Coupling ANFIS with ant colony optimization (ACO) algorithm for 1-, 2-, and 3-days ahead forecasting of daily streamflow, a case study in Poland

Finding an efficient and reliable streamflow forecasting model has always been an important challenge for managers and planners of freshwater resources. The current study, based on an adaptive neuro-fuzzy inference system (ANFIS) model, was designed to predict the Warta river (Poland) streamflow for 1 day, 2 days, and 3 days ahead for a data set from the period of 1993–2013. The ANFIS was additionally combined with the ant colony optimization (ACO) algorithm and employed as a meta-heuristic ANFIS-ACO model, which is a novelty in streamflow prediction studies. The investigations showed that on a daily scale, precipitation had a very weak and insignificant effect on the river’s flow variation, so it was not considered as a predictor input. The predictor inputs were selected by the autocorrelation function from among the daily streamflow time lags for all stations. The predictions were evaluated with the actual streamflow data, using such criteria as root mean square error (RMSE), normalized RMSE (NRMSE), and R(2). According to the NRMSE values, which ranged between 0.016–0.006, 0.030–0.013, and 0.038–0.020 for the 1-day, 2-day, and 3-day lead times, respectively, all predictions were classified as excellent in terms of accuracy (prediction quality). The best RMSE value was 1.551 m(3)/s and the highest R(2) value was equal to 0.998, forecast for 1-day lead time. The combination of ANFIS with the ACO algorithm enabled to significantly improve streamflow prediction. The use of this coupling can averagely increase the prediction accuracies of ANFIS by 12.1%, 12.91%, and 13.66%, for 1-day, 2-day, and 3-day lead times, respectively. The current satisfactory results suggest that the employed hybrid approach could be successfully applied for daily streamflow prediction in other catchment areas.