Experimental Study of Freeze-Thaw/Water Compound Erosion and Hydraulic Conditions as Affected by Thawed Depth on Loessal Slope

Freeze-thaw cycles have significant influences on slope erosion processes. In this study, simulated rainfall laboratory experiments were implemented to investigate erosion processes and the relationship between the soil loss rate and hydraulics conditions under different thawed depths and rainfall intensities. The results indicated that linear regression could be used to describe the relationship between the soil loss rate and runoff time. Soil loss rate, as measured by the curve slope k (represented the increase rate in the soil loss rate), generally increased with runoff time over different thawed depths across all rainfall intensities. The k values generally increased with rainfall intensity from 0.6 to 1.2 mm/min, with the exception of the 4 cm thawed slope, for which the k values initially increased before decreasing with rainfall intensity from 0.6 to 1.2 mm/min. The mean soil loss rate and range also increased with thawed depth under the same rainfall intensity. Finally, the interaction of rainfall intensity and thawed depth had the greatest effect on soil loss rate, while stream erosion power was the hydraulic parameter that exhibited the best soil loss rate prediction performance. The results presented herein improve the understanding of the response of freeze-thaw/water compound erosion to hydraulic conditions.


INTRODUCTION
Soil erosion is one of the main environmental problems facing the world (Batista et al., 2019;Dazzi and Papa, 2019;Shi et al., 2020), and this is especially true in the Loess Plateau of China Guo et al., 2020;Yu et al., 2020;Yue et al., 2020). However, research in this region has focused on hydraulic erosion and wind erosion, while comparatively little is known about freezethaw precipitation compound erosion (Xu et al., 2015a,b;Zhang B.J. et al., 2019;Zhang W. et al., 2019).
Seasonal freeze-thaw (FT) influences soil physical characteristics, such as soil bulk density (Li et al., 2013;Li and Fan, 2014), erodibility (Wang et al., 2017;Cheng et al., 2018), aggregates (Edwards, 2013;Xiao et al., 2019), and water content (Ala et al., 2016;Wang et al., 2019), which make the soil more susceptible to erosion under compound forces (Edwards, 2013;Li and Fan, 2014). As more snow and glaciers melt due to global warming, soil erosion is continually worsening (Ragettli et al., 2015;Wang et al., 2020). Most midlatitude regions also suffer from seasonal FT erosion (Ragettli et al., 2015;Wang et al., 2019). Depending on Second National Soil Erosion Remote Sensing Survey in China, 13.23% of national territorial area is in danger of FT erosion ). In the loess hilly-gully region of Loess Plateau, there are around 105-125 d with average temperatures below 0 • C, and the average annual rainfall is 300-600 mm, which meets the basic conditions necessary for FT erosion . Soil erosion during the thawing period is a unique erosion form known as FT-hydraulic compound erosion.
Previous laboratory rainfall experiments on frozen slopes have shown contrasting patterns. Using control FT-water combined erosion experiments, Wang et al. (2019) found that the total sediment yield of a FT slope exhibited increased soil erosion compared to a control slope . Wang et al. (2020) found that frozen slopes displayed higher sediment yield capacity at equal flow rates when compared with shallow-thawed and unfrozen slopes. However, Zhou et al. (2009) investigated the effects of the thawed depth on black soil erosion under simulated rainfall and found that the erosion amount decreased with increasing thawed depth under lower soil water content. Wei et al. (2015) studied the impacts of FT cycles on runoff and sediment yield of slope land and found that FT cycles greatly increased the sediment yield intensity. In contrast, Ban et al. (2017) found that shallower thawed depths delivered more sediments than deeper thawed depths of high altitude and latitude regions. However, few studies have investigated the effects of thawed depth on soil erosion processes in loess slopes under simulated rainfall.
Generally, hydraulic parameters are essential to describing erosion processes and understanding the hydrodynamic mechanisms of slope erosion (Cuomo et al., 2016;Zi et al., 2016;Xiao et al., 2017;Mirzaee and Ghorbanidashtaki, 2018;Luo et al., 2019). Foster and Meyer (1972) showed that erosion has a positive relationship with shear stress. Govers (1990) found that unit stream power was the best parameter for describing erosion processes. Nearing et al. (1999) andCai (1995) found stream power to be better than other hydraulic parameters for describing erosion processes. Lu et al. (2009) put forward the stream erosion power concept and established the relationship between soil loss rate and stream erosion power. Wang et al. (2020) found that runoff energy loss could predict thawed soil erosion processes under concentrated flow well. Govers (1992) determined that no existing formula could perform efficiently over the entire range of available data. Soil loss by shallow flows is more closely correlated with flow energy than shear stress (Zhang et al., 2002). Some studies have indicated that stream power is better than shear stress for Dc prediction (Knapen et al., 2007;Cao et al., 2009); however, it is still not clear which parameters are suitable for the prediction of FT precipitation compound erosion under simulated rainfall.
Here, we used laboratory experiments of three rainfall intensities to survey erosion processes and assess the relationship between soil loss rate and various hydraulics parameters under four thawed depths and three gradient rainfall intensities. The specific objectives of this study were to (i) assess erosion processes with runoff time under different thawed depths, and (ii) determine the relationships between soil loss rate and hydraulic parameters.

Experimental Materials and Design
We used loessal soil collected from the Wangmaogou catchment (37 • 34 13 -37 • 36 03 N and 110 • 20 26 -110 • 22 46 E) in Shaanxi Province, China. The collected soil was airdried and sieved (10 mm) to remove roots, stones, and other debris. The soil particle with 2 mm distribution was then measured using a Mastersizer2000 particle size analyzer (Malvern Instruments, Malvern, United Kingdom), which showed the mechanical composition of the original soil was 0.02 ± 0.003% clay, 65.28 ± 0.43% silt, and 34.7 ± 0.21% sand depending on USDA classification system of soil texture. We then increased the soil water content to 15% by gravity and kept it indoors for 24 h while covered with plastic.
The experimental soil flume was 2 m long, 0.75 m wide, and 0.3 m deep ( Figure 1A). The skeleton of the soil flume was made of angle steel, and the wall (0.4 m high) was made from wood to reduce heat exchange so that the soil thawed vertically. The bottom of the flume was filled 0.05 m deep with sand to maintain water permeability. Next, experimental soil was added to a depth of 25 cm in 5 cm layers. Quantitative experimental soil for each layer was obtained depending on the soil dry bulk (1.3 g/cm3), soil water content (15%), and volume of each layer. The surface topography on two sides was raised to an experimental slope of 15 • . The area of slope farmland less than 15 • accounts for 43.65% of the total area of slope farmland, and the slope gradient 15 • is a relative threshold of soil erosion modulus.
A FT system, 4.5 m long × 2.5 m wide × 2.5 m high, was used to freeze the experimental soil layer. The FT system could produce temperatures of −40 to 30 • C with an accuracy of ±1 • C. To ensure the soil was completely frozen, the filled soil flume was placed in the FT system for 24 h at −18 to −22 • C. We investigated four thawed depths: 0, 2, 4, and 6 cm. The completely frozen soil-filled flume was then placed at room temperature for thawing, during which time a needle was used to measure the thawed depth every 15 min to meet the requirement of thawed depth during the thawing period. The filled soil flume was then divided into 12 grid cells for testing points of thawed depth. We subjected the slope to three rainfall intensities (0.6, 0.9, and 1.2 mm/min) and set a runoff duration of 60 min for each experiment from the rainfall simulator (Figures 1B,C). Each experiment was repeated two times to give a total of 36 experiments and the results were averaged.
The slope was divided into four transects between 0-0.5, 0.5-1.0, 1.0-1.5, and 1.5-2.0 m. The surface flow velocity of the four transects was measured at 1 min intervals using the KMnO 4 tracer method ( Figure 1D). We multiplied the measured surface flow velocities by a correction factor of 0.65 to obtain the mean flow velocity (Luk and Merz, 1992). The flow widths were measured on the four transects using a ruler at 1-min intervals.
The soil flume bottom was constructed with convergence equipment to collect runoff and sediment at 1 min intervals. The runoff volume was measured in each gathered bucket, and the weight of sediment was recorded after drying in an oven at 105 • C for >24 h.

Methods
The soil loss rate was calculated as the erosion amount per unit area per second: where S r is the soil loss rate (g/m 2 /s); e r is the mass of soil loss during the observation time (g); l and w are the length and width of the experimental flume (m), respectively; and t is the observation time (s).
Shear stress, which is related to soil particle detachment and transport, was calculated as follows (Xiao et al., 2017): where τ is the shear stress (Pa); γ m is the muddy water density (kg/m 3 ); g is the gravitational acceleration (m/s 2 ); J is the slope gradient (m/m); and R is the hydraulic radius, which was considered equal to the flow depth under overland flow conditions (m). It was difficult to directly measure flow depth because the flow depth was shallow and the bed elevation changed with erosion. We calculated flow depth as follows: where h is the flow depth (m); Q is the runoff volume (m 3 ); W is the water width (m); t is the time (s); and V is the mean flow velocity (m/s).
The stream power, which represents power consumed by water flow per unit area, was calculated as previously described (Cao et al., 2009): where ω is the stream power (N/m/s); τ is the shear stress (Pa); V is the mean flow velocity (m/s). The unit stream power, which describes the rate of change of potential energy per unit water mass with time, was calculated as follows (Zhang et al., 2002): where P is the unit stream power (m/s); J is the slope gradient (m/m); V is the mean flow velocity (m/s). The stream erosion power, which comprehensively expresses the efficiency of runoff erosion and sediment transport, was calculated as described by Lu et al. (2009): where E is the stream erosion power [m 4 /(s·m 2 )]; Q m is the runoff peak modulus [m 3 /(s·m 2 )], which is equal to the runoff peak divided by the experimental soil flume area; and H is the mean flow depth (m).

Data Analysis
The regression analyses and associated figures were drawn using OriginPro 8.5 (OriginLab Inc, Northampton, MA, United States), statistical analyses were conducted with SPSS 16.0 (SPSS Inc, Chicago, IL, United States).

Soil Loss Rate Variation With Runoff Time Under Different Thawed Depths
As shown in Figure 2, linear regression was used to describe the relationship between the soil loss rate and runoff time. The determination coefficient (R 2 ) was used to elevate the regression equation (Table 1). Soil loss rate, as measured by the curve slope k (represented the increase rate in the soil loss rate), generally increased with runoff time over different thawed depths across all rainfall intensities (Figure 2 and Table 1), although it plateaued or slightly decreased after 30 min in some trials (e.g., Figure 2C, 4 cm depth). The R 2 values were greater than 0.82 for all tests under 0.6 mm/min intensity. The value of k became greater with deeper thawed depth under 0.6 mm/min intensity and increased to two times when the thawed depth increased from 2 to 4 cm under 0.6 mm/min intensity ( Table 1). The value of k was 2.17 times greater at a thawed depth of 4 cm than at 2 cm under 0.6 mm/min FIGURE 2 | The relationship between soil loss rate and runoff time over different thawed depth at 0.6 mm/min (A), 0.9 mm/min (B), and 1.2 mm/min (C).
Frontiers in Environmental Science | www.frontiersin.org  intensity ( Table 1). As the thawed depth increased from 4 to 6 cm, the value of k increased to 1.31 times under 0.6 mm/min intensity ( Table 1).
The R 2 values were greater than 0.66 for all tests under 0.9 mm/min intensity ( Table 1). The value of k became greater as the thawed depth increased from 0 to 4 cm under 0.9 mm/min intensity (Table 1), while it decreased slightly as the thawed depth increased from 4 to 6 cm under 0.9 mm/min intensity ( Table 1). The value of k increased by 1.63 times when the thawed depth increased from 0 to 2 cm under 0.9 mm/min intensity (Table 1), while it was 1.54 times greater at a thawed depth of 4 cm than 2 cm under 0.9 mm/min intensity ( Table 1).
The R 2 values were 0.56, 0.73 and 0.90 at the thawed depths of 0, 2, and 6 cm under 1.2 mm/min. However, the R 2 was 0.26 at a thawed depth of 4 cm under 1.2 mm/min. Except for the thawed depth of 4 cm, the values of k tended to increase as the thawed depth increased from 0 to 6 cm. As the thawed depth increased from 0 to 2 cm, the value of k increased by 1.56 times under 1.2 mm/min intensity (Table 1). Additionally, the value of k was 3.14 times greater at a thawed depth of 6 cm than 2 cm under 1.2 mm/min intensity ( Table 1).
For the 0, 2, and 6 cm thawed depths, the values of k increased with increasing rainfall intensity from 0.6 to 1.2 mm/min. The values of k also increased when rainfall intensity increased from 0.6 to 0.9 mm/min for the thawed depth of 4 cm. However, the value of k tended to decrease when the rainfall intensity increased from 0.9 to 1.2 mm/min for the thawed depth of 4 cm.  Table 2. The mean soil loss rate increased as thawed depth increased under the same rainfall intensity (Figure 3). A similar phenomenon was also observed for the 1.2 mm/min rainfall intensity except at the thawed depth of 6 cm (Figure 3). At a thawed depth of 0 and 6 cm, the mean soil loss rate increased as rainfall intensity increased. At thawed depths of 2 and 4 cm, the mean soil loss rate increased when the rainfall intensity increased from 0.6 to 0.9 mm/min (Figure 3 and Table 3). However, the mean soil loss rate decreased when the rainfall intensity increased from 0.9 to 1.2 mm/min (Figure 3 and Table 2).

Statistical Analysis of Soil Loss Rate Under Different Thawed Depths
As shown in Figure 3, the median values increased as the thawed depth increased under rainfall intensities of 0.6 and 0.9 mm/min ( Table 2). For the 1.2 mm/min rainfall intensity, the median values tended to increase as the thawed depth increased from 0 to 4 cm ( Table 2). However, decreases in the median value were observed at a rainfall intensity of 0.9 mm/min when the thawed depth was from 4 to 6 cm ( Table 2). Moreover, the median value increased with increasing rainfall intensity at thawed depths of 0, 2, and 6 cm ( Table 2). For a thawed depth of 4 cm, the median value increased as rainfall intensity increased from 0.6 to 0.9 mm/min ( Table 2). However, the median value was lower under 0.9 mm/min than under 1.2 mm/min ( Table 2).
The range was used to describe the variation in soil loss rate for individual groups ( Table 2). The range increased as thawed depth increased under the same rainfall intensity ( Table 2). For thawed depths of 0 and 6 cm, the range values also increased as rainfall intensity increased from 0.6 to 1.2 mm/min ( Table 2). For thawed depths of 2 and 4 cm, the ranges also increased as rainfall intensity increased from 0.6 to 0.9 mm/min ( Table 2); however, the ranges decreased as rainfall intensity increased from 0.9 to 1.2 mm/min ( Table 2). Figure 4 shows the relationship between soil loss rate and shear stress (a), mean stream power (b), mean unit stream power (c), and stream erosion power (d). All the mean hydraulics conditions were found to have a positive relationship with soil loss rate (Figure 4).

Relationships Between Soil Loss Rate and Hydraulic Conditions
Soil loss rate can be linearly described via mean shear stress ( Figure 4A and Table 3). The determination coefficient (R 2 ) is 0.52 and the probabilities test was less than the significance level of 0.01. The erodibility value based on the mean shear stress was 0.17 s/m and the critical shear stress was 0.66 Pa.
The soil loss rate can be fitted to mean stream power with the following power function ( Figure 4B and Table 3). The R 2 was 0.60 and the probabilities test was less than the significance level of 0.01. The erodibility value based on the mean stream power was 0.78 s 2 /m 2 and the power was 0.61.
The soil loss rate showed a linear increase as the mean unit stream power increased, and the relationship could be fitted with the linear expression ( Figure 4C and Table 3). The R 2 of Eq. (3) is 0.57 and the probabilities test was less than the significance level of 0.01. The erodibility value based on the mean unit stream power was 0.78 kg/m 3 and the critical unit stream power was 0.1 cm/s. The power function below effectively described the relationship between the soil loss rate and stream erosion power ( Figure 4D and Table 3). The R 2 value of Eq. (4) was 0.68 and the probabilities test was less than the significance level of 0.01. The erodibility value based on the mean stream power was 0.58 kg/L 4 and the power was 0.52.

The Effect of Rainfall Intensity and Thawed Depth on Soil Loss Rate
Under different rainfall intensities, the k differed with increasing thawed depth. The soil loss rate is determined by hydrodynamic and erosion material conditions. In this study, the hydrodynamic was determined by the rainfall intensity and the soil utilized. For the same rainfall intensity, the k value increased up to a thawed depth of 4 cm. This was likely because shallower thawed soil layers (0 and 2 cm) have slower thawing rates due to heat conduction because the frozen layer will decrease the infiltration ability (Sharratt et al., 2000;Zheng et al., 2001;Wang et al., 2020). As a result, the erodible soil was in short supply, leading to a lower erosion rate. As thawed depth increased (4 and 6 cm), more erodible soil was supplied compared the shallower thawed depths, leading to greater erosion rates. However, the limited hydrodynamic conditions at these depths resulted in decelerating erosion rates. For the 1.2 mm/min rainfall intensity, the erodible soil was still limited for 0 and 2 cm thawed depths.  The 4 cm thawed depth showed a unique trend under high intensity rainfall. Specifically, the soil loss rate began to decrease after 30 min of rainfall, which led to the lowest k value in that trial. The soil loss rate decreased because frozen soil melted slowly in the final 30 min of rainfall, but the soil loss rate was still higher than at thawed depths of 0 and 2 cm.
To clarify the correlation of rainfall intensity and thawed depth, the correlations between soil loss rate and rainfall, thawed depth and rainfall intensity-thawed depth were analyzed. As shown in Table 4, soil loss rate was significantly correlated with rainfall intensity, thawed depth, and rainfall intensity-thawed depth in the following order: I * H > I > H. These findings indicate that interaction of rainfall intensity and thawed depth has the most important effect on soil loss rate.

Response of Soil Loss Rate to Hydraulics Conditions
In this study, the soil loss rate could be robustly predicted as linear functions of previously identified hydraulic conditions, which is similar to the results of previous studies (Laflen et al., 1991;Nearing et al., 1999;Zhang et al., 2003Zhang et al., , 2015. However, we found lower erodibility values than some previous investigations, where erodibility ranged from 8.18 × 10 −4 to 8.4 × 10 −3 s/m Zhang et al., 2013). Additionally, the critical shear stress was only 10% that obtained from a recent laboratory study (Cao et al., 2009). Zhang et al. (2015) found that the critical shear stress was 12.8 Pa under a steep slope accumulation yield experiment (30∼50 • ), while we found that critical shear stress was almost 20 times greater than that obtained in their study at 15 • . Together, these results suggest that FTed soil has a greater erodibility and is less resistant to erosion (Li and Fan, 2014;Ban et al., 2017;Wang et al., 2020).
In addition, the mean stream power coefficient was larger and the power exponent was smaller than in previous studies (Zhang et al., 2008;Mirzaee and Ghorbanidashtaki, 2018;Wang et al., 2018). The larger coefficient mainly resulted from thawed soil having increased susceptibility to provide sediment sources . The smaller power exponent indicated that the increasing amplitude of the loss rate decreased with increased stream power because more energy was used to transport the sediment while the loss energy increased Shen et al., 2016;Xiao et al., 2017).
The erodibility value of unit stream power was larger and the critical unit stream power value was smaller than for previously conducted studies (Wang et al., 2017. This can be attributed to freeze-thawed soil being more easily eroded (Cuomo et al., 2016;Zi et al., 2016). Many erosion models based on processes utilize stream power to establish transport capacity.
In our experiments, stream power could not predict loss rate well, similar to the results of previous studies (Nearing et al., 1999;Zhang et al., 2002Zhang et al., , 2003Wang et al., 2016).
The probabilities test (P < 0.01) indicate that all the hydraulics conditions examined could be used to describe the changes in soil loss rate. However, based on the R 2 values, stream erosion power best described the relationship between the soil loss rate and the hydraulic conditions, followed by stream power, unit stream power and shear stress. Flow energy has been shown to be more closely related to soil loss rate than shear stress, as well as to be a useful indicator for describing soil loss rate (Nearing et al., 1999;Zhang et al., 2002;Wang et al., 2016;Xiao et al., 2017). Shear stress is mainly related to slope and flow depth, and thus reflects the response of eroded slope surfaces to concentrated flow. However, water depth is determined by dividing the runoff by the average water width. As a result, the horizontal and vertical evolution of the rill network cause increased inaccuracy of the measured water width. Hence, shear stress was not good predictive parameter in this study. For mean stream power and unit stream power, flow velocity, which was measured by KMnO 4 tracking, was the crucial parameter. The flow velocity is the average of different rill velocities resulting from eroded surfaces; thus, flow velocity error increases with rill amount. As a result, hydraulic conditions based on flow velocity will also become less robust. However, the predictive power of soil loss rate from stream or unit stream power was still better than that of shear stress. Finally, stream erosion power is calculated from the flow peak and average flow depth. The average flow depth can be obtained from total runoff amount divided by the underlayer area, which has lower measurement error. Thus, stream erosion power is a better hydraulic parameter for predicting soil loss rate.

CONCLUSION
In this study, experimental investigations of erosion processes of different thawed depth loessal slopes were conducted under different rainfall intensities. The results indicated that linear regression could be used to describe the relationship between the soil loss rate and runoff time. The k values increased as rainfall intensity increased from 0.6 to 1.2 mm/min except for the 4 cm thawed depth slope. For the 4 cm thawed depth, the values of k increased first, then decreased as the rainfall intensity increased from 0.6 to 1.2 mm/min. In general, the mean soil loss rate increased with thawed depth under each rainfall intensity. Additionally, the range increased as thawed depth increased under the same rainfall intensity. We observed a significant relationship between soil loss rate and rainfall intensity, thawed depth, and their interaction, and their interaction was found to have the most important effects on soil loss rate. After testing multiple hydraulic conditions, stream erosion power was found to be the best predictor of soil loss rate.

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.