Evaluation of Time Series Analysis Based on Wavelet Function on River Flow Simulation

Using the values analyzed by the wavelet function can increase the accuracy of the simulations. Considering the climatic changes and the increase of extreme values in recent years, in this study, we made an effort that the effect of signal processing under the name of wavelet transformation in improving the performance of random forest model in simulating monthly river flow in Siminehrood and Mahabadchai sub-basins in the south of Lake Urmia has been discussed and investigated in the period of 1971-2019.

In this study, the accuracy of the random forest model has been investigated in two steps of training and testing. At first, the random forest model was evaluated in two phases of training and testing in rainfall-runoff simulation in the south of Lake Urmia basin. Nash-Sutcliffe statistics and root mean square error were used to evaluate the performance and error rate of the studied models, respectively. In the next step, after investigating the performance of the random forest model, the time series of rainfall and river flow in the studied basins were analyzed using the wavelet function. In this regard, two analysis levels (level 1 and 2) and two Haar and Daubechies wavelet functions were used. Finally, using the random forest model, rainfall-runoff simulation based on the wavelet theory was done under the name of W-RF model.

Results and Dissection: 

At First, the random forest model was investigated in two phases of training and testing, and the simulation results of the river flow values showed that the simulated values were within the 95% confidence interval, and the error rate of the river flow simulation using the RMSE statistic is 3.22 and 8.91 cubic meters per second in the test phase for Mahabadchai and Siminehrood sub-basins, respectively. In order to investigate the effect of time series analysis on the performance of the RF model, wavelet theory and Haar and Daubechies 4 wavelet functions were used in decomposition levels 1 and 2. By estimating the accuracy and performance of the hybrid W-RF model in 4 input patterns, the best pattern was selected based on the RMSE and NSE model evaluation criteria. The research results showed that for the Haar wavelet function in level 1 decomposition has better performance and error rate than level 2 type in both sub-basins. In this study, the Daubechies wavelet at level 1 in the test phase has provided the best performance and the lowest error rate in the simulation of the river flow values in the studied sub-basins and has been able to reduce the error rate in the two sub-basins of Mahabadchai and Siminehrood respectively by about 89 and 80 percent compared to the random forest model.

Finally, by comparing the RF and W-RF models, the simulation results of river flow in the two studied sub-basins showed that the integrated W-RF model was able to reduce the error rate in the two sub-basins of Mahabadchai and Siminehrood to reduce by 89 and 80% respectively. Considering the increase in simulation complexity with the involvement of wavelet theory, the error recovery rate and model performance are acceptable. The integrated W-RF model in this study provides reliable results for the simulation of river flow data in order to support decision-making and risk analysis in the exploitation of downstream reservoirs and the management of water resources in sub-basins. The obtained results can be used in the design of water resources systems.