Estimating Tree Biomass, Carbon, 

and Nitrogen in Two Vegetation 

Control Treatments in an 11-YearOld Douglas-Fir Plantation On a 

Highly Productive Site

Warren D. Devine, Paul W. Footen, Robert B. Harrison, 

Thomas A. Terry, Constance A. Harrington, Scott M. Holub, 

and Peter J. Gould

United States 

Department of 

Agriculture

Forest Service

Pacific Northwest 

Research Station

Research Paper

PNW-RP-591

March 2013

DEPAR TMENT OF AGRICULT URE
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been registered. All uses of pesticides must be registered by appropriate state or 

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can be injurious to humans, domestic animals, desirable plants, and fish or other 

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and pesticide containers.

Authors

Warren D. Devine is a postdoctoral research associate, Paul W. Footen is 

a research assistant, and Robert B. Harrison is a professor, University of 

Washington, Box 352100, Seattle, WA 98195; Thomas A. Terry is a senior 

scientist (retired), Weyerhaeuser NR Co., 505 N Pearl St., Centralia, WA 98531-

4660; Constance A. Harrington and Peter J. Gould are research foresters, U.S. 

Department of Agriculture, Forest Service, Pacific Northwest Research Station, 

3625 93rd Ave. SW, Olympia, WA 98512-9193; Scott M. Holub is a silviculture 

research scientist, Weyerhaeuser NR Co., 785 N 42nd Street, Springfield, OR 

97478-5764.

Cover photograph: Rodney Meade.

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Abstract

Devine, Warren D.; Footen, Paul W.; Harrison, Robert B.; Terry, Thomas 

A.; Harrington, Constance A.; Holub, Scott M.; Gould, Peter J. 2013. 

Estimating tree biomass, carbon, and nitrogen in two vegetation control 

treatments in an 11-year-old Douglas-fir plantation on a highly productive site. 

Res. Pap. PNW-RP-591. Portland, OR: U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Research Station. 29 p.

We sampled trees grown with and without competing vegetation control in an 

11-year-old Douglas-fir (Pseudotsuga menziesii var. menziesii (Mirb.) Franco) 

plantation on a highly productive site in southwestern Washington to create diameter-based allometric equations for estimating individual-tree bole, branch, foliar, 

and total aboveground biomass. We used these equations to estimate per-hectare 

aboveground biomass, nitrogen (N), and carbon (C) content, and compared these 

results to (1) estimates based on biomass equations published in other studies, and 

(2) estimates made using the mean-tree method rather than allometric equations. 

Component and total-tree biomass equations were not influenced by the presence 

of vegetation control, although per-hectare biomass, C, and N estimates were 

greater where vegetation control was applied. Our biomass estimates differed 

from estimates using previously published biomass equations by as much as 23 

percent. When using the mean-tree biomass estimation approach, we found that 

incorporating a previously published biomass equation improved accuracy of the 

mean-tree diameter calculation.

Keywords: Douglas-fir, plantation, biomass, allometry, carbon, nitrogen.
ii

Summary

There are few published biomass equations for young Douglas-fir (Pseudotsuga 

menziesii var. menziesii (Mirb.) Franco) plantations. Equations developed from 

regional-scale data, which include older trees, may not produce accurate biomass 

estimates for young, fast-growing trees. We sampled trees grown with and 

without competing vegetation control in an 11-year-old Douglas-fir plantation on 

a highly productive site (Class II+) in southwestern Washington to create diameter-based allometric equations for estimating individual-tree bole, branch, foliar, 

and total aboveground biomass. We used these equations to estimate per-hectare 

aboveground biomass, nitrogen (N), and carbon (C) content, and compared these 

results to (1) estimates based on biomass equations published in other studies, 

and (2) estimates made using the mean-tree method rather than allometric equations. Our component and total-tree biomass equations did not differ between 

treatments with and without 5 years of intensive vegetation control. Estimated 

total aboveground tree biomass at year 11 was 89.7 and 73.2 Mg • ha-1 with and 

without vegetation control, respectively. Total-tree N content was 326 and 256 

kg • ha-1, and C content was 43.7 and 35.5 Mg • ha-1, with and without vegetation 

control, respectively. Per-hectare aboveground tree biomass estimates using previously published Douglas-fir biomass equations differed from those made with 

our equations by -8 to +23 percent; the published equations producing biomass 

estimates most different (≥20 percent) from our estimates included those developed from large, diverse samples. When using the mean-tree biomass estimation approach for our site, we found that incorporating a previously published 

relationship between diameter and biomass for young Douglas-fir improved 

accuracy of the mean-tree diameter calculation. 
iii

Contents

1 Introduction

3 Methods

3 Study Site

4 Experimental Design and Treatments 

4 Data Collection

6 Data Analysis

9 Results and Discussion

9 Objective 1: Estimate Biomass, C, and N By Using Stand-Specific 

Allometric Equations

15 Objective 2: Compare Biomass Estimates From Objective 1 to Estimates Made 

By Using Published Equations From Other Studies

17 Objective 3: Estimate Biomass By Using the Mean Tree Method

19 Conclusions

20 Acknowledgments

21 English Equivalents

21 Literature Cited

25 Appendix

1

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

Introduction

Assessments of forest stand carbon dynamics, nutrient fluxes, and tree growth often 

include estimates of tree biomass. Individual-tree biomass estimates are usually 

based on a known allometric relationship between an easily measurable dimension 

(e.g., diameter at breast height (DBH)) and biomass. These allometric relationships 

are species specific and may be influenced by numerous factors including site quality, associated overstory and understory vegetation, and tree genetics (Bartelink 

1996, Espinosa Bancalari and Perry 1987, Feller 1992, Grier et al. 1984, Petersen 

et al. 2008, St. Clair 1993). The accuracy of a tree biomass estimate depends on 

how well the allometric equation represents the trees to which it is applied. A 

recent project compiled all known diameter-based allometric biomass equations 

(n = 2,640) for tree species in the United States and produced generalized equations 

for common tree species, including Douglas-fir (Pseudotsuga menziesii (Mirb.) 

Franco), and for species groups (Jenkins et al. 2003, 2004).

A commonly applied approach for estimating aboveground tree biomass in 

an even-aged stand or on a sample plot is to measure all trees and then estimate 

the biomass of every tree using an allometric equation that describes the relationship between a measured variable and individual-tree biomass (the “allometric 

method”). Estimated biomass of every tree is summed to create an estimate of 

total biomass. This method can be applied by using a previously published biomass 

equation from other sites, but a site-specific biomass equation, developed from trees 

highly representative of those on the stand or plot, is presumably more accurate. 

Development of site-specific biomass equations can also provide information on 

component (i.e., bole, limbs, foliage) biomass distribution and stand structure. However, development of site-specific biomass equations is generally expensive because 

trees must be destructively sampled across the full range of tree sizes to develop 

the relationship between measured tree size and tree biomass. This expense is 

particularly great where larger trees are sampled. One alternative to the allometric 

method of biomass estimation is the “mean tree” method in which a tree of mean 

size is sampled (often, mean basal area or estimated bole volume) and measured 

for biomass, and the biomass value then multiplied by the number of trees in the 

stand (Attiwill and Ovington 1968, Jolly 1950, Schreuder et al. 1993). This method 

is most accurate in forest plantations where trees are relatively uniform; the method 

becomes less accurate if the relationship between the sampled variable (e.g., basal 

area) and tree biomass changes according to tree size. An advantage of the mean 

tree method is that it has the potential to significantly reduce the number of sampled 

trees, compared to the allometric method.

Individual-tree biomass 

estimates are usually 

based on a known 

allometric relationship 

between an easily 

measurable dimension 

(e.g., diameter at breast 

height) and biomass.
2

RESEARCH PAPER PNW-RP-591

Despite an abundance of Douglas-fir plantations, there are relatively few 

published equations describing the relationship between total aboveground or 

component biomass and DBH, particularly for young plantations (i.e., <30 years) on 

productive sites. The most widely applied DBH-based aboveground biomass equations are those of Gholz et al. (1979) who produced a single set of biomass relationships for Douglas-fir trees 2- to 162-cm DBH using data from five previous studies 

on sites ranging from low to high productivity. Helgerson et al. (1988) developed 

biomass equations for Douglas-fir trees at plantation age 10 by using trees from 

all crown classes (biomass estimates excluded a 15-cm-high stump). Feller (1992) 

developed biomass equations for young Douglas-fir trees on high- and low-productivity sites on Vancouver Island, British Columbia, as well as for Douglas-fir trees 

on a wide range of sites across British Columbia (using data from Standish et al. 

1985). Feller (1992) found that site quality significantly affected biomass equations 

for some tree components, but two other studies found no effect of site quality on 

biomass equations for Douglas-fir in 5-year-old (Devine et al. 2011) and 22-year-old 

(Espinosa Bancalari and Perry 1987) plantations. Combining data from all known 

published studies to date, Jenkins et al. (2003) created a general equation predicting 

total-tree Douglas-fir biomass from DBH.

We are aware of only two published sets of biomass equations for Douglas-fir 

trees that quantified the effects of competing vegetation control on allometry by 

sampling trees grown with and without vegetation control (Devine et al. 2011, 

Peterson et al. 2008). Both studies developed sets of equations using data that 

included the Fall River Long-Term Site Productivity study, which is also the subject 

of this publication. Peterson et al. (2008) sampled 59 trees from the Fall River 

site at plantation age 5 years, and found that the relationship between DBH and 

component and total aboveground biomass differed between trees with 5 years of 

intensive vegetation control and trees grown without vegetation control. Devine et 

al. (2011) developed equations estimating year-5 tree biomass based on diameter at 

15 cm above ground level (D15) and total tree height; these equations used data from 

three sites, including the Fall River data used by Peterson et al. (2008). Devine et 

al. (2011) found that relationships between D15 and biomass, unlike those of DBH, 

were not influenced by vegetation control treatments. The authors observed that 

trees grown with vegetation control had greater bole taper compared to those grown 

without vegetation control, and the DBH measurements did not capture this difference in lower-bole biomass as well as the D15 measurements. For this reason, a 

single D15-based equation was effective in estimating tree biomass for both vegetation control treatments. In assessing tree component biomass, Devine et al. (2011) 
3

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

also found that bole biomass of trees across three sites was best estimated using 

tree height in addition to D15. Although accurate tree biomass equations for a single 

site may use only diameter, additional information, such as tree height, is necessary 

to account for differences in tree allometry that occur across multiple sites and 

management regimes.

This study was initiated to determine tree biomass accumulation and allocation in an 11-year-old Douglas-fir plantation on a highly productive site. We 

had three objectives:

Objective 1: Estimate per-hectare component and total-tree aboveground 

biomass, carbon (C), and nitrogen (N) content of Douglas-fir trees, in treatments 

with or without competing vegetation control. We made biomass estimates using 

the allometric method with equations developed by destructively sampling trees 

from both treatments.

Objective 2: Determine whether stand-specific biomass equations were warranted in this study: could we have made reasonably accurate per-hectare estimates 

using previously published biomass equations? We compared biomass estimates 

made with our stand-specific equations to those made using equations developed 

for other sites.

Objective 3: Compare a biomass estimate made using the mean tree method 

to one made using the allometric method (in objective 1). We applied a speciesspecific adjustment to select the mean tree.

Methods

Study Site

The study took place in a Douglas-fir plantation that was established as an ancillary study site in the North American Long-Term Soil Productivity (LTSP) study. 

The LTSP network was established to evaluate effects of soil compaction, biomass 

removal, and vegetation control on soil processes, nutrient budgets, and tree growth 

across a wide range of sites (Powers et al. 2005). The study site, known as the Fall 

River site, is located on Weyerhaeuser NR Company ownership in the Coast Range 

of Washington (46.72° N.; 123.42° W.) at a mean elevation of 334 m. The site is on 

a 9- to 16-percent slope toward a westerly aspect. The plant association (Henderson 

et al. 1989) is western hemlock (Tsuga heterophylla (Raf.) Sarg.)/swordfern (Polystichum munitum (Kaulf.) C. Presl.)-redwood-sorrel (Oxalis oregano Nutt.).

The site is characterized by a mild, maritime climate; mean January and July 

temperatures, measured onsite, are 3.5 and 16.1 °C, respectively. Mean annual 

precipitation is 181 cm, although an average of only 30 cm precipitation occurs 

between 1 May and 30 September. The soil is formed in residuum of Miocene 
4

RESEARCH PAPER PNW-RP-591

basalt with volcanic ash present in the surface horizons. This silt loam of the Boistfort series is a well-drained Typic Fulvudand (USDA NRCS 1999). The 50-year site 

index for Douglas-fir (King 1966) ranges from 41 to 43 m (Class II+).

The site was previously occupied by a second-growth stand of Douglas-fir and 

western hemlock that was clearcut with chain saws between May and July 1999. 

Merchantable bolewood to an 8- to 13-cm top was removed using a cable-yarding 

system, and logging debris was scattered uniformly across plots. Slash within the 

tree measurements plots was scattered uniformly using a shovel excavator with a 

piling-rake head. Because limited understory vegetation was present after the 1999 

harvest, no general site preparation herbicide treatment was necessary. In March 

2000, the site was planted with 1 + 1 Douglas-fir seedlings on a 2.5- by 2.5-m grid 

(1,600 trees•ha-1). The study area was fenced to eliminate confounding effects that 

could be caused by deer and elk browse.

Experimental Design and Treatments

The study followed a randomized, complete-block design with four experimental 

blocks. Blocking was based on slope position and composition of the previous stand 

(proportion of Douglas-fir and western hemlock). Experimental treatments were 

applied to 30- by 85-m plots, with 15- by 70-m internal measurement plots (168 

planted trees per measurement plot), which were treated in the analysis as experimental units.

The present study includes 2 of a total of 12 planned treatments in the overall 

design (i.e., 2 plots per block): bole-only harvest with and without 5 years of vegetation control (+VC and -VC, respectively). In the -VC treatment, no vegetation control 

was applied. In the +VC treatment, competing vegetation was controlled from the 

time of planting through year 5, with a combination of broadcast and spot-applied 

herbicides designed to eliminate all competing vegetation rather than to simulate 

an operational treatment. During the first 5 years after planting, total cover of 

competing vegetation (sum of the percentage cover of each of five life forms: forbs, 

grasses, vines, shrubs, and nonplanted trees), estimated ocularly within one 176.6-

m2

 circular sample plot per study plot each year and averaged over the 5 years, was 

4 and 74 percent in the +VC and -VC treatments, respectively (Devine et al. 2011). 

Additional background and details of the experiment appear in Ares et al. (2007b).

Data Collection

Following the 10th growing season postplanting, all living trees on the measurement plots were measured for total height (to nearest 0.1 m), height to live crown 

base (HLC; defined as lowest branch whorl with live branches in three quadrants; 
5

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

measured to nearest 0.1 m), and DBH (measured at 1.30 m above ground to nearest 

1 mm). Because we destructively sampled trees at year 11 to develop the biomass 

equations, estimates of biomass per hectare required that we know the year-11 size 

of all study trees. Thus, a subset of trees was remeasured after the 11th growing 

season to develop equations for estimating year-11 tree size using year-10 size. This 

subset of trees consisted of 12 trees per plot (n = 96) selected using a stratified random sampling design to sample across the full range of diameters present on each 

plot; these 96 trees were measured for total height, HLC, DBH, and D15 (measured 

to nearest 1 mm).

In March following the year-11 growing season, 13 trees per treatment were 

destructively sampled to create equations for estimating tree biomass (table 1). 

Twelve of the sampled trees were randomly selected using a stratified sampling 

approach to achieve representation across the full range of diameters present within 

each treatment; the same number of trees was sampled from each block. One 

additional tree per treatment was sampled to meet criteria described for objective 

3 below. The destructive sampling protocol followed the method used by Petersen 

et al. (2008) and is briefly described here. After tree height, HLC, DBH, D15, and 

maximum crown diameter in north-south and east-west directions (nearest 0.1 m) 

were measured, each tree was cut at ground level. In the field, the bole was cut into 

three sections; branches were removed, bundled separately for each bole section, 

and weighed. To estimate dry bole weight, each of the three bole sections was 

weighed in the field; two 5-cm-thick cross-sectional subsamples were cut from each 

section, weighed fresh, returned to the lab, dried to constant weight at 70 °C, and 

reweighed. To estimate branch dry weight, branches from each section were divided 

into three size classes (small, medium, and large), and a number of branches proportional to the number of branches in each size class was subsampled by random 

selection. The bagged subsamples were weighed fresh, returned to the lab, dried 

to constant weight at 70 °C, and then separated into woody and foliar components, 

which were weighed separately. Bole, branch, and foliar components were subsampled for C and N analysis following the procedure described by Petersen et al. 

(2008); subsamples were analyzed by the dry combustion method (Matejovic 1995) 

using a PerkinElmer Model 2400 CHN analyzer1

 at the School of Forest Resources 

Soils Laboratory, University of Washington, Seattle.

1 The use of trade names in this publication is for reader information only and does not 

imply endorsement by the U.S. Department of Agriculture of any product or service.

In the field, the bole 

was cut into three 

sections; branches 

were removed, bundled 

separately for each 

bole section, and 

weighed.
6

RESEARCH PAPER PNW-RP-591

Data Analysis

Objective 1: Estimate biomass, C, and N by using stand-specific 

allometric equations—

Using the 26 destructively sampled trees, we developed individual-tree equations 

predicting component (bole, branch, foliage) and total aboveground tree dry weight 

from tree dimensions measured immediately prior to destructive sampling (data 

appear in the appendix in table 7). Preliminary regression analyses showed that the 

equation form (ln Y = a + b ln X) fit the data best; the fit of this log-log relationship 

was consistently better than the fit of log-linear or linear relationships. Potential 

predictor variables tested in these equations were DBH, D15, and DBH2*height. We 

used PROC REG (SAS 2005) to compare treatment-specific intercepts and slopes 

to determine whether these parameters differed significantly by treatment (Sokal 

and Rohlf 1995). We examined residuals graphically, plotted them against predicted 

values, and tested them using PROC REG and PROC UNIVARIATE to verify 

variance and normality assumptions were met (SAS 2005).

We used PROC REG to determine the relationship between year-10 and year-11 

DBH and height for the subset of 96 trees measured after the year-11 growing season; this analysis included tests for potential effects of vegetation control on these 

relationships. We then used the resulting relationships to estimate year-11 DBH 

and height of all study trees. We used these estimated year-11 values for all trees, 

combined with the biomass equations described above, to estimate component 

Table 1—Summary statistics for destructively sampled 

Douglas-fir trees (13 per treatment) selected using 

stratified random sampling to represent the full range of 

diameters present at plantation age 11 years; treatments 

were 5 years of intensive vegetation control (+VC) and no 

control of competing vegetation (-VC)

Treatment

Variable +VC -VC

- - - Mean (minimum, maximum) - - -

Height (m) 9.5 (7.3, 10.8) 9.8 (7.5, 11.9)

DBH (cm) 13.3 (8.3, 16.8) 13.3 (9.0, 17.6)

D15 (cm) 18.6 (10.5, 26.5) 18.0 (10.9, 25.0)

Height to live crown (m) 1.4 (0.6, 2.4) 1.2 (0.5, 2.5)

Crown width (m) 4.1 (2.8, 5.2) 4.2 (3.5, 5.6)

Note: These data are not intended as a statistical treatment comparison but 

instead show the values for the trees in each treatment resulting from the 

stratified selection.

DBH = diameter at breast height.

D15 = diameter at 15 cm above ground level.
7

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

and total-tree biomass of all live trees on the study plots. This approach for year-11 

biomass estimation ignored any mortality that occurred during year 11; however, 

it is unlikely that mortality increased much between years 10 and 11, as mortality 

increased only 0.3 percentage points in these treatments between years 8 and 10. 

The N and C contents of the components (bole, branch, and foliage) of all study trees 

were estimated using the component concentrations measured for the 26 destructively sampled trees. Individual-tree estimates of biomass and N and C content were 

summed at the plot level.

Estimates of component and total-tree biomass per hectare, N concentration, 

and estimated N and C contents per hectare were analyzed using a randomized, 

complete-block design analysis of variance (ANOVA) model (PROC MIXED; SAS 

2005). We checked all ANOVA data for heteroscedasticity and normality assumptions; data transformation was not necessary. Significance was set at α = 0.05 

throughout the analysis.

Objective 2: Compare biomass estimates from objective 1 to estimates made by 

using published equations from other studies—

Calculations followed the same procedure as that described for objective 1, except 

that instead of using the allometric equations developed from our destructively 

sampled trees, we used previously published equations from other sites that encompassed the range of diameters present at our site (we did not use the year-5 equations 

from the Fall River site because they were developed for much smaller trees).

Objective 3: Compare a biomass estimate made by using the mean tree method 

to one made by using the allometric method—

The first step of the mean tree method was to determine the size (i.e., DBH) of the 

mean tree: the tree representative of the average biomass of all trees in the stand. To 

accurately select the mean tree, we applied an allometric equation relating DBH to 

total-tree biomass (examples of the linearized form of this type of equation appear 

in table 2). Because we did not know this DBH-biomass relationship for our study 

site, we used a preexisting equation. After reviewing the literature, we selected the 

equation of Jenkins et al. (2003) because it included the DBH range of our trees 

and appeared to be relatively robust, as it was based on data derived from 11 previously published Douglas-fir biomass equations, including that of Gholz et al. (1979) 

(Jenkins et al. 2003, 2004).
8

RESEARCH PAPER PNW-RP-591

We began by estimating the DBH of the tree (or trees) representing mean totaltree biomass. Based on year-11 estimated DBH (for this comparison of methods, we 

use only the +VC treatment), we calculated the DBH of the tree of mean biomass 

using the following steps:

1. We applied the slope of the relationship between ln(DBH) and 

ln(biomass) to each study tree to create a “weighted DBH” value:

DBHw = DBHb1

where

DBHw = weighted DBH, and

b1 = slope of the ln(DBH) – ln(biomass) relationship from the Jenkins 

et al. (2003) equation.

2. We calculated the mean DBHw of all trees.

3. We back-converted the mean DBHw to get mean DBH:

DBH = DBHw

(1/ b1)

We then destructively sampled a tree of DBH equal to this value to determine 

biomass, using previously described methods. In practice, more than one tree of this 

DBH would be sampled, but given resource limitations during this sampling effort, 

we sampled only one tree. Finally, we multiplied the measured total-tree biomass 

of this mean tree by the number of live study trees and converted this estimate to a 

per-hectare basis.

Table 2—Equations for estimating dry biomass of individual 

Douglas-fir trees at plantation age 11a

Tree component b0 b1 Adj. R2 CFb

Foliage -4.2488 2.4671 0.888 1.015

Branches -4.4899 2.8001 0.901 1.017

Bole (wood and bark) -2.6623 2.2763 0.968 1.003

Total aboveground -2.5127 2.4807 0.966 1.005

Note: the equation form was ln (biomass) = b0 + b1 ln (DBH); biomass was measured in 

kilograms and diameter at breast height (DBH) was measured in centimeters.

a Trees are described in table 1. Equations were derived from measurements of 26 trees, 13 

with and 13 without 5 years of intensive vegetation control; equations did not differ between 

vegetation control treatments. Equations are plotted in figure 2.

b Correction factor (CF) = exp((SEE2

)/2).
9

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

Results and Discussion

Objective 1: Estimate Biomass, C, and N By Using 

Stand-Specific Allometric Equations

Estimating year-11 DBH and height—

There was a strong, linear relationship between year-10 and year-11 DBH (fig. 1); 

adding tree height to this model did not improve its fit. The intercept of the year-11 

DBH prediction equation differed between treatments, indicating that DBH of trees 

in the -VC treatment increased by an average of 0.36 cm more than those in the 

+VC treatment during the year-11 growing season. This was apparently a result 

of higher relative stand density in the +VC treatment (table 3). The slope of the 

prediction equation did not differ by treatment, indicating that tree size (i.e., DBH) 

did not affect the relationship between year-10 and year-11 DBH differently in the 

two treatments.

Figure 1—Equation developed to estimate year-11 diameter at breast height (DBH) of 96 planted Douglas-fir trees using 

year-10 DBH. -VC = without vegetation control; +VC = with vegetation control.
10

RESEARCH PAPER PNW-RP-591

Year-11 tree height was best predicted from year-10 height by using a 

quadratic equation:

Ht11 = -0.1429 + 1.2504*Ht10 – 0.0153*Ht10

2 (Adj. R2

=0.982)

Vegetation control treatments had no influence on the year-11 height equation. 

Year-11 DBH and height estimates, as well as other estimated parameters, appear in 

table 3. Distributions of estimated year-11 DBH values for both vegetation control 

treatments appear in the appendix (figure 4).

Biomass equations—

Equations for estimating individual-tree foliar, branch, bole, and total aboveground 

biomass appear in table 2 and are shown in figure 2. In each equation, DBH was the 

best predictor of component or total-tree aboveground biomass, based on distribution of residuals and model fit. We detected no difference in slope or intercept 

between the two vegetation control treatments in any of the equations, indicating 

that vegetation control had no significant effect on the relationship between DBH 

and biomass. By contrast, a year-5 study of the same plantation found that DBHbased component and total-tree biomass equations differed between these vegetation control treatments (Peterson et al. 2008). Given two year-5 trees of the same 

DBH, the tree receiving vegetation control had greater bole, branch, foliar, and 

total aboveground biomass than the tree without vegetation control. This vegetation control effect on year-5 allometry was likely influenced by the fact that trees 

receiving vegetation control were significantly taller (Ares et al. 2007a) and had a 

significantly lower mean height: diameter ratio (85) than those without vegetation 

control (97).2

 Additionally, taper of the lower bole, measured as the ratio of D15 to 

Table 3—Summary statistics, based on all study trees, for estimated year-11 

values of diameter at breast height (DBH), height, basal area, and stand density 

index (SDI)a

Treatment

Variable +VC -VC Pr > Fc

- - - - - - - - - - Mean (± standard error) - - - - - - - - -

DBH (cm) 14.0 ± 0.1 12.7 ± 0.2 <0.001

Height (m) 9.7 ± 0.1 9.0 ± 0.1 <0.001

Basal area (m2 ha-1) 23.7 ± 0.3 20.2 ± 0.3 <0.001

SDI (percentage of maximum)b 40.0 ± 0.7 35.3 ± 0.7 <0.001

a Year-11 DBH and height were estimated using equations developed from a subset of 96 trees that were 

measured for both variables in years 10 and 11. Treatments were 5 years of intensive vegetation control (+VC) 

and no control of competing vegetation (-VC). Significance of the treatment effect is shown for each variable.

b Reineke (1933) SDI; value is percentage of maximum SDI for Douglas-fir of 595. Calculation was based on 

estimated year-11 DBH; density was calculated using year-10 survival rate.

c Pr > F = P-value from analysis of variance; values <0.05 indicate a significant difference between treatments.

2 Data are on file at the Forestry Sciences Laboratory, 3625 93rd Ave. SW, Olympia, WA 

98512-9193.

Vegetation control had 

no significant effect 

on the relationship 

between DBH and 

biomass.
11

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

DBH, was greater for trees with vegetation control at year 5 (Devine et al. 2011). At 

year 11, estimated tree height still differed between treatments (table 3), but there 

was no significant difference in estimated height: diameter ratio between treatments 

with vegetation control (71) and without (72), suggesting that differences in allometry had decreased since year 5.

The relationship between DBH and total aboveground biomass, and that found 

in three other studies of similarly sized Douglas-fir, is shown in figure 2. Several 

published Douglas-fir biomass equations for ranges of DBH values that did not fully 

encompass the DBH values of our study trees are included in table 4 and shown 

in the appendix (figs. 5 and 6). Although allometric relationships between DBH 

and total-tree biomass in this study were generally comparable to previous studies, 

Figure 2—Relationship between diameter at breast height (DBH) and component or total aboveground biomass of Douglas-fir trees at 

plantation age 11 (equations in table 2). Relationships are also shown for previous studies of Douglas-fir on other Pacific Northwest sites 

(table 4). The total aboveground biomass equation of Jenkins et al. (2003) is not shown because its predicted biomass is nearly identical 

to that of the equation of Gholz et al. (1979) for this DBH range. -VC = without vegetation control; +VC = with vegetation control.
12

RESEARCH PAPER PNW-RP-591

relationships between DBH and component biomass were less similar, indicating 

a difference in partitioning of biomass (fig. 2). The relationship between DBH and 

branch biomass as well as that between DBH and foliar biomass differed toward the 

high end of the DBH range; equations developed in other studies underestimated 

branch and foliar biomass of Fall River trees. Conversely, previously published relationships between DBH and bole biomass, particularly those of Gholz et al. (1979), 

overestimated bole biomass at Fall River. The trend of greater proportional allocation of biomass to the bole, rather than to foliage and branches (fig. 2) (Gholz et al. 

1979, Standish et al. 1985), may be associated with the fact that equations developed 

in these other studies included older trees, likely from stands at later developmental 

stages with greater intraspecific competition. These differences in site and management influence tree allometry, including height: diameter ratio and crown depth. 

Using data from many of the same Douglas-fir biomass studies referenced here 

(table 4; appendix, figs. 5 and 6), St. Clair (1993) demonstrated that, as intraspecific 

competition for light increases over time in young stands, the receding of tree 

crowns results in a higher proportion of biomass allocated to the bole.

The differences in allometry between trees in this study and those of previous 

studies (fig. 2) may also be associated with relatively high levels of belowground 

resource availability at the Fall River study site (i.e., high available N and soil 

water; Ares et al. 2007a, Roberts et al. 2005). As water becomes increasingly 

growth limiting, trees allocate less C to production of new foliage (Gholz 1982, 

Gower et al. 1992); similarly, availability of nutrients such as N is positively correlated with leaf area index (Gower et al. 1992, Myrold et al. 1989). In our study, 

the presence of vegetation control produced greater leaf area at year 5 (Peterson 

et al. 2008), attributable, at least in part, to greater belowground resource availability (Ares et al. 2007a, Roberts et al. 2005). Conversely, Feller (1992) found that 

Douglas-fir on low-productivity sites had significantly more bole biomass than trees 

of the same DBH on better quality sites. A direct site-quality comparison between 

our site and the sites from which the other equations in figure 2 were derived is not 

possible, as all of the other studies sampled trees from a variety of sites, including low-quality sites. Thus, the differences in allometric equations between our 

study and earlier studies are likely associated with, at least in part, differences in 

belowground resource availability, developmental stage, or relative stand density 

(e.g., Reineke Stand Density Index) (Reineke 1933). Additionally, these factors may 

interact, as faster tree growth potentially decreases the age at which intraspecific 

competition begins.
13

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

Table 4—Published equations for predicting component and total-tree dry biomass of individual 

Douglas-fir trees based only on diameter at breast height (DBH)

Sampled trees

Source DBH Number Site information

Centimeters

Gholz et al. (1979) 2–162 85 Various sites in coastal Washington and Oregon; sites 

 ranged from low to high quality

Grier et al. (1984) 9–30 26 A 23-year-old plantation; site class III; precommercially 

 thinned at year 11

Espinosa Bancalari 10–20 40 Three 22-year-old stands; “low, medium, and fast growing;”

 and Perry (1987) stands were thinned

Feller (1992) / 5–64 43 Sampled codominant trees on a wide range of sites

 Standish et al. (1985)a

 throughout British Columbia

Feller (1992) 5–56 10 Near Port Alberni, Vancouver Island, British Columbia; 

 “high site quality” and “high mineral nitrogen;” dominant 

 and codominant trees

St. Clair (1993) 9–26 240 An 18-year-old plantation; class I site

Jenkins et al. (2003) 2–210 165b Used data from nearly all previously published equations,

 representing a wide range in geographic location and 

 site quality

Harrison et al. (2009) 15–80 31 Sampled stand was adjacent to the study reported here; 

 stand age approximately 47 years; precommercially

 thinned and fertilized

a Ung et al. (2008) published biomass equations apparently derived from the same data set.

b Data points were pseudodata derived from published equations (Jenkins et al. 2003).

Estimated aboveground tree biomass, C, and N content per hectare—

Estimated year-11 tree biomass, measured N concentration, and estimated C and 

N content per hectare are shown in table 5. The presence of vegetation control was 

associated with significant increases in year-11 per-hectare biomass of 22, 26, 20, 

and 23 percent for foliar, branch, bole, and total-tree estimates, respectively. Because 

N and C concentrations (C not shown) did not differ between treatments, the treatment differences in estimated per-hectare N and C content were proportional to 

those for biomass. For total aboveground tree biomass, early vegetation control 

resulted in an additional 70 ± 6 kg•N•ha-1 and 8.2 ± 0.8 Mg•C•ha-1 at year 11.

Year-11 estimated biomass with and without vegetation control was 89.7 and 

73.2 Mg•ha-1, respectively; by contrast, year-5 biomass in these treatments was 7.5 

and 3.1 Mg•ha-1 (Devine et al. 2011). Biomass of the previous stand on the same 

site, harvested at age 47, was 394.9 Mg•ha-1 (Harrison et al. 2009). Compared to 

The presence of 

vegetation control 

was associated with 

significant increases 

in year-11 per-hectare 

biomass.
14

RESEARCH PAPER PNW-RP-591

Table 5—Estimated biomass, nitrogen (N), and carbon (C) per hectare, and N 

concentrations, for Douglas-fir trees at plantation age 11 years with (+VC) and 

without (-VC) 5 years of vegetation controla

Treatment

Tree component +VC -VC Pr > Fb

- - - - - Biomass (Mg • ha-1) - - - - -

Foliage 15.4 ± 0.4 12.6 ± 0.4 <0.001

Branches 29.8 ± 0.7 23.6 ± 0.8 <0.001

Bole 44.4 ± 1.0 36.9 ± 1.0 <0.001

Total aboveground 89.7 ± 2.1 73.2 ± 2.1 <0.001

- - - - - - - - N (g • kg-1) - - - - - - - -

Foliage 11.5 ± 0.1 11.6 ± 0.1 0.700

Branches 4.0 ± 0.3 3.7 ± 0.4 0.203

Bole 0.7 ± 0 0.7 ± 0.1 0.709

- - - - - - - - - N (kg • ha-1) - - - - - - 

Foliage 177 ± 4 146 ± 4 <0.001

Branches 119 ± 3 86 ± 3 <0.001

Bole 30 ± 1 24 ± 1 <0.001

Total aboveground 326 ± 8 256 ± 8 <0.001

- - - - - - - C (Mg • ha-1) - - - - - - -

Foliage 7.7 ± 0.2 6.3 ± 0.2 <0.001

Branches 14.6 ± 0.4 11.6 ± 0.4 <0.001

Bole 21.4 ± 0.5 17.7 ± 0.5 <0.001

Total aboveground 43.7 ± 1.0 35.5 ± 1.0 <0.001

Note: branch and bole values include both wood and bark. a Biomass was estimated by applying the equations shown in figure 2 and table 2 to estimates of year-11 diameter 

at breast height for all study trees; C and N concentrations and estimates were based on samples from each of 

the 26 trees on which the biomass equations were based. Significance of the treatment effect is shown for each 

component. Data have been corrected for log bias.

b Pr > F = P-value from analysis of variance; values <0.05 indicate a significant difference between treatments.

studies that have assessed aboveground biomass in mature Douglas-fir plantations 

(e.g., Acker et al. 2002, Harrison et al. 2009, Keyes and Grier 1981, Mitchell et al. 

1996, Ranger et al. 1995), relatively few studies have estimated biomass of younger 

(≤30 years) plantations, although such information is necessary to validate models 

of stand-level biomass or C accumulation and within-tree allocation. Nine-year-old 

(unthinned) and 19-year-old (thinned) Douglas-fir plantations in the Netherlands 

had 33 and 89 Mg•ha-1, respectively (Bartelink 1996). Three thinned, 22-year-old 

Douglas-fir plantations, differing in site quality, ranged in aboveground biomass 

from 99 to 203 Mg•ha-1 (Espinosa Bancalari and Perry 1987). Trees in 23-yearold plantations represented 58 and 258 Mg•ha-1 on sites of low and high fertility, 

respectively (Binkley 1983), and tree biomass in a 30-year-old plantation (class IV) 

was 169 Mg•ha-1 (Turner and Long 1975). The variability in biomass accumulation among these studies, and the fact that biomass in our 11-year-old plantation 
15

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

is relatively high by comparison, underscores the need for biomass data on highly 

productive sites to validate modeling efforts.

Allocation of estimated year-11 tree biomass among tree components was 

similar between treatments. For foliar, branch, and bole components, allocation was 

17, 32, and 51 percent in the -VC treatment, respectively, and 17, 33, and 50 percent 

in the +VC treatment. There was no relationship between tree size and allocation of 

biomass among the three measured components. The allocation of foliar and branch 

biomass by bole segment followed slightly different trends among treatments, 

although these trends were not statistically significant (fig. 3).

Objective 2: Compare Biomass Estimates From Objective 1 

to Estimates Made By Using Published Equations From 

Other Studies

In table 6, we compare our biomass estimates from objective 1 to estimates made 

using previously published equations that were developed using trees spanning the 

range of DBH present at our site. Total-tree estimates based on these previously 

published equations varied from 8 percent less to 23 percent greater than the estimates based on our site-specific biomass equations. The total-tree equation of Feller 

(1992), using the data set of Standish et al. (1985), produced estimates closest to our 

site-specific equation. The other three previously published equations (Feller 1992, 

Gholz et al. 1979, Jenkins et al. 2003) each overestimated total-tree biomass by 20 

percent or more. Estimated biomass, by DBH class, is shown for these equations 

in the appendix (fig. 7). For component biomass estimates, the differences between 

our equations and those published for other sites were more variable. The greatest 

difference was the overestimation of bole biomass when the Gholz et al. (1979) 

equation was applied to the Fall River trees. The differences in biomass estimates 

are a result of differences in tree allometry among studies that were discussed under 

objective 1. The need for site-specific equations depends on study or management 

objectives, and differences in estimates between our equation and the published 

equations may be acceptable in some situations. However, the biomass estimate 

differences of greater than 20 percent between our site-specific equations and those 

using the equations of Gholz et al. (1979) and Jenkins et al. (2003) indicate that 

these DBH-based equations constructed from regional data were not well suited to 

our study trees. It is possible that regional biomass equations including additional 

variables, such as total height, would better account for site-related differences in 

tree morphology.

Total-tree estimates 

based on these 

previously published 

equations varied from 

8 percent less to 23 

percent greater than 

the estimates based 

on our site-specific 

biomass equations.
16

RESEARCH PAPER PNW-RP-591

Figure 3—Distribution of branch (A), branch + foliar (B), and foliar biomass (C) among bole segments at various heights for 13 trees without vegetation control (-VC; dashed line) and with vegetation control (+VC; solid line) treatments. Points represent the midpoint of each segment. Note that 

length of bole segments was not predetermined; it was influenced by logistical constraints of the field 

sampling procedure and was typically between 1.5 and 3 m.
17

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

Table 6—Estimated biomass per hectare for Douglas-fir trees at Fall River, 

plantation age 11 years, with (+VC) and without (-VC) 5 years of vegetation 

controla

Treatment

Tree component / equation +VC -VC

- - - - - - - - Biomass (Mg•ha-1) - - - - - - - -

Foliage:

 Fall River, year 11 15.4 ± 0.4 12.6 ± 0.4

 Gholz et al. 1979 7.9 (-49%) 6.9 (-45%)

 Feller 1992 / Standish et al. 1985b 13.4 (-13%) 11.8 (-6%)

 Feller 1992 13.2 (-14%) 12.0 (-5%)

Branches:

 Fall River, year 11 29.8 ± 0.7 23.6 ± 0.8

 Gholz et al. 1979 15.4 (-48%) 13.1 (-44%)

 Feller 1992 / Standish et al. 1985 17.1 (-43%) 14.6 (-38%)

 Feller 1992 26.5 (-11%) 22.8 (-3%)

Bole:

 Fall River, year 11 44.4 ± 1.0 36.9 ± 1.0

 Gholz et al. 1979 84.6 (+91%) 68.5 (+86%)

 Feller 1992 / Standish et al. 1985 51.8 (+17%) 41.1 (+11%)

 Feller 1992 67.9 (+53%) 53.4 (+45%)

Total-tree biomass:

 Fall River, year 11 89.7 ± 2.1 73.2 ± 2.1 

 Gholz et al. 1979 107.9 (+20%) 88.5 (+21%)

 Feller 1992 / Standish et al. 1985c 82.3 (-8%) 67.6 (-8%)

 Feller 1992 107.6 (+20%) 88.3 (+21%)

 Jenkins et al. 2003d 109.6 (+22%) 89.7 (+23%)

a Estimates were based on equations developed from on-site trees (means with one standard error shown) and on 

previously published equations (means with percent divergence from the Fall River equation value). Estimates 

were calculated using correction for log bias.

b Equation published in Feller (1992), derived from data published by Standish et al. (1985).

c Ung et al. (2008) published biomass equations apparently derived from the same data set. Because estimates 

using the equations of Ung et al. (2008) were nearly identical to these, they are not presented here.

d Equation for total-tree biomass only; no equations available for component biomass.

Objective 3: Estimate Biomass By Using the Mean Tree Method

Using the slope of the equation from Jenkins et al. (2003), we estimated that the 

tree of mean biomass (the “mean tree”) had a DBH of 14.328 cm. We sampled a 

randomly selected tree of 14.3 cm DBH, and measured its weight: 71.7 kg. Based 

on a year-10 stand density of 1,490 trees ha-1, our estimated biomass using the 

mean tree method was 106.9 Mg•ha-1. This is 19.2 percent greater than the biomass 

estimate using the allometric approach of objective 1 (89.7 Mg•ha-1). There are 

two primary sources of error that could have caused our estimate to be high: (1) an 

incorrect calculation of the mean-tree DBH, and (2) the tree sampled deviated from 

the calculated relationship between DBH and total-tree biomass (i.e., the data point 

was well off the curve).
18

RESEARCH PAPER PNW-RP-591

Could there have been a substantial error in our calculation of mean-tree DBH? 

In this application of the method, we made the assumption that we did not know the 

allometric relationship between DBH and biomass, and therefore selected the most 

appropriate allometric equation from the literature (Jenkins et al. 2003) from which 

to derive a weighting factor. To evaluate how the calculated mean-tree DBH would 

have differed if we had instead used a site-specific weighting factor, we recalculated 

the mean-tree DBH using the weighting factor from our allometric equation developed under objective 1 (table 2). The result was a mean-tree DBH of 14.320 cm; for 

practical purposes, this is no different than the mean-tree DBH of 14.328 cm that 

we derived using the equation of Jenkins et al. (2003). Thus, it is unlikely that our 

calculation of mean-tree DBH was the source of the discrepancy between our meantree biomass estimate and the biomass estimate of objective 1.

To explore the influence of selecting different weighting factors from published 

equations, we then recalculated mean-tree DBH using weighting factors of equations (for Douglas-fir of a DBH range similar to the trees at Fall River) that were 

most different from that of Jenkins et al. (2003) (shown in the appendix, figs. 5 and 

6). The equation of St. Clair (1993) had the shallowest slope (i.e., smallest weighting factor, 2.2985) and produced a mean-tree DBH estimate of 14.291. That of 

Espinosa Bancalari and Perry (1987) had the steepest slope (i.e., largest weighting 

factor, 2.8427) and produced a mean-tree DBH estimate of 14.399. Assuming DBH 

is measured to the nearest 0.1 cm, only the latter equation would have resulted in 

a different mean-tree DBH (i.e., 14.4 cm rather than the 14.3 cm calculated using 

Jenkins et al. (2003)).

We next compared our method of calculating mean-tree DBH with a commonly 

used method: selecting the tree of mean basal area. The mean-tree DBH calculated 

using mean basal area (14.228 cm) differed only slightly from that calculated using 

our site-specific weighting factor from objective 1 (14.328 cm). However, applying 

the allometric equation from objective 1 to these two DBH values shows that the 

estimated difference in biomass between these trees is 1.4 kg, or 1.7 percent of totaltree weight. Thus, a difference of 0.1 cm in the DBH of the mean tree could potentially add a similar amount of error (1.7 percent) to a stand-level biomass estimate.

Based on the above calculations, we concluded that the mean-tree method’s 

19.2 percent overestimation of per-hectare biomass, compared to the allometric 

method, was likely a result of sampling a mean tree that deviated from the site’s 

DBH-biomass regression line. To assess this possibility, we used the allometric 

equation from objective 1 to calculate the hypothetical biomass of a tree equal 

to our calculated mean-tree DBH (14.328 cm). This “perfect mean tree” would 
19

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

have had a biomass of 59.5 kg. The tree that we actually sampled (71.7 kg) was 

20.5 percent greater in biomass than the perfect mean tree. If we had sampled the 

perfect mean tree, our per-hectare biomass estimate using the mean tree method 

would have been 88.7 Mg, only 1.0 Mg less (1.1 percent) than our estimate using the 

allometric method of objective 1. Thus, we can conclude that the vast majority of 

the discrepancy between the biomass estimates of objective 1 and objective 3 was 

associated with our selecting a single mean tree that deviated significantly from the 

measured DBH-biomass regression line. Our selection of the mean tree was based 

only on DBH, and it is certainly possible that mean-tree selection using estimated 

stem volume (requiring height and diameter information) would have resulted in 

selection of a more representative mean tree.

Our example of the mean-tree approach was based on a single-tree sample; in 

practice, estimates using this approach would likely sample multiple mean trees and 

average their biomass, likely resulting in a more representative mean-tree biomass 

value. Sampling of multiple mean trees could also be used to estimate the number 

of mean trees needed to estimate mean tree biomass with a given degree of accuracy and confidence. Our single-tree sample produced a stand biomass estimate that 

diverged from the allometric method estimate by approximately the same amount 

(19 percent) as the estimates based on regional equations (20 to 23 percent; Gholz 

et al. 1979, Jenkins et al. 2003). Therefore, biomass estimation for this stand using a 

regional equation would be similarly accurate and less labor-intensive than a singletree sample using the mean-tree approach.

Conclusions

In contrast to the year-5 DBH-based biomass equations (Petersen et al. 2008), year11 equations did not differ between the vegetation control treatments. Thus, treatment effects on allometry, specifically the relationship between DBH and biomass 

of bole, foliage, branches, and total tree, diminished significantly during the 6-year 

interval. Although tree morphology in these two treatments appears to have largely 

converged at year 11, tree size and plot-level biomass remain significantly higher in 

the treatment that received 5 years of vegetation control.

Our biomass equations, particularly the component biomass equations, differed 

from previously published equations for Douglas-fir, which, for the larger diameter 

trees, would have overestimated bole biomass and underestimated branch and foliar 

biomass. These differences between the allometric relationships in our study and 

those described by the biomass equations of other studies were likely a result of 

differences in intraspecific competition associated with relative stand density, or 

availability of belowground resources.
20

RESEARCH PAPER PNW-RP-591

Plot-level aboveground tree biomass estimates using our biomass equations 

differed from estimates made with previously published equations by -8 to +23 

percent. Component biomass estimates differed by as much as 91 percent. The 

published equations producing biomass estimates most different from ours included 

those of Gholz et al. (1979) and Jenkins et al. (2003), which were equations developed from large, regional data sets. These two sets of equations may not be well 

suited for estimating biomass of young plantations on highly productive sites, which 

are apparently atypical of sites from which these earlier equations were developed. 

Our application of the mean-tree method illustrates the danger of relying on 

a single-tree sample to estimate stand-level biomass, even in a relatively uniform 

plantation. Sampling multiple trees of the mean-tree diameter would likely have 

increased the accuracy of our biomass estimate. If the mean-tree approach is used 

to estimate biomass of young Douglas-fir, our results support the use of a weighting 

factor from a previously published biomass equation, rather than using individualtree basal area to calculate mean-tree DBH. Although we do not know the true 

stand biomass in our study, we found that using a weighting factor from a relevant 

published equation would likely produce a biomass estimate more similar to the 

results of the allometric method.

Acknowledgments

This study is a product of the Sustainable Forestry Component of Agenda 2020, 

a joint effort of the U.S. Department of Agriculture, Forest Service, Research and 

Development and the American Forest and Paper Association. The authors gratefully 

acknowledge the financial support provided by the National Council for Air and 

Stream Improvement, Inc., the Northwest Advanced Renewables Alliance, and the 

Pacific Northwest Stand Management Cooperative. The study site and support for 

experimental treatments were provided by Weyerhaeuser NR Company; the authors 

give particular thanks to Rodney Meade and Glenn Cattnach. We are grateful for 

support from the University of Washington School of Forest Resources and the 

USDA Forest Service Pacific Northwest Research Station. We are grateful for study 

installation and data collection assistance from many employees of these institutions.

Our application of the 

mean-tree method 

illustrates the danger 

of relying on a singletree sample to estimate 

stand-level biomass, 

even in a relatively 

uniform plantation.
21

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

Literature Cited

Acker, S.A.; Halpern, C.B.; Harmon, M.E.; Dyrness, C.T. 2002. Trends in bole 

biomass accumulation, net primary production and tree mortality in Pseudotsuga 

menziesii forests of contrasting age. Tree Physiology. 22: 213–217.

Ares, A.; Terry, T.; Harrington, C.; Devine, W.; Peter, D.; Bailey, J. 2007a.

Biomass removal, soil compaction, and vegetation control effects on five-year 

growth of Douglas-fir in coastal Washington. Forest Science. 53(5): 600–610.

Ares, A.; Terry, T.A.; Piatek, K.B. [et al.]. 2007b. The Fall River Long-Term 

Site Productivity study in coastal Washington: site characteristics, experimental 

design, and biomass, carbon and nitrogen stores before and after harvest. Gen. 

Tech. Rep. PNW-GTR-691. Portland, OR: U.S. Department of Agriculture, 

Forest Service, Pacific Northwest Research Station. 85 p.

Attiwill, P.M.; Ovington, J.D. 1968. Determination of forest biomass. Forest 

Science. 14(1): 13–15.

Bartelink, H. 1996. Allometric relationships on biomass and needle area of 

Douglas-fir. Forest Ecology and Management. 86(1–3): 193–203.

Binkley, D. 1983. Ecosystem production in Douglas-fir plantations: interaction of 

red alder and site fertility. Forest Ecology and Management. 5: 215–227.

Devine, W.D.; Harrington, T.B.; Terry, T.A.; Harrison, R.B.; Slesak, R.A.; 

Peter, D.H.; Harrington, C.A.; Shilling, C.J.; Schoenholtz, S.H. 2011. Fiveyear vegetation control effects on aboveground biomass and nitrogen content and 

allocation in Douglas-fir plantations on three contrasting sites. Forest Ecology 

and Management. 262: 2187–2198.

English Equivalents

When you know: Multiply by: To find:

Millimeters (mm) 0.0394 Inches 

Centimeters (cm) 0.394 Inches

Meters (m) 3.28 Feet

Hectares (ha) 2.47 Acres 

Kilometers (km) 0.621 Miles

Square meters (m2) 10.76 Square feet 

Kilograms (kg) 2.205 Pounds

Megagrams (Mg) 1.102 Tons

Square meters per hectare (m2/ha) 4.37 Square feet per acre

Trees per hectare .405 Trees per acre

Degrees Celsius (°C) 1.8 °C + 32 Degrees Fahrenheit
22

RESEARCH PAPER PNW-RP-591

Espinosa Bancalari, M.A.; Perry, D.A. 1987. Distribution and increment of 

biomass in adjacent young Douglas-fir stands with different early growth rates. 

Canadian Journal of Forest Research. 17(7): 722–730.

Feller, M.C. 1992. Generalized versus site-specific biomass regression equations 

for Pseudotsuga menziesii var. menziesii and Thuja plicata in coastal British 

Columbia. Bioresource Technology. 39(1): 9–16.

Gholz, H.L. 1982. Environmental limits on aboveground net primary production, 

leaf area and biomass in vegetation zones of the Pacific Northwest. Ecology. 

63: 469–481.

Gholz, H.L.; Grier, C.C.; Campbell, A.G.; Brown, A.T. 1979. Equations for 

estimating biomass and leaf area of plants in the Pacific Northwest. Research 

Paper 41. Corvallis, OR: Oregon State University, Forest Research Laboratory. 

39 p.

Gower, S.T.; Vogt, K.A.; Grier, C.C. 1992. Carbon dynamics of Rocky Mountain 

Douglas-fir: influence of water and nutrient availability. Ecological Monographs. 

62(1): 43–65.

Grier, C.C.; Lee, K.M.; Archibald, R.M. 1984. Effect of urea fertilization on 

allometric relations in young Douglas-fir trees. Canadian Journal of Forest 

Research. 14: 900–904.

Harrison, R.; Terry, T.; Licata, C.; Flaming, B.; Meade, R.; Guerrini, 

I.; Strahm, B.; Xue, D.; Lolley, M.; Sidell, A. 2009. Biomass and stand 

characteristics of a highly productive mixed Douglas-fir and western hemlock 

plantation in coastal Washington. Western Journal of Applied Forestry. 24(4): 

180–186.

Helgerson, O.T.; Cromack, K.; Stafford, S.; Miller, R.E.; Slagle, R. 1988.

Equations for estimating aboveground components of young Douglas-fir and 

red alder in a coastal Oregon plantation. Canadian Journal of Forest Research. 

18(8): 1082–1085.

Henderson, J.A.; Peter, D.H.; Lesher, R.D.; Shaw, D.C. 1989. Forested plant 

associations of the Olympic National Forest. Ecol. Tech. Pap. R6-ECOLTP-001-88. Portland, OR: U.S. Department of Agriculture, Forest Service, 

Pacific Northwest Region. 502 p.

Jenkins, J.C.; Chojnacky, D.C.; Heath, L.S.; Birdsey, R.A. 2003. National-scale 

biomass estimators for Unites States tree species. Forest Science. 49(1): 12–35.
23

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

Jenkins, J.C.; Chojnacky, D.C.; Heath, L.S.; Birdsey, R.A. 2004.

Comprehensive database of diameter-based biomass regressions for North 

American tree species. Gen. Tech. Rep. NE-319. Newtown Square, PA: U.S. 

Department of Agriculture, Forest Service, Northeastern Research Station. 45 p.

Jolly, N.W. 1950. The volume line theory in relation to the measurement of the 

standing volume of a forest (with particular reference to Pinus radiata). Adelaide, 

Australia: Woods and Forests Department, University of Adelaide. 37 p.

Keyes, M.R.; Grier, C.C. 1981. Above- and below-ground net production in 

40-year-old Douglas-fir stands on low and high productivity sites. Canadian 

Journal of Forest Research. 11(3): 599–605.

King, J.E. 1966. Site index curves for Douglas-fir in the Pacific Northwest. 

Weyerhaeuser Forestry Paper no. 8. Centralia, WA: Forestry Research Center, 

Weyerhaeuser Co.

Matejovic, I. 1995. Total nitrogen in plant material determinated by means of 

dry combustion: a possible alternative to determination by Kjeldahl digestion. 

Communications in Soil Science and Plant Analysis. 26(13–14): 2217–2229.

Mitchell, A.K.; Barclay, H.J.; Brix, H.; Pollard, D.F.W.; Benton, R.; deJong, 

R. 1996. Biomass and nutrient element dynamics in Douglas-fir: effects of 

thinning and nitrogen fertilization over 18 years. Canadian Journal of Forest 

Research. 26: 376–388.

Myrold, D.D.; Matson, P.A.; Peterson, D.L. 1989. Relationships between soil 

microbial properties and aboveground stand characteristics of conifer forests in 

Oregon. Biogeochemistry. 8: 265–281.

Petersen, K.S.; Ares, A.; Terry, T.A.; Harrison, R.B. 2008. Vegetation 

competition effects on aboveground biomass and macronutrients, leaf area, and 

crown structure in 5-year old Douglas-fir. New Forests. 35(3): 299–311.

Powers, R.F.; Scott, D.A.; Sanchez, F.G.; Voldseth, R.A.; Page-Dumroese, D.; 

Elioff, J.D.; Stone, D.M. 2005. The North American long-term soil productivity 

experiment: findings from the first decade of research. Forest Ecology and 

Management. 220(1–3): 31–50.

Ranger, J.; Marques, R.; Colin-Belgrand, M.; Flammang, N.; Gelhaye, D. 

1995. The dynamics of biomass and nutrient accumulation in a Douglas-fir 

(Pseudotsuga menziesii Franco) stand studied using a chronosequence approach. 

Forest Ecology and Management. 72(2–3): 167–183.
24

RESEARCH PAPER PNW-RP-591

Reineke, L.H. 1933. Perfecting a stand density index for even-aged stands. Journal 

of Agricultural Research. 46: 627–638.

Roberts, S.D.; Harrington, C.A.; Terry, T.A. 2005. Harvest residue and 

competing vegetation affect soil moisture, soil temperature, N availability, and 

Douglas-fir growth. Forest Ecology and Management. 205(1–3): 333–350.

St. Clair, J.B. 1993. Family differences in equations for predicting biomass and 

leaf area in Douglas-fir (Pseudotsuga menziesii var. menziesii). Forest Science. 

39(4): 743–755.

SAS Institute. 2005. The SAS system: SAS OnlineDoc®, Version 9.1, HTML 

format [CD-ROM]. Cary, NC.

Schreuder, H.T.; Gregoire, T.G.; Wood, G.B. 1993. Sampling methods for 

multiresource forest inventory. New York: Wiley. 464 p.

U.S. Department of Agriculture, Natural Resources Conservation Service 

[USDA NRCS]. 1999. Soil taxonomy, a basic system of soil classification 

for making and interpreting soil surveys. 2nd ed. Agric. Handb. No. 436. 

Washington, DC.

Sokal, R.R.; Rohlf, F.J. 1995. Biometry. 3rd ed. New York: W.H. Freeman and 

Company. 880 p.

Standish, J.T.; Manning, G.H.; Demaerschalk, J.P. 1985. Development of 

biomass equations for British Columbia tree species. Information Report BCX-264. Victoria, Canada: Pacific Forest Research Centre, Ministry of State for 

Forestry, Agriculture Canada. 48 p. 

Turner, J.; Long, J.N. 1975. Accumulation of organic matter in a series of 

Douglas-fir stands. Canadian Journal of Forest Research. 5: 681–690.

Ung, C.-H.; Bernier, P.; Guo, X.-J. 2008. Canadian national biomass equations: 

new parameter estimates that include British Columbia data. Canadian Journal of 

Forest Research. 38: 1123–1132.
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Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

Appendix

Table 7—Data from 26 Douglas-fir trees from the Fall River Long-Term Site 

Productivity study sampled at plantation age 11 yearsa

Treatment/

Biomass

tree no. DBH Height Bole Branch Foliage Total

Centimeters Meters - - - - - - - - - - - - Kilograms - - - - - - - - - - - -

+VC

30843 8.3 7.32 8.36 4.14 3.17 15.67

22751 9.0 8.42 11.10 6.05 3.13 20.28

22466 10.6 9.05 15.04 8.36 4.15 27.55

27901 12.5 8.60 24.48 14.34 6.60 45.43

25513 13.2 9.96 24.24 14.79 8.37 47.41

30987 13.6 9.37 28.41 17.87 8.37 54.66

27851 14.3 9.89 32.77 27.17 11.80 71.74

27910 14.6 9.72 32.11 24.64 12.46 69.22

30841 14.6 9.55 30.24 20.39 10.08 60.71

22621 14.7 10.20 34.18 16.18 9.61 59.96

25343 15.4 10.14 32.11 23.35 11.78 67.23

25350 15.6 10.15 32.87 29.52 11.37 73.77

22627 16.8 10.77 39.65 26.79 12.49 78.92

-VC

30596 9.0 7.47 10.11 6.03 4.17 20.30

27364 11.1 8.93 15.39 8.77 5.11 29.27

27370 11.5 9.03 19.18 8.84 4.82 32.84

27253 11.7 10.02 18.27 8.39 4.69 31.35

22387 12.1 8.92 17.54 13.70 6.94 38.18

22219 12.6 10.44 22.65 9.50 6.39 38.54

30601 12.7 9.86 22.20 13.77 8.33 44.30

30670 12.9 9.84 24.97 18.16 9.73 52.86

30682 14.2 9.85 30.82 15.48 10.98 57.28

22329 15.6 11.91 41.63 19.04 11.90 72.56

25207 15.6 8.73 30.29 24.95 9.73 64.98

25097 16.8 11.13 45.70 40.64 19.39 105.74

25107 17.6 11.20 48.75 34.13 24.38 107.26

a Treatments were 5 years of intensive vegetation control (+VC) or no vegetation control (-VC).

DBH = diameter at breast height.
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RESEARCH PAPER PNW-RP-591

Figure 4—Distribution of year-11 estimated diameter at breast height (DBH), by 1-cm DBH class, 

for all study trees. Treatments were: 5 years of intensive vegetation control (+VC) or no vegetation 

control (-VC).
27

Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

Figure 5—Relationships between total aboveground tree biomass and diameter at breast height (DBH) for Douglas-fir; lines are truncated according to the DBH range of the trees from which they were developed. A subset of these equations, which were developed from 

a DBH range encompassing that of the year-11 Fall River plantation, are shown in figure 2.
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RESEARCH PAPER PNW-RP-591

Figure 6—Relationships between total aboveground tree biomass and diameter at breast height (DBH) for Douglas-fir, showing 

only the range of DBH for the trees sampled in this study. Lines are truncated according to the DBH range of the trees from which 

they were developed. A subset of these equations, which were developed from a DBH range encompassing that of the year-11 Fall 

River plantation, are shown in figure 2.
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Estimating Tree Biomass, Carbon, and Nitrogen in Two Vegetation Control Treatments

Figure 7—Estimated total-tree aboveground biomass (Mg•ha-1), using four different equations, by 1-cm diameter at 

breast height (DBH) class for all year-11 Douglas-fir study trees in two vegetation control treatments.

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