Biomass expansion factors (BEFs) for Scots pine, Norway spruce and birch according to stand age for boreal forests

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1 Forest Ecology and Management 188 (2004) Bomass expanson factors (BEFs) for Scots pne, Norway spruce and brch accordng to stand age for boreal forests A. Lehtonen a,*,r.mäkpää b, J. Hekknen b, R. Sevänen a, J. Lsk c a Fnnsh Forest Research Insttute, P.O. Box 18, FIN Vantaa, Fnland b Fnnsh Forest Research Insttute, Unonnkatu 40A, FIN Helsnk, Fnland c European Forest Insttute, Torkatu 34, FIN Joensuu, Fnland Receved 23 September 2002; receved n revsed form 19 March 2003; accepted 14 July 2003 Abstract Assessments of forest resource n natonal nventores provde a frm bass for quantfyng forest bomass and carbon stock. Natonal statstcs on forest resources provde estmates of forest area, tmber volume, and growth of tmber by age classes wth known precson. Estmates of carbon stock are, however, obtaned by expandng the total stemwood volume to total bomass wth smple converson factors. The objectve of ths study was to mprove the accuracy and relablty of the bomass expanson factors (BEFs) and to develop expanson factors that are dependent on stand age and domnant tree speces. For development of BEFs, we appled volume and bomass equatons to descrbe the allometry of sngle trees and a systematc network of forest nventory data to determne varaton n stand structure. The results of ths study ndcate that the proportons of most bomass components vary consderably durng the rotaton. We conclude that the relablty of the natonal carbon stock nventory could be mproved by applyng these age-dependent BEFs, whch are formulated on the bass of representatve data and whch nclude an estmate of uncertanty. # 2003 Elsever B.V. All rghts reserved. Keywords: Boreal forests; Branch; Carbon; Folage; Forest nventory; Kyoto protocol; Roots; Uncertanty 1. Introducton Forest carbon snks were ncluded n the Kyoto Protocol as one of the mechansms for mtgatng clmate change, snce these snks are known to play an mportant role n the global GHG balance. Globally, annual carbon sequestraton by terrestral ecosystems was estmated to be 2.3 Gt C n the 1990s, whle emssons from land-use change were 1.6 Gt C per year (IPCC, 2000). The net terrestral uptake of * Correspondng author. Tel.: þ ; fax: þ E-mal address: aleks.lehtonen@metla.f (A. Lehtonen). 0.7 Gt C per year corresponded to one-tenth of the emssons from combuston of fossl fuels (6.3 Gt C per year) (IPCC, 2000). Currently, the methods for calculatng the carbon content of forests are too mprecse for estmatng the carbon balance at the ecosystem level or the natonal level (Fang et al., 1998). Relable estmates of changes n carbon stocks, and thereby fluxes, are necessary for understandng both the global carbon cycle (Schmel, 1998) and natonal nventores of greenhouse gases (IPCC, 2000). In general, estmates of carbon stocks and stock changes n temperate and boreal forests are based on forest nventory data (Kaupp et al., 1992; Sedjo, 1992; /$ see front matter # 2003 Elsever B.V. All rghts reserved. do: /j.foreco

2 212 A. Lehtonen et al. / Forest Ecology and Management 188 (2004) Dxon et al., 1994; UN-ECE/FAO, 2000; Lsk et al., n press). Systematc assessment of forest resources s a relable source of nformaton for the amounts of stem volume at country and regonal levels and thus a sutable bass for bomass and carbon studes (Kaupp et al., 1992; Sedjo, 1992; Dxon et al., 1994; Latat et al., 2000; Fang and Wang, 2001). As natonal forest nventores (NFI) are usually geared towards estmaton of stem volumes, the dsadvantage of usng NFI data s the lack of drect measurements of bomass. Wth few exceptons (e.g. Graca et al., 1997), representatve estmates of bomass for larger areas do not exst. The bomass stock of forest trees has been calculated by usng bomass expanson factors (BEFs) that convert tmber volumes to dry weght (densty factor) and thereafter to whole tree bomass (expanson factor) (Johnson and Sharpe, 1983; Karjalanen and Kellomäk, 1996; Wess et al., 2000). These two factors can be replaced wth one factor that converts stem volumes drectly to whole tree bomass (e.g. Schroeder et al., 1997; Fang and Wang, 2001). In general, constant BEFs have been appled (UN-ECE/FAO, 2000; FAO, 2001; Lsk et al., n press), although t s known that BEFs vary dependng on growth condtons and phase of stand development (Satoo and Madgwck, 1982). Relable methods are avalable for estmatng both the bomass and volume of sngle tree n boreal forests (Laasasenaho, 1982; Marklund, 1988; Brandel, 1990; Korhonen and Maltamo, 1990; Hakkla, 1991). These sngle tree equatons are not applcable for converson of stem volume to bomass of trees at stand, regonal or natonal scales. In ths study, we developed BEFs for ths task. The objectve was to mprove the accuracy and the relablty of BEFs. We developed BEFs that are dependent on stand age and domnant tree speces. The man results were speces-specfc stand-level BEFs for whole tree bomass, as well as for dfferent bomass components as a functon of stand age, wth known precson. 2. Materal and methods 2.1. Data We used tree and stand varables from 3000 permanent sample plots measured by the Fnnsh Natonal Forest Inventory n Of these sample plots, those located on forest land (tree growth of more than 1m 3 ha 1 per year) ether on mneral sols or peatlands were ncluded n our analyss. Ths systematc samplng grd was denser n southern than n northern Fnland. In southern Fnland there were four plots n each cluster and the dstance between clusters was 16 km. In northern Fnland there were three plots n each cluster and the dstance between clusters vared from 24 to 32 km. The denser samplng grd was located roughly below 668 lattude. The measurements of the permanent sample plots used n ths study were dameter at breast heght (dbh), tree speces, sze of the plot and age of the stand. In the younger stands, age was estmated vsually from the whorls of the trees, and, n the older stands, from drllngs of sample trees. The normal sze of a plot was 300 m 2, but trees wth a dameter less than 10.5 cm were measured from a 100 m 2 plot. Only plots that had more than 70% of the basal area made up of Scots pne, Norway spruce or broadleaved speces were ncluded (Table 1). Snce our analyss was focused on forests that were over 10 years, plots wth a basal area less than 1 m 2 ha 1 were omtted from the sample. Trees wth a dameter less than 5 cm were excluded from the calculatons due to the lmtatons of the appled volume and bomass equatons (Laasasenaho, 1982; Marklund, 1988) Appled volume and bomass equatons The stem volume of each tree was calculated based on dameter at breast heght by usng equatons from Laasasenaho (1982). A smple equaton V ¼ a ðdbhþ b was used n whch V s stem volume over bark, dbh the dameter at breast heght (1.3 m), and a and b are parameters. The bomass of each component of a tree was estmated from dbh usng Swedsh equatons for bomass (Marklund, 1988). These equatons provde bomass estmates for Scots pne (Pnus sylvestrs) and Norway spruce (Pcea abes), for the varous bomass components (stem, stem bark, lvng branches, dead branches, needles, stump, roots more than 5 cm n dameter and roots less than 5 cm n dameter). For brch (Betula pubescens), however, only bomass equatons of stem, stem bark, lvng branches and dead branches were avalable.

3 A. Lehtonen et al. / Forest Ecology and Management 188 (2004) Table 1 Mean densty (trees per ha) and medan dameter of the forest stands used n ths study a Age of stand Domnant tree speces b Scots pne ðn ¼ 782Þ Norway spruce ðn ¼ 459Þ Broadleaved ðn ¼ 153Þ Trees per ha Medan dbh c Trees per ha Medan dbh c Trees per ha Medan dbh c a The age classes of the oldest broadleaved forests were wder than the others due to smaller sample. b The domnant tree speces was defned as havng a threshold of 70% of basal area. c The medan dbh s the basal area medan dameter of trees n each age class BEFs at stand level and by age class In ths study, we were developng stand-level BEFs that convert stem volume drectly to the dry weght of bomass component. We consder expanson from stem volume, V, to dry weght of tree component, W, and consequently defne BEF, B,as B ¼ W (1) V for bomass components (folage, branches, stem, dead branches, bark, stump, coarse roots, small roots or whole tree). Eq. (1) was appled both at stand level and by age classes. In the computaton of stand-level BEFs, W was the sum of the estmated tree level bomasses of component over trees measured n one sample plot and V was the correspondng sum of tree level stem volumes. To obtan BEFs for dfferent age classes (Table 2), these sums were extended over trees measured from all sample plots belongng to the relevant class Error estmates of BEFs by age class The accuracy of BEFs by age classes (Table 2) was assessed, takng nto account samplng error of the nventory, model error of the bomass equatons and model error of the volume equatons (see Appendx A). Model error of the total bomass estmate was assessed by assumng that the errors of the bomass components are mutually uncorrelated at tree level. Ths s not the case exactly, but ths assumpton was made for practcal reasons. Model error was assessed by estmatng both ts maxmum and mnmum values. Ths was done wth two approaches, one n whch we assumed (1) zero correlaton between estmaton errors of trees n a cluster and another where we assumed (2) full correlaton between errors at the cluster level. Samplng error was assessed by estmatng the resdual varance of bomass estmates by age classes (Appendx A, Table 2). Confdence ntervals for BEFs by classes were calculated based on maxmum relatve standard error (RSE) Functons for age-dependent BEFs Modellng of age-dependence n BEFs was based on stand-level BEFs calculated accordng to Eq. (1). Due to the fact that stand age BEF relatons are heteroscedastc and non-lnear, we made comparsons between dfferent logarthmc transformatons of varables and also comparsons between dfferent types of

4 214 A. Lehtonen et al. / Forest Ecology and Management 188 (2004) Table 2 BEFs, ther RSEs, and 95% confdence ntervals (conf. nt.) for Scots pne, Norway spruce and broadleaf domnated forests a Age of stand Domnant tree speces Scots pne Norway spruce Broadleaved BEF Mnmum RSE (%) Maxmum RSE (%) 95% conf. nt. BEF Mnmum RSE (%) Maxmum RSE (%) 95% conf. nt. BEF b Mnmum RSE (%) Maxmum RSE (%) 95% conf. nt a The mnmum and the maxmum RSEs were estmated by assumng ndependence and full correlaton between trees n a cluster of stes of the Natonal Forest Inventory, respectvely. The confdence ntervals (conf. nt.) were calculated on the bass of maxmum relatve standard error. b Accounts for aboveground bomass only. functon forms, n order to obtan the best ft for the data. Eq. (2) was ftted (Tables 3 5) usng lnear regresson wth the tme-dependent term e 0.01t as the ndependent varable. Its rate coeffcent ( 0.01) was determned by tral and error so that t gave the mnmum sum of squares n the regresson ft. The BEF for component as a functon of stand age s thus B ¼ a þ b e 0:01t (2) where a and b are parameters, and s the stem, folage, lvng branches, dead branches, bark, stump, coarse roots, small roots, total bomass or total aboveground bomass BEFs and dameter dstrbuton of stands We tested how detaled nformaton on stand structure (dameter dstrbuton) of each age classes s Table 3 BEFs ¼ B ðtþ for Scots pne (P. sylvestrs) stands a Tree compartment () a S.E. b S.E. r 2 RMSE Mean of response Stem Folage Branches Branches, dead Bark Stump Roots, coarse >5 cm Roots, small <5 cm Total Total ABVG a BEF s expressed n Mg m 3 and the ndependent varable (t) n years. Total ABVG s the total aboveground bomass, ncludng stem, folage, lvng branches, dead branches and bark. Equaton: B ðtþ ¼a þ b e t=100. The functons were developed usng data from stands between 10 and 150 years of age and wth stemwood volume less than 250 m 3 ha 1.

5 A. Lehtonen et al. / Forest Ecology and Management 188 (2004) Table 4 BEFs ¼ B ðtþ for Norway spruce (P. abes) stands a Tree compartment () a S.E. b S.E. r 2 RMSE Mean of response Stem Folage Branches Branches, dead Bark Stump Roots, coarse >5 cm Roots, small <5 cm Total Total ABVG a BEF s expressed n Mg m 3 and the ndependent varable (t) n years. Total ABVG s the total aboveground bomass, ncludng stem, folage, lvng branches, dead branches and bark. Equaton: B ðtþ ¼a þ b e t=100. The functons were developed usng data from stands between 10 and 150 years of age and wth stemwood volume less than 250 m 3 ha 1. needed for calculaton of BEFs. Data were grouped, accordng to domnant tree speces and age of the stand, nto classes wth a 10-year nterval n stand age. For each age class, BEFs were calculated by three dfferent methods (Fg. 1). In the frst method, BEFs were calculated on the bass of the measured dameters of trees on the NFI sample plots, as descrbed earler; ths was used as a reference for comparson wth other methods. The second method was to estmate BEFs usng only basal area medan dameter and stockng densty (trees per ha) of each age class. The thrd method was based on use of the Webull dstrbuton. All the trees of a sngle class were sorted accordng to dameter. Then the shape of the twoparameter Webull dstrbuton was establshed on the medan (d med ) and maxmum dameter (d max ), whch was defned as the 99% percentle dameter. Parameters b ¼ f ðd 50% ; d 99% Þ and c ¼ f ðd 50% ; d 99% Þ were obtaned for each age class. The estmates for parameters were calculated by usng a method based on percentles (Baley and Dell, 1973). Stockng of each class was also used. The estmated Webull dstrbuton was then used to calculate BEFs Bomass as a functon of stem volume We developed equatons at stand-level for the relatonshps between bomass components and stem volume. Eq. (3) was formulated for the relatonshp between stem volume and bomass (Tables 6 8). These equatons are applcable for conferous forests that have a stem volume up to 250 m 3 ha 1. For broadleaved forests the equatons should not be Table 5 BEFs ¼ B ðtþ for broadleaved stands a Tree compartment () a S.E. b S.E. r 2 RMSE Mean of response Stem Branches Branches, dead Bark Total ABVG a BEF s expressed n Mg m 3 and the ndependent varable (t) n years. Total ABVG s the total aboveground bomass, ncludng stem, lvng branches, dead branches and bark (folage excluded). Equaton: B ðtþ ¼a þ b e t=100. The functons were developed usng data from stands between 10 and 100 years of age and wth stemwood volume less than 200 m 3 ha 1.

6 216 A. Lehtonen et al. / Forest Ecology and Management 188 (2004) Fg. 1. The approach to evaluate the effect of dameter dstrbuton on BEFs, usng three methods: (1) estmaton of BEFs based on tree-level data from the Natonal Forest Inventory, (2) estmaton of BEFs based on basal area medan dameter and (3) estmaton of BEFs based on Webull dstrbuton. appled n cases where stem volume s more than 200 m 3 ha 1. The estmate for bomass W s W ðvþ ¼aV b (3) where W s the dry weght of the bomass component ( s the stem, folage, lvng branches, dead branches, bark, stump, coarse roots, small roots) or an aggregate of those components, a and b are parameters and V the stem volume. Formula (3) s a power functon and was estmated n lnear form. Due to ths transformaton of varables, a correcton coeffcent has to be added to parameter a. It was assumed that ln(w ) s normally dstrbuted and therefore varance dvded by 2 was appled as a correcton coeffcent (s 2 /2). 3. Results 3.1. BEFs by stand age and bomass by stem volume The BEF for the total bomass of Scots pne stand was only slghtly age-dependent, whle the BEF for Table 6 Bomass for Scots pne (P. sylvestrs) stands a Tree compartment ln(a) S.E. b S.E. r 2 RMSE Mean of response Stem Folage Branches Branches, dead Bark Stump Roots, coarse >5 cm Roots, small <5 cm Total Total ABVG a Stem volume (V) as an ndependent varable gves bomass components (W ) n tonnes of dry weght. Total ABVG s the total aboveground bomass, ncludng stem, folage, lvng branches, dead branches and bark. Equaton: W ðvþ ¼aV b. The functons were developed usng data from stands between 10 and 250 m 3 ha 1.

7 A. Lehtonen et al. / Forest Ecology and Management 188 (2004) Table 7 Bomass for Norway spruce (P. abes) stands a Tree compartment ln(a) S.E. b S.E. r 2 RMSE Mean of response Stem Folage Branches Branches, dead Bark Stump Roots, coarse >5 cm Roots, small <5 cm Total Total ABVG a Stem volume (V) as an ndependent varable gves bomass components (W ) n tonnes of dry weght. Total ABVG s the total aboveground bomass, ncludng stem, folage, lvng branches, dead branches and bark. Equaton: W ðvþ ¼aV b. The functons were developed usng data from stands between 10 and 250 m 3 ha 1. Norway spruce stands decreased as stand age ncreased (Fg. 2a and b). For the youngest stands, less than 20 years of age, the BEFs were rather mprecse (Table 2). Ths may be a result of hgher varance and greater heterogenty n the structure of these stands and perhaps also of the smaller number of stands n these age classes (Tables 1 and 2). The RSEs of BEFs developed for broadleaved forests were hgher than those for conferous forests. The bomass components of Scots pne, especally stem and folage, were age-dependent; whereas the BEFs of roots and branches vared less durng stand development (Table 3 and Fg. 2). The bomass components of Norway spruce, especally branches and folage, vared accordng to age (Table 4 and Fg. 2). Ths can be seen by comparng the r 2 and parameter b values n the tables mentoned above. In general, our equatons for Scots pne have hgher r 2 values than the equatons for Norway spruce and broadleaved speces (Tables 3 5). Ths s because the development of pne stands over tme s more homogenous and there was a larger number of Scots pne stands n our sample. On the bass of the low values of parameter b and r 2, we conclude that n some cases (e.g. when the bomass of broadleaved speces or that of the stump and bark for Norway spruce are estmated) t s better to apply constant values over the tme of stand development. The mean of the response (see Tables 3 5) can be used as such constant BEF for these components. In the conferous stands, the relatonshp between stem volume and dfferent bomass components was nearly lnear, wth low varance (Tables 6 and 7). The equaton that descrbes the relatonshp between stem Table 8 Bomass for broadleaved stands a Tree compartment ln(a) S.E. b S.E. r 2 RMSE Mean of response Stem Branches Branches, dead Bark Total ABVG a Stem volume (V) as an ndependent varable gves bomass components (W ) n tonnes of dry weght. Total ABVG s the total aboveground bomass, ncludng stem, lvng branches, dead branches and bark. Equaton: W ðvþ ¼aV b. The functons were developed usng data from stands between 10 and 200 m 3 ha 1.

8 218 A. Lehtonen et al. / Forest Ecology and Management 188 (2004) Fg. 2. BEFs for Scots pne (a and c) and Norway spruce (b and d) stands as a functon of stand age. BEF s the rato between the dry weght of bomass and stem volume (Mg m 3 ). Fgures (a) and (b) llustrate the modelled BEFs for whole tree bomass of pne and spruce stands and the actual observatons; (c) and (d) descrbe the modelled BEFs for lvng branches, folage and roots (more than 5 cm n dameter). The parameter values of these functons and ther standard errors are shown n Tables 3 and 4. volume and total bomass started to saturate only slghtly wth hgher stem volumes (Fg. 3). For broadleaved stands the correlaton between stem volume and aboveground bomass was also strong (Table 8) Estmatng dameter dstrbuton In order to understand the role of dameter dstrbuton when BEFs were estmated we compared dfferent methods to generalse nformaton on stand structure (Fg. 4). Comparson of the three methods to descrbe the dameter dstrbuton of stands ndcates that usng Webull, a more sophstcated method compared to use of basal area medan dameter, mproved the accuracy of BEFs only slghtly (Fg. 5). The other method based on the basal area medan dameter and stockng densty resulted n almost equally accurate BEF estmates. If one s lookng for average estmates for large areas, t s feasble to determne volume and bomass based on the basal area medan tree. In most age classes, the relatve dfference of Mg m 3 rato was less than 3% (Fg. 5). On the other hand, when the estmates were made for the youngest age classes, the dfference ncreased to 9%. Thus, for young stands dameter dstrbuton cannot be predcted easly. In general, when representatve treewse nventory data are not avalable, these methods can be appled for estmatng of BEFs. 320 Scots pne Norway spruce Bomass, Mg ha (a) (b) Stem volume of forest stand, m ha Fg. 3. Stand-level bomass (Mg ha 1 ) of Scots pne (a) and Norway spruce (b) stands as a functon of stem volume (m 3 ha 1 ). The parameter values of the functons and ther standard errors are shown n Tables 6 and Bomass, Mg ha

9 A. Lehtonen et al. / Forest Ecology and Management 188 (2004) Frequency of dameter classes Medan Webull NFI Dameter of trees, dbh Fg. 4. Dameter dstrbuton of Scots pne stands of the age class (70 80 years). The grey lne represents the measured dameter dstrbuton on 87 sample plots of the Natonal Forest Inventory. The black lne s an approxmaton of the dameter dstrbuton usng Webull dstrbuton (estmated wth medan and 99th dameter). The black bar ndcates the basal area medan dameter. Relatve dfference of estmaton method, % Pne, Webull Pne, Medan Spruce,Webull Spruce, Medan Age of forest stand, year Fg. 5. Relatve dfferences n BEFs determned wth dfferent methods to descrbe dameter dstrbuton. Medan refers to the method based on a basal area medan dameter and stockng densty, whle Webull s a modelled dameter dstrbuton. The relatve dfference was calculated by dvdng the dfference between the reference and the estmate obtaned wth the method appled (medan or Webull) by the reference (based on measured dameters). 4. Dscusson In general, natonal and regonal estmates of forest carbon stocks and snks are calculated on the bass of growng stock and gross ncrement estmates usng smple converson factors (Kaupp et al., 1992, 1995; Löwe et al., 2000; Tomppo, 2000b; UN-ECE/FAO, 2000; Lsk et al., n press). NFI can provde accurate and unbased estmates of tmber volume and ncrement wth known precson (EC, 1997; Latat et al., 2000). Accordng to a revew by Latat et al. (2000), the RSE n natonal estmates of tmber volume ranges from 0.54% n France to 5.1% n Belgum, whereas errors related to converson factors are unknown. Use of the current converson factors, whch are based on relatvely few stes sampled n varous ecosystem studes, may lead to based estmates of forest carbon stocks.

10 220 A. Lehtonen et al. / Forest Ecology and Management 188 (2004) Relablty of a bomass estmate n the US was facltated by complng of a large dataset on aboveground bomass of temperate forests by poolng publshed and unpublshed bomass studes of the regon (Schroeder et al., 1997). Regonally representatve data on the allometry of trees have been collected and used to develop equatons for tree level volume (e.g. Laasasenaho, 1982; Brandel, 1990; Kaufmann, 1992) and bomass (e.g. Bartelnk, 1997; Ter-Mkaelan and Korzukhn, 1997). In ths study, we have shown that relable standlevel BEFs wth known precson can be formulated on the bass of the nformaton summarsed n the exstng volume and bomass functons. Compared to prevous methods for estmaton of converson factors, the strength of ths study les n (1) the volume and bomass equatons, whch descrbe allometry of trees on the bass of regonally representatve data and n (2) the systematc forest nventory data that descrbe regonal varaton n dameter dstrbuton and stockng densty by stand age. Furthermore, by usng nformaton on model errors and varaton n stand structure, we can provde an estmate of uncertanty for the BEFs. Ths approach can also be used to formulate BEFs n other regons and countres where relable bomass and volume equatons are avalable. The BEFs currently appled n the assessments of forest carbon stocks n Fnland (0.595 Mg m 3 for Scots pne and Mg m 3 for Norway spruce) (Tomppo, 2000b) have been generated on the bass of a few ecosystem studes (Karjalanen and Kellomäk, 1996) and are slghtly lower than those obtaned here. Stump and root BEFs publshed by UN-ECE/ FAO (2000) for Fnland are also lower compared wth the BEFs obtaned n ths study. Accordng to UN- ECE/FAO (2000), for Fnland the stump and root BEF was 0.10 for all tree speces, whereas n the present study t was 0.16 and 0.18 for Scots pne and Norway spruce, respectvely. We were not able to formulate contnuous BEFs for belowground bomass of brch, snce we reled on bomass equatons provded by Marklund (1988), and equatons for roots of brch were not obtaned. Accordng to Latakar (1935), the average estmate for the root system of brch was about half the volume of stem, whch means that BEF for the stump and roots of brch would be 0.19, assumng the same wood densty for roots and stem (Bhat, 1982)and usng our mean of response for estmaton of stem BEF (Table 5). BEFs (bomass component/stem volume) change as a stand ages, especally n Norway spruce stands. The varaton n these factors wth ncreasng stand age was also proposed by Kaupp et al. (1995), who compled nformaton from the lterature. However, they assumed hgher varaton for Scots pne than for Norway spruce stands, manly due to an assumed greater varaton n the proporton of root bomass n Scots pne. In general, BEFs appled for dfferent age classes of Norway spruce stands by Kaupp et al. (1995) were lower than these n ths study. For Scots pne stands ther BEFs by age classes were 0.80 Mg m 3 for stands under 40 years, 0.67 Mg m 3 for year-old stands, and 0.59 Mg m 3 for stands over 81 years, beng hgher for younger stands and lower for mddle aged and old stands than our BEFs were (Table 2). Kaupp et al. (1995) estmated BEFs by age classes, and ther assumpton of decreasng proporton of root bomass over the age gradent was opposte to our results (Fg. 2). Our fndng that BEF decreases n branches and folage s n agreement wth the trend suggested by Kaupp et al. (1995). The proportons of some bomass components (e.g. aboveground bomass of broadleaved speces as well as the stump and bark of Norway spruce) are farly stable durng the rotaton, and constant factors for bomass expanson can be appled for rough estmaton of the bomasses of these components. When stand development and, e.g. bomass turnover are modelled, t s, however, mportant to notce these slght trends n the BEFs. Our functons for BEFs can be appled to conferous forests aged between 10 and 150 years and wth less than 250 m 3 ha 1. An upper lmt s gven snce the number of older stands (>150 years) n our data was small (Fg. 2a and b). For stands less than 10 years, BEF of 10 years should be appled. For a broadleaved forest, the functons are applcable for age classes rangng from 10 to 100 years and wth less than 200 m 3 ha 1. Informaton on forest resources mght be avalable n the form of mean volumes accordng to the development classes. Snce the relatonshp between stem volume and whole tree bomass was found to be very strong, the bomass can be estmated from mean volumes wth the help of equatons presented n Tables 6 8. Stem volume does not determne the

11 A. Lehtonen et al. / Forest Ecology and Management 188 (2004) bomass of the folage and roots, but t certanly has several buld-n factors that affect the bomass of the tree components (e.g. water and nutrent supply, fertlty, competton, mosture and length of growng season) (Mäkelä et al., 1995). The equatons descrbng the relatonshp between bomass of the tree components and stem volume at stand level are applcable for confer forests that have a stem volume up to 250 m 3 ha 1. Wth broadleaved forests, the equatons should not be appled f the stem volume s more than 200 m 3 ha 1. Our equatons may overestmate bomass n stands wth hgh stemwood volumes, because they are based only on dameter. The relatonshp between dameter growth and heght growth changes durng stand development (Assmann, 1970). Ths may not be accounted for adequately, because the tree level equatons we employed have relatvely small sample of larger trees (more than 30 cm dbh) (Marklund, 1988). The BEFs n ths study were formulated on the bass of volume and bomass equatons and on approprate nformaton concernng dameter dstrbuton and stockng densty of the stands, all of whch mght ntroduce some errors n the BEFs. The volume equatons appled n our study (Laasasenaho, 1982) were developed by mnmsng error n large trees, whch consttute the man part of the standng volume. Therefore, volume estmates for small trees mght be based and our BEFs mght ntroduce bas to bomass estmaton n young stands. Appled bomass equatons (Marklund, 1988) are based on a representatve sample of forested stands n Sweden; and dfferences n stem form mght have resulted a systematc bas n our BEF values. The assumpton that the allometry of Swedsh and Fnnsh trees s the same was tested by comparng volume equatons for southern Sweden formulated by Brandel (1990) wth those for Fnland by Laasasenaho (1982). We were especally nterested n the stem form n southern Sweden, snce there the clmatc condtons are more favourable and Marklund s (1988) samplng was qute dense there. We found that the dfference n stem volume based on dameter and heght between trees n southern Sweden and Fnland on the stand level was less than 5% for pne and spruce. The BEF equatons presented here are applcable for a regon where the dameter dstrbuton and tree allometry s smlar to the dameter dstrbuton and tree allometry for whch these volume and bomass equatons were developed and appled (Parresol, 1999). Thus, major changes n slvcultural practces that mght lead to changes n tree allomerty could also nfluence BEF values. In Fnland, the stockng densty of forests has ncreased durng recent decades as a result of ntensfed forest management (Tomppo, 2000a). Ths change may lead to overestmaton of canopy bomass wth our BEFs, snce the rato of canopy bomass to stem volume mght dffer from that n Marklund s and Laasasenaho s data. Furthermore, BEFs by stand age are also senstve to changes n dameter dstrbutons and n stockng densty of the stands. In our study ths nformaton orgnated from the permanent sample plots measured n by the Natonal Forest Inventory. For developng BEFs, we used treewse measurements from the permanent sample plots of the Natonal Forest Inventory, however, detaled nformaton on stand structure mght not always be avalable. Thus, we also tested approaches, n whch the stand structure by age classes was smplfed for a medan tree (assumng all trees n an age class are of equal sze) or where t was descrbed by a Webull dstrbuton (n ths case the nformaton needed was the medan and the 99th percentle of dameter dstrbuton for each age class). Based on ths evaluaton, we conclude that BEFs can also be obtaned wth ths lmted nformaton on stand structure. In addton to regonal carbon stock assessments, the BEFs formulated n our study are needed and can be used n analyss of the carbon dynamcs of forest ecosystems that make use of nventory data on forest resources. Stand-level estmates of bomasses accordng to tree components are needed when bomass producton and ltterfall by bomass components of dfferent qualty are modelled and lnked to a sol (e.g. Lsk et al., 2002) model descrbng decomposton of dead organc matter. For these purposes t s mportant to be able to observe the dynamcs of carbon stocks n dfferent tree components, such as folage, branches, bark, stem, stump and roots, accordng to stand age. Acknowledgements We thank Dr. Rsto Ojansuu, Dr. Annkk Mäkelä and Lc.Sc. Joun Splehto for ther advce through-

12 222 A. Lehtonen et al. / Forest Ecology and Management 188 (2004) out the study and Dr. Joann von Wessenberg for revsng the language. We are grateful to the Academy of Fnland for fnancng project nro Integrated method to estmate carbon budgets of forests whch s part of Research Programme on Sustanable Use of Natural Resources (SUNARE). We also thank the Natonal Forest Inventory group for provdng data on permanent sample plots. Appendx A. Error estmaton of BEFs by age classes Let us denote by v j the estmate of stem volume for tree j n cluster and by m j the bomass estmate for the same tree. An estmate of BEF s P ;j ^b ¼ m P j P ;j v ¼ P m j v ; where v ¼ X v j and m ¼ X m j (A.1) j j and ts varance can be approxmated wth the formula (Cochran, 1977) Varð^bÞ Var P m b P v P v 2 (A.2) Samplng error was estmated by evaluatng the varance of the resduals of bomass by clusters, assumng random samplng X dvar s m b X! v ¼ ndvar s ðe Þ (A.3) where n s the number of clusters and dvar s ðe Þ s estmated by the samplng varance of the resduals e ¼ m ^bv. In ths data there are four sample plots n one cluster n southern Fnland and three sample plots per cluster n northern Fnland. Model errors were estmated by assumng ndependent trees and also by assumng that all trees n one cluster were fully correlated wth each other. Ths approach made t possble to fnd upper and lower lmts for model errors. The assumpton of ndependent trees: Corr m ðv j ; v k Þ¼Corr m ðm j ; m k Þ¼0; k 6¼ j (A.4) gves the formula X Var m m b X! v ¼ X Var m ðm j Þþb 2X Var m ðv j Þ 2b X Cov m ðm j ;v j Þ ;j ;j ;j (A.5) for tree model error. Varance of model errors for volume s Var m ðv j Þ¼ s 2 r;v v2 j (Laasasenaho, 1982) and for bomass Var m ðm j Þ¼s 2 r;m m2 j (Marklund, 1988), where s r,v and s r,m are the relatve mean square errors of the model estmates. Covarance of volume and bomass estmates can be estmated usng the model varances and correlaton of the errors n volume and bomass estmates. dcov m ðm j ; v j Þ qffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ¼ r tree;mv dvar m ðm j ÞdVar m ðv j Þ ¼ s r;m s r;m r tree;mv m j v j (A.6) where r tree,mv s the estmate for the correlaton between bomass and volume models, whch s assumed to be constant for all trees. Assumpton of perfect correlaton between model errors wthn each cluster, Corr m ðv j ; v k Þ¼Corr m ðm j ; m k Þ¼1; k 6¼ j (A.7) leads to X Var m m b X! v ¼ X Var m ðm Þþb 2X Var m ðv Þ 2b X Cov m ðm ;v Þ (A.8) where estmates for varance based on (Laasasenaho, 1982) and (Marklund, 1988) are X dvar m ðv Þ¼s 2 r;v v j v k and j;k X dvar m ðm Þ¼s 2 r;m m j m k (A.9) j;k and where covarance s estmated qffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff dcov m ðm ; v Þ¼r cl;mv dvar m ðm ÞdVar m ðv Þ sffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff X X ¼ s r;m s r;m r cl;mv m j m k v j v k j;k j;k (A.10)

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