In this study, a new hybrid model integrated adaptive neuro fuzzy inference system with Firefly Optimization algorithm (ANFIS-FFA), is proposed for forecasting monthly rainfall with one-month lead time. The proposed ANFIS-FFA model is compared with standard ANFIS model, achieved using predictor-predictand data from the Pahang river catchment located in the Malaysian Peninsular. To develop the predictive models, a total of fifteen years of data were selected, split into nine years for training and six years for testing the accuracy of the proposed ANFIS-FFA model. To attain optimal models, several input combinations of antecedents’ rainfall data were used as predictor variables with sixteen different model combination considered for rainfall prediction. The performances of ANFIS-FFA models were evaluated using five statistical indices: the coefficient of determination (R2), Nash-Sutcliffe efficiency (NSE), Willmott’s Index (WI), root mean square error (RMSE) and mean absolute error (MAE). The results attained show that, the ANFIS-FFA model performed better than the standard ANFIS model, with high values of R2, NSE and WI and low values of RMSE and MAE. In test phase, the monthly rainfall predictions using ANFIS-FFA yielded R2, NSE and WI of about 0.999, 0.998 and 0.999, respectively, while the RMSE and MAE values were found to be about 0.272 mm and 0.133 mm, respectively. It was also evident that the performances of the ANFIS-FFA and ANFIS models were very much governed by the input data size where the ANFIS-FFA model resulted in an increase in the value of R2, NSE and WI from 0.463, 0.207 and 0.548, using only one antecedent month of data as an input (t-1), to almost 0.999, 0.998 and 0.999, respectively, using five antecedent months of predictor data (t-1, t-2, t-3, t-6, t-12, t-24). We ascertain that the ANFIS-FFA is a prudent modelling approach that could be adopted for the simulation of monthly rainfall in the present study region.
Rainfall forecasting Tropical environment Stochastic pattern Hybrid ANFIS-FFA model
This is a preview of subscription content, log in to check access
Authors would like the acknowledge their gratitude and appreciate for the Department of Irrigation and Drainage (DID), Malaysia, for providing the rainfall data set of the studied case study and their admirable cooperation. We thank all Reviewers and the Editor-in-Chief for their insightful comments that improved the clarity of the final paper.
Awadallah MA, Bayoumi EHE, Soliman HM (2009) Adaptive deadbeat controllers for brushless DC drives using PSO and ANFIS techniques. J Electr Eng 60:3–11Google Scholar
Azimi H, Bonakdari H, Ebtehaj I, Michelson DG (2016) A combined adaptive neuro-fuzzy inference system–firefly algorithm model for predicting the roller length of a hydraulic jump on a rough channel bed. Neural Comput & Applic. https://doi.org/10.1007/s00521-016-2560-9
Fahimi F, Yaseen ZM, El-shafie A (2016) Application of soft computing based hybrid models in hydrological variables modeling: a comprehensive review. Theor Appl Climatol:1–29. https://doi.org/10.1007/s00704-016-1735-8
Hong Y, Hsu K, Sorooshian S, Gao X (2005) Self-organizing nonlinear output (SONO): a neural network suitable for cloud patch-based rainfall estimation at small scales. Water Resour Res. https://doi.org/10.1029/2004WR003142
Nhu HN, Nitsuwat S, Sodanil M (2013) Prediction of stock price using an adaptive Neuro-fuzzy inference system trained by firefly algorithm. 2013 Int Comput Sci Eng Conf ICSEC 2013, pp 302–307. https://doi.org/10.1109/ICSEC.2013.6694798
Palit AK, Popovic D (2005) Computational intelligence in time series forecasting: theory and engineering applications (advances in industrial control). Springer-Verlag New York, Inc., SecaucusGoogle Scholar
Prasad R, Deo RC, Li Y, Maraseni T (2017) Input selection and performance optimization of ANN-based streamflow forecasts in the drought-prone Murray Darling Basin region using IIS and MODWT algorithm. Atmos Res 197:42–63Google Scholar
Yaseen ZM, Jaafar O, Deo RC, Kisi O, Adamowski J, Quilty J, El-Shafie A (2016) Stream-flow forecasting using extreme learning machines: a case study in a semi-arid region in Iraq. J Hydrol 542:603–614Google Scholar