Comparing model-based approaches with bucking simulation-based approach in the prediction of timber assortment recovery

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1 Comparing model-based approaches with bucking simulation-based approach in the prediction of timber assortment recovery JUKKA MALINEN *, HARRI KILPELÄINEN, TEPPO PIIRA, VISA REDSVEN, TAPIO WALL and TUULA NUUTINEN The Finnish Forest Research Institute, Joensuu Research Unit, PO Box 68, FI Joensuu, Finland *Corresponding author. Summary The aim of the study was to compare model-based approaches in the prediction of timber assortment recovery with bucking simulation based on detailed stem data. A correction function for the total length of saw log fragments and two optional saw log reduction models, that is, the MELA96 version and MELA05 version, were applied. In the bucking simulation, the volumes by timber assortments were calculated using a bucking-to-value simulator. The prediction of saw log recoveries varied between the bucking simulation and different versions of saw log reduction models. The level of the reduction from the MELA96 version was at the same level as from the bucking simulation where defects were taken into account, but the saw log reduction had a very low variance due to a small amount of independent variables. The saw log reduction of the MELA05 version included more variation although the level of the reductions was higher and the variation did not meet with the bucking simulation. As a conclusion, the model-based approaches seem applicable at least for the prediction of saw log recovery in the large area forest inventories where the variance of the standwise timber assortment recoveries need not be predicted. Introduction Detailed information on wood resources of commercial value is needed when evaluating different harvesting and timber sale options economically (e.g. Maness and Adams, 1991 ; Gobakken, 2000 ; Arce et al., 2002 ). Timber assortment recovery and value predictions are valuable for the forest management planning, timber selling and timber supply chain management purposes. In Finland, different approaches have been applied in the prediction of timber assortment recoveries from cut-to-length harvesting, applied both in thinning and regeneration cuttings. Approaches include timber assortment recovery modelling ( Nyyssönen and Ojansuu, 1982 ; PMP-ohje, 1987 ; Maltamo and Uuttera, 1994 ; Kangas and Maltamo, 2002 ), non-parametric estimation based on existing stem databases including timber assortment recoveries ( Tommola et al., 1999 ; Institute of Chartered Foresters, All rights reserved. Forestry, Vol. 80, No. 3, doi: /forestry/cpm012 For Permissions, please journals.permissions@oxfordjournals.org Advance Access publication date 11 June 2007

2 310 FORESTRY Weijo, 2000 ; Malinen et al., 2001 ) and bucking simulation of individual stems ( Ahonen and Mäkelä, 1995 ; Väätäinen, 1998 ; Malinen et al., 2001 ; Malinen, 2003 ). The last method produces most accurate estimates for specific stands when detailed data on stand or stems are collected, for example, during pre-harvesting inventory. However, non-parametric estimation is applicable only when and where stem databases exist. Although bucking simulation based on detailed stem data including information on the stem defects and their heights would provide accurate prediction on the timber assortment recoveries, this kind of data is seldom available. Pre-harvest measurements are laborious and expensive, and stem databases collected during harvesting include no information on the defects. The defects have a considerable effect on the bucking and timber assortment recoveries and the effect of defects should be considered while predicting the timber assortment recoveries. Due to cost-efficiency requirements in forestry, there is pressure to replace detailed pre-harvest measurements with new remote sensing technology, such as air-borne laser scanning (e.g. Næsset, 2002 ; Maltamo et al., 2006 ) producing either stand-level or stem level data. With remote sensing, it is impossible to detect all stem or stand defects, which is needed in detailed bucking simulation and timber assortment recovery models comprise only rough methods such as reduction factors ( Vähäsaari, 1988 ; Mehtätalo, 2002 ) or a modelling error ( Kangas and Maltamo, 2002 ) in order to take into account defects. There is need to improve methods in the prediction of timber assortment recovery. The aim of the study was to compare modelbased approaches in the prediction of timber assortment recovery with bucking simulation based on detailed stem data in order to evaluate the potential of model-based approaches for the remote sensing-based forest inventory in the conditions where cut-to-length harvesting is applied. In the bucking simulation, the volumes by timber assortments were calculated using a bucking-to-value simulator which maximizes the value of each stem based on the dynamic programming approach (e.g. Näsberg, 1985 ; Ahonen and Mäkelä, 1995 ; Puumalainen, 1998 ) and the stem volumes were calculated using taper curve models as a function of the tree species, the breast height diameter and the height of the trees ( Laasasenaho, 1982 ). In addition, measured external defects were taken into account when bucking the stems. The model-based prediction was implemented in the MELA system ( Siitonen et al., 1996 ; Redsven et al., 2005 ) which is widely used in Finland as a forest management planning system. In the MELA system, the prediction of volumes by timber assortments was based on the same taper curve models as in the bucking simulator. In addition, the total length of saw log fragments was corrected using empirical piecewise correction functions. There were two saw log reduction models examined: the MELA96 version ( Hynynen et al., 2002 ; Redsven et al., 2005 ) and MELA05 version ( Mehtätalo, 2002 ; Redsven et al., 2005 ). Study material and methods Study material The study material consists of 87 clear-cutting stands on mineral soils and ditched peatlands in southern Finland ( Figure 1 ). The data were collected by measurements on standing sample trees from circular sample plots, each of them m 2 (2 5 plots per stand). In this study, all trees from each sample plot with the minimum diameter at breast height (d.b.h.) of 7 cm were measured and graded for the dimensions (d.b.h. and height) and external technical quality affecting the bucking operation. In the fieldwork, particular attention was paid to the occurrence and effective lengths of the technical defects in the tree (e.g. sweep, crooks, branchiness and scars). The number of measured trees totalled to 3486, of which Scots pine ( Pinus sylvestris L.) made up of 1399, Norway spruce ( Picea abies Karst.) 2061 and downy ( Betula pubescens Ehrh.) and Silver birch ( Betula pendula Roth.) 26 ( Table 1 ). Bucking simulation In the bucking-to-value simulator, the stem volumes of sample trees from the stump height to the top were calculated using taper curve models as a function of the tree species, the breast height diameter and the height of the trees ( Laasasenaho, 1982 ). The heights of the stumps were calculated by the stump height models of Laasasenaho (1982) as a function of the tree species and the breast height diameter. Based on the taper curves, the

3 PREDICTION OF TIMBER ASSORTMENT RECOVERY 311 Figure 1. Study stands. Geographic sub-samples 1. South-eastern Finland, 2. Western Finland, 3. Savo-Karelia and 4. Central Finland. Coastal areas are separated by black line. calculated stump heights, the tree measurements and the pre-defined values of different timber assortments, the dynamic programming-based bucking simulator generated several cutting alternatives for each stem; calculated the value of each alternative according to the pre-defined price matrices and selected the optimal alternative maximizing the value of the stem. The volumes by different timber assortments were calculated according to the cutting patterns of the selected alternative. Losses of wood due to kerf were not accounted for. The bucking simulator calculated the volumes and values of timber assortments for each bolt, stem, sample plot and stand. While using taper curves, the simulator took into account the dimensions and the measured external defects (e.g. sweep, crooks, branchiness and scars) of the measured trees. For each timber assortment, possible diameter length combinations and quality requirements had to be defined. The value relations between timber assortments were given as a value matrix in the simulator. The stem parts that contained defects were bucked as pulpwood or non-merchantable wood including jump butts, off-cuts and top-cuts. The stem sections that did not achieve the required dimensions of any timber assortments were classified as non- merchantable wood, that is, wood biomass which can be collected for energy use or left in the forest. The sample trees, in the study stands, were bucked using pre-defined top diameters and log lengths of different timber assortments compatible with the requirements applied in the MELA analyses ( Table 2 ). Timber assortments, in this case, were saw logs, pulpwood and non- merchantable wood. The minimum top diameter of saw logs

4 312 FORESTRY Table 1: Mean stand characteristics by forest site type (fertility level) Oxalis-Myrtillus or corresponding peatland type (OMT), Myrtillus or corresponding peatland type (MT), Vaccinium or corresponding peatland type (VT) and Calluna or corresponding peatland type (CT) based on sample tree measurements Stand characteristics OMT MT VT CT Scots pine dominant stands Norway spruce dominant stands Birch dominant stands 1 Number of stands Mineral soils Ditched peatlands Number of sample trees Mean age of the stand, a Basal area, m 2 ha Stem volume, m 3 ha Tree height, m d.b.h., cm (mean) Scots pine Norway spruce Birch Number of stems per ha Average stem volume, dm 3 (over bark) External defects Stems including any defect (%) Pine stems including any defect (%) Spruce stems including any defect (%) was 14.5 cm for pine, 17.0 cm for spruce and 16.5 cm for deciduous species. The lengths of saw logs were fixed at every 3 dm between 4.3 and 6.1 m. For pulpwood, the minimum top diameter was 6.3 cm for pine and 6.5 cm for other tree species. The allowable lengths of pulpwood were between 2.0 and 5.5 m. The model-based system In the MELA system ( Siitonen et al., 1996 ; Red sven et al., 2005 ), the prediction of timber assortment recovery is also based on the Finnish taper curve and stump height models ( Laasasenaho, 1982 ). The MELA system is originally designed to be used for the inventories over large areas (the whole of Finland) where the speed of the calculation is important. Therefore, for each tree, the stem volume by timber assortments is retrieved from a pre-calculated table as a function of the tree species, the breast height diameter and the height of the tree ( Laasasenaho and Snellman, 1983 ). The breast height diameter is given in centimetre and the height of the tree in decimetre which causes minor accuracy losses due to interpolation. When applying these so-called taper curve models based on two explanatory variables, uniform stem tapering is assumed for all trees of the same size in diameter and height. The minimum top diameters and log lengths applied in the prediction of timber assortment are given in Table 2. To take into account small defects and strong tapering of trees, which cause shorter logs, the total length of saw log fragments derived from taper curve models was corrected using MELAs in-built piecewise functions where explanatory variables are the length of saw log fragments derived from taper curve models and the number of saw logs. The corrections were based on practical inventories conducted in the 1970s and they are dependent on the bucking regimes applied at that time. Corrections do not cover any variation in timber assortment recovery due to the size and age of the tree, or its site conditions. In this study, the performance of both saw log reduction models of the MELA system was

5 PREDICTION OF TIMBER ASSORTMENT RECOVERY 313 evaluated. In the MELA96 version ( Siitonen et al., 1996 ; Redsven et al., 2005 ), explanatory variables are tree species as well as d.b.h. and age at breast height. The model explains the difference between the saw log percentage derived from taper curve models based on two explanatory variables using the bucking algorithm tailored for practical inventories ( Laasasenaho and Snellman, 1983 ; Päivinen, 1983 ) and the saw log percentage assessed for the sample trees in the seventh National Forest Inventory (NFI7). The performance of the model by tree species as a function of the diameter and age of tree is illustrated by Hynynen et al. (2002, see p. 62). The model does not take into account any variation in timber assortment recovery due to site conditions of trees. The MELA05 version ( Mehtätalo, 2002 ; Redsven et al., 2005 ) of the saw log reduction models is composed by tree species and land use categories. The explanatory variables cover both tree and site characteristics correlating with external and internal (i.e. decay) defects assessed for the sample trees in the ninth National Forest Inventory (NFI9). At tree level, independent variables include age (at breast height), d.b.h. and the type of origin. At site level, independent variables consist of x and y coordinates, temperature sum, height above sea level and dummy variables describing site type, soil and peatland category, as well as forestry centre. The details of the models are presented by Mehtätalo (2002, p. 583, Table 3 ). The model explains the proportional difference between the saw log volume derived from taper curves ( Laasasenaho and Snellman, 1983 ) and the saw log volume estimated for the sample trees assessed in the NFI9. In NFI, the trees of saw log size are assessed in stands of different development classes. The bucking regimes applied in the assessment are presented by Mehtätalo (2002, p. 578, Table 1 ). The MELA96 and MELA05 versions of saw log reduction functions are dependent on the bucking regimes applied in the NFI7 or NFI9, respectively. According to the sensitivity analysis of Mehtätalo (2002), the MELA05 version of saw log reduction model is feasible when the minimum top diameter is changed but 30 cm change in the allowed minimum length of saw logs leads to 2 6 percentage unit bias. Table 2: Bucking regimes used in the calculations of volumes of saw logs and pulpwood Tree species Minimum top diameter (cm) Saw logs Length (m) Minimum top diameter (cm) Pulpwood Length (m) Pine Spruce Birch The allowed lengths of saw logs were based on 3 dm classes between the minimum and maximum length. For pulpwood, all lengths between minimum and maximum were possible. Table 3: Averages and SDs for pine saw log recoveries (m 3 ha 1 and %) and saw log reductions (%) from the unconstrained maximum saw log volume due to defects MELA96 MELA05 Bucking simulation Average SD Average SD Average SD Saw log recovery (m 3 ha 1 ) Saw log recovery (%) Saw log reduction (%)

6 314 FORESTRY Comparisons First, stand-level volume comparisons are made without any quality information on the measured trees and without using log volume reduction models. Second, volumes and proportions of the standlevel timber assortments are determined using detailed quality information (in bucking simulation) and log volume reduction models (in modelbased approaches). The results were compared by using averages, standard deviations (SDs), Pearson s correlation analyses and root mean square difference (RMSD). The RMSD is defined as follows: RMSD = 2 ( y ybj ), n n Aj j= 1 where RMSD = root mean square difference, n = number of observations, y Aj = the value of the variable in stand j with method A and y Bj = the value of the variable in stand j with method B. The averages and SDs were studied in different strata (by stand fertility and region). Results Prediction of volume recovery and unconstrained maximum saw log volume Stem volumes were similar between model-based approaches and bucking simulation calculations ( Figure 2 ) due to the reason that both methods used the same stem data and tapering functions introduced by Laasasenaho (1982). However, small differences occurred due to interpolation applied in the model-based approaches. Unconstrained maximum saw log recoveries of pine and birch were systematically smaller in the model-based approaches than in the bucking simulation approach ( Figure 3 ). The modelbased approaches included a correction factor for the unconstrained saw log volume, which led to smaller saw log recoveries. However, for spruce, the model-based approaches produced higher values for small-sized stems and smaller values for large-sized stems. The differences between spruce saw log volumes were considerable concerning the smallest stems. Relative differences were greatest in birch saw log recoveries. Figure 2. The differences (%) between the modelbased and the bucking simulation-based approach in the stand-level volume recoveries for pine, spruce and birch. Prediction of saw log recoveries incorporating the quality information Pine The average saw log recovery for pine was similar between the bucking simulation and model-based approach utilizing the MELA96 version of saw log reduction model ( Table 3 ), but the saw log reductions from the MELA05 version were 33 per cent higher than the saw log reduction of the bucking simulation and 51 per cent higher than saw log reduction of the MELA96 version. The variation of the results was smaller in the model-based approaches, especially when the MELA96 version of saw log reduction function was applied. As a function of stand age, the saw log reduction for pine using the MELA96 version of the model had much less variability than the MELA05 version and bucking simulation ( Figure 4 ). The MELA05 version of the model gave higher saw log reductions for older stands, whereas in the bucking simulation, the effect of external defects on saw log recovery was smaller in those stands. The SD of the pine saw log reduction from the MELA05 version of the model and the bucking

7 PREDICTION OF TIMBER ASSORTMENT RECOVERY 315 Volume difference (%) Volume difference (%) Volume difference (%) Pine y = Ln(x) R 2 = Mean dbh (cm) Spruce y= Ln(x) R 2 = Mean dbh (cm) Birch Mean dbh (cm) y= Ln(x) R 2 = Figure 3. The difference between the model-based (MELA) and the bucking simulation-based approach in the prediction of theoretical maximum saw log recovery for pine, spruce and birch as a function of the mean d.b.h. simulation were considerably higher than from the MELA96 version of the model. The RMSD between the bucking simulation and the results from the MELA96 version was per cent and the correlation was ( P -value 0.086), while the RMSD between the bucking simulation and the results from the MELA05 version was per cent and the correlation was ( P -value 0.004). The different versions of the model-based approaches were more alike, the RMSD was per cent and the correlation was ( P -value 0.005). On average, the variation of the saw log reduction from the MELA05 version Figure 4. Saw log reductions of the model-based approaches (MELA96 and MELA05) and the bucking simulation-based approach for pine as a function of the stand age. followed the variation of the bucking simulation. However, the RMSD indicates that there exist great differences on some saw log reductions. The saw log reductions from the bucking simulation were smaller on lower fertility soils (CT) and higher on rich fertility soils (OMT) ( Table 4 and Figure 5 ). In the model-based approaches, the soil fertility class had no influence on the saw log reductions as expected. For example, lower soil fertility (CT) produced high saw log reductions, and the 95 per cent confidence levels for the mean did not reach the level of the average saw log reduction of the bucking simulation. The saw log reduction from the bucking simulation was highly dependent on the relative length of the dead branch zone ( Table 4 ). For example, pines are expected to have more branches in coastal areas. Both the bucking simulation and the saw log reduction based on the MELA05 version gave clearly higher saw log reductions for the coastal areas. However, there was no difference between the coastal and inland areas in the predictions based on the MELA96 version that has no site or geographical factors as independent variables.

8 316 FORESTRY Table 4: Averages and SDs for pine saw log reductions (%) from the unconstrained maximum saw log volume due to defects MELA96 MELA05 Bucking simulation n Average SD Average SD Average SD Site fertility OMT MT VT CT Dead branch zone >30 (%) (%) <40% Coastal area Inland The results are grouped by site fertility, relative length of the dead branch zone, and maritime vs inland climate. Saw log reduction (%) Bucking Simulation all MELA96 all MELA05 all Bucking Simulation OMT MELA96 OMT MELA05 OMT Bucking SimulationMT MELA96 MT MELA05 MT Bucking Simulation VT MELA96 VT MELA05 VT Bucking Simulation CT MELA96CT MELA05 CT Figure 5. The 95% confidence intervals for the mean saw log reductions (%) for pine from the theoretical maximum saw log volume due to defects grouped by site fertility. Spruce For spruce, both the MELA96 version of the saw log reduction model and bucking simulation gave similar saw log recoveries ( Table 5 ). This was expected as the MELA96 version and bucking simulation predicted saw log reductions based on external characteristics, while the MELA05 version of the model is tailored to take into account also the risk of existing decay (root

9 PREDICTION OF TIMBER ASSORTMENT RECOVERY 317 Table 5: Averages and SDs for spruce saw log recoveries (m 3 ha 1 and %) and saw log reductions (%) from the unconstrained maximum saw log volume due to defects MELA96 MELA05 Bucking simulation Average SD Average SD Average SD Spruce Saw log recovery (m 3 ha 1 ) Saw log recovery (%) Saw log reduction (%) rot). This can be observed from the RMSD of relative saw log reduction. The RMSD between the bucking simulation and the MELA96 version was 8.22 per cent and the correlation was ( P -value 0.669). The RMSD between the bucking simulation and the MELA05 version was per cent and the correlation was ( P -value 0.138), and, furthermore, the RMSD between the MELA96 and MELA05 versions was per cent and the correlation was ( P -value 0.054). The saw log reduction from the MELA96 version of the model is greatly dependent on the stand age ( Figure 6 ). Reductions in the stands below 100 years of age are at the same level as the reductions from the bucking simulation, but the reductions between ages 100 and 120 years are lower. The overall higher level of saw log reduction from the MELA05 version is expected to take into account the average risk of decay over larger areas; however, it may give overestimates on good-quality stands with only a small risk of decay. The influence of soil fertility on the relative saw log reduction for spruce is not as clear as for pine ( Table 6 and Figure 7 ). However, the saw log reductions in the bucking simulation diminished as soil fertility reduced, whereas the saw log reductions for the model-based approaches were greatest on the low fertility soils (VT). The subregional differences were considerable with the bucking simulation: the saw log reduction of the bucking simulation was highest in western Finland and lowest in central Finland. The relative saw log reduction was lowest in central Finland also when the model-based system was applied. However, the model-based system predicted the worst quality for south-eastern Finland which is a well-known risk area for decay. The differences Figure 6. Saw log reductions of the model-based approaches (MELA96 and MELA05) and the bucking simulation-based approach for spruce as a function of the stand age. between the coastal areas and inland were minor with the MELA96 version and bucking simulation. The MELA05 version of the saw log reduction model predicted highest saw log reduction in the coastal areas. Also the saw log predictions for south-eastern Finland and western Finland were greater than those for Savo-Karelia (in eastern Finland) and central Finland. Birch For birch, the saw log recoveries from both versions of the model-based system were the same but

10 318 FORESTRY Table 6: Averages and SDs for spruce saw log reductions (%) from the unconstrained maximum saw log volume due to defects grouped by site fertility, geographical region and maritime vs inland climate MELA96 MELA05 Bucking simulation n Average SD Average SD Average SD Site fertility OMT MT VT Region South-East Finland Western Finland Savo-Karelia Central Finland Costal area Inland Saw log reduction (%) Bucking Simulation all MELA96 all MELA05 all Bucking Simulation OMT MELA96 OMT MELA05 OMT greater than the saw log recoveries from the bucking simulation ( Table 7 ). The RMSD between the MELA96 and MELA05 versions was low (6.63 per cent) while it was per cent between the MELA96 version and the bucking simulation, and per cent between the MELA05 version and the bucking simulation. Moreover, the correlation between the MELA96 and MELA05 Bucking Simulation MT MELA96 MT MELA05 MT Bucking Simulation VT MELA96 VT MELA05 VT Figure 7. The 95% confidence intervals for the mean saw log reductions (%) for spruce from the theoretical maximum saw log volume due to defects grouped by site fertility. versions was high (0.941, P -value 0.000) while it was ( P -value 0.025) between the MELA96 version and the bucking simulation, and ( P -value 0.019) between the MELA05 version and the bucking simulation. However, the proportion of birch was low in the study stands and the properties of individual trees affected greatly the recoveries from the bucking simulation.

11 PREDICTION OF TIMBER ASSORTMENT RECOVERY 319 Table 7: Averages and SDs for birch saw log recoveries (m 3 ha 1 and %) and saw log reductions (%) from the unconstrained maximum saw log volume due to defects MELA96 MELA05 Bucking simulation Average SD Average SD Average SD Birch Saw log recovery (m 3 ha 1 ) Saw log recovery (%) Saw log reduction (%) Discussion The aim of the study was to compare modelbased approaches with bucking simulation-based approaches in the prediction of timber assortment recoveries from cut-to-length harvesting. The bucking simulation was based on detailed stem data, where the occurrence and effective lengths of the technical external defects (e.g. sweep, crooks, branchiness and scars) in the tree were measured. For the model-based approaches, the performance of two separate models for the saw log reduction due to defects was evaluated, that is, the MELA96 version and MELA05 version. Total stem volumes for each species from the model-based approaches and bucking simulation were almost identical due to the same taper functions. However, the predictions of the unconstrained saw log volume and saw log percentages varied due to the MELA correction functions applied for the length of saw log fragments in the model-based approaches resulting in smaller unconstrained saw log recoveries than in the bucking simulation. In the future, sensitivity analysis on the effects of minimum allowable log length and top diameter should be carried out. In the prediction of saw log recoveries, incorporating the quality information, the differences were even greater. The level of the reduction for pine from the MELA96 version was at the same level as from the bucking simulation, but the saw log reduction had a very low variance due to a small amount of independent variables. The saw log reduction of the MELA05 version included more variation; however, the level of the reduction was higher and the variation weakly followed the variation of the bucking simulation. In the future, evaluations should also be extended to comprise stands where thinning operations are carried out. In those stands, the MELA05 version is expected to perform better because of the wide size and age distribution of the trees in the modelling data. To correspond to the modelling data, the MELA05 version was formulated to allow the quality of the stems decrease as a function of the stand age ( Mehtätalo, 2002 ). However, the test data in this study did not support the hypothesis. Moreover, for spruce and birch, the reductions from the MELA05 version of the saw log reduction model and from the bucking simulation are not comparable as the prediction of decay risk is excluded from the bucking simulation. According to Mattila and Nuutinen (2007), the probability of butt rot damage increased on fertile sites, although the probability of damage increased slightly with increasing diameter and age of the tree. In the study, the model-based saw log reductions for lowest fertility spruce stands were opposite. The model-based approaches gave the greatest saw log reductions to the low fertility soils, which were, due to slower growth, older than the stands in more fertile soils. The saw log reductions of MELA05 were larger than the saw log reductions of MELA96. One possible reason for the overestimation of the MELA05 saw log reductions may be due to the effect of the correction factor, which was used in MELA saw log volume calculations and was not used while modelling log reduction models for MELA05. The unconstrained saw log volumes of MELA calculations were, on average, smaller than the saw log volumes of the bucking simulation. The difference was ~ 3 per cent for pine, slightly smaller for spruce and greatest for birch. Consequently, the correction factor for the saw log volume may explain approximately one half of the overestimation on the saw log reduction, the other half can be explained by different data sets.

12 320 FORESTRY The bucking simulation approach with detailed stem data produces relatively reliable estimates on the unconstrained assortment recoveries. However, the effect of a harvester operator cannot be considered. The expertise of the operator affects the observation of the stem defects and, consequently, the recovery of timber assortments. Moreover, the optimization of volume of the most valuable assortments under dimension constraints and stem defects requires experience and, thus, variability between different operators exists. The best validation data would be based on cut and measured stems (stem data bank). However, the acquisition of that kind of data for representative sites would be very expensive. Therefore, the bucking simulation based on measured standing trees of sample stands was chosen as a basis for the validation despite the possible limitations related to the approach. The most probable error with the bucking simulation would be the measurements of the stem defects. However, in the study, the measurers were experienced and, therefore, on the whole, the results should be reliable. The study stands were typical clear-cutting stands in southern and central Finland. The number of measured stands was high considering the number of measured stem details. However, with the bucking simulation approach, in some strata a larger number of stems would be desirable; for example, the small number of birches ( n = 26) stands in the study stands did not enable drawing conclusions from the saw log recovery and saw log reduction models of birch. As a conclusion, the model-based approaches seem applicable at least for the prediction of saw log recovery in the large area forest inventories where the variance of the standwise timber recoveries need not be predicted. Acknowledgements This work was conducted in the Finnish Swedish Wood Material Science and Engineering Research Programme s project VACHA Value-chain analysis for forest management, timber purchasing and timber sale decisions. The sub-project Timber purchasing and sale decision models in accordance with alternative selection of wood assortments was funded by the Ministry of Agriculture and Forestry in Finland and the sub-project A forestry model for the national level analysis of forest management strategies in Finland was funded by the Academy of Finland (Project No ). The authors are grateful to Juha Metros, Eeva Nurmela, Erkki Salo and Tapio Ylimartimo for their assistance in the field data collection, and Hannu Hirvelä and Reetta Lempinen for the assistance with MELA calculations. We are also grateful to Dr Lauri Mehtätalo and Dr W.T. Zakrzewski for their valuable comments on the manuscript and Anne-Marita Järviluoto for revising the English. Conflict of Interest Statement None declared. References Ahonen, O.-P. and Mäkelä, H Etelä-Suomen raakapuuvarat laskennalliseen pölkytykseen perustuen. Metsätieteen Aikak. 3, ( in Finnish). Arce, J.E., Carnieri, C., Sanquetta, C.R. and Filho, A. F A forest-level bucking optimization system that considers customer s demand and transportation costs. For. Sci. 48, Gobakken, T The effect of two different price systems on the value and cross-cutting patterns of Norway spruce logs. Scand. J. For. Res. 15, Hynynen, J., Ojansuu, R., Hökkä, H., Siipilehto, J., Salminen, H. and Haapala, P Models for predicting stand development in MELA System. Metsä ntutkimuslaitoksen Tiedonantoja-835, Research Papers 835. Finnish Forest Research Institute, Vantaa, 116 pp. Kangas, A. and Maltamo, M Anticipating the variance of predicted stand volume and timber assortments with respect to stand characteristics and field measurements. Silva Fenn. 36, Laasasenaho, J Taper curves and volume functions for pine, spruce and birch. Commun. Inst. For. Fenn. 108, 74. Laasasenaho, J. and Snellman, C-G Männyn, kuusen ja koivun tilavuustaulukot. Research Papers 113. Finnish Forest Research Institute, Helsinki, 91 pp [In Finnish]. Malinen, J Locally adaptable non-parametric methods for estimating stand characteristics for wood procurement planning. Silva Fenn. 37 ( 1 ), Malinen, J., Maltamo, M. and Harstela, P Application of most similar neighbor inference

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