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Ring-levelmodelsforpredictingwoodandfibrepropertiesofAbiesbalsamea

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ORI GIN AL

Ring-level models for predicting wood and fibreproperties of Abies balsamea

Francesco Cortini • Arthur Groot • Queju Tong •

Isabelle Duchesne

Received: 12 August 2013

� Crown Copyright 2014

Abstract Wood and fibre properties such as wood density, microfibril angle, and

modulus of elasticity are industrially relevant factors in determining the mechanical

properties of wood. Radial ring-level predictive models of these properties were

developed using balsam fir data from a long-term trial in New Brunswick (Canada),

where precommercial thinning was applied 8 years after the site was harvested. The

mixed effects models developed accounted for most of the variability in wood

density (68 %), microfibril angle (94 %), and modulus of elasticity (77 %) with low

RMSE. This study shows that balsam fir wood and fibre properties are strongly

related to distance from the pith, particularly in the first 20 mm, and much less to

annual ring width. Disk height and selected weather variables related to air tem-

perature during the growing season significantly improved the models, whereas the

effect of precommercial thinning was not significant. These equations can be

incorporated into computer models, such as Optitek, that simulate mill recovery and

wood properties to obtain accurate information on wood products. The unexplained

variation in these models is likely related in part to between-tree genetic variation,

which is unknown in this study.

F. Cortini (&)

Natural Resources Canada, Canadian Wood Fibre Centre, 506 West Burnside Rd., Victoria,

BC V8Z 1M5, Canada

e-mail: fcortini@gmail.com

A. Groot

Natural Resources Canada, Canadian Wood Fibre Centre, 1219 Queen St. E., Sault Ste. Marie,

ON P6A 2E5, Canada

Q. Tong

FPInnovations, 2665 East Mall, Vancouver, BC V6T 1W6, Canada

I. Duchesne

Natural Resources Canada, Canadian Wood Fibre Centre, 1055 Du P.E.P.S. St., Quebec,

QC G1V 4C7, Canada

123

Wood Sci Technol

DOI 10.1007/s00226-014-0664-x

Introduction

Balsam fir (Abies balsamea (L.) Mill.) is a widely distributed and abundant conifer

in eastern Canada and the northeastern United States of America. Balsam fir stands

often regenerate to high densities through plentiful advance regeneration, prolific

seed production, and vigorous growth on a variety of soils. Consequently,

precommercial thinning (PCT) has been increasingly applied to overstocked

balsam fir stands in order to enhance saw log production (e.g. Pitt and Lanteigne

2008). Although stand growth and yield predictions are relatively well documented

for balsam fir, there are still knowledge gaps in terms of its wood quality

attributes.

In eastern Canada, balsam fir is mainly used for lumber and pulp production. The

wood is light in weight, relatively soft, and fairly low in resistance to impact (Burns

and Honkala 1990). Balsam fir has the lowest strength properties of the spruce–

pine–fir (SPF) species group (Zhang and Koubaa 2008) and is therefore a minor

machine stress-rated (MSR) species.

Many studies have already shown a strong relationship between wood and fibre

properties and important attributes of wood and fibre products (e.g. Duchesne et al.

1997; Jansson 2000; Wilhelmsson et al. 2000). Thus, the capability to predict wood

and fibre properties can improve planning of wood flow to industrial plants and can

allow a more in-depth analyses of wood resources (Wilhelmsson et al. 2002).

The differences in wood and fibre properties of the juvenile core of the tree and

that of the outer wood can be relatively large and can influence the processing

properties of each log. Changes in properties from pith to bark are affected by many

factors including site, genotype, and silvicultural management of the stand

(Raymond and Joe 2007). Additionally, the tree crown has long been considered

to have a regulatory influence on wood formation and fibre properties (Larson

1969).

Among the many wood and fibre properties, wood density, microfibril angle,

and modulus of elasticity were found to be relevant factors in determining the

mechanical performance of wood (e.g. Cave and Walker 1994; Reiterer et al.

1999). Wood density is of key importance in forest products manufacturing

because it has a major impact on yield, quality, and value of wood products.

Microfibril angle in the secondary cell wall layer (S2), although not as easily

measurable as density, is known as one of the major determinants of stiffness and

longitudinal shrinkage of wood (Cave and Walker 1994; Harris and Meylan 1965).

Modulus of elasticity, or a material’s tendency to be deformed elastically (non-

permanently), is influenced by the density of wood fibres, and their underlying cell

wall layers composed of cellulose microfibrils embedded in a complex matrix of

lignin and hemicelluloses. The combined effect of these properties determines

product performance.

The purpose of this study was to develop radial ring-level predictive models

of wood density, microfibril angle, and modulus of elasticity using balsam fir

data from a long-term PCT trial in New Brunswick, Canada (Pitt and Lanteigne

2008).

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123

Methods

Study description and sampling

Data for this study came from the Green River precommercial thinning (PCT) trial

that was established between 1959 and 1961 approximately 48 km north of

Edmundston, New Brunswick, Canada (Fig. 1). Soils are predominantly stony

loams and silt-loams. The trial consists of five experimental blocks, each containing

the unthinned control and three nominal thinning spacings: 1.2, 1.8, and 2.4 m.

Thinning was applied to naturally regenerated (largely from preharvest advance

regeneration of variable age) balsam fir approximately 8 years after the site was

harvested. One block was divided into eight treatment plots, whereas all of the other

blocks were divided into four treatment plots. Treatment plots were at least 2 ha in

area, and measurement plots were 0.081 ha in area. In spring 2004, 42–44 years

after the thinning treatments were applied, dominant heights ranged from 20 to

22 m, stand basal area ranged from 40 to 46 m2 ha-1, and mean stem densities

ranged from 1,860 stems ha-1 [ 1.3 m in height in the unthinned control to 1,160

stems ha-1 in the 2.4 m spacing. More information about the PCT trial can be found

in Pitt and Lanteigne (2008).

A total of 20 trees were selected for in-depth analysis of wood and fibre

properties in two steps. The objective was to select a subsample of trees that

represented the range of crown widths within each spacing so that the effects of

crown size and associated growth rates on fibre properties would be represented in

the models. In the first step, five trees were selected for stem analysis and crown

width measurement from each plot (total of 120 trees) in the fall of 2004 (Pitt and

Lanteigne 2008). Selection criteria included representation of the range of DBH

classes within each plot and free from stem defects (Pitt and Lanteigne 2008).

Fig. 1 Location of the five experimental blocks of the Green River precommercial thinning trial

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In the second step, the 30 trees from each spacing were pooled and divided into

five groups of six trees, with each group representing equal intervals of the range of

crown width for that spacing. One tree was randomly selected from each group of

six trees. The result of these two steps was the selection of five trees from each

spacing (total of 20 trees) for laboratory analysis of wood and fibre properties. The

number of disks collected from each tree varied depending on tree height. For trees

taller than 14 m, disks were sampled at 2-m intervals for the first 10 m of the stem,

and at 1-m intervals for the upper part of the tree. For trees shorter than 14 m, disks

were uniformly sampled at 1-m intervals. For each tree, disks were also collected at

stump height and at breast height. Stump height disks were excluded from analysis

because preliminary analysis indicated that fibre properties at stump height

substantially differ from the rest of the tree, likely due to butt flare and frequent

compression wood in this region of the stem. Cortini et al. (2013) also excluded

stump height disks when investigating the longitudinal distribution of ring area.

Sample preparation and analysis

A total of 268 disks were analysed with a SilviScanTM system (Evans et al. 1996)

located at the FPInnovations laboratory in Vancouver, British Columbia, Canada.

The system combines image analysis, X-ray densitometry, and X-ray diffractometry

to provide multiple wood and fibre properties including pith-to-bark profiles of

wood density (WD), microfibril angle (MFA), and modulus of elasticity (MOE).

A 15 9 15 mm2 bark-to-bark block encompassing the pith was cut from the

north side of each wood disk. The blocks were soaked in acetone solution for 12 h

and later extracted for 8 h at 70 �C in a modified Soxhlet extraction system. This

process removes resinous substances that may interfere with density measurements.

After extraction, the blocks were air-dried and conditioned at 20 �C temperature and

40 % relative humidity until the moisture content reached approximately 8 %. The

blocks were then cut into 2 9 7 mm2 (tangentially 9 longitudinally) pith-to-bark

strips with specially designed pneumatic twin blade saws. One cross section of each

strip was polished with various grits of sandpaper (i.e. 400-grit to 1,200-grit) to

obtain a smooth surface for image analysis. Each sample was then scanned for cell

dimensions, WD, and MFA using optical microscopy, X-ray densitometry, and

X-ray diffractometry, respectively. Ring orientation from image analysis was used

as reference for X-ray densitometry and X-ray diffractometry analyses. The samples

were then analysed by the densitometer and diffractometer at variable angles to

correct for annual growth ring orientation. WD was determined at 25-lm resolution,

whereas MFA was determined at 1-mm resolution.

The densitometric measurements were based on Beer’s Law, which states that the

intensity of an X-ray beam that passes through a sample falls off exponentially with

sample thickness, and the extent of that attenuation is related to the density of the

sample.

The diffraction profiles provided information about the orientation of the

cellulose microfibrils in the S2 layer of the secondary cell wall (Evans 1999) in

relation to the longitudinal cell axis. MFA was estimated based on the relationship

between the variance of the 002 azimuthal diffraction profile of cellulose-I and

Wood Sci Technol

123

microfibril orientation distribution. The 002 diffraction patterns were obtained from

the planes whose normal was perpendicular to the microfibril axis. More

information about this technique can be found in Evans et al. (1996) and Evans

(1999).

Wood density (WD) from the X-ray densitometry analysis and the coefficient of

variation of the intensity of the X-ray diffraction profile (ICV) were then combined

to compute the fibre dynamic MOE (Evans 2006):

MOE ¼ A ICVWDð ÞB ð1Þ

The ICV includes the scattering from the S2 layer and the background scattering

from other cell wall constituents such as the S1 and S3 layers, parenchyma, and

amorphous cellulose and lignin present in the fibre wall. The model contains two

statistically determined calibration constants (A and B), which have been shown to

be insensitive to species, and relate to the sonic resonance method used for cali-

bration of MOE (Evans 2006).

Variable selection

For this study, the following wood and fibre properties measured with SilviScanTM

were selected: (1) distance from the pith (DP), (2) ring width (RW), (3) basic wood

density (WD), (4) microfibril angle (MFA), and (5) modulus of elasticity (MOE).

Two disks, from each of two different trees, with a lower ring count than those

disks higher up within the same stem (likely caused by stem defects or extremely

narrow rings) were removed from the analysis. One highly suppressed tree

presented three disks with a lower ring count than those disks higher up within the

same stem, and the entire tree was therefore removed from the analysis. A total of

19 trees, 209 disks, and 6,278 rings were used to develop the predictive models

(Table 1).

Tree and stand attributes including crown radius, crown length, stand dominant

tree height, and basal area of the trees larger than the subject tree (within each of

the four treatment plots) were measured for each tree. Annual weather data relative

to the growing seasons were also available (Table 1) (McKenney et al. 2011). The

weather variables tested included: mean annual temperature, mean temperature

during the growing season, mean annual precipitation, mean precipitation during

the growing season, precipitation of the wettest period, precipitation of the driest

period, number of days of the growing season, GDD (i.e. growing degree

days [ 5 �C), and Julian day number at end of growing season. The growing

season is defined as the period starting when the mean daily temperature is greater

than or equal to 5 �C for five consecutive days from 1 March and ending when

minimum temperatures are below -2 �C after 1 August. Some parameters are

based on time periods associated with the growing season, as follows: period 1

includes the 3 months prior to the growing season; period 2 includes the first

6 weeks of the growing season; period 3 includes the entire growing season; and

period 4 includes the final weeks of the growing season (i.e. period 3–period 2)

(Mackey et al. 1996).

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123

Model development

Given the hierarchical structure of the dataset (i.e. tree rings nested within disks and

disks nested within trees), the parameters were estimated using nonlinear mixed

effect models, which can account for multiple sources of variation and the mutual

dependence of observations. By using tree and disk effects as random subjects in the

models, the parameter estimates can vary around the fixed effects values. Moreover,

the appropriate variance function and correlation structure were included into the

model (as suggested by Pinheiro and Bates 2000) in order to model heterosced-

asticity and unequal variance among within-group errors.

Preliminary analysis indicated that an exponential equation provided the best fit

between the wood and fibre properties investigated (i.e. WD, MFA, and MOE), and

RW and DP. The base model comprises two components, as follows:

Yijz ¼ a0 þ a1 � EXPða2 � RWijzÞ þ a3 � EXPða4 � DPijzÞ þ eijz ð2Þ

where Yijz wood density (kg m-3), or microfibril angle (�), or modulus of elasticity

(GPa) of ring z, in disk j, in tree i, RWijz ring width (mm), DPijz Distance from the

Pith (mm), and an (n = 0, 1, 2, 3, and 4) are the fixed effects parameters; the eijz

term represents the unexplained error.

The sampling strategy did not use the block structure of the original experiment,

but the selected trees were well-distributed across the range of crown widths and

spacing treatments. Consequently, indicator variables were used to test whether

treatment effects were present when the effects of RW and DP were accounted for.

In a subsequent step, the base model was modified by adding one-by-one in separate

steps (in linear form) tree-level attributes such as disk height above ground, tree

height, tree age, live crown length, crown radius, crown ratio (i.e. crown length/tree

height), crown base projected area, height to crown base, crown volume (i.e. volume

of a cone), crown surface area, and diameter at breast height. Only those variables

that contributed significantly (a\ 0.05) to the model were retained.

Table 1 Basic statistical information for selected variables

Minimum Mean Maximum Standard deviation

Wood density (kg m-3) 230.0 403.7 854.0 61.9

Microfibril angle (�) 7.30 13.52 45.30 6.96

Modulus of elasticity (GPa) 1.70 10.97 18.00 2.98

Ring width (mm) 0.050 1.818 7.150 1.103

Distance from pith (mm) 0.05 39.61 144.72 26.83

Disk height (m) 1.3 6.8 19.0 4.5

Growing degree days 796 1,148 1,531 121

Mean growing season temperature (�C) 10.5 12.4 14.8 0.7

Tree age at breast height 48 59 77 7.7

Diameter at breast height 1.3 m (cm) 10.0 19.4 30.6 6.1

Tree height (m) 12.0 17.3 21.4 2.7

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123

Furthermore, other tree attributes were tested relative to the stand characteristics

such as basal area, basal area of the larger trees (i.e. the basal area sum of each tree

larger than the subject tree within the plot) (Biging and Dobbertin 1995), and

dominant height.

In a final step, it was tested whether the inclusion of annual weather information

improved the overall model fit.

The models were then compared using several criteria including: (1) residual

plots, (2) the coefficient of determination (Pseudo-R2), (3) Akaike’s information

criterion (AIC; Burnham and Anderson 1998), and (4) the root mean square error

(RMSE) of each wood and fibre attribute (i.e. absolute values and percentage

relative to the averaged wood and fibre attribute). Parameter estimation was

completed using the NLME statistical package (Pinheiro et al. 2009) in R (version

2.15.1) (The R foundation for Statistical Computing).

Results

The inclusion of indicator variables representing the treatment effects did not

significantly improve the model (p [ 0.05) and were therefore not included in the

final models.

Among the tree-level attributes and the tree attributes relative to the stand

characteristics tested only disk height for MFA and MOE significantly improved the

final model. For MFA, after including disk height, the parameter value related to

ring width (a2) became not significantly different from zero, and therefore, RW was

removed from the final model.

Annual weather information significantly improved the final models. GDD (i.e.

growing degree days [ 5 �C) improved the model fit for WD and MFA, while

MTGS (i.e. mean temperature during the growing season) improved the model fit of

MOE.

The following final model provided the best fit for WD:

Yijz ¼ a0 þ ða1 þ ua1iÞ � EXPða2 � RWijzÞ þ ða3 þ ua3iÞ � EXPða4 � DPijzÞþ a5 � GDDþ eijz ð3Þ

where Yijz wood density (kg m-3) of ring z, in disk j, in tree i, GDD growing degree

days above 5 �C, and an (n = 0, 1, 2, 3, 4, and 5) are the fixed effects parameters.

For tree i, the error structure is defined by an unstructured variance–covariance

matrix of random effects uani with a power variance function Gi (uani, d) = |DPijz|d,

and a serial correlation function Ci(/) = CAR(1) to account for correlation

between disks j within each tree i.

The RMSE for Eq. 3 is 34.15 kg m-3, which represents 8.5 % of the average

wood density value (403.7 kg m-3) across the 19 trees (Table 2). The Pseudo-R2

improves by 15 % moving from the fixed effect model to the mixed effect model

with tree as random subject and improves further by an additional 11 % with the

mixed effect model having tree and disk as random subjects.

The following model provided the best fit for MFA:

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Yijz ¼ a0 þ ðða1 þ ua1iÞ þ a2 � GDDÞ � EXPða3 � DPðða4þua4iÞþa5�DHÞijz Þ þ eijz ð4Þ

where Yijz microfibril angle (�) of ring z, in disk j, in tree i, DH disk height (m), and

an (n = 0, 1, 2, 3, 4, and 5) are the fixed effects parameters. For tree i, the error

structure is defined by an unstructured variance–covariance matrix of random

effects uani with a power variance function Gi (uani, d) = |DPijz|d, and a serial

correlation function Ci(/) = CAR(1) to account for correlation between disks j

within each tree i.

The RMSE for Eq. 4 is 1.64�, which represents 12.1 % of the average microfibril

angle value (13.52�) across the 19 trees (Table 2). The Pseudo-R2 improves by 7 %

moving from the fixed effect model to the mixed effect model with tree as random

subject, and improves further by an additional 6 % with the mixed effect model

having tree and disk as random subjects.

Table 2 Parameter estimates reported with standard error and goodness-of-fit for the disk-level mixed

effects version of Eqs. 3–5

Equations Parameter Estimate Standard

error

RMSE RMSE

(%)

Pseudo-R2

Fixed Mixed

Tree Disk

(3) a0 489.4784 46.884 34.15 kg m-3 8.5 0.430 0.579 0.685

a1 -134.749 46.434

WD a2 0.053 0.016

a3 211.4457 12.383

a4 -0.1855 0.007

a5 0.0389 0.003

(4) a0 9.278583 0.079 1.64� 12.1 0.812 0.880 0.943

a1 24.61626 0.875

MFA a2 -0.00145 0.0004

a3 -0.01248 0.001

a4 1.352283 0.044

a5 0.033897 0.002

(5) a0 7.767211 1.866 1.39 GPa 12.7 0.577 0.781 0.774

a1 5.996475 1.903

MOE a2 -0.02723 0.009

a3 -10.8772 0.520

a4 0.160858 0.026

a5 0.054067 0.022

a6 -0.02539 0.003

a7 1.187729 0.039

Pseudo-R2 values for the fixed effects and tree-level mixed effects versions are included for comparison

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Pn

i¼1yi�yið Þ2

n�k

r

; Pseudo� R2 ¼ 1�Pn

i¼1yi�yið Þ2

Pn

i¼1yi��yð Þ2

where yi observed values, yi predicted values,

�y average, n sample size, k number of model parameters

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123

The following model provided the best fit for MOE:

Yijz ¼ a0 þ ða1 þ ua1iÞ � EXPða2 � RWijzÞ þ ðða3 þ ua3iÞ þ a4 � DH

þ a5 �MTGSÞ � EXPða6 � DPa7

ijzÞ þ eijz ð5Þ

where Yijz modulus of elasticity (GPa) of ring z, in disk j, in tree i, MTGS mean

temperature during the growing season (�), and an (n = 0, 1, 2, 3, 4, and 5) are the

fixed effects parameters. For tree i, the error structure is defined by an unstructured

variance–covariance matrix of random effects uani with a power variance function

Gi (uani, d) = |DPijz|d, and a serial correlation function Ci(/) = CAR(1) to account

for correlation between disks j within each tree i.

The RMSE for Eq. 5 is 1.39 GPa, which represents 12.7 % of the averaged

modulus of elasticity (10.97 GPa) across the 19 trees (Table 2). The Pseudo-R2

improves by 20 % moving from the fixed effect model to the mixed effect model

with tree as random subject and slightly decreases by \1 % with the mixed effect

model having tree and disk as random subjects.

Scatter plots of residuals and studentised residuals suggest that Eqs. 3–5 provided

consistent and unbiased estimates of observed values (Fig. 2). Figures 3, 4 and 5

indicate that rings of similar width have a wide range of wood and fibre properties

depending on their distance from the pith.

Discussion

The equations developed for WD, MFA and MOE accounted for most of the

variability in these wood properties with low RMSE. These equations can be then

incorporated into computer models, such as Optitek (Goulet 2006), that simulate

mill recovery and wood properties to obtain accurate information on wood products

(Zhang and Tong 2005). By matching the wood supply to the industrial

requirements, the forest industry can greatly improve wood flow planning and

therefore reduce costs (e.g. Lindstrom 2000).

The equations developed showed that balsam fir wood and fibre properties were

strongly related to distance from the pith, particularly in the first 20 mm, and much

less to annual ring width. Low stiffness near the pith is common among conifers,

possibly as an adaptation to wind flexing the young leaders (Butterfield 2003). The

formation of wood with large microfibril angles appears to be typical of small

diameter coniferous leaders. As a result, wood and fibre properties are better

captured by distance from the pith than by ring width. The results of the current

study also provided evidence of high WD, high MFA, and low MOE near the pith

(\15–20 mm from the pith), but these wood and fibre attributes quickly changed in

the outer wood where they tend to plateau similar to what Gardiner et al. (2011)

found studying wood density of Sitka spruce (Picea sitchensis (Bong.) Carr.).

Farther from the pith, WD decreased with increasing ring width, but at a rate of only

about 8 kg m-3 for each mm change in ring width. In a similar study, Koga and

Zhang (2002) found no significant correlation between balsam fir wood density and

ring width in neither juvenile wood nor mature wood, which further supports a

Wood Sci Technol

123

general view that relationships between WD and ring width are inconsistent

(Dutilleul et al. 1998; Downes et al. 2002). The results of this study also

demonstrate that the strong influence of distance from pith on WD confounds the

relationship between WD and ring width, particularly near the pith. Alteyrac et al.

(2006) reported for boreal black spruce trees that ring width was not a significant

factor of variation of MOE and MOR measured on small clear specimens. However,

400 500 600 700 800

300

400

500

600

700

800

Fitted Wood Density (Kg/m^3)

Obs

erve

d W

ood

Den

sity

(K

g/m

^3)

400 500 600 700 800

-4-2

02

46

8

Fitted Wood Density (Kg/m^3)

Stu

dent

ized

Res

idua

ls (

Kg/

m^3

)

10 15 20 25 30 35 40

1020

3040

Fitted Microfibril Angle (°)

Obs

erve

d M

icro

fibril

Ang

le (

°)

10 15 20 25 30 35 40

-4-2

02

46

8

Fitted Microfibril Angle (°)

Stu

dent

ized

Res

idua

ls (

°)

(a)

(b)

4 6 8 10 12 14 16

510

15

Fitted Modulus of elasticity (GPa)

Obs

erve

d M

odul

us o

f ela

stic

ity (

GP

a)

4 6 8 10 12 14 16

-4-3

-2-1

01

23

Fitted Modulus of elasticity (GPa)

Stu

dent

ized

Res

idua

ls (

GP

a)(c)

Fig. 2 Plots representing the goodness-of-fit for Eqs. 3 (a), 4 (b), and 5 (c). Each row presents graphs of:(1) observed against predicted together with the fitted lowest line, and (2) scatter plots of residuals againstpredicted together with the fitted Lowess line

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MFA was strongly correlated to wood mechanical performance, explaining 72 and

50 % of the variation in MOE and MOR, respectively.

Among the variables of tree attributes (e.g. tree crown length) and tree attributes

relative to the stand characteristics (e.g. basal area) tested, only disk height

significantly improved the models. The goodness-of-fit information (e.g. Pseudo-R2)

indicated that the intra-tree variability captured by disk height, and the random

300

400

500

600

700

0 15 30 45 60 75 90 105 120 135 150

Fit

ted

Woo

d D

ensi

ty (

m3

Kg-

1)

Distance from the pith (mm)

(a)Minimum Ring Width Average Ring Width Maximum Ring Width

(b)

Fig. 3 For Eq. 3, plots of predicted wood density against distance from the pith. Graph a presents threelevels of ring width (i.e. minimum = dashed line, average = solid line, and maximum = dotted line)calculated using the average value of GDD. Graph b presents three levels of GDD (i.e.minimum = dashed line, average = solid line, and maximum = dotted line) calculated using theaverage value of ring width

Wood Sci Technol

123

Fig. 4 For Eq. 4, plots of predicted wood density against distance from the pith. Graph a presents threelevels of disk height (i.e. minimum = dashed line, average = solid line, and maximum = dotted line)calculated using the average value of GDD. Graph b presents three levels of GDD (i.e.minimum = dashed line, average = solid line, and maximum = dotted line) calculated using theaverage value of disk height

cFig. 5 For Eq. 5, plots of predicted microfibril angle against distance from the pith. Graph a presentsthree levels of ring width (i.e. minimum = dashed line, average = solid line, and maximum = dottedline) calculated using the average value of disk height and MTGS. Graph b presents three levels of diskheight (i.e. minimum = dashed line, average = solid line, and maximum = dotted line) calculated usingthe average value of ring width and MGST. Graph c presents three levels of MTGS (i.e.minimum = dashed line, average = solid line, and maximum = dotted line) calculated using theaverage value of ring width and disk height

Wood Sci Technol

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effects in the mixed effects models, have similar magnitude to the inter-tree

variability. Koga and Zhang (2002) also indicated that the relationship between

wood density and ring width components within a tree (i.e. intra-tree level) was

similar to that at the inter-tree level. The substantial increase of MFA near the pith

with increasing disk height may be a response to increased wind loading at greater

heights above the ground (Booker and Sell 1998; Wimmer et al. 2002).

In this study here, weather variables related to air temperature during the growing

season had a statistically significant role in models for all three wood and fibre

attribute variables. Only for WD, however, was the size of the effect large enough to

suggest that inter-annual variability in weather influenced wood formation, with

WD increasing with GDD. These results are consistent with the positive response of

WD and neutral responses of MFA and MOE in field-grown Norway spruce (Picea

abies) to elevated air temperature (Kostiainen et al. 2009). As other studies have

shown, climatic characteristics during the growing season have a direct effect on the

proportion of earlywood and latewood produced within an annual growth ring,

which consequently have an influence on the overall characteristics of the wood and

fibres (e.g. Kantavichai et al. 2010).

The spacing treatment (i.e. PCT) did not have a significant effect on the modelled

relationships for the wood and fibre properties investigated, likely because the

treatment effects were reflected in ring width. A recent study from the Green River

PCT trial (Duchesne et al. 2013) found that average wood density at the disk level,

cut at stump height, decreased with increasing DBH class (or growth rate), and that

spacing generally resulted in decreased disk density. This outcome is consistent with

the finding from the current study; disk-level wood density averages will result in an

overall lower wood density for larger disks since wood density is relatively constant

after 15–20 mm from the pith. Duchesne et al. (2013) also indicated that the average

wood density measured on the lumber produced along the tree was not influenced by

thinning, which is again consistent with the findings of this study. Another study

(Koga et al. 2002) also found that: (1) the treatment (i.e. PCT) had minimal effect

on balsam fir wood density, and (2) the treatment effect on annual growth lasted for

only 7 years. Correspondingly, the current study did not detect any treatment effects

on wood and fibre properties because (1) treatment effects were already accounted

for in the ring width response, and (2) substantial amount of time had elapsed since

the thinning event.

The unexplained variation in these models is likely related in part to the between-

tree genetic variation, which is unknown in this study. Other studies have shown

that wood and fibre properties are subject to considerable genetic variation (e.g.

Hannrup et al. 2001; Rozenberg et al. 2001).

Conclusion

This study investigated the predictive ability of radial ring-level models of wood

and fibre properties such as wood density, microfibril angle, and modulus of

elasticity for balsam fir. The mixed effects models developed accounted for most of

the variability in wood density (68 %), microfibril angle (94 %), and modulus of

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elasticity (77 %) and included tree and stand level variables such as distance from

the pith, ring width, disk height, and selected weather variables related to air

temperature during the growing season. These equations can be incorporated into

computer models (e.g. Optitek) that simulate mill recovery and wood properties to

obtain accurate information on wood products. The unexplained variation in the

models is likely related to the genetic variation among trees, which is unknown in

this study.

Acknowledgments Special thanks go to Dr. Doug Pitt, Mr. Len Lanteigne, and Mr. Jamie Farell

(Natural Resources Canada, Canadian Wood Fibre Centre) and to FPInnovations (Vancouver) for

supplying the balsam fir data, and to Mr. Gurp Thandi (Natural Resources Canada, Canadian Forest

Service) for creating the map presented in this manuscript. Funding of this research was provided by the

Canadian Wood Fibre Centre (Natural Resources Canada).

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