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The interchange of water vapor between the land and the atmosphere is influenced by actual evapotranspiration (AET). A nonlinear model (AET-SWC-PET-GPP, ASPG) was developed in this study to combine potential evapotranspiration (PET), soil water content (SWC), and gross primary productivity (GPP) in order to quantitatively estimate AET. The Fluxnet Network 2015 global flux station dataset was used to compare the AET models (AET-SWC, AS; AET-SWC-PET, ASP and AET-SWC-PET2, ASP2) with various combinations of influencing factors. The results show that the simulation accuracy of the ASPG model is higher than that of AS, ASP, and ASP2, with improvements in a coefficient of determination (R2) of 45.3, 8.1, and 5.7%, respectively.The ASPG performed well for various vegetation types, geographical regions, and time scales. It was also discovered that the fitting coefficients vary depending on the type of vegetation, each with its own range of values. The ASPG model put forth in this study can be used to more effectively estimate AET quantitatively on a global scale and can serve as a theoretical foundation for the accurate calculation of global evapotranspiration and the wise use of water resources.

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  • Introduction of a new model (ASPG) that integrates potential evapotranspiration (PET), soil water content (SWC), and gross primary productivity (GPP) to quantitatively estimate actual evapotranspiration (AET).

  • Additionally, the study emphasizes the variability of fitting coefficients based on vegetation type, suggesting the model's adaptability to different ecosystems.

actual evapotranspiration, gross primary productivity, potential evapotranspiration, relationship analysis, soil water content
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Actual evapotranspiration (AET) is a key parameter controlling land-atmosphere interaction processes and the water cycle, and quantitative estimation of AET is a challenge in hydrological studies (Han et al. 2021). The study of hydrological, ecological, and surface modeling is greatly aided by accurate AET estimation, which also helps with the sensible distribution and use of water resources and the reduction of ecological pressure (Gao et al. 2018; Liu et al. 2019). The most common traditional techniques for estimating AET are the volumetric evapotranspiration meter, vorticity covariance (Peng et al. 2019), water balance (Liu et al. 2016), energy balance (Liu et al. 2020), and AET simulation utilizing the equations relating physical quantities (Ochoa-Sánchez et al. 2019). However, large-scale AET modeling is difficult because of these methodologies' high data collection requirements. Potential evapotranspiration (PET) is the volume of air needed to evaporate from a vegetated, well-watered land surface; the percentage of PET limited by soil moisture is equal to AET (Liu 2022). Afterwards, by calculating the ratio of AET to PET, scientists were able to verify and improve the modeling of AET (Peng et al. 2019). You et al.(2019) estimated AET using the complementary theory of AET and PET, exposing the features of climate change and the mechanisms influencing variations in AET and PET. To define evapotranspiration from wetland systems, Shoemaker & Sumner (2006) employed modified PET to estimate AET.

It is, however, biased to focus solely on the interaction between AET and PET. AET is produced by regulating the ratio of incident solar energy to longwave radiation (Qiu et al. 2020), and soil water content (SWC) is a crucial component of this process in the hydrologic cycle (Chen et al. 2021). As SWC is nonlinear regarding the soil moisture stress function of AET (Akuraju et al. 2017) and establishes the ratio of AET to PET, examining the pattern of SWC response to AET becomes a crucial component of modeling AET. Rahmati et al. (2020) study of the link between SWC and AET in the Rohrsbrugge region under two different meteorological circumstances revealed that, as a result of increased dryness throughout the measurement period, the phase shift between SWC and AET reduced on an annual scale. In order to mimic AET on a daily basis using soil moisture-limited PET, Liu (2022) built a nonlinear function (NLF). This allowed them to accurately simulate AET in the majority of the world while also coming up with a novel ideal for building AET models. The complexity and variability of the climate, however, reduce the simulation accuracy of AET in the Mediterranean climate zone and in some parts of Australia (Liu 2022). The drawbacks of relying solely on SWC to respond to AET results from ignoring the influence of vegetation, so these models need to be improved and the role that vegetation cover plays in the process of improvement needs to be taken into consideration.

The rate at which carbon is fixed through photosynthesis in vegetation is known as gross primary productivity (GPP), and it can be thought of as a means of mitigating the effects of vegetation deficit (Beer et al. 2010). Additionally, AET and GPP are important flux elements of the global carbon and water cycle, and they are intrinsically linked (Zhang et al. 2016), so understanding how the two interact will be crucial to enhancing the accuracy of AET simulation results. When estimating AET, the Shuttleworth–Wallace (S–W) model makes a distinction between soil moisture and vegetation. According to Zhang et al.'s evaluation (2008), the S–W model performs better overall than other AET models, although it is still subject to the restrictions imposed by canopy stomatal conductance. Hu et al. (2013) enhanced the S–W model by including GPP to lessen the inaccuracy brought on by canopy stomatal conductance. They also effectively calculated AET by utilizing remote sensing products and meteorological data, resolving the coupling issue between GPP and AET in terrestrial ecosystems. Zhang et al. (2016) developed a new monthly coupled carbon and water model to model AET based on GPP and water use efficiency, which improved the simulation efficiency and provided a theoretical basis for predicting human impacts on terrestrial ecosystem functions. Nguyen & Choi (2022) developed an improved Priestley–Taylor algorithm (GPP-PT) that is based on GPP and is robust in estimating the AET. This enhanced algorithm can be a dependable input for conventional hydrological models and increase the accuracy of AET prediction. The enhancement of global forcing data has made it possible to synthesize many elements to simulate AET; therefore, the construction of an AET model under the influence of multiple factors has become essential to increase the simulation stability and accuracy.

In this work, we integrate PET, SWC, and GPP and present a nonlinear model (AET-SWC-PET-GPP, ASPG) for quantitative estimation of AET based on the Fluxnet Network (FLUXNET) 2015 dataset. This approach considers not only the connection between AET and PET, but also the limitations on soil moisture, indicated by SWC, and the equilibrium between CO2 uptake and water transpired during photosynthesis, indicated by GPP, which is enhanced by plants through controlling the opening and closing of their leaf stomata. This study aims to improve the accuracy, stability, and application of the AET model by synthesizing several parameters. The primary objectives are as follows: (1) the aim of this study is to present and thoroughly assess linear and nonlinear models of AET under the influence of various parameters, utilizing the FLUXNET 2015 dataset. (2) Examining the ASPG model's applicability across temporal and spatial dimensions. (3) To investigate the AET models' attribution under various forms of vegetation cover, and the boundary thresholds of fitting coefficients.

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Study area and data sources

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The FLUXNET 2015 dataset is a global resource of ground-based observational data designed to support and facilitate research on carbon, water, and energy fluxes in terrestrial ecosystems. With 212 ecological sites from all over the world, the dataset is collaboratively updated and maintained by the global FLUXNET partners. It is widely used to draw accurate global evaporation maps (Walker & Venturini 2019), as well as the benefits of comparative evaporative physics models, data-driven models, and mixed models (Hu et al. 2021). These data are of academic and scientific value in the fields of global ecology and climate science. It also provides reliable day scale oscillation differential observation data (including net radiation, soil thermal flow, SWC, subheat flow, and heat sensing flow) (Zhang et al. 2017).

In this study, AET, PET, and SWC were calculated based on FLUXNET 2015 mezzo-journal scale data. Since the evapotranspiration process is affected by meteorological factors (e.g., temperature, humidity, wind speed, solar radiation, etc.) and soil moisture, the types of data used in this study are shown in Table 1. All missing and anomalous data were excluded, and a total of 149 usable flux station towers were retained. The towers with the longest time span of data span over 10 years, while the shortest one has one year of data. There are 11 categories of planted cover in the processed dataset, including Croplands (GRO), Closed Shrublands (CSH), Deciduous Broadleaf Forests (DBF), Evergreen Broadleaf Forests (EBF), Evergreen Needleleaf Forests (ENF), Grasslands (GRA), Mixed Forests (MF), Open Shrublands (OSH), Savannas (SAV), Permanent Wetlands (WET), and Woody Savannas (WSA). Figure 1 depicts the positions of the 149 flux station towers. The data are sourced from: https://fluxnet.fluxdata.org/data/download-data/.
Table 1

Data type

VariablesAbbreviationUnitsFrequency
Average air temperature Tmean °C Half-hour 
Net radiant Rn W/m2 Half-hour 
Wind speed U2 m/s Half-hour 
Vapor pressure deficit VPD hpa Half-hour 
Atmospheric pressure P kPa Half-hour 
Latent heat flux LE W/m2 Half-hour 
Sensible heat flux H W/m2 Half-hour 
Soil water content SWC % Half-hour 
Gross primary production GPP gC/mm/year Half-hour 
VariablesAbbreviationUnitsFrequency
Average air temperature Tmean °C Half-hour 
Net radiant Rn W/m2 Half-hour 
Wind speed U2 m/s Half-hour 
Vapor pressure deficit VPD hpa Half-hour 
Atmospheric pressure P kPa Half-hour 
Latent heat flux LE W/m2 Half-hour 
Sensible heat flux H W/m2 Half-hour 
Soil water content SWC % Half-hour 
Gross primary production GPP gC/mm/year Half-hour 
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Figure 1
Geographic location of 149 flux tower stations. (The 149 flux tower stations include 14 CRO stations, 2 CSH stations, 19 DBF stations, 13 EBF stations, 38 ENF stations, 35 GRA stations, 5 MF stations, 8 OSH stations, 7 SAV stations, 2 WET stations, and 6 WSA stations.)
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Geographic location of 149 flux tower stations. (The 149 flux tower stations include 14 CRO stations, 2 CSH stations, 19 DBF stations, 13 EBF stations, 38 ENF stations, 35 GRA stations, 5 MF stations, 8 OSH stations, 7 SAV stations, 2 WET stations, and 6 WSA stations.)

Figure 1
Geographic location of 149 flux tower stations. (The 149 flux tower stations include 14 CRO stations, 2 CSH stations, 19 DBF stations, 13 EBF stations, 38 ENF stations, 35 GRA stations, 5 MF stations, 8 OSH stations, 7 SAV stations, 2 WET stations, and 6 WSA stations.)
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Geographic location of 149 flux tower stations. (The 149 flux tower stations include 14 CRO stations, 2 CSH stations, 19 DBF stations, 13 EBF stations, 38 ENF stations, 35 GRA stations, 5 MF stations, 8 OSH stations, 7 SAV stations, 2 WET stations, and 6 WSA stations.)

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Research methodology

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Determining the real rate of transpiration

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Based on the LE data from eddy covariance observations, the AET is calculated by unit conversion (Liu 2022) as shown in the following equation.
(1)
where AET is the actual evapotranspiration (mm/day); is the conversion factor (value 0.0352); and LE is the latent heat flux (MJ/m2/day).

Potential evapotranspiration computation

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The Food and Agriculture Organization (FAO) in 1998 recommended the Penman–Monteith (PM) standard technique (Allen et al. 1998), which accounts for both physiological mechanisms and aerodynamic features of plants (Dong et al. 2022). This method was used to calculate PET. According to the following equation, soil heat flow (G) is typically negligible on a daily timeframe (Liu 2022).
(2)
(3)
(4)
(5)
where PET is the potential evapotranspiration (mm/day); Rn is the net radiation (MJ/m2/day); G is the soil heat flux (MJ/m2/day); Tmean is the mean air temperature (°C); U2 is the wind speed at 2 m height (m/s); es is the saturated vapor pressure (kPa); ea is the actual vapor pressure (kPa); VPD is the saturated, water-vapor pressure difference (kPa); is the slope of saturated water-vapor pressure curve (kPa/°C); γ is the humidity constant (kPa/°C); and P is at atmospheric pressure (kPa).

AET correlation analysis at various depths with soil water content

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The Pearson correlation coefficient, whose value range is −1 ∼ 1, is used to quantify the degree of correlation between two variables (Pripp 2018). The higher the correlation, the larger the absolute value; the exact calculation is shown below. The next phase of the model input data was to filter out the layer of SWC that had the strongest link with AET using the Pearson correlation coefficient approach.
(6)
where X is the actual evapotranspiration (mm/day) and Y is the soil water content (%).

AET, PET, SWC, GPP relationship fitting

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For solving regression analysis issues that show the relationship between two or more variables, the least squares method is a common approach. The normalization method is adopted to standardize the data and eliminate the influence of dimension. Using Python 3.6, the linear or nonlinear relationship between AET and PET, SWC, and GPP was fitted using the least squares approach, yielding the following formula:
(7)
where AET is the actual evapotranspiration (mm/day) and F (PET, SWC, GPP) is the relationship between PET, SWC, GPP, and AET. With the restriction that AET is smaller than PET, a total of four AET relationship models were presented in this work for the simulation of AET based on the relationship between the four; the model equations are displayed in Table 2.
Table 2

Types of four models

NameModel
AS a × e(SWC-1) 
ASP a × e(SWC-1) + b × PET 
ASP2 a × e(SWC-1) + b × PET + c × SWC2 × PET 
ASPG a × e(SWC-1) + b × PET + c × SWC2 × PET + d × GPP 
NameModel
AS a × e(SWC-1) 
ASP a × e(SWC-1) + b × PET 
ASP2 a × e(SWC-1) + b × PET + c × SWC2 × PET 
ASPG a × e(SWC-1) + b × PET + c × SWC2 × PET + d × GPP 

Note: a, b, c, and d are model fit coefficients.

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Model evaluation

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In order to comprehensively evaluate the performance of the model, Nash–Sutcliffe efficiency (NSE) coefficient and coefficient of determination (R2) are used to evaluate the fitting accuracy of the model, and the closer the value is to 1, the better the fitting effect is; root mean square error (RMSE) and mean absolute error (MAE) are used to evaluate the model error, and the smaller the value is, the smaller the resultant error of the model is, and the formulas are as follows:
(8)
(9)
(10)
(11)
where Yi and Pi are the real and simulated values and Yi' and Pi’ are the average of the real and simulated values.
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AET and PET calculation results and related physical quantity relationship analysis

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Selection of soil water content at different depths

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Among the 149 available sites selected for this study, 44 sites contain multi-layer SWC data, while the remaining sites only contain single-layer SWC data. Pearson's correlation coefficient was used to analyze the correlation of sites containing SWC at different depths. The layer of SWC data with the largest absolute value of the correlation coefficient was chosen to be used in the next step of relationship fitting. The correlation between the AET from some of the sites and the various depths of SWC is shown in Figure 2. The site in Figure 2 is selected on the basis of the selection principle: IT-PT1 station selects the first level, the AT-Neu station selects the first stage, the BE-Lon station selects the fourth level, the BE-Vie station selects the first layer, the FR-LBr station selects the sixth level, and the FR-Gri station selects the third level. The rest of the sites are treated according to the principle.
Figure 2
Pearson correlation coefficients of SWC and AET at different depths. (Sites include IT-PT1, AT-Neu, BE-Lon, BE-Vie, FR-LBr, and FR-Gri.)
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Pearson correlation coefficients of SWC and AET at different depths. (Sites include IT-PT1, AT-Neu, BE-Lon, BE-Vie, FR-LBr, and FR-Gri.)

Figure 2
Pearson correlation coefficients of SWC and AET at different depths. (Sites include IT-PT1, AT-Neu, BE-Lon, BE-Vie, FR-LBr, and FR-Gri.)
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Pearson correlation coefficients of SWC and AET at different depths. (Sites include IT-PT1, AT-Neu, BE-Lon, BE-Vie, FR-LBr, and FR-Gri.)

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A comparison of actual evapotranspiration with other physical quantities to analyze the trends

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The PM equation is utilized to determine the PET, and the unit conversion is used to calculate the AET based on the quantified subheat flow of the turbidity-related system. Figure 3 illustrates the relationship between GPP, PET, SWC, and AET (the figure lists one site each from the northern and southern hemispheres.). Figure 3 illustrates the clear seasonal variations in the northern and southern hemispheres' AET and PET as well as GPP. For the three, the minimum value in the Southern Hemisphere falls between May and June and the greatest value between November and December; for the Northern Hemisphere, the minimum value falls between December and January of the following year and the maximum value falls between July and August. The peak of SWC is earlier than the AET and is influenced by both the plant root system and the soil inclusion zone, albeit with slightly different trends.
Figure 3
Time series data for AET, PET, SWC, and GPP for some of the sites. (Sites include AU-Gin and CN-Qia).
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Time series data for AET, PET, SWC, and GPP for some of the sites. (Sites include AU-Gin and CN-Qia).

Figure 3
Time series data for AET, PET, SWC, and GPP for some of the sites. (Sites include AU-Gin and CN-Qia).
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Time series data for AET, PET, SWC, and GPP for some of the sites. (Sites include AU-Gin and CN-Qia).

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The four model fits' results

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The physical relationship model of AET was fitted using SWC, PET, and GPP as the basis. 80 and 20% of each site's dataset were taken as the rate period and the validation period, respectively. The results of the fitting (one site for each vegetation type was selected as a demonstration example due to space constraints) and the evaluations are displayed in Figure 4 and Table 3, respectively. As can be shown in Figure 4 and Table 3, the adjustment results for AET-SWC (AS) models with only soil moisture do not match the trend of AET; average R2, NSE, RMSE, and MAE are 0.64, 0.01, 1.02, and 0.84 mm, respectively, while rate periodic and validation period R2 are 0.68 and 0.61. Both the ASP and ASP and AET-SWC-PET2 (ASP2) models can roughly represent the trend of AET when taking into account SWC and PET. Their average R2 is 0.86 and 0.88, respectively, which is an increase of 34.4 and 37.5% when compared to the AS model's R2. Their rate periodic R2 are 0.88 and 0.9, and their validation periods R2 are 0.84 and 0.86, respectively. Both models are also not very accurate at every station because of variations in the types of vegetation cover. For instance, SWC and PET under the WSA at the US-Ton station do not fully represent the AET realities. This is because, by virtue of their physiological mechanisms, deep-rooted woody plants in savannas are less susceptible to shallow soil moisture constraints (Shuai et al. 2022). Consequently, the peaks are less well fitted, with many overestimates and underestimates, and fitting errors that may still need to be further reduced. GPP measures how much carbon is taken up overall by all producers in an ecosystem during photosynthesis, which fixes carbon dioxide and fuels transpiration, respiration, and other ecosystem processes (Nguyen & Choi 2022). The ASPG model can more accurately represent the trend of AET because it incorporates SWC, PET, and GPP. The average R2, NSE, RMSE, and MAE reached 0.93, 0.80, 0.42, and 0.31, respectively, which was better than those of the ASP2 model by 5.7, 19.9, 24.6, and 25.4%, respectively. The rate period and validation periods' R2 were 0.94 and 0.93, respectively. With a significantly better fit to the peak and a significantly smaller fitting error, the R2 for the various vegetation cover types revealed WET > EBF > DBF > WSA > CRO > ENF > CSH > GRA > OSH > MF > SAV.
Table 3

Tables of R2, NSE, RMSE, and MAE for models AS, ASP, ASP2, and ASPG

ModelR2
NSE
RMSE (mm)
MAE (mm)
MINMAXAVGMINMAXAVGMINMAXAVGMINMAXAVG
AS 0.41 0.95 0.64 −0.49 0.54 0.01 0.32 2.24 1.02 0.25 1.91 0.84 
ASP 0.58 0.99 0.86 0.32 0.97 0.60 0.19 1.34 0.60 0.13 1.15 0.45 
ASP2 0.66 0.99 0.88 0.43 0.97 0.67 0.17 1.25 0.55 0.11 1.03 0.41 
ASPG 0.73 0.99 0.93 0.51 0.98 0.80 0.14 0.83 0.42 0.09 0.59 0.31 
ModelR2
NSE
RMSE (mm)
MAE (mm)
MINMAXAVGMINMAXAVGMINMAXAVGMINMAXAVG
AS 0.41 0.95 0.64 −0.49 0.54 0.01 0.32 2.24 1.02 0.25 1.91 0.84 
ASP 0.58 0.99 0.86 0.32 0.97 0.60 0.19 1.34 0.60 0.13 1.15 0.45 
ASP2 0.66 0.99 0.88 0.43 0.97 0.67 0.17 1.25 0.55 0.11 1.03 0.41 
ASPG 0.73 0.99 0.93 0.51 0.98 0.80 0.14 0.83 0.42 0.09 0.59 0.31 
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Figure 4
The fitting results of four models under different vegetation coverage types. (One site was selected for each vegetation type to display the results. The red dotted line was about the rate period and the verification period, respectively.)
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The fitting results of four models under different vegetation coverage types. (One site was selected for each vegetation type to display the results. The red dotted line was about the rate period and the verification period, respectively.)

Figure 4
The fitting results of four models under different vegetation coverage types. (One site was selected for each vegetation type to display the results. The red dotted line was about the rate period and the verification period, respectively.)
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The fitting results of four models under different vegetation coverage types. (One site was selected for each vegetation type to display the results. The red dotted line was about the rate period and the verification period, respectively.)

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The four models' attribution analyses and differences in accuracy

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The distribution of the R2 differences of the four models for each flux site globally is displayed in Figure 5. Relative to the AS model, the ASP model exhibits a smaller improvement in simulation accuracy for sites from the equator to 30°S latitude, but a larger improvement for sites between 30°N and 60°N latitude. This is because the ASP model includes a linear relationship between the PET and AET. The reason for this is that the majority of flux stations found between the equator and 30°S are found in tropical rainforest or savannah climates, which are characterized by heavy precipitation and coincident rainfall and heat. Since there is a strong correlation between AET and SWC and a considerable amount of soil water availability due to climatic conditions, only the AS model with soil water limitations can accurately represent the changes in AET. On the contrary, the climatic zones belonging to the stations between 30° and 60° N latitude are complex and numerous, with different rain and heat periods. This is especially true in the Mediterranean climatic zone, where the rain and heat periods are opposite. The SWC alone cannot accurately reflect the actual situation of AET; therefore, the simulation of ASP in this region is more effective in amplifying the effect.
Figure 5
The difference of R2 of models 1–4. (Model-4 AS, ASP, ASP2, and ASPG, respectively. (a–f is the distribution map of each station in parts of North America, Europe, Asia, South America, Africa, and Oceania.)
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The difference of R2 of models 1–4. (Model-4 AS, ASP, ASP2, and ASPG, respectively. (a–f is the distribution map of each station in parts of North America, Europe, Asia, South America, Africa, and Oceania.)

Figure 5
The difference of R2 of models 1–4. (Model-4 AS, ASP, ASP2, and ASPG, respectively. (a–f is the distribution map of each station in parts of North America, Europe, Asia, South America, Africa, and Oceania.)
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The difference of R2 of models 1–4. (Model-4 AS, ASP, ASP2, and ASPG, respectively. (a–f is the distribution map of each station in parts of North America, Europe, Asia, South America, Africa, and Oceania.)

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For North America, Europe, and portions of Oceania, ASP2, which accounts for the nonlinear relationship between SWC, PET, and AET, significantly improves the simulation results, with an increase in R2 of more than 0.15 at most sites. The climates of the alpine plateau and the Mediterranean, where climate change is more complex, account for the majority of the sites with higher accuracy. Since AET has more than a simple linear relationship with SWC and PET, using a nonlinear relationship more accurately captures the situation of AET. Nonetheless, several stations, like CN-Du3 and DK-Fou stations, continue to have R2 below the 0.7 threshold. The reason for the little accuracy gain is because ASP2 finds it difficult to modify the fitting findings due to the small amount of data in these stations – in some cases, the data spans less than a year.

Not only does the ASPG that incorporates SWC, PET, and GPP improve the fitting results, with most sites from 30 to 60° N latitude and Oceania showing a greater improvement in accuracy, but it also has a more significant improvement and higher applicability for sites where there is a data scarcity issue. 95% of the flux locations had an R2 of 0.85 or higher. The few sites that did not perform well were found in southern Australia and southern South America, which is in line with Liu (2022) findings. The station with the lowest R2 (0.73) is AR-SLu. The AR-SLu station is situated in the eastern region of the Cordillera, where it is surrounded by a narrow zone where several climate types converge, primarily tropical desert, Mediterranean, alpine plateau, and temperate continental climates. The vegetation cover of this region is mixed forests. The main causes of the complexity and variability of the AET in the region, as well as the low fit accuracy, are the complex vegetation cover types and the local climate.

In summary, the ASPG is better suited for simulating the change patterns of AET under the 11 planted cover types at the global diurnal scale because it incorporates the physical mechanism of SWC, the nonlinear relationship between AET and PET, and GPP which represents the ability of plants to optimize the balance between CO2 uptake and the amount of water transpired during photosynthesis by regulating the opening and closing of leaf stomata.

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Analysis of model applicability

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In this study, we propose a model to simulate the global AET of each flux station tower at the daily scale (ASPG), based on the linear or nonlinear relationship between PET, SWC, GPP, and AET. The model performs well in North and South America, Eurasia, and Africa, but relatively poorly in some Mediterranean climatic zones and some parts of Australia, even though the lowest NSE reaches more than 0.5. Its regional applicability is in line with the results of an NLF model that Liu (2022) created to simulate AET using PET while taking soil water restrictions into account. While the ASPG suggested in this study achieves an NSE of more than 0.8 in regions with high accuracy, the NLF model only obtains an NSE of more than 0.6 in high accuracy locations. This is a considerable improvement over the AET simulation accuracy.

In terms of time-scale applicability, ASPG was used to fit the FLUXNET 2015 monthly scale correlation data, and the fit was good, with the resultant R2 of minimum 0.71 and maximum 0.99; NSE of minimum 0.56 and maximum 0.93; RMSE of minimum 0.1 mm and maximum 24.46 mm; MAE of minimum 0.1 mm and maximum 20.52 mm. Figure 6 displays the average R2 and NSE under various forms of vegetation cover. It is evident from this figure that the average R2 and NSE under the SAV are lower than those under other types of vegetation cover. The cause is that 71% of SAV vegetation stations are spread throughout Oceania, where they are exposed to Australia's changing climate as well as the Great Dividing Range's blocking of eastern water vapor (Rustomji et al. 2009). As a result, the regional evapotranspiration is complex and variable, increasing the error of the model results. The model performance of the monthly scale AET simulation is lower than that of the daily scale AET model. This is because the monthly scale has less data than the daily scale, which means that more data is needed for model fitting. Consequently, one of the causes of the increase in the model error is the decrease in data. Secondly, the daily scale more accurately depicts the actual state of AET than the monthly scale.
Figure 6
Monthly average R2 and NSE under different vegetation types.
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Monthly average R2 and NSE under different vegetation types.

Figure 6
Monthly average R2 and NSE under different vegetation types.
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Monthly average R2 and NSE under different vegetation types.

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All things considered, ASPG performs better overall across temporal and spatial scales, with greater applicability and dependability.

Effect of different soil moisture content on the results

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In order to investigate the effect of different depths of SWC on the fitting results, this study screened out sites containing multiple layers of SWC (a total of 44 sites), and the correlations between the various SWC layers and AET were calculated separately using Pearson's correlation coefficients, and the SWC with the strongest and weakest correlations were chosen to fit the ASPG model. The strongest correlation refers to the maximum absolute value of the Pearson coefficient, while the weakest correlation refers to the opposite. To account for a single variable, the two types of SWC were kept constant in the time series, and the number of data within each site was equal. Figure 7 displays the NSE of the two SWC fitting findings. It is clear from this that the NSE of the fitting results increases with the strength of the correlation between SWC and AET. The rationale is because diverse vegetation root systems have varying effects on soil hydraulics in various geographic locations (Mair et al. 2022), and deeper root systems might affect deeper soil water movement (Khanal et al. 2023). Consequently, AET fitting results at different SWC depths vary.
Figure 7
The difference in model accuracy due to the strongest and weakest correlations of SWC. (Sites containing multi-layer SWC data, totaling 44.)
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The difference in model accuracy due to the strongest and weakest correlations of SWC. (Sites containing multi-layer SWC data, totaling 44.)

Figure 7
The difference in model accuracy due to the strongest and weakest correlations of SWC. (Sites containing multi-layer SWC data, totaling 44.)
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The difference in model accuracy due to the strongest and weakest correlations of SWC. (Sites containing multi-layer SWC data, totaling 44.)

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Analysis of coefficient variance for ASPG

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Figure 8 displays the box plots of each fitted coefficient for the ASPG model. The fitted coefficient ‘a’, as shown in Figure 8(a), shows the link between SWC and AET. At each site under the EBF and WSA, the coefficients ‘a’ span a wide range of values, whereas at the remaining sites, they span values of 0.2 or less. The stations classified as EBF and WSA are primarily found in coastal regions of South America, Asia, and Oceania, ranging from 30°N to 40°S. These regions are subject to the influence of the South Equatorial Warm Current (Stramma 1991) and the East Australian Warm Current (Kerry et al. 2020), which are characterized by humidification and heat increase. As a result, the SWC in these coastal areas is more likely to vary. The remaining stations are situated inland or on the middle and high-latitude coasts, where the impact of monsoon currents is less pronounced than that of equatorial ocean currents (Wang et al. 2022). Consequently, the equatorial currents mostly affect the range of values of the fitting coefficient ‘a’. The linear relationship between PET and AET is shown in the fitting coefficient ‘b’, which has a median value of 0.4 for each type of vegetation cover. The greatest range of variation in its value is found in GRA, which has stations primarily concentrated around 30° north and south latitudes. Climate types that fall under this category include temperate monsoon, subtropical monsoon, and temperate continental. These climate types are characterized by large annual temperature variations, distinct dry and wet seasons, and large annual variations in PET. These factors ultimately impact the range of values of the coefficient ‘b’. In all vegetative cover types other than the WSA, the distribution of coefficient ‘c’ is more concentrated. Coefficient ‘c’ represents the nonlinear relationship between SWC, PET, and AET. The WSA has more than two meters of forest cover in addition to the influence of ocean currents. The variation in PET in each region is also limited by the physiological mechanism of woody plants (Deng et al. 2021), and because of the more intricate nonlinear link between this mechanism and AET, the WSA's coefficient ‘c’ may vary more widely. The correlation between GPP and AET is represented by the adjustment coefficient ‘d’, as illustrated in Figure 8(d), where the majority of sites have a median value ranging from 0 to 0.2, whereas OSH, SAV, and WSA sites have values between 0.2 and 0.4. Since grassland ecosystems vary significantly from region to region, the GRA sites have the widest range of values. GPP is almost zero in the winter, rises slightly in the spring, and then rapidly declines after reaching its peak in summer (Nguyen & Choi 2022). These seasonal variations vary significantly from one place to another.
Figure 8
The box distribution of the fitting coefficients of ASPG.
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The box distribution of the fitting coefficients of ASPG.

Figure 8
The box distribution of the fitting coefficients of ASPG.
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The box distribution of the fitting coefficients of ASPG.

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The following precise conclusions and findings are presented in this paper, which is based on the 149 flux tower datasets in FLUXNET 2015 and proposes an ASPG model for quantitatively estimating global AET by combining the physical links among SWC, PET, GPP, and AET.

  • (1) The global AET has a distinct seasonal distribution, due to the plantation being rooted in the influence of the soil-covered gas belt, the AET of different geographies has different correlations with the SWC of different depths, and the peak of SWC trend changes generally occur ahead of the trend peak of AET.

  • (2) The ASPG model considers the linear or nonlinear interactions among SWC, PET, GPP, and AET. It outperforms the AS, ASP, and ASP2 models in AET simulation, with R2 > 0.7, NSE > 0.5, RMSE < 0.83 mm, MAE < 0.59 mm, and higher peak simulation accuracy than the other models.

  • (3) On a spatial scale, the ASPG model is suitable for more vegetation-covered areas and has good simulation performance for complex climatically variable areas, such as Mediterranean climate and parts of Australia; on a time-scale, ASPG models are used to simulate the global flow tower day scale and moon scale AET respectively, the R2 of the simulation results can reach 0.7 or more, the NSE can reach 0.5 or more and the RMSE of the daily scale result is reduced by 87% and the MAE scale by more than 89% respectively. In terms of both space and temporal scales, the ASPG model is more effective.

  • (4) The amount of the data volume at each site and the various depths of SWC have an impact on the simulation accuracy of the ASPG model; the greater the correlation between AET and SWC, the more accurate the fitting results. The correlation between AET and SWC, PET, and GPP, respectively, can be reflected by the different fitting coefficients of the ASPG model. These coefficients have varying value spans under different types of vegetation cover, which are primarily influenced by climatic conditions, geographic location, and physiological processes of the vegetation.

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We thank the Hubei Key Laboratory of Intelligent Yangtze and HydroelectricScience, China Yangtze Power Co., Ltd, and Yangtze University for financial support for this study.

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Several authors contributed to create this research article. Detailed contributions were as follows: Yongxi Sun contributed to conceptualization, methodology, software development, and writing the original draft; Yuru Dong contributed to data curation and visualization; Chao He contributed to formal analysis; Yanfei Chen contributed to funding acquisition.

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This research received funding from the Hubei Key Laboratory of Intelligent Yangtze and Hydroelectric Science, China Yangtze Power Co., Ltd open research fund, Fund number: ZH2102000111.

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Data cannot be made publicly available; readers should contact the corresponding author for details.

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The authors declare there is no conflict.

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Author notes

†

These authors contributed equally to the work.

© 2024 The Authors
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