  A rainfall-runoff model predicts surface runoff either using a
physically-based approach or using a systems-based approach. Takagi-Sugeno (TS)
Fuzzy models are systems-based approaches and a popular modeling choice for
hydrologists in recent decades due to several advantages and improved accuracy
in prediction over other existing models. In this paper, we propose a new
rainfall-runoff model developed using Gustafson-Kessel (GK) clustering-based TS
Fuzzy model. We present comparative performance measures of GK algorithms with
two other clustering algorithms: (i) Fuzzy C-Means (FCM), and (ii)Subtractive
Clustering (SC). Our proposed TS Fuzzy model predicts surface runoff using: (i)
observed rainfall in a drainage basin and (ii) previously observed
precipitation flow in the basin outlet. The proposed model is validated using
the rainfall-runoff data collected from the sensors installed on the campus of
the Indian Institute of Technology, Kharagpur. The optimal number of rules of
the proposed model is obtained by different validation indices. A comparative
study of four performance criteria: RootMean Square Error (RMSE), Coefficient
of Efficiency (CE), Volumetric Error (VE), and Correlation Coefficient of
Determination(R) have been quantitatively demonstrated for each clustering
algorithm.
