Browse > Article
http://dx.doi.org/10.3741/JKWRA.2009.42.9.691

Hack's Law and the Geometric Properties of Catchment Plan-form  

Kim, Joo-Cheol (Korea Institute of Water and Environment)
Lee, Sang-Jin (Korea Institute of Water and Environment)
Publication Information
Journal of Korea Water Resources Association / v.42, no.9, 2009 , pp. 691-702 More about this Journal
Abstract
This study makes a systematic approach to Hack's law considering self-affinity and self-similarity of natural basins as well as the elongation of corresponding catchment-plan forms. Catchment-plan forms extracted from DEM appear to be the population come from the interactions of 2 hypotheses on Hack's law. It is judged that the elongation measures based on inertia moments are more intuitive than the ones based on main channel lengths. The exponent of Hack's law, h, seems to be similar to the result of Gray's study (1961). However Hurst exponent, H, being 0.96 imply that catchment-plan forms considered in this study have isotropic increasing properties with scale. From this point of view it is inferred that the shapes of the basins in this study would be more affected from self-similarity of main channel lengths than self-affinity of catchment-plan forms.
Keywords
Hack's law; catchment plan-form; elongation; self-affinity; self-similarity;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Shreve, R.L. (1966). “Statistical law of stream numbers.” Journal of Geology, Vol. 74, pp. 17-37   DOI
2 Tarboton, D.G., Bras, R.L. and Rodríguez-Iturbe, I. (1988). “The Fractal nature of river networks.” Water Resources Research, Vol. 24, No. 8, pp. 1317-1322   DOI
3 Gray, D.M. (1961). “Interrelationships of watershed characteristics.” Journal of Geophysical Research, Vol. 66, No. 4, pp. 1215-1223   DOI
4 Horton, R.E. (1932). “Drainage-basin characteristics.” Transactions of the American Geophysical Union, Vol. 13, pp. 350-361.   DOI
5 Feder, J. (1988). Fractals. Plenum
6 Hack, J.T. (1957). “Studies of longitudinal profiles in Virginia and Maryland.” US Geological Survey Professional Paper, 294-B pp. 45-97
7 Hergarten, S. (2002). Self-organized criticality in earth system. Springer-Verlag, New York
8 양창현 (1996). 구조역학. 청문각
9 Mandelbrot, B.B. (1982). The Fractal geometry of nature. W. H. Freeman, New York
10 김재한 (2005). 수문계의 수학적 모형-선형계를 중심으로-. 새론
11 Abraham, A.D. (1984). “Channel network: A geomorphological perspective.” Water Resources Research, Vol. 20, No. 2, pp. 161-188   DOI
12 Brierley, G.J. and Fryirs, K.A. (2005). Geomorphology and river management. Blackwell
13 Eagleson, P.S. (1970). Dynamic Hydrology. McGraw- Hill
14 Maritan, A., Rinaldo, A., Rigon, R., Giacometti, A. and Rodríguez-Iturbe, I. (1996). “Scaling laws for river networks.” Physical Review E, Vol. 53, No. 2, pp. 1510-1515   DOI   ScienceOn
15 Rigon, R., Rodríguez-Iturbe, I., Maritan, A., Giacometti, A., Tarboton, D.G. and Rinaldo, A. (1996). “On Hack's law.” Water Resources Research, Vol. 32, No. 11, pp. 3367-3374   DOI   ScienceOn
16 Rodriguez-Iturbe, I. and Rinaldo, A. (2003). Fractal river basins-Chance and self-organization. Cambridge
17 Shumm, S.A. (1956). Evolution of drainage systems and slopes in badlands ar Perth Amboy, New Jersey. ” Geological Society of America Bulletin, Vol. 67, pp. 597-646   DOI
18 Smart, J.S. (1972). “Channel Networks.” Advances in Hydroscience, Vol. 8, pp. 305-346   DOI
19 Strahler, A.N. (1964). Quantitative geomorphology of drainage basins and channel networks. In: Handbook of Applied Hydrology. McGraw-Hill, pp. 4.39-4.76
20 Bak, P. (1996). How nature works. Copernicus/ Springer-Verlag, New York
21 Moussa, R. (2003). “On morphometric properties of basins, scale effects and hydrological response.” Hydrological Processes, Vol. 17, pp. 33-58   DOI   ScienceOn