Numerical Assessment of Morphological and Hydraulic Properties of Moss, Lichen and Peat from a Permafrost Peatland
 ^{1}Toulouse Institute of Fluid Mechanics (IMFT), National Polytechnic Institute of Toulouse, Toulouse, F31400, France
 ^{2}Geosciences Environnement Toulouse (GET) Laboratory, University Toulouse III – Paul Sabatier, Toulouse, F31400, France
 ^{3}BIOGEOCLIM Laboratory, Tomsk State University, Tomsk, Russian Federation
 ^{4}N. Laverov Federal Center for Integrated Arctic Research of the Ural Branch – Russian Academy of Science, Russian Federation
 ^{1}Toulouse Institute of Fluid Mechanics (IMFT), National Polytechnic Institute of Toulouse, Toulouse, F31400, France
 ^{2}Geosciences Environnement Toulouse (GET) Laboratory, University Toulouse III – Paul Sabatier, Toulouse, F31400, France
 ^{3}BIOGEOCLIM Laboratory, Tomsk State University, Tomsk, Russian Federation
 ^{4}N. Laverov Federal Center for Integrated Arctic Research of the Ural Branch – Russian Academy of Science, Russian Federation
Abstract. The hydraulic properties of ground vegetation cover are important for high resolution hydrological modeling of permafrost regions, due to its insulating and draining role. In this study, the morphological and effective hydraulic properties of Western Siberian Lowland ground vegetation samples (lichens, Sphagnum mosses, peat) are numerically assessed based on tomography scans. After numerical preprocessing, porosity is estimated through a void voxels counting algorithm, showing the existence of representative elementary volumes (REV) of porosity for most samples. Then, two methods are used to estimate hydraulic conductivity depending on the sample’s homogeneity. For the most homogeneous samples, Direct Numerical Simulations (DNS) of a singlephase flow are performed, leading to a definition of hydraulic conductivity related to REV, which is larger than those obtained for porosity. For more heterogeneous samples, no adequate REV may be defined. To bypass this issue, a pore network representation of the whole sample is created from computerized scans. Morphological and hydraulic properties are then estimated through this simplified representation. Both methods converged on similar results for porosity. Some discrepancies are observed in the morphological properties (specific surface area). Hydraulic conductivity fluctuates by two orders of magnitude, depending on the method used, and yet this uncertainty is less than that found in experimental studies. Therefore, biological and sampling artifacts are predominant over numerical biases. Porosity values are in line with previous values found in the literature, showing that arctic cryptogamic cover can be considered as an open and wellconnected porous medium (over 99 % of overall porosity is open porosity). Meanwhile, digitally estimated hydraulic conductivity is higher compared to previously obtained results based on field and laboratory experiments. This could be related to compressibility effects, occurring during field or laboratory measurements. Thus, some supplementary studies are compulsory for assessing synsampling and synmeasurement perturbations in experimentally estimated, effective hydraulic properties of such a biological porous medium.
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Simon Cazaurang et al.
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RC1: 'Comment on egusphere2022475', Xiaoying Zhang, 24 Aug 2022
Reviewer manuscript #hess2022475 titled “Numerical Assessment of Morphological and Hydraulic Properties of Moss, Lichen and Peat from a Permafrost Peatland” by Simon Cazaurang et al.
General Commentsï¼
This manuscript mainly presents a numerical assessment approach for the morphological and hydraulic properties of Western Siberian Lowland ground vegetation samples (Sphagnum moss, lichens, peat) by tomography scans. The numerical method based on digital XCT recombination of samples can obtain the porosity and hydraulic conductivity. It provides a way to quantify hydrological properties of the bryophytic cover in permafrostdominated peatland catchments. Overall, the contents of the manuscript are interesting. Logicality of the paper is clear, and the results are well discussed and explained. However, there are some issues I concerned after I had read through the paper.
Comments:
 It seems quite complicated to obtain the porosity with the method the authors proposed compared to the traditional experimental method. In general, the advantage of using a nondestructive test is its coverage for large area like remote sensing. However, with the method you proposed, you just measure the properties of samples as the traditional one and even way more complicated. Thus, why this method has superiority?
 The authors stated that they confirmed the REV theory, but in the paper, I only see a schematic representation in Fig.2. Where is the data from the experiments?
 A schematic figure should be given to show the detailed methodology and technologies of PNM.
 The author stated the computation of K is represented in Fig.9, but what I see is a pressure field. What is the connection? And what is the relationship between a and b in Fig.9.
 As we all know, the porosity does not represent the condition of K. In the method, how did you distinguish the effective pores for the estimation of K? and decrease the impact or uncertainty that caused by dead pores as you are only counting the size of the pores?
 For all the bar plot, I suggest you use different patterns instead of colors, as these colors are really hard to distinguish especially in black and white print. Meanwhile, In Fig. 4  Fig.8, one color represents different sample types, such as Lichen2.1, Hollow2.8, and Mound2.6. This can easily cause confusion. The same problem also appears in Fig. 5Fig. 8. It is more appropriate to use one color to represent the same type of sample. Please modify the color of the samplesagain and add the description of types I III in Fig. 4.
 A flowchart is betteradded to show how did you estimate the n and K.
 Line110: "a thorough analysis of sample homogeneity is carried out, based on porosity...." and Line 245: "in the case of a homogeneous porous medium "and Line 25: "the most homogeneous samples" and "more heterogeneous samples", what is the criteria for judging whether the sample is “homogeneous”? Is there a mathematical relationship between the homogeneity of the sample and the porosity? And why do you have to emphasize the homogeneity. Does it mean the method gonna failed if the sample is “heterogeneous”? Is there a condition the method is valid?
 In Fig. 2: the hydrological characteristics of lichen, Sphagnummoss, and peat are studied in this paper. However, Table 2 only collects references and hydraulic conductivity data for sphagnum and peat.
 Line 403405: Specific surface area of the sample obtained usingPNM method is always larger than those obtained by image processing. Besides the explanation from the perspective of porosity, are there any other reasons to prove this phenomenon? Is it true? What is the reason? And how the specific surface area effect the estimation of K.
 Is the application promising like what I proposed in the beginning? Why this hard work is worthy if your only goal is to get same values.
Minor:
 In Table C1, please add the specific surface area and porosity data of samples obtained from image processing.
 In Table C4, Please check whether the symbols are correct, such as dSph, σST, and dThr.
 In the abstract, summary and conclusions, the authors should add supplement contents about the limitations of this proposed model method, as well as the scientific importance of this study.

AC1: 'Reply on RC1', Simon Cazaurang, 08 Nov 2022
Dear Xiaoying Zhang,
On behalf of all the coauthors, I would like to thank you for reviewing this manuscript. Please find below the answers to the questions raised in your review report. In order to make the answers to the questions accessible to everyone, we have chosen to answer each question individually.Sincerely yours,
Simon Cazaurang
General comment:
[XZ]: This manuscript mainly presents a numerical assessment approach for the morphological and hydraulic properties of Western Siberian Lowland ground vegetation samples (Sphagnum moss, lichens, peat) by tomography scans. The numerical method based on digital XCT recombination of samples can obtain the porosity and hydraulic conductivity. It provides a way to quantify hydrological properties of the bryophytic cover in permafrostdominated peatland catchments. Overall, the contents of the manuscript are interesting. The logic of the paper is clear, and the results are well discussed and explained. However, there were some issues I was concerned about after I had read through the paper.
[Authors]: The authors want to thank the reviewer for the appreciation of our work. One can find below our detailed answers to the raised concerns. Each question is answered under the form of a paragraph regarding the raised question.
Questions/Remarks:
[XZ]: It seems quite complicated to obtain the porosity with the method the authors proposed compared to the traditional experimental method. In general, the advantage of using a nondestructive test is its coverage for large areas like remote sensing. However, with the method you proposed, you just measure the properties of samples as the traditional one and even more complicated. Thus, why does this method have superiority?
[Authors]: In this work, we wanted to prove that using a numerical scheme could provide us with data of the same stiffness and quality as traditional methods, which are here field percolation and constanthead permeameter. These methods have one major disadvantage: they can only be performed a few times on a given sample. Using such methods is complicated when field study sites and quantification facilities are far from each other. Often, studies already available in the literature are only dealing with one property at a time for a given sample batch. Thus, experimental methods lead to a result, but they rely on a strong calibration in order to be statistically representative. Intercomparing experimental results is also intricate because experimental devices are different between studies.
Our samples are fragile, requiring extra care during sampling, transportation and analysis. Using nondestructive methods is interesting, even though our measurements heavily rely on samples’ preprocessing after scanning, which is nondeterministic.
Beyond retrieving some values, we want to show through our study that numerical methods are elements of an innovative methodology that only relies on the input tomography. Indeed, numerical methods allow retrieving all usual properties at once using the sample batch, facilitating intercomparisons between them.
[XZ]: The authors stated that they confirmed the REV theory, but in the paper, I only see a schematic representation in Fig.2. Where is the data from the experiments?
[Authors]: A schematic representation of the REV theory is indeed available in Fig.2. Applying our method leads to computation of around 1.5 million of intermediate porosity values, with variable cube length. This process is done for each sample, creating 12 different graphs. Due to the numerous graphs and for the sake of clarity, we decided to put the data of the numerical experiments in Supplement B1 for porosity and in Supplement B2 for hydraulic conductivity. For each sample, the statistic spread as well as the mean porosity value is shown. The black point indicates the minimum REV identified, along with the property variability associated. We will add a sentence to emphasize the presence of the results in Supplement B1 for porosity and in Supplement B2 for hydraulic conductivity.
[XZ]: A schematic figure should be given to show the detailed methodology and technologies of PNM.
[Authors]: In our work, we used some specifically designed Pore Network Model libraries such as PoreSpy (https://porespy.org/) and OpenPNM (https://openpnm.org/) which are opensource and free. Both packages are relying on a dedicated algorithm named SNOW (SubNetwork of the Oversegmented Watershed). Some precision about the construction of such algorithm based on image processing is available in Gostick, 2017 (https://doi.org/10.1103/PhysRevE.96.023307). One can also refer to the following Python tutorial showing the construction of a pore network (https://porespy.org/examples/networks/tutorials/snow_basic.html). Other pore network model generation algorithms are also existing in the literature (such as the “Maximal Ball” algorithm, Silin & Patzek, 2006). However, we decided to give a try to PoreSpy and OpenPNM because of their easy integration to the already existing workflow developed during the implementation of image processing. Many other pore network generators require extensive homemade codes, which makes it difficult to intercompare to other results from different materials.
[XZ]: The author stated the computation of K is represented in Fig.9, but what I see is a pressure field. What is the connection? And what is the relationship between a and b in Fig.9.
[Authors]: The authors warmly thank the reviewer for the careful reading of our manuscript. Unfortunately, this is a typo error in the figure call itself. Indeed, Figure 9 shows pressure fields resulting from a singlephase flow simulation, either through a Representative Elementary Volume of Sphagnum sample using Direct Numerical Simulation for the rightmost figure, or on a Pore Network for the leftmost figure. For both methods, we used a steadystate solver for NavierStokes equations. The pressure field was used to verify the flow equilibrium prior to permeability computations. Then, we used Darcy’s law to compute intrinsic permeability, and then extensively hydraulic conductivity. In our work, we initially represented the velocity field instead of the pressure field. However, this choice was not optimal because velocity field visualization would require vector components. Our figures were then unreadable, as we wanted to show the sample's morphology.
[XZ]: As we all know, the porosity does not represent the condition of K. In the method, how did you distinguish the effective pores for the estimation of K? and decrease the impact or uncertainty that is caused by dead pores, as you are only counting the size of the pores?
[Authors]: In our method, we implement our simulation on pores’ numerical representation, and not on a continuous medium. During morphological analysis, we showed that almost all pores are open and connected to each other. As the proportion of dead pores was often less than 0.1%, we made the assumption that all pores are effectively participating in flow dynamics, as we showed in Table 3.
[XZ]: For all the bar plots, I suggest you use different patterns instead of colors, as these colors are really hard to distinguish, especially in black and white print. Meanwhile, In Fig. 4  Fig.8, one color represents different sample types, such as Lichen2.1, Hollow2.8, and Mound2.6. This can easily cause confusion. The same problem also appears in Fig. 5Fig. 8. It is more appropriate to use one color to represent the same type of sample. Please modify the color of the samples again and add the description of types I III in Fig. 4.
[Authors]: A new color and symbol scheme will be developed in the revised manuscript. Indeed, in the submitted version, we wanted to emphasize on the sample porosity types and not on the sample nature. Here, we will add some symbols to cope with black and white prints.
[XZ]: A flowchart is better added to show how you estimate the n and K.
[Authors]: The authors would like to thank the reviewer for this suggestion. We will add a flowchart describing the method to estimate porosity Representative Elementary Volume. An analogous method is used for the quantification of the hydraulic conductivity K.
[XZ]: Line 110: "a thorough analysis of sample homogeneity is carried out, based on porosity...." and Line 245: "in the case of a homogeneous porous medium "and Line 25: "the most homogeneous samples" and "more heterogeneous samples", what is the criteria for judging whether the sample is “homogeneous”? Is there a mathematical relationship between the homogeneity of the sample and the porosity? And why do you have to emphasize the homogeneity. Does it mean the method is going to fail if the sample is “heterogeneous”? Is there a condition that the method is valid?
[Authors]: In our study, we assume that samples’ variability is conditioned upon porosity spatially varying or not. This condition is a prerequisite, especially in the presence of natural samples, potentially very heterogeneous. Homogeneity criterion is based on the existence of a Representative Elementary Volume. Property homogeneity is required to find a Representative Elementary Volume. Consecutively, if a sample admits no significant variation for a given direction, then we can consider the sample homogeneous for that given axis (i.e., 1Dhomogeneous). In the same way, if this low variability is observed on the three axes, then this sample is considered as homogeneous on the whole sample (i.e., 3Dhomogeneous). Otherwise, convergence cannot be reached, and therefore the method using Representative Elementary Volumes will fail. To illustrate this, it is possible to take the example of samples Peat2.2 and Hollow1.2 that do not satisfy sufficient homogeneity to converge to a Representative Elementary Volume. In this case, apart from doing a computation on the entire sample (which is prohibitive in terms of computational costs), choices are reduced. For both samples, and more widely for the Type II and III samples that are 2Dhomogeneous, Pore Network Modeling is more suitable in the absence of another efficient volume averaging method.
To enhance the classification, we added average and standard deviation values for each sample class in Table 3. This will confirm that X and Y values have very low variability (under 1% for Type I samples, around 1% for Type III and less than 4% for Type II). In terms of vertical porosity, Type I have a low variability as Type III and Type II concentrates the variability.
[XZ]: In Fig. 2: the hydrological characteristics of lichen, Sphagnum moss, and peat are studied in this paper. However, Table 2 only collects references and hydraulic conductivity data for sphagnum and peat.
[Authors]: Indeed, there are only values for Sphagnum and peat in this table. As far as our literature review on lichen hydraulic properties went, we were only able to find one study about macroscale properties of lichens (Voortmann et al., 2014). The authors of this study found a value between 1.8.10^{9 }m.s^{1} to 3.7.10^{9} m.s^{1} using an evaporation experiment and inverse modelling. We will add this value to Table 2 among the other values for Sphagnum moss and peat. However, we express reservations about the representativeness of the obtained value. Indeed, the morphology of the presented samples seems close to those we are studying. The hydraulic conductivity remains nevertheless weak with regard to the observed structure. It would be interesting to apply the numerical scheme developed in the present manuscript in order to compare the results.
[XZ]: Line 403405: Specific surface area of the sample obtained using the PNM method is always larger than those obtained by image processing. Besides the explanation from the perspective of porosity, are there any other reasons to prove this phenomenon? Is it true? What is the reason? And how does the specific surface area affect the estimation of K ?
[Authors]: Even though Pore Network Models are computationally more efficient than Direct Numerical Simulations, they rely on a unidimensional reconstruction of a tridimensional structure. This reconstruction causes structural simplifications and potentially errors.
Specific surface area is important for chemical and thermal reaction studies. They require in essence the most highfidelity surface representation. Finding a specific surface area from a simplified model does not have much sense for comparison. Indeed, the authors will remove the comparison between specific surface obtained by image processing and pore network models in the main text for the revised manuscript.
[XZ]: Is the application promising like what I proposed in the beginning? Why is this hard work worthy if your only goal is to get the same values ?
[Authors]: In our point of view, even though the implementation of such numerical schemes are indeed complex and timeconsuming, we believe that using numerical methods enables a better comparison between samples of different locations. Morphological and hydraulic properties assessments based on field or laboratory experiments have each one their own biases. For these methods, we can identify some possible biases :
 1. Date and time of the sampling;
 2. Experimenter and his/her skills or knowledge;
 3. Transport conditions;
 4. Physical and biological degradation;
 5. Used laboratory hardware to achieve these measurements;
 6. Data postprocessing.
Field experiments also have some limitations. For example, a doublering infiltrometer test was conducted during the sampling field trip next to each sample plot. In this case, the experiment was impossible to conduct for some samples due to a high conductivity. This links well with our results that show high hydraulic conductivity.
When using a numerical scheme, computations can be virtually done as many times as needed. Each computation attempt will produce the same result for a given input dataset. We can also eliminate biases #4 and #5 as the tomography gives us a steadyshot of a given sample, allowing us to study these samples thoroughly, only relying on the minimal resolution of the Xray scanner of 88 µm.voxel1.We found that using numerical schemes enables classifying samples along their homogeneity or heterogeneity, which is not easy if based on experiments only. Our method is valid even for heterogeneous samples, on the condition that sampling and scanning have been conducted thoroughly. A small paragraph will be added in the conclusion to emphasize these points.
Our method allowed to pinpoint the importance of microscale characterization in order to understand macroscale phenomena. We showed that applying an analogous method is potentially valid for all kinds of porous media, even heterogeneous. Such kind of study has not been done so far to our knowledge.
Finally, we assume that the implemented numerical scheme is efficient compared to field and laboratory experiments because such work would require a statistically strong amount of samples. We compensate the low number of samples by the REV survey that validates sufficient statistical representativity of our samples. Collecting such numerous samples is difficult, both for transportation and preservation of this sensitive interface.
Minor remarks:
[XZ]: In Table C1, please add the specific surface area and porosity data of samples obtained from image processing.
[Authors]: We acknowledge this remark. We will include these values in the revised version of our manuscript.
[XZ]: In Table C4, Please check whether the symbols are correct, such as dSph, σST, and dThr.
[Authors]: We acknowledge this remark. The labels of Table C4 will be modified accordingly.
[XZ]: In the abstract, summary and conclusions, the authors should add supplement contents about the limitations of this proposed model method, as well as the scientific importance of this study.
[Authors]: The authors thank the reviewer for this suggestion. Indeed, we wil give some details about the limitations of the proposed model method. Indeed, the main limitation observed in our method is the input data (which is here the tomographic scans). This study highlights the need of a quantitative and reproducible microscale properties' assessment in order to implement values in a macroscale model. Our combined method enable to study any type of sample, even heterogeneous ones. Such inclusive method has not been seen elsewhere by the authors. We will modify the essence of the abstract with a dedicated paragraph. We will also add some information in the conclusion.

RC2: 'Comment on egusphere2022475', Anonymous Referee #2, 23 Oct 2022
The submitted manuscript deals with the assessment of the porosity and hydraulic conductivity of Western Siberian Lowland ground vegetation samples (lichens, Sphagnum mosses, peat). Twelve samples are analysed throughout a numerical method instead of a classical experimental field determination (that they have also carried out). Based on digital XCT reconstructions the study confirms the high values of porosity presented by such a biological media. Due to numerical constraints, a single numerical method could not be implemented and the authors used both Direct Numerical Simulations (DNS) and Pore Network Modeling (PNM), which did not provide the same results… but are closer together for the evaluation of the hydraulic conductivity which is several orders of magnitude lower for the experimental field method.
The subject of the study is interesting and suitable for publication in HESS and as the authors reported in their introduction, the results could be of great importance to model the evolution of these natural environments impacted by climate change. The manuscript is globally well written and of good scientific quality. I think that a few modifications can still be made to improve its quality.
General comments:
References are numerous and I guess that they cover the state of art.
The purpose of the study should be more clearly stated.
The station can be described briefly, the field work is important and deserves a few words.
A complete flowchart describing the different steps of the methodology will be appreciated.
The quality of the figures is good but the use of colors is not always clear and understandable. The works in the supplements are not highlighted enough.
The distinction between homogeneous and heterogeneous is not clearly defined, although this aspect seems to have an impact on the typology and the possibilities of implementing the proposed methods.
Some misunderstandings in the presentation of the results for porosity.
The definition of the sample typology is done twice and is not consistent (?)
Comments:
L 97: I am not a specialist of the topic but what about the study by Potkay et al. (2020) ?
Potkay, A., ten Veldhuis, M. C., Fan, Y., Mattos, C. R., Ananyev, G., & Dismukes, G. C. (2020). Water and vapor transport in algalâfungal lichen: Modeling constrained by laboratory experiments, an application for Flavoparmelia caperata. Plant, cell & environment, 43(4), 945964.
L105: what is the main purpose of the present study? The authors want to assess hydraulic properties of lichens and Sphagnum mosses by numerical methods but I do not understand the “justification” of this way? What kind of problems / difficulties arise from the experimental measurements? The question is of primary goal and I think that the issue of measurements scale should also be mentioned especially if the results are intended to be used in a modelling approach.
L122: please indicate the coordinates of the station where samples were collected. Besides, I would appreciate synthetic details on the climatic condition of this location.
L161: you refer to the drying experiment carried out by Kämäräinen et al. (2018). A different drying temperature (40°C instead of 50°C) has been applied for the preparation of samples that have a larger size in your case. It is not exactly the same protocol. The most important finding is that the morphological structure is preserved, and since you don't expect to know the actual water content of your various samples, this is probably not a critical point.
L190: in the main text, Fig. 4 is used before figures 2 and 3? It is quite difficult to distinguish colors in your picture. Is there a link between the colors used for your planar porosity plots and the averaged versions? I don’t think so, but it‘s not clear.
L202: please indicate that p_{open} refers to the open porosity proportion. In table 3, this variable should be multiply by 100? And to be consistent with equation (2), you should indicate “%” in Table 1.
L258: You should refer to Supplement A. Also, I think you did not mention in the main text supplement B1 where some pictures present the evolution of porosity with the size of measurement. I’m wondering how you fix the final value of the sample’s REV of porosity. It is not obvious to understand your results (final sizes) when comparing curves, for instance, for samples Hollow2.7, lichen1.3 and lichen2.1.
L265: I don't think that figure 3 is required.
L280: I guess the numerical method developed by Patankar (1980) has been improved to solve faster the singlephase flow problem. I understand that the numerical aspects are not a key point of this study but your choice induces limitations in the sample processing capacity (only type I) and that's a bit bothering.
L282: how did you select your 4 REV sizes? If I clearly understand, choosing a small REV size involves performing many simulations. However, are 4 sizes enough to detect the impact of the size on the fluctuation of your variable?
L344354: The conclusion is that DNS and PNM did not lead to compatible results for hydraulic conductivity measurements. The authors should probably indicate a way to  a priori  select the better method for each sample. Is there a link with homogeneity of the sample (the authors have indicated that in the manuscript, L276 for instance) and how can they mathematically or physically define the frontier between homogenous and heterogeneous sample?
L349: Fig. 9Right does not describe the hydraulic conductivity computation as mentioned in the manuscript.
L359: the lowest porosity value is obtained for the Mound1.1 sample.
L365: according to Table 3, the average porosity for mound mosses is 65.8 + 23%?
L373: Lichen1.3 has a total porosity lower than 85%
L375: correct definition is “medium high porosity” or “low basal porosity” (L193) for type II ? Besides, total porosity is not comprised between 70 and 85%.
L376: for type III, the total porosity is lower than 73%
L469: Did Shirokova et al. (2021) make a link between their biological results and the properties you focused on? I don’t think that they talk about porosity, hydraulic conductivity, and specific surfaces. Either you add a reference that show this link, or you add this part later in your discussion…
L472: your experimental results are quite similar than other studies mention in Table 2. I would include them (not only “published results” but experimental results in general, including your own).
L477: What is the interest of subsection “4.1 Numerical reconstruction after scanning” in the discussion part? I have the feeling that the main elements are given again between L 510 and 520?
L523526: I think the main justification and interest of the present study lies in the fact that field experiments carried out to obtain hydraulic conductivity could be inaccurate because of an excessive compression of the biological media. I would appreciate references that could highlight this aspect, also the difference between natural rainfall and field experiments and finally the lack of such kind of experimental measurements. Besides, in the perspective of numerical modelling of these biological media located in the upper part of the soil, is it possible to hide unsaturated flows (cf. L488)? I guess it's not possible to directly measure water flow, but do you know of any experiments or field measurements where high velocity is consistent with your very high hydraulic conductivity?
Minor comments:
L52 “increases”
L93, L109 and in Table 2:Ref. Hamamoto et al. à Date of publication is 2016
L159: IMFT ?
L386: 1.00 mm
L722: “response” a typo in the original title?!
L591: problem with the words in italics “Sphagnum”
L690: problem with the words in italics “Sphagnum”
L770: Date of publication is 2012 instead of 2014 ? (it is correctly mention in the main text: “McCarter & Price, 2012”)
L840841: problem with subscript and italics in the reference title “Extending a landsurface model with Sphagnum moss to simulate responses of a northern temperate bog to whole ecosystem warming and elevated CO_{2}”

AC2: 'Reply on RC2', Simon Cazaurang, 08 Nov 2022
Dear Madam, dear Sir,
On behalf of all the coauthors, I wish to thank you for your careful review of this manuscript. Please find below the answers to the questions raised following the review. In order to make the answers accessible to everyone, we have decided to answer each question individually.
Sincerely yours,
Simon CazaurangGeneral comment:
[AR]: The submitted manuscript deals with the assessment of the porosity and hydraulic conductivity of Western Siberian Lowland ground vegetation samples (lichens, Sphagnum mosses, peat). Twelve samples are analysed throughout a numerical method instead of a classical experimental field determination (that they have also carried out). Based on digital XCT reconstructions the study confirms the high values of porosity presented by such a biological media. Due to numerical constraints, a single numerical method could not be implemented and the authors used both Direct Numerical Simulations (DNS) and Pore Network Modeling (PNM), which did not provide the same results… but are closer together for the evaluation of the hydraulic conductivity, which is several orders of magnitude lower for the experimental field method.
The subject of the study is interesting and suitable for publication in HESS and as the authors reported in their introduction, the results could be of great importance to model the evolution of these natural environments impacted by climate change. The manuscript is globally well written and of good scientific quality. I think that a few modifications can still be made to improve its quality.
 References are numerous, and I guess that they cover the state of the art.
 The purpose of the study should be more clearly stated.
 The station can be described briefly, the field work is important and deserves a few words.
 A complete flowchart describing the different steps of the methodology will be appreciated.
 The quality of the figures is good, but the use of colors is not always clear and understandable. The works in the supplements are not highlighted enough.
 The distinction between homogeneous and heterogeneous is not clearly defined, although this aspect seems to have an impact on the typology and the possibilities of implementing the proposed methods.
 Some misunderstandings in the presentation of the results for porosity.
 The definition of the sample typology is done twice and is not consistent (?)
[Authors]: The authors want to warmly thank the reviewer for the careful and thorough reading of this manuscript. One can find the answers to the raised comments below. Each question is answered through a dedicated paragraph for the question.
Comments:
[AR]: L 97: I am not a specialist of the topic, but what about the study by Potkay et al. (2020) ?
Potkay, A., ten Veldhuis, M. C., Fan, Y., Mattos, C. R., Ananyev, G., & Dismukes, G. C. (2020). Water and vapor transport in algalfungal lichen: Modeling constrained by laboratory experiments, an application for Flavoparmelia caperata. Plant, cell & environment, 43(4), 945964.
[Authors]: The authors want to thank the reviewer for this suggestion. There are some publications about lichen membrane transport properties assessment and modelling (Linefold et al., 1990, Voortmann et al. 2014 and for instance Potkay et al., 2020). However, most of these publications are dealing with transmembrane transport and not macroscale transport. Nonetheless, we will add Potkay et al. (2020) for the sake of completeness of the state of the art. Making the link between transmembrane transport and macroscale transport is a significant clue for understanding the whole atmospheregeosphere transfer phenomenon.
[AR]: L105: what is the main purpose of the present study? The authors want to assess hydraulic properties of lichens and Sphagnum mosses by numerical methods, but I do not understand the “justification” of this way? What kind of problems / difficulties arise from the experimental measurements? The question is of primary goal and I think that the issue of measurements scale should also be mentioned, especially if the results are intended to be used in a modelling approach.
[Authors]: Indeed, we do not emphasize enough the main purpose of the study. The authors want to thank the review to penlight this aspect. We will add a supplementary paragraph to make the link between the state of the art and the main workflow applied for this study, insisting on the gains in terms of reproducibility and intercomparison capability.
[AR]: L122: please indicate the coordinates of the station where samples were collected. Besides, I would appreciate synthetic details on the climatic condition of this location.
[Authors]: The authors will add some supplementary information about the scientific station where the samples were collected and more broadly on northern taiga. Some details are available through various publications such as PayandiRolland et al. (2020), Raudina et al. (2018), Soudzilovskaïa et al. (2013).
[AR]: L161: you refer to the drying experiment carried out by Kämäräinen et al. (2018). A different drying temperature (40 °C instead of 50 °C) has been applied for the preparation of samples that have a larger size in your case. It is not exactly the same protocol. The most important finding is that the morphological structure is preserved, and since you don't expect to know the actual water content of your various samples, this is probably not a critical point.
[Authors]: Actually, the sentence is not wellwritten. It would be more accurate to write “an analogous method than the one used in Kämäräinen et al. (2018) rather than saying that it is the same method. We will correct this sentence in the revised version of the manuscript.
[AR]: L190: in the main text, Fig. 4 is used before figures 2 and 3? It is quite difficult to distinguish colors in your picture. Is there a link between the colors used for your planar porosity plots and the averaged versions? I don’t think so, but it's not clear.
[Authors]: We intended to highlight samples' homogeneity classes through the proposed color scheme. However, this layout was not optimal for black and white prints. A new color palette will be developed to cope with black and white prints and to enhance readability for samples’ nature and homogeneity classes. A sentence will be added in the revised manuscript to emphasize on the manner the color scheme was though out.
[AR]: L202: please indicate that p_{open }refers to the open porosity proportion. In table 3, this variable should be multiplied by 100? And to be consistent with equation (2), you should indicate “%” in Table 1.
[Authors]: The authors want to thank the reviewer for the rigorous reading. We made the choice of keeping popen as a decimal number to avoid confusion with other percentages (especially porosity). We will correct equation (2) accordingly to what is shown in Table 1 and the results of Table 3.
[AR]: L258: You should refer to Supplement A. Also, I think you did not mention in the main text supplement B1 where some pictures present the evolution of porosity with the size of measurement. I’m wondering how you fix the final value of the sample’s REV of porosity. It is not obvious to understand your results (final sizes) when comparing curves, for instance, for samples Hollow2.7, lichen1.3 and lichen2.1.
[Authors]: Indeed, there are missing links to Supplement A and B1. We will make the links between the Supplements and the main text clearer for the reader.
Assessing the REV maximal size is one of the main challenges in REV computations. We presented REV in part 2.4 of the manuscript. Yet, we will reiterate the criteria in this subsection as well as in Supplement B1’s caption.The final REV of porosity size is computed according to the standard deviation values for each study size reduction. Each time when the standard deviation overpasses a certain arbitrary threshold (here, we have decided to take 1, 3 or 5% of porosity variation). In the case of Hollow2.7, Lichen1.3 and Lichen2.1, we observed that these samples are more homogeneous than the others.
To enhance the classification, we added average and standard deviation values for each sample class in Table 3. This confirms that X and Y values have very low variability (under 1% for Type I samples, around 1% for Type III and less than 4% for Type II). In terms of vertical porosity, Type I have a lower variability than Type II and Type III, the latter types concentrating porosity variability.
[AR]: L265: I don't think that figure 3 is required.
[Authors]: Indeed, permeability measurements using pressure gradients (constant and variable head permeameters) are often used in the literature. However, we assume that no standardization is made for such numerical resolution. In this way, we wanted to emphasize boundary and initial conditions to clarify numerical aspects. We will move this figure to the supplemental section, as it is not mandatory for the manuscript itself.
[AR]: L280: I guess the numerical method developed by Patankar (1980) has been improved to solve faster the singlephase flow problem. I understand that the numerical aspects are not a key point of this study, but your choice induces limitations in the sample processing capacity (only type I) and that's a bit bothering.
[Authors]: The actual solver to conduct our computations is simpleFoam, built on the opensource computational fluid mechanics toolbox OpenFoam. The simpleFoam solver is far apart from Patankar’s original algorithm. Nonetheless, simpleFoam still uses the same numerical solving scheme to resolve NavierStokes equations, therefore we thought that it was important to cite Patankar (1980). simpleFoam is nowadays highly parallelizable on many processors so that even big simulations can be conducted fairly easily. In our case, the number of simulations per sample (672) is rather the most limiting factor than the cost of the simulation itself.
However, the sentence could lead to misunderstand our methodology. We will correct this sentence in the revised version of the manuscript.
[AR]: L282: how did you select your 4 REV sizes? If I clearly understand, choosing a small REV size involves performing many simulations. However, are 4 sizes enough to detect the impact of the size on the fluctuation of your variable?
[Authors]: In this study, we assessed hydraulic conductivity REV using an analogous method of the one developed for the REV of porosity. Nonetheless, for the hydraulic conductivity REV, the sizes are assigned from the beginning to shorten computational times. Indeed, this study took 10 days per sample to be conducted. Making a continuous scanning as made for porosity is still prohibitive in terms of computational efficiency.
The sentence on line 282 can be misleading. We will reformulate this sentence in the revised version.
[AR]: L344354: The conclusion is that DNS and PNM did not lead to compatible results for hydraulic conductivity measurements. The authors should probably indicate a way to  a priori  select the better method for each sample. Is there a link with homogeneity of the sample (the authors have indicated that in the manuscript, L276 for instance) and how can they mathematically or physically define the frontier between homogenous and heterogeneous sample?
[Authors]: Indeed, our study spotlights the fact that it is not possible to study a sample in the same way if there is homogeneity or heterogeneity. In our study, we assume that samples’ variability is conditioned upon porosity spatially varying or not. This condition is a prerequisite, especially in the presence of natural samples, potentially very heterogeneous. Homogeneity criterion is based on the existence of a Representative Elementary Volume. Property homogeneity is required to find a Representative Elementary Volume. Consecutively, if a sample admits no significant variation for a given direction, then we can consider the sample homogeneous for that given axis (i.e., 1Dhomogeneous). In the same way, if this low variability is observed on the three axes, then this sample is considered as homogeneous on the whole sample (i.e., 3Dhomogeneous). Otherwise, convergence cannot be reached, and therefore the method using Representative Elementary Volumes will fail. To illustrate this, it is possible to take the example of samples Peat2.2 and Hollow1.2 that do not satisfy sufficient homogeneity to converge to a Representative Elementary Volume. In this case, apart from doing a computation on the entire sample (which is prohibitive in terms of computational costs), choices are reduced. For both samples, and more widely for the Type II and III samples that are 2Dhomogeneous, Pore Network Modeling is appropriate in the absence of another efficient volume averaging method.
To enhance the classification, we will add average and standard deviation values for each sample class in Table 3. This will confirm that X and Y values have very low variability (under 1% for Type I samples, around 1% for Type III and less than 4% for Type II). In terms of vertical porosity, Type I have a low variability as Type III and Type II concentrates the variability.
[AR]: L349: Fig. 9Right does not describe the hydraulic conductivity computation as mentioned in the manuscript.
[Authors]: Indeed, this is a typo error. We will correct this sentence in the manuscript.
[AR] :
 L359: the lowest porosity value is obtained for the Mound1.1 sample.
 L365: according to Table 3, the average porosity for mound mosses is 65.8 ± 23% ?
 L373: Lichen1.3 has a total porosity lower than 85%.
 L375: correct definition is “medium high porosity” or “low basal porosity” (L193) for type II ? Besides, total porosity is not comprised between 70 and 85%.
 L376: for type III, the total porosity is lower than 73%
[Authors]: The authors want to thank the reviewer for the careful reading and verification of the data. We will correct promptly these remarks in the revised version of the manuscript.
For mound mosses, the average porosity is 65.8 ± 23%, including Mound2.6. As the value span is quite significant, we will rework the type definitions to be consistent with the definitions given on lines 192194.
[AR]: L469: Did Shirokova et al. (2021) make a link between their biological results and the properties you focused on? I don’t think that they talk about porosity, hydraulic conductivity, and specific surfaces. Either you add a reference that show this link, or you add this part later in your discussion…
[Authors]: The citation of Shirokova et al. (2021) is not well inserted in our discussion, even though this paper is important because our current study and their study are well linked. Indeed, transmembrane transport properties are required to make a realistic flux and matter balance through arctic vegetation cover. For the sake of clarity, this citation will be presented in the introduction and the linkage will be reinforced.
[AR]: L472: your experimental results are quite similar than other studies mention in Table 2. I would include them (not only “published results” but experimental results in general, including your own).
[Authors]: The authors want to thank the reviewer for this suggestion. We will add our experimental results for each sample in the manuscript. We will add the results of the field work in the discussion part to give some material to discuss the differences between field and numerical experiments. The authors want to thank Georgiy Istigechev for his help in the doublering infiltrometry campaign. We will add him in the contributions as well as in the acknowledgements.
[AR]: L477: What is the interest of subsection “4.1 Numerical reconstruction after scanning” in the discussion part? I have the feeling that the main elements are given again between L 510 and 520?
[Authors]: Section 4.1 describes the drawbacks that were identified from the use of the tomographic plots themselves. Then, between lines 510 and 520, we introduce the differences between DNS and PNM. In our point of view, we think that it is more appropriate to keep these aspects separated, as they are occurring at a different moment in the process.
[AR]: L523526: I think the main justification and interest of the present study lies in the fact that field experiments carried out to obtain hydraulic conductivity could be inaccurate because of an excessive compression of the biological media. I would appreciate references that could highlight this aspect, also the difference between natural rainfall and field experiments and finally the lack of such kind of experimental measurements. Besides, in the perspective of numerical modelling of these biological media located in the upper part of the soil, is it possible to hide unsaturated flows (cf. L488)? I guess it's not possible to directly measure water flow, but do you know of any experiments or field measurements where high velocity is consistent with your very high hydraulic conductivity?
[Authors]: Some few studies deal with compressibility issues occurring in the field measurement (for instance, Weber et al., 2017 and Golubev & Whittington, 2018). These references will be added accordingly in the manuscript. Moreover, this study is a preliminary step of a broader study of transfer properties of this biological media. Here, we assessed fully saturated hydraulic conductivity, which is something occurring in extreme conditions. Hydraulic conductivity will be studied for variably saturated porous media and will be the subject of another study out of the scope of this study.
Minor comments:
L52 “increases” → Will be corrected.
L93, L109 and in Table 2:Ref. Hamamoto et al. à Date of publication is 2016 → Will be corrected.
L159: IMFT ? → Toulouse Fluid Mechanics Institute, will be corrected.
L386: 1.00 mm → Will be corrected.
L722: “response” a typo in the original title?! → Will be corrected.
L591: problem with the words in italics “Sphagnum” → Will be corrected.
L690: problem with the words in italics “Sphagnum” → Will be corrected.
L770:Date of publication is 2012 instead of 2014 ? (it is correctly mention in the main text: “McCarter & Price, 2012”) → Will be corrected.
L840841: problem with subscript and italics in the reference title “Extending a landsurface model with Sphagnum moss to simulate responses of a northern temperate bog to whole ecosystem warming and elevated CO2” → Will be corrected.

AC2: 'Reply on RC2', Simon Cazaurang, 08 Nov 2022
Simon Cazaurang et al.
Simon Cazaurang et al.
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