Prediction of Soil Water Thresholds for Trees in the Semi-Arid Region on the Loess Plateau

Abstract

It is important to obtain the soil water content threshold (θ_THR) for agricultural water management. However, the measurement of θ_THR is time consuming and needs specialized and expensive equipment. The accuracy of the empirical estimates is often low. Therefore, the development of a simple, rapid, and accurate prediction method for θ_THR is the focus of the present study. The value of θ_THR is regarded as the soil water content at the capillary break capacity (θ_CB). A formula based on field capacity (θ_FC) and soil bulk density (D_b) is proposed to calculate θ_CB, expressed as ${\theta }_{CB}={\theta }_{FC}-0.21*\left(1-D_b/2.65\right)$. Six soils from six published studies on the response of tree physiological processes to water deficit were used to calculate θ_CB using this formula. The calculated θ_CB values were compared with the measured θ_THR. The results showed that the calculated θ_CB values were nearly equal to the measured θ_THR. A highly significant (adj R² = 0.9826, p < 0.001) linear relationship with a slope of 0.9506 and a y intercept of 0.0072 was found between the calculated θ_CB and measured θ_THR. The formula proposed in this study provides a novel approach for estimating the θ_THR of trees in the semi-arid regions on the Loess Plateau.

1. Introduction

Soil water content (θ) is important for plant growth [1,2,3]. Plant growth will be inhibited if soil water is deficient [4,5]. There is a threshold θ value (θ_THR) for plant growth and physiological processes [6,7,8]. The shoot growth [9], leaf expansion [8], photosynthetic rate (P_n), and transpiration rate (T_r) will decrease with the decrease in θ if θ is lower than θ_THR [10,11]. However, there are no physiological adjustments pertaining to water availability when θ is within the range of θ_THR–θ_FC (field capacity) [12]. It is thus important to determine or estimate θ_THR for agricultural water management [1]. Usually, the value of θ_THR is calculated by modeling plant physiological responses to soil water content [5,13]. However, specialized and expensive equipment such as a portable photosynthesis system is needed for the determination of plant physiological processes such as P_n and T_r.

Total plant available water, TPAW (cm³ cm⁻³), is defined as the value of θ ranging from θ_FC to the permanent wilting point (θ_PWP). The TPAW indicates the ability of the soil to store and provide water that is available to plant roots. The fraction of plant available water (FPAW) or the fraction of transpirable soil water (FTSW) is usually used to monitor the soil water status [7,9]. The FPAW and FTSW are calculated as the ratio of actual plant available water (APAW) and actual transpirable soil water (ATSW) to the total plant available water (TPAW) and total transpirable soil water (TTSW), respectively [2,7,9]. The APAW and ATSW are calculated as the difference between the actual θ and θ_PWP; therefore, the TPAW and TTSW are calculated as the difference between θ_FC and θ_PWP [2]. The threshold FPAW (FPAW_THR) and threshold FTSW (FTSW_THR) are defined as the values of FPAW and FTSW at θ equal to θ_THR. θ_PWP is estimated as θ, corresponding to 15,000 cm soil water suction [14,15] or to θ at the plant transpiration rate in drying soil less than 10% of that in fully watered soil [4,7,12]. It is time consuming to measure θ_PWP.

As far as soil is concerned, θ_THR should be regarded as the capillary break water (θ_CB) [16]. Soil water cannot be transported to the roots rapidly enough for plants to use when θ is less than θ_CB. The value of θ_CB can be empirically calculated based on a soil water retention curve (SWRC) using an optimum partitioning clustering method [17]. However, time consumption is a common limitation for obtaining the SWRC [18]. The value of θ_CB is estimated empirically and approximately as 0.7–0.75 θ_FC [16]. However, θ_THR has an approximate value of 0.5–0.6 θ_FC for trees such as goldspur apple (Malus pumila cv. Goldspur), Salix matsudana, and Forsythia suspense [10,19,20] in semi-arid regions on the Loess Plateau of northern China. Therefore, the empirical coefficient of 0.7–0.75 between θ_FC and θ_CB may not be suitable for estimating the θ_THR of trees in this region.

The Loess Plateau is located in the arid and semi-arid regions of northern China. Drought and water resource shortages are the main restrictive factors for the sustainable development of vegetation restoration and fruit production in the Loess Plateau [10]. However, insufficient rainfall may also lead to soil erosion. Therefore, the ultimate goal of forest establishment in the semi-arid regions on the Loess Plateau is to conserve soil and to use the water from the inadequate rainfall with higher efficiency [11]. Therefore, water-saving management techniques aimed at improving water use efficiency are very important in this region [10,11,19]. The accurate determination of the θ_THR of plants is a key factor for water-saving management techniques [1,2]. Thus, a calculation formula of θ_CB for the accurate estimation of θ_THR of trees on the Loess Plateau would be conducive to water-saving management in this semi-arid region.

The objectives of this study were (1) to propose a method for calculating θ_CB based on θ_FC and the soil bulk density (D_b) and (2) to compare the calculated θ_CB with the measured θ_THR.

2. Materials and Methods

2.1. Calculation of θ_CB

A theoretical formula for calculating θ was proposed by Qian (1985) [21]. θ comprises two parts, i.e., the part held by the attractive force of the soil particles and the part held by the water surface energy. Thus, the formula of θ is expressed as [21]

$$\theta ={\theta }_{MH}+{\theta }_{HE}$$

(1)

where θ (cm cm⁻³) is the volumetric water content in the soil; θ_MH (cm cm⁻³) is the maximum hygroscopy of the soil, and θ_HE (cm cm⁻³) is the soil water held by surface tension.

The inter-facial free energy of a single soil pore (E_i) is expressed as [21]

$$E_i=S_i\sigma \cos \omega ={\rho }_{w}g{q}_i{h}_i$$

(2)

where S_i (cm²) is the surface area of a single soil pore; σ (g s⁻²) is the surface tension at the air–water interface; ω (°) is the contact angle of the surface of soil particles with water; ρ_w (g cm⁻³) is the water density; g (cm s⁻²) is the gravity acceleration; q_i (cm³) is the soil water volume in a single soil pore; and h_i (cm) is the capillary height. q_i is calculated based on Formula (2), as follows [21]:

$$q_i=\frac{S_i\sigma \cos \omega }{{\rho }_{w}g{h}_i}$$

(3)

The pore number of soil per unit volume is equal to N. θ_HE is calculated as

$${\theta }_{HE}={\displaystyle \sum _{i=1}^N{q}_i}={\displaystyle \sum _{i=1}^N\frac{S_i\sigma \cos \omega }{{\rho }_{w}g{h}_i}}=\frac{N{\overline{S}}_i\sigma \cos \omega }{{\rho }_{w}g{h}_i}$$

(4)

where ${\overline{S}}_i$ (cm²) is the average surface area of a single soil hole. N can be calculated as follows [21]:

$$N=\frac{V_t}{\epsilon {\overline{V}}_i}$$

(5)

where V_t (cm³ cm⁻³) is the total volume of soil per unit volume; ${\overline{V}}_i$ (cm³) is the average volume of a single soil hole; and ε (dimensionless) is the coefficient of the soil particle arrangement in the range of 2.36–2.57 [21]. V_t can be calculated as follows:

$$V_t=1-\frac{D_b}{2.65}$$

(6)

where D_b (g cm⁻³) is the soil bulk density, and 2.65 (g cm⁻³) is the average value of the soil particle density.

Combining Formulas (1), (4), (5), and (6) gives

$$\theta ={\theta }_{MH}+\left(1-\frac{D_b}{2.65}\right)\times \frac{{\overline{S}}_i\sigma \cos \omega }{{\overline{V}}_i{\rho }_{w}g{h}_i}$$

(7)

If a soil hole is regarded as a sphere, the maximum value of θ as calculated from Formula (7) can be considered θ_FC [21]. Using this, the value of ${\overline{S}}_i/{\overline{V}}_i$ can be expressed as

$$\frac{{\overline{S}}_i}{{\overline{V}}_i}=\frac{4\pi {\overline{r}}^2}{\pi {\overline{r}}^{3}4/3}=\frac{3}{\overline{r}}$$

(8)

where $\overline{r}$ is the average of a single soil hole radius. Thus, combining Formulas (7) and (8) gives

$${\theta }_{FC}={\theta }_{MH}+\left(1-\frac{D_b}{2.65}\right)\times \frac{3\sigma \cos \omega }{{\rho }_{w}g{h}_i\overline{r}}$$

(9)

The value of h at 20 °C is given by [22]:

$$h=\frac{0.149}{\overline{r}}$$

(10)

Finally, the assumptions for water at 20 °C are as follows: σ = 72.75 g s⁻², g = 981 cm s⁻², and ω = 0°. One can obtain a simplified theoretical equation for θ_FC calculation by combining Formulas (9) and (10) and by substituting the numerical values for these constants:

$${\theta }_{FC}={\theta }_{MH}+\frac{1.4931}{\epsilon }\times \left(1-\frac{D_b}{2.65}\right)$$

(11)

The θ_CB defines the boundary for the capillary moisture area and characterizes the state in which water in the soil capillary begins to break [16,23]. When θ decreases from θ_FC to θ_CB, the soil pores can be considered to change from a sphere to a cylinder. Therefore, if a soil capillary is regarded as a cylinder, then the θ calculated from Formula (7) can be considered θ_CB. Under this assumption, the values of ${\overline{S}}_i$ and $\overline{V}$ can be calculated as

$${\overline{S}}_i=2\pi r\times 2R$$

(12)

$${\overline{V}}_i=\pi r^2\times 2R$$

(13)

where R (cm) is the average value of the soil particle radius. Combining Formulas (7), (10), (12), and (13) and by substituting numerical values for the constants, the measure θ_CB can be calculated using a simple formula expressed as

$${\theta }_{CB}={\theta }_{MH}+\frac{0.9954}{\epsilon }\times \left(1-\frac{D_b}{2.65}\right)$$

(14)

Combining Formulas (11) and (14) gives

$${\theta }_{CB}={\theta }_{FC}-\frac{0.4799}{\epsilon }\times \left(1-\frac{D_b}{2.65}\right)$$

(15)

The coefficient of ε can be selected as the approximate value of 2.36 for soil in the natural state. Thus, submitting ε = 2.36 into Formula (15) gives

$${\theta }_{CB}={\theta }_{FC}-0.21\times \left(1-\frac{D_b}{2.65}\right)$$

(16)

Formula (16) completes the calculation for θ_CB. It provides a theoretically accurate formula for θ_CB rather than an empirical estimate.

2.2. Data of Soil and Trees

Forests and fruit trees play an important role in soil and water conservation in the Loess Plateau of northern China [10,11]. The water-saving management techniques aimed at the enhancement of water-use efficiency are an effective tool for dealing with the scarce water resources in this semi-arid region [10,11,24]. Thus, literature reports focusing on the relationship between tree physiology and soil moisture in the region were selected. In addition, the values of D_b and θ_FC needed to have been used in these reports because θ_CB is calculated using these two parameters. Based on these criteria, six literature reports [19,25,26,27,28,29] were cited and employed in this study.

The D_b and θ_FC values of the six soils from the six studies ranged from 1.14 to 1.35 g cm⁻³ and from 0.247 to 0.333 cm³ cm⁻³, respectively. The D_b and θ_FC values of the six soils and tree species are listed in

Table 1. Soil bulk density (D_b), field capacity (θ_FC), permanent wilting point (θ_PWP), empirical estimate of capillary break water (θ_CB-E), and total plant available water (TPAW) of six soils and tree types from six published studies.

Soil Number	Plant	Db g cm−3	θFC	1θPWP	2TPAW	References
			cm3 cm−3
1#	Robinia pseudoacacia	1.35	0.321	0.093	0.228	[26]
2#	Ulmus pumila	1.22	0.247	0.053	0.194	[24]
2#	Robinia pseudoacacia	1.22	0.247	0.057	0.190
2#	Pinus tabulaeformis	1.22	0.247	0.045	0.202
2#	Platycladus orientalis	1.22	0.247	0.047	0.200
2#	Prunus armeniaca	1.22	0.247	0.054	0.193
2#	Acer truncatum	1.22	0.247	0.048	0.199
2#	Caragana microphylla	1.22	0.247	0.049	0.198
2#	Hippophae Rhamnoides	1.22	0.247	0.058	0.189
3#	Robinia pseudoacacia	1.20	0.252	0.054	0.198	[25]
3#	Platycladus orientalis	1.20	0.252	0.047	0.205
4#	Salix matsudana	1.24	0.253	0.045	0.208	[19]
5#	Phyllostachys edulis	1.14	0.326	0.057	0.269	[28]
6#	Prunus armeniaca	1.21	0.333	0.076	0.257	[27]

¹ This was estimated as the soil water content when the leaf photosynthetic rate decreased to zero. ² This was the difference between θ_FC and θ_PWP.

. The effects of water deficiency on the tree physiological processes were examined in these studies [19,24,25,26,27,28]. The relationship between the tree physiological indices and θ was modeled using the following linear plus plateau function:

$$R=R_{\max }\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\theta }_{THR}<{\theta }_R\le {\theta }_{FC}$$

(17)

$$R=R_{\max }+S\times \left(\theta -{\theta }_{THR}\right)\hspace{1em}\hspace{1em}\theta <{\theta }_{THR}$$

(18)

where R is the tree physiological index; R_max is the plateau value of R; S is the slope; θ (cm³ cm⁻³) is the soil water content; and θ_THR is the threshold of the soil water content. Thus, θ_THR was identified by locating the intersection of the two lines.

The FTSW is calculated as

$$FTSW=\frac{\theta -{\theta }_{PWP}}{{\theta }_{FC}-{\theta }_{PWP}}$$

(19)

where FTSW is the fraction of transpirable soil water, and θ_PWP was estimated as θ corresponding to P_n = 0. The relationship between the tree physiological indices and FPAW (FTSW) was also modeled using the following linear plus platform function:

$$R=R_{\max }\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}FTS{W}_{THR}<FTSW\le 1$$

(20)

$$R=R_{\max }+S\times \left(\theta -{\theta }_{THR}\right)\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}FTSW<FTS{W}_{THR}$$

(21)

θ_R-CB and θ_R-THR were calculated as follows:

$${\theta }_{R-CB}={\theta }_{CB}/{\theta }_{FC}$$

(22)

$${\theta }_{R-THR}={\theta }_{THR}/{\theta }_{FC}$$

(23)

where θ_FC is the field capacity.

3. Results

3.1. Relationship between θ_THR and θ_CB

The values of θ_THR and θ_CB for six soils are listed in

Table 2. The soil water content threshold (θ_THR), soil water content of capillary break (θ_CB), relative value of θ_CB (θ_R-CB), and threshold fraction of transpirable soil water (FTSW) of six soils.

Soil Number	Plant	θTHR	θCB	θR-THR	θR-CB	FTSWTHR
		cm3 cm−3
1#	Robinia pseudoacacia	0.219	0.218	0.68	0.68	0.55
2#	Ulmus pumila	0.132	0.134	0.53	0.54	0.41
2#	Robinia pseudoacacia	0.137	0.134	0.55	0.54	0.42
2#	Pinus tabulaeformis	0.139	0.134	0.56	0.54	0.46
2#	Platycladus orientalis	0.134	0.134	0.54	0.54	0.43
2#	Prunus armeniaca	0.132	0.134	0.53	0.54	0.41
2#	Acer truncatum	0.137	0.134	0.55	0.54	0.45
2#	Caragana microphylla	0.134	0.134	0.54	0.54	0.43
2#	Hippophae Rhamnoides	0.135	0.134	0.55	0.54	0.41
3#	Robinia pseudoacacia	0.138	0.137	0.55	0.54	0.42
3#	Platycladus orientalis	0.132	0.137	0.52	0.54	0.42
4#	Salix matsudana	0.142	0.141	0.56	0.56	0.47
5#	Phyllostachys edulis	0.209	0.206	0.64	0.63	0.57
6#	Prunus armeniaca	0.206	0.219	0.62	0.66	0.51
Mean		0.152	0.152	0.57	0.57	0.45

. The values of θ_THR ranged from 0.132 to 0.219 cm³ cm⁻³, with a mean of 0.152 cm³ cm⁻³. The values of θ_CB were nearly equal to those of θ_THR. The mean value of θ_CB was 0.152 cm³ cm⁻³, with a range of 0.134–0.219 cm³ cm⁻³.

A highly significant (adj R² = 0.9826, p < 0.001) linear relationship was found between θ_THR and θ_CB (Figure 1). Ideally, if the θ_CB values were exactly the same as θ_THR, then the adj R² would equal 1.0, the slope would equal 1.0, and the y intercept would equal 0. The slope value of 0.9506 and the adj R² of 0.9826 are nearly equal to 1.0. The y intercept of 0.0072 is approximately equal to 0. Thus, the θ_CB estimated from Formula (16) performed well in predicting θ_THR.

Comparison of θ_R-CB with the Empirical Ratio Coefficient of θ_CB to θ_FC

The values of θ_R-CB for soils 1^# and 6^# were 0.68 and 0.66, respectively. These are close to the values of 0.7–0.75, which is the empirical ratio of θ_CB to θ_FC. However, the θ_R-CB values of 2^#, 3^#, 4^#, and 5^# were 0.54, 0.54, 0.56, and 0.63, respectively. These were lower than 0.7–0.75. Thus, the empirical ratio coefficient of θ_CB to θ_FC does not exactly apply to the soil of the Loess Plateau.

3.2. θ_R-CB and FTSW_THR

θ_R-CB ranged from 0.54 to 0.68 for the six soils (Table 2). However, FTSW_THR (FPAW_THR) ranged from 0.41 to 0.46. The mean value of 0.57 of θ_R-CB was higher than 0.47 of FTSW_THR (Table 2). The θ_R-CB of soil 2^# was a fixed value of 0.54. The values of θ_R-THR and FTSW_THR ranged from 0.53 and 0.41 to 0.56 and 0.46, respectively (Table 2). θ_R-CB of soil 3^# was 0.54. The FTSW_THR was 0.42 for Robinia pseudoacacia and Platycladus orientalis in soil 3^#. However, the θ_R-THR values were 0.52 and 0.56 for Robinia pseudoacacia and Platycladus orientalis, respectively (Table 2). Thus, tree species affected FTSW_THR but not θ_R-CB or θ_CB.

3.3. Effects of Soil and Tree on o_ther

The effects of the soil water content on eight trees (Ulmus pumila, Robinia pseudoacacia, Pinus tabulaeformis, Platycladus orientalis, Prunus armeniaca, Acer truncatum, Caragana microphylla, and Hippophae Rhamnoides) were studied in soil 2^#. The θ_THR values of the eight trees ranged from 0.132 to 0.139 cm³ cm⁻³, with a mean of 0.135 cm³ cm⁻³. The θ_CB of the 2^# soil was 0.134 cm³ cm⁻³. The θ_THR values were 98%–104% of θ_CB. Thus, it was θ_CB but not the plant species that affected θ_THR.

The influences of soil water deficiency on Robinia pseudoacacia were determined in soils 1^#, 2^#, and 3^#. The θ_THR values were 0.219, 0.137, and 0.138 cm³ cm⁻³ for soils 1^#, 2^#, and 3^#, respectively (Table 2). The θ_CB values were 0.218, 0.134, and 0.137 cm³ cm⁻³ (Table 2). The D_b and θ_THR values of soil 2^# were 1.22 g cm⁻³ and 0.247 cm³ cm⁻³, very close to the values of 1.20 g cm^–3 and 0.252 cm³ cm⁻³ for soil 3^#, respectively. Thus, the values of θ_THR and θ_CB for soil 2^# were close to those of soil 3^#. However, in soil 1^#, D_b = 1.35 g cm⁻³ and θ_THR = 0.321 cm³ cm⁻³ were significantly higher than the respective values in soils 2^# and 3^#. Therefore, the values θ_THR = 0.219 and θ_CB = 0.218 cm³ cm⁻³ in soil 1^# also were significantly higher than the respective values in soils 2^# and 3^#. This also suggested that θ_CB was the major factor affecting θ_THR.

The values of θ_THR for Platycladus orientalis were 0.134 and 0.132 cm³ cm⁻³ in soils 2^# and 3^#, respectively (Table 2). The values of θ_CB were 0.134 and 0.137 cm³ cm⁻³ (Table 2). This was because the values of D_b (1.22 g cm⁻³) and θ_FC (0.247 cm³ cm⁻³) soil 2^# were approximately equal to the D_b (1.20 g cm⁻³) and θ_FC (0.252 cm³ cm⁻³) values in soil 3^# (Table 2), respectively. The θ_THR and θ_CB values for Prunus armeniaca of 0.132 and 0.134 cm³ cm⁻³ in soil 2^# were significantly lower than the respective values of 0.206 and 0.219 cm³ cm⁻³ in soil 6^# (Table 2). This was because θ_FC = 0.247 cm³ cm⁻³ in soil 2^# was significantly less than θ_FC = 0.333 cm³ cm⁻³ in soil 2^# (Table 2). Additionally, D_b = 1.22 g cm⁻³ in soil 2^# was nearly equal to D_b = 1.21 g cm⁻³ in soil 2^#. Thus, θ_THR was largely determined by θ_CB.

The tree species affected FTSW_THR but not θ_R-CB or θ_CB (Table 2). This was because θ_PWP varied among plant species (Table 2). θ_PWP can be estimated as θ corresponding to 15,000 cm soil water suction [14,15]. Under these circumstances, the FTSW_THR may be equal for the same soil because θ_THR (θ_CB), θ_FC, and θ_PWP do not vary with plant species. However, this does not reflect the differences in the resistance of plants to soil water deficits. Thus, in studies of plant responses to soil water deficits, θ_PWP is usually estimated as the θ measured from the plant transpiration rate in dry soil that is less than 10% of that in fully watered soil [7,9,12]. The θ_PWP is estimated as θ corresponding to leaf P_n = 0 in this study. The FTSW_THR is unequal for different plant species due to different θ_PWP values for the same soil.

4. Discussion

The TPAW is classified into two ranges from the perspective of the soil. One is classified as the water that is easily available for plants (EPAW), and other is classified as the water that is not as easily available to plants (DPAW) [16,29]. The θ_CB value defines the boundaries for the EPAW and the DPAW [16]. Soil water in the range of θ_FC–θ_CB (EPAW) is retained by capillary suction and is in a capillary-suspended state [30]. Thus, soil water can be transported to plant roots easily and quickly. By contrast, soil water in the range of θ_CB–θ_WPW (DPAW) is held by the sorption forces of soil particles and is mainly in the film state [29]. The DPAW is held tightly by soil particles so that it cannot be continuously transported to the roots rapidly enough to meet the needs of the plant [1,16]. Therefore, soil water is inadequate for plant demand when it is in the range of θ_CB–θ_WPW (DPAW). Thus, θ_CB can be regarded as θ_THR in theory.

The θ_THR is a dividing point of the TPAW [1,2]. The TPAW is affected by soil pore properties [15,17,30]. D_b and θ_FC are two main factors affecting soil properties [15,31]. Therefore, the θ_THR is affected by D_b and θ_FC, while the θ_CB is calculated by D_b and θ_FC. That may be another possible reason why θ_CB equals θ_THR. The D_b and θ_FC values in different soils are complex [15,21,31]; thereby, the values of θ_THR and θ_CB are also complex in different soils. Therefore, θ_R-THR and θ_R-CB values may vary with the soil. That is the reason why the θ_R-THR values of six soils taken from Loess Plateau in this study are different. It also explains why the θ_R-CB values of the six soils differ from the empirical coefficient of 0.7–0.75, the mean difference in soil textures [16].

The value of θ_CB is affected by θ_FC and D_b, based on Formula (16). D_b in the range of 1.10–1.35 g cm⁻³ is regarded as the “optimal range” for plant growth [32,33]. If D_b is beyond 1.35 g cm⁻³, then plant growth will be limited by inadequate soil aeration [34,35] or by excessive mechanical resistance to root elongation [32]. If D_b is lower than 1.10 g cm⁻³, the low soil strength will lead to inadequate plant anchoring and reduced plant-available water [33]. $TPAW={\theta }_{FC}-{\theta }_{PWP}\ge 0.20$ cm³ cm⁻³ is often considered “ideal” for maximal root growth and function [36], and 0.15 ≤ TPAW < 0.20 cm³ cm⁻³ is “good” for plant growth, while 0.15 ≤ TPAW < 0.20 cm³ cm⁻³ as well as 0.10 ≤ TPAW < 0.15 and TPAW < 0.10 cm³ cm⁻³ are “limited” and “poor” soils [37,38]. In this study, 1.14 ≤ D_b ≤ 1.35 g cm⁻³ and 0.189 ≤ TPAW ≤ 0.269 cm³ cm⁻³ suggest that Formula (16) is at least suitable for the calculation of θ_CB for “good” soils to estimate θ_THR. Further studies are needed to determine whether it is applicable to “limited” or “poor” soils.

It Is necessary to discuss the feasibility of the method provided in this study for other soils in the Loess Plateau. A data set including seven soils representing the major soil types present on the Loess Plateau [39] was used to evaluate Formula (16) indirectly because there was no other direct experimental evidence. The values of θ_FC for the seven soils were 0.178, 0.218, 0.304, 0.301, 0.328, 0.316, and 0.343 cm³ cm⁻³, corresponding to D_b values of 1.46, 1.28 1.38, 1.40, 1.41, 1.48, and 1.53 g cm⁻³, respectively. Thus, the values of the calculated θ_CB are 0.084, 0.109, 0.203, 0.202, 0.230, 0.223, and 0.254, respectively. The seven mean ranges of the θ_THR values of the seven soils are 0.122–0.072, 0.146–0.083, 0.238–0.165, 0.240–0.171, 0.280–0.221, 0.269–0.223, and 0.300–0.247 cm³ cm⁻³, corresponding to average values of 0.097, 0.114, 0.202, 0.205, 0.250, 0.241, and 0.274 cm³ cm⁻³, respectively. These seven averages are close to those calculated θ_CB values. A highly significant (adjR² = 0.983, p < 0.001) linear relationship with a slope of 1.046 and a y intercept of 0.003 was found between these seven averages (y) and was used to calculate θ_CB (x). Thus, it is feasible to estimate the plant soil moisture threshold on the Loess Plateau using the method proposed in this study.

In addition to soil, θ_THR is also affected by climate, vegetation, and other factors [1,2]. The θ_THR values of trees can be predicted by θ_CB, as calculated by Formula (16), in the semi-arid regions of the Loess Plateau. Whether this method can be applied in other conditions such as in arid regions or with crops requires further research.

5. Conclusions

An approach was provided in this study to predict θ_THR using the estimation of θ_CB based on θ_FC and D_b. The values of θ_THR were nearly equal to those of θ_CB for 10 tree species in six soils in the semi-arid region on the Loess Plateau. θ_THR only changed with θ_CB, but not with tree species. Thus, the estimated θ_CB can be considered as the estimated θ_THR. The estimation only needs to measure θ_FC and D_b. It does not require specialized or expensive equipment and does not need substantial special operational skills. This new method provides an attractive approach for predicting the θ_THR of trees in the studied region.