한국수자원학회논문집 (Journal of Korea Water Resources Association)

  • 제52권10호
  • /
  • Pages.681-695
  • /
  • 2019
  • /
  • 2799-8746(pISSN)
  • /
  • 2799-8754(eISSN)
한국수자원학회 (Korea Water Resources Association)
권호 표지
DOI QR코드

DOI QR Code

저장대모형의 매개변수 산정을 위한 최적화 기법의 적합성 분석

Analysis of the applicability of parameter estimation methods for a transient storage model

  • 노효섭 (서울대학교 건설환경공학부) ;
  • 백동해 (서울대학교 건설환경공학부) ;
  • 서일원 (서울대학교 건설환경공학부)
  • Noh, Hyoseob (Department of Civil and Environmental Engineering, Seoul National University) ;
  • Baek, Donghae (Department of Civil and Environmental Engineering, Seoul National University) ;
  • Seo, Il Won (Department of Civil and Environmental Engineering, Seoul National University)
  • 투고 : 2019.07.16
  • 심사 : 2019.09.20
  • 발행 : 2019.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Transient Stroage Model (TSM)은 하천을 본류대와 저장대로 나누어 각각에 대한 오염물의 혼합거동을 해석함으로써 복잡한 하천에 유입된 오염물질 혼합을 이해하는 데에 가장 많이 이용되는 모형 중 하나이다. TSM의 매개변수들은 역산모형을 통해 산정하게 되는데 이는 자연하천에서 추적자실험을 통해 계측된 농도곡선에 가장 잘 맞는 TSM 모의 농도곡선을 찾는 최적화 문제이다. 저장대모형의 매개변수 산정에 관한 선행 연구들에 의해 매개변수를 산정하는 최적화 문제의 비볼록(non-convex) 특성에서 오는 불확실성이 보고되어 왔다. 본 연구에서는 청미천에서 수행된 추적자실험으로부터 취득된 농도곡선을 이용해 최상의 최적화 기법과 목적함수의 조합에 대해 분석하였다. 최적화 문제의 수렴성과 수렴 속도를 모두 만족하는 최적화 조건을 결정하기 위해 SCE-UA의 CCE와 SP-UCI의 MCCE와 같은 진화 알고리즘 기반의 전역 최적화 방법들과 오차 기반 목적함수들을 Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL)을 활용해 비교하였다. 전반적인 변수 산정 결과 여러 EA를 동시에 적용한 SC-SAHEL을 평균 제곱오차를 목적함수로 한 방법이 가장 빠르고 가장 안정적으로 최적해에 수렴하는 것으로 나타났다.

A Transient Storage Model (TSM) is one of the most widely used model accounting for complex solute transport in natural river to understanding natural river properties with four TSM key parameters. The TSM parameters are estimated via inverse modeling. Parameter estimation of the TSM is carried out by solving optimization problem about finding best fitted simulation curve with measured curve obtained from tracer test. Several studies have reported uncertainty in parameter estimation from non-convexity of the problem. In this study, we assessed best combination of optimization method and objective function for TSM parameter estimation using Cheong-mi Creek tracer test data. In order to find best optimization setting guaranteeing convergence and speed, Evolutionary Algorithm (EA) based global optimization methods, such as CCE of SCE-UA and MCCE of SP-UCI, and error based objective functions were compared, using Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL). Overall results showed that multi-EA SC-SAHEL with Percent Mean Squared Error (PMSE) objective function is the best optimization setting which is fastest and stable method in convergence.

키워드

참고문헌

  1. Arcement, G. J., and Schneider V. R. (1989). Guide for selecting Manning's roughness coefficients for natural channels and flood plains. U.S. Geological Survey, Water-Supply Paper 2339.
  2. Bencala, K. E., and Walters, R. A. (1983). "Simulation of solute transport in a mountain pool-and-riffle stream: A transient storage model." Water Resources Research, Vol. 19, No. 3, pp. 718-724. https://doi.org/10.1029/WR019i003p00718
  3. Boano, F., Harvey, J. W., Marion, A., Packman, A. I., Revelli, R., Ridolfi, L., and Worman, A. (2014). "Hyporheic flow and transport processes: Mechanisms, models, and biogeochemical implications: Hyporheic flow and transport processes." Reviews of Geophysics, Vol. 52, No. 4, pp. 603-679. https://doi.org/10.1002/2012RG000417
  4. Boano, F., Packman, A. I., Cortis, A., Revelli, R., and Ridolfi, L. (2007). "A continuous time random walk approach to the stream transport of solutes: A CTRW approach to stream transport." Water Resources Research, Vol. 43, No. 10.
  5. Choi, J., Harvey, J. W., and Conklin, M. H. (2000). "Characterizing multiple timescales of stream and storage zone interaction that affect solute fate and transport in streams." Water Resources Research, Vol. 36, No. 6, pp. 1511-1518. https://doi.org/10.1029/2000WR900051
  6. Chu, W., Gao, X., and Sorooshian, S. (2010). "Improving the shuffled complex evolution scheme for optimization of complex nonlinear hydrological systems: Application to the calibration of the Sacramento soil-moisture accounting model: improving the shuffled complex." Water Resources Research, Vol. 46, No. 9.
  7. Deng, Z.-Q., Singh, V. P., and Bengtsson, L. (2004). "Numerical solution of fractional advection-dispersion equation." Journal of Hydraulic Engineering, Vol. 130, No. 5, pp. 422-431. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:5(422)
  8. Duan, Q. Y., Gupta, V. K., and Sorooshian, S. (1993). "Shuffled complex evolution approach for effective and efficient global minimization." Journal of Optimization Theory and Applications, Vol. 76, No. 3, pp. 501-521. https://doi.org/10.1007/BF00939380
  9. Eusuff, M. M., and Lansey, K. E. (2003). "Optimization of water distribution network design using the shuffled frog leaping algorithm." Journal of Water Resources Planning and Management, Vol. 129, No. 3, pp. 210-225. https://doi.org/10.1061/(ASCE)0733-9496(2003)129:3(210)
  10. Eusuff, M., Lansey, K., and Pasha, F. (2006). "Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization." Engineering Optimization, Vol. 38, No. 2, pp. 129-154. https://doi.org/10.1080/03052150500384759
  11. Gooseff, M. N., Briggs, M. A., Bencala, K. E., McGlynn, B. L., and Scott, D. T. (2013). "Do transient storage parameters directly scale in longer, combined stream reaches? Reach length dependence of transient storage interpretations." Journal of Hydrology, Vol. 483, pp. 16-25. https://doi.org/10.1016/j.jhydrol.2012.12.046
  12. Hadka, D., and Reed, P. (2013). "Borg: An auto-adaptive many-objective evolutionary computing framework." Evolutionary Computation, Vol. 21, No. 2, pp. 231-259. https://doi.org/10.1162/EVCO_a_00075
  13. Harvey, J. W., and Bencala, K. E. (1993). "The effect of streambed topography on surface-subsurface water exchange in mountain catchments." Water Resources Research, Vol. 29, No. 1, pp. 89-98. https://doi.org/10.1029/92WR01960
  14. Harvey, J. W., Wagner, B. J., and Bencala, K. E. (1996). "Evaluating the reliability of the stream tracer approach to characterize stream-subsurface water exchange." Water Resources Research, Vol. 32, No. 8, pp. 2441-2451. https://doi.org/10.1029/96WR01268
  15. Holland, J. (1975). Adaptation in natural and artificial systems. Ann Arbor, MI: University of Michigan Press.
  16. Jackson, T. R., Haggerty, R., and Apte, S. V. (2013). "A fluid-mechanics based classification scheme for surface transient storage in riverine environments: quantitatively separating surface from hyporheic transient storage." Hydrology and Earth System Sciences, Vol. 17, No. 7, pp. 2747-2779. https://doi.org/10.5194/hess-17-2747-2013
  17. Kerr, P. C., Gooseff, M. N., and Bolster, D. (2013). "The significance of model structure in one-dimensional stream solute transport models with multiple transient storage zones - competing vs. nested arrangements." Journal of Hydrology, Vol. 497, pp. 133-144. https://doi.org/10.1016/j.jhydrol.2013.05.013
  18. Kilpatrick, F. A., and Wilson, J. F. (1989). Measurement of time of travel in streams by dye tracing (Vol. 3). US Government Printing Office.
  19. Mariani, V. C., Luvizotto, L. G. J., Guerra, F. A., and dos Santos Coelho, L. (2011). "A hybrid shuffled complex evolution approach based on differential evolution for unconstrained optimization." Applied Mathematics and Computation, Vol. 217, No. 12, pp. 5822-5829. https://doi.org/10.1016/j.amc.2010.12.064
  20. Marion, A., and Zaramella, M. (2005). "Diffusive behavior of bedform-induced hyporheic exchange in rivers." Journal of Environmental Engineering, Vol. 131, No. 9, pp. 1260-1266. https://doi.org/10.1061/(ASCE)0733-9372(2005)131:9(1260)
  21. Mirjalili, S., Mirjalili, S. M., andLewis, A. (2014). "Grey wolf optimizer." Advances in engineering software, Vol. 69, pp. 46-61. https://doi.org/10.1016/j.advengsoft.2013.12.007
  22. Naeini, M., Yang, T., Sadegh, M., AghaKouchak, A., Hsu, K., Sorooshian, S., Duan, Q., and Lei, X. (2018). "Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL) optimization framework." Environmental Modelling & Software, Vol. 104, pp. 215-235. https://doi.org/10.1016/j.envsoft.2018.03.019
  23. National Institute of Environmental Research (NIER) (2015). Development and application of validation technique for advection-diffusion of dissolved pollutants using tracer experiments (II), Ministry of Environment (in Korean).
  24. Nelder, J. A., and Mead, R. (1965). "A simplex method for function minimization." The Computer Journal, Vol. 7, No. 4, pp. 308-313. https://doi.org/10.1093/comjnl/7.4.308
  25. Runkel, R. L. (1998). One-dimensional transport with inflow and storage (OTIS): A solute transport model for streams and rivers. Water-Resources Investigations Report, 98, 4018.
  26. Seo, I. W., and Maxwell, W. H. C. (1992). "Modeling low-flow mixing through pools and riffles." Journal of Hydraulic Engineering, Vol. 118, No. 10, pp. 1406-1423. https://doi.org/10.1061/(ASCE)0733-9429(1992)118:10(1406)
  27. Storn, R., and Price, K. (1997). "Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces." Journal of Global Optimization, Vol. 11, No. 4, pp. 341-359. https://doi.org/10.1023/A:1008202821328
  28. Vrugt, J. A., and Robinson, B. A. (2007). "Improved evolutionary optimization from genetically adaptive multimethod search." Proceedings of the National Academy of Sciences, Vol. 104, No. 3, pp. 708-711. https://doi.org/10.1073/pnas.0610471104
  29. Vrugt, J. A., Ter Braak, C. J. F., Diks, C. G. H., Robinson, B. A., Hyman, J. M., and Higdon, D. (2009). "Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling." International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 10, No. 3, pp. 273-290. https://doi.org/10.1515/ijnsns.2009.10.3.273
  30. Wagener, T., Camacho, L. A., and Wheater, H. S. (2002). "Dynamic identifiability analysis of the transient storage model for solute transport in rivers." Journal of Hydroinformatics, Vol. 4, No. 3, pp. 199-211. https://doi.org/10.2166/hydro.2002.0019
  31. Wagner, B. J., and Harvey, J. W. (1997). "Experimental design for estimating parameters of rate-limited mass transfer: Analysis of stream tracer studies." Water Resources Research, Vol. 33, No. 7, pp. 1731-1741. https://doi.org/10.1029/97WR01067
  32. Ward, A. S., Kelleher, C. A., Mason, S. J. K., Wagener, T., McIntyre, N., McGlynn, B., Runkel, R. L., and Payn, R. A. (2017). "A software tool to assess uncertainty in transient-storage model parameters using Monte Carlo simulations." Freshwater Science, Vol. 36, No. 1, pp. 195-217. https://doi.org/10.1086/690444
  33. Ward, A. S., Kelleher, C. A., Mason, S. J., Wagener, T., McIntyre, N., McGlynn, B., Runkel, R. L., and Payn, R. A. (2017). "A software tool to assess uncertainty in transient-storage model parameters using Monte Carlo simulations." Freshwater Science, Vol. 36, No. 1, pp. 195-217 https://doi.org/10.1086/690444
  34. Wolpert, D. H., and Macready, W. G. (1997). "No free lunch theorems for optimization." IEEE Transactions on Evolutionary Computation, Vol. 1, No. 1, pp. 67-82. https://doi.org/10.1109/4235.585893
  35. Worman, A., Packman, A. I., Johansson, H., and Jonsson, K. (2002). "Effect of flow-induced exchange in hyporheic zones on longitudinal transport of solutes in streams and rivers: Effect of flow-induced exchange." Water Resources Research, Vol. 38, No. 1, pp. 2-1-2-15.
  36. Zhu, J., Hoi, S. C., and Lyu, M. R. T. (2008). "Robust regularized kernel regression." IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), Vol. 38, No. 6, pp. 1639-1644. https://doi.org/10.1109/TSMCB.2008.927279