Strength Loss Inference Due to Decay or Cavities in Tree Trunks Using Tomographic Imaging Data Applied to Equations Proposed in the Literature

Round 1

Reviewer 1 Report

General:

The work is interesting for the improvement of acoustic tomography image analysis methods and has practical applications. However, the presentation of the introduction or state of the art should be improved. The explanations of the formulas are not easy to follow and in some cases are not understood. Possibly some figures should be incorporated, and the wording improved.

The wording of the method should be revised. The description of section 2.2.6 could be better understood if it is accompanied by figures that explain the equations.

It is advisable to review the text of the discussion to improve and concretize the ideas. The conclusions should be more concrete.

Details:

Line 44: This part of the sentence is left over: Although simplified for the case of trees

L48: equation (1) is not correctly written. It should be: σ=My/I ≤fm

L49: applied bending stress instead of active stress

L50: please revise sentence: …where you want to ….. Better: from the fibre to the axis passing through the center of gravity or similar.

L59: more grades instead of more colors

L66-70: equation 2 is the stiffness loss and not the strength loss. This last one is related with Section modulus more than to Moment of inertia (equation 3). Further, it should be explained that the hollow cylinder is concentric with the circular cross-section. A figure should be included.

L73-75: equation (3) is a simple relation of section modulus loss, and it has no relation with homogeneity or isotropic behaviour of material. Revise it and correct it.

L78: Equation 4, proposed by [35] and adapted from equation [33], includes… Which equation?

L76-78: a figure is required to understand the explanation and terms.

L127-129, figures 2 and caption: The “Scheme of the indirect test with wave propagation in the longitudinal direction and transducers positioned at 45° of inclination” can not be seen in the figure a.

L167: d should be subindex in md

L206-213: a figure should be adequate to understand it.

L218-227: please explain it better. A figure could help. Are the four measurement focused to obtain an equivalent circular cross-section?

Figure 5: caption is repeated. Right part of the figure is not necessary

In general: the word discs is no probably correct. A disc is usually with circular shape, and this is not the case in this work. Probably slice or cross-section should be more correct.

L242-243: the sentence: … and the moment of inertia of 242 the hollow cylinder (Ihc) with cavity centered diameter d is given by Equation 8. Should be: … and the moment of inertia of the cross-section with hollow cylinder (Ihc) with cavity centered diameter d is given by Equation 8.

Equation (8): hc should be subindex

Equation (8): it should be: Ihc=π (D4 - d4) /64, and hc subindex and 4 superindex

L246-253: improve the drafting of this paragraph. In last sentence, “the transport” meaning is not clear. Please revise it.

L266, rewritten equation 4, is not understandable: (3)? Meaning?. Please revise it.

1. 268-281: please revise both paragraphs. Try to avoid the first personal plural mode. L276: what parameters were used?

Equation (10): explain it with a figure.

Table 2: definition of Ca2 is missing

Table 3, title: “Percentage values of” is not necessary and does not apply. (2 to 4) are in percentages, but (5) not.

L320: bur ?

L331: Table 1 should be Table 3?

Author Response

We are very grateful for the suggestions that certainly improved the text.

Attached are our point-by-point responses.

Author Response File: Author Response.pdf

Reviewer 2 Report

Presented article sets a goal to set up a relation or formula to estimate strength loss due to the decay. In my opinion the goal has been achieved However, some changes might be in order, largely formal. I have following remarks:

Keywords: the article does not deal with tree hazard assessment, so despite the link to this is clear, I would suggest to replace “tree hazard” and “tree risk assessment” with “acoustic tomography”, “stem strength loss”, may be “tree stability”. Just a suggestion.

Line 46 – 51, Eq. 1 is not written correctly, as it can be read as stress equals to M to I ratio for y equal or smaller than fm, which does not make sense. I would suggest the correct form will be like this:

σ=M/I⋅y ≤ f_m or σ=( M ⋅ y)/I ≤ f_m, or better as a fraction.

Line 56: it can be agreed, that the equations from beam theory do not deal with the extent of decay. On the other hand it is all coming from the fact, they are technical formulas, used mainly in civil engineering. If applied to tree acoustic tomography, as my knowledge of used methods and devices goes, the area taken into account is only sound wood, so both cavities and decayed wood is taken into consideration. So it might be slightly misleading. I learn it is explained further in the text, but it might be good to stress out that this relates with theory of beams only. Or do I get it wrong?

Line 78: you are referring to the equation by the article reference. This is difficult to follow. I guess, that it would be easier for reader to change the reference [33] (article) to (3) (equation that is referred to).

Line 204, 205 The title 2.2.5. is probably incomplete or there are two sentences unseparated

Lines 229, 230 and 231, 232 are identical, is it on purpose?

Line 245 Formal: Ihc – hc should be a subscript, I_hc

Line 266: more formal, the chosen way of matematical equation transcription will need to be reconsidered for whole article. On this specific line, the double brackets are not necessary and also the last form of the equation is very unhappy. (3)+R-R*(3) made me think about way how the d^3/D^3 become 3. May be without this last part the equation will be better?

Lines 271 and 281 using the same abbreviation (SL) for different version of the calculated parameter might be misleading and I personally would try to include some subscript, perhaps, to distinguish among them. But that is only my personal feeling and this is not an error, as the calculated parameter is basically the same.

Line 287, table 1. In table, the parameter Ct is showed, but in description parameter Cc is mentioned. What is correct? Also, the thickness of the rest wall is denoted as t in description and as T in table. In description of the table the C for trunk circumference is used, but this value is nowhere shown in the table.

Line 298/299 Table 2. All the models are identical. Is it correct? Were they been transcribed correctly? Also, Ca2 is meant to be Ca², I guess, as it is quadratic equation, I suppose?

Line 313 Table 4 Wouldn't be better to exchange the word "Variations" for "Differences"? Is I understood, the values do not show variability or variation od data, but differences between calculated I.

Author Response

We are very grateful for the suggestions that certainly improved the text.

Attached are our point-by-point responses.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

All observations made in the first revision have been corrected. Explanation has greatly improved.

Here are some improvements or comments on your answers:

In relation to equation 2, I understand your explanation and I have verified that the authors (33) relate the strength loss with the relationship between diameters to the fourth power. Therefore, they are making a relationship between moments of inertia of the cross-section that is equivalent to analyzing a stiffness loss, but not strength, which would be related to the decrease in section modulus (with diameters to the third power). But it is to be assumed that this was explained or justified by the authors of that work (33). On the other hand, the term second moment of area is equivalent to moment of inertia.

Lines 404-451: A figure should be included to help explain the eccentric cavity. I understand that it will be a circular cross-section with an eccentric circular cavity, with a ring of degraded wood. In the text it is said that it only has eccentricity in one of the X or Y axes, but in reality, if it is a circular cross-section, the eccentricity can only refer to a single axis.

Figure 7: it would be convenient to add a drawing with the resulting simplification of a circular cross-section with an eccentric cavity, delimiting its dimensions. In the SLD formula, a closing parenthesis is missing.

Author Response

Please see the attachment

Author Response File: Author Response.docx