Extending generalized Horton laws to test embedding algorithms for topologic river networks

Geomorphology

Volumn 151-152, Issue , 2012, Pages 13-26

  Mantilla, Ricardo ^a   Gupta, Vijay K ^b   Troutman, Brent M ^c  

^a UNIVERSITY OF IOWA   (United States)

^b UCB 450   (United States)

^c U S GEOLOGICAL SURVEY   (United States)

Author keywords

Embedding algorithms; Horton laws; Random self similar networks; River networks; Self similar trees

Indexed keywords

ALGORITHM; CATCHMENT; DRAINAGE NETWORK; FLOODING; FLUVIAL GEOMORPHOLOGY; GEOMETRY; LANDSCAPE; PEAK FLOW; RAINFALL; RIVER BASIN; SPATIAL VARIATION; THREE-DIMENSIONAL MODELING; TOPOLOGY;

EID: 84858333947     PISSN: 0169555X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geomorph.2012.01.002     Document Type: Article

References (45)

1. Birnir B., Smith T.R., Merchant G.E. The scaling of fluvial landscapes. Computers and Geosciences 2001, 27:1189-1216.
2. Birnir B., Hernandez J., Smith T.R. The stochastic theory of fluvial land surfaces. Journal of Nonlinear Science 2007, 17(1):13-57.
3. Dodds P.S., Rothman D.H. Scaling, universality, and geomorphology. Annual Review of Earth and Planetary Sciences 2000, 28(1):571-610.
4. Gupta V.K., Waymire E.C. A statistical analysis of mesoscale rainfall as a random cascade. Journal of Applied Meteorology 1993, 32(2):251-267.
5. Gupta V.K., Castro S.L., Over T.M. On scaling exponents of spatial peak flows from rainfall and river network geometry. Journal of Hydrology 1996, 187:81-104.
6. Gupta V.K., Mantilla R., Troutman B.M., Dawdy D., Krajewski W.F. Generalizing a nonlinear geophysical flood theory to medium-sized river networks. Geophysical Research Letters 2010, 37:L11402.
7. Hack J.T. Studies of longitudinal profiles in Virginia and Maryland. USGS Professional Paper 294-B, United States Geological Survey 1957.
8. Holley R., Waymire E. Multifractal dimensions and scaling exponents for strongly bounded random cascades. Annals of Applied Probability 1992, 2(4):819-845.
9. Horton R.E. Erosional development of streams and their drainage basins; hydrophysical approach to quantitative morphology. Geological Society of America Bulletin 1945, 56:275-370.
10. Lee D.T., Schachter B.J. Two algorithms for constructing a delaunay triangulation. International Journal of Parallel Programming 1980, 9(3):219-242.
11. Leopold L.B., Langbein W.B. The concept of entropy in landscape evolution. Professional Paper 500-A 1962, U.S. Geological Survey, Washington D C.
12. Mantilla, R., 2007. Physical basis of statistical scaling in peak flows and stream flow hydrographs for topologic and spatially embedded random self-similar channel networks. Ph.D. thesis, Department of Civil and Environmental Engineering. University of Colorado, Boulder, CO.
13. Mantilla R., Gupta V.K. A GIS framework to investigate the process basis for scaling statistics on river networks. Geoscience and Remote Sensing Letters, IEEE 2005, 2(4):404-408.
14. Mantilla R., Troutman B.M., Gupta V.K. Testing statistical self-similarity in the topology of river networks. Journal of Geophysical Research 2010, 115:F03038.
15. Maritan A., Colaiori F., Flammini A., Cieplak M., Banavar J.R. Universality classes of optimal channel networks. Science 1996, 272(5264):984-986.
16. McConnell M., Gupta V.K. A proof of the Horton law of stream numbers for the Tokunaga model of river networks. Fractals-Complex Geometry Patterns and Scaling in Nature and Society 2008, 16(3):227-233.
17. Meakin P., Feder J., Jøssang T. Simple statistical models of river networks. Physica A 1991, 176:409-429.
18. Menabde M., Sivapalan M. Linking space-time variability of rainfall and runoff fields on a river network: a dynamic approach. Advances in Water Resources 2001, 24:1001-1014.
19. Mesa O.J., Gupta V.K. On the main channel length-area relationship for channel networks. Water Resources Research 1987, 23(11):2119-2122.
20. Molnar P. On geometrical scaling of cayley trees and river networks. Journal of Hydrology 2005, 322(1-4):199-210.
21. Moussa R. Definition of new equivalent indices of Horton-Strahler ratios for the derivation of the Geomorphological Instantaneous Unit Hydrograph. Water Resources Research 2009, 45(9).
22. NIST/SEMATECH e-Handbook of Statistical Methods 2006, NIST. http://www.itl.nist.gov/div898/handbook/.
23. Peckham S. New results for self-similar trees with applications to river networks. Water Resources Research 1995, 31(4):1023-1029.
24. Peckham S., Gupta V.K. A reformulation of Horton's laws for large river networks in terms of statistical self-similarity. Water Resources Research 1999, 35(9):2763-2777.
25. Puente C.E., Castillo P.A. On the fractal structure of networks and dividers within a watershed. Journal of Hydrology 1996, 187(1-2):173-181.
26. Pyke R. Spacings. Journal of the Royal Statistical Society. Series B 1965, 27(3):395-449.
27. Rigon R., Rodríguez-Iturbe I., Ijjasz-Vasquez E. Optimal channel networks: a framework for the study of river basin morphology. Water Resources Research 1993, 29(6):1635-1646.
28. Rinaldo A., Banavar J.R., Maritan A. Trees, networks, and hydrology. Water Resources Research 2006, 42:W06D07.
29. Rodríguez-Iturbe I., Rinaldo A. Fractal River Basins: Chance and Self-organization 1997, Cambridge University Press, New York.
30. Ross S. First Course in Probability 2010, Pearson.
31. Scheidegger A.E. A stochastic model for drainage patterns into an intramontane trench. Bulletin de l'Association Internationale d'Hydrologie Scientifique 1967, 12:15-20.
32. Schumm S.A. Evolution of drainage systems and slopes in badlands at Perth Amboy, New Jersey. Geological Society of America Bulletin 1956, 67:597-646.
33. Shreve R. Statistical law of stream numbers. Journal of Geology 1966, 74:17-37.
34. Shreve R. Infinite topologically random channel networks. Journal of Geology 1967, 75:178-186.
35. Strahler A.N. Quantitative analysis of watershed geomorphology. American Geophysical Union Transactions 1957, 8(6):913-920.
36. Sun T., Meakin P., Jossang T. The topography of optimal drainage basins. Water Resources Research 1994, 30:2599-2611.
37. Tokunaga E. The composition of drainage network in Toyohira river basin and valuation of Horton's first law. Geophysical Bulletin of Hokkaido University 1966, 15:1-19. in Japanese with English summary.
38. Tokunaga E. Concepts and modelling in geomorphology: international perspectives. TERRAPUB, Tokyo, Japan, Ch. Tiling Properties of Drainage Basins and Their Physical Bases 2003, 147-166.
39. Troutman B.M. Scaling of flow distance in random self-similar channel networks. Fractals 2005, 13(4):265-282.
40. Troutman B.M., Karlinger M.R. Inference for a generalized Gibbsian distribution on channel networks. Water Resources Research 1994, 30(7):2325-2338.
41. Troutman B., Karlinger M. Spatial channel network models in hydrology. Vol. 7 of Advanced Series on Statistical Science and Applied Probability 1998, 85-128. World Scientific, Singapore. O.E. Barndorff-Nielsen, V.K. Gupta, V. Pérez-Abreu, E. Waymire (Eds.).
42. Troutman B.M., Over T.M. River flow mass exponents with fractal channel networks and rainfall. Advances in Water Resources 2001, 24:967-986.
43. Veitzer, S., 1999. A theoretical framework for understanding river networks: connecting process, geometry and topology across many scales. Ph.D. thesis, Department of Civil and Environmental Engineering. University of Colorado, Boulder.
44. Veitzer S., Gupta V.K. Random self-similar river networks and derivations of Horton-type relations exhibiting statistical simple scaling. Water Resources Research 2000, 36(4):1033-1048.
45. Veitzer S., Troutman B., Gupta V.K. Power-law tail probabilities of drainage areas in river basins. Physical Review E 2003, 68:016123.