Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
권호 표지
DOI QR코드

DOI QR Code

Analysis of drainage structure for river basin on the basis of power law distribution

멱함수 법칙분포를 기반으로 한 유역의 배수구조에 대한 해석

  • Kim, Joo-Cheol (International Water Resources Research Institute, Chungnam National University) ;
  • Kang, Heeseung (International Water Resources Research Institute, Chungnam National University) ;
  • Jung, Kwansue (Dept. of Civil Engineering, Chungnam National University)
  • 김주철 (충남대학교 국제수자원연구소) ;
  • 강희승 (충남대학교 국제수자원연구소) ;
  • 정관수 (충남대학교 토목공학과)
  • Received : 2016.01.22
  • Accepted : 2016.03.23
  • Published : 2016.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

This study aims at hydrologically demonstrating the universality of power law distribution by analyzing runoff aggregation structures of river basins. Power law distribution is fitted to cumulative drainage area of basins of interest by maximum likelihood, which results in the power law exponents. And then those exponents are assessed in terms of the shape of catchment plan-form. As a main result all of the basins in this study have similar distributions of catchment area. The exponents from this study tend to be higher than the ones from previous researches reflecting self-similar property of the catchment plan-forms of interest. Further study is required about the universality of power law distribution by means of the more realistic flow routing scheme within the framework of DEM.

본 연구의 주목적은 유역의 유출응집구조를 분석하고 이를 기반으로 멱함수 법칙분포의 대표적 특성인 보편성을 수문학적 관점에서 입증해 보고자 하는 것이다. 이를 위하여 최우법에 따라 집수면적의 누가분포에 대한 멱함수 법칙분포의 적합을 수행하였으며 이로부터 도출된 멱함수 법칙분포의 지수를 집수평면의 형상을 기반으로 평가하여 보았다. 주요한 결과로서 본 연구의 대상 유역들은 집수평면의 규모에 대하여 거의 모두 동일한 형태의 분포를 취하고 있음을 확인할 수 있었다. 본 연구에서 얻은 멱함수 법칙분포의 지수는 선행연구에서 제시된 값에 비하여 다소 큰 수치로 나타났는데 이는 본 연구의 대상유역들이 가진 자기상사성의 특징을 반영하는 것으로 판단된다. 향후 DEM을 기반으로 보다 더 실제에 가까운 흐름방향모의를 통한 집수평면의 멱함수 법칙분포의 보편성에 대한 연구가 반드시 수행되어야 할 것이다.

Keywords

References

  1. Bak, P. Tang, C. and Wiessenfeld, K. (1987). "Self-Organized Criticality: An explanation of 1/f noise." Physical Review Letters, Vol. 59, pp.381-384. https://doi.org/10.1103/PhysRevLett.59.381
  2. Bak, P. (1996). How nature works, Copernicus/Springer - Verlag, New York.
  3. Bras, R.L. and Rodriguez-Iturbe, I. (1985) Random Function and Hydrology, Courier Corporation.
  4. Clauset, A., Shalizi, C.R. and Newman, M.E.J. (2009). "Power-Law Distributions in Empirical Data." Siam Review, Vol. 51, No 4, pp. 661-703. https://doi.org/10.1137/070710111
  5. De Vries, H., Becker, T. and Eckhardt, B. (1994). "Power law distribution of discharge in ideal networks." Water Resources Research, Vol. 30, No. 12, pp. 3541-3543. https://doi.org/10.1029/94WR02178
  6. Eagleson, P.S. (1970). Dynamic Hydrology. McGraw-Hill.
  7. Feller, W. (1971). An Introduction Probability Theory and its Applications. Wiley and Sons.
  8. Furey, P.R. and Troutman, B.M. (2008). "A consistent framework for Horton regression statistics that leads to a modified Hack's law." Geomorphology, Vol. 102, pp. 603-614. https://doi.org/10.1016/j.geomorph.2008.06.002
  9. Hack, J.T. (1957). "Studies of longitudinal profiles in Virginia and Maryland." US Geological Survey Professional Paper, 294-B pp. 45-97.
  10. Hergarten, S. and Neugebauer, H. J. (2001). "Self-Organized Critical Drainage Networks." Physical Review Letters, Vol. 86, No. 12, pp. 2689-2692. https://doi.org/10.1103/PhysRevLett.86.2689
  11. Hergarten, S. (2002). Self-organized criticality in earth system. Springer-Verlag, New York.
  12. Inaoka, H. and Takayasu, H. (1983). "Water erosion as a fractal growth process." Physical Review E, Vol. 47, No. 2, pp. 899-910. https://doi.org/10.1103/PhysRevE.47.899
  13. Khan, U., Tuteja, N.K., and Sharma, A. (2013). "Delineating hydrologic response units in large upland catchments and its evaluation using soil moisture simulations." Environmental Modelling & Software, Vol. 46, pp. 142-154. https://doi.org/10.1016/j.envsoft.2013.03.005
  14. Kim, J.C. and Lee, S. (2009). "Hack's Law and the Geometric Properties of Catchment Plan-Form." Journal of Korean Water Resources Association, Vol. 42, No. 9, pp. 691-702. https://doi.org/10.3741/JKWRA.2009.42.9.691
  15. La Barbera, P. and Roth, G. (1994). "Invariance and Scaling Properties in the Distributions of Contributing Area and Energy in Drainage Basins." Hydrological Processes, Vol. 8, pp. 125-135. https://doi.org/10.1002/hyp.3360080204
  16. La Barbera, P. and Lanza, L. G. (2001). "On the cumulative area distribution of natural drainage basins along a coastal boundary." Water Resources Research, Vol. 37, No. 5, pp. 1503-1509. https://doi.org/10.1029/2000WR900382
  17. Mandelbrot, B.B. and Van Ness, J.W. (1968). "Fractional Brownian Motion. Fractional Noises and Applications" Society for Industrial and Applied Mathematics, Vol. 10, No. 4, pp. 427-437.
  18. Mandelbrot, B.B. (1982). The Fractal geometry of nature. W. H. Freeman, New York.
  19. Maritan, A., Rinaldo, A., Rigon, A., Giacometti, A. and Rodriguez-Iturbe, I. (1996). "Scaling laws for river networks." Physical Review E, Vol. 53, No. 2, pp. 1510-1515. https://doi.org/10.1103/PhysRevE.53.1510
  20. McNamara, J.P., Ziegler, A.D., Wood, S.H. and Vogler, J.B. (2006). "Channel head locations with respect to geomorphologic thresholds derived from a digital elevation model: A case study in northern Thailand." Forest Ecology and Management, Vol. 224, pp. 147-156. https://doi.org/10.1016/j.foreco.2005.12.014
  21. Moglen, G.E. and Bras, R. L. (1995). "The importance of spatially heterogeneous erosivity and the cumulative area distribution within a basin evolution model." Geomorphology, Vol. 12, pp. 173-185. https://doi.org/10.1016/0169-555X(95)00003-N
  22. Newman, M.E.J. (2005). "Power laws, Pareto distributions and Zipf's law." Contemporary Physics, Vol. 46, No. 5, pp. 323-351. https://doi.org/10.1080/00107510500052444
  23. Nicholson, B.G., Hancock, G.R., Cohen, S., Willgoose, G.R. and Rey-Lescure, O. (2013). "An assessment of the fluvial geomorphology of subcatchments in Parana Valles, Mars." Geomorphology, Vol. 183, pp. 96-109. https://doi.org/10.1016/j.geomorph.2012.07.018
  24. Paik, K. and Kumar, P. (2007) "Inevitable self-similar topology of binary trees and their diverse hierarchical density" European Physical Journal B, Vol. 60, No. 2, pp. 247-258. https://doi.org/10.1140/epjb/e2007-00332-y
  25. Paik, K. and Kumar, P. (2011). "Power-Law Behavior in Geometric Characteristics of Full Binary Trees." Journal of Statistical Physics, Vol. 142, No. 4, pp. 862-878. https://doi.org/10.1007/s10955-011-0125-y
  26. Perera, H. and Willgoose, G. (1998). "A physical explanation of the cumulative area distribution curve." Water Resources Research, Vol. 34, No. 5, pp. 1335-1343. https://doi.org/10.1029/98WR00259
  27. Rodriguez-Iturbe, I., Ijjasz-Vasquez R, E. J., Bras, R.L. and Tarboton, D.G. (1992). "Power law distributions of discharge, mass, and energy in river basins." Water Resources Research, Vol. 28, No. 4, pp. 1089-1093. https://doi.org/10.1029/91WR03033
  28. Rodriguez-Iturbe, I. and Rinaldo, A. (2003). Fractal river basins-Chance and self-organization. Cambridge.
  29. Scheidegger, A.E. (1967). "A stochastic model for drainage patterns into an intramontane trench." Bull. Assoc. Sci. Hydrol., Vol. 12, pp. 15-20. https://doi.org/10.1080/02626666709493507
  30. Smart, J.S. (1972). "Channel Networks", Advances in Hydroscience, Vol. 8, pp. 305-346. https://doi.org/10.1016/B978-0-12-021808-0.50011-5
  31. Sun, T., Meakin, P. and Jossang, T. (1994). "Minimum energy dissipation model for river basin geometry." Physical Review E, Vol. 49, No. 6, pp. 4865-4872. https://doi.org/10.1103/PhysRevE.49.4865
  32. Takayasu, H., Nishikawa, I. and Tasaki, H. (1988). "Power-law mass distribution of aggregation systems with injection." Physical Review A, Vol. 37, pp. 3110-3117. https://doi.org/10.1103/PhysRevA.37.3110
  33. Willgoose, G., Bras, R.L. and Rodriguez-Iturbe, I. (1991). "A coupled channel network growth and hillslope evolution model, 1. Theory." Water Resources Research, Vol. 27, No. 7, pp. 1671-1684. https://doi.org/10.1029/91WR00935
  34. Yoon Y. (2007). Hydrology, Cheongmoongak.

Cited by

  1. Application of Geomorphologic Factors for Identifying Soil Loss in Vulnerable Regions of the Cameron Highlands vol.10, pp.4, 2018, https://doi.org/10.3390/w10040396
  2. Analysis of Runoff Aggregation Structures with Different Flow Direction Methods under the Framework of Power Law Distribution vol.32, pp.14, 2018, https://doi.org/10.1007/s11269-018-2074-6