United States 

Department of 

Agriculture

Forest Service

Pacific Southwest 

Research Station

Research Paper

PNW-RP-584

November 2009

Estimating Aboveground Tree 

Biomass on Forest Land in 

the Pacific Northwest: A 

Comparison of Approaches

Xiaoping Zhou and Miles A. Hemstrom
The Forest Service of the U.S. Department of Agriculture is dedicated to the principle of 

multiple use management of the Nation’s forest resources for sustained yields of wood, 

water, forage, wildlife, and recreation. Through forestry research, cooperation with the 

States and private forest owners, and management of the National Forests and National 

Grasslands, it strives—as directed by Congress—to provide increasingly greater service to 

a growing Nation.

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activities on the basis of race, color, national origin, age, disability, and where applicable, 

sex, marital status, familial status, parental status, religion, sexual orientation, genetic 

information, political beliefs, reprisal, or because all or part of an individual’s income 

is derived from any public assistance program. (Not all prohibited bases apply to all 

programs.) Persons with disabilities who require alternative means for communication of 

program information (Braille, large print, audiotape, etc.) should contact USDA’s TARGET 

Center at (202) 720-2600 (voice and TDD). To file a complaint of discrimination, write 

USDA, Director, Office of Civil Rights, 1400 Independence Avenue, SW, Washington, DC 

20250-9410 or call (800) 795-3272 (voice) or (202) 720-6382 (TDD). USDA is an equal 

opportunity provider and employer.

Authors 

Xiaoping Zhou is a forester and Miles A. Hemstrom is a research ecologist, 

Forestry Sciences Laboratory, P.O. Box 3890, Portland, OR 97208-3890.
Abstract

Zhou, Xiaoping; Hemstrom, Miles A. 2009. Estimating aboveground tree 

biomass on forest land in the Pacific Northwest: a comparison of approaches. 

Res. Pap. PNW-RP-584. Portland, OR: U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Research Station. 18 p. 

Live tree biomass estimates are essential for carbon accounting, bioenergy feasibility studies, and other analyses. Several models are currently used for estimating 

tree biomass. Each of these incorporates different calculation methods that may 

significantly impact the estimates of total aboveground tree biomass, merchantable 

biomass, and carbon pools. Consequently, carbon markets, bioenergy projects, and 

similar efforts may be affected. In addition to differences in allometric equations, 

the various methods are most suitable for particular geographic scales of analysis. 

We examine three approaches that might be used for midscale analyses (e.g., 

25,000 to several million acres) and compare the regional models with equations 

developed by Jenkins et al. and with the component ratio method (CRM). These 

three methods produce relatively similar estimates of total aboveground biomass 

for softwood species in Oregon, but substantially different estimates for the 

proportion of total biomass that is merchantable. For the major softwood species 

in Oregon, the total aboveground biomass using the CRM is 3 percent lower than 

estimates with regional equations, and the Jenkins models produce estimates that 

are 17 percent higher. However, on average, the proportion of softwood merchantable biomass computed with CRM is about 83 percent of the total aboveground 

biomass with little variation from species to species, whereas regional models 

estimate that 72 percent is merchantable, and the Jenkins equations estimate that 

78 percent is merchantable. 

Keywords: Biomass equations, Jenkins equations, component ratio method, 

forest inventory.

1

Estimating Aboveground Tree Biomass on Forest Land in the Pacific Northwest: A Comparison of Approaches

Introduction

Reasonable methods for estimating tree biomass and carbon stocks1 on forest land 

are increasingly important given concerns of global climate change, increasing 

interest in bioenergy projects, and carbon sequestration protocols for the voluntary 

and regulated markets. During the last two decades, scientists in the U.S. Department of Agriculture, Forest Service have put considerable effort into developing 

models for estimating tree biomass and carbon stock over areas as large as the 

entire United States. However, applying those broad-scale models to regional or 

fine-scale analyses can be challenging. For example, broad-scale estimates of 

merchantable tree biomass based on lumping many species may differ considerably 

from estimates made with more regionally representative models, and the potential 

success of a bioenergy project might hinge on these differences. Therefore, understanding the potential alternative approaches for estimating forest biomass is very 

important for local analyses of biomass supply and forest carbon accounting. We 

review some of the current methods of calculating aboveground live tree biomass 

that might be used in the Pacific Northwest and compare the differences when they 

are applied to Forest Inventory and Analysis (FIA) tree data in Oregon. The three 

most common softwood tree species were analyzed: Douglas-fir (Pseudotsuga 

menziesii (Mirb.) Franco), western hemlock (Tsuga heterophylla (Raf.) Sarg.), and 

ponderosa pine (Pinus ponderosa C. Lawson). 

Current Tree Biomass Calculation Methods Applied on 

Forest Land in United States

Various tree biomass calculation methods are applied on forest lands in the United 

States depending on scale of analysis, need for detail, user group interest, and 

purpose. The USDA Forest Service has used the Jenkins equation system (Jenkins 

et al. 2003, 2004) in recent years to assess national-scale biomass and for forest carbon estimates used in official greenhouse gas inventories of the United States (US 

EPA 2008). The Jenkins model was originally designed for national-scale biomass 

estimation, but the differences in equation forms and species groupings may cause 

differences at fine scales depending on tree size and forest species composition 

(Jenkins et al. 2003). Regional models are usually tree species-specific based on 

various local tree studies, and result in different biomass estimation models for 

1 In general, we calculate biomass to estimate carbon stock (C) and carbon dioxide ( CO2 ) 

emission equivalent: 1 unit of biomass = 0.5 unit carbon stored, and 1 unit carbon stored = 

3.67 units CO2 emission equivalent.
2

RESEARCH PAPER PNW-RP-584

different FIA regions.2 But the regional models lack consistent methodology and 

component definitions, which makes them difficult to use for national estimates. 

National consistency has become a prime concern within FIA (Hansen 2002). 

Therefore, the national forest resources report for the Resources Planning Act has 

used the component ratio method (CRM) to estimate tree biomass for consistency 

across regions, and the CRM approach will be applied to FIA tree data for future 

biomass reporting (Heath et al. 2008). The objective of CRM is to get national 

biomass and carbon estimates that are consistent with FIA tree volume estimates 

(Heath et al. 2008). However, these methods produce generalized biomass estimates 

when compared to more local and detailed allometric equations. Users should 

understand the differences between estimates made with broad-scale methods 

and equations compared to regional representative equations and choose methods 

appropriate to their questions and scale of use.

Live tree biomass is generally divided into five major components, including 

merchantable stem biomass (also called bole biomass including both bark and 

wood), stump biomass, foliage biomass, branches/top biomass, and root biomass. 

We focus on aboveground live tree biomass estimation including stump, stem, 

branch, and top. 

The Regional Approach

The regional volume and biomass models were developed specifically for regional 

tree species (Waddell and Hiserote 2005). In general, these equations were from 

published papers derived from local tree studies and are direct functions of tree 

diameter or both diameter and height. Different regions often pick different 

functions such as logarithmic vs. linear or quadratic forms to fit local tree species. 

The FIA Program in the Pacific Northwest Research Station uses separate sets of 

equations for bole, branch, and bark biomass. Tree bole biomass is scaled directly 

from volume estimates via species-specific wood density factors (USDA FS 1999). 

For example, the suite of equations for lodgepole pine in the Pacific Northwest 

region is: 

CVTS = 10-2.615591 + 1.847504 × log(dbh) + 1.085772 × log(HT)

 (Bracket 1977)

BOLE = (CVTS × Wd)

2 The Forest Inventory and Analysis (FIA) Program in the USA has four regional 

programs based on geographical locations: Northern, Southern, Rocky Mountain, 

and Pacific Northwest.

BRK = 3.2 + 9.1 × 



 





2 dbhcm

100

× HTm (Standish 1985)
3

Estimating Aboveground Tree Biomass on Forest Land in the Pacific Northwest: A Comparison of Approaches

BT = BOLE + BRK + BCH

where 

CVTS = total stem volume from ground to tip (cubic feet),

Wd = wood density (kg/ft3

),3

BOLE = bole biomass (kg),

BRK = bark biomass (kg),

BCH = branch biomass (kg),

BT = total aboveground biomass without foliage (kg)

dbh = diameter at breast height (in)

HT = total height from ground to the tip (ft)

dbhcm = diameter at breast height (cm) 

HTm = total height from ground to the tip (m) 

log is the logarithmic function with base 10.

Each tree species is associated with a set of local volume and biomass equations. Although the particular form of the equations may differ, the biomass calculation of major aboveground biomass components is similar to that for lodgepole pine 

species. Regional equations produce biomass estimates specific to each species and 

separated into major aboveground components. They are useful for people interested in detailed regional estimates and small to midscale studies. Although major 

tree species have separate equations by region or subregion, many minor species 

have no species-specific equations. In such cases, analysts commonly substitute 

the equations for species judged to have similar growth forms. In addition, regional 

equations may apply only to certain diameter ranges, so more than one bole equation may be needed for whole-tree estimates for a given species. Consequently, the 

estimation using regional equations is often fraught with idiosyncrasies and the 

need to reach ad hoc decisions on equation selection. Thus, there are concerns about 

the consistency of estimates among regions, even among trees of a given species. 

The Jenkins Model

The Jenkins model (Jenkins et al. 2003, 2004) was designed for national-level 

biomass estimation. It uses a set of equations for total aboveground biomass 

based on tree diameter. The components of tree biomass for merchantable stem 

wood, stem bark, foliage, and belowground (coarse root) biomass are calculated 

3 This mix of units allows conversion from volume in cubic feet to mass in kilograms.

BCH = 7.8 + 12.3 × 



 





2 dbhcm

100

× HTm (Standish 1985)
4

RESEARCH PAPER PNW-RP-584

as proportions of total aboveground biomass. Branch and stump biomass are 

calculated as a residual after subtracting stem and foliage biomass from total 

aboveground biomass. The Jenkins method was developed by refitting the data 

predicted from various equations found in the literature for different tree species 

that categorized into the same species group. For example, there are about 38 tree 

species in the pine species group, including ponderosa pine from the West, loblolly 

pine (Pinus taeda L.) from the South, and jack pine (Pinus banksiana Lamb.) 

from the East. Forty-three published equations for species in this group were used 

to produce the projection data that were refit into one equation for aboveground 

biomass with diameter as the only independent variable. The general form of the 

Jenkins et al. (2003) equations is: 

Bm = e

(b0 + b1 ln(dbhcm))

where 

Bm = total aboveground biomass (kg) for trees larger than 2.5 cm (1 in) in dbh, 

dbhcm = diameter in centimeter (cm) at breast height, and

b0, b1 = coefficients.

There are 10 aboveground biomass equations associated with 10 tree species 

groups for the United States, including 4 hardwood species groups, 5 softwood 

species groups, and 1 woodland group. The coefficients associated with each 

species group are listed in table 1. 

Because there were too few component-specific equations to use the projection 

data approach for each biomass component (e.g., bole, bark, and branches) in each 

of the above defined 10 species groups, component equations were first pooled into 

hardwood and softwood groups (Jenkins et al. 2003), and projection data were fit 

to a simple equation for each component for each of these two generalized species 

groups. This resulted in two sets of equations for estimating fractions (expressed as 

ratio) of foliage, stem bark, stem wood, and coarse roots in the form (Jenkins et al. 

2003):





 



 

 dbhcm

a a

Ratioi e

1 0

where 

Ratioi = ratio of i

th component (foliage, coarse roots, stem bark, or stem wood) 

 to total aboveground biomass for trees larger than 2.5 cm (1 in) dbh,

dbhcm = diameter (cm) at breast height, and

a0, a1 = regression coefficients. 
5

Estimating Aboveground Tree Biomass on Forest Land in the Pacific Northwest: A Comparison of Approaches

Table 1—Parameters for estimating total aboveground 

biomass for all hardwood and softwood species in the 

United States

Species groups b0 b1

Hardwood:

Aspen/cottonwood/willow -2.2094 2.3867

Soft maple/birch -1.9123 2.3651

Mixed hardwood -2.4800 2.4835

Hard maple/oak/hickory/beech -2.0127 2.4342

Softwood:

Cedar/larch -2.0336 2.2592

	 Douglas-fir	 -2.2304	 2.4435

	 True fir/hemlock	 -2.5384	 2.4814

Pine -2.5356 2.4349

Spruce -2.0773 2.3323

Woodland -0.7152 1.7029

Note: See “Species List” for scientific names.

Source: Jenkins et al. 2003

Bm = e

(b0 + b1 ln(dbhcm))

where 

Bm = total aboveground biomass (kg) for trees larger than 2.5 cm 

 (1 in) dbh, 

dbhcm = diameter (cm) at breast height, and

b0, b1 = coefficients.

The parameters for the component ratios were estimated analogously to how 

coefficients for total aboveground biomass were estimated (table 2).

There are two major concerns about the Jenkins model when it is used for finer 

scale analyses. First, the broad tree species groups may lead to biased biomass 

estimates for a specific tree species in a region when using the nationally averaged 

equation. For example, about 100 hardwood tree species from the East to the West 

are grouped into one hardwood group. Second, the equation only has diameter as 

an explanatory variable, and this fails to account for variation in stem taper. These 

concerns may cause difficulties if the Jenkins methods are used for midscale analyses. For example, because ponderosa pine in the Pacific Northwest is in the same 

group as loblolly pine from the South, the Jenkins equations would predict the same 

biomass for a ponderosa pine and loblolly pine tree with a common diameter even 

though they have significantly different stem forms and consequently quite different actual biomass for a given diameter. Although the Jenkins equations are simple 

and consistent in format across the Nation, they may not be sufficiently accurate for 

mid- to fine-scale analyses. 
6

RESEARCH PAPER PNW-RP-584

Table 2—Parameters for estimating 

component ratios of total aboveground 

biomass for hardwood and softwood 

species in the United States 

Species groups a0 a1

Hardwood:

Foliage -4.0813 5.8816

Coarse roots -1.6911 0.8160

Stem bark -2.0129 -1.6805

Stem wood -0.3065 -5.4240

Softwood:

Foliage -2.9584 4.4766

Coarse roots -1.5619 0.6614

Stem bark -2.0980 -1.1432

Stem wood -0.3737 -1.8055

Source: Jenkins et al. 2003.

where 

Ratioi = ratio of i

th component (foliage, coarse roots, 

 stem bark or stem wood) to total aboveground 

 biomass for trees larger than 2.5 cm (1 in) dbh,

dbhcm = diameter (cm) at breast height, and

a0, a1 = regression coefficients. 

The Component Ratio Method

The component ratio method for estimating aboveground live tree biomass has been 

proposed recently for consistent national projection of tree biomass based on the 

FIA volume estimates. Detailed calculation and examples are described in Heath 

et al. (2008). There are four major steps for the current CRM calculation for trees 

larger than 12.5 cm (5 in) dbh:

1. Calculate base components using Jenkins et al. methods (app. table 4) for 

total aboveground biomass, foliage, stem bark, and stem wood. The stump 

biomass is calculated using Raile’s approach (1982). The branch and top 

biomass are calculated by subtracting stem, stump, and foliage biomass 

from total aboveground biomass. 

2. Recast Jenkins et al. component biomass from step one as the ratio of 

Jenkins bole biomass for trees larger than or equal to 12.5 cm (5 in) (app. 

table 5, fig. 3). In this step, the proposed CRM will calculate the ratio of 

each component relative to merchantable stem (bark and wood) derived 

from Jenkins equations shown in step one: 





 



 

 dbhcm

a a

Ratioi e

1 0
7

Estimating Aboveground Tree Biomass on Forest Land in the Pacific Northwest: A Comparison of Approaches

Stump ratio: STPROP = STP/MST 

Foliage ratio: FLPROP = FOL/MST 

Branch/top ratio: BTPROP = BRT/MST 

Root ratio: RTPROP = RTS/MST 

where: 

MST is merchantable stem biomass based on Jenkins (kg), 

STP is stump biomass with bark based on Raile (kg),

FOL is foliage biomass based on Jenkins (kg),

BRT is branches/top biomass by subtraction based on Jenkins et al. (kg), and

RTS is root biomass based on Jenkins (kg).

3. Calculate component biomass for FIA-measured trees using FIA bole biomass multiplied by the ratios from step two for trees greater than or equal to 

12.5 cm (5 in) in diameter. The volume of sound wood4

 in the central stem 

(sound cubic-foot volume) for the measured FIA trees is used to estimate the 

merchantable stem woody biomass and then the component biomass. The 

components are calculated as follows:

Merchantable stem woody biomass (biomass of the bole): 

MSBIOFIA = VOLCFSND × Rbark × SpGbark × 62.4 + VOLCFSND × SpGwood × 62.4 

Stump biomass: STPBIOFIA = STPROP × MSBIOFIA

Foliage biomass: FOLBIOFIA = FLPROP × MSBIOFIA

Branches/top biomass: TOPBIOFIA = BTPROP × MSBIOFIA

Root biomass: RTSBIOFIA = RTPROP × MSBIOFIA

where: 

VOLCFSND is the volume of sound wood in cubic feet in FIA,

Rbark is the bark ratio on the bole for given species group (10 Jenkins species 

groups),

SpGbark is specific gravity of bark for a given species, 

SpGwood is specific gravity of wood for a given species, and 

62.4 = the pure water weight (lb/ft3).

4. Finally, the total aboveground dry biomass excluding foliage for trees with 

dbh larger than or equal to 5 in using CRM is estimated as: 

DRYBIOT_CRM = MSBIOFIA + STPBIOFIA + TOPBIOFIA 

4 The sound cubic-foot volume is the volume of a sample tree 5.0 in diameter or larger from 

a 1-ft stump to a minimum 4-in top diameter outside of bark (dob) or to where the central 

stem breaks into limbs all of which are less than 4.0 in dob. 
8

RESEARCH PAPER PNW-RP-584

Although this hybrid model appears promising in concept as currently used, its 

limitations resemble those of the Jenkins method when used for mid- and fine-scale 

analysis. In large part, this is because the method uses only the two sets of coefficients from the Jenkins method for component ratios. For example, the foliage 

component ratios will be the same for all species within softwood or hardwood 

groups for a given dbh. There are 10 stump ratio equations and 10 branch/top 

ratio equations corresponding to 10 Jenkins species groups for total aboveground 

biomass. However, the sum of the stump ratio and branch/top ratio collapse to two 

generic softwood and hardwood groups (appendix). The merchantable biomass ratio 

calculated with CRM will also be the same for all softwoods and all hardwoods 

even though they are based on the sound volumes from individually measured trees 

(see appendix for calculation details). 

Comparison of Biomass Estimates Using 

Measured Tree Data

Over 50 tree species contribute to total biomass and sound wood volume on FIA 

plots in Oregon. Douglas-fir, ponderosa pine, and western hemlock are the most 

abundant of those species. Douglas-fir contributes about 51 percent of total aboveground biomass of trees larger than 12.5 cm (5 in) dbh on forest land in Oregon, and 

western hemlock and ponderosa pine contribute around 8 percent each. Hardwoods 

contribute a relatively minor amount to aboveground live tree biomass statewide; 

more than 90 percent is from softwood species. 

The differences among biomass estimates using regional, Jenkins, and CRM 

methods become obvious when all three are used to estimate total live tree aboveground biomass and merchantable biomass of softwoods in Oregon (fig. 1, table 

3). Total aboveground biomass using CRM is about 3 percent lower than estimates 

with regional equations, whereas the estimates using Jenkins’ methods are 17 

percent higher than estimates using regional equations. The merchantable biomass 

from softwoods differs considerably using these three methods. Regional equations 

suggest that merchantable softwood biomass is about 72 percent of total live tree 

aboveground biomass (range 65 to 76 percent). The CRM approach predicts that 

about 83 percent of the total aboveground biomass is merchantable (81 to 83 percent 

range). Estimates from Jenkins’ equations are also considerably higher than those 

from regional equations, producing about 78 percent of total aboveground biomass 

in merchantable biomass (range 76 to 78 percent). 
9

Estimating Aboveground Tree Biomass on Forest Land in the Pacific Northwest: A Comparison of Approaches

0

10

20

30

40

50

60

70

80

90

100

Diameter group (inches)

Merchantable biomass (percent)

Regional Douglas-fir

Regional western hemlock

CRM softwoods Regional ponderosa 

Jenkins softwoods

5 to 7

7 to 9

9 to 11

11 to 13

13 to 15

15 to 17

17 to 19

19 to 21

21 to 29

29 plus

Table 3—Aboveground biomass for trees at least 5 inches dbh on forest land in Oregon by 

major species 

Regional Jenkins CRM Merch to total 

Species Total Merch Total Merch Total Merch Regional Jenkins CRM

- - - - - - - - - - - - - - Million tons - - - - - - - - - - - - - - - - - - - Percent - - - - - 

Douglas-fir 	 899	 684	 1,094	 858	 888	 738	 76	 78	 83

Ponderosa pine 153 104 190 148 148 122 68 78 83

Western hemlock 145 98 130 101 135 112 67 78 83

White fir	 74	 43	 81	 63	 62	 52	 58	 78	 83

Grand fir	 52	 37	 70	 54	 54	 44	 72	 78	 83

Mountain hemlock 50 35 62 48 48 40 70 78 83

Lodgepole pine 44 31 50 38 47 38 70 76 81

Other softwood 203 132 216 168 183 150 65 78 82

 Total softwood 1,620 1,164 1,893 1,478 1,565 1,296 72 78 83

Note: CRM = Component Ratio Method, merch = merchantable.

The ratio of merchantable to total aboveground biomass increases with diameter for all three methods. The ratios from CRM and Jenkins’ equations follow 

the same trajectory with little variation by softwood species trees across diameter 

classes (fig. 1). In fact, the component ratios are the same within the group containing all softwood species and within the group containing all hardwood species for a 

given diameter using the CRM approach (appendix). Conversely, the ratio changes 

significantly among species across diameter groups with regional equations.

Figure 1— Merchantable biomass as a percentage of total aboveground biomass without foliage in Oregon. 

CRM = component ratio method.
10

RESEARCH PAPER PNW-RP-584

Although the CRM estimates show the proportion of merchantable biomass 

to be the same for all the softwood species of a given diameter, estimates from 

regional equations indicate that merchantable biomass differs not only by species 

but also by subregion (fig. 2). For Douglas-fir, the proportion of merchantable biomass to total aboveground biomass in east-side Oregon is lower than the proportion 

in west-side Oregon because the tree forms and stem taper in these two subregions 

are quite different. 

0

10

20

30

40

50

60

70

80

90

100

Diameter group (inches)

Merchantable biomass (percent)

Regional equations, western Oregon

Regional equations, eastern Oregon

CRM Oregon

Jenkins Oregon

5 to 7

7 to 9

9 to 11

11 to 13

13 to 15

15 to 17

17 to 19

19 to 21

21 to 29

29 plus

Figure 2—Merchantable biomass as a percentage of total aboveground biomass without foliage for Douglas-fir, by 

subregion. CRM = component ratio method.

Merchantable biomass with CRM is derived from local merchantable volume. 

Consequently, one would expect the estimates of merchantable biomass to be 

similar or at least to parallel the trends with diameter, but they do not. Two major 

sources might contribute to the differences: (1) CRM uses uniform component 

ratios for softwood and hardwood developed from the Jenkins method over broad 

species groups and (2) 10 bark ratios are used in CRM for species across the United 

States, potentially leading to biases when applied to species in a smaller area. 

Discussion and Conclusion

Biomass estimates are critical for many landscape analysis questions, including 

carbon stock accounting and evaluating biomass potentially available to bioenergy 

projects. The three methods reviewed in this paper were developed for particular 

purposes and are applicable to different analysis scales. The Jenkins and the 
11

Estimating Aboveground Tree Biomass on Forest Land in the Pacific Northwest: A Comparison of Approaches

component ratio methods were targeted at broad-scale analyses across collections of 

states or the entire United States. At those scales, detailed information about differences among tree species and across smaller geographic areas may not be necessary 

for assessments of sufficient accuracy to address issues. In addition, the many equations used to calculate biomass locally are inconsistent, even for the same species, 

across larger areas. Unfortunately, these broad-scale methods may be used more 

generally to compute biomass at a variety of scales and may, at least in our example, 

produce biomass estimates that are significantly different from local estimates at 

least for some diameter classes.

We found, in fact, that both the Jenkins and CRM methods estimate higher 

merchantable biomass, especially in smaller diameter classes, compared to estimates made with regionally derived equations. Jenkins and CRM estimate about 11 

to 13 percent more merchantable volume for softwood biomass in Oregon than the 

regional equations. This difference may or may not be significant at the national 

scale, and to determine this would likely require a comprehensive comparison using 

hundreds of regional equations. However, the differences at local scale, for example 

as when analyzing the carbon dynamics of a proposed management regime on an 

ownership or watershed, or assessing a bioenergy project where profit margins are 

slim, could profoundly affect outcomes. We found that the Jenkins methods estimated about 17 percent more live tree aboveground softwood biomass and carbon 

stock in Oregon compared to that using regional equations, whereas CRM estimates 

were about 3 percent lower than regional estimates. It is unclear to what extent 

carbon flux assessed as stock change would be biased by the use of CRM.

Although it may be true that there is inconsistency of equation forms and 

component definitions among regions, the regional models use the results of local 

species studies and published equations, which will be more suitable for analyses of 

mid- and fine-scale landscapes. Although the Jenkins equations are very simple and 

easy to use, the results may be misleading when applied at fine scales. The CRM 

is a promising approach and may alleviate consistency problems associated with 

regional equations while providing refinement to the generalized Jenkins approach. 

However, the current CRM process uses homogeneous ratios for all softwoods and 

all hardwoods even though they use the locally estimated volumes. Given the highly 

variable form and taper of different tree species, this simplification overestimates 

biomass for some species and underestimates for others. Additional work to include 

more species and regional variability might considerably improve CRM results and 

could provide reasonable national-scale estimates while maintaining simplicity and 

consistency. In addition, analyses of biomass and carbon at the mid and fine scales 

(25,000 to several million acres) might better use locally derived biomass equations, 
12

RESEARCH PAPER PNW-RP-584

especially if the results will be used to evaluate bioenergy projects or carbon 

markets where differences of a few percentage points could be important.

Acknowledgments

This work was supported by funding from the USDA Forest Service, Pacific 

Northwest Research Station.

Metric Equivalents

When you know Multiply by: To get:

Acres (ac) 0.405 Hectares (ha)

Feet (ft) 0.305 Meters (m)

Cubic feet (ft3

) 0.0283 Cubic meters (m3)

Inches (in) 2.54 Centimeters (cm)

Pounds (lb) 0.454 Kilograms (kg)

Tons 0.907 Metric tonnes

Pounds per cubic foot (lb/ft3

) 16.02 Kilograms per cubic meter (kg/m3)

Species List

Common name Scientific name 

Aspen Populus grandidentata Michx

Beech Fagus L.

Birch Betula L.

Cedar Chamaecyparis Spach

Cottonwood Populus L.

Douglas-fir Pseudotsuga menziesii (Mirb.) Franco

Grand fir Abies grandis (Douglas ex D. Don) Lindl.

Hickory Carya Nutt.

Jack pine Pinus banksiana Lamb.

Larch Larix Mill.

Loblolly pine Pinus taeda L.

Lodgepole pine Pinus contorta Douglas ex Louden

Maple Acer L.

Mountain hemlock Tsuga mertensiana (Bong.) Carrière

Oak Quercus L.

Ponderosa pine Pinus ponderosa C. Lawson

Spruce Picea A. Dietr.

True fir Abies Mill.

Western hemlock Tsuga heterophylla (Raf.) Sarg.

White fir Abies concolor (Gord. & Glend.) Lindl. ex Hildebr.

Willow Salix bicolor Fr. 
13

Estimating Aboveground Tree Biomass on Forest Land in the Pacific Northwest: A Comparison of Approaches

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Proc. RMRS-P-56CD. Fort Collins, CO: U.S. Department of Agriculture, 

Forest Service, Rocky Mountain Research Station. [CD–ROM].

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

biomass estimators for United States tree species. Forest Science. 49: 12–35.

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

comprehensive database of 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. [CD-ROM].

Raile, G.K. 1982. Estimating stump volume. Res. Pap. NC-224. St. Paul, MN: 

U.S. Department of Agriculture, Forest Service, North Central Forest 

Experiment Station. 4 p. 

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

biomass equations for British Columbia tree species. Information Report 

BC-X-264. Canadian Forest Service, Pacific Forest Resource Center. 47 p.

Summerfield, E.R. 1980. Volume equations for eastern Washington. Washington 

Department of Natural Resources. Memo. 3 p. On file with: Forest Inventory and

Analysis Program, Pacific Northwest Research Station, 620 SW Main St., Suite

400, Portland, OR 97205.

U.S. Department of Agriculture, Forest Service [USDA FS]. 1999. Wood 

handbook—wood as an engineering material. Gen. Tech. Rep. FPL-GTR-113. 

Madison, WI: Forest Product Laboratory. 463 p
14

RESEARCH PAPER PNW-RP-584

U.S. Environmental Protection Agency [US EPA]. 2008. Inventory of U.S. 

greenhouse gas emissions and sinks: 1990–2006. EPA 430-R-08-005. 

Washington, DC: U.S. Environmental Protection Agency, Office of

Atmospheric Program. http://www.epa.gov/climatechange/emissions/

downloads/08_CR.pdf (April 2009).

Waddell K.L.; Hiserote, B. 2005. The PNW–FIA integrated database user 

guide and documentation: version 2.0. Internal publication. On file with:

Forest Inventory and Analysis Program, Pacific Northwest Research Station,

620 SW Main St., Suite 400, Portland, OR 97205. http://www.fs.fed.us/pnw/

fia/publications/data/data.shtml. (April 2009).
15

Estimating Aboveground Tree Biomass on Forest Land in the Pacific Northwest: A Comparison of Approaches

Appendix: The Math Puzzle of the Current Proposed 

Component Ratio Method (CRM) 

The component ratios are the key for the success of the proposed component ratio 

method (CRM). The current method for calculating component ratios has some 

limitations. Except for the stump, the component ratios of live tree biomass are 

based on the total aboveground tree biomass (TAB) calculated from Jenkins et 

al. (2003, 2004) (table 4), and these ratios are then applied to merchantable stem 

biomass (MST), which is a subset of the total aboveground biomass (table 5). The 

Jenkins equation for total aboveground biomass can be expressed as:

 TAB = e

(b0 + b1 ln(dbh))

 = e

b0 dbhb1

 (1)

Table 4—Equations used in component ratio method step one (biomass in kilograms)

Parts Explanation Equations Equation form

TAB = Total aboveground biomass 10 equations TAB = e

(b0 + b1 ln(dbh))

 (merchantable stem + top/limbs 

 + stump + foliage)

MST = Merchantable stem biomass (Jenkins 2 equations MST = [e

(bmb0 + bmb1/dbh + e(bmw0 + bmw1/dbh)

] × TAB

 stem bark ratio × TAB + Jenkins

 stem wood ratio × TAB)

STP = Stump biomass with bark based 10 equations STP = bst1dia2[(1 – Rb) SGw + RbSGb] × 62.4/2.2

 on Raile

FOL = Foliage biomass (foliage ratio × TAB) 2 equations FOL = [e

(bf0 + bf 1/dbh)

] × TAB

RTS = Root biomass (root ratio × TAB) 2 equations RTS = [e

(br0 + br1/dbh)

] × TAB

BRT = Branches/top biomass By subtraction BRT = TAB – MST – STP – FOL

 (TAB – MST – STP – FOL)

Note: 

[b0 and b1] are coefficients for estimating aboveground biomass (Jenkins) listed in table 1.

[bmb0, bmb1; bmw0, bmw1] are coefficients for estimating biomass of bark and wood (Jenkins) listed in table 2 as a0 and a1.

[bf0 and bf1] are coefficients for estimating foilage biomass (Jenkins) listed in table 2 as a0 and a1.

[br0 and br1] are coefficients for estimating root biomass (Jenkins) listed in table 2 as a0 and a1.

dbh is diameter at breast height in centimeters.

[bst1] is volume coefficient of stump (Raile).

Rb is stump bark ratio to total stump volume.

dia is diameter at breast height in inches, dia = dbh/2.54.

SG is specific gravity (w = wood, b = bark).

62.4 = weight of water per cubic foot (lb/ft3

).
16

RESEARCH PAPER PNW-RP-584

Table 5—Component ratios (step two)

Ratio Explanation Expanded expression

STPROP Stump ratio = STP/MST 

FLPROP Foliage ratio = FOL/MST

BTPROP Branch/top ratio = BRT/MST

RTPROP Root ratio = RTS/MST

Note: 

MST is merchantable stem biomass from Jenkins (2003, 2004).

STP is stump biomass with bark based on Raile (1982) (detail see table 4).

FOL is foliage biomass.

BRT is branches and top biomass.

RTS is root biomass.

Dbh is diameter at breast height in centimeters.

( / ) ( / )

0 1 ( )

b b dbh b b dbh

-b -b

mb0 mb1 mw0 mw1 e e

STP e dbh STPROP   

× 

( / ) ( / )

( / )

b b dbh b b dbh

b b dbh

mb0 mb1 mw0 mw1

f 0 f1

e e

e FLPROP  



 

1 1 ( )

( / ) ( / )

( / ) 0 1

− 

− × −   



b b dbh b b dbh

-b b b dbh

mb0 mb1 mw0 mw1

f0 f1

e e

STP e dbh e BTPROP

-b

( / ) ( / )

( / )

b b dbh b b dbh

b b dbh

mb0 mb1 mw0 mw1

r0 r1

e e

e RTPROP  



+ 

Foliage biomass and merchantable stem biomass use only two sets of coefficients in the Jenkins estimation, one for softwood and one for hardwood species. 

Consequently, there are only two equations for the foliage component ratio of 

foliage biomass to merchantable stem biomass (table 5). That is, the same foliage 

component ratio is applied across all softwood species if the trees have the same 

diameter. The same is true for the hardwood species. Stump ratio and branch/top 

ratio each have 10 equations corresponding to 10 Jenkins species groups for total 

aboveground biomass (table 5). However, the sum of the stump ratio and branch/top 

ratio (STPROP + BTPROP) will collapse to two groups of softwood and hardwood 

based on the formulas in table 5. As a result, the proportion of merchantable biomass to total aboveground biomass either including or excluding foliage with CRM 

will be the same for all softwoods and the same for all hardwoods. It is proved in 

the following section. 

The total aboveground biomass excluding foliage with current CRM 

approach is:

DRYBIOT_CRM = MSBIOFIA + STPBIOFIA + TOPBIOFIA (2)

where

MSBIOFIA is merchantable stem woody biomass (biomass of the bole) from FIA,

STPBIOFIA is stump biomass, and 

TOPBIOFIA is branches and top biomass. 
17

Estimating Aboveground Tree Biomass on Forest Land in the Pacific Northwest: A Comparison of Approaches

Based on the current CRM, the above formula can be expanded as: 

DRYBIOT_CRM = MSBIOFIA + STPROP × MSBIOFIA + BTPROP × MSBIOFIA 

= MSBIOFIA (1 + STPROP + BTPROP) (3)

( / )

( / )

1

1

[ ( ) [ 1

0 1

0

0 +

+ 



 

 −  − × −

+

×

+ +

b b dbh

b dbh

b f f

mb bmb1

STP e

e (bmw0 + bmw1 / dbh) e ( + / ) + bmb0 bmb1 dbh e ( bmw0 + bmw1 / dbh) e

STP e dbh - 1 -b ( 0 ) b e dbh - 1 -b -1





 

   (  / )  bmb0 bmb1 dbh e (bmw0  bmw1 /dbh)

(bf 0  bf 1 / dbh)

e

1 – e -1





 

 = 

(  / ) + bmb0 bmb1 dbh e (bmw0 + bmw1 /dbh)

(bf 0  bf 1 / dbh)

e

1 – e

(4)

where

STPROP is stump biomass ratio, and 

BTPROP is branches and top biomass ratio.

Then, the proportion of merchantable biomass to total aboveground biomass 

with CRM is (refer to the ratio equations in table 5 for STPROP and BTPROP): 

 MSBIOFIA = (1 + STPROP + BTPROP)-1 = DRYBIOT_CRM

That means: 

 MSBIOFIA DRYBIOT_CRM

or 

 MSBIOFIA

DRYBIOT_CRM

As bmb0, bmb1, bmw0, and bmw1 are coefficients for estimating merchantable biomass of bark and wood, and bf0, bf1 are coefficients for foliage from Jenkins et al. 

(2004), there are only two sets of coefficients estimated in Jenkins for merchantable 

biomass (bark and wood) and foliage: all the softwood shares one equation and all 

the hardwood shares another equation. That leads to the merchantable stem biomass 

ratio (equation (4) above) being one for all softwoods and another for hardwoods no 

matter what species for trees. 

Figure 3 shows the component ratios relative to merchantable biomass (MST); 

those are the ratios applied to the FIA tree data. Figure 4 shows the component 

portions relative to total aboveground biomass without foliage. Because the total 

aboveground biomass estimates in the FIA database do not include the foliage, 

the total biomass aboveground using the CRM will also not include the foliage, as 

indicated in equation (2) for comparison. As we discussed, although the individual 

ratios for stump or branch/top are specific to 10 species groups, the sum of these 

two ratios collapse to only two—softwood and hardwood—because branch ratios 
18

RESEARCH PAPER PNW-RP-584

are calculated as a residual after subtracting stumps and other components from 

total aboveground biomass. That is, after all the math manipulations presented 

above, we are going to get two sets of ratios for all components (when considering 

stump and branch/top together), not even the 10 Jenkins species groups.

1.0

0.8

0.6

0.4

0.2

0

5 7 9 11 15 20 25 30 35 40 45 50 60

Diameter at breast height (inches)

Component ratio

Softwood (STPROP + BTPROP)

Softwood FLPROP

Hardwood RTPROP

Softwood RTPROP

Hardwood (STPROP + BTPROP)

Hardwood FLPROP

Figure 3—Softwood and hardwood biomass component relative to merchantable biomass using component ratio method. 

STPROP= stump ratio, BTPROP = branch/top ratio, FLPROP = foliage ratio, RTPROP = root ratio.

Figure 4—Softwood and hardwood biomass component relative to total aboveground biomass without foliage using 

component ratio method.

Softwood (merchantable stem) Softwood (stump + branch/top)

Hardwood (merchantable stem) Hardwood (stump + branch/top)

5 7 9 11 15 20 25 30 35 40 45 50 60

1.0

0.8

0.6

0.4

0.2

0

Component ratio

Diameter at breast height (inches)
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