United States 

Agriculture 

Forest Service 

Northeastern Forest 

Experiment Station 

Research Paper 

N E-564 

Component Biomass Equations - lack Spruce in ~aine 

M. M. Czapowskyj 

D. J. Robison 

R. D. Briggs 

E. H. White 
The Authors I M. M. Czapowskyj, a native of Ukraine and a United States citizen since 

1957, received a Diplomforstwirt degree from Ludwig-Maximilians I University, Munich, Germany, in 1949. He obtained an M.S. degree in 

forestry from the University of Maine in 1958 and a Ph.D. degree in soils 

from Rutgers University in 1962. He joined the Northeastern Forest Experiment Station in 1961 as a research forester and was assigned to the stripmine reclamation project at Kingston, Pennsylvania, for 11 years. In 1973 he 

I was transferred to the Station's project in culture of northeastern conifers 

at Orono, Maine. 

D. J. Robison is a graduate research assistant in forest soils at the 

School of Forestry, SUNY College of Environmental Science and Forestry, 

Syracuse, New York. He holds a B.S. degree from the college of Environmental Science and Forestry and his research efforts have been directed 

toward quantifying relationships between spruce budworm, intensive 

silvicultural treatments, and growth of black spruce in Maine. 

R. D. Briggs received an A.A.S. in forest technology in 1975 from the New 

York State Ranger School. In 1979and 1982, he received B. S. and M.S. 

degrees in forest biology and forest soils, respectively, from SUNY College 

of Environmental Science and Forestry, Syracuse, and currently is a 

candidate for Ph.D. degree in forest soils from SUNY. 

E. H. White is a professor of forest soil science at the School of 

Forestry, College of Environmental Science and Forestry, Syracuse. He 

returned to SUNY at Syracuse after 6 years at the University of Minnesota. 

He previously had worked in Kentucky, Mississippi, Florida, and Alabama. 

White holds B.S. and MS. degrees from SUNY and Ph.D. in soils from 

Auburn University. His principal research interests concern intensive forest 

management, forest soil fertility, and tree nutrition. 

Manuscript received for publication 24 September 1984 

Abstract 

Component biomass prediction equations are presented for young 

black spruce (Picea mariana B.S.P. (Mill.)) in northern Maine. A weighted 

least squares model was used to construct the equations for small trees 

from 1 to 15 cm d.b.h., and an ordinary least squares model for trees less 

than 2 m in height. A linearized allometric model was also tested but was 

not used. Equations were developed for oven-dry needle, branch, bolewood, 

bolebark, aboveground, root, and complete tree biomass components. 

Aboveground components accounted for approximately 80 percent, and 

stump (less than 6 cm in height) plus roots accounted for 20 percent of the 

complete tree oven-dry biomass accumulation. 
Introduction 

Black spruce (Picea mariana 

B.S.P. (Mill.)) is a geographically 

wide-ranging species that occurs on 

76,000 hectares in the State of 

Maine alone (Ferguson and Kingsley 

1972). High fiber quality, ability to 

grow on poor sites, and apparent 

resistance to spruce budworm 

(Choristoneura fumiferana (Clem.)) 

defoliation make black spruce an 

increasingly valuable fiber resource. 

The development of whole-tree 

harvesting and utilization technologies, to make more efficient 

use of wood crops, has created a 

need for reliable estimates of tree 

biomass. Equations relating individual tree diameter and height to 

component biomass dry weight 

have been developed by Young et 

al. (1964, 1980) for mixed species of 

spruce in Maine. Other equations 

have been published for black 

spruce in Minnesota (Schlaegel 

1975) and in Canada (Alemdag 1982, 

Freedman et a/. 1982, Ker 1980, 

1984, Moore and Verspoor 1973, 

Ouellet 1983). 

The objective of this study was 

to develop component biomass 

prediction equations for naturally 

regenerated, unmanaged, poor-site 

black spruce in Maine. The equations were constructed to relate 

component biomass dry weight to 

diameter outside bark at breast 

height and diameter outside bark at 

15 cm above ground line. 

Study Area 

The study was conducted 

immediately north of Square Lake 

(latitude 47"06", longitude 68"23") 

in T-16 R-5 Aroostook County, 

Maine. The climate is characterized 

as humid, cool, continental (Arno 

1964) with a mean yearly temperature of 3.6"C. Annual temperature 

extremes range from a mean low of 

-11.9"C in January to 18.0°C in 

July. A frost-free season of 107 days 

(May 30 to September 16) is typical. 

Average annual precipitation in the 

area is 92 cm (Ruffner 1978). 

The soils are relatively uniform, 

consisting of poorly and very poorly 

drained complexes formed in lakelaid lacustrine deposits and are 

overlain by varying depths of 

organic materials, mostly of 

Sphagnum spp. origin. The microtopography is an intricate association of hummock and hollow relief. 

Overall, the area (1200\ha) is level 

and is situated 6 m above the 

surface of Square Lake at an 

elevation of 183 rn. 

The black spruce stand (98 

percent pure) occupying the site 

developed following clearcutting in 

1957. The stand is even-aged, but 

the age of individual trees varies by 

as much as 20 years due to 

advanced regeneration, layering, 

and ingrowth. A wide range of 

diameters and heights (1 to 11 cm 

and 1 to 8.5 m, respectively) results 

in an uneven canopy surface. 

Density of stems greater than 0.5 m 

in height is as high as 14,000 per 

hectare, and open areas as large as 

4.5 m in diameter occur 

occasionally. 

Methods 

Field and Laboratory Procedures 

A total of 39 trees from 1 to 15 

cm d.b.h. was randomly selected to 

represent the range of diameters 

present. Root systems were 

excavated from 20 of these 39 trees. 

To account for small trees, an additional 25 trees with diameters from 

1 to 3 cm at 15 cm above ground 

were sampled. Trees with broken 

tops and distorted or forked boles 

were excluded from the sample. 

Sample trees came from unmanaged areas, except for the largest 

trees which were located adjacent 

to drainage ditches. In these areas, 

stand development was enhanced 

and larger trees were available for 

sampling. 

Sample trees were measured at 

breast height to the nearest 0.1 cm, 

cut to within 6 cm of the ground, 

and total tree height measured to 

the closest 0.01 m. Dead branches 

and live crown were cut from the 

trees and weighed separately in the 
field (+ 0.01 kg). To account for 

moisture content changes within 

the crown and to accommodate the 

maximum capacity of the field 

scale, crowns of the largest trees 

were cut and weighed in three 

sections, those of moderate size 

trees in two sections, and the 

crowns of the smallest trees were 

weighed as a single unit. A whorl of 

branches was removed from the 

center of each live-crown section 

and from the area of dead crown for 

moisture content and percent 

foliage determination. 

Sampled whorls were sealed in 

double plastic bags and transporteci 

to the laboratory where fresh weight 

(-t 0.1 g) was'recorded within 36 

hours. Branch samples with needles 

were oven-dried at 65°C to constant 

weight and percent moisture 

computed. Moisture content data 

were applied to the fresh weight of 

each crown section and summed to 

obtain the dry weight of the entire 

crown. Needles were separated 

from live-crown sample whorls and 

weighed to determine the percent 

needle component. This ratio was 

used to calculate needle and branch 

dry weight for each crown section 

and then summed for the whole 

crown. 

Boles were cut into 1.22-m 

bolts and weighed (r 0.1 kg) in the 

field. A disk (4 to 7 cm thick) was 

cut from the base of each bolt, 

placed in a double plastic bag, and 

transported to the laboratory. Bark, 

including cambium, was separated 

from the wood of each disk and 

fresh weight (r 0.1 g) of bark and 

wood recorded separately within 36 

hours. Wood and bark were ovendried at 65°C to constant weight 

and percent moisture was calculated. The dry weights of bark and 

wood were calculated for each bolt 

and summed for the entire bole. 

These procedures were 

followed for all aboveground 

sampling except for the smallest 

trees sampled. In these instances, 

the entire tree, by component, was 

transported to the laboratory for 

both fresh and oven-dry weight 

determination. 

Root systems were confined 

almost entirely to the surface 

organic soil with only a few small 

roots extending into the subsurface 

mineral soil. The area of an individual tree root system was estimated as similar in size to the area 

of the trees live crown projected 

onto the ground around its base. 

From within this defined -rea, 

stump and roots were excavated. 

Roots which extended beyond the 

estimated area were traced and 

removed, as well as possible. The 

extracted root systems were 

cleaned of soil, cut into manageable 

pieces, bagged, and taken to the 

laboratory. Roots were then carefully cleaned, weighed, oven-dried at 

65"C, and oven-dry weight recorded 

(-c 0.1 g). Small roots and fine rootlets lost in the excavation were not 

accounted for and are not included 

in the biomass estimates. 

Statistical Procedures 

For trees from 1 to 15 cm 

d.b.h., the diameter outside bark at 

breast height was chosen as the 

independent variable for the 

biomass prediction equations as 

this variable has been shown to be 

strongly correlated with individual 

tree biomass and is an easily 

obtained inventory measurement. 

Graphical analysis of the sample 

data substantiated that the relationship between component biomass 

and d.b.h. was curvilinear and that 

the variation in component biomass 

increased with increasing diameter. 

Two models were tested to fit the 

data: 

(I) weighted least squares 

(11) linearized allometric 

In(y) = In(B1) + Bz*ln(d) + In(e) 

We) * N (0, a2) 

where y = component biomass dry 

weight (kg) 

d = d.b.h. (cm) and 

B1, Bz, and B3 are unknown parameters. 

Graphs of the conditional variance of component biomass by 

diameter class verified that the 

variances were proportional to the 

4th power of diameter. Furnival's 

Index (1961) was used to determine 

whether model I or II best fit the 

data. 

Graphical analysis of sample 

data for trees with diameters from 1 

to 3 cm at 15 cm above ground 

showed that the relationship 

between biomass and tree diameter 

at 15 cm was linear and that the 

conditional variance of component 

biomass was homogeneous. The 

ordinary least squares method was 

used to fit the following linear 

model for these trees: 

where y = component biomass dry 

weight (kg) 

d = diameter (cm) at 15 cm 

and 

B1 and B2 are unknown 

parameters. 
Results and Discussion 

Sample-tree mensurational and 

component biomass data are summarized in Table 1. Complete 

sample-tree dry weight ranged from 

0.1 to 85.4 kg and above ground 

weights from 0.1 to 69.1 kg. 

Model I was selected to construct the prediction equations for 

trees 1 to 15 cm d.b.h. Although 

neither model, based upon 

Furnival's Index (1961), consistently 

provided better results (Table 2), the 

weighted least squares model has 

advantages which favor its 

selection. This model facilitates the 

calculation of unbiased biomass 

prediction and confidence limits 

(Fig. 1). In addition, the model 

provided a statistically better fit to 

the data for bolewood and bolebark, 

the tree components most commonly utilized. The model also 

provided a better fit for root and 

complete tree biomass than did the 

linearized allometric model. Several 

other researchers have supported 

use of the weighted least squares 

model in the construction of 

biomass equations (Crow and 

Laidley 1980, Cunia 1979, Schreuder 

and Swank 1973). 

Table 1 .-Black spruce sample tree mensurational data and mean biomass by component (kg) 

Sample tree Range of Range of Needle Branch Bolewood Bolebark Above- n Stump Complete n 

size class sample sampled ground &root tree 

d.b.h. (cm) d.b.h. height 

Diameter .. Rangeof Above- Stump Complete 

at 15 cm Diameter sampled Needle Branch Bolewood Bolebark ground n & root tree n 

(cm) range height 
Table 2.-Comparison of the fit of weighted least 

squares and linearized allometric 

models to component biomass data 

using Furnival's Indexa 

Model 

Weighted leastb LinearizedC 

Component squares allometric 

Needle 1.82 0.74 

Branch 1.20 .85 

Bolewood .81 1.50 

Bolebark .15 .33 

Aboveground 3.44 2.41 

Stump and root 58 1.05 

Complete Tree 1.55 3.33 

a The smaller value of Furnival's Index, the better the model 

fits. 

by = BY + B2.d + B3+d2 + e e .U N (0, d4 a2) 

c In(y) = In(B1) + B~*ln(d) + In(e) In(e) .U N (0, 02) 

complete 

tree biomass 

Coefficients for the weighted 

least squares regression of 

component biomass on d.b.h. are 

given in Table 3 for trees from 1 to 

15 cm d.b.h.' The coefficients of 

determination for complete tree, 

aboveground,'bolewood, bolebark, 

and root and stump biomass are 

high (0.98, 0.83, 0.96, 0.95, and 0.93, 

respectively) while those for branch 

and needle components are lower 

(0.62 and 0.32, respectively). These 

differences reflect the complexity of 

the stand canopy and thus a high 

degree of variation in crown components. These factors were not 

considered in sample tree selection. 

Prediction equations for small 

trees, diameter measured at 15 cm, 

are presented in Table 4. Height of 

these small trees was also 

considered as an independent 

variable in equation construction. 

However, it did not prove to be a 

good predictor of biomass. It is 

important to measure small trees 

because they can be a significant 

portion of stand biomass. In some 

of the stands sampled, there were 

more than 62,000 stems per hectare 

of these small trees. 

I Confidence and,,prediction limit 

for oven-dry biomass components are 

available upon request from the senior 

author. 

Figure 1.-Relationship of black spruce 

complete tree biomass and d.b.h. with 95 

percent confidence limits (95% C.L.) and 95 

percent prediction limits (95% P.L.). 
Table 3.-Coefficients for the weighted least squares regressions of 

component biomass for black spruce trees on d.b.h., from 

1 to 15cm. 

Component b, b l b2 r2 sZb n 

Needle 

Branch 

Bolewood 

Bolebark 

Aboveground 

Stump and root 

Complete tree 

a The model is: y = b, + b~d + b2d2 

where y = component biomass (kg) 

d = diameter outside bark at breast height (cm) 

b SZy.x = d4s2 

Table 4.-Coefficients for the ordinary least squares regression of 

component biomass of black spruce trees on diameter, from 

1 to 3 cm, at 15 cm. 

Component b 1 r2 s2y.x n 

Needle - 0.1627 0.1583 0.86 0.00143 25 

Branch - .I655 ,1530 .88 .00114 25 

Bolewood - ,1231 .I194 .93 .00037 25 

Bolebark - .0356 .0362 .94 .00003 25 

Aboveground - .4869 ,4669 .92 .00700 25 

Stump and root - ,1231 .1227 .87 .00082 25 

Complete tree - .6100 ,5397 .92 .01149 25 

a The model is: y = b, + bld 

where y = component oven-dry biomass (kg) 

d = diameter outside bark at 15cm (cm) 
Oven-dry biomass distribution 

by component indicates that 

approximately 80 percent of 

complete tree biomass is 

accumulated aboveground and 

approximately 20 percent in the 

stump and roots. Bolewood 

accounts for the largest proportion 

of complete tree biomass (40 

percent) and bolebark the least (7 

percent). 

Oven-dry component biomass 

distribution as a percentage of total 

tree biomass changes with tree size 

(Fig. 2). The percentage of complete 

tree biomass in needles, branches, 

bolebark, and aboveground components decreases (from 19 to 12, 17 

to 15, 8 to 6, and 82 to 79 percent, 

respectively) from size class 1 to 7 

cm d.b.h., to size class 9 to 15 cm 

d.b.h. Bolewood and root biomass 

increase (from 37 to 44 and 19 to 21 

percent, respectively) for the same 

two size classes. Similar biomass 

distributions have been reported for 

black spruce by reed man and 

others (1982) and Ker (1984). 

80 

7 0 

60 

50 

4 0 

30 

20 ~oot & Stump 

10 

0 

0 2 4 6 8 10 12 14 16 

D.b.h. Ccml 

Figure 2.-Relationship of black spruce component biomass and d.b.h. 

as predicted by regression equations. 

Acknowledgment 

The authors gratefully acknowledge the assistance of Dr. L. P. 

Abrahamson in the preparation of 

this manuscript. 
Literature Cited 

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matter of jack pine, black spruce, 

white spruce, and balsam fir trees 

at two localities in Ontario. The 

Forestry Chronicle. 58(1):26-30; 

1982. 

Arno, John R. Soil survey of Aroostook County, Maine, Northeastern part. Washington, 

DC: USDA Soil Conservation 

Service; 1964. 80 p. I 

Crow, T. R.; Laidly, P. R. Alternative 

I models for estimating woody 

plant biomass. Canadian Journal 

of Forest Research. 10:367-370; 

1980. 

Cunia, T. On tree biomass tables 

and regression: some statistical 

1 comments. In W. E. Frayer, ed. 

Forest Resource Inventory Workshop Proceedings, Fort Collins, 

CO: Colorado State University; 

1979. Vol. 2: 643-664. I 

Ferguson, Roland H.; Kingsley, Neal 

P. The timber resources of Maine. 

i Resour. Bull. NE-26. Upper Darby, 

PA: U.S. Department of Agri- 1 culture, Forest Service, Northeastern Forest Experiment I Station; 1972. 129 p. 

Freedman, B.; Duinker, P. N.; 

Barclay, H.; Morash, R.; Prager, U. I Forest biomass and nutrient 

studies in central Nova Scotia. 

I Fredericton, NB: Canadian 

Forestry Service; 1982; Inf. Rep. 

M-X-134,46 p. 

I Furnival, G. M. An index for 

comparing equations used in 

constructing volume tables. 

Forest Science. 7(4):337-341, 1961. 

Ker, M. F. Biomass equations for 

seven major maritimes tree 

species. Fredericton, NB; Canadian Forestry Service; 1984; Inf. 

Rep. M-X-148. 54 p. 

Ker, M. F. Tree biomass equations 

for ten major species in 

Cumberland County, Nova Scotia. 

Fredericton, NB: Canadian Forestry 

Service; 1980; Inf. Rep. M-X-108. 

26 p. 

Moore, T. R.; Verspoor, E. Aboveground biomass of black spruce 

stands in subartic Quebec. 

Canadian Journal of Forest 

Research. 3:596-598; 1973. 

Ouellet, D. Biomass equations for 

black spruce in Quebec. Sainte 

Foy, PQ: Canadian Forestry 

Service; 1983; Inf. Rep. 

LAU-X-60E. 27 p. 

Ruffner, James A. Climates of the 

States, Vol. 1. Detroit, MI: Gale 

Research Co.; 1979. 

Schlaegel, B. E. Yields of four 40- 

year-old conifers and aspen in 

adjacent stands. Canadian Journal 

of Forest Research. 5:278-280; 

1975. 

Schreuder, H. T.; Swank, W. T. 

Statistical considerations in 

sampling biomass and surface 

area over time for a Pinus strobus 

L. forest. In. IUFRO Biomass 

Studies, Orono, ME: University of 

Maine; 1973: 131-141. 

Young, H. E.; Ribe, J. H.; Wainwright, K. Weight tables for tree 

and shrub species in Maine. Life 

Sci. and Agric. Exp. Stn. Misc. 

Rep. 230. Orono, ME: Univ. of 

Maine; 1980. 84 p. 

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76 p. 

*U.S. GOVERNMENT PRINTING OFFICE:^^^^-505-028:20008 
Czapowskyj, M. M.; Robison, D. J.; Briggs, R. D.; White, E. H. Component biomass equations for black spruce in Maine. Res. Pap. NE-564. Broomall, 

PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest 

Experiment Station; 1985.7 p. 

Component biomass prediction equations are presented for young black 

spruce (Picea mariana B.S.P. (Mill,:)) in northern Maine. A weighted least 

squares model was used to construct the eq~iations for small trees from 1 to 

15 cm d.b.h., and an ordinary least squares model for trees less than 2 m in 

height. A linearized allometric model was also tested but was not used. Equations were developed for oven-dry needle, branch, bolewood, bolebark, aboveground, root, and complete tree biomass components. Aboveground components accounted for approximately 80 percent, and stump (less than 6 cm in 

height) plus roots accounted for 20 percent of the complete tree oven-dry biomass accumulation. 

Keywords: Black spruce, biomass distribution 
Headquarters of the Northeastern Forest Experiment Station are in 

Broomall, Pa. Field laboratories are maintained at: 

Amherst, Massachusetts, in cooperation with the University of 

Massachusetts. 

Berea, Kentucky, in cooperation with Berea College. 

Burlington, Vermont, in cooperation with the University of 

Vermont. 

Delaware, Ohio. 

Durham, New Hampshire, in cooperation with the University of 

New Hampshire. 

Hamden, Connecticut, in cooperation with Yale University. 

Morgantown, West Virginia, in cooperation with West Virginia 

University, Morgantown. 

Orono, Maine, in cooperation with the University of Maine, 

Orono. 

0 Parsons, West Virginia. 

Princeton, West Virginia. 

Syracuse, New York, in cooperation with the State University of 

New York College of Environmental Sciences and Forestry at 

Syracuse University, Syracuse. 

University Park, PennsyIvania, in cooperation with the 

Pennsylvania State University. 

Warren, Pennsylvania.