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Temporal variations in runoff and sediment yield associated with soil surface roughness under different rainfall patterns
Journal Pre-proof Temporal variations in runoff and sediment yield associated with soil surface roughness under different rainfall patterns Jian Luo, Zicheng Zheng, Tingxuan Li, Shuqin He
PII:
S0169-555X(19)30406-4
DOI:
https://doi.org/10.1016/j.geomorph.2019.106915
Reference:
GEOMOR 106915
To appear in: Received Date:
26 August 2019
Revised Date:
17 October 2019
Accepted Date:
17 October 2019
Please cite this article as: Luo J, Zheng Z, Li T, He S, Temporal variations in runoff and sediment yield associated with soil surface roughness under different rainfall patterns, Geomorphology (2019), doi: https://doi.org/10.1016/j.geomorph.2019.106915
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Temporal variations in runoff and sediment yield associated with soil surface roughness under different rainfall patterns Jian Luo1, Zicheng Zheng1*, Tingxuan Li1, Shuqin He2 1
College of Resources Science, Sichuan Agricultural University, 211 Huimin Road,
Chengdu, Sichuan 611130, China 2
College of Forestry, Sichuan Agricultural University, 211 Huimin Road, Chengdu,
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Sichuan 611130, China *Corresponding author:
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Tel.: +86-86291371; Fax: +86-86290986 E-mail: [email protected]
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Road, Chengdu, Sichuan 611130, China
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Address: College of Resources Science, Sichuan Agricultural University, 211 Huimin
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Highlights
The temporal changes of runoff and sediment yield were obtained
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from wavelet analysis.
Increased rainfall series was more likely to cause soil erosion.
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The relationships between SSR and runoff, sediment yield could be well described by the parabolic equation.
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ABSTRACT Soil surface roughness (SSR) is one of the topographic factors affecting soil erosion. Currently, temporal variation characteristics of runoff and sediment yield of SSR is still unknown. In this study, ridge tillage (RT) and linear slope (CK) were used to simulate different SSR. Artificial rainfall experiments including increased and decreased rainfall series were conducted in two runoff plots on a slope gradient of 15°. The rainfall
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intensities were 1.0, 1.5 and 2.0 mm min-1 and the rainfall duration were 60, 40 and 30
min, respectively. A method combining of the pin meter and photography was used to
measure micro-topographic changes before and after each run. The results showed that
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the SSR values of RT ranged from 175.94 mm to 181.50 mm and SSR values of CK
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ranged from 75.66 mm to 79.80 mm. The temporal variations of runoff and sediment yield associated with soil surface roughness had positive long-range correlation and
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varied periodically every 9-16 min under different rainfall patterns. There was a critical
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value on the spatial heterogeneity of SSR that affecting soil erosion. SSR reduced the frequency of periodic oscillations of runoff and sediment yield, and then reduced the
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turbulence of runoff and sediment yield during the rainfall, which had good effect of soil and water conservation. When SSR exceeded the certain critical condition, SSR
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served as the source of erosion by increasing the periodic oscillation energy, increased the turbulence of runoff and sediment yield, which led to a large amount of soil and water loss. The findings will help elucidate soil erosion mechanisms in sloping farmland and provide a new insight for understanding of temporal variations in runoff and sediment yield. 2
Keywords: Soil surface roughness; Temporal sequences analysis; Soil erosion; Rainfall pattern
1. Introduction Soil erosion is one of the most concerning environmental problems worldwide (GarciaRuiz et al., 2015; Panagos et al., 2015; Kołodyńska-Gawrysiak et al., 2018). Chinese
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purple soil region suffer from severe soil erosion and significant erosion usually occurs on the tilled slope (Stolte et al., 2009; Wang et al., 2019). On the tilled slopes, due to
the impact of human management and tillage methods, soil surface roughness (SSR)
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describes the small-scale elevation changes in less than 0.05-0.25m (Zhang et al., 2015). SSR will affect the yield of sediment through its influence on the generation, discharge,
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and velocity of runoff, and amount of excavation and filling during the course of the
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soil erosion processes (Kirkby, 2002; Planchon and Darboux, 2002; Darboux et al., 2002; Appels et al., 2011; Morbidelli et al., 2015; Ding and Huang, 2017). Because of
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the random nature of SSR and of the processes involved, the relationship between SSR and soil erosion have produced inconsistent results (Zobeck and Onstad, 1987;
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Römkens et al., 2002; Gómez and Nearing, 2005; Luo et al., 2018a). Quantification of
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spatial variability of SSR is essential to understand the relationship between SSR and soil erosion (He et al., 2018). Several previous studies have applied the SSR index to quantify soil surface microrelief. They found that rougher SSR can reduce soil erosion (Zheng et al., 2014; Vermang et al., 2015). However, Helming et al. (1998) noted that rougher SSR can also increase soil erosion. The result was in accordance with that reported by Römkens et al. (2002). Many studies have pointed out that the SSR index 3
can be utilized to forecast surface runoff and sediment yield (Idowu et al., 2002; He et al., 2018). Luo et al. (2018a) quantified the influence of SSR on soil erosion by using a multifractal approach, the result showed that SSR can increase or decrease soil erosion simultaneously during rainfall. The difference of the above results was due to the lack of appropriate quantitative information about the spatial heterogeneity of SSR and the dynamic interactions of SSR and soil erosion, which is also the main limitation of SSR
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research.
The formation and evolution of water erosion at micro-topographic scale not only
characterized by randomness nature, but also highly non-linear and time-variability
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(Luo et al., 2019). The spatial-temporal evolution of runoff and sediment on slopes is
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the result of the interaction of rainfall and underlying surface factors, and the process is very complicated. The temporal variation of runoff and sediment is not only a
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descriptor that reflects how the erosive agents behave against SSR (Zhang et al., 2017),
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but also a potential index to distinguish different soil surface microrelief. Substantial research investigated the relationship between SSR and soil erosion; however, these
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studies do not adequately convey the occurrence of localised bursts and intermittent time structures in runoff and sediment yield resulted from a spatial and dynamical
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heterogeneity of SSR. Understanding the temporal variation characteristics of runoff and sediment yield of SSR not only can contribute a time-scale representation to reveal the interactions between SSR and soil erosion, but also provide a theoretical guidance for prevention and control of soil and water loss in sloping farmland. Wavelet analysis can distinguish and classify different sequence processes in time series, and identify the 4
principal cycle hidden in the temporal sequence (Labat, 2005). Thus, the multiresolution characteristics of wavelet analysis make it very suitable for dealing with the temporal variation of runoff and sediment yield. Tian et al. (2019) distinguished the temporal variation features of runoff and sediment load in the upper Yellow River based on wavelet analysis. They found the low-frequency periodicities of runoffs increased with the decrease in high-frequency periodicities. Gaucherel (2002) found new
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periodicities on flow curves of remote watersheds using wavelet analysis. In the fields of earth science and hydrology, the feasibility and applicability of using wavelet
analysis to study complex and nonlinear systems with multi-time scale variation
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characteristics have been demonstrated in many studies (Kalbermatten et al., 2012;
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Mount et al., 2013; Kumar et al., 2015; Feng et al., 2015; Pathak et al., 2016). Ridge tillage has been widely used in the hilly region of China with purple soil
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because of its good effect of soil and water conservation (Luo et al., 2017). Generally
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speaking, it can collect rainwater, increase rainwater infiltration, and reduce surface runoff and soil erosion under a ridge-furrow system (Zhang et al., 2014). However, in
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the process of controlling soil and water loss, its water accumulation can also make the ridge collapse with the increase in accumulated rainfall, and its induced seepage can
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accelerate soil erosion on the ridge surface, thereby weakening the water and soil conservation function of the ridge tillage (Liu et al., 2014; Liu et al., 2015). The difference of the above results may be related to the spatial heterogeneity of SSR of ridge tillage slope during the evolution of water erosion. Rainfall pattern refers to the combination of different rainfall intensities varying with the rainfall duration in the 5
process of an individual rainfall event. It is one of the main rainfall parameters affecting soil erosion (Zheng et al., 2016). Two rainfall events with the same or similar rainfall amount have different combinations of rainfall intensities, i.e. rainfall patterns, which have different effects on soil erosion (Wen et al., 2012; He et al., 2018). Zheng et al. (2016) found soil loss of peak rainfall pattern was higher than those of decreased and increased rainfall patterns in Chinese black soil region.
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The specific objectives of present research were to: (1) clarify the spatial variation
of SSR during rainfall, (2) quantify the relationship between SSR and soil erosion, and (3) assess the effects of SSR on temporal variations in runoff and sediment yield under
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different rainfall patterns.
2.1 Experimental soil and soil box
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2. Materials and methods
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The top soil was collected from a sloping land in Ziyang (104° 34' E, 30° 05' N),
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Sichuan Province. The site has a subtropical monsoon climate with an annual precipitation of 980 mm. The study area is a typical purple soil region, and the soil used
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in this study is Entisol (Soil Survey Staff, 2003). The physical and chemical properties of the soil are listed in Table 1. The samples were dried, crushed and passed through a
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10 mm sieve before they were filled layer by layer evenly into the soil box. The bulk density of the soil layers in the soil box was 1.2 g cm-3. The soil box (2.0 m × 1.0 m × 0.5 m) is a portable with an adjustable slope surface (0-25°), V-shape gutter at the foot of the soil box was used to collect runoff and sediment yield.
2.2 Research design 6
After preparation of the soil boxes, ridge tillage (RT) and linear slope (CK) were used to simulate two types of soil surface micro-reliefs (rough vs. smooth). According to the local ridge size with a ridge height of 15 cm and a ridge distance of 40 cm, RT was constructed in the soil box. CK was a relatively flat slope. The rainfall simulator was equipped with two spray nozzles and installed at a height of 6 m that produced raindrops with a mean diameter of 2.50 ± 0.25 mm, which was similar to natural rainfall. In this
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study, two representative erosive rainfall patterns of the increased rainfall series and the decreased rainfall series were conducted in this study. Under the condition of increased rainfall series, a simulation experiment was carried out to apply consecutive artificial
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rainfall with slope gradient at 15° and rainfall intensity at 1.0, 1.5, 2.0 mm min -1
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respectively in 1st, 2nd and 3rd rainfall event. Under the condition of decreased rainfall series, a simulation experiment was carried out to apply consecutive artificial rainfall
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with slope gradient at 15° and rainfall intensity at 2.0, 1.5, 1.0 mm min-1 respectively
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in 1st, 2nd and 3rd rainfall event. The rainfall duration was in accordance with rainfall intensities to keep the total amount of rainfall (60 mm) consistency. For 1.0, 1.5 and 2.0
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mm min-1 rainfall intensity, the rainfall duration were 60, 40 and 30 min, respectively.
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2.3 Experimental measurements 2.3.1 Digital elevation model (DEM) construction and soil roughness analysis This work used a method combining of the pin meter and photography to measure soil surface elevation. Detailed explanations of the measurement procedure have been provided by Luo et al. (2017). Spatial alignment and kriging interpolation were performed to process the surface elevation points, and a micro-topography digital 7
elevation model (M-DEM) of high resolution was generated. Meanwhile, the SSR index was calculated (Luo et al., 2018b): SSR 100 log S
(1)
Where S is the standard deviation of the total surface elevations over an area of 2.0 m2.
2.3.2 Runoff and sediment yield
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At various stages of rainfall events, runoff samples were collected at the downslope outlet of the soil box at 3 min intervals as soon as it had passed from the outlet. The runoff samples were measured using a measuring cylinder. After the upper clear fluid
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was separated, the rest soil sample was put into an oven (at 105℃) to be dried and weighted again for calculation of the sediment yield (He et al., 2014).
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2.4 Wavelet analysis
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The selection of the wavelet type is an essential part of wavelet analysis. The Morlet wavelet has the characteristics of oscillation, rapid decay and good time-frequency
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localization and has been widely applied to reveal periodic features of hydrological processes (Tian et al, 2019). Thus, in this study, the Morlet wavelet was used to
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determine the temporal variations in runoff and sediment yield. Morlet wavelet is a continuous complex wavelet, which defined as:
(t ) ei t et
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0
2
/2
(2)
The fourier transform of Morlet wavelet is as follows:
ˆ ( ) 2 e
( 0 )2 2
(3)
where ω is frequency, ω0 is wavelet central frequency; i is imaginary number; φ(t) is Morlet mother wavelet, ˆ ( ) is the fourier transform of Morlet mother wavelet. 8
For a given Morlet wavelet and hydrological time series f(t), its continuous wavelet transform is defined as:
W f ( a, b)
1 t b ˆ f ( t ) ( )dt a a
(4)
where Wf (a, b) is the wavelet coefficient; ˆ is the complex conjugation of φ; a is the scale factor, which reflects the periodic length of wavelet. b is the time factor, which reflects the translation of time.
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With the change of parameters a and b, a two-dimensional contour map of wavelet coefficients with b as abscissa and a as ordinate can be drawn, which is called wavelet
transform coefficient map. Wavelet transform coefficients can be used to obtain the
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characteristics of time series variation.
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2.5 Rescaled range analysis
Rescaled range analysis can judge the fractal characteristics and long-range correlation
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of time series, distinguish random and non-random systems, and determine the persistence and intensity of trend. For time series {p(t)} with N observations, the time
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series can be equally divided into A continuous subintervals Ia (a=1, 2, …, A) with element pk, a (k = 1, 2, ..., n; 2 ≤ n ＜ L). L is the length of the maximum subinterval.
1 n pk ,a n i 1
(5)
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ea
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The average value ea of Ia time series is as follows:
For each subinterval Ia, SIa is the standard deviation, {xk, a} is the cumulative mean
deviation sequence, and RIa is the range. The calculation formulas are as follows: SIa
1 n ( pk ,a ea )2 n k 1
(6)
k
xk , a ( pk , a ea )
(7)
i 1
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RIa max( xk ,a ) min( xk ,a )
(8)
The R/S statistic - (R/S)n ca be calculated as follows: ( R / S )n
1 A ( RIa / SIa ) A a 1
(9)
Different sub-interval lengths n (i.e. different time scales) correspond to different average R/S statistic. There is a linear relationship between lg(R/S)n and lgn: lg( R / S ) n lg H lg n
(10)
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The scatter plot of lg(R/S)n - lgn was made, and the straight line was fitted by least squares estimation. The slope of the straight line is Hurst exponent H. Hurst exponent is the core parameter describing the long-range correlation of the time sequence, and
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is a constant, which characterizes the inherent characteristics of the system.
Furthermore, the autocorrelation function B and the fractal dimension D can be
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estimated as follows:
D=2-H, D∈[1,2]
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B= 22H-1-1, B∈[-0.5, 1]
(11) (12)
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H can reveal the trend components in the temporal sequence, and can judge the strength of trend components according to the size of H. The autocorrelation function
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B can be used to examine whether the time series is independent, and the fractal dimension D can be used to determine whether the time series is random. When H =
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0.5, B = 0, and D = 1.5, the time series are independent and identically distributed random series, that is, the current trends of runoff and sediment yield have no impact on the future. When 0 ≤ H ＜ 0.5, -0.5 ≤ B < 0 and 1.5 ＜ D ≤ 2, there is a negative correlation between the past increment and the future increment. When 0.5 ≤ H ＜ 1, 0 ≤ B < 1 and 1 ＜ D ≤ 1.5, the time series has a long-range dependence, and there is a positive correlation between the past increment and the future increment (Zhang et al., 10
2016). The closer H is to 1, the stronger the persistence of the temporal sequence. 2.6 Data processing The statistical analyses were conducted using SPSS 22.0. Graphical works were accomplished by Origin 9.0. We used Matlab R2017b software for wavelet analysis.
3. Results 3.1 Characterizing the SSR
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3.1.1 Changes in DEM
For the RT slope under increased rainfall series, the soil surface micro-topography did
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not change significantly during the 1st rainfall event (1.0 mm min-1), while the
depressions were formed on the CK slope (Fig. 1). With the increase of cumulative
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rainfall, one rill formed on the RT slope and three rills formed on the CK slope after the
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2nd rainfall event (1.5 mm min-1). In the 3rd rainfall event (2.0 mm·min-1), the rill formed on the RT slope trended to widen and deepen, and the rill head extended to the furrow.
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While for the CK slope, rills only showed a trend of deepening and widening. Under the condition of decreased rainfall series, one intermittent rill was formed
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on the lower part of the RT slope, while rills were formed on the CK slope during the
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1st rainfall event (2.0 mm·min−1). In the 2nd rainfall event (1.5 mm·min−1), rills formed on lower part of the RT slope and these rills had not changed significantly after the 3rd rainfall event (1.0 mm·min−1). While for the CK slope, the soil surface microtopography changed slightly during the 2nd and 3rd rainfall events. According to Fig. 2, the range of surface elevation change of RT slope showed an increasing first and then decreasing trend with the evolution of slope erosion under 11
different rainfall patterns. During the whole rainfall processes, the variation of surface elevation mainly distributed in the ranges of -20-0 mm and 0-20 mm, accounting for 69.28% to 97.46% of the experimental plot area. Under the condition of increased rainfall series, the ratio of SSR decay were 64.39%, 54.65%, and 60.74% for respectively the 1st, 2nd and 3rd rainfall event. Under the condition of decreased rainfall series, the ratio of SSR decay were 59.08%, 49.71%, and 65.08% for respectively the
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1st, 2nd and 3rd rainfall event. And for the CK slope, the variation of surface elevation
mainly distributed in the range of -5-0 mm during the whole rainfall processes (Fig. 2). Under the condition of increased rainfall series, the ratio of SSR decay were 48.56%,
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45.28%, and 63.14% for respectively the 1st, 2nd and 3rd rainfall event. Under the
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condition of decreased rainfall series, the ratio of SSR decay were 38.59%, 36.59%, and 35.12% for respectively the 1st, 2nd and 3rd rainfall event. It could be seen that soil
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3.1.2 Changes in SSR index
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erosion area of increased rainfall series was higher than that of decreased rainfall series.
According to Fig. 3, for the RT slope under increased rainfall series, the SSR values
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increased gradually with the development of slope erosion and the SSR values ranged
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from 176.77 mm to 181.50 mm. While under the condition of decreased rainfall series, the SSR values showed an increasing first and then decreasing trend with the increase of accumulated rainfall and the SSR values ranged from 175.94 mm to 180.77 mm. The SSR values of different slope positions showed the same trend under different rainfall patterns, that is, the upper slope > the lower slope > the middle slope. For the CK slope under increased rainfall series, the SSR values increased 12
gradually with the evolution of soil erosion and the SSR values ranged from 75.66 mm to 79.31 mm. While under the condition of decreased rainfall series, the SSR values showed an increasing first and then decreasing trend with the increase of accumulated rainfall and the SSR values ranged from 77.67 mm to 79.80 mm. And the SSR of different slope positions had obvious spatial variability. The SSR value of RT slope was
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higher than that of CK slope.
3.2 Characterizing the runoff and sediment yield
According to Fig. 4, for the RT slope under the condition of increased rainfall series,
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initial rainfall mainly entered the soil by infiltration, runoff and sediment yield
increased with the increase of soil water content in the 1st rainfall event (1.0 mm·min−1).
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In the 2nd rainfall event (1.5 mm·min−1), the occurrence of ridge collapse made the
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runoff and sediment yield increased sharply and peaked at 85 min. With the increase of rainfall intensity and cumulative rainfall (2.0 mm·min−1), the variation of runoff and
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sediment yield was quite different. In the later stage of rainfall, the runoff and sediment yield tended to be stable due to the surface micro-topography changed slightly. Under
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the condition of decreased rainfall series, the variation trend of surface runoff and
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sediment yield showed bimodal curves during the rainfall. In the 1st rainfall event (2.0 mm·min−1), the surface runoff increased gradually in 0-25 min, while the change of sediment yield was relatively stable. At 25 min, the formation of rill made the runoff and sediment yield reached their first peak values, and then gradually decreased. In the 2nd rainfall event (1.5 mm·min−1), the change of sediment yield was not obvious at the initial stage of rainfall because of soil crust. With the increase of cumulative rainfall, 13
runoff and sediment yield increased gradually, and ridge collapse occurred in 62 min, which led to reach their second peak values. In the 3rd rainfall event (1.0 mm·min−1), surface runoff fluctuated greatly, while the change of sediment yield was relatively stable. For the CK slope under the condition of increased rainfall series, surface runoff and sediment yield were relatively low in the 1st rainfall event (1.0 mm·min−1), and
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surface runoff and sediment yield increased sharply during the following 2 rainfall
events (1.5 mm·min−1, 2.0 mm·min−1). While under the condition of decreased rainfall
series, surface runoff and sediment yield decreased gradually with the decrease of
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rainfall intensities during various rainfall stages. Increased rainfall series was more
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likely to cause soil erosion. Increased rainfall pattern is similar to the main erosive rainfall pattern in summer in purple soil region of China, which is the main rainfall
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pattern for soil erosion prevention and control in the study area.
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3.3 Periodic features in runoff and sediment yield The periodic behaviors of runoff and sediment yield were obtained from Morlet wavelet
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analysis. Fig. 5 shows the real parts of the wavelet coefficient of runoff and sediment
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yield under different rainfall patterns. The magnitudes (positive or negative) of the real part of the wavelet coefficient in the contour maps reflect the more-than-normal period or less-than-normal period within the rainfall duration. It is easy to locate the dominant periods of runoff based on the structure of the peaks and troughs of the real part of the wavelet at different time scales. For the RT slope under increased rainfall series, the oscillation centers of the 14
wavelet coefficients of surface runoff were mainly distributed in 11 min. The dominant period of runoff was 11 min, moreover, the volatility of the runoff was obvious in the range of 50-120 min. Under the condition of decreased rainfall series, the oscillation centers of the wavelet coefficients of surface runoff were mainly distributed in 16 min, and the volatility of the runoff was obvious in the range of 0-100 min. The variation of sediment yield was basically consistent with runoff under different rainfall patterns.
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For the CK slope under increased rainfall series, the oscillation centers of the
wavelet coefficients of surface runoff were mainly distributed in 9-16 min, thus we can
preliminarily infer that there may be 9-16 min dominant periods of runoff. Under the
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condition of decreased rainfall series, the oscillation centers of the wavelet coefficients
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of surface runoff were mainly distributed in 15-16 min, and the volatility of the runoff was obvious in the range of 0-80 min. The variation of sediment yield were basically
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consistent with runoff under different rainfall patterns. The runoff and sediment yield
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of SSR varied periodically every 9-16 min under different rainfall patterns. On the CK slope, there were multiple dominant periods of runoff and sediment yield, while for the
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RT slope, there was only one dominant period of runoff and sediment yield which was
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closely related to the ridge collapse.
4. Discussion
4.1 The relationship between SSR and soil erosion Compared with the CK slope, the RT slope showed different changes in surface microtopography and sediment transport characteristics due to the existence of ridge-furrow system (Liu et al., 2014). On the RT slope, surface runoff and sediment yield were 15
collected in furrows with the increase of the accumulated rainfall at the early stage of rainfall. The ridge collapse occurred when rainwater volume exceeded the storage capacity of furrows, ridge as the "source" accompanied by strong retrogressive erosion made a large amount of sediment flow out of the experimental plot (Luo et al., 2017). It could be seen that the ridge tillage has good soil and water conservation effect at the early stage of rainfall, however, the effect gradually weakened as the rainfall continued,
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and even increased soil erosion. According to Table 2, compared with the CK slope,
the runoff on the RT slope decreased by 45.32% and 32.85% respectively in the
increased and decreased rainfall series, however, the sediment yield increased by 94.04%
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and 160.11% respectively in the increased and decreased rainfall series. For the
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different tillage practices, the increased rainfall series was more likely to cause soil erosion compared with the decreased rainfall series.
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SSR is an index that describing the distribution and fluctuation of surface soil,
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which has spatial dependence characteristics (Zhao et al., 2018; Zhang et al., 2019a). In this study, the SSR values on CK slope were relatively small during the rainfall, and
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the SSR values on different slope positions had obvious spatial variability, which might have been due to the SSR was mainly composed of random roughness caused by soil
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particles. Compared with the CK slope, RT slope is a horizontal tillage in the direction that is perpendicular to the slope, which changed the spatial distribution pattern of soil surface. It was intuitively shown that the elevation distribution of the RT slope was more discrete and the corresponding SSR values were higher. The variation trend of the SSR indexes of the entire slope were different with the increase of cumulative rainfall 16
under different rainfall conditions, which is mainly due to the difference of rainfall patterns (Luo et al., 2017; He et al., 2018). While the SSR indexes of different slope positions showed the same change trend under different rainfall conditions, that is, upper slope > lower slope > middle slope, which mainly due to the change of SSR was closely related to its spatial location. The response of SSR to rainfall and runoff erosion varied with the shape of surface micro-relief on different slope positions (Zhao et al.,
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2016).
It is generally accepted that the SSR has the effect of reducing soil erosion on the slope surface (Zobeck and Onstad, 1987; Vermang et al., 2015). However, other
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researchers showed that SSR not only can’t reduce the amount of soil erosion, but also
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can promote the occurrence of soil erosion on slope under certain hydrological conditions (Römkens et al., 2002; Luo et al., 2018a). In order to clarify the effect of
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SSR on soil erosion, the empirical relationships between runoff, sediment yield, and
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SSR were obtained through statistical analysis under different rainfall patterns. The results followed:
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MR = 0.0077R2 - 2.1027R + 163.07 MS = 0.0012R2 - 0.2467R + 14.51
r2 = 0.9214
n=12
(13)
r2 = 0.9142
n=12
(14)
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where MR is the runoff yield under different patterns (L m-2), MS is the sediment yield under different rainfall pattern (Kg m-2), R is the SSR index (mm), n is the sample number. According to Eqs. 13 and 14, the relationships between runoff, sediment yield and SSR can be described by parabolic curves, which implied that there was a critical value on the SSR that affecting soil erosion at hillslope scale. 17
4.2 Effects of SSR on temporal variations in runoff and sediment yield The development of hydrological processes at hillslope scale is greatly influenced by underlying surface conditions (Luo et al., 2017). In the past, many studies have explored the relationship between hydrological processes and topography (Vermang et al., 2015; Zhang et al., 2018; Zhang et al., 2019b). However, there are few researches focused on the effects of topography on hydrological temporal sequences, especially at micro-
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topographic scale, and the temporal variation characteristics of runoff and sediment yield was usually neglected in many famous process-based erosion models, such as the
Water Erosion Prediction Project (WEPP) (Nearing et al., 1989) and the European Soil
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Erosion Model (EUROSEM) (Morgan, 1994.). The influence of SSR on runoff and
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sediment yield time series was bound to be reflected in the curves of runoff and sediment yield. However, the phenomena were quite different between smooth and
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rough soil surfaces. According to Fig. 4 and Fig. 5, for the CK slope, there were multiple
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dominant periods of runoff and sediment yield under different rainfall patterns, while for the RT slope, there was only one dominant period of runoff and sediment yield
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which was closely related to the ridge collapse. Generally speaking, the less the change periods were, the more stable the change of runoff and sediment yield was (Zhang et
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al., 2017). Compared to the CK slope, RT slope had stronger soil and water conservation effect before ridge collapse. Once rill occurred, the periodic fluctuation of runoff and sediment yield increased, and the signal oscillation was the most severe when ridge collapse, which led to a large amount of soil and water loss. On the basis of wavelet analysis, we revealed periodic variations of runoff and 18
sediment yield, and the "persistence" characteristics of runoff and sediment yield was further analysed by using rescaled range (R/S) analysis. The two methods complemented each other and could describe the temporal variation characteristics of runoff and sediment yield comprehensively (Luo et al., 2019). R/S analysis is a time series analysis method based on fractal theory and the method is especially suitable for the analysis of long-range correlation of non-linear time series. The R/S analysis has
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been extensively applied in trend analysis of flood, annual runoff time series and
climate change (Hamed, 2007; Szolgayova et al., 2014; Shi et al., 2015). According to
Table 3, all R/S characteristic parameters of runoff and sediment yield are shown 0.5
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≤ H ＜ 1, 0< B≤1, and 1≤D < 1.5, which indicated that runoff and sediment yield
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of SSR exhibited behaviors of persistent fractional Brownian motion and positive longrange correlation under different rainfall patterns. For the RT slope, H∈[0.814, 0.847],
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H value approximated 1, while on the CK slope, H ∈ [0.607, 0.617], H value
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approximated 0.5, which indicated the persistence features of runoff and sediment yield time series on RT slope was stronger than that on CK slope. And the persistence features
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of runoff and sediment yield of increased rainfall series were higher than that of decreased rainfall series, which may be an important way to reveal that increased
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rainfall series was more likely to cause soil erosion. 5. Conclusions The temporal variation of runoff and sediment yield associated with SSR had positive long-range correlation and varied periodically every 9-16 min under different rainfall patterns. The SSR has a great effect on periodic phenomena of runoff and sediment 19
yield. On the CK slope, there were multiple dominant periods of runoff and sediment yield under different rainfall patterns, while for the RT slope, there was only one dominant period of runoff and sediment yield which was closely related to the ridge collapse. The persistence features of runoff and sediment yield time series of increased rainfall series were higher than that of decreased rainfall series. Increased rainfall series was more likely to cause soil erosion. The persistence features of runoff and sediment
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yield time series can be predicted by R/S analysis. Moreover, wavelet analysis satisfactorily represented the temporal variation characteristics of runoff and sediment yield. Therefore, a combination of the two methods is conducive to monitoring the
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impact of SSR on soil and water loss at hillslope scale.
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Declaration of Interest Statement
The authors declare that they have no known competing financial interests
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reported in this paper.
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or personal relationships that could have appeared to influence the work
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Acknowledgements
This study was supported by the National Natural Science Foundation of China (Grant
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28
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Fig. 1. Changes of soil surface micro-reliefs under different rainfall patterns. Note: i represents increased rainfall series, d represents decreased rainfall series, the numbers in parentheses represents serial number of rainfall events
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Fig. 2. Distribution proportion of elevation variation on RT and CK slopes under increased rainfall series (A) and decreased rainfall series (B)
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Fig. 3. Changes of soil roughness indexes in the entire slope (A) and different slope positions (B) on RT and CT slopes under different rainfall patterns
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Fig. 4. Changes of runoff and sediment yield rates on RT and CK slopes under increased rainfall series (A) and decreased rainfall series (B)
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Fig. 5. Time-frequency distribution of real part transformed with Morlet wavelet of runoff and sediment yield on RT and CK slopes under increased rainfall series (A) and decreased rainfall series (B)
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Table 1 Physical-chemical property of experimental soil Soil type
Bulk density
CEC
SOC
CaCO3
Sand
Silt
Clay
(g cm-3)
(cmol Kg-1)
(g Kg-1)
(%)
(%)
(%)
(%)
1.2
21
13
12
49
29
22
7.5
Texture
Clay loam
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Purple soil
pH
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Table 2 Total runoff and sediment yield under different rainfall patterns. Tillage practices
Rainfall patterns
Number of rainfall events
Rainfall intensity (mm min-1)
Total runoff (L m-2)
Sediment yield (Kg m-2)
RT
Increased rainfall series
1st rain 2nd rain 3rd rain Total 1st rain 2nd rain 3rd rain Total 1st rain 2nd rain 3rd rain Total 1st rain 2nd rain 3rd rain Total
1.0 1.5 2.0
1.11 30.51 45.80 77.42 22.18 34.30 33.36 89.84 38.59 50.30 52.69 141.58 40.41 51.84 41.54 133.79
0.0003 2.82 1.74 4.56 1.47 2.25 0.78 4.50 0.22 0.93 1.20 2.35 1.11 0.53 0.09 1.73
2.0 1.5 1.0
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na
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Decreased rainfall series
1.0 1.5 2.0
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Increased rainfall series
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CK
2.0 1.5 1.0
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Decreased rainfall series
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Table 3 R/S characteristic parameters of runoff and sediment yield on RT and CK slopes under different rainfall patterns
Runoff
Sediment yield
CK
Runoff
Autocorrelation Fractal coefficient B dimension D
0.847
0.239
1.214
0.814
0.371
1.333
0.841
0.308
1.214
0.822
0.413
1.464
0.614
0.248
1.289
0.607
0.312
1.296
0.614
0.296
1.323
0.617
0.221
1.247
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na
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Sediment yield
Increased rainfall series Decreased rainfall series Increased rainfall series Decreased rainfall series Increased rainfall series Decreased rainfall series Increased rainfall series Decreased rainfall series
Hurst index
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RT
Rainfall patterns
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Tillage Indexes practices
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PII:
S0169-555X(19)30406-4
DOI:
https://doi.org/10.1016/j.geomorph.2019.106915
Reference:
GEOMOR 106915
To appear in: Received Date:
26 August 2019
Revised Date:
17 October 2019
Accepted Date:
17 October 2019
Please cite this article as: Luo J, Zheng Z, Li T, He S, Temporal variations in runoff and sediment yield associated with soil surface roughness under different rainfall patterns, Geomorphology (2019), doi: https://doi.org/10.1016/j.geomorph.2019.106915
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Temporal variations in runoff and sediment yield associated with soil surface roughness under different rainfall patterns Jian Luo1, Zicheng Zheng1*, Tingxuan Li1, Shuqin He2 1
College of Resources Science, Sichuan Agricultural University, 211 Huimin Road,
Chengdu, Sichuan 611130, China 2
College of Forestry, Sichuan Agricultural University, 211 Huimin Road, Chengdu,
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Sichuan 611130, China *Corresponding author:
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Tel.: +86-86291371; Fax: +86-86290986 E-mail: [email protected]
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Road, Chengdu, Sichuan 611130, China
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Address: College of Resources Science, Sichuan Agricultural University, 211 Huimin
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Highlights
The temporal changes of runoff and sediment yield were obtained
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from wavelet analysis.
Increased rainfall series was more likely to cause soil erosion.
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The relationships between SSR and runoff, sediment yield could be well described by the parabolic equation.
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ABSTRACT Soil surface roughness (SSR) is one of the topographic factors affecting soil erosion. Currently, temporal variation characteristics of runoff and sediment yield of SSR is still unknown. In this study, ridge tillage (RT) and linear slope (CK) were used to simulate different SSR. Artificial rainfall experiments including increased and decreased rainfall series were conducted in two runoff plots on a slope gradient of 15°. The rainfall
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intensities were 1.0, 1.5 and 2.0 mm min-1 and the rainfall duration were 60, 40 and 30
min, respectively. A method combining of the pin meter and photography was used to
measure micro-topographic changes before and after each run. The results showed that
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the SSR values of RT ranged from 175.94 mm to 181.50 mm and SSR values of CK
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ranged from 75.66 mm to 79.80 mm. The temporal variations of runoff and sediment yield associated with soil surface roughness had positive long-range correlation and
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varied periodically every 9-16 min under different rainfall patterns. There was a critical
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value on the spatial heterogeneity of SSR that affecting soil erosion. SSR reduced the frequency of periodic oscillations of runoff and sediment yield, and then reduced the
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turbulence of runoff and sediment yield during the rainfall, which had good effect of soil and water conservation. When SSR exceeded the certain critical condition, SSR
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served as the source of erosion by increasing the periodic oscillation energy, increased the turbulence of runoff and sediment yield, which led to a large amount of soil and water loss. The findings will help elucidate soil erosion mechanisms in sloping farmland and provide a new insight for understanding of temporal variations in runoff and sediment yield. 2
Keywords: Soil surface roughness; Temporal sequences analysis; Soil erosion; Rainfall pattern
1. Introduction Soil erosion is one of the most concerning environmental problems worldwide (GarciaRuiz et al., 2015; Panagos et al., 2015; Kołodyńska-Gawrysiak et al., 2018). Chinese
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purple soil region suffer from severe soil erosion and significant erosion usually occurs on the tilled slope (Stolte et al., 2009; Wang et al., 2019). On the tilled slopes, due to
the impact of human management and tillage methods, soil surface roughness (SSR)
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describes the small-scale elevation changes in less than 0.05-0.25m (Zhang et al., 2015). SSR will affect the yield of sediment through its influence on the generation, discharge,
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and velocity of runoff, and amount of excavation and filling during the course of the
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soil erosion processes (Kirkby, 2002; Planchon and Darboux, 2002; Darboux et al., 2002; Appels et al., 2011; Morbidelli et al., 2015; Ding and Huang, 2017). Because of
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the random nature of SSR and of the processes involved, the relationship between SSR and soil erosion have produced inconsistent results (Zobeck and Onstad, 1987;
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Römkens et al., 2002; Gómez and Nearing, 2005; Luo et al., 2018a). Quantification of
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spatial variability of SSR is essential to understand the relationship between SSR and soil erosion (He et al., 2018). Several previous studies have applied the SSR index to quantify soil surface microrelief. They found that rougher SSR can reduce soil erosion (Zheng et al., 2014; Vermang et al., 2015). However, Helming et al. (1998) noted that rougher SSR can also increase soil erosion. The result was in accordance with that reported by Römkens et al. (2002). Many studies have pointed out that the SSR index 3
can be utilized to forecast surface runoff and sediment yield (Idowu et al., 2002; He et al., 2018). Luo et al. (2018a) quantified the influence of SSR on soil erosion by using a multifractal approach, the result showed that SSR can increase or decrease soil erosion simultaneously during rainfall. The difference of the above results was due to the lack of appropriate quantitative information about the spatial heterogeneity of SSR and the dynamic interactions of SSR and soil erosion, which is also the main limitation of SSR
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research.
The formation and evolution of water erosion at micro-topographic scale not only
characterized by randomness nature, but also highly non-linear and time-variability
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(Luo et al., 2019). The spatial-temporal evolution of runoff and sediment on slopes is
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the result of the interaction of rainfall and underlying surface factors, and the process is very complicated. The temporal variation of runoff and sediment is not only a
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descriptor that reflects how the erosive agents behave against SSR (Zhang et al., 2017),
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but also a potential index to distinguish different soil surface microrelief. Substantial research investigated the relationship between SSR and soil erosion; however, these
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studies do not adequately convey the occurrence of localised bursts and intermittent time structures in runoff and sediment yield resulted from a spatial and dynamical
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heterogeneity of SSR. Understanding the temporal variation characteristics of runoff and sediment yield of SSR not only can contribute a time-scale representation to reveal the interactions between SSR and soil erosion, but also provide a theoretical guidance for prevention and control of soil and water loss in sloping farmland. Wavelet analysis can distinguish and classify different sequence processes in time series, and identify the 4
principal cycle hidden in the temporal sequence (Labat, 2005). Thus, the multiresolution characteristics of wavelet analysis make it very suitable for dealing with the temporal variation of runoff and sediment yield. Tian et al. (2019) distinguished the temporal variation features of runoff and sediment load in the upper Yellow River based on wavelet analysis. They found the low-frequency periodicities of runoffs increased with the decrease in high-frequency periodicities. Gaucherel (2002) found new
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periodicities on flow curves of remote watersheds using wavelet analysis. In the fields of earth science and hydrology, the feasibility and applicability of using wavelet
analysis to study complex and nonlinear systems with multi-time scale variation
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characteristics have been demonstrated in many studies (Kalbermatten et al., 2012;
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Mount et al., 2013; Kumar et al., 2015; Feng et al., 2015; Pathak et al., 2016). Ridge tillage has been widely used in the hilly region of China with purple soil
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because of its good effect of soil and water conservation (Luo et al., 2017). Generally
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speaking, it can collect rainwater, increase rainwater infiltration, and reduce surface runoff and soil erosion under a ridge-furrow system (Zhang et al., 2014). However, in
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the process of controlling soil and water loss, its water accumulation can also make the ridge collapse with the increase in accumulated rainfall, and its induced seepage can
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accelerate soil erosion on the ridge surface, thereby weakening the water and soil conservation function of the ridge tillage (Liu et al., 2014; Liu et al., 2015). The difference of the above results may be related to the spatial heterogeneity of SSR of ridge tillage slope during the evolution of water erosion. Rainfall pattern refers to the combination of different rainfall intensities varying with the rainfall duration in the 5
process of an individual rainfall event. It is one of the main rainfall parameters affecting soil erosion (Zheng et al., 2016). Two rainfall events with the same or similar rainfall amount have different combinations of rainfall intensities, i.e. rainfall patterns, which have different effects on soil erosion (Wen et al., 2012; He et al., 2018). Zheng et al. (2016) found soil loss of peak rainfall pattern was higher than those of decreased and increased rainfall patterns in Chinese black soil region.
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The specific objectives of present research were to: (1) clarify the spatial variation
of SSR during rainfall, (2) quantify the relationship between SSR and soil erosion, and (3) assess the effects of SSR on temporal variations in runoff and sediment yield under
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different rainfall patterns.
2.1 Experimental soil and soil box
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2. Materials and methods
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The top soil was collected from a sloping land in Ziyang (104° 34' E, 30° 05' N),
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Sichuan Province. The site has a subtropical monsoon climate with an annual precipitation of 980 mm. The study area is a typical purple soil region, and the soil used
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in this study is Entisol (Soil Survey Staff, 2003). The physical and chemical properties of the soil are listed in Table 1. The samples were dried, crushed and passed through a
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10 mm sieve before they were filled layer by layer evenly into the soil box. The bulk density of the soil layers in the soil box was 1.2 g cm-3. The soil box (2.0 m × 1.0 m × 0.5 m) is a portable with an adjustable slope surface (0-25°), V-shape gutter at the foot of the soil box was used to collect runoff and sediment yield.
2.2 Research design 6
After preparation of the soil boxes, ridge tillage (RT) and linear slope (CK) were used to simulate two types of soil surface micro-reliefs (rough vs. smooth). According to the local ridge size with a ridge height of 15 cm and a ridge distance of 40 cm, RT was constructed in the soil box. CK was a relatively flat slope. The rainfall simulator was equipped with two spray nozzles and installed at a height of 6 m that produced raindrops with a mean diameter of 2.50 ± 0.25 mm, which was similar to natural rainfall. In this
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study, two representative erosive rainfall patterns of the increased rainfall series and the decreased rainfall series were conducted in this study. Under the condition of increased rainfall series, a simulation experiment was carried out to apply consecutive artificial
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rainfall with slope gradient at 15° and rainfall intensity at 1.0, 1.5, 2.0 mm min -1
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respectively in 1st, 2nd and 3rd rainfall event. Under the condition of decreased rainfall series, a simulation experiment was carried out to apply consecutive artificial rainfall
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with slope gradient at 15° and rainfall intensity at 2.0, 1.5, 1.0 mm min-1 respectively
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in 1st, 2nd and 3rd rainfall event. The rainfall duration was in accordance with rainfall intensities to keep the total amount of rainfall (60 mm) consistency. For 1.0, 1.5 and 2.0
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mm min-1 rainfall intensity, the rainfall duration were 60, 40 and 30 min, respectively.
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2.3 Experimental measurements 2.3.1 Digital elevation model (DEM) construction and soil roughness analysis This work used a method combining of the pin meter and photography to measure soil surface elevation. Detailed explanations of the measurement procedure have been provided by Luo et al. (2017). Spatial alignment and kriging interpolation were performed to process the surface elevation points, and a micro-topography digital 7
elevation model (M-DEM) of high resolution was generated. Meanwhile, the SSR index was calculated (Luo et al., 2018b): SSR 100 log S
(1)
Where S is the standard deviation of the total surface elevations over an area of 2.0 m2.
2.3.2 Runoff and sediment yield
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At various stages of rainfall events, runoff samples were collected at the downslope outlet of the soil box at 3 min intervals as soon as it had passed from the outlet. The runoff samples were measured using a measuring cylinder. After the upper clear fluid
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was separated, the rest soil sample was put into an oven (at 105℃) to be dried and weighted again for calculation of the sediment yield (He et al., 2014).
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2.4 Wavelet analysis
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The selection of the wavelet type is an essential part of wavelet analysis. The Morlet wavelet has the characteristics of oscillation, rapid decay and good time-frequency
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localization and has been widely applied to reveal periodic features of hydrological processes (Tian et al, 2019). Thus, in this study, the Morlet wavelet was used to
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determine the temporal variations in runoff and sediment yield. Morlet wavelet is a continuous complex wavelet, which defined as:
(t ) ei t et
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0
2
/2
(2)
The fourier transform of Morlet wavelet is as follows:
ˆ ( ) 2 e
( 0 )2 2
(3)
where ω is frequency, ω0 is wavelet central frequency; i is imaginary number; φ(t) is Morlet mother wavelet, ˆ ( ) is the fourier transform of Morlet mother wavelet. 8
For a given Morlet wavelet and hydrological time series f(t), its continuous wavelet transform is defined as:
W f ( a, b)
1 t b ˆ f ( t ) ( )dt a a
(4)
where Wf (a, b) is the wavelet coefficient; ˆ is the complex conjugation of φ; a is the scale factor, which reflects the periodic length of wavelet. b is the time factor, which reflects the translation of time.
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With the change of parameters a and b, a two-dimensional contour map of wavelet coefficients with b as abscissa and a as ordinate can be drawn, which is called wavelet
transform coefficient map. Wavelet transform coefficients can be used to obtain the
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characteristics of time series variation.
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2.5 Rescaled range analysis
Rescaled range analysis can judge the fractal characteristics and long-range correlation
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of time series, distinguish random and non-random systems, and determine the persistence and intensity of trend. For time series {p(t)} with N observations, the time
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series can be equally divided into A continuous subintervals Ia (a=1, 2, …, A) with element pk, a (k = 1, 2, ..., n; 2 ≤ n ＜ L). L is the length of the maximum subinterval.
1 n pk ,a n i 1
(5)
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ea
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The average value ea of Ia time series is as follows:
For each subinterval Ia, SIa is the standard deviation, {xk, a} is the cumulative mean
deviation sequence, and RIa is the range. The calculation formulas are as follows: SIa
1 n ( pk ,a ea )2 n k 1
(6)
k
xk , a ( pk , a ea )
(7)
i 1
9
RIa max( xk ,a ) min( xk ,a )
(8)
The R/S statistic - (R/S)n ca be calculated as follows: ( R / S )n
1 A ( RIa / SIa ) A a 1
(9)
Different sub-interval lengths n (i.e. different time scales) correspond to different average R/S statistic. There is a linear relationship between lg(R/S)n and lgn: lg( R / S ) n lg H lg n
(10)
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The scatter plot of lg(R/S)n - lgn was made, and the straight line was fitted by least squares estimation. The slope of the straight line is Hurst exponent H. Hurst exponent is the core parameter describing the long-range correlation of the time sequence, and
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is a constant, which characterizes the inherent characteristics of the system.
Furthermore, the autocorrelation function B and the fractal dimension D can be
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estimated as follows:
D=2-H, D∈[1,2]
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B= 22H-1-1, B∈[-0.5, 1]
(11) (12)
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H can reveal the trend components in the temporal sequence, and can judge the strength of trend components according to the size of H. The autocorrelation function
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B can be used to examine whether the time series is independent, and the fractal dimension D can be used to determine whether the time series is random. When H =
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0.5, B = 0, and D = 1.5, the time series are independent and identically distributed random series, that is, the current trends of runoff and sediment yield have no impact on the future. When 0 ≤ H ＜ 0.5, -0.5 ≤ B < 0 and 1.5 ＜ D ≤ 2, there is a negative correlation between the past increment and the future increment. When 0.5 ≤ H ＜ 1, 0 ≤ B < 1 and 1 ＜ D ≤ 1.5, the time series has a long-range dependence, and there is a positive correlation between the past increment and the future increment (Zhang et al., 10
2016). The closer H is to 1, the stronger the persistence of the temporal sequence. 2.6 Data processing The statistical analyses were conducted using SPSS 22.0. Graphical works were accomplished by Origin 9.0. We used Matlab R2017b software for wavelet analysis.
3. Results 3.1 Characterizing the SSR
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3.1.1 Changes in DEM
For the RT slope under increased rainfall series, the soil surface micro-topography did
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not change significantly during the 1st rainfall event (1.0 mm min-1), while the
depressions were formed on the CK slope (Fig. 1). With the increase of cumulative
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rainfall, one rill formed on the RT slope and three rills formed on the CK slope after the
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2nd rainfall event (1.5 mm min-1). In the 3rd rainfall event (2.0 mm·min-1), the rill formed on the RT slope trended to widen and deepen, and the rill head extended to the furrow.
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While for the CK slope, rills only showed a trend of deepening and widening. Under the condition of decreased rainfall series, one intermittent rill was formed
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on the lower part of the RT slope, while rills were formed on the CK slope during the
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1st rainfall event (2.0 mm·min−1). In the 2nd rainfall event (1.5 mm·min−1), rills formed on lower part of the RT slope and these rills had not changed significantly after the 3rd rainfall event (1.0 mm·min−1). While for the CK slope, the soil surface microtopography changed slightly during the 2nd and 3rd rainfall events. According to Fig. 2, the range of surface elevation change of RT slope showed an increasing first and then decreasing trend with the evolution of slope erosion under 11
different rainfall patterns. During the whole rainfall processes, the variation of surface elevation mainly distributed in the ranges of -20-0 mm and 0-20 mm, accounting for 69.28% to 97.46% of the experimental plot area. Under the condition of increased rainfall series, the ratio of SSR decay were 64.39%, 54.65%, and 60.74% for respectively the 1st, 2nd and 3rd rainfall event. Under the condition of decreased rainfall series, the ratio of SSR decay were 59.08%, 49.71%, and 65.08% for respectively the
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1st, 2nd and 3rd rainfall event. And for the CK slope, the variation of surface elevation
mainly distributed in the range of -5-0 mm during the whole rainfall processes (Fig. 2). Under the condition of increased rainfall series, the ratio of SSR decay were 48.56%,
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45.28%, and 63.14% for respectively the 1st, 2nd and 3rd rainfall event. Under the
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condition of decreased rainfall series, the ratio of SSR decay were 38.59%, 36.59%, and 35.12% for respectively the 1st, 2nd and 3rd rainfall event. It could be seen that soil
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3.1.2 Changes in SSR index
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erosion area of increased rainfall series was higher than that of decreased rainfall series.
According to Fig. 3, for the RT slope under increased rainfall series, the SSR values
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increased gradually with the development of slope erosion and the SSR values ranged
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from 176.77 mm to 181.50 mm. While under the condition of decreased rainfall series, the SSR values showed an increasing first and then decreasing trend with the increase of accumulated rainfall and the SSR values ranged from 175.94 mm to 180.77 mm. The SSR values of different slope positions showed the same trend under different rainfall patterns, that is, the upper slope > the lower slope > the middle slope. For the CK slope under increased rainfall series, the SSR values increased 12
gradually with the evolution of soil erosion and the SSR values ranged from 75.66 mm to 79.31 mm. While under the condition of decreased rainfall series, the SSR values showed an increasing first and then decreasing trend with the increase of accumulated rainfall and the SSR values ranged from 77.67 mm to 79.80 mm. And the SSR of different slope positions had obvious spatial variability. The SSR value of RT slope was
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higher than that of CK slope.
3.2 Characterizing the runoff and sediment yield
According to Fig. 4, for the RT slope under the condition of increased rainfall series,
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initial rainfall mainly entered the soil by infiltration, runoff and sediment yield
increased with the increase of soil water content in the 1st rainfall event (1.0 mm·min−1).
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In the 2nd rainfall event (1.5 mm·min−1), the occurrence of ridge collapse made the
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runoff and sediment yield increased sharply and peaked at 85 min. With the increase of rainfall intensity and cumulative rainfall (2.0 mm·min−1), the variation of runoff and
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sediment yield was quite different. In the later stage of rainfall, the runoff and sediment yield tended to be stable due to the surface micro-topography changed slightly. Under
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the condition of decreased rainfall series, the variation trend of surface runoff and
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sediment yield showed bimodal curves during the rainfall. In the 1st rainfall event (2.0 mm·min−1), the surface runoff increased gradually in 0-25 min, while the change of sediment yield was relatively stable. At 25 min, the formation of rill made the runoff and sediment yield reached their first peak values, and then gradually decreased. In the 2nd rainfall event (1.5 mm·min−1), the change of sediment yield was not obvious at the initial stage of rainfall because of soil crust. With the increase of cumulative rainfall, 13
runoff and sediment yield increased gradually, and ridge collapse occurred in 62 min, which led to reach their second peak values. In the 3rd rainfall event (1.0 mm·min−1), surface runoff fluctuated greatly, while the change of sediment yield was relatively stable. For the CK slope under the condition of increased rainfall series, surface runoff and sediment yield were relatively low in the 1st rainfall event (1.0 mm·min−1), and
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surface runoff and sediment yield increased sharply during the following 2 rainfall
events (1.5 mm·min−1, 2.0 mm·min−1). While under the condition of decreased rainfall
series, surface runoff and sediment yield decreased gradually with the decrease of
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rainfall intensities during various rainfall stages. Increased rainfall series was more
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likely to cause soil erosion. Increased rainfall pattern is similar to the main erosive rainfall pattern in summer in purple soil region of China, which is the main rainfall
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pattern for soil erosion prevention and control in the study area.
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3.3 Periodic features in runoff and sediment yield The periodic behaviors of runoff and sediment yield were obtained from Morlet wavelet
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analysis. Fig. 5 shows the real parts of the wavelet coefficient of runoff and sediment
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yield under different rainfall patterns. The magnitudes (positive or negative) of the real part of the wavelet coefficient in the contour maps reflect the more-than-normal period or less-than-normal period within the rainfall duration. It is easy to locate the dominant periods of runoff based on the structure of the peaks and troughs of the real part of the wavelet at different time scales. For the RT slope under increased rainfall series, the oscillation centers of the 14
wavelet coefficients of surface runoff were mainly distributed in 11 min. The dominant period of runoff was 11 min, moreover, the volatility of the runoff was obvious in the range of 50-120 min. Under the condition of decreased rainfall series, the oscillation centers of the wavelet coefficients of surface runoff were mainly distributed in 16 min, and the volatility of the runoff was obvious in the range of 0-100 min. The variation of sediment yield was basically consistent with runoff under different rainfall patterns.
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For the CK slope under increased rainfall series, the oscillation centers of the
wavelet coefficients of surface runoff were mainly distributed in 9-16 min, thus we can
preliminarily infer that there may be 9-16 min dominant periods of runoff. Under the
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condition of decreased rainfall series, the oscillation centers of the wavelet coefficients
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of surface runoff were mainly distributed in 15-16 min, and the volatility of the runoff was obvious in the range of 0-80 min. The variation of sediment yield were basically
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consistent with runoff under different rainfall patterns. The runoff and sediment yield
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of SSR varied periodically every 9-16 min under different rainfall patterns. On the CK slope, there were multiple dominant periods of runoff and sediment yield, while for the
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RT slope, there was only one dominant period of runoff and sediment yield which was
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closely related to the ridge collapse.
4. Discussion
4.1 The relationship between SSR and soil erosion Compared with the CK slope, the RT slope showed different changes in surface microtopography and sediment transport characteristics due to the existence of ridge-furrow system (Liu et al., 2014). On the RT slope, surface runoff and sediment yield were 15
collected in furrows with the increase of the accumulated rainfall at the early stage of rainfall. The ridge collapse occurred when rainwater volume exceeded the storage capacity of furrows, ridge as the "source" accompanied by strong retrogressive erosion made a large amount of sediment flow out of the experimental plot (Luo et al., 2017). It could be seen that the ridge tillage has good soil and water conservation effect at the early stage of rainfall, however, the effect gradually weakened as the rainfall continued,
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and even increased soil erosion. According to Table 2, compared with the CK slope,
the runoff on the RT slope decreased by 45.32% and 32.85% respectively in the
increased and decreased rainfall series, however, the sediment yield increased by 94.04%
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and 160.11% respectively in the increased and decreased rainfall series. For the
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different tillage practices, the increased rainfall series was more likely to cause soil erosion compared with the decreased rainfall series.
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SSR is an index that describing the distribution and fluctuation of surface soil,
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which has spatial dependence characteristics (Zhao et al., 2018; Zhang et al., 2019a). In this study, the SSR values on CK slope were relatively small during the rainfall, and
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the SSR values on different slope positions had obvious spatial variability, which might have been due to the SSR was mainly composed of random roughness caused by soil
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particles. Compared with the CK slope, RT slope is a horizontal tillage in the direction that is perpendicular to the slope, which changed the spatial distribution pattern of soil surface. It was intuitively shown that the elevation distribution of the RT slope was more discrete and the corresponding SSR values were higher. The variation trend of the SSR indexes of the entire slope were different with the increase of cumulative rainfall 16
under different rainfall conditions, which is mainly due to the difference of rainfall patterns (Luo et al., 2017; He et al., 2018). While the SSR indexes of different slope positions showed the same change trend under different rainfall conditions, that is, upper slope > lower slope > middle slope, which mainly due to the change of SSR was closely related to its spatial location. The response of SSR to rainfall and runoff erosion varied with the shape of surface micro-relief on different slope positions (Zhao et al.,
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2016).
It is generally accepted that the SSR has the effect of reducing soil erosion on the slope surface (Zobeck and Onstad, 1987; Vermang et al., 2015). However, other
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researchers showed that SSR not only can’t reduce the amount of soil erosion, but also
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can promote the occurrence of soil erosion on slope under certain hydrological conditions (Römkens et al., 2002; Luo et al., 2018a). In order to clarify the effect of
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SSR on soil erosion, the empirical relationships between runoff, sediment yield, and
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SSR were obtained through statistical analysis under different rainfall patterns. The results followed:
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MR = 0.0077R2 - 2.1027R + 163.07 MS = 0.0012R2 - 0.2467R + 14.51
r2 = 0.9214
n=12
(13)
r2 = 0.9142
n=12
(14)
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where MR is the runoff yield under different patterns (L m-2), MS is the sediment yield under different rainfall pattern (Kg m-2), R is the SSR index (mm), n is the sample number. According to Eqs. 13 and 14, the relationships between runoff, sediment yield and SSR can be described by parabolic curves, which implied that there was a critical value on the SSR that affecting soil erosion at hillslope scale. 17
4.2 Effects of SSR on temporal variations in runoff and sediment yield The development of hydrological processes at hillslope scale is greatly influenced by underlying surface conditions (Luo et al., 2017). In the past, many studies have explored the relationship between hydrological processes and topography (Vermang et al., 2015; Zhang et al., 2018; Zhang et al., 2019b). However, there are few researches focused on the effects of topography on hydrological temporal sequences, especially at micro-
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topographic scale, and the temporal variation characteristics of runoff and sediment yield was usually neglected in many famous process-based erosion models, such as the
Water Erosion Prediction Project (WEPP) (Nearing et al., 1989) and the European Soil
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Erosion Model (EUROSEM) (Morgan, 1994.). The influence of SSR on runoff and
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sediment yield time series was bound to be reflected in the curves of runoff and sediment yield. However, the phenomena were quite different between smooth and
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rough soil surfaces. According to Fig. 4 and Fig. 5, for the CK slope, there were multiple
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dominant periods of runoff and sediment yield under different rainfall patterns, while for the RT slope, there was only one dominant period of runoff and sediment yield
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which was closely related to the ridge collapse. Generally speaking, the less the change periods were, the more stable the change of runoff and sediment yield was (Zhang et
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al., 2017). Compared to the CK slope, RT slope had stronger soil and water conservation effect before ridge collapse. Once rill occurred, the periodic fluctuation of runoff and sediment yield increased, and the signal oscillation was the most severe when ridge collapse, which led to a large amount of soil and water loss. On the basis of wavelet analysis, we revealed periodic variations of runoff and 18
sediment yield, and the "persistence" characteristics of runoff and sediment yield was further analysed by using rescaled range (R/S) analysis. The two methods complemented each other and could describe the temporal variation characteristics of runoff and sediment yield comprehensively (Luo et al., 2019). R/S analysis is a time series analysis method based on fractal theory and the method is especially suitable for the analysis of long-range correlation of non-linear time series. The R/S analysis has
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been extensively applied in trend analysis of flood, annual runoff time series and
climate change (Hamed, 2007; Szolgayova et al., 2014; Shi et al., 2015). According to
Table 3, all R/S characteristic parameters of runoff and sediment yield are shown 0.5
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≤ H ＜ 1, 0< B≤1, and 1≤D < 1.5, which indicated that runoff and sediment yield
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of SSR exhibited behaviors of persistent fractional Brownian motion and positive longrange correlation under different rainfall patterns. For the RT slope, H∈[0.814, 0.847],
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H value approximated 1, while on the CK slope, H ∈ [0.607, 0.617], H value
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approximated 0.5, which indicated the persistence features of runoff and sediment yield time series on RT slope was stronger than that on CK slope. And the persistence features
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of runoff and sediment yield of increased rainfall series were higher than that of decreased rainfall series, which may be an important way to reveal that increased
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rainfall series was more likely to cause soil erosion. 5. Conclusions The temporal variation of runoff and sediment yield associated with SSR had positive long-range correlation and varied periodically every 9-16 min under different rainfall patterns. The SSR has a great effect on periodic phenomena of runoff and sediment 19
yield. On the CK slope, there were multiple dominant periods of runoff and sediment yield under different rainfall patterns, while for the RT slope, there was only one dominant period of runoff and sediment yield which was closely related to the ridge collapse. The persistence features of runoff and sediment yield time series of increased rainfall series were higher than that of decreased rainfall series. Increased rainfall series was more likely to cause soil erosion. The persistence features of runoff and sediment
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yield time series can be predicted by R/S analysis. Moreover, wavelet analysis satisfactorily represented the temporal variation characteristics of runoff and sediment yield. Therefore, a combination of the two methods is conducive to monitoring the
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impact of SSR on soil and water loss at hillslope scale.
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Declaration of Interest Statement
The authors declare that they have no known competing financial interests
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reported in this paper.
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or personal relationships that could have appeared to influence the work
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Acknowledgements
This study was supported by the National Natural Science Foundation of China (Grant
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Fig. 1. Changes of soil surface micro-reliefs under different rainfall patterns. Note: i represents increased rainfall series, d represents decreased rainfall series, the numbers in parentheses represents serial number of rainfall events
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Fig. 2. Distribution proportion of elevation variation on RT and CK slopes under increased rainfall series (A) and decreased rainfall series (B)
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Fig. 3. Changes of soil roughness indexes in the entire slope (A) and different slope positions (B) on RT and CT slopes under different rainfall patterns
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Fig. 4. Changes of runoff and sediment yield rates on RT and CK slopes under increased rainfall series (A) and decreased rainfall series (B)
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Fig. 5. Time-frequency distribution of real part transformed with Morlet wavelet of runoff and sediment yield on RT and CK slopes under increased rainfall series (A) and decreased rainfall series (B)
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Table 1 Physical-chemical property of experimental soil Soil type
Bulk density
CEC
SOC
CaCO3
Sand
Silt
Clay
(g cm-3)
(cmol Kg-1)
(g Kg-1)
(%)
(%)
(%)
(%)
1.2
21
13
12
49
29
22
7.5
Texture
Clay loam
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Purple soil
pH
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Table 2 Total runoff and sediment yield under different rainfall patterns. Tillage practices
Rainfall patterns
Number of rainfall events
Rainfall intensity (mm min-1)
Total runoff (L m-2)
Sediment yield (Kg m-2)
RT
Increased rainfall series
1st rain 2nd rain 3rd rain Total 1st rain 2nd rain 3rd rain Total 1st rain 2nd rain 3rd rain Total 1st rain 2nd rain 3rd rain Total
1.0 1.5 2.0
1.11 30.51 45.80 77.42 22.18 34.30 33.36 89.84 38.59 50.30 52.69 141.58 40.41 51.84 41.54 133.79
0.0003 2.82 1.74 4.56 1.47 2.25 0.78 4.50 0.22 0.93 1.20 2.35 1.11 0.53 0.09 1.73
2.0 1.5 1.0
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Decreased rainfall series
1.0 1.5 2.0
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Increased rainfall series
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CK
2.0 1.5 1.0
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Decreased rainfall series
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Table 3 R/S characteristic parameters of runoff and sediment yield on RT and CK slopes under different rainfall patterns
Runoff
Sediment yield
CK
Runoff
Autocorrelation Fractal coefficient B dimension D
0.847
0.239
1.214
0.814
0.371
1.333
0.841
0.308
1.214
0.822
0.413
1.464
0.614
0.248
1.289
0.607
0.312
1.296
0.614
0.296
1.323
0.617
0.221
1.247
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Sediment yield
Increased rainfall series Decreased rainfall series Increased rainfall series Decreased rainfall series Increased rainfall series Decreased rainfall series Increased rainfall series Decreased rainfall series
Hurst index
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RT
Rainfall patterns
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Tillage Indexes practices
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