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Contents lists available at SciVerse ScienceDirect
Urban Forestry & Urban Greening
journal homepage: www.elsevier.de/ufug
Relationships between bole and crown size for young urban trees
in the northeastern USA
Blake Troxel a,b,∗ , Max Piana a,b , Mark S. Ashton a , Colleen Murphy-Dunning a,b
a
b
Yale School of Forestry & Environmental Studies, 195 Prospect Street, New Haven, CT 06511, United States
Urban Resources Initiative, Hixon Center for Urban Ecology, 301 Prospect Street, First Floor, New Haven, CT 06511, United States
a r t i c l e
i n f o
Keywords:
Allometry
Growth projection
New Haven
Street tree management
Urban ecology
Urban forestry
a b s t r a c t
Knowledge of allometric equations can enable urban forest managers to meet desired economic, social,
and ecological goals. However, there remains limited regional data on young tree growth within the urban
landscape. The objective of this study is to address this research gap and examine interactions between
age, bole size and crown dimensions of young urban trees in New Haven, CT, USA to identify allometric
relationships and generate predictive growth equations useful for the region. This study examines the
10 most common species from a census of 1474 community planted trees (ages 4–16). Regressions were
applied to relate diameter at breast height (dbh), age (years since transplanting), tree height, crown diameter and crown volume. Across all ten species each allometric relationship was statistically (p < 0.001)
significant at an ˛-level of 0.05. Consistently, shade trees demonstrated stronger relationships than ornamental trees. Crown diameter and dbh displayed the strongest fit with eight of the ten species having
an R2 > 0.70. Crown volume exhibited a good fit for each of the shade tree species (R2 > 0.85), while the
coefficients of determination for the ornamentals varied (0.38 < R2 < 0.73). In the model predicting height
from dbh, ornamentals displayed the lowest R2 (0.33 < R2 < 0.55) while shade trees represented a much
better fit (R2 > 0.66). Allometric relationships can be used to develop spacing guidelines for commonly
planted urban trees. These correlations will better equip forest managers to predict the growth of urban
trees, thereby improving the management and maintenance of New England’s urban forests.
© 2013 Elsevier GmbH. All rights reserved.
Introduction
The composition and arrangement of trees within a city can
provide a range of benefits for the urban community. Urban trees
moderate micro-climate (Rosenfeld et al., 1998; Simpson, 1998;
Akbari et al., 2001; Akbari, 2002; Donovan and Butry, 2009); reduce
energy use and atmospheric carbon dioxide (McPherson, 1998;
McPherson and Simpson, 2000); improve air, soil, and water quality (Beckett et al., 1998; Nowak et al., 2002; Donovan et al., 2005;
Yang et al., 2005; Nowak, 2006; Escobedo and Nowak, 2009); mitigate stormwater runoff (Sanders, 1986; Xiao et al., 1998, 2000a,b);
reduce noise, increase property values, and enhance the social
and aesthetic environment of a city (Nowak et al., 2001; Maco
and McPherson, 2002; Nowak, 2006). These social, economic, and
ecological benefits are often correlated with tree and crown size.
Numerous studies illustrate a direct relationship between the associated benefits of trees and their leaf-atmosphere interactions,
suggesting that each benefit may be a function of tree canopy and
∗ Corresponding author at: Yale School of Forestry & Environmental Studies, 195
Prospect Street, New Haven, CT 06511, United States. Tel.: +1 2036416570.
E-mail addresses: blake.troxel@aya.yale.edu, blake.troxel@gmail.com (B. Troxel).
leaf area (Scott et al., 1998; Dwyer and Miller, 1999; Xiao et al.,
2000a,b; Stoffberg et al., 2010).
Physiological understanding of trees reveals a close relationship
between plant stem growth and photosynthetic area (Berlyn, 1962;
Ashton, 1990). This relationship between bole size and other physical dimensions of growth is fundamental to the study of allometry
in forests. Traditionally associated with rural forests, allometric
models of growth and yield have been developed through relationships between tree dbh, tree height, and crown dimensions to
develop quantitative guidelines for spacing and thinning of managed forests and timber plantations (Furnival, 1961; Curtis, 1967;
Stage, 1973).
The knowledge of size relationships and allometric equations has been recognized as a valuable tool that will enable
professionals to manipulate forest structure and composition to
meet desired economic, social, and ecological benefits (Nowak,
1994; Nowak and Dwyer, 2007). From these equations arborists,
researchers, and urban forest managers can develop appropriate policy, analyze management scenarios, plan for spacing and
infrastructure constraints, and determine best management practices for the selection, sitting, planting, and maintenance of urban
trees (McPherson et al., 2000; Peper et al., 2001a,b; Larsen and
Kristoffersen, 2002; Stoffberg et al., 2008).
1618-8667/$ – see front matter © 2013 Elsevier GmbH. All rights reserved.
http://dx.doi.org/10.1016/j.ufug.2013.02.006
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While allometric equations and their associated models have
great potential to improve urban forest management and planning,
the existing equations from traditional forests do not directly translate to the urban landscape. Differing biophysical conditions impact
tree growth, allocation, and phenology, which result in altered
physical form and altered allometry (Peper and McPherson, 1998;
Nowak, 1994; McHale et al., 2009). The deviations in growth and
size relationships may be explained by the differences associated
with management practices (irrigation, pruning, soil management),
open growing conditions, variable soil structure and composition,
and altered resource competition and resource availability within
cities (McHale et al., 2009; Semenzato et al., 2011).
Urban forestry researchers have responded to this void with the
development of specific allometric equations for urban environments. Over the past two decades predictive allometric equations
have been produced by studies in selective regions of North America, and abroad (Fleming, 1988; Frelich, 1992; Nowak, 1996; Peper
and McPherson, 1998; Peper et al., 2001a,b; Stoffberg et al., 2008;
Semenzato et al., 2011). Despite these efforts there remains limited
species-specific data for a diversity of urban regions, let alone data
that considers varying ages of urban trees, tree conditions, and site
conditions across the urban landscape. This limited understanding presents a major obstacle for the application of models that
quantify urban tree growth and benefits (Peper et al., 2001a,b;
McPherson, 2010). When applying growth models, knowledge of
the relationship between age, dbh, tree height, crown width, and
leaf area must be available for individual species in different cities
within different geographic regions. Ultimately, the predictive allometric modeling of urban trees warrants further research, for both
specific species and specific sites (McHale et al., 2009; Semenzato
et al., 2011).
The objective of this study is to examine interactions between
age (years from transplanting), bole size (dbh) and crown dimensions (tree height, crown diameter, crown volume) of young urban
trees in New Haven, Connecticut, to identify allometric relationships, and to compare growth rates of the 10 most commonly
planted species. This work aims to inform the future management of streetscapes and neighborhood greenspaces throughout
the coastal northeast with an improved knowledge of speciesspecific growth rates and vigor. Such allometric equations will aid
urban foresters with species selection and have the potential to
inform innovative urban ecosystem-service policy and planning.
Finally, this work identifies the need for, and provides a foundation
for future study and establishment of, site-specific and speciesspecific predictive growth curves.
Materials and methods
is a non-profit organization, founded in 1995, in association with
the Yale School of Forestry and Environmental Studies. The initiative seeks to support community forestry and neighborhood
restoration projects, while also acting as the primary contractor for
tree planting within the city. Given URI’s extensive planting records
and wide distribution of plantings across different neighborhoods
and site conditions such plantings offer a unique sampling opportunity.
Since 1995, URI’s Greenspace program has completed more than
300 diverse urban restoration projects with at least 50 community
groups participating each year. Historical records for each restoration project were used to locate all trees planted by community
groups from 1995 to 2007 across the city in 19 neighborhoods.
Most importantly, these records provided information about the
planting date, species type, and location of the planting site.
A total of 1474 URI planted trees were sampled across New
Haven (Fig. 1). Measurements were taken of dbh, tree height, height
to base of live crown, crown width, volumetric shape, and crown
density. From the 1474 trees measured, a subsample of the ten most
frequently planted genera were selected for analysis in this study
(Table 1). Only trees that were qualitatively categorized as either
good, or fair were included in the calculations.
The north–south, east–west crown canopy dimensions of each
tree were mapped using measuring tape that was positioned from
the base of the stem. A percent clinometer (Suunto, Forestry Supplies, Jackson, MS) was used to measure height of the top of the
crown and height to the base of the live crown. Four readings were
taken using a concave densiometer (Forest Densiometers, Forestry
Supplies, Jackson, MS) at each of the north–south and east–west
mid points between the stem and the drip line. Densiometer readings were averaged to assign a plant area index to each crown
(Breda, 2003). These dimensions were then combined with a solid
geometric shape (Fig. 2) to calculate the crown volume of each
individual tree.
The age of each tree was calculated from the date of planting and
does not represent true age. However, URI tree stock is consistently
purchased at 5–6 cm dbh allowing for relative comparisons across
all species over time since planting. Trees in which tree growth and
crown form was significantly impacted by abnormal site conditions
or extreme disturbance were excluded from analysis. Such conflicts
included: mechanical conflict (i.e. wounds caused by lawnmower
or automobile), human conflict (i.e. severe pruning/lifting, tearing
off bark or branches), and infrastructure conflict (i.e. irregular shape
due to building proximity, topping due to overhead power lines).
Most of the trees sampled were single-stemmed, but in some
instances, multi-stemmed measurements were taken and converted to a single diameter by calculating the square root of the
sum of squared stem diameters.
Site description
Tree dimension and crown volume estimation
New Haven, CT (41◦ 18 36 N, 72◦ 55 25 W) is on the Long Island
Sound in northeastern United States. Typical of southern New
England, New Haven experiences a humid continental climate:
Summers are warm to moderately hot, with high levels of humidity, while winters are cold and humid, with frequent snowfalls. The
growing season is from March to September with a mean annual
temperature of 15.7 ◦ C, mean summer highs at 25.6 ◦ C, and mean
winter lows at −2 ◦ C. Monthly precipitation is steady throughout
the year with an annual average of 1336 mm per month.
Sampling design and measurements
The data comes from a completed census of community tree
plantings supported by the Urban Resources Initiative in New
Haven, CT from 1995 to 2007. The Urban Resources Initiative (URI)
For each species the relationship between dbh, age (from
planting), tree height, crown diameter, and crown volume were
evaluated. In order to select an appropriate model for the data,
an exploratory analysis was conducted with equations commonly
used in the allometric estimation of biometric parameters (Peper
et al., 2001a,b; Stoffberg et al., 2008, 2009, 2010; Semenzato et al.,
2011). Using Minitab 16 statistical software (Minitab Inc., 2012),
logarithmic and ordinary least squares (OLS) regressions models
were applied to predict dbh from age after transplantation and to
predict total height, crown diameter, and crown volume from dbh
(Peper et al., 2001a,b; Semenzato et al., 2011):
yi = a[log(xi + 1)]b
(1)
yi = a + b1 (xi )
(2)
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Fig. 1. New Haven, CT: city neighborhoods and sample points.
2
yi = a + b1 (xi ) + b2 xi
(7)
where yi is the observed response for the ith tree, i = 1, 2, . . ., n; n
the number of observations; xi the age or the dbh of the ith tree; a
and b the parameters to be estimated; ε is the residual error.
The quadratic model was selected for this data set in order to:
(1) avoid over-fitting the data with a model that is too complex (the
curvature introduced by the cubic terms was not justified based on
process knowledge and practical significance); (2) reduce standard
error while maintaining a consistent predictive model within and
among species (thereby facilitating the application of the allometric
models); and (3) avoid under-fitting the data with a model that is
too simplistic and misrepresenting the curvature inherent in the
data.
Because the conversion of unbiased logarithmic estimates back
to arithmetic values yields the median of the distribution rather
than the mean, the following bias correction was applied:
(8)
û = log(yi ) = a + b1 log(xi ) + b2 log xi2
(3)
yi = a + b1 (xi ) + b2 xi2 + b3 xi3
(4)
where yi is the observed response for the ith tree, i = 1, 2, . . ., n; n
the number of observations; xi the age or the dbh of the ith tree; a
and b the parameters to be estimated.
To ensure homoscedasticity of the data, the equations were logarithmically transformed, normalizing the variance over the entire
range of predicted values, as:
log(yi ) = log(a) + b1 log(log(xi + 1)) + ε
(5)
log(yi ) = a + b1 log(xi ) + ε
(6)
2
log(yi ) = a + b1 log(xi ) + b2 log xi
+ε
log(yi ) = a + b1 log(xi ) + b2 log xi
+ b3 log xi
2
3
+ε
(9)
Table 1
Subsample of the 10 most frequently planted genera from 1995 to 2007.
Genera/species
Sample size
(n)
% Healthy
treesa
Age range
(yrs)
Acer spp.
Cornus spp.
Gleditsia triacanthos
Malus spp.
Prunus cerasifera
Prunus serrulata
Pyrus calleryana
Quercus spp.
Syringa reticulata
Tilia spp.
56
77
33
45
53
186
97
59
49
43
82
75
97
78
77
84
91
86
80
91
4–16
5–16
4–16
4–16
4–16
4–16
4–16
4–16
4–14
4–14
DBH range
(cm)
3.4–34.5
5.2–27.5
4.0–21.5
5.8–22.4
6.4–23.2
7.3–41.3
7.3–38.8
6.0–29.8
4.5–19.7
8.8–23.4
a
Percentage of healthy trees was calculated by dividing the number of good trees by the total sample number. Tree condition was classified as good, fair, or poor based on
qualitative field observations.
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Fig. 2. Measurements taken at each sample point, and crown volume calculations.
Ŷ = 10(û+MSE/2)
(10)
where Ŷ is the estimated mean in arithmetic units; MSE is the mean
squared error; yi is the observed response for the ith tree, i = 1, 2, . . .,
n; n the number of observations; xi the age or the dbh of the ith tree;
a and b the parameters to be estimated. Table 3 lists the predicted
values (back transformed) for each species at 5 and 15 years after
transplantation (Baskerville, 1972; Peper et al., 2001a,b) (Fig. 3).
Results
All the allometric relationships across each of the growth dimensions were highly significant at an alpha level of 0.05 (˛ = 0.05).
For each of the parameters, shade trees (large trees with spreading
canopies) demonstrated stronger relationships than ornamental
trees (smaller trees with aesthetic features). The strongest fit for
all species, except for Tilia and Prunus cerasifera, was displayed by
the relationship between crown diameter and dbh. Eight of the
ten species had an R2 > 0.700. Quercus species had the highest R2
(0.917), while Syringa reticulata and Cornus species had the lowest
R2 (0.642 and 0.495 respectively) (Table 2). The model for crown
volume exhibited a good fit for each of the shade tree species
(R2 > 0.850), however the coefficients of determination for the ornamentals ranged from 0.377 to 0.730. Similarly, in the model relating
height to dbh, the ornamentals displayed the lowest R2 (between
0.325 and 0.550) while the equations for shade trees represented a
much better fit (R2 > 0.663). When compared to the dbh vs. height
relationships, dbh vs. age exhibited lower R2 values overall with
much greater variation across the 10 species (0.212 < R2 < 0.794).
Using these allometric relationships, dbh, tree height, crown
diameter, and crown volume were estimated at 5 and 15 years
after planting (Table 3). As expected, shade tree species had much
greater absolute dbh growth at the end of the first 15 years than
did ornamentals. Predictions for tree height also followed this same
pattern. Though Gleditsia triacanthos had the smallest dbh of the
shade tree species, its average crown volume was second only to
the Acer species. As P. calleryana and Tilia species are medium sized
trees and exhibit some aesthetic function, it is interesting to note
that dbh, crown diameter, and crown volume of P. serrulata may at
times exceed those of the two aforementioned species.
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Table 2
2
(a and
Listed are the regression coefficients b), adjusted coefficients of determination (R ), and the root mean squared error (RMSE). Regression equations were calculated
using: log(yi ) = a + b1 log(xi ) + b2 log xi2 . All equations were statistically significant at an alpha level of 0.05.
log(yi ) = a + b1 log(xi ) + b2 log xi2
Species
Shade
Ornamental
Parameter
a
b2
R2 (Adj)
RMSE
Quercus spp.
DBH vs. age
Height vs. DBH
Crown diameter vs. DBH
Crown volume vs. DBH
0.269
−0.149
−0.969
−1.946
1.165
1.082
2.157
3.756
−0.192
−0.156
−0.584
−0.480
0.725
0.727
0.917
0.852
0.1023
0.0872
0.0507
0.2143
Acer spp.
DBH vs. age
Height vs. DBH
Crown diameter vs. DBH
Crown volume vs. DBH
1.252
0.686
−0.520
−2.494
−1.148
−0.141
1.361
5.147
1.083
0.276
−0.232
−1.171
0.790
0.762
0.898
0.852
0.0926
0.0595
0.0544
0.1897
Gleditsia
triacanthos
DBH vs. age
Height vs. DBH
Crown diameter vs. DBH
Crown volume vs. DBH
−0.513
0.177
0.007
−1.285
2.923
0.674
0.825
2.743
−1.211
−0.022
−0.077
0.167
0.794
0.849
0.880
0.856
0.1001
0.0588
0.0551
0.2691
Pyrus calleryana
DBH vs. age
Height vs. DBH
Crown diameter vs. DBH
Crown volume vs. DBH
0.084
−0.031
−0.519
−2.601
1.754
0.972
1.130
4.819
−0.589
−0.155
−0.094
−0.927
0.562
0.694
0.872
0.860
0.1174
0.0715
0.0603
0.1833
Tilia spp.
DBH vs. age
Height vs. DBH
Crown diameter vs. DBH
Crown volume vs. DBH
0.837
0.183
−0.275
−2.441
0.069
0.268
0.600
4.193
0.272
0.224
0.161
−0.683
0.396
0.663
0.777
0.855
0.0937
0.0659
0.0619
0.1356
Prunus serrulata
DBH vs. age
Height vs. DBH
Crown diameter vs. DBH
Crown volume vs. DBH
0.918
0.267
−0.792
−1.731
−0.196
0.300
1.591
3.076
0.526
0.046
−0.298
−0.357
0.479
0.381
0.765
0.655
0.1268
0.0909
0.0861
0.2821
Malus spp.
DBH vs. age
Height vs. DBH
Crown diameter vs. DBH
Crown volume vs. DBH
0.894
−0.206
−0.924
0.056
−0.359
1.118
2.212
−0.262
0.493
−0.271
−0.701
1.343
0.481
0.550
0.745
0.377
0.1161
0.0858
0.0823
0.3407
Prunus
cerasifera
DBH vs. age
Height vs. DBH
Crown diameter vs. DBH
Crown Volume vs. DBH
−0.126
−0.246
−1.340
−8.396
2.411
1.155
2.803
15.01
−1.113
−0.279
−0.901
−5.484
0.268
0.383
0.701
0.730
0.1140
0.0887
0.0711
0.2568
Syringa
reticulata
DBH vs. Age
Height vs. DBH
Crown Diameter vs. DBH
Crown Volume vs. DBH
0.351
0.308
−0.273
−0.258
1.117
0.256
0.476
−1.105
−0.448
0.101
0.249
2.260
0.212
0.464
0.642
0.619
0.0976
0.0523
0.0781
0.2588
Cornus spp.
DBH vs. Age
Height vs. DBH
Crown Diameter vs. DBH
Crown Volume vs. DBH
1.211
−0.125
−0.196
−2.753
−1.208
0.930
0.815
5.551
0.953
−0.212
−0.059
−1.679
0.277
0.325
0.495
0.450
0.1391
0.1207
0.1145
0.4209
Discussion
Across all tree species, significant allometric relationships were
found, although with variable R values. Adjusted coefficients of
variation (Table 2) were comparable to those cited in other recent
b1
studies (Peper et al.,2001a,b; Quigley, 2004; Stoffberg et al., 2009;
Semenzato et al., 2011).
Allometric relations for size dimensions (height vs dbh, crown
diameter vs dbh, and crown volume vs dbh) demonstrate stronger
correlations than relationships that were a function of time (dbh vs
Table 3
growth in first 15 years after transplanting. Diameter at breast
Predicted sizes for 10 genera at 5 and 15 years after planting are shown sorted by greatest crown
volume
height, tree height, crown diameter, and crown volume can be predicted by Ŷ = 10
Species
Gleditsia triacanthos
Acer spp.
Quercus spp.
Pyrus calleryana
Prunus serrulata
Tilia spp.
Prunus cerasifera
Malus spp.
Cornus spp.
Syringa reticulata
DBH (cm)
(a+b1 log(xi )+b2 log
Height (m)
x2
i
+MSE/2)
.
Crown diameter (m)
Crown volume (m3 )
5 years
15 years
5 years
15 years
5 years
15 years
5 years
15 years
9.7
10.6
11.0
12.0
12.6
11.6
11.8
8.7
7.9
9.1
19.9
27.9
26.6
24.6
30.1
21.9
16.9
16.3
15.1
12.4
7.1
7.3
7.1
7.5
5.0
5.7
5.2
4.5
4.0
4.7
11.1
12.3
13.2
11.4
7.2
9.5
6.2
6.2
5.5
5.4
5.9
4.6
4.7
4.2
4.4
3.8
4.3
3.8
3.5
2.8
9.5
9.8
8.8
7.9
8.9
7.1
6.0
5.9
5.4
3.8
53
44
35
41
23
21
33
15
12
8
498
393
345
251
150
105
78
76
46
23
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DBH vs. Age
log10(DBH) = 1.252 - 1.148 log10(AGE) + 1.083 log10(AGE)**2
45
Regression
95% CI
95% PI
40
DBH (cm)
35
30
25
20
15
10
RMSE
R-Sq(adj)
5
5.0
7.5
10.0
12.5
0.0926004
79.0%
15.0
17.5
AGE (yrs)
Height vs. DBH
log10(Tree_Height) = 0.6861 - 0.1409 log10(DBH) + 0.2758 log10(DBH)**2
17.5
Regression
95% CI
95% PI
Height (m)
15.0
12.5
10.0
7.5
RMSE
R-Sq(adj)
5.0
10
15
20
25
0.0595101
76.2%
30
35
DBH (cm)
Crown Diameter vs. DBH
log10(Crown_Diameter) = - 0.5198 + 1.361 log10(DBH) - 0.2320 log10(DBH)**2
14
Regression
95% CI
95% PI
Crown Diameter (m)
12
10
8
6
4
RMSE
R-Sq(adj)
0.0543580
89.8%
2
10
15
20
25
30
35
DBH (cm)
age). This suggests that while physical dimensions remain highly
correlated, the pattern of growth for individuals of the same species
(over time) is not always constant (Quigley, 2004). The nature of
site condition (biophysical – impervious surface, shade, street type;
social – neighborhood, stewardship, demographics) may significantly affect the growth of young trees.
Research has found inhibited growth rates to be correlated
with many urban site factors: constrained growing space (Rhoades
and Stipes, 1999), low soil moisture (Whitlow and Bassuck, 1987),
excessive soil moisture (Berrang et al., 1985), increased evaporative demand (Kjelgren and Clark, 1992; Close et al., 1996), limited
nutrient availability (Ruark et al., 1983; Dyer and Mader, 1986), disease and pathogens (Mallett and Volney, 1999), pests (Rhoades and
Stipes, 1999), competition with understory vegetation (Close et al.,
1996), and competition with neighboring trees (Nowak et al., 1990;
Rhoades and Stipes, 1999). At times, urban environmental conditions such as higher temperature, greater CO2 concentrations, and
increased rates of nutrient deposition have been associated with
enhanced growth (Gregg et al., 2003). These inhibiting or enhancing environmental factors may be stunting some individuals while
releasing others and causing some of the variation in stem diameter growth that has been observed within this population of urban
trees (Table 2).
When using age to predict dbh, shade trees (0.396 < R2 < 0.794)
demonstrate stronger correlations than ornamental trees
(0.212 < R2 < 0.481). It may be that ornamental trees are more
susceptible to urban conditions, while shade trees demonstrate
greater tolerance of environmental stressors. Accordingly, studies
have found small diameter trees, as well as younger trees, to be
more greatly impacted by urban site attributes (Quigley, 2004;
Nowak et al., 2004). Of the shade trees only T. species have a lower
R2 value than select ornamentals species. It is possible that the
impacts of urban biophysical factors have a greater effect on T.
species than other common shade tree species.
While in most species, crown volume vs. stem size maintained
a strong relationship, Malus species and C. species displayed significantly weakened crown volume correlations (R2 = 0.377 and
R2 = 0.450 respectively). Given that crown volume is an expression of multiple crown dimensions (height, width, and density)
it may be that the volume value is more sensitive to defects in
crown development. It is likely that these small diameter species
are particularly sensitive to urban conditions, as demonstrated
by the low dbh vs. age correlation. As a result of this stunted
growth and reduced vigor, these trees are more susceptible to
pathogens and other inhibiting environmental factors that negatively effect stem growth and crown development (Semenzato
et al., 2011).
Crown Volume vs. DBH
log10(PAI_Volume) = - 2.494 + 5.147 log10(DBH) - 1.171 log10(DBH)**2
Conclusion
700
Regression
95% CI
95% PI
Crown Volume (m^3)
600
500
400
300
200
100
0
10
15
20
25
RMSE
R-Sq(adj)
0.189698
85.2%
30
35
DBH (cm)
Fig. 3. Actual measurements (points), predicted responses (solid line), 95%
confidence interval (CI), 95% prediction intervals (PI), adjusted coefficient of determination, and RMSE are shown for Acer spp. in New Haven, CT.
Regionally, this work will improve the management of young
trees, allowing urban forest managers to more accurately project
the growth of urban landscapes into the near future. Locally, with
specific allometric equations for New Haven, organizations such as
the Urban Resources Initiative will be better equipped to meet the
community forestry goals and objectives of their organization as
well as those of the city.
It should be noted that while the methods used to develop the
allometric relationships are transferable, the limited study of urban
allometry in the northeast United States makes direct comparisons
of the data difficult. The use of these models for trees growing in
different climate zones or trees outside of the intended age range is
tenuous. Furthermore, because this study was a census of a defined
population of trees, the species composition and sample number
was constrained. With a greater number of sample points and a
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greater range of ages, the observed variation in dbh vs. age may
have been reduced.
This study begins to establish species-specific allometric relations for the northeast region and should be considered a
foundation for further research. Specifically, future efforts should
be directed towards the inclusion of biophysical and social
attributes that impact the growth of trees. This data could then
be used to develop site-specific allometric models. In doing so, it
is theorized that the observed variation between age and size will
be reduced and that there will be greater predictive strength at a
species-specific and site-specific level.
Species
Model
Acer spp.
DBH vs. age
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Height vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown diameter vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown volume vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Cornus spp.
Gleditsia triacanthos
DBH vs. Age
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Height vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown diameter vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown volume vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
DBH vs. Age
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Height vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown diameter vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown volume vs. DBH
a
7
Acknowledgments
This work was initiated and supported by the Urban Resources
Initiative (URI) and the Hixon Center for Urban Ecology at the Yale
School of Forestry and Environmental Studies. Deep gratitude and
appreciation is also given to Elaine Hooper, Chris Ozyck and the
colleagues and classmates who helped to guide the entire process.
Appendix A
Summary of equations for 10 common species predicting DBH,
height, crown diameter and crown volume: estimated parameters
(a, bi ), adjusted coefficient of determination (R2 ) and root mean
squared error (RMSE). All models are significant with an alpha level
of 0.05 (˛ = 0.05).
b1
b2
1.564
0.377
1.252
1.146
0.906
0.852
−1.148
−0.774
1.247
0.291
0.686
−2.537
0.685
0.529
−0.141
8.122
0.739
−0.187
−0.520
−0.826
1.041
0.798
1.361
2.145
0.317
−0.082
−2.494
−11.15
3.011
2.293
5.147
27.31
1.546
0.396
1.211
−3.019
0.617
0.576
−1.208
13.35
1.088
0.064
−0.125
0.277
0.579
0.523
0.930
−0.368
0.089
−0.144
−0.196
1.121
0.772
0.702
0.815
−3.435
0.314
−1.224
−2.753
−1.778
2.579
2.299
5.551
2.400
1.469
0.289
−0.513
−1.925
0.888
0.863
2.923
7.940
1.243
0.197
0.177
0.064
0.708
0.631
0.674
1.046
1.105
0.078
0.007
−1.39
0.757
0.673
0.825
5.42
R2 (Adj)
RMSE
0.156
0.736
0.755
0.790
0.785
0.1045
0.0999
0.0926
0.0935
1.912
0.755
0.760
0.762
0.768
0.0609
0.0598
0.0595
0.0587
0.182
0.873
0.897
0.898
0.896
0.0538
0.0545
0.0544
0.0549
5.121
0.859
0.848
0.852
0.852
0.1876
0.1919
0.1897
0.1897
5.952
0.263
0.263
0.277
0.288
0.1414
0.1404
0.1391
0.1381
−0.451
0.343
0.330
0.325
0.317
0.1120
0.1203
0.1207
0.1215
−1.478
0.506
0.502
0.495
0.496
0.1140
0.1138
0.1145
0.1144
−1.095
0.462
0.441
0.450
0.441
0.4196
0.4242
0.4209
0.4244
2.088
0.799
0.786
0.794
0.787
0.1013
0.1027
0.1001
0.1025
0.136
0.856
0.854
0.849
0.843
0.0583
0.0578
0.0588
0.0598
1.681
0.886
0.883
0.880
0.885
0.0544
0.0543
0.0551
0.0539
b3
1.083
0.658
0.276
−6.666
0.232
−0.891
−1.171
−19.78
0.953
−15.35
−0.212
1.136
−0.059
4.355
−1.679
1.600
−1.211
−6.910
−0.022
−0.418
−0.077
−4.963
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8
Species
Model
a
b
y = a [log(x + 1)]
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Malus spp.
Prunus cerasifera
Prunus serrulata
Pyrus calleryana
DBH vs. Age
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Height vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown diameter vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown volume vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
DBH vs. Age
yva [log(x + 1)]b
yva + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Height vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown diameter vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown volume vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
DBH vs. Age
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Height vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown diameter vs. DBH
yva [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown volume vs. DBH
yva [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
DBH vs. Age
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Height vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
b1
b2
0.263
−1.440
−1.285
−4.525
3.447
3.074
2.743
13.47
1.786
0.530
0.894
−0.324
0.538
0.515
−0.359
4.108
1.063
0.039
−0.206
−0.389
0.661
0.594
1.118
1.780
0.767
−0.288
−0.924
−2.167
0.964
0.858
2.212
6.693
0.327
−1.188
0.056
−11.22
2.609
2.343
−0.262
35.11
2.086
0.703
−0.126
−2.138
0.488
0.457
2.411
9.457
1.055
0.091
−0.246
1.921
0.658
0.536
1.155
−4.870
0.731
−0.251
−1.340
1.654
0.994
0.806
2.803
−5.515
0.122
−1.862
−8.396
14.03
3.638
2.942
15.01
−47.34
1.845
0.541
0.918
1.532
0.736
0.713
−0.196
−2.417
1.168
0.204
0.267
−0.153
0.524
0.410
0.300
1.400
0.612
−0.381
−0.792
0.338
1.135
0.884
1.591
−1.371
0.219
−1.237
−1.731
−4.205
2.865
2.228
3.076
9.570
1.788
0.533
0.084
3.421
0.758
0.699
1.754
−10.09
1.136
0.177
−0.031
−0.723
0.758
0.609
0.972
2.738
R2 (Adj)
RMSE
3.961
0.865
0.863
0.856
0.851
0.2670
0.2624
0.2691
0.2739
2.023
0.486
0.483
0.481
0.472
0.1169
0.1159
0.1161
0.1171
0.274
0.570
0.551
0.550
0.540
0.0848
0.0856
0.0858
0.0868
1.858
0.746
0.714
0.745
0.758
0.0831
0.0872
0.0823
0.0802
0.405
0.392
0.377
0.361
0.3375
0.3365
0.3407
0.3449
0.270
0.246
0.2680
0.263
0.1153
0.1161
0.1140
0.1147
−1.649
0.406
0.391
0.383
0.373
0.0879
0.0881
0.0887
0.0894
−2.278
0.698
0.679
0.701
0.699
0.0722
0.0737
0.0711
0.0714
0.690
0.657
0.730
0.743
0.2786
0.2891
0.2568
0.2502
0.472
0.476
0.479
0.476
0.1280
0.1272
0.1268
0.1271
0.385
0.384
0.381
0.378
0.0909
0.0907
0.0909
0.0912
−0.718
0.767
0.763
0.765
0.764
0.0859
0.0864
0.0861
0.0862
1.578
0.662
0.656
0.655
0.653
0.2808
0.2814
0.2821
0.2828
−5.044
0.614
0.556
0.562
0.576
0.1085
0.1182
0.1174
0.1155
0.437
0.683
0.696
0.694
0.691
0.0708
0.0713
0.0715
0.0718
b3
0.167
−11.30
0.493
−4.798
−0.271
−1.026
−0.701
−5.810
1.343
−35.21
−1.113
−9.134
−0.279
5.210
−0.901
6.690
−5.484
51.42
0.526
3.134
0.046
−0.900
−0.298
2.249
−0.357
−5.950
−0.589
12.99
−0.155
−1.708
12.45
2.981
−17.06
−0.998
0.2667
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Species
Model
a
b1
b2
9
R2 (Adj)
RMSE
−0.265
0.874
0.874
0.872
0.871
0.0603
0.0600
0.0603
0.0606
−2.964
0.829
0.859
0.860
0.859
0.1823
0.1839
0.1833
0.1838
−1.450
0.734
0.728
0.725
0.721
0.1015
0.1016
0.1023
0.1029
−0.480
0.735
0.730
0.727
0.722
0.0865
0.0866
0.0872
0.0879
0.897
0.915
0.899
0.917
0.917
0.0517
0.0557
0.0507
0.0505
6.229
0.858
0.854
0.852
0.858
0.2121
0.2129
0.2143
0.2103
−4.669
0.239
0.218
0.212
0.217
0.0970
0.0973
0.0976
0.0974
0.199
0.482
0.475
0.464
0.452
0.0519
0.0517
0.0523
0.0528
−4.236
0.649
0.648
0.642
0.650
0.0782
0.0774
0.0781
0.0772
0.618
0.620
0.619
0.641
0.2626
0.2586
0.2588
0.2514
2.518
0.417
0.408
0.396
0.384
0.0932
0.0928
0.0937
0.0946
−1.147
0.675
0.671
0.663
0.655
0.0655
0.0652
0.0659
0.0667
7.586
0.785
0.782
0.777
0.785
0.0615
0.0612
0.0619
0.0607
8.530
0.864
0.859
0.855
0.851
0.1333
0.1337
0.1356
0.1373
b3
Crown diameter vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown volume vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Quercus spp.
Syringa reticulata
Tilia spp.
DBH vs. Age
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Height vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown diameter vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown volume vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
DBH vs. Age
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Height vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown diameter vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown volume vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
DBH vs. Age
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Height vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown diameter vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
Crown volume vs. DBH
y = a [log(x + 1)]b
y = a + bx
y = a + b1 x + b2 x2
y = a + b1 x + b2 x2 + b3 x3
0.609
−0.391
−0.519
−0.089
1.158
0.908
1.130
0.016
0.190
−1.373
−2.601
1.837
3.376
2.662
4.819
−6.980
1.626
0.411
0.269
1.231
0.867
0.827
1.165
−2.263
0.995
0.039
−0.149
0.480
0.897
0.733
1.082
−0.685
0.723
−2.660
−0.969
−2.145
1.053
0.855
2.157
5.460
0.219
−1.388
−1.946
−9.734
3.269
2.704
3.756
25.95
2.045
0.692
0.351
3.272
0.341
0.319
1.117
−9.414
1.255
0.213
0.308
0.141
0.504
0.453
0.256
0.796
0.623
−0.505
−0.273
3.227
1.067
0.960
0.476
−11.03
0.124
−2.25
−0.258
17.12
3.448
3.168
−1.105
−58.79
2.003
0.642
0.837
−0.635
0.552
0.536
0.069
5.470
0.844
−0.102
0.183
1.817
0.965
0.776
0.268
−4.120
0.569
−0.479
−0.275
−11.08
1.199
0.964
0.600
29.65
0.163
−1.556
−2.441
−15.14
3.300
2.629
4.193
37.81
−0.094
0.854
−0.927
9.390
−0.192
3.731
−0.156
1.456
−0.584
−3.598
−0.480
−21.06
−0.448
11.85
0.101
−0.471
0.249
12.45
2.260
64.96
0.272
−6.190
0.224
4.130
0.161
−25.66
−0.683
−30.11
−22.36
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References
Akbari, H., 2002. Shade trees reduce building energy use and CO2 emissions from
power plants. Environmental Pollution 116, S119–S126.
Akbari, H., Pomerantz, M., Taha, H., 2001. Cool surfaces and shade trees to reduce
energy use and improve air quality in urban areas. Solar energy 70 (3), 295–310.
Ashton, P.M., 1990. Method for the evaluation of advanced regeneration in forest
types of south and southeast Asia. Forest Ecology and Management 36 (2–4),
163–175.
Baskerville, G.L., 1972. Use of logarithmic regression in the estimation of plant
biomass. Canadian Journal of Forest Research 2, 49–53.
Beckett, K., Freer-Smith, P., Taylor, G., 1998. Urban woodlands: their role in reducing
the effects of particulate pollution. Environmental pollution 99 (3), 347–360.
Berlyn, G.P., 1962. Some size and shape relationships between tree stems and
crowns. Iowa State Journal of Science 37 (1), 7–15.
Berrang, P., Karnosky, D.F., Stanton, B.J., 1985. Environmental factors affecting tree
health in New York City. Journal of Arboriculture 11, 185–189.
Breda, N.J., 2003. Ground-based measurements of leaf area index: a review of methods, instruments and current controversies. Journal of Experimental Botany 54
(392), 2403.
Curtis, R.O., 1967. Height-diameter and height-diameter-age equations for secondgrowth Douglas-fir. Forest Science 13 (4), 365–375.
Close, R., Nguyen, P., Kielbaso, J., 1996. Urban vs. natural sugar maple growth: I.
Stress symptoms and phenology in relation to site characteristics. Journal of
Arboriculture 22, 144–150.
Donovan, G.H., Butry, D.T., 2009. The value of shade: estimating the effect of
urban trees on summertime electricity use. Energy and Buildings 41 (6),
662–668.
Donovan, R.G., Stewart, H.E., Owen, S.M., MacKenzie, A.R., Hewitt, C.N., 2005. Development and application of an urban tree air quality score for photochemical
pollution episodes using the Birmingham, United Kingdom, area as a case study.
Environmental Science & Technology 39 (17), 6730–6738.
Dwyer, M.C., Miller, R.W., 1999. Using GIS to assess urban tree canopy benefits and
surrounding greenspace distributions. Journal of Arboriculture 25, 102–107.
Dyer, S.M., Mader, D.L., 1986. Declined urban sugar maples: growth patterns, nutritional status and site factors. Journal of Arboriculture 12, 6–13.
Escobedo, F.J., Nowak, D.J., 2009. Spatial heterogeneity and air pollution removal by
an urban forest. Landscape and Urban Planning 90 (3–4), 102–110.
Fleming, L.E., 1988. Growth estimates of street trees in Central New Jersey. Rutgers
University, New Jersey.
Frelich, L.E., 1992. Predicting dimensional relationships for Twin Cities shade trees.
University of Minnesota, Department of Forest Resources, St. Paul, MN.
Furnival, G.M., 1961. An index for comparing equations used in constructing volume
tables. Forest Science 7 (4), 337–341.
Gregg, J.W., Jones, C.G., Dawson, T.E., 2003. Urbanization air pollution and tree
growth in the vicinity of New York City. Nature 424, 183–187.
Kjelgren, R., Clark, J.R., 1992. Microclimates and tree growth in three urban spaces.
Journal of Environmental Horticulture 10, 139–145.
Larsen, F.K., Kristoffersen, P., 2002. Tilia’s physical dimensions over time. Journal of
Arboriculture 28 (5), 209–214.
Maco, S.E., McPherson, E.G., 2002. Assessing canopy cover over streets and sidewalks
in street tree populations. Journal of Arboriculture 28 (6), 270.
Mallett, K.J., Volney, W.J.A., 1999. The effect of Armillaria root disease on lodgpole
pine tree growth. Canadian Jouranl of Forest Research 29, 252–259.
McHale, M., Burke, I., Lefsky, M., Peper, P., McPherson, E., 2009. Urban forest biomass
estimates: is it important to use allometric relationships developed specifically
for urban trees? Urban Ecosystems 12 (1), 95–113.
McPherson, E.G., 1998. Atmospheric carbon dioxide reduction by Sacramento’s
urban forest. Journal of Arboriculture 24, 215–223.
McPherson, E.G., Scott, K.I., Simpson, J.R., Peper, P.J., Xiao, Q., 2000. Tree guidelines
for coastal southern California communities. Local Government Commission,
California.
McPherson, E.G., 2010. Selecting reference cities for i-Tree Streets. Arboriculture &
Urban Forestry 36 (5), 230–240.
McPherson, E.G., Simpson, J.R., 2000. Carbon dioxide reduction through urban
forestry: guidelines for professional and volunteer tree planters, vol. 171. US
Department of Agriculture, Forest Service, Pacific Southwest Research Station.
Nowak, D.J., 1994. Understanding the structure. Journal of Forestry 92 (10), 42–46.
Nowak, D.J., 1996. Notes: estimating leaf area and leaf biomass of open-grown deciduous urban trees. Forest Science 42 (4), 504–507.
Nowak, D.J., 2006. Institutionalizing urban forestry as a “biotechnology” to improve
environmental quality. Urban Forestry & Urban Greening 5 (2), 93–100.
Nowak, D.J., Kuroda, M., Crane, D.E., 2004. Tree mortality rates and tree population
projections in Baltimore, Maryland, USA. Urban Forestry & Urban Greening 2 (3),
139–147.
Nowak, D.J., Dwyer, J.F., 2007. Understanding the benefits and costs of urban forest
ecosystems. Urban and community forestry in the Northeast, 25–46.
Nowak, D.J., Crane, D.E, Stevens, J.C, Ibarra, M., 2002. Brooklyn’s urban forest. General
Technical Report GE-290. USDA Forest Service, Northeastern Research Station,
Syracuse, NY.
Nowak, D.J., McBride, J.R., Beatty, R.A., 1990. Newly planted street tree growth and
mortality. Journal of Arboriculture 16 (5), 124–129.
Nowak, D.J., Noble, M.H., Sisinni, S.M., Dwyer, J.F., 2001. People and trees: assessing
the US urban forest resource. Journal of Forestry 99 (3), 37–42.
Peper, P.J., McPherson, E.G., Mori, S.M., 2001a. Predictive equations for dimensions
and leaf area of coastal southern California street trees. Journal of Arboriculture
27, 169–181.
Peper, P.J., McPherson, E.G., Mori, S.M., 2001b. Equations for predicting diameter,
height, crown width, and leaf area of San Joaquin Valley street trees. Journal of
Arboriculture 27 (6), 306–317.
Peper, P., McPherson, E., 1998. Comparison of five methods for estimating leaf
area index of open-grown deciduous trees. Journal of Arboriculture 24,
98–111.
Quigley, M.F., 2004. Street trees and rural conspecifics: will long-lived trees reach
full size in urban conditions? Urban Ecosystems 7 (1), 29–39.
Rosenfeld, A.H., Akbari, H., Romm, J.J., Pomerantz, M., 1998. Cool communities:
strategies for heat island mitigation and smog reduction. Energy and Buildings
28 (1), 51–62.
Rhoades, R.W., Stipes, R.J., 1999. Growth of trees on the Virginia Tech campus in
response to various factors. Journal of Arboriculture 25, 211–215.
Ruark, G.A., Mader, D.L., Veneman, P.L.M., Tattar, T.A., 1983. Soil factors related to
urban sugar maple decline. Journal of Arboriculture 9, 1–6.
Sanders, R.A., 1986. Urban vegetation impacts on the hydrology of Dayton,Ohio.
Urban Ecology 9 (3–4), 361–376.
Scott, K.I., McPherson, E., Simpson, J., 1998. Air pollutant uptake by Sacramento’s
urban forest. Journal of Arboriculture 24, 224–234.
Semenzato, P., Cattaneo, D., Dainese, M., 2011. Growth prediction for five tree
species in an Italian urban forest. Urban Forestry & Urban Greening 10 (3),
169–176.
Simpson, J.R., 1998. Urban forest impacts on regional cooling and heating
energy use: Sacramento County case study. Journal of Arboriculture 24,
201–214.
Stage, A.R., 1973. Prognosis model for stand development. Report no. 137. Intermountain Forest & Range Experiment Station, Forest Service, US Department of
Agriculture.
Stoffberg, G., Van Rooyen, M., Van der Linde, M., Groeneveld, H., 2010. Carbon sequestration estimates of indigenous street trees in the City of Tshwane, South Africa.
Urban Forestry & Urban Greening 9 (1), 9–14.
Stoffberg, G.H., Van Rooyen, M.W., Van der Linde, M.J., Groeneveld, H.T., 2009. Modelling dimensional growth of three street tree species in the urban forest of the
City of Tshwane, South Africa. Southern Forests 71 (4), 273–277.
Stoffberg, G., Van Rooyen, M., Van der Linde, M., Groeneveld, H., 2008. Predicting the
growth in tree height and crown size of three street tree species in the City of
Tshwane, South Africa. Urban Forestry & Urban Greening 7 (4), 259–264.
Whitlow, T., Bassuck, N., 1987. Environmental stress in street trees. Acta Horticulturae (ISHS) 195, 49–58.
Xiao, Q., McPherson, E.G., Simpson, J.R., Ustin, S.L., 1998. Rainfall interception by
Sacramento’s urban forest. Journal of Arboriculture 24, 235–244.
Xiao, Q., McPherson, E.G., Ustin, S.L., Grismer, M.E., Simpson, J.R., 2000a. A new
approach to modeling tree rainfall interception. Journal of Geophysical Research
105 (D23), 29–173.
Xiao, Q., McPherson, E.G., Ustin, S.L., Grismer, M.E., Simpson, J.R., 2000b. Winter
rainfall interception by two mature open-grown trees in Davis,California. Hydrological Processes 14 (4), 763–784.
Yang, J., McBride, J., Zhou, J., Sun, Z., 2005. The urban forest in Beijing and its role in
air pollution reduction. Urban Forestry & Urban Greening 3 (2), 65–78.
Please cite this article in press as: Troxel, B., et al., Relationships between bole and crown size for young urban trees in the northeastern USA.
Urban Forestry & Urban Greening (2013), http://dx.doi.org/10.1016/j.ufug.2013.02.006