Sensitivity analysis of Takagi-Sugeno-Kang rainfall-runoff fuzzy models

Abstract. 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.

[1]  François-Xavier Le Dimet,et al.  Automatic differentiation: a tool for variational data assimilation and adjoint sensitivity analysis for flood modeling , 2006 .

[2]  A. Shamseldin,et al.  River basin modelling for flood risk mitigation , 2005 .

[3]  M. Franchini,et al.  Fuzzy unit hydrograph , 2006 .

[4]  Markus Disse,et al.  Fuzzy rule-based models for infiltration , 1993 .

[5]  C. Fortuin,et al.  Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I Theory , 1973 .

[6]  Thorsten Wagener,et al.  Risk-based modelling of surface water quality: a case study of the Charles River, Massachusetts , 2003 .

[7]  Stefano Tarantola,et al.  A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output , 1999, Technometrics.

[8]  Wayne Woldt,et al.  Fuzzy rule-based approach to describe solute transport in the unsaturated zone , 1999 .

[9]  K. M. O'Connor.  River flow forecasting , 2005 .

[10]  Lucien Duckstein,et al.  A multi-objective fuzzy classification of large scale atmospheric circulation patterns for precipitation modeling , 1998 .

[11]  P. Reed,et al.  Hydrology and Earth System Sciences Discussions Comparing Sensitivity Analysis Methods to Advance Lumped Watershed Model Identification and Evaluation , 2022 .

[12]  Florian Pappenberger,et al.  Multi-method global sensitivity analysis of flood inundation models. , 2008 .

[13]  Max D. Morris,et al.  Factorial sampling plans for preliminary computational experiments , 1991 .

[14]  Bernard De Baets,et al.  Comparison of data-driven TakagiSugeno models of rainfalldischarge dynamics , 2005 .

[15]  G. Hornberger,et al.  Approach to the preliminary analysis of environmental systems , 1981 .

[16]  S. Sorooshian,et al.  The Automatic Calibration of Conceptual Catchment Models Using Derivative‐Based Optimization Algorithms , 1985 .

[17]  Peter C. Young,et al.  Uncertainty , sensitivity analysis and the role of data based mechanistic modeling in hydrology , 2006 .

[18]  Lucien Duckstein,et al.  Fuzzy conceptual rainfall–runoff models , 2001 .

[19]  Asaad Y. Shamseldin,et al.  Development of a possibilistic method for the evaluation of predictive uncertainty in rainfall‐runoff modeling , 2007 .

[20]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[21]  Erwin Zehe,et al.  Predictability of hydrologic response at the plot and catchment scales: Role of initial conditions , 2004 .

[22]  Jan Seibert,et al.  Regionalisation of parameters for a conceptual rainfall-runoff model , 1999 .

[23]  R. Mein,et al.  Sensitivity of optimized parameters in watershed models , 1978 .

[24]  A. Bárdossy,et al.  Development of a fuzzy logic-based rainfall-runoff model , 2001 .

[25]  András Bárdossy,et al.  Modeling of the effect of land use changes on the runoff generation of a river basin through parameter regionalization of a watershed model , 2004 .

[26]  Soroosh Sorooshian,et al.  A framework for development and application of hydrological models , 2001, Hydrology and Earth System Sciences.

[27]  Erwin Zehe,et al.  Modelling of monsoon rainfall for a mesoscale catchment in North-West India I: assessment of objective circulation patterns , 2006 .

[28]  Thorsten Wagener,et al.  Numerical and visual evaluation of hydrological and environmental models using the Monte Carlo analysis toolbox , 2007, Environ. Model. Softw..

[29]  Stefano Tarantola,et al.  Sensitivity Analysis in Practice , 2002 .

[30]  Asaad Y. Shamseldin,et al.  Development of rainfall–runoff models using Takagi–Sugeno fuzzy inference systems , 2006 .

[31]  John R Fieberg,et al.  Assessing uncertainty in ecological systems using global sensitivity analyses: a case example of simulated wolf reintroduction effects on elk , 2005 .

[32]  K. M. O'Connor,et al.  Analysis of the response surface of the objective function by the optimum parameter curve: how good can the optimum parameter values be? , 2000 .

[33]  Stefano Tarantola,et al.  Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models , 2004 .

[34]  Erwin Zehe,et al.  Uncertainty of simulated catchment runoff response in the presence of threshold processes: Role of initial soil moisture and precipitation , 2005 .

[35]  J. E. Nash,et al.  The form of the instantaneous unit hydrograph , 1957 .

[36]  K. Shuler,et al.  Nonlinear sensitivity analysis of multiparameter model systems , 1977 .

[37]  M. Sugeno,et al.  Structure identification of fuzzy model , 1988 .

[38]  A. Saltelli,et al.  Sensitivity Anaysis as an Ingredient of Modeling , 2000 .

[39]  J. Nash,et al.  River flow forecasting through conceptual models part I — A discussion of principles☆ , 1970 .

[40]  A. Saltelli,et al.  Importance measures in global sensitivity analysis of nonlinear models , 1996 .

[41]  Francisco Javier Elorza,et al.  Sensitivity analysis of distributed environmental simulation models: understanding the model behaviour in hydrological studies at the catchment scale , 2003, Reliab. Eng. Syst. Saf..

[42]  Jane R. Frankenberger,et al.  Uncertainties in DRAINMOD predictions of subsurface drain flow for an Indiana silt loam using the GLUE methodology , 2006 .

[43]  R. Spear.  Eutrophication in peel inlet—II. Identification of critical uncertainties via generalized sensitivity analysis , 1980 .

[44]  Interactive comment on "Sensitivity analysis of Takagi-Sugeno-Kang rainfall-runoff fuzzy models" by A. P. Jacquin and A. Y. , 2008 .

[45]  Saltelli Andrea,et al.  Global Sensitivity Analysis: The Primer , 2008 .

[46]  N. Nandakumar,et al.  Uncertainty in rainfall—runoff model simulations and the implications for predicting the hydrologic effects of land-use change , 1997 .

[47]  G. Klir,et al.  Fuzzy logic in geology , 2004 .

[48]  P. Reed,et al.  Characterization of watershed model behavior across a hydroclimatic gradient , 2008 .

[49]  Soroosh Sorooshian,et al.  Model Calibration in Watershed Hydrology , 2009 .

[50]  Pao-Shan Yu,et al.  Fuzzy multi-objective function for rainfall-runoff model calibration , 2000 .

[51]  Henrik Madsen,et al.  Sensitivity of soil parameters in unsaturated zone modelling and the relation between effective, laboratory and in situ estimates , 2005 .

[52]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[53]  Istvan Bogardi,et al.  Fuzzy rule-based prediction of monthly precipitation , 2001 .

[54]  Axel Bronstert,et al.  1-, 2- and 3-dimensional modeling of water movement in the unsaturated soil matrix using a fuzzy approach , 1995 .