Validation of saw log and technological wood assortment recovery and reduction predictions based on cut-to-length harvester data

Accurate information regarding the volumes of growing stock and its wood properties is essential for effective forest management and wood obtainment planning (Malinen et al., 2018). The assessment, based on pre-harvest spatially explicit growing stock assortments of standing wood volumes, becomes imperative in the selection of economically viable and spatially applicable cutting sites (Malinen et al., 2010). It is also crucial in the planning of timber logistics to optimize the flow of raw materials (Kankare et al., 2014). This information holds particular significance when employing the cut-to-length harvesting method (Kankare et al., 2014).

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 et al. (2019) and Kangur et al. (2007). However, the foundation for bucking simulation-based calculations of timber assortment recovery lies in the application of species-specific tree stem form and corresponding taper models for assortment distinction, as described by Malinen et al. (2018). Typically, these taper models are developed based on stem measurements of actual analysis trees (Bravo et al., 2019; Eastaugh et al., 2013). In this context, bucking involves the theoretical simulation of corresponding timber assortment diameters (either the minimal diameter or acceptable diameter range). Actual bucking, where analysis trees are cut to assortment length, occurs only in practical implementation. Literature sources indicate that assortment recovery is influenced not only by tree species but also by its specific average diameter, height, and various other factors, including diameter distribution (Siipilehto & Rajala, 2019), assortment length (Puumalainen, 1998), wood properties, defects (Malinen et al., 2018), and harvester operators (Malinen et al., 2007).

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 et al., 2009). However, the validation of these functions relies on real cut-to-length assortment measurement data. The widespread use of harvesters and thereafter the cut-to-length harvest methods has facilitated the availability of high-precision large datasets for this purpose.

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 et al., 2009). This bucking method has been consistently applied in various analyses, including estimating wood availability for substituting oil shale-based raw material with low-quality wood for energy production in power plants in the Narva region (Kask et al., 2011). The method has also been employed in comparing different management regimes under various nature protection scenarios (Sirgmets et al., 2011), analysing pulp and paper assortment recovery, and predicting reductions for roundwood market pricing studies (Sirgmets et al., 2011). Additionally, it has been used to assess management scenarios for hybrid aspen and silver birch plantations established on abandoned agricultural lands (Tullus et al., 2012) and to estimate the potentials and revenue loss of managed forest sites considered for new nature protection areas (Adermann et al., 2015).

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 et al., 2007). Notably, systematic deviations, either below or above the estimation, have been observed in the case of spruce and birch when comparing pre-harvest bucking with post-harvest cut-to-length data.

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 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.

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: (5) a,b,c=k+l⋅Bn+m⋅Bn2, a,b,c = k + l \cdot Bn + m \cdot B{n^2}, where

a, b, c – Equation 1 coefficient (one of them depending on the formula);

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.

Figure 3.

Figure 4.

Figure 5.

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 H₁₀₀ may be substituted for site index class, as it can be converted into a site index class using the equation provided in Annex 10 to the Forest Inventory Instruction (Metsa korraldamise juhend, 2009): (6) Bn=33.5−H1004, Bn = {{33.5 - {H_{100}}} \over 4}, where

Bn – site index class;

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 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

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.

Figure 12.

Figure 13.

Figure 14.

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.

Figure 15.

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.

Figure 16.

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 Vaccinium myrtillus pine forest in Finland (stand diameter 29.8 cm and height 24.7 m), Vastaranta et al. (2014) found a proportional recovery of 85.5% for saw logs and 14.5% for pulp-wood. The results placed Vastaranta et al. (2014) findings between Siipilehto & Rajala (2019) and the Estonian model. However, the study focused on a single sub-compartment, limiting the generalizability of the results. Kankare et al. (2014) tested terrestrial laser scanning (TLS) and a combination of TLS and airborne laser scanning (ALS) on the same Finnish area, but despite promising results, these methods still lacked accuracy compared to the current methods.

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 et al. (2010) studied cutting scenarios and observed different results for assortment recoveries. Figure 16 shows average saw log recovery for pine, spruce, and birch (a total of 1,399 pines, 2,061 spruces and 26 birches were measured in sample plots) according to Malinen et al. (2007), with detailed stem data producing reliable estimates (Table 7).

The stem quality database employed in Finland contains dimensional and quality information regarding trees harvested in specific thinning and final cutting stands (Malinen et al., 2018). In a previous study (Malinen et al., 2018), external tree defects were estimated, while internal quality was not assessed, resulting in a significantly smaller total saw log reduction of 11.7% for spruce. This current study incorporates actual log recoveries from cutting stands and considers internal defects, as depicted in Figure 3 (C) and Table 7.

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 et al., 2018). Despite testing stem taper curves, this study did not provide model tree dimensions. The absence of diameter values prompted the illustration of saw log recovery in Figure 16 with a red dotted line.

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 Tectona grandis L.f. stands in Brazil (Pelissari et al., 2017). This dataset represents the second thinning stage, enabling commercial volumes. The saw log recoveries observed in Brazil were found to be lower than those in Estonian conifers and grey alder but surpassed the saw log recoveries of other broadleaf trees. The result is presented in Figure 16 with a red plus sign.

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 et al., 2010). While this study delved into the impact of age and quality, it omitted an analysis of the correlation between the assortment recoveries under investigation and site type, harvester operators, and wood buyers. Concurrently, the influence of all these factors remains obscured within the resultant models.

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.