Modelling stage–discharge relationship of Himalayan river using ANN, SVM and ANFIS

Modelling the stage–discharge relationship is vital for precise discharge estimation, which is essential in reservoir operation, design of hydraulic structures, flood and drought control. The study utilised a conventional method, i.e. stage–discharge rating curve (SRC), and three data-driven techniques namely artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS) and support vector machine (SVM), to model the stage–discharge relationship. The input variables used in the ANN, ANFIS and SVM models were selected using the partial autocorrelation function (PACF). Based on PACF, various combinations of stage and antecedent discharge with defined lag time, such as 1-day and 2-day delays, were employed as input parameters for the ANN, ANFIS and SVM models, with the current-day flow data as the output parameter to predict discharge. The quantitative assessment of models demonstrates that the ANFIS model using the Gaussian membership function outperformed the SRC method, ANN and SVM models. The sensitivity analysis was also carried out for the best-performing model. Statistical indicators, i.e. root mean square error (RMSE), mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), and R² values for the best-performed ANFIS model were found to be 0.009, 0.006, 0.982 and 0.994, during testing respectively, which establish the efficacy of the model. Further, the sensitivity analysis of the best-performing ANFIS model infer that the present-day stage parameter is the most sensitive for discharge prediction.