the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Developing Functional Recharge Systems to Repel Saltwater Intrusion via Integrating Physical, Numerical, and DecisionMaking Models for Coastal Aquifer Sustainability
Abstract. Controlling the hydraulic heads along the coastal aquifer may help to effectively manage saltwater intrusion, improve the conventional barrier's countermeasure, and ensure the coastal aquifer's longterm viability. This study proposed a framework that utilizes a decisionmaking model (DMM) by incorporating the results of two other models (physical and numerical) to determine proper countermeasure components. The physical model is developed to analyze the behavior of saltwater intrusion in unconfined coastal aquifers by conducting two experiments: one for the base case and one for the traditional vertical barrier. MODFLOW is used to create a numerical model for the same aquifer, and experimental data is used to calibrate and validate it. Three countermeasure combinations, including vertical barrier, surface, and subsurface recharges, are numerically investigated using three model case categories. Category (a) model cases investigate the hydraulic head’s variation along the aquifer to determine the best recharge location. Under categories (b) and (c), the effects of surface and subsurface recharges are studied separately or in conjunction with a vertical barrier. As a preset of the DMM, evaluation and classification ratios are created from the physical and numerical models, respectively. The evaluation ratios are used to characterize the model cases results, while the classification ratios are used to classify each model case as best or worst. An analytic hierarchy process (AHP) as DMM is built using the classification ratios of hydraulic head (HHR), salt line (SLR), intrusion (IR), repulsion (Rr), wedge area (WAR), and recharge (RER) as selection criteria to select the overall best model case. The optimal recharging location, according to the results, is in the length ratio (LR) range from 0.45 to 0.55. Furthermore, the DMM supports case3b (vertical barrier + surface recharge) as the best model case to use, with a support percentage of 47.93 %, implying that this case has a good numerical model classification with a minimum IR of 67.9 %, a maximum Rr of 29.4 %, and an acceptable WAR of 1.25. The proposed framework could be used in various case studies under different conditions to assist decisionmakers in evaluating and controlling saltwater intrusion in coastal aquifers.
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Interactive discussion
Status: closed

RC1: 'Comment on hess202389', Anonymous Referee #1, 07 Jul 2023

AC1: 'Reply on RC1', Wael Mahmod, 14 Sep 2023
Review of
Developing Functional Recharge Systems to Repel Saltwater Intrusion via Integrating Physical, Numerical, and DecisionMaking Models for Coastal Aquifer Sustainability
By
 Introduction and overall assessment
The authors assess the improvement caused by adding artificial recharge to an impervious barrier as measures to control seawater intrusion (SWI). To this end, they perform sandbox experiments and numerical methods on a highly idealized case. They use this model to compute a number of ratios that are used to feed an “analytic hierarchy process”. They conclude that the combination of physical barrier with artificial recharge is the best option to control SWI.
Overall, the topic is of interest to HESS readers and the conclusion is valid, although somewhat trivial. Since they are not considering construction or operation costs, the more barriers you put (physical and or hydraulic), the better you will control SWI. Furthermore, it is clear that the authors have put a lot of work into this paper. Unfortunately, I believe the paper cannot be published in the present form for several reasons:
1) It is unnecessarily complex and, worse, incomplete. A large number of indicators are defined without a clear reason (no formal dimensional analysis). Yet, the most important parameters (recharge rate) are not defined.
2) The paper contains numerous conceptual errors (not too severe, but unacceptable).
3) It is very poorly written. Worse, it is very poorly organized. I do not just mean the language needs to be improved, but also the logical sequence.
I discuss issues 1) and 2) below and I make a number of writing recommendations in the last section. But the overall recommendation would be to greatly simplify your paper and remove everything that is not related to the main objectives.
The authors put in a lot of effort on this revision to make the manuscript proper for logical sequence, both in terms of the main sections and individual sentences and paragraphs. In addition to the APC language editing service, which the HESS journal will provide if the manuscript is accepted, the writers checked the English language and grammar with native language speakers.
 Conceptual errors:
Introduction
Line 58: It is not true that “Physical and numerical models … reduce the high cost of hydrogeological and environmental investigations”. There is no alternative to scu investigations. If you design a SWI control system without a good understanding of you system, you will waste you money (what is the depth?, how do you know you are intercepting the whole SW flux?, how much you need to recharge?
Reply: The authors agree with the reviewer that hydrogeological and environmental investigations are necessary; yet, this sentence (Line 59) indicates that physical and numerical models decrease expenses rather than eliminating investigations. Using both models aids in understanding hydrogeological systems, eliminating the need to place monitoring wells intensively and identifying where wells should be constructed in order to save money while achieving the same goals. To avoid this conflict, the authors modify the sentence and place a relevant reference:" Physical and numerical models have not only proven to be more effective tools for selecting the optimum solutions for controlling saltwater intrusion, but can also be used to reduce the need for expensive hydrogeological and environmental investigations before constructing a fullscale project (Mantoglou 2003; Zhou, et al. 2003; Abarca et al. 2006; Sutherland and Barfuss, 2011; Singh 2015; AbdElaty et al. 2019; Guo et al. 2019; M Armanuos et al. 2019). "
Methods:
I am not sure what you mean by “dimension analysis”, but none of the dimensional analyses” I know consist of computing model output ratios. Please, do not anticipate results before describing what you do (“The results of the category (a) model cases reveal the location of the minimal hydraulic heads, which are expected to be the locations of the indicated artificial recharge systems” (and we still do not know what model category (a) is).
Reply: Through the experimental phase, the authors suggested dimensionless quantities based on variables, parameters, and constants that influence saltwater intrusion, which are defined and summarized in Figure 5 and Table 2. These suggested dimensionless quantities include three variables called evaluation ratios for analyzing the output results, one parameter that serves as experimental run constraints, and two geometric parameters that are used to assign hydraulic gradient and saltwater profile.
Based on the above explanation, and regards to the reviewer comment, modifications are carried out through the section”2. Materials and Methodologies” as follows:
1 For section “2. Materials and Methodologies”:
 The mentioned sentence of category (a) (line 103) is modified to be “Category (a) model cases are used to determine the location of the minimal hydraulic heads, which are suggested to be the locations of the indicated artificial recharge systems. Categories (b) and (c) investigate the impacts of surface and subsurface recharges on saltwater intrusion at the indicated locations, either alone or in conjunction with a vertical barrier.”
 The word “ratio” in line (97) was replaced with “dimensionless quantities”.
2 For section “2.2 Dimension Analysis and Evaluation Ratios”:
 The subtitle is changed to “Evaluation Ratios”
 The dimensionless quantities are divided into three groups as mentioned to clarify the purpose and physical meaning of each (lines 183188).
 Table3 is renamed “Suggested evaluation ratios, conditional parameters and geometric parameters” and rearranged based on the mentioned three dimensionless groups, as well as adding a new column namely “Physical meaning”
Sand tank:
Note that the selected ratios are arbitrary and do not result from a proper “dimensional analysis”. That is, appropriate rations would result from writing the problem in dimensionless form, so that they would represent the minimum set of variables for definition of the problem. The current definitions are:
(1) arbitrary (e.g., IR is defined with respect to a base case that has not been defined yet, perhaps it would be better to define it with respect to the case without any remediation),
(2) redundant (NAR and NDR are complementary, except that, to make things worse, BDR is defined in terms of cross sectional area),
(3) not really descriptive variables (e.g., the SLR is not a real number, but a function). This is severe, as it invalidates the final results. Worse, the reader is left with the impression that the ratios are improvised.
Reply: The authors would like to confirm that these ratios were not chosen arbitrarily. the authors suggested dimensionless quantities based on variables, parameters, and constants that influence saltwater intrusion, which are defined and summarized in Figure 5 and Table 2. These suggested dimensionless quantities include three variables called evaluation ratios for analyzing the output results, one parameter that serves as experimental run constraints, and two geometric parameters that are used to assign hydraulic gradient and saltwater profile. For that, these changes take place in the manuscript:
1 For section “2. Materials and Methodologies”:
 The mentioned sentence of category (a) (line 103) is modified to be “Category (a) model cases are used to determine the location of the minimal hydraulic heads, which are suggested to be the locations of the indicated artificial recharge systems. Categories (b) and (c) investigate the impacts of surface and subsurface recharges on saltwater intrusion at the indicated locations, either alone or in conjunction with a vertical barrier.”
 The word “ratio” in line (97) was replaced with “dimensionless quantities”.
2 For section “2.2 Dimension Analysis and Evaluation Ratios”:
 The subtitle is changed to “Evaluation Ratios”
 The dimensionless quantities are divided into three groups as mentioned to clarify the purpose and physical meaning of each (lines 183188).
 Table3 is renamed “Suggested evaluation ratios, conditional parameters and geometric parameters” and rearranged based on the mentioned three dimensionless groups, as well as adding a new column namely “Physical meaning”
Concerning comment no. 1 as arbitrary, experiment 1 (the base case) has already been defined before this section at line 175. It is the case where saltwater intrusion through the porous media is being investigated without any countermeasures. Regarding the IR example produced by the reviewer, IR illustrates the variation of intrusion length over time (t) with reference to the maximum intrusion length (base case). Afterwards, IR was used as a comparison analysis for all of the cases covered in this study.
Concerning comment no. 2 as redundant, indeed NAR and BDR are complementary (BDR = 1NAR, where b is constant). The parameter NAR and its components (a/A) are omitted from the whole manuscript as well as in Tables 2, 3, and 4.
Concerning comment no. 3 as not really descriptive variables, the authors agree with the reviewer that SLR is A function demonstrates the variation in intrusion depth as a function of distance X and time (t) due to saltwater boundary head. In the comparative analysis of the results, the average SLR value (SLR_{avg}) will be used. Moreover, HHR is also a function that demonstrates the variation of the hydraulic head due to the influence of the saltwater boundary head at a particular distance X and time (t). In the comparative analysis of the results, the minimum value of HHR and its location will be taken into account. This clarification is explained in the physical meaning column of Table 3.
After devoting some length to describing these ratios in section 2.2, the authors introduce new ratios in section 2.3. Worse, the numbering of the new ratios is inadequate.
Reply: The dimensionless ratios proposed from the experiments are extracted from the geometry shown in Figure 5 to be used for analyzing the output results. From the results themselves, new dimensionless ratios are proposed to classify the model cases as the best or worst models, namely as classification ratios. Lines (250252) explains this in detail. The authors omit the ratio (IR) from the classification ratio because it produces the same classification as Rr (Rr=IRcase1aIRcasek) and add the SLRi instead, which reflects the increase in saltwater level. The SLRi is an important ratio for selecting the best model, which is one of the criteria used in the AHP model. Accordingly, Figure 16a as well as Table 8 are modified.
Recharge through wells is done when you have an aquitard. Furthermore, wells generate a radial
flow around the well. The setting (both the sandbox and the model) are essentially 2D, so that
including wells is not appropriate.
Reply: Wells could be used to recharge any form of aquifer, either naturally or artificially. The physical and numerical models are in 3D (X, Y, and Z directions); however, the hydrogeological conditions in Z directions are constant and have no effect on the outcomes. Furthermore, it is difficult to consider all conditions in experiments. As a result, recharge wells are only used numerically in this study once the numerical model has been calibrated and validated.
Line 132: “The filling process is done in layers of 5cm each, with a falling height of 50 cm for each layer, to ensure a homogeneous hydrogeological property of the media sand”. Actually this procedure may lead to stratification (it depends on the filling rate) with the coarsest material at depth. While this may be adequate (it is similar to what occurs in nature) it does not ensure “a homogeneous … sand”.
Reply: The authors make every effort to obtain accurate physical models. To ensure that stratification did not develop, the filling process was continued from one layer to the next without offering any opportunities for this stratification at a low rate (low rates are ensured due to the usage of funnels). This filling technique, as outlined in the paper, will produce the best results as compared to simply skipping sand at one time in the sandbox. As a result, the authors believe that this method is the best technique to achieve good porous medium homogeneity.
Densities of 0.99 and 1.022 kg/L (not m3/s) are low and high for FW and SW, respectively. Adding 0.15 g/L concentration of green food dye will increase the density of SW.
Reply: At line 144, the units are changed to g/cm^{3}. The main idea in this study is to use variable density flow in porous media. As clearly illustrated in Figure 4, the saltwater density was calibrated after adding the dye, and it was 1.022 g/cm^{3}. On the other hand, the effect of the green food dye is negligible at a concentration of 0.15 g/L (0.00015 g/cm^{3}).
Line 149: You are not verifying saturation, hydraulic heads will equilibrate even if air bubbles are trapped.
Figure 4 can be dropped. It is not necessary.
Reply: The authors demonstrate saturation by monitoring the 14 glass manometer tubes illustrated in Figure 2 until equilibrium is reached and then waiting one hour to confirm that air bubbles have departed. Furthermore, air bubbles will be trapped even in nature. As a result, the experiments are close to nature.
In response to the referee's previous query about saltwater density, the authors consider that this figure supports the experimental section.
In Figure 5, name only variables that you are going to vary (b is fixed, isn’t it?). Also you may add the location of recharge wells here, so that you can eliminate Figure 6.
Reply: The authors omit b, X_{b}, and the highlighted areas (neck area (a) and sand media area( A)) from Figure 5. Regarding omitting Figure 6, concerning the need to clear boundary conditions, the authors restructured this section by including a new section "2.3 Conceptual Model". In this section, a conceptual model based on the experimental set and procedures is proposed to simplify the representation of the groundwater system, its boundary conditions, the use of a vertical barrier, and the use of two artificial recharge systems as presented in the new modified Figure 6. Moreover, Section 2.4's title is modified to "2.4 Numerical Model Development" and a new paragraph about boundary conditions, packages used, and model discretization is added (lines 230–237).
Tables 13 can be blended into 1 (if at all). Table 3 is particularly unfriendly s it forces the reader to check that all cases are identical. It took me a while to realize that you were just varying the barrier depth. In fact, you may just say that you did several runs with varying barrier depth and make them a function of barrier depth.
Reply: The authors were confused by the table numbers provided by the referee (Tables 1–3). If the referee means that Tables 2 and 3 should be combined, the authors prefer to keep them distinct so that the readers are not confused. Table 1 describes the components of the sandbox model. For the second half of the referee question about Table 3, the authors believe that the referee means Table 4. To make the text easier to read in Table 4, the authors omit the values of X_{b}, D_{b}, and NAR from the table, simplifying the table contents. The table listed three distinct groups with clear titles:
Category (a): using vertical barrier
Category (b): using vertical barrier and surface recharge
Category (c): using vertical barrier and subsurface recharge
Please, eliminate Table 5 (textbook and irrelevant for your work)
Reply: The authors eliminate Table 5 and the sentence at lines 242243 is changed to be “Using the experimental results, many trials are carried out to calibrate the model using various hydrogeological properties, with reference to (Domenico et al. 1998; Rotz 2021)”
Numerical Model
The model is not properly described. Beyond formalities, this is severe because the results suggest that boundary conditions in the model /never described) are different to those in the sand tank.
Reply: The authors confirm to the reviewer that the numerical model's boundary conditions are the same as the experiments. However, the authors agree with the reviewer that further details concerning the numerical model and boundary conditions are needed to be clearer. As a result, the authors restructured this section as follows:
 Including a new section "2.3 Conceptual Model". In this section, a conceptual model based on the experimental set and procedures is proposed to simplify the representation of the groundwater system, its boundary conditions, the use of a vertical barrier, and the use of two artificial recharge systems as presented in the new modified Figure 6.
 Section 2.4's title is modified to "2.4 Numerical Model Development" and a new paragraph about boundary conditions, packages used, and model discretization is added (lines 230–237).
AHP technique
The description is too sketchy (I had to read independently to understand it). While, in my understanding, the AHP technique is not appropriate here. It is generally used for multiple criteria that are hard too subjective for quantitative comparison, so that the weights assigned to each criteria are derived from pairwise comparisons by “experts”.
Reply: The authors added more details explaining the scientific background of the AHP model under Section 2.5, "DecisionMaking Model (AHP technique)". AHP is used to arrange the alternatives according to their relative importance, which is considered qualitative based on the subjective opinions of the experts. Through this study, the authors asked several experts to provide the inputs (point scale) for both alternatives and criteria. The authors provided them with the numerical model outputs as a guide.
Results
Model calibration is unclear. For one thing, the authors report a RMSE without having described what errors are being minimized.
Reply: The RMSE is used to assess the quality of fit between the simulated and observed saltwater lines, as clarified at lines 328–330 and in the legends of Figures 8, 9, and 10. Based on these figures and the RMSE values, the employed hydrogeological properties are set as the calibrated parameter of the numerical model, as stated from line 334 to line 339 and shown in Table 5.
The parameters results are unrealistic (Table 6 contains no units, I assume that k is m/s, but a porosity of 0.04, a specific storage of 0.0619 1/m?, and a S_Y of 0.04 are clearly unrealistic). I do not think that these errors affect results severely, but it conveys a poor image of the model.
Reply: The authors added the units of the hydrogeological parameters. The K unit is measured in cm/s, the Ss unit is measured in 1/cm, and the others (Sy and ŋ) are dimensionless.
Of course, the parameters determined during the calibration process are accompanied by inaccuracies, which generally come from two sources. The first is that a model can only represent a simplified version of a complicated natural or experimental reality. The second is that the measurements used to constrain parameter estimations contain noise. To overcome the inaccuracy, the authors conduct numerous trials to obtain numerically calibrated parameters while minimizing the weighted squared difference between measured and simulated data. The model output is evaluated to determine the quality of fit within the meaning of RMSE.
Considering this and according to (Domenico et al. 1998; Rotz 2021):
K value is within the values mentioned by (Domenico et al. 1998; Rotz 2021).
ŋ is not a porosity; it is an effective porosity, so it has less value than porosity and is within the values mentioned by (Domenico et al. 1998; Rotz 2021).
Sy is also within the values mentioned by (Domenico et al. 1998; Rotz 2021).
Ss is considered a complicated parameter as it depends on many parameters as (Aquifer Compressibility, Total Porosity, Water Density (variable densities are found in the study), Gravitational Acceleration, Water Compressibility). The authors tried many values under the consideration of sensitivity analysis to achieve the best of fit between observed and simulated results. Although the authors tried many values and found that there was no effect on the results (as the reviewer indicated), the current value is the calibrated one used in this study.
Probably more severe are the apparent instabilities or the fact that boundary conditions look different. IT is also unfair to the reader to find here, for the first time, that model construction is done under transient conditions, which leaves the reader wondering how are the indices described in Section 2 computed.
Reply: Regarding the boundary conditions, the authors confirm to the reviewer that the numerical model's boundary conditions are the same as the experiments. However, the authors agree with the reviewer that further details concerning the numerical model and boundary conditions are needed to be clearer. As a result, the authors restructured this section as follows:
 Including a new section "2.3 Conceptual Model". In this section, a conceptual model based on the experimental set and procedures is proposed to simplify the representation of the groundwater system, its boundary conditions, the use of a vertical barrier, and the use of two artificial recharge systems as presented in the new modified Figure 6.
 Section 2.4's title is modified to "2.4 Numerical Model Development" and a new paragraph about boundary conditions, packages used, and model discretization is added (lines 230–237).
As mentioned in Section 2.4.1, "Calibration and Verification Processes", a verification procedure is implemented in this study to check two aims,:
1 Confirming the time when a steadystate condition occurs in based the results of experiment 1.
2 Fitting the observed saltwater line in experiments 1 and 2 for the transient and steadystate conditions.
The experimental process is already in a transient state until it achieves a steady state, which is achieved after 90 minutes, as resulted in Section 3.1 “Calibration and Verification of the Numerical Model".
As a result, during the calibration and verification phases, the numerical model is run in a transient state to determine when the steady state condition will be reached when compared to the implemented experiments. The calibration and verification stages' results demonstrate that steady state occurred at 90 minutes as well as in the experiments. All subsequent analyses are based on the data obtained after 90 minutes, as stated at Section 3.1 “Calibration and Verification of Numerical Model” (Lines 338339).
Worse, the flat region of the salt interface (between 30 and 40 cm inland) in the experiment suggests that permeability is higher in this region (probably a consequence of the handling of the barrier). This flat region was reproduced in the numerical model, but nothing is said about heterogeneity.
Reply: As stated in section "2.1.3 Experimental Procedures" the authors attempt to avoid heterogeneity in the experiment 2 part (lines 177181) by first removing sand from the experimental area. The vertical barrier is then placed at the experimental portion, 25cm from the feed chamber. Following that, the experimental section's media sand is replaced. As a result, heterogeneity might be ignored in the numerical model. The results demonstrate that the model has been validated.
The graphs do not appear to make much sense. It is not clear to me what hydraulic grade line is. But if I interpret it to mean head, the paths are inconsistent. You probably do not need the paths.
Reply: The hydraulic grade line (HGL) is the slope of the water table (potentiometric surface), or the change in water level per unit distance along the maximum head decrease direction. According to the graphs, the hydraulic head distribution along the aquifer is necessary to understand in order to locate the ideal place for artificial recharge.
Path lines are utilized to show the flow behavior of both freshwater and saltwater through the sand media under different conditions (using vertical barriers and artificial recharge types), as indicated in Section "2.4 Numerical Model" through lines 224229. The authors believe that these paths represent the hydraulic behavior of freshwater and saltwater in porous media, as well as the effect of these movements on hydraulic heads, particularly near barriers and recharge locations.
Results of each case are hard to read because of the abuse and redundancy of indicators and inconsistencies. For example, IR had been defined the ratio of observed intrusion length at a time (t) to maximum saltwater intrusion length (base case). Yet, for the base case IR is found to be 0.97. I could not follow the last part (new items are introduced and I must confessed that I was exhausted of going back and forth to recall the meanings of all the abbreviations).
Reply: The authors simplify the analysis part by omitting the complex explanation and adding tables with the values of the evaluation ratios and classification ratios, using tables as follows:
Section “3.2.1 Saltwater intrusion and flow behaviors in category(a) model cases”: Table 6 is added
Section “3.2.3 Saltwater intrusion and flow behaviors in categories (b) and (c) model cases”: Table 7 is added
Concerning the value of IR (L(in)/max.L(in) =0.97), after the numerical model has been verified, all of its output values are considered in calculating these evaluation ratios; however, the constant value of max.L(in) is considered from the experimental value (observed value) as stated in Table 2item4, which is nearly the same value as the numerical model. As a result, the ratio is slightly less than 1.00.
Editorial comments and writing
The paper is very poorly written. I am referring not only to the traditional “look for a native speaking person” (being a nonnative myself, I hate when I am told it), but also to the logic. The paper is complex and long, and the writing does not help. Try to simplify it. I understand that you are under pressure to publish quickly, but, please, facilitate the lives of readers by providing an easy to read paper (in the end, it will favor citations). Numerous statements call for a more refined argumentation. I list a few below:
In the abstract: “Three countermeasure combinations, including vertical barrier, surface, and subsurface recharges, are numerically investigated using three model case categories. Category (a) model cases investigate the hydraulic head’s variation along the aquifer to determine the best recharge location. Under categories (b) and (c), the effects of surface and subsurface recharges are studied separately or in conjunction with a vertical barrier”. Perhaps it is sufficient to say "The numerical model is used to investigate the SWI control efficiency of vertical barrier, and optimally located surface and subsurface artificial recharge”.
Reply: The authors believe that the abstract reflects the manuscript contents, and the mentioning of categories of model cases, including the usage of vertical barriers, surface recharge, and subsurface recharge, is important to mention.
Also, in the abstract, try to minimize the use of acronyms (OK in the body of the paper) and too many numbers (they tend to hide, rather that highlight). For example, it is very hard to read: “An analytic hierarchy process (AHP) as DMM is built using the classification ratios of hydraulic head (HHR), salt line (SLR), intrusion (IR), repulsion (Rr), wedge area (WAR), and recharge (RER) as selection criteria to select the overall best model case. The optimal recharging location, according to the results, is in the length ratio (LR) range from 0.45 to 0.55. Furthermore, the DMM supports case3b (vertical barrier + surface recharge) as the best model case to use, with a support percentage of 47.93%, implying that this case has a good numerical model classification with a minimum IR of 67.9%, a maximum Rr of 29.4%, and an acceptable WAR of 1.25”. Instead, you may just say: “An analytic hierarchy process is built to compare SWI control strategies on the basis of head, salt line, intrusion, repulsion, wedge area and recharge. We find that best results are obtained by combining a vertical barrier with surface recharge at a distance from the coast comparable to the thickness (here you have a problem, your LR is a model dependent variable, you must relate it to generic aquifer variables”.
Reply: The authors omit the acronyms from the abstract as much as possible as. This is in the lines 26 and 27.
The introduction is very poorly structured… You start by saying that SWI is a relevant problem, continue with methods to control SWI (but do not mention artificial recharge, which many, including me consider the best control method, as its efficiency is greater than 1, see Abarca et al., WRR, 2006). Then you introduce artificial recharge to conclude that “Although many studies investigate saltwater intrusion in coastal aquifers, only a limited number study the control methods of saltwater intrusion”! This is inconsistent (and false!). I believe that the logical sequence of the introduction needs to be revised.
Reply: In the paragraph from Line 47 to Line 58, the writers described artificial recharge techniques, their efficacy, and the associated problems.
Line 46: “Artificial recharge techniques, such as surface and subsurface recharge systems, are critical for establishing hydraulic barriers and mitigating the effects of saltwater intrusion”. They are not critical… Instead “Artificial recharge techniques can be used for establishing hydraulic barriers and mitigating saltwater intrusion, while recovering SGD”.
Reply: In response to the reviewer's query, the authors changed the sentence.
“These techniques have several advantages compared to traditional methods, including low cost…” what traditional techniques do you refer to?
Reply: Traditional methods have already been mentioned in the second paragraph of the introduction in lines 43 and 46: "reducing pumping rates, relocating pumping wells, changing pumping patterns, constructing physical subsurface barriers, and saltwater abstraction"
“Although many studies investigate saltwater intrusion in coastal aquifers, only a limited number study the control methods of saltwater intrusion”. Indeed, you should cite some of them
Reply: In response to the reviewer's query, the authors added references (line 58).
“Although physical and numerical models are effective economic tools for selecting the best solutions for repelling saltwater intrusion, deficiencies in the acquisition of appropriate evidence to support the final decision are discovered”. What do you mean by discovered… Perhaps you should indicate some of these deficiencies.
Reply: In response to the reviewer's query, the authors changed the sentence to “Although physical and numerical models are useful in determining the optimum solutions for controlling saltwater intrusion, deficiencies in the acquisition of appropriate evidence to support the final decision are discovered. Since the scenarios of hydrogeological models for a specific aquifer cannot agree on minimizing intrusion, improving groundwater availability, being environmentally friendly, and being costeffective”.
The objective statement should be short and to the point. Instead, you list seven goals, which are
really methodological steps.
Reply: The authors omit the objective (III) which may considered as methodology.
Look for appropriate references (this may also help you to simplify the writing by leading the reader to other papers for details). For example, “MODFLOW2005, in conjunction with the SWI2 package, is used in this study for numerical modeling of saltwater intrusion. SWI2 is a software package used to analyze threedimensional groundwater flow, model saltwater intrusion, and calculate hydraulic heads. The main advantage of using the SWI2 package is that it requires fewer cells for the simulation process than variabledensity groundwater flow packages like SEAWAT. The ability of SWI2 to represent each aquifer as a single layer of cells results in significant model runtime savings”. I am not sure this choice is appropriate, but please provide references for all the codes.
Reply: In response to the reviewer's query, the authors added references (lines 220, 221, and 225).
Also, provide a reference for “HM 169 GUNT HAMBURG”
Reply: In response to the reviewer's query, the authors added references (line 119).
There are numerous terms that you must revise (you do not “repel seawater intrusion”, you control it, or minimize it)
Reply: In response to the reviewer's query, the authors change the word repel to control in the whole manuscript.

AC1: 'Reply on RC1', Wael Mahmod, 14 Sep 2023

RC2: 'Comment on hess202389', Anonymous Referee #2, 07 Aug 2023
General comments
 The paper is not well written in terms of the logical flow in the whole paper and in individual sentences and paragraphs.
 The idea of using experimental data to calibrate numerical models of saltwater intrusion is not new. There have been many past studies of numerical modelling of saltwater intrusion and the accuracy of numerical models in this field is well established. The authors could have started with a numerical model of a fullscale project and tested various options for controlling saltwater intrusion on that. The smallscale experiments and smallscale models are not necessary.
 The level of discretisation in the numerical models is not adequate to accurately represent the processes being investigated. The results shown in Figures 8, 9 and 10 show that higher resolution if the vertical direction is required – say five times as many layers.
 In some cases, the key parts of the paper are not clearly explained. For example, what are the nondimensional parameters that were used to assess the merit of the different options?
Detailed comments
Line 1. “Repel” is the wrong word. Use “control” instead.
Line 16. Why use results from the two models? If the numerical model results do not agree with the experimental results, it means that the numerical model needs to be improved. Why and how are the experimental results included in the DMM?
Line 21. Category (a) is not clearly explained here or elsewhere. Table 4 indicates that it includes a vertical barrier but no recharge.
Line 26. It is not clear what is being optimised in the choice of the six parameters. What are the target values for each of the six parameters? And why are they chosen?
Line 39. Replace “potentiality” by “availability”.
Line 46. Add some references for the use of artificial recharge.
Line 59. Change “repelling” to “controlling” (do this throughout the paper). Change to “...reduce the need for expensive hydrogeological and environmental investigations …”.
Line 62. Physical and numerical models are not “economic “ tools.
Line 81. The categories need to be defined here.
Line 82. Why are both experimental and numerical studies required?
Line 84. Item (iii) is meaningless.
Line 104 and Figure 1. There is no explanation of what criteria are used for optimisation. What are the target values for each of the six parameters? And why are they chosen?
Line 135. What does calibration mean here? How is the density changed?
Line 191. The model used is not very large in terms of computational blocks and the results show it requires refinement. Runtime savings is not an important issue for a model of this size.
Line 197. Some discussion in words should be given for the three categories and seven cases. What happens for the surface recharge and borewells recharge?
Line 228263. These sections are very unclear. What are the target values for the parameters? And why?
Line 268. The fit of the model results shown in Figs. 8, 9, 10 and 11 is quite poor and indicates that the model grid is too coarse. Also, the permeability in the experiment may not be uniform.
Line 287321. This discussion is rambling and fails to clearly identify the key conclusions.
Line424434. Very unclear explanation and figures. Without a clear explanation of what the target values for the parameters are the use of terms like “bets” and “worst” is meaningless.
Line 444475. Again, this is very unclear as the optimisation criteria have not been made clear.
Line 484485. It is incorrect to include “numerically” before “proposed”
Line 487. The dimensional analysis was not presented.
Line 489501. The numerical values given for the various parameters (LR.HRR,WAR, SLR,Rr and RER) have little meaning. They are not discussed in physical terms and it is not explained above why these values are desirable.
Citation: https://doi.org/10.5194/hess202389RC2 
AC2: 'Reply on RC2', Wael Mahmod, 14 Sep 2023
General comments
 The paper is not well written in terms of the logical flow in the whole paper and in individual sentences and paragraphs.
Reply: The authors put in a lot of effort on this issue, both in terms of the main sections and individual sentences and paragraphs. In addition to the APC language editing service, which the HESS journal will provide if the manuscript is accepted, the writers checked the English language and grammar with native language speakers.
 The idea of using experimental data to calibrate numerical models of saltwater intrusion is not new. There have been many past studies of numerical modelling of saltwater intrusion and the accuracy of numerical models in this field is well established. The authors could have started with a numerical model of a fullscale project and tested various options for controlling saltwater intrusion on that. The smallscale experiments and smallscale models are not necessary.
Reply: The primary goal of this research is to identify the optimal location for recharging groundwater in order to control saltwater intrusion. The authors use sandbox experiments and numerical approaches to do this. They evaluate the benefit of adding artificial recharge to an impermeable barrier as a strategy to control saltwater intrusion (SWI). This model is used to produce a number of ratios that are fed into an "analytic hierarchy process." They conclude that the combination of physical barriers and artificial recharge is the best solution for controlling SWI. In the future, a largescale model might be utilized to test this concept and examine the outcomes.
 The level of discretisation in the numerical models is not adequate to accurately represent the processes being investigated. The results shown in Figures 8, 9 and 10 show that higher resolution if the vertical direction is required – say five times as many layers.
Reply: The authors investigated various discretization computations in order to provide an accurate diagnostic of variations in head drawdowns and water balances. Calibration and validation are used to ensure the model's validity. Despite its small scale, the model features 8 model layers and 2320 cell of discretization. Furthermore, more refinement is generated at the locations of the vertical barrier and recharge systems to provide more exact outcomes. Finally, the author feels that there is no need to go beyond discretization. Furthermore, the authors revised this section (2.4) in order to clarify the concept of boundary conditions and domain discretization, as follows:
 Including a new section "2.3 Conceptual Model". In this section, a conceptual model based on the experimental set and procedures is proposed to simplify the representation of the groundwater system, its boundary conditions, the use of a vertical barrier, and the use of two artificial recharge systems as presented in the new modified Figure 6.
 Section 2.4's title is modified to "2.4 Numerical Model Development" and a new paragraph about boundary conditions, packages used, and model discretization is added (lines 230–237).
 In some cases, the key parts of the paper are not clearly explained. For example, what are the nondimensional parameters that were used to assess the merit of the different options?
Reply: Through the experimental phase, the authors suggested dimensionless quantities based on variables, parameters, and constants that influence saltwater intrusion, which are defined and summarized in Figure 5 and Table 2. These suggested dimensionless quantities include three variables called evaluation ratios for analyzing the output results, one parameter that serves as experimental run constraints, and two geometric parameters that are used to assign hydraulic gradient and saltwater profile.
Based on the above explanation, and regards to the reviewer comment, modifications are carried out through the section”2. Materials and Methodologies” as follows:
1 For section “2. Materials and Methodologies”:
 The word “ratio” in line (94) was replaced with “dimensionless quantities”.
2 For section “2.2 Dimension Analysis and Evaluation Ratios”:
 The subtitle is changed to “Evaluation Ratios”
 The dimensionless quantities are divided into three groups as mentioned to clarify the purpose and physical meaning of each (lines 183188).
 Table3 is renamed “Suggested evaluation ratios, conditional parameters and geometric parameters” and rearranged based on the mentioned three dimensionless groups, as well as adding a new column namely “Physical meaning”
The dimensionless ratios proposed from the experiments are extracted from the geometry shown in Figure 5 to be used for analyzing the output results. From the results themselves, new dimensionless ratios are proposed to classify the model cases as the best or worst models, namely as classification ratios. Lines (250252) explains this in detail. The authors omit the ratio (IR) from the classification ratio because it produces the same classification as Rr (Rr=IRcase1aIRcasek) and add the SLRi instead, which reflects the increase in saltwater level. The SLRi is an important ratio for selecting the best model, which is one of the criteria used in the AHP model. Accordingly, Figure 16a as well as Table 8 are modified.
Detailed comments
Line 1. “Repel” is the wrong word. Use “control” instead.
Reply: In response to the reviewer's query, the authors change the word repel to control in the whole manuscript.
Line 16. Why use results from the two models? If the numerical model results do not agree with the experimental results, it means that the numerical model needs to be improved. Why and how are the experimental results included in the DMM?
Reply: Physical models are utilized to investigate the hydraulic behavior of saltwater intrusion and to collect data for the numerical model's calibration and validation. In contrast to the limitations of experiments, a numerical model is then employed to extensively study the saltwater intrusion under various conditions. These conditions include the use of vertical barriers, surface recharges, and subsurface recharges, as shown in the suggested model cases (see Table 4).
Regarding DMM, experimental results weren’t included in the AHP model; the numerical model results were included. For more clarification, the authors added more details explaining the scientific background of the AHP model under Section 2.5, "DecisionMaking Model (AHP technique)". AHP is used to arrange the alternatives according to their relative importance, which is considered qualitative based on the subjective opinions of the experts. Through this study, the authors asked several experts to provide the inputs (point scale) for both alternatives and criteria. The authors provided them with the numerical model outputs as a guide.
Line 21. Category (a) is not clearly explained here or elsewhere. Table 4 indicates that it includes a vertical barrier but no recharge.
Reply: In the abstract (line21), the subsequent sentences inform that “Three countermeasure combinations, including vertical barrier, surface, and subsurface recharges, are numerically investigated using three model case categories. Category (a) model cases investigate the hydraulic head’s variation along the aquifer to determine the best recharge location. Under categories (b) and (c), the effects of surface and subsurface recharges are studied separately or in conjunction with a vertical barrier.”. these sentences define the purpose of each proposed category.
To make the text easier to read in Table 4, the authors omit the values of X_{b}, D_{b}, and NAR from the table, simplifying the table contents. The table listed three distinct groups with clear titles:
Category (a): using vertical barrier
Category (b): using vertical barrier and surface recharge
Category (c): using vertical barrier and subsurface recharge
Line 26. It is not clear what is being optimised in the choice of the six parameters. What are the target values for each of the six parameters? And why are they chosen?
Reply: At first, the authors would like to notify the reviewer that they added more details explaining the scientific background of the AHP model under Section 2.5, "DecisionMaking Model (AHP technique)". The authors aim to make it clear that AHP is not an optimization approach but rather a decisionmaking model for selecting the best model case among three categories (a, b, and c). As the AHP is a qualitativebased approach, there are no set targets for these ratios. AHP is used to arrange the alternatives according to their relative importance (lines 275283).
As stated in sections 2.2 and 2.4 of the manuscript, evaluation ratios and classification ratios are proposed to evaluate and classify the model cases included in categories (a, b, and c), respectively. The criteria used in AHP considered 5 parameters (not 6 parameters) among them (Rr, SLRi, Minimum HHR, WAR, and RER). To evaluate and compare alternatives, the AHP determines the relative weights of these parameters. In the model cases of category (a), four criteria (Rr, SLRi, Minimum HHR, and WAR) are employed, while all five criteria are used in the model cases of categories (b) and (c) (lines 309322).
Line 39. Replace “potentiality” by “availability”.
Reply: In response to the reviewer's query, the authors made the changes.
Line 46. Add some references for the use of artificial recharge.
Reply: In response to the reviewer's query, the authors has added references for the use of artificial recharge.
Line 59. Change “repelling” to “controlling” (do this throughout the paper). Change to “...reduce the need for expensive hydrogeological and environmental investigations …”.
Reply: In response to the reviewer's query, the authors change the word repel to control in the whole manuscript. Moreover, the sentence at line 59 is changed to “Physical and numerical models have not only proven to be more effective tools for selecting the optimum solutions for controlling saltwater intrusion but can also be used to reduce the need for expensive hydrogeological and environmental investigations before constructing a fullscale project”
Line 62. Physical and numerical models are not “economic “ tools.
Reply: The authors rephrase the sentence to “Although physical and numerical models are useful in determining the optimum solutions for controlling saltwater intrusion, deficiencies in the acquisition of appropriate evidence to support the final decision are discovered. Since the scenarios of hydrogeological models for a specific aquifer cannot agree on minimizing intrusion, improving groundwater availability, being environmentally friendly, and being costeffective.”
Line 81. The categories need to be defined here.
Reply: In response to the reviewer's query, the authors rephrase the sentence (lines 8486) to “Category (a) model cases explore the variation of hydraulic head along the aquifer in order to determine the appropriate recharging location. The impacts of surface and subsurface recharges are explored separately or in conjunction with a vertical barrier in categories (b) and (c).”.
Line 82. Why are both experimental and numerical studies required?
Reply: Physical models are utilized to investigate the hydraulic behavior of saltwater intrusion and to collect data for the numerical model's calibration and validation. In contrast to the limitations of experiments, a numerical model is then employed to extensively study the saltwater intrusion under various conditions. These conditions include the use of vertical barriers, surface recharges, and subsurface recharges, as shown in the suggested model cases (see Table 4).
Line 84. Item (iii) is meaningless.
Reply: In response to the reviewer's query, The authors omit the objective (III) which may considered as methodology.
Line 104 and Figure 1. There is no explanation of what criteria are used for optimisation. What are the target values for each of the six parameters? And why are they chosen?
Reply: The authors aim to make it clear that AHP is not an optimization approach but rather a decisionmaking model for selecting the best model case among three categories (a, b, and c). As the AHP is a qualitativebased approach, there are no set targets for these ratios. AHP is used to arrange the alternatives according to their relative importance (lines 275283).
As stated in sections 2.2 and 2.4 of the manuscript, evaluation ratios and classification ratios are proposed to evaluate and classify the model cases included in categories (a, b, and c), respectively. The criteria used in AHP considered 5 parameters (not 6 parameters) among them (Rr, SLRi, Minimum HHR, WAR, and RER). To evaluate and compare alternatives, the AHP determines the relative weights of these parameters. In the model cases of category (a), four criteria (Rr, SLRi, Minimum HHR, and WAR) are employed, while all five criteria are used in the model cases of categories (b) and (c) (lines 309322).
To overcome any confusion, added more details explaining the scientific background of the AHP model under Section 2.5, "DecisionMaking Model (AHP technique)".
Line 135. What does calibration mean here? How is the density changed?
Reply: The densities of saltwater and freshwater are known to be 1.025 and 1.00 g/cm3, respectively. Calibration here means measuring the exact density of the saltwater and freshwater, referring to these known values to utilize in the numerical model data set.
Line 191. The model used is not very large in terms of computational blocks and the results show it requires refinement. Runtime savings is not an important issue for a model of this size.
Reply: The authors investigated various discretization computations in order to provide an accurate diagnostic of variations in head drawdowns and water balances. Calibration and validation are used to ensure the model's validity. Despite its small scale, the model features 8 model layers and 2320 cell of discretization. Furthermore, more refinement is generated at the locations of the vertical barrier and recharge systems to provide more exact outcomes. Finally, the author feels that there is no need to go beyond discretization. Furthermore, the authors revised this section (2.4) in order to clarify the concept of boundary conditions and domain discretization, as follows:
 Including a new section "2.3 Conceptual Model". In this section, a conceptual model based on the experimental set and procedures is proposed to simplify the representation of the groundwater system, its boundary conditions, the use of a vertical barrier, and the use of two artificial recharge systems as presented in the new modified Figure 6.
 Section 2.4's title is modified to "2.4 Numerical Model Development" and a new paragraph about boundary conditions, packages used, and model discretization is added (lines 230–237).
Line 197. Some discussion in words should be given for the three categories and seven cases. What happens for the surface recharge and borewells recharge?
Reply: The author added a new section "2.3 Conceptual Model". In this section, a conceptual model based on the experimental set and procedures is proposed to simplify the representation of the groundwater system, its boundary conditions, the use of a vertical barrier, and the use of two artificial recharge systems as presented in the new modified Figure 6. On the other hand, Table 4 is moved under this section and modified to make the text easier to read. The authors simplify the table contents by omitting the values of X_{b}, D_{b}, and NAR from the table,. The table listed three distinct groups with clear titles:
Line 228263. These sections are very unclear. What are the target values for the parameters? And why?
Reply: For section “2.4.1 Classification Ratios”, the authors revise it, trying to make it more clear to the reviewer. In this section, the authors omit the ratio (IR) from the classification ratio because it produces the same classification as Rr (Rr=IRc_{ase1a}IR_{casek}) and add the SLR_{i }instead, which reflects the increase in saltwater level. The SLR_{i} is an important ratio for selecting the best model, which is one of the criteria used in the AHP model. Accordingly, Figure 16a as well as Table 8 are modified. On the other hand, for Section “2.5 DecisionMaking Model (AHP technique)”, the authors added more details explaining the AHP model.
As the AHP is a qualitativebased approach, there are no set targets for these ratios. AHP is used to arrange the alternatives according to their relative importance (lines 275283). The criteria used in AHP considered 5 parameters (not 6 parameters) among them (Rr, SLRi, Minimum HHR, WAR, and RER). To evaluate and compare alternatives, the AHP determines the relative weights of these parameters. In the model cases of category (a), four criteria (Rr, SLRi, Minimum HHR, and WAR) are employed, while all five criteria are used in the model cases of categories (b) and (c) (lines 309322).
Line 268. The fit of the model results shown in Figs. 8, 9, 10 and 11 is quite poor and indicates that the model grid is too coarse. Also, the permeability in the experiment may not be uniform.
Reply: The authors make every effort to obtain accurate physical models. To ensure uniform permeability, the filling process was continued from one layer to the next without offering any opportunities for stratification at a low rate (low rates are ensured due to the usage of funnels) (see Section 2.1.2” Configuration and Experimental Set”. This filling technique, as outlined in the paper, will produce the best results as compared to simply skipping sand at one time in the sandbox. On the other hand, the authors demonstrate saturation by monitoring the 14 glass manometer tubes illustrated in Figure 2 until equilibrium is reached and then waiting one hour to confirm that air bubbles have departed. As a result, the authors believe that this method is the best technique to achieve good porous medium homogeneity.
Line 287321. This discussion is rambling and fails to clearly identify the key conclusions.
Reply: The authors simplify the analysis part by omitting the complex explanation and adding tables with the values of the evaluation ratios and classification ratios, using tables as follows:
Section “3.2.1 Saltwater intrusion and flow behaviors in category(a) model cases”: Table 6 is added
Section “3.2.3 Saltwater intrusion and flow behaviors in categories (b) and (c) model cases”: Table 7 is added
Line424434. Very unclear explanation and figures. Without a clear explanation of what the target values for the parameters are the use of terms like “bets” and “worst” is meaningless.
Reply: The authors would like to clarify that two groups of ratios are recognized in this study: evaluation and classification ratios. The dimensionless ratios proposed from the experiments are extracted from the geometry shown in Figure 5 to be used for analyzing the output results. From the results themselves, new dimensionless ratios are proposed to classify the model cases as the best or worst models, namely as classification ratios. Lines (250252) explains this in detail. Through these lines, it is stated that “The criteria for classifying the best model cases are that they have low values of SLR_{i}, WAR, and RER, as well as the maximum value of Rr. On the other hand, cases with high values of SLR_{i}, WAR, and RER, as well as the lowest value of Rr, are classified as the worst model cases and are not recommended for controlling saltwater intrusion.” at lines (253257).
Line 444475. Again, this is very unclear as the optimisation criteria have not been made clear.
Reply: The authors aim to make it clear that AHP is not an optimization approach but rather a decisionmaking model for selecting the best model case among three categories (a, b, and c). As the AHP is a qualitativebased approach, there are no set targets for these ratios. AHP is used to arrange the alternatives according to their relative importance (lines 275283).
As stated in sections 2.2 and 2.4 of the manuscript, evaluation ratios and classification ratios are proposed to evaluate and classify the model cases included in categories (a, b, and c), respectively. The criteria used in AHP considered 5 parameters (not 6 parameters) among them (Rr, SLRi, Minimum HHR, WAR, and RER). To evaluate and compare alternatives, the AHP determines the relative weights of these parameters. In the model cases of category (a), four criteria (Rr, SLRi, Minimum HHR, and WAR) are employed, while all five criteria are used in the model cases of categories (b) and (c) (lines 309323).
To overcome any confusion, added more details explaining the scientific background of the AHP model under Section 2.5, "DecisionMaking Model (AHP technique)".
Line 484485. It is incorrect to include “numerically” before “proposed”
Reply: In response to the reviewer's query, The authors omit “numerically” from the sentence (line 553).
Line 487. The dimensional analysis was not presented.
Reply: The sentence has changed to “Evaluation ratios are suggested in order to analyze and characterize the numerical model cases' saltwater line and hydraulic head variations.”
The authors would like to notify that modifications are carried out through the Section “2.2 Dimension Analysis and Evaluation Ratios” including:
 The subtitle is changed to “Evaluation Ratios”
 The dimensionless quantities are divided into three groups as mentioned to clarify the purpose and physical meaning of each (lines 183188).
 Table3 is renamed “Suggested evaluation ratios, conditional parameters and geometric parameters” and rearranged based on the mentioned three dimensionless groups, as well as adding a new column namely “Physical meaning”
Line 489501. The numerical values given for the various parameters (LR.HRR,WAR, SLR,Rr and RER) have little meaning. They are not discussed in physical terms and it is not explained above why these values are desirable.
Reply: For the ratios (LR, HRR, and SLR) The authors clarify these parameters through Section “2.2 Dimension Analysis and Evaluation Ratios” while these dimensionless quantities are divided into three groups as mentioned to clarify the purpose and physical meaning of each (lines 183188). Moreover, Table3 is renamed “Suggested evaluation ratios, conditional parameters and geometric parameters” and rearranged based on the mentioned three dimensionless groups, as well as adding a new column namely “Physical meaning”
For the other two ratios (Rr, WAR, and RER) which are mentioned in Section” 2.4.2 Classification Ratios”:
Rr represents the reduction in intrusion length compared with that of the base case as informed by Eq. 2.
WAR represents the variation of the saltwater wedge compared with that of the base case as informed by Eq. 3.
RER represents the variation of recharge rate compared with that which flows across the saltwater boundary as informed by Eq. 4.
Interactive discussion
Status: closed

RC1: 'Comment on hess202389', Anonymous Referee #1, 07 Jul 2023

AC1: 'Reply on RC1', Wael Mahmod, 14 Sep 2023
Review of
Developing Functional Recharge Systems to Repel Saltwater Intrusion via Integrating Physical, Numerical, and DecisionMaking Models for Coastal Aquifer Sustainability
By
 Introduction and overall assessment
The authors assess the improvement caused by adding artificial recharge to an impervious barrier as measures to control seawater intrusion (SWI). To this end, they perform sandbox experiments and numerical methods on a highly idealized case. They use this model to compute a number of ratios that are used to feed an “analytic hierarchy process”. They conclude that the combination of physical barrier with artificial recharge is the best option to control SWI.
Overall, the topic is of interest to HESS readers and the conclusion is valid, although somewhat trivial. Since they are not considering construction or operation costs, the more barriers you put (physical and or hydraulic), the better you will control SWI. Furthermore, it is clear that the authors have put a lot of work into this paper. Unfortunately, I believe the paper cannot be published in the present form for several reasons:
1) It is unnecessarily complex and, worse, incomplete. A large number of indicators are defined without a clear reason (no formal dimensional analysis). Yet, the most important parameters (recharge rate) are not defined.
2) The paper contains numerous conceptual errors (not too severe, but unacceptable).
3) It is very poorly written. Worse, it is very poorly organized. I do not just mean the language needs to be improved, but also the logical sequence.
I discuss issues 1) and 2) below and I make a number of writing recommendations in the last section. But the overall recommendation would be to greatly simplify your paper and remove everything that is not related to the main objectives.
The authors put in a lot of effort on this revision to make the manuscript proper for logical sequence, both in terms of the main sections and individual sentences and paragraphs. In addition to the APC language editing service, which the HESS journal will provide if the manuscript is accepted, the writers checked the English language and grammar with native language speakers.
 Conceptual errors:
Introduction
Line 58: It is not true that “Physical and numerical models … reduce the high cost of hydrogeological and environmental investigations”. There is no alternative to scu investigations. If you design a SWI control system without a good understanding of you system, you will waste you money (what is the depth?, how do you know you are intercepting the whole SW flux?, how much you need to recharge?
Reply: The authors agree with the reviewer that hydrogeological and environmental investigations are necessary; yet, this sentence (Line 59) indicates that physical and numerical models decrease expenses rather than eliminating investigations. Using both models aids in understanding hydrogeological systems, eliminating the need to place monitoring wells intensively and identifying where wells should be constructed in order to save money while achieving the same goals. To avoid this conflict, the authors modify the sentence and place a relevant reference:" Physical and numerical models have not only proven to be more effective tools for selecting the optimum solutions for controlling saltwater intrusion, but can also be used to reduce the need for expensive hydrogeological and environmental investigations before constructing a fullscale project (Mantoglou 2003; Zhou, et al. 2003; Abarca et al. 2006; Sutherland and Barfuss, 2011; Singh 2015; AbdElaty et al. 2019; Guo et al. 2019; M Armanuos et al. 2019). "
Methods:
I am not sure what you mean by “dimension analysis”, but none of the dimensional analyses” I know consist of computing model output ratios. Please, do not anticipate results before describing what you do (“The results of the category (a) model cases reveal the location of the minimal hydraulic heads, which are expected to be the locations of the indicated artificial recharge systems” (and we still do not know what model category (a) is).
Reply: Through the experimental phase, the authors suggested dimensionless quantities based on variables, parameters, and constants that influence saltwater intrusion, which are defined and summarized in Figure 5 and Table 2. These suggested dimensionless quantities include three variables called evaluation ratios for analyzing the output results, one parameter that serves as experimental run constraints, and two geometric parameters that are used to assign hydraulic gradient and saltwater profile.
Based on the above explanation, and regards to the reviewer comment, modifications are carried out through the section”2. Materials and Methodologies” as follows:
1 For section “2. Materials and Methodologies”:
 The mentioned sentence of category (a) (line 103) is modified to be “Category (a) model cases are used to determine the location of the minimal hydraulic heads, which are suggested to be the locations of the indicated artificial recharge systems. Categories (b) and (c) investigate the impacts of surface and subsurface recharges on saltwater intrusion at the indicated locations, either alone or in conjunction with a vertical barrier.”
 The word “ratio” in line (97) was replaced with “dimensionless quantities”.
2 For section “2.2 Dimension Analysis and Evaluation Ratios”:
 The subtitle is changed to “Evaluation Ratios”
 The dimensionless quantities are divided into three groups as mentioned to clarify the purpose and physical meaning of each (lines 183188).
 Table3 is renamed “Suggested evaluation ratios, conditional parameters and geometric parameters” and rearranged based on the mentioned three dimensionless groups, as well as adding a new column namely “Physical meaning”
Sand tank:
Note that the selected ratios are arbitrary and do not result from a proper “dimensional analysis”. That is, appropriate rations would result from writing the problem in dimensionless form, so that they would represent the minimum set of variables for definition of the problem. The current definitions are:
(1) arbitrary (e.g., IR is defined with respect to a base case that has not been defined yet, perhaps it would be better to define it with respect to the case without any remediation),
(2) redundant (NAR and NDR are complementary, except that, to make things worse, BDR is defined in terms of cross sectional area),
(3) not really descriptive variables (e.g., the SLR is not a real number, but a function). This is severe, as it invalidates the final results. Worse, the reader is left with the impression that the ratios are improvised.
Reply: The authors would like to confirm that these ratios were not chosen arbitrarily. the authors suggested dimensionless quantities based on variables, parameters, and constants that influence saltwater intrusion, which are defined and summarized in Figure 5 and Table 2. These suggested dimensionless quantities include three variables called evaluation ratios for analyzing the output results, one parameter that serves as experimental run constraints, and two geometric parameters that are used to assign hydraulic gradient and saltwater profile. For that, these changes take place in the manuscript:
1 For section “2. Materials and Methodologies”:
 The mentioned sentence of category (a) (line 103) is modified to be “Category (a) model cases are used to determine the location of the minimal hydraulic heads, which are suggested to be the locations of the indicated artificial recharge systems. Categories (b) and (c) investigate the impacts of surface and subsurface recharges on saltwater intrusion at the indicated locations, either alone or in conjunction with a vertical barrier.”
 The word “ratio” in line (97) was replaced with “dimensionless quantities”.
2 For section “2.2 Dimension Analysis and Evaluation Ratios”:
 The subtitle is changed to “Evaluation Ratios”
 The dimensionless quantities are divided into three groups as mentioned to clarify the purpose and physical meaning of each (lines 183188).
 Table3 is renamed “Suggested evaluation ratios, conditional parameters and geometric parameters” and rearranged based on the mentioned three dimensionless groups, as well as adding a new column namely “Physical meaning”
Concerning comment no. 1 as arbitrary, experiment 1 (the base case) has already been defined before this section at line 175. It is the case where saltwater intrusion through the porous media is being investigated without any countermeasures. Regarding the IR example produced by the reviewer, IR illustrates the variation of intrusion length over time (t) with reference to the maximum intrusion length (base case). Afterwards, IR was used as a comparison analysis for all of the cases covered in this study.
Concerning comment no. 2 as redundant, indeed NAR and BDR are complementary (BDR = 1NAR, where b is constant). The parameter NAR and its components (a/A) are omitted from the whole manuscript as well as in Tables 2, 3, and 4.
Concerning comment no. 3 as not really descriptive variables, the authors agree with the reviewer that SLR is A function demonstrates the variation in intrusion depth as a function of distance X and time (t) due to saltwater boundary head. In the comparative analysis of the results, the average SLR value (SLR_{avg}) will be used. Moreover, HHR is also a function that demonstrates the variation of the hydraulic head due to the influence of the saltwater boundary head at a particular distance X and time (t). In the comparative analysis of the results, the minimum value of HHR and its location will be taken into account. This clarification is explained in the physical meaning column of Table 3.
After devoting some length to describing these ratios in section 2.2, the authors introduce new ratios in section 2.3. Worse, the numbering of the new ratios is inadequate.
Reply: The dimensionless ratios proposed from the experiments are extracted from the geometry shown in Figure 5 to be used for analyzing the output results. From the results themselves, new dimensionless ratios are proposed to classify the model cases as the best or worst models, namely as classification ratios. Lines (250252) explains this in detail. The authors omit the ratio (IR) from the classification ratio because it produces the same classification as Rr (Rr=IRcase1aIRcasek) and add the SLRi instead, which reflects the increase in saltwater level. The SLRi is an important ratio for selecting the best model, which is one of the criteria used in the AHP model. Accordingly, Figure 16a as well as Table 8 are modified.
Recharge through wells is done when you have an aquitard. Furthermore, wells generate a radial
flow around the well. The setting (both the sandbox and the model) are essentially 2D, so that
including wells is not appropriate.
Reply: Wells could be used to recharge any form of aquifer, either naturally or artificially. The physical and numerical models are in 3D (X, Y, and Z directions); however, the hydrogeological conditions in Z directions are constant and have no effect on the outcomes. Furthermore, it is difficult to consider all conditions in experiments. As a result, recharge wells are only used numerically in this study once the numerical model has been calibrated and validated.
Line 132: “The filling process is done in layers of 5cm each, with a falling height of 50 cm for each layer, to ensure a homogeneous hydrogeological property of the media sand”. Actually this procedure may lead to stratification (it depends on the filling rate) with the coarsest material at depth. While this may be adequate (it is similar to what occurs in nature) it does not ensure “a homogeneous … sand”.
Reply: The authors make every effort to obtain accurate physical models. To ensure that stratification did not develop, the filling process was continued from one layer to the next without offering any opportunities for this stratification at a low rate (low rates are ensured due to the usage of funnels). This filling technique, as outlined in the paper, will produce the best results as compared to simply skipping sand at one time in the sandbox. As a result, the authors believe that this method is the best technique to achieve good porous medium homogeneity.
Densities of 0.99 and 1.022 kg/L (not m3/s) are low and high for FW and SW, respectively. Adding 0.15 g/L concentration of green food dye will increase the density of SW.
Reply: At line 144, the units are changed to g/cm^{3}. The main idea in this study is to use variable density flow in porous media. As clearly illustrated in Figure 4, the saltwater density was calibrated after adding the dye, and it was 1.022 g/cm^{3}. On the other hand, the effect of the green food dye is negligible at a concentration of 0.15 g/L (0.00015 g/cm^{3}).
Line 149: You are not verifying saturation, hydraulic heads will equilibrate even if air bubbles are trapped.
Figure 4 can be dropped. It is not necessary.
Reply: The authors demonstrate saturation by monitoring the 14 glass manometer tubes illustrated in Figure 2 until equilibrium is reached and then waiting one hour to confirm that air bubbles have departed. Furthermore, air bubbles will be trapped even in nature. As a result, the experiments are close to nature.
In response to the referee's previous query about saltwater density, the authors consider that this figure supports the experimental section.
In Figure 5, name only variables that you are going to vary (b is fixed, isn’t it?). Also you may add the location of recharge wells here, so that you can eliminate Figure 6.
Reply: The authors omit b, X_{b}, and the highlighted areas (neck area (a) and sand media area( A)) from Figure 5. Regarding omitting Figure 6, concerning the need to clear boundary conditions, the authors restructured this section by including a new section "2.3 Conceptual Model". In this section, a conceptual model based on the experimental set and procedures is proposed to simplify the representation of the groundwater system, its boundary conditions, the use of a vertical barrier, and the use of two artificial recharge systems as presented in the new modified Figure 6. Moreover, Section 2.4's title is modified to "2.4 Numerical Model Development" and a new paragraph about boundary conditions, packages used, and model discretization is added (lines 230–237).
Tables 13 can be blended into 1 (if at all). Table 3 is particularly unfriendly s it forces the reader to check that all cases are identical. It took me a while to realize that you were just varying the barrier depth. In fact, you may just say that you did several runs with varying barrier depth and make them a function of barrier depth.
Reply: The authors were confused by the table numbers provided by the referee (Tables 1–3). If the referee means that Tables 2 and 3 should be combined, the authors prefer to keep them distinct so that the readers are not confused. Table 1 describes the components of the sandbox model. For the second half of the referee question about Table 3, the authors believe that the referee means Table 4. To make the text easier to read in Table 4, the authors omit the values of X_{b}, D_{b}, and NAR from the table, simplifying the table contents. The table listed three distinct groups with clear titles:
Category (a): using vertical barrier
Category (b): using vertical barrier and surface recharge
Category (c): using vertical barrier and subsurface recharge
Please, eliminate Table 5 (textbook and irrelevant for your work)
Reply: The authors eliminate Table 5 and the sentence at lines 242243 is changed to be “Using the experimental results, many trials are carried out to calibrate the model using various hydrogeological properties, with reference to (Domenico et al. 1998; Rotz 2021)”
Numerical Model
The model is not properly described. Beyond formalities, this is severe because the results suggest that boundary conditions in the model /never described) are different to those in the sand tank.
Reply: The authors confirm to the reviewer that the numerical model's boundary conditions are the same as the experiments. However, the authors agree with the reviewer that further details concerning the numerical model and boundary conditions are needed to be clearer. As a result, the authors restructured this section as follows:
 Including a new section "2.3 Conceptual Model". In this section, a conceptual model based on the experimental set and procedures is proposed to simplify the representation of the groundwater system, its boundary conditions, the use of a vertical barrier, and the use of two artificial recharge systems as presented in the new modified Figure 6.
 Section 2.4's title is modified to "2.4 Numerical Model Development" and a new paragraph about boundary conditions, packages used, and model discretization is added (lines 230–237).
AHP technique
The description is too sketchy (I had to read independently to understand it). While, in my understanding, the AHP technique is not appropriate here. It is generally used for multiple criteria that are hard too subjective for quantitative comparison, so that the weights assigned to each criteria are derived from pairwise comparisons by “experts”.
Reply: The authors added more details explaining the scientific background of the AHP model under Section 2.5, "DecisionMaking Model (AHP technique)". AHP is used to arrange the alternatives according to their relative importance, which is considered qualitative based on the subjective opinions of the experts. Through this study, the authors asked several experts to provide the inputs (point scale) for both alternatives and criteria. The authors provided them with the numerical model outputs as a guide.
Results
Model calibration is unclear. For one thing, the authors report a RMSE without having described what errors are being minimized.
Reply: The RMSE is used to assess the quality of fit between the simulated and observed saltwater lines, as clarified at lines 328–330 and in the legends of Figures 8, 9, and 10. Based on these figures and the RMSE values, the employed hydrogeological properties are set as the calibrated parameter of the numerical model, as stated from line 334 to line 339 and shown in Table 5.
The parameters results are unrealistic (Table 6 contains no units, I assume that k is m/s, but a porosity of 0.04, a specific storage of 0.0619 1/m?, and a S_Y of 0.04 are clearly unrealistic). I do not think that these errors affect results severely, but it conveys a poor image of the model.
Reply: The authors added the units of the hydrogeological parameters. The K unit is measured in cm/s, the Ss unit is measured in 1/cm, and the others (Sy and ŋ) are dimensionless.
Of course, the parameters determined during the calibration process are accompanied by inaccuracies, which generally come from two sources. The first is that a model can only represent a simplified version of a complicated natural or experimental reality. The second is that the measurements used to constrain parameter estimations contain noise. To overcome the inaccuracy, the authors conduct numerous trials to obtain numerically calibrated parameters while minimizing the weighted squared difference between measured and simulated data. The model output is evaluated to determine the quality of fit within the meaning of RMSE.
Considering this and according to (Domenico et al. 1998; Rotz 2021):
K value is within the values mentioned by (Domenico et al. 1998; Rotz 2021).
ŋ is not a porosity; it is an effective porosity, so it has less value than porosity and is within the values mentioned by (Domenico et al. 1998; Rotz 2021).
Sy is also within the values mentioned by (Domenico et al. 1998; Rotz 2021).
Ss is considered a complicated parameter as it depends on many parameters as (Aquifer Compressibility, Total Porosity, Water Density (variable densities are found in the study), Gravitational Acceleration, Water Compressibility). The authors tried many values under the consideration of sensitivity analysis to achieve the best of fit between observed and simulated results. Although the authors tried many values and found that there was no effect on the results (as the reviewer indicated), the current value is the calibrated one used in this study.
Probably more severe are the apparent instabilities or the fact that boundary conditions look different. IT is also unfair to the reader to find here, for the first time, that model construction is done under transient conditions, which leaves the reader wondering how are the indices described in Section 2 computed.
Reply: Regarding the boundary conditions, the authors confirm to the reviewer that the numerical model's boundary conditions are the same as the experiments. However, the authors agree with the reviewer that further details concerning the numerical model and boundary conditions are needed to be clearer. As a result, the authors restructured this section as follows:
 Including a new section "2.3 Conceptual Model". In this section, a conceptual model based on the experimental set and procedures is proposed to simplify the representation of the groundwater system, its boundary conditions, the use of a vertical barrier, and the use of two artificial recharge systems as presented in the new modified Figure 6.
 Section 2.4's title is modified to "2.4 Numerical Model Development" and a new paragraph about boundary conditions, packages used, and model discretization is added (lines 230–237).
As mentioned in Section 2.4.1, "Calibration and Verification Processes", a verification procedure is implemented in this study to check two aims,:
1 Confirming the time when a steadystate condition occurs in based the results of experiment 1.
2 Fitting the observed saltwater line in experiments 1 and 2 for the transient and steadystate conditions.
The experimental process is already in a transient state until it achieves a steady state, which is achieved after 90 minutes, as resulted in Section 3.1 “Calibration and Verification of the Numerical Model".
As a result, during the calibration and verification phases, the numerical model is run in a transient state to determine when the steady state condition will be reached when compared to the implemented experiments. The calibration and verification stages' results demonstrate that steady state occurred at 90 minutes as well as in the experiments. All subsequent analyses are based on the data obtained after 90 minutes, as stated at Section 3.1 “Calibration and Verification of Numerical Model” (Lines 338339).
Worse, the flat region of the salt interface (between 30 and 40 cm inland) in the experiment suggests that permeability is higher in this region (probably a consequence of the handling of the barrier). This flat region was reproduced in the numerical model, but nothing is said about heterogeneity.
Reply: As stated in section "2.1.3 Experimental Procedures" the authors attempt to avoid heterogeneity in the experiment 2 part (lines 177181) by first removing sand from the experimental area. The vertical barrier is then placed at the experimental portion, 25cm from the feed chamber. Following that, the experimental section's media sand is replaced. As a result, heterogeneity might be ignored in the numerical model. The results demonstrate that the model has been validated.
The graphs do not appear to make much sense. It is not clear to me what hydraulic grade line is. But if I interpret it to mean head, the paths are inconsistent. You probably do not need the paths.
Reply: The hydraulic grade line (HGL) is the slope of the water table (potentiometric surface), or the change in water level per unit distance along the maximum head decrease direction. According to the graphs, the hydraulic head distribution along the aquifer is necessary to understand in order to locate the ideal place for artificial recharge.
Path lines are utilized to show the flow behavior of both freshwater and saltwater through the sand media under different conditions (using vertical barriers and artificial recharge types), as indicated in Section "2.4 Numerical Model" through lines 224229. The authors believe that these paths represent the hydraulic behavior of freshwater and saltwater in porous media, as well as the effect of these movements on hydraulic heads, particularly near barriers and recharge locations.
Results of each case are hard to read because of the abuse and redundancy of indicators and inconsistencies. For example, IR had been defined the ratio of observed intrusion length at a time (t) to maximum saltwater intrusion length (base case). Yet, for the base case IR is found to be 0.97. I could not follow the last part (new items are introduced and I must confessed that I was exhausted of going back and forth to recall the meanings of all the abbreviations).
Reply: The authors simplify the analysis part by omitting the complex explanation and adding tables with the values of the evaluation ratios and classification ratios, using tables as follows:
Section “3.2.1 Saltwater intrusion and flow behaviors in category(a) model cases”: Table 6 is added
Section “3.2.3 Saltwater intrusion and flow behaviors in categories (b) and (c) model cases”: Table 7 is added
Concerning the value of IR (L(in)/max.L(in) =0.97), after the numerical model has been verified, all of its output values are considered in calculating these evaluation ratios; however, the constant value of max.L(in) is considered from the experimental value (observed value) as stated in Table 2item4, which is nearly the same value as the numerical model. As a result, the ratio is slightly less than 1.00.
Editorial comments and writing
The paper is very poorly written. I am referring not only to the traditional “look for a native speaking person” (being a nonnative myself, I hate when I am told it), but also to the logic. The paper is complex and long, and the writing does not help. Try to simplify it. I understand that you are under pressure to publish quickly, but, please, facilitate the lives of readers by providing an easy to read paper (in the end, it will favor citations). Numerous statements call for a more refined argumentation. I list a few below:
In the abstract: “Three countermeasure combinations, including vertical barrier, surface, and subsurface recharges, are numerically investigated using three model case categories. Category (a) model cases investigate the hydraulic head’s variation along the aquifer to determine the best recharge location. Under categories (b) and (c), the effects of surface and subsurface recharges are studied separately or in conjunction with a vertical barrier”. Perhaps it is sufficient to say "The numerical model is used to investigate the SWI control efficiency of vertical barrier, and optimally located surface and subsurface artificial recharge”.
Reply: The authors believe that the abstract reflects the manuscript contents, and the mentioning of categories of model cases, including the usage of vertical barriers, surface recharge, and subsurface recharge, is important to mention.
Also, in the abstract, try to minimize the use of acronyms (OK in the body of the paper) and too many numbers (they tend to hide, rather that highlight). For example, it is very hard to read: “An analytic hierarchy process (AHP) as DMM is built using the classification ratios of hydraulic head (HHR), salt line (SLR), intrusion (IR), repulsion (Rr), wedge area (WAR), and recharge (RER) as selection criteria to select the overall best model case. The optimal recharging location, according to the results, is in the length ratio (LR) range from 0.45 to 0.55. Furthermore, the DMM supports case3b (vertical barrier + surface recharge) as the best model case to use, with a support percentage of 47.93%, implying that this case has a good numerical model classification with a minimum IR of 67.9%, a maximum Rr of 29.4%, and an acceptable WAR of 1.25”. Instead, you may just say: “An analytic hierarchy process is built to compare SWI control strategies on the basis of head, salt line, intrusion, repulsion, wedge area and recharge. We find that best results are obtained by combining a vertical barrier with surface recharge at a distance from the coast comparable to the thickness (here you have a problem, your LR is a model dependent variable, you must relate it to generic aquifer variables”.
Reply: The authors omit the acronyms from the abstract as much as possible as. This is in the lines 26 and 27.
The introduction is very poorly structured… You start by saying that SWI is a relevant problem, continue with methods to control SWI (but do not mention artificial recharge, which many, including me consider the best control method, as its efficiency is greater than 1, see Abarca et al., WRR, 2006). Then you introduce artificial recharge to conclude that “Although many studies investigate saltwater intrusion in coastal aquifers, only a limited number study the control methods of saltwater intrusion”! This is inconsistent (and false!). I believe that the logical sequence of the introduction needs to be revised.
Reply: In the paragraph from Line 47 to Line 58, the writers described artificial recharge techniques, their efficacy, and the associated problems.
Line 46: “Artificial recharge techniques, such as surface and subsurface recharge systems, are critical for establishing hydraulic barriers and mitigating the effects of saltwater intrusion”. They are not critical… Instead “Artificial recharge techniques can be used for establishing hydraulic barriers and mitigating saltwater intrusion, while recovering SGD”.
Reply: In response to the reviewer's query, the authors changed the sentence.
“These techniques have several advantages compared to traditional methods, including low cost…” what traditional techniques do you refer to?
Reply: Traditional methods have already been mentioned in the second paragraph of the introduction in lines 43 and 46: "reducing pumping rates, relocating pumping wells, changing pumping patterns, constructing physical subsurface barriers, and saltwater abstraction"
“Although many studies investigate saltwater intrusion in coastal aquifers, only a limited number study the control methods of saltwater intrusion”. Indeed, you should cite some of them
Reply: In response to the reviewer's query, the authors added references (line 58).
“Although physical and numerical models are effective economic tools for selecting the best solutions for repelling saltwater intrusion, deficiencies in the acquisition of appropriate evidence to support the final decision are discovered”. What do you mean by discovered… Perhaps you should indicate some of these deficiencies.
Reply: In response to the reviewer's query, the authors changed the sentence to “Although physical and numerical models are useful in determining the optimum solutions for controlling saltwater intrusion, deficiencies in the acquisition of appropriate evidence to support the final decision are discovered. Since the scenarios of hydrogeological models for a specific aquifer cannot agree on minimizing intrusion, improving groundwater availability, being environmentally friendly, and being costeffective”.
The objective statement should be short and to the point. Instead, you list seven goals, which are
really methodological steps.
Reply: The authors omit the objective (III) which may considered as methodology.
Look for appropriate references (this may also help you to simplify the writing by leading the reader to other papers for details). For example, “MODFLOW2005, in conjunction with the SWI2 package, is used in this study for numerical modeling of saltwater intrusion. SWI2 is a software package used to analyze threedimensional groundwater flow, model saltwater intrusion, and calculate hydraulic heads. The main advantage of using the SWI2 package is that it requires fewer cells for the simulation process than variabledensity groundwater flow packages like SEAWAT. The ability of SWI2 to represent each aquifer as a single layer of cells results in significant model runtime savings”. I am not sure this choice is appropriate, but please provide references for all the codes.
Reply: In response to the reviewer's query, the authors added references (lines 220, 221, and 225).
Also, provide a reference for “HM 169 GUNT HAMBURG”
Reply: In response to the reviewer's query, the authors added references (line 119).
There are numerous terms that you must revise (you do not “repel seawater intrusion”, you control it, or minimize it)
Reply: In response to the reviewer's query, the authors change the word repel to control in the whole manuscript.

AC1: 'Reply on RC1', Wael Mahmod, 14 Sep 2023

RC2: 'Comment on hess202389', Anonymous Referee #2, 07 Aug 2023
General comments
 The paper is not well written in terms of the logical flow in the whole paper and in individual sentences and paragraphs.
 The idea of using experimental data to calibrate numerical models of saltwater intrusion is not new. There have been many past studies of numerical modelling of saltwater intrusion and the accuracy of numerical models in this field is well established. The authors could have started with a numerical model of a fullscale project and tested various options for controlling saltwater intrusion on that. The smallscale experiments and smallscale models are not necessary.
 The level of discretisation in the numerical models is not adequate to accurately represent the processes being investigated. The results shown in Figures 8, 9 and 10 show that higher resolution if the vertical direction is required – say five times as many layers.
 In some cases, the key parts of the paper are not clearly explained. For example, what are the nondimensional parameters that were used to assess the merit of the different options?
Detailed comments
Line 1. “Repel” is the wrong word. Use “control” instead.
Line 16. Why use results from the two models? If the numerical model results do not agree with the experimental results, it means that the numerical model needs to be improved. Why and how are the experimental results included in the DMM?
Line 21. Category (a) is not clearly explained here or elsewhere. Table 4 indicates that it includes a vertical barrier but no recharge.
Line 26. It is not clear what is being optimised in the choice of the six parameters. What are the target values for each of the six parameters? And why are they chosen?
Line 39. Replace “potentiality” by “availability”.
Line 46. Add some references for the use of artificial recharge.
Line 59. Change “repelling” to “controlling” (do this throughout the paper). Change to “...reduce the need for expensive hydrogeological and environmental investigations …”.
Line 62. Physical and numerical models are not “economic “ tools.
Line 81. The categories need to be defined here.
Line 82. Why are both experimental and numerical studies required?
Line 84. Item (iii) is meaningless.
Line 104 and Figure 1. There is no explanation of what criteria are used for optimisation. What are the target values for each of the six parameters? And why are they chosen?
Line 135. What does calibration mean here? How is the density changed?
Line 191. The model used is not very large in terms of computational blocks and the results show it requires refinement. Runtime savings is not an important issue for a model of this size.
Line 197. Some discussion in words should be given for the three categories and seven cases. What happens for the surface recharge and borewells recharge?
Line 228263. These sections are very unclear. What are the target values for the parameters? And why?
Line 268. The fit of the model results shown in Figs. 8, 9, 10 and 11 is quite poor and indicates that the model grid is too coarse. Also, the permeability in the experiment may not be uniform.
Line 287321. This discussion is rambling and fails to clearly identify the key conclusions.
Line424434. Very unclear explanation and figures. Without a clear explanation of what the target values for the parameters are the use of terms like “bets” and “worst” is meaningless.
Line 444475. Again, this is very unclear as the optimisation criteria have not been made clear.
Line 484485. It is incorrect to include “numerically” before “proposed”
Line 487. The dimensional analysis was not presented.
Line 489501. The numerical values given for the various parameters (LR.HRR,WAR, SLR,Rr and RER) have little meaning. They are not discussed in physical terms and it is not explained above why these values are desirable.
Citation: https://doi.org/10.5194/hess202389RC2 
AC2: 'Reply on RC2', Wael Mahmod, 14 Sep 2023
General comments
 The paper is not well written in terms of the logical flow in the whole paper and in individual sentences and paragraphs.
Reply: The authors put in a lot of effort on this issue, both in terms of the main sections and individual sentences and paragraphs. In addition to the APC language editing service, which the HESS journal will provide if the manuscript is accepted, the writers checked the English language and grammar with native language speakers.
 The idea of using experimental data to calibrate numerical models of saltwater intrusion is not new. There have been many past studies of numerical modelling of saltwater intrusion and the accuracy of numerical models in this field is well established. The authors could have started with a numerical model of a fullscale project and tested various options for controlling saltwater intrusion on that. The smallscale experiments and smallscale models are not necessary.
Reply: The primary goal of this research is to identify the optimal location for recharging groundwater in order to control saltwater intrusion. The authors use sandbox experiments and numerical approaches to do this. They evaluate the benefit of adding artificial recharge to an impermeable barrier as a strategy to control saltwater intrusion (SWI). This model is used to produce a number of ratios that are fed into an "analytic hierarchy process." They conclude that the combination of physical barriers and artificial recharge is the best solution for controlling SWI. In the future, a largescale model might be utilized to test this concept and examine the outcomes.
 The level of discretisation in the numerical models is not adequate to accurately represent the processes being investigated. The results shown in Figures 8, 9 and 10 show that higher resolution if the vertical direction is required – say five times as many layers.
Reply: The authors investigated various discretization computations in order to provide an accurate diagnostic of variations in head drawdowns and water balances. Calibration and validation are used to ensure the model's validity. Despite its small scale, the model features 8 model layers and 2320 cell of discretization. Furthermore, more refinement is generated at the locations of the vertical barrier and recharge systems to provide more exact outcomes. Finally, the author feels that there is no need to go beyond discretization. Furthermore, the authors revised this section (2.4) in order to clarify the concept of boundary conditions and domain discretization, as follows:
 Including a new section "2.3 Conceptual Model". In this section, a conceptual model based on the experimental set and procedures is proposed to simplify the representation of the groundwater system, its boundary conditions, the use of a vertical barrier, and the use of two artificial recharge systems as presented in the new modified Figure 6.
 Section 2.4's title is modified to "2.4 Numerical Model Development" and a new paragraph about boundary conditions, packages used, and model discretization is added (lines 230–237).
 In some cases, the key parts of the paper are not clearly explained. For example, what are the nondimensional parameters that were used to assess the merit of the different options?
Reply: Through the experimental phase, the authors suggested dimensionless quantities based on variables, parameters, and constants that influence saltwater intrusion, which are defined and summarized in Figure 5 and Table 2. These suggested dimensionless quantities include three variables called evaluation ratios for analyzing the output results, one parameter that serves as experimental run constraints, and two geometric parameters that are used to assign hydraulic gradient and saltwater profile.
Based on the above explanation, and regards to the reviewer comment, modifications are carried out through the section”2. Materials and Methodologies” as follows:
1 For section “2. Materials and Methodologies”:
 The word “ratio” in line (94) was replaced with “dimensionless quantities”.
2 For section “2.2 Dimension Analysis and Evaluation Ratios”:
 The subtitle is changed to “Evaluation Ratios”
 The dimensionless quantities are divided into three groups as mentioned to clarify the purpose and physical meaning of each (lines 183188).
 Table3 is renamed “Suggested evaluation ratios, conditional parameters and geometric parameters” and rearranged based on the mentioned three dimensionless groups, as well as adding a new column namely “Physical meaning”
The dimensionless ratios proposed from the experiments are extracted from the geometry shown in Figure 5 to be used for analyzing the output results. From the results themselves, new dimensionless ratios are proposed to classify the model cases as the best or worst models, namely as classification ratios. Lines (250252) explains this in detail. The authors omit the ratio (IR) from the classification ratio because it produces the same classification as Rr (Rr=IRcase1aIRcasek) and add the SLRi instead, which reflects the increase in saltwater level. The SLRi is an important ratio for selecting the best model, which is one of the criteria used in the AHP model. Accordingly, Figure 16a as well as Table 8 are modified.
Detailed comments
Line 1. “Repel” is the wrong word. Use “control” instead.
Reply: In response to the reviewer's query, the authors change the word repel to control in the whole manuscript.
Line 16. Why use results from the two models? If the numerical model results do not agree with the experimental results, it means that the numerical model needs to be improved. Why and how are the experimental results included in the DMM?
Reply: Physical models are utilized to investigate the hydraulic behavior of saltwater intrusion and to collect data for the numerical model's calibration and validation. In contrast to the limitations of experiments, a numerical model is then employed to extensively study the saltwater intrusion under various conditions. These conditions include the use of vertical barriers, surface recharges, and subsurface recharges, as shown in the suggested model cases (see Table 4).
Regarding DMM, experimental results weren’t included in the AHP model; the numerical model results were included. For more clarification, the authors added more details explaining the scientific background of the AHP model under Section 2.5, "DecisionMaking Model (AHP technique)". AHP is used to arrange the alternatives according to their relative importance, which is considered qualitative based on the subjective opinions of the experts. Through this study, the authors asked several experts to provide the inputs (point scale) for both alternatives and criteria. The authors provided them with the numerical model outputs as a guide.
Line 21. Category (a) is not clearly explained here or elsewhere. Table 4 indicates that it includes a vertical barrier but no recharge.
Reply: In the abstract (line21), the subsequent sentences inform that “Three countermeasure combinations, including vertical barrier, surface, and subsurface recharges, are numerically investigated using three model case categories. Category (a) model cases investigate the hydraulic head’s variation along the aquifer to determine the best recharge location. Under categories (b) and (c), the effects of surface and subsurface recharges are studied separately or in conjunction with a vertical barrier.”. these sentences define the purpose of each proposed category.
To make the text easier to read in Table 4, the authors omit the values of X_{b}, D_{b}, and NAR from the table, simplifying the table contents. The table listed three distinct groups with clear titles:
Category (a): using vertical barrier
Category (b): using vertical barrier and surface recharge
Category (c): using vertical barrier and subsurface recharge
Line 26. It is not clear what is being optimised in the choice of the six parameters. What are the target values for each of the six parameters? And why are they chosen?
Reply: At first, the authors would like to notify the reviewer that they added more details explaining the scientific background of the AHP model under Section 2.5, "DecisionMaking Model (AHP technique)". The authors aim to make it clear that AHP is not an optimization approach but rather a decisionmaking model for selecting the best model case among three categories (a, b, and c). As the AHP is a qualitativebased approach, there are no set targets for these ratios. AHP is used to arrange the alternatives according to their relative importance (lines 275283).
As stated in sections 2.2 and 2.4 of the manuscript, evaluation ratios and classification ratios are proposed to evaluate and classify the model cases included in categories (a, b, and c), respectively. The criteria used in AHP considered 5 parameters (not 6 parameters) among them (Rr, SLRi, Minimum HHR, WAR, and RER). To evaluate and compare alternatives, the AHP determines the relative weights of these parameters. In the model cases of category (a), four criteria (Rr, SLRi, Minimum HHR, and WAR) are employed, while all five criteria are used in the model cases of categories (b) and (c) (lines 309322).
Line 39. Replace “potentiality” by “availability”.
Reply: In response to the reviewer's query, the authors made the changes.
Line 46. Add some references for the use of artificial recharge.
Reply: In response to the reviewer's query, the authors has added references for the use of artificial recharge.
Line 59. Change “repelling” to “controlling” (do this throughout the paper). Change to “...reduce the need for expensive hydrogeological and environmental investigations …”.
Reply: In response to the reviewer's query, the authors change the word repel to control in the whole manuscript. Moreover, the sentence at line 59 is changed to “Physical and numerical models have not only proven to be more effective tools for selecting the optimum solutions for controlling saltwater intrusion but can also be used to reduce the need for expensive hydrogeological and environmental investigations before constructing a fullscale project”
Line 62. Physical and numerical models are not “economic “ tools.
Reply: The authors rephrase the sentence to “Although physical and numerical models are useful in determining the optimum solutions for controlling saltwater intrusion, deficiencies in the acquisition of appropriate evidence to support the final decision are discovered. Since the scenarios of hydrogeological models for a specific aquifer cannot agree on minimizing intrusion, improving groundwater availability, being environmentally friendly, and being costeffective.”
Line 81. The categories need to be defined here.
Reply: In response to the reviewer's query, the authors rephrase the sentence (lines 8486) to “Category (a) model cases explore the variation of hydraulic head along the aquifer in order to determine the appropriate recharging location. The impacts of surface and subsurface recharges are explored separately or in conjunction with a vertical barrier in categories (b) and (c).”.
Line 82. Why are both experimental and numerical studies required?
Reply: Physical models are utilized to investigate the hydraulic behavior of saltwater intrusion and to collect data for the numerical model's calibration and validation. In contrast to the limitations of experiments, a numerical model is then employed to extensively study the saltwater intrusion under various conditions. These conditions include the use of vertical barriers, surface recharges, and subsurface recharges, as shown in the suggested model cases (see Table 4).
Line 84. Item (iii) is meaningless.
Reply: In response to the reviewer's query, The authors omit the objective (III) which may considered as methodology.
Line 104 and Figure 1. There is no explanation of what criteria are used for optimisation. What are the target values for each of the six parameters? And why are they chosen?
Reply: The authors aim to make it clear that AHP is not an optimization approach but rather a decisionmaking model for selecting the best model case among three categories (a, b, and c). As the AHP is a qualitativebased approach, there are no set targets for these ratios. AHP is used to arrange the alternatives according to their relative importance (lines 275283).
As stated in sections 2.2 and 2.4 of the manuscript, evaluation ratios and classification ratios are proposed to evaluate and classify the model cases included in categories (a, b, and c), respectively. The criteria used in AHP considered 5 parameters (not 6 parameters) among them (Rr, SLRi, Minimum HHR, WAR, and RER). To evaluate and compare alternatives, the AHP determines the relative weights of these parameters. In the model cases of category (a), four criteria (Rr, SLRi, Minimum HHR, and WAR) are employed, while all five criteria are used in the model cases of categories (b) and (c) (lines 309322).
To overcome any confusion, added more details explaining the scientific background of the AHP model under Section 2.5, "DecisionMaking Model (AHP technique)".
Line 135. What does calibration mean here? How is the density changed?
Reply: The densities of saltwater and freshwater are known to be 1.025 and 1.00 g/cm3, respectively. Calibration here means measuring the exact density of the saltwater and freshwater, referring to these known values to utilize in the numerical model data set.
Line 191. The model used is not very large in terms of computational blocks and the results show it requires refinement. Runtime savings is not an important issue for a model of this size.
Reply: The authors investigated various discretization computations in order to provide an accurate diagnostic of variations in head drawdowns and water balances. Calibration and validation are used to ensure the model's validity. Despite its small scale, the model features 8 model layers and 2320 cell of discretization. Furthermore, more refinement is generated at the locations of the vertical barrier and recharge systems to provide more exact outcomes. Finally, the author feels that there is no need to go beyond discretization. Furthermore, the authors revised this section (2.4) in order to clarify the concept of boundary conditions and domain discretization, as follows:
 Including a new section "2.3 Conceptual Model". In this section, a conceptual model based on the experimental set and procedures is proposed to simplify the representation of the groundwater system, its boundary conditions, the use of a vertical barrier, and the use of two artificial recharge systems as presented in the new modified Figure 6.
 Section 2.4's title is modified to "2.4 Numerical Model Development" and a new paragraph about boundary conditions, packages used, and model discretization is added (lines 230–237).
Line 197. Some discussion in words should be given for the three categories and seven cases. What happens for the surface recharge and borewells recharge?
Reply: The author added a new section "2.3 Conceptual Model". In this section, a conceptual model based on the experimental set and procedures is proposed to simplify the representation of the groundwater system, its boundary conditions, the use of a vertical barrier, and the use of two artificial recharge systems as presented in the new modified Figure 6. On the other hand, Table 4 is moved under this section and modified to make the text easier to read. The authors simplify the table contents by omitting the values of X_{b}, D_{b}, and NAR from the table,. The table listed three distinct groups with clear titles:
Line 228263. These sections are very unclear. What are the target values for the parameters? And why?
Reply: For section “2.4.1 Classification Ratios”, the authors revise it, trying to make it more clear to the reviewer. In this section, the authors omit the ratio (IR) from the classification ratio because it produces the same classification as Rr (Rr=IRc_{ase1a}IR_{casek}) and add the SLR_{i }instead, which reflects the increase in saltwater level. The SLR_{i} is an important ratio for selecting the best model, which is one of the criteria used in the AHP model. Accordingly, Figure 16a as well as Table 8 are modified. On the other hand, for Section “2.5 DecisionMaking Model (AHP technique)”, the authors added more details explaining the AHP model.
As the AHP is a qualitativebased approach, there are no set targets for these ratios. AHP is used to arrange the alternatives according to their relative importance (lines 275283). The criteria used in AHP considered 5 parameters (not 6 parameters) among them (Rr, SLRi, Minimum HHR, WAR, and RER). To evaluate and compare alternatives, the AHP determines the relative weights of these parameters. In the model cases of category (a), four criteria (Rr, SLRi, Minimum HHR, and WAR) are employed, while all five criteria are used in the model cases of categories (b) and (c) (lines 309322).
Line 268. The fit of the model results shown in Figs. 8, 9, 10 and 11 is quite poor and indicates that the model grid is too coarse. Also, the permeability in the experiment may not be uniform.
Reply: The authors make every effort to obtain accurate physical models. To ensure uniform permeability, the filling process was continued from one layer to the next without offering any opportunities for stratification at a low rate (low rates are ensured due to the usage of funnels) (see Section 2.1.2” Configuration and Experimental Set”. This filling technique, as outlined in the paper, will produce the best results as compared to simply skipping sand at one time in the sandbox. On the other hand, the authors demonstrate saturation by monitoring the 14 glass manometer tubes illustrated in Figure 2 until equilibrium is reached and then waiting one hour to confirm that air bubbles have departed. As a result, the authors believe that this method is the best technique to achieve good porous medium homogeneity.
Line 287321. This discussion is rambling and fails to clearly identify the key conclusions.
Reply: The authors simplify the analysis part by omitting the complex explanation and adding tables with the values of the evaluation ratios and classification ratios, using tables as follows:
Section “3.2.1 Saltwater intrusion and flow behaviors in category(a) model cases”: Table 6 is added
Section “3.2.3 Saltwater intrusion and flow behaviors in categories (b) and (c) model cases”: Table 7 is added
Line424434. Very unclear explanation and figures. Without a clear explanation of what the target values for the parameters are the use of terms like “bets” and “worst” is meaningless.
Reply: The authors would like to clarify that two groups of ratios are recognized in this study: evaluation and classification ratios. The dimensionless ratios proposed from the experiments are extracted from the geometry shown in Figure 5 to be used for analyzing the output results. From the results themselves, new dimensionless ratios are proposed to classify the model cases as the best or worst models, namely as classification ratios. Lines (250252) explains this in detail. Through these lines, it is stated that “The criteria for classifying the best model cases are that they have low values of SLR_{i}, WAR, and RER, as well as the maximum value of Rr. On the other hand, cases with high values of SLR_{i}, WAR, and RER, as well as the lowest value of Rr, are classified as the worst model cases and are not recommended for controlling saltwater intrusion.” at lines (253257).
Line 444475. Again, this is very unclear as the optimisation criteria have not been made clear.
Reply: The authors aim to make it clear that AHP is not an optimization approach but rather a decisionmaking model for selecting the best model case among three categories (a, b, and c). As the AHP is a qualitativebased approach, there are no set targets for these ratios. AHP is used to arrange the alternatives according to their relative importance (lines 275283).
As stated in sections 2.2 and 2.4 of the manuscript, evaluation ratios and classification ratios are proposed to evaluate and classify the model cases included in categories (a, b, and c), respectively. The criteria used in AHP considered 5 parameters (not 6 parameters) among them (Rr, SLRi, Minimum HHR, WAR, and RER). To evaluate and compare alternatives, the AHP determines the relative weights of these parameters. In the model cases of category (a), four criteria (Rr, SLRi, Minimum HHR, and WAR) are employed, while all five criteria are used in the model cases of categories (b) and (c) (lines 309323).
To overcome any confusion, added more details explaining the scientific background of the AHP model under Section 2.5, "DecisionMaking Model (AHP technique)".
Line 484485. It is incorrect to include “numerically” before “proposed”
Reply: In response to the reviewer's query, The authors omit “numerically” from the sentence (line 553).
Line 487. The dimensional analysis was not presented.
Reply: The sentence has changed to “Evaluation ratios are suggested in order to analyze and characterize the numerical model cases' saltwater line and hydraulic head variations.”
The authors would like to notify that modifications are carried out through the Section “2.2 Dimension Analysis and Evaluation Ratios” including:
 The subtitle is changed to “Evaluation Ratios”
 The dimensionless quantities are divided into three groups as mentioned to clarify the purpose and physical meaning of each (lines 183188).
 Table3 is renamed “Suggested evaluation ratios, conditional parameters and geometric parameters” and rearranged based on the mentioned three dimensionless groups, as well as adding a new column namely “Physical meaning”
Line 489501. The numerical values given for the various parameters (LR.HRR,WAR, SLR,Rr and RER) have little meaning. They are not discussed in physical terms and it is not explained above why these values are desirable.
Reply: For the ratios (LR, HRR, and SLR) The authors clarify these parameters through Section “2.2 Dimension Analysis and Evaluation Ratios” while these dimensionless quantities are divided into three groups as mentioned to clarify the purpose and physical meaning of each (lines 183188). Moreover, Table3 is renamed “Suggested evaluation ratios, conditional parameters and geometric parameters” and rearranged based on the mentioned three dimensionless groups, as well as adding a new column namely “Physical meaning”
For the other two ratios (Rr, WAR, and RER) which are mentioned in Section” 2.4.2 Classification Ratios”:
Rr represents the reduction in intrusion length compared with that of the base case as informed by Eq. 2.
WAR represents the variation of the saltwater wedge compared with that of the base case as informed by Eq. 3.
RER represents the variation of recharge rate compared with that which flows across the saltwater boundary as informed by Eq. 4.
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