The Effect of Empirical Log Yield Observations on Carbon Storage Economics

Round 1

Reviewer 1 Report

The article titled “The effect of empirical log yield observations on carbon storage economics” develops an empirical growth and yield model incorporating carbon storage for boreal spruce. The empirical data indicated that there was a smoother transition from pulpwood to sawlogs and correspondingly the value transition associated with increasing size was also gentler. The author states that the contribution of this paper is to address sources of uncertainty in an analysis of estate-level economics of carbon storage and sequestration (Kärenlampi 2020). This paper addresses these uncertainties by applying a growth model with stem sizes at 25 mm intervals, as opposed to the 50 mm intervals used in Kärenlampi (2020). Also, the yield of sawlogs and pulpwood from trees of different sizes were verified in the experiment, through the collection of empirical log yield data which is used to estimate value for different sized trees. This article looks at results for six different treatment schedules and proposes a carbon sequestration subsidy system. This study finds that (1) all financially feasible treatment cycles terminate in clearcutting and (2) capital return rate is sensitive to rotation age and less sensitive to cutting limit diameter.

Specific editorial suggestions or questions:

Line 7: suggest edit: “An empirical model for log yield from trees is established and applied to microeconomics…”

L27: suggest edit: “Upon the occurrence of clearcutting and soil preparation (for what?), the net..”

L30-31: awkward statement. Essentially, what you are trying to say is, “There is a complex system of industries and human activities that relate (and contribute to) the sequestration of carbon into the atmosphere”.

L40 – 41: Use of designed is awkward here, suggest “The development of the state of any particular estate can be modeled in terms of some sort of dynamic programming.”

L45-46: Are you assuming instead of postulating?

L62-63: Awkward statement, suggest “Increasing the harvesting diameter limit, allows for the economically optimal carbon storage.”

L86: when you refer to quality class, is that grade or just product class (sawtimber, pulpwood)?

L92: odd use of plural, suggest “an (or the) earlier paper [21].”      

L201-203. An inclusion of the modified (or original) harvest supply function from Parkatti et al [33] is desired, so that the reader can know what the model parameter C5 being referred to represents.

L243: When you refer to carbon rents, you are really talking about value associated with storing carbon on the landscape, correct?

L248: Suggest edit: …”carbon sequestration subsidies and taxes [18].”

L289: Suggest edit: “value of capital return rate is greater the smaller the cutting diameter limit.”

L306: Suggest edit: “The higher the cutting limit diameter, the higher the total volume of trees” – remaining on the landscape or removed?

L333 – 334: Suggest edit: …”except for the two lowest cutting diameter limits.”

L 399; Suggest edit: “it is beneficial to plot the annual…”

Author Response

Thank you very much.

There are a few cases where the Reviewer appears to suggest an edit, even if the suggestion is the same as the original text. However, the author has carefully reviewed these cases and modified, if appropriate. Somewhat strangely, many of the statements appear to be carefully formulated and contain significant meaning.

L30-31: awkward statement. Essentially, what you are trying to say is, “There is a complex system of industries and human activities that relate (and contribute to) the sequestration of carbon into the atmosphere”.

OK.

The impression of the author is that dynamic programming is a method of design. Dynamic programming is not supposed to create a model of reality, but rather many different models among which a suitable procedure possibly can be found.

The present author is not assuming or postulating anything related to the ”normal forest principle”. The ”normal forest” is a creature robust in time - time-independent in the statistical sense. Necessary conditions for the time-independency is that the stand ages are evenly distributed, and stand characteristics are determined by stand age. These features being directly derived from the requirement of stability, they are rather postulations than assumptions.

L62-63: Awkward statement, suggest “Increasing the harvesting diameter limit, allows for the economically optimal carbon storage.”

The statement proposed by the Reviewer is incorrect. Microeconomically optimal carbon storage corresponds to the application of multiple repeated thinnings from above, to the transition diameter where sawlogs are gained instead of pulpwood only. Then, carbon storage can be increased. In that case, it differs from the microeconomic optimum. The most economical way of doing it is to increase the harvesting limit diameter.

L86: when you refer to quality class, is that grade or just product class (sawtimber, pulpwood)?

Text has been amended to clarify this.

It is now explained in the text what the parameter C5 of the harvest expense function of Parkatti et al. refers to.

L243: When you refer to carbon rents, you are really talking about value associated with storing carbon on the landscape, correct?

Sort of yes, but the content of the concept is much more specific. Eq. (9) gives the revenue from carbon rentals, and the rent rate is the parameter u in Eq. (9).

Reviewer 2 Report

The author has come up with a very impressive report on log yield and other carbon storage economic analyses, which is the strength of this paper. I like how he tried to make refinements and clarified some uncertainties on the previous reports about log yield to smoothen the curve of log yield trends over the years. I love the concept of carbon rent and carbon sequestration subsidy.  It’s a well-thought-of study. However, I also have a few comments about the results, which I hope the author will address or justify.

Major comments:

• I am a little concerned about the study areas' sampling size and representativeness, mainly relying on the assumed constant age distribution and stand characteristic that may create biases in the report. Please caution the readers on these limitations, especially upon concluding.
• With all these trend analyses, has the author applied any statistical approaches to compare treatments? Any trend analysis, prediction models (linear or non-linear), test for statistical differences, autocorrelations analysis, or curve fittings sort of like that. Any ANOVA or MANCOVA applied? This way, we can be sure that treatments have been treated and analyzed with statistical confidence.

Author Response

Thank you very much.

The author is amazed at how little published information there is regarding the yield of different kinds of logs from trees. Probably there are reasons. The quality of tree trunks varies by stand. Quality requirements of sawlogs vary by sawmill, and are subject to change in time. Geographic areas differ, as well as tree species. The yield of logs from trees does differ depending on type of harvesting (clearcutting, thinning from above/below, continuous cover operation, ..), stand age, and so on. The author does not assume anything, regarding such dependencies. He just has organized and applied the only empirical dataset available to him.

In the geographic area where the dataset has been collected, a national research institute has produced log yield information. However, for some reason, the investigations have not been thoroughly reported; only some coarse-grained tables can be found in the literature.

The above is amazing, considering that the yield of different kinds of logs is essential in the economics of forest management.

The empirical log yield observations used in this paper have been collected for the purposes of the present study. However, the present paper does not intend to provide any detailed discussion of the related problematics. That remains to be done in another paper – this paper focuses on the carbon storage application.

Needless to say, the empirical observations of log yield apply to the circumstances of Eastern Finland, and being collected 2017-2020, may be subject to change in time. This is the first, but possibly not the last log yield dataset collected by the author. The author would like to encourage any practitioner to collect datasets of his or her own. Some difficulties may appear due to classified business information related to crosscutting. The author assumes the datasets (to be reported in more detail in a forthcoming paper) may serve as a starting point for others, possibly widely within the boreal region.

Now, the readers have been cautioned about the above issues in the Discussion.

The other major concern of the Reviewer is of great interest to the author.

The financial treatment used in the paper applies probability theory. The treatment, however, is simplified by introducing the ”normal forest principle”, which refines probability distributions to even distributions, any density function of stand age becoming determined by one parameter (rotation age). Consequently, the financial formulae applied in the paper become deterministic.

The growth model used in the paper applies probability theory. However, the growth model development utilizes expected values and then produces a deterministic outcome.

As a consequence of the above, all the treatments of the paper are deterministic. There are no probabilistic models with statistical scatter.

In real life, there is statistical scatter almost everywhere. As it does not enter the paper from the financial formulae, neither the growth model, does it enter through the forest site characteristics? No, it does not. Analogously to the ”normal forest” principle, a ”normal stand” – concept is introduced. All treatments are deterministic. The deterministic design of the paper does not allow any statistical analysis.

A note clarifying some of the above has now been added to the Discussion. Besides, it is mentioned that scatter in stand characteristics is supposed to be discussed in another paper.

The sampling areas have been described in the text. The log yield data has been collected in two municipalities. Now there is an additional statement that the size of the sampling territory is 100 km wide (West to East) and 30 km tall (South to North), and that the elevations vary from 115 to 205 m above sea level. There also is an additional statement regarding the size of the estate at Vihtari, where tree stand data was recorded.

Fig. 1 shows sawlog proportion within the commercial section of spruce stems. Values naturally run from 0 to 1. Observations are organized according to breast-height diameter in mm (horizontal axis).

The literature curve is actually linearly smoothed by myself. Justified or not, I think I will leave it that way for clarity. The ”original” shape of the curve would be a rectangular graph. This is because any given single value represents all observations within a 50-mm interval. The 50-mm interval centered at 175 mm is represented by sawlog proportion zero. If the reading is an expected value, this indicates NO stem of diameter less than 200 mm should yield any sawlog.

If the data behind the literature values would be available, there would be a variety of methods for the construction of graphs. However, with only 50-mm expected values being available, any attempt to smoothen probably would result in bias (as the linear smoothing has, referring to the above paragraph).

Fig. 2 shows the capital return rate according to Eq. (2) for six different treatments applied on the normal stand representing the example estate. The vertical axis runs from zero to 10%/a. Observations are organized according to stand age. The ISO-standard abbreviation for a year is ”a”. In the file I received from MDPI,  the legend and the plot do match.

In all the Figures of the paper, the vertical axis description is on the top of the axis. There is a better space. I cannot see any need for any special Figure titles, as the axis are specified, and the Figure caption provides further detail.