Calibration and validation of neural networks to ensure physically plausible hydrological modeling Greer B. Kingston * , Holger R. Maier, Martin F. Lambert Centre for Applied Modelling in water Engineering, School of Civil and Environmental Engineering, The University of Adelaide, Adelaide, SA 5005, Australia Received 22 December 2003; revised 16 March 2005; accepted 18 March 2005 Abstract Although artificial neural networks (ANNs) have proven to be useful tools for modeling many aspects of the hydrological cycle, the fact that they do not provide any means of exploiting fundamental knowledge of the system means that they are still viewed with some skepticism. In this paper, an approach is presented for incorporating information about relative input contributions in the development of an ANN during the calibration and validation stages. Two case studies are presented which highlight the uncertainty associated with calibrating and validating an ANN based on predictive error alone and demonstrates the necessity of constraining the calibration of an ANN to ensure physical plausibility. The proposed technique was used in the comparison of three training algorithms in terms of their ability to find a globally optimal solution and it was identified that neither in-sample nor out-of-sample performance measures are very informative about the solutions obtained, nor do they necessarily indicate that a reasonable approximation of the underlying relationship has been achieved. It was shown that by applying constraints to the objective function, an ANN could be developed with physically plausible input contributions and comparable predictive performance to that of an unconstrained model. A sensitivity analysis was carried out to verify the proposed methodology. q 2005 Elsevier B.V. All rights reserved. Keywords: Artificial neural networks; Calibration; Streamflow modeling; Genetic algorithms. 1. Introduction Over the past 15 years, there has been a growing interest in artificial neural networks (ANNs) for simulating, forecasting and predicting hydrological variables (ASCE Task Committee, 2000; Maier and Dandy, 2000). The majority of hydrological processes are highly nonlinear in nature and, in many cases, modeling these variables with more conventional physically based or conceptual models may be limited by a poor understanding of the complex interactions that are involved in the process. In such cases, ANNs are often viewed as an appealing alternative, as they have the ability to extract a nonlinear relationship from data without requiring an in depth knowledge of the physics occurring within the hydrological system (Zhang et al., 1998). Journal of Hydrology 314 (2005) 158–176 www.elsevier.com/locate/jhydrol 0022-1694/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2005.03.013 * Corresponding author. E-mail address: gkingsto@civeng.adelaide.edu.au (G.B. Kingston).