An Assessment of Groundwater Contamination Risk with Radon Based on Clustering and Structural Models

Round 1

Reviewer 1 Report

Good work! I have no more comments.

Author Response

Reviewer #1:

Good work! I have no more comments.

Response: Thank you for recognizing the value of this work on the assessment of groundwater contamination risk with radon based on clustering and structural models.

Reviewer 2 Report

This is a long and complex paper (even without the supplementary information!). I think it has the potential to be a valuable piece of work. Unfortunately the English is in many cases not really good enough for this reviewer to understand the points the authors are trying to make, or follow their descriptions of methodologies and conclusions. The problem with the English is not just that the grammar is not always correct (though this is so), but that the meaning of many sentences is hard to understand. For instance, the passage starting on Line 106 has a mixture of clear sentences and obscure sentences:

"For the assessment of groundwater contamination risk maps, it will be useful to establish a direct comparison between radon concentration in rocks and groundwater." [A clear sentence, though 'it is useful' would be better]. "Then, how is it justified when in this comparison there is a high-radon production in the rocks and a reduced radon concentration in the underground." [Unclear what this means - how is what justified? The sentence is a question and hence should have a question mark (?), but also having raised a question, the authors should answer it in the next sentences.]  "Despite the reduced influence on the overall radon risk, radon concentration in groundwater should be included in geogenic radon hazard index, because there is a human exposure to this gas through ingestion that should not be neglected."[The first phrase is unclear - reduced influence of what? The rest of the sentence is clear, though "geogenic" should be preceded by "the"]. "However, there is a paradigm shift with the role of the groundwater recharge coefficient in the multivariate definition of geogenic radon risk index [35]."[This is totally obscure - some paradigm has shifted, but we are not told what or how]."Understanding the relationship between groundwater radon contamination and radon production in rocks is therefore crucial for the correct planning of groundwater quality protection." [A good clear sentence]. And so on.

For this paper to be acceptable, it needs extensive revision of the English, preferably by a native English speaker with some geochemical expertise. They should have enough expertise to be able to decide what the authors mean and help them express it more clearly. There is some good work here which is likely to be neglected by the scientific community because the writing is so obscure. I also feel that the paper could be more concise - the application of some fairly standard statistical techniques could be described more concisely. Concentrate on the important results and choose the points you want to emphasise. 

More detailed points:

L59 the text implies there are 14 000 new cases of lung cancer every year in Europe. This is a huge underestimate. The UK alone has 46 000 new cases annually.   

Is it a convention in this field to express K as K2O? If not, I would suggest altering K2O references to just K, since K2O will certainly not exist in this environment. 

Equations: define the parameters and constants in each equation immediately before or afterwards, e.g. Eq 1 should say The hydraulic turnover time (t, s) can be estimated through a combination of streamflow constants and average groundwater discharge (Q; m–3.s–1) as proposed by [57]:

 ? = ?.?? /?√????

where a1 is... and a3 is...

Figure legends should just describe the figure and not incorporate other material. So in Fig. 5 the test beginning "These maps were digitally sampled..." should be in the Materials and Methods section.

In Fig. 8, there is no need to write out the latent variables in the legend - we can see what they are in the Figure itself. 

Fig.11 Weights not Weigths

Author Response

Reviewer #2:

This is a long and complex paper (even without the supplementary information!). I think it has the potential to be a valuable piece of work. Unfortunately the English is in many cases not really good enough for this reviewer to understand the points the authors are trying to make, or follow their descriptions of methodologies and conclusions. The problem with the English is not just that the grammar is not always correct (though this is so), but that the meaning of many sentences is hard to understand. For instance, the passage starting on Line 106 has a mixture of clear sentences and obscure sentences:

We thank your kind words for our original manuscript. In the revised manuscript, even considering the requested major changes, we did the utmost to improve the text making it leaner and stronger, also considering the comments and suggestions of other reviewers. Thank you for recognizing the value of this work on the assessment of groundwater contamination risk with radon based on clustering and structural models.

Ad1) 1.      "For the assessment of groundwater contamination risk maps, it will be useful to establish a direct comparison between radon concentration in rocks and groundwater." [A clear sentence, though 'it is useful' would be better].

Response 1. The sentence has been reformulated as the suggestion by the reviewer.

Ad2) "Then, how is it justified when in this comparison there is a high-radon production in the rocks and a reduced radon concentration in the underground." [Unclear what this means - how is what justified? The sentence is a question and hence should have a question mark (?), but also having raised a question, the authors should answer it in the next sentences.]

Response 2. This question is one of the purposes of this paper. The sentence was rephrased:

“Then, how it is justified when in some areas there is a high-radon production in the rocks and a reduced radon concentration in the underground? In order to answer this question, it is important to study the connection between several factors that can increased the radon diffusion from rocks to surface water, namely the weathering of U-bearing minerals under certain specific pH conditions [31–39], the weathering rate and rock hydraulic diffusivity [40–44] and the emanation coefficient [8].”

Ad3) "Despite the reduced influence on the overall radon risk, radon concentration in groundwater should be included in geogenic radon hazard index, because there is a human exposure to this gas through ingestion that should not be neglected."[The first phrase is unclear - reduced influence of what? The rest of the sentence is clear, though "geogenic" should be preceded by "the"]."However, there is a paradigm shift with the role of the groundwater recharge coefficient in the multivariate definition of geogenic radon risk index [35]."[This is totally obscure - some paradigm has shifted, but we are not told what or how].

Response 3. Following the recommendation of the reviewer, the sentence was rephrased:

“Despite the reduced contribution of radon contamination in groundwater on the overall radon risk, the groundwater recharge coefficient was included as a geogenic factor in the geogenic radon hazard index proposed by Bossew et al. [30]. This paradigm shift occurs because there is a radiological exposure through inhalation and ingestion of water that should not be neglected.”

Ad4) "Understanding the relationship between groundwater radon contamination and radon production in rocks is therefore crucial for the correct planning of groundwater quality protection." [A good clear sentence]. And so on.

For this paper to be acceptable, it needs extensive revision of the English, preferably by a native English speaker with some geochemical expertise. They should have enough expertise to be able to decide what the authors mean and help them express it more clearly. There is some good work here which is likely to be neglected by the scientific community because the writing is so obscure. I also feel that the paper could be more concise - the application of some fairly standard statistical techniques could be described more concisely. Concentrate on the important results and choose the points you want to emphasise.

Response 4. This work has undergone an extensive review by a expert in the field of geochemistry. This paper has been extensive revised by a geochemical expert. The whole manuscript was revised in a more concise way, concentrating the most important points of this work.

More detailed points:

Ad5) 7.      L59 the text implies there are 14 000 new cases of lung cancer every year in Europe. This is a huge underestimate. The UK alone has 46 000 new cases annually.  

Response 5. This lapse in the number of deaths was duly removed. According to EPA (1993), radon exposure may cause 14000 deaths per year in the U.S.

The sentence: “In Europe, it is estimated that about 9 to 15% of the approximately 14 000 annual cases of lung cancer can be attributed to radon exposure [3–8]” has been removed and replaced by the following sentence:  

“Approximately 3 to 20% of all lung cancer deaths attributed to radon exposure are estimated Worldwide [3].”

Ad6) Is it a convention in this field to express K as K2O? If not, I would suggest altering K2O references to just K, since K2O will certainly not exist in this environment.

Response 6.  In order to convert the values of the 40K activity in Bq. Kg-1 to K in percentage, the activity of 40K is divided by the value of the specific activity of K (312.5 Bq / kg / 1%). It means, therefore, that for conversion purposes, 1% of K corresponds to 312.5 Bq and as such for the final conversion of K2O (%), multiplies by 1.205. This methodology described for the conversion of gamma spectrometry measurements to % contents obtained recently an accreditation of the international standard ISO 17025 for the standardization of tests and calibration. Currently, the Laboratory of Natural Radioactivity in the Coimbra University (Portugal) is the first laboratory in the Iberian Peninsula to obtain this accreditation for the evaluation of all radiological parameters, responding to the overall requirements imposed by the European Union regarding protection against the hazards of exposure to natural radioactive substances.

Ad7).  Equations: define the parameters and constants in each equation immediately before or afterwards, e.g. Eq 1 should say The hydraulic turnover time (t, s) can be estimated through a combination of streamflow constants and average groundwater discharge (Q; m–3.s–1) as proposed by [57]:

? = ?.?? /?√????

where a1 is... and a3 is...

Response 7. The a1 and a3 constants are retrieved from a scatter plot of ln(ΔQ/Δt) versus. ln(Q), where Q (m3·s−1) is the stream flow discharge rate and t (s) the corresponding time, and correspond to intercept-y values of straight lines with slope 1 and 3 representing the lower envelope to the scatter points.

The sentence “The hydraulic turnover time (t, s) can be estimated through a combination of streamflow constants and average groundwater discharge (Q; m–3.s–1) as proposed by [52]:” is replaced by the following sentence:

“The hydraulic turnover time (t, s) can be estimated through a combination of streamflow discharge rate ( Q, m–3.s–1) and Brutsaert method, where a1 and a3 constants are retrieved from a scatter plot of ln(ΔQ/Δt) versus. ln(Q), a combination of streamflow constants and average groundwater discharge (Q; m–3.s–1) as proposed by [63]:

t=(1.98)/(Q√a_1 a_3 )                                                                         (1)

It should also be noted that a1 and a3 correspond to intercept y values of straight lines with slope 1 and 3 representing the lower envelope to the scatter points.”

Ad8) Figure legends should just describe the figure and not incorporate other material. So in Fig. 5 the test beginning "These maps were digitally sampled..." should be in the Materials and Methods section.

Response 8. The sentence was rephrased and has been included in the Materials and Methods section. (3.4 Dataset preparation):

“These maps were digitally 452 sampled in ArcMap [73] using kriging geostatistical tool and the Zonal Statistics as a Table tool, as to 453 obtain the average value of each feature for the water collection points. These average values were

454 subsequently exported to the Excel worksheet for each cluster with an especific geology groups 455 (Tables S4, S8, S12, S16, S20, and S24) to be used in the Smart PLS-PM software [65].”

To

“In Figure 5a-g, several maps of measured variables were digitally depicted using ArcMap [81] through kriging geostatistical tool and the Zonal Statistics as a Table tool to obtain the average value for each water collection point. These average values were subsequently exported to the Excel worksheet for each cluster with a specific geology group (Tables S4, S8, S12, S16, S20, and S24) to be used in the Smart PLS-PM software [73].”

Ad9) In Fig. 8, there is no need to write out the latent variables in the legend - we can see what they are in the Figure itself.

Response 9. The name of each latent variable was removed in Figure 8.  

Ad11) Fig.11 Weights not Weigths

Response 11. The word was properly modified. 3

Reviewer 3 Report

Review of manuscript Water-488713 “An assessment of groundwater contamination risk

3 with radon based on clustering and structural models” by Martins et al.

This manuscript presents the results of a study aimed at understanding what environmental feature is responsible for the effective transfer of radon contamination to groundwaters. It takes form in a region of Northern Portugal but the statistical methods and approach presented (Hierarchic Agglomerative Clustering, HAC, and Partial Least Squares-Path Modeling, PLS-PM) can be transferred to other locations in the world, and provide a new perspective for groundwater risk modelling. The results show that high radon production from rocks is not necessarily linked to higher groundwater contamination, other factors might be more important (e.g. high fracturing density) while high hydraulic turnover time and high electric conductivity act as barriers to radon transfer to surficial waters

General comment

In my opinion, the paper is very interesting and I see it as a necessary completion of another work from the same group of authors that I had the chance to review some time ago for this same journal. More details have been added relative to the PLS-PM statistical method I am not very much used to, and I think that this is a good way to encourage its application in other areas of the world, making this work of international interest and not only for local use.

However, my biggest concern is relative to the language, since the paper presents a lot of wrong or bad constructed sentences that can be detected also by a non-native speaker like me and that make the comprehension very difficult in some cases.

For instance, the use of “Although” at line 352 creates a suspension and leaves the reader with an unresolved sentence, then it should be deleted.

Again, at line 412 the authors should correct the sentence in order to make it more comprehensible (“ …. One for the radiological data collected in rocks, ONE FOR groundwaterS, and ONE FOR hydraulic turnover timeS.”).

Again, the authors should add “importance of” between “the” and “precipitation” at line 502.

And again, the sentence at lines 721-723 is really confusing and absolutely not straightforward: do the authors mean that the hydrosphere compartment has a significantly higher effect (w=1.380) on radon contamination in groundwater than that produced by radon production potential (w=0.041)? If so, the sentence should be changed accordingly in order to clarify this concept.

Those reported above are only four examples, but the manuscript is plenty of this kind of problems. Therefore, I think that a complete rewriting is absolutely necessary, coupled with the language and grammar check by a native English speaker or a skilled scientist. This rewriting and check is of paramount importance and can not be avoided or quickly solved, given the importance of the paper’s subject. I suggest also to rethink entirely the manuscript’s structure: for example, some parts can be shortened (as the Introduction, very interesting but with way too many details!), others can be better organized in order to avoid repetition. For instance, the parts in sections 4.2.1 and 4.2.2, where equations expressing the influence of exogenous variables over endogenous ones are presented (eqs 4a to 9c), can be summarized in a devoted table, leaving the body of text only for the core discussion.

Specific comments

Line 96: add the acronyms for emanation coefficient (CE) and radon production potential (PRn), since it is the first time they are cited.

Line 200: Please refer also to the work by Martins et al. submitted to revision to Water and entitled “A new framework for the management and radiological protection of groundwater resources: the implementation of a national action plan for radon in drinking water and impacts on human health”. I personally try to avoid citations of PhD or MSc thesis.

Lines 240-242: the sentence “The LSC technique associated with……when compared with other methods” can be deleted.

Lines 248-257: Please, explain here how you provided estimates of hydraulic turnover times for the remaining 52 sampling sites. It is reported in the caption of Figure 5, but it should be presented here first (and only cited in the figure’s caption).

Line 257: explain here what are a₁ and a₃.

Line 330-331: the part of the sentence stating “…, and the migration effect through fracturing density” is a repetition and should be deleted.

Please, provide a better resolution picture of Figure 3b in order to clearly read the writings.

Please, explain what w and pc stand for in Figure 4’s caption.

Table 1: there is no column with n values, please provide it.

Figure 5: instead of using graphical patterns to identify the different geologies of the study area, why not changing the colours of sampling sites (one for each different group) and proveide the relative legend? I suggest to try and then choose the clearer version.

Lines 456-468 I think this part should be moved in the Results’ section, after line 494. It explains why the authors chose to apply the PLS-PM method only to 2 clusters and is therefore better suited for the part relative to the presentation of results.

Lines 482-488 are a repetition of what already written in section 3.3 and should be deleted.

Figure 7: please, explain what is on the y-axis.

Figures 8-10: I suggest to use different colours to identify circles representing latent variables and then add an explanatory legend. In the present form, labels sometime overlap with numbers, resulting in quite confused pictures.

Lines 563 and 565: please refer to Equations 2 and 3 (not 1 and 2) for measured and predicted scores. Equation 1 is that relative to the calculation of hydraulic turnover time (line 257). Correct this mistake throughout the entire manuscript.

Line 565: How can 0.793 provide a substantial deviation between measured and predicted scores, while 0.522 means only some deviation (line 607), and 0.230 an even reduced one (line 682)? In my opinion, the first value (0.793) provides a well overlap between predicted and measured scores (then there is a very reduced deviation) while the last one (0.230) produces a predicted value that is more than 4 times lower than the measured one. Am I right? If so, please correct the text accordingly.

Lines 790, 832, 835: please use “counterbalanced” instead of “countered”.

Line 802: the right citation is Figure 10e.

Line 876: please use “Portuguese” instead of “national”.

Line 902: is “fulfil” the right verb? How can radon concentrations fulfil the EURATOM Directive threshold of 100 Bq/L (meaning they are lower!!) and exceed the value of 500 BQ/L at the same time? Please explain this evident contradiction.

Supplementary Material

Please, homogenize table formats (e.g. Table S9 as format for all other correlation matrices) and provide the graph where one can identify a₁ and a₃ as y-intercepts of the dashed lines reported in Table S3

Conclusive remark

I suggest to accept the paper only after the suggested major revisions are provided.

Comments for author File: Comments.doc

Author Response

Reviewer #3:

This manuscript presents the results of a study aimed at understanding what environmental feature is responsible for the effective transfer of radon contamination to groundwaters. It takes form in a region of Northern Portugal but the statistical methods and approach presented (Hierarchic Agglomerative Clustering, HAC, and Partial Least Squares-Path Modeling, PLS-PM) can be transferred to other locations in the world, and provide a new perspective for groundwater risk modelling. The results show that high radon production from rocks is not necessarily linked to higher groundwater contamination, other factors might be more important (e.g. high fracturing density) while high hydraulic turnover time and high electric conductivity act as barriers to radon transfer to surficial waters

General comment

In my opinion, the paper is very interesting and I see it as a necessary completion of another work from the same group of authors that I had the chance to review some time ago for this same journal. More details have been added relative to the PLS-PM statistical method I am not very much used to, and I think that this is a good way to encourage its application in other areas of the world, making this work of international interest and not only for local use.

However, my biggest concern is relative to the language, since the paper presents a lot of wrong or bad constructed sentences that can be detected also by a non-native speaker like me and that make the comprehension very difficult in some cases.

Ad1) For instance, the use of “Although” at line 352 creates a suspension and leaves the reader with an unresolved sentence, then it should be deleted.

Response 1.The word “Although” was removed, as suggested by the reviewer.

Ad2) Again, at line 412 the authors should correct the sentence in order to make it more comprehensible (“ …. One for the radiological data collected in rocks, ONE FOR groundwaterS, and ONE FOR hydraulic turnover timeS.”).

Response 2. The sentence: “ : one for the radiological data in collected rocks, groundwater and hydraulic turnover time” was removed from the text.

Ad3) Again, the authors should add “importance of” between “the” and “precipitation” at line 502.

Response 3. The word “ importance of” was added, as suggested by the reviewer.

Ad4) And again, the sentence at lines 721-723 is really confusing and absolutely not straightforward: do the authors mean that the hydrosphere compartment has a significantly higher effect (w=1.380) on radon contamination in groundwater than that produced by radon production potential (w=0.041)? If so, the sentence should be changed accordingly in order to clarify this concept.

Response 4. These sentence was changed as suggested by the reviewer.

The sentence “The hydrosphere compartment has a significant positive effect (w = 1.380) than the radon production potential with the insignificant effect (w= 0.041) on radon contamination in groundwater (Figure 10e).” was changed to:

“The hydrosphere compartment has a significantly higher effect (w = 1.380) on radon contamination in groundwater than that produced by radon production potential (w= 0.041) (Figure 10e).”

Ad5) Those reported above are only four examples, but the manuscript is plenty of this kind of problems. Therefore, I think that a complete rewriting is absolutely necessary, coupled with the language and grammar check by a native English speaker or a skilled scientist. This rewriting and check is of paramount importance and can not be avoided or quickly solved, given the importance of the paper’s subject. I suggest also to rethink entirely the manuscript’s structure: for example, some parts can be shortened (as the Introduction, very interesting but with way too many details!), others can be better organized in order to avoid repetition. For instance, the parts in sections 4.2.1 and 4.2.2, where equations expressing the influence of exogenous variables over endogenous ones are presented (eqs 4a to 9c), can be summarized in a devoted table, leaving the body of text only for the core discussion.

Response 5. A skilled scientist checked the entire manuscript. The structure of this manuscript was changed and organized, the introduction was shortened, and the equations are represented in Table 3, as suggested by the reviewer.

Specific comments

Ad6) Line 96: add the acronyms for emanation coefficient (CE) and radon production potential (PRn), since it is the first time they are cited.

Response 6. These  acronyms were added to the manuscript.

Ad7) Line 200: Please refer also to the work by Martins et al. submitted to revision to Water and entitled “A new framework for the management and radiological protection of groundwater resources: the implementation of a national action plan for radon in drinking water and impacts on human health”. I personally try to avoid citations of PhD or MSc thesis.

Response 7. Reference added.

Ad8) Lines 240-242: the sentence “The LSC technique associated with……when compared with other methods” can be deleted.

Response 8. The sentence “The LSC technique associated with……when compared with other methods” was deleted from the manuscript, as suggested by the reviewer.

Ad9) Lines 248-257: Please, explain here how you provided estimates of hydraulic turnover times for the remaining 52 sampling sites. It is reported in the caption of Figure 5, but it should be presented here first (and only cited in the figure’s caption).

Response 9.

The hydraulic turnover time parameter was only used in PLS-PM of the model c2d2, since there is no streamflow discharge data for all the springs sampled. The main purpose for adding this parameter is to see if it improves the model or not.  

As such, it was decided to change the following sentences:

“The total data of hydraulic turnover time on biotitic granites (Group V) springs have been obtained from a study of Pacheco & Van der Weijden [41].”

To

Line: 279“In the absence of streamflow discharge rate data for the calculation of hydraulic turnover time in the total collection points, only data related with Group V was removed from a study of Pacheco & Van der Weijden [41].”

Ad10) Line 257: explain here what are a1 and a3.

Response 10. The explanation for parameters a1, a3 was added.

Line: 276: “Where a1 and a3 correspond to intercept y values of straight lines with slope 1 and 3 representing the lower envelope to the scatter points.”

Ad11) Line 330-331: the part of the sentence stating “…, and the migration effect through fracturing density” is a repetition and should be deleted.

Response 11. Sentence deleted.

Ad12) Please, provide a better resolution picture of Figure 3b in order to clearly read the writings.

Response 12. A new figure 3b with better resolution was added to the manuscript, as suggested by the reviewer.

Ad13) Please, explain what w and pc stand for in Figure 4’s caption.

Response 13 . The figure’s caption was reformulated to clarify what is w and pc:

 “Figure 4.  Schematic representation of Partial Least Squares – Path Modelling (PLS-PM): (a) Panel that illustrates the formative model; (b) Panel that illustrates the relationships (inner model) between latent variables (LV) and the links (outer model), between the LV and the measured values (MV). The strength of those relationships is represented by path coefficients (pc) and weights (w) computed by the PLS-PM model.”

Ad14) Table 1: there is no column with n values, please provide it.

Response 14. The n values were introduced in table 1.

These references are now properly matched to the format requirement

Ad15) Figure 5: instead of using graphical patterns to identify the different geologies of the study area, why not changing the colours of sampling sites (one for each different group) and proveide the relative legend? I suggest to try and then choose the clearer version.

Response 15. According to the suggestions of the reviewer Fig. 5 was changed.

Ad16) Lines 456-468 I think this part should be moved in the Results’ section, after line 494. It explains why the authors chose to apply the PLS-PM method only to 2 clusters and is therefore better suited for the part relative to the presentation of results.

Response 16. The sentence composed by lines 456-468 was moved to the results section, as suggested by the reviewer.

Ad17) Lines 482-488 are a repetition of what already written in section 3.3 and should be deleted.

Response 17. Following the recommendation of the reviewer, this Sentence was deleted from the manuscript.

Ad18) Figure 7: please, explain what is on the y-axis.

Response 18.  y-axis is the mean lines. The following sentence was added to the manuscript to explain the PCV procedure and what is a y-axis.

Line: 565: “According to PCV procedure, when mean lines are activated, the XLSTAT display for each cluster, a line that corresponds to the mean of the multiple measured variables. It means therefore that when the rescale option is activated, it facilitates the visualization of multiple measured variables distribution for each cluster. “

Ad19) Figures 8-10: I suggest to use different colours to identify circles representing latent variables and then add an explanatory legend. In the present form, labels sometime overlap with numbers, resulting in quite confused pictures.

Response 19. Indeed, if it were used different colors for each latent variable, the visual analysis would be eased. Unfortunately, it was decided to use a free version of the software Smart PLS-PM, although with some conditioning factors. It means, therefore, that in this free version, they do not allow us to change the color of the circles, to export the data, or to export the images in another format than PNG.

Ad20) Lines 563 and 565: please refer to Equations 2 and 3 (not 1 and 2) for measured and predicted scores. Equation 1 is that relative to the calculation of hydraulic turnover time (line 257). Correct this mistake throughout the entire manuscript.

Response 20.  This mistake in the number of equations was duly changed throughout the manuscript.

Ad21) Line 565: How can 0.793 provide a substantial deviation between measured and predicted scores, while 0.522 means only some deviation (line 607), and 0.230 an even reduced one (line 682)? In my opinion, the first value (0.793) provides a well overlap between predicted and measured scores (then there is a very reduced deviation) while the last one (0.230) produces a predicted value that is more than 4 times lower than the measured one. Am I right? If so, please correct the text accordingly.

Response 21. Indeed, there is a mistake regarding to the deviation types for each model. We thank  to the reviewer for their detection. The text has been corrected accordingly as recommended by the reviewer.

Ad22) Lines 790, 832, 835: please use “counterbalanced” instead of “countered”.

Response 22. The word “countered” has been replaced by “counterbalanced” as recommended by the reviewer.

Ad23) Line 802: the right citation is Figure 10e.

Response 23. We thank to the reviewer for the detection of this error. The right citation “Figure 10 e” was added to the manuscript. 

Ad24) Line 876: please use “Portuguese” instead of “national”.

Response 24. The word “national” has been replaced by “Portuguese” on the entire  manuscript.

Ad25) Line 902: is “fulfil” the right verb? How can radon concentrations fulfil the EURATOM Directive threshold of 100 Bq/L (meaning they are lower!!) and exceed the value of 500 BQ/L at the same time? Please explain this evident contradiction.

Response 25. Indeed, this sentence is contradictory.

Thus, the sentence:  “Most of these radon concentrations fulfill the Directive 2013/51/EURATOM threshold for drinking water (100 Bq.L-1; [1]) and exceed the parametric value of 500 Bq.L-1 [77] to protect human health against radiological exposure.” Was changed by:

“Most of the sampled springs fulfill the Directive 2013/51/EURATOM threshold for drinking water (100 Bq.L-1; [1]). Although, some springs with radon concentrations higher than 500 Bq.L-1 [85] should not be neglected in order to promote human health protection against radiological exposure.”

Supplementary Material

Ad26) Please, homogenize table formats (e.g. Table S9 as format for all other correlation matrices) and provide the graph where one can identify a1 and a3 as y-intercepts of the dashed lines reported in Table S3

Response 26. All correlation matrices were duly formatted according to table S9, as suggested by the reviewer. Furthermore, we provide in Supplementary material an example of Brutsaert method application to collecting site ID LS5  

Line: 657: “All data for the calculation of hydraulic turnover time are given in Table S3 and an example of Brutsaert method application to collecting site ID LS21 was depicted in Graph S1 of the supplementary material. “.

Furthermore, it already available this example of Brutsaert method in Pacheco & van der Weijden [37].

Fig. 6. Application of Brutsaert method to collecting site ID 144 (name: Guilhado), which is associated to spring site ID 198 (Table 1). The location of these sites is illustrated in Fig. 1. The Q and t data from which the plot was drawn are given in Table 1.

Conclusive remark

I suggest to accept the paper only after the suggested major revisions are provided.

Round 2

Reviewer 3 Report

I have read the revised version of the manuscript and the responses to the reviewers. The authors have provided satisfactory answers to the issues raised by me and the other reviewer and the manuscript has significantly improved. I am happy to suggest its publication

Author Response

Thanks for your kind words about our revised ms. We very much appreciate your recommendation of publishing our ms.