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.


  1. Abdullah, S.S., and Malek, M.A., 2016. Empirical Penman-Monteith equation and artificial intelligence techniques in predicting reference evapotranspiration: a review. International Journal of Water. 10: 1.55-66.
  2. Abrishami, N., Sepaskhah, A.R. and Shahrokhnia, M.H., 2019. Estimating wheat and maize daily evapotranspiration using artificial neural network. Theoretical and Applied Climatology, 135(3-4), pp.945-958.
  3. Adamala, S., Raghuwanshi, N.S. and Mishra, A., 2018. Development of Generalized Higher-Order Neural Network-Based Models for Estimating Pan Evaporation. In Hydrologic Modeling (pp. 55-71). Springer, Singapore.
  4. Aghelpour, P. and Nadi. M., 2018. Comparing the Performance of Autoregressive and Moving Average Models in Predicting Maximum and Minimum Daily Temperature. In Proceeding of 1st National Conference on Water Resources Management and Environmental Challenges. Apr30-May1. Sari Agricultural Sciences and Natural Resources University. Sari. Iran.
  5. Aghelpour, P. and Nadi. M., 2019. Evaluating SARIMA Model Accuracy in Modeling and Long-Term Forecasting of Average Monthly Temperature in Different Climates of Iran. Journal of Climate Research. 35: 113-126. (In Persian with English abstract)
  6. Alves, W.B., Rolim, G.D.S., and Aparecido, L.E.D.O., 2017. REFERENCE EVAPOTRANSPIRATION FORECASTING BY ARTIFICIAL NEURAL NETWORKS. Engenharia Agricola. 37: 6.1116-1125.
  7. Araghinejad, S. 2013. Data-driven modeling: using MATLAB® in water resources and environmental engineering (Vol. 67). Springer Science & Business Media.
  8. Azad, T.N., Behmanesh, J., and Montaseri, M., 2013. Predicting potential evapotranspiration using time series models (case study: Urmia). Journal of Water & Soil. 27: 1.213-223. (In Persian with English abstract)
  9. Azad, T.N., Behmanesh, J., Montaseri, M. and Verdinejad, V.R., 2016. Comparison of Time Series Methods and Artificial Neural Networks in Reference Evapotranspiration Prediction (Case Study: Urmia). Irrigation Science & Engineering. 38: 4.75-85. (In Persian with English abstract).
  10. Babamiri, O., Nowzari, H., and Maroufi, S., 2017. Potential Evapotranspiration Estimation using Stochastic Time Series Models, Watershed Management Research. 8: 15.137-146. (In Persian with English abstract)
  11. Behmanesh, J., Azad, T.N., Montaseri, M. and Besharat, S., 2015. Comparison of Linear and Nonlinear (Bilinear) Time Series Models in Reference Crop Evapotranspiration Prediction in Urmia Synoptic Station. Journal of Water Research in Agriculture. 28(1), 85-96. (In Persian with English abstract).
  12. Dinpashoh, Y. 2006. Study of reference crop evapotranspiration in IR of Iran. Agricultural Water Management. 84(1-2), 123-129.
  13. Eslamian, S.S., Gohari, S.A., Biabanaki, M. and Malekian, R., 2008. Estimation of monthly pan evaporation using artificial neural networks and support vector machines. J Appl Sci. 8(19), 3497-3502.
  14. Feng, Y., Peng, Y., Cui, N., Gong, D., and Zhang, K. 2017. Modeling reference evapotranspiration using extreme learning machine and generalized regression neural network only with temperature data. Computers and Electronics in Agriculture. 136.71-78.
  15. Fooladmand, H. R., 2011. Montly Prediction of Reference Crop Evapotranspiration in Fars Province. Water and Soil Science. 20: 4.157-169. (In Persian with English abstract).
  16. Gautam, R., and Sinha, A.K., 2016. Time series analysis of reference crop evapotranspiration for Bokaro District, Jharkhand, India. Journal of Water and Land Development. 30(1), 51-56.
  17. Goyal, M.K., Bharti, B., Quilty, J., Adamowski, J., and Pandey, A., 2014. Modeling of daily pan evaporation in sub-tropical climates using ANN, LS-SVR, Fuzzy Logic, and ANFIS. Expert systems with applications. 41(11), 5267-5276.
  18. Hasan-Bagloee, M. and Maghsodi, E., 2003. Selection of a suitable method for prediction of reference evapotranspiration of Rasht region. In Proceedings of the 8th national conference on irrigation and evaporation reduction, Shahid Bahonar University, Kerman, Islamic Republic of Irans (pp. 34-43).
  19. Huo, Z., Feng, S., Kang, S. and Dai, X., 2012. Artificial neural network models for reference evapotranspiration in an arid area of northwest China. Journal of arid environments. 82.81-90.
  20. Keshtegar, B., Kisi, O. and Zounemat-Kermani, M., 2019. Polynomial chaos expansion and response surface method for nonlinear modelling of reference evapotranspiration. Hydrological Sciences Journal, pp.1-11.
  21. KIŞI, Ö., 2006. Generalized regression neural networks for evapotranspiration modelling. Hydrological Sciences Journal. 51: 6.1092-1105.
  22. Laaboudi, A., Mouhouche, B., and Draoui, B., 2012. Neural network approach to reference evapotranspiration modeling from limited climatic data in arid regions. International journal of biometeorology. 56: 5.831-841.
  23. Ladlani, I., Houichi, L., Djemili, L., Heddam, S., and Belouz, K., 2012. Modeling daily reference evapotranspiration (ET0) in the north of Algeria using generalized regression neural networks (GRNN) and radial basis function neural networks (RBFNN): a comparative study. Meteorology and Atmospheric Physics. 118: 3-4.163-178.
  24. Lu, X., Ju, Y., Wu, L., Fan, J., Zhang, F. and Li, Z., 2018. Daily pan evaporation modeling from local and cross-station data using three tree-based machine learning models. Journal of Hydrology, 566, pp.668-684.
  25. Pereira, A.R., and Pruitt, W. O. 2004. Adaptation of the Thornthwaite scheme for estimating daily reference evapotranspiration. Agricultural Water Management. 66(3), 251-257.
  26. Rahimi, J., Ebrahimpour, M., and Khalili, A., 2013. Spatial changes of extended De Martonne climatic zones affected by climate change in Iran. Theoretical and applied climatology. 112(3-4), 409-418.
  27. Saggi, M.K. and Jain, S., 2019. Reference evapotranspiration estimation and modeling of the Punjab Northern India using deep learning. Computers and Electronics in Agriculture, 156, pp.387-398.
  28. Salas, J.D., Delleur, W., Yevjevich, V., and Lane, W.L., 1988. Applied modeling of hydrologic time series. Water Resources Publications. Littleton, Colorado, U.S.A. Third prontonh. 484pp.
  29. Salas J. D. 1993. Analysis and modelling of hydrologic time series. In Handbook of hydrology, maidment, D. R. Chapter 19. McGraw-Hill. New York.
  30. Sattari, M.T., Nahrein, F. and Azimi, V. 2013. M5 Model Trees and Neural Networks Based Prediction: of Daily ET0 (Case Study: Bonab Station). Iranian Journal of Irrigation and Drainage. 7: 1.104-113. (In Persian with English abstract).
  31. Shiri, J., 2019. Evaluation of a neuro‐fuzzy technique in estimating pan evaporation values in low‐altitude locations. Meteorological Applications, 26(2), pp.204-212.
  32. Shirvani, A. and Honar, T., 2011. Application of time series models for evapotranspiration forecasting in Bajgah station, Iranian Water Research. 5(8), 135-142. (In Persian with English abstract).
  33. Shirzad, M., and Asadzadeh, B., 2016. Estimating Evapotranspiration Using Meteorological Data by Three Methods: Artificial Neural Nework, FAO Penmann-Montith and GIS (Case Study: Kurdistan Province). The 2nd International Congress on Earth Science & Urban Development. May-12. East Azarbaijan Province Jahad Research Center. Tabriz. Iran. (In Persian with English abstract).
  34. Taylor, K.E., 2001. Summarizing multiple aspects of model performance in a single diagram. Journal of Geophysical Research: Atmospheres. 106: D7.7183-7192.
  35. Torres, A.F., Walker, W.R., and McKee, M., 2011. Forecasting daily potential evapotranspiration using machine learning and limited climatic data. Agricultural Water Management. 98(4), 553-562.
  36. Traore, S., Wang, Y.M., and Kerh, T., 2008. Modeling reference evapotranspiration by generalized regression neural network in semiarid zone of Africa. WSEAS Trans. Inf. Sci. Appl. 6.991-1000.
  37. Verdinejad, V.R., 2015. Evaluation and Comparison of GRNN, MLP and RBF Neural Networks for Estimating Cucumber, Tomato and Reference Crops’ Evapotranspiration in Greenhouse Condition. Water and Soil Science. 25(4), 123-136. (In Persian with English abstract).
  38. Zare, A.H., Afruzi, A., Mirzaei, M., and Bagheri, H., 2016. Forecasting the Reference Evapotranspiration Using Time Series Model. Journal of Water & Soil. 30(1), 99-111. (In Persian with English abstract).
  39. Zare, A.H., Ghasemi, A., Bayat, V.M., and Maroufi, S., 2009. Assessment of artificial neural network (ANN) in prediction of garlic evapotranspiration (ETc) with lysimeter in Hamedan. Journal of Water & Soil. 23(3), 176-185. (In Persian with English abstract).
  40. Zare, A.H., Saghaei, S., Ershad-Fath, F. and Nozari, H., 2014. Modelong and Forecasting of Reference Crop Evapotranspiration Using Time Series, Case Study: Kermanshah Province. Agricultural Meteorology. 2(1), 45-56. (In Persian with English abstract)
  41. Zhao, L., Xia, J., Xu, C.Y., Wang, Z., Sobkowiak, L., and Long, C., 2013. Evapotranspiration estimation methods in hydrological models. Journal of Geographical Sciences. 23(2), 359-369.