Microtopography-Driven Soil Loss in Loess Slopes Based on Surface Heterogeneity with BPNN Prediction

Abstract

Microtopography regulates soil erosion by shaping surface heterogeneity, but the mechanism of loess slope soil loss remains insufficiently quantified. This study combined laboratory rainfall simulations and machine learning to investigate how tillage-induced microtopography modulates soil loss through surface heterogeneity and hydrodynamic processes. Simulations used loess soil (silty loam) with a 5° slope, 60 mm/h rainfall intensity, and 5–30 min rainfall durations (RD). Results indicated that the mean weight diameter (MWD) and aggregate stability index (ASI) of structural, transition, and depositional crusts under micro-terrain decreased by 36~65% and 41~60%, respectively, while the fractal dimension (D) increased by 10~19%. Negative relationships were observed between ASI/MWD and D (R² = 0.83~0.98). Horizontal cultivation (T_HC, surface roughness [SR] = 1.76, average depression storage [ADS] = 2.34 × 10⁻² m³) delayed runoff connectivity and reduced cumulative soil loss (LS) by 42–58% compared to hoeing cultivation (T_HE, SR = 1.47, ADS = 3.23 × 10⁻⁴ m³). Abrupt hydrodynamic transitions occurred at 10 min RD (T_HE) and 15 min RD (artificial digging [T_AD]), driven by trench connectivity and depression overflow. LS exhibited a significant positive correlation with D and RD and was inversely correlated with ASI, MWD, and SR. A three-hidden-layer BPNN exhibited high predictive accuracy for LS (mean square error = 0.07), verifying applicability in complex scenarios with significant microtopographic heterogeneity and multi-factor coupling. This study demonstrated that surface roughness and depression storage were the dominant microtopographic controls on loess slope soil loss. BPNN provided a reliable tool for soil loss prediction in heterogeneous microtopographic systems. The findings provide critical insights into optimizing tillage-based soil conservation strategies for sloping loess farmlands.

1. Introduction

Water erosion is a dominant driver of soil degradation on sloping farmlands, encompassing raindrop splash and sheet erosion, which collectively alter soil structure, reduce fertility, and threaten agricultural sustainability [1,2]. Raindrops transfer kinetic energy to the soil surface, triggering the dispersion and reorganization of soil aggregates and particles at the onset of rainfall [3,4]. As rainfall continues, tillage-induced microtopography, characterized by ridges, transition zones, and ditches, acts as a key regulator of erosion dynamics by reshaping runoff pathways, modifying sediment transport efficiency, and creating spatially heterogeneous surface conditions [5].

Shaped primarily by tillage practices (e.g., depth, intensity, and frequency) on sloping farmlands, surface roughness (SR), defined as micro-scale variations in surface elevation, governs micro-terrain undulations, raindrop impact intensity, surface runoff generation and direction, and the spatial distribution of eroded sediments [6,7]. By altering surface undulations and depression storage capacity, SR can either mitigate or exacerbate water erosion by delaying runoff outflow, trapping sediments in depressions, and reducing raindrop impact via ridge barriers, depending on magnitude and spatial pattern [8,9,10,11,12,13]. Notably, different microtopographic zones exhibit distinct erosion responses. Ridges are vulnerable to raindrop impact despite runoff effects; ditches experience raindrop splash prior to runoff-driven sediment deposition; and transition zones linking ridges and ditches undergo combined processes of raindrop compaction, sheet erosion, and sediment deposition.

Rainfall-driven erosion in heterogeneous micro-terrain generally induces the formation of surface physical crust, a process driven by the fragmentation and recombination of soil aggregates and particles due to raindrop impact and runoff scouring [14,15]. Aggregate swelling, enhanced by water matric potential, increases capillary porosity and modulates crust development [13,16], while the aggregate composition determines the susceptibility to dispersion or retention during erosion [17]. Rainfall characteristics such as intensity and duration govern the direction of aggregate fragmentation, with raindrop impact as the primary driver [4], and tillage practices further shape the aggregate size distribution and soil stability [18]. Aggregate stability, defined as the resistance of macro-aggregates to fragmentation under environmental stressors, is a critical determinant of sediment supply during erosion [19,20]. Generally, the possibility of aggregate fragmentation exceeds combination, reflecting distinct stabilization mechanisms and transformation pathways. Metrics such as the mean weight diameter (MWD) provide static insights into the particle size distribution, and the fractal dimension (D) serves as a critical tool for capturing the continuous, dynamic interplay between dispersion and recombination.

Surface physical crusts, as composite structural units formed by soil particle binding via rainfall impact, runoff scouring, and chemical cementation, link microtopography to soil erosion resistance. It has been confirmed that physical crusts contribute to surface densification and directly affect soil erodibility by altering hydraulic conductivity, detachment capacity, infiltration rate, and sediment transport dynamics [21,22]. Crusts are typically categorized into structural crusts (C_ST), which form on ridges due to raindrop impact, and depositional crusts (C_SD), which develop in ditches via fine-particle deposition within microtopographic zones [23,24]. Inevitably, crusts developed in the transition zone arise from the interaction of raindrop splashing, sheet erosion, and sediment deposition, defined as the transition crust (C_TZ). Despite extensive research on the role of aggregates in crust evolution and erosion [25,26], the dynamic mechanisms underlying crust formation, particularly driving spatial heterogeneity in soil erosion, remain poorly understood. This knowledge gap limits the accuracy of erosion prediction models and hinders the development of targeted soil conservation strategies for microtopographically complex sloping farmlands.

Machine learning models have been increasingly applied to soil erosion prediction, such as Random Forest (RF) and Support Vector Machines (SVMs). RF can capture the aggregate dispersion and recombination features based on tree-based segmentation logic, but it struggles to capture continuous fractal behaviours. SVM requires careful parameter tuning for optimal performance, but it is less effective at handling high-dimensional, spatiotemporally heterogeneous data; dynamic crust development; and runoff–sediment interactions. The Backpropagation Neural Network (BPNN), a gradient-descent-based, multi-layer feedforward model, offers the ability to dynamically adjust weights and thresholds through iterative forward and backward propagation. BPNN excels at capturing dynamic feedback loops between crust evolution and runoff heterogeneity and minimizing prediction errors in high-dimensional systems, making it well-suited to unravel the mechanisms of microtopography-induced erosion variability.

Therefore, this study aimed to advance the mechanistic understanding of microtopography-driven soil erosion and improve predictive capacity for sloping farmlands. Specifically, the objectives were to (1) quantify the effects of tillage-induced microtopography on surface heterogeneity, (2) reveal hydrodynamic mechanisms underlying microtopography-driven soil loss, and (3) develop and validate BPNN for soil loss prediction in complex microtopographic systems. This study links tillage-induced microtopographic zones to zone-specific crust formation and erosion processes, providing a spatially explicit understanding of erosion heterogeneity. The incorporation of dynamic aggregate dispersion and recombination into erosion mechanism analysis overcomes the limitations of static particle-size metrics.

2. Materials and Methods

2.1. Materials

2.1.1. Experimental Area and Soil

The experiment was conducted at the Soil and Water Conservation Laboratory, in Yangling, Shaanxi Province, China (34°16′ N, 108°4′ E). The experimental region is situated within the Cenozoic fault depression zone of the Wei River Valley, characterized by a topography that rises in the northwest and descends in the southeast, with an average elevation of 532 m above sea level (Figure 1). The region has a semi-humid to semi-arid climate, typical of the warm-temperate zone in East Asia, with an average annual temperature of 13 °C. Precipitation averages 641 mm per year, with approximately 60~70% occurring between June and September [27,28].

The experimental soil, classified as loess, was derived from cinnamon soil subjected to long-term cultivation and fertilization. Soil samples were collected at a 0–20 cm depth from the cultivated layer in June 2023. According to USDA Textural Soil Classification standards, the particle size distribution consists of sand (>0.05 mm, 22%), silt (0.002–0.05 mm, 58%), and clay (<0.002 mm, 20%). The loess texture is classified as silty loam, with a specific surface area of 1.17 m²/g and a median particle size of 25 μm.

2.1.2. Experimental Device

Artificial rainfall was simulated using a swing spray rainfall machine manufactured by the Soil and Water Conservation Test Equipment Factory of the Institute of Soil and Water Conservation, Yangling, China. The system comprised power equipment, including a water pump and a 150 L capacity water supply tank, along with control mechanisms featuring adjustable valves to regulate rainfall intensity within a range of 20–250 mm/h. The testing apparatus included four Veejet 80100 nozzles (Spraying Systems Co., Wheaton, IL, USA), which produce raindrop diameters ranging from 2.5 to 5.0 mm. This setup ensured uniform spatial distribution of rainfall intensity, achieving an average Christiansen uniformity coefficient of 90% ± 1.3, exceeding the acceptable minimum threshold of 80% [29]. The effective rainfall area measured 3.0 × 6.0 m, with a height of 8.0 m.

The runoff plot was designed with dimensions of 2.0 m in length, 1.5 m in width, and 0.5 m in height, featuring a slope of 5°. Drainage holes were drilled at 5.0 cm intervals in both longitudinal and lateral directions to facilitate drainage. A 2.0 cm layer of pebbles was placed beneath a geotextile to prevent soil material from obstructing drainage pathways.

2.2. Methods

2.2.1. Experimental Design

To ensure the laboratory results reflected field loess slope conditions (Yangling District, Shaanxi Province), key experimental parameters were aligned with regional field characteristics: (1) the 5° plot slope matched the average slope of Yangling’s sloping farmlands, according to local agricultural extension reports; (2) dimensions of tillage treatments replicated common local tillage practices; (3) a field-realistic simulated rainfall intensity of 60 mm/h was used, corresponding to 90% of summer rainfall events in Yangling, to ensure relevance to natural erosive conditions [13,28]. Six different artificial rainfall durations (5, 10, 15, 20, 25, and 30 min) with an average raindrop diameter of 3.5 mm were repeated three times to eliminate errors.

A layered filling method, with increments of 5 cm, was employed to ensure uniformity, resulting in a gentle, homogeneous slope with a representative loess bulk density of 1.25 g/cm³, consistent with field loess soil properties in the region. Three tillage methods (horizontal cultivation [T_HC], artificial digging [T_AD], and hoeing cultivation [T_HE]) were implemented to build micro-terrain, reflecting typical practices in the Loess Plateau region (Figure 2A). T_HC was configured with alternating ridge-depression microtopography, with ridges 10 cm in height and 20 cm in width, spaced 30 cm apart, forming an undulating slope surface. T_AD featured a staggered slope configuration created via an interlaced excavation method. Based on a pre-established homogeneous slope, T_AD design specifications included depressions with a radius of 15 cm and a depth of 8 cm, with excavated soil naturally piled at the downhill edge of each depression. T_HE adopted an interlaced distribution pattern. Each row contained 4 hoeing depressions, while adjacent rows alternated with 3 depressions of identical specifications. T_HE depressions were constructed using an iron hoe with height-limiting obstacles affixed to ensure a fixed excavation depth, resulting in depressions 20 cm in length, 10 cm in width, and 5 cm in depth.

2.2.2. Measurements and Data Processing

High-resolution overlapping images (80% overlap) of the experimental slope were captured and processed using Agisoft Photoscan Professional 1.2.4 to generate a sparse point cloud via the Structure from Motion (SfM) photogrammetry approach [13]. The point cloud data were then analyzed using 3D surface analysis modules (Figure 2B) and imported into ArcGIS 10.2 for Digital Elevation Model (DEM) generation. The sparse point cloud was georeferenced using 60 ground control points (GCPs; accuracy = ±2 mm) placed on the plot. The point cloud error (root mean square error, RMSE) = 0.8 ± 0.2 mm (meets < 1 mm threshold for microtopography analysis). A dense point cloud (density = 120 points/cm²) was converted to a 1 cm-resolution DEM in ArcGIS 10.2 via multi-view stereo (MVS) algorithms. DEMs were reconstructed using multi-view stereo algorithms, incorporating pre-processing steps [5]. DEM accuracy was validated via independent elevation measurements with a laser distance meter. Surface roughness (SR) was calculated based on the methods described by Kamphorst et al. [30].

C_ST, C_TZ, and C_SD were sampled from the surfaces of ridges, transition zones, and ditches, respectively, based on the mechanisms of aggregate dispersion, transportation, and deposition (Figure 3). Physical crusts were extracted using a 200 cm³ volumetric soil knife, with manipulation to maintain the intact structure of the crust surface using an “S” systematic sampling method to achieve experimental replication and ensure representativeness. A YUY2 digital microscope (ShenHong, Shanghai, China), mounted on a fixed bracket and paired with a calibrated ruler, was used to visualize and delineate the boundary between the physical crust and the underlying undisturbed soil. The physical crust obtained was based on the boundary used to determine the properties. The determination of soil physical crust aggregate composition was conducted using the wet sieve method [31] with sieved sizes of 2, 1, 0.5, 0.25, 0.106, and 0.053 mm. The soil aggregate stability index (ASI), MWD, and D were employed to evaluate the impacts of micro-terrain and rainfall processes on soil structural stability [32,33].

ASI was calculated to assess the stability of soil aggregates and the erosion resistance of soil physical crusts using Equation (1).

$$ASI={\displaystyle \frac{x_{i>250}}{M_T}}\times 100$$

(1)

where $M_T$ is the total mass of water stable aggregates (g), and $x_{i>250}$ is the weight of aggregates > 250 μm (g).

MWD was utilized to evaluate soil aggregate stability and erosion resistance, calculated using Equation (2).

$$MWD={\sum }_{i=1}^n(x_i\times {\omega }_i)$$

(2)

where ${\omega }_i$ represents the weight of i-size aggregates (g), and $x_i$ is the average diameter of i-size aggregates (μm).

D is used to describe the fractal variation in the surface physical crust aggregates, as expressed in Equation (3).

$${\displaystyle \frac{M_{(r<x_i)}}{M_T}}={\left({\displaystyle \frac{x_i}{x_{max}}}\right)}^{3-D}$$

(3)

where $x_{max}$ is the maximum diameter of water stable aggregates (μm), and $M_{(r<x_i)}$ indicates the content of aggregates with diameters < $x_i$ (g).

To quantify the linkage between physical crust aggregate distribution and environmental factors, Mantel’s test, a widely used method in ecology for assessing matrix-based correlations, was applied [34]. Bray–Curtis dissimilarity was computed from the relative abundance of aggregate size classes, treating aggregate variability as a community attribute. Key variables reflected by detachment, transport, and deposition processes were normalized as z-scores to eliminate scale effects. The correlation between two matrices was calculated using Spearman’s rank correlation coefficient. Mantel’s test further elucidated the interaction between aggregate size distribution and environmental factors, with Mantel’s statistic normalized according to Equation (4) to facilitate the interpretation of correlation strength. Additionally, pairwise comparisons of environmental factors were depicted with a color gradient representing Spearman’s correlation coefficients, aiding in the visualization of co-variation among environmental variables.

$$r={\displaystyle \frac{1}{n-1}}{\sum }_{i=1}^n{\sum }_{f=1}^n{\displaystyle \frac{x_{if}-\overline{x}}{S_x}}\times {\displaystyle \frac{y_{if}-\overline{y}}{S_y}}$$

(4)

Backpropagation Neural Network (BPNN) was developed to model the nonlinear, dynamic interactions of microtopography–crust–runoff feedbacks underlying soil loss (LS) prediction by minimizing prediction error for complex coupled systems via iterative weight and threshold adjustment through forward and backward propagation (Figure 4). The input layer consisted of 5 neurons corresponding to key surface heterogeneity and environmental indicators described by SR, RD, ASI, MWD, and D, selected for relevance to microtopographic evolution, crust formation, and erosion dynamics, ensuring comprehensive representation of the system’s driving factors. The hidden layers employ the ReLU activation function (σ(x) = max(0, x)) to reduce the vanishing gradient and accelerate convergence. Three sequential hidden layers were adopted, with neuron counts optimized via a grid search that balances model capacity and generalization, striking an optimal balance and enabling the model to learn hierarchical features, low-level surface roughness patterns, and high-level erosion feedback in this study without overcomplicating the network. The output layer featured 1 neuron that outputted the predicted continuous LS. For model training, a dataset of 162 samples was stratified into 70% training and 30% validation to preserve treatment proportions, with hyperparameters determined via grid search. The output value of the node was calculated using Equation (5).

$$A_j^l=\sigma \left(N_j^l\right)=\sigma \left({\sum }_{k=1}^h{w}_{jk}^{l,l-1}{A}_k^{l-1}+b_j^l\right)$$

(5)

where $A_j^l$ and $A_k^{l-1}$ represent the output of the neuron node j in the layer l and the neuron node k in the layer l − 1, respectively; $\sigma \left(\right)$ is a nonlinear activation function; $N_j^l$ indicates the neuron node j in layer l; $w_{jk}^{l,l-1}$ indicates the weights of neuron node k in layer l − 1 and neuron node j in layer l; and $b_j^l$ is the threshold value of neuron node j in layer l.

During BPNN training, the deviation between the network’s output and actual values was propagated backward through hidden layers to adjust weights and thresholds. The Mean Squared Error (MSE) quantified prediction accuracy, guiding iterative optimization via gradient descent (Equation (6)).

$$MSE\left(w,b\right)={\displaystyle \frac{1}{m\times s}}{\sum }_{i=1}^m{\sum }_{j=1}^s{({y^{\prime }}_{ij}-y_{ij})}^2$$

(6)

where m and s represent the number of samples and neuron nodes in the output layer, respectively; ${y^{\prime }}_{ij}$ is the predicted value of sample i in layer node j; and $y_{ij}$ is the measured value of sample i in layer node j.

2.3. Statistical Analysis

A one-way ANOVA (α = 0.05) was performed to evaluate the effects of tillage practices and microtopographic zones on soil aggregate indices, with the coefficient of determination (R²) used to quantify the proportion of variance explained. Mantel’s test (Spearman correlation, α = 0.05) was applied to assess relationships between Bray–Curtis dissimilarity of aggregate composition and z-scored environmental variables (SR and RD). Pearson’s correlation coefficients calculated in R-Studio were used to analyze associations among RD, SR, and aggregate indices (ASI, MWD, D).

3. Results

3.1. Soil Surface Heterogeneity Under Diverse Erosion Processes

3.1.1. Surface Microstructure and Stability

Under simulated rainfall conditions (5–30 min), MWD of physical crust aggregates exhibited distinct variations across tillage practices (Figure 5). T_HC produced aggregates with the widest MWD range (72–193 μm), though values declined significantly with prolonged rainfall, decreasing by 36%, 42%, and 48% for C_ST, C_TZ, and C_SD, respectively, after 30 min. Correspondingly, T_AD yielded moderately stable aggregates (80–160 μm), with MWD reductions of 34%, 25%, and 38%. In contrast, T_HE resulted in aggregates (84–172 μm) that degraded more uniformly, with declines of 43%, 51%, and 34% for C_ST, C_TZ, and C_SD.

The ASI for three physical crust types across all three micro-topographies is illustrated in Figure 6. Under T_HC, ASI ranges spanned 15–25% for C_ST, 8–23% for C_TZ, and 7–17% for C_SD, decreased by 40%, 61%, and 59%, respectively, from 5 to 30 min of rainfall. T_AD-treated crusts displayed similar declines, with initial ASI ranges of 11–23% (C_ST), 9–18% (C_TZ), and 7–15% (C_SD), diminishing by 52%, 41%, and 46%. T_HE induced the most severe ASI reductions (55–65%), particularly for C_TZ, despite initial values (10–22% for C_ST, 8–24% for C_TZ, and 7–18% for C_SD), underscoring the sensitivity of aggregate stability to both the tillage method and rainfall duration.

3.1.2. Fracture Feature of Surface Aggregates

D of physical crusts varied across tillage practices, with ranges of 2.07–2.71 under T_HC, 2.19–2.65 under T_AD, and 2.22–2.65 under T_HE (Figure 7). As the rainfall duration increased from 5 to 30 min, D exhibited distinct trends for each crust type. Under T_HC, D increased from 2.07 to 2.46 for C_ST, 2.22 to 2.57 for C_TZ, and 2.33 to 2.71 for C_SD. Similarly, T_AD led to increases of 17%, 10%, and 12% for C_ST, C_TZ, and C_SD, respectively, while T_HE resulted in increases of 16%, 19%, and 11%. Notably, C_ST showed more pronounced changes under T_HC, decreasing by 4% and 7% compared to T_AD and T_HE, respectively, whereas C_SD increased by 2% under both T_AD and T_HE. In contrast, C_TZ exhibited no significant variations across the three micro-terrains.

Linear relationships were observed between aggregate stability indices (ASI and MWD) and D, with R² ranging from 0.83 to 0.98, depending on microtopography (

Table 1. Correlation between fractal dimension (D), aggregate stability index (ASI), and mean weight diameter (MWD).

Tillage Method	Formula	R2	Formula	R2
THC	ASI = −33.4D + 95.7	0.89	MWD = −200.6D + 612.9	0.98
TAD	ASI = −35.3D + 100.0	0.83	MWD = −171.1D + 537.4	0.96
THE	ASI = −35.7D + 102.0	0.97	MWD = −193.1D + 596.2	0.98

Note: T_HC, T_AD, and T_HE represent horizontal cultivation, artificial digging, and hoeing cultivation, respectively. MWD, ASI, and D indicate the mean weight diameter, aggregate stability index, and fractal diameter of surface micro-structure.

). Negative correlations dominated, indicating that higher fractal dimensions reflecting more fragmented aggregates were associated with reduced aggregate stability. These trends are further illustrated in Figure 8 and Figure 9, highlighting the inverse linkage between structural complexity and stability.

3.2. Impact of Micro-Terrain on Surface Heterogeneity

SR exhibited distinct spatial characteristics across tillage practices, with values of 1.76 (T_HC), 1.66 (T_AD), and 1.47 (T_HE) (

Table 2. Spatial characteristics of surface roughness under variable micro-terrains.

Tillage Method	SR	SD	Cv	ADS (m3)
THC	1.76	0.04	0.03	2.34 × 10−2
TAD	1.66	0.04	0.03	2.77 × 10−3
THE	1.47	0.04	0.05	3.23 × 10−4

Note: T_HC, T_AD, and T_HE represent horizontal cultivation, artificial digging, and hoeing cultivation, respectively. SR, SD, Cv, and ADS represented surface roughness, standard deviation, coefficient of variation, and average depression storage under micro-terrain, respectively.

). The coefficient of variation (Cv) for SR was lowest under T_HC and T_AD (0.03) and slightly higher under T_HE (0.05), reflecting greater variability in micro-geomorphic features. Depression storage capacity also varied markedly, with T_HC and T_AD retaining 8.4 and 8.6 times retention, respectively, compared to T_HE.

Mantel’s test revealed significant relationships between aggregate distribution and microtopographic factors (Figure 10). Ridges strongly influenced the aggregate size distribution of C_ST, while transition zones primarily affected C_TZ and indirectly controlled C_ST and C_SD. Ditches further modulated the distribution of C_ST and C_SD aggregates, highlighting the role of micro-terrain features in shaping soil structure.

3.3. Response of Soil Loss of Spatial Heterogeneity Under BPNN

Correlations between surface micro-structure (C_ST, C_TZ, and C_SD), rainfall conditions (RD), and micro-terrain (SR) are illustrated in Figure 11. LS was significantly positively correlated with D (r = 0.44, p < 0.001) and RD (r = 0.59, p < 0.001) but exhibited negative correlations with ASI (r = −0.37, p < 0.01), MWD (r = −0.40, p < 0.01), and SR (r = −0.52, p < 0.001).

Figure 11. Relationship between aggregate indicators (aggregate stability index [ASI], mean weight diameter [MWD], and fractal dimension [D]) and soil loss (LS) based on surface micro-terrain roughness (SR) under six artificial rainfall durations (RDs). ** and *** indicate statistically significant difference at the 0.05 level (p < 0.01) and at the 0.001 level (p < 0.001). Input layers incorporated aggregate stability metrics (ASI, MWD, D), while the output layer estimated LS through weighted interactions in hidden layers (Figure 12). The model achieved good performance (MSE = 0.07), effectively capturing the fractal characteristics of aggregates and response to microtopography and rainfall. The BPNN outperformed Random Forest (RF) and Support Vector Machine (SVM) (MSE_BPNN = 0.07, R²_BPNN = 0.89, MSE_RF = 0.12, R²_RF = 0.81, MSE_SVM = 0.15, R²_SVM = 0.76) by capturing dynamic, nonlinear feedback (

Table 3. Comparison of outfit model.

Model	MSE	R2
Backpropagation Neural Network (BPNN)	0.07	0.89
Random Forest (RF)	0.12	0.81
Support Vector Machine (SVM)	0.15	0.76

). BPNN iterative weight adjustment is adapted to the time-dependent nature of erosion and spatial heterogeneity, directly encoding the physical mechanism that cumulative hydrodynamic forcing drives soil loss via aggregate destruction and crust modification.

Figure 11. Relationship between aggregate indicators (aggregate stability index [ASI], mean weight diameter [MWD], and fractal dimension [D]) and soil loss (LS) based on surface micro-terrain roughness (SR) under six artificial rainfall durations (RDs). ** and *** indicate statistically significant difference at the 0.05 level (p < 0.01) and at the 0.001 level (p < 0.001). Input layers incorporated aggregate stability metrics (ASI, MWD, D), while the output layer estimated LS through weighted interactions in hidden layers (Figure 12). The model achieved good performance (MSE = 0.07), effectively capturing the fractal characteristics of aggregates and response to microtopography and rainfall. The BPNN outperformed Random Forest (RF) and Support Vector Machine (SVM) (MSE_BPNN = 0.07, R²_BPNN = 0.89, MSE_RF = 0.12, R²_RF = 0.81, MSE_SVM = 0.15, R²_SVM = 0.76) by capturing dynamic, nonlinear feedback (Table 3). BPNN iterative weight adjustment is adapted to the time-dependent nature of erosion and spatial heterogeneity, directly encoding the physical mechanism that cumulative hydrodynamic forcing drives soil loss via aggregate destruction and crust modification.

Figure 12. BPNN prediction model derived from the number of nodes in three hidden layers, indicating aggregate size distribution of physical crusts (structural [C_ST], transition [C_TZ], and depositional crust [C_SD]) in ridges, transition zones, and ditches formed in variable tillage conditions (horizontal cultivation [T_HC], artificial digging [T_AD], and hoeing cultivation [T_HE]) under six artificial rainfall durations (5, 10, 15, 20, 25, and 30 min). The input layer of the BPNN consisted of five neurons, corresponding to three soil aggregate properties, aggregate stability index (ASI), mean weight diameter (MWD) of aggregates, and fractal dimension (D), as well as two key environmental factors, rainfall duration (RD) and surface roughness (SR). The hidden layer processed weighted signals transmitted from the input layer, where connection weights quantified the intensity of information transfer between adjacent neurons. The network was trained over 1561 iterations, achieving a final mean square error (MSE) of 0.07.

Figure 12. BPNN prediction model derived from the number of nodes in three hidden layers, indicating aggregate size distribution of physical crusts (structural [C_ST], transition [C_TZ], and depositional crust [C_SD]) in ridges, transition zones, and ditches formed in variable tillage conditions (horizontal cultivation [T_HC], artificial digging [T_AD], and hoeing cultivation [T_HE]) under six artificial rainfall durations (5, 10, 15, 20, 25, and 30 min). The input layer of the BPNN consisted of five neurons, corresponding to three soil aggregate properties, aggregate stability index (ASI), mean weight diameter (MWD) of aggregates, and fractal dimension (D), as well as two key environmental factors, rainfall duration (RD) and surface roughness (SR). The hidden layer processed weighted signals transmitted from the input layer, where connection weights quantified the intensity of information transfer between adjacent neurons. The network was trained over 1561 iterations, achieving a final mean square error (MSE) of 0.07.

4. Discussion

4.1. Surface Heterogeneity Evolution Under Microtopography

Soil water-stable aggregates, as fundamental units of soil structure, are porous entities that significantly influence physical, chemical, and biological properties of soil [34,35,36,37,38]. MWD and ASI, key indicators of aggregate stability, are positively correlated with macro-aggregates, determining reliable proxies for soil structural resilience. The stability of physical crusts, as indicated by MWD, suggested that soil aggregates, particularly macro-aggregates, were susceptible to the dispersion process, specifically through raindrop splash and runoff scouring [19,24]. T_HC, with significant surface undulation, exhibited higher MWD (72–193 μm) than T_AD and T_HE, consistent with research by Shi et al. [39], which linked increased MWD to enhanced erosion resistance. Prolonged rainfall intensified erosion processes in undulating microtopography, leading to macro-aggregate dispersion [40]. The observed reduction in ASI with extended rainfall duration suggested that macro-aggregates were predominantly retained in ridges and transition zones instead of being transported and deposited. Through a comprehensive analysis of physical crust aggregate indicators, it could be concluded that crusts formed under T_HC displayed superior erosion resistance compared to T_HE and T_AD. For C_ST, a greater quantity of macro-aggregates was observed under T_HC, followed by T_AD, with T_HE yielding a vulnerable quantity. Analysis of the water-stable macro-aggregates in C_TZ revealed that physical crusts formed under T_HE exhibited greater variability compared to T_HC and T_AD. C_SD in T_HE contained the highest proportion of water-stable aggregates, followed by T_HC and T_AD, which could be attributed to sediment deposition.

D was employed to characterize variations in the stability of soil physical structures by quantifying the distribution of aggregate sizes with fragmented and dispersed soil [41]. Negative correlations were observed between physical crust aggregate indicators and D, consistent with findings by Mikha et al. [19], suggesting that the degree of soil fragmentation and aggregate destruction was influenced by micro-terrain features. This study corroborated that soil surface aggregates and particles undergo dynamic processes of dispersion, reorganization, agglomeration, displacement, and compaction [42,43]. Quantitative analysis revealed that roughness elements increased the Darcy–Weisbach friction coefficient compared to planar surfaces, substantially reducing runoff velocities through micro-eddy generation and sediment detention in depression. Differences in surface roughness directly led to the preferential entrainment of macro-aggregates in high-shear-stress zones, ridges in this study, and the accumulation of fine particles in low-shear-stress zones, ditches in this study, resulting in pronounced sediment selectivity effects. Moreover, the simulated rainfall duration influenced the extent of aggregate dispersion and sedimentation. Notably, mutation points, characterized by increased macro-aggregate content, were identified at 15 and 10 min of rainfall for T_AD and T_HE, respectively. These transitions were primarily attributed to enhanced runoff connectivity, which facilitated sediment accumulation and transfer from the original slope. In contrast, mutation points for T_HC emerged at 20 min of rainfall, coinciding with the observed ridge collapse during the experiment.

4.2. Response of Soil Loss to Surface Spatial Heterogeneity

Tillage practices directly influenced erosion processes on sloping farmlands [44,45,46] by altering the initial surface morphology, which in turn delayed runoff development and generation [47,48,49]. The interaction between tillage and rainfall modified soil microstructure, leading to the formation of ridges, transition zones, and depressions, which facilitated the separation, transportation, and deposition of erosive sediments, which has been indicated in research by Withers et al. [50] and Wang et al. [4,13]. The soil erosion-derived sediment sorting process reflected hillslope erosion intensity under microtopographic conditions [51,52,53,54], ultimately inducing physical crust formation. As a critical soil–atmosphere interface, physical crusts regulate sediment separation and transport, determine the selectivity of disturbed sediments, and influence soil erosion prediction. C_ST in ridges reflected aggregate selectivity and redistribution driven by raindrop splashing [55,56,57], consistent with findings by Lu et al. [23]. C_TZ in ridge-ditch transitions responded to particle size selectivity from combined raindrop impact and runoff transport. C_SD in ditches was linked to sediment deposition [14]. Thus, spatial heterogeneity in physical crusts, driven by sediment separation, transport, and deposition, directly modulates soil loss.

Artificial tillage and management practices have modified the initial surface state of sloping farmlands, leading to SR, which delayed the formation and generation of runoff by altering water storage and infiltration processes [48,49]. Preliminary observations indicated that the presence of surface depressions could delay the onset of slope runoff [45,47], a finding supported by the results of this study. Erosive runoff generation was tightly coupled with microtopography, where the aggregate distribution within soil matrices affected sediment selectivity. Aggregate dispersion and recombination during erosion accompanied physical crust formation, demonstrating that tillage and rainfall jointly reshaped soil microstructure into ridge–depression landforms that mediated sediment separation and deposition [52,54]. LS showed an increase with more dispersed particle distributions, severe aggregate fragmentation, and extended raindrop impact and runoff scour driven by D and RD. Conversely, LS decreased with aggregate resistance to fragmentation. RD had a stronger driving effect on LS than D, while SR exerted a more pronounced inhibitory effect on LS than ASI, indicating that microtopography via flow path modification was more influential than aggregate stability in mitigating erosion.

A three-hidden-layer BPNN was developed to quantify the nonlinear coupling between surface spatial heterogeneity and LS, with iterative adjustment of weights and biases to minimize prediction error. Trained over 1561 steps (error = 0.07), BPNN effectively captured significant microtopographic heterogeneity and multi-factor interactions, overcoming the limitations of traditional erosion models reliant on uniform slope assumptions. Three hidden layers corresponded to distinct physical scales of erosion, mirroring the sequential nature of erosion based on surface heterogeneity, hydrodynamic modification, crust formation, and soil loss, enabling the model to replicate physical causality. The ReLU activation function in hidden layers amplified the influence of ecologically meaningful thresholds described by rainfall duration thresholds for ridge collapse and SR thresholds for runoff connectivity. The linear activation function in the output layer preserved the quantitative relationship between input factors and LS, ensuring predictions aligned with physical erosion magnitudes. Critically, BPNN’s superior performance stemmed from the ability to encode physical mechanisms underlying erosion dynamics, rather than merely fitting statistical correlations (Table 3).

4.3. Implications and Limitations

The laboratory rainfall simulations enabled precise control of key variables to isolate the coupling mechanisms between tillage-induced microtopography, surface heterogeneity, and soil loss, providing mechanistic insights that were challenging to obtain directly from complex field environments. The findings had practical implications for soil conservation on sloping loess farmlands. Additionally, the three-hidden-layer BPNN developed in this study, with input variables including SR, RD, ASI, MWD, and D, provided a tool for soil loss prediction in microtopographically heterogeneous systems, addressing the limitations of traditional models reliant on uniform slope assumptions. However, a key limitation was that the research was based on a single case study specific to loess soil, limiting the transferability of the results to other soil types. The translation of findings to practical field applications requires accounting for natural variability and scale effects, while this study clarified the core mechanisms of microtopography-driven soil loss under controlled conditions. To improve the transferability and broader applicability of the findings, future work should focus on conducting field-scale validation experiments under natural rainfall conditions, incorporating long-term monitoring to capture dynamic microtopographic evolution, and incorporating dynamic microtopographic evolution into the BPNN model to enhance predictive accuracy for long-term field erosion. Despite these limitations, the findings in this study enhance mechanistic predictions of erosion phase transitions under varying rainfall conditions, advance understanding of soil microstructure-erosion relationships, and provide critical insights for adaptive land management strategies tailored to spatial heterogeneity in sloping farmland.

5. Conclusions

This study systematically investigated the effects of three tillage-induced microtopographies (horizontal cultivation [T_HC], artificial digging [T_AD], and hoeing cultivation [T_HE]) on surface heterogeneity, hydrodynamic processes, and soil loss (LS) on sloping loess farmlands via laboratory rainfall duration (RD). Tillage-induced microtopographies significantly modulated the stability and fractal characteristics of structural (C_ST), transition (C_TZ), and depositional (C_SD) crusts. Superior surface roughness (SR) increased the combination of aggregate reflected in the mean weight diameter (MWD) and the aggregate stability index (ASI), which was attributed to runoff connectivity delays and cumulative LS reductions. A relationship between the fractal dimension (D) and RD, MWD, and ASI indicated that aggregate fragmentation intensified with extended erosion. Mantel’s test confirmed that microtopographic zones, ridges, transition zones, and ditches independently regulated aggregate distribution. Ridges (C_ST) preferentially retained macro-aggregates, while ditches (C_SD) accumulated fine particles, reflecting pronounced sediment selectivity. The three-hidden-layer BPNN effectively captured the nonlinear coupling between microtopography, surface heterogeneity, and LS, achieving high predictive accuracy. Overall, this study clarified the mechanistic pathways by which microtopography modulated soil erosion via shaping surface crust properties and hydrodynamic processes. The findings emphasized that enhancing surface roughness and depression storage could be an effective tillage-based soil conservation strategy for sloping loess farmlands, as demonstrated by the application of a BPNN, which would provide a tool for erosion prediction.