Individual Tree Models for the Crown Biomass Distribution of Scots Pine,

7/29/2019 Individual Tree Models for the Crown Biomass Distribution of Scots Pine,

1/13

Individual tree models for the crown biomass distribution of Scots pine,Norway spruce and birch in Finland

Timo Tahvanainen a,*, Eero Forss ba The Finnish Forest Research Institute, P.O. Box 68, FI-80101 Joensuu, Finland

b University of Joensuu, Faculty of Forestry, P.O. Box 111, 80101 Joensuun Yliopisto, Finland

Received 29 November 2006; received in revised form 29 June 2007; accepted 5 September 2007

Abstract

An increase in demand for wood energy is leading to more intensive harvesting of timber, including crown biomasses. In thinning operations,the harvesting method (full tree, part tree, and delimbed stem) and the minimum top diameter for industrial wood strongly affect the amount andquality of harvested biomass. When planning harvest operations, estimates should be based on typically available forest inventory data. InScandinavia, the individual tree approach, with taper curves, is commonly used for the prediction of forest growth and timber assortments.Individual tree stem volume and biomass equations are commonly used to predict the total amount of crown biomass of a tree. To be able to predictthe harvested biomass in integrated industrial and energy wood harvesting, the vertical distribution of crown biomass also needs to be known.

This study presents individual tree models for the prediction of vertical distribution of living crown, needle and dead branch biomasses for Scotspine, Norway spruce and pubescent and silver birch. Mixed linear regression models were produced for the estimation of crown length and theheights to the lowest and highest dead branch. Tree height was the main predictor in the models, but predictors describing the competitive status of the tree and overall competition in the stand were also used. The ChapmanRichards model was used to estimate the distribution of the crownbiomasses between the lower and upper limits of the crown. Data from different geographical regions and with different stand ages were pooled inorder to obtain generally applicable models. The relative root mean square error of the estimate in the crown length models was 23.3% for pine,19.7% for birch and 16.5% for spruce. In the models for the relative cumulative living crown masses the error was 11.7% for pine, 16.2% for birchand 14.3% for spruce. In the models for the relative needle masses the error was 15.1% for pine and 18.6% for spruce. Together with the biomassmodels for total living crown, whole crown, needles and dead branches, the models presented in this paper can be used for the estimation of theharvested volume and energy yield (MWh) using different harvesting methods and bucking options. The models can be used for the planning of harvesting operations, for the selection of feasible harvesting methods, and for the estimation of nutrient removals of different harvesting practises.# 2007 Elsevier B.V. All rights reserved.

Keywords: Branch biomass; Needle biomass; Crown length model; Dead branch height model; Cumulative crown biomass model; Energy wood; ChapmanRichards; Mixed model

1. Introduction

As the demand for using renewable forest biomasses forenergy production to mitigate climate change is growing, crownbiomass is becoming a valuable product. The need for forestenergy boosts the use of intensive harvesting methods like parttree and full tree methods, which increase the harvestedbiomass and, thus, remarkably reduce energy wood harvestingcosts (Hakkila, 2004 ). Harvesting of nutrient-rich crown

biomasses, however, strongly increases nutrient removal,which can reduce the growth of the stand after harvesting

(Malkonen, 1976; Jacobson et al., 2000; Nord-Larsen, 2002 ).The growing interest for forest energy sets new demands forforest inventory, planning and management systems to generatemore detailed information on the different biomass fractionsand crown dimensions. They are needed for more accurateestimates of harvested branch and needle biomasses, theirnutrient contents for the estimation of ecological effects of intensied biomass removal, and for the prediction of the CO 2balances of forested areas.

The crown size is usually described as crown length orcrown ratio. Crown length is calculated as the difference

www.elsevier.com/locate/foreco

Available online at www.sciencedirect.com

Forest Ecology and Management 255 (2008) 455467

* Corresponding author. Tel.: +358 10 211 3267; fax: +358 10 211 3251.E-mail address: timo.tahvanainen@metla. (T. Tahvanainen).

0378-1127/$ see front matter # 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.foreco.2007.09.035
mailto:[email protected]://dx.doi.org/10.1016/j.foreco.2007.09.035http://dx.doi.org/10.1016/j.foreco.2007.09.035mailto:[email protected]


2/13


3/13


4/13

For the modeling of the vertical distribution, branch andneedle biomass accumulation at the top of each 2 m tree

section were transformed into relative cumulative (01)values. Respectively, the heights of the sections weretransformed into proportional heights within the crown. Thus,the relative height for live branch biomass is zero at the crownbase and one at the tree top. The upper limit for dead branchbiomass was not measured, but it was estimated through thefollowing procedure: if the accumulation of dead branchbiomass ends within the same 2 m tree section where theliving crown base is located, the upper limit for dead brancheswas assumed to be equal with the crown base. If theaccumulation ended in a tree section lower than the crownbase, the highest dead branch was assumed to be the upperend of that section. If the accumulation of dead branchbiomass ended above the crown base, the highest dead branch

was assumed to be in the middle of the 2 m section where thehighest dead branch biomass was recorded.

In the second data set, a site index was predicted for eachstand. From ve to seven sample plots with a radius of 5.64 m(100 m2) were measured from each stand, depending on thearea of the stand. The mean stand area was 1.36 ha (0.52.6 ha). Tree species and breast height diameter (cm) wererecorded for every tree with a diameter of at least 25 mmwithin the sample plot. Three trees of each tree species werechosen as sample trees, whose age was estimated and whosetree height (dm), height to crown base (dm) and height to thelowest dead branch (dm) were measured. From the rest of thesample trees only their diameters were measured. Theelectronic Vertex-device was used for height measurementsand the crown base was dened according to the FinnishNational Forest Inventory systems eld instructions. Treeheights were estimated for the trees for which only breastheight diameter was measured. The heights were predictedusing the Na slund height model ( Naslund, 1937 ), based on theheight sample trees of the stand. The predicted heights wereneeded for predicting the stand and plot mean heights. Basalarea and mean height were calculated for both the stand andsample plot levels, including stems of at least 45 mm of breastheight diameter.

The stands had no visible signs of earlier thinnings and thewithin-stand variation in density was large. Almost every standincluded sample plots where the basal area was larger than the

recommended suggesting need for thinning in Finnish

Table 1List of variables

Variables Units Explanations

cf 1 Correction factor for the crown length models of pine and birch and dead branch height modelscf 2 Correction factor for the spruce crown base height modelcf 3 Scaling factor for living crown biomass distribution modelscf 4 Scaling factor for needle biomass distribution modelscf 5 Correction factor for dead branch distribution modelscr Crown ratio (crown length divided by tree height)d 13 cm Tree breast height diameterGplot m2 ha

1 Stand basal area (at breast height level), dened at sample plot levelGstand m2 ha

1 Stand basal area (at breast height level)h m Tree heighth20 m Truncated tree height used in hcr model for spruce ( h20 = h if h < 20, h20 = 20 if h ! 20 m)hcr m Height to crown base; height of the lowest living branchhd Tree height (m) and diameter (cm) ratiohhdb m Height of the highest dead branchhdiff m Height competition factor (difference between tree height and stand/plot medium height); h H plothrel(crown) 0, . . ., 1 Relative height within living crownhrel(db) 0, . . ., 1 Relative height within dead crown H g(plot) m Mean height (the height of the basal area weighted mean diameter tree), dened at sample plot level H g(stand) m Stand mean height (the height of the basal area weighted mean diameter tree)hldb m Height of the lowest dead branchlcr m Crown length (difference between tree height and the base of living crown); h hcrmcrown kg Total dry mass of living crownmcum(crown) 0, . . ., 1 Cumulative relative biomass of live crownmcum(db) 0, . . ., 1 Cumulative relative biomass of dead branchesmcum(needle) 0, . . ., 1 Cumulative relative biomass of needlesT years Average age

Table 2Mean, standard deviation and range of main stand variables

Variables Units Mean S.D. Minmax N

Gplot m2 ha1 21.10 6.43 4.040.0 872

Gstand m2 ha1 21.07 5.73 6.236.6 167

H g(plot) m 13.07 3.67 6.025.0 872 H g(stand) m 13.20 3.55 7.022.6 167T years 62.28 37.2 12200 165

See Table 1 for an explanation of variables.

T. Tahvanainen, E. Forss / Forest Ecology and Management 255 (2008) 455467 458


5/13

silvicultural recommendations. In addition, almost every standincluded at least one sample plot in which the basal area waslower than the recommendation after thinning.

2.2. Crown length modeling

The goal in constructing the crown length models was to ndpredictors that describe the effect of the size of the tree (height,diameter, tree basal area), of its competitive status (tree heightrelative to stand and plot mean height, difference between treeheight and plot mean height, heightdiameter ratio, tree basalarea relative to mean basal area), and of the overall competitionwithin the stand (stand basal area). For spruce, however, theeffect of tree height seemed to be constant after the treesreached about 20 m in height. Therefore, in spruce crown base

models the tree height was substituted by a predictor named h20 ,which is equal to tree height (m) when the height is shorter than20 m, and 20 when the trees are 20 m or higher. The species of competing trees was not taken into account in the heightcompetition factor.

Due to the hierarchical structure of the data, the mixedlinear modeling approach was used ( Lappi, 1986 ; Eerika inen,2001). The residual variation was divided into between-stand,between-plot and between-tree components. The models wereestimated using the Mixed procedure of the SPSS ver 12.0.1computer software ( SPSS Inc., 2003 ). In order to homogenizethe variance of residuals, the dependent variable in the crownlength models for pine and birch was the square root of crownlength (Eq. (1)). For spruce, the dependent variable was thelogarithm of the height to the crown base (Eq. (2)):

ffiffiffiffiffi l crp b 0 b 1h b 2h 2 b 3h diff b 4hd b 5G plot u st u pl e tr (1)

ln h cr b 0 b 1h 20 b 2h220 b 3h diff b 4hd b 5G plot

u st u pl e tr (2)

In Eqs. (1) and (2) , the b 0, . . ., b 5 are coefcients, and thesubscripts st, pl and tr refer to stand, plot and tree, respectively,

ust , upl and etr are independent and identically distributed

random variates that correspond to between-stand, between-plot and between-tree variation with a mean of 0 and constantvariances of dst , dpl and dtr. The estimate of crown length

(Eq. (3)) is the square of the estimate of the xed part of themodel (Eq. (1)) plus a correction term due to the square roottransformation of the dependent variable:

lcr m2 cf 1 (3)

where m b 0 b 1h

b 2h2 b 3h diff

b 4hd b 5G plot is the

estimate of the xed part of the model, and cf 1 dst dpl dtris the sum of the estimates of the variance components.

The estimate of the height to crown base of spruce is

h cr e mcf 2 (4)

where m b0

b1

h 20 b2

h 2

20 b

3h diff b

4hd b

5G plot ;

and cf 2 is a correction coefcient due to the logarithmictransformation of the dependent variable. The value of theempirical correction coefcient ( Snowdon, 1991 ) is

cf 2 P h crP e m

2.3. Dead branch height modeling

The same linear modeling approach as in crown lengthmodeling was used in the modeling of the height of the lowestdead branch ( hldb ) and the height of the highest dead branch(hhdb ). The predictors were chosen among those used in crownlength and crown base models. For estimating the height of thehighest dead branch, a simpler model that uses tree height andthe height of the crown base was selected (Eqs. (5) and (6) ). Thesame method as in the case of crown length estimation was usedto transform the square root of Eqs. (5) and (6) to the arithmeticscale:

ffiffiffiffiffiffiffi h ldbp b 0 b 1h b 2d 13 b 3h 2diff b 4hd b 5G plot u st u pl e tr (5)

ffiffiffiffiffiffiffiffi hhdb

p b0

b1

h b2

hcr

ust

upl

etr

(6)

Table 3Mean, standard deviation and range of main tree variables

Variables Units Pine Birch Spruce

Mean S.D. Minmax N Mean S.D. Minmax N Mean S.D. Minmax N

d 1.3 cm 12.85 6.82 3.00.2 3071 11.72 5.95 3.041.0 2042 12.95 6.58 3.043.1 2802h m 11.63 4.48 4.027.2 3071 13.15 4.71 2.326.6 2042 11.16 5.25 2.129.5 2802

hd 0,. . .

, 1 0.98 0.23 0.402.03 3071 1.23 0.32 0.502.77 2042 0.89 0.18 0.431.53 2802hdiff m 0.92 2.39 11.411.1 3071 0.55 3.01 9.211.4 2042 2.58 4.06 16.89.4 2802lcr m 5.84 2.17 1.019.4 3071 7.44 3.00 1.018.1 2042 8.42 4.25 1.024.4 2802hcr m 5.79 3.23 0.418.8 3071 5.71 2.72 0.116.6 2042 2.73 2.06 0.112.6 2802cr 0, . . ., 1 0.52 0.13 0.140.96 3071 0.57 0.13 0.150.99 2042 0.76 0.13 0.170.98 2802hldb m 2.22 2.49 0.116.6 3059 3.81 2.85 0.115.5 1934 0.66 0.67 0.18.2 2788mcrown kg 10.74 16.24 0.17173.1 2756 12.32 19.39 0.33191.3 1468 26.12 33.93 0.53389.9 2287

See Table 1 for an explanation of variables.



6/13

2.4. Biomass distribution modeling

The cumulative distribution of total living crown mass andneedle mass was found to follow a sigmoid shape from the

crown base to the top of the tree. To describe mass distributions,the exible three-parameter ChapmanRichards function wasused. This model has been commonly used for the description

of stand development ( Pienaar and Turnbull, 1973; Hacker andBilan, 1991; Hui and Gadow, 1993; Forss et al., 1996 ). Themodel was developed for each tree species, assuming that therelative distribution of the crown mass components is the same

in different stands and trees of different sizes. A constant wasadded to the model (Eq. (7)) because there is substantialbiomass at the base of the living crown (rst living branch or

Table 4Crown length models for pine and birch and crown base model for spruce

Variables Parameters Pine (Eq. (1)) Birch (Eq. (1)) Spruce (Eq. (2))

Estimate S.E. Sig. Estimate S.E. Sig. Parameters Estimate S.E. Sig.

Intercept b 0 1.9370 0.0733 0.000 1.4720 0.0696 0.000 b 0 1.4662 0.1308 0.000h b 1 0.1047 0.0083 0.000 0.1885 0.0075 0.000

h2

b 2 0.0016 0.0003 0.000 0.0032 0.0003 0.000h20 b 1 0.1276 0.0121 0.000h 220 b 2 0.0016 0.0004 0.002hdiff b 3 0.0475 0.0043 0.000 b 3 0.0221 0.0076 0.004hd b 4 0.3413 0.0218 0.000 0.3134 0.0228 0.000 b 4 0.3340 0.0638 0.000Gplot b 5 0.0090 0.0020 0.000 0.0115 0.0019 0.000 b 5 0.0202 0.0036 0.000d st 0.0252 0.0045 0.000 0.0107 0.0025 0.000 0.1820 0.0307 0.000d pl 0.0131 0.0016 0.000 0.0093 0.0016 0.000 0.0485 0.0063 0.000d tr 0.0393 0.0011 0.000 0.0532 0.0018 0.000 0.1601 0.0048 0.000cf 1 (m) 0.0525 0.0624cf 2 1.5081 R2 0.63 0.76 0.89RMSE (m) 1.33 1.48 1.39RMSE% 23.3 19.7 16.5Mean estimated (m) 5.69 7.51 8.43

Mean measured (m) 5.84 7.44 8.43Bias (m) 0.15 0.06 0.00Bias% 2.55 0.83 0.00 N 3071 2042 2802

For pine and birch the model parameters are presented for the square root modication of the model (Eq. (1)). For spruce, the logarithmic modication of the crownbase model (Eq. (2)) is presented. The correction factors (cf 1 and cf 2) and the RMSE, RMSE% and bias% are calculated for the metric transformation of the models(Eqs. (3) and (4)). The correction factors are included in the estimates.

Table 5Models for the height of the lowest dead branch for pine, spruce and birch

Variables Parameters Pine Birch Spruce

Estimate S.E. Sig. Estimate S.E. Sig. Estimate S.E. Sig.

Intercept b 0 0.32884 0.04890 0.000h b 1 0.10106 0.00334 0.000 0.08600 0.00321 0.000 0.03420 0.00416 0.000d 13 b 2 0.00396 0.00204 0.053h 2diff b 3 0.046647 0.004405 0.000 0.15734 0.00367 0.000hd b 4 0.13255 0.02796 0.000 0.32955 0.03252 0.000

Gplot b 5 0.011629 0.002878 0.000d st 0.20122 0.02914 0.000 0.08265 0.01600 0.000 0.02281 0.00371 0.000d pl 0.01474 0.00274 0.000 0.02025 0.00388 0.000 0.01147 0.00145 0.000d tr 0.09001 0.00197 0.000 0.14574 0.00513 0.000 0.05284 0.00154 0.000cf 1 (m) 0.10476 0.16599 0.06431 R2 0.542 0.545 0.141RMSE (m) 1.791 2.007 0.620RMSE% 78.7 55.5 104.7Mean estimated (m) 2.27 3.61 0.59Mean measured (m) 2.22 3.81 0.66Bias (m) 0.06 0.19 0.06Bias% 0.03 0.05 0.11 N 3059 1934 2788

The model parameters are presented for the square root modication of the model (Eq. (5)). The correction factor (cf 1) and the RMSE, RMSE% and bias% are

calculated for the metric transformation of the model (Eq. (3)). The correction factor is included in the estimates.



7/13

whorl). The cumulative distribution of dead branches wasestimated with the use of a simple second degree regressionmodel (Eq. (8)).

m cum b 0 b 11 e b 2 h rel

b 3 cf 3 (7)

mcumdb b 1

hrel b 2

h 2rel cf 3 (8)

where mcum is the cumulative relative crown mass components(total crown, needles) along the living crown at a relative heighthrel , mcum(db) the cumulative relative mass of dead branches, hrelthe relative height within the crown, b 0, . . ., b 3 the coefcients,cf 3 is the correction factor for scaling the mcum to value 1 whenhrel = 1.

3. Results

3.1. Crown limit models

Parameter estimates of the crown length (Eq. (1)) and thecrown base (Eq. (2)) models were logical and signicant at the0.05 level ( Tables 4 and 5 ). The higher the stand basal area ormore suppressed the status of the tree (negative heightcompetition index or high heightdiameter ratio) is the shorteris the crown. The R2 values were 0.63 for the pine and 0.76 forthe birch crown length models, and 0.89 for the spruce crownbase model. For the pine and the birch models, the variances of between-stand factors were lower than variances of thebetween-tree factors, but for spruce the between-stand variancewas higher. The between-plot factors were the lowest for allmodels. The relative root mean square error for the crown

length models was 23.3% (1.33 m) for pine, 16.5% (1.39 m) forspruce and 19.7% (1.48 m) for birch.In order to evaluate the differences between the two data

sets, the residuals were produced for both sets separately(Fig. 3). The residuals in the two data sets differ from each othersignicantly and the parameter estimates are dominated by dataset 1, in which the number of sample trees is higher. Pine crownlength was slightly underestimated up to 7 m of crown length.For birch, the residuals were relatively evenly distributed up to10 m of crown length. In data set 1, the model slightlyoverestimated crown lengths of up to 8 m. In the data set 2 themodel gave underestimates for long crown lengths. The largestdifference between the data sets was among spruces; in data set2, the model underestimated all crown lengths, while in data set1 the residuals were quite evenly distributed until 20 m of crown length.

The predictors of models for the lowest dead branch (Eq. (5))and their parameter estimates were quite parallel to those in themodels for the height to the crown base ( Table 5 ). The standdensity (Gplot ), however, was a signicant predictor only forbirch. The parameter estimates were signicant at the 0.05level, except for diameter ( d 13 ) in the spruce model (0.053). The R2 values were lower than for models for the living crown: 0.54for pine and for birch, and 0.62 for spruce. For birch and spruce,the variances of the between-tree factors were greater than the

variances of the between-stand factors, but for the pine the

between-stand variance was higher. The between-plot factorswere the lowest for all models. The root mean square error forlowest dead branch estimates was 78.7% (1.79 m) for pine,55.5% (2.01 m) for birch and 104.7% (0.62 m) for spruce.

The parameter estimates for the highest dead branch models

(Table 6 ) were signicant at the 0.05 level and the R2

values

Fig. 3. Predicted crown length and distribution of residuals for pine, birch andspruce. Residuals are calculated as actual crown lengths minus the predictedcrown lengths. Thegrey small dots representdata set 1 andthe largerblackonesdata set 2. The combined data is presented by the thick line and data set 2 bythinner line.



8/13

were 0.93 for pine, 0.72 for birch, and 0.36 for spruce. Thevariances of the between-tree factors were greater thanvariances of the between-stand factors, and the between-standvariances were lowest for all the models. The root mean squareerror (RMSE%) was 14% (0.85 m) for pine, 21.5% (1.41 m) forbirch, and 38.7% (1.87 m) for spruce.

The average crown limit estimates for different species at agiven tree height ( Fig. 4) were produced using average treedimensions and stand characteristics. For pine, the treediameter varied from 5.5 to 36 cm and stand basal area from

8 to 32 m2

ha1

, for birch, from 5 to 36 cm and from 4.5 to30 m 2 ha1, and for spruce, from 5.5 to 36 cm and from 7 to33.5 m2 ha

1. The competition factor was set to zero. Thedifferences between species are clear: pine and birch are quitesimilar to each other, but birch has a longer live crown thanpine. The crown ratio decreases when the trees get taller. Inyoung trees the highest dead branch is typically inside the livingcrown, but as the trees grow taller the height of the highest deadbranch follows more the crown base level. In tall pines, thehighest dead branches are again located inside the living crown.The length of the living crown of spruce is longer than the otherspecies and the lower limit of the dead branches remains verylow, even in mature trees. The crown base is strongly dependenton tree height up to 1920 m of height, but after that the heightto the lowest live branch increases very slowly.

3.2. Vertical biomass distribution models

The ChapmanRichards function t the sigmoid shape of thecumulative livingcrown and needle biomasses quite well, but inthe upper quarter of the canopy the model was slightly rigid(Fig. 5). A scaling factor has to be applied to the model to makethe predictions consistent at the tip of the crown by forcing themodel through the point (1.0, 1.0). The scaling factor variedbetween 0.984 and 0.993, and was taken into account in the

model t statistics and prediction error terms ( Tables 7 and 8 ).

The root mean square error in the living crown model was11.7% (0.08 relative units) for pine, 14.3% (0.09) for spruce and16.2% (0.11) for birch. The corresponding errors in the needlemodelswere 15.1% (0.09) for pine and 18.6% (0.10) for spruce.The intercept factor for the total living crown biomass modelwas highest for birch (11.9%) and lowest for spruce (5.9%),while pine (7.9%) was in between these two species.

The three tree species also varied in the shape of the livingcrown biomass accumulation: the curve of birch slopedstrongest, forming a clear S-shape correlation ( Fig. 6). The

pine was close to the birch. The relative accumulation of crownbiomass at the relative height zero was about 12% for birch andabout 8% for pine. The accumulation of spruce living crownbiomass was more linear. The relative height, at which theliving crown biomass reached half of the total biomass, was39% for birch, 43% for pine and 47% for spruce. The needlebiomass accumulates slowly in the lower parts of the crowncompared to the total living crown biomass, which alsocorresponds to the lower intercept factors of the needle biomassmodels. Thus, the needle biomass was concentrated more in theupper parts of the living crown: the relative height, at which theneedle biomass reached half of the total needle biomass, was53% for pine and 56% for spruce. The relative height, at whichmaximum crown biomass peaked, was 36% for pine, 33% forbirch and 39% for spruce. Respectively, the maximum needlebiomasses were at a greater relative height: 47% relative heightfor pine and 52% relative height for spruce. The estimates forcumulative dead branch biomass models are presented inTable 9 .

4. Discussion

For energy wood procurement, the living crown measuresare of much higher interest than dead branches. In Hakkilasstudy, the biomass of live branches and needles was about ve

times larger than the biomass of dead branches in pine stands,

Table 6Models for the height of the highest dead branch for pine, birch and spruce

Variables Parameters Pine Birch Spruce


Intercept b 0 1.27200 0.01792 0.000 1.345174 0.041916 0.000 1.66732 0.03727 0.000h b 1 0.02294 0.00239 0.000 0.02236 0.00528 0.000 0.01701 0.00536 0.000

hcr b 2 0.14571 0.00180 0.000 0.130171 0.003746 0.000 0.095715 0.002113 0.000d st 0.00656 0.00127 0.000 0.00579 0.00239 0.015 0.05318 0.01235 0.000d pl 0.00216 0.00043 0.000 0.00381 0.00169 0.025 0.04139 0.00582 0.000d tr 0.02086 0.00061 0.000 0.06437 0.00301 0.000 0.08340 0.00286 0.000cf 1 (m) 0.023 0.068 0.000 R2 0.93316 0.71572 0.36120RMSE (m) 0.85169 1.41033 1.87144RMSE% 14.0 21.5 38.7Mean estimated (m) 6.07 6.55 4.84Mean measured (m) 6.08 6.59 4.66Bias (m) 0.00 0.03 0.18Bias% 0.05 0.52 3.73 N 2668 1069 2117

The model parameters are presented for the square root modication of the model (Eq. (6)). The correction factor (cf 1), and the RMSE, RMSE%, bias and bias% arecalculated for the metric transformation of the model (Eq. (3)). The correction factor is included in the estimates.



9/13

whereas in spruce and birch stands the ratio was about 101(Hakkila, 1991 ). In harvesting removal, the difference is evengreater because the dead branches are mainly located beneaththe living crown or within its lower parts. In the part treeharvesting method, dead branches are usually cut off during thedelimbing of the industrial timber sections. Dead branches alsoeasily drop out during the loading and unloading of timber inforest transportation, even with the use of the full treeharvesting method.

4.1. Modeling data

The two data sets differ remarkably from each other bymeans of the geographical distribution of the stands, selection

criteria of the sample trees and accuracy of sample tree

measurements. Data set 1 covers the geographical area of Finland, and also different stand ages. Data set 2 includes onlyyoung stands located in a relatively small area in Finland. Firstcommercial thinnings are the primary event for which themodels could be utilized. Data set 1 was measured about 20years ago and the increase of mean temperature and nitrogenfall-out during last two decades may have caused changes intypical tree structure. However, larger difference between thetwo data sets exists due to their difference in silviculturalhistory. In the older data set, the stands had been treated withthe traditional thinning from below. Young stands in the seconddata set typically had not yet been thinned and were more orless lacking seedling stage tending.

In data set 1, the sample trees were chosen among trees thatwould be removed in harvesting, being typically suppressedtrees with a small live crown. Currently, especially in earlythinnings, trees are removed more evenly from various dbhclasses than earlier. In data set 2, the trees competitive status orprospects of being removed or left in thinning did not affect the

sampling probability, which makes the sample trees morerepresentative of current thinning operations. The two data setstogether include not only trees of different size anddevelopment phase, but also of highly variable stand density,and therefore of versatile competitive status. Thus, the datamade it possible to develop generally usable models, eventhough the models tended to be slightly inaccurate in the youngand old stands. The stand level accuracy of the estimates can beimproved by measuring sample trees to calibrate the model toparticular stand conditions ( Lappi, 1991 ).

4.2. Crown length and branch height models

Tree height was the most important predictor for crownlength and dbh for crown base models. An increase in the standbasal area decreased the crown length for all the three treespecies as expected. A negative height competition factor,which reects the effect of suppression on a tree, reduced thecrown length estimates for pine and birch and increased theheight of the crown base for spruce. The heightdiameter ratio,which also reects the competition status and growing historyof a tree, was a signicant predictor for all three species. Thehigher the ratio, the shorter the living crown. For spruce, thebetween-stand variances exceeded the between-tree variances,while for pine and birch the between-tree variance wasdominant, indicating a possibility to improve the model forspruce some additional stand level variables. The relationshipsbetween height to lowest living branch and lowest and highestdead branch were in harmony with earlier studies ( Hakkilaet al., 1972; Verkasalo, 1997; Verkasalo and Maltamo, 2002 ).

Verkasalo and Maltamo (2002) and Hynynen et al. (2002)reported differences in crown ratio, crown lengths and heightsto the lowest dead branch between naturally regenerated andplanted birch and spruce stands. The planted trees had longerliving crowns but the difference decreased with increasing treesize. The old spruces in Finland are mainly naturallyregenerated, while during the last decades planting has been

the main regeneration method for spruce. Thus, the regenera-

Fig. 4. Branch heights for pine, birch and spruce.



10/13

Fig. 5. The predicted (curve) and observed accumulation of total living crown biomass for pine, birch and spruce (Eq. (7)).

Table 7Models for the relative cumulative living crown masses for pine, birch and spruce (Eq. (7))

Pine Birch Spruce


Parametersb 0 0.07881 0.00257 0.000 0.11902 0.00431 0.000 0.05892 0.00265 0.000b 1 1.03037 0.00583 0.000 0.96061 0.00851 0.000 1.18495 0.01131 0.000b 2 3.59557 0.05382 0.000 3.90684 0.09381 0.000 2.58915 0.05391 0.000b 3 3.66652 0.09064 0.000 3.65942 0.01515 0.000 2.76521 0.06830 0.000cf 3 0.99071 0.98929 0.98635

R2 0.952 0.899 0.942RMSE 0.077 0.108 0.086RMSE% 11.7 16.2 14.3Mean estimated (m) 0.659 0.667 0.599Mean measured (m) 0.665 0.675 0.608Bias (m) 0.006 0.007 0.008Bias% 0.9 1.1 1.4 N 10301 7125 12305

The scaling factor (cf 3) is included in the estimates of the whole model t and error statistics.



11/13

tion method and genotype might explain part of the differencesfor the spruce crown length estimates in the two data sets(Fig. 3), and also the stabilization of the height to crown base of tall spruces ( Fig. 5). The results suggest that the regenerationmethod might be a relevant independent variable in crownlength models for spruce and birch.

The stands and trees growth history, like earlier thinnings,modify the length of the living crown ( Hynynen et al., 2002 ),allometric relationships and competition factors. Crown lengthand crown base models can only partly reect these differencesin crown dimensions. The stand competition factor ( G) and thetrees competitive status factor did not take into account thedifferences between species. A coniferous mixture and tree agehave been found to have a differentiated effect on the self-pruning of silver birch and pubescent birch ( Hera jarvi, 2001;

Verkasalo, 1997 ) The difference between the two birch species

may have been species based, but they can also be partly causedby differences in soil fertility and growthhistory. Thus, separatemodels for both birch species might be needed.

Crown ratio has been found to decrease with an increasingtemperature sum, and to be greater on fertile sites than on poorsites (Hakkila et al., 1972; Hynynen et al., 2002 ). Predictors likesite index and geographical location, which are commonly usedalso in tree growth models ( Hynynen et al., 2002; Trasobareset al., 2003 ), could have improved the crown length estimates.Unfortunately, the site classication used in data set 1 was not

fully comparable with the classication used in data set 2 and incommon forest management data.The height of the lowest dead branch is much more random

and the models produced weaker correlations than the crownlength estimates. The height of the highest dead branch of pinesand birches seems to closely follow the height to the crownbase, while the highest dead branch of spruce is clearly locatedwithin the living crown. The R2 values of the models were high,but the lack of direct measurements of the height to the highestdead branch and the difculties in placing the relatively smalldead branch biomasses of felled trees to the correct tree sectionsmay cause bias in the models.

4.3. Biomass distribution models

The ChapmanRichards function appeared to be rigid nearthe top of the tree for all three tree species. However, the overallt for modeling the vertical distribution of crown and needlebiomasses was relatively good. A scaling factor was applied tothe model to obtain consistent results at the top of the tree,whose affect on the model predictions below the top isnegligible (on average about 1%). The relative height at whichthe needle biomass reached its maximum point was 47% forpine and 52% for spruce. These results are parallel to previousstudies. In pine stands of various ages, the vertical foliage

density peaked at about 50% relative height ( Makela and

Table 8Models for the relative cumulative needle masses for pine and spruce (Eq. (7))

Pine Spruce

Estimate S.E. Sig. Estimate S.E. Sig.

Parameters

b 0 0.04276 0.00721 0.000 0.04166 0.00717 0.000b 1 1.13650 0.02627 0.000 1.31352 0.05179 0.000b 2 3.43024 0.18470 0.000 2.62216 0.18803 0.000b 3 4.98748 0.45198 0.000 3.96188 0.35821 0.000cf 4 0.99285 0.98435

R2 0.949 0.936RMSE 0.086 0.095RMSE% 15.1 18.6Mean estimated (m) 0.569 0.513Mean measured (m) 0.574 0.521Bias (m) 0.004 0.008Bias% 0.7 1.6 N 1056 1273

The scaling factor (cf 4) is included in the whole model t and error statistics.

Fig. 6. Estimatedrelative accumulation of living crown biomass of pine,spruceand birch and accumulation of needle biomass of pine and spruce.



12/13

Vanninen, 2001 ) and in young pine stands, it peaked just belowthe mid-point of the living crown ( Kelloma ki et al., 1980).Variables describing a trees social status might have explainedvertical distribution of living crown biomasses more accurately.Kelloma ki et al. (1980) and Xu and Harrington (1998) reportedthat in young pine stands the point of maximum needle biomasswas shifted upwards in suppressed trees. These results arecontradictory to Makela and Vanninens (2001) study, in whichthe trees social status did not affect the relative height wherepine needle biomass peaked. In the study of Xu and Harrington(1998) , an increase in the stand density of loblolly pine, dened

as leaf area index, increased the peak relative height of foliagebiomass.The results of other studies suggest that the vertical biomass

distribution models developed in this study can be used for theestimation of biomass removals in thinnings that represent awide range of stand conditions. The models are likely to giveunbiased estimates with different procedures for the selectionof removed trees, although the effect of the trees social statuson vertical biomass distribution requires further studies.

5. Conclusions

The crown length models and relative biomass distributionmodels presented in this study can be utilized for theimprovement of the pre-harvest estimates of harvested volumeand energy yield in Finland. The models can be used forsimulating different harvesting methods and bucking optionsfor planning and developing the energy wood harvestingmethods, and for predicting the costs of different supply chains.The models can also be used for estimating and evaluating thenutrient removals of different logging methods, for eco-physiological studies, such as the estimation of light intercep-tion within the canopy, and for more realistic forestvisualisation. The models are most suitable for standsdominated by conifers with tree heights from 6 to 18 m. They

can also be used in other even-aged, one canopy layer stands

that have not been thinned during the past 510 years, andwhere the between-stem competition for light already affectsthe crown base development after thinning.

Acknowledgements

Financial support for this study was provided by the WoodEnergy Technology Research Programme of the NationalTechnology Agency of Finland, Tekes. We are most grateful forDr. Pentti Hakkila, the leader of the Research Programme, andthe Finnish Forest Research Institute for making the data

available. We also thank Kalle Kaartinen, Hannu Aaltio and AriLauren for their practical assistance with the data. We wouldlike to thank Timo Pukkala and Erkki Verkasalo for theirvaluable comments on the manuscript and Jaakko Heinonen forhis advice and consultation regarding the statistical analysis.We also thank Dr. Greg Watson for his linguistic revision of themanuscript, and Mr. Vertti Tahvanainen for the graphicalillustrations.

References

Assman, E., 1970. The Principles of Forest Yield Study. Pergamon Press,Oxford, p. 506.

Baldwin, V.C., Peterson, K.D., 1997. Predicting the crown shape of loblollypine trees. Can. J. For. Res. 27, 102107.Biging, G.S., Dobbertin, M., 1995. Evaluation of competition indices in

individual tree growth models. For. Sci. 41, 360377.Bjorklund, L., 1999. Identifying heartwood-rich stands or stems of Pinus

sylvestris by using inventory data. Silva Fenn. 33, 119129.Claesson, S., Sahlen, K., Lundmark, T., 2001. Functions for biomass estimation

of Young Pinus sylvestris , Picea abies and Betula spp. from stands innorthern Sweden with high stand densities. Scand. J. For. Res. 16, 138146.

Eerika inen, K., 2001. Stem volume models with random coefcients for Pinuskesya in Tanzania, Zambia and Zimbabwe. Can. J. For. Res. 31, 879888.

Faltinstruktion, 2003. Riksinventering av skog. SLU Institutionen fo r skogligresurshusha llning och geomatik, Umea, Sverige (in Swedish).

Forss, E., Gadow, K.v., Saborowski, J., 1996. Growth models for unthinned Acacia mangium plantations in South Kalimantan, Indonesia. J. Trop. For.

Sci. 8, 449462.

Table 9Models for the relative cumulative dead branch masses for pine, birch and spruce (Eq. (8))

Pine Birch Spruce


Parameters

b 1 0.028 0.010 0.007 0.529 0.030 0.000 0.378 0.013 0.000b 2 0.950 0.011 0.000 0.449 0.031 0.000 0.611 0.014 0.000cf 5 1.02288 1.02233 1.01125

R2 0.900 0.782 0.889RMSE 0.123 0.173 0.120RMSE% 20.5 24.2 17.3Mean estimated (m) 0.602 0.714 0.696Mean measured (m) 0.592 0.712 0.691Bias (m) 0.009 0.003 0.006Bias% 1.6 0.4 0.9 N 6621 2112 4609

The correction factor (cf 5) is included in the estimates of the RMSE%, bias and bias%.



13/13

Gillespie, A.R., Allen, H.L., Vose, J.M., 1994. Amount and vertical distributionof foliage of young loblolly pine trees as affected by canopy position andsilvicultural treatment. Can. J. For. Res. 24, 13371344.

Hacker, W.D., Bilan, M.V., 1991. Site index curves for loblolly and slash pineplantationsin thePostOak Belt of east Texas. South.J. Appl. Forest. 15, 97100.

Hakkila, P., 1991. Hakkuupoistuman latvusmassa. Summary: crown mass of trees at the harvesting phase. Folia For. 773, 24.

Hakkila, P., 2004. Developing technology for large-scale production of forestchips. Wood Energy Technology Programme 19992003. Final Report.Technology Programme Report 6/2004. TEKES, p. 99.

Hakkila, P., Laasasenaho, J., Oittinen, K., 1972. Korjuuteknisia oksatietoja.Summary: branch data for logging work. Folia For. 147, 15.

Hasenauer, H., 1994. A single tree simulator for uneven-aged mixed speciesstands. In: Pinto da Costa, M.E.,Preuhsler, T. (Eds.), Mixed Stands ResearchPlots, Measurement and Results, Models. Inst. Superior de Agronomia,Univ. Technica de Lisboa, Codex, Portugal, pp. 255269.

Hasenauer, H.,Monserud, R.A., 1996.A crown ratio modelfor Austrianforests.For. Ecol. Manage. 84, 4960.

Hasenauer, H., Monserud, R.A., 1997. Biased predictions for tree height incre-ment models developed from smoothed data. Ecol. Model. 98, 1322.

Hera jarvi, H., 2001. Technical properties of mature birch ( Betula pendula and B. pubescens ) for saw milling in Finland. Silva Fenn. 35, 469485.

Hui, G.Y., Gadow, K.v., 1993. Zur modellierung des Oberho hen-wachstums beiCunninghamia lanceolata. Forstarchiv 64, 311313.

Hynynen, J., Ojansuu, R., Ho kka, H., Siipilehto, J., Salminen, H., Haapala, P.,2002. Models for predicting stand development in MELA system. ResearchPapers 835. Finnish Forest Research Institute, p. 116.

Ilomaki, S., Nikinmaa, E., Ma kela, A., 2003. Crown rise due to competitiondrives biomass allocation in silver birch. Can. J. For. Res. 33, 23952404.

Jacobson, S., Kukkola, M., Malkonen, P., Tveite, B.,2000. Impact of whole-treeharvesting and compensatory fertilization on growth of coniferous thinningstands. For. Ecol. Manage. 129, 4151.

Karkkainen, M., 1980. Ma ntytukkirunkojen laatuluokitus. Commun. Inst. For.Fenn. 96, 1152.

Karkkainen, M., 1986. Malli ma nnyn, kuusen ja koivun puuaineen oksaisuu-desta. Abstract: model of knottiness of wood material in pine, spruce andbirch. Silva Fenn. 20, 107116.

Kelloma ki, S., Hari, P., Kanninen, M., Ilonen, P., 1980. Eco-physiologicalstudies onyoung Scots pine stands. II.Distribution of needlebiomassand itsapplication in approximating light conditions inside the canopy. Silva Fenn.14, 243257.

Korhonen, K.T., Maltamo, M., 1990. Ma nnyn Maanpa allisten Osien Kuiva-massat Etela -Suomessa, vol. 371. Metsantutkimuslaitoksen tiedonantoja,Joensuu, p. 29 (in Finnish).

Lappi, J., 1986. Mixed linear models for analyzing and predicting stem formvariation of Scots pine. Commun. Inst. For. Fenn. 134.

Lappi, J., 1991. Calibration of height and volume equations with randomparameters. For. Sci. 37, 781801.

Maguire, D.E.A., Hann, D.W., 1990. Constructing models for direct predictionof 5-year crown recession in southwestern Oregon Douglas-r. Can. J. For.Res. 20, 10441052.

Makela, A., Vanninen, P., 2001. Vertical structure of Scots pine crowns indifferent age and size classes. Trees 15, 385392.

Malkonen, E., 1976. Effect of whole-tree harvesting on soil fertility. Silva Fenn.10, 157164.

Marklund, L.G., 1988. Biomassafunktioner fo r tall, gran och bjo rk I Sverige.

Biomass functions forpine,spruce andbirchin Sweden. Report45. SwedishUniversity of Agricultural Sciences, Department of Forest Survey. Umea , p.73.

Monserud, R.A., Sterba, H., 1999. Modeling individual tree mortality forAustrian forest species. For. Ecol. Manage. 113, 109123.

Naslund, M., 1937. Skogforsokanstaltens gallringsforsok i tallskog. Prima r-bearbetning. Meddelanden fra n Statens Skogfo rsoksanstalt, vol. 29, pp. 1169 (in Swedish, German summary).

Nord-Larsen, T., 2002. Stand and site productivity response following whole-tree harvesting in early thinning of Norway spruce ( Picea abies (L.) Karst.).Biomass Bioenergy 23, 112.

Oker-Blom, P., Pukkala, T., Kuuluvainen, T., 1989. Relationship betweenradiation interception and photosynthesis in forest canopies: effect of standstructure and latitude. Ecol. Model. 49, 7387.

Pienaar, L.V., Turnbull, K.J., 1973. The ChapmanRichards generalization of von Bertalanffys growth model for basal area growth and yield in even-aged stands. For. Sci. 19, 222.

Pukkala,T., Becker, P., Kuuluvainen, T., Oker-Blom, P., 1991. Predictingspatialdistribution of direct radiation below forest canopies. Agric. For. Meteorol.55, 295307.

Snowdon, P., 1991. A ratio estimator for bias correction in logarithmic regres-sions. Can. J. For. Res. 21, 720724.

SPSS Inc., 2003. SPSS 12.0 Command syntax reference.Trasobares, A., Tome, M., Miina, J., 2003. Growth and yield model for Pinus

halepensis Mill in Catalonia, North-East Spain. For. Ecol. Manage. 203, 4962.

Uusitalo, J., 1997. Pre-harvest measurement of pine stands for sawing produc-tion planning. Acta For. Fenn. 259, 56.

Uusvaara, O., 1981. Viljelyma nniko ista Saadun Sahatavaran Laatu ja Arvo, vol.27. Metsa ntutkimuslaitoksen tiedonantoja, p. 108. In Finnish.

Verkasalo, E., 1997. Hieskoivun laatu vaneripuuna. Summary: quality of European white birch ( Betula pubescens Ehrh.) for veneer and plywood.Research Paper 632. Finnish Forest Research Institute, p. 59.

Verkasalo, E., Maltamo, M., 2002. Ojitettujen korpien ja kivenna ismaidenkuusitukkirunkojen ja puuaineen laatu-ja arvoerot. In: Saranpa a, P., Verka-salo, E. (Eds.), Kuusen laatu ja arvo: vuosina 19942001 toteutettujentutkimusten loppuarviointi. Research Paper 841. Finnish Forest ResearchInstitute, pp. 7190 (in Finnish).

Xu, M., Harrington, T.B., 1998. Foliage biomass distribution of loblolly pine asaffected by tree dominance, crown size, and stand characteristics. Can. J.For. Res. 28, 887892.


Individual Tree Models for the Crown Biomass Distribution of Scots Pine,

Documents

Transcript of Individual Tree Models for the Crown Biomass Distribution of Scots Pine,