Long-term forecast of monthly reference evapotranspiration of the period 2018-2027 using SARIMA and GRNN models (case study: Rasht synoptic station)

Document Type : Original Article


Department of Water Science and Engineering, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, Iran


Evapotranspiration is a key principle of water balance and an important element of energy balance. Therefore, forecasting and estimation of evapotranspiration in agricultural water management, forecasting and monitoring drought, and the development and exploitation of effective water resources might be valuable and practical. The purpose of this study was to model the Reference Evapotranspiration time series (ET0) at Rasht Synoptic Station with two SARIMA and GRNN models during 1956-2017 and its forecast for 2018-2027.
Material and methods:
Rasht is located in the temperate and humid parts of northern Iran and in the southern strip of the Caspian Sea. In this study, the Adjusted ThornthWaite method (ATW) was used to estimate ET0, the credibility of which was previously confirmed by researchers for estimation of reference evapotranspiration rate in Rasht. Evapotranspiration values were estimated for the time period of 1956-2017. Two models were selected for modeling and validation of the ET0 series. The SARIMA model is based on seasonal stochastic models, and the GRNN model is based on artificial intelligence. The models’ inputs were selected on the basis of three previous monthly and yearly. The target-input matrices were divided into calibration (75%) and validation (25%) sections. Autocorrelation Function (ACF) indicated a seasonal trend in the ET0 monthly series, with a return period of 12. Four times seasonal differentiation, revealed that the best degree of SARIMA’s seasonal integrated degree was the first-order. Other SARIMA operators, including seasonal and non-seasonal autoregressive, and average seasonal and non-seasonal moving, were selected by trial and error. Optimization of the GRNN model was accomplished by trying and error of the spread parameter. In this study, criteria such as RMSE, NS, and R were used to check the error and correlate the outputs of the model.
Results and discussion:
The best model of SARIMA pattern was SARIMA (0, 0, 1) (0, 1, 1)12 which has RMSE and NS values of 8.89 mm and 0.97, respectively. The GRNN model had its best performance by applying the total inputs. The RMSE and NS values were 9.22 and 0.96, respectively, for GRNN’s best output. The difference between the two models was reported in predicting the year’s minima (January-February), which showed SARIMA’s better performance. To compare these two models, the Taylor diagram was also used, which showed that the accuracy of SARIMA not only in error but also in the correlation and estimation of the true deviation of the real values was slightly more accurate than GRNN. After evaluating the models and assessing their acceptable performances, best extracted models from both SARIMA & GRNN were used for ET0’s long-term forecasting up to the next ten years (for the period of 2018-2027).
The results of the forecasts for Rasht’s future showed a sharp ascending trend in the rate of evapotranspiration in the years 2018-2027 (compared to the period of 1956-2017). This is a warning of a rapid increase in the evapotranspiration rate in the years ahead, in the wet area of Rasht. This issue is very important for the surface water and groundwater resources planning, agricultural uses, and will be a serious warning to farmers and water managers in this area.


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