Reply to Comment on “Potential Evaporation and the Complementary Relationship” by Jozsef Szilagyi

Abstract

The comment by Dr Szilagyi (referred to as S23 hereafter) raised two concerns on our published article (Tu et al., 2023; referred to as T23 hereafter), including (a) the estimation of potential evaporation (E po ); and (b) the calibration of parameters in the complementary relationship (CR) models. Our replies to these two concerns are as follows.For the first concern, S23 discussed different estimates of E po conducted by Szilagyi et al. (2017) (S17 hereafter) and T23, the latter of which adopted the method of Yang and Roderick (2019) (YR19 hereafter). The key difference between the two approaches is that S17 assumes a constant net radiation (R n ) while T23 and YR19 assume a constant net solar radiation (R sn ) and thus allow R n to change, via changes in net longwave radiation (R ln ) at the surface, with surface wetting/drying.The idea underpinning T23 and YR19 is straightforward: surface temperature (T s ) changes during surface wetting/ drying and according to Stefan-Boltzmann's law, so the emitted outgoing longwave radiation (R lo ) directly depends on T s and hence should also change with surface wetting/drying. Moreover, changes in R lo will result in a different amount of longwave radiation being entrapped and re-emitted by the atmosphere, leading to incoming longwave radiation (R li ) changes. This means that the two longwave components must change during surface wetting/drying. YR19 (their Figure 10) and Tu and Yang (2022; their Figures 6 and 7) demonstrated that as T s rises, the increase in R lo outpaces the increase in R li , resulting in a decreased R ln from the surface and therefore a decreased R n . In contrast, S17 assumed a constant R n and argued that the decreased R ln may be counterbalanced by the increased R sn due to less cloud cover as the surface becomes drier (see S23 and Szilagyi (2022) for details). However, numerical experiments indicated that the shortwave transmissivity remained largely unchanged with varying atmospheric humidity (see Figure S2 in Tu & Yang, 2022 and the detailed reply in Yang et al., 2022). Therefore, a perfect offset between changes in R sn and R ln is unlikely to be the normal case and the idea that R n changes with surface wetting/drying is the more physically valid circumstance. To further demonstrate this point, here we use observed radiation components from four low latitude flux sites (Beringer et al., 2016) where the subsolar point throughout the year remains relatively unchanged (Table 1) and assess how the radiation components change with surface moisture conditions (Figure 1). The results clearly show that R sn remains relatively unchanged while R n significantly increases as the surface becomes wetter (indicated by a larger ratio of actual evaporation to apparent potential evaporation, E/E pa ), the latter of which must be induced by an increasing R ln with surface wetting. S23 pointed out that a narrow temporal viewpoint may impede a correct understanding of the CR, and therefore proposed a "spatial angle" of the CR. However, here we argue that nei...