Takagi–Sugeno fuzzy inference system for modeling stage–discharge relationship A.K. Lohani a, * , N.K. Goel b , K.K.S. Bhatia a a National Institute of Hydrology, Jalvigyan Bhawan, Roorkee 247667, India b Indian Institute of Technology, Roorkee 247667, India Received 27 July 2005; received in revised form 10 May 2006; accepted 10 May 2006 Summary Direct measurement of discharge in a stream is not only difficult and time consum- ing but also expensive. Therefore, the discharge in a stream is related to the stage through a number of carefully measured discharge values. A relationship between stages and correspond- ing measured discharges is usually derived using various graphical and analytical methods. As the relationship between stages and measured discharges is not linear, conventional methods based on least squares regression analysis for fitting a relationship are unable to model the non-linearity in the relationship and spatially in the cases when hysteresis is present in the data. The aim of the present study is to investigate the potential of Takagi–Sugeno (TS) fuzzy infer- ence system for modeling stage–discharge relationships and the investigations are illustrated by application of the model to observed gauge and discharges of various gauging stations in Nar- mada river system, India. A step by step procedure for developing TS fuzzy model is also pre- sented. The results show that the TS fuzzy modeling approach is superior than the conventional and artificial neural network (ANN) based approaches. Comparison of the models on hypothet- ical data set also reveals that the fuzzy logic based approach is also able to model the hysteresis effect (loop rating curve) more accurately than the ANN approach.  c 2006 Elsevier B.V. All rights reserved. KEYWORDS Fuzzy logic; Takagi–Sugeno fuzzy inference system; Artificial neural network; Hysteresis effect; Loop rating curve; Clustering Introduction Stream flow information is important for effective and reli- able planning and management of various water resources activities and the assessment, management and control of water resources can be effective if accurate and continuous information on river-flow is available. Generally a network of river gauging stations provides continuous information on river stage and sparse information of corresponding dis- charges. Thus, the continuous discharge data corresponding to observed gauge can be obtained by developing a stage discharge relationship and using this relationship to convert the recorded stages into corresponding discharges. This 0022-1694/$ - see front matter  c 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2006.05.007 * Corresponding author. Tel.: +91 1332 276341; fax: +91 1332 272123. E-mail addresses: akl_nih@yahoo.co.in, lohani@nih.ernet.in (A.K. Lohani). Journal of Hydrology (2006) 331, 146– 160 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/jhydrol