Application of Linearized Calibration Method for Vertically Mixed Runoff Model Parameters
Publication: Journal of Hydrologic Engineering
Volume 19, Issue 8
Abstract
Objective functions are the most important information source for parameter calibration. Current parameter calibration methods mostly employ error sum of squares as the objective function and depend on the information provided by the objective function to search the parameter optima. This kind of method can increase unrelated local optima for nonlinear models. In order to solve the problem, the linearized calibration method of nonlinear model parameters was developed. The purpose of this paper is to investigate the usefulness of the linearized calibration method in the context of calibrating rainfall-runoff models. The new method was first introduced and then used to calibrate vertically mixed runoff model parameters. Two types of analysis were performed. The first refers to an ideal model case free of data and model errors in which the true optimum set of parameter values was known by assumption. The ideal model case was used to examine whether the linearized calibration method is capable of finding that optimum without producing unrelated local optima. Furthermore, it was also applied to validating the advantages and effectiveness of the proposed method through comparison with the shuffled complex evolution (SCE-UA) method and the simplex method. The second refers to a real case in which the data were from four real catchments. It was used to further examine the performance of the linearized calibration method in model parameter calibration. The results show that the linearized calibration method is always able to find the unique global optima with a fast convergence rate and performs better than the SCE-UA method and the simplex method, which demonstrates that the linearized calibration method is an effective parameter optimization technique.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study is supported by the National Natural Science Foundation of China (Grant No. 51279057), Major Program of National Natural Science Foundation of China (Grant Nos. 51190090 and 51190091), the Special Fund of State Key Laboratory of China (Grant Nos. 2009585412 and 2009586412), and Colleges and Universities in Jiangsu Province plans to graduate research and innovation (Grant No. CXZZ13_0250).
References
Bao, W., Li, Q., and Qu, S. (2013b). “Efficient calibration technique under irregular response surface.” J. Hydrol. Eng., 1140–1147.
Bao, W. M. (1986). “Automatic calibration of the Xinanjiang model.” J. Hohai Univ., (4), 22–30.
Bao, W. M. (1989). “The research about calibrating model parameters.” Doctoral dissertation, Hohai Univ., Nanjing, China.
Bao, W. M. (1991). “Parameter estimation of the model with colored noise.” J. Hydraul. Eng., (12), 47–52.
Bao, W. M. (1993). “Improvement and application of the Green-Ampt infiltration curve.” Yellow River, (9), 1–3.
Bao, W. M., Ji, H. X., Hu, Q. M., Qu, S. M., and Zhao, C. (2003). “Robust estimation theory and its application to hydrology.” Adv. Water Sci., 14(4), 133–137.
Bao, W. M., and Li, Q. (2012). “Estimating selected parameters for the XAJ model under multicollinearity among watershed characteristics.” J. Hydrol. Eng., 118–128.
Bao, W. M., Li, Q., Li, C. S., and Si, W. (2013a). “The weighed objective functions based on sensitivity analysis.” J. Hydroelectr. Eng., 32(2), 27–34.
Bao, W. M., Lin, Y., Huang, X. Q., Qu, S. M., and Zhao, C. (2004). “Parameter robust estimation of reach flood concentration model.” Eng. J. Wuhan Univ., 37(6), 13–17.
Bao, W. M., Si, W., and Qu, S. M. (2013c). “The linearized calibration method of nonlinear function parameter.” Chin. J. Comp. Mech., 30(2), 236–241.
Bao, W. M., and Wang, C. L. (1997). “Vertically-mixed runoff model and its application.” Hydrology, (3), 18–21.
Bao, W. M., Wang, H., Zhao, C., and Wen, J. (2006). “Robust estimation of AR model parameters.” J. Hohai Univ., 34(3), 258–261.
Bao, W. M., Zhang, X. Q., and Zhao, L. P. (2013d). “Parameter estimation method based on parameter function surface.” Sci. China Tech. Sci., 56(6), 1485–1498.
Bardossy, A., and Singh, K. (2008). “Robust estimation of hydrological model parameters.” Hydrol. Earth Syst. Sci. Discuss., 5(3), 1641–1675.
Burke, J. V., and Ferris, M. C. (1995). “A Gauss-Newton method for convex composite optimization.” Math. Program., 71(2), 179–194.
Dorigo, M. (1992). “Optimization, learning and natural algorithms.” Doctoral dissertation, Dipartimento di Elettronica, Politecnico di Milano, Milan, Italy.
Dorigo, M., and Birattari, M. (2010). “Ant colony optimization.” Encyclopedia of Machine Learning, Springer, New York, 36–39.
Dorigo, M., Maniezzo, V., and Colorni, A. (1996). “Ant system: Optimization by a colony of cooperating agents,” Syst., Man, Cybern. B: Cybern., IEEE Trans. , 26(1), 29–41.
Duan, Q. Y., Gupta, V. K., and Sorooshina, S. (1993). “Shuffled complex evolution approach for effective and efficient global minimization.” J. Optim. Theory Appl., 76(3), 501–521.
Duan, Q. Y., Sorooshian, S., and Gupta, V. (1992). “Effective and efficient global optimization for conceptual rainfall-runoff models.” Water Resour. Res., 28(4), 1015–1031.
Duan, Q. Y., Sorooshian, S., and Gupta, V. K. (1994). “Optimal use of the SCE–UA global optimization method for calibrating watershed models.” J. Hydrol., 158(3), 265–284.
Eberhart, R. C., and Shi, Y. (2004). “Guest editorial on special issue on particle swarm optimization.” IEEE Trans. Evol. Comput., 8(3), 201–203.
Franchini, M. (1996). “Use of a genetic algorithm combined with a local search method for the automatic calibration of conceptual rainfall-runoff models.” Hydrol. Sci. J., 41(1), 21–40.
Franchini, M., and Galeati, G. (1997). “Comparing several genetic algorithm schemes for the calibration of conceptual rainfall-runoff models.” Hydrol. Sci. J., 42(3), 357–379.
Goldberg, D. E. (1989). Genetic algorithms in search optimization and machine learning, Addison-Wesley, Reading, MA.
Goswami, M., and O’Connor, K. M. (2007). “Comparative assessment of six automatic optimization techniques for calibration of a conceptual rainfallrunoff model.” Hydrol. Sci. J., 52(3), 432–449.
Gupta, H. V., Sorooshian, S., and Yapo, P. O. (1999). “Status of automatic calibration for hydrologic models: Comparison with multilevel expert calibration.” J. Hydrol. Eng., 135–143.
Gupta, V. K., and Sorooshian, S. (1985). “The automatic calibration of conceptual catchment models using derivative-based optimization algorithms.” Water Resour. Res., 21(4), 473–485.
Holland, J. H. (1975). Adaptation in natural and artificial systems, University of Michigan Press, Ann Arbor, MI.
Hopfield, J. J., and Tank, D. W. (1985). “Neural’computation of derisions in optimization problems.” Biol. Cybern., 52(3), 141–152.
Johnston, P. R., and Pilgrim, D. H. (1976). “Parameter optimization for watershed models.” Water Resour. Res., 12(3), 477–486.
Kennedy, J., and Eberhart, R. C. (1995). “Particle swarm optimization.” IEEE Int. Conf. Neural Netwwork, IEEE, Perth, Australia, Vol. 4, 1942–1948.
Kennedy, J. F., Kennedy, J., and Eberhart, R. C. (2001). “Swarm intelligence.” Morgan Kaufmann, San Francisco.
Li, Q., Bao, W. M., Lu, S. F., Mo, J., and Li, C. S. (2011a). “The estimation of concentration parameters based on the Fourier.” Water Resour. Power, 29(2), 7–9.
Li, Q., Bao, W. M., Zhang, B., and Kong, D. Q. (2011b). “Conceptual hierarchical calibration of Xinanjiang model.” 3rd Int. Symp. on Methodology in Hydrology, Vol. 350, International Association of Hydrological Sciences, Wallingford, Royaume-Uni, 690–697.
Lingireddy, S. (1998). “Aquifer parameter estimation using genetic algorithms and neural networks.” Civ. Eng. Syst., 15(2), 125–144.
Nelder, J. A., and Mead, R. (1965). “A simplex method for function minimization.” Comput. J., 7(4), 308–313.
Powell, M. J. D. (1964). “An efficient method for finding the minimum of a function of several variables without calculating derivatives.” Comput. J., 7(2), 155–162.
Rosenbrock, H. H. (1960). “An automatic method of finding the greatest of least value of a function.” Comput. J., 3(3), 175–184.
Spendley, W., Hext, G. R., and Himsworth, F. R. (1962). “Sequential application of simplex designs in optimization and evolutionary design.” Technometrics, 4(4), 441–461.
Wagener, T., Werkhoven, K. V., Reed, P., and Tang, Y. (2009). “Multi-objective sensitivity analysis to understand the information concert in stream flow observations for distributed watershed modeling.” Water Resour. Res., 45(2), 1–5.
Zador, J., Zsely, I. G., and Turanyi, T. (2006). “Local and global uncertainty analysis of complex chemical kinetic systems.” Reliab. Eng. Syst. Saf., 91(10), 1232–1240.
Zhao, C., Bao, W. M., Wang, Y. Q., Wang, H., and Zhang, Y., (2006). “Robust estimation of reach flow concentration parameters.” J. Hohai Univ., 34(1), 14–17.
Zhao, C., Hong, H. S., Bao, W. M., and Zhang, L. P. (2008). “Robust recursive estimation of auto-regressive updating model parameters for real-time flood forecasting.” J. Hydrol., 28(2), 26–29.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 19 • Issue 8 • August 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 14, 2013
Accepted: Feb 14, 2014
Published online: Feb 15, 2014
Published in print: Aug 1, 2014
Discussion open until: Oct 28, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.