Sampling Points

Sampling points are situated in the Qinghai-Tibet Plateau’s central region, characterized by a sub-cold monsoon and semi-humid climate, with minimal seasonal variation and significant diurnal temperature fluctuations (Fig. 2). Point 1 is at 31°3′51″N, 91°41′33″E (4500m elevation), and Point 2 is at 32°33′16″N, 91°49′26″E (5000m elevation). The average annual temperature is -0.6ºC, and the average daily difference in temperature is 16.5ºC [33]. Soil samples were collected from alpine meadow soils during their growing season for this experiment. According to the World Reference Base for Soil Resources (WRB), alpine meadow soils can be classified into one of several categories, with the most relevant classifications likely being “Leptosols” (shallow soils), “Phaeozems” (dark soils), or “Umbrisols” (humus-rich soils), depending on specific features such as the content of organic matter, soil depth, and stone content. Alpine meadow soils have a diverse parent material, including weathered rock, glacial remnants, and mountain sediments. Particle size distribution varies from coarse sand to fine clay, determined by the specific parent material and climatic conditions of the region. These soils typically contain a high level of organic matter, with a significant organic carbon content, attributed to the slow decomposition rates of plant residues under cold climate conditions, facilitating the accumulation of organic matter. The bulk density of alpine meadow soils is relatively low, a consequence of the high organic matter content and loose soil structure, which supports root growth and water retention.

Fig. 1.

Research ideas and calculation flowchart.

Fig. 2.

Specific locations of sampling sites.

Sampling sites were chosen at the Xiangmao Township experimental site and Xiaotanggula Mountain experimental site within the Naqu basin. Soil types at both sampling sites were dominated by alpine meadow soil. They are located in the upper and lower reaches of the Naqu watershed, respectively. The surface of the sampling site in Xiangmao Township was covered with vegetation, while the sampling site in Xiaotanggula Mountain was bare soil. The natural environment of the two places is similar. The Xiaotanggula Mountain sampling site was used as a replication of the Xiangmao Township sampling site. Observations were conducted over two consecutive growing seasons at the experimental sites. As much as possible, we made sure that the changes we observed were caused by changes in time, temperature, and humidity, and not random changes. Over the years, we have been deploying monitoring equipment at two experimental sites, and we have obtained a large amount of soil temperature and moisture data to support this research.

Sample Collection

Field samples were taken in 2021 and 2022 during the regreening and wilting periods at the Xiangmao Town and Xiaotanggula Mountain test sites established by the China Institute of Water Resources and Hydropower Research (IWHR). Before sampling, we removed vegetation and debris from the site’s surface. Using a 1-meter-long auger with a 5-centimeter internal diameter, the auger was slowly advanced vertically over the top of each soil layer to collect the undisturbed soil column from each layer. Then slowly push it into a 5 cm high PVC transparent tube with an inner diameter of 5 cm and wrap it carefully in plastic wrap. The sampling depth was 0-50 cm. Five soil layers (5 cm, 10 cm, 20 cm, 35 cm, 50 cm) were collected. A total of 40 soil samples were collected from the two experimental sites. After each sampling, the soil samples were stored in ice bags and sent to the Nanjing Institute of Soil Sciences of the Chinese Academy of Sciences to obtain soil pore parameters. Soil moisture and soil temperature data acquisition equipment is embedded near the sampling point. The buried depths of the equipment are 5cm, 10cm, 20cm, 35cm, and 50cm. Soil moisture, water potential, and temperature are collected every 1 hour. After continuous soil monitoring, we obtained soil moisture and soil temperature data of different soil layers at the experimental sites during the regreening and wilting periods [33] A double-ring infiltration experiment was carried out near the sampling point. The saturated soil water conductivity of sampled soils was obtained by long-term (4 h) observation [33].

Sample Testing and Image Processing

The undisturbed soil columns were subject to X-ray computed tomography (ZX _ 2014) at the Nanjing Institute of Soil Research, Chinese Academy of Sciences (the Nanotom S model produced by Phoenix, voltage 180kV, power 15W). The device could observe the three-dimensional appearance and internal structure of the undisturbed soil column without destroying its integrity. Meanwhile, pore volume, surface area, length, connectivity, and fractal dimension could be calculated. These scanned images were in TIFF format with a resolution of 25 μm/pixel. In order to improve the precision and eliminate the edge error, the cuboid of 2.5 cm, 2.5 cm, and 5 cm in the center of the soil column was studied. (The cuboid is an undisturbed clod.) Three-dimensional structure images and two-dimensional continuous slice images of soil pores were obtained by using ImageJ software (Fig. 3).

Fig. 3.

Flow chart for soil sample collection and analysis.

Soil Porosity

2D image is transformed into a digital matrix by Image J software. The pixel value 0 represents the solid substance in the soil (the white part in Fig. 4). The pixel value 255 represents the pore in the soil (the black part in Fig. 4). For each soil sample, the ratio of the number of 255 pixels to the number of all pixels in each 2D image was calculated. Repeat this calculation for 1500 images and take the average value, the porosity of this soil sample was obtained.

Where η is the porosity of undisturbed soil blocks; n is the number of images; N₀ refers to the number of pixels with a pixel value of 0; and N₂₅₅ is the number of pixels with a pixel value of 255.

Pore Variability

Pore variability is used to describe the difference in soil porosity between adjacent soil layers. The higher the pore variability, the stronger the soil spatial variability [34]. Which is not conducive to vegetation growth.

Where E is the pore variability; η_u refers to the porosity of the upper soil; and η_u corresponds to the porosity of the lower soil.

Pore Connectivity

The ratio of the largest pore volume in each sample to the total volume of the soil sample [35].

Where R_p is the connectivity of pores; V_PAMAX refers to the volume of the largest pore in the undisturbed soil blocks; and V is the total volume of the undisturbed soil blocks.

Fractal Dimension

Soil pore complexity can be quantitatively evaluated by the relationship between pore surface area and pore circumference [36].

Where D is the pore fractal dimensions; P refers to the pore circumference; and A corresponds to the pore surface area. The larger the fractal dimension, the higher the soil pore complexity.

Pore Curvature

The curvature of soil pores can be quantitatively evaluated by the relationship between the length of the pore path and the Euclidean distance [37-39]. It was computed assuming the geodesic reconstruction algorithm implemented by Roque [32].

Where C_a is the mean soil pore curvature, as follows; P_L refers to the length of the pore path; and E_M refers to the Euclidean distance. The higher the curvature of the pore, the stronger the hygroscopic ability.

Calculate Soil Water-holding Capacity and Hydraulic Conductivity

The Campbell formula has been widely used in soil moisture research since its appearance in 1974 and has achieved fruitful results [36, 40-41]. In the Campbell formula, the empirical constant b is used to describe the complexity of the soil pore distribution. There is a functional relationship between the empirical constant n and b. The fractal dimension D, indicating complex shape irregularity, characterizes soil pore distribution complexity. As a result, Tyler SW first introduced the fractal dimension into the Campbell formula in 1990, which greatly contributed to the study of soil water retention and hydraulic conductivity [42]. They found that the Campbell formula still holds true for parameters

Fig. 4.

Two-dimensional images illustrate the spatial distribution of soil pores in the Little Tanggula Mountains (Figs. a and c) and Xiangmao Township (Figs. b and d). Note: 21XT-G and 21XT-Y in (a) and (b) denote soil samples collected from Xiaotanggula Mountain in 2021 during the regreening and wilting periods respectively, while 21XM-G and 21XM-Y denote soil samples collected from Xiangmao Township in 2021 during the regreening and wilting periods respectively. The black part of the image shows soil pore and the white part shows other solid-phase materials in the soil. 5 cm denotes sampling depth of 5 cm. (c) and (d) are soil samples in 2022, and other representations are consistent with (a) and (b), as follows.

b=1D−2 (1≤D<2), including soil water-holding capacity (Eq. (6)) and soil hydraulic conductivity (Eq. (7)). However, with the deepening of the research on fractal dimension, its connotation and calculation method have changed profoundly. The fractal dimension now represents the quantitative relationship between soil pore path length and Euclidean distance (Eq. (4)) [43]. In addition, when Tyler introduces fractal dimension, the applicable scenario is to assume that the soil pore distribution is in an ideal state of “ Sierpinski carpet” (1≤D<2) [42]. In contrast, alpine meadow soil with extremely complex pore structures does not have this ideal distribution. More importantly, the study of soil pores has moved from 2D to 3D, and the corresponding formula should be adjusted to accommodate the new scene. We suggest that the use of pore curvature instead of fractal dimension in the Campbell formula may be more applicable to the study of alpine meadow soil. Both describe the complexity of soil pore distribution compared to the fractal dimension. However, the fractal dimension represents the complexity of the pore distribution of the whole sample, while pore curvature represents the complexity of the individual pore distribution inside the sample. Our improvement is a shift from external to internal and from whole to individual. Each soil sample contains approximately 100,000 pores, providing data on the pore curvature for a similar number of individual pores. The large amount of data provides the number of samples required for the calculation, which can ensure the accuracy of the results. In contrast, fractal dimensions do not have data volumes of this size. Therefore, we choose pore curvature instead of fractal dimension in many soil-pore characteristic parameters.

Where θ is the soil volumetric water content; η refers to the soil porosity; S_b corresponds to the bubble capillary pressure; S is the soil suction; D refers to the fractal dimension; K(θ) corresponds to the soil water conductivity; Ks is the soil saturation conductivity; as follows.

In the original Campbell formula, the soil porosity was calculated using the ring knife method. The method is time-consuming, the sample cannot be reused, and it is easy to miss the aerated pore, which affects the accuracy. Therefore, the soil porosity was calculated from the two-dimensional X-CT images. The specific method has been described in the previous section, and will not be repeated here. This method is short-lived and the sample can be reused to measure other parameters. The 25 μm resolution of the test instrument is sufficient to guarantee the test accuracy. In summary, the adjusted Campbell formula includes the water-suction curve (Eq. (8)) and the water-conductivity curve (Eq. (9)). On this basis, the soil water-holding capacity (Eq. (10)) and soil hydraulic conductivity (Eq. (11)) of different soil layers are obtained.

Accuracy Verification

The resistance of soil water movement in soil pores is mainly the bubble capillary pressure. The higher the capillary pressure, the slower the soil water flow. Therefore, the soil suction S_sat corresponding to the saturated water content is usually equated with the bubble capillary pressure S_b. The more similar the two, the higher the accuracy [44]. Using this principle, the accuracy of the adjusted Campbell formula is verified. Using the Clapp-Hornberger equation (moisture-suction curve):

Where S_sat is the soil suction corresponding to the saturated moisture content (hereafter referred to as S_sat); θ_s refers to the saturated moisture content; b is the Clapp-Hornberger constant [45].

To further validate the accuracy of the adjusted Campbell formula, we cite data such as saturated water content and saturated hydraulic conductivity used by Deng [33]. in their study. Since they did their study in the same area at a similar time, the relevant data can be quoted. The validation method was to calculate K(θ) using Campbell formula based on pore curvature (Eq. (11)) and fractal dimension (Eq. (13)), respectively, and compare the correlation with an RMSE with the measured data K(θ) from Deng [33].

Quantitative Characterization of Soil Pore

Soil pore numerical characteristics encompass pore number (Fig. 5(a)), ratios of independent (Fig. 5(b)) and connected pores (Fig. 5(c)), average pore junction (Fig. 5(d)), and path branch (Fig. 5(e)). Soil pores can be divided into two types according to their connectivity, independent pores and connected pores [46-48]. Independent pores are dominated by small pores and connected pores by large pores [49]. The mean number of pores in different soil layers decreased in different degrees during the growth period (Fig. 5(a)). Pore numbers significantly vary across soil layers. The pore type is mainly independent pores (Fig. 5(b)). As shown in Table 1 of the appendices, from the regreen to the wilting stage, Xiaotangula Mountain soils showed changes: independent pore ratios decreased from 92.66% to 89.88%, connected pore ratios increased from 7.33% to 10.11%, average pore junctions rose from 1.16 to 3.14, and path branches fell from 42986.5 to 23531.5. In Xiangmao Township, soil layers experienced a decrease in independent pore ratios from 88.95% to 87.10%, an increase in connected pore ratios from 11.04% to 12.89%, pore junctions from 1.84 to 2.27, and path branches from 4091.1 to 4423.2.

In summary, the shift in alpine meadow soil pore characteristics primarily reflects a decrease in independent pores and an increase in connected pores (Fig. 5(b), Fig. 5(c)). However, the number of independent pores still dominates in all soil layers (Fig. 5(b)). During the growing season, we noted a marked decrease in pore path branching and an increase in pore junctions (Fig. 5(d), Fig. 5(e)). This is caused by the change of small pores to large pores in alpine meadow soil. This change was particularly notable in the Xiaotanggula Mountains. We thus infer that soil connectivity will increase. This may be related to the development of root systems in alpine meadows. The development of the root system breaks down the gaps in the separate pores and connects the small pores into large ones.

Fig. 5.

Violin plots illustrating soil pore characteristics. Note: Green denotes the regreening period and Yellow denotes the wilting period, as follows. (a) indicates the mean number of pores, (b) denotes the mean ratio of independent pores, (c) indicates the mean ratio of connecting pores, (d) denotes the average pore junction points, (e) indicates the average path branch, (f) denotes the mean porosity, (g) indicates the mean pore variability, (h) denotes the mean pore curvature, (i) indicates the mean fractal dimension, (j) denotes the mean anisotropy and (k) indicates the mean connectivity.

Morphological Characteristics of Soil Pore

Soil pore morphology parameters comprise porosity (Fig. 5(f)), variability (Fig. 5(g)), curvature (Fig. 5(h)), surface area (Fig. 6(a)), volume (Fig. 6(b)), length (Fig. 6(c)), and sphericity (Fig. 6(d)) [50-52]. As shown in Table 2 of the appendix, the changes in soil pore morphology characteristics from the regreen stage to the wilting stage as follows: soil porosity decreased from 25.02% to 19.10% in Xiaotanggula Mountain and from 24.13% to 18.66% in Xiangmao Township. The mean of pore variability of each soil layer decreased from 10.91% to 4.16% in Xiaotanggula Mountain and from 5.73% to -1.26% in Xiangmao Township. Pore curvature decreased by 3.00% in Xiaotanggula Mountain and by 1.04% in Xiangmao Township. Surface area increased from 0.20 to 0.73 in Xiaotanggula Mountain and from 0.60 to 0.79 in Xiangmao Township. Volume increased from 0.01 to 0.04 in Xiaotanggula Mountain and from 0.04 to 0.05 in Xiangmao Township. Sphericity changed from 62.87±9.96 to 63.66±10.34 in Xiaotanggula Mountain, but decreased from 61.83±10.32 to 60.49±9.83 in Xiangmao Township. Length increased from 0.14±0.19 to 0.15±0.21 in Xiaotanggula Mountain and from 0.15±0.19 to 0.17±0.25 in Xiangmao Township.

Soil porosity in alpine meadow soil decreased during the growing season. Significant decreases in pore variability during the growing seasons suggest stabilization of soil pore development. This stabilization relates to the slowing, stopping, or dying of alpine meadow root systems during wilting periods. Soil pore curvature showed a decreasing trend (Fig. 6(h)). Changes in pore sphericity and pore length were not significant (Fig. 6(c), Fig. 6(d)). This is not conducive to the vertical development of root systems in alpine meadows. We can see that the increase in soil pore surface area was much larger than the increase in pore volume in both experimental sites (Fig. 6(a), Fig. 6(b)). This suggests that horizontal development dominated pore formation [53]. It is inferred that the alpine meadow soil has a strong water-holding capacity.

Spatial Distribution Characterization of Soil Pore

Parameters for pore space distribution are fractal dimension (Fig. 5(i)), anisotropy (Fig. 5(j)), and connectivity (Fig. 5(k)) [54-56]. Fractal dimension and anisotropy quantify the space distribution characteristics of soil pores in the soil structure. As shown in Table 3 of the appendix, the average fractal dimension of pores across Xiaotanggula Mountain’s soil layers remained stable at approximately 2.67 during the growing seasons. Anisotropy in Xiaotanggula Mountain’s soil layers decreased from 0.39 to 0.31 during the growing seasons. Connectivity in each soil layer increased from 4.45% to 16.43% during the growing seasons. In Xiangmao Township, the average fractal dimension slightly decreased during the growing seasons, with no significant change. However, pore anisotropy in each soil layer increased from 0.32 to 0.38, and connectivity from 12.23% to 14.62%.

In summary, the soil pore space distribution characteristics of alpine meadow soil in the growing season were mainly characterized by a complex overall distribution (Fig. 5(i)), reduced anisotropy (Fig. 5(j)), and increased connectivity (Fig. 5(k)). Both soil pore quantity and morphological porosity characterizations indicated a decrease in pore numbers during the growing season. The decrease in pore numbers, alongside the distribution characteristics, is attributed to increased connectivity. The enhanced pore connectivity is manifested in the pore morphology characterized by the appearance of large pores with high surface area and low volume (Fig. 6(a), Fig. 6(b)). Such macropores hinder vertical movement and distribution of soil moisture. Anisotropy’s impact on root characteristics within pore spaces remains unclear. The fractal dimension can reflect the variation in the proportion of clay, silt, and sand in soil texture [36]. A higher fractal dimension means higher clay content. This also hinders the flow of soil moisture. Therefore, it is believed that alpine meadow soil possesses greater water-holding capacity than hydraulic conductivity.

Verifying the Accuracy of The Soil Water-Holding Capacity and Hydraulic Conductivity

Prior to assessing alpine meadow soil’s water-holding capacity and hydraulic conductivity, we verified the adjusted Campbell formula’s outcomes using equations in section 2.4.2. The calculation results are detailed in Table 4 in the appendix. Eq. (12) was used to verify soil water-holding capacity, and Eq. (13) for soil hydraulic conductivity. Soil water-holding capacity and hydraulic conductivity were verified using measured data and data from Deng [33], respectively. Results indicated that for the growing season, S_b1 (soil water-holding capacity), derived from the Campbell formula using fractal dimension, had a correlation (R) of -0.7474 with S_sat, while S_b2 (soil hydraulic conductivity), based on pore curvature, had an R of 0.9948 with S_sat. Fig. 9 shows the scatter plot we plotted. From the Fig. 9, we can see that S_b2 fits better than S_b1 with S_sat. For the soil hydraulic conductivity, we verified the accuracy by calculating the Bias and RMSE of the simulated and measured data. According to Table 1 and Table 5 in the appendices, K2(θ) soil hydraulic conductivity, derived from the Campbell formula using pore curvature, had a Bias of -0.0112 and RMSE of 0.0148; K3(θ), using fractal dimension, had a Bias of 0.0782 and RMSE of 0.0784. In conclusion, Campbell formula based on pore curvature is more accurate than Campbell formula based on fractal dimension. We consider the new method to be reliable.

Fig. 8.

Analysis of the relationship between soil pore characteristics and soil moisture. Note: In the figure, red rectangles signify an increase, blue rectangles a decrease, yellow rectangles soil pore characteristics, and green rectangles soil hydraulic characteristics.

Fig. 9.

Validation of the accuracy of soil water holding capacity. Note: (a) Derived from the Campbell formula using fractal dimension. (b) Derived from the Campbell formula using pore curvature.

Spatiotemporal Variation Analysis of Soil Water-holding Capacity

Using the Campbell formula adjusted for pore curvature (Eq. (10)), we calculated the water holding capacities across different soil horizons in Xiaotanggula Mountain and Xiangmao Township over two growing seasons. The violin plots of soil water-holding capacity of alpine meadow soil with superimposed box plots were drawn (Fig. 10(a)), and the dot-line map indicating the characteristics of temporal and spatial variations of water-holding capacity of alpine meadow soil was plotted (Fig. 11(a), Fig.11(b)). During the regreening periods, water holding capacities in each soil layer initially increased then decreased in both Xiaotanggula Mountain and Xiangmao Township. In the wilting periods, the spatial characteristics of the soil water-holding capacity in Xiaotanggula Mountain were more obvious, which was in the shape of “W”. By the wilting period, the soil water-holding capacity of both sampling sites showed a decrease. This was due to a decrease in independent pores (Fig. 5(b)) and an increase in connected pores (Fig. 5(c)), resulting in lower soil porosity (Fig. 5(f)) and higher pore connectivity (Fig. 5(k)). The decrease in pore variability indicates a stabilization of pore development (Fig. 5(g)). The morphological characteristics of high surface area and low volume of pores indicate that pore development is dominated by the horizontal direction (Fig. 6(a), Fig. 6(b)). Therefore, at the pore scale, the reduction in soil water-holding capacity during the growing season is attributed to the development of flattened, stabilized, and interconnected pores. However, a high fractal dimension indicates a high clay content in the soil. This leads to a decrease in the soil water-holding capacity of alpine meadow soil by the time of wilting, but it still has high water-holding capacity.

The decrease in water-holding capacity can promote the vertical movement and distribution of soil moisture. During the growing season, both sites exhibited high air bubble capillary pressure in the middle soil layers. This indicates that soil moisture in alpine meadow soil is concentrated in the middle of the soil layer. This is also the soil layer where alpine meadow roots are enriched. Enhanced soil water-holding capacity ensures ample moisture, benefiting root development. Additionally, the dense vegetation root system plays a crucial role in maintaining the soil’s high water-holding capacity.

Fig. 10.

A combined box-and-whisker and violin plot illustrates soil hydraulic characteristics. Note: (a) Represents soil water retention capacity, and (b) signifies soil water conductivity.

Fig. 11.

Line charts depict temporal and spatial variations in soil hydraulic properties. Note: (a) Details the distribution of soil water retention during the regreening period, while (b) does so for the wilting period. (c) Describes the distribution of soil water conductivity during the regreening period, and (d) during the wilting period.

Spatiotemporal Variation Analysis of Soil Hydraulic Conductivity

Using the Campbell formula adjusted for pore curvature (Eq. (11)), we calculated soil hydraulic conductivity across various soil layers in Xiaotanggula Mountain and Xiangmao Township over two growing seasons. We then illustrated these findings with violin plots superimposed with box plots (Fig. 10(b)) and dot-line maps showing spatial and temporal variations (Fig. 11(c), Fig. 11(d)). During the regreening period, soil hydraulic conductivity at both sites displayed a notable change at depths of 20-35 cm (Fig. 11(c)), with a decline in conductivity and an increase in water-holding capacity up to 35 cm. Beyond this depth, hydraulic conductivity rose, and water-holding capacity decreased. 0-35cm is the main soil layer for root development in alpine meadows. Therefore, the phenomenon of rising soil water-holding capacity and decreasing soil hydraulic conductivity in the regreening period may be related to root development in alpine meadows. Root development absorbs water and traps it at that location, leading to a reduction in soil hydraulic conductivity. At the pore scale during the regreening period, independent pores constituted over 87% of total pores (Fig. 5(b)), with an average pore intersection below 2.0 (Fig. 5(d)), indicating lower pore connectivity compared to the wilting period (Fig. 5(k)). During the wilting period, soil hydraulic conductivity in the Xiaotanggula Mountains exhibited an “M” shape (Fig. 11(d)). This mirrors the earlier-described “W” shape of soil water-holding capacity in the Xiaotanggula Mountains during the wilting period (see Section 3.2.2). This suggests that in soil layers with high water-holding capacity, soil hydraulic conductivity weakens correspondingly.

Notably, from the regreening to the wilting period, both sampling sites exhibited increased soil hydraulic conductivity and decreased water-holding capacity in the alpine meadow soil layers. Based on the improved Campbell formula, the highly significant negative correlation between soil pore curvature and saturated hydraulic conductivity, and the significant positive correlation between soil suction, we concluded that it was the decrease in soil pore curvature that caused the decrease in soil water-holding capacity and the increase in soil hydraulic conductivity.