Transport/Detachment Regimes of Different Size Class Sediment Particles and Enlightenments for Transport Capacity Prediction for Rain-Induced Overland Flow Erosion

Abstract

The transport/detachment regimes of each particle size vary with size. Moreover, the changing transport/detachment regimes of sediments with size and their related mechanisms considerably affect sediment transport capacity (T_c). To investigate the transport/detachment regimes of each particle size and their explanation for T_c prediction, 27 simulated rainfall experiments were conducted under slope gradients of 8.7%, 17.6%, and 26.7% and rainfall intensities of 60, 90, and 120 mm h⁻¹. The experimental soil was Cumulic Anthrosols, and the duration of each rainfall was 1 h. Results showed that for rain-induced overland flow erosion, the average transport ratios (T_rs) of clay, fine silt, and coarse sand (<0.002, 0.002–0.02, and >0.25 mm, respectively) for rainfall, were greater than 1.0, and their erosion regimes were detachment-limited. The T_rs of coarse silt and fine sand (0.02–0.05 mm and 0.05–0.25 mm, respectively) were less than 1.0, and their erosion regimes were transport-limited. The transport-/detachment-limited degree of each size class of particles, except for coarse sand, increased with the slope gradient, but slightly and complexly changed with rainfall intensity. The T_rs of each size class of particles on the gentle slope (8.7%, 17.6%) increased with the T_rs of total sediments. In the case of the steep slope (27.6%), however, the T_rs of fine silt and clay increased with a decrease in the T_rs of the total sediment particles. Different prediction equations were established to simulate the T_cs of sediments with different sizes in the two slope ranges (R² > 0.823, p < 0.01). The findings will help to elucidate the selective transport mechanisms of all sizes of sediment particles and improve the prediction of T_c in the future.

1. Introduction

Soil erosion is one of the most serious ecological and environmental problems worldwide; it not only restricts the sustainable development of agriculture but also reduces land productivity and increases soil carbon dioxide emissions to the atmosphere [1]. Soil erosion is divided into several processes, namely, sediment detachment, transport, and deposition; each subprocess has different internal mechanisms [2]. Eroded materials from different sources (e.g., raindrop hit or runoff wash) exhibit different transport mechanisms that can be partially reflected by the transport- and detachment-limited erosion regimes [3]. When splash-detached particles are less abundant than runoff-transported ones, partial runoff erosive energy is used to detach slope soil, and the erosion regime is generally detachment-limited. Conversely, most runoff energy is used to transport particles, and the erosion regime is transport-limited. The detachment- and transport-limited processes of rain-induced overland flow can be distinguished by comparing soil losses due to splash detachment and diffuse erosion under different experimental conditions, such as those in [4,5,6,7]. However, only a few studies have considered the effect of the transport- or detachment-limited regime of different particle sizes of sediments on the erosion mechanism and the related erosion prediction.

If specific size class particles from raindrop detachment are greater than runoff-washed ones, then diffuse erosion for the former is perceived as transport-limited; otherwise, it is considered detachment-limited [8,9]. Dominant erosion regimes may not only change with erosion environmental factors and processes but also with the particle size of sediments. Under high rainfall intensities and steep slope gradients, raindrop detachment is a limited factor, and most sand particles are transported while clay and silt are detached by runoff [10]. Under low rainfall intensities and gentle slope gradients, overland flow transport is a limited factor [5], and clay particles are transported by runoff while mobile coarse particles are retained on the splash detachment site [11]. The erosion regime changes with the particle size in soil can be expressed by the difference between sediment size distributions from splash-detached erosion and runoff-washed erosion. Transport- and detachment-limited regimes can exist simultaneously for sediment particles with different particle densities and sizes. However, transport- and detachment-limited regimes between sediment particles are not yet fully understood and still require further investigation.

The effect of the erosion regime on the quantitative relationship between transport capacity (T_c) and hydraulic parameters has elicited research attention [5]. The correlation of hydraulic parameters with T_c varies, e.g., flow velocity > stream power [12]. T_c increases as a linear or power function with the hydraulic parameters, rainfall intensity, raindrop energy, and slope gradient [7,12]. When the erosion regime is transport-limited, hydraulic parameters, such as stream power, shear stress, and mean flow velocity, are evaluated to predict T_c in the Water Erosion Prediction Project (WEPP) model [13] and the European Soil Erosion Model [14], among others. In addition, empirical equations for predicting T_c and soil loss have been widely studied using factor multiplication, e.g., the Universal Soil Loss Equation [15], while the soil erodibility parameter is typically used to modify the equations [13]. Input factors also include the slope gradient, rainfall intensity and raindrop energy, flow discharge, and median particle size [3,4,16,17,18]. T_c is inversely proportional to sediment density or size [19,20,21,22]. In accordance with Govers [23], T_c increases with sediment size. However, the effect of the different mechanisms of each size class of particles associated with transport- and detachment-limited regimes on the T_c of overland flow is not yet fully understood.

Considering the changes in erosion regimes with sediment particle size, their contribution to understanding erosion mechanisms and their possible effect on T_c prediction, the objectives of this experiment were as follows: (1) to distinguish between the transport- and detachment-limited processes of sediment particles of different sizes under rain-induced overland flow, (2) to classify different T_c prediction scenarios in accordance with the erosion mechanisms related to the erosion regimes of each size of particles, and (3) to develop a revised model that incorporates changes in transport- or detachment-limited regimes to predict T_c.

2. Materials and Methods

2.1. Test Soil

In this study, soil samples were collected from Yangling, Shaanxi Province (108°03′ E, 34°18′ N), which is located south of the Loess Plateau in China with a hilly and gully region. The average elevation of the sampling site is about 500 m, belonging to the semi-arid continental monsoon climate. The mean annual rainfall of the region, 60% of which falls between June and September, is approximately 600 mm [24,25]. Crops were rotated for 6 consecutive years, including wheat (Triticum aestivum L.) and corn (Zea mays L.). The typical soil of this area is Cumulic Anthrosols with a high organic matter content (5.68 g kg⁻¹) [26]. The test loess was collected from a 0–20 cm layer of cultivated land in July before corn was planted. Plant residues and pebbles were filtered through a 10 mm sieve and then thoroughly mixed with the soil. The detailed properties of the loess used in the experiment are shown in

Table 1. Basic properties of test soil.

Property	Clay (%)	Fine Silt (%)	Coarse Silt (%)	Fine Sand (%)	Coarse Sand (%)	SOC (g kg−1)	pH (in H2O)	Bulk Density (g cm−3)
Effective values	20.1	11.9	23.1	35.5	9.4	5.68	8.3	1.3
Dispersed values	37.2	30.5	22.2	7.1	3.0

Soil texture is classified based on the USDA soil classification system.

.

2.2. Experiment Equipment

Artificial rainfall simulation experiments were conducted at the Institute of Soil and Water Conservation of the Ministry of Water Resources and Chinese Academy of Sciences in Yangling, Shaanxi, China [27]. Water flowing from these nozzles was approximately 17 m above the surface of the test soil to simulate the final velocity of natural raindrops. The rainfall device can meet the rainfall intensity of 40–260 mm h⁻¹ by changing the nozzle size of two groups of lateral spraying nozzles. The uniformity of the simulated rainfall exceeded 85% [28]. Tap water (electrical conductivity = 0.7 dS m⁻¹) was used in all experiments.

For simultaneously monitoring splash and diffuse erosion, a three-part runoff plot was modified, which was developed from that designed by Meyer and Harmon [29]. A center erosion test area with a length of 100 cm and a width of 35 cm was arranged in the center of the plot (Figure 1). A splash collection trough with a width of 1.5 cm was arranged on the left and right sides; the upper, left, and right parts of the center erosion test area are splash compensation areas. The drainage trough was set between the upper splash compensation area and erosion test area to eliminate the influence of incoming water from above the center erosion test area. According to the maximum distance of the soil particles splashed by raindrops, the width of splash compensation area is set as 35 cm. Thus, the partial missing of the splash soil can be supplemented in the center erosion test area to ensure the accuracy of the splash and diffuse erosion observations. The lower part of the plot was provided with a buffer area enclosed by a “V”-shaped water trough. The “V” fronting effectively reduced the disturbance of runoff to the bottom of the observation area. The narrow runoff outlet facilitated the collection of sediment and runoff samples with large runoff buckets. The slope gradient for the soil pan could be adjusted between 0% and 30%.

2.3. Experiment Design

Soil erosion in the Loess Plateau region is caused by seasonal heavy rainfall [30]. On the basis of the local erosive rainfall intensity, three typical rainfall intensities (60, 90, and 120 mm h⁻¹) in the Loess Plateau region were selected, and three slope gradients (8.7%, 17.6%, and 26.7%) were designed according to the actual situation of the local slope farmland.

2.4. Experiment Procedures

Before loading the test loess into the soil pan, the bottom of the soil pan was lined with a layer of sand 10 cm thick to act as a filter to simulate a drainage system. Then, the soil pan was filled with 30 cm of test soil. The test soil was filled into six layers of 5 cm thick so that the test soil had the same degree of compactness. To reduce discontinuities between layers, the soil was compacted so that the bulk density reached 1.3 g cm⁻³, which is close to the natural soil bulk density. After filling the soil basin, the soil from the top was moistened with water mist to saturate the soil. After pre-rainfall, the surface of the soil was covered with a plastic cloth to prevent the evaporation of soil water and let stand for 24 h. After each rainfall experiment, the soil pan was refilled, and the process was repeated.

Before the formal experiment, the rainfall simulator was adjusted to achieve the required rainfall intensity and maintain uniformity. Before the simulated rainfall began, the slope gradient of the soil pan was calibrated to the required one. The rainfall lasted for 1 h in each experiment. The water temperature was about 18–20 °C. The average daily air temperature during the experiment was approximately 30 °C. Each treatment was repeated three times. Seventeen sediments were collected from the splash erosion and the diffuse erosion at 3 min intervals since the runoff initiation, and a total of 20 runoff or splash erosion samples were collected for each treatment. In order to determine the weight of the sediment, clear supernatant was poured off from the water–sand mixture, and the remaining sediment particles were oven-dried at 105 °C for 24 h. The splash detachment rate was defined as the total splashed material per unit area per unit time. The diffuse erosion rate was defined as the weight of the sediment transported by the rain-induced overland flow per unit area per unit time. Moreover, the surface flow velocity on the test area was measured along the 90 cm distance using KMnO₄ solution as a tracer. The measurement was taken in the area where the stream appeared or in the rill after the development of the interrill. To control the error, all flow velocities were measured by one person and 15 surface flow velocities were obtained for each experiment.

2.5. Measurements

2.5.1. Sample Determination

The sediment samples were analyzed using a Malvern Mastersizer 2000 laser diffractometer (Malvern Instruments Ltd., Worcestershire, UK) without dispersion to obtain the effective sediment particle size distribution. Then, organic matter was removed with H₂O₂ and chemically dispersed with sodium hexametaphosphate. After chemical dispersion, each sample was analyzed with a laser diffraction via supersonic dispersion to obtain the dispersed sediment particle size distribution and median diameter.

2.5.2. Hydraulic Parameters

The mean flow velocity of the overland flow (m s⁻¹) was estimated based on surface flow velocity as follows:

$$V=k{V}_S$$

(1)

where $V$ is the flow velocity of the overland flow (m s⁻¹), $k$ is the correction coefficient, and $V_S$ is the surface flow velocity (m s⁻¹). According to An et al. [31], the $k$ for the sediment-laden flow was 0.67.

The runoff depth was calculated as follows:

$$D=\frac{Q}{V}$$

(2)

where $D$ is the runoff depth (m) and $Q$ is the unit width runoff (m² s⁻¹).

The shear stress of overland flow was calculated using the formula of Yalin [32]:

$$\tau =\rho gDS$$

(3)

where τ is the runoff shear stress (Pa), $\rho$ is the runoff density (kg m⁻³), $g$ is the gravitational constant (9.8 m s⁻²), and $S$ is the slope gradient (mm⁻¹).

The stream power of overland flow was calculated using the formula of Prosser and Rustomji [33]:

$$\Omega =\rho gQS$$

(4)

where $\Omega$ is the runoff stream power (W m⁻²).

To directly reflect that the erosion process belongs to transport- or detachment-limited, the transport ratio (T_r) was defined and calculated as the diffuse erosion rate-to-splash detachment rate ratio.

2.6. Data Analysis

The relationships between T_c and the slope gradient and hydraulic variables were analyzed using a nonlinear regression method. The relationships between T_c and unit width runoff, stream power, runoff depth, shear stress, and flow velocity for different sizes of class sediment particles were analyzed using multivariate regression analysis. For the performance evaluation of the T_c calculation equation, the coefficient of determination (R²) was used. The formulas for R² were as follows:

$$R^2=\frac{{\left[{\sum }_{i=1}^n\left(O_i-\stackrel{-}{O}\right)\left(P_i-\stackrel{-}{P}\right)\right]}^2}{{{\sum }_{i=1}^n\left(O_i-\stackrel{-}{O}\right)}^2{{\sum }_{i=1}^n\left(P_i-\stackrel{-}{P}\right)}^2}$$

(5)

where $O_i$ are the measured values, $\stackrel{-}{O}$ is the mean of the measured values, $P_i$ are the predicted values, and $\stackrel{-}{P}$ is the mean of the predicted values. Visualization was performed using Origin 2022, and IBM SPSS Statistics 26.0 was used for data analysis.

3. Results

3.1. Features of Splash Detachment and Diffuse Erosion during Rainfall

The effects of slope gradients and rainfall intensity on the changes in the diffuse erosion and splash detachment rates with time were investigated (Figure 2). The diffuse erosion and splash detachment rates increased with the slope gradient and rainfall intensity. During the erosion process, the diffuse erosion rate decreased rapidly within the first 15 min of rainfall and then remained stable. However, the splash detachment rate changed slightly with time during the erosion process in most of the erosion situations, especially at the 60 and 90 mm h⁻¹ rainfall intensities. At 120 mm h⁻¹, the splash detachment rate decreased rapidly in the first 15 min, then became stable, and fluctuated slightly with the progress of rainfall.

3.2. Relationships of Percentages of Each Size Class Sediment Particles between Rain-Detached Particles and Runoff-Transported Particles

By comparing the diffuse erosion and splash detachment rates, the erosion regimes of eroded sediments were initially analyzed. At the rainfall intensities of 60 and 90 mm h⁻¹, the diffuse erosion rate was greater than the splash detachment rate during the entire rainfall process, indicating that part of the sediment detachment was caused by runoff scour during erosion. When the rainfall intensity increased to 120 mm h⁻¹, although the diffuse erosion rate was greater than the splash detachment rate in the first 20 min of rainfall, the diffuse erosion rate decreased rapidly, and gradually approached the splash detachment rate.

The T_rs of each size of particles were calculated by dividing the mass percentages of each size class of particles from the rain-induced overland flow erosion by those from the splash detachment (Figure 3). In general, the T_rs of clay, fine silt, and coarse sand (<0.002, 0.002–0.02, and >0.25 mm) was greater than 1.0, indicating that the erosion of these particles was detachment-limited in most situations. The T_rs of coarse silt and fine sand (0.02–0.05 and 0.05–0.25 mm, respectively) was less than 1.0, indicating that the erosion of these large size particles was transport-limited. The T_rs of clay and fine silt increased with the slope gradient and the rainfall intensity. The T_r of coarse silt changed slightly with the slope gradient and the rainfall intensity. However, the T_rs of fine and coarse sand decreased with the increase in the slope gradient and the rainfall intensity. Moreover, interactions existed between the slope gradient and the rainfall intensity for the T_rs of each size class of particles. On the steep slope, rainfall intensity had a greater effect on the T_rs of sediment particle sizes than on the gentle slope. Among all size classes of particles, the slope gradient and rainfall intensity had the least effect on the T_r of coarse silt (0.02–0.05 mm) but the greatest effect on the T_r of coarse sand (>0.25 mm). Overall, the transport-/detachment-limited degree of each size class of particles, except for coarse sand, increased with the slope gradient and the rainfall intensity; coarse sand tended to change from a transport- to detachment-limited process.

3.3. Relations between Detachment-/Transport-Limited Regimes of Each Size Sediment Particles and Those of Total Eroded Sediments

The quadratic regression curve of the T_rs of each size class of particles and those of their corresponding total eroded sediment particles is shown in Figure 4. In the case of a gentle slope (8.7%, 17.6%), the T_rs of each size of particles increased with the T_rs of the total sediments. However, in the case of the steep slope (27.6%), the T_rs of clay and fine silt first increased and then decreased with the increase in the T_rs of the total sediment particles, while those of other size particles always increased. Hence, when the erosion on a large slope gradient was detachment-limited, a great amount of additional runoff energy was used to detach and transport particles with a size of >0.02 mm. When the erosion on the gentle slope was transport−limited, most of the added runoff energy caused by the erosion process or conditions was used to detach and transport <0.02 mm particles. Moreover, the increasing rates of the T_rs of coarse silt and fine sand increased with the T_rs of the total sediment particles, but those of clay, fine silt, and coarse sand first increased and then decreased. The T_rs of clay, fine silt, and coarse sand attained 1.0 before the T_rs of total particles increased to 1.0, while those of the other particles attained 1.0 after the T_rs of total particles increased to 1.0. In addition, on the slope gradients of 8.7% and 17.6%, the T_rs of the total sediment particles were usually less than 1.0 but larger than 1.0 on the slope of 27.6%. Overall, slope gradient had a greater effect on the relationship between the erosion regimes of different particle sizes and those of the total sediment particles than rainfall intensity (

Table 2. Correlation analysis matrix of transport capacity (T_c) with the different sediment particle size classes, slope gradients, rainfall intensities, and hydraulic parameters.

Parameter	Tc (<0.002 mm)	Tc (0.002–0.02 mm)	Tc (0.02–0.05 mm)	Tc (0.05–0.25 mm)	Tc (>0.25 mm)
Slope gradient	0.893 **	0.903 **	0.895 **	0.771 *	0.679 *
Rainfall intensity	0.317	0.346	0.329	0.269	0.346
Flow velocity	0.903 **	0.901 **	0.861 **	0.684 *	0.639
Runoff depth	−0.265	−0.247	−0.253	−0.215	−0.158
Unit width runoff	0.499	0.505	0.459	0.336	0.358
Sheer stress	0.927 **	0.933 **	0.898 **	0.735 *	0.676 *
Stream power	0.933 **	0.936 **	0.899 **	0.727 *	0.695 *

NOTE: ** Correlation is significant at the 0.01 level (two-tailed). * Correlation is significant at the 0.05 level (two-tailed).

). Further investigation of the interactions of rainfall intensity and the slope gradient on the T_rs of different particle sizes revealed that little interactions existed when the slope was below 17.6%, but at a >17.6% slope gradient, the effect of rainfall intensity on the T_rs of different particle sizes increased with the slope gradient (Figure 5).

3.4. Effecting of the Different Erosion Regimes of Each Grain Size on T_c Prediction

Through multiple regression analysis of the relationships among the slope gradient, the rainfall intensity, and the T_c, R² of the equations for <0.002, 0.002–0.02, 0.02–0.05, 0.05–0.25, and >0.25 mm was 0.885, 0.916, 0.896, 0.660, and 0.693, respectively. The exponents of the slope gradient for the sediments with five particle sizes were greater than those of the rainfall intensity, further verifying that the T_c for the overland erosion processes was more sensitive to the slope gradient than rainfall intensity. Moreover, the exponents of the slope gradient first decreased and then increased with an increase in the particle size. This phenomenon is consistent with the influence of the slope on the transport ratios of each grain size mentioned above.

The analysis of the initial relationships between the hydraulic factors and T_cs of each size class of particles indicates a significant power function relationship between T_c and shear stress (R² > 0.469, p < 0.05) or stream power (R² > 0.494, p < 0.05) (

Table 3. Response of T_c to hydraulic parameters.

Parameter	Sediment Sizes (mm)	Function	R2
Slope gradient (%) Rainfall intensity (mm h−1)	<0.002	Tc = 4.93 × 10−7 S1.07 I0.45	0.885
	0.002–0.02	Tc = 5.71 × 10−7 S1.06 I0.48	0.916
	0.02–0.05	Tc = 4.66 × 10−7 S1.10 I0.47	0.896
	0.05–0.25	Tc = 2.33 × 10−7 S1.16 I0.45	0.660
	>0.25	Tc = 3.71 × 10−11 S2.55 I1.14	0.693
Shear stress (Pa)	<0.002	Tc = 4.41 × 10−4 τ1.31	0.863
	0.002–0.02	Tc = 5.47 × 10−4 τ1.27	0.872
	0.02–0.05	Tc = 4.70 × 10−4 τ1.24	0.806
	0.05–0.25	Tc = 2.34 × 10−4 τ1.16	0.537
	>0.25	Tc = 1.58 × 10−4 τ1.88	0.469
Stream power (W m−2)	<0.002	Tc = 1.14 × 10−3 Ω0.80	0.873
	0.002–0.02	Tc = 1.40 × 10−3 Ω0.78	0.880
	0.02–0.05	Tc = 1.19 × 10−3 Ω0.62	0.811
	0.05–0.25	Tc = 5.61 × 10−4 Ω0.72	0.532
	>0.25	Tc = 8.95 × 10−4 Ω1.28	0.494
Flow velocity (m s−1)	<0.002	Tc = 4.09 × 10−3 V1.96	0.822
	0.002–0.02	Tc = 4.88 × 10−3 V1.92	0.822
	0.02–0.05	Tc = 4.08 × 10−3 V1.89	0.751
	0.05–0.25	Tc = 1.77 × 10−3 V1.77	0.476
	>0.25	Tc = 2.29 × 10−2 V3.78	0.484
Runoff depth (m)	<0.002	Tc = 5.01 × 10−6 D−0.32	0.040
	0.002–0.02	Tc = 7.26 × 10−6 D−0.30	0.038
	0.02–0.05	Tc = 4.45 × 10−6 D−0.35	0.045
	0.05–0.25	Tc = 1.51 × 10−6 D−0.40	0.041
	>0.25	Tc = 3.77 × 10−7 D−0.42	0.019
Unit width runoff (m2 s−1)	<0.002	Tc = 0.83 Q0.86	0.246
	0.002–0.02	Tc = 0.91 Q0.84	0.252
	0.02–0.05	Tc = 0.38 Q0.77	0.207
	0.05–0.25	Tc = 0.05 Q0.64	0.110
	>0.25	Tc = 161.70 Q1.51	0.135
Slope gradient (%) Unit width runoff (m2 s−1)	<0.002	Tc = 1.03 × 10−3 S1.01 Q0.51	0.916
	0.002–0.02	Tc = 1.04 × 10−3 S1.00 Q0.48	0.926
	0.02–0.05	Tc = 3.28 × 10−4 S1.04 Q0.40	0.878
	0.05–0.25	Tc = 2.43 × 10−5 S1.12 Q0.23	0.620
	>0.25	Tc = 9.92 × 10−7 S2.45 Q0.44	0.572
Rainfall intensity (mm h−1) Unit width runoff (m2 s−1)	<0.002	Tc = 7.10 × 107 I−1.40 Q1.97	0.421
	0.002–0.02	Tc = 1.75 × 107 I−1.27 Q1.87	0.381
	0.02–0.05	Tc = 2.38 × 106 I−1.17 Q1.74	0.288
	0.05–0.25	Tc = 5.52 × 102 I−0.69 Q1.22	0.125
	>0.25	Tc = 0.431 I0.41 Q1.13	0.138
Slope gradient (%) Rainfall intensity (mm h−1) Unit width runoff (m2 s−1)	<0.002	Tc = 1.326 S0.897 I−0.571 Q0.914	0.814
	0.002–0.02	Tc = 97.54 S0.677 I−0.686 Q1.169	0.662
	0.02–0.05	Tc = 1.61 × 104 S0.664 I−0.939 Q1.534	0.600
	0.05–0.25	Tc = 2.33 × 106 S0.683 I−1.180 Q1.944	0.483
	>0.25	Tc = 363.23 S1.344 I−0.809 Q1.604	0.456

).

Due to the differences in erosion regimes at gentle and steep slope gradients, the hydraulic mechanisms of the transport of sediment particle transport exits under gentle (8.7% and 17.6%) and steep slope gradients (e.g., 26.7%) varied. Thus, different prediction equations were formulated to simulate the T_cs of sediments of each size class in the two slope ranges (

Table 4. Power function of the T_c of different particle sizes with slope gradients, rainfall intensities, and unit width runoff at 8.7% and 17.6%.

Sediments Sizes (mm)	Function	R2
<0.002	Tc = 5.97 × 104 S0.541 I−1.081 Q1.397	0.902
0.002−0.02	Tc = 2.16 × 104 S0.309 I−0.878 Q1.504	0.946
0.02−0.05	Tc = 8.24 × 104 S0.516 I−0.913 Q1.663	0.943
0.05−0.25	Tc = 1.09 × 105 S0.739 I−0.863 Q1.807	0.823
>0.25	Tc = 4.69 × 105 S0.666 I−0.809 Q2.106	0.996

). Under gentle (8.7% and 17.6%) slope gradients and for clay and silt, T_c was correlated with the slope gradient, the rainfall intensity, and the unit width runoff, with R² > 0.902 and p < 0.01, and the correlation was also high for sand with R² > 0.823 and p < 0.01. Given the obvious effect of rainfall intensity on sediment transport under large slope gradients, rainfall intensity, flow velocity, and flow depth were used as independent variables to establish a regression equation to fit the T_c of each size class of particles under the slope gradient of 26.7% (

Table 5. Power function of T_c with the rainfall intensity, flow velocity, and flow depth of different particle sizes at 26.7%.

Sediments Sizes (mm)	Function	R2
<0.002	Tc = 1.059 I−0.273 V−0.440 D0.593	0.984
0.002−0.02	Tc = 1.068 I−0.326 V−0.773 D0.646	0.882
0.02−0.05	Tc = 3.186 I−0.551 V−1.345 D0.876	0.909
0.05−0.25	Tc = 1.143 I−0.960 V−3.204 D1.272	0.955
>0.25	Tc = 2.828 I−8.448 V−34.221 D9.061	0.954

). The equations expressed the T_c of each size of particles well (R² > 0.882, p < 0.01; Figure 6).

To determine the T_c of mixed-size sediment, the T_c of a specific particle size was added up based on the weighted percentage of that size in the total mix:

$$T_c={\sum }_{i=1}^n{T}_{c_i}{P}_i$$

(6)

where $T_{c_i}$ is the T_c of the sediment per particle size (kg m⁻² s⁻¹), $P_i$ is the proportion of each sediment size in the total sediment by mass, and $n$ is the number of different sediment sizes.

Thus, the best fitting power equation among slope gradient, rainfall intensity, unit width runoff, and T_c under gentle slopes (8.7% and 17.6%) is shown as follows:

T_c = 29.048 S^0.490 I^−0.486 Q^1.115 (R² = 0.862, p < 0.01)

(7)

The best fitting power equation between rainfall intensity, flow depth and flow velocity, and T_c under the steep slope (26.7%) is shown as follows:

T_c = 0.01 I^−0.380 V^−0.921 D^0.683 (R² = 0.962, p < 0.01)

(8)

The fitting results of the revised T_c equations were good, with R² > 0.862 and p < 0.01 (Figure 7).

4. Discussion

4.1. Mechanisms of Detachment-/Transport-Limited Regimes for Different Sizes of Sediment Particles

Diffuse erosion is a complex phenomenon that results from soil detachment due to the impact of raindrops and raindrop-affected sheet flow [5,9,11]. Chauhan et al. pointed out that soil erosion is dominated by raindrop splash erosion during its initial stage [34]. From our study, the diffuse erosion rate is typically higher than the splash erosion rate. It initially decreases rapidly during erosion for loess soil, which is consistent with the results of [35], and then gradually approaches the splash detachment rate, because the formation of the non-cohesive crust layer on the soil surface delays the formation of rills and shallow flows [36,37]. Therefore, erosion is both detachment-and transport-limited in most erosion conditions. During erosion, the detachment-limited degree decreases with time, and erosion changes to both detachment- and transport-limited regimes [9]. The development of a non-cohesive crust layer on top of the soil surface also indicates that erosion is transport-limited when raindrop-induced saltation occurs [38]. In such detachment- and transport-limited erosion regimes, most sediment particles are from splash detachment [39,40]. The detachment-limited degree increases, while the transport-limited degree decreases with an increase in the slop gradient [41]. Rainfall intensity exerts a weaker but more complex effect on the transport-/detachment-limited degree of all size classes of particles than the slope gradient. For example, T_cs for all size classes of particles slightly decreased at first and then increased with increasing rainfall intensity; however, it increased considerably with an increase in the slope gradient (Figure 5). Complex interactions occur between raindrop hit and runoff hydraulic characteristics caused by rainfall and the slope on the selective transport of sediment particles [42,43]. The erosion features of the loess soil are different from those of other types of soil [44] but consistent with the results for the same type of soil [10,45]. For example, soil texture exerts a considerable effect on soil loss by affecting soil sealing and crusting [46]. For some soil types, particles are single transport-limited on a gentle slope [47,48]; this phenomenon is related to varying soil erodibility.

From our study, changes in the erosion regimes of detachment-limited particles of each size differed from those of total runoff-eroded sediments. This phenomenon may be the reason behind the bimodal distribution of sediment size [49], which is related to seal development [50]. Under raindrop hit and runoff scour, clay, fine silt, and coarse sand were first detached and transported. However, particles with a size range of 0.02–0.25 mm (coarse silt and fine sand) experience more difficulty in being transported a long way by runoff even if many of these particles were detached and undergoing saltation. This finding may be attributed to particles with a size range of 0.02–0.25 mm having a high organic carbon content and being difficult to detach and transported by runoff. Moreover, the higher the slope, the higher proportion of clay and fine silt detached and transported by runoff scour in the total clay or fine silt of sediments. High slope also enhances the effect of rainfall intensity on the loss features of each size grain.

When erosion power is low on gentle slope gradients, most of the added runoff energy caused by erosion processes or conditions is used to detach and transport <0.02 mm clay and fine silt, and the sand mostly originates from splash detachment [8]. Thus, the mechanisms for different particle transport obviously differ, which is not only related to rainfall intensity and slope but also to soil structure, organic carbon distribution characteristics, and the stress of different particles [51]. The transport modes (i.e., rolling, saltation, and suspension) of different size classes of sediment particles also affect the erosion regimes of these sediment particles [8,35,52]. However, the effects of transport modes or organic carbon content on the erosion regimes of each size class of sediment particles should be investigated further in the future.

4.2. Explanation of the Transport- and Detachment-Limited Erosion Regimes of Each Particle Size on T_c Prediction

Slope gradients, rainfall intensity, and flow discharge characteristics exert different effects on sediment T_c [7,17,53,54,55]. Flow depth affects raindrop detachment and sediment transport through drop impact [43,56]. The median particle size of the sediments exerts a negative or positive effect on T_c [53]. However, the results of the current study show that T_c initially increases and then decreases with an increase in the particle size of sediments (Figure 4). Thus, slope gradient, rainfall intensity, median particle size, and flow hydraulic parameters are incorporated as independent variables for calculating T_cs; this condition is consistent with the study of Kinnell [11]. Furthermore, in accordance with the aforementioned results of the transport mechanisms of different size particles, soil erosion regimes on gentle slope gradients are entirely different from those on steep slope gradients due to the complexity of erosion hydraulic mechanisms [57,58,59]. Even some models, WEPP, have considered distinguishing soil particle size when predicting T_c. The equations do not consider the differentiation of erosion regimes between detachment- and transport-limited particles of different sizes on gentle and steep slopes [60]. Our study verifies that in accordance with the classification of gentle and steep slopes, the accuracy of model prediction can be significantly improved when multiple regression analyses are performed on T_c (Figure 6). The regression results show that the exponent of the slope gradient is higher than that of rainfall intensity, further verifying that T_c is more sensitive to the slope gradient than to rainfall intensity. Thus, the equations are effective and provide unique explanations for improving T_c prediction. Distinguishing gentle and steep slopes for the prediction of all size classes of sediment particles is essential. Overall, the effect of the slope gradient on the erosion regimes of each size class of particles should be considered in future related studies. However, the application of the model results to soil other than loess should be investigated and verified further.

5. Conclusions

The comparison of the erosion regimes of each size of particles and those of the total sediment particles, under rain-induced overland flow, indicates that clay, fine silt, and coarse sand are more easily detached and transported by runoff than coarse silt and fine sand when the erosion is both transport- and detachment-limited for the total sediments. The degree of detachment-limited of each size of particles increased with the slope gradient, while it is changed slightly and complex with rainfall intensity. On the gentle slope, additional runoff energy besides the transport energy was first used to detached clay, fine silt, and coarse sand, while most 0.02–0.25 mm particles detached by splash erosion. On a large slope gradient, a large amount of additional runoff energy was first used to transport residual 0.02–0.25 mm particles and then detach and transport other size particles.

Given the obvious difference in erosion regimes between each size of particles on gentle and steep slope gradients, differences in the hydraulic mechanisms of the transport of different sizes of sediment particles exited under gentle and steep slope gradients. The slope gradient, rainfall intensity, and unit width runoff were used to calculate T_c under the gentle slope gradient (R² > 0.823, p < 0.01), while flow depth, rainfall intensity, and flow velocity were used to calculate the T_c under the steep slope gradient (R² > 0.882, p < 0.01). The regression exponents of each variable further verify their effect on the loss of different sizes of particles. The study will help elucidate the changes in the sediment size distribution and provide a direction for improving the T_c prediction.