Time Series Analysis and Temporal Stability of Shallow Soil Moisture in a High-Fill Slope of the Loess Plateau, China

Abstract

Precipitation-induced soil moisture dynamics are a key factor that plays a critical role in triggering slope failures and geological hazards. This study investigates the response of soil moisture in a high-fill slope to rainfall and explores the influence of the topographic conditions and rainfall characteristics on the soil moisture dynamics. The findings reveal that the topographic conditions significantly influence the soil moisture variability in the high-fill loess slope. The coefficient of variation (CV) follows a decreasing pattern, i.e., slope surface > slope step > flat terrain > slope foot, with the spatial variability diminishing as the depth increases. The response of moisture to rainfall is influenced by the rainfall characteristics. In this study, the peak lag time (PLT), which represents the time interval between the onset of rainfall and the occurrence of the peak cross-correlation coefficient (CCF) between soil moisture and rainfall, is analyzed. The results indicate that, under similar rainfall intensities, the PLT decreases with increasing rainfall amounts. Conversely, for comparable rainfall amounts, a higher rainfall intensity generally shortens the PLT at all positions except the slope step. On the slope scale, the temporal stability of soil moisture exhibits the order flat terrain > slope surface > slope step > slope foot, whereas, in the vertical profile, the temporal stability is positively correlated with the depth. This study provides valuable insights into the hydrological processes of loess high-fill slopes and contributes to understanding slopes’ hydrological transformation and evolution.

1. Introduction

Loess, covering an extensive area of 640,000 km², is one of the most widely distributed soils in Central and Northwestern China [1]. In recent years, rapid urbanization and population growth have intensified the land use pressures on the Loess Plateau. This has led to a contradiction between the increasing demand for land and the limitation of land resources. To alleviate this contradiction, a series of large-scale projects, such as Mountain Excavation and City Construction and Gully Land Consolidation, have been implemented, resulting in the formation of numerous high-fill slopes [2,3,4]. A high-fill slope refers to an artificial slope with a height exceeding 15 m, constructed using soil or other materials through layering or compaction. These slopes are characterized by large engineering volumes, long construction periods, and significant variations in the properties of the fill materials. However, loess high-fill slopes are highly susceptible to landslides, soil erosion, and other types of degradation due to external human activities [5], seasonal groundwater level fluctuations [4], and the collapsibility of loess [6,7,8,9,10,11]. After water infiltration, the structure of loess is disrupted, causing pore collapse. Meanwhile, the increase in the pore water pressure and the reduction in matric suction lead to a decrease in the shear strength of the soil, thereby reducing the slope’s stability [6]. For instance, a step-shaped high-fill slope in Yan’an City failed under continuous heavy rainfall on 19 July 2016, with a landslide volume reaching 1.5 × 10⁴ m³. Research has shown that the soil moisture dynamics play an important role in surface runoff, erosion, and slope failure. Therefore, it is of great significance to investigate the soil moisture dynamics of loess high-fill slopes to understand the soil moisture evolution and refine soil–water conservation.

Soil moisture, as the link between precipitation, surface water, and groundwater, plays an essential role in the hydrological cycle. Its spatial and temporal variability is influenced by various factors, such as the topographic conditions, rainfall characteristics, climate conditions, seasonal variations, and human activities [12,13,14,15]. Among these, the topographic conditions influence the spatial distribution of soil moisture mainly through the slope gradient and position [16,17,18]. Under the influence of gravity, rainfall or surface water infiltrates and flows downward along the slope. Meanwhile, after rainfall redistribution, surface runoff and subsurface flows converge toward the lower position of the slope. These processes collectively transform the lower slope into a water accumulation zone, where the soil often maintains higher moisture content. Rainfall directly impacts the soil moisture dynamics through characteristics such as the rainfall amount, intensity, and duration [19,20]. The soil moisture response amplitude is positively correlated with the rainfall amount and negatively correlated with the soil depth [14]. Although significant progress has been made in understanding the soil moisture dynamics, most research on the Loess Plateau has focused on natural slopes, and further investigation of the moisture distribution characteristics within high-fill slopes is required.

The current research methods for soil moisture mainly include in situ monitoring, remote sensing inversion, and numerical simulation techniques. These methods offer significant advantages in terms of spatial coverage and data precision, enabling the more efficient capture of soil moisture dynamics. The selection of research methods should consider the specific objectives, research scope, and scale. At the slope scale, soil moisture sensors based on time domain reflectometry (TDR) and frequency domain reflectometry (FDR) principles have been applied for long-term field observations. These sensors typically measure the dielectric permittivity of the soil and indirectly obtain the water content by assessing the electrical conductivity, charge storage capacity, or propagation time [21,22]. The main advantage of this method is the ability to continuously monitor dynamic changes in the soil moisture [23] and accurately capture the complex moisture variation. However, the monitoring range is limited, making it difficult to extend to larger scales [22,24,25]. Additionally, the installation, calibration, and maintenance of monitoring equipment are both time-consuming and costly [26]. The remote sensing inversion method estimates the soil moisture content and analyzes its spatial variation characteristics by acquiring surface reflectance and radiation energy [26,27]. Remote sensing data cover the full spectrum, including the visible, infrared, thermal, and microwave bands, enabling the rapid acquisition of soil moisture information at regional and larger spatial scales [26,28]. Furthermore, remote sensing methods offer advantages such as low-cost image acquisition over large areas and multi-resolution capabilities [29]. However, this method has limitations, including a restricted detection depth to the surface layer [27], difficulties in selecting appropriate models [30], and the reliability of the inversion results, which is yet to be validated [29,31]. Numerical simulation is a computational process that includes making assumptions and simplifications based on fundamental mathematical models, selecting numerical calculation methods, and performing program-based computations. Commonly used simulation methods in the field of soil moisture movement include the finite element method, finite difference method, and integral finite difference method. The primary advantage of numerical simulation is its ability to utilize limited moisture data to predict and analyze hydrological dynamics over extended temporal scales and larger spatial extents [32,33]. Additionally, computational software such as HYDRUS 2.0, COMSOL Multiphysics 6.3, and MODFLOW 4.1 has significantly advanced the field of soil moisture movement simulation. However, due to model simplifications and parameter uncertainties, numerical simulations are unable to accurately reflect the actual soil layer characteristics of loess high-fill slopes, leading to discrepancies between the simulation results and real conditions [34,35]. In summary, each method has its unique advantages and limitations depending on the research context. For soil moisture research on loess high-fill slopes, in situ monitoring not only provides accurate time series data but also directly reveals the spatial distribution characteristics of soil moisture, making it particularly suitable for the analysis of the soil moisture dynamics at the slope scale.

The theoretical approaches used to understand soil moisture movement mainly include classical statistical methods, wavelet coherence analysis, and time series analysis. These analytical methods have been widely applied across different research scales, including sample plots, slopes, and watersheds. Classical statistical methods analyze the spatial variability of soil moisture via parameters such as the maximum (Max), minimum (Min), average value (Avg), and coefficient of variation (CV) of soil moisture sequences [36]. However, this approach assumes that soil hydrological properties are independent within a certain spatial range, neglecting the spatial correlation of soil moisture. In contrast, wavelet coherence analysis evaluates the correlation between two data sequences across various time scales by calculating wavelet coefficients and cross-wavelet spectra [37]. It is particularly effective in handling non-stationary time series with random or abrupt events [17]. Challenges such as scale selection, threshold denoising, and wavelet decomposition in wavelet analysis remain significant obstacles [38,39]. Time series analysis is an effective method for the study of soil moisture dynamics at the slope scale. For two time-synchronous sequences, the cross-correlation coefficient (CCF) can quantify their relationship regardless of differences in variability [40,41]. Thus, it can quantitatively reveal the response characteristics of soil moisture to rainfall events. For loess high-fill slopes, time series analysis based on rainfall and soil moisture monitoring data can effectively capture the response of the soil moisture characteristics at different depths and identify the similarities in soil moisture across the slope.

In view of the above, the high-fill slopes on the Loess Plateau have reshaped the original surface morphology and significantly altered the soil hydrological processes. Although previous studies have made progress in understanding the soil moisture dynamics on the slope scale, the soil moisture distribution characteristics within the loess high-fill slopes remain unclear. Meanwhile, as the primary source of water in arid and semi-arid regions, rainfall still remains the subject of conflicting research findings—some studies suggest that intense rainfall promotes rapid infiltration, whereas others argue that surface crusting reduces infiltration and increases runoff [14,42,43]. Therefore, this study selects a loess high-fill slope in Yan’an, Shaanxi Province, as the research site. Based on monitoring data, combined with time series analysis and temporal stability analysis, the relationship between soil moisture and rainfall is investigated. The specific objectives of this study are as follows: (1) to analyze the difference in the soil moisture dynamics under different topographic conditions on the high-fill slope; (2) to explore the correlation, as well as the lag effects, between rainfall and soil moisture under varying rainfall conditions. The findings offer valuable insights into the hydrological processes of loess high-fill slopes and contribute to understanding slopes’ hydrological transformation and evolution.

2. Materials and Methods

2.1. Study Area

The study area is located in the central Loess Plateau in Yanan City (36°35′11.59″ N, 109°18′45.24″ E), which belongs to a semi-arid monsoon climate zone, with an annual average temperature of 7.7–10.6 °C and annual precipitation of 570.6 mm.

The experimental high-fill slope was constructed in 2015 and had a four-step terraced structure. The slope extends 310 m east to west and spans 150 m north to south, with an elevation of roughly 22 m. The projected length is approximately 45 m, and the slope gradient is about 28° (Figure 1). The filling soil primarily originates from the surrounding mountains and has been compacted through simple mechanical methods. During the construction of the high-fill slope, a light roller was used for layered filling and compaction. The compaction process followed the principles of rolling from the slope foot to the slope top, starting at a slow speed and gradually increasing. Each layer was compacted 8–10 times at a speed of 2–3 km/h. Before compaction, the thickness of each soil layer was controlled within 30–50 cm, and the rolling paths overlapped by no less than half the roller width. The physical parameters of the fill material are detailed in

Table 1. Basic properties of the filling soil.

Depth (cm)	Dry Density (g/cm3)	Void Ratio	Hydraulic Conductivity (10−3 cm/s)	Plastic Limit (%)	Plastic Index	Particle Size Distribution (%)
						Clay	Silt	Sand
10	1.42	0.87	0.39	16.59	12.98	12.62	77.41	9.97
50	1.60	0.69	0.09

.

2.2. Research Methods

2.2.1. In Situ Soil Moisture Dynamic Monitoring

This research arranged 12 monitoring points (E1–E4, M1–M4, W1–W4) along four horizontal lines and three vertical lines on the slope to monitor the moisture dynamics. At each monitoring point, MS10 soil moisture sensors were installed at depths of 10, 20, 30, 50, 100, and 200 cm (sensors were set at depths of 10, 20, 30, 50, and 100 cm at M4), with a monitoring frequency of 10 min. Additionally, liquid level sensors (Onset HOBO U20L-01) were also installed at each monitoring point. A tipping bucket rain gauge (JDZ02-1) was placed at the top of the slope, with a tipping increment of 0.2 mm. The detailed characteristics of the monitoring sensors are summarized in

Table 2. Detailed characteristics of monitoring sensors.

Parameter	Sensor	Type	Period	Precision	Resolution	Quantity
Moisture content	Moisture content sensor	MS10	10 min	2–3%	0.03–1%	72
Groundwater level	Liquid level sensor	Onset HOBO U20L-01	10 min	±0.1%FS, 1.0 cm	<0.02 kPa; 0.21 cm	12
Rainfall	Rain gauge	JDZ02-1	0.2 mm	0.2 mm	≤±4%	1

.

The detailed layout of the monitoring points is shown in Figure 2. In this research, monitoring data from the central line (M1–M4) were selected for analysis. M1–M4 were located at the flat terrain, slope step, slope surface, and slope foot, respectively.

2.2.2. Principles of Classical Statistical Methods

Classical statistical methods typically use statistical parameters such as the average value (Avg), maximum value (Max), minimum value (Min), and coefficient of variation (CV) to characterize soil moisture variability. The Avg value reflects the overall soil moisture level in the study area, while the Max and Min values indicate the extreme ranges of soil moisture variation. The CV is used to measure the relative dispersion of soil moisture. The comprehensive application of these statistical parameters helps to fully reveal the distribution characteristics of soil moisture data. The CV is classified as follows: CV < 10% for weak variability; 10% ≤ CV ≤ 100% for moderate variability; CV ≥ 100% for strong variability. This method has been widely used in the soil moisture research field [16,17,44,45].

2.2.3. Principles of Time Series Analysis

For two stationary time series x and y with consistent sampling intervals, the equation for CCF calculation is

$${\rho }_{\mathrm{xy}}={\displaystyle \frac{S_{xy}(h)}{\sqrt{S_{xx}(0)S_{xy}(0)}}}={\displaystyle \frac{S_{xy}(h)}{{\delta }_x{\delta }_y}}$$

(1)

where ρ_xy is the CCF between the two sequences x and y at lag time h; S_xy(h) is the covariance between x and y at lag time h; S_xx(0) and S_yy(0) represent the variances of x and y; δ_x and δ_y represent the standard deviations of x and y; and h is the lag time. In this research, the lag time h is set to 1 h.

For the time series (x₁, y₁), (x₂, y₂), (x₃, y₃), …, (x_n, y_n), the covariance S_xy(h) at a time lag h can be calculated using the following formula:

$$S_{xy}={\displaystyle \frac{1}{n}}{\displaystyle {\sum }_{i=1}^{n-1}(x_i-\overline{x})}(y_{i+h}-\overline{y}) h=1,2,\dots ,n$$

(2)

where $\overline{x}$ and $\overline{y}$ are the mean values of the time series samples x and y, respectively.

Combining the two equations above, the CCF at the lag time h can be calculated, along with the double standard deviation of the sequence. When ρ_xy = 0, the two sequences are significantly uncorrelated; when ρ_xy is greater than twice the standard deviation, it indicates that the two sequences are correlated; and when ρ_xy is less than twice the standard deviation, the two sequences are uncorrelated.

2.2.4. Principles of Temporal Stability

Temporal stability refers to the consistency of soil moisture distribution patterns over time and was proposed by Vachaud in 1985 [46]. The non-parametric Spearman’s test is used to examine the persistence of spatial patterns over the study period. When the rank correlation coefficient r_s approaches 1, it indicates that the soil moisture ranks at different locations are less likely to change during repeated measurements, indicating the stronger temporal stability of the soil moisture [13,36,47].

$$\rho =1-6{\displaystyle \sum _{\mathit{i}=1}^N\frac{{(R_{ij}-R_{il})}^2}{N(N^2-1)}}$$

(3)

where R_ij and R_il are the ranks of the soil moisture observations at monitoring point i at times j and l, respectively, after being arranged in ascending order; N represents the number of measurement points [47].

3. Results

3.1. Rainfall Events and Soil Moisture Dynamics

This study analyzes the monitoring data from 16 July 2019 to 31 December 2019. During this period, 27 rainfall events directly influenced the soil moisture at a depth of 10 cm, with a cumulative rainfall amount of 539.0 mm, accounting for 73.6% of the annual rainfall (732.4 mm). The rainfall pattern was characterized by abundant rainfall in summer and autumn and low precipitation in winter (Figure 3). According to the Chinese Meteorological Industry Standard Grade of Rainfall Processes (QX/T 489-2019) [48], these rainfall events were categorized based on their magnitudes. Independent rainfall events were identified based on the criterion that no other rainfall occurred the day before or after the event.

During the research period, there were 18 light rain events with a cumulative rainfall amount of 76 mm (14.1% of total rainfall), three moderate rain events totaling 72.2 mm (13.4%), three heavy rain events accumulating 190.7 mm (35.4%), and three rainstorm events with a cumulative rainfall amount of 200.1 mm (37.1%). Four representative rainfall events were selected to analyze the impact of the rainfall characteristics on the soil moisture dynamics, as shown in Figure 3. Among them, Events 1 and 2 were short-duration rainstorms with differing rainfall intensities, while Events 3 and 4 were long-duration heavy rain events with varying rainfall amounts.

The soil moisture dynamics at different depths of each monitoring point during the study period are shown in Figure 4. A statistical analysis of the soil moisture data collected during the research period is summarized in

Table 3. Statistical characteristics of moisture content.

	Depth (cm)	Avg (cm3/cm3)	Max (cm3/cm3)	Min (cm3/cm3)	CV (%)
M1	10	19.52	33.91	8.19	25.87
	20	23.29	37.29	9.86	11.90
	30	27.48	32.15	22.22	5.35
	50	28.49	29.93	23.53	3.84
	100	46.16	50.46	34.65	7.83
	200	46.29	47.79	44.33	1.35
M2	10	21.76	32.43	8.78	28.05
	20	17.42	25.84	7.73	23.38
	30	25.48	28.43	13.73	11.25
	50	27.49	30.79	21.71	5.56
	100	27.30	28.71	24.98	4.08
	200	25.56	26.38	24.44	2.60
M3	10	20.42	33.28	7.42	30.36
	20	25.00	35.43	9.63	26.72
	30	24.80	31.41	11.63	19.69
	50	20.07	26.65	9.19	16.45
	100	17.11	20.49	11.17	10.16
	200	31.60	32.31	30.4	1.47
M4	10	34.55	36.34	25.03	5.50
	20	34.35	35.43	28.99	3.47
	30	33.62	35.66	27.82	3.97
	50	35.00	35.43	32.09	1.45
	100	34.83	34.99	34.54	0.22

. The mean soil moisture content at different monitoring points ranged from 7.42 to 50.46 cm³/cm³. The CV ranged from 0.22% to 30.36%, which indicates weak to moderate variability. The CV exhibited a decreasing trend along the vertical profile, suggesting a negative correlation between the CV and soil depth. Shallow soil moisture is more susceptible to rainfall, the temperature, and evapotranspiration, resulting in more active water movement. This effect gradually weakens with increasing depths, and the moisture dynamics become more even.

3.2. Analysis of the Correlation Between Rainfall and Soil Moisture

Based on Equation (1), the autocorrelation of both the rainfall and soil moisture sequences was analyzed, and the results are shown in Figure 5 and Figure 6, respectively. Figure 5 illustrates the autocorrelation of the rainfall sequence at the daily scale. It can be observed that the rainfall sequence exhibits high randomness, meaning that rainfall events are independent and previous rainfall does not correlate with subsequent rainfall. As shown in Figure 6, at different slope positions, the ACF of the soil moisture time series decreases with the depth. This trend suggests that soil moisture movement is a long-term and slow process, with the previous soil moisture conditions significantly influencing subsequent changes. Additionally, it can be observed that the ACF decays most rapidly in the 10 cm and 20 cm soil layers, followed by the 30 cm and 50 cm layers, while the 100 cm and 200 cm layers exhibit the slowest decay rates. This indicates that shallow soil moisture is more affected by external factors and has a weaker self-memory effect, whereas deeper soil moisture is relatively less stable. Therefore, the autocorrelation of rainfall events is not significant, whereas soil moisture shows a high degree of autocorrelation.

Based on Equations (1) and (2), a cross-correlation analysis was conducted on the rainfall and soil moisture time series during the research period, as shown in Figure 7. The cross-correlation dynamics between rainfall and soil moisture exhibit clear stratification: the CCF values at depths of 10–30 cm exceed twice the standard deviation in most cases, indicating a significant correlation in response to rainfall events. In some instances, the soil moisture at 50 cm also occasionally exhibits a distinct response to rainfall, although the CCF value is lower than that of the 10–30 cm layer, suggesting a weaker correlation. Therefore, soil moisture in the shallow layers is more susceptible to rainfall events and shows higher sensitivity in response.

Furthermore, the cross-correlation between rainfall and soil moisture across different monitoring points exhibits similarity. The response pattern of the 10–30 cm soil moisture to the selected rainfall events typically shows a single peak, with the response weakening after reaching the peak CCF. Given that the rainfall response of soil moisture is concentrated at a depth of 10–30 cm, the time interval between rainfall onset and the peak of the cross-correlation coefficient (CCF) between soil moisture and rainfall is defined as the PLT to quantitatively analyze the response time of soil moisture under different rainfall conditions. The results are summarized in

Table 4. Statistics of PLT for selected rainfall events at 10–30 cm depth (unit: h).

	Depth (cm)	M1	M2	M3	M4
Event 1	10	5.2	2.8	3.4	7.9
	20	/	3.8	4.6	/
	30	/	/	5.8	/
	50	/	/	44.2	/
Event 2	10	1.9	5.5	1.8	9.5
	20	2	5.6	2.3	/
	30	2.1	/	2.2	/
	50	/	/	/	/
Event 3	10	6.2	6.3	5.1	33.4
	20	9.3	6.6	5.8	6.7
	30	8.7	8.4	6.1	25.3
	50	/	/	12.2	/
Event 4	10	11.1	11.2	11.8	/
	20	22.8	11.8	20.1	/
	30	21.5	13.0	18.8	/
	50	/	32.4	/	/

Note: / means that no obvious peak was observed.

. The data indicate that the PLT is also depth-dependent on an hourly scale, showing an increasing trend with the depth, and varies across different slope positions. Therefore, it is essential to consider the depth and slope position when selecting the best observation time for soil moisture after rainfall.

3.3. Temporal Stability Analysis of Soil Moisture

Based on Equation (3), a Spearman’s rank correlation analysis was performed on the soil moisture monitoring data, as shown in Figure 8. The results indicate a significant correlation at the 0.001 level across different monitoring points, despite a wide range of fluctuation in the Spearman’s rank correlation coefficients.

The ρ values for M1–M4 ranged as follows: 0.6548–0.9833, −0.0898–0.9763, −0.2232–0.9822, and 0.4798–0.8973, respectively [49].

Similar to the rainfall–soil moisture cross-correlation, the temporal stability exhibits a depth dependency in the vertical profile. It can be observed that, regardless of the depth, the Spearman’s rank correlation coefficient between adjacent depths generally remains above 0.9, indicating a highly significant correlation in soil moisture (p < 0.001). As the distance increases, the Spearman’s rank correlation coefficient between soil layers gradually decreases, and the correlation between shallow and deep soil moisture is significantly reduced. This suggests that the temporal stability of soil moisture tends to diminish with increasing depth intervals, further indicating that shallow and deep soil moisture are influenced by different factors. This finding is consistent with previous studies [17].

4. Discussion

4.1. Influence of Topographic Conditions on Soil Moisture Dynamics

The statistical analysis of soil moisture across different monitoring points revealed spatial variability in the distribution of the CV, as shown in Figure 9. Spatial variability refers to the uneven distribution of soil moisture at different locations and depths of the slope. Despite the similar climatic conditions at the four monitoring points, differences in the soil moisture dynamics are primarily driven by the topographic conditions. The slope position influences surface runoff generation, which subsequently alters the redistribution of rainfall. Additionally, the slope gradient affects the water retention capacity per unit area, impacting the infiltration process [50]. In this study, the CV for soil moisture typically follows the order of slope > slope step > flat terrain > foot of slope (Figure 9). This trend is attributed to the natural slope’s lower position in the landscape, which receives water via both surface and subsurface runoff following rainfall events [51]. The combined effects of the abundant water supply and diverse water movement contribute to more frequent and complex moisture dynamics on the slope, thus increasing the soil moisture variability [36]. In contrast, when the slope gradient decreases, as in the case of flat terrain, soil moisture is only replenished by atmospheric precipitation, lacking the additional input from upslope runoff. This leads to lower soil moisture variability on flat terrain compared to the slope. However, the step intercepts water from the upper slope and reduces surface runoff, promoting deeper infiltration [52]. This process not only enhances the water supply to the step but also prolongs the residence time of water [53], thereby increasing the variation in the soil moisture on the step. Previous studies have shown that the lower slope receives water not only from rainfall and upslope runoff but also from groundwater [54], leading to higher variability in the soil moisture compared to the upper slope. However, in this study, the variability in the soil moisture at the foot of the slope was the lowest. This is mainly due to the shallow groundwater table keeping the soil moisture consistently at higher moisture content. Consequently, significant dry–wet cycling driven by external environmental factors does not occur, which reduces the soil moisture variability at the foot of the slope compared to other positions.

At shallower soil layers, surface evaporation, plant root water uptake, and canopy interception cause the soil to undergo continuous wet–dry cycles, resulting in greater spatial variability in the soil moisture dynamics [47,55]. This finding is consistent with the results of this study: the CV coefficients at different monitoring points exhibited a decreasing trend with increasing depths, indicating a gradual reduction in spatial variability (Figure 9). However, some studies on the Loess Plateau have reported a positive correlation between the CV coefficient and depth, primarily due to differences in vegetation cover and land use types. In these cases, the influence of vegetation factors has overshadowed the effect of terrain factors [36,44]. Therefore, the spatial variability in soil moisture, influenced by the slope position, follows the order of slope surface > slope step > flat terrain > slope foot. In vertical profiles, the soil moisture’s spatial variability exhibits a negative correlation with the depth.

4.2. Influence of Rainfall Characteristics on Soil Moisture Response

The rainfall characteristics significantly affect the transformation of the soil moisture response to rainfall events. Factors such as the rainfall amount [56], rainfall duration [14], and intensity [57] collectively influence the efficiency of rainfall infiltration and the spatial distribution of soil moisture. For instance, light rainfall can effectively replenish moisture in shallow soil layers, whereas heavy rainfall can accelerate the soil moisture response [19].

Based on the observed PLT, differences in the rainfall intensity alter the soil moisture response to rainfall, as shown in Figure 10. Taking Event 1 (67.0 mm, 0.0744 mm/min) and Event 2 (65.1 mm, 0.6510 mm/min) as examples, both events have similar rainfall amounts, but there is a significant difference in rainfall intensity. Typically, as the rainfall intensity increases, the rainfall can quickly and sufficiently supply moisture to the soil, as reflected at the flat terrain (M1) and on the slope surface (M3). Consequently, the PLT in Event 2 is approximately 50% shorter than that in Event 1. However, an excessively high rainfall intensity can lead to raindrop impacts eroding soil aggregates and forming a sealing layer on the soil surface [58]. This process causes the soil moisture to remain on the surface and infiltrate slowly. A larger proportion of the moisture is lost as runoff, reducing the amount of rainfall transformed into soil moisture [59], thus prolonging the PLT. Therefore, an increase in rainfall intensity effectively shortens the PLT, except at the step.

Under similar rainfall intensity conditions, a decrease in rainfall amounts extends the time required for the soil moisture to reach its strongest response. Taking Event 3 (45.4 mm, 0.0229 mm/min) and Event 4 (31.0 mm, 0.0228 mm/min) as examples, in Event 4, the PLT at the 10 cm, 20 cm, and 30 cm depths for M1, M2, and M3 increased compared to Event 3 (Figure 10). This phenomenon occurs because rainfall events with lower amounts provide insufficient moisture after canopy interception by vegetation [51]. Additionally, there is a significant difference in the initial moisture content between Event 3 and Event 4. In Event 3, the soil moisture content was higher due to the influence of prior rainfall, whereas, in Event 4, it was relatively lower. Generally, under higher initial moisture conditions, the infiltration rate of rainfall in the soil is faster. At the same time, the hydraulic gradient at the wetting front and the energy consumption for wetting front advancement decrease, leading to the quicker response of the soil moisture to rainfall [60,61,62]. In this study, the peak response time in Event 3 was significantly shorter than in Event 4, indicating that the combined effect of higher initial moisture content and greater rainfall volumes facilitated the more rapid and pronounced response of the soil moisture to rainfall. As a result, the efficiency of rainfall conversion to soil moisture is reduced under the same depth conditions. Therefore, under a similar rainfall intensity, the time required for soil moisture to reach its peak response to rainfall is negatively correlated with the rainfall amount. However, under similar rainfall amounts, an increasing rainfall intensity shortens the PLT at all locations except the step.

4.3. Soil Moisture Temporal Stability Distribution Characteristics

Previous studies have shown that the temporal stability of soil moisture is influenced by factors such as the soil physicochemical properties and topographic features [29]. In this study, the soil physical and chemical property measurements revealed that the densities of the soil at the 10 cm and 50 cm depths were 1.42 g/cm³ and 1.60 g/cm³, with corresponding porosity values of 0.87 and 0.69. From the vertical profile perspective, the 50 cm soil layer is denser, with poorer internal connectivity, reduced aeration, and lower permeability. This structure hinders soil moisture infiltration but increases its water retention capacity [63], allowing soil moisture to remain relatively stable. Additionally, external factors such as seasonal rainfall, the air temperature, and the wind speed continuously influence the hydrological cycle and moisture dynamics within the slope [64]. However, the impact of these external drivers diminishes with the depth, leading to a more stable spatial distribution of deep soil moisture over time. In summary, the combined effects of the internal soil properties and external climatic influences lead to significantly higher temporal stability in deep soil moisture compared to shallow soil moisture. Therefore, as the depth increases, the temporal stability of the soil moisture gradually strengthens (Figure 8), and the distribution pattern of the soil moisture becomes more stable [65].

At the same time, the temporal stability of the soil moisture varies across different monitoring points, showing a non-monotonic decrease from the top to the foot of the slope. Specifically, the temporal stability of the soil moisture is the highest at the slope top (flat terrain), followed by the slope foot and the slope step, and the lowest at the slope surface. This pattern differs from the findings of other studies, which reported the highest temporal stability of the soil moisture at mid-slope positions, followed by the upper slopes, with the lower slopes being the least stable [66]. This discrepancy may attributed to differences in the slope geometry. The researchers investigated a natural slope for their study, with a gradient of only 20°, which significantly differs from the multi-level slope morphology in this study, resulting in the marked difference in the temporal stability of moisture. Therefore, along the vertical profile, the temporal stability of soil moisture is influenced by the density and porosity, and it increases with the depth. At the slope scale, the temporal stability of soil moisture follows the relative order of flat terrain > slope foot > slope step > slope surface.

4.4. Engineering Significance and Applications

For high-fill slopes in the Loess Plateau, soil moisture is one of the key factors that can trigger slope failures and even geological disasters. With the large-scale implementation of projects in the northwestern regions, such as Gully Land Consolidation, the construction of high-fill slopes has significantly altered the moisture dynamics of the original terrain.

Studies have shown that, compared to natural slopes, the presence of slope steps can significantly reduce the spatial variability of soil moisture. Therefore, in the design of high-fill slopes for agricultural use, a stepped structure can be adopted [67]. This approach helps to mitigate drastic fluctuations in soil moisture and enhance the water retention capacity [68]. Additionally, this study found that, among the different slope positions, the soil moisture variation is the most pronounced on the slope surface and slope step. Therefore, when optimizing soil moisture monitoring schemes, monitoring points should be primarily placed in these areas, while their density can be appropriately reduced in flat terrain and at the foot of the slope. Moreover, as the soil moisture variability decreases with increasing depths, it is recommended to conduct high-frequency monitoring in the shallow layer (0–30 cm), while the sampling frequency in the deeper layer (50 cm and below) can be appropriately reduced.

This study also revealed the impact of the rainfall characteristics on the soil moisture response. The results indicate that, when the rainfall intensity is similar, the PLT is negatively correlated with the rainfall amount. Conversely, when the rainfall amount is similar, an increase in rainfall intensity can shorten the PLT. Therefore, after heavy rainfall events, monitoring should be conducted as soon as possible to capture rapid soil moisture responses, while, during light or continuous rainfall events, sampling can be appropriately delayed to more accurately reflect the infiltration process.

4.5. Future Research Objectives

Based on the results of this study, future research can be further explored in the following aspects.

(1)

Future studies can comprehensively consider the influence of environmental factors. The dynamics of soil moisture in slopes are influenced by multiple environmental factors, including rainfall, the air temperature, the wind speed, and more. In this study, we considered only rainfall and did not account for the interactions among other environmental factors. Future research should integrate multiple influencing factors and quantitatively analyze their relative contributions.

(2)

In future research, the integration of laboratory experiments with in situ monitoring data can be involved. Laboratory model experiments can provide an effective approach to analyzing the impacts of individual influencing factors. Future studies can conduct orthogonal experimental designs to investigate the effects of different rainfall characteristics on soil moisture movement and quantify rainfall thresholds. This would allow for a more precise understanding of the soil moisture responses to rainfall processes.

(3)

When conducting in situ experiments, the monitoring period can be appropriately extended. The study period of this research was six months, which may not fully capture the long-term characteristics of seasonal variations. Future studies should extend the monitoring period to analyze the evolution of soil moisture under seasonal factors (e.g., temperature, atmospheric humidity, and rainfall) from multiple temporal scales.

5. Conclusions

In this study, we focus on a typical high-fill loess slope on the Loess Plateau. We utilize on-site monitoring data spanning six months to investigate the soil moisture dynamics within the slope. By applying time series analysis, the correlation between soil moisture and rainfall, as well as the lag effects, was explored. Additionally, a temporal stability analysis of the soil moisture at different depths and slope positions was conducted. The following conclusions were drawn.

(1)

The topographic conditions significantly affect the spatial variability in the soil moisture, with the relative order being slope surface > slope step > flat terrain > slope foot. The vertical spatial variability in the soil moisture at different positions exhibits a decreasing trend with increasing depths.

(2)

When the rainfall intensity is similar, the PLT of the soil moisture is negatively correlated with the rainfall amount; when the rainfall amount is similar, an increase in the rainfall intensity can shorten the PLT at all positions except the step.

(3)

On the slope scale, the time stability of the soil moisture follows the relative order of flat terrain > slope surface > slope step > slope foot. The time stability of the soil moisture in the vertical profile is positively correlated with the depth.

(4)

When constructing high-fill slopes for agricultural use, it is advisable to construct steps to improve soil moisture conservation. As for soil moisture monitoring, it is recommended to conduct high-frequency monitoring in the shallow layer. The observation timie should be adjusted based on the rainfall conditions: after heavy rainfall events, monitoring should be conducted as soon as possible, while, during light or continuous rainfall events, sampling can be appropriately delayed.