Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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Analysis of runoff aggregation structure and energy expenditure pattern for Choyang creek basin on the basis of power law distribution

멱함수 법칙분포를 기반으로 한 조양하 유역의 유출응집구조와 에너지소비 양상에 대한 해석

  • Kim, Joo-Cheol (International Water Resources Research Institute, Chungnam National University) ;
  • Cui, Feng Xue (Yanbian Water & Electricity Survey Designing Research Institute) ;
  • Jung, Kwan Sue (Department of Civil Engineering, Chungnam National University)
  • 김주철 (충남대학교 국제수자원연구소) ;
  • 최봉학 (연변수리수전탐사설계연구원) ;
  • 정관수 (충남대학교 토목공학과)
  • Received : 2017.06.28
  • Accepted : 2017.09.11
  • Published : 2017.11.30
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Abstract

The main purpose of this study is to analyze runoff aggregation structure and energy expenditure pattern of Choyang creek basin within the framework of power law distribution. To this end geomorphologic factors of every point in the basin of interest, which define tractive force and stream power as well as drainage area, are extracted based on GIS, and their complementary cumulative distributions are graphically analyzed through fitting them to power law distribution. The results indicate that three distinct behavioral regimes are observed from the complementary cumulative distributions of three geomorphogic factors. Based on the parameter estimation of power law distribution by maximum likelihood drainage area and stream power can be judged as scale invariance factor without finite scale while tractive force as scale dependence factor with finite scale. Furthermore, it is judged that tractive force would not follow power law distribution because it shows limited complex system behaviors only within the small extent of scale. The exponent of power law distribution for drainage area obtained in this study by maximum likelihood is larger than the previous researches due to the difference of parameter estimation methodologies. And the exponent for stream power is smaller than the previous researches due to the scaling property of channel slope for the basin of interest.

본 연구의 주목적은 조양하 유역의 유출응집구조와 에너지소비 양상을 멱함수 법칙분포의 틀 내에서 해석하는 것이다. 이를 위하여 GIS를 기반으로 대상유역 내 지점별 배수면적과 함께 소류력 및 수류력을 정의하는 지형학적 인자를 추출하고 해당 인자들의 여누가 분포에 대한 도해적 해석과 함께 멱함수 법칙분포의 적합을 수행하였다. 주요한 결과로서 세 가지 지형학적 인자들의 여누가 분포는 세 개의 개별적인 거동특성 구간으로 구분할 수 있었다. 멱함수 법칙분포 확률밀도함수의 매개변수를 최우도법을 이용하여 추정해 본 결과 배수면적과 수류력은 대표적인 규모를 유한하게 결정할 수 없는 규모 불변성 지형인자이지만 소류력은 유한한 규모를 갖는 규모 종속성 지형학적 인자로 판단할 수 있었다. 또한 소류력의 경우 제한된 범위 내에서만 복잡계 거동을 보여 멱함수 법칙분포를 따르지 않는 것으로 판단되었다. 최우도법을 적용하여 추정한 배수면적의 멱함수 법칙분포 지수는 선행연구에 비하여 큰 수치로서 해당 지수의 추정에 사용된 방법론의 차이에 기인하는 것임을 확인할 수 있었다. 또한 수류력의 멱함수 법칙분포 지수는 선행연구에 비하여 다소 작은 수치로서 대상유역의 규모에 따른 수로경사의 특성에 기인하는 것으로 판단되었다.

Keywords

References

  1. Bak, P. (1996). How nature works. Copernicus/Springer-Verlag, New York.
  2. 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
  3. 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
  4. Flint, J. J. (1974). "Stream gradient as a function of order, magnitude, and discharge." Water Resources Research, Vol. 10, No. 5, 969-973. https://doi.org/10.1029/WR010i005p00969
  5. Horton, R. E. (1945). "Erosional development of streams and their drainage basins; hydrophysical approach to quantitative morphology." Geological Society of America Bulletin, Vol. 56, No. 3, 275-370. https://doi.org/10.1130/0016-7606(1945)56[275:EDOSAT]2.0.CO;2
  6. 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
  7. Kim, J. C., Kang, H., and Jung, K. (2016). "Analysis of drainage structure for river basin on the basis of power law distribution." Journal of Korea Water Resources Association, Vol. 49, No. 6, pp. 495-507. https://doi.org/10.3741/JKWRA.2016.49.6.495
  8. 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
  9. Leopold, L. B., and Maddock, T. (1953). The hydraulic geometry of stream channels and some physiographic implications. US Government Printing Office, Vol. 252.
  10. Mandelbrot, B. B. (1982). The Fractal geometry of nature. W.H. Freeman, New York.
  11. 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.
  12. 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
  13. 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
  14. 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
  15. Montgomery, D. R., and Dietrich, W. E. (1992). "Channel initiation and the problem of landscape scale." Science, Vol. 255, No. 5046, pp. 826-830. https://doi.org/10.1126/science.255.5046.826
  16. Montgomery, D. R., and Foufoula-Georgiou, E. (1993). "Channel network source representation using digital elevation models." Water Resources Research, Vol. 29, No. 12, pp. 3925-3934. https://doi.org/10.1029/93WR02463
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. Pilgrim, D. H. (1977). "Isochrones of travel time and distribution of flood storage from a tracer study on a small watershed." Water Resources Research, Vol. 13, No. 3, 587-595. https://doi.org/10.1029/WR013i003p00587
  23. Rodriguez-Iturbe, I., and Rinaldo, A. (2003). Fractal river basins-Chance and self-organization. Cambridge.
  24. Rodriguez-Iturbe, I., Ijjasz-Vasquez, 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
  25. 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
  26. 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