Surface fractal heterogeneity under microtopography during flow regime transition

While existing studies have explored interactions between microtopography and hydrodynamics, most failed to quantify the continuous dynamic responses of surface fractal heterogeneity along flow transitions triggered by microtopography and prolonged rainfall. This study investigated soil surface microstructure induced by spatial heterogeneity and hydrodynamics, focusing on surface roughness (SR) depicted by flat ( T FC ), horizontal ( T HC ), artificial digging ( T AD ), and hoeing cultivation (T HE ) across variable rainfall duration (RD). The results showed that runoff velocity ( V = 0.16–0.32 m/s) initially increased and stabilized with RD, similar to hydraulic shear stress ( τ = 1.12–1.68 Pa), while it decreased with SR differently from τ . Reynolds number (Re = 184–480) increased quasi-linearly with RD, similar to Froude number (Fr = 1.3–2.7) inverse of Darcy–Weisbach friction coefficient ( f = 0–2). Surface microstructure was dominated by the flow regime shift. Micro-aggregate content and fractal dimension ( D ) positively correlated with environmental factors ( p < 0.05) converse of macro-aggregate. RF analysis and SEM confirmed the positive effects of RD (0.36) and BD (0.44) on D , reverse of Fr (−0.15), f (−0.24*), and TN (−0.14), with acceptable model fit (RMSEA, SRMR < 0.08, CFI, TLI > 0.9). The threshold rainfall duration triggered flow regime conversion under the control of microtopography to quantify surface fractal heterogeneity. The established multi-factor causal framework provides targeted theoretical support for optimizing anti-erosion tillage practices on sloping farmlands.

Microtopography, formed by agricultural tillage, acts as a fundamental geomorphic factor controlling hillslope water erosion (Basic et al., 2004; Hu et al., 2015; Zhao et al., 2014). Composed of ridges, transition zones, and ditches, heterogeneous microtopography modulates raindrop splashing, sheet erosion, and sediment deposition by reshaping the surface undulation patterns, thereby mitigating or exacerbating water erosion (He et al., 2023; Liu et al., 2022; Puustinen et al., 2005; Wang et al., 2024; Withers et al., 2007; Zhang et al., 2020). Micro-ditches are particularly critical due to dual water storage and flow-blocking functions that reshape runoff convergence (Lampurlanes and Cantero-Martinez, 2006; Papanicolaou et al., 2018). Slope catchment area governs total runoff yield during rainfall events, amplifying hydraulic differences across microtopographic zones. Ditch geometry at multiple spatial scales reshapes surface hydraulic pressure, altering runoff connectivity and outflow velocity, thereby driving sediment accumulation, which sequentially generates spatially differentiated surface soil microstructures (Kinnell, 2005; Zhang et al., 2015).

Substantial advances have been made in deciphering the runoff hydrodynamic mechanisms underlying slope erosion (Ali et al., 2013; An et al., 2012; Wang et al., 2018; Zhu et al., 2020), with consistent evidence that hydrodynamic forcing, exerted by runoff, mediating the sequential processes of particle detachment, transport, and deposition (Shen et al., 2021; Tian et al., 2017). Evidence showed that flow velocity (V), hydraulic shear stress (τ), and stream power (ω) showed correlations with sediment transport rate (Liu et al., 2024; Yan et al., 2024; Zhang et al., 2003). Spatiotemporal variations in hydraulic parameters dictate the magnitude on surface erosion, recognized as the primary drivers and initial entrainment of particle detachment. Elevated flow energy over micro-ridges accelerates aggregate mobilization, while flow deceleration within depressions promotes gravitational sediment settling, subsequently reducing turbulent transport capacity.

Under the disturbance of regime transition dynamics, eroded sediments exhibit pronounced particle size selectivity, characterized by vertical stratification (Deal et al., 2023; Kinnell, 2005; Najafi et al., 2021; Perrini et al., 2024). Collectively, existing studies have verified that the coupling interaction between overland hydrodynamics and microtopography directly regulates sediment production and particle size selectivity (Hao et al., 2019; Germain et al., 2020; Shi et al., 2017). The interacting modulation effects of microtopography and runoff flow can be quantified by dimensionless hydrodynamic indices, such as Reynolds number (Re), Froude number (Fr), and Darcy–Weisbach friction coefficient (f) (Liu et al., 2022; Lou et al., 2025; Ni et al., 2026; Schroers et al., 2022). Variations in Re and Fr can distinguish laminar/turbulent and subcritical/supercritical flow states. f quantifies the total hydraulic flow resistance. The hydrodynamics generated by microtopographic ridges, depression ponding, and heterogeneous surfaces further induce differentiated erosion and sedimentation patterns on ridge surfaces, transitional slopes, and micro-depression ditches.

Microtopography-mediated hydrological heterogeneity lays the foundation for subsequent hydrodynamic shifts and subsequent surface flow regime transitions, which are core processes governing hillslope soil erosion and sediment transport. Soil properties interact synergistically with overland flow hydrodynamic forcing to modulate particle detachment efficiency and size-selective transport, accompanied by the dispersion, agglomeration, and recombination of soil aggregates (Barthès and Roose, 2002; Liu et al., 2024). Aggregate retention or breakdown shapes soil pore architecture, water conductivity, and nutrient availability, which can be quantified by fractal dimension (D) (Falsone et al., 2012; Fu et al., 2020; Jasinska et al., 2006; Whalen and Chang, 2002). D with significant correlations to surface fractal heterogeneity quantifies aggregate stability and surface dynamic microstructure, which further initiates physical crusts (Chen et al., 2022).

Physical crusts dominated by aggregate separation and rearrangement during rainfall erosion (Feng et al., 2024; Xu et al., 2026) can be classified into multiple types, such as structural crust and depositional crust. Depositional crust, a dominant subtype formed within stagnant micro-ditches via aggregate sedimentation, migration, and recombination, serves as direct proxies for slope sedimentation processes. The fractal microstructure of depositional crust directly alters soil erodibility by regulating hydraulic conductivity, infiltration rates, and sediment detachment capacity (Bremenfeld et al., 2013; El-Husseiny et al., 2018). Runoff hydraulic heterogeneity drives the initiation and growth of depositional crusts through coupled flow compression, particle sorting, and energy dissipation during sediment deposition (Liu et al., 2024; Yan et al., 2024). This phenomenon verified bidirectional interaction between hydrodynamics and fractal features on surface heterogeneity and microstructure impinged by microtopography. Previous studies have elucidated key links between microtopography, hydrodynamics, and sediment transport process (Falsone et al., 2012; Fu et al., 2020; Hao et al., 2019). However, the dynamic evolution of fractal heterogeneity during surface runoff regime transitions, resulting in incomplete understanding of surface-microstructure-mediated erosion mechanism, was neglected.

Thus, this study aimed to (1) track dynamic fractal heterogeneity alongside progressive laminar to turbulent flow transitions under prolonged rainfall and (2) quantitatively decompose causal pathways linking tillage microtopography, hydrodynamic shifts, and depositional crust fractal heterogeneity. This study would provide empirical statistical evidence clarifying partial causal pathways under simulated rainfall and offer practical guidance for optimizing tillage patterns that delay adverse turbulent flow transitions and mitigate sloping farmland soil loss.

Experimental site and soil

Soil samples were collected from the apical 20-cm layer of cultivated loessal soils in the Loess Plateau (Shaanxi Province, China), characterized by warm-temperate, semi-arid to semi-humid climate, with a mean annual temperature of 13 °C and precipitation of 641 mm, with 60%–70% occurring from June to September (Figure 1) (Lin et al., 2019). The soil, classified as silt loam based on USDA system, with 23% of sand (>50 μm), 57% of silt (2–50 μm), and 20% of clay (<2 μm), had a specific surface area of 1.17 m²/g and median particle size of 25 μm.

Experimental equipment

Artificial rainfall was simulated using a calibrated swing-spray rainfall simulator (Institute of Soil and Water Conservation, China), comprising power, control, and testing integrated systems enabling precise rainfall intensity control (20–250 mm/h). Simulated rainfall was delivered via four Veejet 80100 nozzles (Spraying Systems Co., USA), producing raindrops with diameter ranges from 2.5 to 5.0 mm. The effective rainfall area (3 m × 6 m) was maintained at a height of 8.0 m to ensure terminal raindrop velocity.

The experimental runoff plot was designed to be 2.0 m in length, 1.5 m in width, and 0.5 m in height, with a slope of 5°. To ensure adequate drainage at the bottom of the runoff plot, drainage holes were spaced 5.0 cm apart in both longitudinal and lateral directions. A 2.0-cm layer of pebbles was placed at the bottom, covered with geotextile to prevent soil materials from falling into the interstitial spaces.

Measurements

Spatial data collection and analysis

A layered filling method was employed to create a uniform and gentle homogeneous slope, consisting of five 5.0-cm layers. The designed bulk density (BD) for the experimental original slope was set at 1.25 g/cm³, reflecting the soil structure observed in the field. Four surface roughness types, flat (T FC), horizontal (T HC), artificial digging (T AD), and hoeing cultivation (T HE), were generated based on the homogeneous slope using traditional and classical tillage methods prevalent in the Loess Plateau (Figure 2). T FC was generated by a homogeneous slope surface. T HC was designed with four trapezoidal ditches featuring an upper width of 30 cm, a lower width of 20 cm, and a depth of 10 cm. T AD employed staggered excavation method to construct hemispherical ditches with a radius of 15 cm and a depth of 8 cm. T HE was established with hoe ditches measuring 20 cm in length, 10 cm in width, and 5 cm in depth.

Photogrammetry based on Structure-from-Motion (SfM) multi-view stereo algorithms was used to quantify two core microtopographic indices, surface roughness (SR) (Kamphorst et al., 2000) and surface depression storage (SDS), across four tillage treatments to characterize surface spatial heterogeneity that modulates overland flow dynamics and subsequent depositional crust development. Prior to field image collection, the digital camera underwent strict pre-calibration with a standard chessboard target to eliminate radial and tangential lens distortion, with calibrated intrinsic parameters fixed for all reconstructions to remove systematic geometric bias. Overlapping field imagery with 90% overlap for each plot was captured and all datasets were processed in Agisoft Photoscan Professional 1.2.4 to generate sparse point clouds, followed by multi-view stereo post-processing to produce uniform digital elevation models (DEMs) at a consistent spatial resolution of 0.5 mm (Wang et al., 2024). To rigorously validate the reconstruction methodology itself, 40 high-precision ground control points (GCPs) with manually surveyed total station coordinates were evenly distributed on every plot. SfM-derived point coordinates were cross-compared against independent ground-truth reference datasets to assess absolute reconstruction accuracy. Each plot was reconstructed three independent times to quantify workflow uncertainty. Elevation standard deviation (SD, Equation 1) and coefficient of variation (Cv, Equation 2) calculated across replicate reconstructions were adopted to describe measurement repeatability.

where Z (x i) was the elevation value of the surface space position x i. Z ¯ represented the arithmetic average of surface elevations. N showed the total number of elevation values.

Measurement of surface heterogeneity

Beyond microtopographic indices, depositional crust thickness (TN) and BD were measured to quantitatively represent surface structural heterogeneity, which served as the key intermediate linkage connecting microtopographic hydrodynamic forcing and aggregate fractal characteristics. Depositional crust samples were systematically collected from micro-depression zones of all four tillage plots according to the layered sedimentation pattern of eroded aggregates and fine particles. A calibrated YUY2 ShenHong digital microscope was used to accurately measure TN for a subsequent comparative analysis of crust development differences driven by SR and SDS. For each depositional crust plot under every tillage treatment, five separate crust fragments were stripped to measure TN to minimize measurement errors introduced during manual peeling. BD was determined by wax-coated method according to Archimedes’ principle (Equation 3). Three independent intact crust samples were collected for BD.

where BD, γ w t, and γ n reflected the bulk density of depositional crust, deionized water at temperature T, and the unit weight of paraffin (consistently 0.92 g/cm 3). g 0, g 1, and g 2 indicated the weight of air-dried sample, sample with paraffin film, and paraffin-sealed sample in water (g). ω showed the soil moisture content (%).

The determination of aggregate size distribution was conducted following the foundation of wet sieve method, with soil sieve sizes of 2, 1, 0.5, 0.25, 0.106, and 0.053 mm, respectively. Three parallel subsamples of homogenized crust soil were prepared for aggregate size fractionation tests. D was applied for featuring variation in micro-structure stability by illustrating fragmented changes in aggregate size distribution (Equation 4) (Mikha et al., 2024).

where x i and x max were the average and maximum diameter of aggregates (mm), M r < x i represented the content of aggregates in size i less than x i, and M T was the total aggregate dry weight associated with all aggregate size fractions in depositional crust (g).

Runoff hydrodynamics feature

To replicate high-intensity erosive events occurring frequently in study area (Feng et al., 2024), simulated rainfall was applied at 60 mm/h for six durations (5, 10, 15, 20, 25, and 30 min). During the 5–30-min simulated rainfall monitoring period, hydrodynamic indicators were measured for all four tillage plots. Meanwhile, runoff initiation time of each replicate plot was directly captured to interpret differences in surface depression storage and runoff connectivity. Runoff generation initiated when rainfall interception was modulated by soil hydraulic properties and vertical water movement. Hydrodynamic parameters and runoff movement patterns were acquired to explore the dynamic properties of surface flow regimes (Schroers et al., 2022). Three independent replicate observations were recorded. A regime shift that occurred was quantified using dye-tracing technique to quantify V. τ was calculated to describe the function of runoff in stripping and transporting surface soil aggregates based on Equation 5.

where ρ represented the water mass density (kg/m 3), g was 9.8 m/s 2, h was runoff depth (m), and s was flume slope gradient.

Dimensionless flow regime indicator R e was calculated to determine the state of fluid mechanics according to Equations 6 and 7.

where V m represented kinematic viscosity (function of water temperature, 14 °C in this study).

Flow discriminator, F r, was derived to determine the flow pattern and analyze the similarity of flow based on Equation 8.

f was calculated to conduct resistance features under microtopography control by using Equation 9.

where J was the hydraulic gradient.

Statistical analysis

Differences in bulk density (BD) and thickness (TN) of depositional crusts across rainfall duration gradients under four microtopographies were examined using one-way analysis of variance (ANOVA). Correlation analysis, random forest regression (RF), and structural equation modeling (SEM) were combined to disentangle the regulation of hydrodynamic on surface crusts fractal heterogeneity. RF regression quantified the predictive importance of driving variables for fractal dimension D. Ten-fold cross-validation was applied to assess model reproducibility and assist identification of key coupled driving factors, while mitigating multicollinearity interference. Grid-search hyperparameter tuning was conducted over the candidate space (ntree: 200, 500, 800, 1,000, 1,500; mtry: 1–10). The optimal configuration was selected according to minimum cross-validated prediction error. Predictors with standardized importance >30 % were retained, yielding five core variables for subsequent SEM analysis to reduce model dimensionality and suppress overfitting risk. SEM was fitted with the maximum likelihood estimator to decompose statistical covariation pathways connecting microtopographic and hydrodynamics to fractal dimension D. The dataset contained 216 independent observations for model estimation, with 19 free parameters (12 regression path coefficients, five variances of exogenous predictors, and three residual variances of endogenous variables), producing a ratio of ~11.37, which satisfies the widely recognized 10:1 benchmark for covariance-based SEM. Removal of low-contribution predictors based on RF importance thresholds and cross-validation were performed to evaluate parameter stability across data subsets. Global model-fit indices including RMSEA, SRMR, CFI, and TLI were inspected to verify adequate reproduction of the sample covariance structure.

Characteristics of runoff hydrodynamics

Tillage treatments induced distinct hydrodynamic responses as RD extended from 5 to 30 min (Figure 3). V (0.16–0.32 m/s) and τ (1.12–1.68 Pa) exhibited a consistent trend of initial increase, followed by stabilization with prolonged rainfall. Obvious V was recorded in T FC (0.28 m/s), followed by T HE (0.26 m/s), T AD (0.24 m/s), and T HC (0.19 m/s), a difference attributed to the pronounced surface undulation (SR THC = 1.76, SR TAD = 1.66, SR THE = 1.47, SR TFC = 1.02) (Table 1). In contrast, the relatively homogeneous surface conditions of T FC and T HE yielded lower τ, aligning with SR.

Both Re (184–480) and Fr (1.3–2.7) displayed quasi-linear growth with RD, reflecting a regime transition from laminar-dominated to transitional-turbulent flow (Figure 4). f (0–2) exhibited non-stationary behavior with oscillatory patterns, indicating dynamic interactions between flow inertia and microtopography-induced resistance. Flat surfaces recorded more turbulent flow than undulated surfaces (Re TFC > Re THE > Re TAD > Re THC), accompanied by supercritical flow. The correlation analysis (Figure 5) performed showed that RD was significantly positively correlated with Re (0.74*) and Fr (0.57) and inversely correlated with f (–0.72). The microtopographic indices (SR and SDS) exhibited weaker correlations with the hydrodynamic parameters.

Surface heterogeneity mediated by depositional crust under diversity microtopography

Structural properties

BD and TN of depositional crusts varied significantly across the four distinct microtopographic treatments (Figure 6). BD increased consistently with prolonged RD and peaked in T HC (1.68 g/cm³), followed by T AD (1.67 g/cm³), T HE (1.64 g/cm³), and T FC (1.45 g/cm³), after 30 min of simulated rainfall. In contrast, TN under T HC and T AD exhibited fluctuating increases with RD, while T FC and T HE displayed fluctuating decreases. The thickest depositional crust was observed in T AD (2.7 mm), closely followed by T HC (2.6 mm), T HE (2.3 mm), and T FC (2.2 mm), after 30 min of rainfall.

The correlation analysis (Figure 5) further clarified that BD was significantly positively correlated with RD, SR, and SDS (p < 0.05). TN illustrated no significant correlations. Surface depression specification (SDS THC = 9.36 × 10 -2, SD STAD = 4.65 × 10 -2, SDS THE = 6.42 × 10 -3, SDS TFC = 4.33 × 10 -5) highlighted the role of sediment detention in facilitating microtopographic depressions (Figure 7). SD remained low across all treatments (0.027–0.041), indicating stable surface topography within each tillage plot. The Cv value of surface undulation was lowest for T FC (0.005), demonstrating uniform, flat terrain.

Composition of aggregates

The percentage of macro-aggregates (>0.25 mm) in depositional crusts exhibited a consistently decreasing trend with prolonged simulated RD across all four tillage treatments (Figure 8). The most pronounced reduction was observed in T HC (60%), followed sequentially by T HE (54%) and T AD (46%), while T FC showed negligible variation (6%). T FC maintained the highest macro-aggregate content (26%), which was 2.5, 2.7, and 2.2 times higher than T HC, T AD, and T HE, respectively, reflecting minimal aggregate fragmentation under homogeneous surface conditions.

The correlation analysis between aggregate composition and environmental factors confirmed that spatial heterogeneity dominated macro-aggregate dispersion, manifested that prolonged rainfall and surface roughness promoted fine particle generation and deposition, and identified rainfall as the primary driver of the breakdown and transport of middle aggregates (Figure 9). The macro-aggregate (>0.25 mm) content was not significantly correlated with RD (p > 0.05), whereas it was significantly negatively correlated with SR and SDS (p < 0.05). The intermediate-sized aggregates (0.053–0.25 mm) were significantly negatively correlated with RD (p < 0.05). The micro-aggregate content (<0.053 mm) was significantly positively correlated with RD, SR, and SDS (p < 0.05).

Surface fractal dynamics induced by depositional processes

D was used to quantify the structural complexity of depositional crusts across four tillage treatments, with observed value ranges of 2.22–2.59 (T FC), 2.33–2.71 (T HC), 2.38–2.65 (T AD), and 2.38–2.65 (T HE) (Figure 10). As RD extended from 5 to 30 min, D exhibited an initial increase, followed by gradual stabilization, with relative increments of 16% (T FC), 16% (T HC), 12% (T AD), and 11% (T HE). The correlation revealed significant positive correlations between D and environmental indicators (p < 0.05) as well as all measured hydrodynamic variables (p < 0.01) (Figure 5). Micro-topographic undulation, sediment retention capacity, and flow energy jointly correlated with elevated fractal complexity of surface aggregates. Positive correlations were also detected between D and micro-aggregate proportion and BD (p < 0.001), while macro-aggregate content showed significant negative correlations, consistent with the negative association between f and D (p < 0.001).

Fractal regulation mechanism driven by hydrodynamics forcing

RF analysis identified the primary predictors correlated with D (Figure 11). Combined standardized predictive contributions of f and Fr reached 83%, outperforming Re (22%), shear stress τ (14%), and flow velocity V (14%). Aggregate composition indicators exerted moderate predictive effects (15%–25%). Five predictors (RD, BD, f, Fr, and TN) with standardized importance values exceeding 30% were screened for subsequent SEM. The SEM revealed statistically significant positive correlational pathways linking RD (0.36) and BD (0.44) to D, while non-significant negative associations were observed for Fr (-0.15) and TN (−0.14), alongside a significant negative correlational pathway for f (-0.24) (Figure 12). Statistical covariation suggested that RD was positively associated with fractal complexity via crust-compaction-related pathways, and RD showed linear correlations with the hydrodynamic mediator Fr (-0.57*) and f (0.42*). All model fit indices met acceptable thresholds (RMSEA, SRMR < 0.08; CFI, TLI > 0.9), supporting reliable partitioning of variable covariation patterns associated with surface aggregate fractal characteristics shaped by microstructural and hydrodynamic conditions.

Regulation of runoff hydrodynamic processes by microtopography

Existing research has established that microtopography modulates the storage, conveyance, and dissipation of runoff by altering the physical configuration of sloping farmland surfaces (Lampurlanes and Cantero-Martinez, 2006; Papanicolaou et al., 2018). Specifically, microtopographic surfaces with discrete depressions significantly elevate SR, thereby enhancing water storage capacity, elongating runoff flow paths, and prolonging runoff retention time (Li et al., 2020). The results in this study described that runoff initiation occurred at 5-, 10-, and 15-min rainfall under T FC, T HE, and T AD, respectively, while no continuous outflow was observed for T HC within the 30-min rainfall period. This temporal difference aligns with prior findings (Darboux and Huang, 2005; Govers et al., 2000), which statistically supports the correlational link between depression volume and delayed runoff generation.

Quantitative analysis demonstrated that, in comparison to flat surfaces, rough microtopographic features significantly reduce V through the generation of micro-vortices and sediment deposition in depression zones (Wang et al., 2023, 2025; Zhang et al., 2023a). The mechanism supported the negative correlation between SR and V observed in this study, with significant V recorded in T FC while relatively stable V remained in T HC. Runoff shear stress displayed more pronounced spatiotemporal variability under tillage-modified microtopographic conditions, indicating that microtopography redistributed flow energy across ridges and depressions. T HC generated elevated τ within ditches, consistent with the physical inference that depressions accumulated runoff, subsequently increasing flow depth when undulation amplitudes reach approximately ±10 cm. Conversely, elevated microtopographic zones experience runoff diversion, leading to a reduction in flow depth with increasing surface undulation.

Research has shown that surface-roughness-induced flow perturbations reshape runoff hydrodynamic patterns (Antoine et al., 2012; Myers, 2003), especially under the disturbance of raindrop impact. The conclusion could be conducted that raindrop impact effects dominated runoff dynamics on smooth surfaces, whereas surface roughness exerted pronounced control over laminar flow regimes under highly rough microtopographic conditions. Re and Fr were further employed as diagnostic parameters to characterize surface runoff flow regimes. The probability of flow transition from laminar to turbulent conditions after 15 min of rainfall depicted the influence of prolonged rainfall on fluid momentum. The quasi-linear rising trends of Re and Fr were consistent with results from studies focusing on flow velocity dynamics in sloping landscapes (Abrantes et al., 2018; Pan et al., 2015; Polyakov et al., 2021). Critical hydrodynamic phase transitions were treatment dependent, with T HE and T AD exhibiting abrupt shifts at 10 and 15 min of rainfall, respectively, accompanied by incipient turbulence verified by Re >400 and supercritical flow indicated by Fr. This phenomenon underscored the scale-dependent interaction between microtopography and rainfall regulation in hydraulic process regime transitions.

Response of surface fractal features to hydrodynamics

As the dynamic interface mediating between sediment deposition and rainfall energy dissipation, SR nonlinearly modulates infiltration thresholds, runoff initiation, and drainage network development, shaping the spatiotemporal dynamics in hillslope hydrological connectivity (Bullard et al., 2018; Cerdan et al., 2004; Lampurlanes and Cantero-Martinez, 2006; Liu et al., 2004; Papanicolaou et al., 2018). Tillage-induced microtopography with undulation amplitude of ±5–20 cm significantly altered size-selective sediment transport processes (Darboux and Huang, 2005; Jester and Klik, 2005). In this study, T AD and T HE exhibited apparent shift points at 15 and 10 min RD, respectively, a pattern that correlated with progressive sediment redistribution driven by strengthened runoff connectivity under extended rainfall. Limited variability in BD and TN was observed in T HC, a trend linked to the sediment retention capacity of developed surface undulations. These observational patterns align with the synergistic interactions between tillage microtopography and rainfall duration that jointly regulated particle detachment and sediment deposition (Bronick and Lal, 2005; Okolo et al., 2020).

Rainfall triggers aggregate dispersion, rearrangement, fine-particle translocation, and crust compaction, processes collectively associated with physical crust formation (Chen et al., 2024; Lu et al., 2017; Zhang et al., 2023b). Statistical correlations indicated that macro-aggregate abundance was primarily linked to terrain heterogeneity, while micro-aggregate proportion was closely associated with rainfall duration, highlighting divergent dominant correlates governing aggregate fractionation on heterogeneous sloping land. No statistically significant variations in aggregate size distribution were detected within the initial 5 min of rainfall when the surface runoff remained negligible (p > 0.05). This statistical pattern correlated with the physical pathway by which raindrop splash drove aggregate breakdown, followed by fine-particle translocation via overland flow (Sirjani et al., 2021; Stevens et al., 2009; Vermang et al., 2015). The hydraulic resistance captured by the f originated from two independent mechanisms: form drag generated by topographic ridges and viscous skin friction from ponded surface water, which exerted opposing influences on turbulent particle sorting and fracture. In the present experiment, the significant negative direct effect of f on D (-0.24*) was dominated by friction within ditch ponding. Extended rainfall duration increased the Fr and formed supercritical flow, which weakened viscous friction and reduced flow resistance. This created an offsetting positive indirect mediating pathway of Fr on D through reduced f, partially counteracting the direct inhibitory effect of viscous friction on fractal complexity.

Prolonged rainfall promoted continuous sediment accumulation within micro-depressions, shifting sediment dynamics from high particle detachment and low deposition to low detachment and sustained sediment trapping (Puustinen et al., 2005). Dominant coarse-particle deposition homogenized surface sediment structure, whereas gradual fine sediment accumulation within ditches elevated terrain fractal heterogeneity. RF and SEM covariation analysis indicated that rainfall duration, depositional crust structural properties, and hydrodynamic conditions are the primary variables correlated with D. Fr served as the primary endogenous mediator directly affected by RD, while f acted as the secondary endogenous mediator regulated by Fr, forming a mediating chain shaping fractal complexity. These statistical associations suggested that flow regime transitions modulated by coupled microtopography and sediment deposition may drive temporal shifts in surface fractal characteristics.

Limitations and prospects

This laboratory experiment quantified the effects of flow regime transitions in altering depositional crust fractal heterogeneity across four tillage microtopographies on sloping farmland. However, natural field precipitation features temporally variable, intermittent rainfall with fluctuating kinetic energy, while all leaching tests adopted a fixed single rainfall intensity (60 mm/h) which may shift substantially under low-intensity drizzle or intense storm events. Soil texture strongly mediates aggregate stability, crust formation, and cation exchange capacity. The experiment only utilized homogeneous loess silt loam soil. Other cultivated soils should be included in the observations. Besides that, slope steepness directly modulates runoff velocity, flow depth, and sediment transport capacity. Steeper or gentler slopes would alter hydrodynamic partitioning across ridges and depressions, reshaping the relative contributions of turbulent indices. With these limitations, this work developed a multivariate statistical framework combining RF and SEM to disentangle microtopographic, hydrodynamic, and soil structural variables.

This study investigated the interactive effects of microtopographic disturbance and rainfall duration on surface soil microstructure, hydrodynamic regime transition, and fractal heterogeneity reflected by depositional crust under four typical tillage practices. A hydrodynamic threshold of 15 min of rainfall duration was identified from laminar overland flow to transitional flow, altering soil aggregate redistribution and surface fractal evolution. Microtopographic features (surface depression storage and surface roughness) and rainfall duration (RD) exerted deterministic controls on soil bulk density (BD) and thickness (TN), significantly increasing the micro-aggregate (<0.053 mm) proportion. Fractal dimension (D) was verified for characterizing surface structural heterogeneity, exhibiting significant positive correlations with environmental factors (p < 0.05) and hydrodynamic parameters (p < 0.01). Based on RF and SEM, RD (β = 0.36) and BD (β = 0.44) positively promoted fractal development, whereas hydrodynamic turbulence (β Fr = −0.15, β f = −0.24*) and TN (β = −0.14) exerted negative regulatory effects. The dynamic shift to soil fractal complexity induced by laminar and turbulent flow quantified regulatory trade-offs between microtopographic buffering and surface heterogeneity. This work quantified a multi-factor causal framework for designing erosion-resistant tillage configurations and developing precision soil conservation measures on cultivated hillslopes.