Impact of wavelet on accuracy of estimated models in rainfall-runoff modeling (Case study: Sufi Chay)

Introduction
In recent decades, accurate modeling of runoff has always been one of the hottest topics for researchers in the field of hydrology, as it plays an important role in water resources management, hydropower development, urban planning, irrigation and other hydrological/meteorological activity programs. Concept-based and physical models require huge amounts of data and environmental calculations. The nonlinear nature of the rainfall-runoff process and the complexity of physical models are some of the reasons why researchers have turned to intelligent models. However, these models may not provide logical results for nonlinear hydrological processes. To overcome this shortcoming, nonlinear artificial neural networks (ANNs) have depicted a real success in predicting hydrological time series.
Materials and Methods
The usefulness of wavelet transforms in noise reduction and multi-resolution analysis along with the ability of ANNs to optimize and predict hydrological processes has recently been introduced as a neural network wavelet hybrid model (WANN) and is widely used by hydrologists not only for rainfall-runoff modeling. It has been used to simulate some other components of the hydrological cycle such as river flow, groundwater, precipitation and sediment. In this study, precipitation and discharge data on a monthly scale have been used. For modeling in this research, ANN and WANN have been used. Data were used for Sufi Chay Basin for period 2001-2019.
Results and Discussion
In this study, for modeling rainfall-runoff by neural network in MATLAB 2018 Software and investigating the effect of using wavelet transform on the accuracy of rainfall-runoff model has been done. First, the existence of autocorrelation and its significance in runoff data were investigated using the partial autocorrelation function (PACF). In the hybrid model, Daubechies mother wavelets 3 and 4 are used. Six scenarios were examined for modeling. Among the selected scenarios, scenarios 4 and 5 had the best results in comparison between the two models. The poor accuracy of the first three scenarios (Scenarios 1-3) indicates that using rainfall data alone are not sufficient to model runoff, thus employing the last monthly runoff data into the model made a significant change in the results. In the ANN model, scenario 4 has more acceptable results with correlation coefficient (r), square root mean square error (RMSE) and Nash Sutcliffe coefficient (NSE) of 0.889, 51.574 and 0.788, respectively for the training section, and 0.779, 70.625, and 0.595, respectively for the test section. In the hybrid model WANN, scenario 5 has the best results with the values of r, RMSE and NSE of 0.997, 23.99 and 0.954, respectively for the training section, and 0.829, 62.334 and 0.684, respectively for the test section.
Conclusion
In the present study, the performance of ANN and WANN models for rainfall-runoff modeling in Sufi Chay Basin using different parameters of rainfall and discharge delays during the statistical period (2001-2019) was evaluated. The highest accuracy of the models was provided in combining runoff input with a time delay and monthly precipitation. The purpose of this study is the effect of wavelet on increasing the accuracy of estimation in rainfall-runoff modeling. The results of the present study showed that the hybrid model will increase the accuracy of a model.