2. Material and methods
2.1 Test location and soil
Experiments were conducted within the Simulated Rainfall Hall at the
Institute of Soil and Water Conservation, Chinese Academy of Sciences.
The soil types tested were sand and loessal soils, sourced from Dalad
Banner Province, Inner Mongolia, which intersects the Hobq Desert and
the Loess Plateau (110°31′17″ E longitude, 39°58′12″N latitude) and from
Ansai, Shaanxi Province (110°10′30″E longitude, 38°165′08″N latitude),
respectively. The soil samples were collected from the 0 cm–20 cm soil
layer in abandoned cropland. Table 1 shows the soil mechanical
composition, bulk density and organic carbon. Air-dried soil samples
were filtered through a 2 mm mesh to remove stones, residual roots and
other debris.
2.2 Experimental design
The SDC experiment was conducted in a scour flume. Field investigation
showed that the slope of abandoned land in the study area was generally
less than 15 ° and that the main plant species was Bothriochloa
ischaemum . Therefore, the current study selected a scour test slope of
10 ° and the root system of Bothriochloa ischaemum . Furthermore,
the flow rate was set to 6 L min−1, 12 L
min−1, 18 L min−1 and 24 L
min−1 based on previous research in the study area
(Sun, 2018).
Four tests treatments were conducted
on each soil, and for each treatment, the soil was placed into an iron
box, for a total of eight boxes, with the length, width and depth of
each box of 1.5 m, 1.5 m and 0.2 m, respectively. Soil was compacted
into each box to obtain a bulk density equal to that of the soil in the
field. The inner walls of the boxes were coated with a thermal
insulation material. Several small holes were drilled into the bottom of
each box to prevent water accumulation. The four boxes filled with sand
were labeled as S1, S2, S3 and S4, whereas the four boxes filled with
loessal soil were labeled as L1, L2, L3 and L4, with, S1 and L1
representing the control group of each soil with no treatment measures
(C), S2 and L2 representing the soils treated by freeze-thaw (FT), S3
and L3 representing soil with root systems (R) and S4 and L4
representing soils treated by freeze-thaw combined with root systems (FT
+ R). The seeds of Bothriochloa ischaemum w ere planted in the S2,
S4, L2 and L4 treatments at the optimal density of 50 individuals
m−2 to represent the field growth in the study area.
The B. ischaemum plants were cultivated indoors, with maturity
being reached in October, 2016. During the cultivation period, all test
soil samples were watered twice month to ensure consistent initial water
conditions among the different soil samples. Subsequent to the B.
ischaemum reaching maturity, the S3 and L3 treatments without grass and
the S4 and L4 treatments with grass were placed outdoors to expose them
to natural freeze-thaw conditions from November, 2016 to March, 2017.
The S1, S2, L1 and L2 treatments cultivated indoors were watered with
the amount of water representative of any outside precipitation and snow
during this period. A cylindrical sampler (dimeter and depth of 10 cm
and 5 cm, respectively) was used to collect soil samples for scouring in
April, 2017. The aboveground parts of B. ischaemum plants were
removed from the treatments to eliminate their effects on the test
results, with only the root system retained. A total of 8 soil samples
were collected from each box, for a total of 64 soil samples.
The scouring device comprised a water supply tank, flow meter, steady
flow section and flume, and had a length, width and depth of 400 cm, 15
cm and 8 cm,
respectively
(Fig. 1). Before the scouring experiment for loessal soil was initiated,
dry loessal soil was filtered through a 2 mm mesh, following which the
soil particles were evenly glued to the surface of the flume bed to
simulate the grain roughness of the soil surface under natural
conditions. The same procedure was conducted for the scouring experiment
for sandy soil. For each experiment, the cylindrical sampler packed with
the soil sample was placed into the test area of the flume, with the
soil surface aligned with the flume bed surface. The surface of the soil
sample was covered with a cover panel to prevent the scouring of soil
samples during the adjustment of the flow rate. The panel was removed
once the experiment setup was complete and the flow rate had stabilized
to allow the detachment experiment to begin. Experiments were terminated
when the depth of the eroded soil in the cylindrical sampler reached 2.0
cm, with the duration recorded. For the soil samples containing root
systems, the binding effect of the root systems made it difficult to
measure the eroded soil depth. Therefore, for these samples, the
experiment was halted at 15 min regardless of scour depth. Wet soil was
oven-dried at 105 ℃ for 24 h and then weighed. Two groups of scour tests
were conducted for each flow rate as experiment repetitions, and a total
of 64 groups of tests were conducted for a total of 128 tests.
2.3 Determination of hydraulic parameters and SDC
2.3.1 Water depth and velocity
The below measurements were conducted once for each experimental group,
as defined in the above section.
At flow stabilization, flow depth was measured using a level probe (±
0.01 mm) at points 1.2 m, 2.2 m and 3.2 m above the lower end of the
flume. At each distance, depths were measured three times, at points 1.0
cm from each side and at the center of the flume, resulting in a total
of 9 positions and 27 measurements for each experiment. The mean flow
depth for the experiment was defined as the average of the 27 depth
measurements.
Velocity of the flow was determined using KMnO4 as a
tracer. Velocity measurements were replicated three times for each
experiment group. The water temperature was monitored following which
the Reynolds number (Re ) was calculated. It was
found that the flow regime was mainly laminar flow (Re < 500)
and transitional flow (500 ≤ Re ≤ 2000). Where the flow was laminar, the
mean flow velocity was obtained by multiplying the surface velocity by
0.6, whereas it was multiplied by 0.70 when the flow was transitional
(Abrahams et al., 1985). The mean velocity was defined as the average
corrected velocity of the three times measured velocity for each
experiment group.
2.3.2 Hydraulic parameters
The shear stress (τ), unit energy of the water carrying section (E),
stream power (ω) and unit stream power (P) were calculated as follows:
\(\tau=\rho ghS\) (1)
\(E=\frac{\alpha v^{2}}{2g}+h\cos\theta\) (2)
\(\omega=\tau v\) (3)
\(P=v\times J\) (4)
In Eq. (1)–Eq. (4), τ is the shear stress (Pa), E is the unit
energy of the water carrying section (cm), ω is the stream power
(N·m−1·s−1), P is the unit
stream power (m·s−1), ρ is the water density
(kg·m−3), g is the gravitational acceleration
(m·s−2), h is the flow depth (m), S is
the sine value of slope gradients, V is the mean flow velocity
(m·s−1), α is the kinetic energy correction factor (α
= 1) and θ is the slope gradient (°).
2.3.3 SDC
SDC by overland flow (expressed in
kg·m−2·s−1) was calculated as:
\(D_{c}=\frac{W_{w}-W_{d}}{t\times A}\) (5)
In Eq. (5), WW and Wd are
the weights of the dry soil before and after testing, respectively (kg),t is the duration of the test (s) and A is the sample
cross-section area (m2).
2.4 Root weight
After each group of scouring experiments, roots within each soil sample
were collected by washing over a sieve (1 mm), following which they were
weighted after oven-drying for 12 h at 65 °C (Li et al., 2015).
2.5 Statistical analysis
All statistical analyses were conducted using Excel 2010 and SPSS20.0
software. One-way analysis of variance (ANOVA) was conducted using
SPSS20.0. SigmaPlot12.0 was used for equation regression and mapping.
The general linear model (GML) was used to analyze the effects of soil
type, freeze-thaw, root system and their interactions on the SDC. The
following statistical parameters were used to evaluate the performance
of simulated results:
\(NSE=1-\frac{\sum{(Q_{i}-P_{i})}^{2}}{\sum{(Q_{i}-\overset{\overline{}}{O})}^{2}}\)(6)
\(R^{2}=\frac{\left[\sum_{i=1}^{n}{(O_{i}-\overset{\overline{}}{O})(P_{i}-\overset{\overline{}}{P})}\right]^{2}}{\sum_{i=1}^{n}{(O_{i}-\overset{\overline{}}{O})}^{2}\sum_{i=1}^{n}{(P_{i}-\overset{\overline{}}{P})}^{2}}\)(7)
In Eq. (6) and Eq. (7), NSE is the Nash–Sutcliffe efficiency
index (Wang et al., 2016), R2 is the
coefficient of determination, Oi is the measured
value, Pi is the predicted value,\(\overset{\overline{}}{O}\) is the average measured value,\(\overset{\overline{}}{P}\) is the average predicted value and nis the sample number.
3.
Results
3.1 SDC of different treatments
The SDC of sand soil under each treatment was relatively higher
(1.02–3.40 times) compared to that
of the treatments of loessal soil,
although the differences were not significant (P >
0.05). The SDC values of the two soils showed a similar order of
variation among the four treatments, with R < R+FT <
C < FT (Table 2). Freeze-thaw increased the SDC of sand soil
and loessal soil under the FT treatment by 5.99% and 20.39%,
respectively compared with C, while that under the R + FT treatment
increased by 135.29% and 380.00%, respectively compared with R.
However, the effect of freeze-thaw on SDC was not significant (P> 0.05) compared to the control. Due to the effect of the
root system, the SDC of sand soil and loessal soil under the R treatment
were reduced by 99.00% and 99.66%, respectively compared with C,
whereas that under the R + FT treatment were reduced by 97.82% and
98.76%, respectively compared with FT. Therefore, the root system
reduced SDC significantly (P < 0.05) compared to the
control. During the combined effect of freeze-thaw and the root system,
the contribution of the root system to SDC dominated. The SDC values of
sand soil and loessal soil under the R+FT treatment were reduced
significantly by 97.64% and 98.38% compared with C, respectively.
The relative contributions of soil type, freeze-thaw, root system and
their interactions to the variability of SDC was calculated according to
variance component analysis of the general linear model (GLM). The
contributions of soil type, freeze-thaw and the root system on SDC were
calculated to be 99.95%, 10.64% and 6.00%, respectively; therefore,
the root system had the most significant effect on SDC. The interactions
between the root system and freeze-thaw also explained the variability
of SDC to a high degree (36.90%). whereas the interactions among other
factors explained SDC variability to a much lower degree.
3.2 Predicting SDC using hydraulic parameters
Four hydraulic parameters, namely shear stress (τ), unit energy of the
water carrying section (E ), stream power (ω) and unit stream
power (P ) are often used to describe the soil detachment process
in soil erosion models. Table 3 and Table 4 shows the regression
relationships between SDC and the hydraulic parameters of sand soil and
loessal soil under four treatments, respectively. The two soil types
showed similar regression relationships between SDC and hydraulic
parameters. Shear stress and stream power explained variation in SDC
well in a positive linear function, whereas unit energy of the water
carrying section and unit stream power explained SDC using a power
function. However, there was a weak relationship between the hydraulic
parameters and the SDC of sand soil under the R and R + FT treatments,
with all relationships achieving an R2< 0.01.
3.3 Comparison of the responses of SDC to the different hydraulic
parameters
Table 5 and Table 6 show the prediction accuracies of the regression
equations for SDC of sand soil and loessal soil, respectively. Due to
the fact that the hydraulic parameters showed weak relationships to the
SDC of sand soil treated by R and R+FT, the prediction accuracies of the
regression equations representing the C and FT treatments were analyzed.
Although shear stress and stream power were found to be good predictors
of SDC, shear stress was only a good predictor for rootless soil,
whereas stream power was a good predictor for both rootless soil and
root soil. Therefore, stream power was identified as the most suitable
hydraulic parameter to predict SDC (Fig. 2, Fig. 3). In addition, the
hydraulic parameters had stronger relationships to the SDC of loessal
soil compared to sand soil.
The model to predict SDC of sand soil under the R and R+FT treatments
utilized the regression relationships of both the root weight and stream
power with SDC. The simulation results showed that the regression
relationship effectively predicted the SDC of sand soil treated by R and
R+FT (NSE > 0.6904, R 2> 0.7024) (Table 7). Similarly, root weight and stream
power were used to predict the SDC of loessal soil under the R and R+FT
treatments. The prediction accuracies of the models based on the two
factors of steam power and root weight were greatly improved compared to
those based on either steam power or root weight. Under the R treatment,
the NSE was increased from 0.9144 to 0.9756, whereas theR2 was increased from 0.6477 to 0.9767 under
the two-factor regression compared to the single factor regression for
loessal soil. Under the R + FT treatment, the difference in NSEand R2 between the two-factor and single factor
regression was minimal, although this model still showed a high SDC
prediction accuracy. In summary, the prediction accuracy of the model
was improved when the second factor of root weight was added to steam
power within the SDC prediction model for SDC based on hydraulics
parameters.
The present study explored whether the SDC of root soil and rootless
soil (root weight was set to 0) could be simulated accurately by the
above model. A portion of the test data of SDC, stream power and root
weight under the four treatments in two soils was selected to develop an
SDC prediction model applicable both to sand soil and loessal soil
(Table 8). The results of this model showed higher prediction accuracies
for both the NSE and R2 . The model was
validated using the remaining portion of data not used in model
development. The model validation NSE andR2 prediction accuracies of SDC for loessal
soil were 0.7611 and 0.7861, respectively (Fig. 4a), whereas those for
sand soil were 0.6734 and 0.8513, respectively (Fig. 4b). These results
indicated that the model could simulate the soil SDC under the four
treatments relatively well. A single model applicable to simulating the
SDC of both sand and loessal soils was developed using data that were a
combination of SDC, stream power and root weight data for both soil
types. This model obtained NSE and R2prediction accuracies of 0.8248 and 0.8299, respectively. Therefore, the
single model applicable to both soil types had higher prediction
accuracies relative to the two models developed specifically for the
sand and loessal soils.