Potential evaporation (EP) is an important concept that has been extensively used in hydrology, climate, agriculture and many other relevant fields. However, EP estimates using conventional approaches generally do not conform with the underlying idea of EP, since meteorological forcing variables observed under real conditions are not necessarily equivalent to those over a hypothetical surface with an unlimited water supply. Here, we estimate EP using a recently developed ocean surface evaporation model (i.e., the maximum evaporation model) that explicitly acknowledges the inter‐dependence between evaporation, surface temperature (Ts) and radiation such that is able to recover radiation and Ts to a hypothetical wet surface. We first test the maximum evaporation model over land by validating its evaporation estimates with evaporation observations under unstressed conditions at 86 flux sites and found an overall good performance. We then apply the maximum evaporation model to the entire terrestrial surfaces under both wet and dry conditions to estimate EP. The mean annual (1979–2019) global land EP from the maximum evaporation model (EP_max) is 1,272 mm yr−1, which is 11.2% higher than that estimated using the widely adopted Priestley‐Taylor model (EP_PT). The difference between EP_max and EP_PT is negligible in humid regions or under wet conditions but becomes increasingly larger as the surface moisture availability decreases. This difference is primarily caused by increased net radiation (Rn) when restoring the dry surfaces to hypothetical wet surfaces, despite a lower Ts obtained under hypothetical wet conditions in the maximum evaporation model.

Abstract. State-of-the-art evaporation models usually assume net radiation (Rn) and surface temperature (Ts; or near-surface air temperature) to be independent forcings on evaporation. However, Rn depends directly on Ts via outgoing longwave radiation, and this creates a physical coupling between Rn and Ts that extends to evaporation. In this study, we test a maximum evaporation theory originally developed for the global ocean over saturated land surfaces, which explicitly acknowledges the interactions between radiation, Ts, and evaporation. Similar to the ocean surface, we find that a maximum evaporation (LEmax) emerges over saturated land that represents a generic trade-off between a lower Rn and a higher evaporation fraction as Ts increases. Compared with flux site observations at the daily scale, we show that LEmax corresponds well to observed evaporation under non-water-limited conditions and that the Ts value at which LEmax occurs also corresponds with the observed Ts. Our results suggest that saturated land surfaces behave essentially the same as ocean surfaces at timescales longer than a day and further imply that the maximum evaporation concept is a natural attribute of saturated land surfaces, which can be the basis of a new approach to estimating evaporation.

The complementary relationship (CR) provides a framework for estimating land surface evaporation with basic meteorological observations by acknowledging the relationship between actual evaporation, apparent potential evaporation and potential evaporation (Epo). As a key variable in the CR, Epo estimates by conventional models have a long‐standing problem in practical applications. That is, the meteorological forcings (i.e., radiation and temperature) employed in conventional Epo models are observed under actual conditions that are generally not saturated. Hence, conventional Epo models do not conform to the original definition of Epo (i.e., the evaporation that would occur with an unlimited water supply). Here, we estimate Epo using the maximum evaporation approach (Epo_max) that does follow the original Epo definition. We find that adopting Epo_max considerably reduces the asymmetry of the CR compared to when the conventional Priestley‐Taylor Epo is used. We then employ Epo_max and develop a new physically based, calibration‐free CR model, which shows an overall good performance in estimating actual evaporation in 705 catchments at the mean annual scale and 64 flux sites at monthly and mean annual scales (R2 ranges from 0.73 to 0.75 and root‐mean‐squared error ranges from 9.8 to 18.8 W m−2).Both the 705 catchments and 64 flux sites cover a wide range of climates. More importantly, the use of Epo_max leads to a new physical interpretation of the CR.

The commentary by Jozsef Szilagyi (referred to as JS-2022 hereafter) questioned the estimation of wet surface temperature (T ws ) in Tu and Yang (2022) (TY-2022 hereafter), which adopted the method of Yang and Roderick (2019) (YR-2019 hereafter). The argument outlined in the commentary is mainly based on: (a) the T ws estimates from TY-2022 and YR-2019 are unphysically low, and can be often lower than air temperature and the wet-bulb temperature; (b) the low T ws estimates from TY-2022 and YR-2019 would lead to a negative sensible heat that is unrealistic under a normal atmosphere. However, neither of the above two arguments is correct since JS-2022 interpreted the results of TY-2022 and YR-2019 based on the JS-2022 framework (i.e., Szilagyi & Jozsa, 2008; referred to as SJ-2008 hereafter) instead of the framework of TY-2022 and YR-2019. The underlying key issue is that the framework of SJ-2008 assumes a constant net radiation (R n ), while the framework of TY-2022 and YR-2019 allows R n change with surface wetting/drying.

Abstract. State-of-the-art evaporation models usually assume the net radiation (Rn) and surface temperature (Ts; or near-surface air temperature) to be independent forcings on evaporation. However, Rn depends directly on Ts via outgoing longwave radiation and this creates a physical coupling between Rn and Ts that extends to evaporation. In this study, we test a maximum evaporation theory originally developed for global ocean over saturated land surfaces, which explicitly acknowledges the interactions between radiation, Ts and evaporation. Similar to the ocean surface, we find a maximum evaporation (LEmax) emerges over saturated land that represents a generic trade-off between a lower Rn and a higher evaporation fraction as Ts increases. Compared with flux site observations at the daily scale, we show that LEmax corresponds well to observed evaporation under non-water-limited conditions and that the Ts at which LEmax occurs also corresponds with the observed Ts. Our results suggest that saturated land surfaces behave essentially the same as ocean surfaces at time scales longer than a day and further imply that the maximum evaporation concept is a natural attribute of saturated land surfaces, which can be the basis of a new approach to estimating evaporation.