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.