1. Introduction
The Loess Plateau in northwestern China is suffering from a serious soil erosion problem [
1,
2,
3]. Freeze-thaw (FT) erosion, resulting from melted water, is one of the most important erosion types on the Loess Plateau [
4,
5,
6]. Compound erosion of freeze-thaw and meltwater strips the soil particles from the soil surface on hillslopes, and then moves them into the river [
7].
Field observed experiments on gully erosion resulted from FT [
8]. The results showed 11% of variability in channel erosion, 14% of variability in interfluve erosion, and 26% of variability in side wall erosion using a weekly timescale, which implied that FT processes were a significant contributor to erosion in gully channels, interfluves, and especially the side walls. Gully erosion is one type of linear erosion, where the soil material is detached and transported by overland flow. Several researchers have reported on linear mechanisms, e.g., erosion resulting in headcut and bank retreat due to concentrated surface flow [
9,
10,
11,
12], and landslides that form as a result of the subsurface flow [
13,
14]. Linear erosion, once connected, results from the depression formed, which becomes the main sediment source of the river basin. Rills correspond to the shallowest forms of linear erosion, which are both sediment source areas and sediment transport vehicles on the hillslope. The resulting rills may be persistent and develop into gullies [
15,
16], which will lead to irreversible losses of agricultural land due to not being filled by tillage operations. Therefore, it is important to understand the rill erosion process and spatial distribution for controlling the development of erosion.
Rill erosion accounts for approximately 70% of upland erosion, which is the primary sediment generation on the hillslopes of the Loess Plateau [
17]. Flows in natural rills on hillslopes transport significantly more sediment down slope than overland flows, which in turn affects rill geomorphology that is closely related to the hydraulic conditions [
18,
19,
20]. Therefore, the geomorphic importance of rill erosion has been well-developed [
18,
19,
21]. Surface runoff and soil loss are subjected to rill morphology on the hillslope [
22]. Processes that change the cross-sectional geometry of a rill channel indirectly change the velocity and turbulence [
19]. The importance of the collapse of rill sidewalls resulting in rill widening has received little attention [
23]. Rill length, width, depth, and cross-sections are considered as rill morphology parameters for analyzing the soil erosion rate and hydraulic processes [
21,
24,
25]. Some researchers have focused on the effect of rill morphology on the relationship between the hydraulic and soil erosion rate, such as down-cutting of the rill bed [
26,
27] and widening subprocesses of rill development [
3,
24]. More importantly, rills easily form on soils that have previously experienced FT cycles [
28,
29]. Wischmeier and Smith [
30] reported that frozen strata covered with thawed soil strata were highly susceptible to meltwater erosion. The capability of soil FT processes can affect rill erosion, sediment production, and geomorphic evolution [
20]. At present, research on alternate FT soil erosion, particularly studies on rill erosion and sediment transport process, is limited. However, the processes associated with soil FT that affect rill geometry have received very little attention. Changes in the area-to-perimeter ratios of a V-shaped rill in a frozen fine sandy loam were compared with similar rills that had been never frozen [
31], which showed that after similar flows through each rill, the frozen rill was deeper and narrower throughout its length than the rill that had never been frozen. Gatto et al. [
20] demonstrated that the final x-section of the entire rill was changed from rectangular trapezoidal to triangular as the soil-flows, slides, and slumps filled the rill and increased the width of its top, resulting from the effect of FT cycling. Ban et al. [
32] implemented a laboratory for comparing the rill velocity over frozen and thawed hillslopes and found that the rill morphology without headcuts along the rill on the frozen hillslope promoted an increase in the flow velocity when compared with the erosion of a thawed hillslope with headcuts. Variations in the morphology of rills resulting from freeze-thaw-induced soil erosion under concentrated flow, however, have not been previously investigated, which in turn influence rill erosion and sediment production.
Different relationships between soil detachment and hydraulic parameters have been established to predict the soil erosion rates through concentrated flow experiments [
33,
34,
35,
36]. Therefore, soil erosion rates have been described by several hydraulics parameters, such as shear stress [
37], flow velocity [
38], stream power [
39], unit stream power [
40], and runoff energy consumption [
41]. Flow energy is a better hydraulic parameter than shear stress for describing soil detachment [
42,
43,
44,
45]. Li et al. [
41] demonstrated that the processes of soil erosion accompanied flow energy consumption and consumed energy was used to detach and transport soil particles on the loessal hillslope. Li et al. [
46] calculated the soil erosion and sediment yield through runoff shear stress, runoff energy consumption, and unit stream power, respectively, and indicated that runoff energy consumption in describing the soil erosion process was simpler and more accurate on the loessal hillslope. Experimental results indicated that the soil erosion rate was affected by factors such as soil texture, land use type, bulk density, clay content, organic matter content, and soil moisture [
35,
47,
48]. As the hydraulic parameter does not represent an actual measurable soil property [
43], the values in models are often acquired through calibration in different regions. Therefore, the quantification of soil erosion based on flow hydraulic parameters varies with different soil conditions [
49,
50]. The effect of FT influences soil properties such as soil bulk, water-stable aggregate content, soil cohesion, and soil disintegration [
5,
51,
52,
53], and in turn affects the soil erosion. However, the relative research on the relationship between hydraulic parameters and soil erosion resulting from meltwater is limited. Therefore, the response of meltwater erosion to runoff energy consumption was investigated in this study.
The concentrated flow experiments were conducted under different flow rates and soil conditions (a) to compare the erosion resistance characteristics of soil erosion, rill morphology, and runoff energy consumption; (b) to quantify the relationship between the soil erosion rate and energy consumption; and (c) to analyze the spatial distribution of sediment based on the runoff energy consumption.
5. Conclusions
In this study, the response of the freeze-thaw soil erosion rate to runoff energy consumption was investigated by rill flow under combinations of three flow rates (1, 2, and 4 L/min) and three soil conditions (unfrozen, shallow-thawed, and frozen). The spatial distribution of erosion along the slope was predicted based on the runoff energy consumption. The spatial distribution of erosion along the slope was predicted based on the runoff energy consumption. The results showed that the shallow-thawed and frozen slope produced a mean value of 3.08 and 4.53 times the average soil erosion rate compared to that on the unfrozen slope at the same flow rate, respectively. The width of the rill gradually became larger as the flow rate increased under different soil slopes. There was no significant difference in the rill length on the frozen slope under different flow rates (p > 0.05). The runoff energy consumption in order showed unfrozen > shallow-thawed > frozen slopes at the same flow rate, and runoff energy consumption increased with the increasing flow rate. The runoff energy consumption of the water-carrying section changed linearly with the soil erosion rate. The spatial distribution of the runoff energy implied that soil erosion rates were mainly sourced from the unfrozen down slope, shallow-thawed upper slope, and frozen full slope.
These findings improve our understanding of the effect of freeze-thaw and flow rate on erosion processes and runoff energy consumption for assessing the erosion model for meltwater erosion. These results were only based on one soil type, so varying responses to the soil erosion rate by meltwater-concentrated flow should be investigated in the future.