03 Aug 2021
03 Aug 2021
Rill Erosion on Slope of Spoil tips: experimental study of runoff scouring erosion in multiple times
 ^{1}State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Water and Soil Conservation, Northwest A&F University, Yangling, Shaanxi, China
 ^{2}Institute of Soil and Water Conservation, Chinese Academy of Sciences and Ministry of Water Resources, Yangling, Shaanxi, China
 ^{3}College of Architecture and Plianning, Kunming, Yunnan, China
 ^{1}State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Water and Soil Conservation, Northwest A&F University, Yangling, Shaanxi, China
 ^{2}Institute of Soil and Water Conservation, Chinese Academy of Sciences and Ministry of Water Resources, Yangling, Shaanxi, China
 ^{3}College of Architecture and Plianning, Kunming, Yunnan, China
Abstract. The soil erosion of the spoil tips seriously threatens the safety of people's lives and property and the surrounding ecological environment. Rill erosion is an important cause of water and soil loss in spoil tips. This study was conducted to investigate the process of rill erosion on the slopes of spoil tips, changes in the morphological characteristics of rills and the mechanisms of rill erosion. A Field runoff plot (5 m long, 1 m wide and 0.5 m deep) with three inflow rates (1.6, 2 and 2.4 mm min^{−1}) and three typical slopes (28°, 32° and 36°) was used for runoff simulation experiments. The results showed that, compared with the slope and scouring times, inflow rate was the most important factor affecting rill erosion of the spoil tips. The development of rill mainly goes through three stages: the rill formation stage, the rill development stage and the rill adjustment stage. The overall predominance of parallelshaped rills at all experiments suggested that the formation of rills was dominated by concentrated runoff. The average rill depth was the best indicator of rill morphology for evaluating rill erosion. The flow regimes under the experimental conditions were supercriticallaminar flow and supercriticaltransition flow. The Reynolds number was the best hydraulic parameter for predicting rill erosion. The stream power was the best hydrodynamic parameter to describe rill erosion mechanism. These results contributed to further revealing the rill erosion mechanism on the slope of the spoil tips and provided a scientific basis for its soil erosion control.
Yongcai Lou et al.
Status: open (until 24 Oct 2021)

CC1: 'Comment on hess2021399', Gundy Gu, 09 Aug 2021
reply
It is indeed a interesting topic about soil erosion on spoil slopes that has experienced a long term study history. Rill erosion is also a old topic, and overall the core content is not so innovative. Most importantly, several of the experimental results were not reasonable.
Under a scouring test, the rill developemnt characteristics in this study are obviously different from the actual rill network development. So, this is an unrealistic study, although it shows good results expression. furthermore, the rill hydrodynamics parameters? for me the Reynold number, Frounde shear stress, and so on, they are the derived from the river dynamics, you can ensure that the rill flow is similar with river? Also, there are several rills on a slope (Fig.1), so how did the the rill hydrodynamic parameters obtained? flow velocity of each rill on a slope was measured? and then how did you analysis the data? can it represent the rill flow dynamics? This is not credible. So, the SECTION 3.3 Rill networks and morphology is not so meaningful. the rill network development was significantly affected by the flow characters at the begaining of plot top. Maybe a slight uneven of soil surface (affected by soil structure, soil moisture, mineral content......), the flow along slope showed a completely different results although under the same flow intensity condition. So, it exhabited an extremely random result (rill develoment). Rainfall test or natural rainfall study is a good method for understanding soil erosion mechnism of spoil slopes, because it can represent the actual process of rill developemnt on a spoil slope.

AC1: 'Reply on CC1', Zhaoliang GAO, 24 Sep 2021
reply
Thank for your comments on the article. We would like to respond to your comments in the following aspects.
Comment 1 It is indeed a interesting topic about soil erosion on spoil slopes that has experienced a long term study history. Rill erosion is also a old topic, and overall the core content is not so innovative.
Spoil tips, as anthropogenic landforms formed during development and construction project activities, have become an important source of new soil erosion. In recent years, soil erosion processes on the slope of spoil tips have received widespread attention (Peng et al., 2014; Zhang et al., 2015; Zhang et al., 2016; Niu et al., 2020; Guo et al., 2020; Li et al., 2020). Most of the studies on rill erosion have been based on field runoff monitoring plots, indoor soil tanks using 3D laser scanning technology or photographic photography to characterize the final erosion pattern of slope under a single rainfall or runoff scouring event (Fang et al., 2015; Tian et al., 2020), and also on the dynamic development process of rill erosion on sloping land(Qin et al., 2018; Shen et al., 2020). However, spoil tips, as a unique anthropogenic landform, have a platformsteep slope structure with a significant upslope inflow. This structure leads to the unique characteristics of steepslope rill erosion in the spoil tips, which is different from the traditional gently sloping cultivated land rill erosion (Fig.2b and Fig.3). The rill development process and its erosion hydrodynamic characteristics of the slope of the spoil tips under the upslope inflow conditions are not yet known. This study is important and innovative in the sense that we combined field experiments with theoretical analysis to reveal some of the key characteristics controlling the dynamic development process of rill on the slope of spoil tips.
Comment 2 Most importantly, several of the experimental results were not reasonable.
Question1 Under a scouring test, the rill development characteristics in this study are obviously different from the actual rill network development. So, this is an unrealistic study, although it shows good results expression.
We disagree with these comments. The design and execution of the experiments are appropriate for the purpose of the study and represent real world spoil tips as we show below how our experiments relate to spoil tips in the Loess Plateau of China. The development of traditional sloping land rill head originates from the random strand flow formed in the middle and upper part of the slope under rainfall conditions. The rill starts from the head to converge in the lower part of the slope, and gradually forms the rill network and obvious rill erosion. The rill network is mainly dendritic in general (Fig. 1a). The middle and lower part of the slope is often seriously eroded (Fig. 1a and Fig. 2b). For the slope of the spoil tips, when there is no obvious upslope inflow, the distribution of rills is also random, and the rill network structure has some similarity with the natural slope (Fig. 2a). The above reasons are mainly due to the rainfall generating random strand flow on the slope, and under the random strand flow, the rill develops randomly. However, when there is upslope inflow, the rill network development is different from that under rainfall alone, which is indicating the influence of the upslope inflow on the evolution of rill (Fig. 1b and Fig. 3). It is worth mentioning that the development of rill above the slope in this paper is also random. At the outlet, the water flow is evenly distributed over the entire width of the runoff plot, however, when the water flows through the " soft" part of the slope, the rills are randomly distributed.Figure 1 a: Spatial distribution of the rill network after three rainfall events at a rainfall intensity of 100 mm h^{1} (Shen et al., 2020). b: Spatial distribution of the rill network in this study after three runoff scouring events at a inflow rate of 120 mm h^{1}.
Fig. 2 a: Rill erosion on the slope of the spoil tips (when there is no obvious upslope inflow), b: Rill erosion on gently sloping cultivated land.
Figure 3 Field photo of rill erosion on the slope of the spoil tips (when there is a clear upslope inflow).
In addition, the flow production under rainfall conditions is a fullslope flow production, while the upslope inflow is a linear flow production. Under upslope inflow conditions, due to the attack of rills, it leads to further convergence of runoff, while the runoff in other parts is reduced or disappeared, thus scouring larger rills in the area where runoff converges, as in section 3.3 of this paper for the rill morphology evolution. Where runoff does not converge, the rill development stops.
Spoil tips are a unique manmade mound landform formed by production and construction activities, with a "platformsteep slope" structure. The development of the steepslope rill head of the spoil tips from the large amount of runoff of the platform, and the rill is relatively stable along the development path of the steep slope, showing the overall distribution characteristics of relatively parallel rills from the top to the foot of the slope (Section 3.3 of the article) (Fig.3). Therefore, compared with the traditional sloping land rill erosion, the spoil tips rill erosion has special characteristics. The research on rill erosion and rill morphology evolution of the spoil tips are significant and address some important practical problems in.
Question2 Also, rill hydrodynamic parameters? To me Reynolds number, Froude number, shear stress, etc., they are all derived from river dynamics, can you guarantee that rill flow is similar to a river?
Rill erosion is caused by concentrated flow. Compared with waterflow in river channels, rill development occurs at steeper gradients, the rill flow depth is vastly different and the bank shapes are more irregular. However, rill flow is similar to flow in river channels in terms of sediment transport and deposition (MOSS et al., 1979). Hence, fundamental theories of streams and rivers can be applied to rill flow, and the corresponding methods and governing equations can also be used in studies of rill flow hydraulic characteristics until a more systematic and welldeveloped theory for rill flow hydrology is available. In addition, the rill network is the prototype of the water system development, and is also a microcosm of the water system (Raff et al., 2004). Meanwhile, variables used to characterize flow dynamics can also be used to study rill erosion according to the selfsimilarity theory (Peng et al., 2015).
The descriptions of hydrodynamic parameters in the existing soil erosion studies have been based on the parameters of river dynamics, indicating that they have great potential to be used in slope runoff erosion, which can reflect the soil erosion characteristics and reveal the soil erosion mechanism to a certain extent(Shen et al., 2016; Yang et al., 2020). The application of slope erosion hydrodynamic parameters has a long history. For example, the prediction of soil erosion using simple hydraulic indicators, which are mainly empirical models because they are obtained by looking for the hydraulic indicators which are most correlated to the measured soil loss in statistical terms (KNAPEN et al., 2007). Hairsine and Rose (1992) established a rill erosion model based on runoff power. In the WEPP model, when the sediment concentration of the rill flow is less than the sediment transport capacity and the runoff shear stress of the rill flow is greater than the critical shear stress, the rill erosion is dominated by denudation. The expression of rill erosion rate is：
Where G is the sediment transport amount (kg·s^{1}·m^{1}), Df is the rill erosion rate(kg·s^{1}·m^{2}), Di is the interrill erosion rate(kg·s^{1}·m^{2}), Dc is the denudation rate of rill flow(kg·s^{1}·m^{2}), Tc is the sediment transport capability of rill flow(kg·s^{1}·m^{1}), Kr is the soil erodibility parameter of rill；tf is the runoff shear stress (Pa), tc is the critical shear stress (Pa).
In summary, this paper applies the hydrodynamic parameters to the study of slope rill erosion of the spoil tips with certain applicability and reference.
Question3 they are the derived from the river dynamics, you can ensure that the rill flow is similar with river? Also, there are several rills on a slope (Fig.1), so how did the the rill hydrodynamic parameters obtained? flow velocity of each rill on a slope was measured? and then how did you analysis the data? can it represent the rill flow dynamics? This is not credible.
The runoff velocity measurement scheme is adjusted according to the process of slope erosion rill development.
Runoff velocity were measured for the location of obvious strands of flow on the slope before the appearance of rill on the slope. After the rill formation of the slope, if there were more than one rill in the observed slope section, the runoff velocity of the slope section was represented by measuring the runoff velocity of each rill and calculating the average value. It should be noted that with the increase of duration and scouring times, due to the effect of headcut erosion, downcut erosion and bank landslip, resulting in changes in the rill network and runoff flow path, some rills are not measured for flow velocity when there is no longer runoff in the rill. The average value of the runoff velocity of the four observation sections is used to comprehensively characterize the runoff velocity of the slope (Tian et al., 2017). Due to the shallow runoff depth of the crosssection during the whole test, the error of direct determination is large, so the average runoff depth of the slope is calculated according to the empirical formula to obtain. Other hydrodynamic parameters are obtained based on the average runoff velocity and average runoff depth, which are used to characterize the hydrodynamic properties of the rill flow.Comment 3 Rainfall test or natural rainfall study is a good method for understanding soil erosion mechnism of spoil slopes, because it can represent the actual process of rill developemnt on a spoil slope.
Thank for your suggestion, we agree with the point you mentioned. Rainfall is the main driving force in the field where there is no obvious upslope runoff. The use of simulated rainfall and natural rainfall tests is optimal for studying rill development in this case. However, under field conditions, the runoff collected by the compaction platform of spoil tips is an important factor causing slope scour erosion and accelerating erosion of engineered landscapes (Zhang et al., 2016). The infiltration rate of the platform formed by heavy mechanical rolling is significantly reduced. Under rainfall conditions, the platform produces large concentrated runoff preferentially over the slope, and concentrated runoff rapidly flows along the edge of the platform to the steep slope, thus causing severe slope erosion. Therefore, the runoff from the platform is the main driving force for the slope erosion of the spoil tips. However, it should be noted that the rainfall also plays an important role in the rill erosion on the slope of spoil tips. We will consider a combination of rainfall and runoff in the later experiments to better and more realistically reproduce the field phenomenon.
References
Fang H.Y.,Sun L.Y., and Tang Z.H.: Effects of rainfall and slope on runoff, soil erosion and rill development: an experimental study using two loess soils, Hydrol. Process.,29(11),26492658,doi:10.1002/hyp.10392,2015.
Guo M.M.,Wang W.L.,Li J.M.,Bai Y.,Kang H.L., and Yang B.: Runoff characteristics and soil erosion dynamic processes on four typical engineered landforms of coalfields: An insitu simulated rainfall experimental study, Geomorphology.,349,106896,doi:10.1016/j.geomorph.2019.106896,2020.
Hairsine P.B., and Rose C.W.: Modeling water erosion due to overland flow using physical principles: 2. Rill flow, Water Resour. Res.,28(1),245250,doi:10.1029/91WR02381,1992.
KNAPEN A.,POESEN J.,GOVERS G.,GYSSELS G., and NACHTERGAELE J.: Resistance of soils to concentrated flow erosion: A review, EarthSci. Rev.,80(12),75109,doi:10.1016/j.earscirev.2006.08.001,2007.
Li J.M.,Wang W.L.,Guo M.M.,Kang H.L.,Wang Z.G.,Huang J.Q.,Sun B.Y.,Wang K.,Zhang G.H., and Bai Y.: Effects of soil texture and gravel content on the infiltration and soil loss of spoil heaps under simulated rainfall, J. Soil. Sediment.,20(11),38963908,doi:10.1007/s11368020027296,2020.
MOSS A.J.,WALKER P.H., and HUTKA J.: Raindropstimulated transportation in shallow water flows: an experimental study, Sediment. Geol.,22,165184,1979.
Nearing M.A.,Norton L.D.,Bulgakov D.A.,Larionov G.A.,West L.T., and Dontsova K.M.: Hydraulics and erosion in eroding rills, Water Resour. Res.,33(4),865876,doi:10.1029/97WR00013,1997.
Niu Y.B.,Gao Z.L.,Li Y.H.,Lou Y.C.,Zhang S.,Zhang L.T.,Du J.,Zhang X., and Luo K.: Characteristics of rill erosion in spoil heaps under simulated inflow: A field runoff plot experiment, Soil and Tillage Research.,202,104655,doi:10.1016/j.still.2020.104655,2020.
Peng W.,Zhang Z., and Zhang K.: Hydrodynamic characteristics of rill flow on steep slopes, Hydrol. Process.,29(17),36773686,doi:10.1002/hyp.10461,2015.
Peng X.D.,Shi D.M.,Jiang D.,Wang S.S., and Li Y.X.: Runoff erosion process on different underlying surfaces from disturbed soils in the Three Gorges Reservoir Area, China, Catena.,123,215224,doi:10.1016/j.catena.2014.08.012,2014.
Qin C.,Zheng F.L.,Xu X.M.,Wu H.Y., and Shen H.O.: A laboratory study on rill network development and morphological characteristics on loessial hillslope, J. Soil. Sediment.,18(4),16791690,doi:10.1007/s113680171878y,2018.
Raff D.A.,Ramı́rez J.A., and Smith J.L.: Hillslope drainage development with time: a physical experiment, Geomorphology.,62(34),169180,doi:10.1016/j.geomorph.2004.02.011,2004.
Reichert J.M., and Norton L.D.: Rill and interrill erodibility and sediment characteristics of clayey Australian Vertosols and a Ferrosol, Soil Res.,51(1),1,doi:10.1071/SR12243,2013.
Shen H.O.,Zheng F.L.,Wen L.L.,Han Y., and Hu W.: Impacts of rainfall intensity and slope gradient on rill erosion processes at loessial hillslope, Soil and Tillage Research.,155,429436,doi:10.1016/j.still.2015.09.011,2016.
Shen H.O.,Zheng F.L.,Zhang X.C.J., and Qin C.: Rill network development on loessial hillslopes in China, Earth Surf. Proc. Land.,45(13),31783184,doi:10.1002/esp.4958,2020.
Tian P.,Pan C.Z.,Xu X.Y.,Wu T.N.,Yang T.T., and Zhang L.J.: A field investigation on rill development and flow hydrodynamics under different upslope inflow and slope gradient conditions, Hydrology Research.,51(5),12011220,doi:10.2166/nh.2020.168,2020.
Tian P.,Xu X.,Pan C.,Hsu K., and Yang T.: Impacts of rainfall and inflow on rill formation and erosion processes on steep hillslopes, J. Hydrol.,548,2439,doi:10.1016/j.jhydrol.2017.02.051,2017.
Yang D.M.,Fang N.F., and Shi Z.H.: Correction factor for rill flow velocity measured by the dye tracer method under varying rill morphologies and hydraulic characteristics, J. Hydrol.,591,125560,doi:10.1016/j.jhydrol.2020.125560,2020.
Zhang L.T.,Gao Z.L.,Li Z.B., and Tian H.W.: Downslope runoff and erosion response of typical engineered landform to variable inflow rate patterns from upslope, Nat. Hazards.,80(2),775796,doi:10.1007/s110690151996z,2016.
Zhang L.T.,Gao Z.L.,Yang S.W.,Li Y.H., and Tian H.W.: Dynamic processes of soil erosion by runoff on engineered landforms derived from expressway construction: A case study of typical steep spoil heap, Catena.,128,108121,doi:10.1016/j.catena.2015.01.020,2015.

AC1: 'Reply on CC1', Zhaoliang GAO, 24 Sep 2021
reply

CC2: 'Comment on hess2021399', Lu Zhang, 17 Aug 2021
reply
This paper presents field experiments to quantify erosion processes over spoil tips in the Loess Plateau of China. The authors analysed the experimental data and provided insights into key factors controlling the erosion processes. The paper is well structured and the presentation is mostly clear. However, I have the following specific comments on the manuscript.
Ln 32. Replace “vegetationcovered” with “vegetationcover”
Ln 33, Delete “erosion” before intensity
Ln 46, Replace “which will result in” with “resulting in”
Ln 70, More accurately than what?
Ln 80, Replace “multiple times rainfall” with “multiple rainfall events”
Ln 115, Replace “paper” with “study”
Ln 137, Replace “sheeting” with “sheets”
Ln 156, Do you mean flow hydrodynamic parameters are important for describing runoff and sediment production characteristics?
Ln 231233, These exponents do not necessarily tell us the relative importance of the inflow rate, slope and scouring times as these variables have different dimensions and magnitudes.
Ln 246247, Are these your results or results of Peng et al., 2014 and Niu et al., 2020?
Ln 319, Replace “Eq. (1012) shows” with “Eqs. (1012) show”
Ln 321323, Not sure these interpretations are correct and please see comment above on the same issue.
Ln 333, Delete “function” before relationship
Ln 335, Delete “function” before relationship
Ln 349351, It is not clear what this means. What is a significant variable rule?
Ln 355358, Poor English and please reword
Ln 385, I suggest delete the statement as it does not add any useful information.
Ln 412413, These statements may be correct, but the authors should consider the dimension and magnitude of these variables when comparing them.
Ln 485, Replace “(An et al., 2014)” with An et al., (2014)

AC2: 'Reply on CC2', Zhaoliang GAO, 24 Sep 2021
reply
Thank for your suggestions on this article, and we have revised the content of the article according to your suggestions. The following answers to your questions about the article are provided in detail.
Ln 70, More accurately than what?
Nearing et al. (1997),Reichert and Norton (2013) and Shen et al. (2016) found that stream power can more accurately than other hydrodynamic parameters to characterize the dynamic mechanisms of rill erosion.Ln 156, Do you mean flow hydrodynamic parameters are important for describing runoff and sediment production characteristics?
We consider that mean flow hydrodynamic parameters are important for describing runoff and sediment production characteristics. The slope runoff hydrodynamic characteristics greatly determine the slope rill erosion and morphological characteristics. The hydrodynamic characteristics of runoff can reflect the energy changes of runoff, which in turn have an impact on the stripping, transport and deposition of soil on slopes.Ln 231233, These exponents do not necessarily tell us the relative importance of the inflow rate, slope and scouring times as these variables have different dimensions and magnitudes.
We agree with the views you raised. In order to accurately quantify the effects of inflow rate, slope and scouring times on the slope erosion of the spoil tips, it is necessary to eliminate the effects of the magnitudes between the different influencing factors. For this purpose, we used a multiple linear regression method. The specific steps to calculate the degree of influence or contribution of each independent variable to the dependent variable are: (1) establish a multiple regression equation and obtain its coefficient of determination R^{2}. With R^{2} equal to the sum of the contribution of each independent variable. 1R^{2} being due to other factors that are beyond the scope of the analysis. (2) standardize the regression coefficients of each independent variable in the multiple regression equation to obtain the standardized regression coefficients, which are used to eliminate the effect of the magnitude (Eq. 1). (3) calculate the contribution of the independent variables to the dependent variable in the regression equation using the standardized regression coefficients (Eq. 2)(Nan et al., 2013). The specific formulas are as follows:
where β_{i}is the standardized regression coefficient of the i th independent variable, b_{i}_{}is the regression coefficient of the ith independent variable, σ_{xi }is the standard deviation of the i th independent variable, σ_{y}is the standard deviation of the dependent variable, and P_{i}is the contribution of the i th independent variable.
Ln 246247, Are these your results or results of Peng et al., 2014 and Niu et al., 2020?
These are results we observed during our experiments, and similar phenomena were observed by Peng et al. 2014 and Niu et al. 2020. To avoid misunderstandings, we have modified the original sentence. Specifically, as follows:
“With the blocking and scouring of the side walls, the erosion and collapse occurred repeatedly, and erosion fluctuates, so that multiple peaks and lows occur during the erosion process. Similar phenomena were observed by Peng et al. (2014) and Niu et al. (2020).”
Ln 321323, Not sure these interpretations are correct and please see comment above on the same issue.
As mentioned above, we requantified the effects of different influencing factors on rill width, rill depth and rill widthtodepth ratio based on a multiple linear regression approach.Ln 349351, It is not clear what this means. What is a significant variable rule?
What we want to express is that Fr does not show an obvious variation (increase or decrease) with increasing slope, inflow and scouring number, the reason may be related to the complexity of the development of rill morphology on the slope. we have modified the original sentence. Specifically, as follows:
“No obvious variation existed between Fr and the inflow rate, slope or scouring times may be related to the complexity of the rill morphological development on the slope.”Ln 355358, Poor English and please reword
we have modified the original sentence. Specifically, as follows:
“The DarcyWeisbach coefficient (f) ranged from 1.14 to 3.15. No obvious relationship existed between f and the inflow rate, slope and scouring times (Fig. 10(jl)) because the rill beds became more irregular, resulting in rill development.”Ln 412413, These statements may be correct, but the authors should consider the dimension and magnitude of these variables when comparing them.
As mentioned above, consider the dimension and magnitude of these variables, we used a multiple linear regression method and requantified the effects of different influencing factors on soil erosion of the spoil tips.
References
Nan S.,Wang Z.,Liu J.,Yang X.,Jiao N., and Tan Z.: The Impact and Contribution of Influx of Sediment onto Rill to Rill Erosion on Loess Hillslope, J. Mt. Sci.Engl.,31(2),194199,2013.

AC2: 'Reply on CC2', Zhaoliang GAO, 24 Sep 2021
reply

RC1: 'Comment on hess2021399', Anonymous Referee #1, 27 Aug 2021
reply
This paper presents field experiments to quantify erosion processes over spoil tips in the Loess Plateau of China. The authors analysed the experimental data and provided insights into key factors controlling the erosion processes. The paper is well structured and the presentation is mostly clear. However, I have the following specific comments on the manuscript.
Ln 32. Replace “vegetationcovered” with “vegetationcover”
Ln 33, Delete “erosion” before intensity
Ln 46, Replace “which will result in” with “resulting in”
Ln 70, More accurately than what?
Ln 80, Replace “multiple times rainfall” with “multiple rainfall events”
Ln 115, Replace “paper” with “study”
Ln 137, Replace “sheeting” with “sheets”
Ln 156, Do you mean flow hydrodynamic parameters are important for describing runoff and sediment production characteristics?
Ln 231233, These exponents do not necessarily tell us the relative importance of the inflow rate, slope and scouring times as these variables have different dimensions and magnitudes.
Ln 246247, Are these your results or results of Peng et al., 2014 and Niu et al., 2020?
Ln 319, Replace “Eq. (1012) shows” with “Eqs. (1012) show”
Ln 321323, Not sure these interpretations are correct and please see comment above on the same issue.
Ln 333, Delete “function” before relationship
Ln 335, Delete “function” before relationship
Ln 349351, It is not clear what this means. What is a significant variable rule?
Ln 355358, Poor English and please reword
Ln 385, I suggest delete the statement as it does not add any useful information.
Ln 412413, These statements may be correct, but the authors should consider the dimension and magnitude of these variables when comparing them.
Ln 485, Replace “(An et al., 2014)” with An et al., (2014)

AC3: 'Reply on RC1', Zhaoliang GAO, 24 Sep 2021
reply
Thank for your suggestions on this article, and we have revised the content of the article according to your suggestions. The following answers to your questions about the article are provided in detail.
Ln 70, More accurately than what?
Nearing et al. (1997),Reichert and Norton (2013) and Shen et al. (2016) found that stream power can more accurately than other hydrodynamic parameters to characterize the dynamic mechanisms of rill erosion.
Ln 156, Do you mean flow hydrodynamic parameters are important for describing runoff and sediment production characteristics?
We consider that mean flow hydrodynamic parameters are important for describing runoff and sediment production characteristics. The slope runoff hydrodynamic characteristics greatly determine the slope rill erosion and morphological characteristics. The hydrodynamic characteristics of runoff can reflect the energy changes of runoff, which in turn have an impact on the stripping, transport and deposition of soil on slopes.
Ln 231233, These exponents do not necessarily tell us the relative importance of the inflow rate, slope and scouring times as these variables have different dimensions and magnitudes.We agree with the views you raised. In order to accurately quantify the effects of inflow rate, slope and scouring times on the slope erosion of the spoil tips, it is necessary to eliminate the effects of the magnitudes between the different influencing factors. For this purpose, we used a multiple linear regression method. The specific steps to calculate the degree of influence or contribution of each independent variable to the dependent variable are: (1) establish a multiple regression equation and obtain its coefficient of determination R^{2}. With R^{2} equal to the sum of the contribution of each independent variable. 1R^{2} being due to other factors that are beyond the scope of the analysis. (2) standardize the regression coefficients of each independent variable in the multiple regression equation to obtain the standardized regression coefficients, which are used to eliminate the effect of the magnitude (Eq. 1). (3) calculate the contribution of the independent variables to the dependent variable in the regression equation using the standardized regression coefficients (Eq. 2)(Nan et al., 2013). The specific formulas are as follows:
where βi is the standardized regression coefficient of the i th independent variable, bi is the regression coefficient of the i th independent variable, σ_{xi }is the standard deviation of the i th independent variable, σ_{y }is the standard deviation of the dependent variable, and P_{i }is the contribution of the i th independent variable.Ln 246247, Are these your results or results of Peng et al., 2014 and Niu et al., 2020?
These are results we observed during our experiments, and similar phenomena were observed by Peng et al. 2014 and Niu et al. 2020. To avoid misunderstandings, we have modified the original sentence. Specifically, as follows:
“With the blocking and scouring of the side walls, the erosion and collapse occurred repeatedly, and erosion fluctuates, so that multiple peaks and lows occur during the erosion process. Similar phenomena were observed by Peng et al. (2014) and Niu et al. (2020).”
Ln 321323, Not sure these interpretations are correct and please see comment above on the same issue.
As mentioned above, we requantified the effects of different influencing factors on rill width, rill depth and rill widthtodepth ratio based on a multiple linear regression approach.
Ln 349351, It is not clear what this means. What is a significant variable rule?What we want to express is that Fr does not show an obvious variation (increase or decrease) with increasing slope, inflow and scouring number, the reason may be related to the complexity of the development of rill morphology on the slope. we have modified the original sentence. Specifically, as follows:
“No obvious variation existed between Fr and the inflow rate, slope or scouring times may be related to the complexity of the rill morphological development on the slope.”
Ln 355358, Poor English and please rewordwe have modified the original sentence. Specifically, as follows:
“The DarcyWeisbach coefficient (f) ranged from 1.14 to 3.15. No obvious relationship existed between f and the inflow rate, slope and scouring times (Fig. 10(jl)) because the rill beds became more irregular, resulting in rill development.”
Ln 412413, These statements may be correct, but the authors should consider the dimension and magnitude of these variables when comparing them.As mentioned above, consider the dimension and magnitude of these variables, we used a multiple linear regression method and requantified the effects of different influencing factors on soil erosion of the spoil tips.
References
Nan S.,Wang Z.,Liu J.,Yang X.,Jiao N., and Tan Z.: The Impact and Contribution of Influx of Sediment onto Rill to Rill Erosion on Loess Hillslope, J. Mt. Sci.Engl.,31(2),194199,2013.

AC4: 'Reply on RC1', Zhaoliang GAO, 24 Sep 2021
reply
Thank for your suggestions on this article, and we have revised the content of the article according to your suggestions. The following answers to your questions about the article are provided in detail.
Ln 70, More accurately than what?
Nearing et al. (1997),Reichert and Norton (2013) and Shen et al. (2016) found that stream power can more accurately than other hydrodynamic parameters to characterize the dynamic mechanisms of rill erosion.
Ln 156, Do you mean flow hydrodynamic parameters are important for describing runoff and sediment production characteristics?
We consider that mean flow hydrodynamic parameters are important for describing runoff and sediment production characteristics. The slope runoff hydrodynamic characteristics greatly determine the slope rill erosion and morphological characteristics. The hydrodynamic characteristics of runoff can reflect the energy changes of runoff, which in turn have an impact on the stripping, transport and deposition of soil on slopes.
Ln 231233, These exponents do not necessarily tell us the relative importance of the inflow rate, slope and scouring times as these variables have different dimensions and magnitudes.We agree with the views you raised. In order to accurately quantify the effects of inflow rate, slope and scouring times on the slope erosion of the spoil tips, it is necessary to eliminate the effects of the magnitudes between the different influencing factors. For this purpose, we used a multiple linear regression method. The specific steps to calculate the degree of influence or contribution of each independent variable to the dependent variable are: (1) establish a multiple regression equation and obtain its coefficient of determination R^{2}. With R^{2} equal to the sum of the contribution of each independent variable. 1R^{2} being due to other factors that are beyond the scope of the analysis. (2) standardize the regression coefficients of each independent variable in the multiple regression equation to obtain the standardized regression coefficients, which are used to eliminate the effect of the magnitude (Eq. 1). (3) calculate the contribution of the independent variables to the dependent variable in the regression equation using the standardized regression coefficients (Eq. 2)(Nan et al., 2013). The specific formulas are as follows:
where βi is the standardized regression coefficient of the i th independent variable, bi is the regression coefficient of the i th independent variable, σ_{xi }is the standard deviation of the i th independent variable, σ_{y }is the standard deviation of the dependent variable, and P_{i }is the contribution of the i th independent variable.Ln 246247, Are these your results or results of Peng et al., 2014 and Niu et al., 2020?
These are results we observed during our experiments, and similar phenomena were observed by Peng et al. 2014 and Niu et al. 2020. To avoid misunderstandings, we have modified the original sentence. Specifically, as follows:
“With the blocking and scouring of the side walls, the erosion and collapse occurred repeatedly, and erosion fluctuates, so that multiple peaks and lows occur during the erosion process. Similar phenomena were observed by Peng et al. (2014) and Niu et al. (2020).”
Ln 321323, Not sure these interpretations are correct and please see comment above on the same issue.
As mentioned above, we requantified the effects of different influencing factors on rill width, rill depth and rill widthtodepth ratio based on a multiple linear regression approach.
Ln 349351, It is not clear what this means. What is a significant variable rule?What we want to express is that Fr does not show an obvious variation (increase or decrease) with increasing slope, inflow and scouring number, the reason may be related to the complexity of the development of rill morphology on the slope. we have modified the original sentence. Specifically, as follows:
“No obvious variation existed between Fr and the inflow rate, slope or scouring times may be related to the complexity of the rill morphological development on the slope.”
Ln 355358, Poor English and please rewordwe have modified the original sentence. Specifically, as follows:
“The DarcyWeisbach coefficient (f) ranged from 1.14 to 3.15. No obvious relationship existed between f and the inflow rate, slope and scouring times (Fig. 10(jl)) because the rill beds became more irregular, resulting in rill development.”
Ln 412413, These statements may be correct, but the authors should consider the dimension and magnitude of these variables when comparing them.As mentioned above, consider the dimension and magnitude of these variables, we used a multiple linear regression method and requantified the effects of different influencing factors on soil erosion of the spoil tips.
References
Nan S.,Wang Z.,Liu J.,Yang X.,Jiao N., and Tan Z.: The Impact and Contribution of Influx of Sediment onto Rill to Rill Erosion on Loess Hillslope, J. Mt. Sci.Engl.,31(2),194199,2013.

AC3: 'Reply on RC1', Zhaoliang GAO, 24 Sep 2021
reply
Yongcai Lou et al.
Yongcai Lou et al.
Viewed
HTML  XML  Total  BibTeX  EndNote  

199  55  9  263  1  1 
 HTML: 199
 PDF: 55
 XML: 9
 Total: 263
 BibTeX: 1
 EndNote: 1
Viewed (geographical distribution)
Country  #  Views  % 

Total:  0 
HTML:  0 
PDF:  0 
XML:  0 
 1