Novel approach for streamflow forecasting using a hybrid ANFIS-FFA model

The present study proposes a new hybrid evolutionary Adaptive Neuro-Fuzzy Inference Systems (ANFIS) approach for monthly streamflow forecasting. The proposed method is a novel combination of the ANFIS model with the firefly algorithm as an optimizer tool to construct a hybrid ANFIS-FFA model. The results of the ANFIS-FFA model is compared with the classical ANFIS model, which utilizes the fuzzy c-means (FCM) clustering method in the Fuzzy Inference Systems (FIS) generation. The historical monthly streamflow data for Pahang River, which is a major river system in Malaysia that characterized by highly stochastic hydrological patterns, is used in the study. Sixteen different input combinations with one to five time-lagged input variables are incorporated into the ANFIS-FFA and ANFIS models to consider the antecedent seasonal variations in historical streamflow data. The mean absolute error (MAE), root mean square error (RMSE) and correlation coefficient (r) are used to evaluate the forecasting performance of ANFIS-FFA model. In conjunction with these metrics, the refined Willmott's Index (Drefined), Nash-Sutcliffe coefficient (ENS) and Legates and McCabes Index (ELM) are also utilized as the normalized goodness-of-fit metrics. Comparison of the results reveals that the FFA is able to improve the forecasting accuracy of the hybrid ANFIS-FFA model (r = 1; RMSE = 0.984; MAE = 0.364; ENS = 1; ELM = 0.988; Drefined = 0.994) applied for the monthly streamflow forecasting in comparison with the traditional ANFIS model (r = 0.998; RMSE = 3.276; MAE = 1.553; ENS = 0.995; ELM = 0.950; Drefined = 0.975). The results also show that the ANFIS-FFA is not only superior to the ANFIS model but also exhibits a parsimonious modelling framework for streamflow forecasting by incorporating a smaller number of input variables required to yield the comparatively better performance. It is construed that the FFA optimizer can thus surpass the accuracy of the traditional ANFIS model in general, and is able to remove the false (inaccurately) forecasted data in the ANFIS model for extremely low flows. The present results have wider implications not only for streamflow forecasting purposes, but also for other hydro-meteorological forecasting variables requiring only the historical data input data, and attaining a greater level of predictive accuracy with the incorporation of the FFA algorithm as an optimization tool in an ANFIS model.