River flow forecasting through nonlinear local approximation in a fuzzy model

This study investigates the potential of nonlinear local function approximation in a Takagi–Sugeno (TS) fuzzy model for river flow forecasting. Generally, in a TS framework, the local approximation is performed by a linear model, while in this approach, linear function approximation is substituted using a nonlinear function approximation. The primary hypothesis herein is that the process being modeled (rainfall–runoff in this study) is highly nonlinear, and a linear approximation at the local domain might still leave a lot of unexplained variance by the model. In this study, subtractive clustering technique is used for domain partition, and neural network is used for function approximation. The modeling approach has been tested on two case studies: Kolar basin in India and Kentucky basin in USA. The results of fuzzy nonlinear local approximation (FNLLA) model are highly promising. The performance of the FNLLA is compared with that of a pure fuzzy inference system (FIS), and it is observed that both the models perform similar at 1-step-ahead forecasts. However, the FNLLA performs much better than FIS at higher lead times. It is also observed that FNLLA forecasts the river flow with lesser error compared to FIS. In the case of Kolar River, more than 40 % of the total data are forecasted with <2 % error by FNLLA at 1 h ahead, while the corresponding value for FIS is only 20 %. In the case of 3-h-ahead forecasts, these values are 25 % for FNLLA and 15 % for FIS. Performance of FNLLA in the case of Kentucky River basin was also better compared to FIS. It is also found that FNLLA simulates the peak flow better than FIS, which is certainly an improvement over the existing models.