The Functional Relationship of Sediment Transport under Various Simulated Rainfall Conditions

Round 1

Reviewer 1 Report

This is a revised manuscript after a first round of review. The authors are thanked for making many improving changes and for providing replies to previous raised concerns. I now only suggest six corrections in terms of the language, as follows: - Page 7, line 220: change (analysis of the problem are done) to (analysis of the problem is done). - Page 9, line 272: change (Regression method used are) to (Regression methods used are). - Page 9, line 286: change (value of measured the dependent parameter) to (value of the measured dependent parameter). - Page 9, line 287: change (dividing Q with) to (dividing Q by). - Page 10, line 309: change (Figure 2 (a) and Figure 2 (b) shows) to (Figure 2 (a) and Figure 2 (b) show). - Page 10, line 310: remove (of) in (against of).

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors,

Although this version of the manuscript presents significant improvement compared to the initial version, some of my previous remarks still haven’t been considered. Please find the list of remarks still valid below:

• There is no state-of-the art review which would provide context for the presented research, which is visible from the low number of references in the paper (15). Please add few paragraphs outlining the findings of similar papers and their relevance for your research in the introduction section of the paper.
• Estimation of the critical shear stress (?), considered to be constant by the authors (“because we use the same soil type throughout the experiment thus given the same value of shear stress despite of different rainfall pattern”) cannot be considered valid since for shallow overland flow and low flow rate there is no reliable shear stress estimation methods without velocity measurements. Furthermore, equations used for shear stress estimation are not applicable for rainfall-driven extremely shallow flows, such as the one used in this study.
• Authors state that their findings are in contrast with [16], [17], [18] and consistent with [8]. This needs to be discussed in-depth.
• Conclusion are purely descriptive, lacking connection with the actual research.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The authors have attempted to address the review comments provided in the previous version of this manuscript. Th authors seem to have addressed most of the minor comments. However, the major concerns still remain (see the details below). Hence, I cannot recommend this manuscript for publication at this stage.

Major comments:

1. Since the dimensionless parameters derived in this study are not different from the ones reported in the literature, as the authors themselves state, Sec. 2.3 appears to be redundant. This information can be presented in the introduction as part of literature review.
2. The authors have still not clearly answered how i, Q, and Re are independent of each other. This is a critical concern. Aren't i, Q, and Re dependent on each other for a given rainfall pattern? If so, using three dimensionless parameters based on i, Q, and Re instead of just one seems to be redundant. Please clearly explain how i, Q and Re are calculated from rainfall flow rate for a given rainfall pattern. 
3. It is not clear which data from Ref. 19 have been used in Fig. 5. Please highlight the figure/table in Ref. 19 from which these data have been taken.
4. Shear stress is dependent not just on the soil type but also on the flow velocity gradient at the soil surface. The latter should be dependent on the flow velocity associated with a rainfall pattern -- if not, please clarify how the shear stress at the solid surface is independent of the rainfall pattern.
5. It is not clear if Eq. 19 is dimensionally correct. Please clarify this in the response document. Secondly, is the unit of slope (S) m (line #293)? Please also clarify this.
6. In the previous review comment #31, by 'rate of increase/decrease' it was meant to understand the time rate of change of rainfall rate. From Fig. 1 it seems that these changes are rather abrupt resulting in an instantaneous change in rainfall rate from one value to the next. Please clarify if this is the case.

Minor comments:

1. Please correct Fig. 5 legend: 'Zhang et al., 2010' instead of 'Zhang et al., 2011'.
2. Figure 1 in the new manuscript does not address the comment #7 in the previous review (the old Fig. 1 is not shown in the new manuscript).

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Dear authors,

 

The changes you have introduced into the manuscript compared to the previous version are minor – section 2.2. was moved into introduction and renumerated as 1.1. The rest of the paper remains unchanged, except few minor changes in writing style.

 

In my opinion, lack of the state-of-the art review heavily burdens this manuscript. There is no context for the presented research, and therefore its contribution to the field remains unclear.

 

Authors have used 3 entire paragraphs and 6 references to describe three stages of water-induces erosion which is con tent of elementary engineering textbooks. On the other hand, authors haven’t presented the relevant papers that focus on the same topic, revealing the gap in knowledge they are aiming to bridge. They conclude the introduction with reference to “transfer of solute”, which is a dead-end as they do not address this issue anywhere in the text later on.

 

The aim of the paper is introduced with the following statement: “However, the relationship of rainfall pattern on sediment has rarely been investigated.“. Authors need to present the research they are referring to and highlight the main findings and shortcomings. Otherwise, one can conclude that the presented research is first of its kind.

 

Authors have presented the section 1.1 (Sediment transport prediction and governing equations) as state-of-the-art review, but this section presents equations and assumptions that authors employ in their work, and therefore is actually part of the Methodology as it was in the previous versions.

 

Another of my remarks is questionable estimation of the critical shear stress, and consequently all other hydraulic parameters. From the Figure 2 it can be seen that the flow is highly turbulent (200000< Re<700000). In these flow conditions turbulence is predominant driver of the erosion, and shear stress estimates are not as straightforward as presented here. Authors state “This means that the flow depth contributes to the transport of sediment by saltation and suspension in the flow by increasing the velocity” which shows that they do not understand the main assumptions as flow depth does not directly translate into higher velocity (you can consult the specific energy of cross-section to test this assumption). This misunderstanding is further confirmed with the following statement “The flow depth was calculated by using Manning’s equation as below:”, where authors calculate flow rate (Q) instead of the flow depth.

 

All of the previous remarks indicate that authors haven’t precisely designed their experiment and raises the question if their findings are reliable. Please support your experimental setup and calculations with examples from the literature.

 

Another thing missing are the measured values of the variables used for calculation – flow rate, flow depth, slope, sediment transport, etc. Authors have only presented the derived variable calculated through the dimensional analysis, but their database is missing altogether. Therefore, your approach cannot be repeated or evaluated by the readers.

 

 

“The objective of this paper was to establish the selected parameters that contribute to the sediment transport capacity in overland flow conditions under different rainfall pattern conditions and to evaluate their significance.” In my opinion, in the presented research second part of the objective is not achieved, as authors haven’t evaluated significance for the each of their parameters.

 

I feel that this results of presented research can be published if authors present the framework for their research – i.e. examples from the literature that use same assumptions as them to validate their approach to the problem.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The authors have still not convincingly addressed the major comments 2, 4, and 5 which are critical scientific concerns. Hence I cannot recommend the manuscript to be accepted.

To re-iterate these comments from the previous review:

2. The authors seem to confuse between independent and dependent parameters. The former are the ones which are controlled/varied in experiments whereas the latter are the ones which are measured/predicted. The authors still incorrectly state that iL/ν, Q/Lν, and Re are independent.  

4. A similar comment, as above, can be made for the observations regarding the shear stress.

5. The left-hand side (LHS) of Eq. 19 has units of m³/s, whereas the right-hand side (RHS) of Eq. 19 has units of (m²)(m^2/3) = m^8/3 (as per the authors' response). The dimensions of the LHS and the RHS are, hence, clearly not the same as per the authors' own response. However, the authors state that Eq. 19 is dimensionally correct. This is clearly not correct.

Author Response

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Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Dear authors,

Although your research, in my opinion, still doesn’t provide enough data to be convincing, it is clear that you consider it to be finalized.

In this regard, I have only one minor remark – in the added text in the Introduction combine referencing from [1] in a way that it doesn’t occur 4 times in a single paragraph.

Reviewer 3 Report

The manuscript can be accepted.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

The manuscript reports an experimental investigation on the transport of sediments/soil particles down the slope of a soil surface due to rainfall. The rainfall intensities have been varied through four different types of rainfall (constant, increasing, increasing-decreasing, and decreasing). Other parameters such as the slope of the soil bed, the length of the flow, and the soil type have been kept constant. Dimensional analysis is used to identify the independent and dependent parameters in dimensionless forms. The experimental data of the sediment transport is plotted versus the independent dimensionless parameters, and fitted through regression analysis to obtain correlations connecting sediment transport with Reynolds number, dimensionless rainfall intensity, and dimensionless total discharge.

The topic of this study is interesting. However, the novelty of the study is unclear, the manuscript is poorly written, the presentation and discussion of the results are not convincing. Hence I cannot recommend this manuscript to be accepted. Comments for further improvement of this study and the manuscript are given below.  

Comments:

1. It is not clear how the non-dimensional parameters are different from the ones reported in the literature. The novelty of this study is unclear.
2. This is a critical concern: Are i, Q, and Re truly independent of each other? It seems that the rainfall intensity would have some role in deciding the total discharge as well as the flow velocity used in calculating the Re. Please clarify this in the revised manuscript.
3. The reported correlations seem to have very low R² values. How do these correlations compare with the ones reported in literature, in terms of their predictive capability? Please discuss this in the manuscript.
4. Line 216: Why is the applied shear stress at the surface of the soil/sand considered to be a constant between different rainfall types?
5. What is the difference between 'hydraulic characteristics' and 'hydraulic geometry'? These terms have to be modified to better reflect the intended meaning.
6. The various parameters mentioned in the Abstract are not defined, without which it is rather difficult to understand. Please define these parameters clearly in the abstract!
7. Figure 1: 'a' is rain drop before hitting the soil surface. 'c' is not mentioned in the caption. Please check and make changes appropriately to make the caption reflect the images shown in the figure.
8. Eq. 1: The dimensions of all the parameters have to be explicitly mentioned before the dimensional analysis. Without this, it is difficult to evaluate the equations written down in the manuscript.
9. What does α with an over-bar mean in Eq. 3?
10. It is unclear how Eq. 4 is obtained from Eq. 3. Please provide intermediate steps to clarify this in the manuscript.
11. Line 67: Replace 'principle' with 'principal'.
12. Line 91: It is unclear what the authors mean by 'represented by the term...'. Perhaps, the meaning was lost due to grammatical error. Please revise this statement and clarify this in the revised manuscript.
13. Lines 120-121: The lower limit 0.07 seems to be more than that of the upper limit 0.00207. Please check and correct this. The same is true for S.
14. Line 137: Define/expand GA in GA optimization where it is first used in the manuscript.
15. Is f in Eq.10 and f in Eq. 11 necessarily the same? Perhaps, it is better to use a different letter for the function in Eq. 11.
16. Line 186: τ_c/τ₀ is repeated. Please remove one of these.
17. Eq. 12: The first term within the brackets seems to be incorrect. Please check the dimensions of q_s and correct this accordingly.
18. Eq. 13, line 2: '2' in the superscript should be removed.
19. Eq. 20: Firstly, replace 'initial' with 'inertial' in the definition of Re. Secondly, the definition in terms of the ratio of fluid and flow properties to fluid properties is not correct, since both inertial and viscous forces are dependent on the fluid flow. Thirdly, why was L chosen to define Re rather than the flow depth h?
20. Line 212: The unit of V should be m/s.
21. Line 219: Eq. 1.19 should be replaced with Eq. 19.
22. Why does the subscript of x vary from 1 to k in Eq. 23 whereas it varies from 1 to i in Eq. 24 and Eq. 25? Does this mean the number of independent parameters is different between these two types of regression analyses?
23. Line 232: This is redundant information. Please remove this.
24. Eq. 25: Is it log(x_i)^β_i which can be re-written as β_ilog(x_i) or is it {log(x_i)}^βi? If it is the former, couldn't one incorporate these exponents β_i into the constant factor β₀. Please clarify in the revised manuscript.
25. Line 242: Replace Eq. 1.22 with Eq. 22.
26. Lines 252-253: Is this also true for the 'constant-type' rainfall? Please clarify in the revised manuscript.
27. Table 4: How are these properties measured or from where are they obtained? Please include this info in the revised manuscript.
28. Line 261: What is the purpose of placing the collected samples in the refrigerator? What was the temperature at which the samples were kept? Please clarify this in the revised manuscript.
29. The definition of q_s is not made clear. Please define this parameter clearly in the revised manuscript.
30. Lines 267-268: Please give details of the Manning's equation and how the flow depth was estimated.
    How was it ensured that the flow indeed covered the width of 1 m and not partially filled in the width direction? 
31. Please define the rainfall intensities used in the four types of rainfalls. For example, what were the rates of increase/decrease in ICR, ICRDCR, and DCR? 
Grammatically, this is a poorly written manuscript. There are numerous language-related errors throughout the manuscript which makes it difficult to read and understand. A thorough language check of the manuscript is required.

Reviewer 2 Report

This work presents an experimental and analytical investigation that led to proposed regression models of the sediment transport (as dependent variable) and the Reynolds number, normalized rainfall intensity, and a normalized flow rate (as independent variables), while keeping the surface slope, the shear stress ratio, and the normalized median grain diameter constant.

The work utilized dimensional analysis and statistical regression, with a software package.

Various types of regression functions models were proposed (linear and nonlinear), with quantitative estimation of their prediction accuracy.  

 

The work reflects a lot of efforts and the authors are commended for their study.

 

However, the manuscript suffers from serious linguistic mistakes. The following are just examples

• The final result of established that (should be: The final result established that)
• Statistical method used are (should be Statistical methods used are)
• factor that describing the soil (should be: is a factor that describes the soil)
• soil particle to lose and detached (should be: soil particle to become lose and detached)
• Both graphs showing (should be: Both graphs show)

 

Also, there is a big gap among the repetition of the same experiment, making the results not very reliable (as in Figure 3).

 

Also, there the two independent parameters (Re) and (Q/Lv) appear related, and should not be surprising to see a similarity between Fig. 3b and Fi. 3c.

 

Also, in Figure 4, the same x-axis is used to show variable with huge difference in their range. Thus, the variable (Q/Lv) appears as if (0), but this is not true. Figure 4 does not appear to have a big value.

 

Also, Figure 5 is a probability–probability plot (normal P-P plot), as it shows in its title. But it is interpreted differently, which reflects a lack of understanding of its meaning. The text refers to (linear regression), when discussing that figure.  

Reviewer 3 Report

Dear authors,

The research topic that you presented in this paper, investigation of the sediment transport under various rainfall patterns, is very interesting.

 

Unfortunately, the manuscript in the current version is very poorly written, the results are not clearly presented, discussion is lacking and the conclusion is general. In my opinion, this paper requires major revision, of both methodology and presentation, in order to be suitable for publishing. Please find below few suggestions regarding your work that I feel need to be addressed before publishing.

 

 

General remarks:

 

The whole manuscript is lacking proper structure – there is no state-of-the art review which would provide context for the presented research. Please add few paragraphs outlining the findings of similar papers and their relevance for your research.

 

The factors affecting sediment transport are modelled using study [15], which focuses on bar formation in the sand-bed river. This phenomenon, although similar to yours, is of different time and spatial scale. Please model your approach on study with similar conditions to yours or explain the relevance of the selected paper to your experiment.

 

Paper is lacking Methodology section which would explain your specific approach to the problem, which is currently scattered across sections 2 and 3.

 

The dimensionless parameters you introduced using dimensional analysis need to be explained in more detail – what process each of them present and how does that differ from current approaches in the literature?

 

Regression models are well known, there is no need to present simple equations in your manuscript, a reference would suffice.

 

How is critical shear stress (?) obtained? For your shallow overland flow and low flow rate there is no reliable shear stress estimation methods without velocity measurements.

 

Results presented are purely descriptive. Authors need to elaborate their findings to readers. What are the common characteristics of trend obtained by fitting equation for different sets of variables across the rainfall patterns? Explain the contribution of your research to the respective field.

 

Conclusion is actually introduction, repeating the already known facts. You could have made this conclusion even without conducting the study as it does not reflect your results.

 

 

Specific remarks:

 

The first paragraph of the introduction section contains some strong statements that need to be rephrased, as they are not correct in present form, e.g.:

• “The rainfall that is saturated enough in the soil will become surface runoff; this is known as a partly contributor to soil loss”. The rainfall cannot be saturated, soil can.

 

There are some repetitive sentences – these two sentences on ln 55 are exactly the same:

“Sediment removed in the detachment process is transported by surface runoff. Once detached, sediment particles are transported in the flow.”

 

Figure 2 is simple and there is no need to use external source for it. Please redraw the Figure 2 yourselves and properly reference the source.