Comparison of Automatic Calibration for a Tank Model with Optimization Methods and Objective Functions

  • Kang, Min-Goo (Graduate School, Dept. of Agricultural Engineering, Seoul National University) ;
  • Park, Seung-Woo (Dept. of Agricultural Engineering, Seoul National University) ;
  • Park, Chang-Eun (Dept. of Civil Engineering, Shingu College)
  • Published : 2002.12.01

Abstract

Two global optimization methods, the SCE-UA method and the Annealing-simplex (A-S) method for calibrating a daily rainfall-runoff model, a Tank model, was compared with that of the Downhill Simplex method. The performance of the four objective functions, DRMS (daily root mean square), HMLE (heteroscedastic maximum likelihood estimator), ABSERR (mean absolute error), and NS (Nash-Sutcliffe measure), was tested and synthetic data and historical data were used. In synthetic data study. 100% success rates for all objective functions were obtained from the A-S method, and the SCE-UA method was also consistently able to obtain good estimates. The downhill simplex method was unable to escape from local optimum, the worst among the methods, and converged to the true values only when the initial guess was close to the true values. In the historical data study, the A-S method and the SCE-UA method showed consistently good results regardless of objective function. An objective function was developed with combination of DRMS and NS, which putted more weight on the low flows.

Keywords

References

  1. Cardso, M. F., Salcedo R. L., and Azevedo S. F. (1996). 'The simplex-simulated annealing approach to continuous nonlinear optimization.' Computers and Chemical Engineering, 20(9), 1065-1080
  2. Cooper V. A., Nguyen V. T. V., and Nicell J. A. (1997). 'Evaluation of global optimization methods for conceptual rainfall-runoff model calibration', Water Science and Technology, 36(5), 53-60
  3. Diskin M. H. and Simon E. (1977). 'A procedure for the selection of objective functions for hydrologic simulation models.' Journal of Hydrology, 34, 129-149
  4. Duan Q., Soroooshian S., and Gupta V. K. (1994). 'Optimal use of the SCE-VA global optimization method for calibrating watershed models.', Journal of Hydrology, 158, 265-284
  5. Duan Q., Soroooshian S., and Gupta V. K. (1992). 'Effective and efficient global optimization for conceptual rainfall-runoff models.' Water Resources Research, 28(4), 1015-1031
  6. Franchini, M. and Pacciani M. (1991). 'Comparative analysis of several conceptual rainfall-runoff models.' Journal of Hydrology, 122, 161-219
  7. Freedman V. L., Lopes, V. L., and Hernandez, M. (1998). 'Parameter identifiability for catchment-scale erosion modelling: a comparison of optimization algorithms, Journal of Hydrology, 207, 83-97
  8. Gan T. Y. and Biftu G. F. (1996). 'Automatic calibration of conceptual rainfall-runoff models: Optimization algorithms, catchment conditions, and model structure.' Water Resources Research, 32(12), 3513-3524
  9. Gan T. Y. Dlamini E. M., and Biftu G. F. (1997). 'Effects of model complexity and structure, data quality, and objective functions on hydrologic modeling.' Journal of Hydrology, 192, 81-103
  10. Gribb M. M. (1996). 'Parameter estimation for determining hydraulic properties of a fine sand from transient flow measurements.' Water Resources Research, 32(7), 1965-1974
  11. Gupta H. V., Sorooshian S., and Yapo P. O. (1999). 'Status of automatic calibration for hydrologic model : Comparison with multilevel expert calibration.' Journal of Hydrologic Engineering, 4(2), 135-143
  12. Huh Y. M., Park S. W., and Park C. E. (1993). 'A streamflow network model for daily water supply and demands on small watershed' Journal of The Korean society of agricultural engineers, 35(3), 23-35
  13. Isabel D. and Villeeneuve J. P. (1986). 'Importance of the convergence criterion in the automatic calibration of hydrologic models.' Water Resources Research, 22(10), 1367-1370
  14. Kvasnicka V. and Pospichal J.(1997). 'A hybrid of simplex method simulated annealing.' Chemometrics and Intelligent Laboratory System, 39, 161-173
  15. Lee Y. H. and Singh V. P. (1999). 'Tank model using Kalman filter.' Journal of Hydrologic Engineering, 4(4), 344-349
  16. Liu. P., Chen J., and Hartzell S. H. (1995). 'A improved simulated annealing downhill simplex hybrid global inverse algorithm.' Acta Geophys. Sin., 38, 199-205
  17. Neider J. A and Mead R(1965). 'A simplex method for function minimization.' Computer Journal, 7(4), 308-313
  18. Pan L. and Wu L. (1998). 'A hybrid global optimization method for inverse estimation of hydraulic parameters: Annealing-simplex method.' Water Resources Research, 34(9), 2261-2269
  19. Press, W. H., Teukolsky S. A., Vetterling W. T., and Flannery B. P.(1992). Numerical Recipes in C, 2nd edition, Cambridge University Press, Cambridge, U. K.
  20. Press, W. H. Teukolsky W. T., and Flannery B. P. (1991). 'Simulating annealing optimization over continuous spaces.' Comput. Phys. 5(4), 426
  21. Sorooshian, S., and Gupta V. K. (1983). 'Automatic calibration of conceptual rainfall-runoff models: the question of parameter observability and uniqueness.' Water Resources Research, 19(1), 260-268
  22. Sugawara, M. (1995). 'Tank model.' Computer models of watershed hydrology, V. P. Singh, ed. Water Resource Publications, Littleton, Colo
  23. Thyer M., Kuczera G., and Bates B. C. (1999). 'Probabilistic optimization for conceptual rainfall-runoff models: A comparison of the shuffled complex evolution and simulation annealing algorithms.' Water Resources Research, 35(3), 767-773
  24. World Meteorological Organization (1975). Intercomparison of conceptual models used in operational hydrological forecasting. Operational Hydrology Report No.7, Geneva, Switzerland
  25. Yapo P.O., Gupta H. V., and Sorooshian S. (1996). 'Automatic calibration of conceptual rainfall-runoff models: sensitivity to calibration data.' Journal of Hydrology, 181, 23-48