Modelling the distribution of wood properties along the stems of Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) Karst.) as affected by silvicultural management

Forest Ecology and Management 256 (2008) 1356–1371

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Modelling the distribution of wood properties along the stems of Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) Karst.) as affected by silvicultural management Veli-Pekka Ikonen a,*, Heli Peltola a, Lars Wilhelmsson b, Antti Kilpela¨inen a, Hannu Va¨isa¨nen a, Tuula Nuutinen c, Seppo Kelloma¨ki a a

University of Joensuu, Faculty of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland Skogforsk, The Forestry Research Institute of Sweden, Uppsala Science Park, S-751 83 Uppsala, Sweden c The Finnish Forest Research Institute, Joensuu Research Unit, P.O. Box 68, FI-80101 Joensuu, Finland b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 17 April 2008 Received in revised form 26 June 2008 Accepted 30 June 2008

In this work, empirical ring-based models were developed to predict the distribution of early wood percentage, wood density and fibre length along the stems of Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) Karst.) as affected by silvicultural management. The performance of the ring-based models was also compared for Scots pine and Norway spruce with corresponding disc-based (crosssectional) models. Moreover, both models were integrated with example simulations by a process-based growth and yield model to analyze how management, such as thinning, affects the growth and wood properties of Scots pine trees over a rotation as an average for the tree stem, but also along the stem. The ring-based models built for annual early wood percentage (explained by ring width), air dry wood density (explained by early wood percentage and cambial age) and fibre length (explained by radial growth percentage and cambial age) predicted reasonably well the wood properties both at an intra-ring level, but also at a cross-sectional level. These predictions were also reasonably well in line with corresponding cross-sectional predictions by the disc-based models (which predicted the properties based on the number of annual rings and diameter at breast height and/or the cross-section being considered and temperature sum). The example simulations also demonstrated that both models predicted slightly lower wood density for dominant trees compared to dominated ones grown in thinned and unthinned Scots pine stands over a rotation. Unlike the disc-based model, the ring-based model predicted, on average, higher early wood percentage in dominant trees than in dominated ones. However, fibre length was not significantly affected when the averages of the whole stems were predicted, and this held true for both ring- and disc-based models. In summary, the incorporation of empirical ring-based wood property models into a process-based growth and yield model, offers a means to study in detail how environmental conditions, forest structure and management affect the quantity and properties of stem wood produced over a rotation. The discbased wood property models used in this work are based on data with large geographical and genetic variation, and therefore may turn out to be more applicable for predicting future wood and fibre resources at a regional and national level. This kind of integrated use of wood property models with a process-based growth and yield model could help us to evaluate the forest resources under current and changing climate. ß 2008 Elsevier B.V. All rights reserved.

Keywords: Early wood percentage Wood density Fibre length Tree status Process-based modelling Empirical modelling

1. Introduction * Corresponding author. Tel.: +358 13 251 4401; fax: +358 13 251 4444. E-mail addresses: veli-pekka.ikonen@joensuu.fi (V.-P. Ikonen), heli.peltola@joensuu.fi (H. Peltola), [email protected] (L. Wilhelmsson), antti.kilpelainen@joensuu.fi (A. Kilpela¨inen), hannu.vaisanen@joensuu.fi (H. Va¨isa¨nen), tuula.nuutinen@metla.fi (T. Nuutinen), seppo.kellomaki@joensuu.fi (S. Kelloma¨ki). 0378-1127/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.foreco.2008.06.039

Silvicultural management affects the growth and yield and the consequent stem and wood properties of different genotypes through interactions between biological processes (e.g. height growth, radial growth of the stem and crown development) and environmental conditions (e.g. temperature, precipitation, nutri-

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ents and light). Correspondingly, the stem and wood properties of trees affect the suitability of wood as a raw material for mechanical wood processing and the quality of the end products. The wood and fibre properties also affect the processing as well as the quality and quantity of the pulp and paper and other forest-based products produced. In the forest industry, where even small changes in the material properties of wood may be extremely important, proper information on material properties of raw material would potentially allow the selection of the raw material for its most suitable purposes. Therefore, there exists a need for a deeper understanding of how environmental factors, forest structure and management affect the growth of trees within a stand and consequently the material properties of the stem and wood. Silvicultural management such as the selection of tree species and genotype, spacing, thinning type and its intensity and fertilization are known to affect the growth and formation of wood properties of tree stands by changing the growth rate of the trees within stands. Competition for light tends to modify the allocation of growth along the stem, whereas competition for water and/or nutrients affects the overall growth rate (Cannell et al., 1984; Nilsson and Gemmel, 1993; Nilsson, 1994). Management, such as thinning, increases the living space of individual trees, resulting in faster growth and wider annual rings, having implications also for, e.g. wood density, early wood content and fibre properties. This is because wood properties are linked with the distribution of growth over the stem (Hakkila, 1966; Uusvaara, 1974; Saikku, 1975). However, the magnitude of the effect may vary depending on tree species, type (from above or from below) and intensity of thinning, the length of interval between thinnings, the position of the tree in the stand (dominant, intermediate or suppressed) and the cambial age (i.e. especially the phase of forming juvenile or mature wood) (Olesen, 1977; Moschler et al., 1989; Duchesne et al., 1997; Tasissa and Burkhart, 1998; Pape, 1999a,b; Wilhelmsson et al., 2000; Mo¨rling, 2002; Jaakkola et al., 2005a,b; Peltola et al., 2007). In recent years, interest in models that could predict growth and yield, but also stem and wood properties, has increased and led to the development of various models, e.g. empirical models for timber properties (Leban et al., 1996; Tian and Cown, 1996; Kelloma¨ki et al., 1999; Moberg, 2000, 2001; Ikonen et al., 2003; Kantola et al., 2007). Similarly, models predicting average wood and fibre properties (e.g. wood density, late-wood percentage and fibre length) for cross-sections along the stems of Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) Karst.) have been developed by Wilhelmsson et al. (2002) and Ekenstedt et al. (2003). These models are based on input variables such as number of rings, diameter of stem cross-sections and average climate conditions during growth, expressed by estimated temperature sum according to More´n and Perttu (1994). The models were developed for characterisation of wood and fibre properties of different assortments, type of stands, trees and logs within stems before, during and after harvesting operations. In these models, the most important previously known sources of variation were considered to be geographical location (latitude and altitude), site fertility, inter-tree competition, cambial ages along stems, and genetic variation between individuals (Wilhelmsson et al., 2002). The primary goal with these disc-based models (predicting cross-

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sectional averages) has been to improve efficiency and give added value in industrial wood supply chains by proper selection of wood and fibres for different purposes. On the other hand, process-based growth and yield models, developed in recent years, have also several strengths. They start from processes such as photosynthesis, use weather and soil data and different tree cohorts in a stand as inputs for simulations and could, thus, predict the growth and dynamics of tree stands over a rotation as controlled by environmental conditions and management (Kelloma¨ki and Va¨isa¨nen, 1997; Matala et al., 2003). By relating annual growth to the intra-ring wood properties, they could also offer useful tools to analyze how a selected genotype in interaction with changing environmental conditions (soil and climate) and management (e.g. spacing, thinning and fertilization) affect tree growth within a stand (dominant, co-dominant and suppressed) and the development of stem and wood properties over the trees’ life-span. In this work, empirical ring-based models were developed to predict the distribution of early wood percentage, wood density and fibre length along the stems of Scots pine and Norway spruce as affected by silvicultural management. In the above context, the performance of the ring-based models was analyzed and compared with the corresponding disc-based (cross-sectional) models presented by Wilhelmsson et al. (2002) and Ekenstedt et al. (2003). The model comparison was based on use of Finnish datasets (same as used in development of ring-based models for different properties) and independent Swedish validation dataset (for wood density). Moreover, both ring- and disc-based models were integrated for Scots pine with example simulations by a process-based growth and yield model (FinnFor) to analyze how management, such as thinning, affects the growth and wood properties of Scots pine stems (e.g. in dominant and dominated trees) over a rotation as an average, but also along the stem (e.g. inner part, outer part and top part). 2. Materials and methods 2.1. Development of ring-based properties models 2.1.1. Empirical datasets measured for model development Various datasets were collected in Eastern Finland (close to Mekrija¨rvi Research Station, University of Joensuu, 628470 N, 308580 E, 145 m a.s.l.) for the development of ring-based models for early wood percentage, wood density (air dry) and fibre length in Scots pine and Norway spruce (Tables 1 and 2). The first Scots pine dataset originated from a long-term early thinning experiment established in the summer of 1986 in a naturally regenerated stand of Scots pine (ca. 40-year old) growing on a site with a rather low nitrogen supply (Vaccinium type). The second set of Scots pine data originated from a mature (90-year old, ca. 900 stems ha1) Scots pine dominated stand containing a 20% mixture of Norway spruce growing on a site with a medium fertility (Myrtillus type). The Norway spruce dataset originated from a Norway spruce dominated mature stand (about 80–90-year old, ca. 800 stems ha1) grown on a similar site as the Scots pine trees included in the second Scots pine dataset. These datasets consisted of sample discs taken at various tree heights from breast height to canopy top (Table 2), totalling 337 discs for Scots

Table 1 Numbers and averages from harvested sample trees of Scots pine and Norway spruce in Eastern Finland Tree species

Total number of trees

Tree height (m)

Dbh (cm)

Number of rings at breast height

Total number of discs

Scots pine Norway spruce

136 20

14.0 (10.2–24.0) 17.9 (11.3–24.1)

9.5 (4.1–27.6) 21 (11.3–29.5)

30 (18–83) 63 (19–95)

337 81

Range of variables given by italics.

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Table 2 General information on datasets utilised for laboratory measurements of wood density (air dry), early wood percentage and fibre length as a basis for the parameter estimation of ring-based property models Datasets

Number of trees

Laboratory measurements

Sample heights (m)

Number of discs

Number of annual rings

1. Dataset 1 for Scots pine (1998–1999)

98

ITRAX (e.g. wood density and early wood percentage)

1.3 and 6

180

3891

30a

Light microscope with Image analyses (fibre length)

1.3, 4, 6 and 10

119

1041

8

ITRAX (e.g. wood density and early wood percentage)

1.3, 4, 8 and 12 (in part of trees also 16 and 20)

38

1891

337

6823

81

3988

40

1872

2. Dataset 2 for Scots pine (2002)

Light microscope with Image analyses (fibre length) Total

136

3. Dataset for Norway spruce (2002)

20

ITRAX (e.g. wood density and early wood percentage)

Of which 10

Light microscope with Image analyses (fibre length)

1.3, 4, 8 and 12 (in part of trees also 16 and 20)

a

Unlike in other datasets, image analyses technique WinDendroTM with an Agfa scanner (Regent Instruments Inc.) was used instead of ITRAX in these earlier measurements to provide ring widths for modelling of fibre length.

pine (from 136 trees) and 81 discs from Norway spruce (from 20 trees). For wood density analyses, small rectangular wood specimens, of size 5 mm  5 mm (a radial segment from pith to bark), were cut out of stem discs using a twin-bladed circular saw. Thereafter, these wood specimens were kept for a few weeks at fixed conditions, so that they were stabilised to have moisture content of 12% (air dry). Thereafter, the wood specimens were scanned in batches using a direct scanning ITRAX X-ray microdensitometer (Cox Analytical Systems, Go¨teborg, Sweden), available at the University of Joensuu, Faculty of Forest Sciences. ITRAX works with automatic collimator alignment (Bergsten et al., 2001) at a geometrical resolution of 40 measurements per mm. In this work, the standard X-ray intensity (30 kV, 35 mA) for X-ray measurements was used, with an exposure time of 20 ms based on previous corresponding analyses by Kilpela¨inen et al. (2005) and Peltola et al. (2007). The X-ray radiographic images were further analyzed with the Density software (Bergsten et al., 2001) program to determine the intra-ring density profile for each sample from pith to bark. Based on these radiographic images and intra-ring density profiles and with the help of Excel macros, the following ring width and ring density parameters for each ring were determined: ring width (mm), early- and late-wood widths (mm) and their proportions (%), mean wood density (g cm3), minimum and maximum wood densities (g cm3) and early wood and late-wood densities (g cm3). Similar to previous corresponding analyses, the mean of the maximum and minimum intra-ring densities were used as the threshold for early- and late-wood in each ring, i.e. the values above and below this threshold representing the late- and earlywood (Kilpela¨inen et al., 2005; Peltola et al., 2007). The border between the late- and early-wood of the following year is correspondingly defined as being the point where the sharp decline of the consecutive late-wood density measurements ceases and the decrease in density evens out. These definitions used for early- and late-wood borders were earlier found to work well when ring widths and early- and late-wood widths were compared in several Scots pine samples based on X-ray density profiles and corresponding microscopic measurements (Helama et al., 2008). Intra-ring average fibre lengths were determined with a light microscope and Image Pro Plus 4.0 for Windows (Media Cybernetics, Silver Spring, MD) for each annual ring pair (2 consecutive rings) starting from bark and working towards the pith by averaging lengths of at least 25 undamaged fibres. For analysis of fibre properties, matchstick-sized wood specimens were chipped away from the stem discs and macerated in a boiling

1:1 (v/v) mixture of acetic acid and hydrogen peroxide. Altogether, significantly smaller number of sample trees could be analyzed for fibre length compared to other relevant variables due to the very time-consuming methodology used for this purpose (Table 2). Corresponding ring widths needed for fibre length modelling were measured by ITRAX (datasets 2 and 3) or image analyses technique WinDendroTM with an Agfa scanner (Regent Instruments Inc.) depending on the dataset measured (dataset 1) (Table 2). Fig. 1 shows an example of measured radial profiles of wood density and fibre lengths at different heights within a stem of Scots pine (from dataset 2). 2.1.2. Development of models Based on Finnish datasets measured (Table 2) in Scots pine and Norway spruce, empirical ring-based models for early wood percentage (of ring width), wood density (air dry) and fibre length were formulated. Various variable combinations were tested, with and without logarithmic transformations, for each wood property model based on all the ring-based measurements. Model simplicity and accuracy were the most significant criteria for the acceptance of the final model in addition to their general applicability together with the process-based growth and yield model. Instead of mixed modelling approach, it was preferred to build the models based on pooled observations, without considering variation between the stands, plots, individual trees or individual discs taken from the same tree. Thus, ring width was simply used to explain early wood percentage, whereas early wood percentage and cambial age were used to explain air dry wood density, and radial growth percentage and cambial age to explain fibre length (distance from pith is implicitly included in radial growth percentage). It was also tested other explanatory variables such as distance from pith, height and age at breast height. The parameters of the empirical models were estimated in SPSS based on linear regression methods. The models were evaluated in terms of coefficient of determination (R2), root mean-squared error (RMSE) and residual distributions. Fig. 2 shows how Finnish datasets have been used in model development and in model comparison. 2.2. Comparison of ring- and disc-based property models 2.2.1. Outlines for the disc-based property models used for model comparison The performance of ring-based property models were compared with disc-based models developed by Wilhelmsson et al. (2002) for wood density (kg m3) and late-wood percentage (%) and models developed by Ekenstedt et al. (2003) for fibre length

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Fig. 1. Graphical representation of measured wood densities and fibre lengths from pith to bark at different heights in an example from a Scots pine stem (dataset 2).

(mm) in Scots pine and Norway spruce. These models predict the average properties of a tree at a certain height (cross-section) based on variables such as the number of rings and average growth of the cross-section of discs at various tree heights and temperature sum, for example (for further detail see Appendix A). They are also based on stand and plot data from Sweden (56.6– 65.88N, 12.5–21.58E, 60–440 m a.s.l.) with a large geographical variation and cover trees grown both in younger and older stands on high- and low-fertility sites (i.e. sample trees representing large size variation) (Table 3). Between two and seven cross-sections were cut in each sample tree (i.e. at breast height, at the height of 5 m, close to the top at a diameter of 5 cm under bark and at a number of heights between depending on the size of the tree). Based on these datasets, the number of annual rings and individual ring widths separated into early- and late-wood were measured mainly by surface reflectance intensity analyses (Table 3) using an instrument developed at STFI (Lundqvist et al., 1998). Wood density was measured in terms of basic density by an X-ray and image analyses technique based on comparisons between computed tomography (CT)-scanned green and dry density, while compensating for shrinkage during drying (Lindgren and Lundqvist, 2000; Wilhelmsson et al., 2002). Fibre length, as length-weighted, was determined with the STFI FiberMaster (Ekenstedt et al., 2003). These fibre length measurements were also performed using radial sub-samples for fibres, i.e. they were produced using up to three groups of growth rings from pith to bark (rings 1–15, rings 16–30, and rings 31-bark). 2.2.2. Model comparison In a comparison of ring- and disc-based property models, both Finnish datasets and Swedish validation datasets were used. The

Finnish datasets were the same as those used for parameter estimates in the ring-based model construction for early wood, wood density and fibre length (Table 1), i.e. other independent datasets measured with comparable definitions and within ring resolutions fitting this purpose were not available. The Swedish validation datasets originated from three fast and three slowgrowing Norway spruce and Scots pine stands located in central Sweden (Table 4). Individual ring widths from pith to bark along two radii were measured by a WinDendroTM instrument where after basic densities of discs were determined by volume measurement (by water displacement) after water saturation, oven drying and dry weight measurements. More details about the datasets and measurements are presented by Wilhelmsson et al. (2000). Validation of the disc-based models has also been performed by Wilhelmsson et al. (2002). In model comparison the intra-ring early wood percentage needed for ring-based wood density models were predicted based on the corresponding ring-based model (instead of using measured data). The cross-sectional property averages were calculated based on ring-based models by weighting each predicted ring value with corresponding ring area. In a similar way, the measured crosssectional property averages needed for model comparisons were calculated based on intra-ring measurements of wood properties for both Finnish datasets and Swedish validation datasets. Wood density (air dry versus basic density), early- and latewood and fibre length were measured in the Finnish and Swedish datasets based on very different methodologies, which makes direct comparison of ring- and disc-based models inadequate. Thus, to make comparisons meaningful, it was estimated a simple linear regression model between the cross-sectional averages predicted by ring- (dependent) and disc-based models (indepen-

Table 3 General information on datasets utilised for laboratory measurements of basic density, early wood percentage and fibre length as a basis for the parameter estimation of the disc-based models for wood properties (Wilhelmsson et al., 2002) and fibre lengths (Ekenstedt et al., 2003) Datasets

Number of trees

Stand and sample tree data

Laboratory measurements

1. Scots pine (20 stands, 6 sample trees from each)

120

Height 9–24 m; Dbh 13–32 cm; age (bh) 19–130 years; 340–2923 stems ha1

Surface reflectance intensity analyses (ring width, early- and late-wood width)a Basic density by X-ray and image analyses Fibre length

504 172

Height 5–33 m; Dbh 11–38 cm; age (bh) 17–183 years; 406–3377 stems ha1

Basic density by X-ray and image analyses Late-wood percentage Fibre length

1144 1189 326

2. Norway spruce (42 stands, 6 sample trees from each)

252

Number of discs

515

a Late-wood was determined by a dual, 20–50% reflectance threshold according to Olsson et al. (1998). Moreover, another image analysis instrument operating with a single threshold of reflectance, set to 50% (WinDendroTM) was used to measure wood samples from the northernmost Scots pine stands.

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Fig. 2. Outlines for the work with development and validation of the ring-based models, validation of the disc-based models, model comparisons including residual studies, and simulation of a process-based growth and yield model in order to study effects of forest management on distribution of wood and fibre properties along the stem.

dent) based on Finnish datasets (for this purpose, wood density values in the Finnish datasets were also multiplied by 1000 to change the dimension from g cm3 into kg m3). Thereafter, the cross-sectional averages predicted by the disc-based property models were adjusted for the model comparison by following species-specific conversion factors (regression slope): 0.85 and 0.94 for early wood percentage, 1.08 and 1.09 for wood density and 1.25 and 1.05 for fibre length in Scots pine and Norway spruce, respectively. In a similar way, when the Swedish validation datasets were used as the validation data for the ring-based wood density (air dry) models in Scots pine and Norway spruce, actual

wood density (i.e. basic density of wood) values were also multiplied by the conversion factors given above. Fig. 2 shows outlines for the datasets used for model construction, calculation of predictions, validation and model comparison. 2.3. Integration of property models in Scots pine with the simulations by the process-based growth and yield model 2.3.1. Outlines for the process-based growth and yield model The performance of the ring- and disc-based property models was also demonstrated by the simulation of the development of

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Table 4 Statistics from the Swedish (independent) validation dataset (Wilhelmsson et al., 2000) Property

Species

Stands

Trees

Discs

Max

Min

Number of samples

Pine Spruce

6 6

54 54

194 197

Diameter at breast height (mm)

Pine Spruce

257 232

52 63

Number of annual rings in discs

Pine Spruce

55 50

4 4

Average disc diameter under bark (basal area weighted) (mm)

Pine Spruce

148 160

110 113

Basic density (kg m3)

Pine Spruce

439 421

370 340

Mean annual ring width (mm)

Pine Spruce

growth and wood properties over the Scots pine stems (whole stem, inner part, outer part and top part) and over the life-span of the tree as controlled by tree status in the stand (e.g. dominant and dominated tree) and silvicultural management (spacing and thinning from below). For this purpose, property models were integrated with simulations by a process-based growth and yield model, FinnFor (Kelloma¨ki and Va¨isa¨nen, 1997). In the FinnFor model, the dynamics of the forest ecosystem and stem growth are linked to climate directly through photosynthesis, respiration and transpiration and indirectly through the hydrological and nitrogen cycles. The physiological processes of the model work on an hourly basis, with computations covering an entire year. The stem growth is determined in the FinnFor model in terms of the amount of annual photosynthesis allocated annually to the maintenance and growth of the tree stem. In the current version of the model, the annual growth of stem mass is allocated to the stem as a function of current stem mass and its distribution along the stem, and as a consequence, the growth of stem mass at each height have been converted into the ring width (Ikonen et al., 2006). The modelled distribution of annual diameter growth along the stem provides a useful framework for calculating the distribution of wood properties such as wood density (air dry), early- and late-wood percentage and fibre length along stems based on use of ringbased or disc-based models. This approach is assumed to provide realistic distributions of wood properties as the response of tree growth to thinning (in terms of the distribution of a diameter growth along the tree stem) both in dominant and dominated trees.

3.7 4.2

1.5 1.7

As different tree cohorts can be simulated simultaneously, the FinnFor model can be used to study how the diameter growth and properties of wood such as early wood percentage, wood density (air dry) and fibre length are distributed over the stem as controlled by spacing, thinning and the status of the tree in the stand (dominant, co-dominant or suppressed) (Fig. 3). The input data needed for the model simulations consist of the number of trees in each cohort, their diameter, height and age, the climatic and site characteristics of the stand and the relevant management schedules. Further information on the FinnFor model and its performance are presented by Kelloma¨ki and Va¨isa¨nen (1997), Matala et al. (2003) and Ikonen et al. (2006). 2.3.2. Model simulations In this work, the growth and dynamics of unthinned and thinned Scots pine stands were simulated for a site representing the Myrtillus type in eastern Finland (under current climate, with a temperature sum of 1100 d.d., climatic conditions simulated by weather simulator). These stands were planted with 2500 seedlings ha1. In the thinned stand two thinnings were done during the rotation of 90 years, i.e. first thinning from below was done when the stand reached 40 years of age with 1000 stems ha1 left after thinning and second one when it reached 70 years of age with 500 stems ha1 left after thinning. As inputs for the tree and stand characteristics 3-year-old seedlings (average height of 0.30  0.13 m, average diameter 0.30  0.13 cm at stem base) and stand density 2500 stems ha1 were used in the simulations. The

Fig. 3. Outlines for the integrated modelling of growth and yield and wood properties of tree stands.

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Table 5 Ring-based models developed for Scots pine and Norway spruce (Eqs. (1)–(3)) Tree species

Independent

DF

R2

b0

b1

b2

b3

A. Scots pine Early wood percentage Wood density (air dry) (g cm3) Fibre length (mm)

Ring width Early wood percentage, Cambial age Radial growth percentage, Cambial age

5724 5724 2830

0.48 0.40 0.80

56.193 0.596 1.837

13.564 0.00298 0.0414

– 0.000953 0.0362

– – 0.449

B. Norway spruce Early wood percentage Wood density (air dry) (g cm3) Fibre length (mm)

Ring width Early wood percentage, Cambial age Radial growth percentage, Cambial age

3910 3910 1686

0.53 0.41 0.89

65.183 0.662 1.4761

14.560 0.00330 0.0248

– 0.0000802 0.0391

– – 0.518

material was divided into five cohorts (diameter classes) with 500 seedlings in each. In thinning, trees were assumed to be removed across the whole diameter distribution, with preference for suppressed and intermediate trees, as is typical for thinning from below. At the time of final cutting the stand density was still 500 stems ha1 in the thinned stand and about 800 stems ha1 in the unthinned one. In this work, the differences in wood properties of dominant and dominated trees (i.e. lowest and highest tree cohort) grown in unthinned and thinned stands were compared as both whole stem averages and averages of inner part, outer part or top part of the stem. For this purpose, the top part of the stem was defined to start from where the diameter of the stem is 160 mm (the top diameter limit), thus from that point to the stem apex belonged to the top part. The bottom part (i.e. part of the stem which does not belong to the top part) was further divided into outer part and inner part. The inner part was defined as the part of the bottom partition in which the distance from the pith was less than or equal to the top diameter limit divided by two (i.e. 80 mm). The rest of the stem was taken as the outer part. The average values of these parts were calculated with ring-based models by weighting the values of each wood property by the volumes of the annual rings of each shoot (annual growth unit of the stem). Correspondingly, based on discbased property models (Appendix A), the property averages at different heights (i.e. for each shoot) were calculated separately for the whole stem and the inner part of the stem. Predictions with the disc-based models for the inner part of the stem was calculated for each disc with the number of annual rings with which the stem diameter was as near as possible the diameter limit of 160 mm (for the whole stem all annual rings of each disc were taken into account). Based on these averages, the properties of the outer parts of the stem could be calculated based on corresponding volumes for inner and outer part of the stem. 3. Results 3.1. Ring-based models Final empirical relationships built for different wood properties were in the form: EWW%p ¼ b0 þ b1 lnðring widthÞ

(1)

Wood density ¼ b0 þ b1ðEWW%m Þ þ b2 Cambial age

(2)

Fibre length ¼ b0 þ b1 lnðradial growth %Þ þ b2ðlnðradial growth %ÞÞ þ b3 lnðCambial ageÞ

2

(3)

where EWW%p and EWW%m are percentages of early wood width of total ring width (mm) in a certain annual ring (Cambial age), where subscript p means predicted and m measured, and wood density is air dry density (g cm3), fibre length is average intra-ring

fibre length (mm) and radial growth % is annual radial growth percentage (of that of stem diameter at the end of previous year). Table 5 shows the empirical ring-based models developed for different wood properties for Scots pine and Norway spruce. The early wood percentage was best explained by ring width (in Scots pine and Norway spruce R2 was 0.48 and 0.53). The wood density was best explained by the combined use of measured early wood percentage and cambial age (R2: 0.40 and 0.41). Moreover, the fibre length was best explained by radial growth percentage and cambial age (R2: 0.80 and 0.89). Comparison of predicted results from the ring-based models (early wood percentage, air dry wood density and fibre length) versus correspondingly measured ring-based values from the Finnish datasets of Scots pine and Norway spruce are presented in Figs. 4 and 5 (EWW%m is used when wood density is predicted here, whereas in the following chapters in the comparisons with the disc-based models and in the simulations with the processbased growth and yield model EWW%p is used). The ring-based models developed for fibre length predicted the range from small to large values reasonably well for both species. However, as a consequence of the lower degree of explanation (R2) the models for early wood percentage and wood density had a tendency to overestimate the lowest measured values and underestimate the highest ones. Large variations around the mean values occurred regardless of the property considered, thus relatively large RMSE values were shown for some intra-ring properties predicted by different models (e.g. wood density, see Appendix B, Table B.1). 3.2. Model comparison In model comparison species-specific conversion factors were used in order to make the comparison of models meaningful. Thus all predictions of disc-based models and measured values of Swedish validation datasets were multiplied by conversion factors. This means, in the case of wood density, that basic density values were converted to air dry wood density values. The individual cross-sectional predictions of both ring-based and disc-based models were, in general, well in line with the measurements of Finnish datasets both in Scots pine and Norway spruce (Figs. 6 and 7). When Swedish validation datasets for individual wood density (air dry) predictions of cross-sections were used, especially the ring-based models underestimated the wood densities in both Scots pine and Norway spruce (Fig. 8). The averages of cross-sectional predictions, of both ring- and disc-based models, were mainly in line with corresponding measured values when predictions were based on Finnish datasets, especially in Norway spruce (Fig. 9). However, in Scots pine the disc-based models slightly overestimated early wood percentage and wood density. The variation in individual cross-sectional predictions expressed as standard deviations were significantly lower by disc-based models than by ring-based models in the case of early wood predictions. The standard deviations of individual

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Fig. 4. Predicted values from the ring-based models of Scots pine for early wood percentage (of ring width), air dry wood density and fibre length versus measured ring-based values (A–C) and the residuals (D–F), respectively. The predictions of air dry wood density are based on measured values of both early wood percentage and cambial age.

Fig. 5. Predicted values from the ring-based models of Norway spruce for early wood percentage (of ring width), air dry wood density and fibre length versus measured ring-based values (A–C) and the residuals (D–F), respectively. The predictions of air dry wood density are based on measured values of both early wood percentage and cambial age.

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Fig. 6. Comparison of predicted versus measured disc averages of Scots pine early wood percentage (A), air dry wood density (B) and fibre length (C) calculated by ring-based and disc-based models (Wilhelmsson et al., 2002; Ekenstedt et al., 2003), respectively. Similar comparisons of predicted versus residual values of the corresponding variables are given in (D–F). The measured disc-based averages and the variables used in predictions are based on Finnish datasets. The predictions of air dry wood density by ringbased models are based on measured cambial age but on predicted early wood percentage.

cross-sectional wood density predictions were in general lower than in measured data, especially by the ring-based models based on Finnish datasets. However, the standard deviations of individual cross-sectional wood density predictions were larger based on Swedish validation datasets than Finnish datasets, but still lower than in the measured data (Fig. 9). The RMSE values of individual cross-sectional predictions based on Finnish datasets were 5.4% in Scots pine and 3.8% in Norway spruce for ring-based early wood models, when corresponding values were 6.9% and 4.9% for the validation of the disc-based models (Appendix B, Table B.2). For wood density (air dry) the RMSE values of ring-based (41 kg m3) and disc-based (43 kg m3) models were quite close to each other in Scots pine, while corresponding values in Norway spruce were equal (31 kg m3). For fibre length, the RMSE values in Scots pine were 0.21 mm and 0.22 mm, and in Norway spruce 0.16 mm for both ring- and discbased models. When the cross-sectional predictions for wood density were calculated based on the Swedish validation dataset the RMSE values of ring-based models were larger than those of disc-based models, i.e. in Scots pine 40 kg m3 and 30 kg m3, and in Norway spruce 30 kg m3 and 27 kg m3 for ring- and discbased models, respectively (Appendix B, Table B.3). 3.3. Performance of integrated model The example simulations that were conducted by the integrated use of the physiological growth and yield model and ring-based property models were used to demonstrate the response of Scots pine to thinning in terms of the distribution of annual diameter growth and different wood properties along the stem in trees

representing different status in a stand (Fig. 10). According to these simulations, the sizes of dominated trees grown in both unthinned and thinned stands were remarkably smaller compared to the sizes of dominant trees. The dominated trees also had, to some degree, higher wood density (air dry), but also slightly lower early wood percentage, on average, whereas average fibre lengths did not differ between dominated and dominant trees. Dominant trees grown in the thinned stand were only slightly larger (height 31 m and diameter at breast height (dbh) 33.2 cm) compared to similar kind of trees grown in the unthinned stand (height 30.8 m and dbh 31.8 cm), and subsequently their properties did not differ remarkably from each other at the time of final cutting (Fig. 10). Whereas dominated trees grown in the thinned stand showed remarkably higher diameter growth (dbh 26 cm and height 24.8 m) compared to dominated trees in the unthinned stand (dbh 22.4 cm and height 24 m) with consequent effects especially on wood density (Fig. 10). At the time of first thinning, the average early wood percentage of trees, regardless of tree status in a stand, was higher and wood density and fibre length correspondingly remarkably lower compared to second thinning, and the difference increased until the final cutting (Fig. 11). Predicted wood properties based on ringand disc-based models also differed from each other when averages of the whole stems were studied, and depending on which part of the stem was examined (i.e. inner part, outer part or top part of the stem) (Fig. 11). For example, the average wood density (air dry) predicted by the ring-based model was about 440 kg m3 for the whole stem in dominant trees grown in both the thinned and unthinned stands at the time of final cutting, with corresponding outer part averaging 455–458, inner part 413–416

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Fig. 7. Comparison of predicted versus measured disc averages of Norway spruce early wood percentage (A), air dry wood density (B) and fibre length (C) calculated by ringbased and disc-based models (Wilhelmsson et al., 2002; Ekenstedt et al., 2003), respectively. Similar comparisons of predicted versus residual values of the corresponding variables are given in (D–F). The measured disc-based averages and the variables used in predictions are based on Finnish datasets. The predictions of air dry wood density by ring-based models are based on measured cambial age but on predicted early wood percentage.

and top part about 408 kg m3 in the thinned and unthinned stands, respectively. In dominated trees, corresponding values for the whole stem were 444–450 kg m3 in thinned and unthinned stands, with outer part averages of 469–484 kg m3, inner part 426–438 kg m3 and top part 416–425 kg m3, respectively. Similar to ring-based model predictions, the average values predicted for wood density (air dry) based on the disc-based model varied also less in dominant trees grown in thinned and unthinned stands at the time of final cutting compared to dominated ones. However, the predicted averages were slightly lower in general compared to the ring-based model predictions both in dominant (i.e. average for whole stem of 428 kg m3, with outer part 440– 443 kg m3, inner part 407–409 kg m3 and top part about 396 kg m3) and in dominated trees grown in thinned and unthinned stands (average for whole stem of 435–439 kg m3, with outer part 459–474 kg m3, inner part 419–431 kg m3 and top part 403–410 kg m3). Predicted average early wood percentage of dominant trees did not differ between ring- and disc-based models in thinned and unthinned stands at the time of final cutting. Similarly, only slight differences were observed depending on which part of the stem was examined in dominant trees (i.e. whole stem 65–66%, outer part 63–65%, inner part 67–68% or top part of the stem 68–69%). However, the differences between model predictions were larger in dominated trees, in which ring-based models predicted, to some degree, lower early wood percentages and disc-based models only slightly different to those of dominant trees (i.e. range for whole stem 61–63%, outer part 57–60%, inner part 62–65% or top part of the stem 64–66% in dominated trees grown in unthinned and

thinned stands by ring-based models) (Fig. 11). Predictions of early wood percentages of disc-based models had lower variance, the range of values from 63% (outer part of the dominated tree in unthinned stand) to 68% (top part of the dominant tree in thinned stand) at the time of final cutting. The differences in definitions of early wood (i.e. the threshold for early- and late-wood in each ring) in the Finnish and Swedish datasets must, however, be considered. As a comparison, the fibre length predicted by the ring-based model was, at the time of final cutting, 3.3 mm for the whole stem both in dominant and dominated trees grown in unthinned and thinned stands (i.e. outer part 3.6 mm, inner part 3.0–3.1 mm and top part 2.8–3.0 mm in dominant and dominated trees). Slightly larger fibre lengths were predicted, on average, for whole stems by the disc-based model in dominant and dominated trees (a whole stem 3.6 mm and 3.4 mm, with outer part 3.8 mm, inner part 3.2– 3.3 mm and top part 3.0–3.1 mm) both in unthinned and thinned stands. 4. Discussion and conclusions 4.1. Evaluation of main findings In ring-based models, the early wood percentage was best explained using ring width, whereas the wood density (air dry) was best explained by the combined use of early wood percentage and cambial age. The fibre length was best explained by the combined use of radial growth percentage and cambial age. At the development and parameter estimation of the ring-based models the available dataset of Scots pine represented a broader statistical

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Fig. 8. The validation of the ring-based model of Scots pine for air dry wood density as averaged at disc-level versus disc-based models (A), the residuals (B), and the predictions and the residuals for Norway spruce (C and D). Measured disc-based averages and the variables used in predictions are based on Swedish validation datasets. The predictions of air dry wood density by ring-based models are based on measured cambial age but on predicted early wood percentage.

basis than did the dataset of Norway spruce. Consequently the ring-based models of Norway spruce should be regarded as preliminary. For both species the ring-based models developed for fibre length predicted the measured range in the Finnish datasets from small to large values both at intra-ring level and at the crosssectional average level reasonably well (high degree of determination). The disc-based models of fibre length (Ekenstedt et al., 2003) also were well in line with the cross-sectional averages from the Finnish datasets. As a natural consequence of the lower degree of determination the ring-based models for early wood percentage and wood density overestimated the lowest measured values and underestimated the highest ones both at intra-ring level and at cross-sectional level, as did the corresponding disc-based models (Wilhelmsson et al., 2002). This is also in line with earlier results and can be seen in the intra-ring wood density model developed for Norway spruce by Ma¨kinen et al. (2007). When validating and comparing different models by various datasets, it is important to consider that different ways to measure the property variables (basic density versus air dry density, different definitions of early- and late-wood threshold, and different equipments for measuring fibre lengths) and the methods for making transformations between them, make accurate model comparisons difficult, because there will always be uncertainty due to differences in measurement techniques. However, the discbased models seemed to slightly overestimate the cross-sectional averages of early wood percentage (6%) and wood density (3%) for Scots pine when validated by the Finnish datasets. The corresponding validation of the disc-based models for Norway spruce indicated unbiased results for the cross-sectional averages. Respectively, the ring-based models seemed to underestimate especially the wood density (at cross-sectional level) both in Scots

pine (6%) and Norway spruce (3%) when the Swedish validation datasets were used in model comparison. Another important remark is that the Finnish datasets used in the ring-based model construction and model comparison represented mainly quite slow-growing and young first thinning stands of Scots pine (i.e. typical sites for Scots pine in eastern Finland). For the Swedish validation dataset from central Sweden (also slow-growing, first thinning stands of Scots pine) disc-based models previously underestimated wood density (Wilhelmsson et al., 2000, 2002). The relatively slow growth rate of Scots pines in the Finnish datasets could partially explain why a remarkably larger species-specific multiplier was needed for fibre length of Scots pine compared to Norway spruce to make different kinds of modelling approaches more comparable. Thus, relatively longer fibres in the Finnish datasets in Scots pine seem to be a consequence of relatively low growth rate in naturally regenerated stands. In this work, the performance of ring- and disc-based properties models of Scots pine were also compared with each other in the context of growth and yield simulation over a rotation, although it was not possible to say which predictions were more accurate. As a result of this model comparison, we found that both models predicted slightly lower wood density for dominant trees compared to dominated ones both in thinned and unthinned stands at the time of final cutting (disc-based models also slightly lower values in general than ring-based models). But, unlike the wood density of dominated trees (whole stem of 444–450 kg m3 and 435–439 kg m3 by ring- and disc-based models), the properties of dominant trees (whole stem of 440 kg m3 and 428 kg m3) were not, however, affected by management, as the simulated dominant trees were only slightly larger (4,4% larger diameter at breast height) in the thinned stand than in the

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Fig. 9. Comparison of predicted averages and standard deviations by the ring-based models as averaged at disc-level for early wood percentage, air dry wood density and fibre length, in Scots pine (A–C) and in Norway spruce (D–F), versus predicted averages by disc-based models by Wilhelmsson et al. (2002) and Ekenstedt et al. (2003). Measured disc-based averages and the variables used in predictions are based on Finnish datasets. Moreover, prediction by both ring- and disc-based models of air dry wood densities are compared versus measured disc averages based on Swedish validation datasets, in Scots pine (B) and in Norway spruce (E). Regardless of the datasets used, the predictions of air dry wood density by ring-based models are based on measured cambial age but on predicted early wood percentage.

unthinned stand at the time of final cutting. Ring- and disc-based models predicted, on average, equal early wood percentage for dominant trees (whole stem of 65–66%), but ring-based models predicted, to some degree, lower early wood percentages for dominated trees (whole stem of 61–63%), and disc-based models similar to those of dominant trees. Slightly smaller fibre lengths were also predicted, on average, for whole stems using the ringbased model in dominant and dominated trees (3.3 mm) compared to the disc-based model (3.4–3.6 mm) in unthinned and thinned stands. The predicted wood properties also differed from each other depending on which part of the stem of Scots pine was examined (inner part, outer part or top part of the stem). This result was found both in ring-based and disc-based models (in early wood predictions the variation being larger based on ring-based than disc-based models). This result is in agreement with many previous findings, in which wood density and fibre length has been found to increase and early wood percentage decrease as a function of cambial age and distance from pith to bark (and wood density and fibre length to decrease and early wood percentage to increase from stem base to tree top) in coniferous tree species such as Scots pine and Norway spruce (Tasissa and Burkhart, 1998; Wilhelmsson et al., 2002; Ekenstedt et al., 2003; Jaakkola et al., 2005a; Ma¨kinen et al., 2007; Peltola et al., 2007). Altogether, these example simulations carried out in unthinned and thinned Scots pine stands showed that the response of tree growth to thinning in terms of the annual distribution of diameter growth, but also wood properties along the stem, seemed quite realistic for both

dominant and dominated trees. However, it should be noted that these example scenarios applied in this work presented still quite low differences in management (e.g. stand density 500 stems ha1 and 800 stems ha1 at the time of final cutting), and thus, the differences observed in growth and wood properties of trees were also quite limited. Thus, to study in the future in more detail the sensitivity of growth and wood properties of tree stands to forest management under changing environmental conditions (site and climate), larger variations should be used in initial stand conditions and in management regimes. In this work, the largest effects of tree status in a stand and management on tree growth and distribution of wood properties along the stem could also be seen mainly near the stem base. This may at least partly explain why there was not found, on average, significant differences, for example in the average fibre length of the whole stem in dominated and dominant trees grown in unthinned and thinned stands at the time of final cutting. The relatively small differences found in dominated trees, especially between average properties of the whole stem and the inner part of the stem at the time of final cutting, was also due to the fact that in a relatively small stem, most of the volume of the stem belonged to the inner part (as it was defined by the radius of 80 mm). Consequently, if the stem diameter was rather large, the effect of this inner part on the whole stem average would diminish. Furthermore the simulation results showed that the average early wood percentage was also slightly higher and wood density and fibre length remarkably lower at the time of first thinning when compared to second thinning, and the difference increased at

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Fig. 10. Examples of the performance of the integrated model (FinnFor simulations with ring-based models): early wood percentage (above), air dry wood density (middle) and fibre length (below) in dominant and dominated Scots pine trees grown in unthinned and thinned stands over 90 years rotation. These stands were planted with 2500 seedlings ha1 and in thinned stand two thinnings were done during the rotation (i.e. first thinning from below was done in 40 years old stand with 1000 stems ha1 left after thinning and second one in 70 years old stand with 500 stems ha1 left after thinning). In the unthinned stand there was about 800 stems ha1 at the time of final felling. In the figure, the borders (white squares) for the inner, outer (diameter > 160 mm) and top part of tree stem are shown.

the time of final cutting. The difference in growth and consequently in wood properties, such as wood density between dominant and dominated trees, also increased over time especially in the unthinned stand when the size of trees increased. These effects were previously suggested for Norway spruce by Molteberg and Hoibo (2007). 4.2. Conclusions In ring-based models, the ring width was used alone to predict the early wood percentage, whereas the early wood percentage and cambial age predicted the wood density (air dry), while radial growth percentage and cambial age predicted the fibre length.

Compared to these ring-based models, the disc-based property models used in the model comparison were utilising different variables, i.e. the number of annual rings and diameter at breast height of the individual tree and/or the cross-section being considered, and temperature sum in addition. Moreover, different kinds of measurement instruments were used for the measurements of the Finnish datasets (for construction of ring-based models) and Swedish datasets (for construction of disc-based models). This caused problems for model comparison, which could not have been fully solved by the use of species-specific calibration factors. The use of same Finnish datasets both in the construction of ring-based models and model comparison also favoured the ring-based models in model comparison, as the same datasets

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Fig. 11. Example of wood properties in different parts of the tree stem (inner, outer and top part and as average for whole stem) in dominant and dominated Scots pine trees grown in unthinned and thinned stands, respectively. Simulation results are from first and second thinning and final cutting based on predictions by ring-based (A–C) and disc-based property models (D–F). The simulated trees are the same as in Fig. 10.

were used for parameter estimations, unlike the independent case with the Swedish validation dataset. However, it can be concluded in general that the model predictions were well in line with each other. As it has been previously shown by Ericson (1960) and confirmed by Wilhelmsson et al. (2002) the length of growing season or temperature sum is strongly correlated with basic density and proportions of early- and late-wood as well. It is also shown by Lundqvist et al. (2003) that the disc-based basic density model by Wilhelmsson et al. (2002) has demonstrated reasonably accurate results with Norway spruce samples from Norway, Estonia and France. The disc-based properties models presented by Wilhelmsson et al. (2002) and Ekenstedt et al. (2003) for both Scots pine and Norway spruce are based on data with a large geographical and genetic variation, and they are very useful for forest planning and optimization of the wood and fibre utilization. They could provide predictions on future wood and fibre resources at regional and national levels, e.g. as incorporated into large-scale forestry scenario models. In this study, the variation in climate conditions of the different datasets has been limited. Thus, in the case of predictions over a larger geographic area the present discbased models used in this study as a comparison may have an advantage in comparison with the ring-based models developed in this work. For this reason an addition of, e.g. temperature sum into the ring-based models could increase their generalization. On the other hand, this kind of integrated use of the processbased growth and yield modelling together with empirical ring-

based properties models, as demonstrated in this work, could in the future offer means to study in more detail how environmental conditions (site and climate), forest structure and silvicultural practices (spacing, thinning and fertilization) affect the quantity and properties of stem wood produced over a rotation. This kind of integrated use of wood property models with a process-based growth and yield model could also help us to evaluate the development of forest resources under current and changing climate, which information is crucial for wood utilizing industry. Because the modelling of ring-based wood properties is based on tree growth, vast datasets are not necessarily needed for model construction. However, it should be kept in mind that relatively large variation would still be desirable in datasets used for model construction, i.e. in tree size, age and wood properties and site conditions (climate and site), to make the models more general and applicable for other sites as well. For this purpose, additional datasets should be measured for further development of ringbased models as well as more detailed validation against independent datasets should be carried out. In any case, the risk of obtaining biased results should also be considered if any of these models (i.e. ring- or disc-based) are used outside the range of the sampled material used in their construction. Acknowledgements This work was mainly funded through the Wood Material Science Research Programme promoted by the Academy of Finland

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and Formas (Sweden) (2003–2005), under the projects ‘‘Influence of environmental factors, forest structure and silvicultural practices on Scots pine, Norway spruce and birch properties’’, led by Dr. Heli Peltola, Faculty of Forest Sciences, University of Joensuu and ‘‘Models of wood properties for planning systems’’ led by Dr. Lennart Moberg, Skogforsk. The project belonged to the consortium ‘‘Value-chain analysis for forest management, timber purchasing and timber sale decisions (Vacha)’’, co-ordinated by prof. Tuula Nuutinen, Finnish Forest Research Institute (FFRI)). It was also partly funded through the Centre of Excellence for Forest Ecology and Management (project no. 64308, led by prof. Seppo Kelloma¨ki, University of Joensuu, Faculty of Forest Sciences). Support provided by the Academy of Finland, the National Technology Agency (Tekes), the University of Joensuu, the Graduate School in Forest Sciences, Formas and Skogforsk is acknowledged. Mr. David Gritten is thanked for the English revision of the manuscript.

Appendix A. Outlines for the disc-based models used in model comparison The disc-based models used in the model comparisons for Scots pine (Eqs. (A.1) and (A.2), Wilhelmsson et al., 2002 and Eq. (A.3), Ekenstedt et al., 2003) and Norway spruce (Eqs. (A.4) and (A.5), Wilhelmsson et al., 2002 and Eq. (A.6), Ekenstedt et al., 2003) are as follows:   dh Late wood % ¼ 91:7  31:7 ln 0:5 ch 7 1 þ 2:09eðdh=dbhÞ  224:9 0:5dh=ch þ 2 þ 0:00517 TSum ð%Þ

ðR2 ¼ 0:54Þ

(A.1)

  dh Wood density ¼ 364:4  17:578 0:5 ch  0:6070 lnðcbhÞ þ 0:4172 lnðcbhÞ e þ 0:0578 TSum ðkg m3 Þ

ðR2 ¼ 0:59Þ

When validating these models, and used in model comparison, with data from the Finnish field experiments in this work, a local continental climate correction of +50 day-degrees is applied compared to actual temperature sum of the site according to A˚ngstro¨m (1974) and More´n and Perttu (1994). Appendix B. Root mean-squared error (RMSE) values of each model See Tables B.1–B.3.

Table B.1 RMSE values of ring-based models and prediction errors and RMSE values of discbased models based on predictions made on the basis of datasets used for estimation of models parameters Ring-based models, Finnish datasets Scots pine Early wood percentage (n = 5725) (%) Wood density (n = 5725) (kg m3) a Fibre length (n = 2831) (mm)

7.9 49 0.28

Norway spruce Early wood percentage (n = 3911) (%) Wood density (n = 3911) (kg m3) a Fibre length (n = 1687) (mm)

6.9 41 0.20

Disc-based models, Swedish datasets Scots pine Early wood percentage (n = 507) (%)b Wood density (n = 490) (kg m3)b Fibre length (n = 172) (mm) Norway spruce Early wood percentage (n = 1184) (%)b Wood density (n = 1137) (kg m3) b Fibre length (n = 326) (mm)

3 ðdh=dbhÞ7

3

section. These models are defined for predictions above breast height (values below breast height have been regarded as equal to those at breast height).

(A.2)

  dh Fibre length ¼ 1:21 þ 0:69 lnðchÞ þ 0:33 ln 0:5 ch

2.9(2.4) 26(16) 0.15

3.3(2.6) 26(14) 0.18

a Predictions of wood density have been calculated using measured early wood percentage and measured cambial age (n = number of annual rings). b Prediction errors of mixed models are given as totals (in parentheses: unexplained error component of mixed models, when random effects of tree and stand have been predicted; n = number of discs).

þ 0:65ð1  eðRelHeight=0:13Þ Þ þ 0:00043 TSum ðmmÞ

ðR2 ¼ 0:83Þ

(A.3) 0:5

Late wood % ¼ 6:1  9:183 lnðdhÞ þ 28:885 lnðchÞ þ 0:005911 TSum ð%Þ

ðR2 ¼ 0:52Þ

Wood density ¼ 304:3 þ 10:4437 lnðchÞ þ 0:2957

0:5

(A.4) 1:5

 444:13

TSum ðkg m3 Þ 0:5dh=ch þ 2:3

dh ch  TSum

ðR2 ¼ 0:50Þ (A.5)

Fibre length ¼ 3:06  2:20eðch=29:35Þ  1:55eð0:5dh=ch=0:74Þ  0:70eðRelHeight=0:14Þ þ 0:00056 TSum ðmmÞ

ðR2 ¼ 0:81Þ

(A.6)

where dh is diameter (mm) (under bark) at height h, ch is number of annual rings at height h, cbh is number of annual rings at breast height, dbh is diameter (mm) (under bark) at breast height, TSum is temperature sum, and RelHeight is the relative disc height. In addition, 0.5dh/ch is the average growth ring width in the cross-

Table B.2 RMSE values of the models based on use of Finnish datasets in model comparison Ring-based models, cross-sectional averages, Finnish datasets Scots pine Early wood percentage (n = 218) (%) Wood density (n = 218) (kg m3) a Fibre length (n = 157) (mm)

5.4 41 0.21

Norway spruce Early wood percentage (n = 81) (%) Wood density (n = 81) (kg m3)a Fibre length (n = 39) (mm)

3.8 31 0.16

Disc-based models, Finnish datasets Scots pine Early wood percentage (n = 205) (%) Wood density (n = 205) (kg m3)a Fibre length (n = 157) (mm)

6.9 43 0.22

Norway spruce Early wood percentage (n = 81) (%) Wood density (n = 81) (kg m3)a Fibre length (n = 39) (mm)

4.9 31 0.16

a Predictions of wood density are based on measured cambial age, but on predicted early wood percentage.

V.-P. Ikonen et al. / Forest Ecology and Management 256 (2008) 1356–1371 Table B.3 RMSE values from validation of the models by independent Swedish validation datasets in model comparison Ring-based models, cross-sectional averages, Swedish validation datasets Scots pine: wood density (n = 194) (kg m3) a Norway spruce: wood density (n = 197) (kg m3)a

40 30

Disc-based models, Swedish validation datasets Scots pine: wood density (n = 194) (kg m3) Norway spruce: wood density (n = 197) (kg m3)

30 27

a Predictions of wood density are based on measured cambial age, but on predicted early wood percentage.

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