Quantifying Soil Erosion Processes Based on Micro-ΔDEM

Abstract

The spatial distribution traits of microtopography exert a profound influence on the generation of runoff and sediment. Nevertheless, the underlying mechanism through which microtopography alterations, triggered by diverse factors, impact soil erosion remains largely elusive. In light of that, this study simulated conventional farming practices on the Loess Plateau: artificial backhoe, artificial digging, and contour tillage (CT), with no tillage (CK) designated as the control group. The objective was to meticulously investigate the variations in microtopography, runoff, and sediment yield under disparate treatment conditions, rainfall intensities (60 mm/h and 90 mm/h), and slope gradients (5°, 10°, and 20°). The principal findings were as follows: With the amplification of rainfall intensity, the elevation change rate and fractal dimension of various treatments generally exhibited an upward trend, whereas the structural ratio showed a downward tendency. As the slope gradient increased, the elevation change rate and structural ratio of different treatments typically increased. However, the fractal dimension displayed no conspicuous alteration at a rainfall intensity of 60 mm/h and a decreasing trend at 90 mm/h. Under different rainfall intensity scenarios, a robust linear correlation existed between the fractal dimension and both runoff and sediment yield (R² > 0.73), rendering it an outstanding parameter for estimating these variables within the scope of this research. Path analysis revealed that the indirect effect of microtopography on sediment yield, which was mediated by runoff, constituted 77.80–96.47% of the direct effect. Moreover, under different rainfall intensities, the alterations in runoff and sediment yield ensuing from unit-scale changes in the fractal dimension varied significantly. Specifically, at a rainfall intensity of 90 mm/h, these changes were 1.70-fold and 3.75-fold those at 60 mm/h, respectively. Overall, the CT treatment engendered the lowest runoff and sediment yield, along with the highest fractal dimension, thereby emerging as the most efficacious measure for soil and water conservation in this study. The research outcomes offer valuable perspectives for further elucidating the mechanisms through which tillage practices impinge upon soil erosion.

1. Introduction

Soil erosion is one of the important threats to ecological sustainable development. It not only takes away the fertile topsoil, leading to reduced grain production and intensified poverty and hunger, but also causes reservoir siltation, induces mud and sand disasters, and increases the frequency of flood disasters [1,2]. According to statistics from the International Atomic Energy Agency (IAEA), the economic loss caused by soil erosion each year is as high as 400 billion USD. Among them, the Loess Plateau in China, as the largest loess accumulation area in the world, has an area of 635,000 km². Due to its fragmented and gullied terrain characteristics, it is extremely prone to mud and sand disasters [3]. According to the survey by the Institute of Earth Environment, Chinese Academy of Sciences, the area of soil and water loss in the Loess Plateau is 390,000 km², of which the area of extremely intense soil erosion with an erosion modulus greater than 8000 t/km²·a is 85,000 km², accounting for 64% of the same type of area in China, and it is the most severely eroded area in the country and even in the world. Therefore, research on its soil erosion has always attracted widespread attention [3,4,5]. Soil erosion, as a core process of surface material redistribution, is dynamically coupled with geomorphological evolution. Traditional studies have focused on assessing total erosion at slope or watershed scales; however, recent high-resolution topographic monitoring indicates that morphological variations in microtopographic units, such as gully depth and depression volume, can alter runoff shear stress and sediment transport efficiency, thereby dominating nonlinear responses in the erosion process.

Microtopography refers to the terrain characteristics within a small range, with surface undulations ranging from 5 to 25 cm [6]. On the one hand, the spatial distribution characteristics of surface microtopography affect surface runoff and sediment yield. Zhao et al. set up two types of microtopography treatments, TR (trough and ridge) and DM (depression and mound), and used SS (smooth surface) treatment as a control. Through rainfall experiments, it was found that compared with SS treatment, both DM and TR treatments could delay the onset of runoff, and under the same conditions, TR is more effective in controlling soil and water loss than DM [6]. Wang et al. compared the splash erosion characteristics of three tillage measures, artificial digging (AD), contour tillage (CT), and straight slope conditions (SSCs), and found that tillage microtopography units with high surface roughness produce more splash erosion than flat land [7]. In addition, compared with flat land, the highest surface roughness increased the total splash volume by 102%. Furthermore, some studies have shown that the impact of microtopography on soil erosion depends on the critical slope [8]. When the slope is equal to or less than the critical value, the increase in surface microtopography undulation will reduce soil erosion; when the slope is greater than the critical value, the soil and water conservation benefits of surface microtopography gradually disappear [8]. On the other hand, the rainfall erosion process also affects the spatial distribution of surface microtopography. Rainfall and slope are important factors for surface microtopography and soil erosion [9], which have a strong impact on the spatial distribution of surface microtopography. Yang et al. found that within one rainy season, the average slope of the microtopography of the bare bedrock slope surface increased from 22.76° to 23.09°, the density of fine gullies on the slope surface increased from 0 to 33.73 m/m², and the slope surface microtopography continued to develop in a direction conducive to erosion [10]. Zhang and Xie found that the soil surface roughness index increases exponentially with the increase in slope, while the random roughness value after tillage decreases exponentially over time [9,11].

The above analysis shows that the spatial distribution characteristics of surface microtopography affect the development process of slope runoff and erosion, and these processes also affect the spatial distribution of surface microtopography. This mutual influence process changes with the change in microtopography spatial distribution characteristics, and its final impact on runoff and sediment yield depends on the change characteristics of surface microtopography. Therefore, microtopography is both a direct result of erosion and an important cause of further erosion development. It is a comprehensive factor that can reflect the various elements of slope erosion dynamics and their interactions [12,13]. Research on it is of certain significance for further revealing the mechanism of soil erosion processes and establishing soil erosion models [14,15]. However, due to the relative difficulty of obtaining microtopography data and the complexity of the dynamic interaction between the microtopography of sloped farmland and the water and sand process on the slope, the interaction between microtopography and tillage measures, rainfall intensity, and slope factors is still unclear and needs further study [12,13].

Based on that, this study takes the sloped farmland in the Loess Plateau of China as the research object, sets up three treatments of artificial backhoe (AB), artificial digging (AD), and contour tillage (CT), and uses no tillage (CK) as a control, to explore the changes in microtopography elevation, structural ratio, and fractal dimension under different rainfall intensities and slopes, and it also measures the runoff and sediment yield under different tillage measures. On this basis, the relationship between microtopography changes and runoff and sediment yield under different tillage measures is analyzed, in order to provide a reference for revealing the mechanism of microtopography changes on soil erosion at the microscopic scale and establishing soil erosion process models.

2. Materials and Methods

2.1. Study Area and Soil Properties

This study uses the original surface soil (0~20 cm) of the sloped farmland in Yangling District, Shaanxi Province, as the experimental soil. Yangling District is located on the southern edge of the Loess Plateau, with a longitude of 108.72° E and a latitude of 34.36° N (Figure 1), belonging to the temperate semi-humid continental monsoon climate zone, with an annual rainfall of about 637.6 mm. The dominant soil type is Loutu soil, which has a gray–brown color and a structure characterized by granules or aggregates, with a loose texture, granular or cloddy structure, and soil particles that are mainly silt, accounting for about 70% of the total amount, while clay accounts for about 25%, and the bulk density is about 1.15 g/cm³.

2.2. Experimental Setup and Soil Preparation

The specification of the experimental erosion trough is 2.0 m × 1.0 m × 0.5 m, and the slope can be adjusted between 0° and 30°. When filling the soil, the soil samples are naturally air-dried and passed through a 0.5 cm sieve. The filling depth is 40 cm. To prevent soil stratification, the soil is filled in layers of 5 cm each, and the layers are roughened between each other. The bulk density during filling is 1.15 g/cm³, and the moisture content is controlled at 10%. After filling, a horizontal line is set in the erosion trough to level the surface, making the surface of the test soil sample level with the set horizontal line. The surface is then processed with common tillage methods in the Loess Plateau, including manual hoeing (AB, artificial backhoe), manual excavation (AD, artificial digging), contour tillage (CT, contour tillage), and a straight slope (CK), as shown in Figure 2. In contour tillage, the cross-slope tillage method is used, with ridge height of 7–10 cm and ridge spacing of 20 cm; in manual excavation, the surface is excavated with a hoe, with a depth of 5–8 cm and a spacing of 20–25 cm; in manual hoeing, the surface is hoed in the traditional way, with a depth of 4–5 cm; and in a straight slope, the slope surface is leveled with a level.To ensure data robustness, an untreated control was implemented, and three independent experimental replicates were performed for each condition (Figure 2).

Then, laboratory rainfall experiments were carried out under rainfall at 60 mm‧h⁻¹ and 90 mm‧h⁻¹, with the slope gradient adjusted at 5°, 10°, and 20°, respectively, in different events.

2.3. Artificial Rainfall Simulation

To study the impact of different tillage measures (Figure 2) on slope runoff and sediment yield, this study conducted artificial rainfall simulation experiments at the Soil and Water Conservation Research Institute of Northwest A&F University from July to September 2015. Each soil trough was moistened for half an hour the day before the rainfall experiment to ensure the soil moisture content. The slope was set at 5°, 10°, and 20° during the rainfall experiment. The rainfall intensity was set at 60 and 90 mm/h (an annual rainfall of about 637.6 mm in Yangling District, Shaanxi Province [6]). The height of the simulated rainfall equipment nozzle is 16 m, and the final velocity of the raindrops can reach more than 98% of the natural raindrop falling speed. After the appearance of runoff, timing begins. Every 2 min, a plastic bucket is used to collect runoff and sediment samples, and the rainfall time is 45 min. After that, the plastic bucket is weighed to calculate the total mass of runoff and sediment, and then the runoff and sediment are transferred to an aluminum box for drying to obtain the sediment mass. The runoff mass is obtained by subtracting the sediment mass from the total mass of runoff and sediment, and then the runoff volume is calculated according to the density of water.

2.4. Establishment of Elevation Change Rate (M-ΔDEM)

A 3D laser scanner (GLS-1500, Topcon, Japan) was used to measure the surface elevation data before and after segmented rainfall (sampling interval 2 cm×2 cm). To eliminate the influence of marginal effects, the effective area was set to 174 cm×80 cm, and each slope surface could collect 3480 elevation point data to construct a high-precision microtopography digital elevation model (M-DEM) [13,16]. In the three repeated rainfall experiments, the elevation point data of the same grid unit were averaged. Then, in the ArcGIS 10.7 software, the M-DEM after rainfall was subtracted from the M-DEM before rainfall to generate the M-ΔDEM grid data (Formula (1)) (Figure 3).

M-ΔDEM is M-ΔDEM = M-DEM_after − M-DEM_before

(1)

2.5. Semi-Variance Function

The classic statistical method is used to analyze the surface microtopography with a normal distribution characteristic, which has spatial correlation within a specific range. Therefore, the semi-variance function method can be used to analyze the spatial distribution state of the surface microtopography. The semi-variance function calculation formula is:

$$\gamma (h)={\displaystyle \frac{1}{2N\left(h\right)}}{\sum }_{i=1}^{N\left(h\right)}{\left[Z\left(x_i\right)-Z\left(x_i+h\right)\right]}^2$$

(2)

where$\gamma \left(h\right)$ is a semivariogram;

Z(x_i) and Z(x_i + h) are values for Z at the spatial location of x_i and x_i + h;

N(h) is the total number of sample pairs collected at an interval of h.

The microtopographic characteristics of the spatial distribution of the surface can be characterized by semivariogram models, which include spherical models, exponential models, Gaussian models, and linear models [1,17]. A Gaussian model was used in this study.

Structure ratio C/(C + C_o) and the range are two important coefficients for fitting modeling: (1) C/(C + C_o) is used to quantify the ratio between the autocorrelation-induced spatial variability and total spatial variability. According to the criteria for autocorrelation between regionalized variables, C/(C + C_o) < 25% shows weak autocorrelation, 25% ≤ C/(C + C_o) ≤ 75% a medium autocorrelation, and C/(C + C_o) > 75% a rather strong autocorrelation [18]. (2) represents the scale of spatial autocorrelation, reflecting the range of the continuity of a microtopographic surface. A bigger a means poor continuity while a smaller a better continuity. Variables within are spatially related or dependent, while variables out of a are not spatially related.

2.6. Fractal Dimension

The fractal dimension D is dimensionless and is determined by the relationship between γ(h) and h, 2γ(h) = h^(4−2D). The calculation formula for D is as follows:

D = 2 − m/2

(3)

where m is the slope of the double logarithmic linear regression between the variogram γ(h) and the sampling interval h. The smaller the D value, the more the large-scale variation controls the configuration pattern of surface roughness; the larger the D value, the more significant the small-scale variation, the stronger the spatial heterogeneity caused by random factors, and the more complex the spatial distribution it shows. A higher fractal dimension indicates a more complex surface structure and greater fragmentation, reflecting the nonlinear and irregular nature of slope morphology across multiple scales. It can be used to analyze the dynamic changes in surface fragmentation during erosion processes. The fractal dimension reveals the geometric dynamic evolution mechanism of soil erosion through multi-scale analysis, whereas traditional roughness indices focus on the physical characteristics of the surface at specific scales.

2.7. Data Analysis

Single-factor analysis of variance was used to analyze the differences in different indicators with slope and tillage measures; an independent sample T-test was used to analyze the differences in different indicators with rainfall intensity; correlation analysis was used to analyze the relationship between elevation change rate, structural ratio, fractal dimension, and runoff and sediment yield; statistical analysis was performed using IBM SPSS Statistics 19.0; and drawing was performed using Origin 8.0.

3. Results

3.1. Changes in Elevation Change Rate, Structural Ratio, and Fractal Dimension

From Figure 4, Figure 5 and Figure 6, it can be seen that at the end of the rainfall, in different treatments, with the increase in slope and rainfall intensity, the elevation change rate shows an increasing trend. When the slope is 20°, the elevation change rate is increased by 174.52–584.91% compared with when the slope is 5°. When the rainfall intensity is 90 mm/h, the elevation change rate is increased by 133.33–3379.63% compared with when the rainfall intensity is 60 mm/h. In the change in structural ratio, the structural ratio of the CT measure is the smallest, and it is in the range of moderate spatial autocorrelation. With the increase in slope, the structural ratio shows an overall increasing trend, while with the increase in rainfall intensity, the structural ratio shows an overall decreasing trend. When the rainfall intensity is 60 mm/h, the fractal dimension shows no significant change trend with the increase in slope, but when the rainfall intensity is 90 mm/h, it shows a decreasing trend with the increase in slope. The fractal dimension shows an increasing trend with the increase in rainfall intensity. Overall, in different measures, the CT measure has a larger elevation change rate, a smaller structural ratio, and a relatively larger fractal dimension.

3.2. Runoff and Sediment Yield Characteristics

Compared with CK, the runoff and sediment yield of different treatments show a decreasing trend. The runoff and sediment yield of the AB treatment are reduced by 12.69~42.79% and 10.83~40.86% compared with CK, respectively; the runoff and sediment yield of the AD treatment are reduced by 5.46~36.69% and 7.78–31.38% compared with CK, respectively; and the runoff and sediment yield of the CT treatment are reduced by 29.69~49.86% and 23.04~45.15% compared with CK, respectively. When the slope is 20°, the runoff of different treatments is higher than those of slopes 10° and 5° by 5.41~35.23% and 0.95~24.27%, respectively, and the sediment yield is higher by 9.03~80.36% and 2.75~50.70%, respectively. Overall, the CT treatment has the lowest runoff and sediment yield, and the runoffs and sediment yields of different treatments show an increasing trend with the increase in rainfall and slope (Figure 7 and Figure 8).

3.3. Relationship Between Surface Microtopography and Runoff and Sediment Yield

Under different rainfall intensities, the structural ratio shows a positive correlation with runoff and sediment yield, while the fractal dimension shows a significant negative correlation with sediment yield (

Table 1. Correlation analysis of surface microtopography and sediment yield.

Correlation	Runoff Yield	Sediment Yield
DEM-60	0.05	0.04
DEM-90	0.08	0.48
Structural Ratio-60	0.82 **	0.85 **
Structural Ratio-90	0.88 **	0.84 **
Fractal Dimension-60	−0.89 **	−0.86 **
Fractal Dimension-90	−0.92 **	−0.90 **

Note: Elevation-60 indicates the correlation between elevation change rate and sediment production when rainfall intensity is 60 mm/h. Elevation-90 indicates the correlation between elevation change rate and sediment yield when rainfall intensity is 90 mm/h. And so on. “**” indicates an extremely significant impact (p < 0.01).

). Regression analysis of the two indicators with runoff and sediment yield shows that the R² of the relationship between fractal dimension and runoff and sediment yield is better than that of the structural ratio under different rainfall intensities, and it is a better parameter for simulating the relationship between microtopography and runoff and sediment yield in this study (Figure 9 and Figure 10). Path analysis of the relationship between the fractal dimension and sediment yield shows that under rainfall intensities of 60 mm/h and 90 mm/h, the direct path coefficients are −0.85 and −0.90 (Figure 11), respectively, and the indirect path coefficients are −0.82 and −0.70, respectively. The indirect effect of the fractal dimension on the sediment yield under different rainfall intensities accounts for 96.47% and 77.78% of the direct effect, respectively. Moreover, with the increase in rainfall intensity, the changes in runoff and sediment yield caused by unit changes in fractal dimension are different. When the rainfall intensity is 90 mm/h, the changes in runoff and sediment yield caused by the same size of fractal dimension changes are 1.70 times and 3.75 times those when the rainfall intensity is 60 mm/h, respectively.

4. Discussion

The elevation change rate under different tillage measures shows an increasing trend with the increase in rainfall intensity, which may be because the increase in rainfall intensity often leads to an increase in runoff. Tan et al. (2024) found that as the flow rate increases, the overall depth of surface cutting tends to increase, and the gully erosion becomes more severe, so the elevation change rate increases accordingly [19]. The structural ratio decreases with the increase in rainfall intensity, which may be due to the influence of rainfall and the underlying surface, and the runoff characteristics at different positions on the slope may be different, resulting in different impacts on the microtopography at different positions on the slope. With the increase in rainfall intensity, the runoff volume surges, leading to more significant differences in runoff characteristics at different positions, causing the autocorrelation of the slope surface to weaken, which may be the reason why the structural ratio decreases with the increase in rainfall intensity [20]. The increase in fractal dimension with rainfall intensity may be due to the fact that under a high rainfall intensity, the differences in runoff characteristics at different positions increase, resulting in stronger spatial heterogeneity caused by random factors, which may be the reason why the fractal dimension increases with the increase in rainfall intensity [21,22]. With the increase in slope, the elevation change rate shows an increasing trend, which may be because as the slope increases, the runoff energy tends to increase, and the increase in runoff volume will cause the runoff’s ability to act on the surface to strengthen, which may be the reason why the elevation change rate increases with the increase in slope [23,24]. The larger the slope, the more likely it is to form gully flow, meaning the runoff is concentrated in the gullies, the randomness of runoff distribution on the slope surface is weakened, and the sediment produced is mainly taken away by the runoff, which may be the reason why the structural ratio increases and the fractal dimension decreases with the increase in slope [25].

Among different measures, the CT measure has the largest elevation change rate, the smallest structural ratio, and the largest fractal dimension, which may be because the change in elevation may be related to the energy of rainfall runoff on the slope surface. Since the elevation of the runoff flow is consistent and the rainfall intensity is consistent, the energy difference in the runoff should come from the conversion of potential energy to kinetic energy. In the CT measure, the runoff volume is the lowest, indicating that the energy of the runoff decays the most during the rainfall process in the CT measure, and the greater the decay energy, the more energy the runoff generates on the underlying surface, which may be the reason why the elevation change rate is the largest in the CT measure [23]. Since the CT measure has a strong influence on runoff, and the contour ridge tillage mode can stepwise reduce the energy of runoff, this may make the runoff characteristics at different positions on the slope surface larger. Therefore, the large runoff difference at different slope surface positions in the CT measure and the greater degree of action on the underlying surface may be the reasons for the weak spatial autocorrelation and larger fractal dimension in the CT measure [25,26].

With the increase in rainfall intensity, the increase in slope surface runoff may occur because when the rainfall intensity is high, the impact on the ground is often stronger, accelerating the formation of surface crust, and resulting in a decrease in soil infiltration capacity; therefore, the weakening of soil infiltration capacity and the increase in rainfall may be the reasons for the increase in slope surface runoff with the increase in rainfall intensity [3]. The increase in slope surface runoff makes the erosion capacity of runoff on the underlying surface stronger, which may be the reason for the increase in slope surface sediment yield with the increase in rainfall intensity [2]. In this study, the increase in slope surface runoff with the increase in slope is similar to the results of most studies [27,28]. The increase in sediment yield with the increase in slope may be due to the increase in runoff volume on the one hand, and on the other hand, it may be because as the slope increases, the shear force and sediment carrying capacity of the runoff often increase, which may be the reason for the increase in slope surface sediment yield with the increase in slope [29]. Among different measures, the CT measure has the lowest runoff volume, which may be related to microtopography changes. In the CT measure, its fractal dimension is higher than those of other measures. Most studies have shown that slopes with a larger fractal dimension often form shorter water and sediment paths, and their ability to inhibit soil and water loss is also stronger [13,18,26]. Therefore, the largest elevation change rate and the largest fractal dimension in the CT measure may be the reasons for its lower runoff and sediment yield.

5. Conclusions

At the end of the rainfall, in different tillage measures, except for CK, the elevation change in other treatments is mainly reduced. With the increase in rainfall intensity, the elevation change rate and fractal dimension of different treatments show an overall increasing trend, while the structural ratio shows a decreasing trend. With the increase in slope, the elevation change rate and structural ratio of different treatments show an overall increasing trend. However, the fractal dimension shows no significant change with the increase in slope when the rainfall intensity is 60 mm/h, but shows a decreasing trend with the increase in slope when the rainfall intensity is 90 mm/h. The runoff and sediment yield increase with the increase in slope and rainfall intensity. The structural ratio and fractal dimension show a significant correlation with runoff and sediment yield. Under different rainfall intensities, the empirical equation of fractal dimension with runoff and sediment yield has a higher R² than the empirical equation of structural ratio with runoff and sediment yield, and it was a better microtopography parameter for estimating runoff and sediment yield in this study. Under rainfall intensities of 60 mm/h and 90 mm/h, the indirect effect of the fractal dimension on the sediment yield accounts for 96.47% and 77.78% of the direct effect, respectively. Moreover, when the same size of fractal dimension changes at a rainfall intensity of 90 mm/h, the changes in runoff and sediment yield are 1.70 times and 3.75 times those at a rainfall intensity of 60 mm/h, respectively. Overall, the CT treatment has the smallest runoff and sediment yield and the highest fractal dimension, which is the best measure for soil and water conservation in this study. The results of this study can provide a reference for further revealing the mechanism of the impact of different tillage measures on soil erosion.

6. Study Limitations and Research Prospects

This study employs 3D laser point cloud data and spatial modeling techniques within the ArcGIS platform to systematically quantify the regulatory effects of tillage practices (e.g., CT, AD, AB) on soil erosion under varying rainfall intensity–slope gradients in the Loess Plateau microtopography. It elucidates the coupling mechanisms between micro-geomorphic evolution and erosional dynamics, providing a theoretical foundation for parameterized design of regional soil–water conservation measures. However, limitations persist: (1) Insufficient coupling of ecological processes in model parameterization, notably neglecting vegetation root reinforcement and dynamic anthropogenic disturbances; (2) absence of long-term in situ monitoring data constrains validation of conservation measure durability; and (3) inadequate socioeconomic dimension analysis fails to quantify trade-offs between farmer livelihoods and ecological benefits across tillage regimes. Future research should prioritize interdisciplinary collaboration integrating geography, agronomy, and socioeconomics to establish a multi-source data fusion framework for erosion early-warning decision support systems, alongside developing cost–benefit-optimized tillage modules. Research outcomes should be operationalized through tripartite government–academia–community cooperation, translating into manager-oriented erosion risk classification maps, farmer-targeted scenario simulation decision trees, and policymaker-focused dynamic ecological compensation assessment frameworks. This structured knowledge transfer mechanism will facilitate scientific transformation of ecological restoration strategies from theoretical models to practical implementation.