Estimation of reference evapotranspiration (ET0) is important in hydrological studies. As climate change is predicted to cause changes in water resources and agriculture sectors, the possible implications of changes in different climate variables on ET0 need to be understood. Sensitivity analysis was employed to illustrate the effects of perturbation in meteorological parameters (maximum and minimum air temperature (Tmax and Tmin), sunshine hours (n), maximum and minimum relative humidity (RHmax and RHmin)) and wind speed (uz) on ET0. ET0 was calculated by The Food and Agriculture Organization of the United Nations (FAO) 56 Penman-Monteith approach using climate data from 1979–2017 for the Enbara and Futatsumori watersheds in forested mountain areas in Japan. We quantified the contributions of climatic factors to ET0 at daily, monthly, seasonal and annual time scales. Daily results showed large fluctuations. According to the monthly and seasonal analysis, during warm seasons, Tmax and n had more influence on ET0, especially in May, while for the cold seasons, RH effect was dominant, especially in December. Based on the annual results, the factors most influencing ET0 were Tmax followed by n, uz, RH and Tmin. We also found that the response of ET0 to changes in climatic parameters differs for sites with different topographic and geographic characteristics.