عنوان مقاله [English]
Introduction: Surface water has always been one of the most essential pillars of water projects and, with modeling and predicting the river flow, in addition to the management and utilization of water resources, it is possible to inhibit the natural disasters such as drought and floods. Therefore, researchers have always tried to improve the accuracy of hydrological parameters estimation by using new tools and combining them. In this study, the effect of seasonal coefficients and mathematical methods of signal analysis and signal processing on wavelet transform to improve the performance of the Gene Expression Programming (GEP) model were discussed.
Materials and Methods: In the present study, for the prediction of the monthly flow of Ab Zal River, the information of Pol Zal hydrometric station in period 1972 to 2017 was used. In the next step, different input patterns need to be ready. To this purpose, the data are presented in three different modes: (a) the use of flow data and considering the role of memory up to four delays; (b) the involvement of the periodic term in both linear (?-GEP) and nonlinear (PT-GEP) states, and (c): data analysis using the Haar wavelet, Daubechies 4 (db4), Symlet (sym), Meyer (mey), and Coiflet (coif), was done in two subscales, prepared, and introduced to the GEP model. To better analyze the effect of mathematical functions used in the GEP method, two linear modes (using Boolean functions including addition, multiplication, division, and minus) and nonlinear (including quadratic functions, etc.) were considered. The wavelet transform is a powerful tool in decomposing and reconstructing the original time series. Wavelet function is a type of function that has an oscillating property and can be quickly attenuated to zero. Modeling was done based on 80% of recorded data (432 months) and the validation was done based on the remaining 20% (108 months). To evaluate the performance of each of models, statistical indices such as mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (R) were used.
Results and Dissection: The results of linear and nonlinear GEP models showed that in both cases, the four-delay model achieved the most accuracy in river flow prediction. Still the performance of nonlinear GEP model according to RMSE (4.093 (m3/s)), MAE (2.782 (m3/s)) and R (0.660) were better than another, respectively. In the next step, the periodic term was added to the model inputs. Based on the results, the PT-GEP model with M4 pattern had the lowest error, the highest accuracy and was able to reduce the RMSE index by 8%. Then, in the third step, the river flow data were divided into approximate subdivisions and details using five wavelet functions. The most appropriate level of analysis based on the number of data was considered as number three. The results of the W-GEP modes showed an excellent performance of this method so that the model was able to reduce the RMSE statistics with 48.6%, 41.2%, and 31.1% compared to the L-GEP, NL-GEP and PT-GEP methods, respectively. Also, the best performance of the W-GEP model with the Symlet wavelet and the decomposition level of one had the highest accuracy (R=0.847) and the lowest error (RMSE =2.898 (m3/s) and MAE =1.745 (m3/s) among all models (35 models) such as linear and nonlinear, seasonal and non-seasonal and wavelet hybrid models.
Conclusion: Based on the results, it can be concluded that the overall use of data preprocessing methods (including seasonal coefficients and wavelet functions) has improved the performance of the GEP model. However, the combination of wavelet functions with the GEP model has significantly increased the accuracy of the modeling. Therefore, it is recommended as the most suitable tool for river flow forecasting.