Discussion of “Comparison of Wavelet-Based ANN and Regression Models for Reservoir Inflow Forecasting” by Krishna Budu

Abstract

The discusser wishes to thank the author for investigating the accuracy of the wavelet neural network (WNN) technique in predicting daily reservoir inflows to the Malaprabha Reservoir in Belgaum, India, using daily values of rainfall, inflow, and streamflow at an upstream gauging station. The WNN results were compared with two standard neural network models along with a multiple linear regression (MLR) model and moving average (MA). It was found that the WNN model performed better than the artificial neural network (ANN) and MLR models in inflow forecasting. The discusser would like to point out some important points that the author and other researchers might consider: • According to the author, the testing data-set extremes (Xmin 1⁄4 0 and Xmax 1⁄4 1,016 m=s) fell within the training data-set limits (Xmin 1⁄4 0 and Xmax 1⁄4 1,036.4 m=s) and therefore the trained neural network models did not face difficulties in extrapolating. It is clear from Table 1, however, that Xmin 1⁄4 0.14 m=s, which was higher than the corresponding value of the testing data set and implies that these models faced difficulties in extrapolating low flow values. This can also be seen from Fig. 10, in which the WNN-BP and WNN-RB models (here BP = back propagation and RB = radial basis) slightly overestimated the low flow values. • In the study, the iteration numbers for the optimal ANN-BP, ANN-RB, WNN-BP, and WNN-RB were not provided. As seen from Table 3, the fitting accuracy of the ANN-BP model in the training period was generally similar to that of the ANN-RB model. However, WNN-BP approximated flow values in the training period much better than WNN-RB did. What might be the reason? • According to the author, it is seen from the scatter plot in Fig. 7 that the WMLR model had more values close to its predicted line and its R value was slightly higher. The discusser agrees with the author on this. However, the fit line coefficients should also have been considered in comparing the two methods. It is clear from the scatter plots (assuming that the fit line equation was y 1⁄4 axþ b) that the WNN-BP a and b coefficients were respectively closer to 1 and 0 (the ideal line is y 1⁄4 x) than were the WMLR a and b coefficients. This was also valid for Fig. 9. • The “Conclusion” section states, “Overall analysis indicates that the performance of ANN and regression models using undecomposed data is relatively lower compared to that of wavelet-decomposed data used NN and regression models; this may be plausible due to the variation in nonlinear dynamics of the rainfall runoff process that mapped effectively by waveletbased models.” In the study, however, the WMLR model was found to be better than the WNN model coupled with the RB and BP methods. The discusser wonders how the linear WMLR model could perform better than the nonlinear WNN models in such a nonlinear rainfall-runoff process, as also stated by the author. This needs clarification.