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A long-term estimation of water balance is very important to: 1) understand the hydrological cycles over large temporal scales, 2) describe the dynamics of hydrological systems, and 3) predict the rapidly changing trends of hydro-climatic variables [1]. Water balance is a most basic and important concept for catchment hydrology. Moreover, it is a common concept for studying hydrological behaviors [2][3][4][5]. One of the core questions for estimating long-term water balance is the partition of mean annual precipitation into mean annual evapotranspiration and mean annual streamflow [6]. Until now, none of the methods has been developed for directly measuring evapotranspiration on a large spatial scale [2].In recent times, climate change and human activities have led to a large change in hydrological processes and water availability in many regions of the world [7][8][9][10]. The link between climate change and hydrological response is one of the main questions to be researched in the past and even today in hydrology. Many attempts have been made to formulate the mean annual water-energy balance [11][12][13][14]. Budyko (1974) assumed that the actual evapotranspiration is a function of the aridity index and precipitation, and it can be expressed as E/P=f(E 0 /P) [15].The energy-based theoretical equations, which describe the climate and the water balance, have been developed and applied in a "top-down" fashion [16][17][18]. The developments of Budyko (1974) andFu' (1981) [19] Pol. J. Environ. Stud. Vol. 26, No. 5 (2017) AbstractLong-term water-energy balance is a major concern in hydrology and water resource management. Evapotranspiration is a key factor for achieving water-energy balance. In this study, we used a simple water and energy balance equation to compare the effects of precipitation and potential evapotranspiration on actual evapotranspiration -mathematically and theoretically. The results showed that, in Baiyangdian catchment, a 1 mm or 10% increase in precipitation would lead to a 0.51 mm or 6.6% in actual evapotranspiration, and a 1 mm or 10% increase in potential evapotranspiration would lead to a 0.14 mm or 3.4% in actual evapotranspiration. The regional differences in the 10 regions of China showed that the effects of climate on actual evapotranspiration were significantly influenced by the aridity index. The changes of potential evapotranspiration will lead to more changes in actual evapotranspiration in humid regions, and the changes of precipitation will lead to more changes in actual evapotranspiration in arid regions.