Evapotranspiration Partitioning and Estimation Based on Crop Coefficients of Winter Wheat Cropland in the Guanzhong Plain, China

Abstract

Accurate estimation and effective portioning of actual evapotranspiration (${\mathrm{ET}}_{\mathrm{a}}$) into soil evaporation (E) and plant transpiration (T) are important for increasing water use efficiency (WUE) and optimizing irrigation schedules in croplands. In this study, E/T partitioning was performed on ${\mathrm{ET}}_{\mathrm{a}}$ rates measured using the eddy covariance (EC) technique in three winter wheat growing seasons from October 2020 to June 2023. The variation in the crop coefficients (${\mathrm{K}}_{\mathrm{c}}$, α, and ${\mathrm{K}}_{\mathrm{Hc}}$) were quantified by combining the ${\mathrm{ET}}_{\mathrm{a}}$ and reference evapotranspiration rates using the Penman–Monteith, Priestley–Taylor, and Hargreaves equations. In addition, the application of models based on the modified crop coefficient (${\mathrm{K}}_{\mathrm{c}}$, α, and ${\mathrm{K}}_{\mathrm{Hc}}$) was proposed to estimate the ${\mathrm{ET}}_{\mathrm{a}}$ rates. According to the obtained results, the average cumulative ${\mathrm{ET}}_{\mathrm{a}}$, T, and E rates in the three winter wheat growth seasons were 471.4, 265.2, and 206.3 mm, respectively. The average T/${\mathrm{ET}}_{\mathrm{a}}$ ratio ranged from 0.16 to 0.72 at the different winter wheat growth stages. Vapor pressure deficit (VPD) affected the ${\mathrm{ET}}_{\mathrm{a}}$ rates at a threshold of 1.27 KPa. The average ${\mathrm{K}}_{\mathrm{c}}$, α, and ${\mathrm{K}}_{\mathrm{Hc}}$ values in the middle stage were 1.34, 1.54, and 1.21, respectively. The measured ${\mathrm{ET}}_{\mathrm{a}}$ rates and ${\mathrm{ET}}_{\mathrm{a}}$ rates estimated using the adjusted ${\mathrm{K}}_{\mathrm{c}}$, α, and ${\mathrm{K}}_{\mathrm{Hc}}$ showed regression slope coefficients of 0.96, 0.99, and 0.96, and coefficients of determination (R²) of 0.92, 0.93, and 0.90, respectively. Therefore, the Priestley–Taylor-equation-based adjusted crop coefficient is recommended. The adjusted crop-coefficient-based models can be used as valuable tools for local policymakers to effectively improve water use.

1. Introduction

Evapotranspiration (ET) is a crucial component of the water balance in various agricultural ecosystems and an important link between energy, water, and carbon cycles. In addition, ET is the main factor controlling the dynamic relationship between crop growth and water balance, providing valuable insights into irrigation practices in agroecosystems [1,2,3]. Indeed, about 99% of water in croplands may be lost through the ET process [4]. Evapotranspiration includes soil evaporation (E), plant transpiration (T), and canopy interception evaporation. Several researchers have used T to assess water use efficiency (WUE) and water productivity [5]. Reducing E rates is an important water-saving measure to increase water productivity in croplands, especially in arid and semi-arid agricultural regions [6]. Accurate quantification of ET and effective partitioning between E and T are, therefore, critical. Many studies have assessed the T/ET or E/ET portioning in order to determine effective measures to improve wheat water use efficiency [7,8,9,10,11,12].

Kool et al. [13] showed a wheat T/ET ratio range of 0–0.90 using the ET partitioning method. However, it should be noted that wheat E/T ratios vary greatly depending on the wheat phenological phases [14]. Indeed, several methods can be used to efficiently determine the E and T rates, including direct measurement methods, which involve mainly the determination of the ET and E rates through lysimeter and microlysimeter measurements under the wheat canopy [9,15]. However, to maintain soil conditions inside lysimeters consistent with those outside, soils inside lysimeters need to be replaced every one to two days [16]. Moreover, it is difficult to measure accurately and continuously the daily E rates under precipitation events. On the other hand, the E and T rates can be determined by measuring the plant T rates using the sap flow measurement method. Indeed, this method has been commonly used to estimate the T values in orchards [17] and row crops, such as maize [18]. However, there is still no validated sap flow measurement technique for wheat crops. In addition, although the E and T rates can be determined based on their specific isotopic values (¹⁸O and D) of the total ET flux [11], this method is costly, labor-intensive, and has low temporal resolution [19]. Therefore, indirect measurements can be used as alternative methods to achieve ET partitioning [20]. The absorption and assimilation of carbon dioxide and water losses by T, involved in the photosynthesis process of higher plants, are regulated through stomata and intrinsically linked [21]. Zhou et al. [22] showed that ET is closely related to gross primary production (GPP) and vapor pressure deficit (VPD). In addition, they proposed a potential water use efficiency (uWUE) model based on these parameters using data collected every 30 min from 42 AmeriFlux stations and demonstrated approximatively linear relationships between the ET rates and ${\mathrm{VPD}}^{0.5}$ during the vigorous crop growth stage, in which T accounts for most of the ET. Since the variations in the T and ET rates can induce changes in the uWUE results, the uWUE model is used to achieve ET partitioning based on the principle of the water–carbon coupling processes, particularly when the uWUE values are correlated with the T rates as a relative fraction of ET [23].

Accurate estimation of ET is a prerequisite for optimizing cropland water management measures, determining crop water consumption, and establishing reasonable irrigation schedules [14]. Several researchers have assessed actual evapotranspiration (${\mathrm{ET}}_{\mathrm{a}}$) of wheat using the lysimeter measurement [9,24], water balance [7,10] or soil water balance [11,15], Bowen ratio energy balance [25], and eddy covariance (EC) [8,26] methods. Among these methods, the EC technique is a micrometeorological method that has been commonly used for assessing the turbulent exchanges of water, energy, and trace gases between the land surface and atmosphere, as it is a direct and reliable flux measurement method [27]. The obtained wheat ${\mathrm{ET}}_{\mathrm{a}}$ rates using the above-mentioned measurement methods were very different, showing a cumulative ${\mathrm{ET}}_{\mathrm{a}}$ range for the entire wheat growing season of 192–486 mm. These differences in the ${\mathrm{ET}}_{\mathrm{a}}$ rates may be mainly owing to several factors, including the spatial differences in the climatic conditions, crop variety, crop growth seasons, and agricultural management practices (e.g., fertilization, irrigation, and tillage methods). Among them, climatic conditions, such as solar radiation, air temperature, VPD, and wind speed, may exhibit the greatest influence on the ${\mathrm{ET}}_{\mathrm{a}}$ rates [28,29].

As direct spatiotemporal measurements of ${\mathrm{ET}}_{\mathrm{a}}$ are difficult and costly, many mathematical models have been proposed to estimate ${\mathrm{ET}}_{\mathrm{a}}$ rates [25,30,31]. The FAO-56 crop coefficient model has been widely applied in estimating ${\mathrm{ET}}_{\mathrm{a}}$ because of its convenience, ease of operation, and good repeatability [14]. In this model, ${\mathrm{ET}}_{\mathrm{a}}$ is calculated by multiplying the reference evapotranspiration (${\mathrm{ET}}_0$) by a specific crop coefficient (${\mathrm{K}}_{\mathrm{c}}$). The ${\mathrm{ET}}_0$ rates can be estimated using single or combined temperature-based, radiation-based, and pan-based evaporation equations [32]. Indeed, the temperature-based equation represented by the Hargreaves (HS) equation [33] can be used when only air temperature data are available. Whereas the radiation-based approach represented by the Priestley–Taylor (PT) equation [34] is a simplified version of the Penman–Monteith (PM) equation [14] that can be applied using only radiation data without considering aerodynamic data (e.g., wind speed and vapor pressure deficit data). The most widely used equation for ${\mathrm{K}}_{\mathrm{c}}$ calculation was the PM equation [14]. Because ${\mathrm{K}}_{\mathrm{c}}$ values can vary according to different growth stages of crops, it is important to calculate the specific ${\mathrm{K}}_{\mathrm{c}}$ values of different crop growth stages to accurately estimate the ${\mathrm{ET}}_{\mathrm{a}}$ rates. Kang et al. [9] reported the average monthly ${\mathrm{K}}_{\mathrm{c}}$ during 1987–1997 for lysimeter-based ${\mathrm{ET}}_{\mathrm{a}}$ values and PM-equation-based ${\mathrm{ET}}_0$ values, but the feasibility of ${\mathrm{ET}}_0$ calculation methods with fewer meteorological parameters has not been verified.

The Guanzhong Plain is an important grain production area in Shaanxi Province, China, contributing about two-thirds of the province’s total crop output [35,36]. Wang et al. [37] previously achieved evapotranspiration partitioning and ${\mathrm{K}}_{\mathrm{c}}$ estimations of maize cropland in the Guanzhong Plain. In the present study, the EC method was used to assess the energy, water, and carbon fluxes of a typical winter wheat cropland in the Guanzhong Plain during the period from October 2020 to June 2023, taking into account the different growth stages of winter wheat. Specifically, the present study aims to (1) quantify the seasonal dynamic changes in the E, T, and ${\mathrm{ET}}_{\mathrm{a}}$ rates of the winter wheat cropland; (2) determine the winter wheat ${\mathrm{K}}_{\mathrm{c}}$ value using comparisons of the ${\mathrm{ET}}_{\mathrm{a}}$ versus ${\mathrm{ET}}_0$ values from estimation equations (PM, PT, and HS) at different winter wheat growth stages; and (3) evaluate the accuracies of the three revised ${\mathrm{K}}_{\mathrm{c}}$ estimation equations.

2. Materials and Methods

2.1. Study Site Description

In this study, a field experiment with three winter wheat growing seasons was conducted from October 2020 to June 2023 in the cropland of the Key Laboratory of Agricultural Water and Soil Engineering of the Ministry of Education of Northwest A&F University in Yangling, Shaanxi Province (108°04′07″ E; 34°17′45″ N) (Figure 1). The study region is prone to climatic drought events, characterized by a semi-humid climate, with an average annual sunshine duration, average annual temperature, and frost-free period of more than 2000 h, 12.9 °C, and more than 210 days, respectively. In addition, the average annual precipitation amount over the 1995–2014 period was 560 mm, of which about 65% occurred from June to September, while the average annual pan evaporation was 1500 mm [38]. The dimension of the experimental site was approximately 200 m (north to south) × 250 m (east to west), located at 521 m above sea level. The soil of the experiment site is classified as a silty clay loam texture, according to the USDA soil classification system, with a field capacity and bulk density of 23.5% (mass moisture content) and 1.35 g${\mathrm{cm}}^{-3}$, respectively [39]. The withering moisture content is 8.5% (mass moisture content). The groundwater level in the study region is above 50 m [38], indicating negligible water supply from groundwater.

The experimental site has been continuously conducted over two crop rotation systems in the study site since 2001, including winter wheat (Triticum aestivum L.) and summer maize (Zea mays L.). In addition, straw was chopped by agricultural machinery into fragments of less than 5 cm in length and returned in each crop growing season to the field following harvest. The 0–30 cm soil layer of the experiment site was first plowed once a year following the harvest of maize, then seeds were sown mechanically. In this study, the winter wheat growing season was from mid-to-late October to early June of the following year, with a row spacing of 10 to 15 cm. In addition, a special amino acid calcium combined fertilizer, containing 172.5 kg N ${\mathrm{ha}}^{-1}$, was applied in the winter wheat growing seasons while sowing.

2.2. Meteorological Data and Carbon Flux Measurements

The carbon flux measurement data were obtained from the installed open-path EC device (Figure 1) during the winter wheat seasons at a 2 m height. The device consisted of a three-dimensional wind system (CSAT3, Campbell Scientific., Inc., Logan, UT, USA) for measuring the three components of wind speed and an infrared gas analyzer (IRGA; LI-7500, LI-COR, Inc., Lincoln, NE, USA) for measuring virtual temperature, carbon dioxide fluxes, and water vapor densities. The data were recorded at a frequency of 10 Hz and stored on a 16 GB USB flash drive every 30 min through a LI 7550 box (Campbell Scientific Inc.). In addition, zero and span calibrations were performed semi-annually. Solar radiation (${\mathrm{R}}_{\mathrm{s}}$) and net solar radiation (${\mathrm{R}}_{\mathrm{n}}$) were measured by a four-component radiation sensor (CNR1, Kipp & Zonen, Corp., Delft, The Netherlands) at a 2 m height. Wind speed (${\mathrm{U}}_2$) and wind direction data at 2 m were determined using propeller anemometers (R.M. Young model 03002-5, available from Campbell Scientific, Logan, UT, USA). At the same time, air temperature (${\mathrm{T}}_{\mathrm{air}}$) and relative humidity (RH) were measured at 2 m (HMP-60, Vaisala, Vantaa, Finland), while the precipitation (P) amounts were obtained using a tipping bucket rain gauge (TE525MM-L, Campbell Scientific) at a height of 2 m. Irrigation (I) was measured with an ultrasonic flowmeter (TDS-100P, Haozhi Xinyuan Science and Technology Development Co., Ltd., Beijing, China). The soil temperature and soil water contents (SWCs) were measured at four soil depths (10, 20, 40, and 60 cm) using a time-domain reflectometer (TDR-310s, Beijing Bolun Jingwei Technology Development Co., Ltd., Beijing, China). However, it should be noted that the soil temperature and humidity sensors experienced damage from 12 October 2021 to 13 January 2022. All the meteorological data were recorded using a data collector (Model CR1000) and compiled as 30 min average values. The vapor pressure deficit (VPD) values were calculated using 30 min ${\mathrm{T}}_{\mathrm{air}}$ and RH data according to the method described by Campbell and Norman [40].

2.3. Leaf Area Index Measurements

The leaf area index (LAI) was determined using a plant sampling method. Briefly, five evenly distributed points were first selected in the experimental field around the southern part of the flux tower, then about 5–10 plants were collected from each point [41]. The length and maximum width of green leaves were measured manually every 6–15 days, depending on the maize growth status. Indeed, the area of a single leaf was equal to the length of the green leaf multiplied by the maximum width multiplied by a shape factor (0.74) (Mckee [42]). The total leaf area was equal to the sum of the single leaf areas. The LAI values were determined by dividing the green leaf area by its occupied area. On the other hand, the LAI values during the wheat growing season were determined every 5–15 days using a canopy analyzer with 5 sampling points in each point to the winter wheat growth and developmental status (LAI-2200c, LI-COR Inc., Lincoln, NE, USA). Five LAI values were determined from each sampling point and averaged.

2.4. Flux Data Processing

In this study, the 10 Hz raw data processing, including outlier filtering [43], coordinate rotations (secondary rotation method) [44], sensor separation corrections [45], spectral corrections, Webb–Pearman–Leuning (WPL) calibrations [46], and 30 min block averaging [47], were performed using EddyPro 7.0.4 (LI-COR Inc.). The 0-1-2 system was used for assessing data quality and removing low-quality throughput data, with quality flag 2. Low-mass flux data were filtered based on a friction wind velocity threshold of 0.15 $\mathrm{m}{\mathrm{s}}^{-1}$ [48]. The missing values were filled in this study using the REddyProc package, according to the method described by Wutzler et al. [49]. In addition, the relationship between the daily sensible (H) and latent heat (LE) fluxes was assessed using regression analysis, while the difference between the daily net radiative flux and soil heat flux (${\mathrm{R}}_{\mathrm{n}}$ − G) was determined to evaluate the energy balance closure (EBC) and quality of the data collected from the winter wheat growing seasons. The proposed Bowen ratio method by Twine et al. [50] was used in this study to overcome the energy imbalance problem and adjust the ${\mathrm{ET}}_{\mathrm{a}}$ data.

Net ecosystem exchange (NEE) data were portioned using the short-term temperature response method [51]. The nocturnal deviations were estimated using the temperature response function of TER [52], while the diurnal deviations were estimated based on the NEE-photosynthetic photon flux density (Q) relationship [53]. After interpolation of NEE and TER, the gross primary production (GPP) ($\mathrm{g}\mathrm{C}{\mathrm{m}}^{-2}{\mathrm{day}}^{-1}$) of the ecosystem was calculated using the following formula:

$$\mathrm{GPP}=\mathrm{TER}-\mathrm{NEE}$$

(1)

2.5. Evapotranspiration Partitioning

According to Zhou et al. [22], the ${\mathrm{uWUE}}_{\mathrm{i}}$ values can be determined according to the influence of VPD on the potential water use efficiency (${\mathrm{uWUE}}_{\mathrm{i}}$) at the leaf scale using the following formula:

$${\mathrm{uWUE}}_{\mathrm{i}}=\frac{\mathrm{A}\sqrt{\mathrm{VPD}}}{\mathrm{T}}$$

(2)

where ${\mathrm{uWUE}}_{\mathrm{i}}$ is approximately constant at the leaf scale, while VPD is almost constant from the leaf scale to the ecosystem scale under a unified underlying surface environment; A denotes the assimilated carbon amount. Indeed, the cumulative amounts of carbon assimilation in ecosystems are represented by GPP [54]. It is assumed that the potential water use efficiency (${\mathrm{uWUE}}_{\mathrm{p}}$) is related to T, while the ecosystem apparent water use efficiency (${\mathrm{uWUE}}_{\mathrm{a}}$) is related to ET. Therefore, ${\mathrm{uWUE}}_{\mathrm{p}}$ and ${\mathrm{uWUE}}_{\mathrm{a}}$ can be calculated using the following formulas:

$${\mathrm{uWUE}}_{\mathrm{p}}=\frac{\mathrm{GPP}\sqrt{\mathrm{VPD}}}{\mathrm{T}}$$

(3)

$${\mathrm{uWUE}}_{\mathrm{a}}=\frac{\mathrm{GPP}\sqrt{\mathrm{VPD}}}{{\mathrm{ET}}_{\mathrm{a}}}$$

(4)

where ${\mathrm{ET}}_{\mathrm{a}}$ denotes the actual evapotranspiration rate measured using the EC system. According to Equations (3) and (4), it can be deduced that T/ET can be determined using the ${\mathrm{uWUE}}_{\mathrm{a}}$ to ${\mathrm{uWUE}}_{\mathrm{p}}$ ratio, according to the following formula:

$$\frac{\mathrm{T}}{\mathrm{ET}}=\frac{{\mathrm{uWUE}}_{\mathrm{a}}}{{\mathrm{uWUE}}_{\mathrm{p}}}$$

(5)

where ${\mathrm{uWUE}}_{\mathrm{p}}$ can be estimated using the 95th quantile regression between GPP∙${\mathrm{VPD}}^{0.5}$ and ${\mathrm{ET}}_{\mathrm{a}}$ [54].

In addition, soil evaporation (E) was calculated using the following formula:

$$\mathrm{E}=\mathrm{ET}-\mathrm{T}$$

(6)

2.6. Evapotranspiration Estimation

In this study, the PM [14], PT [34], and HS [33] equations were used to calculate the winter wheat reference ET. In addition, the corresponding ${\mathrm{K}}_{\mathrm{c}}$ values were adjusted in this study according to the different growth stages of the cultivated winter wheat for ${\mathrm{ET}}_{\mathrm{a}}$ estimation.

The PM-based reference ET amounts were calculated as follows:

$${\mathrm{ET}}_0=\frac{0.408\Delta ({\mathrm{R}}_{\mathrm{n}}-\mathrm{G})+900{\mathrm{U}}_2\cdot \mathsf{\gamma }\cdot \mathrm{VPD}/({\mathrm{T}}_{\mathrm{a}}{}_{\mathrm{ir}}+273.3)}{\Delta +\mathsf{\gamma }(1+0.34{\mathrm{U}}_2)}$$

(7)

where ${\mathrm{ET}}_0$ denotes the reference crop ET ($\mathrm{mm}{\mathrm{d}}^{-1}$); ${\mathrm{R}}_{\mathrm{n}}$ denotes the net solar radiation ($\mathrm{MJ}{\mathrm{m}}^{-2}{\mathrm{day}}^{-1}$); G denotes the soil heat flux ($\mathrm{MJ}{\mathrm{m}}^{-2}{\mathrm{day}}^{-1}$); ${\mathrm{T}}_{\mathrm{air}}$ denotes the air temperature ($°\mathrm{C}$); ${\mathrm{U}}_2$ denotes the wind speed at 2 m ($\mathrm{m}{\mathrm{s}}^{-1}$); VPD denotes the vapor pressure deficit (KPa); $\mathsf{\Delta }$ denotes the slope of the water vapor pressure curve ($\mathrm{KPa}{°\mathrm{C}}^{-1}$); $\mathsf{\gamma }$ denotes a psychrometer constant ($\mathrm{KPa}{°\mathrm{C}}^{-1}$).

The PM-based ${\mathrm{K}}_{\mathrm{c}}$ values were determined using the following formula:

$${\mathrm{K}}_{\mathrm{c}}=\frac{{\mathrm{ET}}_{\mathrm{a}}}{{\mathrm{ET}}_0}$$

(8)

The PT-based reference ET rates were determined using the following formula:

$${\mathrm{ET}}_{\mathrm{eq}}=\frac{\mathsf{\Delta }}{\mathsf{\Delta }+\mathsf{\gamma }}\left({\mathrm{R}}_{\mathrm{n}}-\mathrm{G}\right)$$

(9)

The PT coefficient (α) is often used to determine whether the limiting factor of ET is atmospheric demand or surface water supply. Indeed, α values greater than 1 suggest that (${\mathrm{R}}_{\mathrm{n}}$ − G) is the main limiting factor of ET [55]. In the present study, α was calculated as follows:

$$\mathsf{\alpha }=\frac{{\mathrm{ET}}_{\mathrm{a}}}{{\mathrm{ET}}_{\mathrm{eq}}}$$

(10)

On the other hand, the ET calculation using the HS equation was mainly based on the radiation and air temperature data according to the following equation:

$${\mathrm{ET}}_{\mathrm{H}}=0.0135\times {\mathrm{R}}_{\mathrm{s}}{(\mathrm{T}}_{\mathrm{air}}+17.8)$$

(11)

where ${\mathrm{R}}_{\mathrm{s}}$ denotes the solar radiation ($\mathrm{mm}{\mathrm{day}}^{-1}$).

The HS-based Kc values were calculated as follows:

$${\mathrm{K}}_{\mathrm{Hc}}=\frac{{\mathrm{ET}}_{\mathrm{a}}}{{\mathrm{ET}}_{\mathrm{H}}}$$

(12)

2.7. Statistical Analysis

In this study, Pearson correlation analysis and two-tailed significance tests were performed using SPSS software (Version 22, IBM Corp., Armonk, NY, USA) to assess the relationships between the ET rates and the measured environmental biological drivers (i.e., ${\mathrm{T}}_{\mathrm{air}}$, ${\mathrm{T}}_{\max }$, ${\mathrm{T}}_{\min }$, G, ${\mathrm{R}}_{\mathrm{n}}$, VPD, ${\mathrm{U}}_2$, ${\mathrm{SWC}}_{10}$, ${\mathrm{SWC}}_{20}$, ${\mathrm{SWC}}_{40}$, ${\mathrm{SWC}}_{60}$, P, and LAI). In addition, the regression between the GPP∙${\mathrm{VPD}}^{0.5}$ and ${\mathrm{ET}}_{\mathrm{a}}$ values was calculated at the 95th quantile using the R statistical computing environment (version 4.2.0) for ${\mathrm{ET}}_{\mathrm{a}}$ partitioning. All graphs were generated using Origin software (2023a, OriginLab, Northampton, MA, USA). On the other hand, the estimation performance of ${\mathrm{ET}}_{\mathrm{a}}$ was evaluated by using root mean square deviation (RMSD), relative RMSD (RRMSD), and mean deviation (MD) according to the following equations:

$$\mathrm{RMSD}=\sqrt{\frac{1}{\mathrm{n}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{{(\mathrm{ET}}_{\mathrm{ei}}{-\mathrm{ET}}_{\mathrm{ai}})}^2}}$$

(13)

$$\mathrm{RRMSD}=\frac{\mathrm{RMSD}}{{\mathrm{ET}}_{\mathrm{average}}}$$

(14)

$$\mathrm{MD}=\frac{1}{\mathrm{n}}{\displaystyle \sum {(\mathrm{ET}}_{\mathrm{ei}}{-\mathrm{ET}}_{\mathrm{ai}})}$$

(15)

where ${\mathrm{ET}}_{\mathrm{ei}}$ denotes the estimated i-th ET value, ${\mathrm{ET}}_{\mathrm{ai}}$ denotes the observed ith ET value, ${\mathrm{ET}}_{\mathrm{average}}$ denotes the average observed ET value, and n denotes the number of samples. Coefficients of determination (R²) equal or close to 1 and RMSD, RRMSD, and MD values close to 0 indicate good estimation accuracy of the models.

3. Results

3.1. Variation in the Measured Environmental Variables

Figure 2 shows the seasonal dynamic changes in the measured environmental variables (${\mathrm{T}}_{\mathrm{air}}$, ${\mathrm{T}}_{\max }$, ${\mathrm{T}}_{\min }$, ${\mathrm{R}}_{\mathrm{s}}$, ${\mathrm{R}}_{\mathrm{n}}$, VPD, ${\mathrm{U}}_2$, ${\mathrm{SWC}}_{10}$, ${\mathrm{SWC}}_{20}$, ${\mathrm{SWC}}_{40}$, ${\mathrm{SWC}}_{60}$, P, and I) and LAI values over the three winter wheat growing seasons.

Table 1. Energy fluxes, meteorological characteristics, and leaf area index (LAI) average values at different growth stages during the 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons.

	Growth Stage	Period (Month/Day/Year)	Days after Sowing	Rn (MJ m−2)	LE (MJ m−2)	Tair (°C)	VPD (kPa)	P + I (mm)	SWC (m3 m−3)	LAImax (m2 m−2)
2020–2021 Winter wheat	Ini	22 October 2020–11 December 2020	0–50	127.9	125.3	7.3	0.32	44 + 0	25.5	0.11
	Ove	12 December 2020–14 February 2021	51–115	114.0	124.6	1.7	0.40	2 + 90	24.5	0.38
	Dev	15 February 2021–5 April 2021	116–165	265.7	253.7	9.5	0.46	39 + 0	20.9	4.7
	Mid	6 April 2021–25 May 2021	166–215	521.4	534.5	16.4	0.64	97 + 0	20.1	6.23
	Lat	26 May 2021–8 June 2021	216–229	202.0	159.5	23.9	1.87	3 + 0	15.6	5.38
	Seasonal	22 October 2020–8 June 2021	0–229	1231.0	1197.6	9.2	0.52	185 + 90	22.4	6.23
2021–2022 Winter wheat	Ini		0–50	153.2	106.3	7.1	0.39	11 + 0		0.10
	Ove	23 October 2021–12 December 2021	51–115	137.9	99.5	1.2	0.24	23 + 90		0.32
	Dev	13 December 2021–15 February 2022	116–165	338.9	290.9	9.9	0.59	31 + 0	29.3	4.1
	Mid	16 February 2022–6 April 2022	166–215	588.0	521.6	17.1	0.78	97 + 0	26.1	5.01
	Lat	7 April 2022–26 May 2022	216–229	170.4	84.6	23.6	1.56	13 + 0	24.7	4.17
	Seasonal	27 May 2022–9 June 2022	0–229	1388.3	1102.9	9.2	0.53	174 + 90		5.01
2022–2023 Winter wheat	Ini	23 October 2021–9 June 2022	0–50	108.7	98.7	8.1	0.24	17 + 0	29.2	0.07
	Ove		51–115	121.9	104.2	1.0	0.36	7 + 90	28.9	0.35
	Dev	20 October 2022–9 December 2022	116–165	306.7	243.3	9.1	0.54	81 + 0	28.2	4.4
	Mid	10 December 2022–12 February 2023	166–215	531.0	523.4	16.2	0.72	74 + 0	27.2	5.94
	Lat	13 February 2023–3 April 2023	216–230	125.5	74.6	18.7	0.48	121 + 0	28.2	4.97
	Seasonal	4 April 2023–23 May 2023	0–230	1193.7	1044.3	8.7	0.45	300 + 90	28.3	5.94

N.B.: Ini, Ove, Dev, Mid, and Lat denote the initial, overwintering, development, middle, and late winter wheat growth stages, respectively. The initial stage represents the period from winter wheat sowing to the start of the overwintering stage. The development stage represents the beginning of the reviving stage to the end of the jointing stage. The middle stage represents the beginning of booting to the end of the grain-fill stage. T late stage represents the beginning of the winter wheat maturity to harvest. ${\mathrm{R}}_{\mathrm{n}}$, LE, ${\mathrm{T}}_{\mathrm{air}}$, VPD, P, I, SWC, and ${\mathrm{LAI}}_{\max }$ denote net radiation, latent heat flux, air temperature, vapor pressure deficit, precipitation, irrigation, average SWC in the 0–60 cm layer, and maximum leaf area index, respectively.

shows the main energy, climatic, and soil moisture characteristics at each growth stage in the winter wheat growing seasons. During the observation period, the ${\mathrm{T}}_{\max }$, ${\mathrm{T}}_{\min }$, and ${\mathrm{T}}_{\mathrm{air}}$ values ranged from −4.3 to 37.5 °C, −12.3 to 20.9 °C, and −7.1 to 28.6 °C, respectively (Figure 2a). The lowest ${\mathrm{T}}_{\mathrm{air}}$ was observed at the overwintering stage of the winter wheat growing seasons, with an average ${\mathrm{T}}_{\mathrm{air}}$ range of 1.0–1.7 °C. The highest average ${\mathrm{T}}_{\mathrm{air}}$ value at the late stage over the winter wheat seasons ranged from 18.7 to 23.9 °C (Table 1). On the other hand, similar seasonal variation trends of ${\mathrm{R}}_{\mathrm{s}},{\mathrm{R}}_{\mathrm{n}}$, and VPD were observed, showing the highest values at the middle and late stages of the cultivated winter wheat. The average daily ${\mathrm{R}}_{\mathrm{s}},{\mathrm{R}}_{\mathrm{n}}$, and VPD values were about 300, 200, and 1.5 KPa, respectively (Figure 2b). The highest cumulative ${\mathrm{R}}_{\mathrm{n}}$ and LE values of the winter wheat growing seasons were observed during the middle stage, exceeding 500 $\mathrm{MJ}{\mathrm{m}}^{-2}$. The average VPD value at this stage ranged from 0.64 to 0.78 KPa (Table 1). However, ${\mathrm{U}}_2$ had no obvious seasonal variation, showing an average daily range of 0.2–3.5 $\mathrm{m}{\mathrm{s}}^{-1}$ over the observation period (Figure 2c). In the experiment, irrigation was applied annually at the overwintering stage at a rate of 90 mm, maintaining high SWCs over the winter wheat growing seasons without experiencing water stress (Figure 2d). The cumulative P amounts in the 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons were 185, 174, and 300 mm, respectively. Except for the high P amount (121 mm) at the late stage of the 2022–2023 winter wheat season, the P amounts were mainly concentrated at the middle stage of the winter wheat growing seasons, with an average amount of 97 mm (Table 1). There was an increasing trend in the winter wheat LAI that began after the overwintering stage, reaching its peak value at the middle stage (Figure 2e). The ${\mathrm{LAI}}_{\max }$ values of the 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons were 6.23, 5.01, and 5.94 ${\mathrm{m}}^2{\mathrm{m}}^{-2}$, respectively.

Figure 3 shows the energy balance closure (linear regression between H + LE and ${\mathrm{R}}_{\mathrm{n}}$ − G) during the winter wheat growing seasons. The R² value of the winter wheat growing seasons ranged from 0.93 to 0.97 (

Table 2. Energy balance closure analysis of turbulent fluxes (H + LE) and available energy (${\mathrm{R}}_{\mathrm{n}}$ − G) during the 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons.

Winter Wheat Growing Season	Slope	Intercept	${\mathbf{R}}^2$
22 October 2020–8 June 2021	1.02	5.08	0.97
23 October 2021–9 June 2022	0.98	0.01	0.96
20 October 2022–7 June 2023	1.00	4.01	0.93
Average	0.996	3.25	0.95

). The three-year average slope, intercept, and ${\mathrm{R}}^2$ values were 0.996, 3.25 $\mathrm{W}{\mathrm{m}}^2$, and 0.95, respectively (Figure 3), indicating a good energy balance closure. The average daily half-hour ${\mathrm{R}}_{\mathrm{n}}$, LE, H, and G values of each winter wheat growing season showed typical unimodal changes (Figure 4). The ${\mathrm{R}}_{\mathrm{n}}$ and LE peaks were observed at 13:00, while the H peak appeared 30 min (Figure 4b,c) or 1 h (Figure 4a) earlier. However, the G peak showed an obvious time lag (14:00). The H peak value was substantially lower than that of LE. The average daily half-hour ${\mathrm{R}}_{\mathrm{n}}$, LE, H, and G peak ranges were 320.1–374.3, 170.6–193.0, 70.6–87.8, and 35.7–50.9 $\mathrm{W}{\mathrm{m}}^2$, respectively (Figure 4).

3.2. Seasonal Dynamics of the Evapotranspiration, Transpiration, and Soil Evaporation Rates

Figure 5 shows the results of the 95th quantile regression between the half-hour GPP∙${\mathrm{VPD}}^{0.5}$ and measured ET data. There was a linear relationship between the GPP∙${\mathrm{VPD}}^{0.5}$ and EC measured ET values. Indeed, the influence of the ET rates on the GPP∙${\mathrm{VPD}}^{0.5}$ values can be well characterized by the regression slope at the 95th quantile (Figure 5). Therefore, it is reasonable to estimate the ${\mathrm{uWUE}}_{\mathrm{p}}$ values using the quantile regression method applied to the half-hourly data of fluxes. The obtained results showed relatively similar ${\mathrm{uWUE}}_{\mathrm{p}}$ values in the three-year winter wheat growing seasons of 12.75, 13.30, and 12.80 $\mathrm{g}\mathrm{C}·\mathrm{h}{\mathrm{Pa}}^{0.5}/\mathrm{kg}{\mathrm{H}}_2\mathrm{O}$, respectively (Figure 5a–c), with a three-year average ${\mathrm{uWUE}}_{\mathrm{p}}$ value of 13.17 $\mathrm{g}\mathrm{C}·\mathrm{h}{\mathrm{Pa}}^{0.5}/\mathrm{kg}{\mathrm{H}}_2\mathrm{O}$ (Figure 5d).

The T and ${\mathrm{ET}}_{\mathrm{a}}$ values by the EC system showed similar seasonal dynamic changes in the three winter wheat growing seasons. In contrast, the E values exhibited a seasonal variation pattern opposite to that of the T values (Figure 6). The results showed continuous low ${\mathrm{ET}}_{\mathrm{a}}$ and T values over the initial and overwintering stages of the cultivated winter wheat, showing the highest daily values of 3 and 1 $\mathrm{mm}{\mathrm{day}}^{-1}$, respectively. Whereas the E/${\mathrm{ET}}_{\mathrm{a}}$ ratio values ranged from 0.81 to 0.88 and 0.61 to 0.81 at the initial and overwintering stages, respectively (

Table 3. Cumulative actual evapotranspiration (${\mathrm{ET}}_{\mathrm{a}}$), transpiration (T), evaporation (E), T$/{\mathrm{ET}}_{\mathrm{a}}$, and E$/{\mathrm{ET}}_{\mathrm{a}}$ values of the 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons.

	Growth Stage	${\mathbf{ET}}_{\mathbf{a}}$ (mm)	T (mm)	E (mm)	$\mathbf{T}/{\mathbf{ET}}_{\mathbf{a}}$	$\mathbf{E}/{\mathbf{ET}}_{\mathbf{a}}$
2020–2021 winter wheat growing season	Ini	55.2	8.4	46.8	0.15	0.85
	Ove	58.5	23.1	35.4	0.39	0.61
	Dev	103.1	75.1	28.0	0.73	0.27
	Mid	219.6	156.8	62.8	0.71	0.29
	Lat	64.9	15.6	49.3	0.24	0.76
	Seasonal	501.3	279.0	222.3	0.56	0.44
2021–2022 winter wheat growing season	Ini	54.1	10.1	44.0	0.19	0.81
	Ove	61.5	11.4	50.1	0.19	0.81
	Dev	122.9	89.0	33.9	0.72	0.28
	Mid	222.1	165.7	56.5	0.75	0.25
	Lat	37.3	7.6	29.7	0.20	0.80
	Seasonal	497.9	283.8	214.1	0.57	0.43
2022–2023 winter wheat growing season	Ini	40.8	4.8	36.0	0.12	0.88
	Ove	45.0	15.2	29.8	0.34	0.66
	Dev	99.4	65.2	34.2	0.66	0.34
	Mid	194.7	138.0	56.7	0.71	0.29
	Lat	35.2	9.5	25.7	0.27	0.73
	Seasonal	415.1	232.7	182.4	0.56	0.44
Three-year average	Ini	50.0	7.8	42.3	0.16	0.84
	Ove	55.0	16.6	38.4	0.30	0.70
	Dev	108.5	76.4	32.0	0.70	0.30
	Mid	212.1	153.5	58.7	0.72	0.28
	Lat	45.8	10.9	34.9	0.24	0.76
	Seasonal	471.4	265.2	206.3	0.56	0.44

N.B.: Ini, Ove, Dev, Mid, and Lat denote the initial, overwintering, development, middle, and late winter wheat growth stages, respectively.

). On the other hand, the ${\mathrm{ET}}_{\mathrm{a}}$ and T values showed obvious increasing trends with increasing LAI values following the overwintering stage, while the E values exhibited a slight decreasing trend (Figure 6). The highest T/${\mathrm{ET}}_{\mathrm{a}}$ values ranged from 0.66 to 0.73 over the winter wheat developmental stage (Table 3). Both ${\mathrm{ET}}_{\mathrm{a}}$ and T reached their maximum values at the winter wheat middle stage, coinciding with the LAI peak. The highest ${\mathrm{ET}}_{\mathrm{a}}$ values of the 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons were 8.4, 7.2, and 7.0 $\mathrm{mm}{\mathrm{day}}^{-1}$, respectively, with cumulative values at the mid-growth winter wheat stage of 219.6, 222.1, and 194.7 mm, respectively. In contrast, the highest T values of the 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons were 6.3, 5.4, and 4.7 $\mathrm{mm}{\mathrm{day}}^{-1}$, respectively (Figure 6). In addition, the T/${\mathrm{ET}}_{\mathrm{a}}$ and E/ET_a ratios exceeded 0.7 (Table 3). At the late winter wheat stage (leaf senescence), the T and ${\mathrm{ET}}_{\mathrm{a}}$ values decreased rapidly, while E exhibited the highest value. Furthermore, the highest E/${\mathrm{ET}}_{\mathrm{a}}$ values were observed at the late winter wheat stage, ranging from 0.73 to 0.80 (Table 3). Meanwhile the highest E values of the 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons were 5.5, 4.1, and 4.1 $\mathrm{mm}{\mathrm{day}}^{-1}$, respectively (Figure 6). The cumulative ${\mathrm{ET}}_{\mathrm{a}}$ values in the 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons were 501.3, 497.9, and 415.1 mm, respectively. The T/${\mathrm{ET}}_{\mathrm{a}}$ values of the entire 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons were 0.56, 0.57, and 0.56, respectively. The three-year average T and E values were 265.2 and 206.3 mm, respectively, resulting in a difference between the E/${\mathrm{ET}}_{\mathrm{a}}$ and E/${\mathrm{ET}}_{\mathrm{a}}$ values of 12% (Table 3).

3.3. Relationships between the Measured Environmental Factors and Evapotranspiration Rates

The correlation coefficients (r) between ${\mathrm{ET}}_{\mathrm{a}}$ and its controlling environmental factors at different winter wheat growth stages are shown in Figure 7. The ${\mathrm{ET}}_{\mathrm{a}}$ values were significantly and positively correlated with the ${\mathrm{T}}_{\mathrm{air}}$, ${\mathrm{T}}_{\max }$, ${\mathrm{T}}_{\min }$, G, ${\mathrm{R}}_{\mathrm{n}}$, VPD, and LAI values (p < 0.001), while the ${\mathrm{ET}}_{\mathrm{a}}$ values were significantly and positively correlated with ${\mathrm{U}}_2$ (p < 0.05) over the entire winter wheat growing seasons. On the other hand, the ${\mathrm{ET}}_{\mathrm{a}}$ values showed extremely significant negative correlations with the RH, ${\mathrm{SWC}}_{10}$, ${\mathrm{SWC}}_{20}$, ${\mathrm{SWC}}_{40}$, and ${\mathrm{SWC}}_{60}$ values (p < 0.001), as well as with the P amount (p < 0.01). Among the measured environmental factors, ${\mathrm{R}}_{\mathrm{n}}$ was the main dominant factor controlling ${\mathrm{ET}}_{\mathrm{a}}$ over the entire three winter wheat growing seasons, with an r value of 0.94 describing their linear relationship. Although ${\mathrm{SWC}}_{10}$, ${\mathrm{SWC}}_{20}$, ${\mathrm{SWC}}_{40}$, and ${\mathrm{SWC}}_{60}$ had no significant effects on ${\mathrm{ET}}_{\mathrm{a}}$ at the initial, development, and middle stages of the cultivated winter wheat season, they exhibited significant negative effects on ${\mathrm{ET}}_{\mathrm{a}}$ at the late stage (p < 0.01). There was a very significant positive correlation between ${\mathrm{ET}}_{\mathrm{a}}$ and ${\mathrm{T}}_{\max }$, as well as between ${\mathrm{R}}_{\mathrm{n}}$ and VPD, at the different winter wheat growth stages (p < 0.001). The results showed a slight increasing trend of the LAI values with increasing ${\mathrm{R}}_{\mathrm{n}}$ values at the initial winter wheat stage. At this stage, the ${\mathrm{ET}}_{\mathrm{a}}$ values showed a very significant negative correlation with the LAI values (p < 0.001). However, slight variation in the wheat LAI values were observed over the overwintering and middle stages, explaining the lack of an obvious correlation between ${\mathrm{ET}}_{\mathrm{a}}$ and LAI. Notably, ${\mathrm{ET}}_{\mathrm{a}}$ was strongly associated with RH and VPD at the middle stage, showing correlation coefficients of −0.72 and 0.85, respectively (p < 0.001).

3.4. Penman–Monteith-, Priestley–Taylor-, and Hargreaves-Equation-Based Crop Coefficients

The seasonal dynamic changes in the PM-, PT-, and HS-equation-based crop coefficients, namely ${\mathrm{K}}_{\mathrm{c}}$, α, and ${\mathrm{K}}_{\mathrm{Hc}}$, respectively, over the three winter wheat growing seasons are shown in Figure 8. The average ${\mathrm{K}}_{\mathrm{c}}$, α, and ${\mathrm{K}}_{\mathrm{Hc}}$ values at the different winter wheat growth stages are reported in

Table 4. Winter wheat ${\mathrm{K}}_{\mathrm{c}}$, α, and ${\mathrm{K}}_{\mathrm{Hc}}$ coefficients obtained using the Penman–Monteith, Priestley–Taylor, and Hargreaves equations, respectively, for the different growth stages of the 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons.

	Growth Stage	${\mathbf{K}}_{\mathbf{c}}$	α	${\mathbf{K}}_{\mathbf{Hc}}$
2020–2021 winter wheat growing season	Ini	1.16	1.62	1.09
	Ove	1.11	2.10	0.99
	Dev	1.30	1.76	1.18
	Mid	1.46	1.64	1.30
	Lat	0.99	1.15	0.87
	Seasonal	1.20	1.65	1.09
2021–2022 winter wheat growing season	Ini	0.96	1.42	0.77
	Ove	1.23	2.04	1.18
	Dev	1.21	1.70	1.10
	Mid	1.27	1.47	1.18
	Lat	0.68	0.82	0.65
	Seasonal	1.07	1.49	0.98
2022–2023 winter wheat growing season	Ini	1.03	1.37	0.92
	Ove	0.86	1.71	0.79
	Dev	1.11	1.53	1.03
	Mid	1.29	1.51	1.15
	Lat	1.11	1.15	0.89
	Seasonal	1.08	1.45	0.96
Average	Ini	1.05	1.47	0.93
	Ove	1.06	1.95	0.99
	Dev	1.21	1.66	1.10
	Mid	1.34	1.54	1.21
	Lat	0.93	1.04	0.80
	Seasonal	1.12	1.53	1.01

N.B.: Ini, Ove, Dev, Mid, and Lat denote the initial, overwintering, development, middle, and late winter wheat growth stages, respectively.

. The obtained results showed a lack of obvious changes in ${\mathrm{K}}_{\mathrm{c}}$, α, and ${\mathrm{K}}_{\mathrm{Hc}}$ over the initial and overwintering stages. However, sharp decreases in the winter wheat coefficients were observed from the development stage (Figure 8). Among them, ${\mathrm{K}}_{\mathrm{c}}$ and ${\mathrm{K}}_{\mathrm{Hc}}$ exhibited an obvious upward trend over the development stage (Figure 8a,c), while a lack changes were observed in α (Figure 8b). In contrast, continuous constant crop coefficients were observed over the middle stage before decreasing sharply over the late stage (Figure 8). Notably, except for some lower α values less than one at the initial and late stages, all α values at the other winter wheat growth stages were greater than one (Figure 8b). The highest average ${\mathrm{K}}_{\mathrm{c}}$ and ${\mathrm{K}}_{\mathrm{Hc}}$ values were observed at the middle stage, ranging from 1.27 to 1.46 and 1.15 to 1.30, respectively, in the three winter wheat growing seasons, while the highest average α values were observed at the overwintering stage, ranging from 1.95 to 2.10 (Table 4). On the other hand, the lowest average α and ${\mathrm{K}}_{\mathrm{Hc}}$ values were observed at the late stage, ranging from 0.82 to 1.15 and 0.65 to 0.89, respectively. However, the average ${\mathrm{K}}_{\mathrm{c}}$ value at the late stage of the 2022–2023 winter wheat season was 1.11, which was higher than those of the other two winter wheat growing seasons (Table 4). The average winter wheat values of the three growing seasons at the initial, overwintering, development, middle, and late stages were 1.05, 1.06, 1.21, 1.34, and 0.93 for ${\mathrm{K}}_{\mathrm{c}}$; 1.47, 1.95, 1.66, 1.54, and 1.04 for α; and 0.93, 0.99, 1.10, 1.21, and 0.80 for ${\mathrm{K}}_{\mathrm{Hc}}$, respectively. The three average α, ${\mathrm{K}}_{\mathrm{c}}$, and ${\mathrm{K}}_{\mathrm{Hc}}$ coefficients of the entire winter wheat growing seasons were, in descending order, 1.53, 1.12, and 1.01, respectively (Table 4).

3.5. Evapotranspiration Estimation

The seasonal changes in the PT-, PM-, and HS-based ${\mathrm{ET}}_{\mathrm{eq}}$, ${\mathrm{ET}}_0$ and ${\mathrm{ET}}_{\mathrm{H}}$ values, as well as the estimated ET values (${\mathrm{ET}}_{\mathrm{ePT}}$, ${\mathrm{ET}}_{\mathrm{ePM}}$, and ${\mathrm{ET}}_{\mathrm{eH}}$) using the three-year average α, ${\mathrm{K}}_{\mathrm{c}}$, and ${\mathrm{K}}_{\mathrm{Hc}}$ coefficients at the different winter wheat growth stages, are shown in Figure 9. The seasonal dynamic changes in the ET rates estimated by the three calculation methods were consistent with those of ${\mathrm{ET}}_{\mathrm{a}}$. The daily ${\mathrm{ET}}_{\mathrm{eq}}$ rates were less than those of ${\mathrm{ET}}_{\mathrm{a}}$ over the three wheat growing seasons (Figure 9a), while the daily ${\mathrm{ET}}_0$ rates were very close to those of ${\mathrm{ET}}_{\mathrm{a}}$ at the initial and overwintering winter wheat stages. In contrast, the daily ${\mathrm{ET}}_0$ rates were slightly lower than those of ${\mathrm{ET}}_{\mathrm{a}}$ in the development and middle stage (Figure 9b). On the other hand, the daily ${\mathrm{ET}}_{\mathrm{H}}$ rates were slightly higher than those of ${\mathrm{ET}}_{\mathrm{a}}$ at the initial and overwintering stages. Relatively similar daily ET rates to ${\mathrm{ET}}_{\mathrm{a}}$ were observed at the other growth stages using the three estimation methods (Figure 9c). Indeed, the linear regression analysis results showed estimated ${\mathrm{ET}}_{\mathrm{a}}$ rates that were very close to those of ${\mathrm{ET}}_{\mathrm{eq}}$, ${\mathrm{ET}}_0$, and ${\mathrm{ET}}_{\mathrm{H}}$, with ${\mathrm{R}}^2$ values of 0.88, 0.87, and 0.84, respectively (Figure 10a,c,e). The ${\mathrm{ET}}_{\mathrm{a}}$ and ${\mathrm{ET}}_{\mathrm{eq}}$ rates showed the lowest R² and MD, as well as the highest RMSD and RRMSD values, of 0.68 mm, −0.66 mm, 1.00 mm, and 0.49 mm, respectively (Figure 10a). Therefore, the cumulative estimated ${\mathrm{ET}}_{\mathrm{eq}}$ rates of the three winter wheat growing seasons deviated the most negatively from the ${\mathrm{ET}}_{\mathrm{a}}$ rates by an average seasonal cumulative value of 153.1 mm (

Table 5. Cumulative actual evapotranspiration (${\mathrm{ET}}_{\mathrm{a}}$) and estimated ET rates using the PT equation (${\mathrm{ET}}_{\mathrm{eq}}$), PT coefficients (${\mathrm{ET}}_{\mathrm{ePT}}$), PM equation (${\mathrm{ET}}_0$), PM coefficients (${\mathrm{ET}}_{\mathrm{ePM}}$), HS equation (${\mathrm{ET}}_{\mathrm{H}}$), and HS coefficients (${\mathrm{ET}}_{\mathrm{eH}}$) in the 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons.

	${\mathbf{ET}}_{\mathbf{a}}$	${\mathbf{ET}}_{\mathbf{eq}}$	${\mathbf{ET}}_{\mathbf{ePT}}$	${\mathbf{ET}}_0$	${\mathbf{ET}}_{\mathbf{ePM}}$	${\mathbf{ET}}_{\mathbf{H}}$	${\mathbf{ET}}_{\mathbf{eH}}$
2020–2021 winter wheat	501.3	312.5	467.7	407.6	477.9	456.4	456.8
2020–2021 winter wheat	497.9	345.8	526.4	444.0	527.8	507.4	514.6
2020–2021 winter wheat	415.1	296.7	457.1	384.4	460.0	428.6	436.3
Seasonal average values	471.4	318.3	483.7	412.0	488.6	464.1	469.2

). The RMSD and RRMSD values between ${\mathrm{ET}}_{\mathrm{a}}$ and both ${\mathrm{ET}}_0$ and ${\mathrm{ET}}_{\mathrm{H}}$ were relatively similar. In contrast, the absolute MD value between the ${\mathrm{ET}}_{\mathrm{a}}$ and ${\mathrm{ET}}_0$ rates was −0.26 mm, which is substantially higher than that between ${\mathrm{ET}}_{\mathrm{a}}$ and ${\mathrm{ET}}_{\mathrm{H}}$ (Figure 10c,e), indicating a higher difference between the average cumulative ${\mathrm{ET}}_{\mathrm{a}}$ and ${\mathrm{ET}}_0$ rates over the three winter wheat growing seasons (Table 5). The calculated ${\mathrm{ET}}_{\mathrm{ePT}}$, ${\mathrm{ET}}_{\mathrm{ePM}}$, and ${\mathrm{ET}}_{\mathrm{eH}}$ using α, ${\mathrm{K}}_{\mathrm{c}}$, and ${\mathrm{K}}_{\mathrm{Hc}}$ at the different winter wheat stages can better predict the daily ${\mathrm{ET}}_{\mathrm{a}}$ rates. The ${\mathrm{R}}^2$ values of ${\mathrm{ET}}_{\mathrm{a}}$ with ${\mathrm{ET}}_{\mathrm{ePT}}$, ${\mathrm{ET}}_{\mathrm{ePM}}$, and ${\mathrm{ET}}_{\mathrm{eH}}$ all exceeded 0.90, which were 0.93, 0.92, and 0.90, respectively (Figure 10b,d,f). Meanwhile, the slope coefficients were 0.99, 0.96, and 0.96, respectively (Figure 10b,d,f). Hence, ${\mathrm{ET}}_{\mathrm{ePT}}$ had the best goodness-of-fit with the daily ${\mathrm{ET}}_{\mathrm{a}}$ rates, with the lowest RMSD and RRMSD values of 0.51 and 0.25 mm, respectively (Figure 10b). Therefore, the HS-based equation was the optimal method for estimating ET, yielding the lowest MD value of −0.01 mm from the cumulative ${\mathrm{ET}}_{\mathrm{a}}$ value in the three winter growing seasons (Table 5 and Figure 10f).

4. Discussion

4.1. Controlling Factors of the Evapotranspiration Rate and T/ET Ratio

Evapotranspiration (ET) rates are controlled by several factors, including climate, crop species, and soil characteristics [28]. Previous studies have used the EC system and demonstrated that R_n is the main factor controlling the ET rates, showing higher contributions to the ET dynamic changes than that of meteorological variables in crop growing seasons [29,56,57,58]. This finding is consistent with the results of our study, which showed higher α values exceeding one at the main winter heat growth stages (development and middle stages) (Figure 8b), suggesting that energy balance closure was the limiting factor of winter wheat growth in the Guanzhong Plain rather than the SWC. Previous related studies have shown that VPD is one of the main factors controlling the ET rates in winter wheat growing seasons [56,59]. In addition, Chen et al. [60] found an obvious threshold (0.87 and 0.73 Kpa) in the relationship between canopy ET and VPD. Indeed, VPD values below the threshold can increase water vapor flux through plant stomata or the soil surface, thus increasing the ET rates. In contrast, VPD values higher than the threshold result in a decrease in the stomatal aperture size and, consequently, increase the stomatal resistance and decrease the ET rates. In this study, the VPD threshold was 1.27 Kpa, with an ${\mathrm{R}}^2$ value between the ET and VPD values of 0.58 (Figure 11). The linear regression equations between ET and VPD were y = 4.12x + 0.09 and y = −2.43x + 8.41 below and above the defined VPD threshold, respectively. Wang et al. (2022) revealed a great effect of ${\mathrm{T}}_{\mathrm{air}}$ on seed germination, seed dormancy, and greening of wheat. Indeed, ${\mathrm{T}}_{\min }$ is very important in determining whether winter wheat enters dormancy or begins greening over growing seasons. Continuous lower and higher ${\mathrm{T}}_{\min }$ values than 0 °C indicate the occurrence of the wheat dormancy and greening periods, respectively (Figure 2a and Figure 6).

Nelson et al. [20] observed an increasing trend of the T/ET ratio with increasing VAI and LAI values. In the present study, a significant logarithmic relationship was found between the T/ET and VPD values of the winter wheat growing seasons (Figure 12a). The T/ET ratio values increased sharply over the VPD range of 0–0.6 Kpa. However, relatively continuous constant T/ET ratio values were observed with increases in the VPD above 0.6 Kpa. Peng et al. (2023) showed positive and negative correlation coefficients of T rates and GPP, respectively, with VPD. Increases in VPD may decrease crop WUE. Previous studies have shown that WUE is related to VPD in a power function, as demonstrated based on the dynamic change in the GPP/ET ratio obtained from EC data collected in rain-free periods [22,23,61]. The relationship between LAI and T/ET was relatively intuitive. Indeed, the T rates were extremely low when LAI values were low or equal to 0. In contrast, the T rates increased with increasing LAI values, while the E rates decreased with an increase in the vegetation cover, thereby increasing the T/ET ratio (Figure 2e and Figure 6). Unlike the T/ET response to LAI ($\mathrm{T}/\mathrm{ET}=\mathrm{a}·{\mathrm{e}}^{\mathrm{b}\ast \mathrm{LAI}}$) revealed by Wei et al. [62], a logarithmic relationship was observed between T/ET and LAI (Figure 12b). According to the obtained results, the sensitive interval of T/ET to LAI was 0–1 ${\mathrm{m}}^2{\mathrm{m}}^{-2}$ (Figure 12b). However, Berkelhammer et al. [63] revealed similar trends of T/ET and LAI without exhibiting a statistically significant relationship on multiple time scales (day, month, and year). This demonstrates that seasonality and spatial heterogeneity may affect the relationship between the T/ET and LAI.

4.2. Evapotranspiration Partitioning of Winter Wheat Cropland in Other Regions Worldwide

Table 6. Comparison between the seasonal actual evapotranspiration (${\mathrm{ET}}_{\mathrm{a}}$), transpiration (T), evaporation (E), T/${\mathrm{ET}}_{\mathrm{a}}$, and E/${\mathrm{ET}}_{\mathrm{a}}$ obtained in this study and those observed among other regions.

Sites	${\mathbf{ET}}_{\mathbf{a}}$ Measurement Methods	Periods	${\mathbf{ET}}_{\mathbf{a}}$ (mm)	T (mm)	E (mm)	$\mathbf{T}/{\mathbf{ET}}_{\mathbf{a}}$	$\mathbf{E}/{\mathbf{ET}}_{\mathbf{a}}$	References
Yangling, Shaanxi, China (34°17′45″ N, 108°04′07″ E)	EC	2020–2021	501.3	279.0	222.3	0.56	0.44	This study
		2021–2022	497.9	283.8	214.1	0.57	0.43
		2022–2023	415.1	232.7	182.4	0.56	0.44
Weishan, Shandong, China (36°38′55″ N, 116°03′15″ E)	EC	2005–2019	$297\pm$ 21	$229\pm$ 22	$68\pm$ 13	0.65–0.82	0.18–0.35	[8]
Yangling, Shaanxi, China (34°20′ N, 108°04′ E)	Water balance method	2014–2015	413.8	304.1	93.7	0.73	0.27	[10]
		2015–2016	373.6	262.3	98.0	0.70	0.30
Daxing, Beijing, China (39°37′ N, 116°26′ E)	Soil water balance	2013–2014	$270.1\pm$ 27.7	$224.4\pm$ 24.5	$45.7\pm$ 4.5	$0.83\pm$ 0.01		[11]
		2014–2015	$315.4\pm$ 39.9	$252.7\pm$ 34.5	$62.8\pm$ 15.1	$0.80\pm$ 0.04
Nanjing, Jiangsu, China (32.21 ° N, 118.68 ° E)	Bowen ratio energy balance	2016–2017	285.4	149.6	135.8	0.52	0.48	[25]
		2017–2018	279.4	137.0	142.4	0.49	0.51
Daxing, Beijing, China (39°37′ N, 116°26′ E)	Eddy covariance	2007–2008	396.3	287.0	109.3	0.72	0.28	[26]
		2008–2009	437.3	287.0	122.1	0.72	0.28
Ludhiana, Punjab, India (30°56′ N, 75°52′ E)	Water balance method	2006–2007	340–345	210–240	100–135	0.61–0.70	0.30–0.39	[64]
		2007–2008	400–404	243–279	121–161	0.60–0.70	0.30–0.40
Tongzhou, Beijing, China (39°36′ N; 116°48′ E)	Water balance method	2006–2007	219–486		65.7–77.9	0.72–0.79	0.21–0.28	[65]
Luancheng, China (37°50′ N,114°40′ E)	Soil water balance	1999–2000	192.0–464.0	84.0–323.6	108.0–140.4	0.46–0.70	0.30–0.56	[15]
		2000–2001	241.3–443.7	132.6–300.7	108.7–143.0	0.56–0.68	0.32–0.45
		2001–2002	259.7–444.9	161.9–326.2	97.9–139.9	0.64–0.76	0.24–0.37
Yangling, Shaanxi, China (34°20′ N, 108°24′ E)	Lysimeter	1987–1997	$443.6\pm$ 43.9	$297.1\pm$ 46.9	$146.5\pm$ 21.8	0.67	0.33	[9]
Tel Hadya, Syria (35°55′ N 37°10′ E)	Water balance method	1996–1997	367.3–376.7	172.1–184.8	182.5–204.6	0.50–0.55	0.50–0.55	[7]
Luancheng, China (37°50′ N, 114°40′ E)	Lysimeter	1995–2000	401.2–479.2			0.70	0.30	[24]
Tel Hadya, Syria (36°01′ N, 36°56′ E)	Water balance method	1991–1996	295–456	131–358	91–179	0.44–0.80	0.20–0.56	[12]

shows the ET partitioning over winter wheat growing seasons in different regions. In the present study, the T/ET ratios at the initial and overwintering stages of the cultivated winter wheat were 0.16 and 0.30, respectively (Table 3), which were close to those reported by Qiu et al. [25]. In addition, the average seasonal T/ET value of the cultivated winter wheat was 0.56, slightly higher than those reported by Qiu et al. [25] (0.49–0.52) and Eberbach and Pala [7] (0.50–0.55). However, the obtained T/ET values in the present study were lower than those previously observed in North China (Table 6). Sun et al. [15] demonstrated that optimal irrigation practices can increase E and ET, while excessive irrigation rates can reduce wheat yields and WUE. Eberbach and Pala [7] found that winter wheat with different row spacing affected the interception of incident radiation by changing the crop structure and, consequently, increased the E rates slightly. In the present study, the row spacing of the cultivated winter wheat ranged from 10 to 15 cm, which was lower than that adopted by Eberbach and Pala [7] (17 and 30 cm), making it difficult to reduce the E rates in the study area by further improving the row spacing. Zhang et al. (1988) found that nitrogen (N) fertilizer application can reduce E rates by enhancing vegetation cover within crop fields, thereby increasing LAI and dry matter. Straw mulching can also effectively reduce E rates by preventing direct contact between soils and the atmosphere. Balwinder-Singh et al. [64] investigated the effects of rice straw mulching on winter wheat cropland and highlighted a significant increase and decrease in the T and E rates, respectively. Besides the portioning methods used, the deep plowing of the soil at the experimental site before wheat sowing in the present study might be the main reason for the substantially higher E rates than those observed in the other regions. Except for the E rates of the winter wheat growing season in Tel Hadya, Syria [7], which were close to those obtained in this study, the E rates in the other study regions were less than 150 mm (Table 6). In addition, Hu and Lei [8], Ma et al. [10], Ma and Song [11], and Yu et al. [65] reported cumulative E amounts in wheat growing seasons less than 100 mm. However, the observed ET amount in a wheat growing season by Yu et al. [65] was close to that revealed in the present study. Plastic mulch films can prevent the exchange of water and vapor between soils and the atmosphere and reduce thermal radiation reaching the soil surface, thereby significantly reducing E rates [66]. It is, therefore, important to assess the effects of plastic mulch films on the E rates and WUE of the experimental site in the Guanzhong Plain in future research.

4.3. Estimation Performances

The winter wheat coefficient values given in the FAO 56 method are classified according to three growth stages, namely the early (including the initial and overwintering stages), middle, and late stages, corresponding to ${\mathrm{K}}_{\mathrm{c}}$ values of 0.70, 1.15, and 0.25–0.40, respectively [14]. In the present study, the modified ${\mathrm{K}}_{\mathrm{c}}$ values according to the local climate conditions were greater than those obtained by the FAO 56 method, which were 1.05, 1.34, and 0.93 at the initial, middle, and late stages, respectively (Table 4). Qiu et al. [31] proposed a dynamic ${\mathrm{K}}_{\mathrm{c}}$ model based on several factors, including planting density coefficient, temperature limitation, water stress, and leaf senescence, showing ${\mathrm{R}}^2$ and RMSE values between the estimated ${\mathrm{ET}}_{\mathrm{a}}$ rates of the dynamic ${\mathrm{K}}_{\mathrm{c}}$ model and actual ET of 0.85 and 0.55 mm, respectively. The modified ${\mathrm{K}}_{\mathrm{c}}$ model in this study had better estimation performance in the local area, indicating ${\mathrm{R}}^2$ and RMSE values between the ${\mathrm{ET}}_{\mathrm{a}}$ and estimated ET rates of 0.92 and 0.53 mm, respectively (Figure 10d). The improved PT model demonstrated good estimation performance for many types of vegetation cover, including rice and wheat rotation systems [25], film-covered maize [57], grass [67], greenhouse cucumber [30], greenhouse tomato [68], and mixed vegetation cover [69]. The modified PT model usually combines α with various factors to better estimate ${\mathrm{ET}}_{\mathrm{a}}$, including soil cover types (e.g., mulch and straw), solar radiation, LAI, SWC, ${\mathrm{T}}_{\mathrm{air}}$, and RH. On the other hand, the adopted PT model by Qiu et al. [25] comprehensively considers soil water, air temperature, and leaf senescence. The revised PT model demonstrated excellent estimation performance of ${\mathrm{ET}}_{\mathrm{a}}$ under winter wheat, showing slope coefficient and ${\mathrm{R}}^2$ ranges of 0.93–1.09 and 0.92–0.96, respectively. Since there was no water stress at the experimental site of the present study, the PT model was only corrected by calculating α at the different winter wheat growth stages, resulting in a good estimation performance, with slope coefficient and ${\mathrm{R}}^2$ values of 0.99 and 0.93, respectively (Figure 10b). Although the HS model can estimate reference ET rates using only temperature data, it requires calibrations under local conditions [70]. In this study, the original HS model was used to estimate reference ET, and the specific ${\mathrm{K}}_{\mathrm{Hc}}$ values of the different winter wheat growth stages were used to achieve relatively accurate estimated ${\mathrm{ET}}_{\mathrm{a}}$. This approach resulted in slope coefficient and ${\mathrm{R}}^2$ values of 0.96 and 0.90, respectively (Figure 10f), demonstrating that the HS model exhibited good performance for estimating the ${\mathrm{ET}}_{\mathrm{a}}$ rates only by adjusting the crop coefficients without requiring cumbersome parameter calibrations using meteorological input parameters, such as temperature, RH, and wind speed.

5. Conclusions

In the present study, the seasonal dynamics of the ${\mathrm{ET}}_{\mathrm{a}}$ rates were investigated by using EC techniques, as well as E and T based on the conceptual portioning of underlying surface WUE. The winter wheat coefficients, namely ${\mathrm{K}}_{\mathrm{c}}$, α, and ${\mathrm{K}}_{\mathrm{Hc}}$, were determined in this study at the different growth stages by combining the measured ${\mathrm{ET}}_{\mathrm{a}}$ rates with the PM-, PT-, and HS-based ${\mathrm{ET}}_0$ values. The estimated ${\mathrm{ET}}_{\mathrm{a}}$ values using the adjusted ${\mathrm{K}}_{\mathrm{c}}$, α, and ${\mathrm{K}}_{\mathrm{Hc}}$ values were evaluated. The main conclusions are as follows:

(1)

T can be calculated by GPP∙${\mathrm{VPD}}^{0.5}$/${\mathrm{uWUE}}_{\mathrm{p}}$. The energy fluxes were the main limiting factor of ${\mathrm{ET}}_{\mathrm{a}}$ in the three winter wheat growing seasons rather than water. In addition, the VPD values affected the change in the ${\mathrm{ET}}_{\mathrm{a}}$ rates at a threshold of 1.27 KPa. The main limiting factors for T/${\mathrm{ET}}_{\mathrm{a}}$ were VPD and LAI.

(2)

The cumulative ${\mathrm{ET}}_{\mathrm{a}}$ rates of the 2020–2021, 2021–2022, and 2022–2023 winter wheat growing seasons were 501.3, 497.9, and 415.1 mm, respectively, in which E was the main contributor during the initial, overwintering, and late stages, while the T/${\mathrm{ET}}_{\mathrm{a}}$ ratios during the middle stage exceeded 0.7. The average seasonal T/${\mathrm{ET}}_{\mathrm{a}}$ and E/${\mathrm{ET}}_{\mathrm{a}}$ ratios were 0.56 and 0.44, respectively.

(3)

The ${\mathrm{K}}_{\mathrm{c}}$, α, and ${\mathrm{K}}_{\mathrm{Hc}}$ values showed a lack of obvious changes at the initial and overwintering stages of the cultivated winter wheat and tended to be concentrated from the developmental stage. The recommended ${\mathrm{K}}_{\mathrm{c}}$ values for winter wheat in the Guanzhong Plain at the Ini, Ove, Dev, Mid, and Lat stages were 1.05, 1.06, 1.21, 1.34, and 0.93, respectively; the recommended α values at the Ini, Ove, Dev, Mid, and Lat stages were 1.47, 1.95, 1.66, 1.54, and 1.04, respectively; the recommended ${\mathrm{K}}_{\mathrm{Hc}}$ values at the Ini, Ove, Dev, Mid, and Lat stages were 0.93, 0.99, 1.10, 1.21, and 0.80, respectively.

(4)

The models based on the adjusted ${\mathrm{K}}_{\mathrm{c}}$, α, and ${\mathrm{K}}_{\mathrm{Hc}}$ models can reasonably estimate ${\mathrm{ET}}_{\mathrm{a}}$. However, the most accurate ${\mathrm{ET}}_{\mathrm{a}}$ estimation was achieved using the PT-based crop coefficient.

(5)

Therefore, the PT-based method is expected to become a practical tool for formulating irrigation schedules for winter wheat cropland in the Guanzhong Plain and similar regions. We suggest further improvement of WUE in the future by reducing E rates through improved management measures (e.g., film mulch applications). The applicability of ${\mathrm{ET}}_{\mathrm{a}}$ partitioning and model simulation to winter wheat cropland in other regions merits further study.