Development of a Tree Growth Difference Equation and Its Application in Forecasting the Biomass Carbon Stocks of Chinese Forests in 2050
Round 1
Reviewer 1 Report
I appreciate authors’ hard work in revising and resubmitting the manuscript. The manuscript is in acceptable form for publication, but I have some minor comments and edits.
Line 15: between the ratio of tree diameter at breast height to the tree height and age of
Line 17 delete d
Line 73: The main feature of this equation is that it evaluates the relationship between the ratio of DBH and tree height with tree age. We tested and applied this differential equation considering the following aspects.
Line 89: Delete period.
Line 213 Where is the table 3 ?
Line 215: dbh/tree height ratio instead of status; b is the parameter to be estimated; and t is the year or age.
Line 223: Please present table 3 first and then present table 4 (Line 213).
Line 224: ....obtained the Latest results ?? Please explain it. I could not understand what authors are trying to say.
Line 249-250: Please delete this sentence. It is not applicable in this section.
Line 286: Could you please refer the species such as Picea asperata Mas (Fig 1g), Quercus spp. (Fig 1h), .. and so on for other tree species mentioned in this section.
Line 308: Tg = terra gram of carbon.
Line 312: Rewrite this statement that populous is relatively fast. I believe this study is not about comparing the species growth rate, so I would suggest using terms such as high growth rate, low growth rate .
Line 321: difference equations ( Eq. ... ) and equation (10) in order to obtain the net increase.
Line 325: different tree species.
Line 332: relatively large growth (Fig 3(I)) indicating that small trees ..........
Line 334:337: Please refer figures such volume (Fig 3(II)..... while describing the figures in the text. Otherwise, it is difficult to readers to understand.
Line 406: from 2013 to 2050.
Line 415: space after period.
Author Response
Dear Reviewer,
We are grateful to you for your critical comments and constructive suggestion on our manuscript. The comments were very valuable and have played a very important role in improving the level and content of our paper. We have revised and explained our manuscript according to given comments. In order to show the location revision and changes in the manuscript, the “Track changes” option was kept on. The detail of responses against each comment is given below. Thanks again.
Yours sincerely,
(On behalf of all co-authors)
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Brief summary
Aim of this research is to provide parameters of difference equations for main tree species in China.
Broad Comments
STRENGHT
Research computes biomass carbon stocks in entire forest area in China which makes the estimation complete and useful to broad community.
WEAKNESS
Basically, this paper represents a technical report on carbon stocks in forest biomass in China. Method for calculation of carbon stocks is a common method worldwide, e.g. volume derived from allometric equations using DBH and tree height, biomass derived from volume, basic wood density and biomass expansion factors and carbon stocks derived from biomass and carbon content in biomass. Use of difference equations for estimating biomass yearly increment is a static way and it does not account for changes in environment. Forecasting future carbon stocks in changing environment is usually done by process-based or hybrid models which are driven, among other variables, with meteorological data also and therefore can account for response of forest growth to changes in climate. In addition, in this manuscript there is inappropriate use of carbon sink term. Carbon sink in forest ecosystems can only be accounted if all ecosystem compartments are taken into account (biomass and soil) which is not the case here. In this research estimation of soil carbon is missing. Therefore, concluding that Chinas forest will act as carbon sink in the future, not knowing what is happening in the soil, and also assuming a constant (not climate dependant) increment and fixed rate of harvest lost, seems a bit imprudent.
Missing map of the research area. Map of the areas (i.e. provinces) where data were collected should be provided.
Missing chapter on statistical data analysis. Although several times in text it is mentioned that some results are or are not significantly different. Based on what analysis? At least standard errors of fitted parameters should be provided.
Missing result on main forest parameters, e.g. age-class distribution, species composition (by volume, by area), N-G-V table (stand density, basal area and volume), etc.
Missing a list of observed and anticipated short-comings of the calculation method, e.g. constant increment, fixed (assumed) harvest loss, missing soil carbon, etc.
Weak discussion chapter.
Conclusions beyond results.
Concluding remark
Authors did a respective work calculating biomass carbon stocks in Chinas forests and I acknowledge that results of this research could be valuable and could serve as good information. Nevertheless, I think that manuscript, in a present form, does not provide new knowledge. Suggestion is to rewrite the manuscript in a way that it is clear what the limitations of the method are, but at the same time to emphasise when and way this simple calculation could and should be used (assumed for national calculations, e.g. National Inventory Reports for UNFCCC and KP for parties).
Author Response
Dear Reviewer,
We are grateful to you for your critical comments and constructive suggestion on our manuscript. The comments were very valuable and have played a very important role in improving the level and content of our paper. We have revised and explained our manuscript according to given comments. In order to show the location revision and changes in the manuscript, the “Track changes” option was kept on. The detail of responses against each comment is given below. Thanks again.
Yours sincerely,
(On behalf of all co-authors)
Author Response File: Author Response.pdf
Reviewer 3 Report
Brief summary of the paper
The manuscript describes the use of a difference equation for the relationship between tree diameter at breast height (DBH), tree height and age of China’s main arbor species. The method was compared to the logistic and Richards equations representing the traditional tree growth model. Main results showed the proposed method as very precise and suitable for the purpose. The the biomass carbon stocks were calculating supporting the idea that Chinese forests may have an important carbon sequestration ability for future generations.
General comment and remarks
Interesting paper, pretty well written and in agreement with the Journal’s aims and scope. Even if pretty “local” and focused on tree species occurring in China, it is a methodological paper and I believe that very few adjustments could be done in order to accept it for publication. I have just one concern and regarding the training-validation dataset which seems to be extracted just once. Indeed many more runs should be done (30 at least) averaging the results (MAE, RMSE R2, BIAS, etc.). With just one extraction, the probability to extract a biased sample is too high.
Specific comments
L17: a “d” is to be removed between showed and that
L44-56: Concerning this topic I suggest to review also this recent paper on the stand density index and the self thinning rule and the modelling efforts around this topic https://doi.org/10.1007/s11676-019-00967-0
L86-89: please be consistent. You can’t write “the top 10 tree species are” and then to use only the genus such as Quercus spp. or Picea spp. Please rephrase. Maybe “ the top 10 tree genus” is more adequate
L107: was this 20% randomly sampled more times? Actually with just one extraction a biased sample (both 80% and 20%) were very likely to be extracted. Please clarify/solve this issue.
L179-192: the same as above. Please clarify
L376: reference [49] is not Andres et al.
References
please check the references. Some errors were found, e.g. [49]
Author Response
Dear Reviewer,
We are grateful to you for your critical comments and constructive suggestion on our manuscript. The comments were very valuable and have played a very important role in improving the level and content of our paper. We have revised and explained our manuscript according to given comments. In order to show the location revision and changes in the manuscript, the “Track changes” option was kept on. The detail of responses against each comment is given below. Thanks again.
Yours sincerely,
(On behalf of all co-authors)
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
1. Reviewer comment: Missing map of the research area. Map of the areas (i.e.
provinces) where data were collected should be provided.
Author ’s response: We would appreciate the reviewer’s reminder to provide a map
of the research area See P age 4 Line 109 Line 110
Reviewer comment: I appreciate a map that authors have provided. If possible, better resolution should be obtained. I assume that GPS locations of sampled stands are not available? Otherwise, I would strongly recommend to mark the exact locations of sample stands on the Map. In that way a good representation of spatial distribution of sample would be provided.
Considering that you are building a model that needs to predict the increment that will be used on entire China national territory it is important that sample is uniformly distributed across country. I am aware of the huge physical work that is associated with the tree-growth analysis, and I would absolutely understand if sample is bias toward some areas (e.g. forest area nearest to factory or city, etc.). Nevertheless, if there is an intention to extrapolate results beyond its limits, which in this research is the case as you are using DBH increment model to predict future biomass carbon stock at the national level, it is extremely important that you account for all possible factors that could cause uncertainty in the final estimate. E.g. Bias sample toward an area where, due to current favourable climate conditions, growth rate is higher then average, can results with unrealistically higher final biomass carbon stock in 2050 then it would be if you build your model on the sample from area where growth rate is lower then average.
2. Reviewer comment: Missing chapter on statistical data analysis. Although several times in text it is mentioned that some results are or are not significantly different. Based on what analysis? At least standard errors of fitted parameters should be provided.
Author ’s response: The comment is very valuable, and we have elaborated the analytical part.
(…) Part of Author’s response removed in order for the correspondence to be more condense.
Reviewer comment: Thank to the Authors for presenting the analytical part of the manuscript. I think this part clearly and sufficiently described. But, here I did not comment on that part. I showed concern regarding the results of growth difference equation model fitting (chapter 3.1.1.), table 2 and table 3. The use of word significant is not corroborated with statistics.
Line 327-329: The parameter estimation results are shown in Table 2. No significant difference was found in the growth of Abies fabri (Mast.) Craib and Cunninghamia lanceolata in different provinces.
Line 336-337: Picea spp. (Picea asperata, Picea meyeri Rehd. et Wils and Picea wilsonii Mast) and Quercus spp. (Quercus aliena Bl, Quercus dentata Thunb and Quercus wutaishansea Mary) in Shanxi did not significantly differ in the height or DBH models.
Line 367-368: Comparing the models for the same tree species in different areas (shown in Table 2) and the same tree genera in the same area (shown in Table 3) revealed no significant differences.
In table 2 and 3 where model parameters Height(b) and DBH(b) have presented, nor standard error, nor p-value have been provided. High R2 values do not mean that models (i.e. model parameters) do not differ. Without knowing if model parameters are statistically significant (p<0.05) or without knowing the standard errors of estimated parameters, it is not justified to perform further analysis.
I am most concerned about the following decision:
Line 368-371: To improve the precision of the model and expand its applicability, Abies fabri (Mast.) Craib and Cunninghamia lanceolata data from different provinces were merged to establish a tree growth difference model suitable for a wider region.
Parameters in this merged dataset range 0.8-1.231 for Height(b) and 0.78-1.409 for DBH(b) and it seems unlikely that they are not statistically different.
Strongly recommend to provide p-value and standard error of the estimated parameters.
3. Reviewer comment: Missing result on main forest parameters, e.g. age-class distribution, species composition (by volume, by area), N-G-V table (stand density, basal area and volume), etc.
Author ’s response: The question raised is very valuable and critical but, this study mainly takes the individual trees as the research object, that don’t rely on the forest parameters of age-class distribution, species composition (by volume, by area), N-G-V table (stand density, basal area and volume), etc.
The difference equation in this study was developed basing on the harvested trees, obtained via analysis of the analytical wood data from "China's main tree growth compilation," which was compiled by the forestry survey team and other related units. The DBH, size without bark and tree height were actual measured values. See Page 2 Line 82 Line 85
The forest volumes and their areas in 2013 can be obtained using the 8th Chinese Ministry of Forestry data sets. The difference equation was used to predict the DBH growth in China using continuous forest inventory (CFI) data, which were randomly and evenly distributed in various provinces of China. By combining the average DBH with the annual increase in DBH, volume, biomass and BCS in 2013, the increases in the volume, biomass, and BCS were predicted for 2050. See Page 11 Line 313 Line 317
Reviewer comment: Thank to the Authors for explanation. I understand that this study was based on a tree-level data. Consequently, no stand-level characteristics could be provided regarding the sample dataset. Nevertheless, as this research also uses NFI data for prediction of future biomass carbon stock at national level, it would be very useful if data on age-class distribution, species composition (by volume, by area), N-G-V table (stand density, basal area and volume), etc. on the national level from NFI data would be provided.
When making future predictions of carbon stocks on the large-scale one of the most important information is distribution of age-classes (i.e. amount of area under specific age-class), as it is known that biomass is a function of age. Therefore, when having a bias distribution toward young stands and you foresee that in the investigated future period, e.g. 2050, you would have more old-growth forest it is easy to predict that your biomass carbon stock will increase. On contrary, if your forests are approaching their rotation period (if managed) of natural end of a life-time (if unmanaged) then the future of your biomass carbon stock strongly depends on the production potential of young forests. Finally, if your age-class distribution is normal (uniform, stable) then future biomass carbon stock will increase only if some external drivers (e.g. climate) forces stronger C sequestration.
Without knowing current state of the forest ta national level, any predictions and conclusions are incomplete. Figure 4 provide some information but it is not presented in a classical way. Recommend to reorganize the figure in a way that it gives age-class or dbh-class distribution per area, species composition as volume share and biomass carbon stocks in selected time period, e.g. starting and ending point (2013 and 2050). Other graphs can be in Supplement.
4. Reviewer comment: Missing a list of observed and anticipated short-comings of the calculation method, e.g. constant increment, fixed (assumed) harvest loss, missing soil carbon, etc.
Author ’s response: Although some deviations were observed in certain data predictions, these deviations could be due to the heterogeneity of the growth environments, measurement errors or model shortcomings. The influence of different tree shapes and the growth environment (water, nutrients, light, crown and different tree shapes and the growth environment (water, nutrients, light, crown and root space, etc.), which is seen as a fixed value, has been reflected by the difference in the DBH and height at the same age. Additionally, the model assumes that the growth environment of an individual tree will not change suddenly and thus can be expanded for use. Meanwhile, comparing the fitting and validation precision among the Logistic, Richards and difference equations based on the same data reveals that the difference equation had a higher precision than the Logistic and Richards equations for tree height and DBH. This phenomenon may occur because the difference equation was predicted based on the DBH or tree height of a certain year which contained information related to the growth environment/site conditions, etc. Therefore, the difference equation had a remarkable parameter estimation effect and could obtain higher precision for rapid, simple and efficient tree growth predictions. (See Page 14 Line 386-Line 398)
Reviewer comment: Thank to the Authors on the explanation. I agree that difference equations can be used for rapid, simple and efficient tree growth estimates. But, when applying it for predictions, I would recommend addressing main shortcomings of the method, i.e. fixed increment. In current environmental changes assuming that: “…growth environment of an individual tree will not change suddenly…” seems like not very justified assumption. Although I generally agree that in near future growth rates will probably not change significantly, with respect to observed global climate changes it is necessary to address the issue of fixed increment rate, at least in the discussion. Currently, modelling community is struggling with how to model dynamic C allocation in a process-based modelling (i.e. how much of sequestered C will go to above and how much to below ground biomass) as it is found to be highly dependant on the changes in environmental conditions. Therefore, using a fixed increment in today scientific research should be very well elaborated and justified.
Author’s response: The natural growth and the consumption of timber resources result in a certain amount of wood loss per year. According to the wood loss ratio of the annual total volume in 1999-2013, the total loss can be predicted, and the loss of various tree species in 2013-2020, 2020- 2030 and 2030-2050 was predicted according to their proportion, respectively. The DBH growth and the gross growth of timber volume can be predicted by the difference equation (Equation 2) and Equation (10) in order to obtain the net increase. As shown in Figure 3, the volume and proportion of net to obtain the net increase. As shown in Figure 3, the volume and proportion of net growth to gross growth both increased. (See Page 12 Line 333-Line 344)
Due to changes in the calculation method of the total loss, section 3.2 (BCS forecast for Chinese forests in 2050) and 4.2 (BCS forecast for Chinese forests) was modified.
Reviewer comment: Thank to the Authors for the explanation. I am aware of the difficulty to track back or to forecast harvest losses. Nevertheless, assuming that share of harvest losses for each tree species to total harvest loss is equal to their volume share should be additionally corroborated. Otherwise, it is to assume that greatest share in total harvest losses would be from economically more valuable species rather than the ones that have greatest volume share. I understand that in the absence of real data, assumptions should be made. But, they always have to be justified either by some reference or logical explanation.
Is this the way you calculated for example harvest lost for oak in 2013-2020:
oak harvest loss in 2013-2020=total harvest loss in 2013-2020 * (volume of oak in 2013-2020/volume total in 2013-2020)?
Also, Figure 3 is not very good representation of your results. I recommend reorganizing your data as in the following table.
period | balance | Quercus | Pinus |
2013-2020 | growth | 80 | 20 |
loss | -8 | -2 | |
increase | 72 | 18 | |
2020-2030 | growth | 96 | 24 |
loss | -9.6 | -2.4 | |
increase | 86.4 | 21.6 | |
2030-2050 | growth | 115.2 | 28.8 |
loss | -11.52 | -2.88 | |
increase | 103.68 | 25.92 |
Then You can make a figure like Figure 1. It has info on species volume shares and development over time. Note that I used imaginary data.
Figure 1.
Author ’s response: In addition, although soil carbon research is an important aspect of forest C stock and sink studies, the process of soil carbon sink is very complex; thus, this s paper only studied biomass carbon and did not focus on the soil carbon sink.
Reviewer comment: I am aware of the complexity of soil carbon research. Although you did not account it in the study it is important to give a comment on this ecosystem pool when you are predicting future carbon stocks. At least, it is important to stress out that soil carbon is out of the scope of this research.
5. Reviewer comment: Weak discussion chapter.
Author ’s response: Thank you for your concern about the discussion part.
Following your comment the discussion part has been updated and strengthened by adding more literature and references that resonated with our study. In the section
4.1, the following part was modified:
(…) Part of Author’s response removed in order for the correspondence to be more condense.
Reviewer comment: Thank to the Authors for improving the Discussion chapter. Nevertheless, I recommend to cover few more topics:
- proces-based modelling as state-of-the-art in future estimates of carbon stocks (include it in the first paragraph of the 4.2. chapter, as currently there are only references providing estimates until 2008 and not forecasts longer in the future), comparison to this approach
- main advantage and shortcomings of the method (fixed increment, assumption that energy policy would not change causing increased harvest rates, change in species share in total harvest toward more economically utilizable species..) – this can be stand alone paragraph were reader could get short and concise overview of way/when/how to use and not to use this approach
- effect of age –class structure on future biomass carbons stock predictions (when you provide better represented results you can discuss on this topic more under last paragraph of the 4.2. chapter)
Some of the topics can also be included in the Introduction in order to obtain complete “story” when reading the paper.
6. Reviewer comment: Conclusions beyond results.
Author ’s response: This study, which was based on the basic principle of the difference equation and the general law of tree growth and empirical equations, developed and verified a growth difference equation for the main arbour species in China. We found that tree growth was less affected by the spatial position, a certain similarity existed between tree species belonging to a single group, and the tree growth of different species was significantly different. At the same time, the developed model was used to predict China's carbon stocks in 2020, 2030 and 2050. The results show that from 2013 to 2050, the BCS of Chinese forests w ill increase from 7342 to 11,030 TgC and the annual biomass C sink will reach 99.68 TgC∙??−1, which indicates that Chinese land surface forest vegetation have important carbon sequestration capabilities. (See Page 15 Line 448-Line 456)
Reviewer comment: Thank to the Authors for acknowledging that without soil carbon it is impossible to speculate on future carbon sink. Bolded text is in contrast to the sentence in the line 539:
“Table 7 shows that the average growth rates for trees of each species are similar.”
Where did you test effect of spatial position on tree growth?
Overall comment: I would really like to thank to the Authors for all the modifications and explanations that they have provided. This study is interesting and the results will for sure get the interest of the readers. I absolutely support this research, although I have many comments and recommendation. Currently there are many questions that needs to be addressed in the text. Results should be presented in more classical and readable way (resolution is not god so you can not read the graphs properly). Some statistics is still missing in Table 2 and 3 (see comment 2.). Discussion still needs to be improved. By revising the paper in the proposed way I guarantee that manuscript will be more appealing to the readers.
Author Response
Response to Reviewer
Dear Reviewer,
We are grateful to you for your critical comments and constructive suggestion on our manuscript. The comments were very valuable and have played a very important role in improving the level and content of our paper. We have revised and explained our manuscript according to given comments. In order to show the location revision and changes in the manuscript, the “Track changes” option was kept on. The detail of responses against each comment is given below. Thanks again.
Yours sincerely,
(On behalf of all co-authors)
Major comments:
1. Reviewer comment: I appreciate a map that authors have provided. If possible, better resolution should be obtained. I assume that GPS locations of sampled stands are not available? Otherwise, I would strongly recommend to mark the exact locations of sample stands on the Map. In that way a good representation of spatial distribution of sample would be provided.
Author’s response: We are thankful for your reminder to provide GPS locations of sampled stands, that’s a good suggestion. However, the analytical wood data we used in the differential equations was taken in the early days of the founding of the People's Republic of China. Therefore, the GPS coordinates were not recorded unfortunately due to some uncertain limitations. The spatial location information was only specific to the villages. To make the map more readable the resolution and the legend are adjusted as suggested. (See Page 4 Line 109-Line 110)
Figure 1. Distribution areas for model establishment and testing data for different tree species.
2. Reviewer comment: Considering that you are building a model that needs to predict the increment that will be used on entire China national territory it is important that sample is uniformly distributed across country. I am aware of the huge physical work that is associated with the tree-growth analysis, and I would absolutely understand if sample is bias toward some areas (e.g. forest area nearest to factory or city, etc.). Nevertheless, if there is an intention to extrapolate results beyond its limits, which in this research is the case as you are using DBH increment model to predict future biomass carbon stock at the national level, it is extremely important that you account for all possible factors that could cause uncertainty in the final estimate. E.g. Bias sample toward an area where, due to current favourable climate conditions, growth rate is higher then average, can results with unrealistically higher final biomass carbon stock in 2050 then it would be if you build your model on the sample from area where growth rate is lower then average.
Author’s response: We would appreciate the reviewer’s suggestion to consider the biasness in the data. This study purpose at developing a tree growth difference equation and forecasting the biomass carbon stocks of Chinese forests with this equation, thus, some reasonable bias could be accepted, which we are intending to study in our next research project. In future study, we hope to use data that distribute across the whole study area for the difference equation fitting and do some application. (See Page 17 Line 484-Line 485)
Empirical and theoretical equations have been applied mainly to study the population growth of trees, and their differential forms (i.e., the growth status at a certain time) are relatively complex. Difference equations, which reflect one of the essential properties of the real world, occupy an important place in mathematics and in real-world applications due to their discreteness, and these equations open up new approaches in solving one of the central problems of modern science, namely, the problem of turbulence [16]. The difference equation and discrete expression of differential equations belong to the field of nonlinear analysis in mathematics and can elucidate highly complex properties through a simple defined recursive relationship [17-19]. The theory of difference equations arises from the modeling of many aspects, including system theory, economics, inventory analysis, learning probability models, population genetics, and so on [20,21]. The theory of difference equations has been used in forestry and has shown a great advantage despite the fact that these equations have not been widely applied [22]. (See Page 2 Line 50-Line 61)
Based on the general rule of the difference equation and tree growth, including certain empirical and theoretical, equations such as those of Schumacher (1939), the Logistic equation (1838) and Richards (1959) [29], this study proposed a new tree growth difference equation. The main feature of this equation is that it evaluates the relationship between the ratio of DBH and tree height with tree age. (See Page 2 Line 71-Line 74)
3. Reviewer comment:. But, here I did not comment on that part. I showed concern regarding the results of growth difference equation model fitting (chapter 3.1.1.), table 2 and table 3. The use of word significant is not corroborated with statistics.
Line 327-329: The parameter estimation results are shown in Table 2. No significant difference was found in the growth of Abies fabri (Mast.) Craib and Cunninghamia lanceolata in different provinces.
Line 336-337: Picea spp. (Picea asperata, Picea meyeri Rehd. et Wils and Picea wilsonii Mast) and Quercus spp. (Quercus aliena Bl, Quercus dentata Thunb and Quercus wutaishansea Mary) in Shanxi did not significantly differ in the height or DBH models.
Line 367-368: Comparing the models for the same tree species in different areas (shown in Table 2) and the same tree genera in the same area (shown in Table 3) revealed no significant differences.
In table 2 and 3 where model parameters Height(b) and DBH(b) have presented, nor standard error, nor p-value have been provided. High R2 values do not mean that models (i.e. model parameters) do not differ. Without knowing if model parameters are statistically significant (p<0.05) or without knowing the standard errors of estimated parameters, it is not justified to perform further analysis.
I am most concerned about the following decision:
Line 368-371: To improve the precision of the model and expand its applicability, Abies fabri (Mast.) Craib and Cunninghamia lanceolata data from different provinces were merged to establish a tree growth difference model suitable for a wider region.
Parameters in this merged dataset range 0.8-1.231 for Height(b) and 0.78-1.409 for DBH(b) and it seems unlikely that they are not statistically different.
Strongly recommend to provide p-value and standard error of the estimated parameters.
Author’s response: The suggestion has been appreciated and endorsed. The standard errors of the estimated parameters were added in Table 2, Table 3 and Table 4. (See Page 7 Line 228; P7 L241; P8 L259)
Table 2. Two-species growth difference equation to estimate differences between regions
Species | Location | R2 | SE | Height(b) | R2 | SE | DBH(b) |
Abies fabri (Mast.) Craib | Sichuan | 0.986 | 0.065 | 1.174 | 0.986 | 0.069 | 1.273 |
Gansu | 0.994 | 0.032 | 1.231 | 0.99 | 0.04 | 1.409 | |
Cunninghamia lanceolata | Jiangxi | 0.945 | 0.009 | 0.8 | 0.906 | 0.012 | 0.78 |
Fujian | 0.947 | 0.02 | 0.808 | 0.933 | 0.027 | 0.867 | |
Hunan | 0.938 | 0.024 | 0.806 | 0.906 | 0.031 | 0.906 | |
Guizhou | 0.98 | 0.026 | 0.931 | 0.969 | 0.003 | 0.973 | |
Anhui | 0.914 | 0.066 | 0.927 | 0.922 | 0.069 | 0.926 |
Note*: In the equation. Y represents the DBH/tree height ratio; b is the parameter to be estimated; t is the year or age, and SE represents Standard Error.
Table 3. Growth difference equation of similar tree species in the same province
Species | R2 | SE | Height(b) | R2 | SE | DBH(b) |
Quercus aliena Bl | 0.91 | 0.091 | 0.822 | 0.983 | 0.059 | 1.225 |
Quercus dentata Thunb | 0.98 | 0.034 | 0.872 | 0.945 | 0.093 | 1.21 |
Quercus wutaishansea Mary | 0.981 | 0.026 | 0.825 | 0.986 | 0.039 | 1.301 |
Picea asperata | 0.977 | 0.032 | 1.568 | 0.885 | 0.077 | 1.949 |
Picea meyeri Rehd. et Wils | 0.98 | 0.023 | 1.589 | 0.92 | 0.053 | 1.919 |
Picea wilsonii Mast | 0.99 | 0.049 | 1.333 | 0.98 | 0.078 | 1.739 |
Note*: In the equation. Y represents the DBH/tree height ration; b is the parameter to be estimated; and t is the year or age, and SE represents Standard Error.
Table 4. Fitting results for difference equation for different species
Location | Species(groups) | Height | DBH | ||||
R2 | SE | b | R2 | SE | b | ||
Sichuan | Pinus massoniana Lamb. | 0.969 | 0.025 | 0.823 | 0.984 | 0.025 | 1.008 |
Sichuan, Gansu | Abies fabri (Mast.) Craib | 0.991 | 0.034 | 1.186 | 0.991 | 0.038 | 1.338 |
Shandong | Platycladus orientalis (L.) Franco | 0.986 | 0.045 | 0.717 | 0.987 | 0.065 | 0.938 |
Jiangxi,Fujian,Hunan, Guizhou, Anhui | Cunninghamia lanceolata | 0.952 | 0.009 | 0.82 | 0.93 | 0.001 | 0.829 |
Inner Mongolia | Larix gmelinii (Ruprecht) Kuzeneva | 0.979 | 0.019 | 0.785 | 0.984 | 0.002 | 0.906 |
Shanxi | Larix principis-rupprechtii Mayr | 0.949 | 0.032 | 1.348 | 0.918 | 0.045 | 1.578 |
Picea spp. | 0.984 | 0.018 | 1.527 | 0.94 | 0.038 | 1.889 | |
Quercus spp. | 0.965 | 0.026 | 0.842 | 0.966 | 0.041 | 1.250 | |
Pinus tabuliformis Carrière | 0.975 | 0.012 | 1.065 | 0.968 | 0.02 | 1.306 | |
Betula platyphylla Suk. | 0.959 | 0.022 | 1.016 | 0.962 | 0.028 | 1.356 | |
Populus davidiana | 0.94 | 0.03 | 0.981 | 0.964 | 0.033 | 1.405 | |
Populus L. | 0.951 | 0.03 | 0.728 | 0.956 | 0.034 | 1.008 | |
Yunnan | Picea likiangensis | 0.994 | 0.015 | 0.885 | 0.995 | 0.015 | 0.842 |
Pinus yunnanensis | 0.939 | 0.022 | 0.758 | 0.966 | 0.019 | 0.729 | |
Abies georgei Orr | 0.997 | 0.016 | 1.016 | 0.996 | 0.02 | 1.089 | |
Note*: In the equation, Y represents the DBH/tree height ration; b is the parameter to be estimated; and t is the year or age, and SE represents Standard Error. Picea spp. includes Picea asperata, Picea meyeri Rehd. et Wils, and Picea wilsonii Mast. Quercus spp. includes Quercus aliena Bl, Quercus dentata Thunb, and Quercus wutaishansea Mary.
The sentences were modified as following:
“The parameters of Abies fabri (Mast.) Craib showed no significant difference in the Sichuan and Gansu, and the results of Cunninghamia lanceolata also presented the similar growth in five different provinces.” (See Page 7 Line 225-Line 227)
“The results of the R2 and SE to the model showed that the parameter of the model is reliable (Table 3). The parameter of Picea spp. (Picea asperata, Picea meyeri Rehd. et Wils and Picea wilsonii Mast) in Shanxi did not significantly differ in the height or DBH models and the results of Quercus spp. (Quercus aliena Bl, Quercus dentata Thunb and Quercus wutaishansea Mary) presented the same trend. T” (See Page 7 Line 234-Line 238)
“The parameters of Abies fabri (Mast.) Craib in the Sichuan and Gansu province revealed no significant differences and that of Cunninghamia lanceolata in five different areas showed the similar results (shown in Table 2).In addition, the same tree genera such as the three species of Picea spp. in the Shanxi revealed no significant differences and that is similar to Quercus spp. in the Shanxi province (shown in Table 3).” (See Page8 Line 245-Line 249)
“To improve the precision of the model and expand its applicability, the Abies fabri (Mast.) Craib data from the Sichuan and Gansu province were merged to establish a tree growth difference model suitable for a wider region and do the same processing for Cunninghamia lanceolata data from Jiangxi, Fujian, Hunan, Guizhou, Anhui province.” (See Page 8 Line 249-Line 252)
4. Reviewer comment: I understand that this study was based on a tree-level data. Consequently, no stand-level characteristics could be provided regarding the sample dataset. Nevertheless, as this research also uses NFI data for prediction of future biomass carbon stock at national level, it would be very useful if data on age-class distribution, species composition (by volume, by area), N-G-V table (stand density, basal area and volume), etc. on the national level from NFI data would be provided.
Author’s response: The question raised is very valuable and critical but, this study aims at developing a difference equation that rely on the individual trees but not consider stand-level characteristics. In future study, study related to document the stand-level characteristics such as age-class distribution, species composition, stand density, basal area and volume etc. in BCS research, are recommended to be carried out. (See Page 11 Line 318-Line 322; P17 L 486- L 489)
5. Reviewer comment: When making future predictions of carbon stocks on the large-scale one of the most important information is distribution of age-classes (i.e. amount of area under specific age-class), as it is known that biomass is a function of age. Therefore, when having a bias distribution toward young stands and you foresee that in the investigated future period, e.g. 2050, you would have more old-growth forest it is easy to predict that your biomass carbon stock will increase. On contrary, if your forests are approaching their rotation period (if managed) of natural end of a life-time (if unmanaged) then the future of your biomass carbon stock strongly depends on the production potential of young forests. Finally, if your age-class distribution is normal (uniform, stable) then future biomass carbon stock will increase only if some external drivers (e.g. climate) forces stronger C sequestration.
Author’s response: Thank you so much for the suggestion to consider the distribution of age-classes and we are deeply sorry for creating confusion here, this study purposed to develop a reliable and applicable difference equation. In the section 3.2, the difference equation was used to predict the DBH growth in China using continuous forest inventory (CFI) data (individual tree sample), which were randomly and evenly distributed in various provinces of China. The forest volumes and their areas in 2013 was obtained from the 8th Chinese Ministry of Forestry data sets, besides, the affection of age-class distribution to carbon stocks will be researched in our further study. (See Page 11 Line 318-Line 322; P17 L 486- L 489)
6. Reviewer comment: Without knowing current state of the forest ta national level, any predictions and conclusions are incomplete. Figure 4 provide some information but it is not presented in a classical way. Recommend to reorganize the figure in a way that it gives age-class or dbh-class distribution per area, species composition as volume share and biomass carbon stocks in selected time period, e.g. starting and ending point (2013 and 2050). Other graphs can be in Supplement.
Author’s response: Thank you so much for the suggestion to present the current status of the forest. In this study, the forest volumes and their areas in 2013 was obtained from the 8th Chinese Ministry of Forestry data sets in this study, the DBH of individual trees was according to continuous forest inventory (CFI). (See Page 11 Line 318-Line 322)
DBH, volume, biomass, and BCS of Chinese forests in 2013 and 2050 was shown in Table 9 and Figure 4. The table has been reorganized as suggested. (See Page 13 Line 366- Page 14 Line 371)
Table 9. DBH, volume, biomass, and BCS of Chinese forests in 2013 and 2050
Species(groups) | d(cm) | M(m3) | B(Tg) | BCS(TgC) | ||||
2013 | 2050 | 2013 | 2050 | 2013 | 2050 | 2013 | 2050 | |
Quercus spp. | 14.94 | 26.02 | 12.94 | 21.39 | 1305.1 | 2116.09 | 630.63 | 1022.49 |
Betula spp. | 14.08 | 21.38 | 9.14 | 14.57 | 950.53 | 1395.6 | 469.37 | 689.15 |
Larix spp. | 16.75 | 25.48 | 10.01 | 16.05 | 785.67 | 1341.1 | 413.18 | 705.29 |
Pinus massoniana Lamb. | 15.25 | 30.67 | 5.91 | 10.24 | 641.76 | 923.19 | 330.12 | 474.89 |
Pinus yunnanensis | 14.35 | 23.6 | 4.77 | 7.82 | 416.54 | 632.87 | 219.98 | 334.22 |
Picea asperata Mast | 19.26 | 28.2 | 9.87 | 15.65 | 786.16 | 1063.64 | 405.66 | 548.84 |
Abies fabri （Mast.）Craib | 21.64 | 30.54 | 11.65 | 18.3 | 688.14 | 1040.68 | 347.51 | 525.54 |
Cupressus funebris Endl. | 14.27 | 20.79 | 2 | 3.16 | 279.46 | 342.34 | 145.62 | 178.39 |
Cunninghamia lanceolata | 14.29 | 26.94 | 7.26 | 12.37 | 636.59 | 907.31 | 341.53 | 486.77 |
Populus L. | 15.67 | 29.61 | 5.03 | 8.52 | 575.08 | 826.59 | 285.01 | 409.66 |
Pinus tabuliformis Carrière | 14.76 | 26.25 | 0.66 | 1.11 | 73.84 | 108.59 | 39.24 | 57.7 |
Other species | 14.73 | 24.66 | 68.53 | 112.36 | 7227.59 | 10891.71 | 3714.2 | 5597.16 |
Figure 4. DBH, volume, biomass, and BCS of Chinese forests from 2013 to 2050. Meaning of each letter: a: Quercus spp.; b: Betula spp.; c: Larix spp.; d: Pinus massoniana Lamb.; e: Pinus yunnanensis; f: Picea asperata Mast; g: Abies fabri (Mast.) Craib; h: Cupressus funebris Endl.; i: Cunninghamia lanceolata; j: Populus L.; k: Pinus tabuliformis Carrière; l: Other species
7. Reviewer comment: But, when applying it for predictions, I would recommend addressing main shortcomings of the method, i.e. fixed increment. In current environmental changes assuming that: “…growth environment of an individual tree will not change suddenly…” seems like not very justified assumption. Although I generally agree that in near future growth rates will probably not change significantly, with respect to observed global climate changes it is necessary to address the issue of fixed increment rate, at least in the discussion. Currently, modelling community is struggling with how to model dynamic C allocation in a process-based modelling (i.e. how much of sequestered C will go to above and how much to below ground biomass) as it is found to be highly dependant on the changes in environmental conditions. Therefore, using a fixed increment in today scientific research should be very well elaborated and justified.
Author’s response: Thank you so much for the suggestion to address main shortcomings of the method. Because the site conditions, environmental factors, stand conditions and remote sensing information for the same tree will only change very slightly over a certain period of time (except during natural disasters), the influence of external environmental factors can be regarded as a fixed value k [27]. A difference equation is an equation that recursively defines a sequence, and each item of the sequence is a function defined as the previous item [32]. To predict the growth trend of trees over a certain period of time according to the general rule that tree growth is irreversible and slows as trees age, the DBH, tree height and age are taken into account to construct difference equations for the main tree species in China in this study. In addition, although the difference equation can be used for rapid, simple and efficient tree growth estimates, it still has some limitation in forecasting the BCS. For example, the influence of external environmental factors in the equation was regarded as a fixed value k instead of dynamic change. (See Page 4 Line 125-Line 132; P16 L 469-L 471)
8. Reviewer comment: I am aware of the difficulty to track back or to forecast harvest losses. Nevertheless, assuming that share of harvest losses for each tree species to total harvest loss is equal to their volume share should be additionally corroborated. Otherwise, it is to assume that greatest share in total harvest losses would be from economically more valuable species rather than the ones that have greatest volume share. I understand that in the absence of real data, assumptions should be made. But, they always have to be justified either by some reference or logical explanation.
Also, Figure 3 is not very good representation of your results. I recommend reorganizing your data as in the following table.
Author’s response: We would appreciate the reviewer’s suggestion and a reference has been provided in the manuscript.
According to the wood loss ration of the annual total volume in 1999-2013, the total loss can be predicted, and timber harvesting shifted from earlier clearcutting to include selective and staged cuttings, which did not change overall forest cover, thus, the loss of various tree species in 2013-2020, 2020- 2030 and 2030-2050 was predicted according to their proportion in this study [48]. (See Page 12 Line 343-Line 342)
48. Zhang, Y.; Song, C. Impacts of Afforestation, Deforestation, and Reforestation on Forest Cover in China from 1949 to 2003. J FOREST 2006, 104, 383.
The DBH growth and the gross growth of timber volume can be predicted by the difference equation (Equation 2) and Equation (10) in order to obtain the net increase. The results were shown in Table 8 and Figure 3, the volume and proportion of net growth to gross growth both increased (Figure 3). Figure 3 has been reorganized as suggested. (See Page12 Line 346- Page 13 Line 354)
Table 8. The gross growth, loss and net increase of the volume of different tree species in Chinese forests from 2013 to 2050
Species(groups) | 2013-2020 | 2020-2030 | 2030-2050 | ||||||
growth | loss | increase | growth | loss | increase | growth | loss | increase | |
Quercus spp. | 1.89 | 1.07 | 0.82 | 2.83 | 1.29 | 1.54 | 5.01 | 1.94 | 3.07 |
Betula spp. | 2.22 | 1.31 | 0.91 | 3.29 | 1.58 | 1.71 | 5.76 | 2.34 | 3.42 |
Larix spp. | 2.82 | 2.17 | 0.65 | 3.76 | 2.52 | 1.24 | 5.32 | 2.88 | 2.44 |
Pinus massoniana Lamb. | 1.57 | 1.1 | 0.47 | 2.04 | 1.16 | 0.88 | 3.03 | 1.33 | 1.7 |
Pinus yunnanensis | 1.8 | 0.94 | 0.86 | 2.79 | 1.16 | 1.63 | 5.31 | 2.02 | 3.29 |
Picea asperata Mast | 1.77 | 0.78 | 0.99 | 3.1 | 1.2 | 1.9 | 5.68 | 1.92 | 3.76 |
Abies fabri （Mast.）Craib | 0.41 | 0.23 | 0.18 | 0.59 | 0.26 | 0.33 | 1 | 0.35 | 0.65 |
Cupressus funebris Endl. | 3.26 | 2.48 | 0.78 | 4.18 | 2.71 | 1.47 | 5.85 | 2.99 | 2.86 |
Cunninghamia lanceolata | 2.04 | 1.52 | 0.52 | 2.76 | 1.76 | 1 | 4.03 | 2.06 | 1.97 |
Populus L. | 0.22 | 0.15 | 0.07 | 0.32 | 0.19 | 0.13 | 0.52 | 0.27 | 0.25 |
Pinus tabuliformis Carrière | 20.69 | 14.08 | 6.61 | 28.76 | 16.24 | 12.52 | 45.18 | 20.49 | 24.69 |
Other species | 20.69 | 14.07 | 6.62 | 28.77 | 16.23 | 12.54 | 45.19 | 20.44 | 24.75 |
*Note: Loss (mortality and cut) =total loss *(volume of the specie /volume total)
9. Reviewer comment: I am aware of the complexity of soil carbon research. Although you did not account it in the study it is important to give a comment on this ecosystem pool when you are predicting future carbon stocks. At least, it is important to stress out that soil carbon is out of the scope of this research.
Author’s response: Thank you so much for the suggestion, we have stressed out that soil carbon is out of the scope of this research. This has been highlighted as a limitation of the study in the discussion part.
In future study, we hope to (1) use data that distribute across the whole study area for the difference equation fitting and do some application, and (2) investigate the increase of volume, biomass and BCS both for the growth of trees and the expansion of forest area. Moreover, and (3) study related to document the stand-level characteristics such as age-class distribution, species composition, stand density, basal area and volume etc. in BCS research, are also recommended to be carried out. (See Page17 Line 484- Line 489)
10. Reviewer comment: - proces-based modelling as state-of-the-art in future estimates of carbon stocks (include it in the first paragraph of the 4.2. chapter, as currently there are only references providing estimates until 2008 and not forecasts longer in the future), comparison to this approach
Author’s response: The suggestion has been appreciated and endorsed. Thank you for your reminder, the suggested paper has been cited and incorporated in the revised manuscript.
Our estimate is in agreement with the work of Hu et al., who developed a stage-classified matrix model to predict biomass C stocks of China’s forests from 2005 to 2050 by using data from China’s forest inventories between 1994 and 2008, the results showed that total forest biomass C stock would increase from 6430 Tg C in 2005 to 9970 Tg C (95% confidence interval: 898 0~ 1107 Tg C) in 2050, with an overall net C gain of 78.8(56.7 ~ 103.3)[64]. however ,our result is similar than XU et al.[65], who showed that that China’s forest biomass carbon storage will increase by 7230 Pg C in 2000–2050, , with an average carbon sink of 140 Tg C y, and Yao et al.[66],who estimate that age-related forest biomass C sequestration to be 6690 Tg C(170 ) from the 2000s to the 2040s, the total forest biomass in China would increase by 8890–1037 Tg C by the end of 2040s. (See Page16 Line 444-Line 452)
64. Hu, H.; Wang, S.; Guo, Z.; Xu, B.; Fang, J. The stage-classified matrix models project a significant increase in biomass carbon stocks in China’s forests between 2005 and 2050. SCI REP-UK 2015, 5.
65. Xu, B.; Guo, Z.; Piao, S.; Fang, J. Biomass carbon stocks in China’s forests between 2000 and 2050: A prediction based on forest biomass-age relationships. Science China Life Sciences 2010, 53, 776-783.
66. Yao, Y.; Piao, S.; Wang, T. Future biomass carbon sequestration capacity of Chinese forests. SCI BULL 2018, 63, 1108-1117.
11. Reviewer comment: - main advantage and shortcomings of the method (fixed increment, assumption that energy policy would not change causing increased harvest rates, change in species share in total harvest toward more economically utilizable species..) – this can be stand alone paragraph were reader could get short and concise overview of way/when/how to use and not to use this approach
Author’s response: We would appreciate the reviewer’s reminder and add the part of the shortcomings.
Although the difference equation can be used for rapid, simple and efficient tree growth estimates, it still has some limitation in forecasting the BCS. For example, (1) the influence of external environmental factors in the equation was regarded as a fixed value k instead of dynamic change; and (2) the model cannot be used to predict the soil carbon, as soil carbon research is also an important aspect of forest C stock and sink studies. (See Page16 Line 469-Line 473)
12. Reviewer comment: - effect of age –class structure on future biomass carbons stock predictions (when you provide better represented results you can discuss on this topic more under last paragraph of the 4.2. chapter
Author’s response: Thank you so much for the suggestion to consider effect of age –class structure on future biomass carbons stock, but this study relied on the individual tree and did not consider stand-level characteristics. The change has been added in the revised manuscript as below.
In future study, we hope to (1) use data that distribute across the whole study area for the difference equation fitting and do some application, and (2) investigate the increase of volume, biomass and BCS both for the growth of trees and the expansion of forest area. Moreover, and (3) study related to document the stand-level characteristics such as age-class distribution, species composition, stand density, basal area and volume etc. in BCS research, are also recommended to be carried out. (See Page16 Line 481- Page 17 Line 486)
13. Reviewer comment: Bolded text is in contrast to the sentence in the line 539:
“Table 7 shows that the average growth rates for trees of each species are similar.”
Where did you test effect of spatial position on tree growth?
Author’s response: We would apologize to reviewer’s for the confusion and appreciate your suggestion. In the paper, we have modified the sentence to “We found that the parameters of the difference equation for DBH/tree height was less affected by the spatial position, a certain similarity existed between tree species belonging to a single group, and the parameters of different species was significantly different. Besides, the difference equation was used to predict the growth status and BCS of Chinese forests from 2013 to 2050. ” (See Page 16 Line 477-Page 17 Line 481)
Author Response File: Author Response.pdf
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
The manuscript highlighted developing a differential model for the relationship between the DBH/height and age for Chinese main arbor species. The authors collected forest field data from the several sources assessed the differential model performance using some important variables in forests. The results revealed that the differential model shows a higher precision and Chinese forests have critical C sequestration capabilities. This manuscript may display some interest to audiences but it has very limited novelty. From the results, the differential model was of higher accuracy but no traditional models’ comparison. It clearly falls into the scope of journal – Forests, yet it needs to be revised in some places, and some parts require clarification, as outlined in the following.
1. Please add full descriptions for all abbreviations when they are showed in the first time, especially in the title.
2. Please improve the introduction part by adding more background for differential model of the relationship between the DBH/height and age. It seems like the authors are not familiar with traditional DBH/height models.
3. Please make deeper discussion from the forestry aspect but not just statistical points.
4. To be honest, there are numerous DBH/height and biomass C models and I am not sure what novelty and strength for this differential model.
Author Response
Response to Reviewer 1
Dear Reviewer,
Thank you very much for your time and effort reviewing this manuscript. We have responded to the comments below. We believe the edits have resulted in an improved manuscript and our response to all of the comments is provided below.
Yours sincerely,
(on behalf of all co-authors)
Author Response File: Author Response.pdf
Reviewer 2 Report
Manuscript ID: forests-477073
Development of arbor differential growth model and 2 its application in forecasting China's forests BCS in 2014- 2020
Authors: Zhang HanYue, Feng Zhongke*, Chen Panpan and Chen Xiaofeng
I found this paper interesting and not well written with grammatically and fluency issues. I appreciate authors efforts and hard work to develop differential growth models and demonstrate its applicability for predicting biomass carbon storage in China. Please follow the Journals guideline for formatting reference, placing figures and numbering tables.
I could not see the use of Eq.3, might I missed it. However, please state clearly the use of in the methods and also suggest to put Eq. 2 in the results if possible. Discussion section needs more work which needs to be discussed comparing other potential models with authors work. Also, please create two different parts in the discussion one for the model and another for biomass carbon storage. Please fix the table format and increase the figure panel sizes and fonts.
Line: 1 Is this number stands for the biggest age tree or the total number of sampled trees? Could you please provide more information in Table 1 such as Dbh and height ranges as well as age ranges.
Line 115: Could you please explain how the Eq. 1 was derived because I do not see any reference of this equation? Eq. 1 looks like Chapman Richards function, not a differential equation, which is commonly used forest growth modeling. So, I would encourage authors to provide justification that derived Eq 2 is a form of a differential model. Eq. 2 also looks like a time series model form so, should it not be Yt+1?
Line 128: 129- Fix the font sizes.
Line 136: What is N in the Eq. 5and 6?
Line 140: Please, rewrite this sentence. It is not giving information on growth rate although Eq. 8 can be used to obtain net growth.
Line 147. Please Refer to author such as Fang et al. [29]. It is standard to use 0.5 of biomass to obtain C storage; however, it is not clear how the biomass for each species was estimated here. I can assume biomass was estimated from volume but for this species-specific gravity would help to get biomass and carbon storage. Please specify it and for this see the section forest carbon storage of Saud et al. 2013 A life cycle analysis of forest carbon balance and carbon emissions of timber harvesting in West Virginia.
Line 157: Fix the reference style. It should be Haung et al. [33]
Line 160: Could you please refer the nonlinear function as an equation in the text? Or state clearly that eq. is the non-linear model.
Line 160. We cannot use R2 to judge the nonlinear function. However, we can use empirical R2 as Eq. 12 suggested by citation #34. For additional reference see Saud et al. 2016 Using quadratic mean diameter and relative spacing index to enhance height–diameter and crown ratio models fitted to longitudinal data.
Line 175: change it to estimated by
Line 178: Instead of using Table 2-a, Table 2-b, I would suggest authors to use Table 2, Table 3 and so on.
Line 181: What are those two tree species?
Line 185: Please refer to the growth model equation in the Table caption and provide information on response and predicting variables.
Line 186-189: Please rewrite these sentence and do not mix up information here and there. The first piece of information of the second sentence belongs to the first sentence.
Line 195-196: It is not clear how this comparison was made here because Table 2-a and Table 2-b do not share the same tree species.
Line 198: The estimated parameter and model indices of what?
202: Reformat the table 2-c with the content
Line 208-212: Authors have already mentioned about it in the method section, and if needed they can put in that section. This sentence is vague, please simplify it.
Line 214: 215: I did not see Table 3-a and Table-b refereed in the text. State Verification of the accuracy of tree height differential model. Please refer table as 1, 2, 3, 4, 5.... so on instead of -a, -b, -c.
Line 216-219: Please rewrite it in simple language.
Line 221: Abies fabri was the highest, 10.17%.
Line 222: Please provide and compare one information at a time with respect to a tree species. Do not mix it up which make it difficult to understand.
Line 224-227: I could not see that authors have conducted residual analysis and so this statement is not valid here. However, the residual distribution should be homogeneous not approximately to zero. In modeling, we do not observe residual centered to zero. See Saud et al. 2016 and cited reference # 34.
Line 228: Can you create a new sub-heading for this section.
Line 231: and the data from 2004-2008 were used.
Line 232-233- this is a new sentence. The comparison between ............
Please avoid using a semicolon to provide disjoint information. This is a repeated issue in this manuscript.
Line 234-235- Figure 1 shows that the predicted value ...................... What was the predicted and actual value?
Line 238: In addition, Larix gmelini (Ruprecht) Kuzeneva (Figure 1e).....
Please use this format to refer figure in the text and increase the axis font size and figure legend size. Is not that predicted (red line) is plotted from the non-linear model instead of a linear model what is reported in the figure?
Line 252-254: I assume the Chinese Ministry of Forestry combined two different inventory methods instead of the volume of forest and their area. Please rewrite this sentence to provide clear information.
Line 254: Change it to differential model, not capital
Line 258: Provide footnotes for the abbreviated variables used in Table 4.
Line 260-263: Table 4 shows that the average tree growth rate among tree species is similar. Avoid using semicolons;... average annual diameter growth rate is approximately 0.2-0.3 cm/yr for 2014-2020.
Please avoid using a semicolon;... and make different sentences.
Line 265: Explain TgC
Line 266: increased to 1.73.10 ...
Line 268:
Please follow the journal's guideline. Put the figure after introducing it in the text, not before it. Increase the figure sizes and put those labels I- VI within the figure panel. It is difficult to see these figures even with 200% zoom.
Line 277. What is TgC ? Provide full form before using abbreviate terms.
Line 273: Please avoid using "it can be seen from Figure'. Here were are reporting the results to a scientific community.
Line 273-282: While using a figure with multiple panels, please refer the labels (I-IV) in the text with the corresponding statement. Just mentioning figure 3 would not be helpful for readers to understand the message.
Line 289: Not the right place to put this sentence.
Line 292: What..... ? Does verification increase confidence in model development? Please avoid such statement or rewrite it scientifically.
Line 292-294: Rewrite this sentence.
Line 295-297: Please restructure this sentence.
Line 311: Use consistent units for carbon and explain CBEF.
Line 337-338: Please use either use Petagram or Teragram for carbon and do not mix both units. Correct this issue in the above text as well.
Author Response
Response to Reviewer 2
Dear Reviewer,
Thank you very much for your time and effort reviewing this manuscript. We have responded to the comments below. We believe the edits have resulted in an improved manuscript and our response to all of the comments is provided below.
Yours sincerely,
(on behalf of all co-authors)
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
After revision, I think authors have highly improved the manuscript but still not enough. First, it is very tough to read through it as uncleaned tracked changes are shown beside of the manuscript. Second, we already have numerous DBH/height and biomass C models and not sure what novelty and strength for this differential model comparing with other models. In addition, it seems not necessary to predict the biomass carbon stocks in 2020 since this is 2019 now. It is better to make a comparison with observed data or other popular models so we can understand how accurate this model and why we need it and then start a prediction for the next 20 or 30 years. Uncertainty should be considered in the models as well. Anyway, this manuscript may display some interest to some audiences but it has very limited novelty.
Reviewer 2 Report
I appreciate authors’ hard work in revising the manuscript. The manuscript is in acceptable form for publication, but I would encourage authors to conduct a sound proof read before it publishes. The response to reviewers’ shows the comments were well addressed, however the main document that I received for review has some missing pages such as from line 44 to 173, from line 223 to 352 and similarly other pages.
Great work!
