Timber Volume and 

Aboveground Live Tree

Biomass Estimations

for Landscape Analyses

in the Pacific Northwest

Xiaoping Zhou and Miles A. Hemstrom

United States 

Department of 

Agriculture

Forest Service

Pacific Northwest 

Research Station

General Technical Report

PNW-GTR-819

July 2010

DEPAR TMENT OF AGRICULT URE
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.

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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Abstract 

Zhou, Xiaoping; Hemstrom, Miles A. 2010. Timber volume and aboveground live 

tree biomass estimations for landscape analyses in the Pacific Northwest. Gen. 

Tech. Rep. PNW-GTR-819. Portland, OR: U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Research Station. 31 p. 

Timber availability, aboveground tree biomass, and changes in aboveground 

carbon pools are important consequences of landscape management. There are 

several models available for calculating tree volume and aboveground tree biomass 

pools. This paper documents species-specific regional equations for tree volume 

and aboveground live tree biomass estimation that might be used to examine 

consequences of midscale landscape management in the Pacific Northwest. These 

regional equations were applied to a landscape in the upper Deschutes study area 

in central Oregon. We demonstrate an analysis of the changes in aboveground tree 

biomass and wood product availability at the scale of several watersheds on general 

forest lands under an active fuel-treatment management scenario. Our approach 

lays a foundation for further landscape management analysis, such as financial 

analysis of timber product and biomass supply, forest carbon sequestration, wildlife 

habitat suitability, and fuel reduction related studies. 

Keywords: Timber products, biomass supply, volume equation, biomass 

equation, carbon storage, Pacific Northwest, central Oregon.
Contents

1 Introduction

1 Volume Equations for Landscape Analysis

3 Biomass Equations for Midscale Landscape Analysis

4 Case Study

6 Results

9 Discussion

10 Conclusions

11 Equivalents

11 References

17 Appendix
1

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

Introduction

Forest land managers and policymakers face substantial challenges in managing 

forest lands to meet evolving environmental, social, and economic demands. The 

Interagency Mapping and Assessment Project (IMAP) is an interagency1 effort 

to develop midscale assessment and planning tools for addressing fire risks, fuel 

conditions, wildlife habitats, old forests, forest products, potential biomass supplies, and other landscape attributes. Interagency Mapping and Assessment Project 

integrates a suite of vegetation dynamics models with existing and potential 

vegetation information to project potential future vegetation conditions, natural 

disturbances, wildlife habitats, fuel conditions, and other landscape characteristics 

under different management approaches. The outputs from vegetation simulation 

models can be used for a variety of landscape analyses including timber products, 

biomass supply, and carbon accounting. In this report, we document the volume and 

biomass equations that can be used with IMAP models and illustrate the simulated 

changes over time in timber product availability and aboveground tree biomass in 

a central Oregon study area. The volume and biomass equations selected for use 

in the regional landscape study were the subject of comparison in an earlier paper 

(Zhou and Hemstrom 2009), in which the regional model was compared with other 

methods developed for broad-scale estimation.

Volume Equations for Landscape Analysis

Volume equations are expressions of tree forms used to estimate the cubic content 

of a tree with given three-dimensional shapes. Different tree species often have 

different shapes in the same region, or the same species may have different shapes 

in different regions. The Forest Inventory and Analysis (FIA) Program of the USDA 

Forest Service estimates total stem volume, merchantable volume, sawtimber 

volume, and other attributes from tree measurements on inventory plots. Three 

major types of timber volume estimation were summarized in the Timber Volume 

Estimator Handbook (USDA FS 1993). They are (1) stem profile equations, (2) 

direct volume estimators, and (3) product estimators. The Behre (1927) hyperbola, 

one of the stem profile models, has been used by the National Forest Systems in the 

Pacific Northwest Region (USDA FS 1978) for calculating tree volumes, whereas 

1 IMAP partners include USDA Forest Service Pacific Northwest Research Station, Pacific 

Northwest Region, Western Wildland Environmental Threats Center, Oregon Department 

of Forestry, Washington Department of Natural Resources, The Nature Conservancy, and 

others.
2

GENERAL TECHNICAL REPORT PNW-GTR-819

the FIA Program in the Pacific Northwest Research Station (PNW-FIA) is using the 

direct volume equation and the tarif system2 for measured tree volume estimation. 

 For volume estimation in our midscale landscape study, we applied direct 

volume equations and the tarif system (Brackett 1973), the approach used by the 

PNW-FIA Program. Most of the equations were published from local tree studies 

and are documented by Waddell and Hiserote (2005). Two methods were used to 

calculate cubic volume in this approach: (1) using the cubic-foot volume of total 

stem from ground to tree tip (CVTS) to calculate the tarif number and the other 

volumes (table 1a); (2) using the cubic-foot volume from a 1-ft stump to a 4-in top 

(CV4) to calculate tarif number and other volumes (table 1b). These volume equations are for estimation of wood volume without bark. The defect is not included in 

the estimate. 

Equations listed in table 1a allow direct estimation of CVTS for different 

Pacific Northwest tree species, and can be applied to all diameter classes if the 

equations for specified species are available. The tarif numbers are calculated based 

on CVTS (Brackett 1973). The other volumes such as cubic-foot volume from a 1-ft 

stump to the tree tip (CVT) and CV4 are derived from CVTS and tarif numbers. 

Equations shown in table 1b calculate CV4 first, then the tarif numbers are 

derived from CV4 for calculating CVTS and CVT for trees over 5 inches in diameter at breast height (DBH). For trees less than 5 inches in DBH, the CVTS was 

calculated by using direct equations shown in the same table. 

The saw-log volume estimates include saw-log cubic-foot volume (CV), Scribner volume (SV) and international volume (IV) (table 1c). The saw-log volume 

is the volume of wood in the central stem of a sample commercial species tree 

of sawtimber size (9.0 in DBH minimum for softwood and 11.0 in minimum for 

hardwood) from a 1-ft stump to a minimum diameter at top.

Volume equations do not exist for all tree species in the study area. For those 

species without a volume equation, we chose equations from species with similar 

growth forms. The volume estimations for this study may include: 

1. Cubic-foot volume of the total stem from ground to tree tip (CVTS). 

2. Cubic-foot volume from a 1-ft stump to the tree tip (CVT).

3. Cubic-foot volume from a 1-ft stump to a 4-in top (CV4). 

4. Saw-log cubic-foot volume from a 1-ft stump to 6-in top for softwoods 

(CV6) and to an 8-in top for hardwoods (CV8). 

2 The tarif system is a comprehensive tree volume calculation procedure and was adapted 

from the European system to the Pacific Northwest. The tarif system provides a series of 

preconstructed local volume tables applicable to the specific stand. The volume computation procedure of the tarif system was presented in a flow chart by Brackett (1973).
3

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

5. Scribner board-foot volume to a 6-in top in 16-ft logs (SV616) and in 32-ft 

logs (SV632), and to an 8-in top in 16-ft logs (SV816) and in 32-ft logs 

(SV832).

6. International board-foot volume to a 6-in top (IV6) for softwood and to an 

8-in top (IV8) for hardwood.

Biomass Equations for Midscale Landscape Analysis

Tree biomass estimation has become increasingly important for at least two reasons: (1) forest land plays an important role in carbon sequestration for mitigating 

global climate changes, and (2) biomass from forests might be used to generate 

energy. Various tree biomass calculation methods are applied on forest lands in 

the United States. The USDA Forest Service has used the Jenkins equation system 

(Jenkins et al. 2004) to assess forest biomass at national scales and for forest carbon 

estimates used in official greenhouse gas and carbon sequestration assessments for 

the United States (US EPA 2008). The national forest resources report for the Forest 

and Rangeland Renewable Resources Planning Act has used the component ratio 

method (CRM) to estimate tree biomass for consistency across regions. The objective of CRM is to provide national-scale biomass and carbon estimates consistent 

with FIA volume estimates at the tree level (Heath et al. 2008). However, these 

methods produce generalized biomass estimates compared to regional, detailed 

allometric equations (Zhou and Hemstrom 2009). Regional models are usually tree 

species-specific and result from detailed tree studies. We assume these regional 

models will be suitable for analyses of midscale landscapes (e.g., areas of hundreds 

of thousands to a few million acres).

Live tree biomass includes belowground biomass (root biomass) and aboveground biomass. We examined aboveground tree biomass using regional volume 

and biomass models including total stem wood biomass, bark biomass, and branch 

biomass. The foliage biomass is not included in this study. 

 Tree stem wood biomass from ground to tip (including stump) was estimated 

using volume equations (tables 1a, 1b, and 1c) multiplied by the wood density: 

WB = (CVTS × Wd)

where 

CVTS = total stem volume from ground to tip (cubic feet) (tables 1a and 1b),

Wd = wood density (kilogram/cubic foot)3

,

WB = stem wood biomass (kilogram).

3 Wood density is calculated by specific gravity times density of water (62.4 lb/ft3

 or 1000 

kg/m3

).
4

GENERAL TECHNICAL REPORT PNW-GTR-819

The equations for estimating tree branch biomass are listed in table 2, and 

bark biomass equations are in table 3. These biomass equations are also from local 

tree studies, and most of them were from published papers and have been used for 

PNW-FIA live tree biomass estimation (Means et al. 1994, Waddell and Hiserote 

2005). The assignments of volume, biomass equations for each major species 

within different geographic regions of the Pacific Northwest are in table 4. The 

specific gravities of wood and bark by species (Miles and Smith 2009) for calculating wood or bark density are presented in table 5.

There are important constraints to consider when applying these equations to 

measured tree data (tables 1a-c, 2, and 3). For example, bark biomass equations 

(27), (29), and (32) in table 3 may produce negative bark biomass when DBH is less 

than 2 in. We programmed those constraints along with the various volume and 

biomass equations into a SAS®4 (SAS Institute Inc. 2008) script for our analysis. 

4 The use of trade or firm names in this publication is for reader information and does not 

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

Case Study

The upper Deschutes landscape is an area of about 2 million acres that extends 

from just north of Redmond, Oregon, to south of Gilchrist in central Oregon (fig. 

1). We focused on the general forest lands managed by the USDA Forest Service 

for our analysis; about 500,000 ac, or 25 percent of the upper Deschutes landscape. 

General forest lands are outside reserved areas (e.g., late-successional reserves, 

wilderness, national monument). We modeled potential trends in forest vegetation 

structure and vegetation composition under the scenario of active fuel treatment 

management with natural disturbances (wildfire and insect outbreaks) that moved 

dry forests toward more open conditions dominated by large trees of early-seral 

species. This management scenario is likely much more active, in terms of area 

treated per year, than currently occurs on general forest lands. It is assumed in 

this scenario that general forest lands are managed for multiple uses, including 

restoration of forests to conditions more resistant to uncharacteristic wildfire and 

insect outbreaks, recreation, wildlife habitat, and generation of forest products (e.g., 

biomass and timber), and that some level of salvage may occur following standreplacement natural disturbances, but that the level is generally low. The Vegetation 

Dynamics Development Tool (VDDT) (ESSA Technologies Ltd. 2007), a stateand-transition model, was used in this study. VDDT has been used in other similar 

landscape analyses in the interior Pacific Northwest (Hann et al. 1997, Hemstrom et 

al. 2007). We ran this active fuel-treatment scenario for 300 years with 30 Monte 
5

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

Figure 1—The upper Deschutes study area and land ownership/allocation classes in central Oregon.

Land ownership and allocation classes

USDA Forest Service, general forest

USDI Bureau of Land Management

USDA Forest Service, late-successional reserves

State

Wilderness and national monument

Private

Carlo simulations of different combinations of fire and insect outbreaks using 

methods developed by Hemstrom et al. (2008).

Existing vegetation conditions came from Gradient Nearest Neighbor (GNN) 

imputation of inventory plots to 30-m pixels (Ohmann and Gregory 2002; http://

www.fsl.orst.edu/lemma/method/methods.php). Each 30-m pixel with an associated 

inventory plot (PNW-FIA data and USDA Forest Service Pacific Northwest Region 

inventory data) was assigned to one of the state classes in the VDDT model. Then 

area is summarized in each state class within each watershed and ownership/allocation class to develop initial conditions for our models, breaking forest structure into 

classes that combine overstory tree size and canopy density: 

1. Grass/forb, seedling, and sapling—Tree canopy less than 10 percent cover 

but potentially forested or trees less than 1 in DBH.

2. Pole—Tree canopy over 10 percent and dominant/co-dominant tree diameter 1 to 5 in DBH.
6

GENERAL TECHNICAL REPORT PNW-GTR-819

3. Small tree—Tree canopy over 10 percent and dominant/co-dominant tree 

diameter 5 to 10 in DBH.

4. Medium tree—Tree canopy over 10 percent and dominant/co-dominant tree 

diameter 10 to 20 in DBH.

5. Large tree open—Tree canopy 40 to 60 percent cover and dominant/codominant tree diameter >20 in DBH.

6. Large tree closed—Tree canopy >60 percent cover and dominant/co-dominant tree diameter >20 in DBH.

The average volume and biomass are estimated using inventory plot data and 

allometric equations for each VDDT state class, with the same assignment of 

inventory plots to state classes. The result was a large look-up table that linked 

VDDT model state class to volume and biomass estimates. Landscape projections 

of changes to volume and biomass by watershed, ownership/allocation, and state 

class were developed by linking our volume and biomass look-up tables to modeled 

future area in each state class within landscape strata of watersheds and ownership/

allocations. The process was coded and run in the SAS software package.

Results

Forests of seedlings/saplings, poles, small, and medium-sized trees currently 

dominate vegetation conditions in the study area (fig. 2). The active fuel-treatment 

scenario in this study produces a general forest landscape dominated by open 

stands of large trees with abundant openings over the 300-year simulation period.

Figure 2—Proportion of the study area in forest structure classes over a 300-year simulation period 

in the study area. 

0

10.0

20.0

30.0

40.0

50.0

Start 50 100 150 200 250

P

erce

nta

g

e

of l

and

sca

p

e

Simulation year

Grass, shrub, seedling, sapling Pole

Small tree Medium tree

Large closed Large open
7

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

At present, the standing pool of merchantable volume is 571 million cubic 

feet in the study area for general forest land, mostly in forest structure classes of 

small trees and relatively dense stands (figs. 2 and 3). Over the first 50 years of the 

300-year simulation period, the standing pool of merchantable volume declined 

to 460 million cubic feet (fig. 3). Average 47 percent (range from 40 to 59 percent) 

of the total removal of live tree volume from the landscape in the first 50 years 

was from active treatments that generated forest products (including salvage) and 

the remaining from wildfires, insect outbreaks, and other disturbances where no 

salvage occurred. Initially, total loss of live tree volume was 170 million cubic feet 

per decade or 17 million cubic feet per year, but losses slowed and stabilized after 

50 years. For the remaining 250 years of our simulations, the total removal was 

50 million cubic feet per decade, or 5 million cubic feet per year. After 50 years, 

however, growth outpaced volume loss so that the landscape once again contained 

570 million cubic feet of merchantable volume around simulation year 275. Much 

of the recovered volume is in the structure class of large trees of early-seral species 

(e.g., ponderosa pine) by the end of the simulation.

Pools of sawtimber follow a similar trajectory (fig. 4). The landscape sawtimber pool is currently 2.75 billion board feet, much of that in the structure classes 

of small (average 5 to 10 in DBH) and medium (average 10 to 20 in DBH) sized. 

Over the first 30 years, the sawtimber pool declines to 2.33 billion board feet. The 

sawtimber pool then begins to rebound and ends 17 percent above initial conditions 

0

100

200

300

400

500

600

700

Merchantable 

v

olume

(milli

on cubic feet)

Simulation year

Merchantable volume removed by management

Merchantable volume removed by all disturbances including management

Total merchantable volume inventory

25

5

4565

85

105125

145

165

185

205

225

245

265

285

5

Figure 3—Total merchantable volume inventory and 10-year removals by management and natural 

disturbances.
8

GENERAL TECHNICAL REPORT PNW-GTR-819

by the end of the 300-year simulation period. Timber harvest averages 50 percent 

(range from 43 to 62 percent) of the sawtimber removals during the 300-year 

projection period, and the remaining is from natural disturbances.

The pool of aboveground tree biomass in the study area begins at 12.6 million 

tons and declines to 10.2 million tons by the end of the first 50 years (fig. 5). Total 

annual removals of aboveground tree biomass decline from 0.4 million tons (or 4 

million tons per decade) at the start of the simulation period to 0.15 million tons per 

Figure 4—Total sawtimber volume inventory and 10-year removals by management and natural disturbances.

Figure 5—Total biomass inventory and 10-year removals by management and natural disturbances.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Sawti

m

ber

(billi

on b

oard feet)

Simulation year

Sawtimber removed by management

Sawtimber removed by all disturbances including management

Total sawtimber inventory

5

25456585

105125145165185205225245265285

0

2

4

6

8

10

12

14

Bio

mass

(milli

on tons)

Simulation year

Aboveground biomass removed by management

Aboveground biomass removed by all disturbances including management

Total aboveground biomass inventory
9

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

year (or 1.5 million tons per decade) after the third decade. Harvest averages 46 

percent (range from 39 to 60 percent) of aboveground live tree biomass removals 

and the rest is from other natural disturbances. Over the last 250 years of the simulation period, the average annual removal is 1.2 percent of the total aboveground 

live tree biomass inventory. The total aboveground tree biomass pool does not quite 

recover to initial levels after 300 years, instead ending at 11.6 million tons.

Discussion

Active fuel treatment with natural disturbances interacted to produce substantial 

changes to landscape pools of aboveground live tree volume and biomass over 300 

years in our simulations. The combination of timber harvest from fuel treatments 

and natural disturbances (wildfire and insect outbreaks) caused an initial decline 

of 14 to 19 percent in each pool over the first 30 to 50 simulation years. The pools 

then began slow recovery as growth on large, fire-resistant trees in open stands 

outstripped harvest and natural disturbance losses. Since our active fuel-treatment 

scenario was designed to reduce wildfire and insect outbreak losses rather than 

maximize timber output, the forested landscape pools continued to recover to levels 

equal to or above initial conditions over the last 250 years of the simulations. Interestingly, the sawtimber pool exceeded initial conditions by the end of the simulation 

because growth occurred on large trees that contain proportionately more sawtimber than the small and medium-sized trees that currently dominate the landscape.

The results in this study suggest that an active fuel-treatment management 

approach might initially reduce aboveground tree pools of volume, sawtimber, 

and live tree carbon stock but might, over the longer term, move forest conditions 

toward similar pool sizes in more sustainable forest conditions, as suggested by 

Boerner et al. (2008). It seems logical that open forests of large, fire-tolerant tree 

species would be less susceptible to sudden loss to severe wildfire or insect outbreaks (e.g., Hartsough et al. 2008, Hurteau and North 2009) though the effects of 

management on forest carbon pools are debatable (e.g., Finkral and Evans 2008, 

Harmon et al. 1996, Hudiburg et al. 2009, Hurteau and North 2009, Kurz et al. 

1997). For example, Finkral and Evans (2008) estimated that thinning treatments in 

northern Arizona ponderosa pine stands released more carbon than stand-replacing 

wildfire might have, largely owing to the fate of thinned trees sold as firewood 

rather than for longer lasting wood products. They did not examine the longer 

term recovery of carbon on large, fire-tolerant trees. The fate of harvested trees 

was not examined in this active fuel-treatment scenario. It is suspected, however, 

that a similar result would apply; trees sold for firewood could quickly contribute 
10

GENERAL TECHNICAL REPORT PNW-GTR-819

to atmospheric carbon, whereas those destined to become long-term wood products 

would contribute more slowly.

Several cautions and needs are suggested for additional work. This study 

did not include the potential future effects of climate change in our active fueltreatment scenario. Certainly, climate change could alter the rate of natural disturbances and tree growth, changing the aboveground pools. It also did not examine 

soil carbon changes that might accompany an active fuel-treatment management 

approach. It is possible that the active fuel-treatment scenario used in this study 

treats a much higher proportion of the general forest landscape than currently 

occurs and that modeling a current management scenario would produce considerably different results. However, a landscape modeling approach that includes 

dynamic interactions between management activities, natural disturbances, and tree 

growth over a long period is useful for considering management impacts on timber 

volume, aboveground tree biomass, and carbon storage.

Conclusions

Timber supply and biomass estimation can be important to landscape management 

analysis, depending on the questions asked. Although there are several models 

available for calculating tree volume and aboveground biomass, most of the speciesspecific regional volume and biomass equations presented in this paper are applied 

in the PNW-FIA Program (Donnegan et al. 2008), and these regional models would 

be suitable for mid- and fine-scale landscape analyses (Zhou and Hemstrom 2009). 

The application of these regional models to the upper Deschutes area provides an 

example of how such an analysis might be implemented at the scale of several or 

many watersheds. Localized information on trends in these landscape characteristics should help managers, policymakers, and others evaluate different management scenarios in terms of biomass, timber availability, and aboveground tree 

carbon pools over time. Because such analysis provides information at the scale 

of land ownerships within watersheds, the long-term conditions and sustainability 

of these pools could be mapped for midscale analysis and evaluation. This paper 

lays a foundation for further analyses of landscape management practices, such as 

financial analysis of timber products, biomass supply, and aboveground tree carbon 

sequestration for differing landscape management scenarios while including critical 

interactions with natural disturbances. 
11

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

Equivalents

When you know: Multiply by: To get:

Acres (ac) 0.405 Hectares (ha)

Feet (ft) .305 Meters (m)

Cubic feet (ft3) .0283 Cubic meters (m3)

Inches (in) 2.54 Centimeters (cm)

Pounds (lb) .454 Kilograms (kg)

Tons .907 Metric tones

Pounds per cubic 

 foot (lb/ft3) 16.02 Kilograms per cubic meter (kg/m3) 

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Hurteau, M.; North, M. 2009. Fuel treatment effects on tree-based forest carbon 

storage and emissions under modeled wildfire scenarios. Frontiers in Ecology 

and the Environment. 7: 409–414.

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. [1 CD-ROM].

Krumland, B.E.; Wensel, L.E. 1975. Preliminary young growth volume tables for 

coastal California conifers. Res. Note 1. In-house memo. Berkeley, CA: Co-op 

Redwood Yield Research Project, Department of Forestry and Conservation, 

College of Natural Resources, University of California, Berkeley. On file with: 

Forest Inventory and Analysis Program, Pacific Northwest Research Station, 620 

SW Main, Suite 400, Portland, OR 97205.
14

GENERAL TECHNICAL REPORT PNW-GTR-819

Kurz, W.A.; Beukema, S.J.; Apps, M.J. 1997. Carbon budget implications of the 

transition from natural to managed disturbance regimes in forest landscapes. 

Mitigation and Adaptation Strategies for Global Change. 2: 1381–2386.

MacLean, C.; Farrenkopf, T. 1983. Eucalyptus volume equation. In-house 

memo describing the volume equation for CVTS, to be used for all species of 

Eucalyptus. The equation was developed from 111 trees. On file with: Forest 

Inventory and Analysis Program, Pacific Northwest Research Station, 620 SW 

Main, Suite 400, Portland, OR 97205.

Means, J.E.; Hansen, H.A.; Koerper, G.J.; Alaback, P.B.; Klopsch, M.W. 1994.

Software for computing plant biomass—BIOPAK users guide. Gen. Tech. Rep. 

PNW-GTR-340. Portland, OR: U.S. Department of Agriculture, Forest Service, 

Pacific Northwest Research Station. 184 p.

Miles, P.D.; Smith, W.B. 2009. Specific gravity and other properties of wood and 

bark for 156 tree species found in North America. Res. Note NRS-38. Newtown 

Square, PA: U.S. Department of Agriculture, Forest Service, Northern Research 

Station. 35 p.

Ohmann, J.; Gregory, M.J. 2002. Predictive mapping of forest composition and 

structure with direct gradient analysis and nearest neighbor imputation in coastal 

Oregon, U.S.A. Canadian Journal of Forestry. 32: 725–741.

Pillsbury, N.H.; Kirkley, M.L. 1984. Equations for total, wood, and saw-log 

volume for thirteen California hardwoods. Res. Note PNW-RN-414. Portland, 

OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research 

Station. 52 p.

Sachs, D. 1983. Management effects on nitrogen nutrition and long-term 

productivity of western hemlock stands: an exercise in simulation with 

FORCYTE. Corvallis, OR: Oregon State University. 63 p. M.S. thesis.

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Inc.
15

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

Shaw, D.L., Jr. 1977. Biomass equations for Douglas-fir, western hemlock, 

redcedar, and red alder in Washington and Oregon. Centralia, WA: Western 

Forestry Research Center, Weyerhaeuser Company. 18 p.

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

biomass equations for British Columbia tree species. Info. Rep. BC-X-264. 

Victoria, BC: Canadian Forest Service, Pacific Forest Resource Center. 47 p.

Summerfield, E. 1980. In-house memo describing equations for Douglas-fir and 

ponderosa pine. State of Washington, Department of Natural Resources. On 

file with: Forest Inventory and Analysis Program, Pacific Northwest Research 

Station, 620 SW Main, Suite 400, Portland, OR 97205.

U.S. Department of Agriculture, Forest Service [USDA FS]. 1978. Diameter 

and volume procedures. Used by the R-6 timber cruise system. USFS–R6 sale 

preparation and valuation section. Portland, OR, Pacific Northwest Region. 13 p.

U.S. Department of Agriculture, Forest Service [USDA FS]. 1993. Timber 

volume estimator handbook. Forest Service Handb. FSH 2409.12a—Amend. 

2409.12a-93-1. Washington, DC. 

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: Office of Atmospheric Program. 394 p. http://www.epa.gov/

climatechange/emissions/downloads/08_CR.pdf. (September 2009).

Waddell, K.L.; Hiserote, B. 2005. The PNW-FIA integrated database and 

user guide and documentation. Version 2.0. [CD-ROM]. Portland, OR: U.S. 

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

http://www.fs.fed.us/pnw/fia/publications/data/data.shtml. (April 2009).

Zhou, X.; Hemstrom, M.A. 2009. Estimating aboveground tree biomass on forest 

land in the Pacific Northwest: a comparison of approaches. Res. Pap. PNWRP-584. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific 

Northwest Research Station. 18 p. 
16

GENERAL TECHNICAL REPORT PNW-GTR-819
17

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

Table 1a—Pacific Northwest volume equations

—group 1

Eqn CVTS: Cubic-foot volume of total stem, ground to tip (DBH ≥ 1 inch or 2.5 cm) Major speciesa Reference

1  

  2

2

(log(HT)) 0.16185 HT log 1.63408

DBH log 2.02132 )) (log( 0.15664   DBH log   HT log 0.04948 3.21809

10

CVTS × − × 

×  × − × × 

−



DBH Douglas-fir (PNWW) Brackett 1973

2 e   HT ln 1.083884   D

B

H ln 1.81306 110493 . 6 C

V

TS ×  ×  −  Douglas-fir (PNWE) Summerfield 1980

3 e HT   ln 1.2274   DB

H ln 1.7131 5193 . 6 C

V

TS ×  ×  −  Douglas-fir (CA) Krumland and

 Wensel 1975

4 HT log( 1.085681 DBH) log( 1.909478 2.729937 10 CVTS ×  × 

−

 ) Ponderosa pine Brackett 1973

 (PNWE)

6 DBH

HT

DBH × 0.00568 ) log( 1.08620 ) log( 2.00857 72170 . 2 10 C

V

TS −   −  × × Western hemlock Chambers and

 (WA/OR/CA) Foltz 1979

8 ) log( 1.067038 ) log( 1.701993 464614 . 2 10 CVTS HT

DBH ×  × 

−

 Western redcedar Brackett 1973

 (PNWE/CA)

9 ) log( 1.039712 ) log( 1.6823 379642 . 2 10 CVTS HT

DBH ×  × 

−

 Western redcedar Brackett 1973

 (PNWW)

10 ) log( 1.004903 ) log( 1.864963 502332 . 2 10

CVTS

HT

DBH ×  × 

−

 True fir (PNWE) Brackett 1973

11 ) log( 1.094665 ) log( 1.806775 575642 . 2 10 CVTS

HT

DBH ×  × 

−

 True fir (PNWW) Brackett 1973

12 ) log( 1.034051 ) log( 1.841226 539944 . 2 10

CVTS

HT

DBH

×



×



−

 Spruce (PNWE/CA) Brackett 1973

13 ) log( 164531 . 1 ) log( 754171 . 1 700574 . 2 10

CVTS

HT

DBH ×  × 

−

 Spruce (PNWW) Brackett 1973

15 ) log( 085772 . 1 ) log( 847504 . 1 615591 . 2 10 C

V

TS HT

DBH ×  ×  −  Lodgepole pine Brackett 1973 

 (WA/OR/CA)

17    1.

 2744923 1.8140497 001106485 . 0 C

V

TS HT

DBH × ×  Mountain hemlock Bell et al. 1981

 (WA/OR/CA)

18 ln(HT) 1.2979 ln(DBH) 1.7022 6.7013 C

V

TS ×  ×   e − Shasta red fir Krumland and

 (WA/OR/CA) Wensel 1975

21

2

5 4 5 4 00372552 0 000861576 0 307089 . 0 2 005454154 . 0 C

V

TS 







 −

× × − × × ×  × × 

. H

T

HT . H

T

H

T

D

B

H . H

T . D

B

H

H

T − Western juniper Chittester and 

 (WA/OR/CA) MacLean 1984 2

5 4



 −

× ×

. H

T

HT

H

T

22 ) log( 1.044007 ) log( 847123 . 1 624325 . 2 10 C

V

TS HT

DBH ×  ×  −  Western larch (WA/OR) Brackett 1973

24     H

T

D

B

H e ln 0.9642 ln 1.9967 2597 . 6 C

V

TS ×  ×  −  Redwood (CA/WOR) Krumland and

 Wensel 1975

Appendix
18

GENERAL TECHNICAL REPORT PNW-GTR-819 25 ) log( 1.074024 ) log( 1.920617 672775 . 2 10 CVTS HT

DBH ×  × 

−

 Alder (WA) Brackett 1973

27 ) log( 238855 . 1 ) log( 803973 . 1 945047 . 2 10 C

V

TS HT

DBH ×  ×  −  Cottonwood (CA) Brackett 1973

28 ) log( 024793 . 1 ) log( 946034 . 1 635360 . 2 10 C

V

TS HT

DBH ×  ×  −  Aspen (CA) Brackett 1973

29 ) log( 1.105403 ) log( 911681 . 1 757813 . 2 10 C

V

TS HT

DBH ×  ×  −  Birch Brackett 1973

30 ) log( 119043 . 1 ) log( 885813 . 1 770324 . 2 10 C

V

TS HT DBH ×  ×  −  Maple Brackett 1973

31

HT

DBH × ×  2 0016144 . 0 C

V

TS Eucalyptus (CA) MacLean and 

 Farrenkopf 1983

Other cubic foot volume calculated from CVTS (Brackett 1973): 1. CVT: cubic-foot volume above 1-ft stump (DBH ≥ 1 in)

)

) 5. 1 ( 5529 . 0 1051 . 0 9679 . 0( C

V

T

− × − × 

DBH

C

VTS

2. CV4: cubic-foot volume above 1-ft stump to 4-in top  If DBH < 5.0 inches: CV4 = 0  If DBH ≥ 5.0 inches: 

912733 . 0

087266 . 0 C

V4 − ×  B

A

TA

RIF

 Where:   174533 . 0

087266 . 0

) 10

015292 . 4 ( 382937 . 1 0. 1 033 . 1

912

733 . 0

TARIF

−



×





×

−

×



×



×

BA

DBH

e

CVTS

Note: log in base 10, ln in natural base.DBH = diameter at breast height (inches).

HT = total height (feet).

BA = basal area (square feet), BA = 0.005454154 × DBH2. 

Equation numbers may not be in consecutive order.

PNWW = Pacific Northwest West includes western Oregon and Washington.PNWE = Pacific Northwest East includes eastern Oregon and Washington.CA = California, OR = Oregon, WA = Washington, WOR = western Oregon.

a 

Table 1a—Pacific Northwest volume equations

Major species—the species or similar species for which the equation was referred for use in reference. 

—group 1 (continued)

Eqn CVTS: Cubic-foot volume of total stem, ground to tip (DBH ≥ 1 inch or 2.5 cm) Major speciesa Reference
19

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

Table 1b—Pacific Northwest volume equations

—group 2 (Pillsburyand Kirkley 1984)

Eqn CV4: Cubic-foot volume from a 1-foot CVTS: Cubic-foot volume of total stem, ground to tipa Major speciesb

stump to a 4-inch top (DBH ≥ 5.0) (for DBH < 5.0 inch) 

32 77467 . 0 07202 . 2 0055212937 . 0 C

V4 HT

DBH × × 

68638 . 0 02232 . 2

) 90182 . 0 155646 . 0( 0120372263 . 0 C

VTS HT D

B

H × ×  ×  Giant chinkapin

33 05293 . 1 05910 . 2 0016380753 . 0 C

V4 HT

DBH × ×  88389 . 0 94553 . 1

) 96579 . 0 127917 . 0 ( 0057821322 . 0 C

VTS H

T

D

B

H × × + − × = California laurel

34 14078 . 1 19576 . 2 0005774970 . 0 C

V4 HT

DBH × ×  86562 . 0 94165 . 1

) 021968 . 0 95354 . 0 719890 . 1 ( CVTS HT

HT

D

B

H × × + × +

− 0058870024 . 0 × = Tanoak

35 98878 . 0 39565 . 2 0009684363 . 0 C

V4 HT

D

BH × ×  74872 . 0 ) 93545 . 0 382890 . 0 ( 0042870077 . 0 C

V

TS H

T

D

B

H 33631 . 2 × × + − × = California white oak

36 31103 . 0 61268 . 2 0053866353 . 0 C

V4 HT

D

BH × × 

28060 . 0 40248 . 2

) 92472 . 0 785720 . 0 ( 0191453191 . 0 C

V

TS H

T

D

B

H × × + − × = Englemann oak

37 69586 . 0 35347 . 2 0034214162 . 0 C

V4 HT

D

BH × ×  57561 . 0 22462 . 2

) 94782 . 0 083602 . 0( 0101786350 . 0 C

V

TS H

T

D

B

H × × + × = Bigleaf maple

38 83339 . 0 12635 . 2 0036795695 . 0 C

V4 HT

DBH × ×  85034 . 0 97437 . 1

) 95767 . 0 268240 . 0 ( 0070538108 . 0 C

V

TS HT

D

B

H × ×  − ×  California black oak

39 50591 . 0 53987 . 2 0042324071 . 0 C

V4 HT

DBH × × 

46100 . 0 33089 . 2

) 94403 . 0 173240 . 0 ( 0125103008 . 0 C

V

TS H

T

D

B

H × × + − × = Blue oak

40 01532 . 1 99295 . 1 0025616425 . 0 C

V4 HT

DBH × × 

83458 . 0 96628 . 1

) 98155 . 0 013484 . 0 ( 0067322665 . 0 CVTS HT D

B

H × × + − × =

Pacific madrone

41 87108 . 0 25575 . 2 0024277027 . 0 C

V4 HT

D

BH × × 

74220 . 0 14321 . 2

) 95956 . 0 307220 . 0 ( 0072695058 . 0 C

V

TS H

T

D

B

H × × + − × = Oregon white oak

42 74348 . 0 32519 . 2 0031670596 . 0 C

V4 HT

D

BH × × 

61190 . 0 20527 . 2

) 96147 . 0 191276 . 0 ( 0097438611 . 0 C

V

TS H

T

D

B

H × × + − × = Canyon live oak

43 60764 . 0 53284 . 2 0024574847 . 0 C

V4 HT

D

BH × ×  62528 . 0 31958 . 2

) 93475 . 0 757397 . 0 ( 0065261029 . 0 C

V

TS HT

D

BH × × +

− × = Coast live oak

44 77843 . 0 14915 . 2 0041192264 . 0 C

V4 HT

DBH × × 

63257 . 0 02989 . 2

) 92953 . 0 048177 . 0( 0136818837 . 0 C

V

TS H

T

D

B

H × × + × = Interior live oak

Other cubic foot volume calculated from CVTS (Brackett 1973): 1. Volume of total stem (ground to tip) (CVTS):  If DBH < 5.0 inches: use CVTS equations for each species in this table. If DBH ≥ 5.0 inches: 

912733 . 0

174533 . 0 ) 087266 . 0 ( )) 382937 . 1 0. 1( 033 . 1( ) 10 015292 . 4 (

CVTS −

 × ×



× × −

× 

BA e

DBH

TARIF

 Where 087266 . 0

912733 . 0 4 TA

RIF

− × 

B

A

C

V

2. Volume from 1-foot stump to the tip (CVT): )

) 5. 1 ( 5529 . 0 1051 . 0 9679 . 0( C

VT − × − ×  D

B

H

C

VTS

DBH = diameter at breast height.a Total volume in Pillsbury and Kirkley (1984) includes all stem and branch wood plus stump and bark but excludes roots and foliage. It is transformed to inside bark total volume based on the relationship 

between inside bark diameter and outside bark diameter in table 2 (Pillsbury and Kirkley 1984). It is applied only to trees with DBH < 5.0 inch. For trees above 5.0 inches in DBH, the CV4 and Tarif will be applied.

b Major species

—the species or similar species for which the equation was referred for use in reference.

Equation numbers may not be in consecutive order.
20

GENERAL TECHNICAL REPORT PNW-GTR-819 Table 1c—Pacific Northwest volume equations—sawtimber volume calculation Saw-log volume types Saw-log volume equations 

Saw-log cubic feet volume (cubic feet) CV6: Softwood saw-log cubic-foot volume above 1-foot stump to a 6-inch top (DBH ≥ 9 in) 

CV8: Hardwood saw-log cubic foot volume above 1-foot stump to an 8-inch top (DBH ≥ 11 in) )

) 6. 8 ( 65 . 0 983 . 0 983 . 0( 4 C

V8 − × − × 

D

B

H

C

V

Scribner volume Scribner volume to a 6-inch top(board feet) 1. In 16-foot log to 6-inch top (SV616) and to an 8-inch top (SV816):

 SV616 = CV6 × BCU1 SV816 = SV616 × (0.990 – 0.589 × 0.484 (DBH – 9.5))

Where BCU1 is the board-foot Scribner from cubic-foot ratio 

  2 2

2 00001937 . 0 ) 912733 . 0

( 00001345 . 0 0.912733

TARIF log 236693 . 0 210585 . 8

0.912733

TARIF log DBH log 0.117594 174439 . 0 10

DBH

TARIF

DBH × − × − 



 ×  −



 × ×   BCU1

2. In 32-foot log to a 6-inch top (SV632) and to an 8-inch top (SV832): SV632 = SV6 × BF3216 SV832 = SV632 × (0.990 – 0.58 × 0.484 (DBH – 9.5)) 

Where 2 00001351 . 0 924097 . 6 001491 . 1 BF3216 

DBH

TARIF × +

− =

 (TARIF from table 1a and 1b)

International 1. International volume to a 6-inch top (IV6): IV6 = CV6 × BCU2 volume Where 2

29598 . 11 2 00008205 . 0 2765985 . 0 ) log( 466328 . 3 902145 . 2 B

C

U2 DBH

TA

RIF

DBH

TA

RIF

DBH

+ × − × − × × +

−

=

(board feet) (TARIF from table 1a and 1b)

2. International volume to an 8-inch top (IV8): )

) 5.9 ( 485 . 0 55 . 0 990 . 0( 6 IV8 − × − ×  DBH IV

Note: Saw-log volume is the volume of wood in the central stem of a sample commercial species tree of sawtimber size (9.0 inches DBH minimum for softwood and 11.0 inches minimum for hardwood) from a 1-foot stump to a minimum diameter at top.Sources: Brackett 1973, Chambers and Foltz 1979.

)

) 0. 6 ( 62 . 0 993 . 0 993 . 0( 4 C

V6 − × − ×  D

B

H

C

V
21

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

Table 2—Pacific Northwest tree branch biomass (BCH) equations

Eqn Branch equation Major speciesa Reference

1 H m DBH cm BCH _

2

100

_  13.0  12.4 ×  ×



 



 Grand fir Standish et al. 1985

2 H m DBH cm BCH _

2

100

_  3.6  44.2 ×  ×



 



 Subalpine fir Standish et al. 1985

3 DBH cm BCH e − 4 .1817  2 .3324 × ln _  Noble fir Gholz et al. 1979

4 H m DBH cm BCH _

2

100

_  16.8  14.4 ×  ×



 



 Engelmann spruce Standish et al. 1985

5 H m DBH cm BCH _

2

100

_  9.7  22.0 ×  ×



 



 Sitka spruce Standish et al. 1985

6 DBH cm BCH e −3.6941  2.1382 × ln _  Douglas-fir (PNWW) Gholz et al. 1979

7 DBH cm H m BCH e − 4.1068  1.5177 × ln _ )  1.0424 × ln( _  Ponderosa pine Cochran et al. 1984

8 DBH cm BCH e −7.637  3.3648 × ln _  Sugar pine Gholz et al. 1979

9 H m DBH cm BCH _

2

100

_  9.5  16 .8 ×  ×



 





Western white pine Standish et al. 1985

10 BCH DBH cm H_m 2  0.199  0.00381 × _ × Western redcedar Shaw 1977

11 H m DBH cm BCH _

2

100

_  7.8  12.3 ×  ×



 



 Lodgepole pine Standish et al. 1985

12 DBH cm BCH e − 4.570  2.271 × ln _  Western hemlock Sachs 1983

13 DBH cm BCH e − 7.2775  2.3337 × ln _  Western juniper Gholz et al. 1979

14 H m DBH cm BCH _

2

100

_  1.7  26.2 ×  ×



 



 Quaking aspen Standish et al. 1985

15 H m DBH cm BCH _

2

100

_  2.5  36.8 ×  ×



 



 Black cottonwood Standish et al. 1985

16 H m DBH cm BCH _

2

100

_  8.1  21.5 ×  ×



 



 Red alder Standish et al. 1985

17 DBH cm BCH e −5.2581  2.6045 × ln _  Mountain hemlock (CA) Gholz et al. 1979

18 H m DBH cm BCH _

2

100

_  4.5  22.7 ×  ×



 



 Pacific silver fir Standish et al. 1985

19 H m DBH cm BCH _

2

100

_  5.3  9.7 ×  ×



 



 Alaska yellow-cedar Standish et al. 1985
22

GENERAL TECHNICAL REPORT PNW-GTR-819

Table 2—Pacific Northwest tree branch biomass (BCH) equations (continued)

Eqn Branch equation Major speciesa Reference

20 H m DBH cm BCH _

2

100

_  20.4  7.7 ×  ×



 



 Western larch Standish et al. 1985

22 H m DBH cm BCH _

2

100

_  12.6  23.5 ×  ×



 



 Douglas-fir Standish et al. 1985

23 BCH DBH cm H_ m 2  0.047  0.00413 × _ × Western hemlock (OR/WA) Shaw 1977

24 H m DBH cm BCH _

2

100

_  4.2  17.4 ×  ×



 



 Mountain hemlock (OR/WA) Standish et al. 1985

25 H m DBH cm BCH _

2

100

_  −0.6  45.1 ×  ×



 



 White birch (OR/WA) Standish et al. 1985

Note: 

 1. Biomass in kilogram (kg), DBH_cm is diameter in centimeters (cm), H_m is tree height in meters (m).

 2. For branch equation 12, if site is thinned, the coefficient -4.570 will be replaced with -4.876 and all the other items kept the same.

 3. Branch equation 25 may produce negative numbers when DBH < 3.5 inches, so it is suggested to use constraint: branch biomass = 0 

 when formulas produce negative numbers.

 4. PNWW = Pacific Northwest West includes western Oregon and Washington.

 5. CA = California, OR = Oregon, WA = Washington, WOR = western Oregon.

a Major species—the species or similar species for which the equation was referred for use in reference. 
23

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

Table 3—Pacific Northwest tree bark biomass (BRK) equations Eqn Bark equation Major speciesa Reference

1   cm

DBH e BR

K _ ln 7271 . 2 1069 . 2

1000

1 ×   White fir Halpern and Means 2004 

2 m

H cm

DBH

BRK _

2

10

_

0 4. 16 6. 0 × ×   



 Grand fir Standish et al. 1985

3 

m

H cm

DBH

BRK _

2

10

_

0 2. 17 0. 1 × ×   



 Subalpine fir Standish et al. 1985

4   cm DBH e BRK _ ln 8421 . 2 .47146 1

1000

1 ×   California Halpern and Means 2004

 (Shasta) red fir 

5   cm DBH e BRK _ ln 4313 . 2 79189 . 2

1000

1 ×   Noble fir Halpern and Means 2004 

6 m

H cm

DBH

BRK _

2

10

_

0 6. 12 3. 1 × ×   





Sitka spruce Standish et al. 1985

7 m

H cm

DBH

BRK _

2

10

_

0 3. 9 5. 4 × ×   





Engelmann spruce Standish et al. 1985

8 m

H cm

DBH

BRK _

2

10

_

0 6. 15 1. 3 × ×   





Douglas-fir (PNWW/CA) Standish et al. 1985

9   m

H cm

DBH e BRK _ ln( 8567 . 0 ) _ ln 34077 . 1 6263 . 3 ×  ×  −  Ponderosa pine Cochran et al. 1984

10   cm DBH e BRK _ ln 6610 . 2 183174 . 2

1000

1 ×   Sugar pine Halpern and Means 2004 

11

m

H cm

DBH

BRK _

2

10

_

0 2. 11 2. 1 × ×   



 Western white pine Standish et al. 1985

12   cm

DBH e BRK _ ln 8594 . 2 500948 . 0

1000

1 ×   Incense-cedar Halpern and Means 2004 

13   m

H cm

DBH BRK _ 2 _ 00058 . 0 336 . 0 × ×   Western redcedar Shaw 1977

14

m

H cm

DBH

BRK _

2

10

_

0 1. 9 2. 3 × ×   



 Lodgepole pine Standish et al. 1985

15   cm

DBH e BRK _ ln 259 . 2 371 . 4 ×  −  Western hemlock Sachs 1983

16   141593 . 3 _ ln 63333 . 2 175 . 10 × ×  −  cm

DBH e BRK Western juniper Gholz et al. 1979
24

GENERAL TECHNICAL REPORT PNW-GTR-819 17   cm

DBH e BRK _ ln 5837 . 1 189689 . 7

1000

1 ×   Giant sequoia Halpern and Means 2004 

18

m

H cm

DBH

BRK _

2

10

_

0 6. 27 3. 1 × ×   



 Quaking aspen Standish et al. 1985

20

m

H cm

DBH

BRK _

2

10

_

0 0. 24 2. 1 × ×   





Red alder Standish et al. 1985

21

m

H cm

DBH

BRK _

2

10

_

0 4. 27 9. 0 × ×   



 Mountain hemlock Standish et al. 1985

22

m

H cm

DBH

B

R

K _

2

10

_

0 6. 15 0. 1 × ×   



 Pacific silver fir Standish et al. 1985

23

m

H cm

DBH

BR

K _

2

10

_

0 6. 9 8. 1 × ×   



 Alaska yellow-cedar Standish et al. 1985

24

m

H cm

DBH

BRK _

2

10

_

0 0. 15 4. 2 × ×   





Western larch Standish et al. 1985

25

m

H cm

DBH

BRK _

2

10

_

0 2. 18 6. 3 × ×   



 Douglas-fir (PNWE) Standish et al. 1985

26   m

H cm

DBH

BRK _ 2 _ 00134 . 0 025 . 0 × ×   Western hemlock Shaw 1977

 (OR/WA)

27

m

H cm

DBH

B

R

K _

2

100

_ 1. 29 2. 1 × ×   



 Paper birch Standish et al. 1985

28

m

H cm

DBH

B

R

K _

2

10

_

0 5. 15 2. 1 × ×   



 Black cottonwood Standish et al. 1985

29 dB cm

D

B

H cm

D

B

H

m

H

B

R

K × × − − × × 









30 . 35 35347 . 2 _

35347 . 2

94782 . 0

21235 . 0 _ 69589 . 0 _ 0000246916 . 0 Pacific dogwood Pillsbury and Kirkley 1984

30 BRK = 0.0000386403 × H_ m 0.83339 × 



















DBH_cm + 0.68133

0.95767

2.12635

− DBH_cm 2.12635 × 35.30 × Bd California black oak Pillsbury and Kirkley 1984

31 BRK = 0.0000248325 × H_ m 0.74348 × 



















DBH_cm + 0.48584

0.96147

2.32519

− DBH_cm 2.32519 × 35.30 × Bd Canyon live oak Pillsbury and Kirkley 1984

Table 3—Pacific Northwest tree bark biomass (BRK) equations (continued) Eqn Bark equation Major speciesa Reference
25

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

32 BRK = 0.0000568840 × H_ m 0.77467 × 



















DBH_cm + 0.39534

0.90182

2.07202

− DBH_cm 2.07202 × 35.30 × Bd Golden chinkapin Pillsbury and Kirkley 1984

33 BRK = 0.0000237733 × H_ m 1.05293 × 



















DBH_cm + 0.32491

0.96579

2.05910

− DBH_cm 2.05910 × 35.30 × Bd California laurel Pillsbury and Kirkley 1984

34 BRK = 0.0000378129 × H_ m 1.01532 × 



















DBH_cm + 0.03425

0.98155

1.99295

− DBH_cm 1.99295 × 35.30 × Bd Pacific mandrone Pillsbury and Kirkley 1984

35 BRK = 0.0000236325 × H_ m 0.87108 × 



















DBH_cm + 0.78034

0.95956

2.25575

− DBH_cm 2.25575 × 35.30 × Bd Oregon white oak Pillsbury and Kirkley 1984

36 BRK = 0.0000081905 × H_ m 1.14078 × 



















DBH_cm + 4.1177141

0.95354

2.19576

− DBH_cm 2.19576 × 35.30 × Bd Tanoak Pillsbury and Kirkley 1984

Equations 29 to 36 are transformed based on Pillsbury and Kirkley (1984); log in base 10, ln in natural base.

Note: (1) Biomass in kilograms (kg), DBH_cm is diameter in centimeters (cm), H_m is tree height in meters (m).(2) Bd is bark density in kilograms per cubic foot (kg/ft3).

(3) Bark equations 27, 29, and 32 may produce negative bark biomass when DBH < 2 inches, so it is suggested to use constraint: bark biomass = 0 when formulas produce negative numbers.(4) PNWW = Pacific Northwest West includes western Oregon and Washington.PNWE = Pacific Northwest East includes eastern Oregon and Washington.CA = California, OR = Oregon, WA = Washington, WOR = western Oregon.

a Major species

—the species or similar species for which the equation was referred for use in reference. 

Table 3—Pacific Northwest tree bark biomass (BRK) equations (continued) Eqn Bark equation Major speciesa Reference
26

GENERAL TECHNICAL REPORT PNW-GTR-819

Table 4—Assignment of volume and biomass equations to major tree species in the study region

Species Volume equationa Branch equationb Bark equationc

code Common name PNWW PNWE CA PNWW PNWE CA PNWW PNWE CA

11 Pacific silver fir 11 10 11 18 18 18 22 22 22

14 Santa Lucia fir or 

 bristlecone fir 18 18 18 1 1 1 2 2 2

15 White fir 18 18 18 1 1 1 1 1 1

17 Grand fir 11 10 18 1 1 1 2 2 2

19 Subalpine fir 11 10 18 2 2 2 3 3 3

20 California red fir 18 18 18 3 3 3 4 4 4

21 Shasta red fir 18 18 18 3 3 3 4 4 4

22 Noble fir 11 10 18 3 3 3 5 5 5

41 Port-Orford-cedar 9 9 8 10 10 10 13 13 13

42 Alaska yellow-cedar 9 8 8 19 19 10 23 23 13

50 Cypress 9 9 9 10 10 10 13 13 13

51 Arizona cypress 9 9 9 10 10 10 13 13 13

54 Monterey cypress 9 9 9 10 10 10 13 13 13

55 Sargent’s cypress 9 9 9 10 10 10 13 13 13

56 McNab cypress 9 9 9 10 10 10 13 13 13

62 California juniper 21 21 21 13 13 13 16 16 16

64 Western juniper 21 21 21 13 13 13 16 16 16

65 Utah juniper 21 21 21 13 13 13 16 16 16

66 Rocky Mountain juniper 21 21 21 13 13 13 16 16 16

72 Subablpine larch 22 22 22 20 20 20 24 24 24

73 Western larch 22 22 22 20 20 20 24 24 24

81 Incense-cedar 9 9 9 10 10 10 13 13 13

92 Brewer spruce 13 12 12 4 4 4 7 7 7

93 Engelmann spruce 13 12 12 4 4 4 7 7 7

98 Sitka spruce 13 12 12 5 5 5 6 6 6

101 Whitebark pine 15 15 15 9 9 9 11 11 11

102 Bristlecone pine 15 15 15 11 11 11 14 14 14

103 Knobcone pine 15 15 15 11 11 11 14 14 14

104 Foxtail pine 15 15 15 11 11 11 14 14 14

108 Lodgepole pine 15 15 15 11 11 11 14 14 14

109 Coulter pine 4 4 4 7 7 7 9 9 9

113 Limber pine 15 15 15 11 11 11 14 14 14

116 Jeffrey pine 4 4 4 11 11 11 9 9 9

117 Sugar pine 4 4 4 8 8 8 10 10 10

119 Western white pine 15 15 4 9 9 9 11 11 11

120 Bishop pine 15 15 15 11 11 11 14 14 14

122 Ponderosa pine 4 4 4 7 7 7 9 9 9

124 Monterey pine 15 15 15 11 11 11 14 14 14

127 Gray pine 4 4 4 7 7 7 9 9 9

130 Scotch pine 17 17 17 24 24 17 21 21 21

133 Singleleaf pinyon 21 21 21 13 13 13 16 16 16

137 Washoe pine 4 4 4 7 7 7 9 9 9

201 Bigcone Douglas-fir 1 2 3 6 22 6 8 25 8

202 Douglas-fir 1 2 3 6 22 6 8 25 8

211 Redwood 24 24 24 10 10 10 17 17 17

212 Giant sequoia 24 24 24 10 10 10 17 17 17

231 Pacific yew 9 8 8 10 10 10 13 13 13

242 Western redcedar 9 8 8 10 10 10 13 13 13
27

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

251 California nutmeg 9 8 8 10 10 10 13 13 13

263 Western hemlock 6 6 6 23 23 12 26 26 15

264 Mountain hemlock 17 17 17 24 24 17 21 21 21

298 Unknown softwood 17 17 17 24 24 17 21 21 21

312 Bigleaf maple 37 37 37 16 16 16 20 20 20

313 Boxelder 38 38 38 16 16 16 30 30 30

321 Rocky Mountain maple 30 30 30 16 16 16 20 20 20

322 Bigtooth maple 30 30 30 16 16 16 20 20 20

326 Chinkapin oak 43 43 43 16 16 16 31 31 31

330 Buckeye 43 43 43 16 16 16 31 31 31

333 California buckeye 43 43 43 16 16 16 31 31 31

341 Tree of heaven 28 28 28 14 14 14 18 18 18

351 Red alder 25 25 25 16 16 16 20 20 20

352 White alder 25 25 25 16 16 16 20 20 20

361 Pacific madrone 40 40 40 16 16 16 34 34 34

374 Water birch 25 25 25 25 25 25 27 27 27

375 Paper birch 25 25 25 25 25 25 27 27 27

376 Western paper birch 25 25 25 25 25 25 27 27 27

431 Golden chinkapin 32 32 32 16 16 16 32 32 32

475 Curlleaf mountain-mahogany 32 32 32 16 16 16 32 32 32

492 Pacific dogwood 25 25 25 16 16 16 29 29 29

500 Hawthorn 34 34 34 15 15 15 36 36 36

510 Eucalyptus 31 31 31 15 15 15 36 36 36

511 Tasmanian bluegum 31 31 31 15 15 15 36 36 36

540 Ash 38 38 38 16 16 16 20 20 20

542 Oregon ash 38 38 38 16 16 16 20 20 20

591 Holly 29 29 29 25 25 25 27 27 27

600 Walnut 38 38 38 16 16 16 30 30 30

603 Northern California walnut 38 38 38 16 16 16 30 30 30

631 Tanoak 34 34 34 15 15 15 36 36 36

660 Apple 42 42 42 15 15 15 31 31 31

730 California sycamore 27 27 27 15 15 15 28 28 28

740 Cottonwood and poplar spp. 27 27 27 15 15 15 28 28 28

741 Balsam poplar 27 27 27 15 15 15 28 28 28

742 Eastern cottonwood 27 27 27 15 15 15 28 28 28

745 Plains cottonwood 27 27 27 15 15 15 28 28 28

746 Quaking aspen 28 28 28 14 14 14 18 18 18

747 Black cottonwood 27 27 27 15 15 15 28 28 28

748 Fremont cottonwood 27 27 27 15 15 15 28 28 28

755 Mesquite 27 27 27 15 15 15 28 28 28

756 Western honey mesquite 27 27 27 15 15 15 28 28 28

758 Screwbean mesquite 27 27 27 15 15 15 28 28 28

760 Cherry 27 27 27 15 15 15 28 28 28

763 Chokecherry 27 27 27 15 15 15 28 28 28

768 Bitter cherry 27 27 27 15 15 15 28 28 28

800 Oak-deciduous 43 43 43 15 15 15 31 31 31

801 California live oak 43 43 43 15 15 15 31 31 31

805 Canyon live oak 42 42 42 15 15 15 31 31 31

807 Blue oak 39 39 39 15 15 15 30 30 30

Table 4—Assignment of volume and biomass equations to major tree species in the study region (continued)

Species Volume equationa Branch equationb Bark equationc

code Common name PNWW PNWE CA PNWW PNWE CA PNWW PNWE CA
28

GENERAL TECHNICAL REPORT PNW-GTR-819

810 Emory oak 39 39 39 15 15 15 30 30 30

811 Englemann oak 36 36 36 15 15 15 30 30 30

815 Oregon white oak 41 41 41 15 15 15 35 35 35

818 California black oak 38 38 38 15 15 15 30 30 30

821 California white oak 35 35 35 15 15 15 35 35 35

839 Interior live oak 44 44 44 15 15 15 31 31 31

901 Black locust 41 41 41 15 15 15 35 35 35

920 Willow 40 40 40 15 15 15 34 34 34

922 Black willow 40 40 40 15 15 15 34 34 34

926 Balsam willow 40 40 40 15 15 15 34 34 34

928 Scouler's willow 40 40 40 15 15 15 34 34 34

981 California-laurel 33 33 33 14 14 14 33 33 33

990 Tesota (desert ironwood) 33 33 33 14 14 14 33 33 33

998 Unknown hardwood 25 25 41 16 16 16 20 20 20

999 Unknown tree 25 25 25 16 16 16 20 20 20

Note: Tree species code (SPP) 298 and 326 in the table are not in the Forest Inventory and Analysis tree species list, but are defined in the study area. 

PNWW = Pacific Northwest West includes western Oregon and Washington.

PNWE = Pacific Northwest East includes eastern Oregon and Washington.

CA = California, 

a Equation numbers refer to those in table 1a and 1b.

b

 Equation numbers refer to numbers in table 2.

c Equation numbers refer to numbers in table 3. 

Table 4—Assignment of volume and biomass equations to major tree species in the study region (continued)

Species Volume equationa Branch equationb Bark equationc

code Common name PNWW PNWE CA PNWW PNWE CA PNWW PNWE CA
29

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

Table 5—Specific gravity for major tree species wood and bark 

 Wood- BarkFIA specific specific

code Common name Scientific name gravity gravity 

11 Pacific silver fir Abies amabilis (Douglas ex Louden) Douglas ex Forbes 0.4 0.44

14 Santa Lucia or 

 bristlecone fir Abies bracteata (D. Don) D. Don ex Poit. 0.36 0.49

15 White fir Abies concolor (Gord. & Glend.) Lindl. ex Hildebr. 0.37 0.56

17 Grand fir Abies grandis (Douglas ex D. Don) Lindl. 0.35 0.57

19 Subalpine fir Abies lasiocarpa (Hook.) Nutt. 0.31 0.5

20 California red fir Abies magnifica A. Murray 0.36 0.44

21 Shasta red fir Abies x shastensis (Lemmon) Lemmon [magnifica × procera] 0.36 0.49

22 Noble fir Abies procera Rehd. 0.37 0.49

41 Port-Orford-cedar Chamaecyparis lawsoniana (A. Murr.) Parl. 0.39 0.4

42 Alaska yellow-cedar Chamaecyparis nootkatensis (D. Don) Spach 0.42 0.4

50 Cypress Cupressus L. 0.41 0.42

51 Arizona cypress Cupressus arizonica Greene ssp. arizonica 0.41 0.42

54 Monterey cypress Cupressus macrocarpa Hartw. ex Gord. 0.41 0.42

55 Sargent's cypress Cupressus sargentii Jeps. 0.41 0.42

56 MacNab's cypress Cupressus macnabiana A. Murray 0.41 0.42

62 California juniper Juniperus californica Carrière 0.45 0.4

64 Western juniper Juniperus occidentalis Hook. 0.45 0.4

65 Utah juniper Juniperus osteosperma (Torr.) Little 0.68 0.4

66 Rocky Mountain 

 juniper Juniperus scopulorum Sarg. 0.45 0.4

72 Subalpine larch Larix lyallii Parl. 0.49 0.32

73 Western larch Larix occidentalis Nutt. 0.48 0.33

81 Incense-cedar Calocedrus decurrens (Torr.) Florin 0.35 0.25

92 Brewer spruce Picea breweriana S. Watson 0.36 0.44

93 Engelmann spruce Picea engelmannii Parry ex Engelm. 0.33 0.51

98 Sitka spruce Picea sitchensis (Bong.) Carr. 0.33 0.55

101 Whitebark pine Pinus albicaulis Engelm. 0.43 0.4

102 Rocky Mountain 

 bristlecone pine Pinus aristata Engelm. 0.43 0.4

103 Knobcone pine Pinus attenuata Lemmon 0.39 0.38

104 Foxtail pine Pinus balfouriana Balf. 0.43 0.4

108 Lodgepole pine Pinus contorta Douglas ex Louden 0.38 0.38

109 Coulter pine Pinus coulteri D. Don 0.43 0.4

113 Limber pine Pinus flexilis James 0.37 0.5

116 Jeffrey pine Pinus jeffreyi Grev. & Balf. 0.37 0.36

117 Sugar pine Pinus lambertiana Dougl. 0.34 0.35

119 Western white pine Pinus monticola Dougl. ex D. Don 0.36 0.47

120 Bishop pine Pinus muricata D. Don 0.45 0.45

122 Ponderosa pine Pinus ponderosa P. & C. Lawson 0.38 0.35

124 Monterey pine Pinus radiata D. Don 0.4 0.4

127 Gray or California 

 foothill pine Pinus sabiniana Douglas ex Douglas 0.4 0.4

130 Scotch pine Pinus sylvestris L. 0.43 0.4

133 Singleleaf pinyon Pinus monophylla Torr. & Frém. 0.43 0.4

137 Washoe pine Pinus washoensis H. Mason & Stockw. 0.43 0.4

201 Bigcone Douglas-fir Pseudotsuga macrocarpa (Vasey) Mayr 0.45 0.44

202 Douglas-fir Pseudotsuga menziesii (Mirb.) Franco 0.45 0.44
30

GENERAL TECHNICAL REPORT PNW-GTR-819

211 Redwood Sequoia sempervirens (Lamb. ex D. Don) Endl. 0.36 0.43

212 Giant sequoia Sequoiadendron giganteum (Lindl.) J. Buchholz 0.34 0.34

231 Pacific yew Taxus brevifolia Nutt. 0.6 0.59

242 Western redcedar Thuja plicata Donn ex D. Don 0.31 0.37

251 California torreya

 (nutmeg) Torreya californica Torr. 0.41 0.42

263 Western hemlock Tsuga heterophylla (Raf.) Sarg. 0.42 0.5

264 Mountain hemlock Tsuga mertensiana (Bong.) Carr. 0.42 0.41

312 Bigleaf maple Acer macrophyllum Pursh 0.44 0.48

313 Boxelder Acer negundo L. 0.42 0.5

321 Rocky Mountain maple Acer glabrum Torr. 0.47 0.53

322 Bigtooth maple Acer grandidentatum Nutt. 0.47 0.53

330 Buckeye, 

 horsechestnut spp. Aesculus spp. 0.33 0.5

333 California buckeye Aesculus californica (Spach) Nutt. 0.33 0.5

341 Tree of heaven 

 (Ailanthus) Ailanthus altissima (Mill.) Swingle 0.46 0.45

351 Red alder Alnus rubra Bong. 0.37 0.56

352 White alder Alnus rhombifolia Nutt. 0.37 0.56

361 Pacific madrone Arbutus menziesii Pursh 0.58 0.6

374 Water birch Betula occidentalis Hook. 0.51 0.58

375 Paper birch Betula papyrifera Marsh. 0.48 0.56

431 Giant chinkapin, 

 golden chinkapin Chrysolepis chrysophylla (Dougl. ex Hook.) Hjelmqvist 0.42 0.42

475 Curlleaf mountain-

 mahogany Cercocarpus ledifolius Nutt. 0.52 0.53

492 Pacific dogwood Cornus nuttallii Audubon ex Torr. & Gray 0.58 0.58

500 Hawthorn spp. Crataegus spp. 0.52 0.53

510 Eucalyptus spp. Eucalyptus fruticetorum F. Muell. 0.52 0.53

511 Tasmanian bluegum Eucalyptus globules Labill. 0.52 0.53

540 Ash spp. Fraxinus spp. 0.51 0.46

542 Oregon ash Fraxinus latifolia Benth. 0.5 0.5

591 Holly Ilex spp. 0.5 0.5

600 Walnut spp. Juglans spp. 0.44 0.37

603 Northern California 

 black walnut Juglans hindsii (Jeps.) Jeps. ex R.E. Sm. 0.44 0.37

631 Tanoak Lithocarpus densiflorus (Hook. & Arn.) Rehd. 0.58 0.62

660 Apple spp. Malus spp. 0.61 0.5

730 California sycamore Platanus racemosa Nutt. 0.46 0.6

740 Cottonwood and poplar Populus spp. 0.35 0.46

741 Balsam poplar Populus balsamifera L. 0.31 0.5

742 Eastern cottonwood Populus deltoides Bartram ex Marsh. 0.37 0.38

745 Plains cottonwood Populus deltoides Bartram ex Marsh. ssp. monilifera

 (Aiton) Eckenwalder 0.35 0.46

746 Quaking aspen Populus tremuloides Michx. 0.35 0.5

747 Black cottonwood Populus balsamifera L. ssp. trichocarpa

 (Torr. & A. Gray ex Hook.) Brayshaw 0.31 0.4

748 Fremont cottonwood Populus fremontii S. Watson 0.41 0.41

Table 5—Specific gravity for major tree species wood and bark (continued)

 Wood- BarkFIA specific specific

code Common name Scientific name gravity gravity 
31

Timber Volume and Aboveground Live Tree Biomass Estimations for Landscape Analyses in the Pacific Northwest

755 Mesquite Prosopis spp. 0.78 0.65

756 Honey mesquite Prosopis glandulosa var. torreyana (L.D. Benson) M.C. Johnst. 0.78 0.65

758 Screwbean mesquite Prosopis pubescens Benth. 0.78 0.65

760 Cherry and plum Prunus spp. 0.47 0.63

763 Chokecherry Prunus virginiana L. 0.47 0.63

768 Bitter cherry Prunus emarginata (Dougl. ex Hook.) D. Dietr. 0.47 0.63

800 Oak Quercus spp. 0.59 0.58

801 California live oak Quercus agrifolia Née 0.59 0.58

805 Canyon live oak Quercus chrysolepis Liebm. 0.7 0.64

807 Blue oak Quercus douglasii Hook. & Arn. 0.59 0.58

810 Emory oak Quercus emoryi Torr. 0.59 0.58

811 Engelmann oak Quercus engelmannii Greene 0.59 0.58

815 Oregon white oak Quercus garryana Dougl. ex Hook. 0.64 0.63

818 California black oak Quercus kelloggii Newberry 0.51 0.45

821 California white oak Quercus lobata Née 0.55 0.55

839 Interior live oak Quercus wislizeni A. DC. 0.59 0.58

901 Black locust Robinia pseudoacacia L. 0.66 0.29

920 Willow Salix spp. 0.36 0.5

922 Black willow Salix nigra Marsh. 0.36 0.5

926 Balsam willow Salix pyrifolia Andersson 0.36 0.5

928 Scouler's willow Salix scouleriana Barratt ex Hook. 0.36 0.5

981 California-laurel Umbellularia californica (Hook. & Arn.) Nutt. 0.51 0.55

990 Desert ironwood Olneya tesota Barratt ex Hook. 0.52 0.53

998 Unknown hardwood Unknown 0.52 0.53

999 Other or unknown

 live tree Unknown 0.52 0.53

Note: Tree species code (SPP) 298 and 326 are not listed in the table (Miles and Smith 2009) and the specific gravities from similar tree species were 

applied.

Sources: Miles and Smith 2009. Missing species assigned specific gravity with similar species.

Table 5—Specific gravity for major tree species wood and bark (continued)

 Wood- BarkFIA specific specific

code Common name Scientific name gravity gravity 

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