Two hybrid Artificial Intelligence approaches for modeling rainfall–runoff process

The need for accurate modeling of the rainfall–runoff process has grown rapidly in the past decades. However, considering the high stochastic property of the process, many models are still being developed in order to define such a complex phenomenon. Recently, Artificial Intelligence (AI) techniques such as the Artificial Neural Network (ANN) and the Adaptive Neural-Fuzzy Inference System (ANFIS) have been extensively used by hydrologists for rainfall–runoff modeling as well as for other fields of hydrology. In this paper, two hybrid AI-based models which are reliable in capturing the periodicity features of the process are introduced for watershed rainfall–runoff modeling. In the first model, the SARIMAX (Seasonal Auto Regressive Integrated Moving Average with exogenous input)-ANN model, an ANN is used to find the non-linear relationship among the residuals of the fitted linear SARIMAX model. In the second model, the wavelet-ANFIS model, wavelet transform is linked to the ANFIS concept and the main time series of two variables (rainfall and runoff) are decomposed into some multi-frequency time series by wavelet transform. Afterwards, these time series are imposed as input data to the ANFIS to predict the runoff discharge one time step ahead. The obtained results of the models applications for the rainfall–runoff modeling of two watersheds (located in Azerbaijan, Iran) show that, although the proposed models can predict both short and long terms runoff discharges by considering seasonality effects, the second model is relatively more appropriate because it uses the multi-scale time series of rainfall and runoff data in the ANFIS input layer.