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Spatial variation of microtopography and its effect on temporal evolution of soil erosion during different erosive stages
Catena 190 (2020) 104515
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Spatial variation of microtopography and its effect on temporal evolution of soil erosion during different erosive stages
T
⁎
Jian Luoa, Zicheng Zhenga, , Tingxuan Lia, Shuqin Heb a b
College of Resources Science, Sichuan Agricultural University, 211 Huimin Road, Chengdu, Sichuan 611130, China College of Forestry, Sichuan Agricultural University, 211 Huimin Road, Chengdu, Sichuan 611130, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Microtopography Fractal model Temporal sequences analysis Soil erosion Purple soil
Microtopography significantly influences soil erosion at hillslope scale. Currently, the influence of microtopography on temporal evolution of soil erosion is still unclear. A set of simulated rainfall experiments on three 2 m long, 1 m wide soil boxes under a rainfall intensity of 1.5 mm min−1 on a 20° slope were conducted in the Chinese purple soil region to quantify the spatial variation of microtopography and its effect on temporal variations of runoff and sediment yield during water erosion processes. Three local tillage practices: conventional tillage (CT), artificial digging (AD), and ridge tillage (RT) with different initial microrelief (smooth, rough, and very rough) were designed. The spatial heterogeneity of microtopography was characterized by directional derivatives, semivariogram, and fractal information dimension in terms of morphology and quantity. And we identified the temporal variability characteristics of runoff and sediment yield based on wavelet and rescaled range (R/S) analyses. The results indicated that the spatial variability of different tillage practices had strong or medium autocorrelations during different water erosive stages. The spatial autocorrelation scales of CT, AD, and RT were 6.10, 5.32, and 4.01 m, respectively. The fractal information dimensions of tillage practices at various erosive stages were RT > AD > CT. There was a certain range of Di critical values, which reflected the positive or negative effect on soil erosion. The Hurst indexes of the runoff time series were in the section between 0.632 and 0.718, and that of the sediment yield time series ranged between 0.741 and 0.846. The time series of runoff and sediment yield had long-range persistence and varied periodically every 12–16 min during water erosion processes. Overall, the dominant period and the persistence of runoff tended to decrease and increase respectively with the increase in microrelief, while the temporal variation in sediment yield was opposite to that of runoff. Characterization of the temporal variability characteristics of runoff and sediment yield response to microrelief changes would contribute to a better understanding of the hydro-geomorphological processes at hillslope scale.
1. Introduction Sloping farmland in Purple Hilly Area of Sichuan Basin is not only the major grain-producing area, but also the main sediment source in the Upper Yangtze River Basin (Long et al., 2006; Zheng et al., 2007). Soil erosion in sloping farmland greatly restricts ecological environment and food security in the area (Stolte et al., 2009). Intensive cultivation and unreasonable tillage practices have accelerated soil erosion in sloping farmland (Wang et al., 2017; Luo et al., 2018a). Tillage operations disturb the original form of surface soil, and make the soil surface appear microtopography with high and low fluctuations (Moreno et al., 2008). The study of water erosion process mechanisms at microtopographic scale is an important issue in the field of soil erosion, and it is also a crucial scientific problem urgently needed to be ⁎
solved in the quantitative study of soil erosion. Microtopography describes the micro-variation in surface elevation caused by tillage practices and soil erosion, which is identified as a key factor in water erosion evolution (Govers et al., 2000). Previous studies have shown that microtopography can significantly affect runoff, soil loss and deposition (Cogo et al., 1984; Darboux et al., 2002; Zhao et al., 2014). Dynamic erosion pattern continuously creates and alters microrelief. Meanwhile, microrelief will in turn change the erosion patterns. Hence, the spatial variation of microtopography is a descriptor that reflects how the soil surface behaves against the soil erosion. Currently, opposing results for the effect of microtopography on soil erosion were reported in many studies. Some researchers indicated that the increasing microrelief is expected to impose greater resistance to flow velocities, and hence reduce the soil and water loss (Cogo et al.,
Corresponding author at: College of Resources Science, Sichuan Agricultural University, 211 Huimin Road, Chengdu, Sichuan 611130, China. E-mail address: [email protected] (Z. Zheng).
https://doi.org/10.1016/j.catena.2020.104515 Received 24 June 2019; Received in revised form 1 February 2020; Accepted 9 February 2020 0341-8162/ © 2020 Elsevier B.V. All rights reserved.
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1984; Römkens et al., 2001). However, other researchers reported that the increasing microrelief may even increase the soil erosion (Gómez and Nearing, 2005; Ding and Huang, 2017). Insights into the interaction between microtopography and soil erosion require an understanding of spatial variation characteristics of microtopography. At present, soil roughness (SR), semivariable function and multifractal analysis are widely used to analyze the spatial variation characteristics of surface microtopography during water erosion processes (Shen et al., 2009; Zhang et al. 2015; Luo et al., 2018b). Many researchers have systematically studied the characterization of runoff and sediment from catchment and hillslope scales. The results showed that the generation and evolution of runoff and sediment under the condition of continuous rainfall was a complex process affected by many internal and external factors, and the runoff and sediment processes exhibited complex nonlinear and multi-time scale variation characteristics (Tian et al., 2019; Luo et al., 2020). This situation is more obvious at hillslope scale due to the complex material composition, poor uniformity and the interference of artificial farming management on slope surface. Traditional Euclidean geometry is difficult to describe the complicated and high-dimensional nonlinear process of runoff and sediment accurately. Wavelet analysis is a kind of multiresolution analysis method, which can reveal the localized characteristics of time series from temporal and frequency domains at the same time, so it is suitable for the study of hydrological time series with multi-time scale changes and non-stationary characteristics (Labat, 2005). The correlation between wavelet analysis and fractal theory is very strong. Wavelet transform has scaling invariance, which is consistent with the characteristics of fractal structure. Wavelet analysis can distinguish the dominant periods hidden in the time series, which is of guiding significance to predict the trend of runoff and sediment yield in the future. Furthermore, rescaled range (R/S) analysis can detect the long-term correlation or “memory” of a time series. Up until now, these methods have applied to many fields in the earth sciences (Peng et al., 2012; Shi et al., 2015; Karmakar et al., 2019; Luo et al., 2019). The objectives of the study are as follows: 1) to investigate the spatial variation characteristics of microtopography during different water erosive stages, 2) to analyze the temporal variation characteristics of runoff and sediment yield at hillslope scale, and 3) to clarify the effect of microtopography on temporal evolution of soil erosion during water erosion processes.
Table 2 Rainfall durations for three tillage practices at different water erosive stages. Tillage practices
Rainfall Duration (min)
CT AD RT
SpE
ShE
RE
4.0 4.8 5.8
15.1 12.4 19.7
21.7 26.9 27.5
Note. CT: conventional tillage; AD: artificial digging; RT: ridge tillage; SpE: splash erosion; ShE: sheet erosion; RE: rill erosion.
different initial microrelief (smooth, rough, and very rough) were designed based on the local custom. CT creates a smooth slope using rake wear. AD is a manual tillage practice which uses a hoe to cultivate the soil depression at a depth of 5 cm and a width of 15 cm. The distance between depressions is 20 cm. RT is traditional tillage practice which uses a plow to create ridge-furrow systems, with a ridge height of 15 cm, a ridge width of 50 cm and a ridge distance of 40 cm. The slope gradient and rainfall intensity were designed based on the study area was characterized by steep slopes and experienced high rainfall intensities. The slope gradient of the soil box was 20° and a representative erosive rainfall intensity of 1.5 mm min−1 was employed in this study. The rainfall simulator was similar to that described by He et al. (2018). The water erosive stages were: (a) splash erosion (SpE), the phase prior to the initiation of runoff; (b) sheet erosion (ShE), the phase when the drop pits started to appear; and (c) rill erosion (RE), the phase when the fish-scale shaped pits and overfall formed the rills (Zhang et al., 2015). Information regarding the rainfall duration for each event is presented in Table 2. All experiments were repeated twice. 2.3. Experimental measurements 2.3.1. Construction of soil surface microtopography The microtopography was measured with a laser scanner (Maptek isite-8820). Accordingly, 486,453 surface elevation data points for each slope were collected and each point represented an area of 6 mm × 6 mm. After a series of pre-processing procedures (spatial alignment, cross validation and Kriging interpolation), the original microtopography digital elevation model (M−DEM) was constructed by ArcGIS 3D analyst.
2. Materials and methods 2.3.2. Runoff and sediment yield Soil splash erosion was used to be determined by the hanging splash erosion boards and oven-dried at 105 °C to a constant weight (Zheng et al., 2014). During the sheet and rill erosive stages, each flow generation duration was recorded, runoff samples were collected continuously at the outlet of the soil box at intervals of 3 min. The runoff samples were measured using a measuring cylinder and then settled for 12 h so that the suspended sediments could settle out. After decanting the clear supernatant, the sediment samples were dried in an oven at 105 °C and weighed to determine the sediment yield (He et al., 2014).
2.1. Study site and soil sampling The study area was located in a sloping farmland around Ziyang, China (104° 34ʹ E, 30° 05ʹ N). The purple soil used in this study was Entisol (USDA Soil Taxonomy) with 22 % clay, 29 % silt, and 49 % sand (Soil Survey Staff, 2010) (Table 1). Air-dried soil was crushed before being passed through a 10 mm sieve. Each soil box with an area of 2 m2 was filled with 10 cm layers of soil to a depth of 50 cm. The soil moisture content was 5 % before rainfall events. The details of the soil preparation have been described by Luo et al. (2017).
2.4. Calculating horizontal directional derivatives based on DEM 2.2. Research design First derivative: The slope of DEM grid surface along the horizontal direction is calculated, which is equal to the product of the slope vector and the unit vector in the specified direction. In a particular grid, along
After packing the box with soil, three tillage practices, i.e. conventional tillage (CT), artificial digging (AD), and ridge tillage (RT) with Table 1 Physical-chemical properties of experimental soil. Soil type
pH
Bulk density (g cm−3)
CEC (cmol kg−1)
SOC (g kg−1)
CaCO3 (%)
Sand (%)
Silt (%)
Clay (%)
Texture
Purple soil
7.5
1.2
21
13
12
49
29
22
Clay loam
2
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Fig. 1. Contour maps of first directional derivatives of three tillage practices in horizontal direction at different water erosive stages. Note. BR: before rainfall; SpE: splash erosion; ShE: sheet erosion; RE: rill erosion; CT: conventional tillage; AD: artificial digging; RT: ridge tillage.
directional derivative of the first derivative. In a particular grid, the larger the second derivative value in the horizontal direction, which indicates that the grid is at the turning point of the surface morphology. The second derivative can be denoted as:
the positive direction of X axis, the rise of slope at the grid is expressed as positive value, and the decline of slope is expressed as negative value, which can be used to determine the location of rill channel and the fluctuation degree of microrelief. The first derivative can be denoted as:
cos(α ) ⎤ ⎡ dy df ⎤ ⎡ cos(α ) ⎤ df df df , · ·cos(α ) + ·sin(α ) = = = g·⎡ ⎥ ⎥ ⎢ ⎢ ⎢ ⎥ sin( ) sin( ) α α dy ds dx dy dx ⎦⎣ ⎦ ⎦ ⎣ ⎣
df
df
df d ⎡ ·cos(α ) + dy ·sin(α ) ⎤ d ⎡ ds ⎤ d 2f ⎣ ⎦ = ⎣ dx ⎦ = 2 ds ds ds d 2f d 2f d 2f ·cos2 (α ) + 2 ·cos(α )·sin(α ) + ·sin2 (α ) = 2 dy 2 dxdy dx
(1)
Second derivative: The change rate of the slope along the horizontal direction on the surface of DEM grid is calculated, which is the
(2)
where g is the gradient vector of the grid point; α is the angle value 3
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Fig. 2. Rill distributions obtained for three tillage practices during ShE and RE stages. Note. ShE: sheet erosion; RE: rill erosion; CT: conventional tillage; AD: artificial digging; RT: ridge tillage. nε
of the specified direction. In this paper, the horizontal direction, i.e. the positive direction of the X-axis, is selected, thus α = 0; x, y are the distances in the horizontal and vertical directions, respectively.
μi (q, ε ) =
∑ μi (ε )q i=1
(3)
where q is the weight factor and the q values ranged from − 3 to + 3 with increments of 0.5; ε is size of the box, in this study, the box size was 10, 30, 60, 90… 270, and 300 mm, respectively; μi(ε) is elevation distribution probability of i-th subarea; n(ε) is the number of boxes in which μi(ε) greater than 0. The fractal information dimension can be denoted as:
2.5. Fractal analysis of microtopography The box counting method is used to determine the fractal information dimension of microtopography (Ferreiro and Vázquez, 2010; Torre et al., 2018). The partition function μi(q, ε) can be obtained from the weighted summation of q-th power of elevation distribution probability. 4
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Fig. 3. Contour maps of second directional derivatives of three tillage practices in horizontal direction at different water erosive stages. Note. BR: before rainfall; SpE: splash erosion; ShE: sheet erosion; RE: rill erosion; CT: conventional tillage; AD: artificial digging; RT: ridge tillage. n (ε )
1 D (q) = lim q − 1 ε→0
2.6. Semivariogram analysis
ln ∑ μi (q, ε ) i=1
ln(ε )
,q≠1
The distribution of relative elevation of soil surface is not only random, but also correlated in a certain range of space. Therefore, semivariogram model (SM) is used to analyze the spatial variation structure characteristics of microtopography. SM is defined as:
(4)
n (ε )
∑ μi (ε ) ln μi (ε ) Di = lim ε→0
i=1
ln(ε )
,q=1
(5)
γ (h) =
where D(q) is the general fractal dimension, Di is the fractal information dimension.
1 2N (h)
N (h)
∑ i=1
[Z (x i ) − Z (x i + h)]2
(6)
Where γ(h) is the semivariance for the lag distance between 5
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Fig. 4. Relationships between D(q) and q of three tillage practices at different water erosive stages. Note. A: conventional tillage (CT); B: artificial digging (AD); C: ridge tillage (RT); BR: before rainfall; SpE: splash erosion; ShE: sheet erosion; RE: rill erosion.
The mean rescaled range (R/S)n can be estimated by:
sampling elevation data points (h); Z(xi) is the relative elevation at the location xi; and N(h) is the number of data pairs for the lag distance h. The semivariogram model mainly has the following parameters: (a) sill, total spatial variability of microtopography; (b) nugget, spatial variability caused by random factors; (c) base effect, proportion of spatial variability caused by structural factors to total spatial variability of microtopography. The base effects of greater than 75 %, 25–75 %, and < 25 % indicate strong, medium, and weak spatial autocorrelations of microtopography, respectively; (d) codomain, spatial autocorrelation scale of microtopography (Zhang et al., 2015).
(R/ S )n =
Wavelet analysis is an appropriate method to solve the multi-time scale nonlinear response of a time series. Wavelet analysis is closely related to wavelet type. Morlet wavelet can eliminate the false oscillation generated by using the real wavelet transform coefficients as the criterion. Morlet wavelet is defined as: 2
/2
1 a
∞
∫−∞ f (t ) eic ( t−ab ) e at ( t−ab ) dt
3. Results
2
(8) 3.1. Spatial variation of microtopography during different water erosive stages 3.1.1. Spatial distribution of directional derivatives based on DEM According to Figs. 1 and 2, the first derivative contour map can reflect the slope distribution in the horizontal direction. The denser the contour lines are, the larger the topographic fluctuation is. For the CT slope, during the SpE and ShE stages, intermittent rills occurred in the middle and lower sections of the plot. During the RE stage, continuous rills were formed by the connection of runoff paths on slope. For the AD slope, during the SpE and ShE stages, intermittent rills occurred at surface depressions in the plot and continuous rills were formed that cut through the surface during the RE stage. For the RT slope, during the SpE and ShE stages, intermittent rills occurred in the middle section of the plot. During the RE stage, rills formed on the ridge lateral slope. The occurrence of ridge collapse aggravated the fluctuation degree of microtopography. The second derivative contour map reflects the change rate of gradient in the horizontal direction (Fig. 3). At the same time, it also reflects the most serious part of slope erosion. For the CT slope, the erosion distribution on the whole slope was relatively uniform at different water erosive stages. For the AD slope, during the SpE and ShE stages, soil erosion mainly occurred near the surface depressions and around the intermittent rills. And the length and width of rills on the slope significantly increased at the RE stage. For the RT slope, during the SpE and ShE stages, soil erosion mainly occurred on ridges. At the
2.8. Rescaled range analysis Rescaled range (R/S) analysis can detect the future trends of a time series. The time series {p(t)} was divided into A sub series Ia (a = 1, 2, …, A) with element pk, a (k = 1, 2, …, n). The mean sequence ea of Ia can be denoted as:
1 n
n
∑ pk,a
(9)
i=1
For each sub series Ia, the standard deviation sequence SIa can be denoted as:
S Ia =
1 n
n
∑ (pk,a
− ea)2
k=1
(10)
The cumulative mean deviation sequence {xk, a} can be denoted as: k
xk , a =
∑ (pk,a
− ea)
i=1
(11)
The range sequence RIa can be denoted as:
R Ia = max(xk, a) − min(xk, a)
(13)
All data analyses were carried out using SPSS 22.0. Graphic works were performed by Origin Pro 9.0 and Surfer 16. Wavelet analysis of the time series data was conducted using Matlab 2017b software.
where Wf (a, b) is the wavelet coefficient; a is the scale factor; b is the time factor; i is the imaginary number; c is a constant.
ea =
a=1
2.9. Data analysis
(7)
Wavelet transform can decompose time series data in multiple time scales by scaling and shifting wavelet functions, and then get the periodic change characteristics of the original signal in different scales. The continuous wavelet transform of a time series f(t) can be denoted as:
Wf (a, b) =
A
∑ (R Ia /SIa)
H is the Hurst exponent, B is the autocorrelation coefficient of differential sequence, and D is the fractal dimension. The calculation formulas are as follows: (R/S)n = C × nH (14) B = 22H-1 –1, B ∈ [-0.5, 1] (15) D = 2 - H, D ∈ [1,2] (16) where C is a constant. H has the following characteristics with the help of B and D: (a) 0 ≤ H ＜ 0.5, −0.5 ≤ B < 0 and 1.5 ＜ D ≤ 2, the time series have long range anti-persistence; (b) 0.5 ≤ H ＜ 1, 0 ≤ B < 1 and 1 ＜ D ≤ 1.5, the time series have long range persistence; (c) H = 0.5, B = 0, and D = 1.5, the time series are independent without long range persistence (Zhang et al., 2017).
2.7. Wavelet analysis
ϕ (t ) = eict e−t
1 A
(12) 6
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generalized dimension spectra Dq ~ q could be described by a linear curve. While for the AD and RT slopes, their generalized dimension spectra Dq ~ q could be described by S-shaped curves. The fractal information dimension Di can be used to qualify the degree of disorder present in microtopography distribution. For the CT slope, the fractal information dimension Di values were 2.1556, 2.1556, 2.1557, and 2.1558 for respectively BR, SpE, ShE, and RE stages. For the AD slope, the fractal information dimension Di values were 2.2007, 2.1914, 2.1864, and 2.2119 for respectively BR, SpE, ShE, and RE stages. For the RT slope, the fractal information dimension Di values were 2.2003, 2.2000, 2.2085, and 2.2193 for respectively BR, SpE, ShE, and RE stages.
3.1.3. Semivariogram analysis of microtopography According to Fig. 5, nugget values of tillage practices increased with the evolution of water erosion. Meanwhile, sill values of different tillage practices increased with the increase in nugget values during water erosion processes. Overall, sill values for the tillage practices were RT > AD > CT. Base effect values were more than 75 % except for the ShE and RE stages of CT slope, which indicated that the spatial variability of different tillage practices had strong or medium autocorrelations during different water erosive stages. For the CT slope, codomain values were 6.14, 6.10, 6.09, and 6.05 m for respectively BR, SpE, ShE, and RE stages. For the AD slope, codomain values were 5.44, 5.50, 5.22, and 5.11 m for respectively BR, SpE, ShE, and RE stages. For the RT slope, codomain values were 4.36, 4.30, 3.97, and 3.41 m for respectively BR, SpE, ShE, and RE stages.
3.2. Temporal evolution of soil erosion Morlet wavelet analysis was used to interpret the time-varying characteristics of runoff and sediment yield during water erosion processes. Fig. 6 shows the changes in runoff at different time scales over time, and the magnitudes (positive or negative) of the real parts of the wavelet coefficients in the contour map represent the periods in which runoff increase or decrease. At the same time, the contour density reflects the fluctuation intensity, the change periods of runoff can be located. For the runoff, the oscillation centers of the wavelet coefficients were located at 14, 13 and 12 min for the CT, AD, and RT slopes, respectively. For the sediment yield, the oscillation centers of the wavelet coefficients were located at 12, 15 and 16 min for the CT, AD, and RT slopes, respectively (Fig. 7). We estimated the H, B and D values of time series of runoff and sediment yield based on R/S analysis (Table 3). For the runoff, H ∈ [0.632, 0.718], 0 < B ≤ 1, and 1 ≤ D < 1.5. For the sediment yield, H ∈ [0.741, 0.846], 0 < B ≤ 1, and 1 ≤ D < 1.5. 3.3. Effect of soil microtopography on soil erosion Table 4 shows the changes in runoff and sediment yields for three tillage practices during ShE and RE stages. With the increasing in microrelief, the runoff showed a decreasing first and then increasing trend during ShE stage. The variation trend of runoff in RE stage was similar to that in ShE stage. For the sediment yield, it showed a decreasing first and then increasing trend during ShE stage. While at the RE stage, the sediment yield increased gradually with the increase in microrelief. The interaction between microrelief and soil erosion was quantified based on fractal information dimension. As shown in Fig. 8, the runoff and sediment yield showed an initial decreasing and a subsequent increasing trend with the increase in the fractal information dimensions. This implied that there was a critical value of Di that affecting soil erosion. Within a certain range of fractal information dimension, soil erosion decreased with the increase in microrelief. When the fractal information dimension exceeded the critical range, soil erosion increased with the increase in microrelief.
Fig. 5. Parameters of the semivariogram models of three tillage practices at different water erosive stages. Note. CT: conventional tillage; AD: artificial digging; RT: ridge tillage; BR: before rainfall; SpE: splash erosion; ShE: sheet erosion; RE: rill erosion; S: strong autocorrelation; M: medium autocorrelation.
RE stage, it showed the location of the ridge collapse where the erosion was the most serious. 3.1.2. Fractal characteristics of microtopography Fig. 4 shows generalized dimension spectra Dq ~ q of different tillage practices with the evolution of water erosion and these Dq decreased monotonically with the increase in q. For the CT slope, the 7
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Fig. 6. Time-frequency distributions of real parts transformed with Morlet wavelet of surface runoff for three tillage practices. Note. A: conventional tillage (CT); B: artificial digging (AD); C: ridge tillage (RT).
4. Discussion
indicated that tillage practice was the crucial factor affecting the microrelief, and rainfall process also had a significant impact on the microrelief. Spatial heterogeneity of microtopography was affected by both structural factors and random factors (Bullard et al., 2018). In this study, base effect values were all more than 50 %, the spatial variability of different tillage practices had strong or medium autocorrelations during water erosion processes. The results provided further evidence that the effect of tillage practice on microtopography was much greater than that of rainfall event. Based on the results of semivariogram analysis, the overall spatial variability and spatial autocorrelation of microtopography both displayed a general trend: RT > AD > CT. The multifractal method was further used to interpret complex spatial structures of microtopography. According to Fig. 4, the generalized fractal dimension D values of CT slope at various water erosive stages were within in the range of 2.1554–2.1571, and the Dq ~ q curve displayed a linear relation. The D values of AD slope were within in the range of 2.1786–3.0961, the D
4.1. Spatial heterogeneity of microtopography in the process of water erosion Relative to the megarelief, the microtopography describes the micro-variation in surface elevation (5–25 cm) caused by tillage practices (Vermang et al., 2015). Zhang et al. (2015) proposed that the following basic problems can be solved using semivariogram analysis in the study of spatial variation characteristics of microtopography in the process of water erosion: base effect problem (i.e., proportion of spatial variability caused by structural factors to total spatial variability of microtopography) and scale problem (i.e., the spatial autocorrelation scale of microtopography). Many previous studies showed that tillage practice was the main factor affecting the spatial variation of microtopography based on the semivariogram method (Zhang et al., 2015; Luo et al., 2017). Jia et al. (2013) using swath profile methodology 8
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Fig. 7. Time-frequency distributions of real parts transformed with Morlet wavelet of sediment yield for three tillage practices. Note. A: conventional tillage (CT); B: artificial digging (AD); C: ridge tillage (RT). Table 3 R/S characteristic parameters of runoff and sediment yield for three tillage practices. Indexes
Tillage practices
Hurst index H
Autocorrelation coefficient B
Fractal dimension D
Runoff
CT AD RT CT
0.718 0.654 0.632 0.741
0.225 0.324 0.398 0.521
1.415 1.329 1.302 1.245
AD RT
0.814 0.846
0.224 0.355
1.312 1.368
Sediment yield
Table 4 Total runoff and sediment yields of three tillage practices at different water erosive stages. Tillage practices
Erosive stages
CT
AD
RT
Note. CT: conventional tillage; AD: artificial digging; RT: ridge tillage.
Total runoff (L m−2)
Sediment yield (kg m−2)
SpE ShE RE
29.15 35.48
0.0004 0.32 0.41
SpE ShE RE
9.57 31.68
0.0012 0.06 0.43
SpE ShE RE
28.47 67.96
0.0057 0.42 0.82
Note. CT: conventional tillage; AD: artificial digging; RT: ridge tillage; SpE: splash erosion; ShE: sheet erosion; RE: rill erosion. 9
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Fig. 8. Relationships of Di with runoff yield (A) and sediment yield (B) at different water erosive stages. Note. Di: the fractal information dimension.
with R/S analysis, 0.5 ≤ H ＜ 1, 0 < B ≤ 1, and 1 ≤ D < 1.5, which indicated that the runoff time series of tillage practices had long-range persistence during water erosion processes. Meanwhile, H ∈ [0.632, 0.718], H values approximated 0.5 and H values decreased gradually with the increase in microrelief, which indicated that although runoff will increase with an increase in rainfall duration, this trend is weak. Due to the high content of soil clay and the formation of soil crust, the runoff increased rapidly after the beginning of rainfall. The runoff fluctuated upwards with the increase in rainfall duration. However, the increasing trend of runoff gradually weakened, and tended to be stable in the later stage of rainfall. This phenomenon may be related to different erosive stages of water erosion (Zheng et al., 2014). With the evolution of water erosion, soil microtopography gradually formed a stable spatial structure, which made the runoff changes tend to be stable. At the same time, the persistence of runoff time series decreased with the increase in microrelief. The variation in sediment yield time series was quite different from that of runoff. The dominant sediment yield periodicities were 12, 15 and 16 min for the CT, AD, and RT slopes, respectively (Fig. 7). Overall, the dominant period of sediment yield tended to increase with the increase in microrelief. Combined with R/S analysis, 0.5 ≤ H ＜ 1, 0 < B ≤ 1, and 1 ≤ D < 1.5, which indicated that the sediment yield time series of tillage practices had positive long-range correlations during water erosion processes. However, H ∈ [0.741, 0.846], H values approximated 1 and H values increased gradually with the increase in microrelief, which indicated that sediment yield will increase with the increase in rainfall duration, this trend is strong, and the persistence of sediment yield time series increased with the increase in microrelief. The soil we used was characterized by lithologic soil and was regarded as a typical erodible soil, as was confirmed by Chen et al. (2015). The sediment loss increased gradually with the increase in rainfall duration. With the development of water erosion, greater erosion was occurred on rougher surface, especially for the RT slope. Wavelet analysis satisfactorily interpreted the multi-time scale structures of runoff and sediment yield. Furthermore, R/S analysis could detect the persistence features of runoff and sediment yield. This study confirmed the validities of wavelet and R/S analyses to reflect the temporal variation characteristics of runoff and sediment yield at hillslope scale. There were few studies that had explicitly tried to link the spatio-temporal changes in microtopography with those of runoff and sediment discharge. This study provided a new insight for clarifying the coupling relationships between microtopography changes and temporal evolution of soil erosion in sloping farmland.
values of RT slope were within in the range of 2.1924–3.9830, and the Dq ~ q curves of AD and RT slopes had typical S shapes. That indicated that the multifractal behaviours were gradually enhanced from CT, AD to RT. Meanwhile, the fractal information dimension Di values for the tillage practices were RT > AD > CT. These results demonstrated that RT had the highest spatial variability and the most complex spatial structure of microtopography. Many researches showed that microtopography with higher spatial variability can result in the shortest path of runoff and sediment, thus it can prevent soil erosion (Moreno et al., 2012; Zhang et al., 2015). As a result, RT slope should have the largest restraining effect on water erosion. However, RT may even accelerate soil erosion once ridge collapse according to Table 4. This phenomenon was confirmed by the relationship between Di and soil erosion. There was a certain range of Di critical values, which reflected the positive or negative effect on soil erosion at the centimetre scale. The spatial autocorrelation scales for different tillage practices were CT > AD > RT. The average codomains of CT, AD, and RT were 6.10, 5.32, and 4.01 m, respectively. That indicated that spatial continuity of microtopography was gradually reduced from CT, AD to RT and the complexity of the spatial variability of microtopography was gradually strengthened in turn. The microtopography combined with rainfall resulted in enhanced spatial variability from the SpE stage to the RE stage and reduced the spatial autocorrelation with the evolution of water erosion. At the RE stage, microtopography had the highest spatial heterogeneity structure and the lowest spatial dependence. The spatial variation of microtopography varied with the changes in slope steepness and rainfall intensity. Zhang et al. (2015) proposed that the spatial heterogeneity of microtopography at 15° slope was stronger than those of 10° and 20° slope gradients, while Luo et al. (2018b) indicated that the spatial variation of microtopography increased with the increase in slope gradients. Römkens et al. (2001) reported that decreasing rainfall sequence on a smooth surface caused more soil erosion than increasing rainfall sequence. In contrast, He et al. (2018) suggested that the increasing rainfall sequence was more likely to cause soil erosion. This could be attributed to the differences in initial roughness and soil texture. The current research studied the spatial heterogeneity of microtopography under a rainfall intensity of 1.5 mm min−1 on a 20° slope. Thus, further study should investigate the variability of microtopography under different slope gradients or rainfall intensities. 4.2. Effects of microtopography on temporal variations of runoff and sediment yield
5. Conclusions
According to Fig. 6, the dominant runoff periodicities were 14, 13 and 12 min for the CT, AD, and RT slopes, respectively. In general, the dominant period of runoff tended to decrease and the runoff turbulence tended to increase with the increase in microrelief. Especially for RT slope, the strong oscillation of signal occurred within 40–45 min, which might be related to the sudden change of microtopography. Combined
Three tilled slopes: conventional tillage (CT), artificial digging (AD), and ridge tillage (RT) had strong or medium spatial autocorrelations during water erosion processes. The fractal information dimensions of tillage practices at various erosion stages were RT > AD > CT. At the 10
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same time, we used the directional derivatives to describe the spatial distribution of microtopography in term of microrelief morphology. There was a certain range of Di critical values, which reflected the positive or negative effect on soil erosion at hillslope scale. During water erosion processes, the time series of runoff and sediment yield of tillage practices had long-range persistence, and Morlet wavelet analysis indicated that there were 12–16 min dominant periods in the time series of runoff and sediment yield. Microtopography remarkably influenced the temporal evolution of soil erosion. The higher microrelief led to the shorter dominant period and weaker the persistence of runoff, while the temporal variation in sediment yield was opposite to that of runoff.
and soil erosion in the upper reaches of the Yangtze River: some socio-economic considerations on China's Grain-for-Green Programme. Land Degrad. Dev. 17 (6), 589–603. https://doi.org/10.1002/ldr.736. Luo, J., Zheng, Z., Li, T., He, S., 2017. Spatial heterogeneity of microtopography and its influence on the flow convergence of slopes under different rainfall patterns. J. Hydrol. 545, 88–99. https://doi.org/10.1016/j.jhydrol.2016.12.018. Luo, J., Zheng, Z., Li, T., He, S., 2018a. Assessing the impacts of microtopography on soil erosion under simulated rainfall, using a multifractal approach. Hydrol. Process. 32 (16), 2543–2556. https://doi.org/10.1002/hyp.13175. Luo, J., Zheng, Z., Li, T., He, S., 2018b. Changes in micro-relief during different water erosive stages of purple soil under simulated rainfall. Sci. Rep. 8 (1), 3483. https:// doi.org/10.1038/s41598-018-21852-6. Luo, J., Zheng, Z., Li, T., He, S., 2020. Temporal variations in runoff and sediment yield associated with soil surface roughness under different rainfall patterns. Geomorphology 349, 106915. https://doi.org/10.1016/j.geomorph.2019.106915. Luo, J., Zheng, Z., Li, T., He, S., Wang, Y., Zhang, X., Huang, H., Yu, H., Liu, T., 2019. Characterization of runoff and sediment associated with rill erosion in sloping farmland during the maize-growing season based on rescaled range and wavelet analyses. Soil Till. Res. 195, 104359. https://doi.org/10.1016/j.still.2019.104359. Moreno, R.G., Álvarez, M.C.D., Alonso, A.T., Barrington, S., Requejo, A.S., 2008. Tillage and soil type effects on soil surface roughness at semiarid climatic conditions. Soil Till. Res. 98, 35–44. https://doi.org/10.1016/j.still.2007.10.006. Moreno, R.G., Burykin, T., Diaz Alvarez, M.C., Crawford, J.W., 2012. Effect of management practices on soil microstructure and surface microrelief. Appl. Environ. Soil Sci. 2012, 1–9. https://doi.org/10.1155/2012/608275. Peng, J., Liu, Z., Liu, Y., Wu, J., Han, Y., 2012. Trend analysis of vegetation dynamics in Qinghai-Tibet Plateau using Hurst Exponent. Ecol. Indic. 14 (1), 28–39. https://doi. org/10.1016/j.ecolind.2011.08.011. Römkens, M.J., Helming, K., Prasad, S.N., 2001. Soil erosion under different rainfall intensities, surface roughness, and soil water regimes. Catena 46 (2–3), 103–123. https://doi.org/10.1016/S0341-8162(01)00161-8. Shen, Z.Y., Li, Z.B., Li, P., Lu, K.X., 2009. Multifractal arithmethic for watershed topographic feature. Adv. Water Sci. 20 (3), 385–391. https://doi.org/10.14042/j.cnki. 32.1309.2009.03.001. Shi, P., Wu, M., Qu, S., Jiang, P., Qiao, X., Chen, X., Zhou, M., Zhang, Z., 2015. Spatial distribution and temporal trends in precipitation concentration indices for the Southwest China. Water Resour. Manage. 29 (11), 3941–3955. https://doi.org/10. 1007/s11269-015-1038-3. Soil Survey Staff, 2010. Keys to Soil Taxonomy (11th ed.). USDA/ NRCS. Washington, D.C. Stolte, J., Shi, X., Ritsema, C.J., 2009. Introduction: Soil erosion and nutrient losses in the Hilly Purple Soil area in China. Soil Till. Res. 105, 283–284. https://doi.org/10. 1016/j.still.2009.09.010. Tian, S., Xu, M., Jiang, E., Wang, G., Hu, H., Liu, X., 2019. Temporal variations of runoff and sediment load in the upper Yellow River China. J. Hydrol. 568, 46–56. https:// doi.org/10.1016/j.jhydrol.2018.10.033. Torre, I.G., Losada, J.C., Heck, R.J., Tarquis, A.M., 2018. Multifractal analysis of 3D images of tillage soil. Geoderma 311, 167–174. https://doi.org/10.1016/j.geoderma. 2017.02.013. Vermang, J., Norton, L.D., Huang, C., Cornelis, W.M., Da Silva, A.M., Gabriels, D., 2015. Characterization of soil surface roughness effects on runoff and soil erosion rates under simulated rainfall. Soil Sci. Soc. Am. J. 79 (3), 903–916. https://doi.org/10. 2136/sssaj2014.08.0329. Wang, L., Dalabay, N., Lu, P., Wu, F., 2017. Effects of tillage practices and slope on runoff and erosion of soil from the Loess Plateau, China, subjected to simulated rainfall. Soil Till. Res. 166, 147–156. https://doi.org/10.1016/j.still.2016.09.007. Zhang, H., Zhang, H., Dong, Y., Zhang, Q., 2017. Characterization of runoff and sediment yield in farmlands on loess slopes based on R/S and wavelet analysis. Acta Pedol. Sin. 54 (6), 1345–1356. https://doi.org/10.11766/trxb201704190031. Zhang, Q., Wang, J., Zhao, L., Wu, F., Zhang, Z., Torbert, A.H., 2015. Spatial heterogeneity of surface roughness during different erosive stages of tilled loess slopes under a rainfall intensity of 1.5 mm min-1. Soil Till. Res. 153, 95–103. https://doi. org/10.1016/j.still.2015.05.011. Zhao, L.S., Liang, X.L., Wu, F.Q., 2014. Soil surface roughness change and its effect on runoff and erosion on the Loess Plateau of China. J. Arid Land 6 (4), 400–409. https://doi.org/10.1007/s40333-013-0246-z. Zheng, J.J., He, X.B., Walling, D., Zhang, X.B., Flanagan, D., Qi, Y.Q., 2007. Assessing soil erosion rates on manually-tilled hillslopes in the Sichuan Hilly Basin using 137Cs and 210 Pbex measurements. Pedosphere 17 (3), 273–283. https://doi.org/10.1016/S10020160(07)60034-4. Zheng, Z.C., He, S.Q., Wu, F.Q., 2014. Changes of soil surface roughness under water erosion process. Hydrol. Process. 28 (12), 3919–3929. https://doi.org/10.1002/hyp. 9939.
Declaration of interest statement The authors declare that they have no known competing interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This study was supported by the National Natural Science Foundation of China (Grant No. 41271307 and 40901138) and the Key R & D Project of Sichuan Province (Grant No. 2019YFS0463). References Bullard, J.E., Ockelford, A., Strong, C.L., Aubault, H., 2018. Impact of multi-day rainfall events on surface roughness and physical crusting of very fine soils. Geoderma 313, 181–192. https://doi.org/10.1016/j.geoderma.2017.10.038. Chen, X.Y., Huang, Y.H., Zhao, Y., Mo, B., Mi, H.X., 2015. Comparison of loess and purple rill erosions measured with volume replacement method. J. Hydrol. 530, 476–483. https://doi.org/10.1016/j.jhydrol.2015.10.001. Cogo, N.P., Moldenhauer, W.C., Foster, G.R., 1984. Soil loss reductions from conservation tillage practices. Soil Sci. Soc. Am. J. 48 (2), 368–373. https://doi.org/10.2136/ sssaj1984.03615995004800020029x. Darboux, F., Davy, P., Gascuel-Odoux, C., Huang, C., 2002. Evolution of soil surface roughness and flowpath connectivity in overland flow experiments. Catena 46, 125–139. https://doi.org/10.1016/S0341-8162(01)00162-X. Ding, W., Huang, C., 2017. Effects of soil surface roughness on interrill erosion processes and sediment particle size distribution. Geomorphology 295, 801–810. https://doi. org/10.1016/j.geomorph.2017.08.033. Ferreiro, J.P., Vázquez, E.V., 2010. Multifractal analysis of Hg pore size distributions in soils with contrasting structural stability. Geoderma 160 (1), 64–73. https://doi.org/ 10.1016/j.geoderma.2009.11.019. Gómez, J.A., Nearing, M.A., 2005. Runoff and sediment losses from rough and smooth soil surfaces in a laboratory experiment. Catena 59 (3), 253–266. https://doi.org/10. 1016/j.catena.2004.09.008. Govers, G., Takken, I., Helming, K., 2000. Soil roughness and overland flow. Agronomie 20, 131–146. https://doi.org/10.1051/agro:2000114. He, J., Li, X., Jia, L., Gong, H., Cai, Q., 2014. Experimental study of rill evolution processes and relationships between runoff and erosion on clay loam and loess. Soil Sci. Soc. Am. J. 78 (5), 1716–1725. https://doi.org/10.2136/sssaj2014.02.0063. He, S., Qin, F., Zheng, Z., Li, T., 2018. Changes of soil microrelief and its effect on soil erosion under different rainfall patterns in a laboratory experiment. Catena 162, 203–215. https://doi.org/10.1016/j.catena.2017.11.010. Jia, T.B., Wu, F.Q., Zhao, L.S., Wang, L.H., 2013. Micro-relief slope surface complexity characteristics of sloping farm land under different tillage practices. J. Soil Water Conserv. 27 (4), 152–156. https://doi.org/10.13870/j.cnki.stbcxb.2013.04.039. Karmakar, S., Goswami, S., Chattopadhyay, S., 2019. Exploring the pre-and summermonsoon surface air temperature over eastern India using Shannon entropy and temporal Hurst exponents through rescaled range analysis. Atmos. Res. 217, 57–62. https://doi.org/10.1016/j.atmosres.2018.10.007. Labat, D., 2005. Recent advances in wavelet analyses: Part 1. A review of concepts. J. Hydrol. 314 (1–4), 275–288. https://doi.org/10.1016/j.jhydrol.2005.04.003. Long, H.L., Heilig, G.K., Wang, J., Li, X.B., Luo, M., Wu, X.Q., Zhang, M., 2006. Land use
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Spatial variation of microtopography and its effect on temporal evolution of soil erosion during different erosive stages
T
⁎
Jian Luoa, Zicheng Zhenga, , Tingxuan Lia, Shuqin Heb a b
College of Resources Science, Sichuan Agricultural University, 211 Huimin Road, Chengdu, Sichuan 611130, China College of Forestry, Sichuan Agricultural University, 211 Huimin Road, Chengdu, Sichuan 611130, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Microtopography Fractal model Temporal sequences analysis Soil erosion Purple soil
Microtopography significantly influences soil erosion at hillslope scale. Currently, the influence of microtopography on temporal evolution of soil erosion is still unclear. A set of simulated rainfall experiments on three 2 m long, 1 m wide soil boxes under a rainfall intensity of 1.5 mm min−1 on a 20° slope were conducted in the Chinese purple soil region to quantify the spatial variation of microtopography and its effect on temporal variations of runoff and sediment yield during water erosion processes. Three local tillage practices: conventional tillage (CT), artificial digging (AD), and ridge tillage (RT) with different initial microrelief (smooth, rough, and very rough) were designed. The spatial heterogeneity of microtopography was characterized by directional derivatives, semivariogram, and fractal information dimension in terms of morphology and quantity. And we identified the temporal variability characteristics of runoff and sediment yield based on wavelet and rescaled range (R/S) analyses. The results indicated that the spatial variability of different tillage practices had strong or medium autocorrelations during different water erosive stages. The spatial autocorrelation scales of CT, AD, and RT were 6.10, 5.32, and 4.01 m, respectively. The fractal information dimensions of tillage practices at various erosive stages were RT > AD > CT. There was a certain range of Di critical values, which reflected the positive or negative effect on soil erosion. The Hurst indexes of the runoff time series were in the section between 0.632 and 0.718, and that of the sediment yield time series ranged between 0.741 and 0.846. The time series of runoff and sediment yield had long-range persistence and varied periodically every 12–16 min during water erosion processes. Overall, the dominant period and the persistence of runoff tended to decrease and increase respectively with the increase in microrelief, while the temporal variation in sediment yield was opposite to that of runoff. Characterization of the temporal variability characteristics of runoff and sediment yield response to microrelief changes would contribute to a better understanding of the hydro-geomorphological processes at hillslope scale.
1. Introduction Sloping farmland in Purple Hilly Area of Sichuan Basin is not only the major grain-producing area, but also the main sediment source in the Upper Yangtze River Basin (Long et al., 2006; Zheng et al., 2007). Soil erosion in sloping farmland greatly restricts ecological environment and food security in the area (Stolte et al., 2009). Intensive cultivation and unreasonable tillage practices have accelerated soil erosion in sloping farmland (Wang et al., 2017; Luo et al., 2018a). Tillage operations disturb the original form of surface soil, and make the soil surface appear microtopography with high and low fluctuations (Moreno et al., 2008). The study of water erosion process mechanisms at microtopographic scale is an important issue in the field of soil erosion, and it is also a crucial scientific problem urgently needed to be ⁎
solved in the quantitative study of soil erosion. Microtopography describes the micro-variation in surface elevation caused by tillage practices and soil erosion, which is identified as a key factor in water erosion evolution (Govers et al., 2000). Previous studies have shown that microtopography can significantly affect runoff, soil loss and deposition (Cogo et al., 1984; Darboux et al., 2002; Zhao et al., 2014). Dynamic erosion pattern continuously creates and alters microrelief. Meanwhile, microrelief will in turn change the erosion patterns. Hence, the spatial variation of microtopography is a descriptor that reflects how the soil surface behaves against the soil erosion. Currently, opposing results for the effect of microtopography on soil erosion were reported in many studies. Some researchers indicated that the increasing microrelief is expected to impose greater resistance to flow velocities, and hence reduce the soil and water loss (Cogo et al.,
Corresponding author at: College of Resources Science, Sichuan Agricultural University, 211 Huimin Road, Chengdu, Sichuan 611130, China. E-mail address: [email protected] (Z. Zheng).
https://doi.org/10.1016/j.catena.2020.104515 Received 24 June 2019; Received in revised form 1 February 2020; Accepted 9 February 2020 0341-8162/ © 2020 Elsevier B.V. All rights reserved.
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1984; Römkens et al., 2001). However, other researchers reported that the increasing microrelief may even increase the soil erosion (Gómez and Nearing, 2005; Ding and Huang, 2017). Insights into the interaction between microtopography and soil erosion require an understanding of spatial variation characteristics of microtopography. At present, soil roughness (SR), semivariable function and multifractal analysis are widely used to analyze the spatial variation characteristics of surface microtopography during water erosion processes (Shen et al., 2009; Zhang et al. 2015; Luo et al., 2018b). Many researchers have systematically studied the characterization of runoff and sediment from catchment and hillslope scales. The results showed that the generation and evolution of runoff and sediment under the condition of continuous rainfall was a complex process affected by many internal and external factors, and the runoff and sediment processes exhibited complex nonlinear and multi-time scale variation characteristics (Tian et al., 2019; Luo et al., 2020). This situation is more obvious at hillslope scale due to the complex material composition, poor uniformity and the interference of artificial farming management on slope surface. Traditional Euclidean geometry is difficult to describe the complicated and high-dimensional nonlinear process of runoff and sediment accurately. Wavelet analysis is a kind of multiresolution analysis method, which can reveal the localized characteristics of time series from temporal and frequency domains at the same time, so it is suitable for the study of hydrological time series with multi-time scale changes and non-stationary characteristics (Labat, 2005). The correlation between wavelet analysis and fractal theory is very strong. Wavelet transform has scaling invariance, which is consistent with the characteristics of fractal structure. Wavelet analysis can distinguish the dominant periods hidden in the time series, which is of guiding significance to predict the trend of runoff and sediment yield in the future. Furthermore, rescaled range (R/S) analysis can detect the long-term correlation or “memory” of a time series. Up until now, these methods have applied to many fields in the earth sciences (Peng et al., 2012; Shi et al., 2015; Karmakar et al., 2019; Luo et al., 2019). The objectives of the study are as follows: 1) to investigate the spatial variation characteristics of microtopography during different water erosive stages, 2) to analyze the temporal variation characteristics of runoff and sediment yield at hillslope scale, and 3) to clarify the effect of microtopography on temporal evolution of soil erosion during water erosion processes.
Table 2 Rainfall durations for three tillage practices at different water erosive stages. Tillage practices
Rainfall Duration (min)
CT AD RT
SpE
ShE
RE
4.0 4.8 5.8
15.1 12.4 19.7
21.7 26.9 27.5
Note. CT: conventional tillage; AD: artificial digging; RT: ridge tillage; SpE: splash erosion; ShE: sheet erosion; RE: rill erosion.
different initial microrelief (smooth, rough, and very rough) were designed based on the local custom. CT creates a smooth slope using rake wear. AD is a manual tillage practice which uses a hoe to cultivate the soil depression at a depth of 5 cm and a width of 15 cm. The distance between depressions is 20 cm. RT is traditional tillage practice which uses a plow to create ridge-furrow systems, with a ridge height of 15 cm, a ridge width of 50 cm and a ridge distance of 40 cm. The slope gradient and rainfall intensity were designed based on the study area was characterized by steep slopes and experienced high rainfall intensities. The slope gradient of the soil box was 20° and a representative erosive rainfall intensity of 1.5 mm min−1 was employed in this study. The rainfall simulator was similar to that described by He et al. (2018). The water erosive stages were: (a) splash erosion (SpE), the phase prior to the initiation of runoff; (b) sheet erosion (ShE), the phase when the drop pits started to appear; and (c) rill erosion (RE), the phase when the fish-scale shaped pits and overfall formed the rills (Zhang et al., 2015). Information regarding the rainfall duration for each event is presented in Table 2. All experiments were repeated twice. 2.3. Experimental measurements 2.3.1. Construction of soil surface microtopography The microtopography was measured with a laser scanner (Maptek isite-8820). Accordingly, 486,453 surface elevation data points for each slope were collected and each point represented an area of 6 mm × 6 mm. After a series of pre-processing procedures (spatial alignment, cross validation and Kriging interpolation), the original microtopography digital elevation model (M−DEM) was constructed by ArcGIS 3D analyst.
2. Materials and methods 2.3.2. Runoff and sediment yield Soil splash erosion was used to be determined by the hanging splash erosion boards and oven-dried at 105 °C to a constant weight (Zheng et al., 2014). During the sheet and rill erosive stages, each flow generation duration was recorded, runoff samples were collected continuously at the outlet of the soil box at intervals of 3 min. The runoff samples were measured using a measuring cylinder and then settled for 12 h so that the suspended sediments could settle out. After decanting the clear supernatant, the sediment samples were dried in an oven at 105 °C and weighed to determine the sediment yield (He et al., 2014).
2.1. Study site and soil sampling The study area was located in a sloping farmland around Ziyang, China (104° 34ʹ E, 30° 05ʹ N). The purple soil used in this study was Entisol (USDA Soil Taxonomy) with 22 % clay, 29 % silt, and 49 % sand (Soil Survey Staff, 2010) (Table 1). Air-dried soil was crushed before being passed through a 10 mm sieve. Each soil box with an area of 2 m2 was filled with 10 cm layers of soil to a depth of 50 cm. The soil moisture content was 5 % before rainfall events. The details of the soil preparation have been described by Luo et al. (2017).
2.4. Calculating horizontal directional derivatives based on DEM 2.2. Research design First derivative: The slope of DEM grid surface along the horizontal direction is calculated, which is equal to the product of the slope vector and the unit vector in the specified direction. In a particular grid, along
After packing the box with soil, three tillage practices, i.e. conventional tillage (CT), artificial digging (AD), and ridge tillage (RT) with Table 1 Physical-chemical properties of experimental soil. Soil type
pH
Bulk density (g cm−3)
CEC (cmol kg−1)
SOC (g kg−1)
CaCO3 (%)
Sand (%)
Silt (%)
Clay (%)
Texture
Purple soil
7.5
1.2
21
13
12
49
29
22
Clay loam
2
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Fig. 1. Contour maps of first directional derivatives of three tillage practices in horizontal direction at different water erosive stages. Note. BR: before rainfall; SpE: splash erosion; ShE: sheet erosion; RE: rill erosion; CT: conventional tillage; AD: artificial digging; RT: ridge tillage.
directional derivative of the first derivative. In a particular grid, the larger the second derivative value in the horizontal direction, which indicates that the grid is at the turning point of the surface morphology. The second derivative can be denoted as:
the positive direction of X axis, the rise of slope at the grid is expressed as positive value, and the decline of slope is expressed as negative value, which can be used to determine the location of rill channel and the fluctuation degree of microrelief. The first derivative can be denoted as:
cos(α ) ⎤ ⎡ dy df ⎤ ⎡ cos(α ) ⎤ df df df , · ·cos(α ) + ·sin(α ) = = = g·⎡ ⎥ ⎥ ⎢ ⎢ ⎢ ⎥ sin( ) sin( ) α α dy ds dx dy dx ⎦⎣ ⎦ ⎦ ⎣ ⎣
df
df
df d ⎡ ·cos(α ) + dy ·sin(α ) ⎤ d ⎡ ds ⎤ d 2f ⎣ ⎦ = ⎣ dx ⎦ = 2 ds ds ds d 2f d 2f d 2f ·cos2 (α ) + 2 ·cos(α )·sin(α ) + ·sin2 (α ) = 2 dy 2 dxdy dx
(1)
Second derivative: The change rate of the slope along the horizontal direction on the surface of DEM grid is calculated, which is the
(2)
where g is the gradient vector of the grid point; α is the angle value 3
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Fig. 2. Rill distributions obtained for three tillage practices during ShE and RE stages. Note. ShE: sheet erosion; RE: rill erosion; CT: conventional tillage; AD: artificial digging; RT: ridge tillage. nε
of the specified direction. In this paper, the horizontal direction, i.e. the positive direction of the X-axis, is selected, thus α = 0; x, y are the distances in the horizontal and vertical directions, respectively.
μi (q, ε ) =
∑ μi (ε )q i=1
(3)
where q is the weight factor and the q values ranged from − 3 to + 3 with increments of 0.5; ε is size of the box, in this study, the box size was 10, 30, 60, 90… 270, and 300 mm, respectively; μi(ε) is elevation distribution probability of i-th subarea; n(ε) is the number of boxes in which μi(ε) greater than 0. The fractal information dimension can be denoted as:
2.5. Fractal analysis of microtopography The box counting method is used to determine the fractal information dimension of microtopography (Ferreiro and Vázquez, 2010; Torre et al., 2018). The partition function μi(q, ε) can be obtained from the weighted summation of q-th power of elevation distribution probability. 4
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Fig. 3. Contour maps of second directional derivatives of three tillage practices in horizontal direction at different water erosive stages. Note. BR: before rainfall; SpE: splash erosion; ShE: sheet erosion; RE: rill erosion; CT: conventional tillage; AD: artificial digging; RT: ridge tillage. n (ε )
1 D (q) = lim q − 1 ε→0
2.6. Semivariogram analysis
ln ∑ μi (q, ε ) i=1
ln(ε )
,q≠1
The distribution of relative elevation of soil surface is not only random, but also correlated in a certain range of space. Therefore, semivariogram model (SM) is used to analyze the spatial variation structure characteristics of microtopography. SM is defined as:
(4)
n (ε )
∑ μi (ε ) ln μi (ε ) Di = lim ε→0
i=1
ln(ε )
,q=1
(5)
γ (h) =
where D(q) is the general fractal dimension, Di is the fractal information dimension.
1 2N (h)
N (h)
∑ i=1
[Z (x i ) − Z (x i + h)]2
(6)
Where γ(h) is the semivariance for the lag distance between 5
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Fig. 4. Relationships between D(q) and q of three tillage practices at different water erosive stages. Note. A: conventional tillage (CT); B: artificial digging (AD); C: ridge tillage (RT); BR: before rainfall; SpE: splash erosion; ShE: sheet erosion; RE: rill erosion.
The mean rescaled range (R/S)n can be estimated by:
sampling elevation data points (h); Z(xi) is the relative elevation at the location xi; and N(h) is the number of data pairs for the lag distance h. The semivariogram model mainly has the following parameters: (a) sill, total spatial variability of microtopography; (b) nugget, spatial variability caused by random factors; (c) base effect, proportion of spatial variability caused by structural factors to total spatial variability of microtopography. The base effects of greater than 75 %, 25–75 %, and < 25 % indicate strong, medium, and weak spatial autocorrelations of microtopography, respectively; (d) codomain, spatial autocorrelation scale of microtopography (Zhang et al., 2015).
(R/ S )n =
Wavelet analysis is an appropriate method to solve the multi-time scale nonlinear response of a time series. Wavelet analysis is closely related to wavelet type. Morlet wavelet can eliminate the false oscillation generated by using the real wavelet transform coefficients as the criterion. Morlet wavelet is defined as: 2
/2
1 a
∞
∫−∞ f (t ) eic ( t−ab ) e at ( t−ab ) dt
3. Results
2
(8) 3.1. Spatial variation of microtopography during different water erosive stages 3.1.1. Spatial distribution of directional derivatives based on DEM According to Figs. 1 and 2, the first derivative contour map can reflect the slope distribution in the horizontal direction. The denser the contour lines are, the larger the topographic fluctuation is. For the CT slope, during the SpE and ShE stages, intermittent rills occurred in the middle and lower sections of the plot. During the RE stage, continuous rills were formed by the connection of runoff paths on slope. For the AD slope, during the SpE and ShE stages, intermittent rills occurred at surface depressions in the plot and continuous rills were formed that cut through the surface during the RE stage. For the RT slope, during the SpE and ShE stages, intermittent rills occurred in the middle section of the plot. During the RE stage, rills formed on the ridge lateral slope. The occurrence of ridge collapse aggravated the fluctuation degree of microtopography. The second derivative contour map reflects the change rate of gradient in the horizontal direction (Fig. 3). At the same time, it also reflects the most serious part of slope erosion. For the CT slope, the erosion distribution on the whole slope was relatively uniform at different water erosive stages. For the AD slope, during the SpE and ShE stages, soil erosion mainly occurred near the surface depressions and around the intermittent rills. And the length and width of rills on the slope significantly increased at the RE stage. For the RT slope, during the SpE and ShE stages, soil erosion mainly occurred on ridges. At the
2.8. Rescaled range analysis Rescaled range (R/S) analysis can detect the future trends of a time series. The time series {p(t)} was divided into A sub series Ia (a = 1, 2, …, A) with element pk, a (k = 1, 2, …, n). The mean sequence ea of Ia can be denoted as:
1 n
n
∑ pk,a
(9)
i=1
For each sub series Ia, the standard deviation sequence SIa can be denoted as:
S Ia =
1 n
n
∑ (pk,a
− ea)2
k=1
(10)
The cumulative mean deviation sequence {xk, a} can be denoted as: k
xk , a =
∑ (pk,a
− ea)
i=1
(11)
The range sequence RIa can be denoted as:
R Ia = max(xk, a) − min(xk, a)
(13)
All data analyses were carried out using SPSS 22.0. Graphic works were performed by Origin Pro 9.0 and Surfer 16. Wavelet analysis of the time series data was conducted using Matlab 2017b software.
where Wf (a, b) is the wavelet coefficient; a is the scale factor; b is the time factor; i is the imaginary number; c is a constant.
ea =
a=1
2.9. Data analysis
(7)
Wavelet transform can decompose time series data in multiple time scales by scaling and shifting wavelet functions, and then get the periodic change characteristics of the original signal in different scales. The continuous wavelet transform of a time series f(t) can be denoted as:
Wf (a, b) =
A
∑ (R Ia /SIa)
H is the Hurst exponent, B is the autocorrelation coefficient of differential sequence, and D is the fractal dimension. The calculation formulas are as follows: (R/S)n = C × nH (14) B = 22H-1 –1, B ∈ [-0.5, 1] (15) D = 2 - H, D ∈ [1,2] (16) where C is a constant. H has the following characteristics with the help of B and D: (a) 0 ≤ H ＜ 0.5, −0.5 ≤ B < 0 and 1.5 ＜ D ≤ 2, the time series have long range anti-persistence; (b) 0.5 ≤ H ＜ 1, 0 ≤ B < 1 and 1 ＜ D ≤ 1.5, the time series have long range persistence; (c) H = 0.5, B = 0, and D = 1.5, the time series are independent without long range persistence (Zhang et al., 2017).
2.7. Wavelet analysis
ϕ (t ) = eict e−t
1 A
(12) 6
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generalized dimension spectra Dq ~ q could be described by a linear curve. While for the AD and RT slopes, their generalized dimension spectra Dq ~ q could be described by S-shaped curves. The fractal information dimension Di can be used to qualify the degree of disorder present in microtopography distribution. For the CT slope, the fractal information dimension Di values were 2.1556, 2.1556, 2.1557, and 2.1558 for respectively BR, SpE, ShE, and RE stages. For the AD slope, the fractal information dimension Di values were 2.2007, 2.1914, 2.1864, and 2.2119 for respectively BR, SpE, ShE, and RE stages. For the RT slope, the fractal information dimension Di values were 2.2003, 2.2000, 2.2085, and 2.2193 for respectively BR, SpE, ShE, and RE stages.
3.1.3. Semivariogram analysis of microtopography According to Fig. 5, nugget values of tillage practices increased with the evolution of water erosion. Meanwhile, sill values of different tillage practices increased with the increase in nugget values during water erosion processes. Overall, sill values for the tillage practices were RT > AD > CT. Base effect values were more than 75 % except for the ShE and RE stages of CT slope, which indicated that the spatial variability of different tillage practices had strong or medium autocorrelations during different water erosive stages. For the CT slope, codomain values were 6.14, 6.10, 6.09, and 6.05 m for respectively BR, SpE, ShE, and RE stages. For the AD slope, codomain values were 5.44, 5.50, 5.22, and 5.11 m for respectively BR, SpE, ShE, and RE stages. For the RT slope, codomain values were 4.36, 4.30, 3.97, and 3.41 m for respectively BR, SpE, ShE, and RE stages.
3.2. Temporal evolution of soil erosion Morlet wavelet analysis was used to interpret the time-varying characteristics of runoff and sediment yield during water erosion processes. Fig. 6 shows the changes in runoff at different time scales over time, and the magnitudes (positive or negative) of the real parts of the wavelet coefficients in the contour map represent the periods in which runoff increase or decrease. At the same time, the contour density reflects the fluctuation intensity, the change periods of runoff can be located. For the runoff, the oscillation centers of the wavelet coefficients were located at 14, 13 and 12 min for the CT, AD, and RT slopes, respectively. For the sediment yield, the oscillation centers of the wavelet coefficients were located at 12, 15 and 16 min for the CT, AD, and RT slopes, respectively (Fig. 7). We estimated the H, B and D values of time series of runoff and sediment yield based on R/S analysis (Table 3). For the runoff, H ∈ [0.632, 0.718], 0 < B ≤ 1, and 1 ≤ D < 1.5. For the sediment yield, H ∈ [0.741, 0.846], 0 < B ≤ 1, and 1 ≤ D < 1.5. 3.3. Effect of soil microtopography on soil erosion Table 4 shows the changes in runoff and sediment yields for three tillage practices during ShE and RE stages. With the increasing in microrelief, the runoff showed a decreasing first and then increasing trend during ShE stage. The variation trend of runoff in RE stage was similar to that in ShE stage. For the sediment yield, it showed a decreasing first and then increasing trend during ShE stage. While at the RE stage, the sediment yield increased gradually with the increase in microrelief. The interaction between microrelief and soil erosion was quantified based on fractal information dimension. As shown in Fig. 8, the runoff and sediment yield showed an initial decreasing and a subsequent increasing trend with the increase in the fractal information dimensions. This implied that there was a critical value of Di that affecting soil erosion. Within a certain range of fractal information dimension, soil erosion decreased with the increase in microrelief. When the fractal information dimension exceeded the critical range, soil erosion increased with the increase in microrelief.
Fig. 5. Parameters of the semivariogram models of three tillage practices at different water erosive stages. Note. CT: conventional tillage; AD: artificial digging; RT: ridge tillage; BR: before rainfall; SpE: splash erosion; ShE: sheet erosion; RE: rill erosion; S: strong autocorrelation; M: medium autocorrelation.
RE stage, it showed the location of the ridge collapse where the erosion was the most serious. 3.1.2. Fractal characteristics of microtopography Fig. 4 shows generalized dimension spectra Dq ~ q of different tillage practices with the evolution of water erosion and these Dq decreased monotonically with the increase in q. For the CT slope, the 7
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Fig. 6. Time-frequency distributions of real parts transformed with Morlet wavelet of surface runoff for three tillage practices. Note. A: conventional tillage (CT); B: artificial digging (AD); C: ridge tillage (RT).
4. Discussion
indicated that tillage practice was the crucial factor affecting the microrelief, and rainfall process also had a significant impact on the microrelief. Spatial heterogeneity of microtopography was affected by both structural factors and random factors (Bullard et al., 2018). In this study, base effect values were all more than 50 %, the spatial variability of different tillage practices had strong or medium autocorrelations during water erosion processes. The results provided further evidence that the effect of tillage practice on microtopography was much greater than that of rainfall event. Based on the results of semivariogram analysis, the overall spatial variability and spatial autocorrelation of microtopography both displayed a general trend: RT > AD > CT. The multifractal method was further used to interpret complex spatial structures of microtopography. According to Fig. 4, the generalized fractal dimension D values of CT slope at various water erosive stages were within in the range of 2.1554–2.1571, and the Dq ~ q curve displayed a linear relation. The D values of AD slope were within in the range of 2.1786–3.0961, the D
4.1. Spatial heterogeneity of microtopography in the process of water erosion Relative to the megarelief, the microtopography describes the micro-variation in surface elevation (5–25 cm) caused by tillage practices (Vermang et al., 2015). Zhang et al. (2015) proposed that the following basic problems can be solved using semivariogram analysis in the study of spatial variation characteristics of microtopography in the process of water erosion: base effect problem (i.e., proportion of spatial variability caused by structural factors to total spatial variability of microtopography) and scale problem (i.e., the spatial autocorrelation scale of microtopography). Many previous studies showed that tillage practice was the main factor affecting the spatial variation of microtopography based on the semivariogram method (Zhang et al., 2015; Luo et al., 2017). Jia et al. (2013) using swath profile methodology 8
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Fig. 7. Time-frequency distributions of real parts transformed with Morlet wavelet of sediment yield for three tillage practices. Note. A: conventional tillage (CT); B: artificial digging (AD); C: ridge tillage (RT). Table 3 R/S characteristic parameters of runoff and sediment yield for three tillage practices. Indexes
Tillage practices
Hurst index H
Autocorrelation coefficient B
Fractal dimension D
Runoff
CT AD RT CT
0.718 0.654 0.632 0.741
0.225 0.324 0.398 0.521
1.415 1.329 1.302 1.245
AD RT
0.814 0.846
0.224 0.355
1.312 1.368
Sediment yield
Table 4 Total runoff and sediment yields of three tillage practices at different water erosive stages. Tillage practices
Erosive stages
CT
AD
RT
Note. CT: conventional tillage; AD: artificial digging; RT: ridge tillage.
Total runoff (L m−2)
Sediment yield (kg m−2)
SpE ShE RE
29.15 35.48
0.0004 0.32 0.41
SpE ShE RE
9.57 31.68
0.0012 0.06 0.43
SpE ShE RE
28.47 67.96
0.0057 0.42 0.82
Note. CT: conventional tillage; AD: artificial digging; RT: ridge tillage; SpE: splash erosion; ShE: sheet erosion; RE: rill erosion. 9
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Fig. 8. Relationships of Di with runoff yield (A) and sediment yield (B) at different water erosive stages. Note. Di: the fractal information dimension.
with R/S analysis, 0.5 ≤ H ＜ 1, 0 < B ≤ 1, and 1 ≤ D < 1.5, which indicated that the runoff time series of tillage practices had long-range persistence during water erosion processes. Meanwhile, H ∈ [0.632, 0.718], H values approximated 0.5 and H values decreased gradually with the increase in microrelief, which indicated that although runoff will increase with an increase in rainfall duration, this trend is weak. Due to the high content of soil clay and the formation of soil crust, the runoff increased rapidly after the beginning of rainfall. The runoff fluctuated upwards with the increase in rainfall duration. However, the increasing trend of runoff gradually weakened, and tended to be stable in the later stage of rainfall. This phenomenon may be related to different erosive stages of water erosion (Zheng et al., 2014). With the evolution of water erosion, soil microtopography gradually formed a stable spatial structure, which made the runoff changes tend to be stable. At the same time, the persistence of runoff time series decreased with the increase in microrelief. The variation in sediment yield time series was quite different from that of runoff. The dominant sediment yield periodicities were 12, 15 and 16 min for the CT, AD, and RT slopes, respectively (Fig. 7). Overall, the dominant period of sediment yield tended to increase with the increase in microrelief. Combined with R/S analysis, 0.5 ≤ H ＜ 1, 0 < B ≤ 1, and 1 ≤ D < 1.5, which indicated that the sediment yield time series of tillage practices had positive long-range correlations during water erosion processes. However, H ∈ [0.741, 0.846], H values approximated 1 and H values increased gradually with the increase in microrelief, which indicated that sediment yield will increase with the increase in rainfall duration, this trend is strong, and the persistence of sediment yield time series increased with the increase in microrelief. The soil we used was characterized by lithologic soil and was regarded as a typical erodible soil, as was confirmed by Chen et al. (2015). The sediment loss increased gradually with the increase in rainfall duration. With the development of water erosion, greater erosion was occurred on rougher surface, especially for the RT slope. Wavelet analysis satisfactorily interpreted the multi-time scale structures of runoff and sediment yield. Furthermore, R/S analysis could detect the persistence features of runoff and sediment yield. This study confirmed the validities of wavelet and R/S analyses to reflect the temporal variation characteristics of runoff and sediment yield at hillslope scale. There were few studies that had explicitly tried to link the spatio-temporal changes in microtopography with those of runoff and sediment discharge. This study provided a new insight for clarifying the coupling relationships between microtopography changes and temporal evolution of soil erosion in sloping farmland.
values of RT slope were within in the range of 2.1924–3.9830, and the Dq ~ q curves of AD and RT slopes had typical S shapes. That indicated that the multifractal behaviours were gradually enhanced from CT, AD to RT. Meanwhile, the fractal information dimension Di values for the tillage practices were RT > AD > CT. These results demonstrated that RT had the highest spatial variability and the most complex spatial structure of microtopography. Many researches showed that microtopography with higher spatial variability can result in the shortest path of runoff and sediment, thus it can prevent soil erosion (Moreno et al., 2012; Zhang et al., 2015). As a result, RT slope should have the largest restraining effect on water erosion. However, RT may even accelerate soil erosion once ridge collapse according to Table 4. This phenomenon was confirmed by the relationship between Di and soil erosion. There was a certain range of Di critical values, which reflected the positive or negative effect on soil erosion at the centimetre scale. The spatial autocorrelation scales for different tillage practices were CT > AD > RT. The average codomains of CT, AD, and RT were 6.10, 5.32, and 4.01 m, respectively. That indicated that spatial continuity of microtopography was gradually reduced from CT, AD to RT and the complexity of the spatial variability of microtopography was gradually strengthened in turn. The microtopography combined with rainfall resulted in enhanced spatial variability from the SpE stage to the RE stage and reduced the spatial autocorrelation with the evolution of water erosion. At the RE stage, microtopography had the highest spatial heterogeneity structure and the lowest spatial dependence. The spatial variation of microtopography varied with the changes in slope steepness and rainfall intensity. Zhang et al. (2015) proposed that the spatial heterogeneity of microtopography at 15° slope was stronger than those of 10° and 20° slope gradients, while Luo et al. (2018b) indicated that the spatial variation of microtopography increased with the increase in slope gradients. Römkens et al. (2001) reported that decreasing rainfall sequence on a smooth surface caused more soil erosion than increasing rainfall sequence. In contrast, He et al. (2018) suggested that the increasing rainfall sequence was more likely to cause soil erosion. This could be attributed to the differences in initial roughness and soil texture. The current research studied the spatial heterogeneity of microtopography under a rainfall intensity of 1.5 mm min−1 on a 20° slope. Thus, further study should investigate the variability of microtopography under different slope gradients or rainfall intensities. 4.2. Effects of microtopography on temporal variations of runoff and sediment yield
5. Conclusions
According to Fig. 6, the dominant runoff periodicities were 14, 13 and 12 min for the CT, AD, and RT slopes, respectively. In general, the dominant period of runoff tended to decrease and the runoff turbulence tended to increase with the increase in microrelief. Especially for RT slope, the strong oscillation of signal occurred within 40–45 min, which might be related to the sudden change of microtopography. Combined
Three tilled slopes: conventional tillage (CT), artificial digging (AD), and ridge tillage (RT) had strong or medium spatial autocorrelations during water erosion processes. The fractal information dimensions of tillage practices at various erosion stages were RT > AD > CT. At the 10
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same time, we used the directional derivatives to describe the spatial distribution of microtopography in term of microrelief morphology. There was a certain range of Di critical values, which reflected the positive or negative effect on soil erosion at hillslope scale. During water erosion processes, the time series of runoff and sediment yield of tillage practices had long-range persistence, and Morlet wavelet analysis indicated that there were 12–16 min dominant periods in the time series of runoff and sediment yield. Microtopography remarkably influenced the temporal evolution of soil erosion. The higher microrelief led to the shorter dominant period and weaker the persistence of runoff, while the temporal variation in sediment yield was opposite to that of runoff.
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Declaration of interest statement The authors declare that they have no known competing interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This study was supported by the National Natural Science Foundation of China (Grant No. 41271307 and 40901138) and the Key R & D Project of Sichuan Province (Grant No. 2019YFS0463). References Bullard, J.E., Ockelford, A., Strong, C.L., Aubault, H., 2018. Impact of multi-day rainfall events on surface roughness and physical crusting of very fine soils. Geoderma 313, 181–192. https://doi.org/10.1016/j.geoderma.2017.10.038. Chen, X.Y., Huang, Y.H., Zhao, Y., Mo, B., Mi, H.X., 2015. Comparison of loess and purple rill erosions measured with volume replacement method. J. Hydrol. 530, 476–483. https://doi.org/10.1016/j.jhydrol.2015.10.001. Cogo, N.P., Moldenhauer, W.C., Foster, G.R., 1984. Soil loss reductions from conservation tillage practices. Soil Sci. Soc. Am. J. 48 (2), 368–373. https://doi.org/10.2136/ sssaj1984.03615995004800020029x. Darboux, F., Davy, P., Gascuel-Odoux, C., Huang, C., 2002. Evolution of soil surface roughness and flowpath connectivity in overland flow experiments. Catena 46, 125–139. https://doi.org/10.1016/S0341-8162(01)00162-X. Ding, W., Huang, C., 2017. Effects of soil surface roughness on interrill erosion processes and sediment particle size distribution. Geomorphology 295, 801–810. https://doi. org/10.1016/j.geomorph.2017.08.033. Ferreiro, J.P., Vázquez, E.V., 2010. Multifractal analysis of Hg pore size distributions in soils with contrasting structural stability. Geoderma 160 (1), 64–73. https://doi.org/ 10.1016/j.geoderma.2009.11.019. Gómez, J.A., Nearing, M.A., 2005. Runoff and sediment losses from rough and smooth soil surfaces in a laboratory experiment. Catena 59 (3), 253–266. https://doi.org/10. 1016/j.catena.2004.09.008. Govers, G., Takken, I., Helming, K., 2000. Soil roughness and overland flow. Agronomie 20, 131–146. https://doi.org/10.1051/agro:2000114. He, J., Li, X., Jia, L., Gong, H., Cai, Q., 2014. Experimental study of rill evolution processes and relationships between runoff and erosion on clay loam and loess. Soil Sci. Soc. Am. J. 78 (5), 1716–1725. https://doi.org/10.2136/sssaj2014.02.0063. He, S., Qin, F., Zheng, Z., Li, T., 2018. Changes of soil microrelief and its effect on soil erosion under different rainfall patterns in a laboratory experiment. Catena 162, 203–215. https://doi.org/10.1016/j.catena.2017.11.010. Jia, T.B., Wu, F.Q., Zhao, L.S., Wang, L.H., 2013. Micro-relief slope surface complexity characteristics of sloping farm land under different tillage practices. J. Soil Water Conserv. 27 (4), 152–156. https://doi.org/10.13870/j.cnki.stbcxb.2013.04.039. Karmakar, S., Goswami, S., Chattopadhyay, S., 2019. Exploring the pre-and summermonsoon surface air temperature over eastern India using Shannon entropy and temporal Hurst exponents through rescaled range analysis. Atmos. Res. 217, 57–62. https://doi.org/10.1016/j.atmosres.2018.10.007. Labat, D., 2005. Recent advances in wavelet analyses: Part 1. A review of concepts. J. Hydrol. 314 (1–4), 275–288. https://doi.org/10.1016/j.jhydrol.2005.04.003. Long, H.L., Heilig, G.K., Wang, J., Li, X.B., Luo, M., Wu, X.Q., Zhang, M., 2006. Land use
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