Forecasting of Daily Reference Evapotranspiration at Ahvaz synoptic station using wavelet-GMDH hybrid model

Reference evapotranspiration is one of the most effective components of agricultural water use and management of water resources. Determination of the water requirements of various plants during the growing season is necessary in order to prevent water waste and proper planning (7). In recent years the use of artificial intelligence technics and hybrid model in forecasting of hydrological parameters has become very popular (12). The objective of this study is to evaluate GMDH neural network and wavelet-GMDH hybrid models in forecasting of daily reference evapotranspiration at Ahvaz synoptic station.
For this purpose, 10-year period (2000 to 2009), 7 years (2000-2006) for training and 3 years (2007-2009) to test different models were considered. Reference crop evapotranspiration time series generated using standard penman-monteith equation. Different combinations of inputs (different delays) and various mother wavelets were examined. To test different models were considered different combinations of inputs (9 different delays); and different mother wavelets (13 mother wavelets). A total of 126 models 117 of them related to hybrid models wavelet- GMDH and 9 for GMDH neural network were carried out. To choose the best model, statistical criteria such as coefficient of determination (R2), root mean square error (RMSE) and the mean percentage error (MARE) was used.
The results showed that wavelet-GMDH hybrid model (RMSE = 0.31 mm / day) compared with GMDH neural network (RMSE = 1.22 mm / day) has higher accuracy in forecasting daily reference evapotranspiration. The results showed that use of delays longer than four days have little effect on the accuracy of models and in some cases can result in reduced accuracy. The results of similar studies that have used wavelet transform to preprocessing data are in correspondence with our findings (1, 4, 5 and 12). Results of GMDH neural network showed that number of delays did not affect the accuracy of model. This study evaluates the accuracy of the wavelet-artificial neural network hybrid model for different mother wavelets. Results showed that Meyer mother wavelet due to its complexity and its shape improved the accuracy of models. These findings correspond with the findings of Rajaee and Ebrahimi(2014), Shoaib et al(2015) and Toofani et al (2012) (13, 15 and 17).
Results of this study showed that, at the forecasting of one day ahead reference evapotranspiration Wavelet-GMDH model (MAPE=5.53%) has significant superiority to GMDH model (MAPE=22.11%). The results of this study can be used in the planning of irrigation water in this area. At the end it is recommended that proposed models has been evaluated in different climate conditions of Iran.