Discussion of “Comparative Analysis of Event-based Rainfall-runoff Modeling Techniques—Deterministic, Statistical, and Artificial Neural Networks” by Ashu Jain and S. K. V. Prasad Indurthy

Abstract

The discusser appreciates the exhaustive efforts undertaken by the authors for a comparative analysis of techniques based on deterministic (unit hydrograph theory), statistical (regression analysis), and artificial neural networks (ANN) for better representation of an event-based rainfall-runoff process. Of late, the ANN model, among the black-box models, has gained wider applicability, because the functional form between the input variable and the output is not required to be defined a priori, and it involves minimal knowledge of the underlying process to model such hydrologic problems. The present study is yet another addition to many other studies on the application of ANN in modeling hydrologic inputoutput relationships (Zhu et al. 1994; Smith and Eli 1995; Hsu et al. 1995; Minns and Hall 1996; Tokar and Johnson 1999; Anmala et al. 2000). Although the efforts of the authors are laudable, the discusser has certain reservations on the applicability of methodology applied by the authors for comparing the predictive performance of the various models. The ANN model, even with only three layers, results in a nonlinear relationship between input and output with a very large number of connection weights wij relating to the ith neuron of the input layer, to jth neuron of the hidden layer, and wjk relating to the jth neuron of the hidden layer, to kth neuron of the output layer. Due to the presence of such nonlinearity, the ANN model is very sensitive to the values of input neurons. Obviously, if the input values are subjected to large errors, then the functional form, which the ANN evolves at the training stage, may perform poorly at the validation stage. This calls for careful selection of input neurons for such complex studies. In rainfall-runoff modeling, the effective rainfall eff Pt= sPt-lossesd results in direct surface runoff. The eff Pt is, of course, difficult to estimate because it depends on the antecedent moisture conditions (AMC) of the catchment. For the same value of total precipitation Pt, one may get a very wide variation of eff Pt ranging from zero to Pt depending on AMC, which in turn depends on preceding hydrological conditions. The authors, in the ANN (regression) modeling procedure, have taken nine rainfall neurons (explanatory variables): Pt , Pt−1 , . . . Pt−8, besides one neuron (explanatory variable), viz., runoff Rt−1. As the authors have not taken the most important causal variable “rainfall excess” ef f Pt for prediction of runoff, the variables Pt , Pt−1 , . . . Pt−8 of the models are likely to have significant differencs compared to the corresponding rainfall excess values. Thus the discusser is of the opinion that formulating a relationship between such input and runoff in regression and