1Belowground biomass functions and expansion factors in high elevation
2Norway spruce.
3
4Bohdan Konôpka1, Jozef Pajtík1, Vladimír Šebeň1, Martin Lukac2,*
5
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
9
10*Corresponding author: Martin Lukac
11 tel. number: +44 -118-378 8470
12 fax: +44 -118-935 2421
13 e-mail: [email protected]
14
15Number of tables: 2
16Number of figures: 5
17
18
1 19Summary
20
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.
36
37Introduction
38
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.
87
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.
104
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:
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 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.
142
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.
155
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 dbhb2 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).
182
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).
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 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.
249
250Discussion
251
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.
335
336 Conclusions
337
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.
348
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).
353
354References
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443
17 17 444Figure legends:
445
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.
449
450Figure 2. A comparison of allometric models describing the relationship between DBH and
451belowground biomass in individual trees.
452
453Figure 3a, 3b. Relationship between BCEF and DBH (3a) and tree height (3b) calculated for
454whole stem volume and merchantable volume of individual trees.
455
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).
460
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
21 21