Spatial Prediction of Diameter Distributions for the Alpine Protection Forests in Ebensee, Austria, Using ALS/PLS and Spatial Distributional Regression Models

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a set of models to predict the gamma function mean and variance parameters. These parameters then provide a distributional approach for modelling the diameter distribution of stems in the measured plots. The models are estimated using linear parametric and spline smoothing in a Bayesian framework.

While I agree that the distributional modelling is a modern and interesting approach for the old and often studied problem, I partly disagree with the authors concerning the PPM and PRM methods. I think the authors have mixed the methods: in the parameter recovery method (PRM) the parameters of a selected function are solved directly from the measured characteristics, and in the parameter prediction method (PPM) the parameters are regressed against suitable forest characteristics. (see e.g. Siipilehto J, Mehtätalo L (2013). Parameter recovery vs. parameter prediction for the Weibull distribution validated for Scots pine stands in Finland. Silva Fennica vol. 47 no. 4 article id 1057. https://doi.org/10.14214/sf.1057, or Mehtätalo L, Lappi J (2020) Biometry for forestry and environmental data. CRC Press. 411 p. chapter 11).

The PRM also provides exact solution to the variables used to solve the parameter values. For instance, if the authors now would estimate a model for the stem number and mean diameter (if those are not available from field measurements), PRM can fit a Weibull or gamma distribution that is compatible with both of them, and, as a result, provides quite a realistic diameter distribution. The parameters could also be solved based on the basal area or total volume, even with the mean height. On the contrary, if the models proposed by the authors were used to predict the stem numbers by diameter classes based on the field-measured or predicted (using the model they propose in lines 345-360) stem number, it is clear that the total basal area calculated from the diameter distribution would not be compatible with the one field-measured or predicted (with a model). Some of the plot from Appendix 1 look particularly non-compatible in this sense. While I do not suggest the authors should be able to provide compatible diameter distribution, they should mention this aspect when discussing the (older and proposed) methods.

When I looked at the results, I was surprised to see the erratic behavior of the "best" models. I do not believe for a second that the behavior presented in Figure 2 is reasonable. It looks (to an outsider) as a classic case of overfitting a model, and I assume that this kind of model simply cannot work outside the modelling data. Especially the cyclic behavior of ASP looks highly suspicious. I assume that it is possible, even if highly unlikely, that some kind of explanation for this behavior can be found, but I assume it is far more likely that the shape of the models is a result of pure happenstance. Therefore, I think the authors should test their model in independent data (which is likely a difficult requirement, unless smaller NFI plots could be used for that purpose). As a minimum requirement, I see that the authors should e.g., divide their data to two and use part of the data as a test data and part as modelling data, or utilize k-fold cross-validation or something. Unless otherwise proven (with such an analysis or logical reasoning), I interpret the models as grossly overfitted.

The result table 1 is difficult to read as the variables are not presented, but they need to be searched for in the text.

The results section between lines 238-250 is a tedious read and should be shortened. All the local minima and maxima (that I find irrational) can be much better seen from Figure 2.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Comments for author File: Comments.pdf

Comments on the Quality of English Language

1.          Writing specifications: The sentence expressions throughout the text need further polishing to avoid grammatical errors and ensure that the writing style meets the requirements of the journal，such as：

l  “Characterizing such structurally diverse forests is best accomplished using more detailed summaries of possibly complex size-class distributions.”.

l   “The parameters are usually not directly formed by a regression predictor, but often through a monotonically increasing response function,”  

l   “When a spatially structured effect was considered, a Gaussian process proved more appropriate than a tensor product smooth;”

l   “This suggests the gamma distributional assumptions fit very well to the data and the distributional regression model m_14 was adequately specified.”

l  The verb tense is confusing, such as “our findings also suggest that a spatially structured effect always enhanced the model performance” ;  In“Forest inventory data was collected on n = 273 sample plots”，"was" should be changed to "were", because the subject is plural "data"; In “For each of the prediction pixels the same set of covariates as used in the candidate models were derived.”，“were derived”should be replaced by“was derived”.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The article deals with the prediction of stem diameters in forest stands in the Ebensee region, Austria. A distribution-based regression model is used for the prediction, which models linear, non-linear and spatial effects.

The introduction provides a comprehensive overview of the objectives and the state of the art. In the methodology section, the concept and the procedure applied to the collected data are explained very well and comprehensively. The results are discussed and the conclusions are justified by the results.

All in all, a well-written and scientifically sound work that is suitable for publication after the correction of a few minor comments:

- western, eastern etc. should not be capitalised in the contexts used

- line62 … approach to estimate …

- Line 141 x'_i is used in two different contexts: full vector of covariates and its linear part. It is better to use a different symbolism for one of the two.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The paper has been revised as required, and I do not have any suggestions for further revision.