# Predicting the internal quality and value of Norway spruce trees by using two non-parametric nearest neighbor methods.

Abstract

End-use oriented sawing, which has become more and more popular for Norway spruce, demands more accurate evaluation of the inner quality of trees to be logged. The needed description includes characteristics such as wood density, decay, amount of heartwood, and knottiness. The prediction of these variables using commonly measured tree- and stand wise variables has been found very difficult. Due to the complex correlation of the variables, the use of non-parametric regression methods in the prediction of properties of spruce trees is one alternative. The emphasis of this study was to test possibilities to predict the yield and internal quality of spruce trees and value of lumber and side products by stand and tree factors for traditionally oriented sawing with two non-parametric nearest neighbor methods: k-nearest-neighbor (k-nn) most similar neighbor (MSN) and locally adaptable neighborhood (LAN) MSN method, by using data that were collected in a large research project performed by the Finnish Forest Research Institute. The methods were compared by using treewise and standwise information in prediction. According to the results of this study, the non-parametric nearest neighbor methods seem to provide one interesting option to estimate the internal quality and value of Norway spruce trees. The (LAN) MSN method was found to be slightly better than the k-an MSN method inmost cases when using relative root mean square error as the criteria to compare results. Treewise information improved the accuracy of the methods compared to the results of standwise input information.

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Norway spruce became the most important species for the Finnish sawmilling industries at the beginning of the 1990s, after the dominant period of Scots pine from the start-up of industrial export sawing in the 1850s. During recent years, spruce has been sawn more than pine, excluding the later half of 2001 (Sevola 2001). The average unit price of spruce lumber also exceeded that of pine lumber, at least for a period in 1998, as well (Sevola 2001; Wood Focus 2001, 2000). In this situation, increasing attention must be paid to the improved utilization of the properties and quality of spruce trees and logs, to maximize the net revenue from the wood raw materials available. For sawmilling, this means embarking on an end-use-oriented philosophy for further processing, and, simultaneously, a market-oriented approach (e.g., Verkasalo et al. 200 la, b).

It is commonly acknowledged in Finland that there is a considerable lack of knowledge concerning the factors for the quality of Norway spruce, compared with Scots pine and European birch species, in particular. It is not only for the lack of research but, thus far, somewhat biased uses as well. Spruce timber has mainly been used for mechanical pulping and further for wood-containing paper grades and sawn goods for structural uses. Accordingly, it is not unexpected that the control of timber flow by its quality was considered a secondary issue. Moreover, variation in the unit price of timber assortments and lumber grades was relatively small, compared, again, with pine and birch (Sevola 2001; Wood Focus 2001, 2000). The potential to predict the internal quality of spruce is also considered relatively weak, particularly for knottiness (e.g., Verkasalo et al. 2001a,b; Makinen et al. 2001; Karkkainen 1986a,b).

Growth and diversification in the end uses of and markets for spruce products were relatively rapid during the 1990s. Building products, i.e., structural uses, continue to be the predominant end uses of spruce lumber, but the importance of joinery, interior panels, furniture, glued products, log houses, and miscellaneous special products is growing. In addition to lumber, industries started to produce structural plywood, laminated veneer lumber (LVL) (Kertowood), and novel Kraft pulps (armoring fiber) in large amounts. Now, the implementation of dedicated spruce plywood mills and LVL mills has greatly solved the problem of the underutilized resources of big-dimensioned spruce in southern Finland (e.g., Pennanen and YliHukkala 1994, Verkasalo 1992).

All this resulted in an increased need for end-use-oriented procurement of spruce timber, evaluation and pricing of spruce timber by quality, and forest management toward high-quality spruce. Accordingly, proper prediction of the properties and quality, both internal and external, is needed to analyze their potential for different end uses of mechanical processing. This is needed to select the appropriate stands, trees, and logs for the appropriate production plants and end products, and for bucking, sorting, and grading logs, controlling timber storage, and planning sawing operations.

The description of internal quality includes characteristics such as wood density, decay, amount of heartwood, and knottiness. The prediction of these variables using commonly measured tree-and standwise variables was generally found very difficult. Regression models were constructed but correlation between tree variables (diameter at breast height (DBH) for example) and these characteristics were found weak and complex. Moreover, the separate prediction of these variables did not guarantee logical dependent estimates between these variables.

Most of the regression models describing quality in boreal conditions were constructed for external variables and for Scots pine. These equations included different models for crown height and branchiness (Makinen and Colin 1999, 1998; Uusitalo and Kivinen 1998; Hynynen 1995; Karkkainen 1986a). In the studies of Makinen and Colin (1999, 1998), the size, birth, death, and pruning of Scots pine branches were considered. Corresponding models were constructed also for Norway spruce in Finland (Makinen et al. 2001, Karkkainen 1986a). Different kinds of branchiness models were constructed for Norway spruce by Houllier et al. (1995) and Karkkainen (1986a, 1972), and for Douglas-fir by Maguire et al. (1994). In the case of internal quality, heartwood curves of Scots pine (Ojansuu and Maltamo 1995) and different models describing wood density (e.g. Hakkila

1979, 1966) were created.

Although a nationwide taper curve model exists for Norway spruce in Finland (Laasasenaho 1982), there are only a few models considering internal quality of Norway spruce. Karkkainen (1986a) presented a way to divide stems to zones of dead and living branches. These models considered Scots pine, Norway spruce, and birch species. The wood density of Norway spruce was examined in Finland by Hakkila (2001, 1979, 1968, 1966), Saranpaa (1994), Karkkainen (1984), and Hakkila and Uusvaara (1968). Different models also exist for describing decaying of Norway spruce. These studies include the probability of the existence of decay, the amount of decay, and the spread of butt rot (Moykkynen et al. 1998, Tamminen 1985, Hypponen and Norokorpi 1979, Norokorpi 1979, Tuimala 1979, Kallio and Norokorpi 1972).

Due to the complex correlation of internal variables, the use of non-parametric regression methods in the prediction of properties concerning spruce trees is one alternative. According to Altman (1992), these methods are suitable especially for complex situations and for comparing different models. These methods predict the value of the variable of interest as the weighted average of the values on most identical observations, the neighbors being defined with the predicting variables (Altman 1992, Hardle 1989). All variables of interest can be predicted simultaneously and the original covariance structure of variables remains. Furthermore, unrealistic estimates cannot be produced because they are based on measured observations.

The non-parametric prediction methods used in forestry include, for example, k-nearest neighbor (k-nn) and most similar neighbor (MSN) (Moeur and Stage 1995, Kilkki and Paivinen 1987). The accuracy of the non-parametric methods was observed to be similar to the compared parametric methods (Haara et al. 1997, Moeur and Stage 1995) or even better (Maltamo and Kangas 1998) and they were found useful in many forestry applications (e.g. Malinen et al. 2001, Tommola et al. 1999). In the case of tree quality, the non-parametric two-dimensional kernel regression was used by Uusitalo and Kivinen (1998) to generalize sample tree information of crown heights for tally trees. The results were very promising but this approach cannot not be used for prediction but only for generalization.

However, there are some disadvantages in the use of non-parametric methods. These methods require comprehensive reference material in applications. In addition, it is not ensured that the estimates are unbiased. At the boundary of the predictor space, the neighborhood is asymmetric and models tend to be highly biased. Bias can be a problem concerning the interior as well if the predictors are non-uniform or if the regression function has substantial curvature. By increasing the number of neighbors, we can enhance the local validity of a model but at the same time the bias of results increases.

The emphasis of this study was to test possibilities to predict the yield and internal quality of Norway spruce trees and the value of lumber and side-products by stand and tree factors for traditionally oriented sawing with the non-parametric k-nn MSN (Malinen et al. 2003) and locally adaptable neighborhood (LAN) MSN methods (Malinen 2001).

Material and methods

Study material

At the Finnish Forest Research Institute, a large research project on predicting and controlling the properties and quality of trees and logs of Norway spruce for mechanical wood processing was performed in 1994 to 1998. For the project, 240 sawn timber trees were sampled from 48 spruce-dominated mature or nearly mature stands in southern Finland (five trees per stand).

The entire range of diameter distribution of the sawn timber trees was covered in each stand, with the minimum and maximum of 18 and 40 cm, respectively. Only dominant and co-dominant, visually healthy trees, whose neighboring trees were all spruces and that met the minimum commercial requirements for sawn timber trees were accepted. However, limits for knottiness could be exceeded; this was even desirable for the objectives of the study. Trees meeting all these requirements were divided by descending DBH into five groups, of which one tree was selected for the material by random sampling.

The sample of the study was evenly divided into four geographic regions in the southern half of Finland: 1) southern Finland, coastal area; 2) southern Finland, inland; 3) western Finland, Suomenselka; and 4) eastern Finland, Savo (Fig. 1). Regions 2 and 4 are considered to represent good growth and quality potential for Norway spruce in Finland, whereas regions 1 and 3 are considered fringe areas for producing spruce timber.

For each region, the subsamples were evenly divided by soil and regeneration types into: 1) mineral uplands, naturally regenerated stands; 2) mineral uplands, planted stands; and 3) fertile peatlands, naturally regenerated stands. Soil fertility was, in each stand, at the level of Vaccinium myrtillus type (MT) or Oxalis-Myrtillus type (OMT), which correspond to semifertile and fertile soil types in Finland. Each stand had been treated in accordance with the principles of regular silviculture, i.e., by appropriate tending, spacing, and thinning operations. The years of silvicultural operations and timber cuttings were recorded for each stand. The desired interval in the age of the stands was 50 to 120 years for each stratum of geographic region and type of soil and regeneration. Means and standard deviations of selected properties for the sample trees by using the previously mentioned classification are shown in Table 1.

Field and laboratory measurements

DBH was measured on all trees at each sample plot of 30 m by 30 m, which were placed into a visually representative part of a stand. The following stand-level factors were determined for each sample plot: soil type, spacing (number of trees per hectare), basal area and its distribution by tree species, and mean age, height, and DBH of spruces among dominant trees.

The following factors were determined for each of the five sample trees on a plot: biological crown type (five categories) and crown level class (four categories), both by using the classification by Ilvessalo (1929); biological age at the stump; height; lower level of dead branches; lower limit of living crown; lowest dead branch; lowest living branch; external defects and their heights; selected diameters at the fixed heights in a tree (0.1,0.5,1.3,2,3,4,5,6,8, ... in); maximum crown width and its compass reading; perpendicular to the maximum crown width and its compass reading; distances and their compass readings to the closest five trees; vertical locations of and average branch angles in all whorls; and the types and diameters of branches recorded to the 6-cm diameter.

Laboratory measurements were performed on sample discs at the before-mentioned heights from all sample trees for diameters, bark thickness, cross-sectional geometry, pith eccentricity, and extent of heartwood and compression wood, and on sample whorls (over-healed, self-pruned, and un-pruned) closest to the before-mentioned wood samples for the diameters and quality of knots at fixed radial locations (on the surface under bark and at consecutive 3-cm distances perpendicular to the stem axis). For the investigations on the vertical and radial frequency, extent, and quality of adventive knots (compared with whorl knots), 1-in logs were cut at 3 heights from 20 trees from 4 selected stands. The logs were rotary-cut into 1.5-aim thickness and the number of whorls and adventive knots were separately recorded by diameter class (5-mm classification) at each consecutive half of the logs.

Spatial pattern of forest

For each sample tree, according to the distances and their compass readings to the closest five trees, the spatial pattern of forest was analyzed by using angle indices ([W.sub.i]) (Gadow et al. 1998). Each intermediate angle from tree I to two of its neighbors was calculated, and that value was compared to the so-called standard angle ([[alpha].sub.0]), which is equal to 360[degrees]/n, where n is the selected number of neighboring trees. The spatial structure described by angle index of the ith tree with its n nearest neighbors is the following:

[W.sub.i] = 1/n [summation over (n/j=1)] [Z.sub.y] (1)

where:

[Z.sub.ij] 1, if the jth angle c~ is less than [[alpha].sub.0].

[Z.sub.ij] = 0, otherwise

The value of the angle index describes the regularity of the distribution of trees. Value zero means that the spatial pattern is very regular, values close to 0.5 means a randomly distributed forest, and 1 means a very clumped forest.

Generating the internal structure for sample trees

Field and laboratory data were used to generate the external and internal structure of trees by computer calculations. The stem curve over and under bark and the limit between heartwood and sapwood was generated for each sample tree by polynomial spline functions based on diameters on the sample discs at the before-mentioned heights, and total tree height (Lahtinen and Laasasenaho 1979). For the limit of heartwood and sapwood, means of minimum and maximum diameter on each disc were used. Zones of compression wood were placed into trees by linear smoothing from the consecutive measurements on vertical discs. The area of compression wood was planimetrically measured at each disc by using visual evaluation of the boundaries.

Internal knots were created for all trees by multivariate polynomial regression models based on the sample whorl measurements. The following models were generated to predict the relative diameter of internal knots, in comparison with the diameter of each knot on the tangential surface of tree without bark (Eq. (2), Verkasalo et al. 2001b), and, for dry knots and knot bumps, the relative distance from point of death for internal knots from the tangential surface of tree under bark, in comparison with the radius without bark (Eq. (3), Verkasalo et al. 2001b):

[Y.sub.1] = 0.270 + 1.119[X.sub.1] + 0.4053[X.sup.1.sub.2] - 0.7347[X.sup.3.sub.1] - 0.1945[X.sub.2]

N = 4218, [r.sup.2] = 0.74, [S.sub.E] = 0.139 (2)

where:

[Y.sub.1] = relative diameter of knot, in comparison with the diameter of each knot on the tangential surface of tree (without bark)

[X.sub.1] = for green knots, relative distance from the tangential surface of tree (without bark), in comparison with the radius (without bark); for dry knots, relative distance from the point of death, in comparison with the distance from the pith to the point of death

[X.sub.2] = relative height in a tree, in comparison with the total height from the felling height to the tip

[Y.sub.2] = 0.5188 - 0.5479[X.sub.1] +

0.001373[X.sup.-1.sub.1] - 8.0212 * [l0.sup.-6][X.sup.-2.sub.1] +

5.293 * [10.sup.9][X.sup.-3.sub.1] - 0.01165[X.sub.2] +

0.7879[X.sup.-1.sub.2] - 0.5353[X.sup.-2.sub.2]

N = 2320, [r.sup.2] = 0.54, [S.sub.E] = 0.133 (3)

where:

[Y.sub.2] = relative distance of point of death from the tangential surface of tree under bark, in comparison with the radius (without bark)

[X.sub.1] = relative height in a tree, in comparison with the total height from the felling height to the tip

[X.sub.2] = knot diameter on the tangential surface of tree (without bark)

So far, the frequency or maximum diameter of sound and dead adventive knots in different radial zones could not be predicted satisfactorily by tree or stand factors. This was probably due to two factors: 1) obviously, their start and death are not regulated by the variables measured in the study material; and 2) for technical reasons, logs could not be rotary-cut to diameters less than 8 cm. Instead, the frequency of sound and dead adventive knots at different heights could be predicted by DBH and diameter at the particular height. These relationships were used to create internal adventive knots.

Simulating cross-cutting trees and sawing logs

The predicted stems were bucked theoretically to logs by particular simulating programs for this research (Verkasalo et al. 200 la,b). In this study, the conventional dimensions of sawlogs were used: six lengths (4.3 to 5.8 in), minimum top diameter 16 cm (on the bark); small-dimensioned sawlogs: one length (4.3 in), minimum top diameter 12 cm (o.b.); pulpwood: minimum length 3 m, minimum top diameter 7 cm (o.b.).

The logs were theoretically sawn by simulating computer programs, by using sawing patterns of a traditionally operating large sawmill (Verkasalo et al. 2001 a,b). Primary sawing is based on cant chipper and band sawing techniques. Sawing direction was determined according to the minimum and maximum diameter of the log.

Lumber grading and pricing, determining the gross value of trees

The simulated sawn goods were fresh-graded according to the rules of the Nordic Timber Grading Rules (1994) (Verkasalo et al. 2001a,b). For grading, knots generated into the trees were projected on the faces and edges of each piece of lumber for the diameter and quality of the knot. Zones of heartwood and compression wood were placed within each piece of lumber as well. Grade for each piece of lumber was determined by using dimension, knottiness, compression wood, and wane. The simulated sawn goods were priced by using dimension and grade, in accordance with the price list of a particular sawmill. The average prices of the lumber grades from the years 1994 and 1995 were used. Sideproducts were priced according to the actual market prices for each sawmill at that time.

These procedures produce grade distribution of lumber, and gross value of lumber, chips, sawdust, bark and pulpwood. These data were used to compute the gross value of trees.

Non-parametric estimation methods

The non-parametric estimation methods used in this study are based on distance-weighted nearest neighbors estimation, where the search for similar reference trees is done by using easily measurable mean stand and tree variables. Reference trees are used to characterize the target tree properties (Fig. 2). The distance measure of similarity is needed to compare different trees and their characteristics and is calculated for each stand. In the estimation phase, differences across all reference trees are calculated and properties are formed using chosen neighbor trees.

The variables describing a tree used in the similarity distance function were chosen with two different principles. In the first model, the model has been constructed with the concept that information on a tree and its surroundings can be measured (Table 2). In the second model, this kind of treewise information is not available, but the stand characteristics are known. However, in the standwise model, diameter distribution is expected to be measured or estimated as well as tree heights.

Before the nearest neighbors method can be applied, it is necessary to decide:

1. the form of distance function to be used for finding the most similar reference trees;

2. the number of nearest neighbors or process for selecting an appropriate neighborhood;

3. the form of weight function for weighting the reference trees.

In this study, the similarity of target and reference trees was measured according to the MSN inference (Moeur and Stage 1995). The similarity function used in the MSN method is a generalized Mahalanobis distance (Mahalanobis 1936). A canonical correlation analysis provides a unified multivariate approach to the computation of the weighting matrix in the distance function, by summarizing the relationship between a set of search attributes and a set of design attributes simultaneously. The MSN similarity measure derived from the canonical correlation analysis is:

[D.sup.2.sub.uj] = [([X.sub.u] - [X.sub.j]).sub.lxp][GAMMA] [[LAMBDA].sup.2.sub.pxp] [LAMBDA]'

[[X.sub.u] - [X.sub.j]'.sub.pxi] [4] where:

D = distance between observations

X = vector of known search variables from target observation

[X.sub.j] = vector of search variables from reference observations

[GAMMA] = matrix of canonical coefficients of indicator variables

[LAMBDA] = diagonal matrix of squared canonical correlation

In the MSN similarity function, the weighting matrix weights the elements of search variables according to their predictive power for all elements of design variables simultaneously, while incorporating the covariance between the elements of design attributes.

The optimal number of neighbors used in the k-nn MSN method can be determined by using the cross-validation method, for example by minimizing the relative root mean square error (RMSE) (Eq. [5]) of certain characteristics. The minimization of relative RMSE emphasizes local accuracy of estimates more than average accuracy of estimates. In the used cross-validation method, a target tree is a tree that is excluded from reference trees and for which estimates are calculated. Each tree from reference data is, in turn, used as the target tree.

RMSE% = 100 x [square root][[summation over](n/j=1)] [y.sub.ij] - [[y.sub.ij].sup.2]/n-1/[y.sub.i] [5]

where:

n = number of observations

[y.sub.ij] = real value of the variable in tree j

[y.sub.ij] = estimated value of the variable i in tree j

[y.sub.i] = mean of estimates of variable i

Large neighborhoods can affect the bias in the boundary situations or in the situations where the reference data are distorted. The nearest neighbors may be located on the same side of the input space, even in the situations where observations exist on the other side of the input space (Fig. 3). Recognizing these situations and adjusting locally the amount of the neighbors and selecting the combination of neighbors symmetrically can reduce the bias of estimates.

The information used in the selection of the local neighborhood must be produced from neighborhood observations and predictor variables of the target stand. In the LAN MSN method, every possible combination of neighborhood is examined, in turn, and the averages of predictor variables of neighborhood combinations are calculated. Every vector of average predictor variables of possible neighborhood combinations is compared to the vector of predictor variables of the target stand with MSN metrics and the combination of neighbors that is most identical to the target stand is chosen to be used in the calculation of estimates.

The neighborhood, from which the optimal neighborhood is selected, is limited to 15 neighbors due to computer time consumption. Demand for computer time increases by 2", when the size of the neighborhood (n) is expanded.

Results

The performance of the nearest neighbor methods is greatly affected by the number of selected neighbors in the estimation process. The optimal number depends on the objectives of the user. When the used criterion is average goodness, the optimal number of neighbors is larger. Vice versa, if the user minimizes bias, the optimal number of neighbors is smaller, usually one. RMSE is located between these two ends. It weights average goodness of estimates but uses square errors to punish large variation of bias.

In this study, the optimal number of neighbors varied around five (e.g., Fig. 4) and, therefore, the size of the neighborhood was set to be five in the k-nn MSN method. In the LAN MSN method, the optimal number and combination of neighbors is set in each estimation situation according to the shape of the surrounding neighborhood. The average number of used neighbors was four and number of neighbors used varied between one and eight.

For the study, two different models were used:

1. the treewise model, where treewise information, such as spatial information and crown information, was available;

2. the standwise model, where treewise information was not available; however, the breast height diameter distribution and heights were assumed to be known or estimated.

The yield estimates for the treewise model were clearly more accurate than the standwise model estimates for the sawlog volume, bark volume, and chips volume (Table 3). However, pulpwood estimates did not differ in these models.

The nearest neighbor MSN method can be tailored to every estimation situation according to user preferences by input variable selection. When optimizing the model with emphasis on the internal quality, the error of sawlog volume estimates were relatively high compared to the model, where accurate sawlog volume estimates were preferred (Table 3). While the sawlog volume and pulpwood volume includes the volume of bark and chips, the accuracy of the bark and chips volume estimates is strongly correlated with the sawlog volumes.

There was no difference between the optimized treewise model and standwise model, when the sawlog volume was preferred. The treewise data made estimates less accurate and the optimal model includes only tree size information, which was assumed to be known in both situations.

When estimating the internal quality of spruce trees, the results were slightly more preferable for the treewise model than for the standwise model (Table 4). When accuracy of sawlog volume estimates was preferred, the estimates were clearly more inaccurate, except for basic density in the rest of the wood and volume of heartwood. It could be assumed that density, as an average in the rest of the wood, depends more on the size of the estimated tree than on the properties of the surroundings and the tree itself. When the volume of heartwood is concerned, it was quite expected that estimates are better, due to the more accurate overall volume estimates.

Estimating the total value derived from products greatly depended on volume estimates, and therefore, the emphasis on the sawlog volume (Table 5) produced most accurate total value estimates. Sawn timber value per cubic meter was dependent on the quality of input information, but it was unexpected that the total value per cubic meter did not seem to correlate with the predictor variables. A reason for this unexpected result might be that the total value per cubic meter also depends on the obtained amount of sideproducts (bark and chips) and the relative amount of sideproducts depends on the size of the tree.

Discussion

This study examined the use of two non-parametric nearest neighbors methods in the context of prediction of yield and internal quality of Norway spruce trees and value of lumber and sideproducts according to selected stand- and treewise predictors. The fundamental idea in these methods is to find trees similar to the tree that is the subject of interest from empirical data and to use measured empirical data from similar trees to produce estimates.

According to the results obtained in the present study, the tested methods seem to provide an interesting option to estimate the internal quality of trees. The use of the large empirical data as reference material ensured that estimates were always reasonable and impossible predictions, as with the case of parameter estimators, didn't occur. When considering different level input information, the treewise input data produced more accurate estimates, as expected, but standwise input data may be used as well.

Although results were promising, it must be kept in mind that there are many possible sources of error. It is not ensured that data measurements are totally unbiased, the simulation procedure may involve unsure assumptions and resultant inaccuracy and systematic errors, and models may include bias. The efficiency of these methods could be improved by increasing the number and diversity of reference trees, by measuring new variables to be used as predictor variables, or by tailoring methods to be more appropriate for every estimation situation.

In the non-parametric methods, the reference data used are crucial in many ways. Methods are, even at their best, only as good as the data used. These methods only point out the most similar trees and if the data does not include similar trees, then the target tree estimates may be inaccurate. In the case of inner quality, the measurement of representative data is expensive and laborious. However, this might not be the situation in the future. One interesting possibility to collect usable data is to use an ultra-sound-based or x-ray-based wood scanner that is can be placed in the harvester head of a modern harvester.

If methods of this kind are used in practice, it would be necessary to have:

1. comprehensive data from the application area;

2. three-dimensional models of tree properties, including, for example, branch models and heartwood models etc.

3. simulating software, which is capable of bucking trees according to customer demands and sawing bucked trees into products according to desired sawing parameters.

With an application of this kind, it is possible to create a practical application to be used in wood procurement planning purposes.

[FIGURE 4 OMITTED]

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Moeur, M. and A.R. Stage. 1995. Most similar neighbour: An improved sampling inference procedure for natural resource planning. Forest Sci. 41(2):337-359.

Moykkynen, T., J. Miina, T. Pukkala, and K. von Weissen berg. 1998. Modelling the spread of butt rot in a Picea abies stand in Finland to evaluate the profitability of stump protection against Heterohasidium annosum. Forest Ecol. Manage. 106:247-257.

Nordic Timber Grading Rules. 1994. Foreningen Svenska Sagverksman, Suomen Sahateollisuusmiesten Yhdistys, Treindustriens Tekniske Forening. (The Finnish Forest Industries Federation), Stockholm, Helsinki, Oslo, Sweden. (in Finnish).

Norokorpi, Y. 1979. Old Norway spruce stands, amount of decay and decay-causing microbes in northern Finland, Commun. Inst. For. Fenn. 97(6): 1-77.

Ojansuu, R. and M. Maltamo. 1995. Sapwood and heartwood taper in Scots pine stems. Can. J. Forest Res. 25:1928-1943.

Pennanen, O. and T. Yli-Hukkala. 1994. Utilisation of large spruce. Metsateho Review 4/1994. Helsinki, Finland. (in Finnish with English summary).

Saranpaa, P. 1994. Basic density, longitudinal shrinkage and tracheid length of juvenile wood of Picea abies (L.) Karst. Scand. J. Forest Res. 9: 68-74, 1994.

Sevola, Y. (ed.). 2001. Finnish Statistical Yearbook of Forestry. SVT Agriculture, Forestry and Fishery 2000:14.

Tamminen, P. 1985. Butt-rot in Norway spruce in southern Finland. Commun. Inst. For. Fenn. 127.

Tommola, M., NI. Tynkkynen, J. Lemmetty, P. Harstela, and L. Sikanen. 1999. Estimating the Characteristics of a Marked Stand Using K-Nearest-Neighbour Regression. J. of Forest Engineering 10:75-81.

Tuimala, A. 1979. Changes in timber assortments and loss in stumpage prices caused by decay in growing spruce timber. Silva Fenn. 13(4):333-342. (in Finnish with English summary).

Uusitalo, J. and V.-P. Kivinen. 1998. Constructing bivariate dbh/dead branch height distribution of pines for use in sawing production planning. Scand. J. Forest Res. 13:509-514.

Verkasalo, E. 1992. American ways to manufacture plywood from softwoods - models to rotary-cut Finnish spruce. Puumies 37(3): 2-6. The Association of Finnish Wood Engineers and Technicians. Jyvaskyla, Finland. (in Finnish).

_____, P. Sairanen, and P. Melen. 2001a. Dependence of the value of the stems and logs of Norway spruce on the properties of stands, stems and logs. Value of the stems and logs of Norway spruce in traditional and specialising sawmilling. In: Proc. Quality and Value of Norway Spruce. Research Day in Lahti. M. Heino, P. Saranpaa, and E. Verkasalo, eds. The Finnish Forest Research Institute, Joensuu, Finland.

_____, P. Sairanen, and P. Melen, 2001b. Predicting the value of Norway spruce trees and saw log sections for traditional and end-use oriented sawing. In: Proc. 4th Meeting COST El0 Wood Properties for Industrial Uses, Bordeaux, France. R. Birkeland, and G. Chantre, eds. Cost E10 & AFOCEL, Labortoire qualite du bois, Nangis. pp. 134-145.

Wood Focus. 2000. Overviews of the line of business of wood product industries of 2000. Wood Focus Ltd., Puuinfo and Finnish Forest Industries Federation, Helsinki, Finland. (in Finnish).

_____. 2001. Overviews of the line of business of wood product industries of 2001. Wood Focus Ltd., Puuinfo and Finnish Forest Industries Federation, Helsinki, Finland. (in Finnish).

The authors are, respectively, Senior Scientist and Professor, Faculty of Forestry, Univ. of Joensuu, Box 111, FIN-80101 Joensuu, Finland; and Professor, Finnish Forest Research Institute, Joensuu Research Centre, Box 68, FIN-80101 Joensuu, Finland. Research data collection and data analyses were mainly funded through the research projects of the Finnish Forest Research Institute I 994-2000. Financial and labor support for sampling the empirical materials in forest was received from UPM-Kymmene Corp., Forest Dept., Enso-Gutzeit Ltd., Forest Dept., and Metsaliitto Co-op. The prediction calculations were performed at the Univ. of Joensuu in the research projects "Databases of timber procurement enterprise and forest mensuration as a basis for operational planning" and "Group decision support in wood procurement," funded by the Academy of Finland. This paper was received for publication in January 2002. Article No. 9430.

[C] Forest Products Society 2003.

End-use oriented sawing, which has become more and more popular for Norway spruce, demands more accurate evaluation of the inner quality of trees to be logged. The needed description includes characteristics such as wood density, decay, amount of heartwood, and knottiness. The prediction of these variables using commonly measured tree- and stand wise variables has been found very difficult. Due to the complex correlation of the variables, the use of non-parametric regression methods in the prediction of properties of spruce trees is one alternative. The emphasis of this study was to test possibilities to predict the yield and internal quality of spruce trees and value of lumber and side products by stand and tree factors for traditionally oriented sawing with two non-parametric nearest neighbor methods: k-nearest-neighbor (k-nn) most similar neighbor (MSN) and locally adaptable neighborhood (LAN) MSN method, by using data that were collected in a large research project performed by the Finnish Forest Research Institute. The methods were compared by using treewise and standwise information in prediction. According to the results of this study, the non-parametric nearest neighbor methods seem to provide one interesting option to estimate the internal quality and value of Norway spruce trees. The (LAN) MSN method was found to be slightly better than the k-an MSN method inmost cases when using relative root mean square error as the criteria to compare results. Treewise information improved the accuracy of the methods compared to the results of standwise input information.

**********

Norway spruce became the most important species for the Finnish sawmilling industries at the beginning of the 1990s, after the dominant period of Scots pine from the start-up of industrial export sawing in the 1850s. During recent years, spruce has been sawn more than pine, excluding the later half of 2001 (Sevola 2001). The average unit price of spruce lumber also exceeded that of pine lumber, at least for a period in 1998, as well (Sevola 2001; Wood Focus 2001, 2000). In this situation, increasing attention must be paid to the improved utilization of the properties and quality of spruce trees and logs, to maximize the net revenue from the wood raw materials available. For sawmilling, this means embarking on an end-use-oriented philosophy for further processing, and, simultaneously, a market-oriented approach (e.g., Verkasalo et al. 200 la, b).

It is commonly acknowledged in Finland that there is a considerable lack of knowledge concerning the factors for the quality of Norway spruce, compared with Scots pine and European birch species, in particular. It is not only for the lack of research but, thus far, somewhat biased uses as well. Spruce timber has mainly been used for mechanical pulping and further for wood-containing paper grades and sawn goods for structural uses. Accordingly, it is not unexpected that the control of timber flow by its quality was considered a secondary issue. Moreover, variation in the unit price of timber assortments and lumber grades was relatively small, compared, again, with pine and birch (Sevola 2001; Wood Focus 2001, 2000). The potential to predict the internal quality of spruce is also considered relatively weak, particularly for knottiness (e.g., Verkasalo et al. 2001a,b; Makinen et al. 2001; Karkkainen 1986a,b).

Growth and diversification in the end uses of and markets for spruce products were relatively rapid during the 1990s. Building products, i.e., structural uses, continue to be the predominant end uses of spruce lumber, but the importance of joinery, interior panels, furniture, glued products, log houses, and miscellaneous special products is growing. In addition to lumber, industries started to produce structural plywood, laminated veneer lumber (LVL) (Kertowood), and novel Kraft pulps (armoring fiber) in large amounts. Now, the implementation of dedicated spruce plywood mills and LVL mills has greatly solved the problem of the underutilized resources of big-dimensioned spruce in southern Finland (e.g., Pennanen and YliHukkala 1994, Verkasalo 1992).

All this resulted in an increased need for end-use-oriented procurement of spruce timber, evaluation and pricing of spruce timber by quality, and forest management toward high-quality spruce. Accordingly, proper prediction of the properties and quality, both internal and external, is needed to analyze their potential for different end uses of mechanical processing. This is needed to select the appropriate stands, trees, and logs for the appropriate production plants and end products, and for bucking, sorting, and grading logs, controlling timber storage, and planning sawing operations.

The description of internal quality includes characteristics such as wood density, decay, amount of heartwood, and knottiness. The prediction of these variables using commonly measured tree-and standwise variables was generally found very difficult. Regression models were constructed but correlation between tree variables (diameter at breast height (DBH) for example) and these characteristics were found weak and complex. Moreover, the separate prediction of these variables did not guarantee logical dependent estimates between these variables.

Most of the regression models describing quality in boreal conditions were constructed for external variables and for Scots pine. These equations included different models for crown height and branchiness (Makinen and Colin 1999, 1998; Uusitalo and Kivinen 1998; Hynynen 1995; Karkkainen 1986a). In the studies of Makinen and Colin (1999, 1998), the size, birth, death, and pruning of Scots pine branches were considered. Corresponding models were constructed also for Norway spruce in Finland (Makinen et al. 2001, Karkkainen 1986a). Different kinds of branchiness models were constructed for Norway spruce by Houllier et al. (1995) and Karkkainen (1986a, 1972), and for Douglas-fir by Maguire et al. (1994). In the case of internal quality, heartwood curves of Scots pine (Ojansuu and Maltamo 1995) and different models describing wood density (e.g. Hakkila

1979, 1966) were created.

Although a nationwide taper curve model exists for Norway spruce in Finland (Laasasenaho 1982), there are only a few models considering internal quality of Norway spruce. Karkkainen (1986a) presented a way to divide stems to zones of dead and living branches. These models considered Scots pine, Norway spruce, and birch species. The wood density of Norway spruce was examined in Finland by Hakkila (2001, 1979, 1968, 1966), Saranpaa (1994), Karkkainen (1984), and Hakkila and Uusvaara (1968). Different models also exist for describing decaying of Norway spruce. These studies include the probability of the existence of decay, the amount of decay, and the spread of butt rot (Moykkynen et al. 1998, Tamminen 1985, Hypponen and Norokorpi 1979, Norokorpi 1979, Tuimala 1979, Kallio and Norokorpi 1972).

Due to the complex correlation of internal variables, the use of non-parametric regression methods in the prediction of properties concerning spruce trees is one alternative. According to Altman (1992), these methods are suitable especially for complex situations and for comparing different models. These methods predict the value of the variable of interest as the weighted average of the values on most identical observations, the neighbors being defined with the predicting variables (Altman 1992, Hardle 1989). All variables of interest can be predicted simultaneously and the original covariance structure of variables remains. Furthermore, unrealistic estimates cannot be produced because they are based on measured observations.

The non-parametric prediction methods used in forestry include, for example, k-nearest neighbor (k-nn) and most similar neighbor (MSN) (Moeur and Stage 1995, Kilkki and Paivinen 1987). The accuracy of the non-parametric methods was observed to be similar to the compared parametric methods (Haara et al. 1997, Moeur and Stage 1995) or even better (Maltamo and Kangas 1998) and they were found useful in many forestry applications (e.g. Malinen et al. 2001, Tommola et al. 1999). In the case of tree quality, the non-parametric two-dimensional kernel regression was used by Uusitalo and Kivinen (1998) to generalize sample tree information of crown heights for tally trees. The results were very promising but this approach cannot not be used for prediction but only for generalization.

However, there are some disadvantages in the use of non-parametric methods. These methods require comprehensive reference material in applications. In addition, it is not ensured that the estimates are unbiased. At the boundary of the predictor space, the neighborhood is asymmetric and models tend to be highly biased. Bias can be a problem concerning the interior as well if the predictors are non-uniform or if the regression function has substantial curvature. By increasing the number of neighbors, we can enhance the local validity of a model but at the same time the bias of results increases.

The emphasis of this study was to test possibilities to predict the yield and internal quality of Norway spruce trees and the value of lumber and side-products by stand and tree factors for traditionally oriented sawing with the non-parametric k-nn MSN (Malinen et al. 2003) and locally adaptable neighborhood (LAN) MSN methods (Malinen 2001).

Material and methods

Study material

At the Finnish Forest Research Institute, a large research project on predicting and controlling the properties and quality of trees and logs of Norway spruce for mechanical wood processing was performed in 1994 to 1998. For the project, 240 sawn timber trees were sampled from 48 spruce-dominated mature or nearly mature stands in southern Finland (five trees per stand).

The entire range of diameter distribution of the sawn timber trees was covered in each stand, with the minimum and maximum of 18 and 40 cm, respectively. Only dominant and co-dominant, visually healthy trees, whose neighboring trees were all spruces and that met the minimum commercial requirements for sawn timber trees were accepted. However, limits for knottiness could be exceeded; this was even desirable for the objectives of the study. Trees meeting all these requirements were divided by descending DBH into five groups, of which one tree was selected for the material by random sampling.

The sample of the study was evenly divided into four geographic regions in the southern half of Finland: 1) southern Finland, coastal area; 2) southern Finland, inland; 3) western Finland, Suomenselka; and 4) eastern Finland, Savo (Fig. 1). Regions 2 and 4 are considered to represent good growth and quality potential for Norway spruce in Finland, whereas regions 1 and 3 are considered fringe areas for producing spruce timber.

For each region, the subsamples were evenly divided by soil and regeneration types into: 1) mineral uplands, naturally regenerated stands; 2) mineral uplands, planted stands; and 3) fertile peatlands, naturally regenerated stands. Soil fertility was, in each stand, at the level of Vaccinium myrtillus type (MT) or Oxalis-Myrtillus type (OMT), which correspond to semifertile and fertile soil types in Finland. Each stand had been treated in accordance with the principles of regular silviculture, i.e., by appropriate tending, spacing, and thinning operations. The years of silvicultural operations and timber cuttings were recorded for each stand. The desired interval in the age of the stands was 50 to 120 years for each stratum of geographic region and type of soil and regeneration. Means and standard deviations of selected properties for the sample trees by using the previously mentioned classification are shown in Table 1.

Field and laboratory measurements

DBH was measured on all trees at each sample plot of 30 m by 30 m, which were placed into a visually representative part of a stand. The following stand-level factors were determined for each sample plot: soil type, spacing (number of trees per hectare), basal area and its distribution by tree species, and mean age, height, and DBH of spruces among dominant trees.

The following factors were determined for each of the five sample trees on a plot: biological crown type (five categories) and crown level class (four categories), both by using the classification by Ilvessalo (1929); biological age at the stump; height; lower level of dead branches; lower limit of living crown; lowest dead branch; lowest living branch; external defects and their heights; selected diameters at the fixed heights in a tree (0.1,0.5,1.3,2,3,4,5,6,8, ... in); maximum crown width and its compass reading; perpendicular to the maximum crown width and its compass reading; distances and their compass readings to the closest five trees; vertical locations of and average branch angles in all whorls; and the types and diameters of branches recorded to the 6-cm diameter.

Laboratory measurements were performed on sample discs at the before-mentioned heights from all sample trees for diameters, bark thickness, cross-sectional geometry, pith eccentricity, and extent of heartwood and compression wood, and on sample whorls (over-healed, self-pruned, and un-pruned) closest to the before-mentioned wood samples for the diameters and quality of knots at fixed radial locations (on the surface under bark and at consecutive 3-cm distances perpendicular to the stem axis). For the investigations on the vertical and radial frequency, extent, and quality of adventive knots (compared with whorl knots), 1-in logs were cut at 3 heights from 20 trees from 4 selected stands. The logs were rotary-cut into 1.5-aim thickness and the number of whorls and adventive knots were separately recorded by diameter class (5-mm classification) at each consecutive half of the logs.

Spatial pattern of forest

For each sample tree, according to the distances and their compass readings to the closest five trees, the spatial pattern of forest was analyzed by using angle indices ([W.sub.i]) (Gadow et al. 1998). Each intermediate angle from tree I to two of its neighbors was calculated, and that value was compared to the so-called standard angle ([[alpha].sub.0]), which is equal to 360[degrees]/n, where n is the selected number of neighboring trees. The spatial structure described by angle index of the ith tree with its n nearest neighbors is the following:

[W.sub.i] = 1/n [summation over (n/j=1)] [Z.sub.y] (1)

where:

[Z.sub.ij] 1, if the jth angle c~ is less than [[alpha].sub.0].

[Z.sub.ij] = 0, otherwise

The value of the angle index describes the regularity of the distribution of trees. Value zero means that the spatial pattern is very regular, values close to 0.5 means a randomly distributed forest, and 1 means a very clumped forest.

Generating the internal structure for sample trees

Field and laboratory data were used to generate the external and internal structure of trees by computer calculations. The stem curve over and under bark and the limit between heartwood and sapwood was generated for each sample tree by polynomial spline functions based on diameters on the sample discs at the before-mentioned heights, and total tree height (Lahtinen and Laasasenaho 1979). For the limit of heartwood and sapwood, means of minimum and maximum diameter on each disc were used. Zones of compression wood were placed into trees by linear smoothing from the consecutive measurements on vertical discs. The area of compression wood was planimetrically measured at each disc by using visual evaluation of the boundaries.

Internal knots were created for all trees by multivariate polynomial regression models based on the sample whorl measurements. The following models were generated to predict the relative diameter of internal knots, in comparison with the diameter of each knot on the tangential surface of tree without bark (Eq. (2), Verkasalo et al. 2001b), and, for dry knots and knot bumps, the relative distance from point of death for internal knots from the tangential surface of tree under bark, in comparison with the radius without bark (Eq. (3), Verkasalo et al. 2001b):

[Y.sub.1] = 0.270 + 1.119[X.sub.1] + 0.4053[X.sup.1.sub.2] - 0.7347[X.sup.3.sub.1] - 0.1945[X.sub.2]

N = 4218, [r.sup.2] = 0.74, [S.sub.E] = 0.139 (2)

where:

[Y.sub.1] = relative diameter of knot, in comparison with the diameter of each knot on the tangential surface of tree (without bark)

[X.sub.1] = for green knots, relative distance from the tangential surface of tree (without bark), in comparison with the radius (without bark); for dry knots, relative distance from the point of death, in comparison with the distance from the pith to the point of death

[X.sub.2] = relative height in a tree, in comparison with the total height from the felling height to the tip

[Y.sub.2] = 0.5188 - 0.5479[X.sub.1] +

0.001373[X.sup.-1.sub.1] - 8.0212 * [l0.sup.-6][X.sup.-2.sub.1] +

5.293 * [10.sup.9][X.sup.-3.sub.1] - 0.01165[X.sub.2] +

0.7879[X.sup.-1.sub.2] - 0.5353[X.sup.-2.sub.2]

N = 2320, [r.sup.2] = 0.54, [S.sub.E] = 0.133 (3)

where:

[Y.sub.2] = relative distance of point of death from the tangential surface of tree under bark, in comparison with the radius (without bark)

[X.sub.1] = relative height in a tree, in comparison with the total height from the felling height to the tip

[X.sub.2] = knot diameter on the tangential surface of tree (without bark)

So far, the frequency or maximum diameter of sound and dead adventive knots in different radial zones could not be predicted satisfactorily by tree or stand factors. This was probably due to two factors: 1) obviously, their start and death are not regulated by the variables measured in the study material; and 2) for technical reasons, logs could not be rotary-cut to diameters less than 8 cm. Instead, the frequency of sound and dead adventive knots at different heights could be predicted by DBH and diameter at the particular height. These relationships were used to create internal adventive knots.

Simulating cross-cutting trees and sawing logs

The predicted stems were bucked theoretically to logs by particular simulating programs for this research (Verkasalo et al. 200 la,b). In this study, the conventional dimensions of sawlogs were used: six lengths (4.3 to 5.8 in), minimum top diameter 16 cm (on the bark); small-dimensioned sawlogs: one length (4.3 in), minimum top diameter 12 cm (o.b.); pulpwood: minimum length 3 m, minimum top diameter 7 cm (o.b.).

The logs were theoretically sawn by simulating computer programs, by using sawing patterns of a traditionally operating large sawmill (Verkasalo et al. 2001 a,b). Primary sawing is based on cant chipper and band sawing techniques. Sawing direction was determined according to the minimum and maximum diameter of the log.

Lumber grading and pricing, determining the gross value of trees

The simulated sawn goods were fresh-graded according to the rules of the Nordic Timber Grading Rules (1994) (Verkasalo et al. 2001a,b). For grading, knots generated into the trees were projected on the faces and edges of each piece of lumber for the diameter and quality of the knot. Zones of heartwood and compression wood were placed within each piece of lumber as well. Grade for each piece of lumber was determined by using dimension, knottiness, compression wood, and wane. The simulated sawn goods were priced by using dimension and grade, in accordance with the price list of a particular sawmill. The average prices of the lumber grades from the years 1994 and 1995 were used. Sideproducts were priced according to the actual market prices for each sawmill at that time.

These procedures produce grade distribution of lumber, and gross value of lumber, chips, sawdust, bark and pulpwood. These data were used to compute the gross value of trees.

Non-parametric estimation methods

The non-parametric estimation methods used in this study are based on distance-weighted nearest neighbors estimation, where the search for similar reference trees is done by using easily measurable mean stand and tree variables. Reference trees are used to characterize the target tree properties (Fig. 2). The distance measure of similarity is needed to compare different trees and their characteristics and is calculated for each stand. In the estimation phase, differences across all reference trees are calculated and properties are formed using chosen neighbor trees.

The variables describing a tree used in the similarity distance function were chosen with two different principles. In the first model, the model has been constructed with the concept that information on a tree and its surroundings can be measured (Table 2). In the second model, this kind of treewise information is not available, but the stand characteristics are known. However, in the standwise model, diameter distribution is expected to be measured or estimated as well as tree heights.

Before the nearest neighbors method can be applied, it is necessary to decide:

1. the form of distance function to be used for finding the most similar reference trees;

2. the number of nearest neighbors or process for selecting an appropriate neighborhood;

3. the form of weight function for weighting the reference trees.

In this study, the similarity of target and reference trees was measured according to the MSN inference (Moeur and Stage 1995). The similarity function used in the MSN method is a generalized Mahalanobis distance (Mahalanobis 1936). A canonical correlation analysis provides a unified multivariate approach to the computation of the weighting matrix in the distance function, by summarizing the relationship between a set of search attributes and a set of design attributes simultaneously. The MSN similarity measure derived from the canonical correlation analysis is:

[D.sup.2.sub.uj] = [([X.sub.u] - [X.sub.j]).sub.lxp][GAMMA] [[LAMBDA].sup.2.sub.pxp] [LAMBDA]'

[[X.sub.u] - [X.sub.j]'.sub.pxi] [4] where:

D = distance between observations

X = vector of known search variables from target observation

[X.sub.j] = vector of search variables from reference observations

[GAMMA] = matrix of canonical coefficients of indicator variables

[LAMBDA] = diagonal matrix of squared canonical correlation

In the MSN similarity function, the weighting matrix weights the elements of search variables according to their predictive power for all elements of design variables simultaneously, while incorporating the covariance between the elements of design attributes.

The optimal number of neighbors used in the k-nn MSN method can be determined by using the cross-validation method, for example by minimizing the relative root mean square error (RMSE) (Eq. [5]) of certain characteristics. The minimization of relative RMSE emphasizes local accuracy of estimates more than average accuracy of estimates. In the used cross-validation method, a target tree is a tree that is excluded from reference trees and for which estimates are calculated. Each tree from reference data is, in turn, used as the target tree.

RMSE% = 100 x [square root][[summation over](n/j=1)] [y.sub.ij] - [[y.sub.ij].sup.2]/n-1/[y.sub.i] [5]

where:

n = number of observations

[y.sub.ij] = real value of the variable in tree j

[y.sub.ij] = estimated value of the variable i in tree j

[y.sub.i] = mean of estimates of variable i

Large neighborhoods can affect the bias in the boundary situations or in the situations where the reference data are distorted. The nearest neighbors may be located on the same side of the input space, even in the situations where observations exist on the other side of the input space (Fig. 3). Recognizing these situations and adjusting locally the amount of the neighbors and selecting the combination of neighbors symmetrically can reduce the bias of estimates.

The information used in the selection of the local neighborhood must be produced from neighborhood observations and predictor variables of the target stand. In the LAN MSN method, every possible combination of neighborhood is examined, in turn, and the averages of predictor variables of neighborhood combinations are calculated. Every vector of average predictor variables of possible neighborhood combinations is compared to the vector of predictor variables of the target stand with MSN metrics and the combination of neighbors that is most identical to the target stand is chosen to be used in the calculation of estimates.

The neighborhood, from which the optimal neighborhood is selected, is limited to 15 neighbors due to computer time consumption. Demand for computer time increases by 2", when the size of the neighborhood (n) is expanded.

Results

The performance of the nearest neighbor methods is greatly affected by the number of selected neighbors in the estimation process. The optimal number depends on the objectives of the user. When the used criterion is average goodness, the optimal number of neighbors is larger. Vice versa, if the user minimizes bias, the optimal number of neighbors is smaller, usually one. RMSE is located between these two ends. It weights average goodness of estimates but uses square errors to punish large variation of bias.

In this study, the optimal number of neighbors varied around five (e.g., Fig. 4) and, therefore, the size of the neighborhood was set to be five in the k-nn MSN method. In the LAN MSN method, the optimal number and combination of neighbors is set in each estimation situation according to the shape of the surrounding neighborhood. The average number of used neighbors was four and number of neighbors used varied between one and eight.

For the study, two different models were used:

1. the treewise model, where treewise information, such as spatial information and crown information, was available;

2. the standwise model, where treewise information was not available; however, the breast height diameter distribution and heights were assumed to be known or estimated.

The yield estimates for the treewise model were clearly more accurate than the standwise model estimates for the sawlog volume, bark volume, and chips volume (Table 3). However, pulpwood estimates did not differ in these models.

The nearest neighbor MSN method can be tailored to every estimation situation according to user preferences by input variable selection. When optimizing the model with emphasis on the internal quality, the error of sawlog volume estimates were relatively high compared to the model, where accurate sawlog volume estimates were preferred (Table 3). While the sawlog volume and pulpwood volume includes the volume of bark and chips, the accuracy of the bark and chips volume estimates is strongly correlated with the sawlog volumes.

There was no difference between the optimized treewise model and standwise model, when the sawlog volume was preferred. The treewise data made estimates less accurate and the optimal model includes only tree size information, which was assumed to be known in both situations.

When estimating the internal quality of spruce trees, the results were slightly more preferable for the treewise model than for the standwise model (Table 4). When accuracy of sawlog volume estimates was preferred, the estimates were clearly more inaccurate, except for basic density in the rest of the wood and volume of heartwood. It could be assumed that density, as an average in the rest of the wood, depends more on the size of the estimated tree than on the properties of the surroundings and the tree itself. When the volume of heartwood is concerned, it was quite expected that estimates are better, due to the more accurate overall volume estimates.

Estimating the total value derived from products greatly depended on volume estimates, and therefore, the emphasis on the sawlog volume (Table 5) produced most accurate total value estimates. Sawn timber value per cubic meter was dependent on the quality of input information, but it was unexpected that the total value per cubic meter did not seem to correlate with the predictor variables. A reason for this unexpected result might be that the total value per cubic meter also depends on the obtained amount of sideproducts (bark and chips) and the relative amount of sideproducts depends on the size of the tree.

Discussion

This study examined the use of two non-parametric nearest neighbors methods in the context of prediction of yield and internal quality of Norway spruce trees and value of lumber and sideproducts according to selected stand- and treewise predictors. The fundamental idea in these methods is to find trees similar to the tree that is the subject of interest from empirical data and to use measured empirical data from similar trees to produce estimates.

According to the results obtained in the present study, the tested methods seem to provide an interesting option to estimate the internal quality of trees. The use of the large empirical data as reference material ensured that estimates were always reasonable and impossible predictions, as with the case of parameter estimators, didn't occur. When considering different level input information, the treewise input data produced more accurate estimates, as expected, but standwise input data may be used as well.

Although results were promising, it must be kept in mind that there are many possible sources of error. It is not ensured that data measurements are totally unbiased, the simulation procedure may involve unsure assumptions and resultant inaccuracy and systematic errors, and models may include bias. The efficiency of these methods could be improved by increasing the number and diversity of reference trees, by measuring new variables to be used as predictor variables, or by tailoring methods to be more appropriate for every estimation situation.

In the non-parametric methods, the reference data used are crucial in many ways. Methods are, even at their best, only as good as the data used. These methods only point out the most similar trees and if the data does not include similar trees, then the target tree estimates may be inaccurate. In the case of inner quality, the measurement of representative data is expensive and laborious. However, this might not be the situation in the future. One interesting possibility to collect usable data is to use an ultra-sound-based or x-ray-based wood scanner that is can be placed in the harvester head of a modern harvester.

If methods of this kind are used in practice, it would be necessary to have:

1. comprehensive data from the application area;

2. three-dimensional models of tree properties, including, for example, branch models and heartwood models etc.

3. simulating software, which is capable of bucking trees according to customer demands and sawing bucked trees into products according to desired sawing parameters.

With an application of this kind, it is possible to create a practical application to be used in wood procurement planning purposes.

[FIGURE 4 OMITTED]

Table 1 Means and standard deviations of selected properties of sample trees by geographic region and type of soil and regeneration of the stand. DBH Type of soil/ Geographic Number of regeneration region sample trees Mean SD (cm) Mineral upland/ natural regener. 1 20 30.6 8.3 2 25 26.9 6.5 3 25 27.6 5.2 4 20 27.3 5.9 Total 90 28.0 6.5 Mineral upland/planted 1 20 24.9 4.9 2 15 24.3 4.5 3 15 25.4 3.8 4 20 29.6 5.8 Total 70 26.2 5.2 Fertile peatland/ natural regener. 1 20 27.6 6.8 2 20 27.1 4.9 3 20 26.4 4.5 4 20 23.8 4.3 Total 80 26.2 5.0 Age Hight Type of soil/ regeneration Mean SD Mean SD (yr.) (m) Mineral upland/ natural regener. 86 24 24.4 2.6 81 28 23.4 3.4 108 21 22.5 2.3 102 13 22.9 2.8 94 25 23.2 2.9 Mineral upland/planted 66 10 24.1 3.2 57 12 22.3 2.4 70 6 21.8 2.9 66 8 24.6 3.0 65 10 23.4 3.1 Fertile peatland/ natural regener. 789 27 23.9 3.0 99 34 23.0 2.7 126 25 21.7 2.5 107 16 20.1 2.3 111 26 22.0 2.9 Volume Type of soil/ regeneration Mean SD ([dm.sup.3]) Mineral upland/ natural regener. 930 501 698 371 664 256 705 318 742 375 Mineral upland/planted 653 337 528 233 571 249 962 348 668 325 Fertile peatland/ natural regener. 769 424 715 324 595 281 473 224 627 321 Table 2 Predictor variables used in estimation. Predictor variables in treewise Predictor variables in standwise model model Relative proportion of tree species Relative proportion of tree species Number of stems/hectare Number of stems/hectare Basal area ([m.sup.2] ) Basal area ([m.sup.2]) Stand age (yr.) Stand age (yr.) Mean diameter Mean diameter Forest site type Forest site type Mean distance of five nearest trees Diameter Angle index Height Diameter Height Volume Age Contraction Slenderness Lower level of dead branches Lower limit of living crown Table 3 Relative RMSE (%) of estimated yield of timber assortments. Emphasison the internal quality,treewise model k-nn MSN LAN MSN % Sawlog volume 17.33 14.04 Pulpwood volume 32.39 34.38 Bark volume 22.09 20.59 Chips volume 18.67 16.00 Emphasis on the internal quality, standwise model k-nn MSN LAN MSN % Sawlog volume 23.23 17.70 Pulpwood volume 32.88 34.51 Bark volume 28.30 24.94 Chips volume 24.70 19.80 Emphasis on the sawlog volume k-nn MSN LAN MSN % Sawlog volume 8.24 6.69 Pulpwood volume 35.40 34.02 Bark volume 19.43 19.23 Chips volume 12.17 10.53 Table 4 Relative RMSE (%) of estimated internal structure of trees. Emphasis on the internal quality, treewise model k-nn MSN LAN MSN % Ring width in base log 22.16 23.29 Ring width in rest of wood 22.37 22.08 Basic density in base log 7.90 8.02 Basic density in rest of wood 20.59 19.02 Volume of heartwood 30.45 33.25 Width of sapwood in breast height 24.93 24.45 Width of sapwood in 5.5 m 24.10 23.03 Emphasis on the internal quality, standwise model k-nn MSN LAN MSN % Ring width in base log 26.51 25.31 Ring width in rest of wood 26.84 27.55 Basic density in base log 8.26 8.24 Basic density in rest of wood 20.76 22.66 Volume of heartwood 38.04 33.50 Width of sapwood in breast height 25.46 26.35 Width of sapwood in 5.5 m 24.07 24.70 Emphasis on the sawlog volume k-nn MSN LAN MSN % Ring width in base log 36.81 37.67 Ring width in rest of wood 36.82 36.65 Basic density in base log 8.56 8.38 Basic density in rest of wood 16.74 18.15 Volume of heartwood 27.88 24.97 Width of sapwood in breast height 27.62 25.89 Width of sapwood in 5.5 m 25.88 25.30 Table 5 Relative RMSE (%) of estimated value of trees derived from the products. Emphasison the internal quality,treewise model k-nn MSN LAN MSN (%) Total value 17.17 13.76 (solid) 7.66 7.47 Euro/[m.sup.3] 6.08 5.88 Emphasis on theinternal quality, standwisemodel k-nn MSN LAN MSN (%) Total value 22.48 17.12 (solid) 8.40 8.50 Euro/[m.sup.3] 6.66 6.64 Emphasis on the sawlog volume k-nn MSN LAN MSN (%) Total value 10.13 9.48 (solid) 7.83 8.01 Euro/[m.sup.3] 6.98 7.06

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The authors are, respectively, Senior Scientist and Professor, Faculty of Forestry, Univ. of Joensuu, Box 111, FIN-80101 Joensuu, Finland; and Professor, Finnish Forest Research Institute, Joensuu Research Centre, Box 68, FIN-80101 Joensuu, Finland. Research data collection and data analyses were mainly funded through the research projects of the Finnish Forest Research Institute I 994-2000. Financial and labor support for sampling the empirical materials in forest was received from UPM-Kymmene Corp., Forest Dept., Enso-Gutzeit Ltd., Forest Dept., and Metsaliitto Co-op. The prediction calculations were performed at the Univ. of Joensuu in the research projects "Databases of timber procurement enterprise and forest mensuration as a basis for operational planning" and "Group decision support in wood procurement," funded by the Academy of Finland. This paper was received for publication in January 2002. Article No. 9430.

[C] Forest Products Society 2003.

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Author: | Malinen, Jukka; Maltamo, Matti; Verkasalo, Erkki |
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Publication: | Forest Products Journal |

Geographic Code: | 4EXNO |

Date: | Apr 1, 2003 |

Words: | 7107 |

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