A comparative analysis of training methods for artificial neural network rainfall–runoff models Sanaga Srinivasulu a , Ashu Jain b, * a Center for Spatial Information Technology, Institute of Post Graduate Studies and Research, Jawaharlal Nehru Technological University, Hyderabad 500 028, India b Department of Civil Engineering, Indian Institute of Technology, Kanpur 208016, India Received 9 June 2004; received in revised form 14 December 2004; accepted 14 February 2005 Abstract This paper compares various training methods available for training multi-layer perceptron (MLP) type of artificial neural networks (ANNs) for modelling the rainfall–runoff process. The training methods investigated include the popular back- propagation algorithm (BPA), real-coded genetic algorithm (RGA), and a self-organizing map (SOM). A SOM was used to first classify the input–output space into different categories and then develop feed-forward MLP models for each category using BPA. The daily average rainfall and streamflow data derived from an existing catchment were employed to develop all ANN models investigated in this study. A wide variety of standard statistical performance evaluation measures were employed to evaluate the performances of various ANN models developed. The results obtained in this study indicate that the approach of first classifying the input–output space into different categories using SOM and then developing separate ANN models for different classes trained using BPA performs better than the approach of developing a single ANN rainfall–runoff model trained using BPA. The ANN rainfall–runoff model trained using RGA was able to provide a better generalization of the complex, dynamic, non-linear, and fragmented rainfall–runoff process in comparison with the other approaches investigated in this study. It has been found that the RGA trained ANN model significantly outperformed the ANN model trained using BPA, and was also able to overcome certain limitations of the ANN rainfall–runoff model trained using BPA reported by many researchers in the past. It is noted that the performances of various ANN models should to be evaluated using a wide variety of statistical performance indices rather than relying on a few global error statistics normally employed that are similar in nature to the global error minimized at the output layer of an ANN. # 2005 Elsevier B.V. All rights reserved. Keywords: Artificial neural networks; Rainfall–runoff modelling; Real-coded genetic algorithms; Self-organizing maps; Back-propagation training algorithm 1. Introduction Water is essential to all kinds of lives on the earth. The total quantity of available water is estimated to be about 1386 million cubic kilometers (MKm 3 ). Out of www.elsevier.com/locate/asoc Applied Soft Computing 6 (2006) 295–306 * Corresponding author. Tel.: +91 512 259 7411; fax: +91 512 259 7395. E-mail address: ashujain@iitk.ac.in (A. Jain). 1568-4946/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2005.02.002