Evapotranspiration (ET) is an important element in the water and energy cycle. Potential evapotranspiration (PET) is an important measurement of ET. Its accuracy has significant influence on agricultural water management, irrigation planning, and hydrological modelling. However, whether current PET models are applicable under climate change or not, is still a question. In this study, five frequently used PET models were chosen, including one combination model (the FAO Penman-Monteith model, FAO-PM), two temperature-based models (the Blaney-Criddle and the Hargreaves models) and two radiation-based models (the Makkink and the Priestley-Taylor models), to estimate their appropriateness in the historical and future periods under climate change impact on the Yarlung Zangbo river basin, China. Bias correction methods were not only applied to the temperature output of Global Climate Models (GCMs), but also for radiation, humidity, and wind speed. It was demonstrated that the results from the Blaney-Criddle and Makkink models provided better agreement with the PET obtained by the FAO-PM model in the historical period. In the future period, monthly PET estimated by all five models show positive trends. The changes of PET under RCP8.5 are much higher than under RCP2.6. The radiation-based models show better appropriateness than the temperature-based models in the future, as the root mean square error (RMSE) value of the former models is almost half of the latter models. The radiation-based models are recommended for use to estimate PET under climate change in the Yarlung Zangbo river basin.Atmosphere 2019, 10, 453 2 of 24 management and irrigation planning [21][22][23]. A number of models have been proposed to estimate PET and these models can be divided into four categories: (1) Temperature-based models, such as the Blaney-Criddle model [24]; (2) radiation-based models, including the Makkink model [25]; (3) mass transfer-based models, such as the Rohwer model [26]; (4) combined energy-mass balanced models, such as the Penman-Monteith (PM) model [27]. The PM model is used widely and has been commonly adopted as a reference, owing to the fact that it is a physical-based model and combines both energy and mass balances [28][29][30]. Correspondingly, its requirement of climate variables data is much stricter than other models, including relative humidity and wind speed [27]. These climate data may not be available in many regions or even may not be measured at all. Thus, models with less data demand were developed, such as models from categories 2 and 3. These simple models only need temperature data or solar radiation data [31][32][33]. However, they were proposed under specific climate conditions, which may have impact on their applicability for various conditions. Therefore, understanding the behavior of these models has been a major concern.Many studies have compared the performance of different PET models under various regions and under different climate conditions for historical periods [19,[31][32][33][34][35]. Xu and...