To fully utilize the existing EC measurements, this study collected the half-hourly or hourly FLUXNET2015 Tier-2 (http://fluxnet.fluxdata.org/data/fluxnet2015-dataset/, last access: 30 August 2022), LaThuile (https://fluxnet.org/data/la-thuile-dataset/, last access: 20 August 2022), AsiaFlux (http://asiaflux.net/?page_id=23, last access: 21 July 2022), and OzFlux (https://data.ozflux.org.au/portal/home.jspx, last access: 15 June 2022) datasets. Following Maes et al. (2019), we processed the four datasets to provide the necessary inputs and the ET observations without water limits (i.e., PET) for calibrating the SW model.

First, we screened the measurements using data quality control. Sites lacking one or more of the basic measurements required for our analysis, i.e., latent heat (LE), sensible heat (H), soil heat flux (G), the net radiation fluxes (Rn), wind speed (u), air temperature, relative humidity (RH), actual vapor pressure (ea), and atmospheric water concentration and vapor pressure deficit (D), were not considered further. Considering potential impacts of surface energy imbalance on the results, the corrected half-hourly or hourly LE and H (Pastorello et al., 2020) were used here. Regarding the major heat fluxes (LE, H, and G), good gap-filled records were retained according to the quality flags provided by the four datasets. When the flags for Rn observations were unavailable, the flags of the downward shortwave radiation were used instead. Mainly due to the impacts of interception loss and condensation on the accuracy of H or LE measurements (Mizutani et al., 1997), the negative values were masked out. Likewise, all Rn negative values were masked out.

Second, the half-hourly or hourly measurements were aggregated to daytime records. Only days on which more than 70 % of the basic data were measured directly were retained, and days with rainfall during midnight–sunset were excluded from the analyses to remove the effects of rainfall interception. Moreover, we only retained sites with 80 or more days for the processing below. Taking 5 W m-2 of top-of-atmosphere incoming shortwave radiation as a minimum threshold, the half-hourly or hourly measurements were aggregated to daytime composites, and then the daytime values were obtained by subtracting measurements at the first and last (half-)hours for these aggregates.

Third, we identified days with no soil water limits. This study employed an energy-balance-based approach to select unstressed days rather than the soil moisture criterion. The major considerations were three-fold: (a) no soil moisture measurements existed at most of the EC sites; (b) the energy-balance-based method could effectively remove days on which the ecosystem is not limited by soil moisture availability but is stressed by other environmental factors (e.g., insect plagues, phenological leaf-out, fires, heat and atmospheric dryness stress, nutrient limitations); and (c) soil moisture may not be a good indicator of water stress due to variable rooting depth and its inaccurate measurements (Powell et al., 2006; Douglas et al., 2009; Martínez-Vilalta et al., 2014). The evaporative fraction, i.e., EF = LE/(LE+H), was selected as the energy balance criterion, and we assumed that under conditions of no water limits a larger fraction of the available energy should be used for evaporating water (Gentine et al., 2007, 2011; Maes et al., 2011). Taking a site as an example, a day was identified as having no water limits when its corresponding EF exceeded the 95th percentile EF threshold. Notably, if fewer than 15 d fulfilled this criterion at some particular sites, the 15 d with the highest EF were used as unstressed days.

Finally, the sites used for further analyses were selected. Despite the usage of the corrected half-hourly or hourly LE and H here, we found that an evident surface energy imbalance still existed in the daytime, with a Bowen ratio between 0.60 and 1.80. To further reduce the potential impacts of this issue, we retained records with a Bowen ratio between 0.90 and 1.10. After this, if a certain site had fewer than 8 unstressed days, it was removed. Because the LAI and the CO2 concentration were unavailable at some sites, the Global LAnd Surface Satellite (GLASS) LAI and CO2 concentration (ρCO2, ppm) observed at Mauna Loa were used instead. Finally, 96 sites were retained, including 73, 5, 3, and 18 sites from the FLUXNET2015 Tier-2, AsiaFlux, OzFlux, and LaThuile datasets, respectively (Fig. 1). Their basic information is shown in Table S2.

Meteorological inputs are necessary for generating the SW PET and, moreover, to reduce uncertainties, we collected four monthly or 3-hourly meteorological datasets, i.e., Multi-Source Weather (MSWX)-Past (Beck et al., 2022), National Aeronautics and Space Administration (NASA) Modern Era Reanalysis for Research and Applications (MERRA)-2 (Molod et al., 2015), European Centre for Medium-Range Weather Forecasts Reanalysis (ERA)-5 (Hersbach et al., 2020), and Climatic Research Unit (CRU) TS4.06 (Harris et al., 2020). The detailed information of these datasets is shown in Table 1. The directly used meteorological variables to drive the SW model mainly include air temperature, u, D, Rn, and G. Except for air temperature and u, the meteorological datasets provide different D-related and radiation-related variables (Table 1), and therefore different methods were utilized to estimate D and Rn (details in Supplement Sects. S1 and S2). Regarding G, the mean air-temperature-based method was used here (Allen et al., 1998; details in Supplement Sect. S3). Notably, because CRU TS4.06 lacked direct radiation records, the algorithm of Reddy (1974) was employed here to estimate Rn based on the Clouds and the Earth's Radiant Energy System (CERES) satellite-based monthly net shortwave radiation records (https://asdc.larc.nasa.gov/project/CERES, last access: 12 June 2022) and the CRU TS4.06 cloud cover data (algorithm and validation in Supplement Sect. S1 and Fig. S1, respectively). Moreover, due to no wind speed records in CRU TS4.06, we used the mean wind speed from the other three meteorological datasets as a proxy.

Considering the time span of the available LULC products at present, the 1982–2015 yearly GLASS-Global Land Cover (GLC) dataset developed by Liu et al. (2020a, b) at a spatial resolution of 5000 m was used here (Table 1), though it has a coarse LULC classification ecosystem (including cropland (CRO), forest (FR), grassland (GRA), shrubland (SHRB), tundra, barren land, and snow or ice). Some studies stated that the accuracy of the GLASS LAI is clearly better than that of others (e.g., the Moderate-resolution Imaging Spectroradiometer (MODIS) LAI), especially for forested areas with more realistic and reasonable trajectories representing seasonal variations (Fang et al., 2013; Liang et al., 2013; Xiao et al., 2014, 2016, 2017). Thus, the 1981–2018 8 d GLASS Advanced Very High Resolution Radiometer (AVHRR) LAI product at a spatial resolution of 0.5∘ was selected in this study (Xiao et al., 2016, 2017; Table 1). The global saturated soil water content in the first soil layer (i.e., 0–0.0451 m) was collected from http://globalchange.bnu.edu.cn/research/soil5.jsp (last access: 30 December 2021​​​​​​​) (Dai et al., 2019a, b; Table 1), while the 1850–2013 monthly CO2 concentration at 1∘ × 1∘ spatial resolution was downloaded from 10.5281/zenodo.5021361 (Cheng et al., 2022; Table 1). Because this CO2 dataset missed the data in 2014 and 2015, the 1985–2021 monthly Global CO2 Distribution (GCD) product from the Japan Meteorological Agency at a 2∘ × 2∘ spatial resolution (https://www.data.jma.go.jp/ghg/kanshi/co2data/co2_mapdata_e.html, last access: 5 July 2023; Maki et al., 2010; Nakamura et al., 2015; Table 1) was used to estimate the monthly CO2 concentration in the 2 missing years by the linear regression method. In detail, we firstly resampled the GCD data into a 1∘ × 1∘ resolution and used the 1985–2013 GCD as an independent variable and Cheng's data as a dependent variable to fit the linear regressions for each month and each grid. Subsequently, based on the GCD data, these regressions were used to calculate the monthly CO2 concentration on each grid in 2014 and 2015. The validation results of the established regression are in Fig. S2.

To date, the vegetation canopy height (h) maps to fully cover the whole globe are still lacking, although they are needed for the SW model to estimate some key parameters. Therefore, we made use of the existing datasets, mainly including the remote-sensing-based forest h datasets of Potapov et al. (2020), Wang et al. (2016), Simard et al. (2011), and Lang et al. (2021, 2022), respectively named h-Potapov, h-Wang, h-Simard, and h-Lang (Table 1), and the Spatial Production Allocation Model (SPAM) V2.0 crop distribution map (Yu et al., 2020; Table 1) to reconstruct the global vegetation h maps. For each year, the detailed procedures are four-fold. (1) Map FR and SHRB h. To reduce uncertainties related to the retrieval algorithms and source data, the h-Potapov, h-Wang, h-Simard, and h-Lang datasets were used in this procedure. Notably, we ignored differences in periods of source data for producing the forest h datasets. That is, we assumed that the changes in forest h due to vegetation natural growth were limited during the study period. To match GLASS-GLC, the four forest h datasets were firstly resampled to a spatial resolution of 5000 m. If two or more h datasets showed non-missing values at a certain FR (SHRB) grid cell, the average of these non-missing values represented the final h at this grid cell. After this, if some FR (SHRB) grid cells still had missing values, then the h value at each of these grid cells was filled with the mean h at the four nearest FR (SHRB) grid cells around this grid cell. (2) Map GRA and tundra h. Although the h-Lang product provided GRA and tundra h values over a few regions, there were still large areas with missing values, and even large uncertainties existed (Huang et al., 2017). Therefore, we specified the GRA and tundra h based mainly on the Comprehensive Sequential Classification System (CSCS)-based GRA groups and the typical GRA and tundra h measured at the EC sites and records from the literature. Using vegetation bioclimate characteristics and hydrothermal indictors (e.g., temperature and precipitation), the CSCS method was employed to classify the GLASS-GLC GRA and tundra into 10 groups (Li and Ma, 2009; Liang et al., 2011; Gang et al., 2016). According to the map of the CSCS-based GRA groups and the locations of the EC sites, the h value for each CSCS-based GRA group was estimated as the mean h from the EC sites with such a GRA group, and lastly the h values for seven CSCS-based GRA groups were determined. As for the remaining three CSCS-based GRA groups (i.e., frigid desert GRA, warm desert GRA, and tropical zonal forest steppe GRA), their h values were from White (1983), Suttie et al. (2005), Kadeba et al. (2015), Yin et al. (2019), and Prakash et al. (2020). The h values of all the CSCS-based GRA groups can be found in Table S3. (3) Map CRO h. By overlaying the SPAM V2.0 and GLASS-GLC maps, CRO was further classified into 42 types, and the h for each type was specified based on Table S4 (Allen et al., 1998). (4) Map the h of barren land and snow or ice. As for the barren land and snow or ice regions, the h was set to 0. Notably, regardless of the h map reconstructed for each year, this dataset could not reflect interannual variations of h except for regions with LULC changes, where the h values varied due to LULC changes. In the grid with LULC changes in a certain year, its new h value was assigned as the mean h value of its four nearest-neighbor grids with the same LULC. An example of the reconstructed canopy h map in 1982 is shown in Fig. S3.

Based on the assumption that the water vapor arriving at the reference height is a mixture of evaporation from soil and transpiration from the vegetation layer (Fig. 3; Shuttleworth and Wallace, 1985; Wallace et al., 1990), the SW model can be expressed as where λET is the total latent heat flux (W m-2), i.e., the sum of the canopy (λTr) and vegetation latent heat fluxes (λE), where Tr and E represent transpiration and soil evaporation, respectively; PMc and PMs are the closed vegetation and bare soil latent heat fluxes (W m-2), respectively, which can be calculated by the Penman formulas under conditions of bare soil (i.e., Eq. 1d) and closed canopy (i.e., Eq. 1e); Cc and Cs represent soil surface resistance (i.e., Eq. 1f; unitless) and canopy resistance coefficients (i.e., Eq. 1g; unitless), respectively; Δ denotes the slope of the saturated vapor pressure curve (kPa K-1); γ is the humidity constant (kPa K-1); λ is the latent heat of evaporation (MJ kg-1); ρ is the air density (kg m-3); cp is the constant pressure-specific heat (1013 J kg-1 K-1); raa, rac, and ras are the aerodynamic resistance (s m-1), the vegetation boundary layer resistance (s m-1), and the soil boundary layer resistance (s m-1), respectively; and rss is the soil surface resistance, while rsc is the vegetation canopy resistance (s m-1). Based on Eq. (1b) (Eq. 1c), Tr (E) can be obtained with CcPMc (CsPMs) divided by λ.

In Eq. (1b) and (1c), A and Asoil are the available energy for the canopy and soil layers (W m-2), respectively, and are defined as where Rn,soil is the net radiation fluxes into the soil (W m-2) and can be computed with Beer's law (i.e., Eq. 2c; Mo et al., 2004); kex represents the light extinction coefficient, which varies with the LULC types (Table S5).

Previous studies have stated that determining the five resistance parameters is the key to successfully running the SW model (Hu et al., 2009; Chen et al., 2022). Of these resistance parameters, raa and ras are estimated using Shuttleworth and Gurney (1990), while rac and rss are calculated based on Shuttleworth and Wallace (1985), Brisson et al. (1998), and Villagarcía et al. (2010), respectively. Detailed information about equations for parameterizing the four resistance parameters can be found in Supplement Sects. S4–S6 and Table S5. Considering large uncertainties of rsc (Fisher et al., 2005; Hu et al., 2009, 2013; Wei et al., 2020), this study used the EC measurements to calibrate its value for each LULC type, and the detailed procedures can be found in Sect. 2.2.2.

In this study, the parameterization of rsc is mainly based on a Jarvis-type model, which is based on the hypothesis that stomatal resistance is independently affected by every environmental variable (Jarvis, 1976; Shuttleworth and Wallace, 1985). Here, we considered effects of the LAI, D, air temperature (T, ∘C), soil moisture, and ρCO2 on rsc, which correspond to stress functions of F1 (Noilhan and Planton, 1989), F2 (Raab et al., 2015), F3 (Zhou et al., 2006), F4, and F5 (Neitsch et al., 2002). Notably, this study focuses on ET under a condition with no soil water limits (namely PET), and thus F4 is set to 1 here. The specific equations are shown as follows: where rsmax is the maximum canopy resistance (s m-1) and is fixed at 5000 s m-1 here (Crow and Kustas, 2008); LAIe denotes the effective LAI (Gardiol et al., 2003); Rds is the downward shortwave radiation (W m-2); Rds,dbl is the minimum shortwave radiation threshold for vegetation to carry out photosynthesis (W m-2), which is set to 30 W m-2 for forests and 100 W m-2 for other vegetation (Noilhan and Planton, 1989; Lo Seen et al., 1997); and Δg1,CO2 is the multiple of leaf stomatal conductance reduction when ρCO2 is doubled (Table S5; Morison and Gifford, 1984; Field et al., 1995; Saxe et al., 1998; Neitsch et al., 2002; Eckhardt and Ulbrich, 2003; Wu et al., 2017).

Finally, we determined the values of rsmin. Here, the Monte Carlo method was used to calibrate this parameter using the identified PET observations at each EC site (Hu et al., 2009). The following five steps were taken to determine the rsmin values: (1) giving a rough range for rsmin (i.e., rsmin between 1 and 500 s m-1) with reference to previous studies (e.g., Zhou et al., 2006; ECWMF, 2007); (2) conducting 5000 Monte Carlo simulations with the parameter sets randomly sampled from uniform distributions within the given ranges; (3) comparing the estimated SW model-based PET (SW PET) and the EC PET after each simulation based on a validation metric of the Kling–Gupta efficiency (KGE; see Eq. 4d; Gupta et al., 2012; 5000 parameter sets corresponded to 5000 KGEs after this step); (4) selecting the mean of rsmin with the 10 highest KGEs as the optimal value for each site; and (5) classifying the 96 EC sites into four types (i.e., FR, SHRB, CRO, and GRA) based on the GLASS-GLC classification system (Liu et al., 2020a, b) and then determining the best-fit parameter sets for a given LULC type by averaging the optimal parameter values at the sites with this LULC type. In this way, the final parameter values for FR, CRO, GRA, and SHRB were obtained and are illustrated in Table S6. Notably, the rsmin for the tundra, barren land, and snow or ice types of GLASS-GLC are from Zhou et al. (2006) and Zhang et al. (2008), mainly due to the lack of the corresponding EC observations.

Several validation metrics were employed to evaluate the performance of the simulated SW PET. Mean error (ME) provides a way of quantifying the biases of the estimates relative to the measurements, while root-mean-square error (RMSE) describes the accuracy of the estimations. In addition, the correlation coefficient (R) and KGE (with a range between -∞ and 1.0, the optimal value) were used to measure the capability of capturing the spatiotemporal variability and the overall performance of the SW PET, respectively. The metrics are expressed as where N is the sample number; S denotes the mean of the SW-PET-averaged N samples; O is for the measured PET; i is the ith sample; α is S/O; and β is σS/σO, where σS and σO are the standard deviations of the estimated and measured PET, respectively.

These metrics were first computed based on the daily estimates with the optimal parameters for each site, i.e., parameters obtained in step (4) of the Monte Carlo method, and the observations from the 96 EC sites, and then validation in site-calibration mode was performed. Notably, to evaluate the transferability of the calibrated parameters from known observations to any location and then the robustness of the established SW model, the “leave-one-out” cross-validation method was utilized here (Zhang et al., 2019). For each LULC type, the data from one “ungauged” observation were excluded from the Monte Carlo method-based optimization, while the data from all other observations of the same LULC type were used for model calibration to obtain the simulated one in the ungauged position. All four LULC types were actualized in this way. Then, the daily SW PET estimates in cross-validation mode were compared against the daily observations from the 96 EC sites to further explore the model performance.

Considering that the SW model was calibrated with the daily EC measurements, it was necessary to examine whether this model could be applicable at the monthly scale. Therefore, we firstly compared the monthly PET estimated based on the daily and monthly meteorological variables from MSWX-Past, MERRA-2, and ERA-5 (not including CRU TS4.06, mainly due to it being at a monthly scale). Various validation metrics showed that there were generally no evident differences in the two PET estimates (Fig. S4). That is, the model established with the daily EC measurements could be driven using the monthly meteorological variables. Mainly due to GLASS-GLC having the shortest time span, the global SW PET was produced at the GLASS-GLC grid and monthly scale during 1982–2015. Therefore, before running the calibrated SW model, the meteorological, GLASS LAI, and CO2 concentration datasets were resampled to a spatial resolution of 5000 m. The monthly mean meteorological and LAI datasets were taken as inputs to run the calibrated model for estimating the monthly mean SW PET, PT, and PE. Finally, the total SW PET values (PT and PE) of a certain month were obtained by the monthly mean value multiplied by the days of this month. Additionally, to reduce uncertainties from the meteorological datasets, the ensemble means of PET, PT, and PE based on the four meteorological datasets were provided. Using the ensemble mean PET, PT, and PE, we analyzed climatological characteristics and spatiotemporal changes in PET and its two components together with climatological characteristics of PET partitioning. Notably, the area-weighted method was used to estimate the regional mean PET, PT, and PE.

A relatively simple Jarvis-type empirical formula was employed here to describe the impacts of environmental conditions (i.e., temperature, vapor pressure deficit, solar radiation, soil moisture content, and CO2 concentration) on rac. While the better performance is with the Jarvis-type formula in simulating the impacts of environmental conditions on water and carbon fluxes (Jarvis, 1976; Lhomme, 2001; Wang et al., 2020), the interactive effects between environmental factors on rac are not taken into account by this empirical formula. In reality, environmental factors are interdependent, and hence their interaction in the Jarvis-type empirical formula cannot be easily separated. In one word, the “multiplication” form of the Jarvis-type empirical formula potentially biases the estimated rac (Damour et al., 2010; Chen et al., 2022) and then the SW PET estimates.

As an important and undetermined parameter within the Jarvis-type empirical formula for estimating rac, rsmin was optimized for FR, SHRB, GRA, and CRO, and the calibrated SW model performance was satisfactory (details in Sect. 3.1). However, it should be noted that this optimized parameter may be the main hindrance to SW model application over the globe (Liu et al., 2003; Mo et al., 2004; Chen et al., 2022). First, rsmin was estimated using EC observations that generally cover the period after 2000 assuming stationary environmental conditions. Environmental conditions were shown to have greatly changed during the past several decades, especially climate conditions such as global warming (IPCC, 2014), brightening or dimming (Wild, 2009), and frequent extreme events (e.g., droughts; Sheffield et al., 2012; Trenberth et al., 2012). Therefore, rsmin may have interannual variations due to the changes in these variables (Wever et al., 2002; Winkel et al., 2001), and this finally introduces biases into the PET product, particularly for years with evidently different environmental conditions relative to the period after 2000 (Aschonitis et al., 2017). Second, rsmin was fixed throughout the year in the SW model, regardless of seasonal variations of this parameter with environmental and vegetation conditions (Winkel et al., 2001; Wever et al., 2002; Douglas et al., 2009). Therefore, no consideration of the seasonal cycle of rsmin may impact the quality of the PET product (Hu et al., 2009; Zhu et al., 2013; Elfarkh et al., 2021). For instance, Hu et al. (2009) and Zhu et al. (2013) found that ET was systematically overestimated or underestimated using the SW model with fixed parameters.

The canopy light extinction coefficient of kex, which represents a partitioning of radiant energy over the vegetation canopy and the soil surface, is a key factor affecting ecosystem carbon, water, and energy processes (Tahiri et al., 2006; Zhang et al., 2014). As a result, the accuracy of the SW model was believed to be associated with the kex parameterization used in this study. Considering the physiological and morphological differences between terrestrial ecosystems (Emami-Bistghani et al., 2012; Zhang et al., 2014), we followed the popular biogeochemical models and the remote-sensing models of ET and gross primary productivity (e.g., the Lund-Potsdam-Jena Dynamic Global Vegetation Model or the Vegetation Photosynthesis Model; Xiao et al., 2004; Sitch et al., 2003) and assumed this coefficient to be a constant for every LULC type (Table S1). Despite this, it is notable that the kex values vary with the growth of plant and/or vegetation coverages (Lindroth and Perttu, 1981; Aubin et al., 2000; Maddoni et al., 2001; Emami-Bistghani et al., 2012; Fauset et al., 2017). Emami-Bistghani et al. (2012) stated that, with an increase in vegetation coverages, the kex values decreased, especially at the early reproductive stage in sunflower cultivars. This suggested that the fixed kex within the SW model potentially led to uncertainties in the PET estimates. As shown by Tahiri et al. (2006), relative to the values of the variable kex, the fixed values gave a less precise estimation of plant transpiration under irrigated maize.

Notably, the SW model only focuses on two processes of ET, i.e., soil evaporation and vegetation transpiration (Shuttleworth and Wallace, 1985). Other parts of ET, vegetation canopy interception and nighttime ET (ETn), are ignored in this study. It is reported that vegetation canopy interception can occupy a certain proportion in the total ET, especially for regions with a high LAI and frequent rainfall (Gash et al., 1995; Tourula and Heikinheimo, 1998; Lawrence et al., 2007; Wang and Dickinson, 2012). On rainy days, the vegetation canopy interception may account for a considerable fraction of the total ET (Tourula and Heikinheimo, 1998; Hu et al., 2009). On average, the fraction of ETn accounts for approximately 6.3 % of the total ET informed by the FLUXNET2015 dataset, while 7.9 % is based on multiple global models (Padrón et al., 2020). This fraction may exceed 15 % in a mountain forest with a snowy and windy winter. Despite this, accurately representing the ETn process is still difficult at present, mainly because the related controlling mechanisms are still not clear (Han et al., 2021). For example, Novick et al. (2009) and Groh et al. (2019) found that vapor pressure deficit (VPD) and wind speed had a significant impact on ETn, while Groh et al. (2019) stated that the contributions of night dew could not be ignored. As an important component of ETn, the nighttime transpiration is related not only to the incomplete stomatal closure (Dawson et al., 2007; Duursma et al., 2019), but also to the circular regulation of nighttime water uses by plants (De Dios et al., 2015). However, how the environmental factors alter nighttime transpiration is still disputed. Dawson et al. (2007) and Moore et al. (2008) reported a positive correlation between nighttime transpiration, VPD, and soil moisture content, while Barbour and Buckley (2007), N. G. Phillips et al. (2010), and De Dios et al. (2015) found no or a negative correlation between nighttime transpiration and the two aforementioned variables. Moreover, the biological factors (e.g., plant species and ecosystem types) can also significantly influence nighttime transpiration (O'Keefe and Nippert, 2018; Zeppel et al., 2014). Therefore, establishing a common model for estimating ETn across various ecosystems remains challenging. All in all, ignoring vegetation canopy interception and ETn may underestimate PET (Tourula and Heikinheimo, 1998; Lawrence et al., 2007; Mu et al., 2011; Padrón et al., 2020; Singer et al., 2021). Subsequent research will be done to integrate these two processes into the SW model to further enhance the model's physical mechanism.

The uncertainties in the EC observations for calibrating the SW model and in inputs for producing the global PET can be propagated into the PET estimates. As for the EC observations, the uncertainties mainly come from the selection of unstressed days for obtaining the observed PET, the issue of non-closure of the energy balance at the EC system level, and the gap-filling methods (e.g., the marginal distribution sampling (MSD) method; Reichstein et al., 2005). The energy-balance-based criterion employed in this study proved to be efficient at selecting unstressed days (Maes et al., 2019), but this method may still result in two uncertainties. First, we should note that the higher the LAI or normalized difference vegetation index (NDVI) is, the larger the EF will be (Gentine et al., 2007; Nutini et al., 2014). This suggests that the larger EF will likely frequently happen during the growing season, which usually corresponds to a higher LAI or NDVI. Therefore, the identified unstressed days tended to involve fewer ones within the non-growing season, potentially introducing large biases into the estimated PET during this season. Second, due to frequent water deficits in arid regions, the EF threshold may exceed the 95th percentile. What is more, there may be no unstressed days in extremely arid regions, mainly because the soil moisture can hardly reach the field capacity or saturation due to the very limited precipitation. Thus, the identified unstressed days using the energy-balance-based criterion may actually include stressed days in arid regions and potentially bias the PET estimates. In order to reduce the impacts of the non-closure of the energy balance in the EC system (Wilson et al., 2002; Foken, 2008), we used the corrected half-hourly or hourly EC LE and H observations and only retained daytime records with a Bowen ratio between 0.90 and 1.10 to calibrate the SW model. Although such processing could reduce uncertainties, the energy imbalance was not fully solved in our study and may lead to inevitable errors in the calibrated parameter of rsmin and therefore the global PET estimates (Hu et al., 2009; Elfarkh et al., 2021; Chen et al., 2022). In this study, to maximize the use of data, the MSD method was employed to fill the gaps in the EC LE measurements. However, we should note that if the controlling thermodynamic and kinetic factors of the atmosphere and soil moisture conditions are different between the missing and retrieved moments, the gap-filled LE based on the MSD method may have low confidence, especially when soil moisture has abrupt changes (Jiang et al., 2022). Recently, Jiang et al. (2022) developed a physics-based full-factorial scheme to fill gaps in ET from EC observations, and they found that the gap-filled ET with this scheme showed higher confidence relative to the existing typical gap-filling methods. Therefore, to reduce the uncertainties from the MSD-based gap-filled LE, the physics-based full-factorial scheme could be a good candidate in the future to fill the ET gaps. Here, to quantify potential impacts of the MSD-based gap-filled values, the SW model was re-calibrated and re-validated against the data points without gap-filling. Relative to the SW model used in this study, the new rsmin and the validation metrics changed insignificantly (Figs. S6 and S7), suggesting that the uncertainties induced by the gap-filled LE were limited.

The SW model used various datasets as inputs, including LULC, LAI, canopy height, and meteorological data (e.g., MSWX-Past, CRU TS4.06, ERA5, and MERRA-2), albeit with some uncertainties (Fang et al., 2013; Xiao et al., 2017; Liu et al., 2018; Xu et al., 2018). As a reflection of vegetation growth, the accuracy of the LAI can affect several key parameters (e.g., rac, rsc, raa, or ras) and input variables (e.g., A or Asoil) and influence the quality of the PET estimates. To reduce uncertainties from LAI datasets, this study selected the GLASS AVHRR LAI product with a better overall performance (relative to other popular products, e.g., MODIS, FSGOM, GLOBMAP, and GIMMS3g; Fang et al., 2013; Xiao et al., 2017; Liu et al., 2018; Xu et al., 2018). However, we should note that this LAI product slightly underperformed over grassland compared to the other products (Liu et al., 2018). Considering that this LAI product was based on the 8 d maximum value composite for removing the impacts of cloudy days, the LAIe (based on Eq. 3b) was potentially larger than its authentic value due to some leaves being covered by rain or snow. Thus, from Eq. (3b), rsc may be slightly underestimated, leading to an overestimation of PT and PET. Considering the impacts of LULC changes on PET across the globe, we used the 1982–2015 yearly GLASS-GLC dataset developed by Liu et al. (2020a, b) to separately estimate the PET for each LULC type. Although the average overall accuracy for the 34 years with seven classes each is 83 % based on 2431 test sample units, the misclassification issues still existed, e.g., in Africa, eastern and southern South America, southern Alaska, northern and eastern Australia, and southwestern Indonesia (Liu et al., 2020a, b). The reconstructed global vegetation canopy height also has limitations, which may arise from (1) uncertainties in the retrieval algorithms and remote-sensing data (Simard et al., 2011; Wang et al., 2016; Potapov et al., 2020; Lang et al., 2021, 2022), (2) neglecting the spatial differences in CRO and GRA heights and using an alternative specific value, and (3) not considering the interannual changes in the FR and SHRB canopy heights and the intra-annual cycle in the CRO and GRA heights. These limitations undermine the accuracy of the PET estimates. Recently, Peng et al. (2022) proposed a practical method for global estimates of 500 m daily aerodynamic roughness length with a combination of machine-learning techniques, a wind profile equation, observations from 273 sites, and MODIS remote-sensing data. Their results showed that the random forest model could reproduce well the magnitude and temporal variability of the daily aerodynamic roughness length at most of the sites for all of the land cover types. We believe that the aerodynamic roughness length produced by this method has the potential to replace vegetation canopy height as an input to run the SW model and thus reduce the aforementioned vegetation canopy height-related uncertainties and improve the accuracy of the PET estimates. A series of evaluations of various meteorological datasets across the world suggested the discrepancies among these datasets (Urraca et al., 2018; Hinkelman, 2019; Jourdier, 2020; Zhang et al., 2021). Although the ensemble mean used here may reduce uncertainties from the meteorological datasets, there is still the likelihood that the remaining uncertainties will be propagated into the PET estimates. In this study, even though soil does experience water stress, we assumed that the soil water supply for ET was unconstrained in estimating PET. As a result, the two conditions with and without soil water stress corresponded to different meteorological variables when considering land–atmosphere interaction (Crago and Crowley, 2005; Kahler and Brutsaert, 2006; Aminzadeh et al., 2016; Maes et al., 2019). For example, air temperature under the unstressed condition will likely be lower than that under the stressed condition because of the lower sensible heating and the stronger evaporative cooling from the wetter land surface to the atmosphere (Maes and Steppe, 2012; Maes et al., 2019). Thus, the mismatch between the assumption of no soil water stress and the observed meteorological variables will likely introduce biases into our PET estimates.