Hydrology and Earth System Sciences www.hydrol-earth-syst-sci.net 1027-5606 1607-7938 13 11 2009 10.5194/hess-13-2137-2009 http://www.hydrol-earth-syst-sci.net/13/2137/2009/ http://www.hydrol-earth-syst-sci.net/13/2137/2009/hess-13-2137-2009.html http://www.hydrol-earth-syst-sci.net/13/2137/2009/hess-13-2137-2009.pdf 2137 2149 2009-11-12 Multi-objective calibration of a distributed hydrological model (WetSpa) using a genetic algorithm M. Shafii mshafiih@vub.ac.be F. De Smedt Department of Hydrology and Hydraulic Engineering, Vrije Universiteit Brussel, Belgium A multi-objective genetic algorithm, NSGA-II, is applied to calibrate a distributed hydrological model (WetSpa) for prediction of river discharges. The goals of this study include (i) analysis of the applicability of multi-objective approach for WetSpa calibration instead of the traditional approach, i.e. the Parameter ESTimator software (PEST), and (ii) identifiability assessment of model parameters. The objective functions considered are model efficiency (Nash-Sutcliffe criterion) known to be biased for high flows, and model efficiency for logarithmic transformed discharges to emphasize low-flow values. For the multi-objective approach, Pareto-optimal parameter sets are derived, whereas for the single-objective formulation, PEST is applied to give optimal parameter sets. The two approaches are evaluated by applying the WetSpa model to predict daily discharges in the Hornad River (Slovakia) for a 10 year period (1991–2000). The results reveal that NSGA-II performs favourably well to locate Pareto optimal solutions in the parameters search space. Furthermore, identifiability analysis of the WetSpa model parameters shows that most parameters are well-identifiable. However, in order to perform an appropriate model evaluation, more efforts should be focused on improving calibration concepts and to define robust methods to quantify different sources of uncertainties involved in the calibration procedure. Ajami, N. K., Gupta, H. V., Wagener, T., and Sorooshian, S.: Calibration of a semi-distributed hydrologic model for streamflow estimation along a river system, J. Hydrol., 298, 112–135, 2004. Baginska, B., Milne-Home, W., and Cornish, P.: Modelling nutrient transport in Currency Creek, NSW with AnnAGNPS and PEST, Environ. Model Softw., 18, 801–808, 2003. Bahremand, A., De Smedt, F., Corluy, J., and Liu, Y. B.: WetSpa Model Application for Assessing Reforestation Impacts on Floods in Margecany-Hornad Watershed, Slovakia, Water Resour. Manag., 21, 1373–1391, 2007. Bekele, E. G. and Nicklow, J. W.: Multi-objective automatic calibration of SWAT using NSGA-II, J. Hydrol., 341(3–4), 165–176, 2007. Beven, K. J.: Prophesy, reality and uncertainty in distributed hydrological modelling, Adv. Water Resour., 16, 41–51, 1993. Beven, K. J. and Binley, A. M.: The future of distributed models: model calibration and uncertainty prediction, Hydrol. Processes, 6, 279–298, 1992. Boyle, D. P., Gupta, H. V., and Sorooshian, S.: Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods, Water Resour. Res., 36, 3663–3674, 2000. Cheng, C. T., Ou, C. P., and Chaw, K. W.: Combining a fuzzy optimal model with a genetic algorithm to solve multi-objective rainfall-runoff model calibration, J. Hydrol., 268(1–4), 72–86, 2002. Cieniawski, S. E., Eheart, J. W., and Ranjithan, S. R.: Using genetic algorithms to solve a multiobjective groundwater monitoring problem, Water Resour. Res., 31, 399–409, 1995. Coello, C. C.: An updated survey of GA-based multiobjective optimization techniques, ACM Comput. Surv., 32(2), 109–143, 2000. Cunha, A. G., Oliviera, P., and Covas, J.: Use of genetic algorithms in multicriteria optimization to solve industrial problems, in: Proceedings of the Seventh International Conference on Genetic Algorithms, edited by: Bäck, T., San Francisco, California, 682–688, Morgan Kaufmann, 1997. De Smedt, F., Liu, Y. B., Gebremeskel, S., Hoffmann, L., and Pfister, L.: Application of GIS and remote sensing in flood modeling for complex terrain, in: GIS and Remote Sensing in Hydrology, edited by: Chen, Y. B., Takara, K., Cluckie, I., and De Smedt, F., Water Resources and Environment, IAHS Publ., 289, 23–32, 2004. De Smedt, F., Liu, Y. B., and Gebremeskel, S.: Hydrologic modeling on a basin scale using GIS and remote sensed land use information, in: Risk Analysis II, edited by: Brebbia, C. A., 295–304, WTI press, Southampton, Boston, 2000. Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II, IEEE Trans. Evol. Computation, 6(2), 182–197, 2002. Doherty, J. and Johnston, J. M.: Methodologies for calibration and predictive analysis of a watershed model, J. Am. Water Resour. Assoc., 39, 251–265, 2003. Fonseca, C. and Fleming, P. J.: An overview of evolutionary algorithms in multiobjective optimization, Evolutionary Comput., 3(1), 1–16, 1995. Fourman, M. P.: Compaction of symbolic layout using genetic algorithms, in: Proceedings of an International Conference on Genetic Algorithms and Their Applications, edited by: Grefenstette, J. J., Pittsburgh, PA, 141–153, sponsored by Texas Instruments and US Navy Center for Applied Research in Artificial Intelligence (NCARAI), 1985. Gen, M. and Cheng, R.: Genetic algorithms and engineering optimization, New York, John Wiley &Sons, 2000. Goldberg, D. E.: Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Co., Inc., Redwood City, CA, USA, 1989. Goldberg, D. E. and Deb, K.: A comparative analysis of selection schemes used in genetic algorithms, in: Foundations of Genetic Algorithms, edited by: Rawlins, G. J. E., Morgan Kaufmann, San Mateo, CA, 1991. Gupta, H. V., Beven, K. J., and Wagener, T.: Model Calibration and Uncertainty Estimation, Encyclopedia of Hydrological Sciences, Part 11, Rainfall-Runoff Modeling, John Wiley & Sons, Ltd, 2005. Gupta, H. V., Sorooshian, S., and Yapo, P. O.: Toward improved calibration of hydrological models: multiple and noncommensurable measures of information, Water Resour. Res., 34(4), 751–763, 1998. Iman, R. L. and Conover, W. J.: Small sample sensitivity analysis techniques for computer models, with an application to risk assessment, Communication in Statistics, A9(17), 1749–1842, 1980. Ishibuchi, H. and Murata, T.: Multi-objective genetic local search algorithm, in: Proceedings of 1996 IEEE International Conference on Evolutionary Computation (ICEC'96), Piscataway, NJ, 119–124, 1996. Kavetski, D., Franks, S. W., and Kuczera, G.: Confronting input uncertainty in environmental modeling, in: Calibration of Watershed Models, edited by: Duan, Q., Gupta, H. V., Sorooshian, S., Rousseau, A. N., and Turcotte, R., AGU Water Science and Applications Series, 6, 49–68, 2002. Khu, S. T., Savic, D., and Liu, Y.: Evolutionary-based multi-objective meta-model approach for rainfall-runoff model calibration, Geophys. Res. Abstr., 7, 09858, 2005. Lindstorm, G.: A simple automatic calibration routine for the HBV model, Nordic Hydrology, 28, 153–168, 1997. Liu, Y. B., Gebremeskel. S., De Smedt, F., Hoffmann, L., and Pfister, L.: A diffusive transport approach for flow routing in GIS-based flood modelling, J. Hydrol., 283, 91–106, 2003. Liu, Y. B., De Smedt, F., Hoffmann, L., and Pfister, L.: Parameterization using ArcView GIS in medium and large watershed modelling, in: GIS and Remote Sensing in Hydrology, edited by: Chen, Y. B., Takara, K., Cluckie, I., and De Smedt, F., Water Resources and Environment, IAHS Publ., 289, 50–58, 2004. Liu, Y. B., Batelaan, O., De Smedt, F., Poorova, J., and Velcicka, L.: Automated calibration applied to a GIS-based flood simulation model using PEST, in: Floods, from Defence to Management, edited by: van Alphen, J., van Beek, E., and Taal, M., Taylor & Francis Group, London, 317–326, 2005. Liu, Y. B. and De Smedt, F.: WetSpa extension, documentation and user manual, Department of Hydrology and Hydraulic Engineering, Vrije Universiteit Brussel, Belgium, 2004. Liu, Y. B. and De Smedt, F.: Flood modeling for complex terrain using GIS and remote sensed information, Water Resour. Manag., 19(5), 605–624, 2005. Madsen, H.: Parameter estimation in distributed hydrological catchment modeling using automatic calibration with multiple objectives, Adv. Water Resour., 26, 205–216, 2003. Madsen, H.: Automatic calibration of a conceptual rainfall-runoff model using multiple objectives, J. Hydrol., 235, 276–288, 2000. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs, AI Series, Springer-Verlag, New York, 1994. Muleta, M. and Nicklow, J.: Decision Support for Watershed Management Using Evolutionary Algorithms, J. Water Res. Pl., 131, 35–44, 2005a. Muleta, M. K. and Nicklow, J. W.: Sensitivity and uncertainty analysis coupled with automatic calibration for a distributed watershed model, J. Hydrol., 306, 127–145, 2005b. Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual models. Part 1: A discussion of principles, J. Hydrol., 10, 282–290, 1970. Osyczka, A.: Multicriteria Optimization for Engineering Design, Academic Press, 1985. Pareto, V.: The Rise and Fall of the Elites, Totowa, N. J., Bedminster Press, 1968. Reed, P. and Minsker, B. S.: Striking the Balance: Long-Term Groundwater Monitoring Design for Conflicting Objectives, J. Water Res. Pl., 130, 140–149, 2004. Reed, P., Minsker, B. S., and Goldberg, D. E.: A multiobjective approach to cost effective long-term groundwater monitoring using an Elitist Nondominated Sorted Genetic Algorithm with historical data, J. Hydroinform., 3, 71–90, 2001. Ritzel, B. J., Eheart, J. W., and Ranjithan, S. R.: Using genetic algorithms to solve a multiple objective groundwater pollution containment problem, Water Resour. Res., 30, 1589–1603, 1994. Schaffer, J. D.: Multiple objective optimization with vector evaluated genetic algorithms, in: Proceedings of an International Conference on Genetic Algorithms and Their Applications, edited by: Grefenstette, J. J., Pittsburgh, PA, 93–100, sponsored by Texas Instruments and US Navy Center for Applied Research in Artificial Intelligence (NCARAI), 1984. Seibert, J.: Multi-criteria calibration of a conceptual runoff model using a genetic algorithm, Hydrol. Earth Syst. Sci., 4, 215–224, 2000. Singh, A. and Minsker, B. S.: Uncertainty-based multiobjective optimization of groundwater remediation design, Water Resour. Res., 44, W02404, doi:10.1029/2005WR004436, 2008. Srinivas, N. and Deb, K.: Multiobjective optimization using nondominated sorting in genetic algorithms, Tech. Rep., Indian Institute of Technology, Delhi, India, 1993. Syvoloski, G., Kwicklis, E., Eddebbarh, A. A., Arnold, B., Faunt, C., and Robinson, B.: The site-scale saturated zone flow model for Yucca Mountain: calibration of different conceptual models and their impact on flow paths, J. Contam. Hydrol., 62–63, 731–750, 2003. Tang, Y., Reed, P., and Wagener, T.: How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration?, Hydrol. Earth Syst. Sci., 10, 289–307, 2006. Valenzuela-Rend'on, M. and Uresti-Charre, E.: A nongenerational genetic algorithm for multiobjective optimization, in: Proc. 7th Int. Conf. Genetic Algorithms, edited by: Bäck, T., San Francisco, CA, Morgan Kaufmann, 658–665, 1997. Vrugt, J., Gupta, H. V., Bastidas, L. A., Bouten, W., and Sorooshian, S.: Effective and efficient algorithm for multiobjective optimization of hydrologic models, Water Resour. Res., 39, 1214, doi:1210.1029/2002WR001746, 2003. Vrugt, J. A., Schoups, G., Hopmans, J. W., Young, C., Wallender, W. W., and Harter, T.: Inverse modeling of large-scale spatially distributed vadose zone properties using global optimization, Water Resour. Res., 41, W06003, doi:10.1029/2004WR003698, 2005. Vrugt, J. A. and Robinson, B. A.: Improved evolutionary optimization from genetically adaptive multimethod search, Proc. Natl. Acad. Sci. USA, 104, 708–711, doi:10.1073/pnas.0610471104, 2007. Wagener, T., Boyle, D. P., Lees, M. J., Wheater, H. S., Gupta, H. V., and Sorooshian, S.: A framework for development and application of hydrological models, Hydrol. Earth Syst. Sci., 5, 13–26, 2001. Wang, Z., Batelaan, O., and De Smedt, F.: A distributed model for Water and Energy Transfer between Soil, Plants and Atmosphere (WetSpa), Phys. Chem. Earth 21(3), 189–193, 1997. Wöhling, Th., Barkle, G. F., and Vrugt, J. A.: Comparison of three multiobjective optimization algorithms for inverse modeling of vadose zone hydraulic properties, Soil Sci. Soc. Am. J., 72(2), 305–319, 2008. Yapo, P. O., Gupta, H. V., and Sorooshian, S.: Multi-objective global optimization of hydrological models, J. Hydrol., 204, 83–97, 1998. Zitzler, E., Deb, K., and Thiele, L.: Comparison of Multiobjective Evolutionary Algorithms: Empirical Results, Evolutionary Comput., 8(2), 173–195, 2000. Zitzler, E. and Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach, IEEE Trans. Evol. Computation, 3(4), 257–271, 1999.