The energy and water cycles are interconnected in the Earth system and need to be represented accurately in Earth system models (Clark et al., 2015). Understanding the primary drivers of energy and water cycles is essential for hydrological studies. The fluxes of energy and water can be considered as a coupled problem (Koppa et al., 2021). This coupled water-energy system includes two partitioning relationships, namely the water partitioning of precipitation into runoff and evaporation and the energy partitioning of net radiation into sensible heat and latent heat over long timescales. Evaporation and the related latent heat flux are common to both the water and energy balance partitioning relationships, which are fundamental in hydrological systems and the Earth system in general.The water partitioning relationship has been extensively studied. One classic conceptual framework adopted for the study of long-term water partitioning is that of Budyko (1974). The Budyko curve indicates that the long-term water partitioning is primarily controlled by climate, represented by the aridity index. In the original study the Budyko framework was applied to large catchments (Budyko, 1974). In recent decades, the framework has been applied to medium sized catchments as well (e.g., Yang et al., 2006;Yin et al., 2019). Furthermore, the aridity index was originally described as a ratio between net radiation over latent heat of vaporization (R n /λ) and precipitation (P), where R n /λ represents energy supply and P represents water supply. In subsequent hydrological studies, aridity index has been usually described as a ratio between potential evaporation (E P ) and precipitation (P), in order to show the energy/water relationship explicitly in terms of water fluxes (e.g.,