Assessment of the Performance of Various Wavelet Transforms in Combined Wavelet-neural Network Modeling for Monthly River Flow Prediction (Case Study: Kardeh Watershed)

Predicting river flow is one of the most crucial aspects in water resources management. Improving forecasting methods can lead to a reduction in damages caused by hydrological phenomena. Studies indicate that artificial neural network models provide better predictions for river flow compared to physical and conceptual models. However, since these models may not offer reliable performance in estimating unstable data, using preprocessing techniques is necessary to enhance the accuracy and performance of artificial neural networks in estimating hydrological time series with nonlinear relationships. One of these methods is wavelet transformation, which utilizes signal processing techniques.

In this study, to evaluate the efficiency of discrete and continuous wavelet types in the Wavelet-Artificial Neural Network (WANN) hybrid model for monthly flow prediction, a case study was conducted on the Kardeh Dam watershed in the northeast of Iran, serving as a water source for part of Mashhad city and irrigation downstream agricultural lands. Monthly streamflow estimates for the upstream sub-basin of the Kardeh Dam were obtained from the meteorological and hydrometric stations' monthly statistics over a 30-year period (1991-2020). The WANN model is a hybrid time series model where the output of the wavelet transform serves as a data preprocessing method entering an artificial neural network as the predictive model. The combination of wavelet analysis and artificial neural network implies using wavelet capabilities for feature extraction, followed by the neural network to learn patterns and predict data, potentially enhancing the models' performance by leveraging both methods. The 4-fold cross-validation method was employed for the artificial neural network model validation, where the model underwent validation and accuracy assessment four times, each time using 75% of the data for training and the remaining 25% for model validation. The final results were presented by averaging the validation and accuracy results obtained from each of the four model runs. To evaluate and compare the performance of the models used in this study, three evaluation indices, Nash-Sutcliffe Efficiency (NSE), Root Mean Square Error (RMSE), and Pearson correlation coefficient (R), were employed.

The analysis of meteorological and hydrometric data in this study revealed that monthly streamflow in two time steps, T-1 and T-2, were the most effective predictive variables. Each of the two runoff variables of the previous month (Qt-1) and the previous two months (Qt-2) were analyzed by each of the Haar and Fejer-Korovkin2 discrete wavelet transforms and the two continuous Symlet3 and Daubechies2 wavelets at three levels. The results of each level of decomposition was given as input to the ANN model. The presented results at each decomposition level indicated that hybrid models could accurately predict lower flows compared to the single ANN model, and the estimation of maximum values also significantly improved in the hybrid models. Among the wavelets used, Haar wavelets exhibited the weakest performance, and the less commonly employed Kf2 wavelet showed a moderate performance. Since the Haar and Fk2 wavelets, with their discrete structure, did not perform well in decomposing continuous monthly streamflow data, continuous wavelet models outperformed discrete wavelet models. The hybrid models, combining wavelet analysis and artificial neural networks, demonstrated up to an 11% improvement over the performance of the single neural network model.

Streamflow is a crucial element in the hydrological cycle, and predicting it is vital for purposes such as flood prediction and providing water for consumption. The objective of this research was to evaluate the performance of different types of discrete and continuous wavelet models at various decomposition levels in enhancing the efficiency of artificial neural network (ANN) models for streamflow prediction. Since climate and watershed characteristics can influence the nature of data fluctuations and, consequently, the results of the wavelet model decomposition, choosing an appropriate wavelet model is essential for obtaining the best results. Considering the existing variations in the results of different studies regarding the selection of the best wavelet type, it is suggested to use both continuous and discrete wavelet types in modeling to achieve the best predictions and select the optimal results. Given that a lower number of input variables in neural network models lead to higher accuracy in modeling results, it is recommended to perform decomposition at a two-level depth to reduce input components to the neural network model, thereby reducing the model execution time.