Round 1

Reviewer 1 Report

This manuscript shows an interesting exercise of estimating the root distribution of some crops by using some assumptions applied in a water balance model. Although the results can barely say whether we are in the right direction of estimating the correct root distribution, I believe that this effort is worth publishing after considering a few remarks:

a)    The work is densely based on modelling. For this reason, the methodology needs to be more explicit about how the equations of section 2.1 were considered in the SWAP model. In fact, the SWAP model needs its own section with all parameters used to the simulation (can be included in the supplementary material – for example (but not the only one): table 4 for all crops, not only maize), otherwise, it will not be reproducible;

b)    It reads as part of the results are already in the methodology (e.g., L215-232). As much as this support other methodological statements, this needs to be rewritten and any results of this study should be in the results section;

c)    The methodology says that this work has taken into account a large dataset on crop root distribution. However, it is not possible to see how the model performs against these data. It would be interesting to see this graphically;

d)    The discussion is very short. It will be necessary to include how the uncertainties of the model can be circumvented by both fieldwork and model approaches; otherwise this study is not helping further work.

Author Response

Observation: Line numbers indicated in the authors’ responses refer to the submitted version of the manuscript with track changes option.

General comment from the reviewer

“This manuscript shows an interesting exercise of estimating the root distribution of some crops by using some assumptions applied in a water balance model. Although the results can barely say whether we are in the right direction of estimating the correct root distribution, I believe that this effort is worth publishing after considering a few remarks”.

 

General authors’ response

We would like to thank this reviewer for supporting our research approach and for his analysis on our manuscript.

Specific comments from Reviewer 1

 

Comment 1 -“The work is densely based on modelling. For this reason, the methodology needs to be more explicit about how the equations of section 2.1 were considered in the SWAP model. In fact, the SWAP model needs its own section with all parameters used to the simulation (can be included in the supplementary material – for example (but not the only one): table 4 for all crops, not only maize), otherwise, it will not be reproducible”.

Authors’ response

We appreciate this suggestion. However, as we used well-documented parameterization retrieved from the standard SWAP input files (as cited, downloaded directly from the Alterra website: http://www.swap.alterra.nl/) and from Taylor and Ashcroft (1972) and Boons-Prins et al. (1993), we think that it is not necessary to reproduce all the parameterization as a supplementary material. Heading of Table 4 and shortly after Eq. 21, we cited the main sources of the adopted parameterization. We simulated only a maize crop. Therefore, the reviewer´s observation “table 4 for all crops, not only maize” seems based on a misunderstanding.

  

Comment 2 - “It reads as part of the results are already in the methodology (e.g., L215-232). As much as this support other methodological statements, this needs to be rewritten and any results of this study should be in the results section”.

Authors’ response

The referred lines are in the sub-section 2.5, and there we report the main patterns of the climate data for the 38-year period used in our simulation, e.g., wettest and driest year, annual precipitation average and potential evapotranspiration averages for the two simulated seasons. Therefore, we think that this information fits well in the M&M section.

 

Comment 3 - “The methodology says that this work has taken into account a large dataset on crop root distribution. However, it is not possible to see how the model performs against these data. It would be interesting to see this graphically”.

Authors’ response

If the reviewer is referring to the functions used to define the root distribution, Table 5 gives the goodness of fit for the derived functions against the database retrieved from literature. Nevertheless, if by the term “model” the reviewer is referring to the SWAP, in general it adopts the root distribution information generated by the fitted functions to simulate the root water uptake, therefore, it would be necessary a database with relative transpiration of a specific crop to allow a comparison between SWAP simulations and measured values. When using the SWAP model, we did not aim to compare the fit of root density distribution functions with the quality of transpiration simulation; instead, we were looking at the sensitivity of the transpiration simulation data to the shape of those functions, in particular the logistic function.

 

Comment 4 – “The discussion is very short. It will be necessary to include how the uncertainties of the model can be circumvented by both fieldwork and model approaches; otherwise this study is not helping further work”.

Authors’ response

We thank the reviewer for this suggestion. In the updated version of the manuscript we added to the discussion (please see lines 359-369 and lines 397-402). In general, in the discussion we give elements to show to the reader that among the several presented functions, the logistic one is the most appropriate function. In the second part of the discussion, we detail the sensitivity of the agro-hydrological model transpiration outputs to the different scenarios of root distribution shapes based on the logistic dose response function. In lines 397-402, we discuss some shortcomings of the transpiration reduction function implemented in the SWAP model and call attention for the importance of correct root profile representation and the adoption of mechanistic transpiration reduction functions.  

 

 

Reviewer 2 Report

Metselaar et al.

The paper gives an interesting overview of different functions that can be used to describe root density distributions. A dataset is compiled of experimental data on root distributions for agricultural crops and this data is used derive a dataset of root distribution parameters. Such a dataset is very important when simulation studies on crop water status and water management have to be carried out.

I think that the paper has some deficiencies which should be addressed before it can be published. There is a lack of consistency in the paper. First, different functions to describe cumulative root density distributions are discussed. But, one of these functions is not fitted to the dataset that was compiled. Yet, this function was later used in the sensitivity analysis in which the sensitivity of a simulation model to the parameterization of the root distribution was evaluated. How the sensitivities were actually calculated and what the numbers that are given actually mean is not described in the paper. In order to interpret the results, more information on this issue should be given.  

In the introduction, I would propose that the authors also touch the impact of considering absolute root density rather than relative or normalized root density distributions in root water uptake models.  In most root water uptake models that are currently implemented in land surface models or field water balance models, the normalized root density distribution is considered. This implies that these models cannot make use of the extra information that is contained in root density distributions. In their study, the authors do not consider this issued either but they refer to other studies in which this aspect was investigated. I think this requires some more discussion

 

Section 2.1 should best be restructured. First, the authors start with the log-logistic function (which they call the logistic dose response function which is confusing since this function is not the same as the logistic function) and give the impression that this is the model that will be used. Later, they introduce other distributions. Finally they summarize the distributions in a table but do not include in this table the distribution they started with at the beginning of this chapter. This gives a bit an unstructured impression of this section. It should also be made clear what the purpose of presenting all these functions is. Why are these functions presented, what will the authors do further with it in the paper?

 

Detailed comments.

Ln 33: I think there are more recent publications on datasets and parameterisations of root denstiy distributions that can be used in models. See for instance the work of Schenk and of Yan.

H.J. Schenk. The shallowest possible water extraction profile: A null model for global root distributions. Vadose Zone Journal, 7,(3),doi:10.2136/vzj2007.0119, 1119-1124, (2008).

Y. Fan, G. Miguez-Macho, E.G. Jobbagy, R.B. Jackson and C. Otero-Casal. Hydrologic regulation of plant rooting depth. Proceedings of the National Academy of Sciences of the United States of America, 114,(40),doi:10.1073/pnas.1712381114, 10572-10577, (2017).

J. Fan, B. McConkey, H. Wang and H. Janzen. Root distribution by depth for temperate agricultural crops. Field Crops Research, 189,doi:https://doi.org/10.1016/j.fcr.2016.02.013, 68-74, (2016). (I am not sure whether this study was included in the set of studies that were included in the data set).

 Ln 86, Eq. 2: Although it is called in the paper of Schenk a logistic dose response function, I think it should be called a log-logistic dose response function. The problem is that it seems that a logistic dose response function is not the same as a logistic function. In other words, the dose response function does not that the form of a logistic function but it takes the form of a logistic function with a logarithmic argument. That is confusion and I think that for that reason, the term log-logistic dose response function is used. See for instance: Ritz C, Baty F, Streibig JC, Gerhard D. Dose-Response Analysis Using R. PLoS One. 2015;10(12):e0146021. Published 2015 Dec 30. doi:10.1371/journal.pone.0146021

Ln 90: Rx is the maximal cumulative root density but according to equation 2, this is reached at infinite D. That means that a ‘maximal’ root depth, Dx, does not exist according to Eq. (2).  So I suppose that Dx is defined in terms of a certain percentile of the cumulative distribution. But, looking at figure 1, this assumption was apparently not correct since R/Rx at D = Dx varied for different values of the c-parameter. Therefore I think it is necessary that the authors define Dx clearly.

Ln 128: This is confusing. First reading this sentence, it is not clear to which two functions is referred to here.  Strictly following the text, it should be Eq. 2 and Eq. 13 which are identical functions. I think the authors are referring here to the logistic function and the log-logistic function. The question is why one would fit one function and transfer then the parameters to another function which is not identical.

Ln 144: From reading the sentence, it is not clear which function requires an additional parameter: the Gompertz function or the generalized logistic function? Or the log-logistic function?

Table 1: I think that the log-logistic function should also be included in this table.

ln 171: Since the half distance between the roots is non-linearly dependent on the root density, I do not think that the mean half distance can be calculated from the mean root density using equation 16.

 

Ln 191 and section 2.4: In this section, four distribution models are checked and compared but the log-logistic distribution model is not included in this comparison. This is however the model that is later used in the sensitivity analysis. This is not really consistent. I think that the log-logistic function should also be evaluated.

Ln 248: According to Eq. 21, Rz could also be the root density (not the relative or normalized one). If Rz is the normalized one, there is no need to divide by the sum of Rz over the different soil layers since that should be 1. Therefore, I propose changing Rz by rho.  It should be noted that Rx half mean root distance do not appear in the model. Were these properties of the root system not considered then?

ln 300 Table 7: Could it be explained how the average differences were actually calculated? I don’t know how to interpret the numbers in table 7.

Ln332: Can the authors give some evidence that the importance of the root distribution will increase when mechanisms like root water uptake compensation are included in the model? I think that such processes rather decrease the sensitivity of root water uptake to the root density distribution.

 

Author Response

Observation: Line numbers indicated in the authors’ responses refer to the submitted version of the manuscript with track changes option.

General comment from the reviewer

“The paper gives an interesting overview of different functions that can be used to describe root density distributions. A dataset is compiled of experimental data on root distributions for agricultural crops and this data is used derive a dataset of root distribution parameters. Such a dataset is very important when simulation studies on crop water status and water management have to be carried out”.

General authors’ response

We thank this reviewer for his detailed evaluation of our manuscript. His suggestions and comments were much appreciated and most of them inserted in the updated version of the manuscript. 

Specific comments from Reviewer 2

 

Comment 1 – “I think that the paper has some deficiencies which should be addressed before it can be published. There is a lack of consistency in the paper. First, different functions to describe cumulative root density distributions are discussed. But, one of these functions is not fitted to the dataset that was compiled. Yet, this function was later used in the sensitivity analysis in which the sensitivity of a simulation model to the parameterization of the root distribution was evaluated. How the sensitivities were actually calculated and what the numbers that are given actually mean is not described in the paper. In order to interpret the results, more information on this issue should be given”.

Authors’ response

We thank the reviewer for pointing out this issue. The logistic dose response function, as referred to by the reviewer, was in fact fitted as well. In Table 1, we give some expressions to calculate the parameters D₅₀ and D₉₅ using the four functions (Generalized logistic, Logistic, Exponential/Mitscherlich, and Gompertz). With these two parameters, we could employ Eq. 11 to calculate the parameter c of the logistic dose response function. Therefore, as explained throughout the manuscript, we adopted D₅₀ and D₉₅ calculated by the logistic function due to its higher consistency and less extrapolation need (D₉₅ < D_max for the majority of the database). For more details, we refer to Table 1, lines 245-248, lines 307-310, and the heading of Table 6.

Comment 2 - “In the introduction, I would propose that the authors also touch the impact of considering absolute root density rather than relative or normalized root density distributions in root water uptake models.  In most root water uptake models that are currently implemented in land surface models or field water balance models, the normalized root density distribution is considered. This implies that these models cannot make use of the extra information that is contained in root density distributions. In their study, the authors do not consider this issued either but they refer to other studies in which this aspect was investigated. I think this requires some more discussion.

Authors’ response

We added a new sentence in the introduction emphasizing the importance of considering absolute root distribution for better predictions of root water uptake by detailed reduction functions. Lines 49-57 now read: … “Detailed root water uptake reduction functions, which usually describe compensation mechanisms, are dependent on the absolute values of root length density distribution over the soil profile. This will determine the rhizosphere radius and the distribution of root water uptake. In this sense, crops with low root density will need higher hydraulic gradients between roots and the surrounding bulk soil in order to attend the atmospheric water demand. On the other hand, crops with higher root density can maintain the root water potential closer to that of the bulk soil and then postponing the drought stress [23]. Those mechanisms are highly dependent on the soil hydraulic properties, and for this reason, well-represented root distribution allows accounting for the hydraulic ability of each soil layer in supplying water to plants. ”   

 

Comment 3 - “Section 2.1 should best be restructured. First, the authors start with the log-logistic function (which they call the logistic dose response function which is confusing since this function is not the same as the logistic function) and give the impression that this is the model that will be used. Later, they introduce other distributions. Finally they summarize the distributions in a table but do not include in this table the distribution they started with at the beginning of this chapter. This gives a bit an unstructured impression of this section. It should also be made clear what the purpose of presenting all these functions is. Why are these functions presented, what will the authors do further with it in the paper?”

Authors’ response

We thank the reviewer for this suggestion. Section 2.1 was rearranged, and now we started with the general case (generalized logistic) and then we derived the specific cases from it; and last we show the case of the exponential sigmoid function (Gompertz, Eq. 14).   

Regarding the purpose of dealing with the different functions and what we intend to do with them, we think it is described in the last paragraph of the introduction, where we list the objectives of the MS.

 

Comment 4 – “Ln 33: I think there are more recent publications on datasets and parameterisations of root denstiy distributions that can be used in models. See for instance the work of Schenk and of Yan.”

H.J. Schenk. The shallowest possible water extraction profile: A null model for global root distributions. Vadose Zone Journal, 7,(3),doi:10.2136/vzj2007.0119, 1119-1124, (2008).

Y. Fan, G. Miguez-Macho, E.G. Jobbagy, R.B. Jackson and C. Otero-Casal. Hydrologic regulation of plant rooting depth. Proceedings of the National Academy of Sciences of the United States of America, 114,(40),doi:10.1073/pnas.1712381114, 10572-10577, (2017).

J. Fan, B. McConkey, H. Wang and H. Janzen. Root distribution by depth for temperate agricultural crops. Field Crops Research, 189,doi:https://doi.org/10.1016/j.fcr.2016.02.013, 68-74, (2016). (I am not sure whether this study was included in the set of studies that were included in the data set).

Authors’ response

We thank the reviewer for the suggestion. We now cite some of these papers in our MS. We think that it is very likely that part of the dataset used by the last cited paper (Fan et al., 2016), were also included in our analysis.

 

Comment 5 – “Ln 86, Eq. 2: Although it is called in the paper of Schenk a logistic dose response function, I think it should be called a log-logistic dose response function. The problem is that it seems that a logistic dose response function is not the same as a logistic function. In other words, the dose response function does not that the form of a logistic function but it takes the form of a logistic function with a logarithmic argument. That is confusion and I think that for that reason, the term log-logistic dose response function is used. See for instance: Ritz C, Baty F, Streibig JC, Gerhard D. Dose-Response Analysis Using R. PLoS One. 2015;10(12):e0146021. Published 2015 Dec 30. doi:10.1371/journal.pone.0146021”.

Authors’ response

According to Table 1, the four equations (Generalized logistic, Logistic, Exponential (Mitscherlich), and Gompertz) allow to calculate D₅₀ and D₉₅ using the rearranged expressions of Table 1. Once D₅₀ and D₉₅ were calculated, we used Eq. 11 to obtain the parameter c of the logistic dose response function. We think this also clarifies the misperception about the nomenclature for eq. 7.

 

Comment 6 – “Ln 90: Rx is the maximal cumulative root density but according to equation 2, this is reached at infinite D. That means that a ‘maximal’ root depth, Dx, does not exist according to Eq. (2).  So I suppose that Dx is defined in terms of a certain percentile of the cumulative distribution. But, looking at figure 1, this assumption was apparently not correct since R/Rx at D = Dx varied for different values of the c-parameter. Therefore I think it is necessary that the authors define Dx clearly”.

Authors’ response

We slightly reworded lines 99-100, in fact, R tends to R_x at D=D_x.

 

Comment 7 – “Ln 128: This is confusing. First reading this sentence, it is not clear to which two functions is referred to here.  Strictly following the text, it should be Eq. 2 and Eq. 13 which are identical functions. I think the authors are referring here to the logistic function and the log-logistic function. The question is why one would fit one function and transfer then the parameters to another function which is not identical”.

Authors’ response

We rearranged section 2.1. In the updated version, Eq. 13 became Eq. 2 and Eq. 2 became Eq. 7. Regarding the claim that Eq. 4 assumes the same form of Eq. 7 (new numbering), it is clear that this is only true with the insertion of the log-transformed argument. We also made clear that the two referred equations are not equal, but the interchangeability of parameters can be an option (lines 116-119). However, we did not use this approach in our manuscript. The parameters D₅₀ and D₉₅ were calculated using the relations given in Table 1, and then we used these values given by the logistic function (Eq. 4), the most consistent one, to obtain the parameter c (using Eq. 11) of the logistic dose response function; lines 245-248 highlights this procedure.

 

Comment 8 – “Ln 144: From reading the sentence, it is not clear which function requires an additional parameter: the Gompertz function or the generalized logistic function? Or the log-logistic function?”

Authors’ response

We refer to the generalized logistic function and its special cases. We think this is unambiguously stated.

 

Comment 9 – “ln 171: Since the half distance between the roots is non-linearly dependent on the root density, I do not think that the mean half distance can be calculated from the mean root density using equation 16”.

Authors’ response

We agree with the reviewer. However, the calculated average can be in a range when the root density is roughly linear. We added this note of caution shortly after Eq. 19 of the updated MS version.

 

Comment 10 – “Ln 191 and section 2.4: In this section, four distribution models are checked and compared but the log-logistic distribution model is not included in this comparison. This is however the model that is later used in the sensitivity analysis. This is not really consistent. I think that the log-logistic function should also be evaluated”.

Authors’ response

Please see the reply to the comment #1 and #5.

 

Comment 11 – “Ln 248: According to Eq. 21, Rz could also be the root density (not the relative or normalized one). If Rz is the normalized one, there is no need to divide by the sum of Rz over the different soil layers since that should be 1. Therefore, I propose changing Rz by rho.  It should be noted that Rx half mean root distance do not appear in the model. Were these properties of the root system not considered then?”.

Authors’ response

We agree with the reviewer’s suggestion. We replaced the term R_z in equation 21 by the term r. As the Feddes reduction function adopts normalized root length density, it does not make use of the information regarding the half-distance between roots (r_m), which may limit predictions by this reduction function.

 

Comment 12 – “ln 300 Table 7: Could it be explained how the average differences were actually calculated? I don’t know how to interpret the numbers in table 7”.

Authors’ response

We slightly reworded the caption of table 7 to make this clearer. It should now be clear that the numbers shown in table 7 are the relative transpiration differences between the arbitrary “standard” simulation using D₅₀ = 0.45 m and c = -1 and the other combinations of D₅₀ (0.15 and 0.30 m) and c (-3 and -5), followed by the respective standard deviation over the 38-year period.

 

Comment 13 – “Ln332: Can the authors give some evidence that the importance of the root distribution will increase when mechanisms like root water uptake compensation are included in the model? I think that such processes rather decrease the sensitivity of root water uptake to the root density distribution”.

Authors’ response

We added a sentence in lines 355-360 discussing a bit more this issue. The citations numbered as 23, 25, 60 and 61 give complete details on how root water uptake distribution over the soil profile is highly dependent on the absolute root length density.

Round 2

Reviewer 1 Report

I acknowledge that the authors clarified many of my concerns. However, the lack of clarity of the manuscript was interpreted as a misunderstanding on my side, and very few changes in the manuscript were conducted to circumvent this problem.

I still have concerns about how the SWAP model is being presented in this manuscript. I understand that the model is well-known and that the authors are advanced users of it, but it does not reduce the need to give the model a proper introduction and explain clearly how this was integrated to the description of the root density profiles.

The authors “think that it is not necessary to reproduce all the parameterization as a supplementary material”. However, I am concern about the reproducibility of this study. As long as they state all parameters that are out of the standard model parameterization with their respective values, I think that it will be no problem.

The authors state that “We simulated only a maize crop. Therefore, the reviewer´s observation “table 4 for all crops, not only maize” seems based on a misunderstanding.” – I do understand now what they mean. However, it not trivial to understand how the data from Table 2, which contains many crops, is used in this work that only deals with maze. The methodology seems complete, but there is a lack in structure showing a step-by-step procedure and how each methodology component is connected.

Author Response

Observation: Line numbers indicated in the authors’ responses refer to the submitted version of the manuscript with track changes option.

General comment from the reviewer

“I acknowledge that the authors clarified many of my concerns. However, the lack of clarity of the manuscript was interpreted as a misunderstanding on my side, and very few changes in the manuscript were conducted to circumvent this problem.

 

I still have concerns about how the SWAP model is being presented in this manuscript. I understand that the model is well-known and that the authors are advanced users of it, but it does not reduce the need to give the model a proper introduction and explain clearly how this was integrated to the description of the root density profiles.

 

The authors “think that it is not necessary to reproduce all the parameterization as a supplementary material”. However, I am concern about the reproducibility of this study. As long as they state all parameters that are out of the standard model parameterization with their respective values, I think that it will be no problem.

 

The authors state that “We simulated only a maize crop. Therefore, the reviewer´s observation “table 4 for all crops, not only maize” seems based on a misunderstanding.” – I do understand now what they mean. However, it not trivial to understand how the data from Table 2, which contains many crops, is used in this work that only deals with maze. The methodology seems complete, but there is a lack in structure showing a step-by-step procedure and how each methodology component is connected.”

General authors’ response

We would like to thank this reviewer for his suggestions and for giving us the opportunity to make our MS clearer. We acknowledge that we might have overlooked some of the reviewer’s concerns in the first reviewing round. We apologize for lacking more clarity in our previous replies.

We agree that some more information about the model and simulated scenario´s is necessary for reproducibility and in this updated version we added more information regarding the SWAP model and the parameterization used (please see section 2.5). We added a new table (Table 5) with values of crop parameters adopted in our simulation. Now this section gives: (i) a general idea about the SWAP model with its main equations used to solve water flow in the unsaturated zone; (ii) the transpiration reduction function embedded in the SWAP model with the respective values of its parameters; (iii) an overview on the upper and lower boundary conditions and growth seasons; (iv) soil hydraulic properties; (v) period of simulation with parameter values for each development stage; (vi) parameters for calculating root distribution profiles; and (vii) general crop simulation parameters.

We think that with this added information the results are now reproducible and we hope the reviewer agrees.

Regarding the reviewer’s concern about Table 2, it gives a general overview on the database used in our study, i.e., species, relative proportion of cropped area, and number of sources in the database for each individual crop group. In Table 7 the fitted parameters that describe the root distribution over the soil profile for all crop groups from Table 2 are shown, individually and pooled. For the next step of our study, we selected maize for our simulation exercise, the reason for this particular crop is due to its large importance worldwide and due to available parameterization (please see lines 259-261). However, the same exercise could have be done for the other crops from Table 7, as long as the required parameters by the simple crop file of SWAP were available.

Reviewer 2 Report

The authors carefully responded to all my comments and changed their manuscript appropriately. The only issue that still remains unclear to me is why the authors first evaluate the goodness of fit of four distribution functions to a dataset of root length distributions to evaluate which function is most appropriate to represent root length distribution. Once they have identified this function, they use percentiles that are calculated by this function to parameterize another distribution function (the logistic dose response function). This other function is then used in a senstivity analysis. But, it remains unclear to me how well this function describes the actual root density profiles and why not the simple logistic function was used in the sensitivity analysis. Probably, it will be difficult to clarify this issue conclusively but it would be good if the authors could point at it.

Author Response

Observation: Line numbers indicated in the authors’ responses refer to the submitted version of the manuscript with track changes option.

General comment from the reviewer

“The authors carefully responded to all my comments and changed their manuscript appropriately. The only issue that still remains unclear to me is why the authors first evaluate the goodness of fit of four distribution functions to a dataset of root length distributions to evaluate which function is most appropriate to represent root length distribution. Once they have identified this function, they use percentiles that are calculated by this function to parameterize another distribution function (the logistic dose response function). This other function is then used in a senstivity analysis. But, it remains unclear to me how well this function describes the actual root density profiles and why not the simple logistic function was used in the sensitivity analysis. Probably, it will be difficult to clarify this issue conclusively but it would be good if the authors could point at it.”

General authors’ response

We thank the reviewer for his comment. We understand his concern, however, we think that using the parameters (percentiles) calculated by equations in Table 1, which have the same meaning of those percentiles expressed in equations (7) and (11), did not diminish the results presented by the logistic dose-response function. In fact, once values of D₅₀ and D₉₅ are known, equation 11 allows finding the shape parameter c analytically. It is also interesting to point out that although all the equations presented in our study are well accepted, the logistic dose-response function seems to be more common in the literature, and it is also the preferred one in studies aiming to compile large dataset describing root distribution over the soil profile. We slightly addressed this issue in lines 278-280 of the updated version.

Round 3

Reviewer 1 Report

Dear authors, I'm glad you worked in making the manuscript clearer. I have no further comments to do besides congratulate you with your nice manuscript.