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Application of Entropy Concept for Input Selection of Wavelet-ANN Based Rainfall-Runoff Modeling

V. Nourani*,T. R. Khanghah and A. H. Baghanam

Department of Water Resources Engineering, Faculty of Civil Engineering, University of Tabriz, Tabriz 51666-16471, Iran

*Corresponding author. Tel: +98-411-3392409 Fax: Email:


This paper presents a Wavelet-based Artificial Neural Network (WANN) approach to model rainfall-runoff process of the Delaney Creek and Payne Creek watersheds with distinct hydro-geomorphological characteristics, located in Florida. Wavelet is utilized to handle the multi-frequency characteristics of the process in daily and monthly time scales. Thus, rainfall and runoff time series were decomposed into several sub-series by various mother wavelets. Due to multiple components obtained through wavelet decomposition, input sets to the Feed Forward Neural Network (FFNN) were enhanced. The application of two information content based criteria (i.e., entropy, H, and mutual information, MI) to select more reliable input sets (among all potential input sets) and to have better insight into the physics of process is considered as the basic innovation of the study which led to a more accurate and compact model. The increase in the number of input of the FFNN might lead to a complex structure and low performance. The results demonstrated that MI  as a supervised feature extraction criterion could lead to more reliable outcomes due to its non-linear nature. Furthermore, results indicated the superiority of proposed entropy-based WANN model (EWANN) in comparison to simple FFNN. Moreover, multi-step-ahead FFNN, conventional WANN and classic Auto Regressive Integrated Moving Average with eXogenous inputs (ARIMAX) models could not reveal appropriate forecasting results with regard to EWANN model. The superiority of the EWANN over the WANN and FFNN models is not only in terms of efficiency criteria, but also due to its appropriate ability to provide information about the physics of the process. The consequences of EWANN for rainfall-runoff modeling of two watersheds revealed that the proposed EWANN could simulate the process of a small and flat sub-basin slightly reliable than a sloppy and wild watershed. The poor outcome of monthly modeling in regard to daily modeling might be due to involvement of more uncertainty in the monthly data.

Keywords: rainfall-runoff modeling, Feed Forward Neural Network, wavelet transform, feature extraction, Shannon entropy (information content), multi-step-ahead forecasting

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