Accurate information regarding the volumes of growing stock and its wood properties is essential for effective forest management and wood obtainment planning (Malinen
All decisions related to forest management depend on stand-level characteristics, such as species-specific mean diameter at breast height (DBH) or basal area, mean height, and age, as documented by Bravo
In the evaluation of standing wood volumes, which is based on pre-harvest stand growing stock assortments, bucking is executed using species-specific generalized assortment calculation models. In these models, the differences between assortments, arising from damage or defects, are either incorporated based on inventory information or through an age-dependent reduction function (Padari
In the Baltic countries, the current methodology for dividing standing wood volume into roundwood timber assortments (including log, small-dimension log, pulpwood, firewood, and logging residues) has been in use since the adoption of the cut-to-length system in the 1990s, a practice implemented in Scandinavia over a decade earlier. The initial cut-to-length assortment functions in Finland were developed and published in 1982 (Nyyssonen & Ojansuu, 1982). In Estonia, the bucking models applied were documented in the analysis of growing stock assessment for comparing allowable stand-replacing cuttings (Padari & Muiste, 2003).
Enhanced bucking models, also employed in the current study, (Kinnisasja erakorralise hindamise kord, 2023) have been utilized for assessing wooden biomass availability in Estonia since 2009 (Padari
In the present day, approximately 98% of the cuttings conducted by the Estonian State Forest Management Centre (RMK) involve the use of harvesters (Kaivapalu, 2017). The implementation of the cut-to-length harvesting method in the 1990s has revealed a gradual realization that the existing volume correction-based bucking model does not accurately represent the practical bucking activities carried out in the field (Kangur
In the contemporary context, obtaining actual assortment bucking information is facilitated by real harvest measurements collected from cut-to-length harvester data. RMK has introduced a certified harvester for validating the machinery and operators of partners. Concurrently, a harvester data collection database has been implemented to compile genuine bucking data from across Estonia. For the current study, a dataset comprising real bucking data from RMK was utilized, covering clear-cuts conducted from 2011 to 2017 and encompassing pre-harvest conditions from over 27.5 thousand stand elements. While studies based on harvester bucking data are limited, some case studies, such as the one conducted in Finland by Siipilehto & Rajala (2019), using seven clear-cut sites, have explored comparisons between theoretical bucking and actual bucking.
The objective of this study is to analyse and validate the prevailing methodology employed in predicting saw log assortment recovery and reduction, utilizing cut-to-length harvester data.
The current method for timber assortment recovery, extensively elucidated by Padari Timber is categorized into diameter classes, determined as the ratio of a diameter class to the square mean diameter of a stand element (d/D). A relevant Finnish study emphasized the impact of diameter distribution on saw log and pulpwood recovery (Siipilehto & Rajala, 2019). However, due to the unavailability of diverse diameter distribution data, a uniform distribution was employed for all cases. Height is computed for each diameter class using a height curve derived from Prodan’s book (1965) and referred to as the Levakovic II function (Kiviste Assortment recovery is then calculated for each diameter class based on diameter and height values. The taper curve equation developed by Latvian researcher Ozolinš (2002; Silava, 1988), commonly used in Estonia for growing forest volume calculation, is employed. Padari (2020) has presented a mathematical algorithm for utilizing this taper curve to determine volumes of wood assortments. Subsequently, the bark proportion equation is applied to compute the diameters of assortments under the bark (Padari For saw log assortments, a selected length ranging from 3.1 to 6.1 m (0.3 m increment) is chosen, while pulpwood and firewood assortments are set at a fixed length of 3 m. Assortment distribution is carried out based on the small end diameter under the bark, determined using the taper curve equation. The specified assortment lengths and diameters are detailed in Table 2. Assorting begins with the widest assortment of the respective tree species and proceeds in descending order until the last assortment (Table 2). The assorting process initiates at stump height (one-third of the diameter at breast height, but not below 10 cm). The determination of a single assortment length involves the following considerations:
calculating the diameter at the height of the end of the last assortment (stump in the first case) to which the minimum length of the assortment was added; if the diameter was larger than the minimum diameter of the respective assortment, calculations with this assortment were continued (otherwise, the next assortment was selected, and step a) was repeated); performing a calculation cycle in which stem diameters were calculated by incrementing assortment length by assortment step until the stem diameter was shorter than the minimum diameter of the log. In this case, the assortment length applied in the diameter calculation that preceded the last calculation was used. If the stepwise increase in length reached the maximum assortment length, but the diameter still remained larger than the minimum diameter of the assortment, the calculation cycle was restarted. The minimum length applied was the twofold minimum length of the assortment, and the maximum length was the twofold maximum length of the assortment. If necessary, the cycle made use of multiple log minimum and maximum lengths until the stem diameter was smaller compared to the log minimum diameter. In accordance with the taper curve presented above, the volumes of the assortments were computed utilizing the integral method, as outlined by Ozolinš (2002) and Padari (2020).
The previously outlined methodology has been retained in the new model. However, as part of this project, the segment addressing the correction of assortment volume resulting from damage and bending underwent revision and replacement.
Historically, theoretical models for correcting assortment recovery in the context of damage and bending were employed. These models, as published by Padari
Following the determination of the proportion of damaged trees, assortment damage was rectified according to the methodology outlined by Padari The volumes of saw logs and pulp-wood were both multiplied by the proportion of damaged trees (depicted in Figure 1), resulting in theoretical volumes for the saw logs of the damaged trees (Vdam_log) and pulpwood (Vdam_pulp). The obtained results (Vdam_log and Vdam_pulp) underwent further adjustment by multiplying them by the coefficient 0.5, denoted as 0.5Vdam_log and 0.5Vdam_pulp, respectively. These adjusted volumes were then subtracted from the saw log or pulp-wood assortment and added to the firewood assortment. The saw log assortment volumes of the remaining damaged trees (0.5Vdam_log) underwent additional modification. Specifically, for pine, a multiplication factor of 0.5 was applied; for spruce, a factor of 0.75 was used, and for broadleaf trees, a factor of 1.0 was employed. The resulting volumes were subtracted from saw log assortments and added to pulpwood assortments. To account for trunk curvature, 5% of pine and spruce saw logs, 10% of aspen saw logs, and 25% of birch saw logs were adjusted, being transferred from the log assortment to the pulpwood assortment. Similarly, 25% of black alder and 50% of grey alder saw log volumes were relocated from the log assortment to the firewood assortment.
Data on assortments felled from clear-cutting areas were retrieved from the RMK for analysis. Clear-cuttings were carried out from 2011 to the first half of 2017. Only stand elements from the first layer were selected for analysis. However, the stand elements that included tree species represented also in the second layer or single-tree layer were neglected. This was done due to the fact that assortments of the same tree species were aggregated and thus, distributing obtained roundwood data between different layers proved impossible. All stand elements which had stand data but lacked felled assortments were also excluded from the analysis. Firewood was considered by tree species in several stands, but aggregated in a group named ‘mixed species’. Firewood volumes of the mixed tree species were weighted by a composition coefficient and divided to the stand elements.
In total, 27,514 felled stand elements were analysed, comprising 14,013 pine elements, 3,045 spruce elements, 7,145 birch elements, 1,862 aspen elements, 679 black alder elements, and 770 grey alder elements (Table 1). Only firewood was salvaged from stand elements of other tree species. These 27,514 analysed stand elements were distributed across 21,057 stands. The geographical distribution of the felled stands is depicted on a map (Figure 2).
General data on felled elements included in the analysis. Site index class and site index
Tree species | No. of elements | Age, years | Site index class | ||
---|---|---|---|---|---|
minimum | maximum | maximum | minimum | ||
Scots pine ( |
14,013 | 21 | 219 | 1A | 5A |
Norway spruce ( |
3,045 | 16 | 177 | 1A | 5 |
Silver and downy birch ( |
7,145 | 22 | 153 | 1A | 5 |
European aspen ( |
1,862 | 23 | 140 | 1A | 3 |
Black alder ( |
679 | 37 | 138 | 1A | 4 |
Grey alder ( |
770 | 18 | 75 | 1A | 4 |
Total | 27,514 | 16 | 219 | 1A | 5A |
Site index classes and site index
Site index |
Site index class | Site index class in calculations |
---|---|---|
< 11.5 | 5A | 6 |
11.5…15.5 | 5 | 5 |
15.5…19.5 | 4 | 4 |
19.5…23.5 | 3 | 3 |
23.5…27.5 | 2 | 2 |
27.5…31.5 | 1 | 1 |
> 31.5 | 1A | 0 |
To identify the assortments mentioned above, a table compiled based on round-wood parameters sourced from the RMK database was utilized, as presented in Table 3.
Parameters of timber assortments (roundwood) used in the analysis.
Tree species | Assortment | Top diameter, cm | Length, m | ||
---|---|---|---|---|---|
minimum | step | Maximum | |||
Scots pine | Log | 28–… | 3.1 | 0.3 | 6.1 |
Log | 23–28 | 3.1 | 0.3 | 6.1 | |
Log | 18–23 | 3.1 | 0.3 | 6.1 | |
Log | 13–18 | 3.1 | 0.3 | 6.1 | |
Log | 10–13 | 3.1 | 0.3 | 6.1 | |
Pulpwood | 5 | 3.0 | 3.0 | ||
Firewood | 3 | 3.0 | 3.0 | ||
Norway spruce | Log | 25–… | 3.1 | 0.3 | 6.1 |
Log | 18–25 | 3.1 | 0.3 | 6.1 | |
Log | 13–18 | 3.1 | 0.3 | 6.1 | |
Log | 10–13 | 3.1 | 0.3 | 6.1 | |
Pulpwood | 5 | 3.0 | 3.0 | ||
Firewood | 3 | 3.0 | 3.0 | ||
Silver and downy birch | Log | 14–… | 3.1 | 0.3 | 6.1 |
Pulpwood | 5 | 3.0 | 3.0 | ||
Firewood | 3 | 3.0 | 3.0 | ||
European aspen | Log | 14–… | 3.1 | 0.3 | 6.1 |
Pulpwood | 5 | 3.0 | 3.0 | ||
Firewood | 3 | 3.0 | 3.0 | ||
Black alder | Log | 18–… | 3.1 | 0.3 | 6.1 |
small log | 14–18 | 3.1 | 0.3 | 6.1 | |
Firewood | 3 | 3.0 | 3.0 | ||
Grey alder | Log | 18–… | 3.1 | 0.3 | 6.1 |
small log | 14–18 | 3.1 | 0.3 | 6.1 | |
Firewood | 3 | 3.0 | 3.0 |
In order to ensure comparability of the data, the results of all elements were converted to percentages, ensuring that the total of logs, pulpwood, and firewood equalled 100. This conversion was applied both to the results obtained through the described methodology and to the actual felling volumes obtained from RMK.
Additionally, the minimum diameters of spruce and pine logs in use at the respective felling areas were monitored. Theoretical assortment volumes for each stand were calculated based on the dimensions of assortments cut in the corresponding stand. For instance, if pine assortments in the database had a minimum diameter of 18 cm, smaller diameter log assortments were categorized as pulpwood to enable a comparison between actual and theoretical assortment volumes.
Two correction models were formulated for each tree species: 1) a firewood increase model and 2) a log volume reduction model.
Initially, an appropriate form for the regression equation was sought to conduct the modelling. The following equation was selected as the primary equation for regression:
Δ
To find coefficients Δ
To find coefficients
The equation parameters derived from the regression analysis conducted using the data collected from RMK are presented in Table 4. Equation 2 was utilized in the regression analysis.
Equation parameters obtained by comparing roundwood assortment volumes.
Tree species | Assortment | p-value | |||||||
---|---|---|---|---|---|---|---|---|---|
Scots pine | Log volume reduction | −0.4560 | −6.7947 | −46.8016 | 99 | 100 | 1 | 0.0356 | < 0.0001 |
Firewood increase | 2.7817 | 1.0015 | 267.0156 | 99 | 100 | 1 | 0.0233 | < 0.0001 | |
Norway spruce | Log volume reduction | 0.2145 | 6.7871 | −0.0656 | 1 | 20 | 1.1 | 0.0158 | < 0.0001 |
Firewood increase | −3.1086 | 17.2571 | −91.9444 | 49 | 50 | 0.1 | 0.0195 | < 0.0001 | |
Silver and downy birch | Log volume reduction | 1.0622 | 9.1595 | 0.3487 | 10 | 50 | 1 | 0.0945 | < 0.0001 |
Firewood increase | 0.1733 | 3.2363 | 0.0063 | 0,1 | 1 | 1 | 0.0052 | < 0.0001 | |
Veneer log | −3.6396 | 10.4272 | −2.6481 | 10 | 20 | 0.1 | 0.1445 | < 0.0001 | |
European aspen | Log volume reduction | 1.0522 | 12.6587 | 15.8415 | 49 | 50 | 1 | 0.1991 | < 0.0001 |
Firewood increase | −1.0607 | 28.4761 | −0.0969 | 0.1 | 0.2 | 0.1 | 0.0381 | < 0.0001 | |
Black alder | Log volume reduction | 0.6106 | 22.1975 | −0.0837 | 1 | 2 | 1 | 0.0789 | < 0.0001 |
Grey alder | Log volume reduction | −6.106 | 12.485 | −61.485 | 90 | 100 | 1 | 0.0353 | 0.0257 |
Note.
The error encountered in the regression equations stemmed from instances where certain young stand ages (where initial data were absent) led to the production of negative results. Consequently, a novel model was devised to yield logical outcomes even for young stands, replacing negative results with zeros. This involved utilizing Equation 1 to compute results separately for each site index class across ages ranging from 1 to 200 years. Subsequently, all negative values were adjusted to zero. Regression analysis was then conducted for each age class (Equation 4). While the specifics of the regression results are not elaborated upon here, it is noteworthy that the determination coefficients approached unity (R2 > 0.99) across all cases. The following relationships between the model coefficients (a, b, c) and the site index class were established, employing a square parabolic function to depict the association:
The parameter
Tree species | Formula | Constant | Equation coefficients | |||
---|---|---|---|---|---|---|
Scots pine | log volume reduction | a | −2.259 | 0.24693 | −0.01345 | 3 |
b | 11.35752 | −2.10076 | 0.1712 | |||
c | 894.235 | −304.766 | 28.869 | |||
firewood increase | a | −3.3503 | 0.0159 | −0.0013 | 2 | |
b | 1.5375 | −0.0271 | 0.0022 | |||
c | 1.5328 | −0.0261 | 0.0021 | |||
Norway spruce | log volume reduction | a | −0.89371 | −0.13886 | 0.01049 | 4 |
b | 29.4603 | 4.36432 | −0.33114 | |||
c | −366800 | −228124 | −4093 | |||
firewood increase | a | −1.66542 | −0.06081 | 0.0012 | 4 | |
b | 29.59224 | 0.27817 | 0.09189 | |||
c | −115756 | −24063 | 89.533 | |||
Silver and downy birch | log volume reduction | a | −0.39607 | 0.06595 | −0.0032 | 5 |
b | 28.784 | −1.088 | 0.042 | |||
c | 3829316 | 885112 | 80082 | |||
firewood increase | a | −1.67591 | 0.01012 | −0.00097 | 4 | |
b | 25.21899 | −0.21777 | 0.02076 | |||
c | −211985 | 7782.9 | −749.88 | |||
veneer block recovery | a | −2.7282 | −0.2457 | −0.0683 | 4 | |
b | 30.281 | 12.921 | −1.639 | |||
ln(-c) | 12.655 | 0.8226 | 0.2254 | |||
European aspen | log volume reduction | a | 0.09015 | 0.01429 | −0.00061 | 4 |
b | 27.49482 | −0.06593 | −0.01049 | |||
c | −150369 | 7285 | −387 | |||
firewood increase | a | −1.34789 | −0.01386 | 0.0011 | 5 | |
b | 46.31225 | 0.04688 | −0.00447 | |||
c | 10507971 | 920148 | −82200 | |||
Black alder | firewood increase | a | 0.1209 | −0.09111 | 0.01198 | 10 |
b | 73.66109 | −4.70172 | 0.78866 | |||
c | −2.703·1015 | −5.258·1015 | 6.974·1014 | |||
Grey alder | firewood increase | a | −0.82187 | −0.30129 | 0.00434 | 7 |
b | 58.03680 | −0.13325 | 5.87003 | |||
c | 3.048·1011 | −2.887·1011 | 4.242·1012 |
Consequently, the site index class serves as the basis for determining coefficients a, b, and c when applying Equation 5. Subsequently, volume variation is calculated using Equation 3, which is contingent upon age.
Figures 3 to 5 describe the results of the equations obtained with regression analyses. Figure 3 graphically illustrates the models created for correcting the stand element assortment of pine, spruce, birch and aspen, and Figure 5 that of black alder and grey alder. The parts A, C, E and G of Figure 3 are for log volume reduction (by considering injuries, curvatures and other defects) and the parts B, D, F and H are for increasing the volume of firewood. The amount of pulpwood is obtained by subtracting the volumes of logs and firewood from the total volume of the assortments.
Although log assortments are reduced after removing defects, not all of them qualify for firewood. In addition, there is Figure 4 which describes the birch veneer log recovery. The veneer logs were mostly cut from IA site index class forests, but also to a small extent from I and II site index class birch forests. Thus, it is not reasonable to calculate veneer logs for birch forests of the site index class III or lower.
In the application of correction equations, the variable
In this context, employing integer values for site index class becomes redundant; instead, it is advisable to utilize site index class, preferably as decimal numbers.
Based on data from RMK, only firewood had been harvested from all stand elements where other tree species were present; hence, this study did not develop the correction equation for other tree species.
In order to compare the old and new assortment models, both were compared against actual logging data, utilizing stand elements with a minimum volume of 25 m3/ha in the sample. Assortment volumes and the discrepancies between these volumes and the actual assortments were computed for both models. The outcomes of the three scenarios (actual, old model, and new model) are depicted in Figures 6–11 for Scots pine, Norway spruce, birch species, European aspen, black alder, and grey alder, respectively. These figures delineate the results by diameter class, incorporating the distribution of diameters, as well.
Figure 12 presents a comparison of log, pulpwood, and firewood assortment outputs calculated using both the old and new models for Scots pine and Norway spruce species, while Figure 13 illustrates the comparison for birch species and European aspen using the initial dataset. Additionally, Figure 14 depicts the disparities in log and firewood volumes of assortments calculated using both the old and new models from the initial dataset for black alder and grey alder.
In the analysis, model prediction residuals were computed for both the old and new model. The arithmetic means of these residuals, expressed as percentages, are presented in Table 6, and the same information is graphically depicted in Figure 15.
Average model residuals for different models for calculating assortment volumes by tree species.
Tree species | Assortment | Average model residuals, % | |
---|---|---|---|
old model | new model | ||
Scots pine | saw log | 6.74 | −0.01 |
firewood | −1.33 | −0.82 | |
Norway spruce | saw log | 7.78 | 2.40 |
firewood | −3.67 | −2.55 | |
Birch species | saw log | 11.83 | 1.23 |
firewood | 2.21 | −0.16 | |
European aspen | saw log | 0.75 | 0.42 |
firewood | 22.48 | −2.34 | |
Black alder | saw log | −17.98 | −7.84 |
Grey alder | saw log | −33.45 | −2.99 |
The comparative data in Table 6 and Figure 15 clearly demonstrate that the new model provides better description of the actual assortment outcomes when compared to the old model.
Figures 6–11 provide a comparison of models for different tree species, namely Scots pine, Norway spruce, birch spp. (downy and silver birch), European aspen, black alder, and grey alder. In Figure 6, it can be observed that the new model for pine yields more accurate results in assortment distribution when the stand diameter ranges from 10 to 40 cm. Below 10 cm, both models significantly underestimate log output, but the old model provides slightly more accurate estimates. Conversely, for stand diameters exceeding 40 cm, the models overestimate log output, with the old model overestimating less than the new model.
The comparison of models for spruce (Figure 7) and birches (Figure 8) assortment output indicates that the new model provides more accurate estimates for log output in the 10–30 cm diameter range. Similar trends are observed for other diameter ranges, as seen with pine. The comparison of models for aspen assortment output (Figure 9) reveals that the distribution calculated by the new model is much more accurate than that obtained from the old model, and closely aligns with actual results for stand diameters ranging from 10 to 60 cm. For stands with diameters below 10 cm, the old model overestimates log and pulpwood output, while the new model underestimates log output and overestimates pulpwood output.
The comparison of output for black alder assortments (Figure 10) demonstrates that the new model underestimates log output for stand diameters between 20 and 40 cm, whereas the old model underestimates log output even more. For stands with diameters between 10 and 20 cm, the new model underestimates log output more than the old model. In the case of grey alder (Figure 11), the new model overestimates log output for stands with diameters between 20 and 30 cm, performs reasonably well for diameters between 10 and 20 cm, and underestimates output for diameters below 10 cm. The old model yields almost negligible log output for all stand diameters.
Given that the mean diameter of mature stands generally lies within the 20–40 cm range, the novel model yields more precise assortment output calculations in comparison to its predecessor. Additionally, as illustrated in Table 6 and Figure 15, the new model more effectively characterizes the real assortment outcomes than the outdated model.
Several scientific articles, including the current work, have focused on stand diameter and height data analysis. This study aims to calculate the proportion of sawlog output in relation to the sum of all assortments, allowing for a comparison with a previous Finnish study by Nyyssonen & Ojansuu (1982) (Figure 16). The figure illustrates differences between the Estonian and Finnish models, particularly in the diameter range of 20–25 cm, where the Estonian model estimates higher log output for smaller diameter stands and lower for larger diameter stands compared to the Finnish model.
Siipilehto & Rajala (2019) conducted a study adjusting diameter distributions for each stand individually, resulting in precise saw log and pulpwood recoveries. The comparison with the Estonian model (Figure 16) indicates higher pine and spruce saw log recoveries in the Finnish study. These differences may originate from stem defects and rots more prevalent in Estonia.
In a 75-year-old 3 ha
Puumalainen (1998) studied the theoretical dependence of assortment recovery on minimum diameter and length values. They found that shortening the minimum saw log length had a greater impact on saw log recovery than reducing diameter. The new Estonian model represents actual saw log recovery, considering variations in saw log lengths based on orders. For most data, it is unknown which cuttings were carried out according to which orders. This is the reason why using different saw log lengths is a supplementary factor increasing recovery divergence.
Malinen
Saw log proportion reduction.
Tree species | Age used in the Estonian model | Malinen |
Estonian model (Figure 3) | ||
---|---|---|---|---|---|
MELA-96 | MELA-05 | Bucking simulation | |||
Pine | 60–100 | 16.04 | 24.25 | 18.17 | 9–28% |
Spruce | 60–80 | 2.35 | 17.79 | 6.38 | 10–29% |
Birch | 50–70 | 30.27 | 29.35 | 41.46 | 38–64% |
The stem quality database employed in Finland contains dimensional and quality information regarding trees harvested in specific thinning and final cutting stands (Malinen
For context, a brief comparison with tree species from other regions is presented. A study in Brazil examined 30 Japanese cedars in a plantation, revealing saw log, pulpwood, and firewood recoveries of 66.1%, 32.0%, and 1.9%, respectively, out of all roundwood assortments (Sanquetta
In another analysis, a dataset of 1,038 trees was utilized to fit taper models and estimate saw log and firewood volumes in 273 plots within eight-year-old
It would be intriguing to compare developed models with practical bucking outcomes. However, owing to variables impacting the actual assortment recovery, the dataset should encompass a representative sample of diverse stand types, harvester operators, and wood buyers. Acquiring such extensive data poses significant challenges (Malinen
In conclusion, the practical applicability of the assortment recovery model developed in this study can be assessed. However, it is essential to acknowledge that over time, the dimensions of timber and veneer log have undergone changes. With the adoption of newer technologies, the diameters of timber logs have progressively decreased. Sawmills now purchase logs with diameters as small as 8–10 cm, while the plywood industry starts from 16-cm-wide logs. Additionally, quality criteria for logs have been reduced. Some sawmills, for instance, cut boards from curved logs, with saws following the curvature of the log. The boards obtained through this method, known as curve sawing, straighten during stacking and drying. All such changes impact the output of logs from the forest. Therefore, periodic studies are necessary to calculate the proportions of log assortments under these evolving conditions.
In modern harvesting operations, the diameters, lengths, and assortment names of all trees are measured. It would be wise to compile detailed data and use it not only for assortment recovery studies but also for various other data analyses.
The steps for programmers to utilize the developed model are outlined in the Appendix 1.