Efficient Uncertainty Analysis of TOPMODEL Using Particle Swarm Optimization

입자군집최적화 알고리듬을 이용한 효율적인 TOPMODEL의 불확실도 분석

  • Cho, Huidae (Staff Water Resources Engineer, Dewberry) ;
  • Kim, Dongkyun (Department of Civil Engineering, Hongik University) ;
  • Lee, Kanghee (Department of Civil Engineering, Hongik University)
  • 조희대 (미 듀베리사 수자원부) ;
  • 김동균 (홍익대학교 공과대학 토목공학과) ;
  • 이강희 (홍익대학교 공과대학 토목공학과)
  • Received : 2013.11.28
  • Accepted : 2014.02.07
  • Published : 2014.03.31


We applied the ISPSO-GLUE method, which integrates the Isolated-Speciation-based Particle Swarm Optimization (ISPSO) with the Generalized Likelihood Uncertainty Estimation (GLUE) method, to the uncertainty analysis of the Topography Model (TOPMODEL) and compared its performance with that of the GLUE method. When we performed the same number of model runs for the both methods, we were able to identify the point where the performance of ISPSO-GLUE exceeded that of GLUE, after which ISPSOGLUE kept improving its performance steadily while GLUE did not. When we compared the 95% uncertainty bounds of the two methods, their general shapes and trends were very similar, but those of ISPSO-GLUE enclosed about 5.4 times more observed values than those of GLUE did. What it means is that ISPSOGLUE requires much less number of parameter samples to generate better performing uncertainty bounds. When compared to ISPSO-GLUE, GLUE overestimated uncertainty in the recession limb following the maximum peak streamflow. For this recession period, GLUE requires to find more behavioral models to reduce the uncertainty. ISPSO-GLUE can be a promising alternative to GLUE because the uncertainty bounds of the method were quantitatively superior to those of GLUE and, especially, computationally expensive hydrologic models are expected to greatly take advantage of the feature.

멀티모달 최적화 알고리듬의 일종인 ISPSO와 불확실도 분석기법인 GLUE를 결합한 ISPSO-GLUE 기법을 TOPMODEL의 불확실도 분석에 적용하였으며, 그 결과를 GLUE 기법과 비교하였다. 두 기법 모두 같은 횟수만큼 모형을 실행하였을 때 ISPSO-GLUE 기법의 누적성능이 더 좋아지는 시점을 발견할 수 있었으며, 그 이후로도 ISPSO-GLUE 기법은 GLUE 기법과는 달리 점진적인 성능의 향상을 보여 주었다. 두 기법이 비슷한 모양과 양상의 95% 불확실도 구간을 생성하였다. 하지만 ISPSO-GLUE 기법이 약5.4배 더 많은 관측치를 포함하는 것으로 나타났으며 GLUE 기법에 비해 훨씬 적은횟수의 모형실행으로도 좋은 성능의 불확실도 구간을 얻을 수 있는 것으로 나타났다. ISPSO-GLUE 기법과 비교했을 때GLUE 기법이 최대 첨두유량의 감쇠곡선 부분에서 불확실도를 과대평가하였다. 이 시간대에 대해서는 GLUE의 경우 불확실도 를 줄이기 위해 더 많은 행동모형들을 찾을 필요가 있다. ISPSO-GLUE 기법이 정량적인 성능평가에서 훨씬 많은 관측치를 포함할 수 있었다는 것은 이 기법의 가능성을 잘 보여 주었다고 할 수 있으며, 특히 계산적으로 값비싼 수문모형에서는 보다 큰 성능의 차이를 보일 것으로 기대된다.



Supported by : 한국연구재단


  1. Arnold, J.G., Srinivasan, R., Muttiah, R.S., and Williams, J.R. (1998). "Large Area Hydrologic Modelling and Assessment, Part I: Model Development." Journal of the American Water Resources Association, Vol. 34, No. 1, pp. 73-89.
  2. Beven, K.J., and Kirkby, M.J. (1979). "A Physically Based, Variable Contributing Area Model of Basin Hydrology." Hydrological Sciences Bulletin, Vol. 24, pp. 43-69.
  3. Beven, K., and Binley, A. (1992). "The Future of Distributed Models: Model Calibration and Uncertainty Prediction." Hydrological Processes, Vol. 6, pp. 279-298.
  4. Beven, K.J., Quinn, P., Romanowicz, R., Freer, J., Fisher, J., and Lanb, R. (1995). TOPMODEL and GRIDATB: A User's Guide to the Distribution Versions, Lancaster University, p. 31.
  5. Beven, K., Smith, P., and Freer, J. (2008). "So Just Why Would A Modeller Choose To Be Incoherent?" Journal of Hydrology, Vol. 354, pp. 15-32.
  6. Blasone, R.-S., Vrugt, J.A., Madsen, H., Rosbjerg, D., Robinson, B.A., and Zyvoloski, G.A. (2008). Generalized Likelihood Uncertainty Estimation (GLUE) Using Adaptive Markov Chain Monte Carlo Sampling. Advances in Water Resources, Vol. 31, pp. 630-648.
  7. Cho, H. (2000). Development of a GIS Hydrologic Modeling System by Using the Programming Interface of GRASS GIS, Master's Thesis. Department of Civil Engineering, Kyungpook National University.
  8. Cho, H., Lee, D., Lee, K., Lee, J., and Kim, D. (2013). "Development and Application of a Storm Identification Algorithm that Conceptualizes Storms by Elliptical Shape." Journal of the Korean Society of Hazard Mitigation, Vol. 13, No. 5, pp. 325-335.
  9. Cho, H., and Olivera, F. (2009). "Effect of the Spatial Variability of Land Use, Soil Type, and Precipitation on Streamflows in Small Watersheds." Journal of the American Water Resources Association, Vol. 45, No. 3, pp. 673-686.
  10. Cho, H., Kim, D., Olivera, F., and Guikema, S.D. (2011). "Enhanced Speciation in Particle Swarm Optimization for Multi-Modal Problems." European Journal of Operational Research, Vol. 213, No. 1, pp. 15-23.
  11. Cho, H., and Olivera, F. (2014). "Application of Multimodal Optimization for Uncertainty Estimation of Computationally Expensive Hydrologic Models." Journal of Water Resources Planning and Management, Vol. 140, No. 3, pp. 313-321.
  12. Conrad, O. (2003). System for Automated Geoscientific Analyses Module Library: sim_hydrology, topmodel.cpp., accessed in October 2013.
  13. Draper, N.R., and Box, G.E. (1987). Empirical Model-Building and Response Surfaces. John Wiley and Sons Inc.
  14. Evans, M. (1991). Adaptive Importance Sampling and Chaining." Contemporary Mathematics, Vol. 115, pp. 137-143.
  15. GRASS Development Team. (2012). Geographic Resources Analysis Support System(GRASS GIS) Software. Open Source Geospatial Foundation Project.
  16. Hornik, K. (2008). Changes on CRAN. R News 8(2), 60-68., accessed in October 2013.
  17. Kim, D., Olivera, F., Cho, H., and Socolofsky, S. (2013). "Regionalization of the Modified Bartlett-Lewis Rectangular Pulse Stochastic Rainfall Model." Terrestrial, Atmospheric and Oceanic Sciences, Vol. 24, No 3, pp. 421-436.
  18. Mantovan, P., and Todini, E. (2006). Hydrological Forecasting Uncertainty Assessment: Incoherence of the GLUE Methodology. Journal of Hydrology, Vol. 330, pp. 368-381.
  19. McKay, M.D., Beckman, R.J., and Conover, W.J. (1979). "A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code." Technometrics Vol. 21, No. 2, pp. 239-245.
  20. Muleta, M.K., and Nicklow, J.W. (2005). "Sensitivity and Uncertainty Analysis Coupled with Automatic Calibration for a Distributed Watershed Model." Journal of Hydrology Vol. 306, pp. 127-145.
  21. Nash, J.E., and Sutcliffe, J.V. (1970). River Flow Forecasting Through Conceptual Models, Part I-A Discussion of Principles. Journal of Hydrology, Vol. 10, pp. 282-290.
  22. NOAA-CPC. (2013). National Oceanic & Atmospheric Administration-Climate Prediction Center. Joint Agricultural Weather Facility, U.S. Evaporation Data., accessed in September 2013.
  23. NOAA-NCDC. (2013). National Oceanic & Atmospheric Administration-National Climatic Data Center. Surface Data, Daily US., accessed in September 2013.
  24. Olaya, V. (2004). A Gentle Introduction to SAGA GIS., Accessed on September 13, 2013.
  25. R Development Core Team. (2006). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0.
  26. Thiessen, A.H., and Alter, J.C. (1911). Climatological Data for July, 1911: District No. 10, Great Basin. Monthly Weather Review July 1911:1082-1089.
  27. USGS. (2013a). U.S. Geological Survey. National Elevation Dataset (NED)., accessed in September 2013
  28. USGS. (2013b). U.S. Geological Survey. Surface-Water Daily Data for the Nation., accessed in September 2013.
  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 & Numerical Simulation, Vol. 10, No. 3, pp. 271-288.
  30. Zheng, Y., and Keller, A.A. (2007). Uncertainty Assessment in Watershed-Scale Water Quality Modeling and Management: 1. Framework and Application of Generalized Likelihood Uncertainty Estimation (GLUE) Approach. Water Resources Research 43, W08407.