Climatic and Topographic Variables Improve Estimation Accuracy of Patula Pine Forest Site Productivity in Southern Mexico

Round 1

Reviewer 1 Report

I would like to thank the authors for working on such an interesting and important work, considering how topography and climate can impact site index.  I also appreciate the use of the GADA approach while incorporating climate variables.  Much appreciated!

General Comments:

Alas, I do have some significant concerns about the presentation and discussion of results.  The first relates to model selection.  In the text, the authors suggest the best performing model is M1b, the GADA model based on the Chapman-Richards formula that includes topographic and climatic variables.  However, a close examination of Table 3 shows that M1a and M2a (GADA models without topographic or climatic variables) had the lowest RMSE, bias, AIC, and DW of all six models.  The only model improved through the addition of topographic and climatic variables was M3, but as the authors noted, the model behavior was inferior.  Thus, the results strongly suggest the addition of topographic and climatic variables did not improve the models, but if anything lowered their predictive ability.  Thus, I cannot agree with much of the discussion stating the importance of including topographic and climatic variables in the models, unless substantial revisions occur that recognize the lack of benefit they provided (in terms of traditional model fitting evaluations).  Given the importance of parsimony and ease of application, I would argue for M1a being the best model, at least based on the results given in the text.

Second, the authors appeared to conduct and interpret a correlation analysis in the Discussion section, based on Table 4.  I was curious as to why this was done?  The results from Table 3 should have been interpreted in terms of sign and magnitude, as these partial regression coefficients account for the influence of the other variables.  I do think Table 4 is interesting and warrants inclusion, but Table 4 should only be used to setup the main interpretation based on Table 3.

Third, the study did not include model validation.  Conclusions were based on fit statistics (unfortunately incorrectly so), figures, and correlations, but there was no holdout sample or cross-validation employed to verify results.  Without validation, the results cannot be independently verified, and the credibility of the research suffers.

Fourth, a few more minor comments.  Although I cannot point to specific papers, most studies I have seen over the years have suggested that climate variables provide little in terms of model improvement.  The culprit may be the typical shorter time frame the data covers, with climate factors potentially increasing their effect over longer time horizons.  All the papers cited in this work pointed to the improvement, but not the magnitude of the gains from using climate variables.  There seems to be room for improvement by discussing the magnitude of improvement and/or including more studies that showed no affect.  In addition, the 99.4% adjusted R2 values for nearly all the models seems extraordinarily high, given the spread of the raw data in Figure 2.  These consistent R2 values also point to the negligible effect of the topographic and climatic variables.  Also, how were the topographic and particularly the climate variables selected?  Were other variables tried besides PTm and Tmin?  Finally, Goelz and Burk (1996) provide a numeric list of considerations when evaluating height or site index models.  I would encourage the authors take a look at this list when evaluating the models.

Specific Comments:

L 27-28: Consider replacing “… temperature suggested fastest-growing rates for the dominant tree height” with “temperature suggested the fastest-growing rates for dominant tree height.”

L 41: There are likely more foundational, or at least additional, sources for referencing growth and yield systems.

L 62: Remove “climate”

L 85-86: Consider replacing “for temporary plots data” with “for the temporary plots” or “for the temporary plot data”

L 87-88: Replace the author list with Nava-Nava, et al., as was done elsewhere.

Section 2.2: Why was it necessary to estimate the height trajectories for the temporary plots?  Was the height data missing?  Was height needed at a second time?  What were the 77 pairs of data (two height values?)?  I feel this section needs some more clarity on why the heights were projected and what the final dataset represents.

L 97-98: Consider replacing “established in stands of patula pine randomly distributed” with “randomly distributed in stands of patula pine”

L106-107: The first sentence of the paragraph reads as if the authors used individual tree height data to estimate mean age.  Consider rewording.

Table 2: Under the Site-specific parameter column, some of the alphas are represented by a’s, rather than alphas.  There are multiple alpha 3’s, but no alpha 3 appears in the base model.  For the Chapman model, alpha 2 came before alpha 1.  The authors will want to double check to ensure all the listed models are correct, allowing others to quickly replicate and use these models.  In addition, did the authors derive the x0 solutions and the subsequent GADA formulations, or were they borrowed from others’ work?  If the latter, please cite the sources, as GADA models can be difficult to formulate.

L 127-129: Consider replacing “Expansion of the GADA model parameters was re-parameterized as a multiple regression model…” with “The GADA model parameters were re-parameterized as multiple regression models…”

L 131 & 135-136: Were the Bi,j’s topographic and climatic variables, or parameters?  The wording implies they were variable combinations, not parameters.

L 134: Consider replacing “parameters as follows:” with “parameters, which was the following:”

L 145-146: Was RMSE (Eq. 6) also used for making the selection of the best model?

L 150-153: The Wi’s need defined (are they weights? how are they used?).  Some additional text to clarify is needed.

L 156: Needs “where” at the beginning of the explanations.

Results Section: When I looked at Table 3, I had a difficult time tracking what topographic and climatic variables were actually included in each model.  The explanations in the methods detailed the process, but the reader is left to interpret Table 3 by looking back into the methods, and I had trouble interpreting.  Please consider listing out the Mib models explicitly in the results before Table 3, allowing the reader ready access to the exact forms of the best topographic and climatic models.

L 163: Why a base age of 40 years?  Typically, studies use 50 years, or perhaps 25 or 100 years.

L 165: Replace the author list with Kiviste, et al., as done previously.

L 180-181: Autocorrelation in regression does not affect the parameter estimates (they remain unbiased), but does inflate the standard errors.

L 189-195: See my general comments for discussion on the best model selection.

L 189: Replace “fitting” with “fit”, drop “the” before SI, and add a period after “vs”.

L 190: Replace “trend” with “trends” and “plot” with “plots”.

L 192-193: Both M3 models, though in particular M3b, do not show signs of an asymptote, a desirable feature of height models.

Figure 4: The resolution was poor, making identifying the model curves difficult.

L 198-199: Replace the author list with Nava-Nava, et al.

L 202-212: The emphasis of this paragraph appears to be the comparison of the M1b model to the one previously published by Nava-Nava, et al.  This is how I read the paragraph.  However, after looking over Figure 4, I realized (I believe) the focus is on demonstrating that including climatic variables effects estimates (i.e., Lines 210-212).  The Nava-Nava, et al. model was constant regardless of changing topographic and climatic variables.  Unfortunately, the use of Nava-Nava, et al. here may not be helpful.  It would be better to use M1a for that comparison, because everything is equal between the two models (e.g., data, base form used, etc.), except for the inclusions of topographic and climatic variables in M1b.  I strongly suggest replacing the Nava-Nava, et al. model with M1a for this comparison (unless M1a is the Nava-Nava, et al. model, then this should be clearly stated).

L 203-305: Replace the author list with Nava-Nava, et al.

L 210: Considering changing “e.g., a 10-year stand with SI = 30 m the model…” to “e.g., for a 10-year stand with SI = 30 m, the model…”

L 211: Consider changing “…while at lower…” with “…while at a lower…”

L 224: Since the AIC values are negative, they actually increased for M1b and M2b, suggesting the remainder of the sentence may not be true.

L 227: Replace “distribution” with “distributions” and add a reference to Figure 3.

L 230-231: Replace author list with Mensah, et al.

L 242: Remove the comma.

L 246-247: Move “accordingly” to after “modify”

L 248: Consider changing “who consider that site index play” to “who consider site index to play”

L 250-252: See general comments.

Table 4: Since this table provides analysis results, place the table and initially reference to it in the Results section, rather than the Discussion section. 

L 272-274: Consider rewording to remove the “nots” and improve the flow (e.g., “most species will be strongly affected…”; “or will demand immediate…”)

L 275-283: Why did the results show this negative relationship, particularly since other studies showed the opposite?  Please provide some conjectures.

L 280-281: Replace the author list with Elli, et al.

L 289: Replace the last comma with a period.

L 295: Consider replacing “(Figure 4b)” with “(Figure 4)”

L 295-296: Replace author list with Özel, et al.

L 297-298: Is this last sentence based on examination of Figure 4a, or based on the collected data?  I do not think one can draw this conclusion from Figure 4a, so the authors may consider removing that reference.  The data may support this conclusion, however.

L 299-301: Unfortunately, the results from Table 3 suggest the opposite.  The models showed poorer fits when including the topographic and climatic variables.  The correlations and Figure 4 suggest including the extra variables allows for more flexibility, but these facts do not improve the models’ statistical properties.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

Journal: Forests (ISSN 1999-4907)

Manuscript ID: forests-1813973

Title: Climatic and topographic variables improve estimation accuracy of patula pine forest site productivity in southern Mexico

Overall  Comments and Suggestions for Authors

Dear authors,

Regarding the estimation of site productivity for patula pine forest in southern Mexico, this manuscript may be interesting to the relevant researchers who deals with similar issues such as forest biometrician, growth and yield modeler, and silviculturist. Also, the approach with climatic and topographic variables was interesting enough. Overall, the context was acceptable, and the logic was easy to understand. I suggested a few comments to update the manuscript. Although I offered a few comments, I think it’s significant for this type of manuscript. Please consider the comments carefully. I wish the models in this study will serve for estimating site index for patula pine in the region.

I hope that this manuscript can be improved based on peer-review’s comments. My specific comments were provided in detail as follows.

Kind regards,

Reviewer

Point 1.

I don’t really understand how authors argued that models with b type were superior to the models with a type. When I checked the goodness-of-fit statistics in Table 3, I evaluated models with a type were better except for M3a vs M3b. For example, RMSE and AIC were lower in a type than in b type for M1.

Point 2.

I would like to recommend changing the figures with higher resolution. The current Figures 2 and 4 are not easy to see. If possible, it should be changed.

Point 3.

It’s required to check the residual plots over the predicted as well as stand age. In the current manuscript, I can see only the residual plots over  age in Figure 3. I assumed authors already check the residuals over the predicted value, but it should be convinced. I recommend authors to include the Figure in the manuscript or in the supplementary file at least.

Point 4.

It would be good to provide some discussion regarding applicability and practicability. Authors may be able to suggest the spatial and temporal range in model application. In addition, the available range of climatic and topographic variables can be discussed.

Point 5.

If I understand the models and outputs correctly, the interpretation must be proceeded before discussing other analysis. Still, the objectives of this study and contents were interesting regardless of the output.

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.docx