Belowground Biomass Functions and Expansion Factors in High Elevation Norway Spruce

1Belowground biomass functions and expansion factors in high elevation2Norway spruce. 34Bohdan Konôpka1, Jozef Pajtík1, Vladimír Šebeň1, Martin Lukac2,*561National Forest Centre, Forest Research Institute, T.G. Masaryka 22, 960 92 Zvolen,7Slovakia82Department of Agriculture, Development and Policy, University of Reading, RG6 6AR, UK910*Corresponding author: Martin Lukac11 tel. number: +44 -118-378 8470 12 fax: +44 -118-935 242113 e-mail: [email protected]1415Number of tables: 216Number of figures: 517181 19Summary2021Biomass allocation to above- and belowground compartments in trees is thought to be22affected by growth conditions. To assess the strength of such influences, we sampled six23Norway spruce forest stands growing at higher altitudes. Within these stands, we randomly24selected 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 observations26with models parameterised for lower altitudes shows that models developed for specific27conditions may be applicable to other locations. Using our observations, we developed28biomass functions (BF) and biomass conversion and expansion factors (BCEF) linking29belowground biomass to stem parameters. While both BF and BCEF are accurate in30belowground biomass predictions, using BCEF appears more promising as such factors can be31readily used with existing forest inventory data to obtain estimates of belowground biomass32stock. As an example, we show how BF and BCEF developed for individual trees can be used33to estimate belowground biomass at the stand level. In combination with existing34aboveground models, our observations can be used to quantify total standing biomass of high35altitude Norway spruce stands.3637Introduction3839The root system is important not only for anchoring trees in the soil, but it also fulfils a40variety of physiological functions such as water and nutrient absorption from the soil and41storage of carbohydrates. Trees therefore transfer a considerable proportion of assimilates to42their belowground compartments. Tree roots significantly contribute to the total biomass and43carbon 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, partly45due 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 accurately47estimate the amount of carbon held in forests (Brunner and Godbold, 2007). A further impetus48is provided by the proposed utilization of whole tree biomass as a renewable material for49bioenergy generation (Schlamadinger and Marland, 1996). 50Studies dealing with biomass functions for Norway spruce (Picea abies (L.) Karst) during the51past 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). There53are several publications which also estimate the biomass of belowground compartments54(Drexhage and Colin, 2001; Offenthaler and Hochbichler, 2006; Repola, 2009), however their55general weakness is that they do not consider the full range of tree sizes, usually omitting56early growth stages (Pajtík et al., 2008). There are two established approaches to estimating57the biomass of particular tree compartments, making use of (a) allometric biomass functions58and (b) expansion factors. Both methods can be used to calculate tree biomass at the tree or59stand levels and can be readily adapted to calculate tree carbon stock. While biomass60functions are invariably based on diameter (usually at breast height, i.e. DBH) and/or tree61height, the definitions and usage of expansion factors varies among countries or authors (see62for 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 the64most widely available forest mensuration data on stem volume directly to whole tree or65compartment biomass (including belowground compartments, if parameterized). Here, a66substantial variation in BCEF calculations may be related to inconsistent definition of stem67volume (above or over bark, with or without the aboveground part of stump, including or68excluding the stem top). To illustrate this point, we established BCEFs based both on stem3 3 69volume (stem only, including aboveground stump and bark) and on merchantable volume70(stem and branches above 7 cm, excluding stump and bark).71This paper focuses on developing root system biomass functions and BCEFs for Norway72spruce, 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 Norway74spruce growing at high elevations in Central Europe . This area is typical for its abundance of75spruce forests in mountainous regions in countries such as Austria, Czech Republic, Romania76and 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 data79availability, we constructed root system (defined as belowground stump plus roots over 0.580cm diameter) biomass models for Norway spruce growing at high elevations in Central81Europe and compared them with models parameterized for other European regions. We82utilized data from 6 stands to establish biomass functions and BCEFs for belowground83biomass of Norway spruce and compared their predictive power. We hypothesised that using84both DBH and stem height as predictor variables does not lead to improved model85predictions. In addition, we used developed models to illustrate their applicability to86calculations of belowground biomass in conjunction with forest inventory data. 8788 Materials and methods89 Location and sites90The research was conducted between 1998 and 2005 on six sites located in four separate91mountain ranges in Slovakia, offering a good coverage of soil and climatic conditions at the92higher end of natural Norway spruce distribution. The altitudes of selected sites were between93626 and 1171 m above sea level. The prevailing bedrock was granodiorit and the soils were4 4 94classified as Cambisol, Podzol and Psedogley (Table 1). The climate at this range of altitudes95is characterised by low average temperatures (annual means between 4.0 and 5.2 C) and96medium to high precipitation (ranging between 870 – 1080 mm per year). Studied stands were97composed of Norway spruce, often with an admixture of other tree species not exceeding 1098% stocking density and ranged from 3.4 to 6.0 ha in size. Stands 1-4 were uneven aged99(originating from combined natural regeneration and planting), while stands 5 and 6 were100even aged, originating from planting (stand 5) and natural regeneration (stand 6, Table 1). In101each stand, a random sample of between 5 and 25 trees representing equal number of102dominant, co-dominant and subdominant competitive status was selected in as wide an area as103possible and destructively sampled. 104105Sampling and measurement106To reflect site conditions and management history at each site, we varied the sampling design107and the root excavation methods. Stands 1 to 4 were located in an area severely damaged by108windthrow in November 2004. Utilising the exposed root plates of uprooted trees, all109branches were removed from selected trees and stem height was measured using a tape.110Diameter measurements were taken using a calliper (two perpendicular measurements) from111all sampled trees at the following locations: tree base (ground level) and then at 20 and 130112cm (diameter at breast height, DBH) from ground level. In addition, we recorded two113diameters of every 100 cm stem section from stem base to the top of the tree. The position of114the ground level was identified on each stem and trees were cut at this point to separate stems115from the belowground compartments (belowground part of the stump and roots). A horizontal116line was drawn through the centre of the stump to divide the root plate into two equal halves117and all roots found above this line were harvested. Roots which were broken-off from the root118plate were excavated and paired up with fresh root injuries on the exposed part of the root5 5 119system. All roots thicker than 0.5 cm were collected and divided into the following diameter120classes: 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 of1210.5 cm was applied to avoid technical difficulties when collecting thinner root fragments and122is in agreement with the general definition of medium and large roots (Böhm, 1979). The total123length of roots in each diameter class was measured and the volume was calculated as:124 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 diameter130classes 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 affected132by 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 recovered134half of the root system gives us a good estimate of the total.135Diameters of belowground stump cylinders were measured at the top (ground level), bottom136and in the middle, together with the cylinder height. The volume of the stump cylinder was137then 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. 1426 6 143The volumes of all 1 m stem sections were calculated in the same fashion, with the exception144of stem base where stem volume was described by a curve fitted to the following four stem145radiuses: 0, 20, 100 and 130 cm from the ground level. Total stem volume was then calculated146by summing the volumes of all stem sections. 147Biomass samples corresponding to approximately 10% of the total root system, stump and148stem were taken to establish their density. The samples were transported to the laboratory, air149dried 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 we152manually excavated entire coarse root systems for all sampled trees. Aboveground stem153parameters, stump and coarse root volume and specific weight were all measured as described154above, apart from stem volume in stand 6 where stems were divided into 0.5 m sections. 155156Belowground biomass functions and BCEF157Observations of tree height, DBH, stem volume and dry weight of belowground biomass of158all 77 sampled trees were used to describe the relationship between aboveground parameters159and belowground biomass. First, we established allometric biomass functions using tree160height and/ or DBH as independent variables. Second, we expressed BCEF as dependent on161DBH, tree height or a combination of the two variables. BCEF (in Mg m-3), which converts162stem 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, stem164volume 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 stem166thinner than 7.0 cm in diameter, but included the volume of all branches over 7.0 cm in167diameter. Stem volume used to calculate BCEFstem originated from our measurements (as7 7 168described above), while merchantable volume used to establish BCEFmerchantable was obtained169from local stem volume models (Petráš and Pajtík, 1991). As well as DBH, we measured tree170height and compared the accuracy of biomass functions based on DBH, height or both The171following 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)175where176Y = dependent variable, either belowground compartment biomass (B, kg) or biomass177conversion and expansion factor (BCEF, Mg m-3)178dbh = stem base diameter (cm)179h = tree height (m)180b0, b1, b2 = coefficients181λ = logarithmic retransformation correction factor after Marklund (1987).182183Model validation 184A variation of K-fold model validation procedure (Mosteller and Turkey, 1968) was applied185to compare the accuracy of developed biomass functions and BCEF models. In brief, out of186the total of 6 stands we used data from 5 stands to ‘train’ the model and then compared the187measured data from the 6th stand with model predictions. This procedure was repeated 6188times, leaving out each of the stands in turn. All 6 stands were used for biomass function and189BCEFstem cross-validation, stand 6 was omitted from cross-validation of BCEFmerchantable models190since trees in this stand were too small to include any merchantable biomass. 191 192Model application8 8 193To illustrate potential application of developed belowground biomass models, we utilised194forest inventory data from 32 intensively monitored forest stands from High and Low Tatra195mountains in Northern Slovakia. All of these stands were located between 600 and 1200 m196above sea level and contained at least 90% Norway spruce. Within each stand, all trees inside197a 500 m2 monitoring area and thicker than 7 cm DBH were measured for height, DBH, age198and stocking density. Aboveground merchantable biomass was calculated separately for each199tree from volume table models (Petráš and Pajtík, 1991), average diameter and height for each200stand were calculated as quadratic mean. Stocking density data were used to transform201estimated biomass to full stocking density. Aboveground parameters were then used to202calculate belowground biomass on a stand basis by biomass functions and by BCEF to203compare the accuracy of these two methods. In addition, we compared BCEF predictions of204stand biomass calculated on the basis of average tree with stand biomass obtained by205summing separately calculated biomass of all trees within a stand.206All model fits, estimations and model comparisons were carried out using the least squares207non-linear regression model in Statistica 7.0 (StatSoft, Oklahoma, USA). 208 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 in212Central Europe (Table 1). Although DBH and tree height are usually strongly correlated, we213used both of these variables as predictors in biomass functions and BCEF models because214their relationship was shown to be affected by harsh climatic conditions at higher elevations215(Socha and Kulej, 2005). A comparison of allometric biomass functions shows that DBH is a216slightly 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 over9 9 218the DBH based model. We were able to demonstrate that both tree height and DBH predict219belowground biomass in the sampled altitudinal range of Norway spruce trees (Figures 1a and2201b). K-fold validation of constructed models confirmed the fact that combining tree height221and DBH in a single model does not improve the predictive power of the model. In fact, using222our dataset from Slovakia, the predictor of choice in belowground biomass functions and223BCEFstem is DBH, while the most accurate BCEFmerchantable predictions were attained when224using height as the single independent variable (Table 3).225We compared our model of the relationship between belowground biomass and DBH226parameterised for high altitude Norway spruce with published models of the same species227originating from lower altitude forests (Figure 2). Our observations fall between published228models, perhaps suggesting that the relative size of coarse root systems is not modified by229climatic conditions. 230Figure 3 illustrates the dependence of biomass factors on tree size parameters. After a steep231decrease 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 30233cm (Figure 3a) or height above 20 m (Figure 3b). Small trees, on the other hand, were234characterized by much higher values of BCEFmerchantable than BCEFstem.235Based on our sample of 77 uprooted and excavated trees, we parameterised biomass functions236and BCEFs for predicting belowground biomass of high altitude Norway spruce. Based on237models combining both DBH and height, Figure 4a shows the influence of tree size on the238relative under- or overestimation of individual tree biomass by allometric function when239compared to an estimate by BCEFmerchantable. By applying both types of models to inventory240data from 32 intensively monitored stands, we also compared the relative discrepancy241between the two methods when predicting belowground biomass at the stand level (Figure10 10 2424b). Here, biomass function predicts lower stand biomass in younger stands, while in older243stands the two methods predict the same biomass. 244In order to illustrate potential application of individual tree equations and BCEFs to stand245level estimations, we predicted belowground biomass of 32 intensively monitored forest246stands. As can be seen from Figure 5, the ratio between merchantable and belowground247biomass is dependent on mean tree size, but tends to stabilise once the stands reach ca. 65248years or 35-40 cm DBH.249250Discussion251252The observation that stem diameter is the most reliable predictor of biomass of nearly all tree253components 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 little255change once a critical tree size has been reached. Lacointe (2000) indicated that the growth of256structural roots is proportional to stem diameter and that the above- and below-ground stump257development of trees maintains an allometric balance. Root biomass was successfully258predicted 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 its260close 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, of262course, not universal and may be modified by several environmental variables, such as263prevailing climate, soil characteristics and stand management. Carbon partitioning to roots264may 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 conditions266Puhe (2003). Bolte et al. (2004) have shown that the relationship between DBH and coarse11 11 267root biomass is significantly modified by climatic and soil conditions, but less strongly in268Norway 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 and270birch in Finland was affected by stand density, which may change due to varying forest271management intensity. When considering site index as an indicator of prevailing site272conditions, Teobaldelli et al. (2009) did find greater biomass of non-stem compartments in273stands growing on less productive sites, especially in mature or older stands. However, this274pan-European study was based on aboveground data only. To assess the strength of the275environmental influence on belowground allocation, we compared our allometric model276developed for mountainous Central Europe with other models originating from several West277European 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, falls279in 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 lower281than those of Wirth et al. (2004) and Dieter et al. (2002), but higher than those of Drexhage et282al. (2001) and Bolte et al. (2004). This suggests that root/shoot ratios in mature Norway283spruce trees may not respond to environmental signals and that models parameterised for284specific climatic conditions might, with caution, be applicable in other areas.285To complement our biomass functions, we constructed BCEF based on two stem286characteristics: stem volume and merchantable volume. Stem volume, expressed as the entire287stem volume from the base to the tip, is interesting from the physiological point of view as it288reflects belowground allocation in proportion to the stem defined as a functional unit. Its289estimation is fairly straightforward in Norway spruce since it rarely forms multi-stem290individuals and all branches are well defined against the stem. Merchantable volume, on the291other hand, is a ubiquitous volumetric unit used in commercial forestry to describe timber12 12 292stock held in a forest stand. Trees in initial stages of growth are characterised by a very small293volume of merchantable wood, because of the minimum 7 cm diameter definition. As trees294mature, 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 showed297slightly greater variation between 0.10 and 0.25 Mg.m-3. There is a general lack of BCEF298observations for belowground tree compartments, however the findings of Lehtonen (2005)299corroborate our observations. When plotting the values of BCEFmerchantable for Norway spruce300belowground biomass and aboveground stump versus tree age, he showed that the values301decreased from 0.19 Mg.m-3 at the age of 15 years to 0.17 Mg.m-3 at 145 years. The slightly302higher values of Lehtonen (2005), when compared to our observations, may be explained by303the inclusion of aboveground stump mass in the belowground biomass compartment.304Recently, usage of BCEF is gaining prominence over biomass functions, mainly because they305allow for easy estimation of tree biomass or carbon stock held in a forest stand (Somogyi et306al., 2007). Since we used our observations of spruce root systems to establish both biomass307functions and BCEFs, we were able to directly compare the predictions obtained by the two308methods at individual tree level (Figure 4a), but also at stand level in 32 Norway spruce309stands (Figure 4b). Although the discrepancy between the two approaches is clearly310dependent on the size of the tree, it does not convey any biological meaning, as it driven by311the mathematical definitions of the models. Biomass functions slightly underestimate the312belowground biomass of smaller trees when compared to BCEFmerchantable, however the313divergence of the two methods is minimal and we contend that both can be used to estimate314belowground biomass in Norway spruce. 315As an example of using biomass functions and BCEF with existing inventory data to estimate316belowground biomass at stand level, we predicted belowground biomass of 3213 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 the319stand level appears to be mean height, perhaps because mean stand age can be difficult to320ascertain accurately and mean DBH is somewhat sensitive to stem slenderness. Given that we321knew the DBH and height of every tree in all monitored stands, we could assess the error in322belowground biomass estimates due to using mean tree size. First, we calculated stand323biomass by summing up individual biomass predicted for all trees in each stand. Second, by324calculating the quadratic mean of the DBH distribution of each stand, we found the size of the325mean tree which, together with the stocking density, formed the basis of the second stand326belowground biomass estimate. In our test sample of Norway spruce stands, the mean tree327method underestimated root and belowground stump biomass by 2.08% (st.dev. 1.23%) when328compared to the sum of individual trees. Arguably, this small error justifies using mean tree329size and stocking density to predict belowground biomass at the stand level, especially when330we consider excellent availability of these two stand parameters in Norway spruce stands in331Europe. To date, several studies have shown that using BCEF to estimate total stand biomass332or 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 of334BCEF models is available.335336 Conclusions337338Our results indicate that usage of locally parameterised BF and BCEF may not be necessary to339obtain meaningful estimates of belowground biomass in mature Norway spruce. Despite the340fact that BCEF are based on stem volume, which is an allometrically derived parameter, we341contend that presented BCEF offer reasonable accuracy for estimating coarse root and14 14 342belowground stump biomass in Norway spruce growing at high elevations. Using available343inventory data to calculate stand belowground biomass from average tree dimensions, as344opposed to individual tree calculation, leads to a very small bias and represents a viable345method of biomass estimation at this scale. The established BF and BCEF are clearly age and346tree size dependent, highlighting the importance of considering these parameters when347estimating biomass of Norway spruce stands. 348349Acknowledgements350This research was supported by the Research & Development Operational Programme of the Slovak351Ministry of Education through its Centre of Excellence project ‘Adaptive Forest Ecosystems’ (ITMS:35226220120006).353354References355Albaugh, T.J., et al. 2009 Do biological expansion factors adequately estimate stand-scale 356 aboveground component biomass for Norway spruce? Forest Ecology and 357 Management 258, 2628-2637. 358Böhm, W. 1979 Methods of studying root systems. 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European Journal of Forest Research 126, 189- 435 196. 436Wirth, C., Schumacher, J. and Schulze, E.D. 2004 Generic biomass functions for Norway 437 spruce in Central Europe - a meta-analysis approach toward prediction and uncertainty 438 estimation. Tree Physiol 24, 121-139. 439Zianis, D., Muukkonen, P., Mäkipää, R. and Mencuccini, M. 2005 Biomass and stem volume 440 equations for tree species in Europe. Silva Fennica Monographs. 441 44244317 17 444Figure legends:445446Figure 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. 449 450Figure 2. A comparison of allometric models describing the relationship between DBH and451belowground biomass in individual trees. 452453Figure 3a, 3b. Relationship between BCEF and DBH (3a) and tree height (3b) calculated for 454whole stem volume and merchantable volume of individual trees. 455456Figure 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). 460461Figure 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 46518 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 47119 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). 475Predictor 2 RESIDUAL bo (S. E.) P b1 (S. E.) P b2 (S. E.) P R MSE λ S. D. variableD -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 0.319D -1.815 (0.083) <0.001 -0.155 (0.033) <0.001 0.235 0.097 1.047 0.320BCEFstem H -1.742 (0.094) <0.001 -0.188 (0.039) <0.001 0.245 0.096 1.047 0.321D, 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 0.324D -1,009 (0,332) 0.004 -0.375 (0.108) 0.001 0.206 0.120 1.060 0.396BCEFmerchantable H -0.536 (0.405) 0.191 -0.553 (0.138) <0.001 0.258 0.113 1.054 0.353D, 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 47820 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 48621 21

Belowground Biomass Functions and Expansion Factors in High Elevation Norway Spruce

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