Belowground Biomass Functions and Expansion Factors in High Elevation Norway Spruce

1Belowground biomass functions and expansion factors in high elevation

2Norway spruce.

4Bohdan Konôpka1, Jozef Pajtík1, Vladimír Šebeň1, Martin Lukac2,*

61National Forest Centre, Forest Research Institute, T.G. Masaryka 22, 960 92 Zvolen,

7Slovakia

82Department of Agriculture, Development and Policy, University of Reading, RG6 6AR, UK

10*Corresponding author: Martin Lukac

11 tel. number: +44 -118-378 8470

12 fax: +44 -118-935 2421

13 e-mail: [email protected]

15Number of tables: 2

16Number of figures: 5

1 19Summary

21Biomass allocation to above- and belowground compartments in trees is thought to be

22affected by growth conditions. To assess the strength of such influences, we sampled six

23Norway spruce forest stands growing at higher altitudes. Within these stands, we randomly

24selected a total of 77 Norway spruce trees and measured volume and biomass of stem, above-

25and belowground stump and all roots over 0.5 cm diameter. A comparison of our observations

26with models parameterised for lower altitudes shows that models developed for specific

27conditions may be applicable to other locations. Using our observations, we developed

28biomass functions (BF) and biomass conversion and expansion factors (BCEF) linking

29belowground biomass to stem parameters. While both BF and BCEF are accurate in

30belowground biomass predictions, using BCEF appears more promising as such factors can be

31readily used with existing forest inventory data to obtain estimates of belowground biomass

32stock. As an example, we show how BF and BCEF developed for individual trees can be used

33to estimate belowground biomass at the stand level. In combination with existing

34aboveground models, our observations can be used to quantify total standing biomass of high

35altitude Norway spruce stands.

37Introduction

39The root system is important not only for anchoring trees in the soil, but it also fulfils a

40variety of physiological functions such as water and nutrient absorption from the soil and

41storage of carbohydrates. Trees therefore transfer a considerable proportion of assimilates to

42their belowground compartments. Tree roots significantly contribute to the total biomass and

43carbon storage in forests (Li et al., 2003). In spite of this significance of root systems,

2 2 44researchers have traditionally paid only scant attention to the ‘invisible’ part of the tree, partly

45due to the laborious and time consuming research methods involved (Levy et al., 2004).

46Recently, a substantial interest in tree root systems has been sparked by the need to accurately

47estimate the amount of carbon held in forests (Brunner and Godbold, 2007). A further impetus

48is provided by the proposed utilization of whole tree biomass as a renewable material for

49bioenergy generation (Schlamadinger and Marland, 1996).

50Studies dealing with biomass functions for Norway spruce (Picea abies (L.) Karst) during the

51past decade relate almost exclusively to aboveground biomass (Albaugh et al., 2009;

52Fehrmann and Klein, 2006; Muukkonen, 2007; Wirth et al., 2004; Zianis et al., 2005). There

53are several publications which also estimate the biomass of belowground compartments

54(Drexhage and Colin, 2001; Offenthaler and Hochbichler, 2006; Repola, 2009), however their

55general weakness is that they do not consider the full range of tree sizes, usually omitting

56early growth stages (Pajtík et al., 2008). There are two established approaches to estimating

57the biomass of particular tree compartments, making use of (a) allometric biomass functions

58and (b) expansion factors. Both methods can be used to calculate tree biomass at the tree or

59stand levels and can be readily adapted to calculate tree carbon stock. While biomass

60functions are invariably based on diameter (usually at breast height, i.e. DBH) and/or tree

61height, the definitions and usage of expansion factors varies among countries or authors (see

62for instance Somogyi et al. (2007); Tobin and Nieuwenhuis (2007)). Teobaldelli et al. (2009)

63defined the biomass conversion and expansion factor (BCEF) as an index which converts the

64most widely available forest mensuration data on stem volume directly to whole tree or

65compartment biomass (including belowground compartments, if parameterized). Here, a

66substantial variation in BCEF calculations may be related to inconsistent definition of stem

67volume (above or over bark, with or without the aboveground part of stump, including or

68excluding the stem top). To illustrate this point, we established BCEFs based both on stem

3 3 69volume (stem only, including aboveground stump and bark) and on merchantable volume

70(stem and branches above 7 cm, excluding stump and bark).

71This paper focuses on developing root system biomass functions and BCEFs for Norway

72spruce, which is one of the most important forest species in western and central Eurasia (EEA,

732006). At present, we are lacking belowground biomass models parameterised for Norway

74spruce growing at high elevations in Central Europe . This area is typical for its abundance of

75spruce forests in mountainous regions in countries such as Austria, Czech Republic, Romania

76and Slovakia. Use of Norway spruce biomass model parameters originating from other areas,

77for example from Western Europe (Drexhage and Colin, 2001) or Scandinavia (Repola,

782009), may introduce a significant bias to biomass estimates. To close the existing gap in data

79availability, we constructed root system (defined as belowground stump plus roots over 0.5

80cm diameter) biomass models for Norway spruce growing at high elevations in Central

81Europe and compared them with models parameterized for other European regions. We

82utilized data from 6 stands to establish biomass functions and BCEFs for belowground

83biomass of Norway spruce and compared their predictive power. We hypothesised that using

84both DBH and stem height as predictor variables does not lead to improved model

85predictions. In addition, we used developed models to illustrate their applicability to

86calculations of belowground biomass in conjunction with forest inventory data.

88 Materials and methods

89 Location and sites

90The research was conducted between 1998 and 2005 on six sites located in four separate

91mountain ranges in Slovakia, offering a good coverage of soil and climatic conditions at the

92higher end of natural Norway spruce distribution. The altitudes of selected sites were between

93626 and 1171 m above sea level. The prevailing bedrock was granodiorit and the soils were

4 4 94classified as Cambisol, Podzol and Psedogley (Table 1). The climate at this range of altitudes

95is characterised by low average temperatures (annual means between 4.0 and 5.2 C) and

96medium to high precipitation (ranging between 870 – 1080 mm per year). Studied stands were

97composed of Norway spruce, often with an admixture of other tree species not exceeding 10

98% stocking density and ranged from 3.4 to 6.0 ha in size. Stands 1-4 were uneven aged

99(originating from combined natural regeneration and planting), while stands 5 and 6 were

100even aged, originating from planting (stand 5) and natural regeneration (stand 6, Table 1). In

101each stand, a random sample of between 5 and 25 trees representing equal number of

102dominant, co-dominant and subdominant competitive status was selected in as wide an area as

103possible and destructively sampled.

105Sampling and measurement

106To reflect site conditions and management history at each site, we varied the sampling design

107and the root excavation methods. Stands 1 to 4 were located in an area severely damaged by

108windthrow in November 2004. Utilising the exposed root plates of uprooted trees, all

109branches were removed from selected trees and stem height was measured using a tape.

110Diameter measurements were taken using a calliper (two perpendicular measurements) from

111all sampled trees at the following locations: tree base (ground level) and then at 20 and 130

112cm (diameter at breast height, DBH) from ground level. In addition, we recorded two

113diameters of every 100 cm stem section from stem base to the top of the tree. The position of

114the ground level was identified on each stem and trees were cut at this point to separate stems

115from the belowground compartments (belowground part of the stump and roots). A horizontal

116line was drawn through the centre of the stump to divide the root plate into two equal halves

117and all roots found above this line were harvested. Roots which were broken-off from the root

118plate were excavated and paired up with fresh root injuries on the exposed part of the root

5 5 119system. All roots thicker than 0.5 cm were collected and divided into the following diameter

120classes: 0.5 – 2.5 cm, 2.6 – 5.0 cm, 5.1 – 7.5 cm, 7.5 – 10.0 cm and so on. The lower limit of

1210.5 cm was applied to avoid technical difficulties when collecting thinner root fragments and

122is in agreement with the general definition of medium and large roots (Böhm, 1979). The total

123length of roots in each diameter class was measured and the volume was calculated as:

2 125 V =  * r 0.5 * l (1)

126 where:

127 r0.5 - average radius between the lower and upper end of each root diameter class,

128 l – total root length in the diameter class.

129Subsequently, total volume of the root system was calculated as the sum of all diameter

130classes and multiplied by 2 to account for the other half of the root system still in the soil,

131assuming equal distribution of roots around the tree. Coarse root distribution may be affected

132by environmental conditions, notably prevailing wind direction which is westerly in stands 1-

1334. Since the destructive storm featured northerly winds, we are confident that the recovered

134half of the root system gives us a good estimate of the total.

135Diameters of belowground stump cylinders were measured at the top (ground level), bottom

136and in the middle, together with the cylinder height. The volume of the stump cylinder was

137then expressed by applying the Newton’s formula:

2 2 2 138 V =  * l * (r1 + r2 + 4r3 ) / 6 (2)

139 where:

140 l – stump length

141 r – stump radius in top (r1), bottom (r2) and middle (r3) part of the stump.

6 6 143The volumes of all 1 m stem sections were calculated in the same fashion, with the exception

144of stem base where stem volume was described by a curve fitted to the following four stem

145radiuses: 0, 20, 100 and 130 cm from the ground level. Total stem volume was then calculated

146by summing the volumes of all stem sections.

147Biomass samples corresponding to approximately 10% of the total root system, stump and

148stem were taken to establish their density. The samples were transported to the laboratory, air

149dried at room temperature for 10 days and then oven-dried at 95˚C until constant weight.

150Specific weight of belowground compartment was then calculated separately for each tree.

151Plots 5 and 6 were not damaged by windthrow, in contrast to previous four stands we

152manually excavated entire coarse root systems for all sampled trees. Aboveground stem

153parameters, stump and coarse root volume and specific weight were all measured as described

154above, apart from stem volume in stand 6 where stems were divided into 0.5 m sections.

156Belowground biomass functions and BCEF

157Observations of tree height, DBH, stem volume and dry weight of belowground biomass of

158all 77 sampled trees were used to describe the relationship between aboveground parameters

159and belowground biomass. First, we established allometric biomass functions using tree

160height and/ or DBH as independent variables. Second, we expressed BCEF as dependent on

161DBH, tree height or a combination of the two variables. BCEF (in Mg m-3), which converts

162stem volume directly to dry biomass of the belowground compartment (Lehtonen et al.,

1632004), were calculated for each sampled tree. For the purpose of our calculations, stem

164volume was defined as the entire stem including aboveground stump, stem top and bark.

165Merchantable volume did not include bark, aboveground stump or upper part of the stem

166thinner than 7.0 cm in diameter, but included the volume of all branches over 7.0 cm in

167diameter. Stem volume used to calculate BCEFstem originated from our measurements (as

7 7 168described above), while merchantable volume used to establish BCEFmerchantable was obtained

169from local stem volume models (Petráš and Pajtík, 1991). As well as DBH, we measured tree

170height and compared the accuracy of biomass functions based on DBH, height or both The

171following functions were tested:

172 Y  e(b0 b1 ln dbh) (3)

173 Y  e(b0 b1 ln h) (4)

174 Y  e(b0 b1 ln dbhb2 ln h) (5)

175where

176Y = dependent variable, either belowground compartment biomass (B, kg) or biomass

177conversion and expansion factor (BCEF, Mg m-3)

178dbh = stem base diameter (cm)

179h = tree height (m)

180b0, b1, b2 = coefficients

181λ = logarithmic retransformation correction factor after Marklund (1987).

183Model validation

184A variation of K-fold model validation procedure (Mosteller and Turkey, 1968) was applied

185to compare the accuracy of developed biomass functions and BCEF models. In brief, out of

186the total of 6 stands we used data from 5 stands to ‘train’ the model and then compared the

187measured data from the 6th stand with model predictions. This procedure was repeated 6

188times, leaving out each of the stands in turn. All 6 stands were used for biomass function and

189BCEFstem cross-validation, stand 6 was omitted from cross-validation of BCEFmerchantable models

190since trees in this stand were too small to include any merchantable biomass.

191 192Model application

8 8 193To illustrate potential application of developed belowground biomass models, we utilised

194forest inventory data from 32 intensively monitored forest stands from High and Low Tatra

195mountains in Northern Slovakia. All of these stands were located between 600 and 1200 m

196above sea level and contained at least 90% Norway spruce. Within each stand, all trees inside

197a 500 m2 monitoring area and thicker than 7 cm DBH were measured for height, DBH, age

198and stocking density. Aboveground merchantable biomass was calculated separately for each

199tree from volume table models (Petráš and Pajtík, 1991), average diameter and height for each

200stand were calculated as quadratic mean. Stocking density data were used to transform

201estimated biomass to full stocking density. Aboveground parameters were then used to

202calculate belowground biomass on a stand basis by biomass functions and by BCEF to

203compare the accuracy of these two methods. In addition, we compared BCEF predictions of

204stand biomass calculated on the basis of average tree with stand biomass obtained by

205summing separately calculated biomass of all trees within a stand.

206All model fits, estimations and model comparisons were carried out using the least squares

207non-linear regression model in Statistica 7.0 (StatSoft, Oklahoma, USA).

209Results

210In our dataset, tree heights varied between 1.7 and 33.5 m and DBH between 2.6 and 33.5 cm,

211offering a good coverage of Norway spruce size distribution found in mountainous regions in

212Central Europe (Table 1). Although DBH and tree height are usually strongly correlated, we

213used both of these variables as predictors in biomass functions and BCEF models because

214their relationship was shown to be affected by harsh climatic conditions at higher elevations

215(Socha and Kulej, 2005). A comparison of allometric biomass functions shows that DBH is a

216slightly better predictor of root biomass than tree height (R2 = 0.986 versus 0.975, Table 2).

217Combining the two predictor variables in a single model did not show any improvement over

9 9 218the DBH based model. We were able to demonstrate that both tree height and DBH predict

219belowground biomass in the sampled altitudinal range of Norway spruce trees (Figures 1a and

2201b). K-fold validation of constructed models confirmed the fact that combining tree height

221and DBH in a single model does not improve the predictive power of the model. In fact, using

222our dataset from Slovakia, the predictor of choice in belowground biomass functions and

223BCEFstem is DBH, while the most accurate BCEFmerchantable predictions were attained when

224using height as the single independent variable (Table 3).

225We compared our model of the relationship between belowground biomass and DBH

226parameterised for high altitude Norway spruce with published models of the same species

227originating from lower altitude forests (Figure 2). Our observations fall between published

228models, perhaps suggesting that the relative size of coarse root systems is not modified by

229climatic conditions.

230Figure 3 illustrates the dependence of biomass factors on tree size parameters. After a steep

231decrease in small trees, BCEF tend to stabilise once the trees reach certain size. Moreover,

232the values of both types of BCEF in our study were very similar in trees with DBH above 30

233cm (Figure 3a) or height above 20 m (Figure 3b). Small trees, on the other hand, were

234characterized by much higher values of BCEFmerchantable than BCEFstem.

235Based on our sample of 77 uprooted and excavated trees, we parameterised biomass functions

236and BCEFs for predicting belowground biomass of high altitude Norway spruce. Based on

237models combining both DBH and height, Figure 4a shows the influence of tree size on the

238relative under- or overestimation of individual tree biomass by allometric function when

239compared to an estimate by BCEFmerchantable. By applying both types of models to inventory

240data from 32 intensively monitored stands, we also compared the relative discrepancy

241between the two methods when predicting belowground biomass at the stand level (Figure

10 10 2424b). Here, biomass function predicts lower stand biomass in younger stands, while in older

243stands the two methods predict the same biomass.

244In order to illustrate potential application of individual tree equations and BCEFs to stand

245level estimations, we predicted belowground biomass of 32 intensively monitored forest

246stands. As can be seen from Figure 5, the ratio between merchantable and belowground

247biomass is dependent on mean tree size, but tends to stabilise once the stands reach ca. 65

248years or 35-40 cm DBH.

250Discussion

252The observation that stem diameter is the most reliable predictor of biomass of nearly all tree

253components was noted by a variety of authors (e.g. (Hochbichler et al., 2006; Pajtík et al.,

2542008). The relative proportion of tree components is largely species specific, with little

255change once a critical tree size has been reached. Lacointe (2000) indicated that the growth of

256structural roots is proportional to stem diameter and that the above- and below-ground stump

257development of trees maintains an allometric balance. Root biomass was successfully

258predicted on the basis of DBH for instance by Drexhage and Colin (2001) and Tobin et al.

259(2007). DBH is therefore widely used as the predictor variable of choice, not only due to its

260close link to tree biomass allocation, but also due to the ease with which it can be measured.

261The relationship between aboveground stem parameters and belowground biomass is, of

262course, not universal and may be modified by several environmental variables, such as

263prevailing climate, soil characteristics and stand management. Carbon partitioning to roots

264may increase under general conditions of stress, leading to an increase in the root/shoot ratio,

265which contrasts with 'reduced' root systems of trees growing in favourable growth conditions

266Puhe (2003). Bolte et al. (2004) have shown that the relationship between DBH and coarse

11 11 267root biomass is significantly modified by climatic and soil conditions, but less strongly in

268Norway spruce than in European beech (Fagus sylvatica). Similarly, Lehtonen et al. (2004)

269showed that allocation to other compartments relative to that of the stem in pine, spruce and

270birch in Finland was affected by stand density, which may change due to varying forest

271management intensity. When considering site index as an indicator of prevailing site

272conditions, Teobaldelli et al. (2009) did find greater biomass of non-stem compartments in

273stands growing on less productive sites, especially in mature or older stands. However, this

274pan-European study was based on aboveground data only. To assess the strength of the

275environmental influence on belowground allocation, we compared our allometric model

276developed for mountainous Central Europe with other models originating from several West

277European countries (Bolte et al., 2004; Dieter and Elsasser, 2002; Drexhage and Colin, 2001;

278Wirth et al., 2004). Figure 2 shows that our model, parameterised for continental climate, falls

279in the middle of the distribution of models from lower altitudes and more oceanic climates.

280Our predictions of belowground biomass based on the same aboveground stem size are lower

281than those of Wirth et al. (2004) and Dieter et al. (2002), but higher than those of Drexhage et

282al. (2001) and Bolte et al. (2004). This suggests that root/shoot ratios in mature Norway

283spruce trees may not respond to environmental signals and that models parameterised for

284specific climatic conditions might, with caution, be applicable in other areas.

285To complement our biomass functions, we constructed BCEF based on two stem

286characteristics: stem volume and merchantable volume. Stem volume, expressed as the entire

287stem volume from the base to the tip, is interesting from the physiological point of view as it

288reflects belowground allocation in proportion to the stem defined as a functional unit. Its

289estimation is fairly straightforward in Norway spruce since it rarely forms multi-stem

290individuals and all branches are well defined against the stem. Merchantable volume, on the

291other hand, is a ubiquitous volumetric unit used in commercial forestry to describe timber

12 12 292stock held in a forest stand. Trees in initial stages of growth are characterised by a very small

293volume of merchantable wood, because of the minimum 7 cm diameter definition. As trees

294mature, the volume of merchantable wood is roughly proportional to the volume of the stem,

295branches thicker than 7 cm making up for the volume of stem tip and the stump. Our values of

-3 296BCEFstem varied between 0.10 and 0.15 Mg.m , while the values of BCEFmerchantable showed

297slightly greater variation between 0.10 and 0.25 Mg.m-3. There is a general lack of BCEF

298observations for belowground tree compartments, however the findings of Lehtonen (2005)

299corroborate our observations. When plotting the values of BCEFmerchantable for Norway spruce

300belowground biomass and aboveground stump versus tree age, he showed that the values

301decreased from 0.19 Mg.m-3 at the age of 15 years to 0.17 Mg.m-3 at 145 years. The slightly

302higher values of Lehtonen (2005), when compared to our observations, may be explained by

303the inclusion of aboveground stump mass in the belowground biomass compartment.

304Recently, usage of BCEF is gaining prominence over biomass functions, mainly because they

305allow for easy estimation of tree biomass or carbon stock held in a forest stand (Somogyi et

306al., 2007). Since we used our observations of spruce root systems to establish both biomass

307functions and BCEFs, we were able to directly compare the predictions obtained by the two

308methods at individual tree level (Figure 4a), but also at stand level in 32 Norway spruce

309stands (Figure 4b). Although the discrepancy between the two approaches is clearly

310dependent on the size of the tree, it does not convey any biological meaning, as it driven by

311the mathematical definitions of the models. Biomass functions slightly underestimate the

312belowground biomass of smaller trees when compared to BCEFmerchantable, however the

313divergence of the two methods is minimal and we contend that both can be used to estimate

314belowground biomass in Norway spruce.

315As an example of using biomass functions and BCEF with existing inventory data to estimate

316belowground biomass at stand level, we predicted belowground biomass of 32

13 13 317aforementioned stands and established its ratio to merchantable biomass (Figure 5).

318Surprisingly, the best predictor of the ration of belowground to merchantable biomass at the

319stand level appears to be mean height, perhaps because mean stand age can be difficult to

320ascertain accurately and mean DBH is somewhat sensitive to stem slenderness. Given that we

321knew the DBH and height of every tree in all monitored stands, we could assess the error in

322belowground biomass estimates due to using mean tree size. First, we calculated stand

323biomass by summing up individual biomass predicted for all trees in each stand. Second, by

324calculating the quadratic mean of the DBH distribution of each stand, we found the size of the

325mean tree which, together with the stocking density, formed the basis of the second stand

326belowground biomass estimate. In our test sample of Norway spruce stands, the mean tree

327method underestimated root and belowground stump biomass by 2.08% (st.dev. 1.23%) when

328compared to the sum of individual trees. Arguably, this small error justifies using mean tree

329size and stocking density to predict belowground biomass at the stand level, especially when

330we consider excellent availability of these two stand parameters in Norway spruce stands in

331Europe. To date, several studies have shown that using BCEF to estimate total stand biomass

332or C stock on the basis of forest mensuration data gives reasonable estimates (de Wit et al.,

3332006; Green et al., 2007; Lehtonen et al., 2007), but only if accurate parameterisation of

334BCEF models is available.

336 Conclusions

338Our results indicate that usage of locally parameterised BF and BCEF may not be necessary to

339obtain meaningful estimates of belowground biomass in mature Norway spruce. Despite the

340fact that BCEF are based on stem volume, which is an allometrically derived parameter, we

341contend that presented BCEF offer reasonable accuracy for estimating coarse root and

14 14 342belowground stump biomass in Norway spruce growing at high elevations. Using available

343inventory data to calculate stand belowground biomass from average tree dimensions, as

344opposed to individual tree calculation, leads to a very small bias and represents a viable

345method of biomass estimation at this scale. The established BF and BCEF are clearly age and

346tree size dependent, highlighting the importance of considering these parameters when

347estimating biomass of Norway spruce stands.

349Acknowledgements

350This research was supported by the Research & Development Operational Programme of the Slovak

351Ministry of Education through its Centre of Excellence project ‘Adaptive Forest Ecosystems’ (ITMS:

35226220120006).

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17 17 444Figure legends:

446Figure 1. The relationship between DBH (1a), tree height (1b) and belowground biomass of

447individual Norway spruce trees. Insets show observations between 0-4 cm DBH and 0-4 m

448height.

450Figure 2. A comparison of allometric models describing the relationship between DBH and

451belowground biomass in individual trees.

453Figure 3a, 3b. Relationship between BCEF and DBH (3a) and tree height (3b) calculated for

454whole stem volume and merchantable volume of individual trees.

456Figure 4a, 4b. A comparison of theoretical size dependent bias in belowground biomass

457predicted by an allometric relationship (biomass function) over BCEFmerchantable in individual

458Norway spruce trees (4a) and prediction bias when using inventory data from 32 Norway

459spruce stands in northern Slovakia (4b).

461Figure 5. Ratio of estimated dry belowground biomass to merchantable biomass in Norway

462spruce stands, as dependent on stand age (R2=0.84), mean DBH (R2=0.75) and mean height

463(R2=0.95).

464 465

18 18 466 467 468 469Table 1. Site description of Norway spruce stands used to construct BF and BCEF models. 470 Plot Site location Geographic Altitude Number of Mean height Mean DBH Soil type number (° ' N, ° ' E) unit (m a.s.l.) sampled trees (m) (cm) 1 49 09, 19 58 Vysoké Tatry 1171 11 24.5 33.3 Humic Podzol 2 49 08, 19 56 Podtatranská nížina 1012 10 17.9 20.6 Cambic Podzol 3 49 08, 20 14 Vysoké Tatry 975 12 16.5 19.5 Haplic Cambisol 4 49 11, 20 18 Podtatranská nížina 897 14 14.0 16.0 Stagnic Pseudogley 5 48 50, 19 06 Veľká Fatra 626 5 20.9 23.1 Dystric Cambisol 6 48 39, 19 36 Slovenské Rudohorie 977 25 2.44 2.9 Humic Cambisol 471

19 19 472Table 2. Model parameters for the calculation of belowground biomass in Norway spruce (D=DBH; H=height; b0, b1 and b2=parameters from 473equations 3-8; R2=goodness of fit, MSERESIDUAL=residual sum of squares; λ= logarithmic retransformation correction factor; S.D. = standard 474deviation). 475

Predictor 2 RESIDUAL bo (S. E.) P b1 (S. E.) P b2 (S. E.) P R MSE λ S. D. variable

D -3,634 (0,081) <0.001 2.319 (0.032) <0.001 0.986 0.094 1.046 0.320 Allometric H -4.555 (0.124) <0.001 2.737 (0.051) <0.001 0.975 0.166 1.075 0.397 equation D, H -3.639 (0.155) <0.001 2.306 (0.310) <0.001 0.015 (0.368) 0.967 0.986 0.095 1.046 0.319

D -1.815 (0.083) <0.001 -0.155 (0.033) <0.001 0.235 0.097 1.047 0.320

BCEFstem H -1.742 (0.094) <0.001 -0.188 (0.039) <0.001 0.245 0.096 1.047 0.321

D, H -1.654 (0.156) <0.001 0.223 (0.313) 0.479 -0.451 (0.371) 0.228 0.250 0.097 1.047 0.324

D -1,009 (0,332) 0.004 -0.375 (0.108) 0.001 0.206 0.120 1.060 0.396

BCEFmerchantable H -0.536 (0.405) 0.191 -0.553 (0.138) <0.001 0.258 0.113 1.054 0.353

D, H -0.174 (0.497) 0.728 0.526 (0.425) 0.223 -1.224 (0.560) 0.034 0.282 0.111 1.052 0.337 476 477 478

20 20 479Table 3. K-fold cross-validation of biomass functions, BCEFstem and BCEFmerchantable models. All 6 sampled stands were used for biomass

480functions and BCEFstem cross-validation, stand 6 was omitted from cross-validation of BCEFmerchantable model since the trees were too small to have 481merchantable biomass (D=DBH; H=height; Mean Prediction Error (MPE) and absolute Root Mean Square Prediction Error (RMSPE) are in kg 482for model (1) and Mg.m-3 for models (2) and (3); relative RMSPE in %). 483 Predictor Model MPE absolute RMSPE relative RMSPE variable D -2.1815 11.9877 30.2 Allometric (1) H 0.4008 10.9675 31.5 equation D, H -2.3606 12.2530 32.4 D -0.0095 0.0417 37.4

(2) BCEFstem H -0.0123 0.0441 39.0 D, H -0.0147 0.0471 41.4 D -0.0019 0.0448 33.9

(3) BCEFmerchantable H -0.0001 0.0424 31.8 D, H 0.0005 0.0440 33.5 484 485 486