United States Department of Agriculture

Forest Service

Comparing Algorithms 

for Estimating Foliar 

Biomass of Conifers in 

the Pacifi c Northwest

Crystal L. Raymond and Donald McKenzie

Pacifi c Northwest 

Research Station

Research Paper

PNW-RP-595

November 2013
Authors

Crystal L. Raymond is a research biologist and Donald McKenzie is a research 

ecologist, Pacifi c Wildland Fire Sciences Laboratory, 400 N 34th Street, Suite 

201, Seattle, WA 98103. Raymond is currently located at the Rocky Mountain 

Research Station, Forestry Sciences Laboratory, 507 25th Street, Ogden, UT 

84401. 

Cover photograph by Tom Iraci.

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Abstract

Raymond, Crystal L.; McKenzie, Donald. 2013. Comparing algorithms for 

estimating foliar biomass of conifers in the Pacifi c Northwest. Res. Pap. 

 PNW-RP-595. Portland, OR: U.S. Department of Agriculture, Forest Service, 

 Pacifi c Northwest Research Station. 23 p.

Accurate estimates of foliar biomass (FB) are important for quantifying carbon 

storage in forest ecosystems, but FB is not always reported in regional or national 

inventories. Foliar biomass also drives key ecological processes in ecosystem 

models. Published algorithms for estimating FB in conifer species of the Pacifi c 

Northwest can yield signifi cantly different results, but have not been rigorously 

compared for species other than Douglas-fi r (Pseudotsuga menziesii (Mirb.) 

Franco). We compared fi ve algorithms for estimating FB for seven common coniferous species in the Pacifi c Northwest. Algorithms based on diameter at breast 

height (DBH), or on DBH and height, consistently yield higher estimates of FB 

than algorithms based on sapwood area. At the tree level, differences between 

algorithms increased with increasing DBH for all species, but their order and 

magnitude differed by species. At the stand level, differences among algorithms 

were muted by the mix of species and diameter classes that contributed to total 

FB of stands of different seral stages and species composition. Signifi cant differences among estimates of FB from different algorithms show the need for consistent methods for estimating FB for carbon accounting, tests of the sensitivity of 

ecosystem models to these differences, and more fi eld observations to compare 

algorithms.

Keywords: foliar biomass, carbon, Pacifi c Northwest, allometry.
ii

Summary

Accurate estimates of foliar biomass (FB) are important for quantifying carbon 

storage in forest ecosystems, but FB is not always reported in regional or national 

inventories. In the Pacifi c Northwest (PNW), inventory data for Washington, 

Oregon, and California do not include estimates of carbon in tree canopies; 

although FB represents a small proportion of total stand biomass, it is important 

for estimating productivity and proportional changes in biomass. Foliar biomass 

also drives key ecological processes in ecosystem models. Published algorithms 

for estimating FB in conifer species of the PNW can yield signifi cantly different 

results, but have not been compared rigorously for species other than Douglas-fi r 

(Pseudotsuga menziesii (Mirb.) Franco). We compared fi ve algorithms for estimating FB for seven common coniferous species in the PNW: two that used only diameter and height; two that used sapwood area and leaf area, respectively; and one that 

calculated foliar biomass from alternate estimates of crown dimensions. Algorithms 

based on diameter at breast height (DBH), or on DBH and height, consistently yield 

higher estimates of FB than algorithms based on sapwood area. At the tree level, 

differences between algorithms increased with increasing DBH for all species, but 

their order and magnitude differed by species. For example, in coastal Douglas-fi r, 

estimates for large-diameter trees based on diameter alone were higher by a factor 

of fi ve than those that incorporated crown dimensions. In contrast, for lodgepole 

pine (Pinus contorta Douglas ex Loudon), estimates from the different algorithms 

were barely distinguishable. At the stand level, differences among algorithms were 

muted by the mix of species and diameter classes that contributed to total FB of 

stands of different seral stages and species composition. Signifi cant differences 

among estimates of FB from different algorithms demonstrate the need for consistent methods for estimating FB for carbon accounting and further documentation of 

the uncertainties associated with each method. Tests of the sensitivity of forest-succession models to these differences are also needed, as projections of future carbon 

dynamics depend on carbon accounting within the models, which is sensitive in 

turn to species-specifi c allometries. More fi eld observations are also needed to 

compare algorithms and inform and validate theoretical models, such as pipe-model 

theory, that could improve our understanding of carbon dynamics within forests.
1

Comparing Algorithms for Estimating Foliar Biomass of Conifers in the Pacifi c Northwest

Introduction

Accurate inventories of carbon in forest ecosystems require accounting for carbon 

in many ecosystem pools. The foliar biomass (FB) pool is particularly diffi cult 

to estimate and is not always reported as a stand attribute in regional inventories. 

For example, the Pacifi c Northwest Integrated Database (PNW-IDB) (Waddell 

and Hiserote 2005), which includes federal forest inventory data for Washington, 

Oregon, and northern California, does not include an estimate of carbon or biomass 

in the foliage of trees, leaving users to estimate it themselves. Although FB is a 

small proportion of total stand biomass, it is important for calculating annual productivity or proportional changes in biomass stocks in forest ecosystems. Accounting for carbon in FB is also important for quantifying the effects of disturbances, 

such as fi re and defoliators, on forest carbon stocks. Disturbances can affect foliage 

carbon pools greatly, and accurate estimates of FB before and after disturbance are 

necessary for quantifying this change in carbon pools. 

Estimating FB, leaf area (LA) of an individual tree, or leaf area index (LAI) 

of a stand are also key steps in modeling forest succession and carbon dynamics. 

Ecosystem process models often use these variables to calculate productivity, and 

some forest gap and succession models depend on estimates of LA for calculating 

growth, recruitment, stress, and mortality (e.g., Urban 1993). Fire models may use 

FB to calculate fuel mass and fi re hazard (Reinhardt and Crookston 2003), and 

hydrology models often require LAI or FB to simulate evapotranspiration and 

snowpack dynamics (Tague and Band 2004).

Inventories of FB and LAI for large forested areas can be done by either 

ground-based measurements or remotely sensed data. Light detection and ranging 

(LiDAR) and satellite imagery are commonly used to estimate FB (Lefsky et al. 

2002, Means et al. 1999) and LAI (Lefsky et al. 1999) over large geographic areas, 

and if temporal sequences of remotely sensed data are available, changes in canopy 

attributes over time can be detected (Turner et al. 2004). Remotely sensed data 

should be verifi ed with fi eld measurements, however, and are often not feasible 

to collect for fi ne-scale carbon accounting. Thus, there continues to be a need for 

accurate estimates of LAI and FB from ground-based measurements.

Foliar biomass of individual crowns is diffi cult to measure directly without 

destructive sampling, so it must be estimated from other more easily measured 

tree dimensions with species-specifi c allometric equations (Gholz et al. 1979, Grier 

and Logan 1977, Jenkins et al. 2004, Standish et al. 1985). Independent variables 

for these equations include diameter at breast height (DBH), tree height (HT), and 

crown dimensions. Foliar biomass can then be converted to LA by using a speciesspecifi c value of specifi c leaf area (SLA), which has units of mass per unit area. 
2

RESEARCH PAPER PNW-RP-595

Simulation models also use these allometric equations to estimate canopy attributes from other tree or stand attributes that are predicted by the models or input 

variables. 

An alternative method for estimating FB for individual trees relies on the crosssectional area of sapwood (SA) at a specifi c height on the tree, usually breast height 

(1.37 m) or crown base height (Grier and Waring 1974, Marshall and Waring 1986, 

Smithwick et al. 2002, Snell and Brown 1978). For this method of estimating FB 

from SA, SA was measured in several ways, including destructive sampling with 

staining techniques (Snell and Brown 1978), destructive sampling with a visual estimate of SA based on color (Grier and Waring 1974), with increment cores (Marshall 

and Waring 1986), or by estimating SA based on species and DBH (Smithwick et 

al. 2002). With this method, LA of individual crowns is estimated from SA fi rst, 

and then converted to FB with SLA (the reverse of what is described above). The 

SA-based method has its origin in the “pipe model” theory, which states that a given 

unit of foliage is maintained by a corresponding unit of water-conducting sapwood 

tissue (Shinozaki et al. 1964, Waring et al. 1982), i.e., LA above a specifi c height on 

a tree is a linear function of SA at that height. 

Methods that use different tree dimensions to estimate FB can yield widely different estimates (Marshall and Waring 1986, Turner et al. 2000, Van Pelt and Sillett 

2008). Previous studies have been limited in one of four ways: (1) mainly qualitative 

comparisons, (2) comparisons for only small DBH trees, (3) comparisons for only 

a few species, and (4) comparisons of LA only and not FB. For example, Grier and 

Waring (1974) developed regression equations to estimate FB as a function of SA 

at breast height for four common PNW conifers with a large range of DBH values 

(4 to 112 cm). They suggested that SA predicted FB more accurately than DBH 

alone, particularly for larger and older trees that typically have less uniform crowns, 

but they offered little quantitative analysis to support this conclusion. 

In coastal Douglas-fi r (Pseudotsuga menziesii [Mirb.] Franco var. menziesii) 

and western hemlock (Tsuga heterophylla [Raf.] Sarg.) forests of the western PNW, 

DBH-based equations consistently yield higher estimates of LA in large trees and 

LAI of old-growth forests than SA-based algorithms and other fi eld-based methods 

of measuring LAI (Marshall and Waring 1986, Turner et al. 2000, Van Pelt and 

Sillett 2008). These studies focused on LA rather than FB, however, and compared 

algorithms for only Douglas-fi r, western hemlock, and western redcedar (Thuja 

plicata Donn ex D. Don). 

Marshall and Waring (1986) compared four methods for estimating LAI of 

old-growth Douglas-fi r forests: (1) litterfall measurements, (2) light interception 

under the canopy, (3) regression on SA, and (4) regression on DBH. They found that 
3

Comparing Algorithms for Estimating Foliar Biomass of Conifers in the Pacifi c Northwest

the fi rst three methods gave similar estimates of LAI, but these estimates were half 

that of the estimate from regression on DBH. Similarly to Grier and Waring (1974), 

Marshall and Waring (1986) suggested that DBH-based regressions overestimate 

LA of large trees, and therefore LAI of mature stands, because (1) most DBH-based 

equations were derived from small-DBH trees, and (2) large-DBH trees tend to have 

more variable crowns because of competition, disturbance, and breakage. Smithwick et al. (2002) presented an approach, derived from the methods of Gholz et al. 

(1976), for estimating FB from SA that does not require sampling SA directly but 

uses regressions of sapwood width (SW) on DBH.

Allometry based on DBH is frequently used to estimate LA and FB, despite 

evidence that these equations overestimate foliar characteristics for both Douglasfi r and western hemlock and that SA is a better predictor. This may be because (1) 

the equations are readily available in comprehensive syntheses and databases of 

biomass equations (Means et al. 1994, Standish et al. 1985), (2) more variables need 

to be measured or estimated to use SA-based algorithms, and (3) SA is often not 

measured in forest inventories, being eschewed for the more easily measured DBH, 

HT, and crown dimensions.

In this study, we expand on previous research by comparing fi ve allometric 

methods (table 1) for estimating FB for seven common PNW conifers over a large 

range of DBH. We also compare the aggregate effects of these methods at the stand 

level for early-, mid-, and late-seral stands in the western and eastern Cascade 

Range of Washington state. We discuss potential biases associated with each 

method, but do not extend the analysis to fi eld-based methods of measuring FB, 

which are subject to their own sources of error. We also demonstrate the sensitivity of SA-based algorithms to two intermediate variables: (1) the ratio of the leaf 

area to sapwood area (LA:SA) and (2) specifi c leaf area (SLA). We seek to enable 

researchers, modelers, and forest managers to make informed decisions about which 

methods to use when estimating FB of different species and stands of different seral 

stages. 

We compile and document variables necessary to apply SA-based algorithms 

to the seven PNW conifers. These variables are available in the literature but have 

not been synthesized in one publication. We also rebuild regression equations for 

estimating SA from DBH for these seven conifer species, using the summary data 

of Lassen and Okkonen (1969). These equations are embedded in some forest gap 

models (e.g., Urban 1993), but not published independently. This study complements 

other regional (Means et al. 1994) and national (Jenkins et al. 2003) syntheses of 

allometric equations for estimating FB that do not include alternative methods 

based on SA. 
4

RESEARCH PAPER PNW-RP-595

Methods

Inventory Data

We used data from the Pacifi c Northwest Integrated Database (PNW-IDB) (Waddell 

and Hiserote 2005) to determine characteristic ranges of independent variables for 

each species for use in the algorithms. The PNW-IDB combines forest inventory 

data from the federal inventories on private and public lands. We used measured 

(DBH and HT) inventory data from the PNW-IDB to obtain characteristic ranges 

of DBH and total HT for the seven species growing in the PNW. For total HT, 

we used the mean HT of all trees in each 1-cm DBH class, for each species. For 

Table 1―Summary of algorithms used to calculate foliar biomass (FB)

Algorithm Description Equation form Source

FBdbh FB is estimated ln(FB)= a + b ln(D) Jenkins et al. 2004,

 with regression equations Means et al. 1994 

 based on diameter (D).

FBdbh+ht FB is estimated with FB = a + b (D/100)2 H Standish et al. 1985

 equations based on 

 diameter (D) and 

 height (H).

FBsa FB is estimated with FB = a (SA) + b Grier and Waring 

 equations based on 1974, Snell and

 sapwood cross-sectional or Brown 197)

 area (SA). 

 SA is estimated from ln (FB) = a + b ln(SA)

 diameter (D) and bark 

 thickness.

FBla Leaf area (LA) is FB = LA:SA (SA)/SLA (0.1) Gholz et al. 1976,

 estimated as a ratio of SA. Smithwick et al. 

 2002

 SA is estimated from 

 diameter and bark 

 thickness.

 LA is then converted to 

 FB using specifi c leaf 

 area (SLA). 

FBcrown FB is estimated with FB = a (CDb) + c(Dd

) + e(CW f) Van Pelt and 

 regression equations Sillett 2008

 based on diameter (D) or

 or SA and crown 

 dimensions (crown depth, FB = a(SAb

) + c(CDd)

 CD, and crown width,

 CW). SA is estimated from 

 DBH and bark thickness. 

Note: Coeffi cients a through f are species-specifi c (Van Pelt and Sillet 2008) (table 4). Diameter is diameter at 1.37 m. 

Not all algorithms were used for all species. FBsa was not used to estimate FB for western hemlock, Engelmann spruce, 

or lodgepole pine. FBcrown was only used to estimate FB for coastal Douglas-fi r. 
5

Comparing Algorithms for Estimating Foliar Biomass of Conifers in the Pacifi c Northwest

crown dimensions, each tree in the PNW-IDB has a value for crown width (CW) 

and crown ratio. Crown ratio is estimated ocularly in the fi eld as the percentage of 

the tree bole supporting healthy foliage. Crown width was either measured in the 

fi eld or estimated with equations from the Forest Vegetation Simulator. The equations used in this analysis require crown depth (CD) rather than crown ratio, so we 

multiplied the crown ratio (percentage, to the nearest 10 percent, of total HT that 

supports living crown) by total HT to calculate CD.

For the stand-level analysis, we selected 30 stands from the PNW-IDB that were 

primarily composed of two to four of the seven species. We selected 15 stands from 

the western Cascade Range region that were dominated by Douglas-fi r, western 

redcedar, and western hemlock (table 2). Some of these stands also included low 

densities of Pacifi c silver fi r (Abies amabilis [Dougl. ex Loud.] Dougl. ex J. Forbes). 

We selected 15 stands from the eastern Cascade Range region that were dominated 

by Douglas-fi r, western larch (Larix occidentalis Nutt.), or Engelmann spruce 

(Picea engelmannii Parry ex Engelm.1) (table 2). These stands also included low 

densities of ponderosa pine (Pinus ponderosa P.&C. Lawson), lodgepole pine (Pinus 

contorta Dougl. ex Loud. var. latifolia Engelm.), or grand fi r (Abies grandis (Dougl. 

ex D. Don) Lindl.). Of the 15 stands in each region, we selected 5 stands from each 

of three seral stages: young (0 to 80 years), mid (80 to 200 years), and late (>200 

years). 

Estimating Sapwood Area (SA)

The forest inventories in the PNW-IDB did not measure sapwood width (SW) 

or SA, so we used data from Lassen and Okkonen (1969) to estimate SA. They 

reported the number of samples (ni

), mean, and standard deviation (si) of SW by 

DBH-class (2.5-cm classes for DBH <76 cm and 12.7-cm classes for DBH >76 cm) 

for each species, from which we developed species-specifi c regression equations of 

SW on DBH. Ideally, we would have used direct measurements of SW or SA, but 

they are not available in the PNW-IDB and are often not included in standard forest 

Table 2―Stand characteristics by region and seral stage for the 30 stands used in the stand-level 

analysis

Region Seral stage Mean density Mean basal area Max DBH Mean DBH

 Stems/ha-1 m2

/ha-1 - - - - Centimeters - - - -

Western Cascade Range Early 2,316 23.0 35.6 8.9

 Middle 1,109 59.9 96.6 21.6

 Late 1,539 78.4 155.4 25.4

Eastern Cascade Range Early 856 13.0 32.3 10.7

 Middle 849 6.3 72.4 17.0

 Late 1,538 41.3 88.5 12.5

DBH = diameter at breast height.
6

RESEARCH PAPER PNW-RP-595

inventories for carbon because of time and expense. Regressions of SW on DBH 

provide an alternative.

We estimated SW by using species-specifi c bark-thickness coeffi cients and 

species-specifi c regressions of SW on DBH. Nonlinear regression models assume 

that the errors are independent, normally distributed, with constant variance. 

Residual diagnostics indicated increasing variance in SW with increasing DBH 

(heteroscedasticity). Furthermore, the data had large differences in sample size 

for different levels of DBH. For these two reasons, we used a weighted nonlinear 

regression model. For each species, we regressed mean SW of the DBH class on 

the midpoint of that DBH class using the equation.

 SW = b1(1 – exp(b2 × D)) (1) 

where D is diameter (cm) outside of the bark at 1.37 m, b1 is the asymptotic maximum SW (cm) reached in large trees, and b2 (dimensionless) controls the curve 

shape. We estimated all species-specifi c equations with weighted nonlinear regression by using the nls function in R (Bates and Watts 1988, R Development Core 

Team 2008). We assigned weights (wi) as

 wi = (si2

/ni)-1 (2)

where ni

 is the sample size and si is the standard deviation (cm) of each DBH class 

(i). The weights are proportional to both the sample size and the variance, so this 

weighted regression corrects for both the large differences in ni and the heteroscedasticity of the data (Neter et al. 1996).

We calculated SA (cm2

) from SW and species-specifi c coeffi cients for bark 

thickness.

 SA = (π(D(1 – b3)/2)2

) – (π((D(1 – b3)/2) – SW)

2

) (3)

where b3 is the bark thickness coeffi cient (dimensionless), D is diameter (centimeters) outside the bark at 1.37 m, and SW is the predicted sapwood width (centimeters). We used bark thickness coeffi cients from Lassen and Okkonen (1969), which 

were the mean ratio of diameter inside bark to diameter outside bark. 

Algorithms for Estimating Tree-Level Foliar Biomass

We selected equations that fi t the following three criteria: the equations (1) are 

available in syntheses of allometric equations (Jenkins et al. 2004, Means et al. 

1994), (2) are specifi c to the PNW, and (3) were developed based on a large range 

of DBH values. The fi rst algorithm (FBdbh) estimates FB based on DBH alone 

(table 1). The second algorithm (FBdbh+ ht) predicts FB based on DBH and total HT 

(Standish et al. 1985) (table 1). These are general equations intended to represent a 

species over a broad geographic range in the PNW. 
7

Comparing Algorithms for Estimating Foliar Biomass of Conifers in the Pacifi c Northwest

Table 3―Ratios of projected leaf area (LA) to sapwood cross-sectional area (SA) for seven common 

Pacifi c Northwest conifers

 LA:SA State LA:SA State

Species at 1.37 m (region) Source crown base (region) Source

 m2 cm-2 m2 cm-2

Western larch 0.29 Washington Gower et al. 1987

 (east)

Engelmann spruce .34 Oregon Waring et al. 1982 0.35 Oregon Waring

 (west) (west) et al. 1982

 .29a Colorado Kaufmann and

 Troendle 1981

Lodgepole pine .18a

 Colorado Kaufmann and 0.15 Oregon Waring

 Troendle 1981 (west) et al. 1982

 .14 Washington Gower et al. 1987

 (east)

 .11–0.3 Margolis et al. 1995

Ponderosa pine .19 Oregon Waring et al. 1982 0.25 Oregon Waring

 (west) (west) et al. 1982

 .17 Oregon Kimmins 2004 0.1–0.2 Nevada Callaway

 (east) et al. 1994

 .47 Oregon Waring et al. 1982 0.54 Oregon Waring

 (west) (west) et al. 1982

 .35 Washington Gower et al. 1987

 (east)

 .34 Oregon Waring et al. 1982

 (east)

 .25–0.7 Montana Callaway et al. 2000

Western redcedar .50 Oregon Callaway et al. 2000, 

 (west) Turner et al. 2000

Western hemlock .41 Oregon Waring et al. 1982 0.46 Oregon (Waring

 (west) (west) et al. 1982)

a Original ratios in Kaufmann and Troendle (1981) were converted from all-sided leaf area to projected leaf area in Waring et al. (1982) by 

dividing by 2.5. 

Note: Oregon (west) and Washington (west) indicate the western Cascade Range region in those states, respectively. Oregon (east) and Washington 

(east) indicate the eastern Cascade Range region in those states, respectively.

The third (FBsa) and fourth algorithms (FBla) were based on SA rather than 

DBH (table 1). The FBsa algorithm, which was not available for all species, estimates FB directly as a function of SA. These equations were originally developed 

from regressing FB on SA values that were measured directly (Grier and Waring 

1974, Snell and Brown 1978). The FBla algorithm also predicts FB as a function of 

SA, but it includes two intermediate steps (Smithwick et al. 2002). First, we used 

SA (square centimeters) to predict LA (square meters) of an individual tree using 

species- and region-specifi c values for LA:SA ratios (square meters:square centimeters) (table 3). Then we converted LA to FB using species- and region-specifi c 
8

RESEARCH PAPER PNW-RP-595

values for SLA (cm2 g-1) (table 4). SLA is the ratio of LA (square cemtimeters) to 

leaf dry mass (grams) (Gholz et al. 1976). FB kilograms per tree) was calculated as

 FB = (LA:SA × SA) / (0.1 × SLA) (4)

whereby SLA in square centimeters per gram (the units with which it is typically 

reported in the literature) is converted to square meters per kilogram.

The fi fth algorithm (FBcrown) uses two equations that estimate FB from DBH or 

SA and additional variables for crown dimensions (Van Pelt and Sillett 2008). These 

equations were available for only coastal Douglas-fi r. Van Pelt and Sillett (2008) 

developed the FBcrown equations based on an extensive data set of Douglas-fi r trees 

(n = 70) with a wide range of DBH (19 to 237 cm) and age, detailed crown measurements, and destructive samples of FB. One equation predicts FB as a function of SA 

and crown depth (m). For this equation, we used the same estimates of SA that were 

used for the FBsa and FBla algorithms. The second equation provides an alternative 

if SA estimates are not available. This equation estimates FB as a function of DBH, 

crown depth (m), and crown width (m). 

Table 4―Published values of specifi c leaf area (SLA) for common conifers in 

the Pacifi c Northwest

Species SLA Region Source

 cm2 g-1

Western larch 83.7 Washington (east) Gower et al. 1987

 76.0 Washington (east) Gower and Richards 1990

Engelmann spruce 43.5a

 Colorado Kaufmann and Troendle 1981

Lodgepole pine 41.4a Colorado Kaufmann and Troendle 1981

 39.5 Washington (east) Gower et al. 1987

 38.0 Washington (east) Gower and Richards 1990

Ponderosa pine 36.3 Oregon (east) Bond et al. 1999

 48.9 General Cregg 1994

 25.8 Idaho Cregg 1994, Marshall 

 and Monserud 2003

Coastal Douglas-fi r 82.4a

 Oregon (coast) Gholz et al. 1976

 73.9a Oregon (west) Gholz et al. 1976

 70.8a Oregon (central) Gholz et al. 1976

 74.0a Oregon (east) Gholz et al. 1976

 44.7 Washington (east) Gower et al. 1987

Rocky Mountain 34.3 Idaho Marshall and Monserud 2003

 Douglas-fi r

Western redcedar 82.6 Oregon (west) Gholz et al. 1976

Western hemlock 81.2a

 Oregon (coast) Gholz et al. 1976

 91.3a

 Oregon (west) Gholz et al. 1976 a Converted from all-sided leaf area to projected leaf area. SLA values in the literature for all-sided leaf area 

can be converted to SLA for projected leaf area by dividing by two times a species-specifi c needle crosssection correction factor to account for curved, rather than planar, needle surfaces (Gholz et al. 1976).

Note: Oregon (west) and Washington (west) indicate the western Cascade Range region in those states, 

respectively. Oregon (east) and Washington (east) indicate the eastern Cascade Range region in those states, 

respectively.
9

Comparing Algorithms for Estimating Foliar Biomass of Conifers in the Pacifi c Northwest

Sensitivity Analysis of the FBla Algorithm 

We tested the sensitivity of the FBla algorithm to variation in the values of LA:SA 

ratios and SLA by comparing predicted FB with a wide range of LA:SA ratios and 

SLA values reported in the literature for two species (ponderosa pine and coastal 

Douglas-fi r). The FBla algorithm makes two assumptions about the LA:SA ratio 

and SLA: the values (1) are reasonably consistent within a species and (2) remain 

constant with succession. Intraspecifi c variation has been observed, however, for 

both variables and could introduce uncertainty in results of the FBla algorithm. 

LA:SA ratios vary by species, with late-seral shade-tolerant species in light-limited 

environments having higher LA:SA ratios than early-seral species in moisturelimited environments (Kaufmann and Troendle 1981, Waring et al. 1982). A threefold difference in the LA:SA ratio has been observed between genera and a fi vefold 

difference across all genera (table 3). 

Similarly, intraspecifi c variation in SLA has been attributed to variations in 

seral stage, site or region, and stand density (Pearson et al. 1984, Whitehead et al. 

1984). The SLA is generally higher for shade-tolerant and late-seral species and 

lower in regions with moisture limitations. The SLA also varies within a species by 

tree age (Gholz et al. 1976), and within crowns of individual trees, decreasing with 

increasing branch height within the crown (Marshall and Monserud 2003). 

Stand-Level Analysis

We tested differences in stand-level estimates of FB for stands of different successional stages and species composition. We calculated FB for all trees in the stand 

by using the four algorithms (minus the algorithm for only coastal Douglas-fi r). 

Within-genus substitutions were made for species that did not have published equations for all four algorithms. We used analysis of variance (ANOVA) to compare 

the differences in FB estimates among algorithms within regions and seral stages. 

Thus we conducted six ANOVA tests, one for each of the two regions (western 

and eastern Cascade Range, respectively) and three seral stages (early, middle, and 

late). We used a Tukey HSD test for a post hoc analysis to determine which pairs 

of algorithms were different when signifi cant differences between algorithms were 

found in ANOVA. We used an alpha level of 0.10 because we could thereby control 

for Type II error better, with Type I error not being the concern it would be, for 

example, in a biomedical study or a fi eld experiment.

Results

Estimation of Sapwood Area 

The nonlinear regressions of SW on DBH explained a high proportion of the variance of mean SW for coastal Douglas-fi r, Rocky Mountain Douglas-fi r (Pseudotsuga 
10

RESEARCH PAPER PNW-RP-595

menziesii [Mirb.] Franco var. glauca [Beissn] Franco), ponderosa pine, lodgepole 

pine, and Engelmann spruce (table 5) (fi g. 1). In contrast, they explained a low proportion of the variance of mean SW for western larch and western redcedar (table 5) 

(fi g. 1). Asymptotic values of SW ranged from a low of 2.2 cm for western larch to a 

high of 16.6 cm for ponderosa pine (table 5).

Algorithms for Estimating Tree-Level Foliar Biomass

The FBdbh and FBdbh+ht algorithms yield consistently higher estimates of tree-level 

FB than the SA-based algorithms (FBsa and FBla) for all species (fi g. 2), although 

the order of differences between the FBdbh and FBdbh+ht algorithms was not the 

same for all species. Of the four algorithms, FBdbh gave the highest estimates of 

FB for western hemlock, western larch, and Engelmann spruce and FBdbh+ht gave 

intermediate estimates. In contrast, FBdbh+ht gave the highest estimates of all four 

algorithms for both varieties of Douglas-fi r. The FBdbh+ht and FBdbh algorithms gave 

similar estimates for western redcedar, ponderosa pine, and lodgepole pine. The 

two SA-based algorithms gave the lowest estimates of FB for all species, and were 

similar for all species for which both were available, except for Rocky Mountain 

Douglas-fi r.

Differences between FB estimates from different algorithms increased with 

increasing DBH for all species, but the DBH at which the algorithms diverged 

differed between species. For all species, the four algorithms gave similar estimates 

of FB at small DBH (< ca 40 cm) (fi g. 2). The algorithms diverged at a DBH of 

about 40 cm for Rocky Mountain Douglas-fi r, western redcedar, western larch, and 

Engelmann spruce, but about 70 cm for coastal Douglas-fi r and ponderosa pine 

Table 5―Coeffi cients of regression equations for sapwood width (SW) as a 

function of diameter at breast height (DBH) for common conifer species in the 

Pacifi c Northwest

 DBH

Species Min Max b1 b2

 b3 adj. R2

 - - Centimeters - - 

Coastal Douglas-fi r 15 213 5.51 -0.043 0.11 0.95

Rocky Mountain Douglas-fi r 16 129 4.57 -.037 .11 .97

Ponderosa pine 16 138 16.55 -.026 .11 .97

Lodgepole pine 14 70 7.08 -.045 .03 .96

Engelmann spruce 15 97 5.56 -.039 .04 .85

Western larch 16 85 2.19 -.111 .13 .19

Western redcedar 15 175 2.43 -.097 .05 .19

Western hemlock 16.30 -.018 .04

Note: All coeffi cients except western hemlock were estimated from nonlinear models fi t to the data published 

in Lassen and Okkonen (1969). Coeffi cients for western hemlock are cited in Turner et al. (2000) and originally 

from Urban (1993). Sapwood width (SW) (cm) is calculated as: SW = b1× (1 – exp(b2 × DBH)). Sapwood area 

(SA) (cm2) is calculated from SW: SA = (π × (DBH × (1 – b3)/2)2) − (π × ((DBH × (1 – b3)/2) – SW)

2

).
11

Comparing Algorithms for Estimating Foliar Biomass of Conifers in the Pacifi c Northwest

0 50 100 150 200 0 50 100 150 200

0

1

2

3

4

5

6

7

Coastal Douglas-fir

Ponderosa pine

Engelmann spruce

Lodgepole pine

Rocky Mountain Douglas-fir

0

5

10

15

20

Sapwood width (cm) Sapwood width (cm) Sapwood width (cm)

0

5

10

15

20

Diameter (cm)

0

1

2

3

4

5

6

7

0

1

2

3

4

5

6

7

0 50 100 150 200 0 20 40 60 80 100

Diameter (cm)

0 20 40 60 80 100

Figure 1—Regression models of sapwood width as a function of diameter at breast height (DBH) class for seven conifer species in

the Pacifi c Northwest. Models are fi t to the mean values for each DBH class as reported in Lassen and Okkonen (1969). DBH-classes 

are 2.5-cm classes for DBH <76 cm and 12.7-cm classes for DBH >76 cm. The sizes of the circles are proportional to the weights 

used in the nonlinear regression models.

(fi g. 2). The FBdbh+ht and FBla algorithms gave similar estimates over a wide range 

of DBH for lodgepole pine, Engelmann spruce, and western hemlock, diverging 

only above 80 to 100 cm (fi g. 2). 

For large DBHs, range width of estimates of FB also varied by species, with 

western larch and Rocky Mountain Douglas-fi r having the largest differences. For 

western larch the highest estimate of FB was 24 times that of the smallest estimate; 
12

RESEARCH PAPER PNW-RP-595

a difference of 365 kg for a 140-cm-DBH tree. For Rocky Mountain Douglas-fi r, 

the highest estimate of FB was 16 times that of the lowest estimate; a difference of 

1100 kg for a 180-cm-DBH tree. These differences were smaller for ponderosa pine, 

lodgepole pine, and Engelmann spruce, with the highest being only two to three 

times the lowest, a difference of 150 to 300 kg for a 140-cm-DBH tree. 

0

200

400

600

800

1000

1200

0

200

400

600

800

1000

1200

0 50

&RDVWDO'RXJODVíILU

:HVWHUQUHGFHGDU

3RQGHURVDSLQH

:HVWHUQODUFK

0

200

400

600

800

1000

1200

Foliar biomass (kg / tree)

Diameter (cm) Diameter (cm)

100 150

0 50 100 150

0 50 100 150

)%GEKKW

)%GEK

FB sa

)%ODL

0

200

400

600

800

1000

1200

0 50 100 150

0

200

400

600

800

1000

1200

0 50 100 150

0

200

400

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800

1000

1200

0 50 100 150

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200

400

600

800

1000

1200

0 50 100 150

0

200

400

600

800

1000

1200

0 50 100 150 200

200

200

200

5RFN\0RXQWDLQ'RXJODVíILU

:HVWHUQKHPORFN

/RGJHSROHSLQH

(QJHOPDQQVSUXFH

Figure 2—Estimates of foliar biomass (FB) made with four algorithms for eight conifer species common in the Pacifi c Northwest. The 

dotted line is FBdbh, the dashed line is FBsa, the solid line is FBla, and the circles are FBdbh+ht, which was calculated for the mean model 

term (HT) of each 1-cm DBH class. The scatter of points for FBdbh+ht is due to the HT not shown.
13

Comparing Algorithms for Estimating Foliar Biomass of Conifers in the Pacifi c Northwest

Foliar biomass (kg per tree)

0

200

400

600

800

1000

0 50 100 150 200 250 300

Diameter (cm)

FB crown sa

FB crown dbh

FA sa

FB sa

FB la

Figure 3—Estimates of foliar biomass (FB) made with fi ve algorithms for coastal Douglas-fi r. The two FBcrown

algorithms use mean crown dimensions (crown width or crown height) for each 1-cm diameter at breast height 

(DBH) class. The scatter of points is due to the model terms not shown (crown width and crown height).

Generally, both FBcrown equations for coastal Douglas-fi r agreed well with the 

FBla and FBsa algorithms (fi g. 3). The FBla and FBsa algorithms gave slightly higher 

estimates of FB than the FBcrown algorithm for trees with DBH greater than about 

200 cm. 

Sensitivity Analysis of the FBla Algorithm 

The selection of LA:SA ratios and SLA values affected the magnitude of differences between the FBla algorithm and the FBdbh algorithm (fi g. 4). Ranges of 

estimates were considerably higher for ponderosa pine than for Douglas-fi r. For 

ponderosa pine FBla estimates using a higher LA:SA ratio and a higher SLA were 

greater than the estimates with the FBdbh algorithm up to a DBH of about 175 cm, 

whereas for coastal Douglas-fi r, the FBdbh algorithm gave higher estimates than the 

FBla algorithm, regardless of LA:SA or SLA values, for DBH greater than about 

125 cm.

Stand-Level Analysis 

We rejected the null hypothesis (p < 0.10) of no differences between estimates of 

FB by using different algorithms for all six ANOVAs (two regions and three seral 
14

RESEARCH PAPER PNW-RP-595 Foliar biomass (kg / tree)

Foliar biomass (kg / tree)

0

200

400

600

800

1000

1200

0 50 100 150 200 250

Diameter (cm)

0

200

400

600

800

1000

1200

0 50 100 150 200 250

Diameter (cm)

&RDVWDO'RXJODVíILU 3RQGHURVDSLQH

FB dbh

LA:SA = 0.35, SLA = 44.7

LA:SA = 0.47, SLA = 44.7

LA:SA = 0.35, SLA = 82.4

LA:SA = 0.47, SLA = 82.4

FB dbh

LA:SA = 0.17, SLA = 25.8

LA:SA = 0.25, SLA = 25.8

LA:SA = 0.17, SLA = 48.9

LA:SA = 0.25, SLA = 48.9

Figure 4—Sensitivity of FBlai algorithm to sapwood area ratios (LA:SA) and specifi c leaf area (SLA) for (a) coastal Douglas-fi r 

and (b) ponderosa pine. The FBdbh algorithm is shown for comparison. FB = foliar biomass, DBH = diameter at breast height.

Table 6―Estimates of mean stand foliar biomass (FB) by region and 

seral stage for four algorithms

 Foliar biomass

Region Seral stage FBdbh FBdbh+ht FBsa FBla

 Mg/ha-1

Western Cascades Early 7.5a 19.1b 6.1a 6.1a

 Middle 16.9a 19.6b 16.0a 12.8c

 Late 21.9a 32.7b 16.6a,c 14.5c

Eastern Cascades Early 5.3a 10.6b 6.0a,b 4.5a

 Middle 6.6a 10.4b 5.7a 4.5a

 Late 10.5a 21.4b 8.3a 7.7a

a b c Estimates across a single row are not signifi cantly different from one another (α = 0.10) if 

they share a superscript letter. The analysis of variance tested for differences in algorithms only. 

We did not compare differences in FB between regions or seral stages.

stages). The FBdbh+ht algorithm yields signifi cantly higher values of total FB for 

stands of both regions and all three seral stages than the other three algorithms 

(table 6). The Tukey HSD test for post hoc pair-wise comparisons indicated that the 

FBdbh+ht algorithm’s estimates of stand-level FB were greater (p < 0.10) (as much as 

three times) than the estimates of the FBla algorithm. The FBdbh algorithm also gave 

signifi cantly higher (p < 0.10) estimates of FB than the FBla algorithm in the midand late-seral stands of the western Cascades. The FBla and FBsa algorithms gave 

similar estimates of stand-level FB for stands of both regions and all seral stages, 

except the mid-seral stands of the western Cascades.
15

Comparing Algorithms for Estimating Foliar Biomass of Conifers in the Pacifi c Northwest

Discussion

Estimating Sapwood Area

The regression models of SW as a function of DBH provide an alternative for 

estimating SA when it cannot be measured directly, but there are three reasons to 

be cautious when using them. First, the data we used to develop the models did not 

include trees with DBH less than 15 cm (Lassen and Okkonen 1969), so they are 

less appropriate for use with small-DBH trees. Second, the sample sizes of the large 

DBH trees were small, so outliers with large DBH could be much more infl uential 

than the many trees in the mid-range of DBH (fi g. 1). Third, direct measurements of 

SW or SA, if available, should yield more accurate estimates of FB than regressions 

on DBH. Turner et al. (2000) found that using SW from regression models overestimated LA compared to fi eld-measured SW. The applicability of the FBla and FBsa

algorithms is limited when SA is estimated from regression models rather than 

measured directly. The use of predicted values of SW to estimate FB eliminates 

tree-level variability that might be observed if SW or SA were measured directly. 

The ability of SA-based algorithms to capture this variability is one reason that 

these algorithms estimate FB better than DBH (Grier and Waring 1974). 

Diameter was a good predictor of SW for all species except western larch and 

western redcedar, introducing considerable uncertainty in the end calculation of FB 

for these two species. For both species, there is a clear tradeoff between the probable bias associated with estimating FB directly from DBH and the low explanatory power and associated uncertainty with the intermediate step via SW and SA. 

Furthermore, regression models of SW as a function of DBH are available for only a 

few species in the PNW (notably absent is any species of Abies), so species substitutions are required to use this method to calculate SA for other species, introducing 

even more uncertainty. 

Algorithms for Estimating Tree-Level Foliar Biomass

Algorithms based on DBH or DBH and HT gave higher estimates of FB for all 

species than the algorithms based on SA, although the magnitudes of divergence 

and the DBH at which the equations diverged differed among species. Divergence 

between algorithms increases with DBH for two reasons: (1) the exponential form 

of the DBH- and HT-based equations, and (2) because most of the equations were 

developed based on only trees with small DBH. Small trees can experience large 

increases in FB with relatively small increases in DBH, which suggests an 

exponential response, but that relationship will not hold for large DBH trees 

because FB growth becomes limited by other factors (Van Pelt and Sillett 2008). 

Therefore, there is a physiological reason to believe that DBH-based equations may 

be biased for large trees. More variability in the crowns of large trees is explained 
16

RESEARCH PAPER PNW-RP-595

by the FBdbh+ht algorithm, which gave intermediate estimates between the FBdbh

and the SA-based algorithms for some species. For Douglas-fi r and western redcedar, however, the FBdbh+ht algorithm gave even higher estimates of FB than FBdbh. 

In contrast to DBH- or HT-based allometry, SA-based algorithms for estimating 

FB invoke a direct physiological mechanism because they are based on the pipe 

model theory (Shinozaki et al. 1964). The pipe model theory does, however, assume 

that LA and FB are limited only by water availability. 

The FBcrown algorithms for Douglas-fi r that included both crown dimensions 

and DBH gave similar estimates to those of the SA-based algorithms for diameters 

up to about 200 cm. Intuitively, models with explicit crown dimensions should be 

closest to “truth,” given their direct geometric translation to crown volume and 

reasonable estimates of crown density. The similarity between estimates of the 

FBcrown algorithm and those of the FBla and FBsa algorithms suggests that the SAbased algorithms may be more robust than those based solely on DBH and HT. The 

FBcrown algorithms did, however, give even lower estimates of FB than SA-based 

algorithms for the largest DBH trees (DBH greater than about 200 cm). The SAbased algorithms may overestimate FB in the oldest and largest trees because they 

do not capture loss of crown biomass from disturbance and crown breakage, which 

can be captured with measurements of CW and CD. 

The FBcrown algorithms are a promising alternative to SA-based algorithms 

because CD and CW are easier to measure than SA and estimating FB using 

measured crown variables likely introduces less error than the two-step process of 

estimating SA from DBH. Defi nitive answers will require more fi eld observations 

and destructive sampling, which are currently available for only coastal Douglasfi r, but fi eld-based observations and destructive sampling of tree crowns are also 

subject to error, because large crowns often must be subsampled, with ratios then 

used to calculate full crown weight. 

In their comparison of DBH and SA as predictors of FB for several coniferous species in the Rocky Mountains, Snell and Brown (1978) found that SA was 

a better predictor of FB for some species, but SA and DBH were not signifi cantly 

different predictors of FB for other species. They concluded that the marginal 

increase in predictive power achieved when using SA was not worth the additional 

effort required to measure SA. A key limitation of their study, however, was that 

it included only trees with DBH less than 20 cm. Foliar biomass in mature trees 

can be much more complicated to estimate or measure, particularly in species like 

Douglas-fi r that have epicormic branching (Ishii et al. 2002).

Despite their apparent bias, simple allometric equations based on HT and DBH 

have three advantages over SA-based algorithms. First, they exist for more tree 
17

Comparing Algorithms for Estimating Foliar Biomass of Conifers in the Pacifi c Northwest

species in the PNW than do SA-based equations, so they may require fewer species 

substitutions. Second, they are readily available in syntheses and databases of equations commonly used to calculate FB. Third, they require only tree measurements 

that are commonly collected in the most basic forest inventories. The similarity 

between DBH-based equations and other algorithms for small DBH trees suggests 

that DBH-based algorithms are appropriate for estimating FB for smaller trees (less 

than about 50 cm DBH) and early seral stands in the PNW, whereas FB of largerDBH trees and mature stands in the PNW calls for SA-based algorithms.

Sensitivity Analysis of the FBla Algorithm 

Algorithms based on SA are sensitive to user-selected values of LA:SA ratios and 

SLA. When they were initially developed, LA:SA ratios and SLA values were 

assumed to be constant for a species, but as these values were measured over a 

wider range of environments, more variability was observed (Margolis et al. 1995 

and citations therein). Ideally, site-specifi c values would be measured when applying SA-based algorithms to specifi c stands. Alternatively, care should be taken to 

select variables from the literature that are from environments similar to a given 

study area. 

The pipe model theory, the justifi cation for SA-based algorithms, applies 

strictly only when SA and LA:SA ratios are measured at the base of the crown. 

We did not account for differences in LA:SA ratios between breast height and 

crown base height in our use of SA-based algorithms; such accounting would likely 

improve the accuracy of estimates of FB, because LA:SA ratios depend on how far 

from the crown base stem SA is measured (Whitehead et al. 1984). The SA-based 

algorithms can also be improved if the predicted SA contains an adjustment for 

taper between breast height and the crown base (Waring et al. 1982), via speciesspecifi c taper equations (Maguire and Hann 1987, Urban 1993). Alternatively, Dean 

and Long (1986) accounted for stand- and tree-level differences in LA:SA ratios 

with a nonlinear model of LA as a function of SA rather than a constant LA:SA 

ratio. 

Stand-Level Analysis of Foliar Biomass Estimates

Some differences among the algorithms for FB at the stand level were large, up to 

threefold (table 6), especially for stands with high densities of large-DBH (>20 cm) 

trees and composed primarily of Douglas-fi r (either variety), western redcedar, or 

western larch. For most regions and seral stages, however, estimates of FB at the 

stand level were not signifi cantly different between the FBla and FBdbh algorithms. 

At the stand level, the differences between these two algorithms are neutralized 
18

RESEARCH PAPER PNW-RP-595

because the FBdbh algorithm predicts lower FB for trees with the smallest DBH (less 

than about 15 to 20 cm) for some species than the SA-based algorithms. Therefore 

the differences in FB for small DBH trees compensate for the large differences 

between the large DBH trees. The late-seral stands used in this analysis had a high 

density of small DBH trees, as well as large DBH trees, which accounts for the lack 

of signifi cant differences between the FBla and FBdbh. Differences in the estimates 

of stand-level FB also depend on species composition. This stand-level analysis 

should be considered preliminary and can inform future studies that go into greater 

detail and account for differences in species composition. More detailed work at the 

stand level is needed to understand the effects of varying species composition and 

stand structure.

Implications for Ecological Modeling and Carbon Accounting

Foliar biomass is a relatively small component of total ecosystem carbon in lateseral forests of the western PNW (Grier and Logan 1977, Smithwick et al. 2002), 

but it is a larger proportion of total ecosystem carbon in early-seral forests. The proportion of aboveground biomass estimated to be FB depends on species composition and seral stage of the stand, but also on how it is estimated, as we have shown. 

The DBH-based algorithms estimate FB to be a larger portion of total biomass than 

do SA-based algorithms. In this study, FB calculated with SA-based algorithms 

was about 10 percent of aboveground biomass in early-seral stands of the western 

Cascades, 6 percent in early-seral stands in the eastern Cascades, and 3 percent to 

5 percent in the mid- and late-seral stands of both regions. In contrast, FB calculated with the FBdbh+ht algorithm was 28 percent in early-seral stands of the western 

Cascades and 15 percent in early-seral stands of the eastern Cascades. 

More research is needed on the sensitivity of ecological models to the algorithms they use to calculate FB and LAI. For example, when forest gap and succession models calculate FB, LA, or LAI with algorithms based on DBH, the modeled 

understory light environment is likely to be too dark, especially when overstory 

trees are large. This could lead to unrealistic stand structure because of the effect 

of light on recruitment and growth stress, thereby overestimating the proportion of 

late-seral species. Similarly, succession models that include fi re may overestimate 

crown fuels (and therefore crown bulk density) if using DBH-based algorithms 

to predict FB. More fi ne fuels increase fi re severity, altering carbon stocks, forest 

demography, and age and stand structure. The SA-based algorithms may improve 

model results, but then species substitutions may introduce new uncertainties if 

a model simulates species not in the limited database for SA-based models. Finescale (30-m) hydrological models, such as the regional hydro-ecological simulation 
19

Comparing Algorithms for Estimating Foliar Biomass of Conifers in the Pacifi c Northwest

system (RHESSys) (Tague and Band 2004) and the distributed hydrology-soilvegetation model (DHSVM) (Wigmosta et al. 1994), use LAI to calculate evapotranspiration, interception, and snowpack energy dynamics, and will be similarly 

affected. Modelers should be aware of the origins of the LA and FB data and of 

their sensitivity to three sources of uncertainty: (1) choice of FB-estimation algorithms, (2) parameters used in SA-based algorithms, and (3) species substitutions. 

Forests are being proposed as carbon storage offsets, thus accurate and reliable 

methods are needed to account for carbon in all FB pools. We have documented 

differences among algorithms that estimate FB for seven species in the PNW. 

These methods actualize the FB component in forest carbon accounting, but the 

signifi cant differences between stand-level estimates of FB for different algorithms 

show the need for their informed use. Consistent methods are needed for estimating FB when comparing different stands, monitoring the same stand over time, or 

comparing stands with established baselines above which additional carbon storage 

is measured. Which of these methods is generally more accurate is not known 

because independent measures of FB (e.g., destructive sampling or litter fall) are 

not available except for Douglas-fi r, for which SA-based algorithms are more 

accurate (Marshall and Waring 1986, Turner et al. 2000). Direct measurements of 

FB on other species are needed to confi rm if a more mechanistic approach, based 

on pipe-model theory, proves indeed to be superior. 

Acknowledgments

This publication was supported by the University of Washington, Joint Institute for 

the Study of the Atmosphere and Ocean (JISAO), under NOAA Cooperative Agreement No. NA17RJ1232, contribution number 1834; the U.S. Department of Agriculture, Forest Service, Pacifi c Northwest Research Station; and the U.S. Geological 

Survey, Global Change Research Program. It is a product of the Western Mountain 

Initiative. James K. Agee, Timothy B. Harrington, Maureen C. Kennedy, Douglas 

A. Maguire, and David L. Peterson provided helpful comments on an earlier draft.

English Equivalents 

When you know: Multiply by: To fi nd:

Millimeters (mm) 0.0394 Inches

Centimeters (cm) .394 Inches

Grams (g) .0352 Ounces

Kilograms (kg) 2.205 Pounds

Hectares (ha) 2.47 Acres

Megagrams per hectare .446 Tons per acre
20

RESEARCH PAPER PNW-RP-595

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