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Two sets of initial conditions on boreal forest carbon storage economics

['Petri P. Kärenlampi', 'Lehtoi Research', 'Lehtoi']

Date: 2022-02 

Abstract Two sets of initial conditions are used in the investigation of capital return rate and carbon storage in boreal forests. Firstly, a growth model is applied in young stands as early as the inventory-based model is applicable. Secondly, the growth model is applied to observed wooded stands. Four sets of thinning schedules are investigated in either case. The two sets of initial conditions yield similar results. The capital return rate is a weak function of rotation age, which results in variability in the optimal number of thinnings. Reducing the number of thinnings to one increases timber stock but induces a capital return rate deficiency. The deficiency per excess volume unit is smaller if the severity of any thinning is restricted by the removal of large trees only. Omission of thinnings best applies to spruce-dominated stands with stem count less than 2000/ha. Restricted thinning intensity applies to deciduous stands and dense pine stands. The albedo effect increases the benefits of restricted thinnings and increased clearcuttings instead of contradicting the carbon storage.

Citation: Kärenlampi PP (2022) Two sets of initial conditions on boreal forest carbon storage economics. PLOS Clim 1(2): e0000008. https://doi.org/10.1371/journal.pclm.0000008 Editor: Abdul Rehman, Henan Agricultural University, CHINA Received: July 22, 2021; Accepted: November 8, 2021; Published: February 1, 2022 Copyright: © 2022 Petri P. Kärenlampi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: Data enclosed as a supplementary file. Funding: This work was partially funded by Niemi foundation, grant II (PPK). The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The author has declared that no competing interests exist.

1. Introduction There are two large sinks of atmospheric carbon on planet Earth: the oceans and the forests [1–4]. It is difficult to manipulate oceans, whereas forests can be managed. By definition, a carbon sink is a system with a positive time change rate of stored carbon. This paper discusses the microeconomics of boreal forests as a carbon sink. A particular benefit of the boreal forest is carbon storage in the soil; the amount of soil carbon may exceed the carbon storage in living biomass [5–10]. However, living biomass produces litter resulting in soil carbon accumulation, and consequently, the rate of carbon storage depends on the rate of biomass production on the site. The biomass production rate is related to the amount of living biomass [6, 9, 11, 12]. As the time change rate of storage constitutes a sink, this paper focuses on changes in living biomass. In the case of trees, one of the most straightforward indicators of living biomass per surface area unit is the commercial volume of tree trunks. The outcome of any process depends on the essential contributing mechanisms. Such mechanisms can often be described in terms of a process model. However, the outcome also depends on the occurring initial conditions, or more broadly, boundary conditions. In real-life applications, the initial conditions vary. Results of model-based investigations can be considered robust (or non-chaotic) if they are coherent under realistically varying sets of initial conditions [13]. This paper investigates carbon storage in boreal forests using a growth model based on large inventory datasets [14]. To gain possibly robust results, two different sets of initial conditions are used. Both sets of initial conditions have been described in recent investigations [15–17], but have not been applied simultaneously in the clarification of any single problem. The process model, together with the initial conditions, could produce an outcome. However, in this paper, there are more elements. There are objective functions. The objective functions are partially microeconomic, partially of a physical character. The microeconomic objective function is the capital return rate [16–20]. The physical objective functions are carbon storage area densities, discussed in terms of living biomass, and measured in area densities of commercial trunk volumes. There is a hierarchy between the objective functions. Firstly, the capital return rate is maximized. Then, deviations are introduced, and the relationship of capital return rate deficiency to excess commercial volume is investigated. The deviations are introduced in terms of four additional sets of boundary conditions. These are constituted by four sets of restrictions applied to intermediate harvesting practices, or, in other words, thinning restrictions. Some of the restrictions may result in a favorable combination of carbon storage and capital return deficiency, in which case the deficiency could be compensated in terms of a carbon rent [21]. There are many previous investigations discussing the economic feasibility of thinning practices [22–30]. Some of them also discuss carbon storage features [31–35]. However, a few studies contain deficiencies restricting their applicability. Common deficiencies are unrealistic assumptions regarding the yield of various timber assortments, as well as pricing assumptions not adhering with reality [35–39]. It also appears that the optimal number of thinnings, thinning intensity, as well as selection between continuous-cover forestry and clearcuttings, depends on the applied discounting interest rate [22–30]. The capital return rate in forestry has been investigate sparsely [16–20, 40, 41]. Results regarding the relationship of capital return rate and carbon storage are still more sparse [16–20]. Again, some of the available results are deficient due to unrealistic yield assumptions [15, 19]. Others have used financial boundary conditions not considered appropriate in this investigation [16, 20]. There is one earlier study discussing capital return rate deficiency per excess volume unit appearing with the intent of carbon storage where the financial boundary condition meets that one here considered appropriate [17]. That study, however, did not discuss eventual thinning restrictions in detail [17].

2. Materials and methods The two different sets of initial conditions have been described in three earlier investigations [15–17]. Firstly, a group of nine setups was created, containing three tree species and three initial sapling densities [17]. The idea was to apply the inventory-based growth model as early in stand development as it is applicable, to avoid approximations of stand development not grounded on the inventory-based growth model [14]. This approach also allowed an investigation of a wide range of stand densities, as well as a comprehensive description of the application of three tree species. The exact initial conditions here equal the ones recommended in [17], appearing there in Figs 8 and 9. The second set of initial conditions is here reported in more detail. The tree species distribution was not accounted for in previous publications [15, 16]. Within the seven wooded, commercially unthinned sample plots of age from 30 to 45 years, located in Eastern Finland, the total stem count varied from 1655 to 2451 per hectare. A visual quality approximation was implemented. The number of stems deemed suitable for growing further varied from 1050 to 1687 per hectare. The distribution of the basal area (cross-sectional area of all trees at breast height) of these acceptable-quality trees into tree species is shown in Fig 1; the basal area of the acceptable-quality trees varied from 28 to 40 m2/ha, in all cases dominated by spruce (Picea abies) trees. PPT PowerPoint slide

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TIFF original image Download: Fig 1. Distribution of basal area of acceptable-quality trees into tree species at seven sample plots. https://doi.org/10.1371/journal.pclm.0000008.g001 The growth model—the process model acting on the initial conditions—used in this study has been established in 2008 by Bollandsås et al. [14], based on a comprehensive forest inventory in Norway. The growth model has been applied in a variety of earlier investigations [15, 17, 42]. In this study, it is used exactly in the same form as in [17]. To clarify the capital return rate, a financial treatment is needed. We apply a procedure first mentioned in the literature in 1967, but applied only recently [16–20, 40, 41]. Instead of discounting revenues, the capital return rate achieved as relative value increment at different stages of forest stand development is weighed by current capitalization, and integrated. The procedure applies to forest estates of any distribution of site properties, but the result is stationary in time only if the stand age distribution within the forest estate is even. Assumption of even age distribution of stands within an estate corresponds to the “normal forest principle” [43], where any established stand setup or observed sample plot serves as a “normal stand” of an estate [16, 17, 19, 20]. Regeneration expenses are capitalized at the time of regeneration and amortized at the end of any rotation [17]. It is, however, not necessary to adopt the “normal forest principle” in the application of the financial theory [16–20, 40, 41]. This fundamental viewpoint is here presented as an addition to the theory. Instead of discussing an estate with a constant-valued density function of stand ages, let us discuss a single stand, observed at an arbitrary time. The momentary capital return rate is (1) where κ in the numerator considers value growth, operative expenses, interests and amortizations, but neglects investments and withdrawals. In other words, it is the change of capitalization on an economic profit/loss basis. K in the denominator gives capitalization on a balance sheet basis, being directly affected by any investment or withdrawal. One single observation of the stand at an arbitrary time however does not represent the expected value of the capital return rate within the stand. The expected value can be produced by integrating over the rotation as (2) where a is stand age (or time elapsed since the latest regeneration harvesting), and τ is rotation age. Now, however, time proceeds in a linear manner. Consequently, the probability density function p(a) is constant within the interval [0, τ]. Then, it becomes canceled from Eq (2). Further assuming real-valued prices and expenses, as well as growth functions, to be time-independent, the expected value of capital return rate becomes independent of time as (3) In other words, Eq (3) does not require the application of the “normal forest principle”. Finally, as the initial conditions and the growth process function have been established, as well as the objective function as the expected value of capital return rate, four sets of operative boundary conditions are applied. First, intermediate harvesting events (thinnings) are designed for any normal stand to maximize the capital return rate, without any restriction. Second, the number of thinnings is restricted to one. Third, the severity of any thinning is restricted by removing large trees only. A breast-height diameter limit of 238 mm is used. The fourth boundary condition consists of the omission of commercial thinnings. The three latter of the four boundary conditions defined above in general result as a deficient capital return rate, in comparison to the first (with no restriction). However, at the expense of a capital return deficiency, the magnitude of carbon storage may be increased.

5. Conclusions The results above indicate that restricting thinnings may result in significant additional carbon storage at a capital return deficiency in the vicinity of a Euro per excess commercial cubic meter of standing timber storage. Such a level of carbon rent [21] would be well in concert with the 2021 European carbon emission prices in the vicinity of 50 Eur per ton of CO 2 . Naturally, such climate benefits are achievable only if the carbon rent arrangements can be materialized. From the viewpoint of the society, an important finding is that restriction of thinnings as a means of increasing carbon storage does not jeopardize the wood supply of the relevant industries.

Supporting information S1 Table. Measurement data of trees on wooded stands. Koealan säde = experimental plot radius. Tila = estate name. Koealanro = experimental plot number. BA = basal area. Numerical tree species codes: 1 = Pinus sylvestris, 2 = Picea abies, 3 = Betula pendula, 4 = Betula pubescens, 5 = Populus tremula, 6 = other species. 10.1371/journal.pclm.0000008.s001 (XLSX)

Acknowledgments Prof. Dr. Lauri Mehtätalo is gratefully acknowledged for fruitful discussions.

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