United States Department of Agriculture

DEPAR TMENT OF AGRICULT URE

Forest 

Service

Pacific Southwest 

Research Station

General Technical Report

PSW-GTR-253

October

2016

Urban Tree Database and 

Allometric Equations

E. Gregory McPherson, Natalie S. van Doorn, and Paula J. Peper
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Authors

E. Gregory McPherson is a research forester, 1731 Research Park Dr., Davis,

CA 95618; Natalie S. van Doorn is a research urban ecologist, 800 Buchanan St.,

Albany, CA 94710; Paula J. Peper is an urban ecologist (retired), 1731 Research

Park Dr., Davis, CA 95618.

Cover photos: top—Mature street trees frame a view down a residential street in 

Bismarck, North Dakota. Bottom right—Young street trees shade a sidewalk and 

parked cars in Glendale, Arizona. Bottom left—Street and front yard trees join 

to provide continuous shade in this Indianapolis, Indiana, neighborhood. (Photos 

courtesy of Pacific Southwest Research Station.)
Abstract

McPherson, E. Gregory; van Doorn, Natalie S.; Peper, Paula J. 2016. Urban 

Tree Database and Allometric Equations. Gen. Tech. Rep. PSW-GTR-235. 

Albany, CA: U.S. Department of Agriculture, Forest Service, Pacific Southwest 

Research Station. 86 p.

Information on urban tree growth underpins models used to calculate the effects 

of trees on the environment and human well-being. Maximum tree size and other 

growth data are used by urban forest managers, landscape architects, and planners 

to select trees most suitable to the amount of growing space, thereby reducing costly 

future conflicts between trees and infrastructure. Growth data are used to examine 

relationships between growth and influencing factors such as site conditions and 

stewardship practices. Despite the importance of tree growth data to the science 

and practice of urban forestry, our knowledge in this area is scant. Over a period of 

14 years, scientists with the U.S. Forest Service Pacific Southwest Research Station 

recorded data from a consistent set of measurements on over 14,000 trees in 17 U.S. 

cities. Key information collected for each tree species includes bole and crown size, 

location, and age. From this Urban Tree Database, 365 sets of tree growth equations 

were developed for the 171 distinct species. Appendices contain field data collection 

protocols, foliar biomass data that are fundamental to calculating leaf area, tree 

biomass equations for carbon storage estimates, and a user guide that illustrates 

application of the equations to calculate carbon stored over many years for tree 

species that were measured in multiple cities. An online database at http://dx.doi.

org/10.2737/RDS-2016-0005 includes the raw data, growth equations, coefficients, 

and application information for each species’ volume and dry-weight-biomass 

equations for urban and rural forest trees; and an expanded list of biomass density 

factors for common urban tree species.

Keywords: Allometry, growth models, predictive equations, tree growth, 

urban trees.
Contents

1 Chapter 1: Introduction

1 Uses of Urban Tree Growth Equations

4 Development of Urban Tree Growth Equations

6 Origin of These Urban Tree Growth Equations

8 Limitations of Urban Tree Growth Equations

11 Foliar Biomass

12 Woody Biomass

15 Chapter 2: Sampling Design and Data Collection

15 Climate Zones and Reference Cities

17 Species and Tree Sampling

18 Tree Data Collection

22 Foliar Sampling and Data Collection

23 Chapter 3: Development of Tree Growth Equations

25 Database Description

26 Data Limitations and Future Research Needs

29 Chapter 4: Conclusions

30 Acknowledgments

30 English Equivalents

31 References

38 Appendix 1: Trees Sampled by Species and Region

48 Appendix 2: Field Data Collection Protocols

56 Appendix 3: Foliar Biomass

64 Appendix 4: Growth Equation Coefficients and Application Information

68 Appendix 5: User Guide

68 Calculating Bole Diameter and Height, Crown Dimensions, and Leaf Area

69 Estimating Dry-Weight Biomass and Carbon

80 Error in Predicting Future Growth, Carbon, and Biomass

80 Case Study
1

Urban Tree Database and Allometric Equations

Tree size and age influence management costs and ecosystem services derived from 

urban trees. Urban forest researchers have developed allometric equations for trees 

in urban environments, but their range of application and predictive power are limited owing to small sample sizes, few species, young trees only, excellent-condition 

trees only, and narrow geographic region. This research overcomes many of these 

limitations. Based on measurements of 14,487 urban street and park trees, an Urban 

Tree Database (UTD) was constructed. From the UTD, 365 sets of allometric equations were developed for tree species from around the United States. Each “set” 

consists of eight equations for each of the approximately 20 most abundant species 

in each of 16 climate regions. Tree age is used to predict species diameter at breast 

height (d.b.h.), and d.b.h. is used to predict tree height, crown diameter, crown 

height, and leaf area. Diameter at breast height is also used to predict age. For 

applications with remote sensing, average crown diameter is used to predict d.b.h. 

There are 171 distinct species represented within this database. Some species grow 

in more than one region and tend to grow differently from one region to another 

owing to environmental and management differences. Thus, there are multiple 

equations for the same species that reflect those differences, and it is important to 

select the equation for the appropriate region. The UTD contains foliar biomass 

data that are fundamental to calculating leaf area, as well as tree biomass equations 

for carbon storage estimates. Also, a user guide illustrates application of the equations to calculate carbon stored over many years for tree species that were measured 

in multiple cities. The raw data and equations may be accessed and downloaded at 

http://dx.doi.org/10.2737/RDS-2016-0005.

Uses of Urban Tree Growth Equations

Information on urban tree growth is indispensable to modeling urban forest 

function and value. The economic, social, and ecological benefits of trees are 

directly related to their size, as indicated by leaf area, crown volume, and biomass (Scott et al. 1998, Stoffberg et al. 2010, Xiao et al. 2000a). Growth equations underpin the calculations produced by many computer models used in 

urban forestry, such as i-Tree, National Tree Benefit Calculator, OpenTreeMap, 

and ecoSmart Landscapes (fig. 1).

Urban tree growth and size data can assist municipal foresters because the 

costs for pruning and removing trees tends to increase with tree size (O’Brien et 

al. 1992). For example, accurate projections of size-related costs for pruning species that require frequent care can improve budgeting. Sanders et al. (2013) noted 

that managers are hindered in developing tree removal and replacement plans and 

obtaining public acceptance when they lack empirical data on each species’ useful 

Chapter 1: Introduction
2

GENERAL TECHNICAL REPORT PSW-GTR-253

service life. Without maximum size end points that are linked to constraints posed 

by the designed space, it is difficult to plan for phased removal and replacement that 

minimizes liability and maintains continuous tree canopy cover.

Knowledge of maximum tree size can inform tree selection to avoid conflicts 

between tree roots and nearby sidewalks or between crowns and utility lines 

(Randrup et al. 2001). Conversely, field-based predictions of crown projection area 

at 10, 15, and 20 years after planting can help designers select species to achieve 

targeted tree canopy cover in parking lots (McPherson 2001). Other examples of 

design and management issues influenced by tree growth and size include spacing 

between trees and in relation to building infrastructure, soil volumes required, 

irrigation demands, and pest-control and fertilization dosages (fig. 2). A better 

understanding of tree allometry by landscape architects and arborists can potentially reduce management costs, improve functional performance, and increase the 

benefits derived from healthy and sustainable urban forests (Clark et al. 1997).

Allometric equations that describe the bole and crown growth of different urban 

tree species can be used to create more realistic animations that compress years of 

growth into seconds (Peper et al. 2007). Landscape architects and planners are 

increasingly using three-dimensional models to visualize alternative landscapes (fig. 

3). Incorporating empirically derived allometric equations to simulate development of 

the tree canopy can allow designers to anticipate spatial impacts and potential conflicts 

between maturing trees and other design elements (Larsen and Kristoffersen 2002).

Figure 1—Computer programs such as i-Tree use tree growth equations when calculating annual 

carbon dioxide sequestration by trees.

i-Tree.org
3

Urban Tree Database and Allometric Equations

Figure 2—Urban tree growth equations can 

be used to estimate the maximum trunk 

diameter of different aged trees to help 

managers reduce infrastructure repair costs.

Figure 3—Tree growth equations underpin three-dimensional models that are used to visualize the 

spatial and economic impacts of alternative landscapes. (Linsen et al. 2005) Pacific Southwest Research Station
4

GENERAL TECHNICAL REPORT PSW-GTR-253

Analyses of allometric and site data can find correlations between variables that 

will inform management (Grabosky and Gilman 2004). Moreover, tree size and age 

data can be used to form local baselines for cities. Repeated measurements of the 

same trees can identify trends in growth, survival, and replacement. By building 

upon these baseline data, long-term tree growth and demographic studies could fill 

important knowledge gaps in urban forestry.

Development of Urban Tree Growth Equations

Although tree growth is the result of very complex processes, growth equations 

capture changes in tree size with age in a surprisingly simple and accurate way. 

Growth equations contain two components that reflect the interaction of two opposing biological forces. The expansion component is responsible for the increase in 

the increment with age, and growth expansion is proportional to the current size of 

the tree (Zeide 1993). The growth-decline component is responsible for the decrease 

in the increment with age from constraints imposed by internal (aging) and external 

(stress) factors. Hence, growth equations bring together these two biological forces 

over the entire lifespan of a species. Because tree growth reflects the unique genetic 

traits of trees, as well as their responses to environmental trends and management, 

no one growth equation suits all species, sites, or growth processes. Growth equations are best applied when the scope of analysis includes many individual trees 

over long time periods.

Growth equations are traditionally associated with rural forests, where they 

provide quantitative guidelines for planting, thinning, and harvesting. Growth equations for forest trees may not be directly transferable to open-grown urban trees 

because they grow and partition bole, branch, twig, and leaf biomass differently 

(Anderegg et al. 2015, Nowak 1994a, Peper and McPherson 1998) (fig. 4). For 

example, in forests, tree crowns compete for limited space and may not reach their 

maximum expansion potential (Martin et al. 2012). 

The development of allometric equations for urban open-grown trees has 

been sporadic. Fleming (1988) measured trees in New Jersey having full healthy 

crowns to develop linear relationships between d.b.h., height, crown spread, 

and age. Frelich (1992) measured only healthy trees (12 species, 221 trees total) 

growing in Minneapolis and St. Paul, Minnesota, to predict linear size relationships. Nowak (1994b) developed an allometric equation for leaf area based on 

data from park trees in Chicago. Tree dimensions and leaf area were predicted 
5

Urban Tree Database and Allometric Equations

for the most abundant street tree species in Modesto and Santa Monica, California (Peper et al. 2001a, 2001b). In New Haven, Connecticut, Troxel et al. (2013)

developed allometric equations for predicting d.b.h. from age and height, crown 

diameter, and crown volume from d.b.h. for early growth (15 years) of 10 street 

tree species. 

Outside of North America, growth equations have been developed for 

street-side Tilia species in Copenhagen, Denmark (Larsen and Kristoffersen 

2002), and T. cordata Mill., Fraxinus excelsior L. and Aesculus hippocastanum

L. in Warsaw, Poland (Lukaszkiewicz and Kosmala 2008, Lukaszkiewicz et al. 

2005). Predictive models were developed from allometric data for five street 

tree species in northeastern Italy by Semenzato et al. (2011). Stoffberg et al. 

(2008) used allometric relationships between age and d.b.h., height, and crown 

diameter to estimate dimensions at 10, 15, and 30 years after planting for three 

street tree species in Tshwane, South Africa. The allometric equations from all 

these studies reflect the effects of local site conditions, management practices, 

and growing season on growth, limiting application outside their region of 

origin (fig. 5).

Crown base and height (m)

Years after planting

Cheyenne

Ft. Collins

25

20

15

10

5

0

0 5 10 15 20 25

15.9 m

20.5 m

13.7 m

55%

100%

8.8 m

30 35 40 45 50 55 60 65 70 75 80

Figure 4—The form of red maple trees (Acer rubrum) can vary from relatively upright in forest stands (left) (Zimmerman 2011) to 

spreading when growing in the open (right). 

Pacific Southwest Research Station
6

GENERAL TECHNICAL REPORT PSW-GTR-253

Origin of These Urban Tree Growth Equations

For this report, the need to develop urban tree growth equations was first 

prompted by a grant that required calculating the 40-year annual stream of carbon 

stored by urban trees across the United States (McPherson and Simpson 1999). 

Measured data were lacking for most regions. Following Frelich (1992), d.b.h. was 

predicted using a power function with age and two constants (fig. 6). Coefficients 

were adjusted for different regions based on the number of frost-free days, and 

calibrated with the few data points that were available. This absence of reliable 

data led the U.S. Forest Service to undertake a 14-year campaign that measured 

more than 14,000 trees in cities across the United States. Crews began systematically sampling street and park trees in 1998. The initial tree growth equations 

were used with numerical models to calculate the annual stream of benefits 

associated with energy effects, air pollutant uptake and emissions, carbon storage, 

rainfall interception, and effects on property values (Maco and McPherson 2003, 

McPherson et al. 2005). 

Crown base and height (m)

Years after planting

Cheyenne

Ft. Collins

25

20

15

10

5

0

0 5 10 15 20 25

15.9 m

20.5 m

13.7 m

55%

100%

8.8 m

30 35 40 45 50 55 60 65 70 75 80

Figure 5—Urban tree growth modeling has shown how crown dimensions for trees of the same age 

and species can vary due to differences in climate and management practices (McPherson and Peper 

2012). Upper and lower lines represent height and height to first branch, respectively. Cheyenne green 

ash (Fraxinus pennsylvanica) have 55 percent of the Fort Collins’ ash leaf area after 60 years.
7

Urban Tree Database and Allometric Equations

Diameter at breast height (inches)

Age (years)

25

30

35

20

15

10

5

0

0 10 20 30 40

North

NJ-ash

South

NJ-plane

Central

Sac-ash Sac-plane

Minn-ash

This work evolved into the i-Tree Streets (formerly STRATUM) software 

program and a series of related products that are highlighted below. 

• Sixteen regional tree guides quantified the long-term benefits and costs 

for trees and provided information on program design and implementation, optimal configurations of trees, tree species for different situations, 

techniques for successful establishment of new trees, and sources of funding and technical assistance. These technical reports provide regionally 

specific science-based information for elected officials, planners, landscape architects and contractors, urban foresters, arborists, and nonprofit 

tree organizations (McPherson et al. 2000, 2010; Peper et al. 2009; Vargas 

et al. 2007) (http://www.fs.fed.us/psw/topics/urban_forestry/products/

tree_guides.shtml). 

• Seventeen municipal forest resource assessments combined results of 

citywide street/park tree inventories with benefit-cost modeling to describe 

structure, function, and value, along with resource management needs 

(McPherson and Simpson 2002, McPherson et al. 1999) (http://www.fs.fed.

us/psw/topics/urban_forestry/products/mfra.shtml).

Figure 6—Initial efforts to model tree growth to calculate carbon storage were limited by a scarcity 

of measured data (McPherson and Simpson 1999).
8

GENERAL TECHNICAL REPORT PSW-GTR-253

• Trees in Our City PowerPoint presentations (http://www.fs.fed.us/

psw/topics/urban_forestry/TreesInOurCity/index.shtml) and Trees Pay 

Us Back brochures (http://www.fs.fed.us/psw/topics/urban_forestry/

products/treebrochures.shtml) translated regional results into customized 

images and figures for audiences such as city councils and homeowners 

(McPherson et al. 2011). 

In 2008, the U.S. Forest Service Pacific Southwest Research Station received 

funding from CAL FIRE to develop a tree carbon calculator to predict carbon 

stored by tree planting, following guidance in the Urban Forest Greenhouse Gas 

Reporting Protocol (Climate Action Reserve 2008). The Center for Urban Forestry 

Research (CUFR) Tree Carbon Calculator was released in 2010 and incorporated 

revised tree growth equations for the most abundant tree species in each of 16 U.S. 

climate zones (http://www.fire.ca.gov/resource_mgt/resource_mgt_urbanforestry). 

This report presents the third, most recent and most complete sets of growth 

equations. The equations presented in this report were developed using more 

sophisticated statistical methods than before. For example, in the first studies, 

logarithmic regression and exponential models predominantly provided the best 

fits to measured data (Peper et al. 2001a, 2001b). In these equations, the best 

model fits ranged from polynomials (from simple linear to quartic) to logarithmic 

and exponential models (Peper et al. 2014). The newest equations have been 

integrated with numerical models of tree benefits in the ecoSmart Landscapes 

software (McPherson et al. 2014).

Limitations of Urban Tree Growth Equations

The biophysical, social, and economic forces that influence tree growth are highly 

variable within and among cities. Consequently, large sample sizes are required to 

fully capture overall growth trends within a species. In rural forests, relatively uniform 

growing conditions allow foresters to create site indices and generate site-specific 

growth equations for each species in the stand. This has not been done for trees in the 

urban forest because of their heterogeneity and limited resources for measurements.

Management practices can differ widely among the arborists and amateurs who 

plant and maintain trees. For example, pruning practices such as topping trees to 

reduce their height can affect tree growth and size (fig. 7). Crown damage from 

storms, pests, drought, and other stressors can result in highly variable height and 

diameter dimensions among trees of the same species and age. The presence of 

trees with dimensions that deviate from the norm can result in growth equations 

that produce less reliable size predictions.
9

Urban Tree Database and Allometric Equations

Figure 7—Tree management practices, especially pruning, can affect crown size. The two Chinese 

elms (Ulmus parvifolia) before (above) and after (below) pruning in Claremont, California.

Pacific Southwest Research Station
10

GENERAL TECHNICAL REPORT PSW-GTR-253

Another limitation to the development of robust growth equations for urban 

trees is the difficulty of obtaining accurate age data for older trees. In the context of 

this research, tree age refers to years after planting, not after germination or propagation. Records of planting dates seldom extend beyond 30 to 40 years. Similarly, 

detecting the presence and size of individual trees using high-resolution aerial 

imagery becomes difficult prior to 1990. As a result, predictions of urban tree 

dimensions reflect the increasing uncertainty about true tree age compounded by 

naturally increasing variability associated with aging (fig. 8).

Allometric equations for urban tree species have many valuable uses. Although 

researchers have developed such equations, their range of application and predictive 

power are limited by small sample sizes, few species, young and excellent-condition 

trees only, and narrow geographic range. This research overcomes some of these 

limitations by presenting 365 sets of allometric equations for the most abundant tree 

Diameter at breast height

Crown diameter

FRPE: Linear Adj R2 = 0.0880

Weight = 1 /d.b.h.ˆ2

20

15

10

5

0 20 40 60 80

Figure 8—Tree crown measurements typically reflect increased variability with age. In this scatter 

plot of green ash diameter at breast height (d.b.h.) (in centimeters) and crown-diameter data 

(in meters) the variability is greatest for trees with d.b.h. in the 20-to 60-cm range. Accordingly, 

the prediction interval increases with d.b.h. size (Peper et al. 2014).
11

Urban Tree Database and Allometric Equations

species in cities from around the United States. Also, this report illustrates application of these growth equations by calculating the predicted amounts of carbon 

dioxide stored over 50 years by the same species of trees growing in cities with 

different climates, soils, and management practices. 

Foliar Biomass

Accurate estimates of leaf area are fundamental to modeling physiological and functional processes of urban forests. For example, the volume of rainfall intercepted 

by a tree crown is related to the amount of leaf area as well as the foliage surface 

saturation storage capacity, both of which are species dependent (Xiao et al. 2000b). 

Leaf area is used to calculate dry deposition rates of air pollutants and emissions of 

biogenic volatile organic compounds (BVOC) for different tree species (Benjamin 

and Winer 1998). Hirabayashi et al. (2012) used a regression equation to estimate 

leaf area that uses crown dimensions and a species-specific shade factor (Nowak 

1996). Bottom-up modeling approaches such as this calculate interception, uptake, 

and emissions of individual trees and scale-up these estimates to the region. This 

approach allows for modeling future effects of different management strategies. 

The accuracy, precision, efficiency, and other practical considerations associated with four methods of estimating leaf area of open-grown urban trees were 

evaluated with a completely destructive sample of 50 trees (Peper and McPherson 

2003). The color digital image processing method was the only method to produce 

estimates within 25 percent of mean true leaf area and meet additional requirements 

for precision and efficient use in urban settings. The regression equation that is currently applied in the i-Tree Eco dry deposition model (Cabaraban et al. 2013, Nowak 

et al. 2014) had the lowest correlation of the four approaches. 

Isoprene and other BVOC emission factors are important components of air quality 

models because tree emissions can occur at levels that influence atmospheric composition (Geron et al. 2001). Isoprene emission rates of different plant species range from 

<0.1 to >100 μg· m-2 · h-1. Species-specific emission factor data have been summarized 

and measurement techniques detailed (Ortega et al. 2008). Allometric relationships 

between leaf area, fresh and dry leaf weight make it possible to estimate values of these 

important model parameters from measurements on a related parameter. For example, 

emission factors are expressed in units for dry foliar weight (g-C · kg-1 · dry leaf day-1). 

To scale-up the emission calculation to an entire tree, one can estimate its total dry 

foliar weight if the kilogram of dry leaf to square meter leaf area is known, as well as 

total tree leaf area. Similarly, if total tree foliar dry weight is unknown but the foliar 

dry weight to fresh weight ratio is known, total tree foliar dry weight can be estimated 

by sampling and weighing leaves in quadrats within the crown volume. 
12

GENERAL TECHNICAL REPORT PSW-GTR-253

The UTD described in this report contains allometric equations that can be used 

to calculate tree leaf area by d.b.h. for selected species. Also, it contains species-specific ratios for foliar dry weight to fresh weight and dry weight to leaf area. The UTD 

is the most extensive compilation of these ratios for urban trees published to date.

Woody Biomass

Tree species, wood density, moisture content, and size data (d.b.h. and height) are 

used with biomass equations and other information (e.g., condition) to calculate tree 

wood volume and stored carbon. Because wood densities and moisture contents can 

vary within and among species, there is error associated with the use of average 

values in allometric equations (Yoon et al. 2013). Volumetric equations calculate 

the aboveground green wood volume of a tree using species d.b.h. and height. Total 

biomass and carbon stored are estimated by converting green volume to dry weight 

using density conversion factors, adding the biomass stored belowground, and 

converting total biomass to carbon. 

Direct equations, a second type of equation, yield the aboveground dry weight 

of a tree, eliminating the need for density conversion factors. Direct equations are 

very site specific, and they assume that wood density value does not change. This 

is a limitation if the equations are to be applied across a variety of trees, sites, and 

climate zones because wood density varies within a tree and by site. Our focus has 

been on using volume equations and species-specific wood density factors obtained 

from the Global Wood Density Database (Zanne et al. 2009). This allows the user to 

select a volume equation from a species whose structure most resembles the structure of the subject tree, then apply the density factor for the subject tree’s species. 

Destructive sampling methods used to develop biomass equations in forests 

are occasionally used in urban forests, such as for Quercus virginiana Mill. and 

Q. laurifolia Michx. in Florida (Timilsina et al. 2014). Pillsbury et al. (1998) took 

nondestructive manual measurements of 15 species of street and park trees in 

California. Terrestrial LiDAR was used to develop biomass equations for 11 species 

in Fort Collins, Colorado (Lefsky and McHale 2008). A laser dendrometer was used 

for measurements on the five most abundant street tree species in Daegu, Korea 

(Yoon et al. 2013). 

Application of forest-based biomass equations for tree species is less desirable 

than applying urban-based equations because of differences in tree architecture 

(McHale et al. 2009, Yoon et al. 2013). Nowak (1994c) recommended multiplying 

forest-based equation results by a correction factor of 0.80 because they overestimated actual biomass. However, McHale et al. (2007) found that standard application of the correction factor may lead to underestimates of biomass at the city 
13

Urban Tree Database and Allometric Equations

scale. Yoon et al. (2013) found that the urban-based biomass equation for Zelkova 

serrata (Thunb.) Makino produced estimates 4.7 to 6.0 times lower than one 

from plantation-grown trees, but was similar to the equation for urban Zelkova in 

California (Pillsbury et al. 1998). However, the allometric equations for open- and 

plantation-grown Ginkgo biloba L. were similar, implying greater architectural and 

genetic uniformity for this species.

Urban general equations have been developed as an alternative to applying 

species-specific equations when many species do not have an equation. Aguaron 

and McPherson (2012) compiled urban general equations from 26 urban-based 

equations that were species specific. They found that these direct general equations underestimated carbon storage relative to species-specific equations at the 

city scale. Differences between the structure of the species used to generate the 

urban general equations and the city’s tree population may be responsible. Yoon 

et al. (2013) compiled species-specific urban equations into a general equation and 

found that the difference in values estimated using species-specific values was less 

than 1 percent at the citywide scale. However, Aguaron and McPherson’s (2012) 

general equation for urban broadleaf species overestimated aboveground biomass 

by 50 percent. The uncertainty associated with application of urban general equations underscores the need for more urban equations that are species specific. For 

improved accuracy, the urban general equations in this UTD are volume equations 

that allow users to apply species-specific dry weight density factors.
14

GENERAL TECHNICAL REPORT PSW-GTR-253
15

Urban Tree Database and Allometric Equations

Climate Zones and Reference Cities

The United States was divided into 16 national climate zones by aggregation of 

45 Sunset climate zones (Brenzel 1997). The climate zone map demarcates each 

zone (fig. 9). Sunset zones were aggregated based on factors that influence plant 

distribution, such as length of growing season and minimum temperature, as well 

as cooling degree days (CDD) and heating degree days (HDD), which are indicators of the potential effects of trees on building heating and cooling loads (table 

1). The CDD and HDD values are the summation of degrees of the average 

temperature per day above and below 18.5 °C (65 °F) for the year, respectively

(McPherson 2010). 

Chapter 2: Sampling Design and Data Collection

Figure 9—Climate zones were aggregated from 45 Sunset climate zones into 16 zones. Each zone has a reference city where tree growth 

data were collected. Sacramento, California, was added as a second reference city (with Modesto) to the Inland Valleys zone.
16

GENERAL TECHNICAL REPORT PSW-GTR-253 Table 1—Information on the reference city in each climate zone Climate zone (code) Reference city Years data collected Reference city code Sunset zonesa USDA hardiness zonesb CDDc HDDc Annual precipitation Millimeters Central Florida (CenFla) Orlando, FL 2008 ORL 26 9-10 1,806 289 1367 Coastal Plain (GulfCo) Charleston, SC 2004 CHS 27, 28 8-9 1,124 1,221 1555 Inland Empire (InlEmp) Claremont, CA 2000 CLM 18, 19, 20, 21 9 134 872 523 Inland Valleys (InlVal) Modesto, CA Sacramento, CA 1998 2010 2012 MOD SMF 7, 8, 9, 14, 8-9 1,052 773 1,439 1,718 315 470 Interior West (InterW) Albuquerque, NM 2005 ABQ 2, 10 5-6 677 2,416 250 Lower Midwest 

(LoMidW)

Indianapolis, IN 2006 IND 35 6-7 510 3,153 392

Midwest (MidWst) Minneapolis, MN 2004 MSP 36, 41, 43 4-6 355 4,436 622North (NMtnPr) Fort Collins, CO 2002 FNL 1, 44, 45 1-4 349 3,332 452Northern California Coast 

(NoCalC)

Berkeley, CA 2003 JBK 15, 16, 17 9-10 39 1,786 564

Northeast (NoEast) Queens, New 

York city, NY

2005 JFK 34, 37, 38, 39, 

40, 42

2-5 560 2,819 1041

Pacific Northwest 

(PacfNW)

Longview, WA 2001 LOG 4, 5, 6 8-9 157 2,468 1059

South (Piedmt) Charlotte, NC 2004 CLT 29, 30, 31, 32, 

33

6-8 847 1,891 1426

Southern California Coast 

(SoCalC)

Santa Monica, CA 1999 SMA 22, 23, 24 10-11 266 710 570

Southwest Desert 

(SWDsrt)

Glendale, AZ 2003 GDL 11, 12, 13 9-10 2,128 637 174

Temperate Interior West 

(TpIntW)

Boise, ID 2005 BOI 3 7 387 3,325 417

Tropical (Tropic) Honolulu, HA 2005 HNL 25 11 2,416 0 2206a From Brenzel (1997).b From http://planthardiness.ars.usda.gov/PHZMWeb/.c From McPherson (2010), cooling degree days (CDD) and heating degree days (HDD) are the summation of degrees of the average temperature per day above and below 18.5 °C for the year, respectively.
17

Urban Tree Database and Allometric Equations

“Reference city,” refers to one city selected for intensive study within each 

climate zone (McPherson 2010). Data were collected for a second reference 

city in the Inland Valleys climate zone, Sacramento, California, because tree 

growth data were required for several ongoing studies. Criteria for selecting a 

reference city included (1) an updated computerized tree inventory with location 

information for each tree (20,000 to 250,000 street/park trees); (2) information 

to accurately age a sample of about 900 trees by the city forester; (3) large, old 

trees present in the community; and (4) an aerial lift truck available for 1 week to 

sample foliage. 

Species and Tree Sampling

The trees sampled in each reference city were obtained from the computerized tree 

inventory. First, the inventory was cleaned to remove stumps, dead trees (shown 

as scheduled for removal), and vacant sites. It was sorted by species to identify the 

most abundant species for sampling. About 20 of the most abundant species were 

selected for sampling in each city. Appendix 1 lists the number of trees of each 

species sampled in each city (available for download as table S2). The sampled 

species accounted for 50 to 95 percent of all trees in the municipal tree inventories. To obtain information spanning the life cycle of each of the predominant tree 

species, a stratified random sample was drawn. The sample was stratified into nine 

diameter at breast height (d.b.h.) classes (0 to 7.6, 7.6 to 15.2, 15.2 to 30.5, 30.5 to 

45.7, 45.7 to 61.0, 61.0 to 76.2, 76.2 to 91.4, 91.4 to 106.7, and >106.7 cm). Thirty 

to 70 trees of each species were randomly selected to survey, about 5 to 10 trees 

in each d.b.h. class. Smaller samples of 30 trees were drawn for small-growing 

species such as Prunus spp. and Malus spp. Seventy trees were drawn for species 

with individuals represented in all size classes. An equal number of alternative 

trees were selected as replacement trees in the event that the originally sampled 

trees could not be located. 

Although 30 to 70 trees were randomly selected for sampling each species, 

the final samples ranged from 22 to 79 trees. The lower number resulted when 

the original and replacement trees could not be located. The higher numbers 

occurred when the sample trees were actually in a different size class than 

reported in the inventory. These trees were measured in case viable replacements could not be found. In fact, replacements were found and sample numbers 

became greater than expected.
18

GENERAL TECHNICAL REPORT PSW-GTR-253

Tree Data Collection

Each variable in the UTD, as well as its definition, abbreviation, and potential use, 

is listed in table 2. Protocols for data collection are in appendix 2. Metrics recorded 

for each tree sampled included species, address/location, d.b.h. (to nearest 1.0 cm by 

tape), tree crown, and bole height (to nearest 0.5 m by clinometer or sonar measuring device), crown diameter in two directions (parallel and perpendicular to nearest 

street to nearest 0.5 m by sonar measuring device) (table 2). Observational information was recorded on crown shape, land use, distance and direction from nearest 

air-conditioned/heated building, car shade, and conflicts with utility lines. Other 

data are presently being analyzed and will be added to the UTD upon publication 

including sidewalk damage, site type, the amount of planting space, condition of 

wood and foliage, whether the tree is city or privately managed, maintenance needs, 

and photograph numbers for the one or two photographs that were taken of each tree 

and processed in the laboratory to calculate leaf area and crown volume. This photographic method is described in Peper and McPherson (2003) and was found more 

accurate than other techniques (±25 percent of actual leaf area) for open-grown 

trees. The tree growth equations and raw data collected for each tree are available 

for download in the online supplement http://dx.doi.org/10.2737/RDS-2016-0005.

Tree age was determined from local residents, the city’s urban forester, street 

and home construction dates, historical planting records, and aerial and historical 

photos. In two cases, extra effort was required to obtain age information. Tree 

coring was used in Queens, New York City, to estimate planting dates instead of 

relying solely on historical research. Unlike other cities, where streets are lined 

with trees of the same age because they were all planted at the time of development, 

street trees in Queens were of all ages because several episodes of planting had 

ocurred. Dendrologists at the Lamont-Doherty Earth Observatory’s Tree Ring Laboratory cored 150 randomly sampled trees to establish mean tree age. These trees 

represented a subsample of the original 910 sample trees. One to two trees in size 

classes 2 through 9 were cored for each species. Cores were analyzed in the lab and 

tree age established. Urban foresters provided tree ages for an additional 104 sample 

trees in d.b.h classes 8 and 9 (91.4 to 106.7 cm and >106.7 cm), based on building 

records, and 34 trees in d.b.h. classes 1 and 2 based on planting records. These data 

were pooled with ring-count data to develop regressions based on the mean age 

for each d.b.h. size class. Thus, the online data for Queens, New York City, shows 

two sets of data, one for data directly collected from each tree and one for tree ages 

collected from a combination of coring a subsample of the measured trees and aging 

information provided by New York City Parks and Recreation. Although more 

accurate aging of trees is required for that region, equations relationships between 

d.b.h. and parameters other than age reflect actual measured data.
19

Urban Tree Database and Allometric Equations

Table 2—Abbreviations, names, descriptions, and uses for each variable in the Urban Tree Database (UTD)

Abbreviation Name Description Use

DbaseID UTD ID number Unique ID number for each tree To track tree

Region Climate region 16 U.S. climate regions, abbreviations are used 

(see table 1)

To identify geographic 

region and climate

City Reference city/state City/state names where data were collected To identify city where data 

were collected, associated 

management practices, 

climate, etc.

Source Original file name .xls file name To identify locations of 

original data sets

TreeID Inventory ID 

number

Number assigned to each tree in inventory by city To link to other tree 

inventory data

Zone Inventory 

management or 

nursery number

Number of the management area or zone that 

the tree is located in within a city or nursery if 

young tree data are collected there

To identify where data were 

collected

Park/street Inventory data for 

park, street, or 

nursery trees

Data listed as park or street or nursery (for young 

tree measurements)

To identify where data were 

collected

SpCode Species code Four- to six-letter code consisting of the first two 

letters of the genus name and the first two letters 

of the species name followed by two optional 

letters to distinguish two species with the same 

four-letter code

To have a stable 

abbreviation for each 

species name

ScientificName Scientific name Botanical name To group by taxon

CommonName Common name Common name To group by taxon

Treetype Tree type Three-letter code where first two letters refer 

to life form (BD = broadleaf deciduous, BE = 

broadleaf evergreen, CE = coniferous evergreen, 

PE = palm evergreen), and the third letter is 

mature height (S = small [<8 m], M = medium [8 

to 15 m], (L = large [>15 m])

To assist with matching 

species that were not 

measured

Address Address number From inventory, street number of the building 

where the tree is located

To relocate the tree

Street Street name From inventory, the name of the street on which 

the tree is located

To relocate the tree

Side Side of building or 

lot

From inventory, side of building or lot on which 

the tree is located: F = front, M = median, S = 

side, P = park

To relocate the tree

Cell Tree number when 

multiple trees are at 

the same address

From inventory, the cell number (i.e., 1, 2, 3, ...), 

where protocol determines the order trees at same 

address are numbered (e.g., driving direction or 

as street number increases)

To relocate the tree

OnStreet Name of the street 

the tree is on

From inventory (omitted if not a field in city’s 

inventory), for trees at corner addresses when 

tree is on cross street rather than addressed street

To relocate the tree
20

GENERAL TECHNICAL REPORT PSW-GTR-253

Abbreviation Name Description Use

FromStreet Name of cross street 

where first tree is 

inventoried

From inventory, the name of the first cross 

street that forms a boundary for trees lining 

unaddressed boulevards. Trees are typically 

numbered in order (1, 2, 3 ...) on boulevards 

that have no development adjacent to them, no 

obvious parcel addresses

To relocate the tree

ToStreet Name of last cross 

street

From inventory, the name of the last cross 

street that forms a boundary for trees lining 

unaddressed boulevards

To relocate the tree

Age Tree age Number of years since planted For allometric equations

DBH (cm) Trunk diameter 

at breast height 

(d.b.h.)

D.b.h. (1.37 m) measured to nearest 0.1 cm (tape). 

For multistemmed trees forking below 1.37 m 

measured above the butt flare and below the 

point where the stem begins forking, as per 

protocol

For allometric equations

TreeHt (m) Tree height From ground level to tree top to nearest 0.5 m 

(omitting erratic leader)

For allometric equations

CrnBase (m) Height to crown 

base

Average distance between ground and lowest 

foliage layer to nearest 0.5 m (omitting erratic 

branch)

For allometric equations

CrnHt (m) Height of crown 

from crown base 

to top

Calculated as TreeHT minus Crnbase to nearest 

0.5 m

To calculate crown volume

CdiaPar (m) Crown diameter 

measured parallel 

to the street

Crown diameter measurement taken to the nearest 

0.5 m parallel to the street (omitting erratic 

branch)

For average crown diameter

CDiaPerp (m) Crown diameter 

measured 

perpendicular to 

the street

Crown diameter measurement taken to the nearest 

0.5 m perpendicular to the street (omitting 

erratic branch)

For average crown diameter

AvgCdia (m) Average crown 

diameter

The average of crown diameter measured parallel 

and perpendicular to the street

For allometric equations

Leaf (m2) Leaf surface area 

(one side)

Estimated using digital imaging method to 

nearest 0.1 m2

Air pollutant and property 

value effects

Setback Tree distance 

from conditioned 

building

Distance from tree to nearest airconditioned/

heated space (may not be same address as tree 

location): 1 = 0 to 8 m, 2 = 8.1 to 12 m, 3 = 12.1 

to 18 m, 4 = >18 m.

Energy effects

TreeOr Tree orientation 

(compass bearing)

Taken with compass, the coordinate of tree taken 

from imaginary lines extending from walls of 

the nearest conditioned space (may not be same 

address as tree location)

Energy effects

CarShade Number of parked 

vehicles in tree 

shade

Number of parked automotive vehicles with 

some part under the tree’s drip line. Car must be 

present: 0 = no autos, 1 = 1 auto, etc.

Air pollutant effects

Table 2—Abbreviations, names, descriptions, and uses for each variable in the Urban Tree Database (UTD) 

(continued)
21

Urban Tree Database and Allometric Equations

Abbreviation Name Description Use

LandUse Land use type where 

tree is located

Predominant land use type where tree is growing: 

1 = single-family residential, 2 = multifamily 

residential (duplex, apartments, condos), 3 

= industrial/institutional/large commercial 

(schools, government, hospitals), 4 = park/

vacant/other (agric., unmanaged riparian areas 

of greenbelts), 5 = small commercial (minimart, 

retail boutiques, etc.), 6 = transportation corridor.

Energy and property value 

effects

Shape Crown shape Visual estimate of crown shape verified from 

each side with actual measured dimensions of 

crown height and average crown diameter: 1 

= cylinder (maintains same crown diameter in 

top and bottom thirds of tree), 2 = ellipsoid, the 

tree’s center (whether vertical or horizontal) is 

the widest, includes spherical), 3 = paraboloid 

(widest in bottom third of crown), 4 = upside 

down paraboloid (widest in top third of crown).

For crown volume and 

energy effects

WireConf Tree crown conflict 

with overhead 

wires

Utility lines that interfere with or appear above 

tree: 0 = no lines, 1 = present and no potential 

conflict, 2 = present and conflicting, 3 = present 

and potential for conflicting.

Pruning owing to conflicts 

may affect crown 

dimensions

d.b.h.1 to 

d.b.h.8

Trunk d.b.h. D.b.h. (cm) for multistemmed trees; for nonmultistemmed trees, d.b.h.1 is same as d.b.h.For d.b.h. calculation

Note: “-1” for all fields except leaf area, and “-100” for leaf area indicate no data collected.

Table 2—Abbreviations, names, descriptions, and uses for each variable in the Urban Tree Database (UTD) 

(continued)

In the Lower Midwest zone, the age of 337 of the 911 sampled trees was identified across d.b.h. ranges through local resources. This represented enough data to 

develop age to d.b.h equations for 12 of the 20 species sampled. For the remaining 

eight species, analysis was run testing available measured data with the same 

species measured in the other 15 climate regions to find the closest relationships. 

Closest relationships were found for Catalpa speciosa and Juglans nigra with same 

species in Boise, Idaho; with Magnolia grandiflora, Picea pungens, Pyrus sp., and 

Ulmus pumila in Fort Collins, Colorado; with Celtis occidentalis in Minneapois, 

Minnesota; and with Pinus strobus in Queens, New York City. However, these 

relationships were based on a comparison of minimal data from Indianapolis and 

should not be construed to be accurate until additional data are available for analysis from Indianapolis. These data are presented in the online UTD database and 

annotated in the “Notes” column as to origin. Age to d.b.h. equations shown here 

for these eight species, therefore, should be regarded as first-order approximations 

until more definitive data are available. For these reasons, tree age is probably the 

least accurate metric in this database.
22

GENERAL TECHNICAL REPORT PSW-GTR-253

Foliar Sampling and Data Collection

For each species, one to three trees—typical of species in age, size, and condition—

were selected for foliar sampling. Sampling was done from a bucket truck that 

required room to maneuver to reach the areas of the crown to be sampled. Foliar 

samples were taken at different locations within each tree crown to capture differences between sun and shade, as well as juvenile and mature foliage. By sampling 

leaves of different size and maturity, it was possible to obtain relationships between 

leaf area and dry weight that were representative of the tree’s foliar biomass over 

time. One set of 10 random quadrat (a cube 30 by 30 by 30 cm) samples were 

clipped from each tree—three from the lower one-third of the crown, four from the 

middle section, and three from the top one-third. Within each crown stratum, at 

least one sample was from the outer, middle, and inner portions. Leaves and stems 

were clipped along the outside of the cube, and each sample was stored in a labeled 

ziplock bag. The bags were stored in an ice chest and shipped by overnight delivery 

to the cold-storage site in Davis, California. 

The foliar samples were processed to develop relationships between leaf area 

and foliar biomass for each tree species. The leaves in each bag were separated from 

stems and twigs, then weighed (fresh weight) and run through the leaf area meter 

to obtain the sample’s total surface area (leaf area). The foliage was returned to the 

paper bag and dried in an oven at 65 °C (149 °F) for 3 days (72 hours minimum). 

On the fourth day, the bag was removed from the oven and weighed (dry weight). 

The bag was returned to the oven and dried 24 hours then removed from the oven 

and weighed. If the bag weighed less than its previous weight, it was returned to the 

oven and dried. This process was repeated until the weight no longer changed. The 

fresh weight, dry weight, and leaf area were recorded for the foliar samples in each 

of the 10 bags per species. Leaf area to dry weight and fresh weight to dry weight 

relationships were calculated for each species using standard descriptive statistics. 

Resulting data are shown in appendix 3.
23

Urban Tree Database and Allometric Equations

Six models were tested for seven parameters at four weights. Predicted parameters 

included the following: using tree age to predict diameter at breast height (d.b.h.); 

and using d.b.h. to predict tree height, crown height, crown diameter, and leaf 

area. In addition, crown diameter was used to predict d.b.h. for use with remote 

sensing imagery and age predicted from d.b.h. for use in backcasting. Prior to 

analysis, raw data points from each region were plotted to examine potential 

outliers. Following methods described by Martin et al. (2012), we eliminated from 

our analysis those observations identified on residual plots that were greater than 

two units larger than the general spread of observations for that parameter. Models 

tested included four polynomial models (linear, quadratic, cubic, and quartic), as 

well as log-log and exponential: 

Linear (1)

Quadratic (2)

Cubic (3)

Quartic (4)

Log-log (5)

Exponential (6)

Where yi is the measurement of tree i, a is the mean intercept, b is the mean slope, 

xi is the d.b.h. or age of tree i, is the random error for tree i with j ~N(0,σ2), σ2

is the variance of the random error, and wi is a known weight that takes on one of 

the following forms: wi = 1, wi = 1/√xi , wi = 1/xi , wi = 1/x2.

Analysis was conducted using SAS® 9.2 MIXED procedure (SAS 2008). The 

bias-corrected Aikaike’s information criterion (AICc) was used to compare and 

rank the models because of smaller sample sizes (Akaike 1974). The models with 

the “best” fit as indicated by having the smallest AICc were selected. Additional 

steps were needed to obtain comparable AICc values for log-log and exponential 

models (eqs. 7 and 8). Otherwise AICc values would not be comparable across all 

models. Multiplying by the geometric mean allows the AICc values to be compared 

with the models where yi is not transformed (Draper and Smith 1998). 

Chapter 3: Development of Tree Growth Equations
24

GENERAL TECHNICAL REPORT PSW-GTR-253

Log-log (7)

Exponential (8)

Where is the geometric mean of the yi values. 

All weightings for polynomials are built into the coefficients (unlike the exponential and log-log formulas). The equations are translated to Excel format in table 

3 (available for download as table S4).

The resulting best fitting model is listed for each measured species and region 

in the online supplement, table S6 (an example is shown in app. 4), with the measured parameter, predicted tree component, model weight, equation name, the 

coefficients to use in each model, the minimum and maximum values to estimate 

between, mean square error, sample size, adjusted R2, the raw data range, and the 

degrees of freedom. The model weights are already accounted for in the equation 

coefficients. The equation name represents the general form of the equation, the 

details of which are in table 3. Note that log-log and exponential models require an 

input for mean-squared error (mse), which is listed in table 7 (app. 4) column “c or 

mse” (i.e., do not calculate and use sigma2).

For palms, there is no discernable relationship between age and d.b.h. In contrast, age is an adequate predictor of tree height. Therefore, equations were developed to predict palm height from age, and subsequently, to predict other parameters 

such as biomass from palm height. 

Table 3—Excel-formatted equations for predicting open-grown tree 

growth parameters

Model name Equation

lin a + b × (age or dbh)

quad a + b × x + c ×x^2

cub a + b × x + c ×x^2 + d × x^3

quart a + b × x + c ×x^2 + d × x^3 + e × x^4

log-logw1 EXP(a + b × LN(LN(age or dbh +1) + (mse/2)))

log-logw2 EXP(a + b × LN(LN(age or dbh +1)) + (SQRT(age or dbh) + (mse/2)))

log-logw3 EXP(a + b × LN(LN(age or dbh +1)) + (age or dbh) + (mse/2))

log-logw4 EXP(a + b × LN(LN(age or dbh +1)) + (age^2 or dbh^2) + (mse/2))

expow1 EXP(a+ b × (age or dbh) + (mse/2))

expow2 EXP(a + b × (age or dbh) + SQRT(age or dbh) + (mse/2))

expow3 EXP(a + b × (age or dbh) + (age or dbh) + (mse/2))

expow4 EXP(a + b × (age or dbh) + (age^2 or dbh^2) + (mse/2))
25

Urban Tree Database and Allometric Equations

An important constraint to consider when applying the growth equations to 

measured tree data is that equations predicting d.b.h. from age may produce negative values for young ages. Negative values in d.b.h. estimates may cause continued 

problems for predicting tree height and other variables from d.b.h. These values 

should take on the first instance of a positive value.

In the Urban Tree Database (UTD), two sets of data ranges are reported. One 

shows the actual range of the data collected and is labelled “Data min” and “Data 

max.” To reduce the risk of overextending the application of the equations, we 

report application ranges for the equations used to predict each parameter. The 

“Apps min” and “Apps max” range informs users on a reasonable range for use of 

the equations—sometimes extending beyond collected data points, and sometimes 

not reaching those points. Values extending beyond the range of collected data were 

considered because there was sufficient knowledge of how large trees grow from 

measurements taken in local parks and neighborhoods. 

Database Description

The core of the UTD consists of two large data tables that can be downloaded in 

ASCII format through the online supplement. The first table (app. 3 and available 

for download as table S5) shows summarized results from the foliar sampling for 

each species and region. The second table displays equations and coefficients for 

predicting tree-growth parameters by species and predicted parameter (table S6). 

An excerpt from table S6 for two species in one climate zone is shown in appendix 4. A User Guide (app. 5) provides step-by-step instructions and examples for 

applying the growth equations to trees of interest using the core data tables. In 

addition, appendix 5 demonstrates how to estimate dry weight biomass and carbon 

using allometric equations (tables S7 and S8). Table S9 provides an expanded list 

Table 4—Percentage of best fitting model types for tree growth parameters by 

measured and predicted parameters

Relationship cub expow lin log-log quad quart

Percent

Age to diameter at breast height (d.b.h.) 27 0 31 13 28 0

Crown diameter to d.b.h. 26 1 23 35 15 0

D.b.h. to age 38 1 22 14 25 0

D.b.h. to crown diameter 22 16 23 38 0

D.b.h. to crown height 13 4 26 24 33 0

D.b.h. to leaf area 15 2 1 72 10 0

D.b.h. to tree height 16 3 14 30 35 2

Total 22 2 19 31 26 0
26

GENERAL TECHNICAL REPORT PSW-GTR-253

of dry-weight biomass density factors for common urban species. Lastly, a case 

study demonstrates differences in d.b.h., tree height, and total carbon across the 

different climate zones, highlighting the importance of developing region-specific 

growth models. 

Data Limitations and Future Research Needs

Accurately predicting d.b.h and tree height leads to better estimates of total carbon 

storage and carbon sequestration. This section describes where uncertainty is greatest and additional research is needed to improve estimates.

Tails—

In the context of estimating tree size, as well as carbon storage and sequestration for 

applications such as calculating tree benefits, it is important to continue to improve 

the accuracy of the equations at the extreme ends of the age spectrum. With limited 

measurements at the extreme ends of the age spectrum, there is the risk of a few 

extreme points driving the equation form selection. It is particularly important to 

sample from larger/older trees because small changes in growth equations can cause 

large absolute differences in carbon estimates. As trees age, the differences typically increase owing to temporal autocorrelation and differences in equation form. 

Each additional data point obtained at the upper age range is therefore critical for 

increasing accuracy of growth and volumetric equations. 

Age—

Sampling from large trees does not guarantee the addition of old trees to the database. One practical limitation of the age-to-d.b.h.-regression approach (from size 

curves instead of real growth curves) is that age data are often difficult to acquire. 

The lack of age information can limit the use of predictions in applications. For 

example, not all of the large trees randomly selected for coring in New York City 

were successfully cored. The length of the coring instrument and pockets of decay 

inside the tree limited the effectiveness of coring and thus makes this research 

dependent on people recording tree planting dates. Predictions for d.b.h. from the 

best model for Platanus × acerifolia in New York City estimated an end d.b.h. 

growth at and end d.b.h. of 61 cm as predicted from age, even though the largest tree 

measured was 165 cm d.b.h. This occurred because the largest tree was not cored 

successfully. Until additional data are collected to represent a larger and more robust 

sample of tree ages and sizes for each species, the level of inference drawn from 

these model fits should be limited by staying within the Apps min and Apps max 

ranges listed in the database. 
27

Urban Tree Database and Allometric Equations

Size—

Selecting a robust sample of trees that captures a range of sizes is important for 

smaller-growing species as well. We found that smaller-growing species, particularly Prunus and Lagerstroemia were problematic for model-fitting. Typically, 

there were few specimens smaller than 7.6 cm d.b.h. and many in the 15.2 to 30.5 

cm d.b.h. range. In addition, because these trees were often pruned by homeowners, crowns rarely followed a more natural form, resulting in a large variety of 

forms and heights. This problem of form manipulation was even greater with 

Lagerstroemia, which also might be present as either a single- or multistemmed 

plant. Lagerstroemia were often pollarded every year, affecting height and crown 

measurements as well as slowing d.b.h. growth.

It was also more difficult to find good model fits for several of the small- and 

medium-growing conifers like Pinus brutia, P. edulis, and P. contorta because 

there were few representatives in the 0 to 15.2 cm size class or, as in the case of 

P. edulis, most representatives were in the 10.2 to 30.5 cm d.b.h. range with few 

samples available below or above that.

Palms—

Palms represent another sampling gap. In the UTD (app. 4), palms do not have mse 

or adjusted R2 because the equations were not calculated from measurements, but 

from information provided by palm nurseries and experts in the region. This was 

done because the majority of palms were transplanted at anywhere from 5 to 40 

years of age, and d.b.h. recorded in tree inventories showed no relationship to other 

crown dimensions. Also, city foresters had very little information on the ages of 

palms at time of planting. Although the UTD contains measurements for more species than ever reported, much more information is needed for truly accurate growth 

representation within regions of the country.

Volumetric equations—

The results from the case study (app. 5) demonstrate the differences in growth 

patterns among climate zones/regions. Besides improving on the growth equation 

database, there is work to be done to expand volumetric equations. As described in 

the user guide (app. 5), the volumetric equations used to predict tree volume from 

measured parameters are not region specific, because differences between regions 

have not yet been tested and localized equations have not been developed. Developing a more extensive database of volumetric equations for open-grown urban tree 

species is a high-priority research need.
28

GENERAL TECHNICAL REPORT PSW-GTR-253
29

Urban Tree Database and Allometric Equations

Information on urban tree growth underpins models such as i-Tree that calculate 

effects of trees on the environment and human well-being. Data about tree growth 

are used to create realistic animations that depict landscape change over decades. 

Maximum tree size and other growth data are used by urban forest managers, 

landscape architects, and planners to select trees most suitable to the amount of 

growing space, thereby reducing costly future conflicts between trees and infrastructure. Growth data may be used to characterize relationships between growth 

and influencing factors such as site conditions and stewardship practices. Despite 

the importance of tree growth data to the science and practice of urban forestry, 

our knowledge is scant. For example, data have been lacking to specify the range 

of bole and crown dimensions for an open-grown red oak (Quercus rubra) tree 

exhibiting “normal” growth in New York City.

Over a period of 14 years, the U.S. Forest Service recorded data from a 

consistent set of measurements on over 14,000 trees in 17 U.S. cities. This 

network of cities represents municipal forests with different climates, forest 

structures, and management histories and practices. Key information collected 

for each tree species includes bole and crown size, location, and age. From this 

Urban Tree Database (UTD), 365 sets of tree-growth equations were developed 

for the predominant species. Although the UTD contains measurements for more 

species than ever reported, much more information is needed to better model tree 

growth within regions of the country. Tree planting dates are seldom recorded 

but remain fundamental to establishing relations between age and size. Capturing the range of ages that exist within the population promises to improve the 

lower and upper ends of the growth predictions where most of the uncertainty 

currently resides. Also, the value of the UTD can be expanded with new information on site conditions (e.g., soil type, microclimate, amount of growing space) 

and management practices (e.g., pruning dose, irrigation regime). With such 

information, analysts can better predict the effects of practices on tree growth 

and the services their trees provide. 

The UTD is not a static repository. Already remeasurements have been conducted on originally measured trees in two cities (Claremont and Santa Monica, 

California) to update these equations and better understand the long-term demographics of street tree populations. These new data, as well as contributions from 

other researchers, will be incorporated into the UTD. Continued updating will 

ensure that the UTD remains a valuable resource for urban and community forestry.

Chapter 4: Conclusions
30

GENERAL TECHNICAL REPORT PSW-GTR-253

Acknowledgments

This research was supported by the U.S. Department of Agriculture Forest Service, Pacific Southwest Research Station, and State Private Forestry’s Urban and 

Community Forestry Program. We are indebted to the many states and cities that 

provided support and resources that were vital to this research, not to mention the 

many seasonal data collectors and analysts. 

English Equivalents

When you know: Multiply by: To find:

Millimeters (mm) 0.0394 Inches (in)

Centimeters (cm) 0.394 Inches (in)

Meters (m) 3.281 Feet (ft)

Square meter (m2) 10.76 Square feet

Cubic meters (m3) 35.315 Cubic feet (ft3)

Grams (g) 35.315 Ounces (oz)

Micrograms or microns (μg) 3.527 x 108 Ounces (oz)

Kilograms (kg) 2.205 Pounds (lb)

Kilograms per square meter 

(kg/m2)

0.205 Pounds per square foot (lb/ft2)

Metric tonne (t) 1.102 Tons (ton)

Degrees Celsius (°C) °C × 1.8 + 32 Degrees Fahrenheit (°F)
31

Urban Tree Database and Allometric Equations

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GENERAL TECHNICAL REPORT PSW-GTR-253

Appendix 1: Trees Sampled by Species and Region

Table 5—Numbers of trees sampled by species and region (continued)

Scientific name Common name SpCode Samples

Central Florida (CenFla):

Acer rubrum L. red maple ACRU 56

Cinnamomum camphora (L.) J. Presi camphor tree CICA 63

Eriobotrya japonica (Thunb.) Lindl. loquat tree ERJA 31

Juniperus virginiana L. southern redcedar JUSI 50

Koelreuteria elegans (Seem.) A.C. Sm. Chinese rain tree KOELFO 43

Lagerstroemia indica L. common crapemyrtle LAIN 35

Liquidambar styraciflua L. sweetgum LIST 48

Magnolia grandiflora L. southern magnolia MAGR 51

Pinus elliottii Engelm. slash pine PIEL 37

Platanus occidentalis L. American sycamore PLOC 44

Platycladus orientalis (L.) Franco Oriental arborvitae THOR 37

Prunus caroliniana (Mill.) Aiton Carolina laurelcherry PRCA 39

Quercus laurifolia Michx. laurel oak QULA2 67

Quercus shumardii Buckley Shumard oak QUSH 37

Quercus virginiana Mill. live oak QUVI 65

Sabal palmetto (Walter) Lodd. ex Schult. & Schult. f. cabbage palmetto SAPA 45

Syagrus romanzoffiana (Cham.) Glassman queen palm SYRO 30

Triadica sebifera (L.) Small tallowtree TRSE6 40

Ulmus parvifolia Jacq. Chinese elm ULPA 37

Washingtonia robusta H. Wendl. Mexican fan palm WARO 40

Coastal Plain (GulfCo):

Acer rubrum L. red maple ACRU 36

Butia capitata (Mart.) Becc. jelly palm BUCA 33

Carya illinoinensis (Wangenh.) K.Koch pecan CAIL 36

Celtis laevigata Willd. sugarberry CELA 37

Cornus florida L. flowering dogwood COFL 34

Gleditsia triacanthos L. honeylocust GLTR 37

Ilex opaca Aiton American holly ILOP 37

Juniperus virginiana L. eastern red cedar JUVI 43

Lagerstroemia indica L. common crapemyrtle LAIN 42

Liquidambar styraciflua L. sweetgum LIST 50

Magnolia grandiflora L. southern magnolia MAGR 40

Pinus taeda L. loblolly pine PITA 47

Platanus occidentalis L. American sycamore PLOC 56

Pyrus calleryana Decne. Callery pear PYCA 36

Quercus laurifolia Michx. laurel oak QULA2 79
39

Urban Tree Database and Allometric Equations

Table 5—Numbers of trees sampled by species and region (continued)

Scientific name Common name SpCode Samples

Quercus nigra L. water oak QUNI 68

Quercus phellos L. willow oak QUPH 45

Quercus virginiana Mill. live oak QUVI 76

Sabal palmetto (Walter) Lodd. ex Schult. & Schult. f. cabbage palmetto SAPA 40

Inland Empire (InlEmp):

Brachychiton populneus (Schott & Endl.) R.Br. kurrajong BRPO 37

Cinnamomum camphora (L.) J. Presl camphor tree CICA 57

Eucalyptus sideroxylon A. Cunn. ex Woolls red ironbark EUSI 37

Fraxinus uhdei (Wenz.) Lingelsh. evergreen ash FRUH 37

Fraxinus velutina ‘Modesto’ Torr. Modesto ash FRVE_G 36

Ginkgo biloba L. ginkgo GIBI 37

Jacaranda mimosifolia D. Don jacaranda JAMI 63

Lagerstroemia indica L. common crapemyrtle LAIN 61

Liquidambar styraciflua L. sweetgum LIST 38

Liriodendron tulipifera L. tulip tree LITU 37

Magnolia grandiflora L. southern magnolia MAGR 37

Pinus brutia Ten. Turkish pine; east 

Mediterranean pine

PIBR2 37

Pinus canariensis C. Sm. Canary Island pine PICA 39

Pistacia chinensis Bunge Chinese pistache PICH 40

Platanus racemosa Nutt. California sycamore PLRA 37

Platanus × acerifolia (Aiton) Willd. London planetree PLAC 38

Pyrus calleryana Decne. Callery pear PYCA 39

Quercus agrifolia Née coastal live oak; 

California live oak

QUAG 37

Quercus ilex L. holly oak QUIL2 35

Schinus molle L. California peppertree SCMO 37

Schinus terebinthifolius Raddi Brazilian pepper SCTE 36

Washingtonia robusta H. Wendl. Mexican fan palm WARO 36

Inland Valleys (InlVal):

Acer saccharinum L. silver maple ACSA1 29

Betula pendula Roth European white birch BEPE 29

Celtis sinensis Pers. Chinese hackberry CESI4 30

Cinnamomum camphora (L.) J. Presl camphor tree CICA 31

Fraxinus angustifolia ‘Raywood’ Vahl Raywood ash FRAN_R 31

Fraxinus excelsior ‘Hessei’ L. Hesse ash FREX_H 27

Fraxinus holotricha Koehne Moraine ash FRHO 29
40

GENERAL TECHNICAL REPORT PSW-GTR-253

Table 5—Numbers of trees sampled by species and region (continued)

Scientific name Common name SpCode Samples

Fraxinus pennsylvanica Marshall Marshall ash FRPE_M 28

Fraxinus velutina Torr. Modesto ash FRVE_G 28

Ginkgo biloba L. ginkgo GIBI 32

Gleditsia triacanthos L. honeylocust GLTR 27

Koelreuteria paniculata Laxm. goldenrain tree KOPA 29

Lagerstroemia indica L. common crapemyrtle LAIN 26

Liquidambar styraciflua L. sweetgum LIST 30

Magnolia grandiflora L. southern magnolia MAGR 29

Pinus thunbergii Parl. Japanese black pine PITH 26

Pistacia chinensis Bunge Chinese pistache PICH 30

Platanus × acerifolia (Aiton) Willd. London planetree PLAC 27

Prunus cerasifera Ehrh. cherry plum PRCE 27

Pyrus calleryana ‘Bradford’ Decne. Callery pear ‘Bradford’ PYCA_B 30

Quercus ilex L. holly oak QUIL2 28

Zelkova serrata (Thunb.) Makino Japanese zelkova ZESE 31

Interior West (InterW):

Chilopsis linearis (Cav.) Sweet desert willow CHLI 30

Elaeagnus angustifolia L. Russian olive ELAN 30

Fraxinus americana L. white ash FRAM 28

Fraxinus angustifolia ‘Raywood’ Vahl Raywood ash FRAN2 30

Fraxinus pennsylvanica Marshall green ash FRPE 31

Fraxinus velutina Torr. velvet ash FRVE 69

Gleditsia triacanthos L. honeylocust GLTR 68

Koelreuteria paniculata Laxm. goldenrain tree KOPA 28

Malus sp. apple MA2 30

Pinus edulis Engelm. pinyon pine PIED 29

Pinus nigra Arnold Austrian pine PINI 28

Pinus ponderosa Douglas ex P. Lawson & C. Lawson ponderosa pine PIPO 30

Pinus sylvestris L. Scotch pine PISY 30

Pistacia chinensis Bunge Chinese pistache PICH 30

Platanus × acerifolia (Aiton) Willd. London planetree PLAC 70

Populus angustifolia E. James narrowleaf cottonwood POAN 70

Populus fremontii S. Watson Fremont cottonwood POFR 70

Prunus cerasifera Ehrh. cherry plum PRCE 30

Pyrus calleryana Decne. Callery pear PYCA 32

Ulmus pumila L. Siberian elm ULPU 70
41

Urban Tree Database and Allometric Equations

Table 5—Numbers of trees sampled by species and region (continued)

Scientific name Common name SpCode Samples

Lower Midwest (LoMidW):

Acer platanoides L. Norway maple ACPL 34

Acer rubrum L. red maple ACRU 35

Acer saccharinum L. silver maple ACSA1 54

Acer saccharum Marsh. sugar maple ACSA2 37

Catalpa speciosa (Warder) Warder ex Engelm. northern catalpa CASP 49

Celtis occidentalis L. northern hackberry CEOC 56

Cercis canadensis L. eastern redbud CECA 33

Fraxinus americana L. white ash FRAM 55

Fraxinus pennsylvanica Marshall green ash FRPE 49

Gleditsia triacanthos L. honeylocust GLTR 35

Juglans nigra L. black walnut JUNI 34

Malus sp. apple MA2 36

Morus sp. mulberry MO 48

Picea pungens Engelm. blue spruce PIPU 35

Pinus strobus L. eastern white pine PIST 39

Populus deltoides Bartram ex Marsh eastern cottonwood PODE 59

Pyrus calleryana ‘Bradford’ Decne. Callery pear ‘Bradford’ PYCA_B 39

Quercus rubra L. northern red oak QURU 60

Tilia cordata Mill. littleleaf linden TICO 36

Ulmus pumila L. Siberian elm ULPU 54

Midwest (MidWst):

Acer negundo L. Boxelder ACNE 43

Acer platanoides L. Norway maple ACPL 48

Acer rubrum L. red maple ACRU 46

Acer saccharinum L. silver maple ACSA1 41

Acer saccharum Marsh. sugar maple ACSA2 48

Celtis occidentalis L. northern hackberry CEOC 49

Fraxinus americana L. white ash FRAM 38

Fraxinus pennsylvanica Marshall green ash FRPE 46

Ginkgo biloba L. ginkgo GIBI 48

Gleditsia triacanthos L. honeylocust GLTR 48

Malus sp. apple MA2 50

Quercus palustris Münchh. pin oak QUPA 47

Quercus rubra L. northern red oak QURU 45

Tilia americana L. American basswood TIAM 46

Tilia cordata Mill. littleleaf linden TICO 38

Ulmus americana L. American elm ULAM 42
42

GENERAL TECHNICAL REPORT PSW-GTR-253

Table 5—Numbers of trees sampled by species and region (continued)

Scientific name Common name SpCode Samples

Ulmus pumila L. Siberian elm ULPU 37

North (NMtnPr):

Acer platanoides L. Norway maple ACPL 60

Acer saccharinum L. silver maple ACSA1 66

Acer saccharum Marsh. sugar maple ACSA2 22

Celtis occidentalis L. northern hackberry CEOC 67

Fraxinus americana L. white ash FRAM 31

Fraxinus pennsylvanica Marshall green ash FRPE 65

Gleditsia triacanthos L. honeylocust GLTR 64

Gymnocladus dioicus (L.) K. Koch Kentucky coffeetree GYDI 31

Malus sp. apple MA2 31

Picea pungens Engelm. blue spruce PIPU 34

Pinus nigra Arnold Austrian pine PINI 33

Pinus ponderosa Douglas ex P. Lawson & C. 

Lawson

ponderosa pine PIPO 31

Populus sargentii Dode plains cottonwood POSA 54

Prunus sp. plum PR 25

Pyrus sp. pear PY 29

Quercus macrocarpa Michx. bur oak QUMA1 34

Tilia americana L. American basswood TIAM 33

Tilia cordata Mill. littleleaf linden TICO 34

Ulmus americana L. American elm ULAM 61

Ulmus pumila L. Siberian elm ULPU 62

Northern California Coast (NoCalC):

Acacia melanoxylon R. Br. black acacia ACME 35

Acer palmatum Thunb. Japanese maple ACPA 38

Cinnamomum camphora (L.) J. Presl camphor tree CICA 70

Eucalyptus globulus Labill. blue gum eucalyptus EUGL 67

Fraxinus velutina Torr. velvet ash FRVE 33

Ginkgo biloba L. ginkgo GIBI 36

Liquidambar styraciflua L. sweetgum LIST 37

Liriodendron tulipifera L. tulip tree LITU 34

Magnolia grandiflora L. southern magnolia MAGR 38

Pinus radiata D. Don Monterey pine PIRA 35

Pistacia chinensis Bunge Chinese pistache PICH 37

Pittosporum undulatum Vent. Victorian box PIUN 31

Platanus × acerifolia (Aiton) Willd. London planetree PLAC 70
43

Urban Tree Database and Allometric Equations

Table 5—Numbers of trees sampled by species and region (continued)

Scientific name Common name SpCode Samples

Prunus cerasifera Ehrh. cherry plum PRCE 31

Pyrus calleryana Decne. Callery pear PYCA 30

Pyrus kawakamii Hayata evergreen pear PYKA 35

Quercus agrifolia Née coastal live oak; 

California live oak

QUAG 66

Robinia pseudoacacia L. black locust ROPS 34

Sequoia sempervirens (Lamb. ex D. Don) Endl. coast redwood SESE 62

Ulmus americana L. American elm ULAM 60

Ulmus parvifolia Jacq. Chinese elm ULPA 33

Northeast (NoEast):

Acer platanoides L. Norway maple ACPL 42

Acer rubrum L. red maple ACRU 46

Acer saccharinum L. silver maple ACSA1 53

Acer saccharum Marsh. sugar maple ACSA2 31

Aesculus hippocastanum L. horsechestnut AEHI 33

Fraxinus pennsylvanica Marshall green ash FRPE 44

Ginkgo biloba L. ginkgo GIBI 33

Gleditsia triacanthos L. honeylocust GLTR 34

Liquidambar styraciflua L. sweetgum LIST 41

Malus sp. apple MA2 32

Pinus strobus L. eastern white pine PIST 32

Platanus × acerifolia (Aiton) Willd. London planetree PLAC 53

Pyrus calleryana Decne. Kwanzan cherry PRSE2 34

Quercus palustris Münchh. Callery pear PYCA 33

Quercus phellos L. pin oak QUPA 54

Quercus rubra L. willow oak QUPH 33

Tilia cordata Mill. northern red oak QURU 51

Tilia tomentosa Moench littleleaf linden TICO 48

Ulmus americana L. silver linden TITO 30

Zelkova serrata (Thunb.) Makino American elm ULAM 40

Acer platanoides L. Japanese zelkova ZESE 34

Pacific Northwest (PacfNW):

Acer macrophyllum Pursh bigleaf maple ACMA 40

Acer platanoides L. Norway maple ACPL 74

Acer rubrum L. red maple ACRU 39

Acer saccharum Marsh. sugar maple ACSA2 37

Betula pendula Roth European white birch BEPE 41
44

GENERAL TECHNICAL REPORT PSW-GTR-253

Table 5—Numbers of trees sampled by species and region (continued)

Scientific name Common name SpCode Samples

Calocedrus decurrens (Torr.) Florin incense cedar CADE2 38

Carpinus betulus ‘Fastigiata’ L. columnar hornbeam CABEF 39

Crataegus × lavallei Hérincq ex Lavallée Carriere hawthorn CRLA 74

Fagus sylvatica L. European beech FASY 38

Fraxinus latifolia Benth. Oregon ash FRLA 39

Liquidambar styraciflua L. sweetgum LIST 73

Malus angustifolia (Aiton) Michx. southern crabapple PYAN 39

Morus alba L. white mulberry MOAL 38

Pinus contorta var. bolanderi (Parl.) Vasey Bolander beach pine PICO5 39

Populus balsamifera subsp. Trichocarpa L. black cottonwood POTR2 36

Prunus cerasifera Ehrh. cherry plum PRCE 74

Prunus serrulata Lindl. Kwanzan cherry PRSE2 38

Pseudotsuga menziesii (Mirb.) Franco Douglas-fir PSME 39

Quercus rubra L. northern red oak QURU 39

Tilia americana L. American basswood TIAM 39

Tilia cordata Mill. littleleaf linden TICO 40

Ulmus americana L. American elm ULAM 41

South (Piedmt):

Acer rubrum L. red maple ACRU 44

Acer saccharinum L. silver maple ACSA1 48

Acer saccharum Marsh. sugar maple ACSA2 41

Betula nigra L. river birch BENI 39

Cornus florida L. flowering dogwood COFL 34

Ilex opaca Aiton American holly ILOP 34

Juniperus virginiana L. eastern red cedar JUVI 39

Lagerstroemia sp. common crapemyrtle LA6 40

Liquidambar styraciflua L. sweetgum LIST 43

Magnolia grandiflora L. southern magnolia MAGR 42

Malus sp. apple MA2 29

Pinus echinata Mill. shortleaf pine PIEC 36

Pinus taeda L. loblolly pine PITA 37

Prunus sp. plum PR 36

Prunus yedoensis Matsum. Yoshino flowering cherry PRYE 39

Pyrus calleryana Decne. Callery pear PYCA 34

Quercus alba L. white oak QUAL 47

Quercus nigra L. water oak QUNI 45

Quercus phellos L. willow oak QUPH 49

Quercus rubra L. northern red oak QURU 40
45

Urban Tree Database and Allometric Equations

Table 5—Numbers of trees sampled by species and region (continued)

Scientific name Common name SpCode Samples

Ulmus alata Michx. winged elm ULAL 32

Inland Valleys (SacVal):

Cedrus deodara (Roxb. ex D. Don) G. Don deodar cedar CEDE 61

Celtis occidentalis L. northern hackberry CEOC 37

Celtis sinensis Pers. Chinese hackberry CESI4 60

Cinnamomum camphora (L.) J. Presl camphor tree CICA 63

Fraxinus velutina Torr. Modesto ash FRVE_G 40

Ginkgo biloba L. ginkgo GIBI 60

Lagerstroemia indica L. common crapemyrtle LAIN 28

Liquidambar styraciflua L. sweetgum LIST 44

Liriodendron tulipifera L. tulip tree LITU 64

Magnolia grandiflora L. southern magnolia MAGR 67

Pistacia chinensis Bunge Chinese pistache PICH 38

Platanus × acerifolia (Aiton) Willd. London planetree PLAC 54

Prunus cerasifera Ehrh. cherry plum PRCE 34

Pyrus calleryana Decne. callery pear PYCA 31

Quercus agrifolia Née coastal live oak; 

California live oak

QUAG 65

Quercus lobata Née valley oak QULO 53

Quercus rubra L. northern red oak QURU 41

Sequoia sempervirens (Lamb. ex D. Don) Endl. coast redwood SESE 52

Ulmus parvifolia Jacq. Chinese elm ULPA 62

Zelkova serrata (Thunb.) Makino Japanese zelkova ZESE 47

Southern California Coast (SoCalC):

Callistemon citrinus (Curtis) Skeels lemon bottlebrush CACI 31

Cedrus deodara (Roxb. ex D. Don) G. Don deodar cedar CEDE 28

Ceratonia siliqua L. algarrobo Europeo CESI3 31

Cinnamomum camphora (L.) J. Presl camphor tree CICA 29

Cupaniopsis anacardioides (A. Rich.) Radlk. carrotwood CUAN 30

Eucalyptus ficifolia F.Muell red flowering gum EUFI81 32

Ficus thonningii Blume figueira benjamin FIMI 34

Jacaranda mimosifolia D. Don jacaranda JAMI 33

Liquidambar styraciflua L. sweetgum LIST 33

Magnolia grandiflora L. southern magnolia MAGR 33

Melaleuca quinquenervia (Cav.) S.T. Blake punk tree MEQU 31

Metrosideros excelsa Sol. ex Gaertn. New Zealand christmas tree MEEX 32

Phoenix canariensis Chabaud Canary Island date palm PHCA 32
46

GENERAL TECHNICAL REPORT PSW-GTR-253

Table 5—Numbers of trees sampled by species and region (continued)

Scientific name Common name SpCode Samples

Pinus canariensis C. Sm. Canary Island pine PICA 30

Pittosporum undulatum Vent. Victorian box PIUN 36

Podocarpus macrophyllus (Thunb.) Sweet yew podocarpus POMA 31

Prunus caroliniana (Mill.) Aiton Carolina laurelcherry PRCA 32

Schinus terebinthifolius Raddi Brazilian pepper SCTE 31

Tristaniopsis conferta L.A.S.Johnson & K.D.Hill Brisbane box TRCO 28

Washingtonia robusta H. Wendl. Mexican fan palm WARO 30

Southwest Desert (SWDsrt):

Acacia farnesiana L. sweet acacia ACFA 31

Acacia salicina Lindl. willow acacia ACSA3 37

Brachychiton populneus (Schott & Endl.) R.Br. kurrajong BRPO 35

Chilopsis linearis (Cav.) Sweet desert willow CHLI 34

Eucalyptus microtheca F. Muell. coolibah tree EUMI2 36

Fraxinus uhdei (Wenz.) Lingelsh. evergreen ash FRUH 32

Fraxinus velutina Torr. velvet ash FRVE 59

Morus alba L. white mulberry MOAL 39

Olea europaea L. olive OLEU 36

Parkinsonia aculeata L. Jerusalem thorn PAAC 34

Parkinsonia florida (Benth. ex A. Gray) S. Watson blue paloverde CEFL 32

Phoenix dactylifera L. date palm PHDA4 56

Pinus eldarica Medw. Afghan pine PIEL2 30

Pinus halepensis Mill. Aleppo pine PIHA 34

Pistacia chinensis Bunge Chinese pistache PICH 33

Prosopis chilensis (Molina) Stuntz algarrobo PRCH 31

Quercus virginiana Mill. live oak QUVI 36

Rhus lancea L.f. African sumac RHLA 32

Ulmus parvifolia Jacq. Chinese elm ULPA 36

Washintonia filifera (Linden) Wendl. California palm WAFI 71

Washingtonia robusta H. Wendl. Mexican fan palm WARO 63

Temperate Interior West (TpIntW):

Acer platanoides L. Norway maple ACPL 62

Acer saccharinum L. silver maple ACSA1 58

Acer saccharum Marsh. sugar maple ACSA2 30

Catalpa speciosa (Warder) Warder ex Engelm. northern catalpa CASP 59

Crataegus sp. hawthorn CR 33

Fraxinus americana L. white ash FRAM 32

Fraxinus pennsylvanica Marshall green ash FRPE 60
47

Urban Tree Database and Allometric Equations

Table 5—Numbers of trees sampled by species and region (continued)

Scientific name Common name SpCode Samples

Gleditsia triacanthos L. honeylocust GLTR 33

Juglans nigra L. black walnut JUNI 57

Liquidambar styraciflua L. sweetgum LIST 33

Malus sp. apple MA2 30

Picea pungens Engelm. blue spruce PIPU 29

Pinus sylvestris L. Scotch pine PISY 29

Platanus × acerifolia (Aiton) Willd. London planetree PLAC 64

Platanus occidentalis L. American sycamore PLOC 48

Pyrus calleryana Decne. Callery pear PYCA 34

Quercus rubra L. northern red oak QURU 56

Robinia pseudoacacia L. black locust ROPS 62

Tilia americana L. American basswood TIAM 59

Ulmus pumila L. Siberian elm ULPU 55

Tropical (Tropic):

Bauhinia × blakeana Dunn Hong Kong orchid tree BABL 37

Calophyllum inophyllum L. kamani CAIN4 62

Cassia × nealiae H. S. Irwin & Barneby rainbow shower tree CANE33 41

Casuarina equisetifolia L. Australian pine CAEQ 62

Citharexylum spinosum L. fiddlewood CISP2 35

Cocos nucifera L. coconut palm CONU 34

Conocarpus erectus L. var. argenteus Millsp. silver buttonwood COERA2 37

Cordia subcordata Lam. kou COSU2 33

Delonix regia (Bojer) Raf. royal poinciana DERE 59

Elaeodendron orientale Jacq. false olive ELOR2 34

Ficus benjamina L. Benjamin fig FIBE 60

Filicium decipiens (Wight & Arn.) Thwaites fern tree FIDE6 35

Ilex paraguariensis A. St.-Hil. Paraguay tea ILPA2 36

Lagerstroemia speciosa (L.) Pers. giant crapemyrtle LASP 37

Melaleuca quinquenervia (Cav.) S.T. Blake punk tree MEQU 59

Samanea saman (Jacq.) Merr. monkeypod PISA2 62

Swietenia mahagoni (L.) Jacq. West Indian mahogany SWMA 54

Tabebuia aurea (Silva Manso) Benth. & Hook. f. ex S. silver trumpet tree TAAR 37

Tabebuia heterophylla (DC.) Britton pink trumpet tree TAPA 36

Tabebuia ochracea (Cham.) Standl. subsp. 

neochrysantha (A.H. Gentry) A.H. Gentry 

golden trumpet tree TACH 36

Veitchia merrillii H.E. Moore Christmas palm VEME 32

Total 14,487

SpCode = four- to six-letter code consisting of the first two letters of the genus name and the first two letters of the species name followed by two 

optional letters to distinguish two species with the same four-letter code. 
48

GENERAL TECHNICAL REPORT PSW-GTR-253

Appendix 2: Field Data Collection Protocols

The following data will be recorded for each tree (note: highlighted fields 1 through 

9 will be uploaded from inventory onto your palmtop and are for locating trees. You 

will collect data for the remaining items:

1. TreeID—from inventory, unique number assigned to each tree by city in 

inventory.

2. SpCode—four- to six-letter code consisting of the first two letters of the 

genus name and the first two letters of the species name followed by two 

optional letters to distinguish two species with the same four-letter code. 

3. AddressNum–from inventory, street number of building where tree is located. 

4. Street–from inventory, the name of the street on which the tree is located–

from inventory. 

5. Side—from inventory, indicates side of building or lot on which the tree is 

located (see fig. 10):

F = front

M = median

S = side

P = park

6. Cell—from inventory, the cell number where the tree is located (1, 2, 3, 

etc). Obtain city inventory protocols to determine what order the trees are 

numbered in (e.g., sometimes they are assigned in driving direction or, 

alternatively, as street number increases, depending upon city).

7. OnStree—from inventory (omit if not included as a field in city’s inventory), for trees at corner addresses when the tree is actually on a cross street 

rather than the addressed street (see fig. 10).

8. FromStreet/ToStreet—from inventory, the names of the cross streets that 

form boundaries for trees lining unaddressed boulevards. For example, on 

boulevards that have no development adjacent to them, therefore no obvious 

parcel addressing, trees are typically numbered in order. By including closest cross streets in the inventory, one will not have to begin counting trees 

from No. 1 in order to locate No. 333, which is 10 blocks up the boulevard 

from No. 1.
49

Urban Tree Database and Allometric Equations

9. DBHinv—the diameter at breast height (d.b.h.) from the city inventory, 

usually expressed as classes from one to nine, but class system specific 

to city. Sometimes expressed as d.h.h. to nearest inch or centimeter. Data 

are used to help locate the desired size of tree in the field for sampling.

10. Diameter at breast height—measure the d.b.h. (1.37 m) to nearest 0.1 cm (tape). 

Where possible for multistemmed trees forking below 1.37 m, measure above 

the butt flare and below the point where the stem begins forking. When this is 

not possible, measure diameter root collar (DRC) as described below. Saplings 

(d.b.h./DRC 2.54 to 12.5 cm) will be measured at 1.37 m unless falling under 

multistemmed/unusual stem categories requiring DRC measurements (per 

Forest Health Monitoring (FHM) Field Methods Guide). 

1415 1420

1410 1405

285 295

280 290 300

305

Apple Street

Maple StreetBirch Street

F1 F1

F1

F1

F1

F1

F1

F1

F1 F1

S1

S1 S1

S2

S2

F2

F2

F2 F2

F2

Figure 10—Treeloc tree 295 Apple S1 is actually the first tree (in driving direction) on Birch Street 

side of house.

Pacific Northwest Research Station
50

GENERAL TECHNICAL REPORT PSW-GTR-253

DIAMETER at ROOT COLLAR–adapted from Forest Health and Monitoring 

(FHM) Field Methods Guide:

For species requiring DRC, measure the diameter at the ground line or at the stem 

root collar, whichever is higher. For these trees, treat clumps of stems having a 

unified crown and common rootstock as a single tree; examples include mesquite 

and juniper. For multistemmed trees, compute and record a cumulative DRC (see 

below); record individual stem diameters and a stem status (live or dead) on a 

separate form or menu as required.

Measuring DRC: Before measuring DRC, remove the loose material on the ground 

(e.g., litter) but not mineral soil. Measure just above any swells present, and in a 

location where the diameter measurements are reflective of the volume above the 

stems (especially when trees are extremely deformed at the base).

Stems must be at least 0.3 m in length and 2.54 cm in diameter at breast height 

to qualify for measurement; stems that are missing owing to cutting or damage are 

not included in measurement.

Additional instructions for DRC measurements are illustrated in figure 11.

Computing and recording DRC: For all tally trees requiring DRC, with at least 

one stem 2.54 cm in diameter or larger at the root collar, DRC is computed as the 

square root of the sum of the squared stem diameters. For a single-stemmed DRC 

tree, the computed DRC is equal to the single diameter measured.

Use the following formula to compute DRC:

DRC = SQRT [SUM (stem diameter2)]

Round the result to the nearest 2.54 cm. For example, a multistemmed woodland tree with stems of 12.2, 13.2, 3.8, and 22.1 would be calculated as:

DRC = SQRT (12.22 + 13.22 + 3.82 + 22.12)

= SQRT (825.93)

= 28.74

= 28.7

11. TreeHt—from ground level to treetop to nearest 0.5 m (omit erratic leader 

as shown in fig. 12 with rangefinder).

12. CrnBase—with rangefinder, average distance between ground and lowest 

foliage layer (omitting erratic branch) to nearest 0.5 m.

13. CDiaPar—(crown diameter) crown diameter measurement taken to the 

nearest 0.5 m parallel to the street. The occasional erratic branch should not 

be included (see fig. 13). 

14. CDiaPerp—(crown diameter) crown diameter measurement taken to the 

nearest 0.5 m perpendicular to the treet. The occasional erratic branch 

should not be included (see fig. 13). 
51

Urban Tree Database and Allometric Equations

1. Measure at ground line when 

reasonable.

2. Measure above root collar.

3. Multistemmed above diameter.

5. Measure missing stem(s).

Compute DRC.

6. Multistemmed at or below ground. 

Compute DRC.

4. Excessive diameter below stems.

Measure stems. Compute DRC.

Figure 11—How to measure Diameter at Root Collar (DRC) in a variety of situation. 

U.S. Forest Service
52

GENERAL TECHNICAL REPORT PSW-GTR-253

15. Setback—distance from the tree to the nearest air conditioned/heated space 

(be aware that this may not be the same address as the tree location).

Evaluate as:

1 = 0 to 8 m

2 = 8.1 to 12 m

3 = 12.1 to 18 m

4 = >18 m

Use: assess effects of shade on energy use.

16. TreeOr—Tree orientation—taken with compass, as in figure 14 the coordinate of tree taken from imaginary lines extending from walls of the nearest conditioned space (heated or airconditioned space—may not be same 

address as tree location):

17. CarShade—Number of autos where any portion of any parked automotive 

vehicle is under the tree’s drip line. Car must be present:

0 = no autos

1 = one auto

2 = two autos, etc.

Use: vehicle hydrocarbon emissions reduction.

Figure 12—Tree with erratic leader that should 

not be included in height measurement.

Figure 13—Erratic branch (in box at left) is omitted from crown 

diameter measurement. Distance measured is represented by white line.

Pacific Southwest Research StationPacific Southwest Research Station
53

Urban Tree Database and Allometric Equations

18. Land use—Area where tree is growing:

1 = single-family residential

2 = multifamily residential (duplex, apartments, condos)

3 = industrial/institutional/large commercial (schools, government, hospitals)

4 = park/vacant/other (agricultural, unmanaged riparian areas of greenbelts)

5 = small commercial (minimart, retail boutiques, etc.)

6 = transportation corridor.

Use: energy, property value.

Garage without 

air conditioning or heat

Tree is southeast 

of air conditioned 

portion of house

Tree is west

of air conditioned 

portion of house

Tree is northeast of air 

conditioned portion of house

Tree is south 

of air conditioned 

portion of house

Trees are east of air 

conditioned portion 

of house

Tree is north of 

air conditioned 

portion of house

Northwest 

facing air 

conditioned 

house

South facing 

air conditioned 

house

Southeast facing 

air conditioned 

house 

Garage without 

air conditioning or heat

Figure 14—Shows imaginary lines extending from walls and associated tree orientation
54

GENERAL TECHNICAL REPORT PSW-GTR-253

19. Shape–visual estimate of crown shape verified when different from each 

side with actual measured dimensions of crown height and average crown 

diameter. If in doubt, determine shape using average crown diameter and 

crown height measurements. See figure 15. Use: energy (shadow patterns)

20. 1 = cylinder = maintains same crown diameter in top and bottom thirds of tree

21. 2 = ellipsoid (horizontal or vertical; also includes spherical)—for ellipse the 

tree’s center (whether vertical or horizontal) should be the widest)

22. 3 = paraboloid—widest in bottom third of crown

23. 4 = upside down paraboloid—widest in top third of crown

24. WireConf—utility lines that interfere with or appear above tree

0 = no lines

1 = present and no potential conflict

2 = present and conflicting

3 = present and potential for conflicting

25. Image1—select position for best possible photo of tree crown, keeping in 

mind that you must try to obtain two perpendicular views of the tree that 

are as free of background noise as possible. Try to position yourself so the 

tree crown is as isolated as possible from neighboring tree crowns and other 

crowns in background:

26. Distance from tree that photo is taken at increments of 5 m (5, 10, 15, 20 m, 

etc) and accurate within 0.05 m.

27. Camera zoom should be set to full wide angle

28. First image must include entire tree (bole and crown) for backup measurements and should fill as much of viewfinder as possible

29. Kneel to take images so more sky is included in background

30. Dist1—Measure distance from camera back (the point where image is actually recorded) to point equivalent to center of tree bole (fig. 16). Measure 

accurately within 0.05 m.

31. Image2—taken as perpendicularly (90°) as possible to Image 1.

32. Dist2—distance as per Dist1 for Image 2.

33. PlantDate—Date tree was planted. As you collect data, talk with residents 

and see if you can find name and address of the oldest person on street or in 

neighborhood, or if residents know age of tree. We will review methods for 

aging trees during training.

34. Notes: any pertinent notes—if tree is replacement and what tree was 

replaced—give address of replacement tree. 

35. dbh1, dbh2, dbh3, etc., are for individual stem diameter entries for multistemmed trees being recorded using DRC methods. These cells are linked to 

the formula in field #10 (d.b.h.) column calculating the final d.b.h.
55

Urban Tree Database and Allometric Equations

Cylindrical Horizontal

ellipsoid

Vertical

ellipsoid

Paraboloid Upside down

paraboloid

1 2 2 4 5

Figure 15—Shapes of tree crowns.

Figure 16—Showing how to measure distance (in 5-m increments) 

between camera back and tree center.

Measuring devise placed 

adjacent to tree center

Tree center

Measuring devise placed 

adjacent to camera back
56

GENERAL TECHNICAL REPORT PSW-GTR-253

Appendix 3: Foliar Biomass

Table 6 shows the mean and standard deviations for dry-weight to fresh-weight 

ratios for foliar biomass and the average foliar biomass factors (gram of dry weight 

per square meter of leaf area) for each species and region. Average foliar biomass 

factors range from a low of 76.1 g/m2 for climate zone MidWst to a high of 222.7 g/

m2 for TpIntW. Across climate zones, there is a range of average foliar biomass factor values by species tree type from a high of 481.9 g/m2

 in large conifer evergreen 

species to a low of 99.3 g/m2 in large broadleaf deciduous species. Within climate 

zones, there is also high variability, influenced by tree type. For example, although 

the average foliar biomass factor for NoCalC is 214.4 g/m2, the range is from a high 

of 659.7 g/m2 (driven by Sequoia sempervirens and Pinus radiata, both factors 

over 500.0 g/m2) to a low of 73.2 g/m2 Prunus cerasifera. It is important to note 

the sample number (n) and documented sampling notes when applying these data. 

Foliar samples were not collected in four of the reference cities (InlVal, InterW, 

PacfNW, SacVal).

Table 6—Average dry-weight to fresh-weight (dw:fw) ratios for foliar biomass and average 

foliar biomass factors (gram of dry weight per square meter of leaf area) for each species 

and region (continued)

Regiona SpCodeb Avg dw/fw (g) dw/fw SD Avg dw g/m2 dw g/m2 SD No.

CenFla ACRU 0.46 0.04 102.75 12.28 10

CenFla CICA 0.48 0.04 116.42 6.64 10

CenFla ERJA 0.41 0.06 162.48 26.87 10

CenFla JUSI 0.50 0.03 405.68 48.08 10

CenFla KOELFO 0.49 0.04 68.35 12.55 10

CenFla LAIN 0.34 0.03 81.38 18.16 10

CenFla LIST 0.31 0.02 93.74 15.48 10

CenFla MAGR 0.35 0.03 144.87 22.25 10

CenFla PIEL 0.44 0.01 107.74 11.50 10

CenFla PLOC 0.38 0.04 74.60 13.45 10

CenFla THOR 0.42 0.01 207.09 29.85 10

CenFla PRCA 0.45 0.05 118.66 19.20 10

CenFla QULA2 0.48 0.01 117.81 37.87 10

CenFla QUSH 0.50 0.02 110.12 16.49 10

CenFla QUVI 0.49 0.04 135.18 51.85 10

CenFla SAPA 0.41 0.16 207.21 83.86 7

CenFla SYRO 0.46 0.03 132.76 59.85 7

CenFla TRSE6 0.36 0.03 73.87 10.81 10

CenFla ULPA 0.42 0.04 130.78 37.30 10
57

Urban Tree Database and Allometric Equations

Table 6—Average dry-weight to fresh-weight (dw:fw) ratios for foliar biomass and average 

foliar biomass factors (gram of dry weight per square meter of leaf area) for each species 

and region (continued)

Regiona SpCodeb Avg dw/fw (g) dw/fw SD Avg dw g/m2 dw g/m2 SD No.

CenFla WARO 0.42 0.07 149.50 18.68 4

GulfCo ACRU 0.32 0.02 72.68 14.58 10

GulfCo BUCA 0.71 331.74 1

GulfCo CAIL 0.45 0.03 104.35 16.85 10

GulfCo CELA 0.33 0.04 58.41 11.16 10

GulfCo COFL 0.39 0.03 78.34 21.27 10

GulfCo GLTR 0.40 0.03 159.31 142.22 10

GulfCo ILOP 0.52 0.02 206.95 13.51 10

GulfCo JUVI 0.45 0.02 357.56 46.51 10

GulfCo LAIN 0.30 0.03 78.58 13.71 10

GulfCo LIST 0.35 0.04 98.90 24.22 10

GulfCo MAGR 0.43 0.02 221.77 17.98 10

GulfCo PITA 0.39 0.01 572.86 25.14 10

GulfCo PLOC 0.40 0.06 71.94 15.67 10

GulfCo PYCA 0.49 0.02 154.87 22.36 10

GulfCo QULA2 0.53 0.02 135.55 14.41 10

GulfCo QUNI 0.53 0.01 147.77 14.32 10

GulfCo QUPH 0.50 0.03 100.79 10.68 10

GulfCo QUVI 0.52 0.01 255.19 197.58 10

GulfCo SAPA 0.63 303.42 1

InlEmp BRPO 0.35 122.79 20

InlEmp CICA 0.46 176.12 20

InlEmp EUSI 0.47 179.20 20

InlEmp FRUH 0.45 164.23 20

InlEmp FRVE 0.53 144.64 20

InlEmp GIBI 0.41 176.63 20

InlEmp JAMI 0.36 114.76 20

InlEmp LAIN 0.46 256.51 20

InlEmp LIST 0.46 145.46 20

InlEmp LITU 0.34 89.61 20

InlEmp MAGR 0.54 289.27 20

InlEmp PIBR2 0.36 446.89 20

InlEmp PICA 0.50 342.79 20

InlEmp PICH 0.45 118.87 20

InlEmp PLAC 0.55 128.41 20

InlEmp PLRA 0.56 139.39 20

InlEmp PYCA 0.59 186.43 20

InlEmp QUAG 0.52 358.25 20
58

GENERAL TECHNICAL REPORT PSW-GTR-253

Table 6—Average dry-weight to fresh-weight (dw:fw) ratios for foliar biomass and average 

foliar biomass factors (gram of dry weight per square meter of leaf area) for each species 

and region (continued)

Regiona SpCodeb Avg dw/fw (g) dw/fw SD Avg dw g/m2 dw g/m2 SD No.

InlEmp QUIL2 0.60 202.39 20

InlEmp SCMO 0.31 166.69 20

InlEmp SCTE 0.43 153.77 20

InlEmp WARO 0.47 0.05 271.45 52.90 4

LoMidW ACPL 0.31 0.12 101.52 53.63 10

LoMidW ACRU 0.32 0.05 108.69 16.68 10

LoMidW ACSA1 0.29 0.07 85.92 15.37 10

LoMidW ACSA2 0.38 0.06 122.58 30.86 10

LoMidW CASP 0.25 0.03 72.01 16.29 10

LoMidW CEOC 0.31 0.05 72.60 13.00 10

LoMidW CECA 0.27 0.04 95.05 9.89 10

LoMidW FRAM 0.37 0.02 102.43 16.89 10

LoMidW FRPE 0.33 0.04 116.06 22.56 10

LoMidW GLTR 0.32 0.07 114.58 29.89 10

LoMidW JUNI 0.30 0.03 87.52 10.82 10

LoMidW MA2 0.23 0.07 105.13 21.14 10

LoMidW MO 0.26 0.04 99.88 22.03 10

LoMidW PIPU 0.42 0.04 340.97 169.38 10

LoMidW PIST 0.34 0.03 250.60 32.06 10

LoMidW PODE 0.28 0.03 122.01 20.47 10

LoMidW PYCA 0.30 0.03 115.70 25.59 10

LoMidW QURU 0.34 0.05 109.22 21.66 10

LoMidW TICO 0.28 0.06 100.13 37.61 10

LoMidW ULPU 0.26 0.05 106.42 13.37 10

MidWst ACNE 0.30 0.03 52.94 10.21 10

MidWst ACPL 0.39 0.03 49.84 7.50 10

MidWst ACRU 0.46 0.02 83.29 11.79 10

MidWst ACSA1 0.44 0.03 85.83 14.78 10

MidWst ACSA2 0.42 0.04 53.62 11.55 10

MidWst CEOC 0.40 0.02 68.23 6.79 10

MidWst FRAM 0.40 0.03 71.40 15.16 10

MidWst FRPE 0.34 0.03 68.62 13.05 10

MidWst GIBI 0.31 0.03 91.24 14.10 10

MidWst GLTR 0.39 0.02 89.52 12.86 10

MidWst MA2 0.40 0.05 67.53 20.50 10

MidWst QUPA 0.44 0.02 84.97 10.85 10

MidWst QURU 0.45 0.02 85.06 16.44 10
59

Urban Tree Database and Allometric Equations

Table 6—Average dry-weight to fresh-weight (dw:fw) ratios for foliar biomass and average 

foliar biomass factors (gram of dry weight per square meter of leaf area) for each species 

and region (continued)

Regiona SpCodeb Avg dw/fw (g) dw/fw SD Avg dw g/m2 dw g/m2 SD No.

MidWst TIAM 0.37 0.03 77.04 22.04 10

MidWst TICO 0.35 0.03 57.33 15.11 10

MidWst ULAM 0.36 0.02 82.30 9.63 10

MidWst ULPU 0.41 0.02 124.67 18.41 10

NMtnPr ACPL 0.40 0.03 68.23 19.36 10

NMtnPr ACSA1 0.48 0.09 83.03 29.01 10

NMtnPr ACSA2 0.36 0.06 75.73 11.58 10

NMtnPr CEOC 0.45 0.04 76.18 16.71 10

NMtnPr FRAM 0.42 0.06 74.91 11.40 10

NMtnPr FRPE 0.39 0.08 84.76 20.89 10

NMtnPr GLTR 0.44 0.03 96.98 21.79 10

NMtnPr GYDI 0.36 0.03 58.25 13.26 10

NMtnPr MA2 0.31 0.09 54.94 13.70 10

NMtnPr PIPU 0.45 0.01 428.00 29.51 10

NMtnPr PINI 0.43 0.04 411.32 41.37 10

NMtnPr PIPO 0.44 0.02 399.01 31.95 10

NMtnPr POSA 0.27 0.04 70.73 12.52 10

NMtnPr PR 0.41 0.09 71.12 15.74 10

NMtnPr PY 0.42 0.02 120.06 14.26 10

NMtnPr QUMA1 0.53 0.11 122.42 14.97 10

NMtnPr TIAM 0.33 0.03 69.46 8.30 10

NMtnPr TICO 0.33 0.07 57.75 14.78 10

NMtnPr ULAM 0.43 0.04 84.33 22.85 10

NMtnPr ULPU 0.33 0.04 70.29 15.34 10

NoCalC ACME 0.56 0.05 219.54 23.17 10

NoCalC ACPA 0.51 0.02 90.67 10.69 10

NoCalC CICA 0.53 0.05 167.57 18.93 9

NoCalC EUGL 0.55 0.03 338.48 28.62 10

NoCalC FRVE 0.60 0.05 184.02 18.19 10

NoCalC GIBI 0.38 0.02 156.00 60.01 10

NoCalC LIST 0.48 0.04 125.75 18.38 10

NoCalC LITU 0.36 0.01 83.00 5.16 10

NoCalC MAGR 0.48 0.02 232.77 15.65 10

NoCalC PIRA 0.52 0.03 762.71 127.18 10

NoCalC PICH 0.51 0.04 143.94 25.88 10

NoCalC PIUN 0.49 0.01 149.41 11.55 10

NoCalC PLAC 0.42 0.14 107.74 12.69 10
60

GENERAL TECHNICAL REPORT PSW-GTR-253

Table 6—Average dry-weight to fresh-weight (dw:fw) ratios for foliar biomass and average 

foliar biomass factors (gram of dry weight per square meter of leaf area) for each species 

and region (continued)

Regiona SpCodeb Avg dw/fw (g) dw/fw SD Avg dw g/m2 dw g/m2 SD No.

NoCalC PRCE 0.45 0.02 73.19 27.38 10

NoCalC PYCA 0.57 0.03 175.06 34.38 10

NoCalC PYKA 0.58 0.09 243.93 48.81 10

NoCalC QUAG 0.60 0.02 251.98 9.65 10

NoCalC ROPS 0.42 0.03 86.20 8.34 10

NoCalC SESE 0.52 0.03 556.77 94.40 10

NoCalC ULAM 0.79 1.19 160.98 243.30 9

NoCalC ULPA 0.46 0.01 192.29 16.69 10

NoEast ACPL 0.41 0.04 62.05 18.87 10

NoEast ACRU 0.37 0.13 72.68 16.10 10

NoEast ACSA1 0.41 0.04 89.82 18.86 10

NoEast ACSA2 0.44 0.02 80.77 13.07 10

NoEast AEHI 0.43 0.06 85.38 10.89 10

NoEast FRPE 0.44 0.02 109.44 12.42 10

NoEast GIBI 0.35 0.08 130.59 31.82 10

NoEast GLTR 0.44 0.03 124.66 21.56 10

NoEast LIST 0.35 0.08 93.78 25.84 10

NoEast MA2 0.50 0.05 109.68 23.11 10

NoEast PIST 0.38 0.10 717.94 376.53 10

NoEast PLAC 0.41 0.01 110.02 20.02 10

NoEast PRSE2 0.43 0.03 99.32 19.35 10

NoEast PYCA 0.46 0.06 130.15 35.72 10

NoEast QUPA 0.45 0.05 88.17 28.31 10

NoEast QUPH 0.46 0.03 183.61 278.65 10

NoEast QURU 0.46 0.03 96.79 24.42 10

NoEast TICO 0.38 0.04 141.78 236.15 10

NoEast TITO 0.38 0.01 73.85 8.99 10

NoEast ULAM 0.40 0.01 99.77 20.85 10

NoEast ZESE 0.45 0.05 73.05 39.55 10

Piedmt ACRU 0.44 0.04 86.92 21.30 10

Piedmt ACSA1 0.40 0.03 84.77 9.26 10

Piedmt ACSA2 0.36 0.12 57.99 30.52 10

Piedmt BENI 0.35 0.07 69.63 15.32 10

Piedmt COFL 0.35 0.05 54.49 14.71 10

Piedmt ILOP 0.34 0.05 124.53 32.68 10

Piedmt JUVI 0.40 0.02 559.08 78.10 10

Piedmt LA6 0.32 0.03 112.76 18.18 10
61

Urban Tree Database and Allometric Equations

Table 6—Average dry-weight to fresh-weight (dw:fw) ratios for foliar biomass and average 

foliar biomass factors (gram of dry weight per square meter of leaf area) for each species 

and region (continued)

Regiona SpCodeb Avg dw/fw (g) dw/fw SD Avg dw g/m2 dw g/m2 SD No.

Piedmt LIST 0.33 0.04 80.11 20.74 10

Piedmt MAGR 0.40 0.04 165.31 26.11 10

Piedmt MA2 0.28 0.06 57.71 19.52 10

Piedmt PIEC 0.38 0.02 706.35 201.79 10

Piedmt PITA 0.39 0.03 525.79 98.03 10

Piedmt PR 0.29 0.05 57.86 17.15 10

Piedmt PRYE 0.40 0.05 116.85 28.23 10

Piedmt PYCA 0.37 0.08 113.74 41.72 10

Piedmt QUAL 0.42 0.05 73.03 17.37 10

Piedmt QUNI 0.44 0.08 91.73 20.63 10

Piedmt QUPH 0.42 0.04 86.21 18.50 10

Piedmt QURU 0.42 0.06 71.81 16.01 10

Piedmt ULAL 0.50 0.03 84.65 16.63 10

SoCalC CACI 204.01 10

SoCalC CEDE 390.93 11.19 3

SoCalC CESI3 233.23 22.20 3

SoCalC CICA 129.86 1

SoCalC CUAN 178.53 20.01 3

SoCalC FIMI 141.50 7.04 3

SoCalC JAMI 115.85 1

SoCalC LIST 124.00 4.85 3

SoCalC MAGR 235.45 13.78 3

SoCalC MEQU 201.99 1

SoCalC MEEX 219.06 1

SoCalC PHCA 226.15 1

SoCalC PIBR2 0.36 446.89 1

SoCalC PICA 371.31 1

SoCalC PIUN 143.46 1

SoCalC POMA 200.41 13.34 2

SoCalC SCTE 121.99 1

SoCalC TRCO 174.30 1

SoCalC WARO 216.16 1

SWDsrt ACFA 0.48 0.08 178.75 42.23 10

SWDsrt ACSA3 0.32 0.02 187.23 16.85 10

SWDsrt BRPO 0.37 0.02 86.14 6.40 10

SWDsrt CHLI 0.40 0.02 159.62 25.89 10

SWDsrt EUMI2 0.48 0.08 145.29 12.16 10
62

GENERAL TECHNICAL REPORT PSW-GTR-253

Table 6—Average dry-weight to fresh-weight (dw:fw) ratios for foliar biomass and average 

foliar biomass factors (gram of dry weight per square meter of leaf area) for each species 

and region (continued)

Regiona SpCodeb Avg dw/fw (g) dw/fw SD Avg dw g/m2 dw g/m2 SD No.

SWDsrt FRUH 0.47 0.02 126.35 11.21 10

SWDsrt FRVE 0.44 0.02 120.11 13.48 10

SWDsrt MOAL 0.49 0.04 153.46 30.14 10

SWDsrt OLEU 0.52 0.02 256.39 18.88 10

SWDsrt PAAC 0.40 0.06 586.32 126.61 10

SWDsrt CEFL 0.51 0.05 181.85 40.64 10

SWDsrt PHDA4 0.68 0.02 309.49 5.62 2

SWDsrt PIEL2 0.43 0.02 452.68 142.21 10

SWDsrt PIHA 0.47 0.02 515.04 199.92 10

SWDsrt PICH 0.47 0.06 132.31 27.57 10

SWDsrt PRCH 0.45 0.03 177.36 21.06 10

SWDsrt QUVI 0.52 0.10 185.64 29.68 10

SWDsrt RHLA 0.46 0.04 132.57 15.47 10

SWDsrt ULPA 0.53 0.01 203.71 20.19 10

SWDsrt WAFI 0.52 0.01 193.01 27.01 2

SWDsrt WARO 0.54 0.06 192.46 2.98 2

TpIntW ACPL 0.43 0.02 68.37 13.43 10

TpIntW ACSA1 0.46 0.12 83.03 11.59 7

TpIntW ACSA2 0.43 0.03 59.23 12.41 10

TpIntW CASP 0.32 0.05 81.09 35.25 10

TpIntW CR 0.48 0.03 113.36 25.49 10

TpIntW FRAM 0.41 0.03 101.97 12.78 10

TpIntW FRPE 0.39 0.02 78.97 15.26 10

TpIntW GLTR 0.45 0.03 113.71 30.52 10

TpIntW JUNI 0.41 0.03 97.23 21.33 10

TpIntW LIST 0.38 0.03 99.82 17.96 10

TpIntW MA2 0.42 0.06 81.29 21.26 10

TpIntW PIPU 0.49 0.03 562.63 28.25 10

TpIntW PISY 0.46 0.02 477.71 70.45 10

TpIntW PLAC 0.40 0.02 101.34 18.50 10

TpIntW PLOC 0.38 0.03 91.63 21.75 10

TpIntW PYCA 0.42 0.03 93.42 14.80 10

TpIntW QUAL 0.47 0.02 91.68 16.86 10

TpIntW QURU 0.47 0.06 89.61 13.81 10

TpIntW ROPS 0.42 0.11 64.84 14.25 10

TpIntW TIAM 0.37 0.03 60.00 13.58 10

TpIntW TICO 0.39 0.03 63.38 16.17 10
63

Urban Tree Database and Allometric Equations

Table 6—Average dry-weight to fresh-weight (dw:fw) ratios for foliar biomass and average 

foliar biomass factors (gram of dry weight per square meter of leaf area) for each species 

and region (continued)

Regiona SpCodeb Avg dw/fw (g) dw/fw SD Avg dw g/m2 dw g/m2 SD No.

TpIntW ULPU 0.40 0.02 118.79 27.30 10

Tropic BABL 0.43 0.03 121.05 10.66 10

Tropic CAIN4 0.41 0.06 173.82 16.25 10

Tropic CANE33 0.45 0.03 99.05 10.73 10

Tropic CAEQ 0.45 0.17 1466.27 561.35 10

Tropic CISP2 0.35 0.02 109.36 19.44 10

Tropic CONU 0.45 0.06 200.91 28.09 2

Tropic COERA2 0.34 0.02 194.06 87.11 10

Tropic COSU2 0.20 0.02 50.06 9.58 10

Tropic DERE 0.38 0.02 125.06 26.21 10

Tropic ELOR2 0.44 0.01 216.18 14.57 10

Tropic FIBE 0.39 0.02 130.09 22.03 10

Tropic FIDE6 0.42 0.02 151.57 27.80 10

Tropic ILPA2 0.42 0.02 164.33 12.96 10

Tropic LASP 0.31 0.04 99.35 26.17 10

Tropic MEQU 0.40 0.14 189.66 48.45 10

Tropic PISA2 0.41 0.03 118.04 21.74 10

Tropic SWMA 0.45 0.02 110.92 15.42 10

Tropic TAAR 0.34 0.02 155.75 18.22 10

Tropic TAPA 0.36 0.02 136.29 21.70 10

Tropic TACH 0.48 0.03 154.16 31.80 10

Tropic VEME 0.41 0.02 170.11 10.17 2

SD = standard deviation.

a CenFla = Central Florida, GulfCo = Coastal Plain, InlEmp = Inland Empire, LoMidW = Lower Midwest, MidWst = Midwest, 

NMtnPr = North, NoCalC = Northern California Coast, NoEast = Northeast, Piedmt = South, SoCalC = Southern California 

Coast, SWDsrt = Southwest Desert, TpIntW = Temperate Interior West, Tropic = Tropical.

b SpCodes = Four- to six-letter code consisting of the first two letters of the genus name and the first two letters of the species 

name followed by two optional letters to distinguish two species with the same four-letter code.
64

GENERAL TECHNICAL REPORT PSW-GTR-253

Appendix 4: Growth Equation Coefficients and 

Application Information

Appendix 4 and the corresponding online supplement report the growth equation coefficients from the best fitting models for each species and region. Table 

7 illustrates the parameters predicted by the growth equations for two species, 

ACME and ACPA, in the Northern California Coast climate zone. The full table of 

coefficients for all species measured in each reference city is available in table S6 

of the online supplement.

Twelve combinations of equation forms and model weights were tested for 

predicting seven parameters for each species and region. Thirty-one percent of all 

region-species combinations are best-fit (as measured by AICc values) by log-log 

(primarily unweighted) equations, followed closely by polynomial quadratic (26 

percent), cubic (22 percent), and linear (19 percent) equations (app. 4, table 8). However, there is considerable variation in best-fit equation form among measured and 

predicted parameter types. For example, d.b.h. to leaf area relationship are typically 

best described by a log-log relationship (72 percent of the best-fit models across 

species are log-log equations), while d.b.h. to age relationships are most frequently 

described by cubic equations (38 percent). There is also variation in best-fit model 

frequency based on tree type, such as evergreen or deciduous, large, medium or 

small, and broadleaf, conifer, or palm. For example, the relationship between d.b.h. 

and tree height is most frequently best fit with quadradic models (50 percent) in 

medium coniferous evergreen species, but small coniferous evergreen species are 

best fit with linear models (83 percent). Meanwhile, log-log models are the most 

frequently chosen models for medium broadleaf deciduous species (43 percent).
65

Urban Tree Database and Allometric Equations

Table 7—Example of equations for predicting tree-growth parameters by species and predicted parameter in Northern California Coast climate zoneSpecies

Ind. 

var. Pred.a

Model 

weightb EqNamec A b c or mse d e

Apps 

min

Apps 

max Sigma No.

adj 

R2 DF

ACME dbh age 1/dbh quad -0.07717 1.03847 -0.00387 1 74 1.13403 35 0.941 32ACME cdia dbh 1/cdia^2 quad 0.48486 2.88322 0.17048 2.78 99.02 1.28772 31 0.927 28ACME dbh crown dia 1/sqrt(dbh) quad 0.72517 0.23255 -0.00072 1.37 16.71 0.31444 31 0.941 28ACME dbh crown ht 1/sqrt(dbh) log-logw2 0.33845 1.43614 0.01374 2.14 13.47 0.1172 31 0.911 29ACME age dbh 1/age^2 cub 2.85114 -0.12224 0.05596 -0.0005 2.78 99.03 0.11337 35 0.907 31ACME dbh leaf area 1 log-logw1 0.38175 3.72792 0.30567 6.38 491.2 0.55287 25 0.895 23ACME dbh tree ht 1/sqrt(dbh) log-logw2 0.50713 1.54757 0.00894 2.6 18.45 0.09454 31 0.948 29ACPA dbh age 1/dbh cub -2.14827 1.39244 0.00738 -0.00021 0 64 0.70595 38 0.97 34ACPA cdia dbh 1/cdia^2 lin -0.767 4.15225 2.85 47.38 0.67011 35 0.931 33ACPA dbh crown dia 1 log-logw1 -1.01932 2.48188 0.03998 0.78 10.57 0.19994 35 0.928 33ACPA dbh crown ht 1/dbh lin 0.90353 0.11475 1.23 6.34 0.05462 35 0.771 33ACPA age dbh 1/age^2 cub 2.84767 0.23083 0.02511 -0.00028 2.85 47.39 0.02437 38 0.944 34ACPA dbh leaf area 1 log-logw1 -2.21556 5.79413 0.37159 1.3 368.78 0.60958 33 0.888 31ACPA dbh tree ht 1/sqrt(dbh) lin 2.02054 0.15818 2.47 9.52 0.36403 35 0.819 33ACME, ACPA = Acacia melanoxylon and Acer palmatum, respectively.a Units of predicted components: age = years, dbh = centimeters, crown dia = meters, crown height = meters, la = m2.b Model components: dbh = diameter at breast height, crown dia = crown diameter, crown ht = crown height, tree ht = tree height, la = leaf area, Ind.var. = independent variable; Pred. = predicts component; EqName = equation name referring to equations in table 3.c Log-log and exponential models require an input for mean-squared-error (mse), which is listed in column ”c or mse” (do not calculate and use sigma2).
66

GENERAL TECHNICAL REPORT PSW-GTR-253

Table 8—Percentage frequency of best-fit equation forms by measured/predicted parameter and tree type

Relationship BDL BDM BDS BEL BEM BES CEL CEM CES PEL PEM PES Total

Percent

Age to d.b.h.:

cub 33 26 16 33 25 5 12 67 6 27 

expow 0 2 0 0 0 0 0 0 0 0 

lin 24 35 50 33 36 58 36 6 12 31 

log-log 9 11 18 3 3 0 16 22 82 13

quad 34 26 16 30 36 37 36 6 0 28

quart 0 0 0 0 0 0 0 0 0 0

Total 100

Crown diameter to d.b.h.:

cub 35 25 8 21 33 21 28 22 0 26

expow 1 0 5 0 0 0 0 0 0 1

lin 11 21 39 24 33 26 36 50 12 23

log-log 35 33 34 42 28 37 28 17 82 35

quad 19 21 13 12 6 16 8 11 6 15

quart 0 0 0 0 0 0 0 0 0 0

Total 100

D.b.h. to age:

cub 43 37 32 27 42 32 28 6 94 38

expow 1 0 5 0 0 0 4 0 0 1

lin 23 19 29 21 17 21 24 28 6 22

log-log 7 14 18 12 17 26 12 50 0 14

quad 26 30 16 39 25 21 32 17 0 25

quart 0 0 0 0 0 0 0 0 0 0

Total 100

D.b.h. to crown diameter:

cub 29 21 24 12 3 0 16 0 0 14 93 33 22

expow 0 0 0 3 0 0 0 0 0 0 0 0 0

lin 6 25 26 9 25 32 36 28 18 7 0 0 16

log-log 31 26 24 15 25 47 24 17 0 0 0 0 23

quad 34 28 26 61 47 21 24 56 82 79 7 53 38

quart 0 0 0 0 0 0 0 0 0 0 0 13 0

Total 100
67

Urban Tree Database and Allometric Equations

Relationship BDL BDM BDS BEL BEM BES CEL CEM CES PEL PEM PES Total

Percent

D.b.h. to crown height

cub 13 9 3 15 6 0 8 22 0 14 73 33 13

expow 0 2 8 0 8 21 8 0 12 0 0 0 4

lin 17 25 45 18 36 42 40 22 82 7 0 0 26

log-log 29 35 29 36 25 26 16 6 6 0 0 0 24

quad 40 30 16 30 25 11 28 50 0 79 27 53 33

quart 0 0 0 0 0 0 0 0 0 0 0 13 0

Total 100

D.b.h. to leaf area:

cub 5 5 5 9 3 0 8 39 0 100 73 93 15

expow 1 2 0 3 6 5 0 0 12 0 0 0 2

lin 1 2 5 3 0 0 0 0 0 0 0 0 1

log-log 85 75 87 67 81 89 84 44 88 0 0 0 72

quad 8 16 3 18 11 5 8 17 0 0 27 7 10

quart 0 0 0 0 0 0 0 0 0 0 0 0 0

Total 100

D.b.h. to tree height:

cub 18 12 5 15 6 0 24 17 0 7 93 33 16

expow 0 0 8 3 8 21 0 6 0 0 0 0 3

lin 10 12 29 9 8 5 16 22 82 0 0 0 14

log-log 33 33 42 36 36 47 28 6 18 7 0 0 30

quad 39 42 16 36 42 26 32 50 0 86 7 20 35

quart 0 0 0 0 0 0 0 0 0 0 0 47 2

Total 100

Tree types: BDL = broadleaf deciduous large, BDM = broadleaf deciduous medium, BDS = broadleaf deciduous small, BEL = broadleaf evergreen 

large, BEM = broadleaf evergreen medium, BES = broadleaf evergreen small, CEL = conifer evergreen large, CEM = conifer evergreen medium, CES = 

conifer evergreen small, PEL = palm evergreen large, PEM = palm evergreen medium, PES= palm evergreen small.

Table 8—Percentage frequency of best-fit equation forms by measured/predicted parameter and tree type 

(continued)
68

GENERAL TECHNICAL REPORT PSW-GTR-253

Appendix 5: User Guide

This guide provides step-by-step instructions on how to use the allometric equations 

to estimate tree component dimensions. Predicted parameters included using tree 

age to predict diameter at breast height (d.b.h.); using d.b.h. to predict tree height, 

crown height, crown diameter, and leaf area. In addition, crown diameter was used 

to predict d.b.h., and age from d.b.h. The guide is divided into sections based on the 

tree components that are to be estimated. In the first section, we show tree diameter, 

height, crown dimensions, and leaf area from d.b.h. and/or tree height. In the second 

section, we demonstrate how to estimate dry-weight biomass and carbon using 

the table of equations presented in appendix 5. Lastly, we present a case study that 

illustrates the importance of developing region-specific growth models. 

Calculating Bole Diameter and Height, Crown Dimensions, 

and Leaf Area

Example 1. Calculating d.b.h. and tree height from tree age (d.b.h. and height not 

measured). 

In this example, we aim to predict tree dimensions d.b.h., tree height, crown 

diameter, crown height, and leaf area for a 33-year-old Liquidambar styraciflua 

(American sweetgum) in the Northern California Coast (NoCalC) region.

Step 1. Look up the species and region specific age to d.b.h. equation in table S5 in 

the online supplement at http://dx.doi.org/10.2737/RDS-2016-0005. The equation 

name is “quad” for which the equation form is listed in table 3: 

d.b.h. (Liquidambar styraciflua in NoCalC) = a + b × age + c × age2

d.b.h. = 2.80359 + 1.29151 × 33 + 0.00299 × (33)2 = 42.2 cm 

Step 2. Calculate tree height (ht) from d.b.h. by looking up the equation name and 

coefficients in table S5 and equation form (cubic) in table 3:

ht (Liquidambar styraciflua in NoCalC) = a + b × dbh + c × dbh2 + d × dbh3

ht = 0.57478 + 0.62687 × 42.16 + (-0.00837) × (42.2)2 + 0.00004 × (42.2)3 = 15.1 m 

Having calculated tree d.b.h (and in some cases tree height), it is now possible 

to skip ahead to section 2 if the goal is to estimate dry-weight biomass and carbon 

storage/sequestration. To estimate other tree dimensions, continue with steps 3 

through 6.

Step 3. Calculate crown diameter (cdia) from d.b.h. by looking up the equation 

name and coefficients in table S5 and equation form (cubic) in table 3:

cdia (Liquidambar styraciflua in NoCalC) = a + b × dbh + c × dbh2

cdia = 0.42238 + 0.29796 × 42.2 +(-0.00131) × 42.22 = 10.7 m
69

Urban Tree Database and Allometric Equations

Step 4. Calculate crown height (cht) from d.b.h. by looking up the equation name 

and coefficients in table S5 and equation form in table 3:

cht (Liquidambar styraciflua in NoCalC) = a + b × dbh + c × dbh2 + d × dbh3

cht = (-0.54095) + 0.53287 × 42.2 + (-0.00872) × 42.22+0.00005 × 42.23 = 10.2 m 

Step 5. Calculate leaf area (la) from d.b.h. by looking up the equation name and coefficients in table S5 and equation form (log-log) in table 3:

la = e (a + b × ln (ln (dbh +1) + (mse/2)) 

la = e (-1.47634) + 5.49634×LN(LN(42.2+1) + (0.29671/2)) = 413.2 m2

where e is a mathematical constant equal to 2.71828182845904, the base of the 

natural logarithm.

Step 6. To calculate foliar biomass (fb), multiply leaf area (m2) from step 4 by the 

average foliar biomass factor (g/m2 leaf area) in appendix 3:

fb = leaf area × average foliar biomass factor

fb = 413.2 m2 × 125.75 (g/m2) = 51959.9 g 

Estimating Dry-Weight Biomass and Carbon

To estimate the aboveground volume of wood in a tree, measured tree size data are 

used with biomass equations. While the growth equations are region-specific, biomass 

equations are not. Biomass equations are presented for 26 open-grown urban trees species (table 9). Most of these equations are compiled from literature sources described 

in the table, while the general equations (Urb Gen Broadleaf and Urb Gen Conifer) 

were developed through data collection and analyses. To be consistent with equations 

used in the Urban Forest Project Protocols (Climate Action Reserve 2008) for carbon 

projects, mass is not included in the formulations. All urban equations predict aboveground volume in square meters per tree. To convert from volume to dry-weight (DW) 

biomass, the predicted volume is multiplied by a DW density factor (table 9). 

In addition to equations developed specifically for urban trees, biomass equations have been adapted from literature on rural forest biomass and applied for 

use in the urban setting (table 10). These equations may produce either volume or 

DW biomass directly. Equations predicting DW biomass directly do not need to be 

multiplied by a DW density factor. 

Complete listings of equations are available in tables 9 and 10 (downloadable 

as tables S6 and S7). All equations are listed in an Excel-ready form so they may be 

copied and pasted into an Excel cell. Measurements required for using the biomass 

equations are either d.b.h. and tree height, or d.b.h. alone. If data availability 

permits, it is recommended that users select the d.b.h. and height equations over the 

d.b.h. only equations as they tend to produce more accurate results, particularly for 

trees with crowns that have been heavily pruned or topped. 
70

GENERAL TECHNICAL REPORT PSW-GTR-253 Table 9—Volume equations for 26 urban tree species requiring diameter at breast height (d.b.h.) (cm) only or d.b.h. (cm) and height (m) measurements to calculate volume Equation species SpCode D.b.h. range Equationa Predictsb DW density Equation sourcec D.b.h. and height: Centimeters Acacia longifolia ACLO 15 to 57 =0.0000904 × dbhcm^2.18649 × htm^0.46736 V 510 3 Acer platanoides ACPL 10 to 102 =0.001011 × dbhcm^1.533 × htm^0.657 V 520 2 Acer saccharinum ACSA1 13 to 135 =0.0002383 × dbhcm^1.998 × htm^0.596 V 440 2 Celtis occidentalis CEOC 11 to 119 =0.0022451 × dbhcm^2.118 × htm^ to 0.447 V 490 2 Ceratonia siliqua CESI3 16 to 74 =0.0001368 × dbhcm^1.79584 × htm^0.92667 V 520 3 Cinnamomum camphora CICA 13 to 69 =0.0000807 × dbhcm^2.1348 × htm^0.63404 V 520 3 Cupressus macrocarpa CUMA 16 to 147 =0.0000419 × dbhcm^2.2604 × htm^0.6301 V 410 3 Eucalyptus globulus EUGL 116 to 130 =0.0000318 × dbhcm^2.15182 × htm^0.83573 V 620 3

Fraxinus pennsylvanica FRPE 15 to 123 =0.0004143 × dbhcm^1.847 × htm^0.646 V 530 2Fraxinus velutina ‘Modesto’ FRVE_G 15 to 85 =0.0000385 × dbhcm^1.76296 × htm^1.42782 V 510 3Gleditsia triacanthos GLTR 9 to 98 =0.0004891 × dbhcm^2.132 × htm^0.142 V 600 2Gymnocladus dioicus GYDI 10 to 37 =0.000463 × dbhcm^1.545 × htmet^0.792 V 530 2Jacaranda mimosifolia JAMI 17 to 60 =0.0000801 × dbhcm^2.18578 × htm^0.548045 V 490 3Liquidambar styraciflua LIST 14 to 54 =0.0000631 × dbhcm^2.31582 × htm^0.41571 V 460 3Magnolia grandiflora MAGR 15 to 74 =0.0000504 × dbhcm^2.07041 × htm^0.84563 V 460 3Pinus radiata PIRA 17 to 105 =0.0000419 × dbhcm^2.226808 × htm^0.668993 V 400 3Pistacia chinensis PICH 13 to 51 =0.0000329 × dbhcm^2.19157 × htm^0.94367 V 685 3Platanus × acerifolia PLAC 16 to 74 =0.0000485 × dbhcm^2.43642 × htm^0.39168 V 500 3Populus sargentii POSA 6 to 137 =0.0019055 × dbhcm^1.806 × htm^0.134 V 370 2Quercus ilex QUIL2 13 to 52 =0.0000789 × dbhcm^1.82158 × htm^1.06269 V 820 3Quercus macrocarpa QUMA1 11 to 100 =0.0001689 × dbhcm^1.956 × htm^0.842 V 580 2Tilia cordata TICO 11 to 65 =0.0009453 × dbhcm^1.617 × htm^0.59 V 420 2Ulmus americana ULAM 18 to 114 =0.0012 × dbhcm^1.696 × htm^0.405 V 460 2Ulmus parvifolia ULPA 17 to 56 =0.0000609 × dbhcm^2.32481 × htm^0.49317 V 730 3Ulmus pumila ULPU 16 to 132 =0.000338 × dbhcm^0.855 × htm^2.041 V 540 2Zelkova serrata ZESE 15 to 86 =0.0000401 × dbhcm^2.36318 × htm^0.5519 V 520 3Urban Gen broadleaf UGEB 6 to 135 =0.0001967 × dbhcm^1.951853 × htm^0.664255 V Jenkins, DRYADd 1Urban Gen conifer UGEC 16 to 147 =0.0000426 × dbhcm^2.24358 × htm^0.64956 V Jenkins, DRYADd 1
71

Urban Tree Database and Allometric Equations

Equation species SpCode D.b.h. range Equationa Predictsb DW density Equation sourcecD.b.h. only:

Acacia longifolia ACLO 15 to 57 =0.000154 × dbhcm^2.34725 V 510 3Acer platanoides ACPL 10 to 102 =0.0019421 × dbhcm^1.785 V 520 2Acer saccharinum ACSA1 13 to 135 =0.000363 × dbhcm^2.292 V 440 2Celtis occidentalis CEOC 11 to 119 =0.0014159 × dbhcm^1.928 V 490 2Ceratonia siliqua CESI3 16 to 74 =0.0002579 × dbhcm^2.128861 V 520 3Cinnamomum camphora CICA 13 to 69 =0.0000839 × dbhcm^2.53466 V 520 3Cupressus macrocarpa CUMA 16 to 147 =0.0000985 × dbhcm^2.495263 V 410 3Eucalyptus globulus EUGL 116 to 130 =0.000161 × dbhcm^2.43697 V 620 3Fraxinus pennsylvanica FRPE 15 to 123 =0.0005885 × dbhcm^2.206 V 530 2Fraxinus velutina ‘Modesto’ FRVE_G 15 to 85 =0.000054 × dbhcm^2.633462 V 510 3Gleditsia triacanthos GLTR 9 to 98 =0.0005055 × dbhcm^2.22 V 600 2Gymnocladus dioicus GYDI 10 to 37 =0.0004159 × dbhcm^2.059 V 530 2Jacaranda mimosifolia JAMI 17 to 60 =0.0001005 × dbhcm^2.486248 V 490 3Liquidambar styraciflua LIST 14 to 54 =0.0000799 × dbhcm^2.560469 V 460 3Magnolia grandiflora MAGR 15 to 74 =0.0000559 × dbhcm^2.622015 V 460 3Pinus radiata PIRA 17 to 105 =0.0000469 × dbhcm^2.666079 V 400 3Pistacia chinensis PICH 13 to 51 =0.0000392 × dbhcm^2.808625 V 685 3Platanus × acerifolia PLAC 16 to 74 =0.000059 × dbhcm^2.673578 V 500 3Populus sargentii POSA 6 to 137 =0.0020891 × dbhcm^1.873 V 370 2Quercus ilex QUIL2 13 to 52 =0.0000627 × dbhcm^2.607285 V 820 3Quercus macrocarpa QUMA1 11 to 100 =0.0002431 × dbhcm^2.415 V 580 2Tilia cordata TICO 11 to 65 =0.0009359 × dbhcm^2.042 V 420 2Ulmus americana ULAM 18 to 114 =0.0018 × dbhcm^1.869 V 460 2Ulmus parvifolia ULPA 17 to 56 =0.000069 × dbhcm^2.639347 V 730 3Ulmus pumila ULPU 16 to 132 =0.0048879 × dbhcm^1.613 V 540 2Zelkova serrata ZESE 15 to 86 =0.0000502 × dbhcm^2.674757 V 520 3Urban Gen broadleaf UGEB 6 to 135 =0.0002835 × dbhcm^2.310647 V Jenkins, DRYADd 1Urban Gen conifer UGEC 16 to 147 =0.0000698 × dbhcm^2.578027 V Jenkins, DRYADd 1

a dbhcm = diameter at breast height in centimeters; htm = tree height in meters; dwdensity = dry weight-density factor. b DWdensity = dry weight biomass in kg/ m3 ; V = aboveground volume in cubic meters per tree.c Equation source: 1 = Aguaron and McPherson 2012; 2 = Lefsky and McHale 2008; 3 = Pillsbury et al. 1998. d Look up the dw density factor in McHale et al. (2009) first, but if not available, then the Global Wood Density Database (Zeng 2003).Table 9—Volume equations for 26 urban tree species requiring diameter at breast height (d.b.h.) (cm) only or d.b.h. (cm) and height (m) measurements to calculate volume (continued)
72

GENERAL TECHNICAL REPORT PSW-GTR-253 Table 10—Dry-weight biomass and volume equations derived from rural forests Equation species SpCode D.b.h. range (cm) Equationa Predictsb Dry-weight density Equation sourcec Acer rubrum ACRU 0 to 35 =0.1970 × dbhcm^2.1933 DW N/A 6 Fagus grandifolia FAGR 1 to 60 =0.1957 × dbhcm^2.3916 DW N/A 6 Fraxinus americana FRAM 5 to 50 =0.1063 × dbhcm^2.4798-EXP(-4.0813+5.8816/dbhcm) DW N/A 6,A Juniperus virginiana JUVI 14 to 43 =dbhcm+0.1632 × dbhcm^2.2454-(dbhcm+0.1244 × dbhcm^1.5549) DW 440 4,B Liriodendron tulipifera LITU 5 to 50 =0.0365 × (dbhcm)^2.7324-EXP(-4.0813+5.8816/dbhcm) DW N/A 6,A Melaleuca quinquenervia MEQU 0.5 to 39 =EXP(-1.83+2.01 × LN(dbhcm)) DW N/A 7 Quercus agrifolia QUAG 20 to 140 =0.0000447 × (dbhcm)^2.31958 × (htm)^0.62528 V 590 5 Quercus garryana QUGA4 20 to 140 =0.0000674 × (dbhcm)^2.14321 × (htm)^0.74220 V 640 5 Quercus lobata QULO 20 to 140 =0.0000763 × (dbhcm)^1.94165 × (htm)^0.86562 V 550 5

Quercus rubra QURU 5 to 50 =0.1130 × (dbhcm)^2.4572-EXP(-4.0813+5.8816/dbhcm) DW N/A 6,AUmbellularia californica UMCA 20 to 140 =0.0000763 × (dbhcm)^1.94553) × (htm)^0.88389 V 510 5Gen Hdwd aspen/alder/cottonwood/

willow

GNHDAA 12 to 50 =EXP(-2.2094+2.3867 × LN(dbhcm))-EXP(-4.0813+5.8816/dbhcm) DW N/A 4,B

Gen Hdwd Harris GNHDH >10 =EXP(-2.437+2.418 × LN(dbhcm))+EXP(-3.188+2.226 × LN(dbhcm)) DW N/A 3Gen Hdwd maple/oak/hickory/beech GNHDHM 14 to 34 =EXP(-2.0127+2.4342 × LN(dbhcm))-EXP(-4.0813+5.8816/dbhcm) DW N/A 4,BGen Hdwd soft maple/birch GNHDSM 12 to 42 =EXP(-1.9123+2.3651 × LN(dbhcm))-EXP(-4.0813+5.8816/dbhcm) DW N/A 4,BGen Sftwd cedar/larch GNSWCL 3 to 61 =EXP(-2.0336+2.2592 × LN(dbhcm))-EXP(-2.9584+4.4766/dbhcm) DW N/A 4,BGeneral Sftwd doug-fir GNSWDF 3 to 190 =EXP(-2.2304+2.4435 × LN(dbhcm))-EXP(-2.9584+4.4766/dbhcm) DW N/A 4,BGen Sftwd pine GNSWP 3 to 99 =EXP(-2.5356+2.4349 × LN(dbhcm))-EXP(-2.9584+4.4766/dbhcm) DW N/A 4,BGen Sftwd spruce GNSWS 3 to 78 =EXP(-2.0773+2.3323 × LN(dbhcm))-EXP(-2.9584+4.4766/dbhcm) DW N/A 4,BGen Sftwd truefir/hemlock GNSWTF 3 to 111 =EXP(-2.5384+2.4814 × LN(dbhcm))-EXP(-2.9584+4.4766/dbhcm) DW N/A 4,BGen Trop Chave GNTRC 4 to 148 =0.112 × ((dw density/1000) × dbhcm^2 × htm)^0.916 DW Jenkins, 

DRYADd

1

Gen Wdlnd juniper/oak/mesquite GNWDJO NA =EXP(-0.7152+1.7029 × LN(dbhcm))-EXP(-4.0813+5.8816/dbhcm) DW N/A 4,BGenl palms GNP to 17 m ht =(6 × htm+0.8)+(0.8 × htm+0.9) DW N/A 2Gen spiny dry climate GNHDV 2 to 32 =EXP(-1.103+1.994 × LN(dbhcm)+0.317 × LN(htm)+1.303 × 

LN(dwdensity/1000))

DW Jenkins, 

DRYADd

8

N/A = not applicable.a dbhcm = diameter at breast height in centimeters; htm = tree height in meters; dwdensity = dry-weight density factor.b DW density = dry-weight biomass in kiligrams per cubic meter; V = aboveground volume in cubic meters per tree.c Equation source: 1 = Chave et al. 2005, 2 = Frangi and Lugo (1985), 3 = Harris et al. (1973), 4 = McHale et al. (2009), 5 = Pillsbury and Kirkley (1984), 6 = Ter-Mikaelian and Korzukhin 1997, 7 = Van et al. 2000, 8 = Vieilledent et al. 2012, A = minus Jenkins foliage, B = minus foliage ratio. d Look up the dry-weight density factor in McHale et al. (2009) first, but if not available, then look it up in the Global Wood Density Database (Zeng 2003). 
73

Urban Tree Database and Allometric Equations

We developed two general volume equations from the urban species equations, 

one for urban broadleaf species and one for conifers. These equations can be used 

if the species of interest cannot be matched taxonomically or through wood form 

to the species listed in the tables of biomass equations derived from urban or rural 

forests (table 10). The general equations predict cubic meters of fresh-wood volume. 

Fresh-wood volume is then multiplied by the species’ DW density factor to obtain 

aboveground DW biomass. The urban general equations require looking up a dryweight density factor (in Jenkins et al. 2004 first, but if not available then the Global 

Wood Density Database).

To estimate total carbon and stored carbon dioxide (CO2) equivalents, dryweight biomass (either calculated directly or from fresh-wood volume) is converted 

using constants. The DW biomass is multiplied by 1.28 to incorporate belowground 

biomass (Husch et al. 2003, Tritton and Hornbeck 1982, Wenger 1984), multiplied 

by the constant 0.5 to convert to total carbon stored (Leith 1963, Whittaker et al. 

1973), and multiplied by the constant 3.67 (molecular weight of CO2) to convert to 

total CO2 stored. 

Dry-weight densities are unique to each tree species and can vary extensively 

among species. Volume equations can be applied to other species based on taxonomy if a species-specific DW density factor is not known. For example, because 

many of the species measured in each of the reference cities were not represented 

in tables 9 and 10, it was necessary to assign biomass equations to species for 

which there were no available data. Table 11 provides examples of species matching for volume or biomass estimation (see column “Equation Species Code” for 

species to which species without information are matched). If the form of the 

tree is completely different than any species listed, we recommend using the 

general equations for urban broadleaf and conifer trees and look up the speciesspecific dry-weight-wood density value in DRYAD, the Global Wood Density 

Database (Chave et al. 2005, Frangi and Lugo 1985, Harris et al. 1973, Higuchi 

et al. 2005, Jenkins et al. 2004, Pillsbury and Kirkley 1984, Ter-Mikaelian and 

Korzuhkhin 1997, Van et al. 2000, Vieilledent et al. 2012, Zanne et al. 2009, Zeng 

2003) available as a downloadable Excel spreadsheet at http://datadryad.org/repo/

handle/10255/dryad.235. 
74

GENERAL TECHNICAL REPORT PSW-GTR-253

Table 11— Expanded list of biomass density factors for common urban species (continued)

SpCode Scientific name DW densitya

Matched 

equation SpCode

Equation 

sourceb

ACFA Acacia farnesiana 520 ACLO 8

ACLO Acacia longifolia 520 ACLO 8

ACMA Acer macrophyllum 440 ACPL 6

ACME Acacia melanoxylon 573 ACLO 8

ACNE Acer negundo 420 ACPL 6

ACPA Acer palmatum 450 ACPL 6

ACPL Acer platanoides 520 ACPL 6

ACRU Acer rubrum 490 ACRU 9

ACSA1 Acer saccharinum 440 ACSA1 6

ACSA2 Acer saccharum 560 ACPL 6

ACSA3 Acacia salicina 473 ACLO 8

AEHI Aesculus hippocastanum 500 UGEB 1

BABL Bauhinia x blakeana 527 GNTRC 2

BENI Betula nigra 490 UGEB 1

BEPE Betula pendula 530 UGEB 1

BRPO Brachychiton populneus 387 UGEB 1

BUCA Butia capitata 370 PRACM 3

CABEF Carpinus betulus ‘Fastigiata’ 598 UGEB 1

CACI Callistemon citrinus 690 UGEB 1

CADE2 Calocedrus decurrens 350 GNSWCL 5,B

CAEQ Casuarina equisetifolia 728 GNTRC 2

CAIL Carya illinoinensis 600 UGEB 1

CAIN4 Calophyllum inophyllum 560 GNTRC 2

CANE33 Cassia x nealiae 670 GNTRC 2

CASP Catalpa speciosa 380 UGEB 1

CECA Cercis canadensis 520 UGEB 1

CEDE Cedrus deodara 410 GNSWCL 5,B

CEFL Parkinsonia florida 619 GNHDV 11

CELA Celtis laevigata 490 CEOC 6

CEOC Celtis occidentalis 490 CEOC 6

CESI3 Ceratonia siliqua 520 CESI3 8

CESI4 Celtis sinensis 490 CEOC 6

CHLI Chilopsis linearis 600 GNHDV 11

CICA Cinnamomum camphora 520 CICA 8

CISP2 Citharexylum spinosum 700 GNTRC 2

COERA2 Conocarpus erectus var. argenteus 690 GNTRC 2

COFL Cornus florida 640 UGEB 1

CONU Cocos nucifera 520 PRACM 3

COSU2 Cordia subcordata 640 GNTRC 2
75

Urban Tree Database and Allometric Equations

Table 11— Expanded list of biomass density factors for common urban species (continued)

SpCode Scientific name DW densitya

Matched 

equation SpCode

Equation 

sourceb

CR Crataegus species 520 UGEB 1

CRLA80 Crataegus laevigata 620 UGEB 1

CUAN Cupaniopsis anacardioides 520 UGEB 1

CUMA Cupressus macrocarpa 410 CUMA 8

DERE Delonix regia 479 GNTRC 2

ELAN Elaeagnus angustifolia 520 UGEB 1

ELOR2 Elaeodendron orientale 676 GNTRC 2

ERJA Eriobotrya japonica 520 UGEB 1

EUFI81 Eucalyptus ficifolia 794 EUGL 8

EUGL Eucalyptus globulus 620 EUGL 8

EUMI2 Eucalyptus microtheca 994 EUGL 8

EUSI Eucalyptus sideroxylon 932 EUGL 8

FAGR Fagus grandifolia 585 FAGR 9

FASYAT Fagus sylvatica ‘Atropunicea’ 585 FAGR 9

FIBE Ficus benjamina 460 GNTRC 2

FIDE6 Filicium decipiens 805 GNTRC 2

FIMI Ficus thonningii 432 GNTRC 2

FRAM Fraxinus americana 550 FRAM 9,A

FRAN_R Fraxinus angustifolia ‘Raywood’ 510 FRVE_G 8

FRAN2 Fraxinus angustifolia 510 FRVE_G 8

FREX_H Fraxinus excelsior ‘Hessei’ 560 FRVE_G 8

FRHO Fraxinus holotricha 510 FRVE_G 8

FRLA Fraxinus latifolia 500 FRAM 9,A

FRPE Fraxinus pennsylvanica 530 FRPE 6

FRPE_M Fraxinus pennsylvanica ‘Marshall’ 530 FRPE 6

FRUH Fraxinus uhdei 510 FRPE 6

FRVE Fraxinus velutina 510 FRVE_G 8

FRVE_G Fraxinus velutina ‘Modesto’ 510 FRVE_G 8

GIBI Ginkgo biloba 520 UGEB 1

GLTR Gleditsia triacanthos 600 GLTR 6

GNHDAA General hardwood jenkins N/A GNHDAA 5,B

GNHDH General hardwood harris N/A GNHDH 4

GNHDHM General hardwood jenkins N/A GNHDHM 5,B

GNHDSM General hardwood jenkins N/A GNHDSM 5,B

GNHDV General spiny dry vieilledent N/A GNHDV 11

GNSWCL General softwood jenkins N/A GNSWCL 5,B

GNSWDF General softwood jenkins N/A GNSWDF 5,B

GNSWP General softwood jenkins N/A GNSWP 5,B

GNSWS General softwood jenkins N/A GNSWS 5,B
76

GENERAL TECHNICAL REPORT PSW-GTR-253

Table 11— Expanded list of biomass density factors for common urban species (continued)

SpCode Scientific name DW densitya

Matched 

equation SpCode

Equation 

sourceb

GNSWTF General softwood jenkins N/A GNSWTF 5,B

GNTRC General tropical chave N/A GNTRC 2

GNWDJO General woodland jenkins N/A GNWDJO 5,B

GYDI Gymnocladus dioicus 530 UGEB 1

ILOP Ilex opaca 500 UGEB 1

ILPA2 Ilex paraguariensis 565 GNTRC 2

JAMI Jacaranda mimosifolia 490 JAMI 8

JUNI Juglans nigra 510 UGEB 1

JUSI Juniperus virginiana var. silicicola 420 JUVI 5,B

JUVI Juniperus virginiana 440 JUVI 5,B

KOEL Koelreuteria elegans 595 UGEB 1

KOPA Koelreuteria paniculata 620 UGEB 1

LA6 Lagerstroemia species 571 UGEB 1

LAIN Lagerstroemia indica 571 UGEB 1

LASP Lagerstroemia speciosa 612 GNTRC 2

LIST Liquidambar styraciflua 460 LIST 8

LITU Liriodendron tulipifera 400 LITU 9,A

MA2 Malus species 610 UGEB 1

MAGR Magnolia grandiflora 460 MAGR 8

MEEX Metrosideros excelsa 1150 UGEB 1

MEQU Melaleuca quinquenervia 520 MEQU 10

MO Morus species 520 UGEB 1

MOAL Morus alba 520 UGEB 1

OLEU Olea europaea 700 UGEB 1

PAAC Parkinsonia aculeata 610 GNHDV 11

PHCA Phoenix canariensis 370 PRACM 3

PHDA4 Phoenix dactylifera 370 PRACM 3

PIBR2 Pinus brutia 430 UGEC 1

PICA Pinus canariensis 610 UGEC 1

PICH Pistacia chinensis 685 PICH 8

PICO5 Pinus contorta var. bolanderi 380 UGEC 1

PIEC Pinus echinata 470 UGEC 1

PIED Pinus edulis 500 UGEC 1

PIEL2 Pinus eldarica 540 UGEC 1

PIHA Pinus halepensis 460 UGEC 1

PINI Pinus nigra 430 UGEC 1

PIPO Pinus ponderosa 380 UGEC 1

PIPU Picea pungens 360 UGEC 1

PIRA Pinus radiata 400 PIRA 8
77

Urban Tree Database and Allometric Equations

Table 11— Expanded list of biomass density factors for common urban species (continued)

SpCode Scientific name DW densitya

Matched 

equation SpCode

Equation 

sourceb

PISA2 Samanea saman 520 GNTRC 2

PIST Pinus strobus 340 UGEC 1

PISY Pinus sylvestris 430 UGEC 1

PITA Pinus taeda 470 UGEC 1

PITH Pinus thunbergiana 430 UGEC 1

PIUN Pittosporum undulatum 745 UGEB 1

PLAC Platanus × acerifolia 500 PLAC 8

PLOC Platanus occidentalis 480 PLAC 8

PLRA Platanus racemosa 480 PLAC 8

POAN Populus angustifolia 350 POSA 6

PODE Populus deltoides 370 POSA 6

POFR Populus fremontii 410 POSA 6

POMA Podocarpus macrophyllus 470 UGEB 1

POSA Populus sargentii 370 POSA 6

POTR2 Populus balsamifera ssp. trichocarpa 310 POSA 6

PR Prunus species 560 UGEB 1

PRACM Prestoea montana 370 PRACM 3

PRCA Prunus caroliniana 560 UGEB 1

PRCE Prunus cerasifera 470 UGEB 1

PRCEKW Prunus cerasifera ‘Thundercloud’ 560 UGEB 1

PRCH Prosopis chilensis 740 GNHDV 11

PRSE2 Prunus serrulata 560 UGEB 1

PRYE Prunus yedoensis 470 UGEB 1

PSME Pseudotsuga menziesii 450 GNSWDF 5,B

PY Pyrus species 600 UGEB 1

PYAN Malus angustifolia 610 UGEB 1

PYCA Pyrus calleryana 600 UGEB 1

PYCA_B Pyrus calleryana ‘Bradford’ 600 UGEB 1

PYKA Pyrus kawakamii 600 UGEB 1

QUAG Quercus agrifolia 590 QUAG 7

QUAL Quercus alba 600 QUGA4 7

QUGA4 Quercus garryana 640 QUGA4 7

QUIL2 Quercus ilex 820 QUIL2 8

QULA2 Quercus laurifolia 560 QULO 7

QULO Quercus lobata 550 QULO 7

QUMA1 Quercus macrocarpa 580 QUMA1 6

QUNI Quercus nigra 560 QUAG 7

QUPA Quercus palustris 580 QUAG 7

QUPH Quercus phellos 560 QUAG 7
78

GENERAL TECHNICAL REPORT PSW-GTR-253

Table 11— Expanded list of biomass density factors for common urban species (continued)

SpCode Scientific name DW densitya

Matched 

equation SpCode

Equation 

sourceb

QURU Quercus rubra 560 QURU 9,A

QUSH Quercus shumardii 590 QUAG 7

QUVI Quercus virginiana 800 QUGA4 7

RHLA Rhus lancea 540 GNHDV 11

ROPS Robinia pseudoacacia 660 GLTR 6

SAPA Sabal palmetto 520 PRACM 3

SCMO Schinus molle 650 UGEB 1

SCTE Schinus terebinthifolius 650 UGEB 1

SESE Sequoia sempervirens 360 GNSWCL 5,B

SWMA Swietenia mahagoni 750 GNTRC 2

SYRO Syagrus romanzoffiana 370 PRACM 3

TAAR Tabebuia aurea 520 GNTRC 2

TACH Tabebuia ochracea subsp.

neochrysantha

960 GNTRC 2

TAPA Tabebuia heterophylla 520 GNTRC 2

THOR Platycladus orientalis 527 UGEC 1

TIAM Tilia americana 320 TICO 6

TICO Tilia cordata 420 TICO 6

TITO Tilia tomentosa 320 TICO 6

TRCO Tristaniopsis conferta 750 UGEB 1

TRSE6 Triadica sebifera 520 UGEB 1

UGEB Urban general broadleaf DRYADc UGEB 1

UGEC Urban general conifer DRYADc UGEC 1

ULAL Ulmus alata 600 ULPU 6

ULAM Ulmus americana 460 ULAM 6

ULPA Ulmus parvifolia 730 ULPA 8

ULPU Ulmus pumila 540 ULPU 6

UMCA Umbellularia californica 510 UMCA 7

VEME Veitchia merrillii 370 PRACM 3

WAFI Washingtonia filifera 370 PRACM 3

WARO Washingtonia robusta 370 PRACM 3

ZESE Zelkova serrata 520 ZESE 8

Notes: Species without a specific equation or dry-weight density factor are matched to known species. N/A = not applicable.

a

 DW density = dry-weight biomass kilograms per cubic meter. b

 Equation source: 1 = Aguaron and McPherson 2012, 2 = Chave et al. 2005, 3 = Frangi and Lugo 1985, 4 = Harris et al. 1973, 5 

= Jenkins et al. 2004, 6 = Lefsky and McHale 2008, 7 = Pillsbury and Kirkley 1984, 8 = Pillsbury et al. 1998, 9 = Ter-Mikaelian 

and Korzukhin 1997, 10 = Van et al. 2000, 11 = Vieilledent et al. 2012, A = minus Jenkins foliage, B = minus foliage ratio.

c For equations UGEC and UGEB, look up correct dry-weight density factor for species of interest in DRYAD (the Global Wood 

Density Database).
79

Urban Tree Database and Allometric Equations

Example 2. Calculating dry-weight biomass and carbon stored based on either calculated or measured d.b.h. and/or tree height.

Once d.b.h. and height have been measured or calculated (as in example 1), the 

next step entails using either d.b.h. or d.b.h. and height to calculate the dry-weight 

biomass. For species assigned biomass equations, skip to example 3. For species 

assigned volumetric equations, follow this example. 

In this example, we continue with a sample tree Liquidambar styraciflua

(sweetgum) located in the Northern California Coast region. It is 33 years of age 

and has an estimated d.b.h. equal to 42.2 cm and tree height equal to 15.3 m, as 

calculated in example 1. 

Step 1. Select the equation for d.b.h. and height to calculate aboveground fresh 

wood volume (table 9). Fresh-wood volume in cubic meters (V) for a 15.3-m tall 

sweetgum with a 42.2-cm d.b.h. is calculated as: 

V = 0.0000631 × (42.2) 2.31582 × (15.1) 0.41571 = 1.13 m3 

Note that the volumetric equations are not region specific, so the fact that our 

sample tree is located in the Northern California Coast region does not play a role in 

this example. If the tree had not been measured and we were predicting d.b.h. and/

or ht from age or d.b.h., we would need to select a region-specific growth equation. 

Step 2. Convert from fresh-wood volume to dry-weight biomass by multiplying V 

by the species-specific DW density factor, which for sweetgum is 460 kg/m3 (from 

table 9)

DW = 1.13 m3 × 460 kg/m3 = 519.80 kg

Step 3. Thus far, we have calculated the biomass for the aboveground portion of 

the tree. To convert from DW biomass to carbon stored, the belowground biomass 

should be incorporated. The biomass stored belowground is calculated by multiplying the DW biomass by 1.28:

Total DW = 519.80 kg × 1.28 = 665.34 kg

Step 4. Next, the DW biomass is converted into kilograms of carbon (C) by multiplying by the constant 0.5:

C = 665.34 kg × 0.5 = 332.67 kg

Step 5. Convert stored carbon into stored carbon dioxide (CO2) by multiplying by 

the constant 3.67 as follows: 

CO2 = 332.67 kg × 3.67 = 1220.89 kg

Note that in this case, results were rounded at each step. Users will achieve 

slightly different results when using Excel or programming language to calculate 

the final amounts. 
80

GENERAL TECHNICAL REPORT PSW-GTR-253

Example 3. Estimating DW biomass directly from tree size parameters. 

In this variation of example 2, we measure a Liriodendron tulipifera, which has 

a d.b.h. of 35.0 cm. Select the equation from table 10 for estimating the direct DW 

biomass of this species. The calculation is as follows: 

DW = 0.0365 × (35.0)2.7324- e (-4.0813+5.8816/35.0) = 604.4 kg 

where e is a mathematical constant equal to 2.71828182845904.

To estimate total DW, total carbon stored, and CO2 stored, continue with steps 3 

through 5 in example 2. 

Error in Predicting Future Growth, Carbon, and Biomass

The volume equations were developed from trees that may differ in size from 

the trees in the user’s sample or inventory. The d.b.h. ranges for trees sampled to 

develop the volume and biomass equations are listed in columns labelled “Dbh 

lower (cm)” and “Dbh upper (cm)” (tables 9 and 10). Applying the equations to trees 

with d.b.h. outside of this range may increase the prediction error. Tree growth 

as modelled or estimated by the user may deviate significantly from tree growth 

models generalized here. In general, it is better to err on the side of underestimating 

carbon stocks rather than overestimating. Recommended ways of evaluating the 

growth data presented here include contacting local arborists and other tree experts 

(e.g., university extension offices, city tree managers) or from repeated measurements of inventoried trees.

Case Study

To demonstrate the species-level differences in d.b.h., tree height, and total carbon 

across regions, we selected the top three species most commonly measured in the 

17 reference cities (16 reference cities and SacVal): Acer saccharinum (silver maple), 

Liquidambar styraciflua (sweetgum), and Magnolia grandiflora (southern magnolia). We estimated the d.b.h., tree height, and total carbon at 10-year intervals up to 

the maximum age recommended for the application of the developed equations (i.e., 

“AppMax”). Silver maple was measured in 7 reference cities, southern magnolia in 

8 cities, and sweetgum in 12 cities. 

At age 40, the oldest age for which data were available across regions, the 

estimated total carbon stored in silver maple was between 378.1 kg in the Northeast 

and 4505.6 kg in the Midwest regions, an 11-fold difference (fig. 17). Estimated 

d.b.h range was between 34.8 cm in Northeast and 101.6 cm in the Midwest; tree 

height ranged from 13.3 m in Northeast and 23.4 m in Midwest (table 12). The 

growth patterns of silver maple are similar in three regions: Inland Valley, North, 

Tropical Interior West and Lower Midwest, where there is only a twofold difference 

at age 40. Over the same time period, the quickest accumulation of carbon in silver 
81

Urban Tree Database and Allometric Equations

Age

Climate zone

InlVal

LoMidW

MidWst

NMtnPr

NoEast

Peidmt

TpIntW

Total carbon (kg)

0

5000

4000

6000

7000

8000

9000

3000

2000

1000

0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

maple occurred in the Midwest and South. Silver maple growing in the Northeast is 

on the lowest trajectory for carbon stored, amounting to only 1222.3 kg at the oldest 

age for which the growth equations could be applied, age 150. 

Of the regions and reference cities in which sweetgum is planted abundantly, 

the highest amount of carbon stored was in the southeastern region of the United 

States followed by regions in California (Northern California Coast; Inland Valleys 

including Sacramento Valley; Inland Empire) (fig. 18). Sweetgum in the Northeast 

and Southern California Coast stored noticeably less carbon than in the other 

regions as trees grew older. At age 60, the difference between highest and lowest 

estimates of carbon storage was ninefold, ranging from 238.6 kg in Southern California Coast (d.b.h. = 37.3; tree height = 13.3 m) to 5451.5 kg in the South region 

(d.b.h. = 121.4 cm; tree height = 34.8 m (fig. 18; table 13).

The regional differences in total carbon stored by magnolia become evident 

within 30 years of planting, with trees in Central Florida, South (Piedmont), Coastal 

Plain, and Sacramento Valley increasing at a faster rate than in Southern California 

Coast, Northern California Coast, and Inland Valleys (fig. 19). It takes magnolia 

approximately 30 additional years in Northern California Coast to attain similar 

levels of total carbon storage amount as in Central Florida and South regions. By 

age 50, the oldest age for which estimates were available across regions, magnolia is 

Figure 17—Total stored carbon by age for silver maple in regions where it was measured.
82

GENERAL TECHNICAL REPORT PSW-GTR-253

Age

Climate zone

CenFla

GulfCo

InlEmp

InlVal

NoCalC

NoEast

PacfNW

Peidmt

SacVal

SoCalC

TpIntW

Total carbon (kg)

0

5000

4500

4000

6000

5500

3500

3000

2500

2000

500

1500

1000

0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

Age

Climate zone

CenFla

GulfCo

InlEmp

InlVal

NoCalC

Peidmt

SacVal

SoCalC

Total carbon (kg)

2500

2000

1500

500

0

1000

0 10 20 30 40 50 60 70 80 90 100 110

Figure 18—Total stored carbon by age for sweetgum in regions where it was measured.

Figure 19—Total stored carbon by age for southern magnolia in regions where it was measured.
83

Urban Tree Database and Allometric Equations

expected to accumulate six times more carbon in the Central Florida (1596.2 kg) 

than in the Inland Valleys region (271.9 kg), nearly a sixfold difference. Estimated 

d.b.h ranged from 41.2 cm (tree height = 12.2 m) in the Inland Valleys to 97.8 cm in 

Central Florida region (tree height = 15.7 m) (table 14).

Species that are highly abundant in the reference cities (i.e., silver maple, sweetgum, and magnolia) accumulated carbon at a higher rate in the southeastern regions 

of the Unites States, namely South, Central Florida, and Coastal Plain regions. The 

ability of trees to store a large amount of carbon in the southeastern United States 

is likely due in part to the combination of high precipitation (>1300 mm per year), 

high temperatures in the summer and relatively warm temperatures in the winter 

(cooling degree days [CDD] > 847; heating degree days [HDD] < 2000), and long 

growing seasons. Central Florida, for example, has low HDD and high CDD, signifying a warm climate year round, where cooling would be required in the summers, 

but heating would not be needed as much in the winter. 

Another region in which our case study species have accumulated relatively 

large amounts of carbon is the Midwest. This is surprising owing to the shorter 

growing seasons and cooler temperatures. One factor that likely played a role was 

the lack of limitations on growing space in Minneapolis, Minnesota. Very few sites 

had visible limitations on growth. In contrast, in Queens, New York city, only 44 

percent of the sites had no apparent limitations. The species analyzed in our case 

study accumulated consistently less carbon in Queens than in the other reference 

cities. Santa Monica, reference city for the Southern California Coast region, also 

had lower estimates of carbon storage by sweetgum, likely resulting from too heavy 

pruning owing to hazard potentials (e.g., trees planted very close to curbs on busy 

commercial boulevards) (personal communication, P. Peper). Additional regions 

that had lower total carbon storage were the Inland Empire, Inland Valleys, and 

Lower Midwest. Although the inland regions of California have many warm days 

conducive to plant growth, low precipitation can result in high evaporative demand. 

Prolonged drought stress can restrict tree growth and carbon storage (Anderegg et 

al. 2015). For example, in the Inland Valleys region, CDD is 3153 mm, but annual 

precipitation is only 315 mm, most of which comes during the leaf-off season.
84

GENERAL TECHNICAL REPORT PSW-GTR-253

Table 12—Diameter at breast height (d.b.h.) and tree height estimates for Acer saccharinum in 

regions where these species were measured

Age

Inland 

Valleys

Lower 

Midwest Midwest North Northeast South

Temperate 

Interior West

Year - - - - - - - - - - - - - - - - - - - - - Diameter at breast height (cm) - - - - - - - - - - - - - - - - - - - - -

0 2.5 1.4 2.2 2.8 2.2 1.3 4

10 19 10 22.5 19.6 16.5 22.4 15.2

20 35.5 23.5 52.6 35.5 24.8 43.5 28.4

30 52 36.2 81.4 50.3 30.4 64.6 42.8

40 68.5 48 101.6 64.2 34.8 85.7 57.9

50 85 58.9 77.2 38.4 106.7 72.8

60 101.5 69.1 89.1 41.5 127.8 87

70 118 78.7 100.1 44.1 99.7

80 87.8 110.2 46.5 110.3

90 96.4 119.2 48.7 118

100 104.7 127.3 50.6 122.2

110 112.6 134.4 52.4

120 120.1 140.6 54.1

130 55.7

140 57.1

150 58.5

- - - - - - - - - - - - - - - - - - - - - - - - - - -Tree height (m) - - - - - - - - - - - - - - - - - - - - - - - - - - -

0 2.2 1.3 3 2.8 2 2.6 6.4

10 10.6 6.9 10.4 11.2 9.1 8.7 9.3

20 14.7 11.2 18.3 15 11.3 13.7 12.4

30 17.5 13.8 22.5 17.5 12.5 17.8 15.4

40 19.8 15.7 23.4 19.3 13.3 20.9 18.1

50 21.6 17.1 20.8 13.9 23 20.4

60 23.2 18.2 21.9 14.4 24.2 22.1

70 24.5 19.2 22.9 14.8 23.3

80 20 23.7 15.2 24

90 20.7 24.4 15.5 24.4

100 21.3 24.9 15.7 24.6

110 21.9 25.4 16

120 22.4 25.8 16.2

130 16.4

140 16.6

150 16.7
85

Urban Tree Database and Allometric Equations

Table 13—Diameter at breast height (d.b.h.) and tree height estimates for Liquidambar styraciflua in regions where these species were measuredAge

Central 

Florida

Coastal 

Plain

Inland 

Empire

Inland 

Valleys Northeast

Northern 

CA Coast

Pacific 

Northwest

Sacramento 

Valley South

Southern 

CA Coast

Temperate 

Interior West

Year - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Diameter at breast height (cm) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 0.9 2.6 2.5 2.5 3.4 2.8 2 3.7 2.3 1.8 2.810 21.9 24.5 15.1 14.5 12.1 15.4 18.4 20.4 18.7 14.9 13.720 41 42.9 26.4 26.4 20.2 27.4 34.8 35.3 39.3 22.3 26.130 56.2 58 36.3 38.4 27.8 38.9 51.3 48.4 59.8 27.4 36.840 68.9 69.7 45 50.3 35 49.7 67.7 59.6 80.3 31.4 46.150 80.1 77.9 52.4 62.3 41.6 59.9 69 100.8 34.6 53.860 90 82.8 58.4 74.2 47.7 69.5 76.5 121.4 37.3 6070 99 63.2 53.4 78.5 82.2 39.7 64.780 66.6 58.5 87 86 41.9 67.990 68.8 63.1 94.8 88.1 43.8100 69.6 67.2 102 45.5110 69.6 70.8120 69.6 73.9130 69.6 76.5140 69.6 78.6150 80.1

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Tree height (m) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

0 0.6 1.8 2.9 4.8 2.7 2.3 2.4 3.5 1.8 2.6 1.610 9.9 12.7 9.2 7.9 5.9 8.4 9.5 10 12.6 7.3 8.120 13.6 17.7 12.9 11.1 8.5 12.4 14.5 15.2 19.9 9.6 12.930 15.7 20.7 15.2 14.2 10.6 14.8 17.6 19.2 24.9 11 16.240 17.2 22.7 16.6 17.4 12.3 16.3 18.6 22.2 28.8 12 18.650 18.3 23.9 17.7 20.5 13.7 17.3 24.5 32 12.7 20.360 19.2 24.6 18.6 23.7 14.9 18 26.1 34.8 13.3 21.670 19.9 19.4 15.9 18.8 27.3 13.8 22.580 20 16.8 19.8 28 14.2 23.190 20.5 17.6 21.1 28.3 14.6100 20.6 18.3 22.7 14.9110 20.6 18.9120 20.6 19.4130 20.6 19.9140 20.6 20.2150 20.5
86

GENERAL TECHNICAL REPORT PSW-GTR-253 Table 14—Diameter at breast height (d.b.h.) and tree height estimates for Magnolia grandiflora in regions where these species were measured Age Central Florida Coastal Plain Inland Empire Inland Valleys Lower Midwest Midwest North Northeast Northern California Coast Sacramento Valley South Year - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Diameter at breast height (cm) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 3 2.5 2.2 2.5 3.1 3.1 3.1 3.1 3 1.2 3.1 10 21.2 14.7 13.3 10.3 14.5 14.5 14.5 14.5 7.7 18.8 14.5 20 41.6 26.9 21.9 18 27.9 27.9 27.9 27.9 14.1 32.4 27.9 30 59.4 39.1 29.3 25.7 43.2 43.2 43.2 43.2 22.3 42.6 43.2 40 74.7 51.3 36.7 33.5 60.5 60.5 60.5 60.5 32.3 50.9 60.5 50 87.5 63.5 45.6 41.2 79.6 79.6 79.6 79.6 44.1 57.9 79.6 60 97.8 57.1 49 57.6 64.1

70 105.5 72.6 72.9 69.680 90.1 74.690 79.2100 83.4110 87.4

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Tree height (m) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

0 1.1 1.2 2.8 1.8 1.6 1.6 1.6 1.6 1.9 0.7 1.610 6.6 5.7 5.6 4.4 6.1 6.1 6.1 6.1 4.1 8 6.120 10.3 9.2 7.5 6.8 10.5 10.5 10.5 10.5 6 10.8 10.530 12.7 11.8 8.9 8.9 14.4 14.4 14.4 14.4 7.8 12.4 14.440 14.4 13.5 10.2 10.7 17.3 17.3 17.3 17.3 9.4 13.4 17.350 15.7 14.2 11.4 12.2 18.7 18.7 18.7 18.7 10.8 14.3 18.760 16.5 12.5 13.5 12.1 14.970 16.5 13.2 13.3 15.580 14.5 15.990 16.3100 16.7110 17
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