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8/10/2019 Relationships between bole and crown size for young urban trees in northeastern USA(4).pdf
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Urban Forestry & Urban Greening 12 (2013) 144–153
Contents lists available at SciVerse ScienceDirect
Urban Forestry & Urban Greening
journa l 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-Dunninga,b
a Yale School of Forestry & Environmental Studies, 195 Prospect Street, New Haven, CT 06511, United Statesb Urban Resources Initiative, Hixon Center for Urban Ecology, 301Prospect Street, First Floor, NewHaven,CT 06511, United States
a r t i c l e i n f o
Keywords:
AllometryGrowth 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,
andecological 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 diam-
eter 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 orna-
mental 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;
Akbariet al., 2001; Akbari, 2002; Donovan andButry, 2009); reduce
energy use and atmospheric carbon dioxide (McPherson, 1998;
McPherson and Simpson, 2000); improve air, soil, and water qual-
ity (Beckett et al., 1998; Nowak et al., 2002; Donovan et al., 2005;
Yang et al., 2005; Nowak, 2006; Escobedo and Nowak, 2009); miti-
gate 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 asso-
ciated benefits of trees and their leaf-atmosphere interactions,
suggesting that each benefit may be a function of tree canopy and
∗ Corresponding authorat: Yale Schoolof Forestry & Environmental Studies, 195
Prospect Street, NewHaven, CT 06511, United States. Tel.: +1 2036416570.
E-mailaddresses: [email protected], [email protected](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 growthand photosynthetic area (Berlyn, 1962;
Ashton, 1990). This relationship between bole size and other phys-
ical 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 rela-
tionships between tree dbh, tree height, and crown dimensions to
develop quantitative guidelines for spacing and thinning of man-
aged forests and timber plantations (Furnival, 1961; Curtis, 1967;
Stage, 1973).
The knowledge of size relationships and allometric equa-
tions 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 appropri-
ate policy, analyze management scenarios, plan for spacing and
infrastructure constraints, and determine best management prac-
tices 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/$ – seefront matter© 2013 Elsevier GmbH. All rights reserved.
http://dx.doi.org/10.1016/j.ufug.2013.02.006
8/10/2019 Relationships between bole and crown size for young urban trees in northeastern USA(4).pdf
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B. Troxel et al. / Urban Forestry & Urban Greening 12 (2013) 144–153 147
Fig. 2. Measurements taken at each sample point, and crown volume calculations.
Y = 10(u+MSE/2) (10)
where Y is theestimated mean in arithmetic units;MSE isthe mean
squared error; yi is theobservedresponsefor the ith tree, i =1,2, . . .,n; n the number of observations; xi theageorthedbhofthe ith tree;
a and b the parameters to be estimated. Table 3 lists the predictedvalues (back transformed) for each species at 5 and 15 years after
transplantation (Baskerville, 1972; Peper et al., 2001a,b) (Fig. 3).
Results
Allthe allometricrelationshipsacrosseach of the growth dimen-
sions 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 coefficientsof determination for the orna-
mentals rangedfrom0.377to 0.730.Similarly,in themodel relating
height to dbh, the ornamentals displayed the lowest R2 (between
0.325 and 0.550) while the equations for shade trees represented amuch 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 heightalso 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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148 B. Troxel et al. / Urban Forestry & Urban Greening 12 (2013) 144–153
Table 2
Listed are the regression coefficients (a and b), adjusted coefficients of determination (R2 ), and the root mean squared error (RMSE). Regression equations were calculated
using: log( yi) = a+ b1 log( xi)+ b2 log x2
i
. Allequations were statisticallysignificant at an alpha level of 0.05.
Species log( yi) = a+ b1 log( xi)+ b2 log x2
i
Parameter a b1 b2 R2 (Adj) RMSE
Shade Quercus spp. DBH vs. age 0.269 1.165 −0.192 0.725 0.1023
Heightvs. DBH −0.149 1.082 −0.156 0.727 0.0872
Crown diameter vs.DBH −0.969 2.157 −0.584 0.917 0.0507
Crown volume vs.DBH −1.946 3.756 −0.480 0.852 0.2143
Acer spp. DBH vs. age 1.252 −1.148 1.083 0.790 0.0926
Height vs. DBH 0.686 −0.141 0.276 0.762 0.0595
Crown diameter vs.DBH −0.520 1.361 −0.232 0.898 0.0544
Crown volume vs.DBH −2.494 5.147 −1.171 0.852 0.1897
Gleditsia
triacanthos
DBH vs. age −0.513 2.923 −1.211 0.794 0.1001
Height vs. DBH 0.177 0.674 −0.022 0.849 0.0588
Crown diameter vs. DBH 0.007 0.825 −0.077 0.880 0.0551
Crown volume vs.DBH −1.285 2.743 0.167 0.856 0.2691
Pyrus calleryana DBH vs. age 0.084 1.754 −0.589 0.562 0.1174
Heightvs. DBH −0.031 0.972 −0.155 0.694 0.0715
Crown diameter vs.DBH −0.519 1.130 −0.094 0.872 0.0603
Crown volume vs.DBH −2.601 4.819 −0.927 0.860 0.1833
Tilia spp. DBH vs. age 0.837 0.069 0.272 0.396 0.0937
Height vs. DBH 0.183 0.268 0.224 0.663 0.0659
Crown diameter vs.DBH −0.275 0.600 0.161 0.777 0.0619Crown volume vs.DBH −2.441 4.193 −0.683 0.855 0.1356
Ornamental Prunus serrulata DBH vs. age 0.918 −0.196 0.526 0.479 0.1268
Height vs. DBH 0.267 0.300 0.046 0.381 0.0909
Crown diameter vs.DBH −0.792 1.591 −0.298 0.765 0.0861
Crown volume vs.DBH −1.731 3.076 −0.357 0.655 0.2821
Malus spp. DBH vs. age 0.894 −0.359 0.493 0.481 0.1161
Heightvs. DBH −0.206 1.118 −0.271 0.550 0.0858
Crown diameter vs.DBH −0.924 2.212 −0.701 0.745 0.0823
Crown volume vs. DBH 0.056 −0.262 1.343 0.377 0.3407
Prunus
cerasifera
DBH vs. age −0.126 2.411 −1.113 0.268 0.1140
Heightvs. DBH −0.246 1.155 −0.279 0.383 0.0887
Crown diameter vs.DBH −1.340 2.803 −0.901 0.701 0.0711
Crown Volume vs.DBH −8.396 15.01 −5.484 0.730 0.2568
Syringa
reticulata
DBH vs. Age 0.351 1.117 −0.448 0.212 0.0976
Height vs. DBH 0.308 0.256 0.101 0.464 0.0523Crown Diameter vs.DBH −0.273 0.476 0.249 0.642 0.0781
Crown Volume vs.DBH −0.258 −1.105 2.260 0.619 0.2588
Cornus spp. DBH vs. Age 1.211 −1.208 0.953 0.277 0.1391
Heightvs. DBH −0.125 0.930 −0.212 0.325 0.1207
Crown Diameter vs.DBH −0.196 0.815 −0.059 0.495 0.1145
Crown Volume vs.DBH −2.753 5.551 −1.679 0.450 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
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 3Predicted sizes for 10 genera at 5 and 15 years after planting are shown sorted by greatest crown volume growth in first 15 years after transplanting. Diameter at breast
height, tree height, crown diameter,and crown volumecan be predicted by Y = 10(a+b1 log( xi )+b2 log
x2i
+MSE/2)
.
Species DBH (cm) Height (m) Crown diameter (m) Crown volume(m3)
5 years 15 years 5 years 15 years 5 years 15 years 5 years 15 years
Gleditsia triacanthos 9.7 19.9 7.1 11.1 5.9 9.5 53 498
Acer spp. 10.6 27.9 7.3 12.3 4.6 9.8 44 393
Quercus spp. 11.0 26.6 7.1 13.2 4.7 8.8 35 345
Pyrus calleryana 12.0 24.6 7.5 11.4 4.2 7.9 41 251
Prunus serrulata 12.6 30.1 5.0 7.2 4.4 8.9 23 150
Tilia spp. 11.6 21.9 5.7 9.5 3.8 7.1 21 105
Prunus cerasifera 11.8 16.9 5.2 6.2 4.3 6.0 33 78
Malus spp. 8.7 16.3 4.5 6.2 3.8 5.9 15 76
Cornus spp. 7.9 15.1 4.0 5.5 3.5 5.4 12 46
Syringa reticulata 9.1 12.4 4.7 5.4 2.8 3.8 8 23
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B. Troxel et al. / Urban Forestry & Urban Greening 12 (2013) 144–153 149
17.515.012.510.07.55.0
45
40
35
30
25
20
15
10
5
AGE (yrs)
D B H
( c m )
RMSE 0.0926004
R-Sq(adj) 79.0%
Regression
95% CI
95% PI
DBH vs. Agelog10(DBH) = 1.252 - 1.148 log10(AGE) + 1.083 log10(AGE)**2
353025201510
17.5
15.0
12.5
10.0
7.5
5.0
DBH (cm)
H e i g h t (
m )
RMSE 0.0595101
R-Sq(adj) 76.2%
Regression
95% CI
95% PI
Height vs. DBH
log10(Tree_Height) = 0.6861 - 0.1409 log10(DBH) + 0.2758 log10(DBH)**2
353025201510
14
12
10
8
6
4
2
DBH (cm)
C r o w n D i a m e t e r ( m )
RMSE 0.0543580
R-Sq(adj) 89.8%
Regression
95% CI
95% PI
CrownDiameter vs. DBHlog10(Crown_Diameter) = - 0.5198 + 1.361 log10(DBH) - 0.2320 log10(DBH)**2
353025201510
700
600
500
400
300
200
100
0
DBH (cm)
C r o w n V o l u m e ( m ^ 3 )
RMSE 0.189698
R-Sq(adj) 85.2%
Regression
95%
CI
95% PI
Crown Volume vs.
DBHlog10(PAI_Volume) = - 2.494 + 5.147 log10(DBH) - 1.171 log10(DBH)**2
Fig. 3. Actual measurements (points), predicted responses (solid line), 95%
confidence interval (CI), 95% prediction intervals (PI), adjusted coefficient of deter-
mination, and RMSE areshownfor Acer spp. in New Haven,CT.
age). This suggests that while physical dimensions remain highly
correlated, thepatternof growthfor individuals of thesamespecies
(over time) is not always constant (Quigley, 2004). The nature of
site condition (biophysical – impervioussurface, shade, street type;
social – neighborhood, stewardship, demographics) may signifi-
cantly 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 evapora-
tive demand (Kjelgren and Clark, 1992; Close et al., 1996), limited
nutrient availability (Ruark et al., 1983;Dyer andMader, 1986), dis-
ease andpathogens (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 condi-
tions 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 enhanc-
ing environmental factors may be stunting some individuals while
releasing others and causing some of the variation in stem diame-
ter 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 sig-
nificantly weakened crown volume correlations (R2 =0.377 and
R2 = 0.450 respectively). Given that crown volume is an expres-sion 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 neg-
atively effect stem growth and crown development (Semenzato
et al., 2011).
Conclusion
Regionally, this work will improve the management of youngtrees, 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
allometricrelationships 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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150 B. Troxel et al. / Urban Forestry & Urban Greening 12 (2013) 144–153
greater range of ages, the observed variation in dbh vs. age may
have been reduced.
This study begins to establish species-specific allometric rela-
tions 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.
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). Allmodels aresignificant with an alpha level
of 0.05(˛ =0.05).
Species Model a b1 b2 b3 R2 (Adj) RMSE
Acer spp. DBHvs. age
y = a [log( x +1)]b 1.564 0.906 0.736 0.1045
y = a + bx 0.377 0.852 0.755 0.0999
y = a + b1 x + b2 x2 1.252 −1.148 1.083 0.790 0.0926
y = a + b1 x + b2 x2 + b3 x3 1.146 −0.774 0.658 0.156 0.785 0.0935
Heightvs. DBH
y = a [log( x +1)]b 1.247 0.685 0.755 0.0609
y = a + bx 0.291 0.529 0.760 0.0598
y = a + b1 x + b2 x2 0.686 −0.141 0.276 0.762 0.0595
y = a + b1 x + b2 x2 + b3 x3−2.537 8.122 −6.666 1.912 0.768 0.0587
Crown diameter vs. DBH
y = a [log( x +1)]b 0.739 1.041 0.873 0.0538
y = a + bx −0.187 0.798 0.897 0.0545
y = a + b1 x + b2 x2−0.520 1.361 0.232 0.898 0.0544
y = a + b1 x + b2 x2 + b3 x3−0.826 2.145 −0.891 0.182 0.896 0.0549
Crown volumevs. DBH
y = a [log( x +1)]b 0.317 3.011 0.859 0.1876
y = a + bx −0.082 2.293 0.848 0.1919
y = a + b1 x + b2 x2−2.494 5.147 −1.171 0.852 0.1897
y = a + b1 x + b2 x2 + b3 x3−11.15 27.31 −19.78 5.121 0.852 0.1897
Cornus spp. DBH vs. Age
y = a [log( x +1)]b 1.546 0.617 0.263 0.1414
y = a + bx 0.396 0.576 0.263 0.1404
y = a + b1 x + b2 x2 1.211 −1.208 0.953 0.277 0.1391 y = a + b1 x + b2 x2 + b3 x3
−3.019 13.35 −15.35 5.952 0.288 0.1381
Heightvs. DBH
y = a [log( x +1)]b 1.088 0.579 0.343 0.1120
y = a + bx 0.064 0.523 0.330 0.1203
y = a + b1 x + b2 x2−0.125 0.930 −0.212 0.325 0.1207
y = a + b1 x + b2 x2 + b3 x3 0.277 −0.368 1.136 −0.451 0.317 0.1215
Crown diameter vs. DBH
y = a [log( x +1)]b 0.089 0.772 0.506 0.1140
y = a + bx −0.144 0.702 0.502 0.1138
y = a + b1 x + b2 x2−0.196 0.815 −0.059 0.495 0.1145
y = a + b1 x + b2 x2 + b3 x3 1.121 −3.435 4.355 −1.478 0.496 0.1144
Crown volumevs. DBH
y = a [log( x +1)]b 0.314 2.579 0.462 0.4196
y = a + bx −1.224 2.299 0.441 0.4242
y = a + b1 x + b2 x2−2.753 5.551 −1.679 0.450 0.4209
y = a + b1 x + b2 x2 + b3 x3−1.778 2.400 1.600 −1.095 0.441 0.4244
Gleditsia triacanthos DBHvs. Age
y = a [log( x +1)]b 1.469 0.888 0.799 0.1013
y = a + bx 0.289 0.863 0.786 0.1027
y = a + b1 x + b2 x2−0.513 2.923 −1.211 0.794 0.1001
y = a + b1 x + b2 x2 + b3 x3−1.925 7.940 −6.910 2.088 0.787 0.1025
Height vs.DBH
y = a [log( x +1)]b 1.243 0.708 0.856 0.0583
y = a + bx 0.197 0.631 0.854 0.0578
y = a + b1 x + b2 x2 0.177 0.674 −0.022 0.849 0.0588
y = a + b1 x + b2 x2 + b3 x3 0.064 1.046 −0.418 0.136 0.843 0.0598
Crown diameter vs. DBH
y = a [log( x +1)]b 1.105 0.757 0.886 0.0544
y = a + bx 0.078 0.673 0.883 0.0543
y = a + b1 x + b2 x2 0.007 0.825 −0.077 0.880 0.0551
y = a + b1 x + b2 x2 + b3 x3−1.39 5.42 −4.963 1.681 0.885 0.0539
Crown volumevs. DBH
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B. Troxel et al. / Urban Forestry & Urban Greening 12 (2013) 144–153 151
Species Model a b1 b2 b3 R2 (Adj) RMSE
y = a [log( x +1)]b 0.263 3.447 0.865 0.2670
y = a + bx −1.440 3.074 0.863 0.2624
y = a + b1 x + b2 x2−1.285 2.743 0.167 0.856 0.2691
y = a + b1 x + b2 x2 + b3 x3−4.525 13.47 −11.30 3.961 0.851 0.2739
Malus spp. DBHvs. Age
y = a [log( x +1)]b 1.786 0.538 0.486 0.1169
y = a + bx 0.530 0.515 0.483 0.1159
y = a + b1 x + b2 x2 0.894 −0.359 0.493 0.481 0.1161
y = a + b1 x + b2 x2 + b3 x3−0.324 4.108 −4.798 2.023 0.472 0.1171
Height vs. DBH
y = a [log( x +1)]b 1.063 0.661 0.570 0.0848
y = a + bx 0.039 0.594 0.551 0.0856
y = a + b1 x + b2 x2−0.206 1.118 −0.271 0.550 0.0858
y = a + b1 x + b2 x2 + b3 x3−0.389 1.780 −1.026 0.274 0.540 0.0868
Crown diameter vs. DBH
y = a [log( x +1)]b 0.767 0.964 0.746 0.0831
y = a + bx −0.288 0.858 0.714 0.0872
y = a + b1 x + b2 x2−0.924 2.212 −0.701 0.745 0.0823
y = a + b1 x + b2 x2 + b3 x3−2.167 6.693 −5.810 1.858 0.758 0.0802
Crown volumevs. DBH
y = a [log( x +1)]b 0.327 2.609 0.405 0.3375
y = a + bx −1.188 2.343 0.392 0.3365
y = a + b1 x + b2 x2 0.056 −0.262 1.343 0.377 0.3407
y = a + b1 x + b2 x2 + b3 x3−11.22 35.11 −35.21 12.45 0.361 0.3449
Prunus cerasifera DBHvs. Age yva [log( x +1)]b 2.086 0.488 0.270 0.1153
yva + bx 0.703 0.457 0.246 0.1161
y = a + b1 x + b2 x2−0.126 2.411 −1.113 0.2680 0.1140
y = a + b1 x + b2 x2 + b3 x3−2.138 9.457 −9.134 2.981 0.263 0.1147
Height vs. DBH
y = a [log( x +1)]b 1.055 0.658 0.406 0.0879
y = a + bx 0.091 0.536 0.391 0.0881
y = a + b1 x + b2 x2−0.246 1.155 −0.279 0.383 0.0887
y = a + b1 x + b2 x2 + b3 x3 1.921 −4.870 5.210 −1.649 0.373 0.0894
Crown diameter vs. DBH
y = a [log( x +1)]b 0.731 0.994 0.698 0.0722
y = a + bx −0.251 0.806 0.679 0.0737
y = a + b1 x + b2 x2−1.340 2.803 −0.901 0.701 0.0711
y = a + b1 x + b2 x2 + b3 x3 1.654 −5.515 6.690 −2.278 0.699 0.0714
Crown volumevs. DBH
y = a [log( x +1)]b 0.122 3.638 0.690 0.2786
y = a + bx −1.862 2.942 0.657 0.2891 y = a + b1 x + b2 x2
−8.396 15.01 −5.484 0.730 0.2568
y = a + b1 x + b2 x2 + b3 x3 14.03 −47.34 51.42 −17.06 0.743 0.2502
Prunus serrulata DBHvs. Age
y = a [log( x +1)]b 1.845 0.736 0.472 0.1280
y = a + bx 0.541 0.713 0.476 0.1272
y = a + b1 x + b2 x2 0.918 −0.196 0.526 0.479 0.1268
y = a + b1 x + b2 x2 + b3 x3 1.532 −2.417 3.134 −0.998 0.476 0.1271
Height vs. DBH
y = a [log( x +1)]b 1.168 0.524 0.385 0.0909
y = a + bx 0.204 0.410 0.384 0.0907
y = a + b1 x + b2 x2 0.267 0.300 0.046 0.381 0.0909
y = a + b1 x + b2 x2 + b3 x3−0.153 1.400 −0.900 0.2667 0.378 0.0912
Crown diameter vs. DBH
yva [log( x +1)]b 0.612 1.135 0.767 0.0859
y = a + bx −0.381 0.884 0.763 0.0864
y = a + b1 x + b2 x2−0.792 1.591 −0.298 0.765 0.0861
y = a + b1 x + b2 x2 + b3 x3 0.338 −1.371 2.249 −0.718 0.764 0.0862
Crown volumevs. DBH
yva [log( x +1)]b 0.219 2.865 0.662 0.2808
y = a + bx −1.237 2.228 0.656 0.2814
y = a + b1 x + b2 x2−1.731 3.076 −0.357 0.655 0.2821
y = a + b1 x + b2 x2 + b3 x3−4.205 9.570 −5.950 1.578 0.653 0.2828
Pyrus calleryana DBHvs. Age
y = a [log( x +1)]b 1.788 0.758 0.614 0.1085
y = a + bx 0.533 0.699 0.556 0.1182
y = a + b1 x + b2 x2 0.084 1.754 −0.589 0.562 0.1174
y = a + b1 x + b2 x2 + b3 x3 3.421 −10.09 12.99 −5.044 0.576 0.1155
Height vs. DBH
y = a [log( x +1)]b 1.136 0.758 0.683 0.0708
y = a + bx 0.177 0.609 0.696 0.0713
y = a + b1 x + b2 x2−0.031 0.972 −0.155 0.694 0.0715
y = a + b1 x + b2 x2 + b3 x3−0.723 2.738 −1.708 0.437 0.691 0.0718
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152 B. Troxel et al. / Urban Forestry & Urban Greening 12 (2013) 144–153
Species Model a b1 b2 b3 R2 (Adj) RMSE
Crown diameter vs.DBH
y = a [log( x +1)]b 0.609 1.158 0.874 0.0603
y = a + bx −0.391 0.908 0.874 0.0600
y = a + b1 x + b2 x2−0.519 1.130 −0.094 0.872 0.0603
y = a + b1 x + b2 x2 + b3 x3−0.089 0.016 0.854 −0.265 0.871 0.0606
Crown volume vs.DBH
y = a [log( x +1)]b 0.190 3.376 0.829 0.1823
y = a + bx −1.373 2.662 0.859 0.1839
y = a + b1 x + b2 x2−2.601 4.819 −0.927 0.860 0.1833
y = a + b1 x + b2 x2 + b3 x3 1.837 −6.980 9.390 −2.964 0.859 0.1838
Quercus spp. DBH vs. Age
y = a [log( x +1)]b 1.626 0.867 0.734 0.1015
y = a + bx 0.411 0.827 0.728 0.1016
y = a + b1 x + b2 x2 0.269 1.165 −0.192 0.725 0.1023
y = a + b1 x + b2 x2 + b3 x3 1.231 −2.263 3.731 −1.450 0.721 0.1029
Heightvs. DBH
y = a [log( x +1)]b 0.995 0.897 0.735 0.0865
y = a + bx 0.039 0.733 0.730 0.0866
y = a + b1 x + b2 x2−0.149 1.082 −0.156 0.727 0.0872
y = a + b1 x + b2 x2 + b3 x3 0.480 −0.685 1.456 −0.480 0.722 0.0879
Crown diameter vs.DBH
y = a [log( x +1)]b 0.723 1.053 0.915 0.0517
y = a + bx −2.660 0.855 0.899 0.0557
y = a + b1 x + b2 x2−0.969 2.157 −0.584 0.917 0.0507
y = a + b1 x + b2 x2 + b3 x3−2.145 5.460 −3.598 0.897 0.917 0.0505
Crown volume vs.DBH y = a [log( x +1)]b 0.219 3.269 0.858 0.2121
y = a + bx −1.388 2.704 0.854 0.2129
y = a + b1 x + b2 x2−1.946 3.756 −0.480 0.852 0.2143
y = a + b1 x + b2 x2 + b3 x3−9.734 25.95 −21.06 6.229 0.858 0.2103
Syringa reticulata DBH vs. Age
y = a [log( x +1)]b 2.045 0.341 0.239 0.0970
y = a + bx 0.692 0.319 0.218 0.0973
y = a + b1 x + b2 x2 0.351 1.117 −0.448 0.212 0.0976
y = a + b1 x + b2 x2 + b3 x3 3.272 −9.414 11.85 −4.669 0.217 0.0974
Heightvs. DBH
y = a [log( x +1)]b 1.255 0.504 0.482 0.0519
y = a + bx 0.213 0.453 0.475 0.0517
y = a + b1 x + b2 x2 0.308 0.256 0.101 0.464 0.0523
y = a + b1 x + b2 x2 + b3 x3 0.141 0.796 −0.471 0.199 0.452 0.0528
Crown diameter vs.DBH
y = a [log( x +1)]b
0.623 1.067 0.649 0.0782 y = a + bx −0.505 0.960 0.648 0.0774
y = a + b1 x + b2 x2−0.273 0.476 0.249 0.642 0.0781
y = a + b1 x + b2 x2 + b3 x3 3.227 −11.03 12.45 −4.236 0.650 0.0772
Crown volume vs.DBH
y = a [log( x +1)]b 0.124 3.448 0.618 0.2626
y = a + bx −2.25 3.168 0.620 0.2586
y = a + b1 x + b2 x2−0.258 −1.105 2.260 0.619 0.2588
y = a + b1 x + b2 x2 + b3 x3 17.12 −58.79 64.96 −22.36 0.641 0.2514
Tilia spp. DBH vs. Age
y = a [log( x +1)]b 2.003 0.552 0.417 0.0932
y = a + bx 0.642 0.536 0.408 0.0928
y = a + b1 x + b2 x2 0.837 0.069 0.272 0.396 0.0937
y = a + b1 x + b2 x2 + b3 x3−0.635 5.470 −6.190 2.518 0.384 0.0946
Heightvs. DBH
y = a [log( x +1)]b 0.844 0.965 0.675 0.0655
y = a + bx −0.102 0.776 0.671 0.0652
y = a + b1 x + b2 x2 0.183 0.268 0.224 0.663 0.0659
y = a + b1 x + b2 x2 + b3 x3 1.817 −4.120 4.130 −1.147 0.655 0.0667
Crown diameter vs.DBH
y = a [log( x +1)]b 0.569 1.199 0.785 0.0615
y = a + bx −0.479 0.964 0.782 0.0612
y = a + b1 x + b2 x2−0.275 0.600 0.161 0.777 0.0619
y = a + b1 x + b2 x2 + b3 x3−11.08 29.65 −25.66 7.586 0.785 0.0607
Crown volume vs.DBH
y = a [log( x +1)]b 0.163 3.300 0.864 0.1333
y = a + bx −1.556 2.629 0.859 0.1337
y = a + b1 x + b2 x2−2.441 4.193 −0.683 0.855 0.1356
y = a + b1 x + b2 x2 + b3 x3−15.14 37.81 −30.11 8.530 0.851 0.1373
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