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There are a lot of investigations to select the best model to estimate potential evapotranspiration (ETo) in a certain climate or region. In this paper, the types of climate include arid, semiarid, Mediterranean, and very humid. A spatial and temporal study of the ETo is the aim of this paper, according to the peak and low events (extreme events) and climate change alarms. For this purpose, 50 years (1961-2010) monthly meteorological data of 18 regions in Iran, with various climates, were collected. For estimating the ETo, 5 temperature-based, 5 radiation-based, and 5 mass transfer-based models, were selected with respect to better performance of them in different climates on the basis of past investigations. The results will especially be useful in the regions where the monthly (rather than daily) meteorological data are available. The results appear that the Blaney-Criddle (BC) (root mean square error (RMSE)= 1.32 mm day(-1)) and Abtew (Ab) (RMSE= 0.83 mm day(-1)) are the best models for estimating the ETo in the arid and semiarid regions, respectively. While, modified Hargreaves-Samani 2 (MHS2) represents the best performance in the Mediterranean and very humid regions (RMSE= 0.30 mm day(-1) & 0.68 mm day(-1), respectively). In addition, radiation-and mass transfer-based models are proper tools to estimate the ETo in warm and cold seasons on the basis of improving values of evaluation indices in 40% and 70% of the study area, respectively. Increasing air temperature and decreasing minimum relative humidity for best performance of most models alarms a climate change in most regions of Iran. As a result, the radiation-based models were adapted with climate change better than the temperature-based and particularly mass transfer-based models. Finally, a step by step flowchart was presented for selecting the best model to estimate the ETo in each climate. (C) 2016 Elsevier B.V. All sights reserved.