Tree Biomass Modeling Based on the Exploration of Regression and Artificial Neural Networks Approaches
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis manuscript is concerned with tree biomass modelling. Different modelling strategies were applied such as NSUR, the generalized regression (GRNN), the resilient propagation (RPNN) and the Bayesian regularization (BRNN). Some inspiration can be drawn from this work, which could provide a possible alternative for choosing machine learning methods for tree biomass modelling. However, there are some significant flaws in the manuscript. I advised this paper a major revision. The specific revision suggestions can be found as follows:
1. The most important issue of this article is that the authors say “to construct reliable and accurate estimation and prediction models”. However, there is no experimental design on reliability in this paper, and there is no explicit index to verify the reliability of each model. I think the author only compares the accuracy of these models and therefore only shows the effectiveness of them.
2. The authors introduce NSUR clearly, there is no doubt about it. But here comes the second important issue of the paper, why did the author choose these machine learning models as examples (GRNN, RPNN, BRNN), and what are the differences among them? Are there any model algorithms that represent the state of the art?
3. In this paper, 55 trees are selected as samples. What is the spatial distribution of these trees? How were these field plots arranged? How to ensure that the samples collected are representative and universal? The geographical description and a spatial distribution map of the study area should be required in the materials and methods subsection.
4. The paragraph from Line 409 to 414 should not appear in result, it should be included in introduction or methods subsection.
5. In table 3, I don't think it's a good idea to put the Network architecture in a table, it should be included in "Artificial Neural Network Modelling".
6. In Figure 2, it is not easy to compare the error of each model in this 3D chart. Please make the diagram more clearly.
7. The figure resolutions in this manuscript are too coarse for publication purposes, and the authors should resubmit the figures with finer resolution during the revision round.
8. In table 1, “Tables may have a footer”?
Comments on the Quality of English LanguageI don't think there is any big problem with the English language of this paper. Only minor editing of English language is required.
Author Response
This manuscript is concerned with tree biomass modelling. Different modelling strategies were applied such as NSUR, the generalized regression (GRNN), the resilient propagation (RPNN) and the Bayesian regularization (BRNN). Some inspiration can be drawn from this work, which could provide a possible alternative for choosing machine learning methods for tree biomass modelling. However, there are some significant flaws in the manuscript. I advised this paper a major revision. The specific revision suggestions can be found as follows:
- The most important issue of this article is that the authors say “to construct reliable and accurate estimation and prediction models”. However, there is no experimental design on reliability in this paper, and there is no explicit index to verify the reliability of each model. I think the author only compares the accuracy of these models and therefore only shows the effectiveness of them.
The comment of the reviewer makes us think that we maybe could not make clear the way we test the reliability of the ANN constructed models. Of course, we have tested their reliability. The Reviewer is right. If we didn't proceed to this control, this would be a real shortcoming to the quality of the ANN constructed models.
Please, let us explain: The constructed machine learning models’ reliability focuses on assessing the stability and consistency of these models across different data sets and in forestry the different data sets are initially, and by the book, coming from the same forest region and the same tree species, due to the variability of the biological data. In order for the generalization ability of the neural network models to be assessed (that is their ability to accurately extrapolate using new “never seen” data by the model in its construction phase), the available data set was randomly divided into fitting data which constitutes 70% of the total dataset and test data which consists of the remaining 30% data sets. The first dataset was used for the choice of the “best” model, while the latter was used for the exploration of the predictive ability of the constructed model. This means that the test data set was a brand-new data set that the constructed model applied to, in order for its generalization ability to be assessed. This handle can ensure the control of the stability and consistency of the ANN constructed models.
Further, the methodology of the k-fold cross validation was used for the fitting data set, with k=10, in order for all the available information of the fitting data (in this data set the training and the validation data sets are included in order to enrich the training and support the accuracy of the final constructed model) set to be included in the training process of the models.
In order to follow the Reviewer’s comment and make our manuscript clearer, relative explanations have been included in the text.
Please see lines 346 – 356: “ In order for the generalization …………reliability of the ANN constructed model was revealed” of the revised manuscript
- The authors introduce NSUR clearly, there is no doubt about it. But here comes the second important issue of the paper, why did the author choose these machine learning models as examples (GRNN, RPNN, BRNN), and what are the differences among them? Are there any model algorithms that represent the state of the art?
As we have already mentioned in our manuscript, that the three algorithms used (Generalized Neural Network (NN), Resilient Backpropagation NN, and Bayesian Regression NN) are different techniques within the realm of machine learning, having their own both advantages and drawbacks. State of the art could be any ANN approach depending on a given problem. Considering the available information from the relative literature (is been given in our manuscript), we chose to use these specific methodologies because a) they have the potential to address the tree biomass estimation problem comprehensively, from different methodological perspectives, b) each one of them has shown its potential to model forest attributes, c) the number of hyperparameters that must be tuned is low for each one of them making their application, more or less, simple, and d) we felt that the usage of all three algorithms for modeling the same attribute which is the tree biomass, can produce significant result and conclusion on which algorithm could most scientifically serve the problem of estimating standing tree biomass. Finally, a pathway for their effective application is described, as well. Let’s be more specific:
- Generalized Neural Network (NN) Algorithm: encompasses traditional feedforward neural networks, with the flexibility to be applied to non-linear regression type problems, however if the algorithm not properly treated, it may be trapped into local minima or can be overfitted.
- Resilient Backpropagation NN Algorithm: it is a variant of the traditional backpropagation algorithm. It is robust in the training phase of the network and its efficiency to overcome problems of the traditional backpropagation algorithm, such as slow at converging, effort at parameter tuning, stuck in local minima, is considered significant.
- Bayesian Regression NN Algorithm: is combine the principles of Bayesian statistics with neural networks to provide a probabilistic framework for modeling uncertainty by producing probability distributions over predictions and not a single estimation.
In order to follow the Reviewer’s comment relative information has been included in the text.
Please see lines 534 – 556: “These are different techniques within ………… application is described, as well.” of the revised manuscript.
- In this paper, 55 trees are selected as samples. What is the spatial distribution of these trees? How were these field plots arranged? How to ensure that the samples collected are representative and universal? The geographical description and a spatial distribution map of the study area should be required in the materials and methods subsection.
We have been followed the reviewer comment. We have added a map to show location of the sample trees. The sample trees were taken Interior of Mediterranean growing zone (Kantarcı 1991). The sample trees were distributed as equally as possible to represent different stand structure in these areas. The sample trees were subjectively selected among the dominant or co-dominant trees so as to represent all diameter and height classes and site conditions in the growing zone.
- The paragraph from Line 409 to 414 should not appear in result, it should be included in introduction or methods subsection.
The comment has been followed and the paragraph has been transferred into the Introduction section.
Please see lines 99-104: “It is well-known that tree……. aforementioned difficulties” of the revised manuscript.
- In table 3, I don't think it's a good idea to put the Network architecture in a table, it should be included in "Artificial Neural Network Modelling".
The Reviewer is right. The proper section of a model architecture to be given is into the methods. However, we think our perspective was not clear. Let us explain.
In Artificial Neural Network Modelling we give the general details of each neural network algorithm. In Table 3 we give the specific structure of the constructed models according to our problem and our data. As can be seen the input layer includes the specific input variables, the hidden layer includes the specific number of nodes, etc. These architectures give an illustration of the specific information of Table 3.
Despite the explanation given, in an effort to follow the Reviewer’s comment, we will remove the ANN architectures from the Table3 and these are going to be transferred to the “Artificial Neural Network Modelling” sub-section.
Please see lines 343-344 and Figure 2 of the revised manuscript.
- In Figure 2, it is not easy to compare the error of each model in this 3D chart. Please make the diagram more clearly.
The comment has been followed. Please see the revised Figure 5 (previous ver. Figure 2)
- The figure resolutions in this manuscript are too coarse for publication purposes, and the authors should resubmit the figures with finer resolution during the revision round.
The comment has been followed. Please see our revised figures.
- In table 1, “Tables may have a footer”?
It escaped our attention. Thank you. Please see line 207.
Reviewer 2 Report
Comments and Suggestions for AuthorsThis manuscript focuses on tree biomass modeling based on the exploration of regression and artificial neural network approaches. There are many defects in it.
1.In Eq. (2), what is the value of "x_i" for the vector x?
2.There are p values of "sigma_j" in Eq. (2), but there is only one value of "sigma" in lines 286-288. Why?
3.In line 308, the first "w^t_ij" should be replaced by "w^(t+1)_ij".
4.In Eq. (4), "delta^(t-1)_ij" should be replaced by "delta^t_ij". Or, "delta^0_ij" is needed.
5.In Eq. (7), what is "- over y"?
6.In Eqs. (7)-(12), all variables must be tilt letters.
7.In line 364, "value" should be replaced by "values".
8."w_stem" is used in Eq. (1), but "w_s" is used in Table 2. They are the same one.
9."W_total" is used in Eq. (1), but "w_t" is used in Table 2. They are the same one.
10.In Table 2, "wcrown", "wcrown", "ws", "wbark", and "wt" should be respectively replaced by "w_crown", "w_stem", "w_bark", and "w_total"/"W_total".
11.In Table 2, what does "41.2232(7.6996)" mean?
12.In Table 2, the condition "<0001" is strange.
13.In Table 2, "<0001" is used for "a_0", "a_1", "a_2", "b_0", "b_1", "b_2", and "c_1", but ".1110" is for "c_0". It is strange.
14.In Table 2, why can the models for "w_s", "w_bark", and "w_bark" be used?
15.In Table 3, what does "2(38)" mean?
16."w_stem", "w_bark", and "w_crown" are biomasses in Table 2, but "dw_stem", "dw_bark", and "dw_crown" are biomasses in Table 3. Why?
In conclusion, major revision is necessary.
Author Response
This manuscript focuses on tree biomass modeling based on the exploration of regression and artificial neural network approaches. There are many defects in it.
1.In Eq. (2), what is the value of "x_i" for the vector x?
xi are the i input sample of the x vector variable.
2.There are p values of "sigma_j" in Eq. (2), but there is only one value of "sigma" in lines 286-288. Why?
The Reviewer is right. In this equation, a smoothing factor was associated with each feature. For this reason, we have more than one smoothing factors. This approach was applied in order to have an indication of the importance of each feature to the configuration of the output variable in order for the most significant features to be included in our final model. Then we use one smoothing factor for the final model, as the GRNN standard methodology requires. Many sigma values tested during the GRNN training and at the end, when the prerequisites of the error value that has been set is satisfied, the sigma value for the “best” model is only one value, different for each biomass component (output variable).
We realize that this formula can lead to misunderstandings. Therefore, in order to be consistent with our results we replaced this formula with addition of more information.
Please see lines 273 – 281: “mean value (E[y/x]) of the output (y),……… the transposed action.” of the revised manuscript
3.In line 308, the first "w^t_ij" should be replaced by "w^(t+1)_ij".
The reviewer is right. The correction is made. Please see line 308 of the revised manuscript.
4.In Eq. (4), "delta^(t-1)_ij" should be replaced by "delta^t_ij". Or, "delta^0_ij" is needed.
The reviewer is right. The correction is made. Please see equ. 4 of the revised manuscript.
5.In Eq. (7), what is "- over y"?
We are sorry but we have not found the “over y”, therefore we could not understand the comment
6.In Eqs. (7)-(12), all variables must be tilt letters.
The comment has been followed. Please see the eqs 7-12 of the revised paper.
7.In line 364, "value" should be replaced by "values".
The comment has been followed. Please see line 369 of the revised paper.
8."w_stem" is used in Eq. (1), but "w_s" is used in Table 2. They are the same one.
The comment has been followed. Please see Table 2 of revised paper.
9."W_total" is used in Eq. (1), but "w_t" is used in Table 2. They are the same one.
The comment has been followed. Please see Table 2 of the revised paper.
10.In Table 2, "wcrown", "wcrown", "ws", "wbark", and "wt" should be respectively replaced by "w_crown", "w_stem", "w_bark", and "w_total"/"W_total".
The comment has been followed. Please see Table 2 of the revised paper.
11.In Table 2, what does "41.2232(7.6996)" mean?
Values in parantheses indicates the standard errors for each parameter estimates. Corresponding column header revised as “Estimate (SE)”
12.In Table 2, the condition "<0001" is strange.
The comment has been followed. <0001 corrected as <0.0001
13.In Table 2, "<0001" is used for "a_0", "a_1", "a_2", "b_0", "b_1", "b_2", and "c_1", but ".1110" is for "c_0". It is strange.
This a statistical representation. All parameters is significant at P<0.0001 except for c0
14.In Table 2, why can the models for "w_s", "w_bark", and "w_bark" be used?
Necessary explanations about why we use these tree components were given lines 195-199 of revised paper.
15.In Table 3, what does "2(38)" mean?
As we have mentioned in the footnote of the Table 3 2(38) means “* variables introduced to the input layer: 2: D, H with 38 rows “. That is, 2 means the two input variables and 38 are the values of the input variables used in rows by the system. The rows are 38 because we have used the 70% of the available data set.
16."w_stem", "w_bark", and "w_crown" are biomasses in Table 2, but "dw_stem", "dw_bark", and "dw_crown" are biomasses in Table 3. Why?
The comment has been followed. Please see Table 3 of the revised paper.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe authors used different regression and artificial neural networks (ANN) for tree biomass modeling using fifty-five sample trees of different diameter and height classes. The manuscript is well written and it is an interesting case study for biomass modeling.
My major concern is how the total 55 tree samples were divided into training and testing for accuracy assessment and which technique was used for sampling.
There should be a study area map with spatial distribution of trees location because it provides location of study area in relation to globe.
Minor Comments:
Line 11: Please use high quality of Figures 1 and 2 for clarity.
Figure 497: Please use figure 3 ïstead of figure 2 in caption as it is a third figure.
Author Response
The authors used different regression and artificial neural networks (ANN) for tree biomass modeling using fifty-five sample trees of different diameter and height classes. The manuscript is well written and it is an interesting case study for biomass modeling.
My major concern is how the total 55 tree samples were divided into training and testing for accuracy assessment and which technique was used for sampling.
As we have mentioned in our manuscript “the available data set was randomly divided into fitting data which constitutes 70% of the total dataset and test data which consists of the remaining 30% data sets. The first dataset was used for the choice of the “best” model, while the latter was used for the exploration of the predictive ability of the constructed model”
The test data set is totally independent from the fitting procedure and is only used for the evaluation of the constructed model. In order to explain the whole procedure, the following figure is presented.
In order to follow the comment, text was added to the revised manuscript. Please see lines 347-354: “the available data set… training process of the models” of the revised manuscript.
There should be a study area map with spatial distribution of trees location because it provides location of study area in relation to globe.
A map representing the study area has been added as suggested. Please see Figure 1 in revised paper.
Minor Comments:
Line 11: Please use high quality of Figures 1 and 2 for clarity.
The comment has been followed. Please see our revised figures
Figure 497: Please use figure 3 ïstead of figure 2 in caption as it is a third figure.
The comment has been followed. Please see our revised manuscript.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe author has answered all my questions in a precise and detailed way. This manuscript can be accept in present form. However, there is a small problem, figure 1 the map of the research area needs a north pointer and a scale, and I hope the editor can review it after the author has modified it in this round.
Reviewer 2 Report
Comments and Suggestions for AuthorsThis revised manuscript is ready to be published.
