W. I. Newman (1998), Networks with side branching in biology, J. Theor. Biol., 193, 577-592.
54. Turcotte, D. L., B. D. Malamud, G. Morein, and W. I. Newman (1999), An inverse cascade model for self-organized critical behavior, Physica A, 268, 629-643.
55. Turner, J. R., and J. F. Thayer (2001), Introduction to Analysis of Variance: Design, Analyis and Interpretation, 192, Sage Publ., Thousand Oaks, Calif.
56. Veitzer, S., and V. K. Gupta (2000), Random self-similar river networks and derivations of generalized Horton laws in terms of statistical simple scaling, Water Resour. Res., 36, 1033-1048.
57. Veitzer, S., and V. K. Gupta (2001), Statistical self-similarity of width function maxima with implications to floods, Adv. Water Resour., 24(9-10), 955-965, doi:10.1016/S0309-1708(01)00030-6.
58. Westfall, P. H., R. D. Tobias, and R. D. Wolfinger (2011), Multiple Comparisons and Multiple Tests Using the SAS System, 2nd ed., SAS Publ., Cary, N. C.
59. Yakovlev, G., W. I. Newman, D. L. Turcotte, and A. Gabrielov (2005), An inverse cascade model for self-organized complexity and natural hazards, Geophys. J. Int., 163, 433-442.
60. Zaliapin, I., and Y. Kovchegov (2011), Tokunaga and Horton self-similarity for level set trees of Markov chains, Chaos Solitons Fractals, 45, 358-372, doi:10.1016/j.chaos.2011.11.006.
61. Zaliapin, I., H. Wong, and A. Gabrielov (2006a), Inverse cascade in percolation model: Hierarchical description of time-dependent scaling, Phys. Rev. E., 71, 066118.
62. Zaliapin, I., H. Wong, and A. Gabrielov (2006b), Hierarchical aggregation in percolation model, Tectonophysics, 413, 93-107.
63. Zanardo, S., C. Harman, P. A. Troch, S. C. Rao, and M. Sivapalan (2012), Intra-annual rainfall variability controls on inter-annual variability of catchment water balance: A stochastic analysis, Water Resour. Res., 48(6), doi:10.1029/2010WR009869.