1. Introduction
Soil erosion by water leads to land degradation, reduced crop yields, water pollution, threatening biodiversity and sustainability of environmentally protected areas, and other problems, which have made it a serious global problem [
1,
2,
3,
4,
5]. A soil erosion model is essential for understanding the erosion process and implementing effective soil conservation measures [
6,
7,
8]. The Universal Soil Loess Equation (ULSE) and revised ULSE (RULSE) were widely applied to predict soil erosion [
5]. However, ULSE and RUSLE were empirical and lacked deep recognition of erosion processes and erosion mechanisms [
5,
8]. Thus, many studies in recent decades have been concerned with process-based models, which were physically-based and could model erosion processes [
9,
10]. In these models, represented by the Water Erosion Prediction Project (WEPP), the rill erosion of overland flow is the most important process that influences sediment production [
11]. Rill erodibility (K
r, s m
−1) and critical shear stress (τ
c, Pa) (both refer to soil resistance to overland flow) are crucial parameters for modeling rill erosion [
7]. K
r and τ
c are usually determined by the linear regression of soil detachment capacity (D
c, kg m
−2 s
−1) and flow shear stress (τ, Pa) [
12].
Generally, K
r and τ
c are greatly influenced by soil properties (such as soil texture, soil cohesion, soil organic matter (SOM), plant roots, etc.) [
13,
14,
15].
In past decades, researchers have done significant work on the influencing factors of K
r and have reached a consensus about the effects of these influencing factors on K
r [
16,
17,
18]). Soil texture was widely used in the prediction of K
r [
16]. Geng et al. [
18] studied the response of K
r to landscape positions in a small watershed and found K
r decreased and increased with increasing clay content and sand content, respectively. Soil cohesion reflects the cohesive forces among soil particles [
19]. Wang et al. [
20] found a negative relationship between K
r and soil cohesion. SOM affects soil resistance to overland flow by functioning as a cementing agent among soil particles [
17]. Geng et al. [
21] proposed a significant correlation between K
r and SOM. Plant roots also impose great influence on K
r due to their chemical bonding effect and physical bonding effect [
14,
22]. K
r usually increases exponentially with root mass density [
20].
Significant disagreement remains, however, regarding other crucially important parameters of soil resistance to overland, namely τ
c [
23,
24]. Generally speaking, these disagreements can be categorized as follows: (1) Unlike K
r, the relationships between τ
c and its potential influencing factors were rather confusing [
21,
25]. For example, Gilly et al. [
25] quantified the τ
c of 36 soils throughout the United States and indicated that τ
c could be predicted by clay content, linear extensibility coefficient, and soil water content. Nonetheless, Geng et al. [
21] showed no significant relationship between τ
c and 17 measured soil properties for 36 soil types across Eastern China. (2) There is also no general agreement on the relationship between K
r and τ
c. Many studies indicated that soils with higher τ
c correspond to less erodibility [
26,
27]. Knapen et al. [
17] found that no significant relationship existed between K
r and τ
c for both laboratory (
n = 179) and field experiments (
n = 151). Additionally, Mamo and Bubenzer’s [
27] findings did not support the opinion that when τ
c was smaller, K
r would be larger. (3) In the WEPP, τ
c does not change with the variation of slope gradient (S) and hence is considered to be a constant [
28]. Nevertheless, in developing a rational method for predicting τ
c, Lei et al. [
29] suggested that τ
c increased when S changed from 0.087 to 0.423 and attributed this increase to the fact that the force along the slope enhanced when S was raised. Moreover, the critical shear stress of sediment particles in rivers mostly depended on bed S [
30,
31].
Due to the limitations of determining critical shear stress in rills by linear regression [
32,
33], some researchers have tried to determine critical shear stress by gradually increasing flow shear stress until an obvious detachment of soil particles is observed [
34,
35]. The critical shear stress of rill erosion determined by this method was called τ
o. Nouwakpo et al. [
36] considered τ
c was not capable of detecting small variations in real critical shear stress because of its projected characteristic. Thus, they determined the τ
o of different hydraulic gradients and demonstrated a good linear relationship with the hydraulic gradient that was in line with the changing trend of K
r. Lei and Nearing [
34] designed an apparatus to control flow discharge for well determining the τ
o of loose material. Although these studies presented satisfactory results, they only used the method of observing the initial detachment of soil particles to determine τ
o and did not compare these results with the widely used τ
c [
17,
21]. Thus, it is of paramount importance to investigate whether the method determining τ
o in rills is reliable.
Different from determining τ
o in rills, the method of determining critical shear stress in rivers by observing initial sediments has been extensively used [
37,
38,
39], and a great deal of knowledge has been gained [
40,
41,
42]. However, there are distinct discrepancies in hydraulic environments between rivers and rills [
43]. Typical flow depths in rills are several centimeters or less, which is several orders of magnitudes lower than that of rivers [
7]. The S of rivers was generally gentle (usually less than 0.01) [
31], while it was steep for rills (up to 0.46) [
44]. What is more, distinguishing differences exist between soils in rills and sediments in rivers [
20,
31]. Considering the great discrepancies between rivers and rills, the knowledge obtained from rivers may not be valid in rills [
7,
43]. Therefore, the reliability of the method determining τ
o in rills is in need of exploration.
For the purpose of exploring the reliability of the method determining τ
o in rills, undisturbed soils were preferable, considering the extrapolation of research results [
24,
45]. However, as mentioned above, K
r and τ
c of undisturbed soils were affected by numerous soil properties and plant roots [
17]. These influencing factors of K
r and τ
c were various, complicated, and, at times, greatly correlated [
21]. Specifically designed experiments, which controlled influenced factors, were usually aimed at establishing an accurate relationship between K
r and τ
c and their influencing factors [
21,
27,
46]. Clear relationships between τ
o and τ
c and their influencing factors were pivotal to estimating the reliability of the method determining τ
o. Disturbed soils, compared with undisturbed soils, could well control influencing factors, whereby the clear relationships between τ
o and τ
c and some fundamental factors (e.g., soil texture and SOM) could be more easily established with relatively lesser soil samples [
24,
47]. Therefore, disturbed soils, standing for the freshly tilled condition, were used in this study [
21].
As mentioned earlier, a lot of disagreement exists regarding the usually used method (linear regression) to determine the critical shear stress of rills (τ
c), whereas the method measuring critical shear stress of rills by observing the start of soil particle detachment (τ
o) has shown promising results [
36]. However, the reliability of the method determining τ
o was still unknown. Therefore, this study aimed to identify the reliability of the method determining τ
o in rills by comparing (1) the values of τ
o and τ
c, (2) the relationship between τ
o and τ
c, and K
r, and (3) the relationship between τ
o and τ
c and their influencing factors. This study’s findings have important implications for recognizing rill erosion mechanisms and enhancing the prediction accuracy of erosion models.
4. Discussion
Nearing et al. [
12] defined τ
c as the threshold of rill detachment below in which soil detachment is zero. In this study, nearly all sampling sites had obviously greater τ
c than τ
o. Interestingly, an obvious soil detachment was apparent for sampling sites with higher τ
c, which might contradict the definition of τ
c [
12]. This result meant that τ
c calculated by Equation (3) could not represent the critical condition of the start of soil detachment. The definition of τ
c has been contested [
33,
56]. For example, Knapen et al. [
46] and Wang et al. [
57] have stated that τ
c represented the appearance of significant detachment, which still did not explain why significant detachment was observed at the sampling sites with higher τ
c. Therefore, the reliability of τ
c determined by Equation (3) was probably controversial. Nearing et al. [
32] also indicated τ
c had no actual meaning, as it was calculated by linear regression, and a large regression slope would lead to a large value (τ
c).
The gradually increasing trend of K
r could be well explained by the soil properties. Specifically, K
r was negatively correlated to clay content and silt content, and a positive relationship was observed between sand content and K
r (
Table 6). This finding was consistent with the results of Geng et al. [
21]. Some previous studies have shown K
r decreased with τ
c, implying that factors that influenced K
r also affected τ
c [
58]. Although K
r showed an increasing trend from south to north and had a satisfactory relationship with soil properties, no significant relationship was observed between K
r and τ
c. Furthermore, Knapen et al. [
59] indicated that the K
r of deep noninversion tillage was 10 times lower than that of conventional plowing, but the differences in τ
c between these two tillage practices were not significant. Additionally, Geng et al. [
21] calculated K
r and τ
c of 36 soil types across eastern China and also found no significant relationship between K
r and τ
c. For the relationship between K
r and τ
o, K
r increased with an increase of τ
c from Yijun to Zizhou, which supported the perception that the higher τ
o corresponded to the lower K
r. The increasing trends of τ
o and K
r from Zizhou to Yunlin barely supported the inverse relationship between τ
o and K
r, which could be attributed to the low clay content and high sand content in Yulin (
Table 5). Sand particles need higher flow shear stress to be detached because of their high ratio of mass to surface area [
60]. Although Yulin has high τ
o, Yulin also showed high K
r. The low clay content of this sampling site may explain both the high K
r and τ
o of Yulin [
21].
For τ
c, the widely applied WEPP model considered that τ
c did not change with the variation of S [
14,
25,
34]. This study, however, found a significantly positive relationship between τ
o and S. This result was the opposite of the common-sense understanding that the gravitational force along a flume bed increases with S, which makes soil particles detach more easily [
31]. Lei and Nearing [
34] also found an increase of τ
o with S for loose material. In this study, the ratios of the H
o (S, 42.26%) to the H
o (S, 3.49%) for Yijun, Fuxian, Yanan, Zichang, Zizhou, and Yulin were 31.08%, 34.30%, 54.12%, 61.04%, 58.14%, and 58.37%, respectively. Nonetheless, the S (42.26%) was 12.11 times that of the S (3.49%). Thus, the influence of S on τ
o was much greater than H
o and explained why τ
o increased with S [
34]. This statement was inconsistent with the findings of some researchers who found that the critical shear stress was related only to soil properties [
25,
28]. Nonetheless, hydraulic parameters and S also have been used to calculate the critical shear stress [
24,
61]. This discrepancy has probably reflected the lack of clarity regarding the significance of the critical shear stress [
7].
Numerous disputes have existed with regard to the influence of soil properties on τ
c [
21,
24]. This study demonstrated a poor relationship between τ
c and measured soil properties. Our results, however, agreed with the findings of Geng et al. [
21]. They explored the relationship between τ
c and 17 soil properties of 36 soil types and also did not find a significant relationship between τ
c and the 17 soil properties. For the relationship between τ
o and measured soil properties, τ
o increased exponentially and SOM (
Figure 5), which agreed with the findings of Kimiaghalam et al. [
62] and Grabowski et al. [
63]. The poor relationship between τ
o and soil texture was probably caused by the fact that both the cohesive effect of clay particles and the ratio of mass to surface area of sand particles determined τ
o, and their interaction was complicated [
59].
Generally speaking, τ
o, compared with τ
c, did not present significantly better results with regard to the relationships with K
r, S, and soil properties. This finding could deepen the recognition of erosion processes and improve the precision of process-based soil erosion models. In this study, however, only the relationships between critical shear stress and some basic soil properties (soil texture and SOM) were established and compared, and the relationships with other key soil properties (such as soil cohesion, aggregate stability, plant root, etc.) were not investigated [
64]. Therefore, further research should be conducted to compare the relationships between τ
o and τ
c and these influencing factors. Even though τ
o was more reliable compared to τ
c, observing the start of soil particle detachment was subjective [
54]. Thus, it was meaningful to develop an objective method to ascertain the beginning of soil particle detachment [
39,
65]. Additionally, some researchers have argued that the critical shear stress had a relationship only with soil properties, which as well revealed the uncertainty of using a method to determine τ
o that was related to hydraulic parameters and S [
28].