Particle size distribution (PSD) of sediment by sheet erosion not only indicates erosion behaviors, but also provides a basis for potential nutrient losses. PSDs are significantly influenced by topographic, rainfall, and associate runoff characteristics, such as rainfall intensity (I), rainfall kinetic energy (KE), slope gradient (S), runoff velocity (v), and stream power (Ω), while their effects have not been fully understood so far. To fill this research gap, in this study, simulated rainfall experiments were conducted to investigate the characteristics of effective and ultimate PSDs of sediments, as well as their responses to related parameters, under five levels of I and S. The results showed that (1) for effective PSDs, there was a significant enrichment of clay-sized and silt-sized fractions (P<2μm and P2–50μm) in sediment (percentage range: 12.11–20.64% and 57.09–65.94%), whereas there was a depletion of sand-sized fractions (P50–250μm and P250–2000μm). The ultimate PSDs of sediment were, however, similar to the soil matrix under experimental conditions. (2) With an increase in I and S, P<2μm and P2–50μm decreased exponentially or logarithmically, and P50–250μm and P>250μm increased correspondingly. The contribution rates (PCs) of the effect of I on clay-, silt-, fine-sand-, and coarse-sand-sized fractions in sediment were 23.44, 35.45, 29.09, and 56.82%, respectively, whereas the PCs of that of S were 56.54, 24.42, 59.89, and 31.47%, respectively, indicating that S plays a more pivotal role in influencing P<2μm and P50–250μm, whereas P2–50μm and P>250μm were more sensitive to I than to S. (3) The aggregation ratio (AR) for the fractions of different sizes indicated that clay-sized particles tend to be transported as aggregates, while silt-sized particles tend to be transported as primary particles. A higher I or steeper S leads to a larger proportion of particles being transported as aggregates. (4) KE, Ω, and unit stream power (U) were the most correlated parameters influencing effective PSDs. Equations were finally established using KE, Ω, and U to predict the effective PSDs of sediment by sheet erosion. This study can further the understanding of the sheet erosion process and provide a scientific basis for the establishment of a sheet erosion model.

  • The effective PSD of sediment by sheet erosion was more sensitive to external conditions than ultimate PSD.

  • The contribution rates of the effect of rainfall intensity and slope gradient on the effective PSDs of sediment were quantified.

  • An equation set was established to predict the effective PSDs of sediment by sheet erosion using rainfall kinetic energy, stream power, and unit stream power.

Graphical Abstract

Graphical Abstract
Graphical Abstract

Soil erosion has been considered as a widespread ecological and environmental problem due to its on-site and off-site adverse impacts at the global scale. It not only causes land degradation, but also threatens local food security and social sustainability (Wang et al. 2013a; Keesstra et al. 2016; Kiani-Harchegani et al. 2021). Rainfall-induced sheet erosion is of common occurrence on a hillslope. It is usually implicated in the movement of nutrients and contaminants that bind tightly to soil particles in fertile topsoil (Kuhn et al. 2012; Rienzi et al. 2015; Koiter et al. 2017). In this regard, particle size distribution (PSD) is an important characteristic index of eroded sediment, which can not only provide a basic understanding of the sheet erosion process (Proffitt & Rose 1991; Wan & EI-Swaify 1998; Asadi et al. 2011; Wang et al. 2014b), but also help in quantifying non-point source pollution (Foster et al. 1985; Walling 1988). Likewise, information about erosive selective behavior, as well as the erosive form of soil particles (eroded as aggregates or primary particles), reflected by the above comparison of the PSDs of eroded sediment and soil matrix, is necessary for the development of improved soil erosion models (Martinez-Mena et al. 1999, 2002).

Several studies have investigated the PSDs of sediment yielded by sheet erosion processes. To sum up, their data can be classified into two categories. One is termed ‘ultimate PSD’ or ‘primary PSD’, in which sediments are measured after being physically or chemically dispersed into their individual primary mineral particles. The other is termed ‘effective PSD’, in which sediments are measured directly without any dispersion (Martinez-Mena et al. 1999, 2002; Shi et al. 2017). These two categories are important. Ultimate PSD can reflect the enrichment/depletion of clay, silt, and sand, which provides a basis for potential nutrient losses and pollution hazards to the environment. Effective PSD more intuitively describes the actual status and behavior of sediment in sheet erosion processes. Indeed, a comparison between the two kinds of PSDs can reflect the erosive form of soil particles in sheet erosion processes, i.e., whether soil particles tend to be eroded as aggregates or as primary particles. Such information is important for a better understanding of sheet erosion mechanisms (Walling & Moorehead 1989; Martinez-Mena et al. 1999, 2002; Hao et al. 2018).

Some previous studies paid attention to the effective PSDs of eroded sediment (Sutherland et al. 1996; Leguédois & Bissonnais 2004; Kiani-Harchegani et al. 2018). Some gained an insight into ultimate PSDs (Warrington et al. 2009; Zhang et al. 2015a). A few studies were available on both ultimate and effective PSDs of eroded sediment, as well as their comparisons, in the sheet erosion process (Martinez-Mena et al. 1999, 2002; Hao et al. 2018; Shi et al. 2017). Martinez-Mena et al. (2002) found that the median effective particle was coarser than the median ultimate particle for almost all rainfall events with different rainfall intensities and soil types, confirming that much of the sediment in the runoff includes a substantial proportion of aggregates. Shi et al. (2017) investigated the particle size selectivity effects during erosion of purple soils in south-western China, and they found that most of the mobilized and exported sediment was transported as primary particles, while substantial proportions of aggregates were present in the deposited sediment. Hao et al. (2018) investigated the effective and ultimate PSDs of sediment eroded from five typical soils in China under natural rainfalls. They found that in terms of effective PSD, clay- and silt-sized particles were enriched in the sediment for all five soils; however, the ultimate PSDs of eroded sediments were almost similar to the soil matrix. These indicated the discrepancy between variations in effective and ultimate PSDs during the erosion process.

Rainfall and subsequent runoff are the drivers for the occurrence and development of sheet erosion. Slope gradient (S) is an important topographic factor influencing erosive behavior. Thus, their effects on the PSDs of sediment by sheet erosion have been investigated by many researchers. Shi et al. (2012) conducted simulated rainfall experiments to study the variations in the effective PSDs of sediment with four steep slope gradients in the Loess Plateau, as well as the transport mechanism of sediment particles of different sizes (suspension–saltation or rolling load). They found that most of the sediment particles (>87%) were transported by suspension–saltation in all simulations, while transport by rolling load significantly increased with S, resulting in a coarser sediment in a steeper S. A strong relationship was found between stream power and rolling load sediment (coarser than 0.152 mm). Similar results were obtained by others (Kiani-Harchegani et al. 2018; Sadeghi et al. 2018). Higher rainfall intensity (I) often leads to a coarser sediment due to the stronger runoff power generated (Martinez-Mena et al. 2002; Cui et al. 2015; Sadeghi et al. 2018). On the other hand, Wang & Shi (2015) performed rainfall simulations for a loess soil to study the effects of rainfall kinetic energy (KE) on the PSDs of sediment. They found that 105 J m−2 h−1 appeared to be a threshold beyond which the disintegration of aggregates was severe and the influence of KE on sediment selectivity may change. Most studies, including the above, qualitatively assessed the effects of external factors on the PSDs of sediment. Recently, Kiani-Harchegani et al. (2019) quantitatively calculated the effects of I and S on percentages of <2, 2–4, 4–8, 8–16, 16–32, 32–63, and >63 μm of sediment using partial η2, which further improved the study accuracy.

Overall, not much information is available on particle size characteristics of sediment by way of sheet erosion data that include both effective and ultimate PSDs of eroded sediment in sheet erosion, as well as their comparisons, especially in regard to loessal soils from the Loess Plateau of China, and this gap needs to be addressed. Likewise, the contribution rate of effect of the controlling factors (e.g., I and S) on fractions of different sizes of sediment needs to be further quantified. Besides, during the erosion process, the degree of erosion of soil particles in sheet flow may be different in different-sized particles. Which hydraulic parameters could be the fittest for representing the water power to erode different-sized soil particles in the related prediction model are not clear. Furthermore, a border area surrounding the test area, which is used to equalize the opportunity for splashing both onto and off the test area, is very important and necessary when studying rainfall-induced sheet erosion by indoor simulation experiment at a plot scale. Certain experimental plots in the previous related studies did not include a border area, which may not result in an accurate observation and collection of sediments by sheet erosion and, thus, not result in an accurate measurement of PSDs of sediment and accurate models of sheet erosion.

Against this background, a detailed laboratory study was conducted on a soil tray with a buffer area to observe the PSDs of sediment yielded by sheet erosion under five levels of I and five levels of S on a clayey loessal soil collected from the Loess Plateau of China. The objectives of this study were to (1) investigate the variations in the effective and ultimate PSDs of sediment with I and S; (2) explore the contribution rate of effects of I and S to different-sized fractions of sediment; (3) use an index, an aggregation ratio (AR), to evaluate whether certain classes in the eroded sediment tend to be eroded as primary particles or as aggregates under different levels of I and S; (4) analyze the responses of the PSDs of sediment to hydraulic and rainfall parameters and find the most relevant parameters to finally establish the prediction model.

Soils

The soils were collected from the top surface layer (0–25 cm) of sloping cultivated land in the experimental site of the Zhongliang Test Station, Tianshui Institute of Agricultural Science in Gansu Province (34°35′N, 105°40′E), which was located in the southwest of the Loess Plateau in China. The average annual temperature and precipitation in this area were 11.5 °C and 500 mm, respectively. After analysis, the test soil consisted of 7.02% sand (diameter: 0.05–2 mm), 68.52% silt (diameter: 0.002–0.05 mm), 24.46% clay (diameter: <0.002 mm), and 9.13 g kg−1 organic matter. Based on the soil texture classification system of the United States Department of Agriculture, the test soil belonged to silt loam (Huang & Zhan 2002). The effective and ultimate PSDs of the test soil are shown in Figure 1.

Figure 1

Effective and ultimate PSDs of the test soil.

Figure 1

Effective and ultimate PSDs of the test soil.

Close modal

Rainfall simulator and soil tray

A side-spraying rainfall simulator operated by the rainfall simulation laboratory of the State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau in Yangling, China, was used in this study. The simulator system comprised power supply, water supply, nozzles, and bracket. Rainfall with different intensities and drop-size distributions can be produced by changing water pressure and nozzle sizes/numbers using a computer. Tap water (electrical conductivity = 0.7 dS m−1) was supplied to produce rainfall. The produced rainfall has a height of 16 m above the soil surface, which ensures that all raindrops reach their terminal velocity when they fall to the ground. The uniformity of the produced rainfall was higher than 85% (Zhang et al. 2018). A disdrometer (Thies Clima, Germany), which measures the diameter, velocity, as well as the number of raindrops/minute passing through the disdrometer measurement area (46.46 cm2), was used to measure the rainfall characteristics in this study (Figure 2).

Figure 2

Disdrometer used in this study.

Figure 2

Disdrometer used in this study.

Close modal

The simulated rainfall experiments were conducted on a soil tray with a dimension of 1.4 m (length) × 1.2 m (width) × 0.25 m (depth). The test area, being the collection area of sheet erosion, was set at the center of the soil tray with a dimension of 0.8 m (length) × 0.6 m (width) × 0.25 m (depth). A trough was designed at the lower end of the test area to collect the runoff and sediment. Around the test area was the border area, which was filled with soil in the same manner as the test area to equalize the opportunity for splash onto and off the plots. The designed border area was similar to that in Bradford & Foster (1996). Detailed information was provided by Zhang et al. (2018, 2019, 2020) and a picture of the soil tray can be seen in Figure 3.

Figure 3

Rainfall simulator and soil tray used in this study.

Figure 3

Rainfall simulator and soil tray used in this study.

Close modal

Experimental procedures

Soils taken from the farmland were air-dried and passed through a sieve with 5-mm openings. Then, they were thoroughly mixed and prepared to be packed into the soil tray. A 5-cm sand layer was placed at the bottom of the soil tray to provide free drainage before soil packing. Then, four 5-cm soil layers were sequentially packed into the soil tray. Before packing the next soil layer, the surface of the lower soil layer was scraped gently to diminish the discontinuity between the two soil layers. A similar packing procedure was used in previous studies (Kiani-Harchegani et al. 2018, 2021; Wang et al. 2019; Quan et al. 2020). The soil layers were packed to a bulk density of approximately 1.2 g cm−3 to simulate those found in the field. After the above procedures, the packed soil erosion tray was adjusted to the designed S and positioned under the rainfall simulator to begin the simulated rainfall experiments. A complete combination of five I (0.7, 1.0, 1.5, 2.0, and 2.5 mm min−1) and five S (7°, 10°, 15°, 20°, and 25°) were designed in this study. Two replications were performed for each I and S combination.

The duration of each rainfall event was 40 min based on the pre-experiment results. During each rainfall event, runoff and sediment samples were collected at 1- and 2-min intervals for the first two samples within 3 min after the onset of runoff and then at 3-min intervals for the remaining samples (Liu et al. 2014). Totally, 14 or 15 samples were collected for each rainfall event, and the last sample was collected in less than 3 min for some rainfall events (which varied depending upon the onset time of runoff). Meanwhile, surface runoff velocities were measured using a KMnO4 solution as a tracer along a 50-cm segment at two positions simultaneously during the rainfall. The measuring positions were 15 cm from the upper boundary of the test area and 15 cm from each side wall of the test area (Figure 3). The mean values of the two measured surface runoff velocities were used to calculate the final runoff velocity, represented as Equation (3).

Once runoff and sediment samples were collected, they were first weighed by an electronic scale with high accuracy and then kept aside and allowed to settle for several hours. The deposited sediment was separated from the water. Then, a part of the sediment was transported to the laboratory immediately to measure their PSDs. A Master sizer 2000 laser diffraction device (Malvern Instruments Ltd, Malvern, UK) was used to measure both effective and ultimate PSDs of sediment (Sadeghi et al. 2018). The effective PSD was first measured without any dispersion treatment; then, the sediment was treated with hydrogen peroxide to remove organic matter, dispersed in sodium hexametaphosphate, and then subjected to ultrasonic dispersion to determine the ultimate PSD (Wang et al. 2014b). The residual sediment was dried in an oven at 105 °C for several hours until constant weight was achieved and then weighed by an electronic scale to calculate soil loss, runoff volume, etc. It should be noted that, the weight of sediments, that used for measuring effective and ultimate PSDs, was also added into total weight of sediments to accurately calculate soil loss, runoff volume, etc. Also, when the runoff and sediment parameters, such as PSDs, were obtained for each sample during a rainfall event, their mean values were calculated as the parameters for this rainfall event to do the final analysis in this study.

Calculation

Hydraulic parameters

The hydraulic parameters of sheet flow such as runoff volume (Q, m3 s−1), runoff coefficient (R), flow velocity (v, m s−1; Horton et al. 1934), flow depth (h, mm), Reynolds number (Re), Froude number (Fr), Darcy–Weisbach resistance coefficient (f), flow shear stress (τ, Pa), stream power (Ω, W m−2), and unit stream power (U, m s−1) were calculated. The equations are as follows:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
where Ri is the total weight of the runoff and sediments during sampling time (kg), mi is the weight of the sediments during sampling time (kg), ρi is the mass density of the runoff (kg m−3), ti is the sampling time (s), W is the runoff width (it is equal to the width of test area of experimental soil tray, 0.6 m), L is the runoff length (it is equal to the length of test area of experimental soil tray, 0.8 m), I is the rainfall intensity (m s−1), α is the correction factor of 0.67 (Horton et al. 1934), vsur is the surface velocity measured by KMnO4 solution (m s−1), R′ is the hydraulic radius (m); v′ is the kinematical viscosity coefficient of the sheet flow (cm2 s−1), g is the acceleration of gravity (cm s−2), J is the hydraulic slope and the sine function of slope gradient, and γ is the unit weight of water (N m−3).

Aggregation ratio

The AR was used to express the sediment characteristics of sheet erosion. The equation for the AR was the same as that in Martinez-Mena et al. (2002) and Xu et al. (2021), which is as follows:
(11)
where Effi is the percentage of particles of the ith size class in the effective sediment and Ulti is the percentage of particles of the ith size class in the ultimate sediment. The AR value of 1 indicates that the size class in sediment is transported as primary particles. Values lower than 1 indicate an increase in the percentage of these sized particles after dispersion, and values higher than 1 indicate the opposite, both of which suggest that they are transported as aggregates rather than as primary particles (Martinez-Mena et al. 2002). The closer the AR value is to 1, the larger will be the sediment transport as primary particles; otherwise, the sediment will tend to be transported as aggregates.

Contribution rate

The contribution rates of the effects of I, S, as well as their interactions on PSDs, were calculated by using Equation (12), which was also used in the studies of Sadeghi et al. (2012) and Zhang et al. (2015b).
(12)
where, for a given factor, SSF is the factorial sum of squares, DF is the degree of freedom, VEr is the variance of error, and SST is the total sum of error. The output of ANOVA gives the values of SSF, DF, VEr, and SST.

Fitting goodness indicators

The determination coefficient (R2) and Nash–Sutcliffe Efficiency Index (NSE) (Nash & Sutcliffe 1970) were used to evaluate the performance of the empirical equations based on the experimental data. R2 and NSE are expressed as follows:
(13)
(14)
where Oi represents the measured values, Pi represents the calculated values, represents the mean of measured values, and represents the mean of calculated values.

Variations in the effective and ultimate PSDs with I and S

Both effective and ultimate particle sizes were grouped as clay-sized fraction (<2 μm), silt-sized fraction (2–50 μm), fine-sand-sized fraction (50–250 μm), and coarse-sand-sized fraction (>250 μm). Figure 4 illustrates the variations in the percentage of the clay-sized fraction (P<2μm) in effective and ultimate sediments under different I and S. P<2μm in the effective sediment ranged from 12.11 to 20.64%, which was higher than that in the soil matrix (9.39%) (Figure 4(a) and 4(b)). With the increase in I, P<2μm tended to decrease, which can be described by an exponential function equation under a different S (Figure 4(a) and Supplementary Material, Table S1). Similarly, it decreased with the increase in S, which can be described by a logarithmic equation under a different I (Figure 4(b) and Supplementary Table S1). P<2μm in the ultimate sediment was slightly lower than or even similar to that in the soil matrix (24.46%) and shows no significant tendency with the increase in I or S (Figure 4(c) and 4(d) and Supplementary Table S2). Comparing Figure 4(a) and 4(b) and Figure 4(c) and 4(d), it is shown that the percentage of the clay fraction (<2 μm) in the ultimate sediment was obviously higher than that in the effective sediment.

Figure 4

Percentage of clay-sized fraction (P<2μm) in effective and ultimate sediments.

Figure 4

Percentage of clay-sized fraction (P<2μm) in effective and ultimate sediments.

Close modal

Similar to that of P<2μm, P2–50μm also decreased with the increase in I and S, with the tendency being described by a logarithmic equation (Figure 5(a) and 5(b) and Supplementary Table S3). The percentage of the silt-sized fraction in the ultimate sediment was similar to that in the soil matrix (68.52%), and it shows no significant tendency with the increase in I or S (Figure 5(c) and 5(d) and Supplementary Table S4). The percentage of the silt-sized fraction (2–50 μm) in the ultimate sediment was obviously higher than that in the effective sediment (Figure 5(a) and 5(b) and Figure 5(c) and 5(d)).

Figure 5

Percentage of silt-sized fraction (P2–50μm) in effective and ultimate sediments.

Figure 5

Percentage of silt-sized fraction (P2–50μm) in effective and ultimate sediments.

Close modal

With the increase in I or S, P50–250μm tended to increase (range: 13.46–25.49%), which can be described by a logarithmic equation (Figure 6(a) and 6(b) and Supplementary Table S5). It was significantly lower than that in the soil matrix (33.63%) (Figure 6(a) and 6(b) and Supplementary Table S5). The percentage of the fine-sand-sized fraction in the ultimate sediment was similar to or a little higher than that in the soil matrix (7.02%) and shows no significant tendency with the increase in I or St (Figure 6(c) and 6(d) and Supplementary Table S6). Comparing Figure 6(a) and 6(b) and Figure 6(c) and 6(d), it is shown that the percentage of the fine-sand-sized fraction (50–250 μm) in the ultimate sediment was obviously lower than that in the effective one.

Figure 6

Percentage of fine-sand-sized fraction (P50–250μm) in effective and ultimate sediments.

Figure 6

Percentage of fine-sand-sized fraction (P50–250μm) in effective and ultimate sediments.

Close modal

The percentage of the coarse-sand-sized fraction (>250 μm) in both the dispersed soil matrix and the ultimate sediment was 0; thus, Figure 7 illustrates only the variations in the percentage of the effective coarse-sand-sized fraction (P>250μm) under different I and S. P>250μm ranged from 0.56 to 5.21% under experimental conditions, which was lower than that in the soil matrix (10.64%) (Figure 7(a) and 7(b)). With the increase in I and S, P>250μm increased linearly, exponentially, or logarithmically, with R2 ranging from 0.92 to 0.99 (Figure 7(a) and 7(b) and Supplementary Table S7).

Figure 7

Percentage of coarse-sand-sized fraction (P>250μm) in the effective sediment.

Figure 7

Percentage of coarse-sand-sized fraction (P>250μm) in the effective sediment.

Close modal

As also obtained above, the sensitivity of the different fractions in the effective sediment to I and S may differ. To study this, the mean values of each-sized fractions and decrease/increase rate under different I and S were calculated, as shown in Figure 8. The decrease rate of P<2μm with I and S ranged from 4.27 to 7.28% and 4.58 to 11.33%, respectively (Figure 8(a) and 8(b)), whereas the decrease rate of P2–50μm with I and S ranged from 0.26 to 1.98% and 0 to 2.65%, respectively (Figure 8(c) and 8(d)). This indicates that the <2 μm fractions were more sensitive to the changes in I and S than 2–50 μm fractions in this study. Likewise, the increase rate of P20–250μm with I and S ranged from 3.15 to 10.30% and 6.47 to 13.96%, respectively (Figure 8(e) and 8(f)). The increase rate of P>250μm with I and S ranged from 20.93 to 41.91% and 12.84 to 47.97%, respectively (Figure 8(g) and 8(h)). The discrepancy showed that the contents of the >250 μm fractions in sediment were more sensitive to the changes in I and S than 50–250 μm fractions.

Figure 8

Variations in mean values of different-sized fraction and decrease/increase rate with rainfall intensity regardless of the effect of slope gradient (a, c, e, g) and with slope gradient regardless of the effect of rainfall intensity (b, d, f, h).

Figure 8

Variations in mean values of different-sized fraction and decrease/increase rate with rainfall intensity regardless of the effect of slope gradient (a, c, e, g) and with slope gradient regardless of the effect of rainfall intensity (b, d, f, h).

Close modal

Contribution rate (PC) of the effects of I and S on the effective PSDs of sediment

Figure 8 also shows, to a certain degree, the effects of the two basic factors (I and S) in varying degrees on different-sized fractions in the effective sediment. For further quantifying the PC of the effects of I and S on the PSDs of sediment, as well as assessing if there were interactive effects between I and S on PSDs, ANOVA was conducted first and then the results were used to calculate the contribution of the two factors using Equation (12). The results are shown in Table 1. It is revealed that both I and S have a significant influence on the percentage of the different-sized fractions in sediment (sig. <0.001), while their performances are different. For P<2μm and P2–50, S plays a more important role than I, with the PC being 23.44, 56.54, 29.09, and 59.89%, respectively. However, for P50–250μm and P>250μm, I plays a more pivotal role than S, with the PC being 35.45, 24.42, 56.82, and 31.47%, respectively. The interaction effects between I and S do not have a significant effect on the PSDs of sediment, except for a relatively little effect on the percentage of the coarse-sand-sized fraction (sig. = 0.023, PC = 3.71%).

Table 1

Significance and contribution rate of effects of rainfall intensity and slope gradient on the percentage of different-sized fractions in sediment by sheet erosion based on ANOVA

VariableSourceDFType III sum of squaresMean squareFSig.PC
P<2μm I 86.082 21.520 13.611 0.000 23.44% 
S 198.726 49.681 31.421 0.000 56.54% 
I × S 16 15.944 0.996 0.630 0.830 
Error 25 39.529 1.581    
Total 49 340.280     
P2–50μm I 69.143 17.286 10.483 0.000 35.45% 
S 49.684 12.421 7.533 0.000 24.42% 
I × S 16 16.380 1.024 .621 0.838 
Error 25 41.224 1.649    
Total 49 176.430     
P50–250μm I 128.674 32.168 27.625 0.000 29.09% 
S 259.993 64.998 55.818 0.000 59.89% 
I × S 16 8.548 .534 .459 0.945 
Error 25 29.112 1.164    
Total 49 426.326     
P>250μm I 38.833 9.708 88.032 0.000 56.82% 
S 21.704 5.426 49.201 0.000 31.47% 
I × S 16 4.273 .267 2.422 0.023 3.71% 
Error 25 2.757 .110    
Total 49 67.567     
VariableSourceDFType III sum of squaresMean squareFSig.PC
P<2μm I 86.082 21.520 13.611 0.000 23.44% 
S 198.726 49.681 31.421 0.000 56.54% 
I × S 16 15.944 0.996 0.630 0.830 
Error 25 39.529 1.581    
Total 49 340.280     
P2–50μm I 69.143 17.286 10.483 0.000 35.45% 
S 49.684 12.421 7.533 0.000 24.42% 
I × S 16 16.380 1.024 .621 0.838 
Error 25 41.224 1.649    
Total 49 176.430     
P50–250μm I 128.674 32.168 27.625 0.000 29.09% 
S 259.993 64.998 55.818 0.000 59.89% 
I × S 16 8.548 .534 .459 0.945 
Error 25 29.112 1.164    
Total 49 426.326     
P>250μm I 38.833 9.708 88.032 0.000 56.82% 
S 21.704 5.426 49.201 0.000 31.47% 
I × S 16 4.273 .267 2.422 0.023 3.71% 
Error 25 2.757 .110    
Total 49 67.567     

Note: P<2μm, P2–50μm, P50–250μm, and P>250μm are the percentages of the clay-, silt-, fine-sand, and coarse-sand-sized fractions in effective sediment yield by sheet erosion, respectively, I is the rainfall intensity (mm min−1), S is the slope gradient (°), DF is the degree of freedom, and PC is the percentage contribution of each factor (%), calculated by using Equation (12).

ARs for different-sized fractions in sediment

Figure 9 illustrates the ARs for the different-sized fractions under experimental conditions. All AR values for the clay-sized fractions were less than 1, with a range of 0.50 to 0.93 (Figure 9(a) and 9(b)). As I and S increased, the AR tended to decrease and deviate from value 1, which indicated that the clay-sized fractions were likely to be transported as aggregates with the increase in I and S. The ARs for the silt-sized fraction (2–50 μm) ranged from 0.97 to 0.85 and showed a slight decrease with the increase in I and S, indicating that most of the silt-sized fractions were transported as primary particles (Figure 9(c) and 9(d)). The fine-sand-sized fraction (50–250 μm) and coarse-sand-sized fraction (>250 μm) were added together to calculate the AR for the total sand-sized fraction (>50 μm). They were significantly larger than 1 (range: 1.39–3.52) and increased with the increase in I and S (Figure 9(e) and 9(f)), which indicates that the steeper the S or the higher the I is, the more sand-sized fractions are to be transported as aggregates.

Figure 9

ARs under different rainfall intensities and slope gradients.

Figure 9

ARs under different rainfall intensities and slope gradients.

Close modal

Responses of effective PSDs in sediment to hydraulic and rainfall parameters

Hydraulic and rainfall parameters are frequently used to represent erosive force/power to sheet erosion. Finding the closest parameter relating to sediment characteristics can effectively reveal the mechanism of erosion. As effective PSDs more intuitively describe the actual status and behavior of sediment during erosion processes, relationships between effective PSDs and corresponding flow hydraulic and rainfall parameters (including R, h, Re, Fr, f, τ, Ω, U, D50, KE, and Vt) were investigated. The Pearson correlation analysis results are shown in Figure 10. For flow hydraulic parameters, Ω is the closet parameter related to the percentage of silt-sized and coarse sand-sized fractions in sediment (P2–50μm, P>250μm) at P < 0.001 level. U is the closet parameter related to the other two-sized fractions (P<2μm and P50–250μm) at the P < 0.001 level. For rainfall parameters, KE and Vt are the closet parameters related to the percentage of four-sized fractions at the P < 0.001 level.

Figure 10

Pearson correlation coefficients between the percentages of different-sized fractions in the effective sediment (P<2μm, P2–50μm, P50–250μm, and P>250μm) and rainfall and hydraulic parameters as the variables. R indicates the runoff coefficient; h indicates the sheet flow depth; Re indicates the Reynolds number; Fr indicates the Froude number; f indicates the Darcy–Weisbach resistance coefficient; v indicates the sheet flow velocity; τ indicates the sheet flow shear stress; Ω indicates the stream power; U indicates the unit stream power; D50 indicates the median diameter of raindrops; Vt indicates the mean terminal velocity of raindrops; KE indicates the rainfall kinetic energy. *Significant level of P < 0.001.

Figure 10

Pearson correlation coefficients between the percentages of different-sized fractions in the effective sediment (P<2μm, P2–50μm, P50–250μm, and P>250μm) and rainfall and hydraulic parameters as the variables. R indicates the runoff coefficient; h indicates the sheet flow depth; Re indicates the Reynolds number; Fr indicates the Froude number; f indicates the Darcy–Weisbach resistance coefficient; v indicates the sheet flow velocity; τ indicates the sheet flow shear stress; Ω indicates the stream power; U indicates the unit stream power; D50 indicates the median diameter of raindrops; Vt indicates the mean terminal velocity of raindrops; KE indicates the rainfall kinetic energy. *Significant level of P < 0.001.

Close modal

Comparisons between effective PSDs of sediment and soil matrix

Effective PSD is a parameter that reflects the actual status and behavior of sediment in erosion processes (Martinez-Mena et al. 1999, 2002; Hao et al. 2018). In this study, when compared with the soil matrix, the clay- and silt-sized fractions (<2 and 2–50 μm) are enriched, whereas sand-sized fractions (50–250 and >250 μm) are depleted in sediment by rainfall-induced sheet erosion. It is implied that particle size selectivity occurs (smaller particles are prone to be detached and transported) during the erosion process. There are several important reasons that account for this phenomenon. Firstly, an insufficient ability of sheet flow to transport large particles and selective deposition of large particles are the most important reasons (Parsons et al. 1991; Proffitt & Rose 1991; Larionov et al. 2007; Wang et al. 2014b). Similar results were reported by previous studies, such as by Wan & EI-Swaify (1998), Jiang et al. (2014), and Koiter et al. (2017). Secondly, as particles are transported by sheet flow to the outlet, they are constantly colliding with the soil surface, which causes large particles (aggregates) to be denuded and rounded gradually, and there is a decrease in their sizes (Larionov et al. 2007; Wang et al. 2014a). Thirdly, detached particles could be destroyed by the continuous hitting of raindrops when they are transported by sheet flow to the outlet. Fourthly, the rainfall energy may be insufficient to overcome stronger bonding forces that hold particles at the soil surface and can detach only small particles from the surface, resulting in detached sediment by raindrops (sediment source for sheet flow transport) being smaller than that of the soil matrix, which was reported by Zhang et al. (2020). However, conflicting results were reported by Young & Onstad (1978), who found that sediment by sheet erosion was coarser than the soil matrix. This contradiction might be due to the difference in test soil texture and experimental conditions (experiment setups, rainfall properties, etc.). In addition, some finer particles might be carried downward by infiltration flows, resulting in sediment to be collected in the outlet that was coarser than the soil matrix, which was mentioned in the studies of Young & Onstad (1978) and Posen & Savat (1981). More studies about particle size selectivity during erosion under different conditions of rainfall property, soil texture, and near surface hydrological condition should be conducted in the future.

Variations in effective PSDs of sediment with I and S

In the rainfall-induced sheet erosion process, I is a fundamental control of sheet runoff and erosion (Parsons & Stone 2006; Gholami et al. 2021). A higher I generally corresponds to higher rainfall kinetic energy and stronger surface flow power (Komatsu et al. 2018). Positively, higher rainfall kinetic energy, which is reported to be used to overcome the bonding forces that hold particles on the soil surface and detach soil particles (Wuddivira et al. 2009), could detach larger and more soil particles; then, stronger sheet flow power transports larger and more soil particles to the outlets. While negatively, higher rainfall kinetic energy may also cause severe aggregate breakdown (Wang & Shi 2015); and stronger sheet flow power can also peel and disintegrate aggregates down during sediment transportation to the outlets (Wang et al. 2012, 2013b). Actually, whether the effect of I on sediment size is positive or negative, depends on the above-mentioned relative magnitude. In this study, the positive effect of I on sediment size plays a more important role than its negative effect, thus resulting in a higher percentage of sand-sized fractions in sediment in this study. Similar results were found in many other studies (Meyer et al. 1980; Hao et al. 2018; Xue et al. 2017; Sadeghi et al. 2018).

S is a basic topographic factor that influences the sheet erosion process. Similar to the tendency that appeared in I, the percentage of the sand-sized fraction increased and that of clay- and silt-size fractions decreased in sediment as S increased. This may be explained by the following: (1) a steeper S caused a stronger shear force and higher velocity of sheet flow, which, in turn, caused a higher stream power that benefited the transport of large aggregates; (2) likewise, large-sized particles tend to be easily transported on steeper slopes due to the intense gravity and force of inertia in the direction along the slope (Kiani-Harchegani et al. 2018); and (3) rolling transport modes of large-sized particles functioned more effectively with the increase in S (Asadi et al. 2011; Wang & Shi 2015). All of these caused sediment size to be larger and the sheet erosion process less selective when S became steeper. Similar results were obtained in other studies (Wang & Shi 2015; Kiani-Harchegani et al. 2018). However, Fullen et al. (1996) found that the clay and silt content of sediment increased with S. Their explanation for this was increased runoff velocities, and, therefore, erosivity on steeper S would be increasingly competent to detach clays from soil aggregates. The difference between the results obtained by Fullen et al. (1996) and our study were mostly attributed to the different soil textures used in the two studies. The test soil used by us in this study contained more aggregates and was more stable than that used by Fullen et al. (1996); thus, less aggregates were peeled and even broke down to release small particles.

Variations in ultimate PSDs under different I and S

Ultimate PSDs represent discrete mineral particles (Shi et al. 2018). An interesting phenomenon is that ultimate PSDs in sediment are similar to the ultimate PSDs of the soil matrix. In this study, no such obvious characteristic of ultimate PSDs with the increase in I and S was noticed. This similarity characteristic is quite different from the characteristic of the effective PSD. The possible reason is that much of the soil erodes in aggregate form and larger soil aggregates often get enrich in silt or sand particles, which, in turn, increase the ultimate sediment size. Similar results were reported by Young & Onstad (1978), who found that the ultimate sediment size was similar to or coarser than that of the soil matrix. Hao et al. (2018) studied the ultimate PSDs of sediment eroded from five typical soils in China under natural rainfall, and they found that the ultimate PSDs of eroded sediments were similar to those of the soil matrix for four soils, and there was only a slight enrichment of silt and clay in sediment for one soil. Martinez-Mena et al. (1999) found that the ultimate sediment size was finer than that of the matrix soil, with a depletion of clay and sand in exchange for an enrichment in silt. Warrington et al. (2009) conducted simulated rainfall experiments on three types of soils (loam, sandy clay, and clay soils), and found that most of the eroded sediments had larger clay contents than the soil matrix used. These different results highlight the high dependence of sediment size on soil texture.

Comparison of effective PSDs and ultimate PSDs

The results showed that the percentage of the clay- and silt-sized fractions in the effective sediment was obviously lower than that in ultimate sediment, and correspondingly, the percentage of the sand-sized fractions in the effective sediment was obviously higher than that in ultimate sediment under different I and S, which indicates that sediment by sheet erosion is a combination of primary particles and aggregates under experimental conditions. Similar results were found in other studies (Young & Onstad 1978; Mitchell et al. 1983; Martinez-Mena et al. 1999, 2002; Wang & Shi 2015; Shi et al. 2017). The AR values for the clay-, silt-, and sand-sized fractions indicated that clay-sized particles tended to be transported as aggregates, while silt-sized particles tended to be transported as primary particles in this study, which agree with the findings in other studies such as by De Ploey (1981), Loch & Donnollan (1983), Martinez-Mena et al. (2002), and Wang & Shi (2015). The results further showed that the effective PSDs of eroded sediment were more sensitive than the ultimate PSDs, thus inducing curiosity to study the real status of sediment in sheet erosion.

Prediction of effective PSDs of sediment by sheet erosion

Effective PSDs more intuitively describe the actual status and behavior of sediment during sheet erosion processes. There is significant value in developing a model to predict it. In this study, the effective PSDs are influenced significantly by the hydraulic characteristics of sheet flow and rainfall characteristics (Figure 10). I and S are important variables that determine the hydraulic characteristics of sheet flow and rainfall characteristics, and they are the most easily obtained hydraulic parameters. It is both feasible and practical to introduce slope gradient and flow discharge when simulating effective PSDs. Multivariate nonlinear regression analysis for the effective PSDs showed that the effective PSDs of sediment by sheet erosion could be modeled by the quaternary power functions of I and S, as shown by Equations (15)–(17).
(15)
(16)
(17)
(18)

The predicted percentage of the different-sized fractions in sediment using Equations (15)–(18) satisfactorily matched those measured with high R2 and NSE. Figure 11 displays the agreement between measured and predicted values by using Equations (15)–(18), in which data points were distributed near the 1:1 line. All these indicated that Equations (15)–(18) were reliable equations that could well describe the effective PSDs of sediment by sheet erosion using I and S.

Figure 11

Measured versus predicted percentage of clay-, silt-, fine-sand-, and coarse-sand-sized fractions in the effective sediment using Equations (15)–(18), respectively.

Figure 11

Measured versus predicted percentage of clay-, silt-, fine-sand-, and coarse-sand-sized fractions in the effective sediment using Equations (15)–(18), respectively.

Close modal
Stream power (Ω), which proved to be the best hydraulic parameter, and KE, which proved to be the best rainfall parameter, were selected as two factors to simulate P2–50μm and P>250μm (Figure 10). Meanwhile, U and KE were selected to simulate P<2μm and P>250μm (Figure 10). The functions obtained were as follows:
(19)
(20)
(21)
(22)

The predicted percentage of the different-sized fractions in sediment using Equations (19)–(22) satisfactorily matched the measured (R2 = 0.821–0.945, NSE = 0.821–0.953). It is indicated that Equations (19)–(22) can be used to calculate the effective PSDs of sediment by sheet erosion for various hydraulic and rainfall conditions in similar climate and soil texture regions.

To some certain extent, Equations (15)–(22) can deepen the understanding of the mechanism in the sheet erosion process and demonstrates some scientific significance for the establishment of sheet erosion models.

Implications for providing the basis of rainfall event–based nutrient loss estimation

Among the types of water erosion on hillslopes, sheet erosion is often considered the most harmful for carrying off fertile topsoil with soil nutrients, which results in land degradation, thereby affecting soil productivity and crop yield (Gilka et al. 2012). Modeling nutrient loss driven by sheet erosion is an important and effective tool for the design of efficient soil and water conservation practices that mitigate land degradation. As soil nutrients are lost in two forms during erosion, sediment-bound nutrient loss and soluble nutrient loss with runoff, runoff and soil loss models are often used as an integral part of nutrient loss models (Shi et al. 2018). The content and form of soil nutrients bound in sediment particles is heterogeneous, due to the difference in sediment size classes and aggregation. Thus, models that contain sediment size characteristics (like Equations (15)–(22) in this study) rather than models that contain only soil loss rate may be more accurate and may form an integral part of sediment-bound nutrient loss models. However, we have to admit that out research findings were not deep enough in this regard, and, therefore, more research should be done in the future.

The effective and ultimate PSDs of sediments by sheet erosion, as well as their responses to related parameters under five levels of I and S on a silt loam loessal soil from the Loess Plateau of China, were investigated based on simulated rainfall experiments. In terms of effective PSDs, P<2μm and P2–50μm in sediment were higher than those in the soil matrix, and these fractions decreased exponentially or logarithmically with increasing I and S; inversely, P50–250μm and P>250μm were depleted in sediments. Compared with I, S played a more important role in influencing P<2μm and P50–250μm, whereas P2–50μm and P>250μm were more sensitive to I than to S. The ultimate PSDs of sediment were similar to those of the soil matrix under experimental conditions, which indicates that the effective PSD of eroded sediment is more sensitive than the ultimate PSD, inducing curiosity to study the real status of sediment in sheet erosion. The aggregation ratio for the different-sized fractions indicated that clay-sized particles tended to be transported as aggregates, while silt-sized particles tended to be transported as primary particles. A higher I or steeper S leads to a larger proportion of particles being transported as aggregates. Two models that could effectively predict the effective PSDs were established based on the rainfall intensity, slope gradient, stream power, unit stream power, and rainfall kinetic energy. The results obtained can not only further the understanding of sediment characteristics in sheet erosion, but also provide a scientific basis for soil erosion control and sustainable agricultural development in the study area.

The paper was supported by the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, the China Institute of Water Resources and Hydropower Research (Grant no. IWHR-SKL-KF202005), the National Natural Science Foundation of China funded project (Grant nos 42107362 and 41830758), the Open Research Fund of State Key Laboratory of Soil Erosion and dryland Farming on the Loess Plateau (Grant no. A314021402-202213), and the Chinese Universities Scientific Fund (Grant no. 2452020248).

The authors declare that they have no financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data cannot be made publicly available; readers should contact the corresponding author for details.

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Supplementary data