A Graphical Interpretation of the Rescaled Complementary Relationship for Evapotranspiration

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.

Section: Discussionmentioning

confidence: 62%

Section: Discussionmentioning

confidence: 99%

On the Estimation of Potential Evaporation Under Wet and Dry Conditions

2022

“… Saturation vapor pressure ( e* ) curve, air (blue) and surface (green) isenthalps (Crago & Qualls, 2021; Szilagyi, 2021) during a full drying‐out of the environment from completely wet to a completely dry state. The vertical and horizontal projections of the dotted lines are proportional (∝) to the different latent ( E ≤ E w ≤ E p ≤ E p dry ) and corresponding sensible (the latter negative–directed toward to surface–for E p and E p dry ) heat fluxes.…”

Section: A Concise Thermodynamical Derivation Of the Nondimensional P...mentioning

confidence: 99%

“…With the help of the two isenthalps, Qualls and Crago (2020) graphically illustrated how evaporation occurs from saturated surfaces. Using a similar approach, Crago and Qualls (2021) reproduced an existing linear nondimensional formulation of the CR (Crago & Qualls, 2018), while Szilagyi (2021) independently of them and by a different approach replicated both the existing linear as well as the polynomial formulation of the CR (Szilagyi et al., 2017), the latter having been inspired by the study of Brutsaert (2015).…”

Section: Introductionmentioning

confidence: 99%

Power‐Function Expansion of the Polynomial Complementary Relationship of Evaporation

Szilágyi

Crago

et al. 2022

Self Cite

The complementary relationship (CR) of evaporation is a powerful tool [see the latest global studies by Brutsaert et al. (2020) and Ma et al. (2021)] for predicting actual land evaporation (E) rates with the help of basic meteorological variables (i.e., air temperature, humidity, net surface radiation and wind speed) all obtained at a single elevation above the ground. Since its original formulation by Bouchet (1963) and subsequent practical early versions by Brutsaert and Stricker (1979) as well as Morton (1983), it has evolved into various forms based on different intuitive, sometimes heuristic arguments. The interest in the CR increased significantly with the publication of Brutsaert and Parlange (1998) who elegantly demonstrated why generally plummeting pan evaporation rates signify an intensification of the global hydrologic cycle. See Han and Tian (2020) for a concise overview of the relevant CR studies.After almost six decades of the groundbreaking study by Bouchet (1963), and encouraged by the apparent success of Brutsaert and Parlange (1998) of solving even climate change issues by the CR, Szilagyi (2021) as well as Crago and Qualls (2021) engaged in finding a thermodynamic foundation for it, following the lead of Monteith (1981) who first defined the thermodynamic pathway a parcel of air near the evaporating drying surface must follow under unchanging wind conditions and constant available energy (Q n ) at the surface during an adiabatic and isobaric (i.e., isenthalpic) process. A constancy of Q n can only be expected on the daily or longer time steps (as averaging periods) with which the CR is typically applied, although Katul and Parlange (1992) and Parlange and Katul (1992) presented guidelines for sub-daily applications as well.

“…Figure 2. Saturation vapor pressure (e*) curve, air (blue) and surface (green) isenthalps(Crago & Qualls, 2021;Szilagyi, 2021) during a full drying-out of the environment from a completely wet to a completely dry state. The air and surface (T, e) value pairs move along the same respective isenthalps during wetting/drying cycles as long as R n does not change.…”

mentioning

confidence: 99%

Comment on “On the Estimation of Potential Evaporation Under Wet and Dry Conditions” by Z. Tu and Y. Yang

Szilágyi

2022

Tu and Yang (2022) employ the wet-surface temperature estimation method of Yang and Roderick (2019) in their potential evaporation estimation approach and frequently end up with wet-surface (T ws ) temperatures 10-12 K lower (seen e.g., in their Figure 9) than the actual air temperature (T a ). In their example of Figure 9, their estimates of T ws under dry conditions drop below even the actual wet-bulb temperature, T wb (compare Figure 9 with Figure 1 here). Note that between days 40 and 91 the T ws values of Yang and Roderick (2019) stay predominantly below 285 K, while it never happens with T wb in Figure 1. T wb represents the lowest possible temperature the air can be cooled by evaporation under an isenthalpic (i.e., adiabatic and isobaric) process (Figure 2) and zero net radiation (R n ) at the evaporating surface (i.e., at the wet-bulb of the thermometer). The hypothetical wet land surface however cannot be cooler than T wb (Monteith, 1981;Szilagyi, 2021) since at the land surface R n on a daily basis is almost always positive under typical conditions (and it is definitely so in each single day in Figure 1), raising its temperature above that of the wet-bulb of the thermometer (Monteith, 1981) where R n is zero, achieved by double metal tubing of the for example, aspirated psychrometer (e.g., Stull, 2000). Also, during wet environmental conditions (starting with Day 211 in Figure 9 with rains almost every day and relative humidity values often exceeding 85% in Figure 1) T ws cannot be expected (as seen in Figure 9) to be (significantly) lower than the actual air temperature measured over the wet land and therefore yielding downward sensible heat (H) fluxes. It would contradict the common observation that even over extensive wet surfaces the equilibrium air (potential) temperature profile near the surface is decreasing with elevation facilitating an upward H.Tu and Yang (2022) dismisses the T ws estimation method of Szilagyi and Jozsa ( 2008) that assumes unchanging net radiation (R n ) during drying/wetting of the environment, by arguing that net radiation would increase with decreasing surface temperatures (due to declining thermal radiation of the surface, R lo ) as the surface becomes wetter. However, they did not take into consideration that a weakening incoming shortwave radiation can counteract the effect of dropping R lo on R n as cloudiness and humidity typically increase with a regional wetting of the land surface, thus making it possible to leave R n practically intact (Brutsaert, 1982).In summary, the wet-surface temperature estimation method of Yang and Roderick (2019) as employed by Tu and Yang (2022) appears to significantly underestimate the wet surface temperature leading to physical/thermodynamical contradictions. At the same time the Szilagyi and Jozsa (2008) estimated T ws values always stay above T wb and predominantly above T a (depending on e.g., the degree of saturation of the air) under wet conditions, as demonstrated in Figure 1 and therefore claimed to be a more realistic wet-surf...