Runoff prediction using an integrated hybrid modelling scheme Renji Remesan a, * , Muhammad Ali Shamim a , Dawei Han a , Jimson Mathew b a Water and Environmental Management Research Centre, Department of Civil Engineering, University of Bristol, Lunsford House, Cantocks Close, Clifton Bristol BS8 1UP, United Kingdom b Department of Computer Science, University of Bristol, Merchant Venture’s Building, Woodland Road, Bristol BS8 1UB, United Kingdom article info Article history: Received 10 May 2008 Received in revised form 10 March 2009 Accepted 30 March 2009 This manuscript was handled by P. Baveye, Editor-in-Chief, with the assistance of Juan V Giraldez, Associate Editor Keywords: Rainfall runoff modelling Gamma test Wavelet Hybrid model summary Rainfall runoff is a very complicated process due to its nonlinear and multidimensional dynamics, and hence difficult to model. There are several options for a modeller to consider, for example: the type of input data to be used, the length of model calibration (training) data and whether or not the input data be treated as signals with different frequency bands so that they can be modelled separately. This paper describes a new hybrid modelling scheme to answer the above mentioned questions. The proposed meth- odology is based on a hybrid model integrating wavelet transformation, a modelling engine (Artificial Neural Network) and the Gamma Test. First, the Gamma Test is used to decide the required input data dimensions and its length. Second, the wavelet transformation decomposes the input signals into differ- ent frequency bands. Finally, a modelling engine (ANN in this study) is used to model the decomposed signals separately. The proposed scheme was tested using the Brue catchment, Southwest England, as a case study and has produced very positive results. The hybrid model outperforms all other models tested. This study has a wider implication in the hydrological modelling field since its general framework could be applied to other model combinations (e.g., model engine could be Support Vector Machines, neuro-fuzzy systems, or even a conceptual model. The signal decomposition could be carried out by Fou- rier transformation). Ó 2009 Elsevier B.V. All rights reserved. Introduction Rainfall–runoff dynamics is usually highly nonlinear, time- dependent and spatially varying. Significant advancements in hydrological modelling started with the introduction of unit hydrograph model and its related impulse response functions (Sherman, 1932), and is considered to be the first data driven mod- el in hydrology. In the last four decades, mathematical modelling of rainfall–runoff series, for reproducing the underlying stochastic structure of this type of hydrological process, has been performed to a great extent. Models of AR (autoregressive) and ARMA (auto- regressive moving average) class (Box and Jenkins, 1970) have played a key role in this kind of approach, producing runoff predic- tion for many different time step cases (Bartolini et al., 1988). Variant forms of these models like PAR (periodic AR), PARMA (peri- odic ARMA), DARMA (discrete ARMA) etc. were introduced with some considerable improvements in prediction (Tao and Delleur, 1976; Chang et al., 1987). Moss and Bryson (1974) introduced a bivariate character to the conventional way of adopting ARX (Auto- Regressive with eXogenous input) concept in hydrological time series modelling. ARX and its variant form ARMAX (autoregressive moving average with exogenous input) were considered as much as a success for runoff predictive tools as other models compared in its generation (Todini, 1978). Furthermore, they are still in use even in a plethora of new sophisticated mathematical tools (Jonsdottir et al., 2007; Karamouz et al., 2008; Young and Garnier, 2006). Over the last decades, data mining techniques have been introduced and widely applied in hydrological studies as powerful alternative modelling tools, such as Artificial Neural Networks (ANN) (Dawson and Wilby, 2001; Han et al., 2007a, 2007b; Bray and Han, 2004; Nayak et al., 2005, 2007), fuzzy inference system (FIS) (Zadeh, 1965; See and Openshaw, 2000; Xiong et al., 2001; Han et al., 2002; Nayak et al., 2004, 2005, 2007), and Data Based Mechanistic (DBM) models (Young, 2002; Young and Garnier, 2006). A comprehensive review by ASCE Task Committee on Appli- cation of Artificial Neural Networks in Hydrology (ASCE, 2000a,b) shows the acceptance of ANN technique among hydrologists. A major criticism of ANN models is of their limited ability to account for any physics of the hydrologic processes in a catchment (Aksoy et al., 2007, 2008a,b; Koutsoyiannis, 2007). That concern is par- tially ruled out through a study by Jain et al. (2004), which proves that the distributed structure of the ANN is able to capture certain hydrological processes such as infiltration, base flow, delayed and quick surface flow, etc. These artificial intelligent techniques exhi- bit many advantages over conventional modelling techniques, including the ability to handle enormous amounts of noisy data 0022-1694/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2009.03.034 * Corresponding author. Tel.: +44 (0)117 9289768; fax: +44 (0)117 9289770. E-mail address: Renji.Remesan@bristol.ac.uk (R. Remesan). Journal of Hydrology 372 (2009) 48–60 Contents lists available at ScienceDirect Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol