Wood energy fuel cycle optimization in beech and spruce forests

During the initial stages of this research, relevant analytical boundaries were established. These included: the wood species analysed, the region of production, the harvesting method employed and the destination of the wood produced. In the interests of preparing a simple, yet relevant model we settled on the analysis of high beech and spruce forests, grown in the Swiss Mittelland. Regionally, wood production in Switzerland is separated into five regions with the dominant region being the Swiss Mittelland (or Plateau). This region encompasses the plain to the north of the Alps, extending from Geneva in the south-west through the populated Zurich and Bernese regions into the Appenzell region bordering Austria in the north-east. The Plateau generates 2.90 Mm³ of wood products [23] including 41% of total Swiss wood energy production [22]. In all regions in Switzerland, high forests are dominant [36].

Wood production (thinning) characteristics of a single forest stand of one hectare were acquired from the Swiss Federal Institute for Forest, Snow and Landscape Research (WSL) permanent plot yield tables [37–39]. The yield table describes the growth of high timber forests located in the Swiss Plateau region at altitudes of 400–1000 m.a.s.l. during a growth period of ∼120 yr. The tables give the density of the stand every 10 yr in the entire rotation period of the forest. In addition to the thinning tables, additional tables provide information on the remaining trees in the forest after each thinning episode. Adding the two tables together, it was possible to calculate total tree numbers at the beginning of, and during, the cycle. The production and thinning processes used in this work were based on yield tables for beech and spruce forests of average and high quality. In forestry terminology, these forests are classified as having site index of H₁₆ and H₂₂ respectively. Site indices H₁₆ and H₂₂ describe average and high forest stand growth conditions, respectively.

Wood products are defined by their potential usage and these can be specified by diameter. Using assumptions based on Swiss commercial standards for beech and spruce [40–44] we dimensionally classified the wood according to its usage profile (table 1). Roundwood is suitable for industry and construction purposes. Primary fuel wood derives from both fuel stem wood and branches. Branch sections having diameter greater than 7 cm are classified as primary fuel wood. Smaller branch material (e.g. twigs) is classified as secondary fuel. Utilizing available data [36, 45], good quality and high quality beech were found to constitute 41.1% and 55.4% of all beech in the Swiss Mittelland. The quality of spruce in the Mittelland is estimated to be extremely high, with H₂₂ contributing 94.3.

To assess the potential of FCO, separate models characterizing both single trees and a typical forest stand were required. The single tree (micro) model was used to quantify the production of round wood, fuel wood, bark and chips (as well as waste) from trees of user-defined diameter. The forest stand (macro) model incorporated output from the individual single tree models. Based upon stock levels and thinning operations, the stand model enabled production per hectare (m³ ha⁻¹) to be quantified.

2.2.1. Single tree model.

The single tree model was developed to calculate the total volume of a tree (stem, branches and twigs), with and without bark. Our initial premise was to utilize a conical taper model to determine the volume of stem intervals (V_i), with and without bark. Primary inputs to the model were diameter at breast height (d_b), in centimetres, and total height (h_t), in metres. Existing work in this area includes assessments of average [46] and diameter dependent [40, 47] bark percentage by species.

The method employed in this letter evolved from an existing method. The Lemm method describes a taper function with and without bark for a given tree species as a function of tree height and breast height, d(h_t,d_b) [48]. These diameters were then used to determine the volume of a user-defined beech tree with and without bark. However, estimates of the volume of the tree without bark were found to be unrealistically low. The bark volume estimate used by Lemm derives from the tree diameter without bark, which is a function of a percentage bark fraction. In this method, the term is diameter independent. That is, the formula returned a fixed bark percentage for a given height, regardless of the diameter of the tree. (i.e. both small trees and large trees exhibited the same bark fraction at a selected height). This led to an underestimation of the calculated bark fraction for small trees.

In consultation with Lemm, it seemed more appropriate to reparameterize the bark terms in the formula. Single large trees (d_b ∼ 60 cm) were modelled and their percentage bark versus diameter was plotted and parameterized as a function of diameter. This new function was then used as a guide to determine bark percentage at a given diameter, rather than for a given height. The beech bark function was fitted using third order polynomials, while the spruce bark function was fitted using a second order polynomial. Coefficients of the parameterizations are given in table 2.

Table 2.  Coefficients of the reparameterization of the bark terms in the taper model.

	a1	a2	a3	a4	db range (cm)
Beech fbark (db)	0.000 0359	−0.002 7104	−0.055 4414	8.156 0223	2–60
Spruce fbark (db)	−0.000 33	−0.079 21	10.307 49	—	2–55
Spruce fbark (db)	0.0126	−1.544 84	51.6037	—	55–60

Applying the new bark parameterizations, a modified version of the taper function was used to calculate the volumes of a series of stem intervals, with and without bark. The sum of the intervals gives the total volume of the stem and its bark fraction. Interval volumes were calculated using the volume formula of a truncated conical section. During methodology development, the height interval used for each truncated section (δh) was 10 cm. Intervals were summed from the base of the tree up to a user-defined reference height. This height was estimated using the SILVA 2.2 single tree simulator [49] and represented the base height of the branches, otherwise known as the crown height (h_crown). In this work h_crown is determined as a function of h_t, d_b and species and location dependent constants c_1–3, such that

$$\begin{eqnarray*} &&{h}_{\mathrm{crown}}({h}_{t},{d}_{b})={h}_{t}(1-{\mathrm{e}}^{({c}_{1}+{c}_{2}({h}_{t}/{d}_{b})+{c}_{3}{d}_{b})}) \end{eqnarray*}$$

c₁ =− 0.5478 ± 0.0229; c₂ =− 0.1094 ± 0.0158; c₃ =− 0.0023 ± 0.0003.

Using h_crown as the maximum height of the stem it was possible to calculate the volume of a series of truncated conical sections (V_i) from the ground up to h_crown. The sum of the section volumes gave the stem volume V_stem. The same procedure was performed for bark free conical sections. The volume difference between each of the two sections was calculated, from which the volume fraction of bark (%bark_vol) in each section was determined.

$$\begin{eqnarray*} &&{V}_{\mathrm{stem}}={\mathop{\sum }\nolimits }_{h=0}^{{h}_{\mathrm{crown}}}{V}_{i}(\delta h) \end{eqnarray*}$$

$$\begin{eqnarray*} &&{V}_{i}=\frac{\pi }{3}h({r}_{1}^{2}+{r}_{1}{r}_{2}+{r}_{2}^{2}). \end{eqnarray*}$$

Revision of existing literature and consultation with experts did not reveal any direct methods for estimating the bark fraction of the branches (diameter > 7 cm) or twigs (diameter < 7 cm). However, the Brassel–Lischke method models the volume relationship between stem wood, branches and twigs [50]. For each species, Brassel–Lischke incorporates regression coefficients (k₁ and k₂) that describe the volume relationship of branches and twigs to a corresponding stem (table 3). These constants are representative of beech and spruce trees in the Swiss Mittelland [42, 50]. Based on assumptions made in the Swiss National Forestry Inventory, spruce trees are considered not to have branches of >7 cm diameter, and therefore no coefficients exist [50].

Table 3.  Branch and twig regression coefficients for beech and spruce.

	Branches		Twigs
	K1	K2	K1	K2
Beech	−5.990 3924	0.101 889 09	−0.759 6139	0.033 555 23
Spruce	—	—	−1.206 1326	−0.019 1865

Utilizing this method, the volume of the branches was calculated as follows

$$\begin{eqnarray*} &&{V}_{\mathrm{branches}}({d}_{b})=\left(\frac{\omega }{1+\omega }\right){V}_{\mathrm{stem}} \end{eqnarray*}$$

where ω is equal to:

$$\begin{eqnarray*} &&\omega ={\mathrm{e}}^{{k}_{1}+{k}_{2}{d}_{b}}. \end{eqnarray*}$$

Combining the modified taper function and the Brassel–Lischke method the total volume of a typical tree as a function of its height and d_b can be determined as follows:

$$\begin{eqnarray*} &&{V}_{\mathrm{total}}({h}_{t},{d}_{b})={V}_{\mathrm{stem}}+{V}_{\mathrm{branches}}+{V}_{\mathrm{twigs}}. \end{eqnarray*}$$

In the absence of empirical or modelled data, the bark fraction in the branches was taken as the average of percentage bark volume (%bark_vol) in the tree section ranging from crown height to the point where the taper thins to 7 cm. The volume of the bark fraction in the twigs was taken as the average of %bark_vol in the taper section from 7 cm to the apex. As such, the volume with and without bark for each tree segment (stem wood, branches and twigs) can be determined as a function of h_t and d_b. By summing each segment, the total bark and wood fractions can be quantified.

Based upon assumptions given in section 2.1 the entire volume of the tree can be allocated to one of the following usage profiles: stem wood, fuel wood (stem and branch), bark and chips. For each profile the wood and bark volumes can be modelled, and as such, the total volume of wood and bark for a given tree can be estimated. In total 18 trees with d_b ranging from 2 to 60 cm were modelled, with δh, the height interval, set to 1 m. During methodology preparation, comparisons of δh set at 10 cm and 1 m were made and the stem volume variance was found to be less than 1%. The characteristics of these trees were used to prepare the forest stand model and are presented in section 3.1.

2.2.2. Forest stand model.

Estimates of the total volume of beech and spruce trees in the range 2–60 cm were generated. Each diameter class was apportioned, by volume, into one of the four usage profiles (figures 1(a) and (b)). For both beech and spruce trees, the smallest trees (2–6 cm d_b) contribute solely to the chip/waste profile. Trees from 10–22 cm (beech) and 10–14 cm (spruce) d_b are predominantly used as fuel wood. For d_b of 25 cm (beech) and 18 cm (spruce), trees are suitable for construction (e.g. lumber) use and contribute to the roundwood profile. For beech trees, a second regime of fuel wood production can be attributed to fuel coming from the branches. As such, fuel stem wood (F_sw) dominates the volume contribution to fuel wood for trees having diameter less than 41 cm while for trees of larger diameter, fuel wood is primarily sourced from branches (F_b). For spruce trees, all branches are considered to have diameter less than 7 cm and are corralled into the chips/waste supply chain. As such, spruce fuel wood production is derived solely from F_sw.

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Analysis of bark production with respect to fuel wood produced by single trees confirms the existence of two bark production regimes in beech trees and one production regime in spruce trees. For a single beech tree (H₂₂), the percentage of fuel wood bark is at a minimum at the intersection of the two fuel wood regimes, d_b ∼ 41 cm (figure 2(a), upper panel). Fuel wood bark is comprised of bark from stem wood (B_sw) and bark from branches (B_b). For a H₁₆ beech tree, the minima (or rather a shoulder) occurs at d_b ∼ 32 cm (figure 2(a), lower panel). Spruce trees do not exhibit explicit minima. However a region of minimal bark production exists from 35 to 50 cm d_b for H₂₂ and from 30 to 50 cm for H₁₆ classed spruce. These minima were used as guide for optimizing the fuel wood production.

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The tendency of these species to produce less fuel wood bark at a certain point in their lifetimes was analysed to find optimum conditions for reducing the bark fraction. Utilizing the combined single tree and stand models, the production of wood and bark for each of the profiles was determined for beech and spruce trees. As an example, the absolute production (m³) of roundwood, fuel wood and fuel wood bark for beech H₂₂ is reported in table 6. The upper section shows the original production, based on the yield tables, while the lower section shows the results of the optimizing the thinning to reduce bark. As far as was possible, absolute production of fuel wood was held constant during the optimization process. For the case presented in table 6, this led to a 7% reduction in bark fraction. The bark reduction was calculated as a weighted average of the production. Applying the same method, bark reductions of 13.1% were found for the beech H₁₆ stands, while spruce H₂₂ and H₁₆ exhibited reductions of 0.5% and 3.6% across the cycle. A positive side effect of the optimization process is an ∼340% increase in round wood production. We believe that this change has the potential to increase the carbon storage potential of forests managed in this way. In fact, the extension of forest cycles and corresponding increases in forest density has been shown increase carbon storage [51, 52]. Further, increasing the availability of sustainably grown wood for production purposes, particularly as a substitute for alternate materials (e.g. concrete), has been shown to have significant lifecycle benefits [53].

The values presented in table 6 summarize the production curves shown in figure 3. Figure 3(a) shows a single mode of production for roundwood and the now expected dual production mode of fuel wood. Alternatively, figure 3(b) shows the single productions modes for both roundwood and fuel wood from spruce, with the majority of fuel wood produced by trees having d_b less than 20 cm.

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For each of the tree species, the initial inputs for the dynamic thinning model were the original starting values (tree numbers) of each of the cycles. These were manually adjusted and fine tuned to find the minimum value of the bark production for each cycle. Examples of the influence of the original and optimized thinning processes upon beech fuel wood and fuel bark are shown for cycles C₁ and C₅ (figure 4(a) and (b)). Fuel wood production in cycle C₁ is initially in the d_b range 10–30 cm, as is the bark production. Varying the thinning strategy so that the majority of remaining trees are thinned at d_b between 20 and 40 cm leads to an 8% reduction in the relative production of bark.

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Applying the same method to C₅, a significant shift to the right in fuel wood production was observed. This led to a 5% reduction in bark fraction. Similar analysis was conducted for beech and spruce (H₁₆ and H₂₂) cycles, the results of which are summarized in figure 5.

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Bark reduction due to FCO for each of the beech and spruce stands is presented in figure 5. Significant differences between beech and spruce are immediately apparent. Beech responds well to FCO while spruce was found to be less sensitive. Comparing beech H₂₂ and H₁₆, it is clear that the lower quality H₁₆ benefits most from FCO. This of some importance, given that a not insignificant volume of Swiss fuel wood is derived from beech H₁₆ stands. A similar relationship exists between the spruce coming from H₂₂ and H₁₆ stands. The different responses of beech and spruce to FCO should be taken into account when considering which fuels have the potential for lower emissions. Generally, for RWC, hardwoods are preferential to softwood and they also exhibit lower emissions [54]. As such, FCO complements the existing support for the use of hardwood RWC fuels.

Further analysing figure 4, the differences between, for example, C₁ and C₅ can be explained as follows. For C₁, production lies to the left of the 41 cm optimum, while for C₅, the production is distributed fairly evenly around this diameter. For C₁, the distribution provides space to shift production to the right and the significantly lower bark production regime. For C₅, the distribution is already centred around d_opt and, as such, only limited gain can be had by shifting production to the right. In summary, forests with dominant fuel wood allocations are most responsive to FCO (e.g. beech H₁₆).

Extending the concept beyond the beech and spruce cases discussed here, FCO could also be applied to forest stands solely grown to produce fuel wood. In the Swiss case however, no such plantation forests exist. However, in other countries, forests that solely produce fuel wood and are characterized by short forest cycles do exist (e.g. Italian beech coppice with 10–30 yr cycles) [55]. In principle FCO could be extended to, and would well suit, these solely fuel producing rotation forests. Additionally, FCO could be applied to fuel wood plantations (short rotation); these are relatively widespread throughout Europe. Given the standardized management techniques employed in plantation forests, applying FCO would be simpler than for natural forests. These applications of FCO could be extended throughout continental Europe and North America. Further, FCO could be further applied to Swiss forests where stem defects exist. In this case, entire tree stems are downgraded to fuel quality wood [41, 44] and these could be managed similar to fuel wood plantation forests. Finally, combining cleaner fuels, modern combustion appliances and after-treatment devices leads to a comprehensive emission reduction suite (and lowest possible emissions).