The deviations of the Priestley–Taylor (PT) coefficient from a fixed value around 1.26 indicate a nonlinear dependence of wet surface evaporation (E) on the equilibrium evaporation (Erad, which is the radiation term in Penman potential evaporation (EPen)). The linear PT equation with a fixed coefficient underestimates E for small E_rad but overestimates E for large Erad. In this study, the sigmoid generalized complementary (SGC) equation by Han and Tian (2018) was applied to estimate the wet surface evaporation by setting its asymmetric parameter to infinity. The SGC equation with one parameter captures the nonlinear dependence of E on Erad over the wet surface by including the aerodynamic component of EPen and amends the shortage of the linear PT equation. By using datasets over open water surfaces of lakes and ocean, wetlands, and paddy fields, the validation results indicate that the wet surface SGC equation performed better than the linear PT equation on evaporation estimation, especially over open water surfaces, where advections or large-scale synoptic changes are more substantial. The success of the wet surface SGC equation has implications for the extension of the complementary principle to consider above processes.

Evaporation is the key to the basin’s water cycle. Agricultural irrigation has resulted in a significant variation of regional potential evaporation (Epen). The spatiotemporal variation of Epen and the influencing factors in the natural, agricultural, and desert areas in different developmental stages of irrigation in the Heihe River Basin (HRB) from 1970 to 2017 are comparatively analyzed in this study. This work focused on the correction effect of irrigation on the variation of Epen. The agricultural water consumption in HRB significantly varied around 1998 due to the agricultural development and water policy. Under the influence of irrigation, the annual variation of Epen in the agricultural, natural, and desert areas was significantly different. From 1970 to 1998, the annual trend slope of Epen in the natural area only reduced by 1 mm decade-1, while that in the agricultural area significantly decreased by 39 mm decade-1. After the implementation of water-saving irrigation, the Epen in the natural and agricultural areas increased by 11 and 54 mm decade-1, respectively, from 1998 to 2017. In contrast with the natural and agricultural areas, Epen in the desert area decreased by 80 mm decade-1 from 1970 to 1998 and continuously decreased by 41 mm decade-1 from 1998 to 2017. However, the regulatory effect of irrigation on Epen in the desert area started to manifest due to the expansion of the cultivated land area in the desert area from 2010 to 2017. Irrigation has a significant regulatory effect on the variation of Epen in HRB. The regulatory effect is mainly reflected on the aerodynamic term (Eaero). The analytical results of the main meteorological factors affecting Epen in different regions indicated that the main meteorological factors influencing the variation of Epen in each region are the wind speed 2 m above the surface (U2) and the water vapor pressure difference (VPD).

The response of meteorological elements to potential evapotranspiration(ET0) varies greatly from different time-scale perspectives, but current research are mainly focused on a certain time-scale and lack the study on the response of various meteorological elements to ET0 variations based on different time-scale perspectives. This situation results in the unilateral perception of variations in ET0 caused by climate change. Therefore, this study qualitatively explore the sensitive factors of ET0 on different time scales by sensitivity coefficients, and quantitatively characterize the actual contribution amounts of major meteorological elements to variations in ET0 on different time scales by contribution rate combining the sensitivity coefficients with the relative variation rates of meteorological elements. Results are listed as follows. (1) The SRH is always negative, but SRn, ST and SU are positive. The main sensitivity factors of ET0 vary on different time scales. Specifically, RH and Rn become the major sensitive factors alternately within a year. On an interannual basis, the Rn was the most sensitive factor from 1958 to 1963, and the most sensitive factor became RH from 1964 to 1978. RH and Rn became the most sensitive factors to ET0 alternately from 1979 to 2017. (2) The contributions of each meteorological element fluctuate significantly. On the daily time scale, the GT and GU are large at the beginning and end of the year. The GRn and GRH are dominant in the middle of the year. On the monthly and seasonal time scales, RH contributes the most in spring and autumn and Rn does in summer. The GT and GU are dominant in winter. On the yearly and multi-yearly time scales, the main contributing factors are RH and T. In summary, the increase in ET0 in Beijing area is mainly caused by the decrease in RH and the increase in T. The decreases in U and Rn also slow down the further increase in ET0 in this area. This blocking effect caused by Rn in summer is highly evident.