Comparison of Linear and Nonlinear (Bilinear) Time Series Models in Reference Crop Evapotranspiration Prediction in Urmia Synoptic Station

Comparison of Linear and Nonlinear (Bilinear) Time Series Models in Reference Crop Evapotranspiration Prediction in Urmia Synoptic StationReference crop evapotranspiration (ETo) prediction is one of the important elements in optimizing agricultural water consumption. In this regard, one of the prediction approaches is to use the stochastic time series methods. In this research, AR (p) and ARMA(p,q) linear models and Bilinear nonlinear model were compared in predicting the monthly values of  ETo in Urmia synoptic station. To conduct the present research, the monthly values of ETo from 1971 to 2010 were calculated and data between 1971-2005 and 2006-2010 were used for models calibration and validation, respectively. In the next step, the suitable linear model was selected and the results of this model and Bilinear nonlinear model were compared with the values of FAO Penman-Monteith method. The results showed that the AR(11) time series model had better results than the other linear models. The comparison of the results of AR(11) model and BL(11,0,1,1) model with the monthly values of the ETo using FAO Penman-Monteith method showed that the value of root mean square error (RMSE) and relative error (VE) in AR(11) model were 1.85 mm and 3.8 %, respectively, and in BL(11,0,1,1) model, they were 1.76 mm and 3.6 %, respectively. Therefore, Bilinear nonlinear model had more capability in modeling and predicting of the monthly values of ETo values in comparing with linear models. In the next step, the monthly values of ETo for five future years were predicted by using the Bilinear nonlinear model.