Modeling Water Flow in Variably Saturated Porous Soils and Alluvial Sediments
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis is a review manuscript, so there is no novelty in our understanding of the subject.
The literature review is not critical although it is supposed that a review manuscript shows weak and strong points of each equation. What is the necessity of this study? No data is used to justify the selected equations for a specific objective.
Why does one need such a review?
The authors should mention the assumptions and limitations of each equation critically. Many factors affect the performance of each equation which have not been considered in this study. Discussion about the equations is not deep and most of time refers the journal reader to the existing references.
It is very difficult to draw any conclusion based on the results.
The author may use a data bank to justify his results about each equation.
Conclusion should be rewritten showing better contribution of this research. The authors present three objectives in lines 94-98, however, they do not reply to these objectives
The most innovative content of this work needs to be more discussed.
In summary:
The superiority of this study and methodology is not clear in comparison to existing ones.
The literature review is not critical regarding the existing methods.
The authors should present more profound investigation around his innovation, comparing their results with existing studies through a data set.
What is the main contribution of this study in our knowledge and understanding?
Some parts of the conclusion is based on current knowledge however, the journal readers need more innovative comparison and results from the existing literature.
Therefore, abstract and conclusions need to be rewritten by revealing the contribution of this study.
Author Response
Please, see the attachment.
Attachment File:
I thank the reviewers for their comments and suggestions. They were very useful to improve the manuscript during the revision. I also fixed some typos throughout the whole manuscript.
REVIEWER #1
I thank the reviewer for having dedicated his/her time to read and comment my manuscript. I did my best to improve the manuscript by profiting from his/her remarks and suggestions, as specified in detail below.
This is a review manuscript, so there is no novelty in our understanding of the subject.
I partially agree with the reviewer, as a “review manuscript” does not provide novelties, but it can provide a particular vision on the treated topic. In particular, I am not aware of any paper or textbook, which shows in a single publication, the four different formulations of the flow equations in unsaturated porous media, as it is done here.
The literature review is not critical although it is supposed that a review manuscript shows weak and
strong points of each equation.
Some remarks have been added, also on the basis of other reviewers’ suggestions and comments.
What is the necessity of this study?
I was invited to contribute to the special issue on “Groundwater, Soil and Sustainability” and I proposed the topic of this paper, which was considered to be suitable by the associate editors of the issue.
No data is used to justify the selected equations for a specific objective.
Some references to papers providing insight into the measurement of soil hydraulic properties and the reciprocal relationships have been added.
Why does one need such a review?
Please, see the answer to question “What is the necessity of this study?” few lines above.
The authors should mention the assumptions and limitations of each equation critically. Many factors
affect the performance of each equation which have not been considered in this study. Discussion about
the equations is not deep and most of time refers the journal reader to the existing references. It is very
difficult to draw any conclusion based on the results.
I revised the conclusions and hope that the link with the work’s objective is now more clear.
The author may use a data bank to justify his results about each equation.
The application of the four formalism presented in this manuscript to real field cases would require a very long work and would introduce also several critical aspects related to the numerical solution of the non-linear partial differential equations. Therefore, this would require a much longer time than that allowed from the publisher for a major revision and it would require to heavily increase the length of the paper. Although I agree with the reviewer that numerical aspects are at least as important as the identification of the partial differential equations which properly describe the physics of flow in unsaturated soil, I prefer to stick to the original . However, I included some references to papers which provide an interesting and useful insight into the measurement of soil hydraulic properties and the reciprocal relationships.
Conclusion should be rewritten showing better contribution of this research. The authors present three
objectives in lines 94-98, however, they do not reply to these objectives
Conclusions have been modified.
Sorry, but in the version that I uploaded on the journal website and I checked once again, lines 94 to 98 correspond to few points of the list of assumptions on which equation (3) is based. Probably, there is a discrepancy between the version I see and the version examined by the reviewer. However, in the revision of the conclusions, I tried to improve the correspondence of the comments to the goals of the paper stated in the introduction.
The most innovative content of this work needs to be more discussed.
I agree. The last sentence of the introduction has been modified, in order to provide a partial
answer to this comment.
In summary:
The superiority of this study and methodology is not clear in comparison to existing ones.
I agree with the reviewer, and in fact, I do not claim this work to be “superior” to any other work, but I hope it can contribute with some aspects which are sometimes left aside in the scientific literature.
The literature review is not critical regarding the existing methods.
This is basically due to the fact that I preferred to refer to seminal papers and to acknowledge researchers who published pioneering works in this research field.
The authors should present more profound investigation around his innovation, comparing their results with existing studies through a data set.
Please, see the answer to the comment “The author may use a data bank to justify his results about each equation” above.
What is the main contribution of this study in our knowledge and understanding? Some parts of the
conclusion is based on current knowledge however, the journal readers need more innovative comparison and results from the existing literature.
I hope this is now more clear from the conclusions.
Therefore, abstract and conclusions need to be rewritten by revealing the contribution of this study.
Abstract and conclusions have been revised, following the reviewers’ suggestion.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for Authors1. Abstract
The abstract section should be streamlined to highlight the key findings of the paper.
Line 5, “……quantity which is considered as independent variable”, the formulation of (3) in the scientific literature varies mainly depending on the dependent variable, so the statement here is inaccurate and contrary to follows.
Line 10, “Different types of initial and boundary conditions will be examined……”, the initial conditions required to solve the evolutionary equations are simply described in the text as the state of the system at t=0. A detailed overview of the initial conditions for the four equations is not carried out, which is contrary to the description here.
2. Introduction
Equations of water flow are not addressed in the status of research in the introduction, and the current state of research on the behavior of water flow in variably saturated porous soils and alluvial sediments is unclear, and more literature should be reviewed.
3. Discussion about initial and boundary conditions and about phenomenological relationships among θ, h and K
There is no clear conclusion in subsection 3.1, what does the focus here want to emphasize?
Line 170-173, whether θirr is a self-defined symbol, what is the basis and significance of the definition, and what is the reason for the volumetric water content to be somewhere in between? secondly, the definition of θirr is poorly expressed in the later text.
Line 176-177, it was mentioned earlier that he is a minimum, so why can ˆh(θ) lie between 0 and he, and this is inconsistent with Eq. 23 above.
Equation 25 cannot be deduced from Equation 24, how Equation 25 is derived?
“Both experimental evidence and studies on capillary bundle models show that ˆθ is a monotonously non-increasing function”, references should be added here, as well as ˆh(θ) should be described instead of ˆθ, and monotonically non-increasing functions are contrary to Equation 26.
“The first trivial condition for ˆK is that it should be positive, but for θ=θirr”, it is contrary to Eq. 29 with ˆK(θirr)=0.
“It is experimentally verified that K increases with soil water content”, please add the appropriate reference.
Line 181, “so that ˆh(θ) is always invertible in the interval (θirr, θsat)”, it should be monotonically increasing, what does invertible mean, the expression is not clear.
Line 186, “……which are based on the results of several studies which show that water infiltration in an initially dry soil creates a wetting front”, please add the appropriate reference.
“Instead, the study of non-linear systems by……”, the twist is not appropriate here.
Line 198-200, “The limitations of (39) are due to the fact that it does not obey (27)……it does not show any inflection point, contrary to what is expected from (28)”, equations 28 and 29 in the previous section are not sufficiently well founded, while the reasons for the discrepancy between equation 39 and the previous analysis need to be analyzed here.
Line 217, “3.3.1. Prescribed value of θ”, this subsection is mainly written about the boundary conditions under different conditions for the four equations, which does not correspond to the title.
4. Conclusions
Lines 245 and 247, “……the most natural formulations of (3)……”, and “……simultaneous saturated-unsaturated flow……”, the conclusion is not mentioned in the previous text, please verify.
In line 258, "at teh water tabel" is suggested to be changed to "at the water table".
5. References
Most of the citations in the article are old references and the reference section should be increased with the number of recent studies.
Comments on the Quality of English LanguageMinor editing of English language required.
Author Response
Please, see the attachment.
Attachment File:
I thank the reviewers for their comments and suggestions. They were very useful to improve the manuscript during the revision. I also fixed some typos throughout the whole manuscript.
REVIEWER #2
I thank the reviewer for having dedicated his/her time to read and comment my manuscript. I did my best to improve the manuscript by profiting from his/her remarks and suggestions, as specified in detail below.
1. Abstract
The abstract section should be streamlined to highlight the key findings of the paper.
Abstract have been revised, following the reviewers’ suggestion.
Line 5, “……quantity which is considered as independent variable”, the formulation of (3) in the scientific
literature varies mainly depending on the dependent variable, so the statement here is inaccurate and
contrary to follows.
I agree, there was a typo that has been corrected.
Line 10, “Different types of initial and boundary conditions will be examined……”, the initial conditions required to solve the evolutionary equations are simply described in the text as the state of the system at t=0. A detailed overview of the initial conditions for the four equations is not carried out, which is contrary to the description here.
I agree: initial conditions are not mentioned here in the revised version.
2. Introduction
Equations of water flow are not addressed in the status of research in the introduction, and the current state of research on the behavior of water flow in variably saturated porous soils and alluvial sediments is unclear, and more literature should be reviewed.
Indeed, the paper is not expected to provide a thorough review of the status of research on water flow in variably saturated porous media, but it is focused on a specific topic. However, further references have been added.
3. Discussion about initial and boundary conditions and about phenomenological relationships among θ, h and K
There is no clear conclusion in subsection 3.1, what does the focus here want to emphasize?
A sentence has been added at the end of the subsection to stress the value and relevance of the obtained conditions.
Line 170-173, whether θirr is a self-defined symbol, what is the basis and significance of the definition, and what is the reason for the volumetric water content to be somewhere in between? secondly, the definition of θirr is poorly expressed in the later text.
The sentences have been rephrased.
Line 176-177, it was mentioned earlier that he is a minimum, so why can ˆh(θ) lie between 0 and he, and this is inconsistent with Eq. 23 above.
I agree, the sentence was somehow jargony. I modified it.
Equation 25 cannot be deduced from Equation 24, how Equation 25 is derived?
Equation (25) depends on equation (24), in the sense that equation (24) implies that suction has a vertical asymptote for θirr. This is now stated explicitly and I hope that this clarify the derivation.
“Both experimental evidence and studies on capillary bundle models show that ˆθ is a monotonously non-increasing function”, references should be added here, as well as ˆh(θ) should be described instead
of ˆθ, and monotonically non-increasing functions are contrary to Equation 26.
References have been added. I thank the reviewer for finding the typo: “increasing” has been substituted with “decreasing”.
“The first trivial condition for ˆK is that it should be positive, but for θ=θirr”, it is contrary to Eq. 29 with ˆK(θirr)=0.
I rephrased the sentence, in order to avoid misunderstanding.
“It is experimentally verified that K increases with soil water content”, please add the appropriate reference.
References has been added.
Line 181, “so that ˆh(θ) is always invertible in the interval (θirr, θsat)”, it should be monotonically increasing, what does invertible mean, the expression is not clear.
This is used in mathematical sense and it is now specified in the text.
Line 186, “……which are based on the results of several studies which show that water infiltration in an initially dry soil creates a wetting front”, please add the appropriate reference.
References have been added.
“Instead, the study of non-linear systems by……”, the twist is not appropriate here.
The sentence has been rephrased in active form.
Line 198-200, “The limitations of (39) are due to the fact that it does not obey (27)……it does not show any inflection point, contrary to what is expected from (28)”, equations 28 and 29 in the previous section are not sufficiently well founded, while the reasons for the discrepancy between equation 39 and the previous analysis need to be analyzed here.
The sentence has been slightly modified, so that it should be now more clear.
Line 217, “3.3.1. Prescribed value of θ”, this subsection is mainly written about the boundary conditions under different conditions for the four equations, which does not correspond to the title.
The title of the subsection has been changed in order to be more consistent with the final result and the text has been modified accordingly.
4. Conclusions
Lines 245 and 247, “……the most natural formulations of (3)……”, and “……simultaneous saturated-unsaturated flow……”, the conclusion is not mentioned in the previous text, please verify.
The conclusions have been revised and hopefully this problem has been fixed.
In line 258, "at teh water tabel" is suggested to be changed to "at the water table".
Thank you, the typo has been fixed.
5. References
Most of the citations in the article are old references and the reference section should be increased with the number of recent studies.
This is due to the fact that in the original version I preferred to refer to seminal papers and to acknowledge researchers who published pioneering works in this research field. However, in this revised version, some further references have been added.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsDear Authors,
The presented study describes theoretical work on bounduary condition of selected equation. In my opinion there is no clear highlight/intended contribution pointed out (diffrent keywords ?)
The article consists of the same sentences written twice .
English language needs to be improved. Some sentences are to long and difficult to understand main idea. eg. I do not understand the point of the sentence: lin 3-5 ..Modelling...
All abbreviations and acronyms should be explained at their first use in the text.
Comments on the Quality of English Language
There are some problems in English expression, which makes some sentences difficult to understand. The expression needs to be more standardized and more concise.
Author Response
Please, see the attachment.
Attachment File:
I thank the reviewers for their comments and suggestions. They were very useful to improve the manuscript during the revision.
I also fixed some typos throughout the whole manuscript.
REVIEWER #3
I thank the reviewer for having dedicated his/her time to read and comment my manuscript. I did my best to improve the manuscript by profiting from his/her remarks and suggestions, as specified in detail below.
Dear Authors,
The presented study describes theoretical work on bounduary condition of selected equation. In my opinion there is no clear highlight/intended contribution pointed out (diffrent keywords ?)
Abstract, introduction and conclusions have been revised, following the reviewers’ suggestion.
The article consists of the same sentences written twice .
I agree and I tried to reduce the repetitions in the body of the text.
English language needs to be improved. Some sentences are to long and difficult to understand main idea. eg. I do not understand the point of the sentence: lin 3-5 ..Modelling...
The text has been modified, in order to use a better and more clear language. In particular, I agree that the sentence in the abstract, which was explicitly mentioned by the reviewer, was too synthetic and cryptic, so that it has been modified and slightly expanded.
All abbreviations and acronyms should be explained at their first use in the text.
I agree. The definitions of some symbols have been moved, in order to be given exactly at the first use in the text of the symbols themselves.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe author replied to my comments. I recommend the acceptance of this manuscript. .
Author Response
Please, see the attached file.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for Authors1. Abstract
The abstract section is cumbersome and should be streamlined to highlight the key findings of the paper.
2. Introduction
The research status on water flow equations in variably saturated porous soils and alluvial sediments is unclear and should be supplemented.
3. References
There are few references published in the recent five years, and it is recommended to supplement them.
Author Response
Please, see the attached file.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsDear Authors,
The paper has been clearly improved. Nevertheless, I have some suggestions:
I still do not see a clear statement for the intended contribution. I have seen other reviewers point this out as well. In my opinion, the authors answer that “I was invited to contribute to the special issue on “Groundwater, Soil and Sustainability” and I proposed the topic of this paper, which was considered to be suitable by the associate editors of the issue.” Is no explanation of the contribution of this work mentioned in the reviewer's comments "What is the need for this study? Why is such a review needed?"
Author Response
Please, see the attached file.
Author Response File: Author Response.pdf
