Hydrology and Earth System Sciences Discussions www.hydrol-earth-syst-sci-discuss.net 1812-2108 1812-2116 5 4 2008 10.5194/hessd-5-1967-2008 http://www.hydrol-earth-syst-sci-discuss.net/5/1967/2008/ http://www.hydrol-earth-syst-sci-discuss.net/5/1967/2008/hessd-5-1967-2008.html http://www.hydrol-earth-syst-sci-discuss.net/5/1967/2008/hessd-5-1967-2008.pdf 1967 2003 2008-07-18 Sensitivity analysis of Takagi-Sugeno-Kang rainfall-runoff\ fuzzy models A. P. Jacquin A. Y. Shamseldin Departamento de Obras Civiles, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile Department of Civil and Environmental Engineering, The University of Auckland, Private Bag 92019, Auckland, New Zealand This paper is concerned with the sensitivity analysis of the model parameters of the Takagi-Sugeno-Kang fuzzy rainfall-runoff models previously developed by the authors. These models are classified in two types of fuzzy models, where the first type is intended to account for the effect of changes in catchment wetness and the second type incorporates seasonality as a source of non-linearity. The sensitivity analysis is performed using two global sensitivity analysis methods, namely Regional Sensitivity Analysis and Sobol's variance decomposition. The data of six catchments from different geographical locations and sizes are used in the sensitivity analysis. The sensitivity of the model parameters is analysed in terms of several measures of goodness of fit, assessing the model performance from different points of view. These measures include the Nash-Sutcliffe criteria, volumetric errors and peak errors. The results show that the sensitivity of the model parameters depends on both the catchment type and the measure used to assess the model performance. Bárdossy, A., Bronstert, A., and Merz, B.: 1-, 2- and 3-dimensional modelling of water movement in the unsaturated soil matrix using a fuzzy approach, Adv. Water Resour., 18(4), 237–251, 1995. Bárdossy, A. and Disse, M.: Fuzzy rule-based models for infiltration, Water Resour. Res., 29(2), 373–382, 1993. Bárdossy, A., Mascellani, G., and Franchini, M.: Fuzzy unit hydrograph, Water Resour. Res., 42(2), W02401, doi:10.1029/2004WR003751, 2006. Beven, K. J.: Rainfall-runoff modelling: the primer, John Wiley and Sons, Chichester, UK, 360 pp., 2001. Castaings, W., Dartus, D., Honnorat, M., Le Dimet, F. X., Loukili, Y., and Monnier, J.: Automatic differentiation: a tool for variational data assimilation and adjoint sensitivity analysis for flood modelling, in: Automatic differentiation: applications, theory, and tools, edited by: Bücker, H. M., Corliss, G., Hovland, P., Naumann, U., and Norris, B., Springer, Chicago, USA, 249–262, 2005. Chan, K., Tarantola, S., Saltelli, A., and Sobol, I. M.: Variance-based methods, in: Sensitivity Analysis, edited by: Saltelli, A., Chan, K., and Scott, E. M., John Wiley and Sons, Chichester, UK, 167–197, 2000. Cukier, R. I., Fortuin, C. M., Shuler, K. E., Petschek, A. G., and Schaibly, J. H.: A Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients, I: Theory, J. Chem. Phys., 59(8), 3873–3878, 1973. Cukier, R. I., Levine, H. B., and Shuler, K. E.: Nonlinear sensitivity analysis of multiparameter model systems, J. Comput. Phys., 26, 1–42, 1978. Demicco, R. and Klir, G.: Fuzzy Logic in Geology, Academic Press, Amsterdam, The Netherlands, 347 pp., 2004. Dou, X., Wouldt, W., and Bogardi, I.: Fuzzy rule-based approach to describe solute transport in the unsaturated zone, J. Hydrol., 220, 74–85, 1999. European Union Joint Research Centre: SIMLAB: simulation environment for uncertainty and sensitivity analysis (version 2.2), Applied Statistics Sector, Institute for Systems, Informatics and Safety, European Union Joint Research Centre, Ispra, Italy, 2004. Fieberg, J. and Jenkings, K. J.: Assessing uncertainty in ecological systems using global sensitivity analyses: a case example of simulated wolf reintroduction effects on elk, Ecol. Model., 187, 259–280, 2005. Francos, A., Elorzab, F. J., Bouraouia, F., Bidoglioa, G., and Galbiatia, L.: Sensitivity analysis of distributed environmental simulation models: understanding the model behaviour in hydrological studies at the catchment scale, Reliab. Eng. Syst. Safe., 205–218, 2003. Gupta, V. K. and Sorooshian, S.: The automatic calibration of conceptual catchment models using derivative-based optimization algorithms, Water Resour. Res., 21(4), 473–485, 1985. Homma, T. and Saltelli, A.: Importance measures in global sensitivity analysis of model output, Reliab. Eng. Syst. Safe, 52, 1–17, 1996. Hornberger, G. M. and Spear, R. C.: An approach to the preliminary analysis of environmental systems, J. Environ. Manage., 12, 7–18, 1981. Hundecha, Y., Bárdossy, A., and Theisen, H.-W.: Development of a fuzzy logic-based rainfall-runoff model, Hydrolog. Sci. J., 46(3), 363–376, 2001. Hundecha, Y. and Bárdossy, A.: Modeling of the effect of land use changes on the runoff generation of a river basin through parameter regionalization of a watershed model, J. Hydrol., 292, 281–295, 2004. Jacquin, A. P. and Shamseldin, A. Y.: Development of rainfall-runoff models using Takagi-Sugeno-Kang fuzzy inference systems, J. Hydrol., 329, 154–173, 2006. Jacquin, A. P. and Shamseldin, A. Y.: Development of a possibilistic method for the evaluation of predictive uncertainty in rainfall-runoff modelling, Water Resour. Res., 43(4), W04425, doi:10.1029/2006WR005072, 2007. Kanso, A., Chebboa, G., and Tassina, B.: Application of MCMC-Global sensitivity analysis method for model calibration to urban runoff quality model, in: Sensitivity Analysis of Model Output, edited by: Hanson, K. M. and Hemez, F. M., Los Alamos National Laboratory, 17–26, available at: http://library.lanl.gov, 2005. McIntyre, N. R., Wagener, T., Wheater, H., and Chapra, S. C.: Risk-based modelling of surface water quality: a case study of the Charles River, Massachussetts, J. Hydrol., 274, 225–247, 2003. Mein, R. G. and Brown, B. M.: Sensitivity of optimized parameters in watershed models, Water Resour. Res, 14(2), 299–303, 1978. Mertens, J., Madsen, H., Kristensen, M., Jacques, D., and Feyen, J.: Sensitivity of soil parameters in saturated zone modelling and the relation between effective, laboratory and in situ estimates, Hydrol. Process., 19(8), 1611–1633, doi:10.1002/hyp.5591, 2005. Morris, M. D.: Factorial sampling plans for preliminary computational experiments, Technometrics, 33(2), 161–074, 1991. Nandakumar, N. and Mein, R. G.: Uncertainty in rainfall-runoff model simulations and the implications for predicting the hydrologic effects of land-use change, J. Hydrol., 192, 211–232, 1997. Nash, J. E.: The form of the instantaneous unit hydrograph, IASH Publication, 45(3), 114–118, 1957. Nash, J. E. and Foley, J. J.: Linear models of rainfall-runoff systems, in: Proceedings of the International Symposium on Rainfall-Runoff Modeling, Mississippi State University, USA, 18–21 May 1981, 51–66, 1982. 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. O'Connor, K. M.: River flow forecasting, in: River Basin Modelling for Flood Risk Mitigation, edited by: Knight, D. W. and Shamseldin, A. Y., Taylor and Francis, London, UK, 197–213, 2005. Özelkan, E. C. and Duckstein, L.: Fuzzy conceptual rainfall-runoff models, J. Hydrol., 253, 41–68, 2001. Özelkan, E. C., Galambosi, A., Duckstein, L., and Bárdossy, A.: A multi-objective fuzzy classification of large scale atmospheric circulation patterns for precipitation modelling, Appl. Math. Comput., 91, 127–142, 1998. Pappenberger, F., Beven, K. J., Ratto, M., and Matgen, P.: Multi-method global sensitivity analysis of flood inundation models, Adv. Water Resour., 31(1), 1–14, 2008. Pongracz, R., Bartholy, J., and Bogardi, I.: Fuzzy rule-based prediction of monthly precipitation, Phys. Chem. Earth Pt. B, 26(9), 663–667, 2001. Ratto, M., Young, P. C., Romanowicz, R., Pappenberger, F., Saltelli, A., and Pagano, A.: Uncertainty, sensitivity analysis and the role of data based mechanistic modelling in hydrology, Hydrol. Earth Syst. Sci., 11, 1249–1266, 2007. Saltelli, A., Tarantola, S., and Campolongo, F.: Sensitivity analysis as an ingredient of modelling, Stat. Sci., 15(4), 377–395, 2000. Saltelli, A., Tarantola, S., Campolongo, F., and Ratto, M.: Sensitivity analysis in practice: a guide to assessing scientific models, John Wiley and Sons, Chichester, UK, 219 pp., 2004. Saltelli, A., Tarantola, S., and Chan, K.: A quantitative, model independent method for global sensitivity analysis of model output, Technometrics, 41(1), 39–56, 1999. Seibert, J.: Regionalization of parameter of a conceptual rainfall-runoff model, Agr. Forest Meteorol., 98-99, 279–293, 1999. Sobol, I. M.: Sensitivity analysis for non-linear mathematical models, Math. Mod. Comput. Exp., 1(4), 407–414, 1993. Sorooshian, S. and Gupta, V. K.: Model calibration, in: Conceptual Models of Watershed Hydrology, edited by: Singh, V. P., Water Resources Publications, Colorado, USA, 23–67, 1995. Spear, R. C. and Hornberger, G. M.: Eutrophication in Peel Inlet, II: Identification of critical uncertainties via generalised sensitivity analysis, Water Resour. Res., 14, 43–49, 1980. Sugeno, M. and Kang, G. T.: Structure identification of fuzzy model, Fuzzy Set. Syst., 28, 15–33, 1988. Takagi, T. and Sugeno, M.: Fuzzy identification of systems and its application to modeling and control, IEEE T. Syst. Man Cyb., SMC-15(1), 116–132, 1985. Tang, Y., Reed, P., Wagener, T., and van Werkhoven, K.: Comparing sensitivity analysis methods to advance lumped watershed model identification and evaluation, Hydrol. Earth Syst. Sci., 11, 793–817, 2007. Vernieuwe, H., Georgieva, O., De Baets, B., Pauwels, V. R. N., Verhoest, N. E. C., and De Troch, F. P.: Comparison of data-driven Takagi-Sugeno models of rainfall-discharge dynamics, J. Hydrol., 302, 173–186, 2005. Wagener, T., Boyle, D., 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, 2001a. Wagener, T., Lees, M. J., and Wheater, H. S.: MCAT: Monte-Carlo Analysis Toolbox (version 3), Civil and Environmental Engineering Department, Imperial College of Science Technology and Medicine, London, UK, 2001b. Wagener, T., Wheater, H. S., and Gupta, H. V.: Identification and evaluation of watershed models, in: Calibration of Watershed Models, edited by: Duan, Q., Gupta, H. V., Sorooshian, S., Rousseau, A. N., and Turcotte, R., American Geophysical Union, Washington, USA, 29–47, 2002. Wang, X., Frankenberger, J. R., and Kladivko, E. J.: Uncertainties in DRAINMOD predictions of subsurface drain flow fr and Indiana silt loam using the GLUE methodology, Hydrol. Process., 20(14), 3069–3084, 2006. Xiong, L. and O'Connor, K. M.: Analysis of the response surface of the objective function by the optimum parameter curve: how good can the optimum parameter values be?, J. Hydrol., 234, 187–207, 2000. Yu, P.-S. and Yang, T. C.: Fuzzy multi-objective function for rainfall-runoff model calibration, J. Hydrol., 238, 1–14, 2000. Zadeh, L. A.: Fuzzy Sets, Inform. Control, 8(3), 338-353, 1965. Zehe, E. and Blöschl, G.: Predictability of hydrologic response at the plot and catchment scales: the role of initial conditions, Water Resour. Res., 40(10), W10202, doi:10.1029/2003WR002869, 2004. Zehe, E., Becker, R., Bárdossy, A., and Plate, E.: Uncertainty of simulated catchment runoff response in the presence of threshold processes: role of initial soil moisture and precipitation, J. Hydrol., 315, 183–202, 2005. Zehe, E., Singh, A. K., and Bárdossy, A.: Modelling of monsoon rainfall for a mesoscale catchment in North-West India, I: assessment of objective circulation patterns, Hydrol. Earth Syst. Sci., 10, 797–806, 2006.