Comprehensive Response of Daily Transpiration from Armeniaca sibirica Plantations to Meteorological and Soil Moisture/Temperature Conditions on the Semi-Arid Loess Plateau, China

Abstract

Forest transpiration plays a vital role in the regional water budget and water supply security of the semi-arid Loess Plateau of northwest China. A thorough understanding and accurate predictions of the variation in the transpiration of forests with important tree species, e.g., Armeniaca sibirica (L.) Lam., are critical for land and water management. Owing to the extreme climatic seasonality and interannual variability, detailed information on the seasonal variation in the transpiration of Armeniaca sibirica plantations and its response to climatic and soil moisture/temperature fluctuations is limited. Therefore, in this study, the sap flux density and meteorological and soil moisture/temperature conditions were continuously monitored during the growing season (May to October) in 2019–2020. The results show the four following features: (1) The mean daily transpiration of the Armeniaca sibirica plantation was 0.31 mm·day⁻¹; (2) the daily transpiration varied nonlinearly with increasing potential evapotranspiration (PET). Transpiration first increased rapidly until reaching the PET threshold of 4 mm·day⁻¹ and then slowly increased within the PET range of 4–8.5 mm·day⁻¹, but thereafter, it decreased slightly when PET exceeded 8.5 mm·day⁻¹; (3) the daily forest transpiration varied with increasing relative extractable soil water content (REW) and soil temperature (ST) following a saturated exponential function; i.e., it first increased until reaching a threshold of 0.5 of REW or 14 °C of ST, but thereafter tended to stabilize; (4) models for estimating the daily forest transpiration were established. According to these models, PET had the greatest limiting effect (32.17%) on forest transpiration during the observation period, while REW and ST showed lower limits at 7.03% and 3.87%, respectively. The findings of this study are useful for understanding and managing the hydrological effects of forests in the semi-arid Loess Plateau as a typical dryland with seasonal droughts.

1. Introduction

The Loess Plateau, with its arid and semi-arid climate, is significantly affected by global climate changes and suffers from the world’s most serious water and soil losses due to long-term ecological destruction [1,2,3]. Currently, the plateau area is about 650,000 km², and the erodible area is about 470,000 km² [4]. To improve the ecological environment, the Chinese government has been implementing large-scale afforestation since the late 1950s [5,6]. In addition, since 2000a, the Chinese government has also implemented a large-scale project to return farmland to forests in the Loess hilly area. A large area of ecological economic forest has been planted, which aims to improve the living standards of 70 million farmers on the Loess Plateau while protecting the environment. Important economic tree species, such as apples, walnuts, jujubes, and apricots, have been widely planted [7]. Due to the high input and yield of these species, their planted area has been increasing since the 1980s [8]. Large-scale afforestation relevant to these high-yield species has achieved some significant achievements, such as increasing vegetation coverage, which has made a significant contribution to global “greening” and plays a positive role in increasing carbon sinks and mitigating climate changes [5,9].

Nevertheless, increasing numbers of studies have shown that large-scale planting of ecological, economic forests can lead to increased water consumption and reduced watershed water resources [10], along with causing soil desiccation and “little old trees”, affecting the survival, growth, and function of trees [11]. Moreover, the increased degree and frequency of droughts caused by global climate changes have exacerbated the contradiction between vegetation and water in this region [12,13]. Although numerous studies have been conducted on water consumption and climate changes in ecological forests in the Loess Plateau, studies on the response of economic forests to changing environments remain inadequate [2]. Therefore, to apply soil moisture information and to understand the response to climate changes, more information on sustainable water use by economic tree species needs to be quantified, thereby allowing for rational planning of commercial plantations in this region.

Accounting for over 60% of evapotranspiration, plant transpiration is an important component in the hydrological cycle [14], which is a complex process jointly affected by vegetation characteristics (forest age, density, leaf area index, etc.) [15,16], management measures, and environmental factors (atmospheric temperature, precipitation, soil moisture, soil temperature, etc.) [17]. For plantations with simple structures, environmental factors can be divided into two types based on differences in the influencing mechanisms [18]. One is the demand for atmospheric evaporation, which is jointly determined by meteorological conditions, such as atmospheric temperature, radiation, and wind speed driving transpiration, and can be characterized by a composite index, namely, potential evapotranspiration (PET) [19]. Another is the available soil water content, which is jointly determined by soil conditions, such as soil temperature (ST) and humidity [20]. It is generally believed that atmospheric evaporation potential can promote forest transpiration. However, the impact of soil moisture on forest transpiration is complex. It has been shown that forest transpiration gradually increases with the increase in soil moisture [21,22]. Some scholars have found that forest transpiration first rapidly increases with the increase in soil moisture and then gradually decreases after exceeding a specific threshold [23]. In contrast, other researchers believe that there is no significant correlation between forest transpiration and soil moisture [24]. In addition, an ST that is too low can limit vegetation transpiration, especially in spring [25]. These factors may be caused by stressful environments with different growth periods and soil moisture contents changing the factors that control transpiration. Consequently, it is necessary to quantify the impacts of meteorology, soil moisture, and ST on daily, seasonal, and annual transpiration through long-term observations during multiple seasons.

In order to accurately quantify the changes in transpiration of the main ecological and economic forest and its environmental influencing factors in the Loess Plateau, with the aim of serving the understanding of forest–water relationships in this region, the major ecological, economic forest species Armeniaca sibirica (L.) Lam was selected as the subject. During the 2019 to 2020 growing seasons, the changes in the transpiration rate, soil temperature, moisture, and meteorological factors in the economic forests of Armeniaca sibirica were observed and recorded. The main objectives of this effort were as follows: (1) to estimate the daily, and seasonal variation in the transpiration of the Armeniaca sibirica economic forests on the Loess Plateau; and (2) to analyze the response of Armeniaca sibirica transpiration to various single environmental factors, such as meteorology and soil; and (3) to couple the effects of various single factors to establish a composite model of forest transpiration in response to multiple environmental factors so as to provide a theoretical basis for the accurate prediction of forest transpiration and its rational management in the study region.

2. Materials and Methods

2.1. Study Area

The study area is in the Pengyang County (PYC) (105°09′–106°58′ E, 34°14′–37°04′ N) of Ningxia, northwest China. The elevation range of the PYC is within 1248–2418 m. The climate type is typical temperate semi-arid monsoon climate, and the mean annual potential evaporation is 1360.6 mm, the mean annual air temperature is 7.4~8.5 °C, the annual accumulated temperature (≥10 °C) is 2500~2800 °C, the frost-free period is 140~170 days, and the annual precipitation is 350~550 mm, and unevenly distributed mainly within June~September. The soil types are mainly Loessial soil and black Loessial soil, and the pH value is between 8 and 8.5. The typical vegetation belonging to the typical steppe consists mainly of Thymus mongolicus, Potentilla acaulis, Stipa capillata, and so on. At the beginning of the 21st century, a large area of slope farmland was returned to forest with the main tree species of Armeniaca sibirica, Amygdalus davidiana, Robinia pseudoacacia, Hippophae rhamnoides, Caragana korshinskii and so on. Due to the limited natural conditions of sloped farmland and considering the ecological and economic value of apricot (Armeniaca sibirica L.) trees, most trees are sparsely planted in a single manner, resulting in a forest coverage rate in this area that remains below 30%.

2.2. Data Collection

2.2.1. Sample Plots

In total, 1 plot of Armeniaca sibirica plantation with a size of 30 m × 30 m was investigated in PYC in 2019 and 2020. The investigated items include geographic location, site factors (elevation, slope aspect, slope gradient), and tree/vegetation growth parameters (tree age, density, height, ground diameter, canopy diameter, canopy density, etc.). Characteristics of trees in the apricot plantation plot are shown in

Table 1. Basic information on the trees in the apricot plantation plot.

Year	Canopy Density	Mean of Tree Ground Diameter/cm	Mean of Tree Height/m	Mean Clear Length of Trees/m	Mean Canopy Diameter/m	Total Sapwood Area/cm2
2019	0.39	11.3	3.9	0.7	3.3	2062
2020	0.40	11.8	3.9	0.7	3.5	2160

. The average elevation of the sample plot is 1714 m. The forest age is 18 years in 2019, and the forest density is 500 trees·hm⁻². The soil type is Loessial soil with a thickness greater than 10 m.

2.2.2. Sap Flow Measurement and Transpiration Calculation

Four healthy individual trees of Armeniaca sibirica with different sizes were selected for sap flow measurement in the monitoring plot, and their growth characteristics are shown in

Table 2. Features of sample trees for sap flow measurements.

Year	Sample Tree/No.	Ground Diameter/cm	Height/m	Clear Length/m	Canopy Diameter/m
2019	1	10.4	4.5	1.6	3.8
	5	17.3	6.0	1.5	3.7
	7	14.6	5.1	1.7	6.0
	16	16.4	6.3	1.2	3.9
2020	1	11.2	4.7	1.6	4.0
	5	17.8	6.0	1.5	4.2
	7	15.2	5.2	1.7	6.2
	16	16.8	6.3	1.2	4.1

. The sap flow density of the sample trees was measured at breast height (1.0 m aboveground) using a thermal diffusion probe (SF-L, Ecomatik, Munich, Germany). These probes consisted of two sensors 20 mm long and 2 mm in diameter (S0, a heated sensor powered by a constant current of 12 volts; S1, an unheated sensor). These sensors were inserted 20 mm outside the xylem at breast height on the north-facing side of the trunk (rather than the side exposed to sunlight). Before insertion, the outer bark was peeled off. Each probe was coated with silicone gel to ensure good thermal contact between the probe element and the sapwood. After insertion, the exposed bark was covered with silicone gel to reduce evaporation from the wood surface and then covered with aluminum foil to avoid physical damage and the thermal effects of solar radiation. Sap flow data were recorded every 10 min using a logger (CR1000x, Campbell Scientific Inc., Salt Lake City, UT, USA).

The sap flow meter operates on the principle of thermal diffusion, wherein two probes are strategically positioned at different locations above and below the trunk to establish a temperature gradient. As water ascends, it absorbs heat, resulting in a reduction of the temperature differential between the probes. A functional correlation exists between this temperature difference and trunk flow. The sap flow rate can be determined by measuring the aforementioned temperature differential. The sap flow density of individual trees was calculated using Equation (1) [26,27]:

$$J_s=0.714\times {(\frac{d_{t\max }}{d_{tact}}-1)}^{1.231}$$

(1)

where J_s is the sap flux density (mL·cm⁻²·min⁻¹), and d_tmax is the maximum temperature difference when the sap flow is 0, namely, the maximum d_t value. In this study, transpiration from the trees is calculated on a daily scale, and the d_tmax value is selected daily; d_tact is the temperature difference between the two needles.

Since the trees in this study area grow sparsely, it is unnecessary to consider the difference in tree dominance. The relationship between the average sap flow rate in the four sample trees and the sapwood area is used to estimate the daily transpiration from the trees.

The daily transpiration (T, mm·day⁻¹) of the forest plot was calculated using Equation (2):

$$T=\frac{J_{s\text{-}mean}\times 60\times 24\times 10\times A_{s\text{-}all}}{Plo{t}_s}$$

(2)

where T is the daily transpiration from the forest trees (mm·day⁻¹), J_s-mean is the daily average sap flow rate for all samples (mL·cm⁻²·min⁻¹), A_s-all is the total sapwood area within the sample plot (cm²), and Plot_s is the sample plot area (cm²).

2.2.3. Weather and Soil Moisture/Temperature Measurements

The weather conditions, including the precipitation (TE525MM, P (mm)), air temperature (°C), solar radiation (w·m⁻²), relative humidity (%), and wind speed (m·s⁻¹), were monitored for the period from May to October in 2019 and 2020, and they were recorded every 10 min with an automatic weather station (CR1000X, Campbell Scientific Inc., Salt Lake City, UT, USA) in an open area 100 m away from the sample plots.

The daily potential evapotranspiration (PET; mm·day⁻¹) was estimated using Equation (3) based on the measured weather data [28]:

$$PET=\frac{0.408\Delta \left(R_n-G\right)+\gamma \frac{900}{T_a+273}{U}_2\times \left(e_s-e_a\right)}{\Delta +\gamma \left(1+0.34U_2\right)}$$

(3)

where ∆ (Kpa/°C) is the slope of the relationship between the vapor pressure and the air temperature, R_n (MJ·m⁻²·day⁻¹) is the net radiation, G (MJ·m⁻²·day⁻¹) is the soil heat density, γ (Kpa/°C) is the psychrometric constant, T_a (°C) is the mean air temperature at 2 m height, U₂ (m·s⁻¹) is the wind speed at 2 m height, e_s (kPa) is the saturation vapor pressure, and e_a (kPa) is the actual vapor pressure.

Soil volumetric moisture in the root zone (soil layers 10–20, 20–30, 30–40, 40–50, 50–60, 60–70, and 70–80 cm) was simultaneously monitored using soil moisture and temperature sensors (5-TE, Decagon, Pullman, WA, USA) in the two intensive-study plots. Data were collected every 10 min using a data logger (EM50, Decagon, Pullman, WA, USA). The relative extractable soil water content (REW) [26,29] was calculated as the ratio of the actual extractable water to the maximum extractable water.

The REW of the forest plot was calculated using Equation (4):

$$REW=\frac{{\theta }_{act}-{\theta }_{wp}}{{\theta }_{fc}-{\theta }_{wp}}$$

(4)

where θ_act is the actual soil volume water content (%), θ_fc is the field volumetric water content (%, with a value of 25.3% in this sample), and θ_wp is the wilting volumetric water content (%, with a value of 6.4% in this sample). Field moisture capacity and wilting moisture are measures of soil volumetric moisture content determined by a soil moisture characteristic curve when the soil water potential is −0.01 and −1.5 MPa, respectively [30].

2.3. Data Processing

2.3.1. Establishment of Daily Transpiration Model of Forest Trees

The daily transpiration of forests is influenced by many factors, such as meteorological elements, soil moisture, and soil temperature. In previous works, the continued multiplication model has been broadly employed to explore various responses of coupled canopy conductance to different influencing factors [30,31]. However, the present study does not consider canopy conductance because it cannot be directly measured but instead is determined from the calculated forest transpiration [32]. Thus, it is supposed that the responses of daily forest transpiration to PET, REW, and ST align with the continued multiplication coupling model extensively adopted in several other works [20,29,33].

$$T=f(PET)\times f(REW)\times f(ST)$$

(5)

where T is the daily forest transpiration (mm·day⁻¹), and f (PET), f (REW), and f (ST) are the variation functions of forest transpiration with PET, REW, and ST, respectively.

2.3.2. Data Processing and Model Validation

Excel 2016 and Origin 21.0 were used for data processing and mapping. The data points on the upper boundary lines were filtered using an Excel 2016 macro program, and then, the software 1stOpt 1.5 (developed by 7D-Soft High Technology Inc., Zhongguancun, China) was used to fit the parameters in Equation (5), with field-measured data from 2019. Then, the model was validated with field-measured data from 2020. The fitting effect of the model was evaluated using a dimensionless Nash–Sutcliffe coefficient (NS), which varies between 0 and 1, as shown in Equation (6):

$$NS=1-\frac{{\displaystyle \sum _{i=1}^n\left(M_i-{\mathrm{C}}_i\right)}}{{\displaystyle \sum _{i=1}^n(M_i-M_{av})}}$$

(6)

where M_i and C_i refer to the measured value of the i-th daily transpiration from trees and the calculated value of the corresponding model, M_av is the mean value of all measured values, and n is the number of samples used to verify the model. The closer the value is to 1, the higher the model accuracy. It has been shown that model prediction is better with an NS exceeding 0.6 [34,35].

Using the forest transpiration model constructed based on the method described above, the optimal PET, REW, and ST during the research period were introduced to calculate the (potential) effect on forest transpiration (T_max, mm·day⁻¹) for each factor in an ideal state during the growing seasons, as shown in Equation (7). In the analysis of the limiting effect of PET (T_limit-PET, mm·day⁻¹) on forest transpiration, the actual observed PET and the optimal REW and ST during the research period were introduced into the model, as shown in Equation (8). The limiting effect of REW (T_limit-REW, mm·day⁻¹) on forest transpiration, the actual observed REW, and the optimal PET and ST during the research period were introduced into the model, as shown in Equation (9). The limiting effect of ST (T_limit-ST, mm·day⁻¹) on forest transpiration, the actual observed ST, and the optimal PET and REW during the research period were introduced into the model, as shown in Equation (10).

$$T_{max}=f(PE{T}_{max})\times f(RE{W}_{max})\times f(S{T}_{max})$$

(7)

$$T_{Limit\text{-}PET}=T_{max}-f(PET)\times f(RE{W}_{max})\times f(S{T}_{max})$$

(8)

$$T_{Limit\text{-}REW}=T_{max}-f(PE{T}_{max})\times f(REW)\times f(S{T}_{max})$$

(9)

$$T_{Limit\text{-}ST}=T_{max}-f(PE{T}_{max})\times f(RE{W}_{max})\times f(ST)$$

(10)

where T_max is the maximum forest transpiration when PET, REW, and ST are the optimal conditions, f (PET_max), f (REW_max), and f (ST_max) are the specific values calculated in this relation when the three factors are at their optimal value, and f (PET), f (REW), and f (ST) are the values calculated in this relation when the three factors are at their measured value.

3. Results

3.1. Changes in Meteorological Factors, REW and ST

The mean daily PET in the growing season of 2019 and 2020 was 5.09 mm·day⁻¹ (Figure 1a) and 4.78 mm·day⁻¹ (Figure 1b), respectively. From 1 May to 19 August, it was relatively high, and the means were 6.47 and 5.86 mm·day⁻¹ in 2019 and 2020, respectively. Within the period from 20 August to 31 October, it was relatively low, and the means were 2.99 and 3.15 mm·day⁻¹ in 2019 and 2020, respectively.

As shown in Figure 1c,d, the total precipitation in 2019 and 2020 during the research period was 554.0 and 426.4 mm, respectively. The precipitation from 15 July to 9 September 2019 was 315.6 mm, accounting for 56.97% of the total precipitation. The total precipitation from 26 June to 17 August 2020 was 236.8 mm, accounting for 55.53% of the total precipitation.

Owing to the effect of pulsed precipitation, REW presented an undulating change during the research period (Figure 1e,f). Overall, the high REW in 2019 (with an average of 0.67) was larger than that in 2020 (with an average of 0.55). From 1 May to 2 August 2019, REW was relatively low and showed a gradually decreasing trend, with an average of 0.57. From 3 August to 31 October, REW was relatively high and fluctuated, with an average of 0.77. From 1 May to 15 August 2020, REW was relatively low, with an average of 0.42. From 16 August to 31 October, REW was relatively high, with an average of 0.74.

ST first increased and then decreased (Figure 1g,h). Its maximum values in 2019 and 2020 occurred on July 28 (21.74 °C) and July 9 (21.67 °C), respectively, with small fluctuations. The averages were 16.36 and 16.46 °C and varied in the ranges 7.42–21.74 and 7.83–21.67 °C, respectively.

3.2. Changes in Tree Transpiration

The variation in daily forest transpiration rates during the growing season is shown in Figure 2. The variation range of forest transpiration was large, with an undulating trend of first rising and then falling in 2019 (Figure 2a), and an upward trend was observed from early May to the end of May, which was related to high REW and the upward trends of PET and ST. The change from early June to the end of August presented a slow decrease, mainly related to the first increase and then decrease in PET and relatively low REW. The change from early September to the end of October showed a rapid decline, mainly related to significant decreases in PET and ST.

In 2020, there was basically an upward–downward–upward–downward trend (Figure 2b). From the beginning to the middle of May, a rising trend was observed, which was related to a significant increase in PET. There was a downward trend from mid-May to the end of June, related to a linear decrease in REW to its minimum. The change from early July to the end of August presented a slow increase, with both PET and ST at a high level in this region, mainly related to a significant increase in REW. From early September to the end of October, there was a significant downward trend, with a relatively high REW during this period, which was mainly related to significant declines in PET and ST.

The maximums in 2019 and 2020 occurred on June 6 (0.61 mm·day⁻¹) and May 16 (0.62 mm·day⁻¹), with averages of 0.35 and 0.32 mm·day⁻¹ and variation ranges of 0.03–0.61 and 0.02–0.62 mm·day⁻¹, respectively.

3.3. Response of Tree Transpiration to PET, REW, and ST

Forest transpiration is co-influenced by multiple factors, such as vegetation characteristics and the external environment. It was difficult to accurately evaluate the impact of PET as a single factor on forest transpiration based on the figure. To exclude the effects of other factors, an upper enveloping curve was used to analyze the impact of single factors on forest transpiration, which to some extent could reflect the response of forest transpiration to single factors (such as PET) when other factors, except for PET, were at the optimal levels. There was a binomial relationship between forest transpiration and PET.

Figure 3a displays the impact of PET on forest transpiration. When PET was <4 mm·day⁻¹, forest transpiration increased approximately linearly. When PET was between 4 and 8.5 mm·day⁻¹, forest transpiration increased slowly. When PET was >8.5 mm·day⁻¹, forest transpiration showed a slow decline. The upper boundary line was derived as Equation (11):

$$T=0.139PET-0.00823PE{T}^2 R^2=0.886$$

(11)

The response of forest transpiration to REW tended to be a saturated exponential function (Figure 3b). When REW was <0.3, forest transpiration increased rapidly. When REW was between 0.3 and 0.5, forest transpiration slowly increased. When REW was >0.5, forest transpiration tended to stabilize. The upper boundary line was derived as Equation (12):

$$T=0.655\times \left[1-\exp \left(-4.178REW\right)\right] R^2=0.790$$

(12)

The response of forest transpiration to ST also tended to be a saturated exponential function (Figure 3c). When ST was <10 °C, forest transpiration increased rapidly. When ST was between 10 °C and 14 °C, forest transpiration slowly increased. When ST exceeded 14 °C, forest transpiration tended to stabilize. The upper boundary line was derived as Equation (13):

$$T=0.655\times \left[1-\exp \left(-0.119ST\right)\right] R^2=0.769$$

(13)

3.4. Construction and Verification of Model of Forest Transpiration Response to Multiple Factors

To determine the compound effects of atmospheric evaporation potential and soil conditions on forest transpiration, it is necessary to construct a model that comprehensively considers meteorological conditions and soil factors. A coupling model of forest transpiration in response to multiple factors was constructed by successively multiplying the relationships of forest transpiration in response to single factors such as PET, REW, and ST (Equations (11)–(13)). The model was constructed using the data from 2019 (n = 160), and the following relationship was obtained (Equation (14)) with a high fitness (R² = 0.856):

$$T=\left(0.156\times PET-0.009077\times PE{T}^2-0.08595\right)\times \left[1-\exp \left(-4.616\times REW\right)\right]\times \left[1-\exp \left(-0.1959\times ST\right)\right] R^2=0.856$$

(14)

The total forest transpiration observed in 2019 was 56.49 mm, and that calculated using the model was 56.25 mm, which was 0.42% lower than the measured value. The average daily forest transpiration observed in 2019 was 0.3531 mm, and that calculated using the model was 0.3516 mm, which was 0.42% lower than the measured value. The difference between 89.38% of the simulated value and the measured value was smaller than 0.1 mm·day⁻¹ (Figure 4a), with an NS of 0.856.

The accuracy of the model was verified using the data from 2020 (n = 169), and the results are shown in Figure 4b. The difference between 81.66% of the simulated and measured values was below 0.1 mm·day⁻¹. The average value calculated from all data (0.3409 mm·day⁻¹) was 5.28% higher than the measured value (0.3238 mm·day⁻¹). The calculated total forest transpiration in 2020 (57.61 mm) was 5.30% higher than the measured value (54.71 mm), with an NS of model verification of 0.825. These results indicate that the accuracy of the comprehensive multifactor model is high and that it can accurately predict forest transpiration with known PET, REW, and ST data.

3.5. Restrictions on Transpiration by PET, REW and ST

During the research period, the optimal PET was 8.6 mm·day⁻¹, and the optimal REW and ST were 0.92 and 21.7 °C, respectively. After introducing the three factors into the constructed forest transpiration model, the maximum potential daily forest transpiration was calculated to be 0.568 mm·day⁻¹. The optimal values of the three factors during the research period could be used to calculate their limiting effects on daily forest transpiration. As shown in Figure 5, the limiting effect of PET on forest transpiration was the largest and most complex, with a roughly undulating trend, first decreasing and then increasing. The limiting effect of REW presented an overall trend that first increased and then decreased. The limiting effect of ST was the smallest, with an overall trend that first decreased and then increased.

Table 3. Tree transpiration reductions by the limit of potential evapotranspiration (PET), relative extractable soil water content (REW), and soil temperature (ST) during the growing season of 2019 and 2020.

Year	Month	PET Limit		REW Limit		ST Limit
		T/mm	Percent/%	T/mm	Percent/%	T/mm	Percent/%
2019	May	4.19	23.78	0.33	1.87	1.24	7.04
	Jun	3.45	20.23	1.57	9.25	0.32	1.88
	Jul	2.12	12.03	1.92	10.93	0.11	0.60
	Aug	4.28	24.32	0.67	3.81	0.10	0.54
	Sep	7.08	41.58	0.16	0.93	0.52	3.07
	Oct	11.14	63.32	0.21	1.22	1.87	10.64
	May–Oct	32.25	30.88	4.87	4.66	4.16	3.98
2020	May	2.72	15.43	1.52	8.62	0.83	4.72
	Jun	3.14	18.46	4.16	24.40	0.26	1.50
	Jul	3.89	22.12	2.45	13.90	0.13	0.72
	Aug	6.19	35.16	0.96	5.43	0.16	0.89
	Sep	7.20	42.25	0.37	2.15	0.48	2.82
	Oct	11.83	67.21	0.39	2.24	2.09	11.88
	May–Oct	34.97	33.47	9.83	9.41	3.94	3.77

shows the monthly limiting effects of PET, REW, and ST on tree transpiration. Overall, the limiting effect of PET was significantly greater than that of REW and ST. In 2019, the limiting effect of REW was 17.09% greater than that of ST, and in 2020, it was 149.60%, which was mostly related to 2019 being a wet year and 2020 being a normal year. In October 2019 and 2020, the limiting effect of PET was the greatest, exceeding 30% in both years. The limiting effect of PET in September and October exceeded 40%. The least PET-restrictive months were July in 2019 and May in 2020. In 2019 and 2020, the most restrictive months of REW were July and June, respectively, while the least restrictive month was September. In 2019 and 2020, the most restrictive month of ST was October, while the least restrictive months were August and July, respectively.

4. Discussion

4.1. Response of Tree Transpiration to PET

Forest transpiration has been previously shown to be affected by meteorological factors such as air temperature [36], solar radiation intensity [37], water vapor pressure deficits [37,38], and wind speed. PET can represent the comprehensive effect of various meteorological factors [39], and it can reflect the atmospheric evaporation demand and water absorption capacity of plants [20]. It can affect the difference in water vapor concentration between leaf stomata and the atmosphere, along with the stomatal action in leaves, thereby affecting forest transpiration [40]. Generally, as PET increases, the difference in water vapor concentration between leaf stomata and the atmosphere gradually increases, and stomatal resistance decreases, resulting in a gradual increase in the transpiration rate. However, when PET is particularly high, intense transpiration can reduce water potential, leading to a decrease in stomatal conductance and an increase in stomatal resistance, which, in turn, inhibits transpiration, thence resulting in a decrease in the transpiration rate [41,42]. In this study, the analysis based on the upper outer envelope revealed a binomial relationship between PET and forest transpiration that first rose and then decreased. That is, when PET was less than 4 mm d⁻¹, forest transpiration increased rapidly, and when PET was 4–8.5 mm d⁻¹, forest transpiration increased slowly and then decreased slowly. Some scholars have found similar changing trends in Larix principis-rupprechtii plantations at Liupan Mountain, Ningxia, China [20,43,44].

Here, the forest transpiration variation trend along with PET is still consistent with those verified by many other scholars. For instance, Bréda et al. [42] investigated the transpiration of Quercus petraea in Nancy, southeastern France, and Granier et al. [45] conducted related research in French Guiana. As they have confirmed, the threshold at which forest transpiration no longer increases as PET increases is 4 mm/day in all cases. In addition, Wu et al. [36] have conducted controlled experiments on the transpiration of nursery-grown Robinia pseudoacacia on the Loess Plateau in northwest China and have reported that PET thresholds under clay and sandy loam conditions are 3.2 and 4.0 mm/day, respectively.

In the above studies, the PET threshold corresponding to the maximum forest transpiration is lower than that in our study, which may be caused by the differences in biological characteristics between tree species and environmental conditions in the research areas. In other studies, however, transpiration (T) linearly increases as PET increases and no apparent thresholds at which PET stops increasing have ever been found. For instance, Granier et al. [46,47] have investigated the transpiration of Pinus pinaster Ait. in southern France, demonstrating that T/PET is 0.55 when PET changes in the range of 0–7 mm·day⁻¹, but measured a T/PET of 0.75 on the tropical rainforest in French Guiana. The main reason for this may lie in the fact that the air humidity in the research area is high, and the difference in water vapor concentration cannot reach the state of stomatal closure; the VPD exhibits minimal stomatal inhibition.

4.2. Response of Tree Transpiration to REW

Soil moisture directly influences forest transpiration and canopy conductance [48,49]. In related studies, the available soil moisture is the indicator generally used and is the ratio of the water content held in soil and available for plants [50]. In addition, REW indicates the water content that a plant root system can absorb and use. A low REW means that capillary conductivity and the root system of soil are rather poor in soil moisture absorption, which probably results in water content and water potential reduction in leaves. Therefore, stomatal guard cells shrink due to water loss, the stomatal aperture of leaves decreases, and water transport resistance increases. Under these circumstances, the forest transpiration rate is very low. As REW increases, the soil moisture absorbed and utilized by the root system increases, as does the water potential and stomatal aperture of leaves. Accordingly, the forest transpiration rate increases [51]. As revealed in studies on forests of Pinus sylvestris L. in Scotland, Picea abies in Sweden, Acer saccharum in Quebec, Canada, Pinus halepensis in Israel, and Populus tremuloides and Pinus banksiana in Canada [52,53,54,55,56], forest transpiration may increase as REW increases; however, once it exceeds a certain threshold, it no longer increases [57,58]. As shown in the above studies, this threshold has a range of 0.2–0.5.

In this study, an exponential growth relationship inclined towards the saturated has been observed in forest transpiration responses to REW. Specifically, forest transpiration increases at a rather high rate as REW increases in a range below 0.3. For REW at 0.3–0.5, forest transpiration increases slowly when REW increases. Once REW exceeds 0.5, it no longer rises when REW increases. Such an outcome is still consistent with those of previous studies. For instance, Granier et al. [30] have investigated how the ratio of canopy stomatal conductance of 21 varieties of trees to the maximum canopy stomatal conductance varies with REW. As far as coniferous and broad-leaf species are concerned, such a ratio increases when REW is increased; however, once REW exceeds 0.4, it tends to be stable [30,59]. For instance, tree transpiration affects the threshold of REW, and a threshold of 0.4 was used for the Robinia pseudoacacia plantations on the Loess Plateau [60]. Our study shows that forest transpiration presented a slight increase as REW increased, mainly due to the fact that the precipitation (554.0 mm in 2019 and 426.4 mm in 2020) during the research period was higher than or similar to that in normal years (350–550 mm), and REW was always at a relatively high level. It remains undetermined whether there is a threshold for forest transpiration in response to REW or whether the magnitude of the threshold is caused by differences in meteorological factors (precipitation, solar radiation, atmospheric temperature, etc.), tree species, or soil characteristics.

4.3. Response of Tree Transpiration to ST

On the one hand, soil temperature plays a role by influencing the water absorption temperature of the root layer and changing the hydraulic conductivity of the plants [61]; on the other hand, soil temperature can affect both the pore structure and the water supply capacity of soil and place further influences on water movement characteristics and moisture availability in the soil to eventually impact forest transpiration. High soil temperature can easily result in plant root scorching; therefore, water absorption can be hindered due to the self-protection feature of the root system. In the case of low soil temperature, the glutinousness and membrane permeability of soil moisture is increased [62]; thus, the hydraulic conductivity of soil and plants can be decreased, which allows the root system to absorb less water and hinders the generation of new fine roots [63,64].

In recent decades, the impacts of soil warming on transpiration in mountain and boreal forests have been extensively investigated using various models and sap flow techniques [65,66,67,68]. Several experiments have confirmed that increasing soil temperature positively influences tree transpiration [36,69]. Based on Schwarz et al. [63], soil temperature forms a significant correlation with sap flow when the temperature is below 10 °C. Clements et al. [70] have found that if soil temperature drops from 45 °C to approximately 10 °C, its impact on vegetation transpiration can be minor. However, once the temperature decreases to approximately 1 °C from 10 °C, vegetation transpiration significantly reduces.

Our study demonstrates that, as ST increased, forest transpiration first increased and then stabilized nonlinearly. The corresponding thresholds are 10 °C and 14 °C. This may result from the inhibitory effects of low available soil moisture and high PET (above the threshold) on forest transpiration during the highest ST periods (July and August). These differences in the above studies clearly indicate that the control of transpiration may be different across species and temperature gradients.

4.4. Multi-Factor Coupling Model of Forest Transpiration

In areas of light deficiency, forest transpiration is primarily confined to meteorological conditions such as PET in general cases. In arid regions with serious water deficits, soil moisture (e.g., REW) is a major constraint on forest transpiration, and in cold regions, forest transpiration is mainly influenced by temperature (e.g., ST). However, forest transpiration is under the joint actions of various factors, such as PET and soil moisture. Considering this, we are less likely to learn about real forest transpiration variations based on the effect of a single factor on forest transpiration.

The controlling effects of transpiration mainly included meteorological factors such as solar radiation and vapor pressure deficit and soil conditions such as soil water availability [26] and soil temperature [71,72]. Currently, the responses of forest transpiration to various factors are seldom explored, and most related research puts emphasis on the environmental responses of forest stand canopy conductance. For forest canopy, stomatal conductance variations of leaves in the light can be expressed in a continued multiplication equation of photon flux density, temperature, VPD, leaf water potential, and ambient CO₂ concentration, which has been increasingly applied [31]. Based on observation data of 12 varieties of trees on 17 sample plots, Granier has constructed a model to reflect the combined influence of different meteorological factors (e.g., radiation, vapor pressure deficit, and temperature), soil moisture, and leaf area index [30]. This approach has been extensively applied in relevant studies on canopy conductance and influencing factors. However, simultaneous responses of forest transpiration to all major influencing factors are comparatively seldom explored in the current literature.

In this study, a daily forest transpiration model was constructed along with the impacts of PET, REW, and ST on forest transpiration (R² = 0.856). The model preferably describes how daily forest transpiration responds to the influencing factors. Moreover, the abovementioned studies have a characteristic in common; that is, they assume that no synergistic interaction takes form in the corresponding effect variables. As for whether such an assumption can be established, this warrants further experimental investigations. If the assumption fails, this means that a synergistic interaction is present among them.

4.5. Limitations of This Study and Future Research Suggestions

This study is limited to analyzing the comprehensive response of forest transpiration to environmental factors exclusively during wet and average water years. Future research should, therefore, encompass long-term and inclusive observations to develop coupled models that adeptly simulate forest transpiration’s response to environmental fluctuations, particularly extreme climate events. Such events include the onset of drought, where soil moisture in the root zone approaches or hits the wilting point, as well as the physiological underpinnings that lead to the establishment of the relative extractable water (REW) threshold and its environmental interactions. Additionally, as the distribution of active root depths is not uniform, the influence of soil moisture and temperature at various depths on forest transpiration is correspondingly inconsistent. Subsequent research should prioritize assessing the varied responses of trees of different heights and root depth profiles to soil moisture shortages. In this study, soil moisture (for REW calculation) and temperature were measured within the 0.1 to 0.8 m range of the root zone in apricot trees. It is conceivable that soil moisture and temperature at greater depths, which can differ with the tree’s age, size, and location on the slope, may affect apricot forest transpiration. Consequently, it may be necessary to adjust current models or their parameters to more accurately represent the interplay between forest transpiration, PET, REW, and ST. When considering a single 30 m × 30 m plot, the model parameters derived from this study may not be fully representative of other artificial forests with varying site conditions and growth stages in the study area or elsewhere.

Furthermore, the limited number of sap flow measurement devices available and the challenges of installing sensors on trees with small diameters meant that sap flow density results were based on a small sample of just four trees with either average or dominant heights. This sampling limitation might lead to an overestimation of stand transpiration, though the impact of tree size may be negligible due to the low stand density and closure. The importance of this research stems from creating a coupled model framework informed by mechanistic understanding, which is instrumental in depicting the combined effects of PET, REW, and ST on forest transpiration. The way forest transpiration reacts to environmental factors changes with local conditions like aspect, slope position, and gradient. Without data from diverse locations, the broad applicability and precision of the forest transpiration coupled model remain untested. Nonetheless, the model’s variables—PET, REW, and ST—are expected to vary with site conditions, suggesting that the model could potentially be used for forecasting forest transpiration across different sites. More empirical observations across varied sites are recommended to confirm the model’s utility in broader contexts and to further refine the transpiration modeling approach.

The TD method proposed by Granier has been widely used to estimate forest stand scale transpiration. In addition, the empirical equation for the method was originally developed by Granier for conifers and broad-leaved trees. At the moment, the sap flow rate is generally calculated using a universal formula that applies to all tree species. However, this formula has limitations and often results in significant errors when estimating the sap flow rate in different regions and with different tree species, sometimes exceeding 30%. Therefore, experts recommend correcting for specific tree species to obtain reliable formulas and estimates. The sap flow formula of the main economic tree species in the Loess Plateau has not been subject to specific research. In future studies, it is imperative to conduct a dedicated correction of its sap flow formula in order to enhance the accuracy of transpiration measurement.

The VPD affects tree transpiration in two ways: firstly, it is accompanied by an increase in evaporation demand, resulting in a greater force of water loss through stomata; secondly, it induces stomatal closure by impacting leaf water status. Consequently, the response of transpiration to changes in VPD exhibits a non-linear pattern, initially increasing until reaching a certain threshold of maximum value, beyond which stomatal closure may lead to reduced transpiration. Drought-stressed trees respond to soil water deficiency by inducing stomatal closure, thereby causing reductions in both transpiration and photosynthesis. Therefore, the regulation of water use through stomatal control plays a crucial role in maintaining the balance between carbon gain and water loss at the individual, stand, and landscape scales. Although this study provides a relatively comprehensive understanding of the response mechanism of short-term transpiration to variations in tree-level VPD and soil water content, there remains a dearth of research on the regulatory impact of stomatal conductance. This represents a limitation in our current study and highlights an area for future investigation.

5. Conclusions

The intricate influence of environmental forces on forest transpiration can be distilled into three primary components: PET, REW, and ST. In semi-arid apricot plantations, transpiration response to increasing PET is characterized by a quadratic relationship, with a decreasing trend beyond a PET threshold of 8.5 mm·day⁻¹. Similarly, transpiration response to REW and ST adheres to a saturation exponential curve, plateauing when REW and ST reach thresholds of 0.5 and 14 °C, respectively. Integrating these single-factor response equations has yielded a mechanistic multiplicative daily transpiration model for the apricot plantation. The model demonstrates high fidelity in both fitting (R² = 0.856) and validation (NS = 0.825), predicting forest transpiration responses to shifts in meteorological conditions and soil environments with considerable accuracy. Although the wider application of the model requires validation with data from additional sites, it provides a viable approach to quantify the concurrent impact of variations in PET, REW, and ST on forest transpiration, as well as to estimate daily forest transpiration using daily data of PET, REW, and ST.