Triangular Fuzzy Finite Element Solution for Drought Flow of Horizontal Unconfined Aquifers

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

• (1) It was claimed that “Compared to traditional numerical approaches,it provides a more robust and flexible framework capable of handling irregular geometries, highly variable hydraulic properties, and the inherent uncertainties in hydrological By integrating fuzzy logic with FEM analysis, this method enhances predictive accuracy and improves decision-making in water resource management by quantifying uncertainties through probability-based confidence intervals.” However, based on current evaluations, the computational outcomes of the proposed method show high consistency with those of the comparison methods. Since prototype observation data is lacking for validation and support, the reliability of the model's calculations remains undemonstrated, and the advantages of the proposed method are not fully emphasized. It is recommended to utilize field data from actual groundwater flow cases or experimental data to better evaluate the practical applicability and reliability of the model.
• (2) As mentioned in the manuscript, this method has a higher computational cost and requires a large amount of data for calibration. On the other side, the difference in calculation accuracy is small according to manuscript. Therefore, I am curious about the specific significance and value of this research, particularly how it addresses practical issues and contributes to academic innovation and practical application. In my humble opinion, the author needs to provide additional explanation about this.
• (3) It contains numerous formulas throughout the model construction and mathematical expression sections, but lacks sufficient explanation of notation. It is recommended to add explanations of key parameters or variable symbols.
• (4) The presentation of the results in the manuscriptis somewhat simplistic. It is suggested to use more intuitive flow field visualization diagrams to depict the simulation outcomes, thereby enhancing the manuscript's visual clarity and overall readability.
• (5) There are some equations which were not numbered, such as those appearing on lines 152-153.Please ensure all displayed equations are properly numbered for cross-referencing purposes.
• (6) The visual representation in Figure 1 does not align with or properly illustrate the mathematical relationship expressed in equation (5) of the manuscript: Equation in the text but in the figure, which may cause confusion. The use of italic and roman font styles for parameters needs to be standardized.
• (7) In Figure 2(a), shouldn't the transition from jto j+1/2 be immediately followed by j+1? Furthermore, Figure 2(c) exhibits an unexplained spacing between "j+1/2" and "j+1". Kindly clarify this spacing decision or make corrections if unintended.
• (8) In Figure 5, shouldn't the S-axis in Figure 5 be “i”? According to my personal understanding, the axis where variablejis locate should be labeled as “τ” but not “T”, and the label for the H-axis has disappeared.
• (9) Please review allfiguresthroughout the manuscript and standardize the legends, label fonts, and font sizes.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Paper "Triangular Fuzzy Finite Element Solution for drought flow of Horizontal Unconfined Aquifers" presents research related to the field of hydrogeology. A very interesting combination of fuzzy logic and the groundwater flow equation.

 

• Check that there are no more citations from the same journal or author. It is suggested that the percentage should not exceed 10% - 15%.
• The conclusion should not be in the form of a summary. Here it is necessary to precisely emphasize the scientific contribution of the conducted research, as well as the contribution to the academic community.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

What is the main question addressed by the research?

 

The article analyzes flows through aquifers. The problem is analyzed in drought conditions. The authors set themselves the goal of finding a solution for the following flow conditions: one-dimensional, non-stationary problem, non-linear analysis solved by fuzzy methods of the second order partial differential equation. The authors carried out a numerical analysis with the adopted initial and boundary assumptions. Modeling was carried out based on triangular elements.

 

• Do you consider the topic original or relevant to the field? Does it address a specific gap in the field? Please also explain why this is/ is not the case. • What does it add to the subject area compared with other published material?

The authors discuss in detail the history of research conducted in the analyzed field. It is worth noting that the first author has been dealing with the subject for 50 (!) years and his position in this field is well-established. The authors draw attention to the inconveniences of the models used so far. The problem they try to solve in the current article is the existence of an impervious wall.

 

• What specific improvements should the authors consider regarding the methodology? What further controls should be considered?

 

The authors describe the initial and boundary conditions and the formulas used in a mathematical manner. The formulas provided do not exhaust the entire model used to conduct the analysis. Information about the model is sufficient and the introduced restrictions are justified – there is no need to provide a full model with all the details, because the methodology is familiar to scientists dealing with similar topics. An interesting concept is the authors' use of selected definitions for "the readers non-familiar with the fuzzy and possibility theory" (chapter 2.2.1),

Because the model used is very complex, there is a risk of an error in the implemented code. The authors rightly tested the created software on a case that has an analytical solution.

 

• Are the conclusions consistent with the evidence and arguments presented and do they address the main question posed? Please also explain why this is/is not the case.

A numerical analysis was carried out in the paper – the results were compared with the analytical solution. Conclusions regarding individual calculation cases are given below the graphs illustrating the obtained results. The “discussion” chapter contains general recommendations resulting from the entire analysis and valuable tips on cases for which the presented model is recommended. The authors also discuss the limitations of the proposed method and the stated goals of further research. The “conclusions” chapter summarizes the conducted research, which is discussed in the article.

 

• Are the references appropriate?

The selection of literature is appropriate for this type of scientific article.

The list of references includes 52 items. The authors refer to most of them in the initial description of the current state of knowledge. The rest are necessary due to the mathematical model used.

 

Eight items are co-authored by the first author. Considering the long-term work on the issue and the author's great contribution to the development of the issue, such a large number should not be considered as “unjustified self-citation”.

 

Final conclusion:

The article is scientifically correct. The whole meets the criteria required for scientific works and in my opinion qualifies for publication. Due to the precisely provided mathematical model, the article can be a valuable source for other researchers.

It is recommended to make only minor corrections and conduct careful editorial proofreading. Detailed comments are given below.

 

DETAILED COMMENTS.

Comments on references.

Line 88 indicates that the item [16] is from 1976. Meanwhile, in the list of references (line 593), item [16] is from 1975.

 

Editorial comments

Particular care should be taken when dividing paragraphs into lines. Automatic division generates errors (see e.g. lines 92/93, 202, 220, 262, 265, 431 etc.). After automatic division by the text editor, the entire document should be carefully checked and corrections made manually.

Figures: 3, 6, 9, 10 – please consider enlarging the figure or using larger letters inside the figure.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf