Contrasting Land and Atmospheric Controls on the Generalized Complementary Relationship of Evaporation Over Grasslands and Forests

The generalized complementary relationship (CR) rooted on land–atmosphere coupling has been widely used to study evaporation over various ecosystems. Evaporation estimation models based on CR usually contain two parameters. The first one controls the shape of CR, and the second one is related to potential evaporation (Epo). Previous studies have found substantial variations in these parameters, but how they are affected by land surface and/or the atmosphere under conditions with varying land–atmosphere coupling remains unclear. In this study, the land and atmospheric controls for the generalized CR were comparatively investigated focusing on the two parameters of the sigmoid type function by using the data of 24 grassland and 19 forest flux sites and by considering the contrasting land–atmosphere coupling strength. The strong coupling to the outer atmosphere at the forest sites resulted in a large variation in the Epo‐related parameter and its significant correlation with the mean relative humidity. The shape parameter had a large variation at the grassland sites due to the weak coupling with the outer atmosphere and was significantly correlated with the mean soil water content. The simple parameterizations for the two parameters based on the correlations improved the predictions of monthly actual evaporation compared with the parameterizations for the fixed parameters corresponding to ecosystem types. The effects of land surface wetness and local advections on the generalized CR over grasslands and forests were also discussed respectively.

enhance the evaporation demand by changing the atmospheric conditions.A complementary relationship (CR) between changes in actual evaporation   and changes in apparent potential evaporation   from potential evaporation   has been proposed with a symmetric deviation (Bouchet, 1963) and modified to allow for asymmetry (Brutsaert & Parlange, 1998;Kahler & Brutsaert, 2006)  −  = ( − ), (1) where b adjusts the asymmetry of CR.E pa can be measured by the evaporation pan or represented by Penman's (1948) open-water evaporation (E Pen ) with a two-term structure containing equilibrium evaporation E eq and aerodynamic component E aero where Q n = R n − G is the available energy, with R n and G being the net radiation and soil heat flux, respectively; L is the latent heat of vapourization; Δ is the slope of the saturation vapor curve; γ is a psychrometric constant; ρ is air density; c p is specific heat; D i is the vapor pressure deficit at the screen level; and r a is aerodynamic resistance.
Equilibrium evaporation E eq is also used to formulate E po with a parameter (Priestley & Taylor, 1972;Yang & Roderick, 2019), such as the Priestley-Taylor equation where α PT is the Priestley-Taylor coefficient.
The original CR shown in Equation 1 has evolved to a generalized nonlinear one, namely, E = f(E pa ,E po ).Given that it is usually utilized to represent E pa by using E Pen and E po on the basis of E eq , the generalized CR in the dimensionless form can be expressed as Most existing complementary equations can be accommodated by Equation 4 in the form of linear (Brutsaert & Stricker, 1979), polynomial (Brutsaert, 2015), sigmoid (Han et al., 2012), or exponential (Bing Gao, 2020) functions.As shown in Table 1, two parameters are contained in complementary equations; one is for adjusting the shape of CR (we use the term 'shape parameter' by considering that the nonlinear generalized CR makes the term 'asymmetric parameter' inappropriate), and the other is related to potential evaporation E po (analogous to α PT in Equation 3) (Brutsaert, 2015;Han et al., 2011Han et al., , 2012;;Kahler & Brutsaert, 2006).The two-parameter scheme is also used and recommended for the complementary equation following the scaling approach (Szilagyi  9, and α HT and b HT are the parameters analogous to α PT and b (we use the symbols to distinguish them from α PT and b).c α B is the parameter analogous to α PT , and c is the parameter adjusting the normalized complementary relationship (Brutsaert, 2015).d X is the independent variable by using the rescaled method proposed by Crago et al. (2016); Szilagyi et al. (2017), with the parameter α PT included in X. b S is the parameter used by Szilagyi et al. (2022) to adjust the equation to cope with the line one (b S = 1) (Crago & Qualls, 2018) or the polynomial one (b S = 2) (Crago et al., 2016;Szilagyi et al., 2017).et al., 2022).The corresponding shape and E po -related parameters of these equations are comparable (Han & Tian, 2018a;Szilagyi et al., 2022;Wang et al., 2021).
Although default values were used in the past to achieve calibration-free evaporation estimation models based on the complementary principle (Anayah & Kaluarachchi, 2014;Brutsaert & Stricker, 1979;Morton, 1983;Szilagyi et al., 2017), the parameters are site-specific (Han & Tian, 2018a;Liu et al., 2016) and need to be determined as prior knowledge for applications.The parameters would be related to land and/or atmospheric properties since the CR is affected by the land surface (Pettijohn & Salvucci, 2006) and/or atmospheric sub-processes (Parlange & Katul, 1992;Tu et al., 2023).However, existing parameterizations differ considerably (Table 1).The shape parameter is believed to be the unity in the linear function by assuming changeless land-atmosphere coupling (Brutsaert & Stricker, 1979), and it is fixed in the polynomial function and its rescaled versions (Brutsaert, 2015;Crago et al., 2016;Szilagyi et al., 2017).Meanwhile, E po -related parameters need to adjust to different conditions.However, arguments exist about the controls on the E po -related parameter, which is considered to be affected by water vapor transport or advection in linear and rescaled polynomial functions (Crago et al., 2022;Crago & Qualls, 2018;Yang et al., 2012) but is thought to be related to land surface properties, such as the surface dryness index, vegetation characteristics, or surface roughness, in the polynomial function (Brutsaert et al., 2020;Gan, Liu, Chen, & Zheng, 2021;Li et al., 2021;Liu et al., 2016;Zhang & Brutsaert, 2021;Zhang et al., 2017;Zhou et al., 2020).Following an opposite direction, the E po -related parameter is fixed in view of the constant Priestley-Taylor coefficient (Priestley & Taylor, 1972), leaving the shape parameter to cope with different conditions (Han et al., 2012;Han & Tian, 2018a;Szilagyi, 2015;Wang et al., 2020) (Table 1).Given that the E po -related parameter (α HT ) is approximately 1.26, the shape parameter was believed to be related to land surface properties, such as vegetation type or mean soil water content (    ) (Wang et al., 2020(Wang et al., , 2022) ) or land surface temperature (Szilagyi, 2007), but was considered to be driven by the atmospheric conditions, like the mean wind speed and relative humidity (   ) in the linear function (Aminzadeh et al., 2016;Szilagyi, 2015) and thought to reflect the advection effect of moisture transport in the power function expansion of the polynomial function (Szilagyi et al., 2022).The contrasting parameterization strategies and different matchings between shape/E po -related parameters and land/atmospheric factors (Table 1) imply that the understanding of land/atmosphere controls on CR is lacking (Han & Tian, 2020).
Rooted on land-atmosphere coupling, the complementary principle requires that the contributions of land surface properties on evaporation can be effectively captured by the changes of the atmospheric evaporation demand.However, in addition to the processes related to land-atmosphere coupling at the landscape scale, the atmospheric evaporation demand changes can also arise by the processes admixing outside air with different humidity and temperature into the atmosphere boundary layer.This advection effects related to horizontal water vapor transport or the large-scale atmospheric process were thought to be negligible or changeless in the CR (Brutsaert & Stricker, 1979;Morton, 1983) by supposing fully or fixed land-atmosphere coupling (Han & Tian, 2018b).But the land-atmosphere coupling would be disrupted by advected atmosphere moisture (McNaughton & Jarvis, 1983), which substantially affects the evaporation process (Han et al., 2023;Szilagyi et al., 2022).The arguments on parameterizations and the substantial biases of the CR equations with fixed parameters under conditions with varying land-atmosphere coupling (Han et al., 2023;Ma et al., 2021;Zhu et al., 2016) indicates that the land/ atmospheric controls on CR need to be reexamined by considering the land-atmosphere coupling strength, especially the advection effects.
Aside from the complementary principle, another framework based on the widely used Penman-Monteith equation (Monteith, 1965) was proposed by McNaughton and Jarvis (1983) to describe the effects of land-atmosphere coupling on evaporation.They derived a decoupling factor (Ω) ranging from 0 to 1 to quantify how tightly atmospheric conditions (mainly the water vapor saturation deficit of air) on the evaporating surface are coupled with those at the screen level and mixed boundary layer (Jarvis & McNaughton, 1986;McNaughton & Jarvis, 1983).This framework successfully interprets the contrasting land-atmosphere coupling strength over grasslands and forests.Accordingly, it would have the potential to assist in the investigation of land and atmospheric controls on CR.
The sigmoid generalized complementary (SGC) equation is derived based on boundary conditions by assuming different land-atmosphere coupling strengths (Han et al., 2012;Han & Tian, 2018a), which is consistent with McNaughton-Jarvis's framework (1983).In this study, we conducted a pairwise study by using the data of 24 grassland and 19 forest eddy flux sites in Asia to investigate how land-atmosphere coupling influences land and atmospheric controls on the generalized CR on the basis of the SGC equation.The correlations between the shape/E po -related parameters and the land/atmospheric factors at grassland and forest sites were compared and explained, and different simple parameterization methods for the two parameters over grasslands and forests were proposed.The effects of land surface wetness at the grasslands and local advections over the forests on the generalized CR were also discussed.

SGC Equation With Land and Atmospheric Controls
McNaughton and Jarvis (1983) proposed an equation equivalent to the Penman-Monteith equation to describe the departure of actual evaporation from E eq as follows: where is the evaporation imposed by the outer atmosphere on the surface with no local adjustment with canopy resistance r c , and D i is the water vapor saturation deficit at the reference level.Equation 5 also describes the coupling between the saturation deficit on surface D 0 and that in the outer atmosphere as where is the equilibrium saturation deficit.A small value of the decoupling coefficient Ω indicates that the evaporation and air conditions near the evaporating surface are closely coupled with the outer atmosphere via advection processes, and the lower limit of Ω = 0 represents complete coupling (Jarvis & McNaughton, 1986;McNaughton & Jarvis, 1983).A large value indicates weak coupling with the outer atmosphere; the air conditions on the canopy surface are completely decoupled from outer atmosphere at the other extreme of Ω = 1.
In the generalized CR of Equation 4, approaches the minimum and maximum values under an extremely arid condition (E/E Pen = 0) and a completely wet condition (E/E Pen = 1), respectively (Han et al., 2012).Han and Tian (2018a) derived the boundary conditions by considering different land-atmosphere coupling, which can also be derived using McNaughton and Jarvis's framework.Notably, E/E Pen is equivalent to Ω.At the lower limit of Ω = 0 with complete coupling between the air just above the evaporation surface and the outer atmosphere (Equation 6), a change in evaporation does not cause a general change in D 0 (as well as in the vapor pressure deficit at the screen level and in the mixed layer).This situation implies that the air just above the surface is controlled by the outer atmosphere and has no relation to the land surface conditions.Given that D 0 is equal to D i , a fractional change in canopy conductance causes an fractional change in evaporation (Jarvis & McNaughton, 1986) but does not change the evaporation demand.Thus, ∂E/∂E Pen = 0.At the other extreme of Ω = 1 with complete decoupling, the air just above the evaporation surface is independent of the outer atmospheric conditions but controlled by local land surface conditions.D 0 tends to approach the equilibrium value D eq but is not affected by D i .Hence, evaporation is independent of the canopy resistance.At this extreme, a small change in the land surface condition does not cause any change in the evaporation rate.On the contrary, evaporation is controlled by atmospheric evaporation demand E Pen rather than the land surface, and ∂E/∂E Pen = 1.The boundary conditions can be derived in accordance with ∂E/∂E Pen (Han & Tian, 2018a).
where x = E eq /E Pen and y = E/E Pen .x min and x max are the minimum and maximum values of x, and can be regarded as 0 and 1, respectively, under general conditions (Han & Tian, 2018a).A sigmoid function can be derived by invoking the boundary conditions (Han et al., 2012;Han & Tian, 2018a) HAN ET AL.

10.1029/2023WR035501
5 of 17 where m and n can be obtained as where α HT and b HT are the parameters analogous to the Priestley-Taylor coefficient α PT and the asymmetric parameter b (we use the symbols to distinguish them from α PT and b), and x 0.5 is the corresponding x value of y = 0.5, 0.5 = 0.5 + −1 (1 + −1 ) .
Equation 8 is equal to E = E eq when α HT = 1 and   −1  = 0 , which is the 1:1 line in the state space of .
The resulting curves for selected values of α HT and   −1  are shown in Figure 1.Under the condition of   −1  = 0 , the curves move to the left as the value of α HT increases (from 1.05, 1.26, and 2 to 2.5).Under the condition of α HT = 1, the curves move to the right with increasing   −1  (from 0.05, 0.25, and 0.5 to 1 and 2).The two groups of curves imply two types of departure of evaporation from equilibrium: an enhancing one with increasing α HT and a HAN ET AL. 10.1029/2023WR035501 6 of 17 depressing one with increasing   −1  .Evaporation can be enhanced to exceed E eq by large-scale or regional advection effects in the atmosphere (Brutsaert, 1982), and can be depressed to a value below E eq because of the soil moisture deficit and canopy resistance (Denmead & McIlroy, 1970).Thus, α HT is expected to be highly sensitive when evaporation is closely coupled to the outer atmosphere.By contrast,   −1  would be highly sensitive when evaporation is closely coupled to the land surface.Previous studies on the SGC equation have confirmed that   −1  can be effectively determined by land surface properties (Wang et al., 2020(Wang et al., , 2022)), while α HT is highly correlated with advection effects (Han et al., 2021;Han & Guo, 2023).

Data and Methods
The observed data of 43 eddy covariance flux sites in Asia, including 24 grassland and 19 forest sites ( The monthly flux and meteorological data processed from 10-or 30-min data were used.These data included net radiation, soil heat flux, latent heat flux, sensible heat flux, precipitation, air temperature, relative humidity or water vapor pressure, wind speed, and air pressure.The REddyProc online tool (http://www.bgc-jena.mpg.de/REddyProc/brew/REddyProc.rhtml) was employed to fill the missing data.The ground heat flux data of three grassland sites (HBG, NQ, and NMC) were unavailable, and G was assumed to be 5% of R n rather than being completely disregarded (Brutsaert et al., 2017;Ma et al., 2019).At the seven forest sites with unavailable ground heat flux data, G was assumed to be a fixed proportion of R n in accordance with the published energy balance closure (Text S1 in Supporting Information S1).Surface energy closure corrections were applied on a monthly basis by preserving the Bowen ratio (Twine et al., 2000) where the subscript u denotes the unadjusted fluxes from the flux tower measurements.
The plant available water sustaining evaporation is determined by soil water content in the whole root zone.The long-term mean soil water content (    ) of around 20 cm below the ground was determined and used to reflect the land surface water availability at the grassland sites by considering the shallow root depth.However, the soil water content data in the deep root zone is not available at the forest sites.Total precipitation was usually used to represent the long-term water availability for evaporation at the forest sites or catchments (Rungee et al., 2018;Zhou et al., 2008).The aridity index, the ratio of the mean potential evaporation and the mean precipitation, was also widely used to represent the water availability for the forests (Gan, Liu, & Sun, 2021;Zhang et al., 2001), and was used to determine the parameters of the CR equations (Liu, Liu, & Brutsaert, 2018;Zhang & Brutsaert, 2021).Thus, the mean annual precipitation (   ) and the wetness index (the ratio of the mean annual precipitation and potential evaporation,   ∕ ) are also used to represent the water availability, especially for the forest sites.In addition, the vegetation conditions were represented by the average values of the normalized difference vegetation index (NDVI) of the grids where the sites were located from two data sets: Global Inventory Modeling and Mapping Studies (GIMMS) NDVI version 3 (NDVI3g) (Pinzon & Tucker, 2014) and NOAA Climate Data Record (CDR) of the AVHRR NDVI product (Vermote, 2019).The 300-m resolution European Space Agency global land cover data set (Arino et al., 2012) according to UN Food and Agriculture Organization's Land Cover Classification was used.

Aerodynamic resistance 𝐴𝐴
was derived through Monin-Obukhov similarity theory by assuming neutral conditions as follows:  where κ = 0.41 is von Karman's constant, u is the wind speed at height z v , and z m is the measurement height of humidity (m).z ov and z om are the roughness lengths of momentum and water vapor, respectively, and d 0 is the displacement height; they can be determined from vegetation canopy height (h c ) as follows: d 0 = 0.67h c , z 0v = 0.123h c , and z 0m = 0.1z 0v (Allen et al., 1998).
The parameters of the SGC equation were calibrated by minimizing the mean absolute error (MAE) of monthly evaporation.We also used the Nash-Sutcliffe coefficient (NSE) for a performance evaluation.The simple linear regression was conducted to investigate the dependence of parameters α HT and .The significance of the regression with determination coefficient R 2 was verified through a conventional F-test, which was also used by Han and Guo (2023).A stepwise regression at the significance level of 1% was used to test whether the factors should be added to determine the parameters α HT and   −1  .

Site-Specific Generalized CRs
The mean actual evaporation (1.38 ± 0.46 mm day −1 ) and equilibrium evaporation (1.60 ± 0.24 mm day −1 ) at the 24 grassland sites were smaller than those at the 19 forest sites (2.00 ± 0.81 and 2.10 ± 0.72 mm day −1 ), so the mean     differed slightly (Table 3).Meanwhile, the mean E Pen at the grassland sites (3.79 ± 0.98 mm day −1 ) was much smaller than that at the forest sites (7.51 ± 2.78 mm day −1 ), which could be attributed to the high aerodynamic components because of the small aerodynamic resistance of tall forests.As a result, the mean values of   S1 in Supporting Information S1), with MAE ranging within 0.12-0.38mm day −1 (mean value of 0.21 ± 0.07 mm day −1 ) and 0.11-0.40mm day −1 (mean value of 0.22 ± 0.08 mm day −1 ), respectively.The calibrated α HT at the grassland sites ranged from 1.02 to 1.59 and had a mean value of 1.23 ± 0.15, whereas α HT at the forest sites (between 0.0.94 and 2.28, with a mean value of 1.28 ± 0.30) had a much larger variation.The calibrated   −1  showed a large variation from 0 to 1.08 (with a mean value of 0.46 ± 0.32) at the grassland sites but a small variation at the forest sites (between 0.01 and 0.46, with a mean value of 0.16 ± 0.16).Figure 4a

Contrasting Land-Atmosphere Coupling
The contributions of equilibrium and imposed evaporation to the actual evaporation at the grassland and forest sites were evaluated based on Equation 5.The mean values of the contribution of E eq to the actual evaporation were close at the grassland (0.67 ± 0.36 mm day −1 ) and forest (0.70 ± 0.61 mm day −1 ) sites because of the larger decoupling coefficient Ω (0.41 ± 0.20) of the grassland sites compared with that of the forest sites (0.30 ± 0.10) (Table 3).However, The mean imposed evaporation (1.50 ± 1.06 mm day −1 ) at the grassland sites was smaller than that at the forest sites (2.02 ± 0.91 mm day −1 ; Table 3).The contributions of the imposed evaporation were much larger at the forest sites (1.30 ± 0.31 mm day −1 ) than those at the grassland sites (0.72 ± 0.19 mm day −1 ).The magnitudes of Ω and the contributions of the imposed evaporation confirmed a weak coupling of the evaporation and air conditions near the surface with the outer atmosphere at the grassland sites but a close coupling at the forest sites (McNaughton & Jarvis, 1983).
After the rearrangement of Equation 5, was much more significantly correlated with  Ω (y = 1.085x + 0.421, R 2 = 0.772, p < 0.001) at the grassland sites than at the forest sites (y = 0.517x + 0.799, R 2 = 0.184, p = 0.086).By contrast, the actual evaporation is much more significantly correlated with the imposed evaporation at the forest sites (y = 0.878x + 0.237, R 2 = 0.974, p < 0.001), and the R 2 is much larger than that at the grassland sites (R 2 = 0.672) (Figure 5).The results imply that the imposed evaporation by the outer atmosphere played much more important roles on evaporation at the forest sites than that at the grassland sites.The contrasting land-atmosphere coupling can also be detected from the much more significant correlations between  ∕ and the land surface water availability represent by    ,   and   ∕ over the grassland sites (Table 4).

Different Correlations Between Parameters and Land/Atmosphere Factors
Consistent with the fact that evaporation is closely coupled to the outer atmosphere over forests and closely coupled to local conditions over grasslands, the calibrated parameter α HT in this study was much highly variable over the forests (the standard derivation is 0.30) than that over the grasslands (the standard derivation is 0.15 respectively), and   −1  was highly variable over the grasslands (the standard derivation is 0.16 vs. 0.32 over the forests) (Table 3).In addition, different correlations between the parameters and land/atmospheric  properties were found at the grassland and forest sites (Table 4).No statistically significant correlations were observed between α HT and the land/atmospheric factors at the grassland sites.By contrast, α HT was statistically significantly correlated with   (   = 2.41 − 1.74 , p < 0.01) at the forest sites (Figure 6), followed by land surface factors   ,   ∕ ,    and    with the correlation coefficient around −0.65.At the grassland sites, the calibrated   −1  was significantly correlated with    (p < 0.01) (Figure 6), but no statistically significant correlations were observed between   −1  and the atmospheric factors, except for wind speed (p < 0.05) (Table 4).By contrast, the correlations between   −1  and the atmospheric variables at the forest sites were significant for The relatively low variation in α HT at the grassland sites (Table 3) and the absence of a correlation with the land/ atmosphere factors imply that α HT could be fixed for approximation.The stepwise regression at the significance level of p = 0.01 suggested that none of the factors should be added to determine α HT at the grassland sites, whereas    should be added to determine   −1  at the first step.Then, the parameters at the grassland sites can be simply determined as The reductions in performance of the SGC equation with parameters determined by Equations 12 or 13 compared with that with calibrated parameters were acceptable, with the mean MAE increasing from 0.21 ± 0.07 mm day −1 to 0.32 ± 0.13 mm day −1 at the grassland sites and from 0.22 ± 0.08 mm day −1 to 0.38 ± 0.17 mm day −1 at the forest sites.The performance was improved compared with that with fixed parameters corresponding to ecosystem types (Figure 7).

Local Advection Effect on the Generalized CR Over Forests
The local horizontal advection effects related to the canopy disturbance of the profiles of specific humidity, wind and temperature should be carefully considered over forests because of the strong coupling of evaporation to the outer atmosphere.The significant dependence of atmospheric parameter α HT on   (Table 4) revealed increasing local advection effects on the generalized CR curve with decreasing   .At the two sites in Northwest China over the mixed forest of Populus euphratica and Tamarix (HHL) and Populus euphratica (HYL) from the Heihe Integrated Observatory Network (Liu, Li, et al., 2018), the forest land where the sites were located was surrounded by extremely arid bare areas and   are only 29% and 27.7% respectively.The large spatial heterogeneity of the land surface conditions at the two sites (Figure 8) indicated that the substantial horizontal advections of hot dry air originated from the surrounding dry desert and extended to the forest land.Due to the substantial local advection effect, the decoupling factor Ω was very low at the two sites (i.e., 0.14 and 0.12), and the calibrated α HT was high (2.28 and 1.73).As shown in Figure 4b, the curve for HHL departed sharply from the equilibrium line after the intersection point.By contrast, the spatial heterogeneity was less  HAN ET AL. 10.1029/2023WR035501 13 of 17 substantial at the Changbaishan (CBS) site (Wu et al., 2013) Northeast China with a subhumid climate with   of 61.7%.The curve departed from the equilibrium line with a calibrated α HT of 1.34 implying a mild advection effect.The heterogeneity was insignificant at the site in Xishuangbanna rubber plantations (XJL) in South China (Yu et al., 2021) with a tropic humid climate and mean   of 79.6%, and the curve was close to the equilibrium line with a calibrated α HT of 1.13, implying that the effect of any possible horizontal advection was weak.The local advections of heat and water vapor at the forests need to be further investigated based on detailed analyses on the vertical profiles of wind, air temperature, vapor pressure and saturation deficit.
We also tested the performance of the SGC equation in evaporation estimation with fixed α HT = 1.26 and calibrated   −1  at HHL.We found substantial reductions in MAE from 0.40 mm day −1 to 0.71 mm day −1 without considering the local advection effect by varying α HT .Previous studies have shown that a significant underestimation of evaporation by the CR equation will be achieved if the advection effects are not well addressed (Szilagyi et al., 2022;Zhu et al., 2016).A similar failure of the generalized CR in this study has been found in regions near areas with sudden changes in surface moisture conditions (Ma et al., 2021).Our results demonstrate that the advection effects need to be carefully considered when evaporation is tightly coupled to the outer atmosphere, and the   above the canopy is crucial when parametrizing the local advection effect for α HT over forests.

Effect of Long-Term Land Surface Wetness on the Generalized CR Over Grasslands
The fact that evaporation is tightly coupled to the local land surface and the significant dependence of the parameter   −1  on the land surface water availability at the grassland sites (Table 4 and Figure 6) demonstrate that long-term land surface wetness would affect the generalized CR over grasslands.The fixed generalized CR at landscapes located in different climate regions, or at the same landscape during periods with different atmospheric circulations (Han et al., 2023).Then, the generalized CR would be varying, as shown in Figure 4a, and needs to be described with the help of land surface wetness., thus resulting in a varying generalized CR among them.As shown in Figure 4a, when    decreased from 35.6% at a meadow steppe in Mongolia (MN-MDW) (Shao, Chen, Chu, et al., 2017) to 18.6% at a marsh alpine meadow in Northwest China (DSL) (Liu, Li, et al., 2018) and 6.5% at a shrubland in Mongolia (MN-SHB) (Shao, Chen, Chu, et al., 2017), the scatter plots and generalized CR curve moved from above the equilibrium line to closely intersect the line with and to below the line, with the mean     decreases from 1.25 to 1.00 and 0.59.Accordingly, the calibrated   −1  increased from 0.08 to 0.41 and 0.87 with α HT weakly decreased from 1.36 to 1.26 and 1.17.Our results demonstrate that the effects of land surface wetness on the generalized CR over the grasslands can be represented by the dependence of the shape parameter   −1  of the SGC equation on    .

Summary
1.The analysis and comparison of the 24 grassland and 19 forest flux sites indicated that the generalized CR was site-specific and controlled differently by land and atmospheric characteristics over grasslands and forests.2. The generalized CR was substantially controlled by the atmosphere at the forest sites because of the strong coupling of evaporation to the outer atmosphere conditions.Atmospheric control was applied via the local advection effect and could be detected by the E po -related parameters.The calibrated E po -related parameter α HT of the SGC equation showed a large variation at the forest sites and was significantly correlated with the mean   (   = 2.41 − 1.74 ). 3. The generalized CR was substantially controlled by the long-term mean land surface wetness at the grassland sites because of the weak coupling of evaporation to the outer atmosphere.The shape parameter   −1  of the SGC equation exhibited remarkable variation at the grassland sites and was significantly correlated with    (   −1  = 0.87 − 2.49  ).By contrast, α HT can be fixed at the grassland sites because of its small variation and no significant correlation with the land/atmosphere factors.
eq /E Pen , y = E/E Pen .α PT is the Priestley-Taylor coefficient and b is the asymmetric parameter in the Advection-aridity model.b m and n are obtained from the parameters α HT and b HT by Equation

Figure 2 .
Figure 2. Spatial distribution of the 43 flux sites in this study.
had a scattered distribution (Figure3), implying that the generalized CR among the grassland and forest sites could vary.The size and color of the circles proportional to the mean soil water content    and relative humidity   of the sites indicated that the distributions of the points may be related with    and   at the grassland and forest sites, respectively.The SGC equation performed well in estimating the monthly actual evaporation at the grassland and forest sites by calibrating parameters α HT and   −1  (Table over (a) grassland and (b) forest sites.The size and color of the circles are proportional to the mean soil water content    and relative humidity   of the sites respectively.
sites and three forest sites with different land and atmospheric conditions.It shows that the generalized CRs were site-specific, and the SGC equation with calibrated α HT and   −1  effectively captured the variability of the generalized CRs across the sites.

Figure 4 .
Figure 4. Plots of      with respect to       at selected (a) grassland and (b) forest sites, compared with the calibrated sigmoid generalized complementary curves.The line of the equilibrium evaporation (red dash line) is also shown.

Figure 5 .
Figure 5. Plots of (a)     against the decoupling coefficient Ω and (b) evaporation E against the imposed evaporation E imp at the grassland and forest sites.

Figure 6 .
Figure 6.Plots of the calibrated parameter (a) α HT with respect to the mean relative humidity (   ) and (b)   −1  with respect to the mean soil water content (    ) at the grassland sites and to the mean air temperature   at the forest sites.The regression lines are also shown.

Figure 7 .
Figure 7. Comparing the mean actual evaporation estimated by using the SGC equation with parameters determined by Equation 12 and Equation13with the observed mean actual evaporation at the grassland and forest sites.

Figure 8 .
Figure 8. Locations of the selected forest sites (XJL, CBS, HHL, and HYL) within the 0.5° grid-cells of covering them.The land cover category is same as that in Figure 2.

Table 1
Selected Generalized Complementary Equations and the Determinants of Their Parameters From Published Papers Table 2 and Figure2), were used in this study.The 24 grassland sites were distributed between 30.42°N and 48.11°N and 79.7°E−123.3°E,with the mean annual precipitation ranging from 91 to 507 mm.Mean canopy height h c ranged from 0.05 to 0.61 m at the grassland sites.The 19 forest sites were distributed in a wide range between 2.32°S and 62.26°N and 100.25°E−142.32°Eand included deciduous broadleaf forest (six sites), deciduous needleleaf forest (two sites), evergreen broadleaf forest (five sites), evergreen needleleaf forest (four sites), and mixed forest (two sites).The mean annual precipitation ranged from 31 to 2,331 mm, and canopy height ranged 5-35 m at the forest sites.

Table 2
Description of the Sites presents the monthly  and E II are the contribution of the equilibrium and imposed evaporation to the actual evaporation based on Equation5.
a E I

Table 3
Mean Actual and Apparent Potential Evaporation (mm Day −1 ) and Their Components, as Well as the Calibrated Parameters at the Grassland and Forest Sites

Table 4
Correlation Coefficient Between the MeanFor the forest sites, the stepwise regression suggested that only   should be added to determine α HT and only   to determine   −1  at p = 0.01 respectively.Then, α HT and   −1  can be determined as