Optimal Methods for Estimating Shortwave and Longwave Radiation to Accurately Calculate Reference Crop Evapotranspiration in the High-Altitude of Central Tibet

Abstract

The FAO56 Penman–Monteith model (FAO56-PM) is widely used for estimating reference crop evapotranspiration (ET₀). However, key variables such as shortwave radiation (R_s) and net longwave radiation (R_ln) are often unavailable at most weather stations. While previous studies have focused on calibrating R_s, the influence of large R_ln, particularly in high-altitude regions with thin air, remains unexplored. This study investigates this issue by using observed data from Bange in central Tibet to identify the optimal methods for estimating R_s and R_ln to accurately calculate ET₀. The findings reveal that the average daily R_ln was 8.172 MJ m⁻² d⁻¹ at Bange, much larger than that at the same latitude. The original FAO56-PM model may produce seemingly accurate ET₀ estimates due to compensating errors: underestimated R_ln offsetting underestimated net shortwave radiation (R_sn). Merely calibrating R_s does not improve ET₀ accuracy but may exacerbate errors. The Liu-S was the empirical model for R_s estimation calibrated by parameterization over the Tibetan Plateau and the Allen-LC was the empirical model for R_ln estimation calibrated by local measurements in central Tibet. The combination of the Liu-S and Allen-LC methods showed much-improved performance in ET₀ estimation, yielding a high Nash–Sutcliffe Efficiency (NSE) of 0.889 and a low relative error of −5.7%. This strategy is indicated as optimal for ET₀ estimation in central Tibet. Trend analysis based on this optimal strategy indicates significant increases in ET₀ in central Tibet from 2000 to 2020, with projections suggesting a continued rise through 2100 under climate change scenarios, though with increasing uncertainty over time. However, the rapidly increasing trends in precipitation will lead to decreasing trends in agricultural water use for highland parley production in central Tibet under climate change scenarios. The findings in this study provide critical information for irrigation planning to achieve sustainable agricultural production over the Tibetan Plateau.

1. Introduction

Evapotranspiration is a crucial component of the water balance in various agricultural systems and also plays an important role in the hydrological cycle [1,2,3]. In recent decades, the hydrological cycle has intensified over the last century due to climate change [4,5,6]. Therefore, accurate calculation of evapotranspiration is essential for reliable investigation of future trends in the hydrological cycle under various climate change scenarios [7]. Moreover, water security is fundamental to food security [8], both of which have been severely threatened by climate change in recent decades [9,10]. These threats highlight the importance of precise evapotranspiration data for irrigation planning to ensure water security and sustainable agricultural development [11,12]. Additionally, as a key process in the water movement module, evapotranspiration also plays a vital role in crop growth modelling [13,14,15].

Crop evapotranspiration includes both soil evaporation and crop transpiration. Despite the significance of evapotranspiration across various fields, measured data are often unavailable due to the scarcity of lysimeters and the high cost associated with their maintenance [16]. Currently, the most common approach to estimating evapotranspiration is by using reference crop evapotranspiration (ET₀) multiplied by a crop coefficient [17,18]. ET₀ refers to the evapotranspiration of the reference crop. The reference crop is defined as a hypothetical crop with a height of 0.12 m, a surface resistance of 70 s m⁻¹ and an albedo of 0.23, closely resembling the evaporation from an extensive surface of green grass of uniform height [17]. Thus, accurately estimating ET₀ is a critical step in determining evapotranspiration.

To date, numerous methods have been developed for estimating ET₀, which can be categorized into groups based on their input requirements [7] and include the following: (1) temperature-based models [19,20]; (2) radiation-based models [21,22,23]; (3) mass transfer-based (or pan evapotranspiration-based) models [24,25]; and (4) combination models [17,26,27]. Among these, the FAO56 Penman–Monteith model (FAO56-PM) is widely recognized as the most robust due to its strong physical basis [17,28,29] and high accuracy across diverse climate conditions [28,30]. The FAO56-PM model is now widely used worldwide [31,32,33] and serves as the standard against which other empirical models are evaluated [34,35,36,37,38,39].

However, compared to some empirical models, such as temperature-based ones, the FAO56-PM requires a broader range of meteorological variables, including maximum and minimum temperature, vapor pressure deficit, wind speed, shortwave radiation (R_s) and net longwave radiation (R_ln) [17]. Among these variables, R_s and R_ln are particularly challenging to obtain at most weather stations due to the high costs associated with the required instruments and their maintenance. They are not inputs for calculating ET₀ but are estimated by some other easily obtained inputs. Allen et al. [17] provided a set of empirical models to estimate R_s and R_ln using more accessible variables, such as sunshine duration and temperature. While default coefficients are available for these empirical models, they should be locally calibrated when the observational data are available [17]. However, most calibrations to date have focused on R_s [40,41,42,43,44,45], with few efforts directed towards calibrating R_ln [46]. An experiment in the Liz experimental catchment area highlighted the critical role of R_ln in ET₀ estimation [46]. Thus, it is reasonable to hypothesize that calibrating R_ln could significantly enhance the accuracy of ET₀ estimation by FAO56-PM in high-altitude regions like the Tibetan Plateau, where the R_ln is expected to be higher than that at lower elevations at the same latitude [47].

The Tibetan Plateau (TP), located in southwestern China, is the largest plateau in China and the highest in the world. It covers approximately 25% of China’s land area and is characterized by highly complex terrain [48]. Central Tibet is a key region for highland barley (Hordeum vulgare var. coeleste Linnaeus) production on TP. Highland barley is the staple food for Tibetan people, but it is severely limited by the local water conditions. Accurate evapotranspiration data are vital for local government water planning to achieve sustainable development. However, only about 40 weather stations are sparsely distributed across Tibet, with only four located in the central part. Moreover, none of these stations record radiation-related meteorological data. Fortunately, during the third scientific expedition over the Tibetan Plateau, complete data required for FAO56-PM, including all radiation-related variables, were continuously measured for nearly a year at Bange in central Tibet.

In 1998, Allen et al. [17] provided a set of empirical models to estimate shortwave and longwave radiation for the application of the FAO56-PM equation. However, Allen et al. (1998) could not ensure the accuracy and applicability of these empirical models and pointed out “where measurements of incoming and outcoming short and longwave radiation during bright sunny and overcast hours are available, calibration of the coefficients can be carried out” [17] (p. 52). In China, shortwave radiation is only observed at about 100 out of a total of 2500 weather stations. In contrast, longwave radiation has never been observed at any weather station in China. In recent years, the relevant research has mainly focused on the calibration of shortwave radiation for ET₀ estimation [40,41,42,43,44,45]. Very few calibrations have been made for longwave radiation due to the paucity of longwave radiation observations. For the first time, supported by the comprehensive dataset from Bange, we calibrated empirical models for both shortwave and longwave radiation estimation, in order to find the best method for accurately estimating reference crop evapotranspiration in central Tibet. With the optimal strategy for estimating reference crop evapotranspiration, the data from four weather stations in central Tibet, and projected data under climate change scenario data, this study aimed to assess the impact of R_ln on ET₀ estimation across TP and identify the optimal strategy for ET₀ estimation in central Tibet, based on which the trends in ET₀ and agricultural water use were preliminarily investigated to provide valuable insights for climate adaptation in this highland region.

2. Materials and Methods

2.1. Study Area

Located in southwest China, TP, often referred to as the “Third Pole” due to its high elevation, is the highest plateau in the world. The region has only about 40 weather stations, which are sparsely distributed, with just four weather stations in central Tibet (Figure 1). Detailed information on these stations is shown in Table 1.

2.2. Data Collection

The third scientific expedition over the Tibetan Plateau was conducted in 2014. During the expedition, an automated weather station (AWS) was installed near the Bange weather station. Various meteorological parameters, including upward and downward shortwave radiation, upward and downward longwave radiation, temperature, vapor pressure, wind speed and precipitation, etc., were measured at 0.1-s intervals. The air temperature and vapor pressure were measured by VAISALA-HMP155, and the wind speed was measured by GILL-WINDSONIC. The shortwave radiation was measured by Kipp&zonen-CM21, while the longwave radiation was measured by Eppley-PIR. These instruments were calibrated every month with a set of standard instruments to ensure high data quality. The collected data were averaged or accumulated every half hour and recorded by the AWS. The measurements were conducted continuously from 13 July 2014 to 23 September 2015, with half-hourly data further averaged or accumulated to generate the daily values. After strict data quality control, 365 daily values were used to validate the empirical models for the shortwave radiation estimation. Up to now, the empirical models for longwave radiation estimation have never been calibrated in central Tibet due to a lack of observation. Thus, the data set was first listed in sequence according to the observation date; the daily observations at odd numbers were used for calibration to obtain the coefficients of the empirical models (n = 183), while those at even numbers were used for model validation (n = 182).

At the weather stations in central Tibet, routine observations of meteorological parameters such as sunshine duration, maximum and minimum temperature, vapor pressure and wind speed were conducted, although radiation-related parameters were not measured. Data from these stations, recorded between 1961 and 2020, were collected by the National Meteorological Information Center (NMIC) and the China Meteorological Administration (CMA). As quality assurance and quality control (QAQC) play a very important role in the research work [49], the NMIC has established the Tianqi platform, which includes a comprehensive meteorological data quality control system to ensure high quality of daily weather observations. Daily weather observations were provided by the NMIC for a preliminary trend analysis in central Tibet over recent decades.

Additionally, climate data from 12 global climate models (GCMs) under SSP245 and SSP585 scenarios were downscaled to daily values for each station [50,51]. These projected daily data, spanning from 1961 to 2100, were used for preliminary trend analysis of ET₀ and agriculture water use in central Tibet under climate change scenarios. Firstly, the period from 1961 to 1990 was set as the base period; the monthly climatic data from GCMs were downscaled to specific weather stations using the inverse distance weighted interpolation method. Subsequently, we applied bias correction to the monthly values of climatic factors for each station and used a stochastic weather generator to produce daily climate variables for each station. Detailed information on the downscaling method was described by Liu et al. [50]. The 12 GCMs are described in Table 2.

2.3. Description of FAO56-PM

The widely used FAO56-PM equation is expressed as [17]:

(1)${ET}_0={\displaystyle \frac{0.408∆\left(R_n-G\right)+\left(\frac{900\gamma u_2\left(e_s-e_a\right)}{T}+273\right)}{∆+\gamma \left(1+0.34u_2\right)}}$

where ET₀ is the reference crop evapotranspiration (mm d⁻¹); Δ is the slope of saturated vapor pressure-temperature curve (kPa °C⁻¹); R_n is net radiation (MJ m⁻² d⁻¹); G is soil heat flux (MJ m⁻² d⁻¹); e_s and e_a are saturated and actual vapor pressure (kPa), respectively; γ is the psychrometric constant (kPa °C⁻¹); and T is mean air temperature (°C); u₂ is wind speed at the height of 2 m (m s⁻¹). For standardization, Allen et al. [17] defined T as the mean value of the daily maximum (T_max) and minimum temperature (T_min), rather than as the average of the hourly temperature measurements.

(2)$T={\displaystyle \frac{T_{max}+T_{min}}{2}}$

The slope of the saturated vapor pressure-temperature curve Δ can be calculated as:

(3)$∆={\displaystyle \frac{2504\exp \left(17.27T/T+237.3\right)}{{\left(T+237.3\right)}^2}}$

At the daily scale, the soil heat flux G can be neglected [17], so G = 0 in Equation (1). The psychrometric constant γ is obtained as follows:

(4)$\gamma =0.665\times {10}^{-3}p$

where p is atmospheric pressure (kPa), which can be calculated as [17]:

(5)$p=101.3{\left({\displaystyle \frac{293-0.0065H}{293}}\right)}^{5.26}$

where H is the altitude (m) of the study site. Wind speed at 2 m (u₂) can be calculated from the wind speed measured at height of z m (u_z) using the following equation:

(6)$u_2={\displaystyle \frac{4.87}{\mathrm{l}\mathrm{n}(67.8z-5.42)}}{u}_z$

The saturated vapor pressure e_s is the average of e_s(T_max) and e_s(T_min), calculated as:

(7)$e_s\left(t\right)=0.6108exp\left({\displaystyle \frac{17.27t}{t+237.3}}\right)$

where t represents either T_max or T_min. All values except R_n are readily available for ET₀ calculation. The net radiation R_n is obtained as follows:

(8)${R_n=R_{sn}-R}_{ln}$

where R_sn and R_ln are net shortwave and longwave radiation, respectively. R_sn can be calculated as:

(9)$R_{sn}=\left(1-\alpha \right)\times R_s$

where α is albedo and R_s is the downward shortwave radiation (the solar radiation). Allen et al. [17] fixed α as 0.23 for the reference crop, simplifying the calculation of R_sn to 0.77 R_s. If both R_s and R_ln are available, ET₀ can be directly calculated.

However, obtaining R_s and R_ln, especially R_ln, is challenging at most weather stations. They are typically estimated using empirical models. In this study, four empirical models were used to estimate R_s and another four to estimate R_ln, resulting in 16 combined strategies for ET₀ estimation. Detailed descriptions of the empirical models are presented below.

2.4. Empirical Models for Caculating R_s

Many empirical models have been developed for estimating R_s [52,53,54,55,56,57]. Allen et al. [17] recommended the widely accepted Angstrom–Prescott model for estimating R_s, providing default coefficients for direct application. To identify possible discrepancies from the direct application of the recommended model, the Angstrom–Prescott model was selected for estimating R_s in this study. As the Angstrom–Prescott model must be calibrated locally for accurate application, two parametrization models were also used for regional application. The original Angstrom model was established by Angstrom [52] and revised by Prescott [53] as follows:

(10)${\displaystyle \frac{R_s}{R_0}}=a+b\times {\displaystyle \frac{S}{S_0}}$

where R_s is solar radiation, R₀ is extraterrestrial radiation, S is sunshine hours, and S₀ is potential sunshine hours. a and b are coefficients.

• (1). Allen-S: the original Angstrom–Prescott model with coefficients recommended by Allen et al. [17] is referred to as Allen-S.

  (11)${\displaystyle \frac{R_s}{R_0}}=0.250+0.500\times {\displaystyle \frac{S}{S_0}}$

  where 0.250 and 0.500 are the default coefficients of a and b, respectively.

• (2). Allen-SC: the coefficients in the Angstrom–Prescott model were calibrated using data from the Bange experiment. The calibrated model is referred to as the Allen-SC model:

  (12)${\displaystyle \frac{R_s}{R_0}}=0.310+0.550\times {\displaystyle \frac{S}{S_0}}$

  where 0.310 and 0.550 are the calibrated coefficients for a and b, respectively, at Bange weather station [17,58].

• (3). Gopinathan-S: the coefficients in the Angstrom–Prescott model can be also calibrated by the parameterization method suggested by Gopinathan [59], referred to as Gopinathan-S, as follows:

  (13)${\displaystyle \frac{R_s}{R_0}}=0.012+0.854\times {\displaystyle \frac{S}{S_0}}$

  where 0.012 and 0.854 are the coefficients of a and b, respectively [58]. These coefficients are calculated according to the following parameterization equations [59]:

  (14)$a=-0.309+0.539\times cos\varphi -0.0693\times H+0.290\times \overline{{\displaystyle \frac{S}{S_0}}}$

  (15)$b=1.527-1.027\times cos\varphi +0.0926\times H-0.359\times \overline{{\displaystyle \frac{S}{S_0}}}$

  where φ is latitude, H is altitude, and $\overline{S/S_0}$ is the long-term annual average daily sunshine fraction at the calibration site.

• (4). Liu-S: when the coefficients were calibrated using the parameterization equation suggested by Liu et al. [57,58], the following model is referred to as Liu-S:

  (16)${\displaystyle \frac{R_s}{R_0}}=0.238+0.598\times {\displaystyle \frac{S}{S_0}}$

  where the coefficients were calculated from the following parameterization functions based on the observations over the TP [58,60]:

  (17)$\left(a+b\right)=0.106\times \ln \left(H\right)-0.060$

  (18)$b=0.373\times {\displaystyle \frac{1}{\mu }}+0.483$

  where µ is the average daily water vapor pressure (hPa).

2.5. Empirical Models for Estimating Longwave Radiation (R_ln)

R_ln is usually estimated using models such as FAO56 and FAO24 models. The FAO56 model for calculating longwave radiation is formulated as follows [17]:

(19)$R_{ln}=\sigma \left({\displaystyle \frac{{T_{max,k}}^4+{T_{min,k}}^4}{2}}\right)\left(c_1-c_2\sqrt{e_a}\right)\left(d_1{\displaystyle \frac{R_s}{R_{s0}}}-d_2\right)$

where σ is the Stefan–Boltzmann constant (4.903 × 10⁻⁹ MJ K⁻⁴ m⁻² d⁻¹); T_max,k and T_min,k are the absolute maximum and minimum temperature in the unit of K, respectively; R_s is the observed solar radiation (the downward shortwave radiation); and R_s0 is the calculated clear solar radiation (MJ m⁻² d⁻¹), typically using the Angstrom–Prescott model assuming full sunshine, i.e., S = S₀.

The FAO24 model [61] offers an alternative formulation for estimating R_ln:

(20)$R_{ln}=\left(\sigma T_K^4\right)\left(e_1-e_2\sqrt{e_a}\right)\left(f_1+f_2{\displaystyle \frac{S}{S_0}}\right)$

where T_K is the absolute air temperature in the unit of K. In these equations, c₁, c₂, d₁, d₂, e₁, e₂, f₁ and f₂ are model coefficients that can be calibrated using observational data when available.

• (1). Allen-L (Original FAO56 model): the FAO56 model with the original coefficients proposed by Allen et al. [17] is referred to as Allen-L and is as follows:

  (21)$R_{ln}=\sigma \left({\displaystyle \frac{{T_{max,k}}^4+{T_{min,k}}^4}{2}}\right)\left(0.34-0.14\sqrt{e_a}\right)\left(1.35{\displaystyle \frac{R_s}{R_{s0}}}-0.35\right)$

The coefficients 0.34, 0.14, 1.35 and 0.35 are default values recommended by Allen et al. [17].

• (2). Allen-LC (Calibrated FAO56 Model): this version of the FAO56 model is calibrated using the observational data from Bange, and is referred to as Allen-LC. It is as follows:

  (22)$R_{ln}=\sigma \left({\displaystyle \frac{{T_{max,k}}^4+{T_{min,k}}^4}{2}}\right)\left(0.854-0.346\sqrt{e_a}\right)\left(0.505{\displaystyle \frac{R_s}{R_{s0}}}+0.047\right)$

Here, the same coefficients as in the Allen-L model are adjusted based on the data measured in the Bange experiment.

• (3). Doorenbos-L (Original FAO24 Model): the FAO24 model for estimating R_ln, as developed by Doorenbos et al. [61], is referred to as Doorenbos-L and is as follows:

  (23)$R_{ln}=\left(\sigma T_K^4\right)\left(0.34-0.044\sqrt{e_a}\right)\left(0.1+0.9{\displaystyle \frac{S}{S_0}}\right)$

  where T_K is the mean temperature in the unit of K, and the default coefficients were suggested by Doorenbos et al. [61].

• (4). Doorenbos-LC (Calibrated FAO24 Model): the Doorenbos-LC is a calibrated version of the FAO24 model (Equation (23)). Similar to the Allen-LC model, this version calibrated the default coefficients by the observational data from the Bange experiment using the following equation:

  (24)$R_{ln}=\left(\sigma T_K^4\right)\left(0.402-0.164\sqrt{e_a}\right)\left(0.487+0.691{\displaystyle \frac{S}{S_0}}\right)$

2.6. Model Evaluation

The performance of these models was evaluated using the Nash–Sutcliffe Efficiency (NSE), the coefficient of determination (R²), the Mean Bias Error (MBE), and the Root Mean Squared Error (RMSE) metrics [62,63]:

(25)$NSE=1-{\displaystyle \frac{{\sum }_{i=1}^n{\left(O_i-S_i\right)}^2}{\sum _{i=1}^n{\left(O_i-\overline{O}\right)}^2}}$

(26)$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(O_i-S_i)}^2}$

(27)$R^2={\left({\displaystyle \frac{\sum _{i=1}^n\left(O_i-\overline{O}\right)\left(S_i-\overline{S}\right)}{{\left(\sum _{i=1}^n{\left(O_i-\overline{O}\right)}^2\sum _{i=1}^n{\left(S_i-\overline{S}\right)}^2\right)}^{0.5}}}\right)}^2$

(28)$MBE={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left(S_i-O_i\right)$

where $O_i$ is the observed value; $S_i$ is the simulated value; $\overline{O}$ is the average value of the observed radiation; and n is the number of observations. The higher the NSE and R², the better the performance of the model. The lower RMSE means less error in estimation. The value of MBE indicates underestimation (negative value) or overestimation (positive value) by the empirical models.

Linear regressions were also conducted between observed and simulated values, with the slope and intercept of the regression line (denoted as Slope and Inter) serving as auxiliary indicators to assess the overall accuracy of the model simulations.

3. Results

3.1. Variation in R_ln and ET₀ at Bange

Significant fluctuations were observed in daily R_sn, R_ln and R_n (Figure 2). R_sn varied from 6.613 to 26.645 MJ m⁻² d⁻¹, with an average of 15.866 MJ m⁻² d⁻¹. The mean daily R_ln was 8.172 MJ m⁻² d⁻¹, comparable to the R_n of 7.694 MJ m⁻² d⁻¹. The substantial R_ln values indicate its potential importance in ET₀, highlighting the need for R_ln calibration over TP. Daily ET₀ also showed considerable fluctuations, ranging from 0.714 to 6.594 mm d⁻¹, with an average of 2.618 mm d⁻¹ (Figure 2). Seasonal variations were evident in R_sn, R_ln, R_n and ET₀, with the lowest values in January (winter) and the highest in July (summer), indicating a consistent seasonal trend across these variables.

3.2. Performance of the Empirical Models

For R_s estimation, the Allen-S model had a lower performance on NSE of 0.631 (Figure 3a). After calibration, the Allen-SC model showed improved performance, with an increased NSE of 0.847. The Gopinathan-S model, calibrated using global parametrization equations, performed the worst with the lowest NSE of 0.349. In contrast, the Liu-S, calibrated using TP-specific data, performed well with an NSE of 0.814, close to that of the Allen-SC. Furthermore, the Allen-S and the Gopinathan-S showed large discrepancies between estimated and observed R_s (Figure 3a,c), whereas the Allen-SC and the Liu-S had much smaller discrepancies (Figure 3b,d). Thus, the Allen-SC model and the Liu-S models are considered suitable for R_s estimation in central Tibet.

For R_ln estimation, the original Allen-L and Doorenbos-L models performed poorly, with low NSE of −2.514 and −0.417, respectively (Figure 4a,c). The negative values of NSE suggest these models performed worse than a simple average of observations. However, when calibrated, both the Allen-LC and Doorenbos-LC models performed significantly better, with NSE values of 0.697 and 0.695, respectively (Figure 4b,d). Higher NSE means better model performance, so the Allen-LC and Doorenbos-LC models have obvious advantages over the Allen-L and Doorenbos-L models in estimating R_ln in central Tibet.

3.3. Reliability of the Previous Standard for ET₀

R_s is more readily available than R_ln at most weather stations. Consequently, researchers often calibrate the Allen-S model for accurate estimation of R_s, while leaving the Allen-L model unchanged for R_ln estimation. This approach, using observed R_s to drive the FAO56-PM model and treating calculated ET₀ as the standard for model evaluation, overlooks potential R_ln estimation errors caused by the Allen-L model, assuming that any ET₀ estimation errors are solely due to R_s estimation inaccuracies. In this context, improved R_s estimation directly translates to more accurate ET₀ estimation.

In this scenario, observed R_s was used to estimate the FAO56-PM while R_ln was calculated using the Allen-L model. Treating observed R_s and calculated R_ln as actual values yielded zero error for both R_s and the calculated R_ln, resulting in zero error for R_n and ET₀ as well. Since the Allen-SC performed the best in R_s estimation (Figure 3a), it resulted in the smallest ET₀ estimation error of 0.02 mm d⁻¹ (Table 3). Conversely, the Gopinanthan-S model, which performed the worst in R_s estimation (Figure 3c), produced the largest ET₀ estimation error of −0.43 mm d⁻¹ (Table 3).

When both observed R_s and R_ln were used to drive the FAO56-PM model, the resulting ET₀ was based on all observed meteorological data, representing the real standard for ET₀. Under this real standard, the evaluation results differed significantly from the previous approach. While the Gopinathan-S model performed the worst in estimating in R_s estimation (Figure 3a), when combined with the Allen-L, it appeared to perform the best in ET₀ estimation, with the smallest error of 0.22 mm d⁻¹ (Table 4). This accuracy was due to its high precision in R_n estimation, with the smallest error of 1.37 MJ m⁻² d⁻¹ (Table 4), achieved by offsetting the largest errors in R_sn (−2.61 MJ m⁻² d⁻¹) and R_ln (−3.97 MJ m⁻² d⁻¹). Therefore, under the real standard, errors in both R_s and R_ln can affect ET₀ estimation. A large error in R_sn estimation does not necessarily lead to a large ET₀ error if it is offset by an R_ln error, and vice versa. For example, the Allen-SC model performed the best in R_sn estimation, with the smallest error of 0.11 MJ m⁻² d⁻¹, but this error was amplified by a −3.97 MJ m⁻² d⁻¹ error in R_ln estimation, resulting in a large ET₀ estimation error of 4.08 mm d⁻¹ (Table 4).

3.4. Comparison of Different Strategies for ET₀ Estimation

Combining the four empirical models for R_s estimation with four for R_ln estimation resulted in 16 strategies for ET₀ estimation (Table 5, Figure 5 and Figure 6). According to the FAO56-PM, errors in ET₀ estimation are primarily due to inaccuracies in R_n estimation. Thus, calibrating both R_s and R_ln models yields the most accurate ET₀ estimations. For instance, the combination of the Allen-SC and Allen-LC models performed best, with the smallest errors of 0.1 MJ m⁻² d⁻¹ and 0.02 mm d⁻¹ for R_n and ET₀, respectively (Table 5). Conversely, calibrating only R_s or R_ln does not guarantee accurate ET₀ estimation. The combination of the Allen-SC and Allen-L models, for example, resulted in the largest error of 4.08 MJ m⁻² d⁻¹ for R_n and 0.66 mm d⁻¹ for ET₀ (Table 5).

Evaluating model performance solely based on the final error in ET₀ estimation may lead to incorrect conclusions. For example, the combination of the Gopinathan-S and Doorenbos-L models resulted in the most inaccurate R_sn and R_ln estimations, with errors of −2.61 MJ m⁻² d⁻¹ and −2.3 MJ m⁻² d⁻¹, respectively. However, these errors offset each other, resulting in relatively accurate R_n and ET₀ estimates, with small errors of −0.3 MJ m⁻² d⁻¹ and −0.05 mm d⁻¹, respectively (Table 5 and Figure 5). Thus, relying solely on final ET₀ estimation errors can lead to misjudgment. Similarly, the Allen-S and Doorenbos-L combination produced accurate R_n and ET₀ estimations, but with large errors in R_sn and R_ln estimation (Table 5 and Figure 5).

From a scientific perspective, the final accuracy achieved by offsetting large errors during the calculation processes is not an ideal evaluation model criterion. Therefore, for optimal ET₀ estimation, only the Allen-SC and Liu-S models were selected as the suitable methods for R_s estimation, while the Allen-LC and Doorenbos-LC were regarded as the suitable methods for R_ln estimation. Based on these models, four combinations were identified as candidates for optimal ET₀ estimation strategies. Notably, the combinations of the Allen-SC and Allen-LC with the Allen-SC and Doorenbos-LC performed the best, with the smallest ET₀ estimation errors of 0.02 mm d⁻¹, attributable to minimal differences in R_n estimates between these two combinations (Table 5). Although the combinations of the Liu-S with Allen-LC and the Liu-S with Doorenbos-LC did not perform very well, they were still acceptable, with a small ET₀ estimation error of 0.15 mm d⁻¹, corresponding to a relative error of −5.7% (−0.15/2.62). Given that R_sn is more easily obtained by the empirical models than by measurements of sunshine duration, the Allen-LC model is preferred over the Doorenbos-LC. Therefore, the combination of the Allen-SC and Allen-LC is considered the most suitable strategy for ET₀ at Bange (Figure 6). However, the Allen-C model requires local calibration and cannot be applied regionally. In contrast, the Liu-S can be easily obtained from local altitude and vapor pressure at any station on the TP, making the Liu-S and Allen-LC combination the optimal strategy for regional ET₀ estimation in central Tibet (Figure 6).

3.5. Preliminary Analysis of the Trends in ET₀ and Agricultural Water Use in Central Tibet

Using the optimal strategy, ET₀ was calculated from 1961 to 2020 at four weather stations in central Tibet (Figure 7). During this period, slightly increasing trends were observed at Bange and Dangxiong, while a slight decrease was noted at Nanmulin. Shenzha showed a clear decreasing trend, with a rate of 0.002 mm d⁻¹ per year. However, from 2000 to 2020, all stations exhibited significant increasing trends, with rates ranging from 0.009 to 0.030 mm d⁻¹ per year, and with a mean rate of 0.019 mm d⁻¹ per year (Figure 7).

The trends in ET₀ under different climate change scenarios are shown in Figure 8 and Figure 9. Under the SSP245 scenario, the changes in ET₀ were not obvious from 1961 to 2020 but became notable from 2020 to 2100 at all stations, especially at Dangxiong and Nanmulin (Figure 8). It should be noted that a large discrepancy existed among the ET₀ calculated by different GCMs, and the discrepancy became larger as time progressed (Figure 8 and Figure 9). The large discrepancy resulted in great uncertainty in the changes of ET₀. In some periods, the bottom boundary of the gray area even exhibited a decreasing trend, which was especially obvious at Nanmulin (Figure 8d). The trends in ET₀ under the SSP585 showed a similar changing pattern, but the increasing trends from 2021 to 2100 became more obvious than those under the SSP245 scenario (Figure 9). For each station, the discrepancy among different GCMs was smaller than that under the SSP245 scenario. In addition, no obvious decreasing trend was identified at the bottom boundary of the canyon area, indicating that the increasing trends in ET₀ became more significant under the SSP585 scenario (Figure 9).

Agricultural water use in Tibet is influenced by many factors, but the main factors are crop evapotranspiration and precipitation [64]. Liu et al. [64] conducted a field experiment in Tibet, finding that the crop coefficient of highland barley was 0.87. Liu et al. defined water demand as the difference between crop evapotranspiration and precipitation [64]. For simplicity, we used a similar method and defined agricultural water use as the difference between crop evapotranspiration and precipitation. The highland barley grows from April to August in central Tibet, and the crop evapotranspiration was calculated with the reference crop evapotranspiration and the crop coefficient of 0.87 in the growth period of the highland barley.

Under the SSP245 scenario, changes in crop evapotranspiration in the growth period of highland barley were not obvious at Bange and Shenzha, while the crop evapotranspiration showed slightly increasing trends at Dangxiong and Nanmulin (Figure 10). In contrast, changes in precipitation showed obvious increasing trends at all stations, which resulted in decreasing trends in agricultural water use at all stations, especially at Bange and Shenzha (Figure 10). The trends under the SSP585 showed a similar pattern, but the increasing trends in precipitation became more significant, resulting in significant decreasing trends in agricultural water use at all stations in central Tibet (Figure 11).

4. Discussion

4.1. Large R_ln in Central Tibet

Due to the high altitude of the TP, the atmosphere is significantly thinner compared to regions at the same latitude. This thinner atmosphere results in reduced downward longwave radiation, which, in turn, leads to elevated net longwave radiation. In central Tibet, the average daily R_ln was measured as 8.172 MJ m⁻² d⁻¹ in Bange, which is comparable to an average daily R_ln of 9.73 MJ m⁻² d⁻¹ measured at six stations in the eastern and western TP [47]. These values are considerably higher than those at similar latitudes worldwide [65,66,67]. For instance, in the North China Plain, the mean R_ln was only 4.043 MJ m⁻² d⁻¹ during the period from 15 June to 28 October 2003 [68], which is approximately half of that observed in Bange. Additionally, spatial distribution estimates of R_ln across China indicate that the R_ln over the TP is significantly higher than that in the Sichuan Basin, which lies at the same latitude [69]. The elevated R_ln plays a crucial role in both sensible heat and latent heat (evapotranspiration) processes [47], highlighting the importance of accurately calibrating R_ln over the TP.

4.2. Necessity of Comprehensive Calibration for Both Rs and Rln

The FAO56-PM model is widely regarded as the standard for evaluating the performance of empirical models in ET₀ estimation [34,35,37]. Typically, the methods introduced by Allen et al. [17] were directly applied for both R_s and R_ln estimation or coefficients from other studies were used without further local calibration [39,40,70]. However, the variability of the coefficients might be quite obvious (see Equations (10)–(16)). According to the atmospheric theory, the coefficient of a is the solar radiation reaching the earth's surface on cloudy days, while the coefficient of b can be viewed as a kind of transmission of solar radiation under cloudless conditions [58,71]. These coefficients are influenced by many environmental factors such as local cloud conditions, air mass, altitude, water vapor content and aerosol density, etc.. Therefore, the coefficients would be quite different if they were calibrated with data from different locations. Both the Allen-S and Gopinathan-S were calibrated with data from many locations around the world [17,59], but the calibration data did not include any observations from the Tibetan Plateau. The Tibetan Plateau is famous for its large solar radiation in the world due to its high altitude and clean sky conditions [57,58], which makes the coefficients quite different from those calibrated in the other regions. Variations in the coefficients make it very important to calibrate them locally over the Tibetan Plateau.

While local calibration is often deemed essential, many scientists focused solely on calibrating R_s, assuming that this would improve ET₀ estimation accuracy [41,42,44]. However, this assumption does not necessarily hold true for TP. As shown in Table 5 and Figure 6a, the original methods by Allen et al. [17] for estimating R_s and R_ln, (Allen-S and Allen-L) resulted in significant estimation errors (Table 5). Nevertheless, these errors in R_s and R_ln estimation tended to offset each other, leading to relatively high accuracy in ET₀ estimation (Figure 6a). When R_s was calibrated using the Allen-SC model, the accuracy of R_s estimation improved significantly (Table 5). However, this also amplified the discrepancy in R_n estimation, causing the FAO56-PM model to perform worse in ET₀ estimation (Table 5 and Figure 6b).

In summary, for ET₀ estimation, it is essential to calibrate both R_s and R_ln simultaneously. While the original method by Allen et al. [17] might provide plausible accuracy in ET₀ estimation, it might introduce significant process errors in R_s and R_ln estimation. Calibrating R_s alone may improve ET₀ estimation accuracy by previous standards (Table 3). However, large errors may exist when validated against actual ET₀ values calculated with observed R_s and R_ln data (Table 4). Consequently, conclusions drawn using the previous standards should be reexamined [39,41,44,70,72], as these standards may contain substantial errors compared to the real ET₀ standard.

4.3. Uncertainties and Future Research

Compared to R_s, R_ln is more challenging to measure due to the high cost of instruments and maintenance, leading to limited observations and empirical models for R_ln [46]. While the Liu-S and Allen-SC methods accurately estimated R_s (Figure 3), the Allen-LC and Doorenbos-LC methods did not perform as well in estimating R_ln (Figure 4). The discrepancies between observed and estimated R_ln in Figure 4b,d suggested that these empirical models cannot accurately estimate R_ln in central Tibet, even after local calibration. The study by Kofronva et al. [46] also found that, while local calibration improved these models’ performance, significant discrepancies remained between observations and estimations. Up to now, most of the calibrations have been focused on the shortwave radiation models, as shortwave radiation data are available at some weather stations. Various kinds of empirical models for shortwave radiation estimation were put forward and validated in different regions around the world [40,41,42,43,44,45,52,53,54,55,56,57,58,59,60]. In contrast, very little research has been conducted on longwave radiation estimation due to the lack of longwave radiation observation at weather stations. Therefore, rather than merely calibrating coefficients in existing models like the Allen-L and Doorenbos-L, developing new empirical models for R_ln estimation is essential for future research. In addition, the measurement only lasted for about one year in Bange due to the high cost of the experiment. Calibration and validation of the empirical models with multiple years of observation data can lead to more reliable results, meaning that further experiments on shortwave and longwave radiation measurement are necessary for future scientific expeditions over the Tibetan Plateau.

There is considerable uncertainty regarding ET₀ trends under climate change scenarios (Figure 8 and Figure 9). While significant increasing trends were observed in central Tibet in the last two decades (Figure 7), these trends were not mirrored in ET₀ estimates based on climate change projections (Figure 8 and Figure 9). The discrepancy suggests that historical data projected by GCMs may differ significantly from actual historical records. Moreover, although increasing ET₀ trends were identified at all stations under different climate change scenarios, the uncertainty in ET₀ projections grew over time. In addition, large uncertainties also exist in the changes in precipitation over the Tibetan Plateau. Simulated by GCMs, the precipitation is projected to increase with the radiation forcing, as a response to the enhanced evaporation [73,74,75]. These findings agreed well with our results in this study, but the increasing rates of precipitation ranged from 7.4% to 21.6% under different scenarios [76], making it urgent to improve the relevant skills in the projection of future climate scenarios. Since this study primarily focused on identifying the optimal strategy for ET₀ estimation in central Tibet, trends in ET₀ and agricultural water use were only preliminarily analyzed based on 12 GCMs. More GCMs might lead to more reliable results. Thus, future research should involve more GCMs and include ensemble studies and attribution analysis of the changes in ET₀ and agricultural water use to address these uncertainties.

5. Conclusions

Observations at Bange, collected during the third scientific expedition over the TP, were used to analyze R_ln variations and identify the optimal strategy for ET₀ estimation in central Tibet. The results showed that the average daily R_ln was 8.172 MJ m⁻² d⁻¹ at Bange, much higher than that at the same latitude elsewhere. When calibrated, the Allen-SC and Liu-S methods performed well in estimating R_s, with NSE of 0.847 and 0.814, respectively. Local calibration also improved the accuracy of R_ln estimation using the Allen-LC and Doorenbos-LC models, with NSE values of 0.697 and 0.695, respectively.

The combination of the Allen-S and Allen-L methods resulted in high ET₀ estimation accuracy, but this was due to large errors in R_sn and R_ln estimates offsetting each other. In contrast, merely calibrating R_s does not improve ET₀ accuracy but may exacerbate error. This highlights that accurate ET₀ estimation requires simultaneous calibration of both R_s and R_ln. Following this principle, the combination of the Liu-S and Allen-LC methods was determined to be the optimal strategy for ET₀ estimation in central Tibet.

ET₀ changes in central Tibet from 1961 to 2020 were not significant. From 2000 to 2020, significant increasing trends were observed, with rates ranging from 0.009 to 0.030 mm d⁻¹ per year. These trends were pronounced under the SSP245 climate change scenario and even more significant under the SSP585 climate change scenario. However, rapidly increasing trends in precipitation were projected under climate change scenarios, resulting in obvious decreasing trends in agricultural water use for highland barley production in the future climate change context. As the uncertainty in ET₀ projections under different climate scenarios increases over time, ensemble studies and attribution analysis will be critical in addressing these uncertainties in future research.

Author Contributions

Conceptualization, J.L., J.D., F.W., J.T., D.L., Y.T., L.S., Q.Y. and D.L.L.; methodology, J.L., J.D., F.W., D.L.L., J.T., L.S., D.L., Y.T. and Q.Y.; software, J.L.; validation, J.T., D.L. and Y.T.; formal analysis, J.L.; writing—original draft preparation, J.L.; writing—review and editing, Q.Y. and D.L.L. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Acknowledgments

The authors would like to show special gratitude to the scientists for their experiments conducted under extremely harsh environments during the third scientific expedition over the Tibetan Plateau. We also acknowledge support from the CMA Key Innovation Team (CMA2022ZD10) and the WMC Innovation Team (WMC2023IT03).

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Tables

Figure 1. Distribution of weather stations in central Tibet. The black dots denote all weather stations distributed over Tibet, while the red ones denote stations in central Tibet.

Figure 2. Variations in net radiation and reference crop evapotranspiration at Bange.

Figure 3. Validation of different empirical models for shortwave radiation estimation.

Figure 4. Validation of different empirical models for net longwave radiation estimation.

Figure 5. Performance of different strategies for estimation of ET0. Numbers in the table refer to Table 5. The top dot marks the maximum value, the vertical line from top to bottom marks the 95th, 75th, 50th, 25th and 5th percentiles, and the bottom dot marks the minimum value.

Figure 6. Validation of different strategies for estimating reference crop evapotranspiration.

Figure 7. The annual average daily ET0 in central Tibet from 1961 to 2020.

Figure 8. The annual average daily ET0 under the SSP245 climate change scenario.

Figure 9. The annual average daily ET0 under the SSP585 climate change scenario.

Figure 10. Crop evapotranspiration, precipitation and agricultural water use in the growth period of highland barley under the SSP245 climate change scenario.

Figure 11. Crop evapotranspiration, precipitation and agricultural water use in the growth period of highland barley under the SSP585 climate change scenario.

Table 1

Detailed information on the weather stations in central Tibet.

Station	Latitude/° N	Longitude/° E	Altitude/m (a.s.l 1)
Bange	31.38	90.02	4700.0
Dangxiong	30.48	91.10	4200.0
Nanmulin	29.68	89.10	4000.0
Shenzha	30.95	88.63	4672.0

¹ a.s.l is the acronym for above sea level.

Table 2

Information on 12 global climate models (GCMs) used in this study.

Model No.	Name of GCM	Abbreviation of GCM	Institute	Country
1	ACCESS-CM2	ACC1	ACCESS	Australia
2	ACCESS-ESM1-5	ACC2	ACCESS	Australia
3	CMCC-CM2-SR5	CMCS	CMCC	Italy
4	CNRM-ESM2-1	CNR1	CNRM-CERFACS	France
5	CNRM-CM6-1	CNR2	CNRM-CERFACS	France
6	FGOALS-g3	FGOA	IAP, CAS	China
7	GISS-E2-1-G	GISS	NASA-GISS	USA
8	HadGEM3-GC31-LL	HadG	MOHC	UK
9	MIROC6	MIR1	MIROC	Japan
10	MIROC-ES2L	MIR2	MIROC	Japan
11	MRI-ESM2-0	MTIE	MRI	Japan
12	UKESM1-0-LL	UKES	MOHC	UK

Table 3

Evaluation of the effect of estimated R_sn on EP₀ with the previous standard for ET₀ *.

Method		Rsn (MJ m−2 d−1)		Rln (MJ m−2 d−1)		Rn (MJ m−2 d−1)		ET0 (mm d−1)
R sn	R ln	Value	Error	Value	Error	Value	Error	Value	Error
Observed	Allen-L	15.87 ± 4.47	0.00 ± 0.00	4.20 ± 1.57	0.00 ± 0.00	11.67 ± 3.94	0.00 ± 0.00	3.26 ± 1.10	0.00 ± 0.00
Allen-S	Allen-L	13.74 ± 3.96	−2.13 ± 1.68	4.20 ± 1.57	0.00 ± 0.00	9.54 ± 3.48	−2.13 ± 1.68	2.92 ± 1.05	−0.34 ± 0.28
Allen-SC	Allen-L	15.97 ± 4.51	0.11 ± 1.75	4.20 ± 1.57	0.00 ± 0.00	11.77 ± 4.05	0.11 ± 1.75	3.28 ± 1.11	0.02 ± 0.29
Gopinathan-S	Allen-L	13.26 ± 5.37	−2.61 ± 2.49	4.20 ± 1.57	0.00 ± 0.00	9.06 ± 4.32	−2.61 ± 2.49	2.84 ± 1.20	−0.43 ± 0.41
Liu-S	Allen-L	14.93 ± 4.49	−0.94 ± 1.69	4.20 ± 1.57	0.00 ± 0.00	10.73 ± 3.88	−0.94 ± 1.69	3.11 ± 1.11	−0.15 ± 0.28

* The previous standard for ET₀ is calculated by observed R_sn and estimated R_ln according to Allen et al. [17]. In A ± S, A and B denote the average value and the standard deviation, respectively.

Table 4

Evaluation of the effect of estimated R_sn on EP₀ with the real standard for ET₀ *.

Method		Rsn (MJ m−2 d−1)		Rln (MJ m−2 d−1)		Rn (MJ m−2 d−1)		ET0 (mm d−1)
R sn	R ln	Value	Error	Value	Error	Value	Error	Value	Error
Observed	Observed	15.87 ± 4.47	0.00 ± 0.00	8.17 ± 2.34	0.00 ± 0.00	7.69 ± 3.30	0.00 ± 0.00	2.62 ± 1.01	0.00 ± 0.00
Allen-S	Allen-L	13.74 ± 3.96	−2.13 ± 1.68	4.20 ± 1.57	−3.97 ± 1.43	9.54 ± 3.48	1.85 ± 1.68	2.92 ± 1.05	0.30 ± 0.29
Allen-SC	Allen-L	15.97 ± 4.51	0.11 ± 1.75	4.20 ± 1.57	−3.97 ± 1.43	11.77 ± 4.05	4.08 ± 1.96	3.28 ± 1.11	0.66 ± 0.33
Gopinathan-S	Allen-L	13.26 ± 5.37	−2.61 ± 2.49	4.20 ± 1.57	−3.97 ± 1.43	9.06 ± 4.32	1.37 ± 2.72	2.84 ± 1.20	0.22 ± 0.45
Liu-S	Allen-L	14.93 ± 4.49	−0.94 ± 1.69	4.20 ± 1.57	−3.97 ± 1.43	10.73 ± 3.88	3.04 ± 1.88	3.11 ± 1.11	0.49 ± 0.32

* The real standard for ET₀ is calculated by both observed R_sn and observed R_ln. In A ± S, A and B denote the average value and the standard deviation, respectively.

Table 5

Comparison of different strategies for estimation of ET₀.

	Method		Rsn (MJ m−2 d−1)		Rln (MJ m−2 d−1)		Rn (MJ m−2 d−1)		ET0 (mm d−1)
No.	Rsn	Rln	Value	Error	Value	Error	Value	Error	Value	Error
	Observed	Observed	15.87 ± 4.47	0.00 ± 0.00	8.17 ± 2.34	0.00 ± 0.00	7.69 ± 3.30	0.00 ± 0.00	2.62 ± 1.01	0.00 ± 0.00
1	Allen-S	Allen-L	13.74 ± 3.96	−2.13 ± 1.68	4.20 ± 1.57	−3.97 ± 1.43	9.54 ± 3.48	1.85 ± 1.68	2.92 ± 1.05	0.30 ± 0.29
2	Allen-S	AllenL-C	13.74 ± 3.96	−2.13 ± 1.68	8.18 ± 1.78	0.01 ± 1.30	5.56 ± 3.42	−2.13 ± 1.63	2.27 ± 1.06	−0.35 ± 0.28
3	Allen-S	Doorenbos-L	13.74 ± 3.96	−2.13 ± 1.68	5.87 ± 1.90	−2.30 ± 1.41	7.87 ± 3.16	0.18 ± 1.68	2.65 ± 1.01	0.03 ± 0.28
4	Allen-S	Doorenbos-LC	13.74 ± 3.96	−2.13 ± 1.68	8.17 ± 1.78	0.00 ± 1.30	5.57 ± 3.43	−2.13 ± 1.64	2.28 ± 1.06	−0.34 ± 0.28
5	Allen-SC	Allen-L	15.97 ± 4.51	0.11 ± 1.75	4.20 ± 1.57	−3.97 ± 1.43	11.77 ± 4.05	4.08 ± 1.96	3.28 ± 1.11	0.66 ± 0.33
6	Allen-SC	Allen-LC	15.97 ± 4.51	0.11 ± 1.75	8.18 ± 1.78	0.01 ± 1.30	7.79 ± 3.98	0.1 ± 1.88	2.64 ± 1.12	0.02 ± 0.32
7	Allen-SC	Doorenbos-L	15.97 ± 4.51	0.11 ± 1.75	5.87 ± 1.90	−2.30 ± 1.41	10.10 ± 3.71	2.41 ± 1.84	3.01 ± 1.07	0.39 ± 0.31
8	Allen-SC	Doorenbos-LC	15.97 ± 4.51	0.11 ± 1.75	8.17 ± 1.78	0.00 ± 1.30	7.80 ± 3.98	0.11 ± 1.89	2.64 ± 1.12	0.02 ± 0.32
9	Gopinathan-S	Allen-L	13.26 ± 5.37	−2.61 ± 2.49	4.20 ± 1.57	−3.97 ± 1.43	9.06 ± 4.32	1.37 ± 2.72	2.84 ± 1.19	0.22 ± 0.45
10	Gopinathan-S	Allen-LC	13.26 ± 5.37	−2.61 ± 2.49	8.18 ± 1.78	0.01 ± 1.30	5.08 ± 4.19	−2.61 ± 2.56	2.19 ± 1.19	−0.43 ± 0.43
11	Gopinathan-S	Doorenbos-L	13.26 ± 5.37	−2.61 ± 2.49	5.87 ± 1.90	−2.3 ± 1.41	7.39 ± 3.91	−0.3 ± 2.48	2.57 ± 1.14	−0.05 ± 0.41
12	Gopinathan-S	Doorenbos-LC	13.26 ± 5.37	−2.61 ± 2.49	8.17 ± 1.78	0.00 ± 1.30	5.09 ± 4.12	−2.6 ± 2.56	2.19 ± 1.19	−0.42 ± 0.43
13	Liu-S	Allen-L	14.93 ± 4.49	−0.94 ± 1.69	4.20 ± 1.57	−3.97 ± 1.43	10.73 ± 3.88	3.03 ± 1.88	3.11 ± 1.11	0.49 ± 0.32
14	Liu-S	Allen-LC	14.93 ± 4.49	−0.94 ± 1.69	8.18 ± 1.78	0.01 ± 1.30	6.75 ± 3.80	−0.94 ± 1.78	2.47 ± 1.11	−0.15 ± 0.30
15	Liu-S	Doorenbos-L	14.93 ± 4.49	−0.94 ± 1.69	5.87 ± 1.90	−2.3 ± 1.41	9.06 ± 3.53	1.37 ± 1.73	2.84 ± 1.06	0.22 ± 0.29
16	Liu-S	Doorenbos-LC	14.93 ± 4.49	−0.94 ± 1.69	8.17 ± 1.78	0.00 ± 1.30	6.76 ± 3.81	−0.93 ± 1.78	2.47 ± 1.11	−0.15 ± 0.30

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