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Growth prediction for five tree species in an Italian urban forest
Urban Forestry & Urban Greening 10 (2011) 169–176
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Urban Forestry & Urban Greening journal homepage: www.elsevier.de/ufug
Growth prediction for five tree species in an Italian urban forest Paolo Semenzato ∗ , Dina Cattaneo, Matteo Dainese Department TeSAF, University of Padova, Viale dell’Università 16, 35020 Legnaro, PD, Italy
a r t i c l e Keywords: Predictive equations Tree growth Urban forest Allometry
i n f o
a b s t r a c t Modeling the environmental benefits of urban trees requires data which relate crown height, crown diameter, and leaf area to tree age or stem diameter (DBH). Growth prediction curves, that can be derived from the same data, can also be very useful for a better planning, design and development of the urban forest. However, very little information is available on the growth behavior of urban trees, and limited to few species and regional contexts. The aim of this study was to determine the relationships between tree age and various parameters of tree size in order to develop models to predict the growth of the most important species of an urban forest in northeastern Italy. The logarithmic regression model, proposed by Peper et al. (2001a,b) and applied by Stoffberg et al. (2008, 2009), and other equations were tested in order to obtain the best fit for each species and parameter. All the models provided a better fit for the larger species (Tilia x vulgaris Hayne, Fraxinus angustifolia Vahl., Acer platanoides L.) than for the smaller ones (Prunus cerasifera “pissardi” (Carriere) L.H. Bailey and Lagerstroemia indica L.). The equations for predicting tree sizes and leaf area are presented and applied to compare size and growth 15 and 25 years after planting. According to the models A. platanoides attained the largest average annual DBH growth with values ranging from an average of 1.25 cm years−1 between 0 and 15 years after planting and 1.52 cm years−1 between 15 and 25 years after planting. L. indica showed the smaller DBH growth, ranging from 0.34 cm years−1 in the first period to 0.48 cm years−1 in the second period. 25 years after planting. A. platanoides L. is the tallest species and reaches the largest crown diameter, whith the largest average annual growth, followed by F. angustifolia and Tilia x vulgaris that show similar growth patterns. A comparison with predicted sizes in other studies confirms the need to extend the knowledge to the behavior of more species and more site specific conditions. © 2011 Elsevier GmbH. All rights reserved.
Introduction Most of the environmental benefits associated with urban trees, such as CO2 sequestration (McPherson, 1998; McPherson and Simpson, 2000; Nowak and Crane, 2000), air pollution removal (Beckett et al., 1998; Nowak, 1994, 2006; Nowak et al., 2002; Donovan et al., 2005; Yang et al., 2005; Escobedo and Nowak, 2009), reduction of stormwater runoff (Sanders, 1986; Xiao et al., 1998, 2000a,b), microclimate modification and reduction of the urban heat island through shading and evaporative cooling (Rosenfeld et al., 1998; Simpson, 1998; Akbari et al., 1998; Akbari, 2002; Donovan and Butry, 2009), are related to their size, and particularly to the size of their crowns. Many of the benefits are directly related to leaf-atmosphere processes and thus they are a function of tree canopy cover and leaf area (Scott et al., 1998; Dwyer and Miller, 1999; Xiao et al., 2000a,b; Stoffberg et al., 2010). Estimating the environmental benefits of urban trees is particularly important in strengthening the position of the green
∗ Corresponding author. E-mail address: [email protected] (P. Semenzato). 1618-8667/$ – see front matter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.ufug.2011.05.001
infrastructure in the political agenda of public administrations and gaining more substantial financial and technical support for the planning, development and management of the urban forest, through evidence of economic return for the resources allocated, and of forgone benefits when green spaces are not adequately supported (Wolf, 2004; Schwab, 2009). Models have been developed to assess costs and benefits of the existing urban forest, compare alternative management scenarios, and determine the best management practices to maximize the environmental benefits of urban trees (Nowak and Crane, 2000; Nowak and Dwyer, 2000; Nowak et al., 2008; McPherson et al., 1999, 2000; McPherson and Simpson, 2000; Peper et al., 2001a,b; Maco and McPherson, 2003). Such models have been applied to many case studies, mainly in North America but also in other countries (McPherson et al., 2008; Nowak et al., 2002, 2007a,b; Peper et al., 2009; Soares, 2006; Siena and Buffoni, 2007). Many of the existing models are based on tree inventories and rely on algorithms and allometry that estimate canopy cover and leaf area from easily measured parameters such as DBH (Maco and McPherson, 2003) and, in some cases, crown shape and density descriptors (Nowak, 2006). Since these parameters are already often collected in inventories conducted for tree management
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purposes, they do not require additional data collection and associated cost for the municipalities. The relationships between such parameters are likely to be not only species-specific but also site specific, since growth behavior is influenced by climate and management practices (irrigation, pruning, soil management). Therefore, in applying, the models knowledge of the relationship between age, DBH, tree height, crown width and leaf area, must be available for different species in different geographic areas. The size of trees at maturity and their growth rate have also a considerable importance in guiding planning and design decisions and management practices (Larsen and Kristoffersen, 2002; Stoffberg et al., 2008). Decisions regarding tree spacing and setbacks from buildings, distances from overhead utilities, parking lot shading ordinances, landscape requirement regulations, should be based on reasonable assumptions on tree canopy growth rate. More reliable information on the growth of urban trees makes it possible to develop more feasible requirements (McPherson, 2001). Scientific evidence of urban tree growth is however available only for a limited number of species and for specific geographic areas. Data are available for North America (Frelich, 1992; Peper et al., 2001a,b), while few studies have been carried out in other countries (Stoffberg et al., 2008, 2009). The lack of regional specific data on urban tree growth is a major obstacle to the application of models that quantify tree benefits (McPherson, 2010). In southern Europe and specifically in Italy, scant information on urban tree population, composition and urban street species behavior makes it therefore difficult to estimate their potential environmental role. Growth prediction equations exist for only few of the species found in the urban forest that was studied (Frelich, 1992; Peper et al., 2001a), but not for the specific climatic zone. The purpose of this paper is to study the relationship between age and allometric parameters for the most important species identified in a typical urban forest population of northeastern Italy and provide growth prediction equations for these species. Methods Data collection The age and allometric data for the urban trees derived mostly from a series of inventories that were carried out in previous years (between 2003 and 2006) to develop urban forest plans for the cities of Piazzola sul Brenta (45◦ 32 31.21 N, 11◦ 47 .70 E), Pontelongo (45◦ 15 0.28 N, 12◦ 1 11.28 E), Vigonovo (45◦ 23 21.80 N, 12◦ 0 22.51 E) and Piove di Sacco (45◦ 17 46.20 N and 12◦ 2 5.38 E). The towns selected for the study represented fairly typical examples of urban development for north-eastern Italy. The public urban forest in the area is mainly characterized by linear planting along urban and suburban streets, and by relatively sparse tree patches in urban parks, historical gardens and city squares. The towns are in the same geographical area, in the adjacent provinces of Padua and Venice. They are all characterized by a similar climate, typical of the eastern Po Valley: growing season from March to October with mean annual temperature of 13 ◦ C; mean winter lows at −1 ◦ C, and mean summer highs at 30 ◦ C, mean annual precipitation at 900 mm with two peaks, the higher in the spring and the lower in the fall. The trees selected for the study are not subject to irrigation. The following variables were obtained from the tree inventory database that contained 7278 records: tree species and variety, stem diameter at breast height to the nearest 1 cm (DBH), tree height to the nearest 10 cm, height to base of live crown to the nearest 10 cm, the average of two crown diameters (N–S; E–W) to the nearest 10 cm, and crown height to the nearest 10 cm.
Tree age was also available for a large sample of the population as obtained through tree planting records provided by the city administrators. It must be pointed out that the age obtained through planting records refers to the age since planting date and not to the true age. It was assumed, based on the type of nursery stock used in recent public urban planting in the area, the majority of trees were between 3 and 5 years old when planted. The difference in age of planting is believed to have a minor effect on the mean growth rates calculated over a 15 year period from actual planting. The records were also used to identify the most important species in the urban tree population. In urban forestry, species importance values (IV) have been calculated in different ways (Miller and Winer, 1984; Rowntree, 1984; Welch, 1994; Maco and McPherson, 2003) to quantify the relative degree to which a species dominates a population also in terms of the potential environmental services it can provide. Because tree services are mainly linked to crown dimensions, IV has been calculated in recent studies as the average of relative abundance, relative crown projection area and/or relative leaf area (Nowak and Crane, 2000; McPherson et al., 2005; Nowak et al., 2007a,b, 2008). In our case, leaf area measurements or estimates were unavailable prior to the study, thus IV was calculated as the average of relative abundance (RA) and relative crown projection area (RC). The species were selected for the study based on the following criteria: (1) high importance value, considering also trends in species selection for the new plantings (species with a larger number of individuals in the lower DBH classes); (2) availability of reliable information on tree age/planting dates; (3) relatively wide range in age and diameter in the population; and (4) the inclusion of species pertaining to different size groups (large, medium, small). Five species met the criteria described in the methods and were used in the growth prediction study (Tables 1 and 2). Common lime (Tilia x vulgaris Hayne) was selected because it is the most important species in the study area with a RA of 15% and a RC of 23%, it also presents a good distribution of individuals in age classes (Table 2). The second and third species in the list ordered by species importance, European hornbeam and southern magnolia (Carpinus betulus L. and Magnolia grandiflora L.), were not considered, because their populations in the study area are characterized by very few age classes. Narrowleaf ash (Fraxinus angustifolia Vahl.), Norway maple (Acer platanoides L.) and Purple leaf plum (Prunus cerasifera “pissardi” (Carriere) L.H. Bailey) were selected because they were 4th, 5th and 6th, respectively, within the species importance list, characterized by a wide range of age classes in the population and extensively used in new plantings. Crapemyrtle (Lagerstroemia indica L.) was selected to include a small size species in the study having the highest IV among that category. All the inventoried trees of the five species were used in the growth study. Only trees with significant crown defects (mainly deriving from topping), trees whose age could not be determined, and those with evident space constraints physically limiting the crown growth were excluded. The tree sampled were all single stemmed, with the exception of the crapemyrtles that included a few multistemmed trees. Leaf area had to be estimated, since this parameter was not measured nor estimated in the original inventory. The image processing method proposed by Peper and McPherson (2003) was used. The protocol was slightly changed by using newer technology. A SONY alpha 700 DSRL camera with a 50 mm focal length equivalent was used to capture the images, and the public domain software ImageJ was employed to measure the crown silouette in the digital photos on an apple MacBook pro. Due to limited resources for the analysis and limited availability of images where the crown could be clearly identified, leaf area estimation was performed on a subsample of trees (between 10 and
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Table 1 Most important tree species in the inventoried urban forest (the species selected for the study are bolded). SPECIES
RA
RC
IV
Tilia x vulgaris Hayne Carpinus betulus L. Magnolia grandiflora L. Fraxinus angustifolia Vahl. Acer platanoides L. Prunus cerasifera “pissardi” (Carriere)L.H. Bailey Aesculus hippocastanum L. Cedrus deodara G. Don Robinia pseudoacacia L. Acer campestre L. Lagerstroemia indica L. Liquidambar styraciflua L. Populus nigra L. var. italica Prunus avium L. Quercus rubra L. Acer saccarinum L. Picea abies (L.) Karst Salix alba L. Pinus pinea L. Crataegus monogyna Jacq. Platanus hybrida Brot. Tilia cordata Miller Ulmus minor Miller Populus nigra L. Populus alba L. Albizzia julibrissin (Willd.) Durazzo Prunus laurocerasus L. Taxus baccata L. Acer pseudoplatanus L. Ginkgo biloba L.
0.152 0.095 0.024 0.051 0.031 0.045 0.037 0.012 0.023 0.032 0.023 0.016 0.022 0.022 0.017 0.011 0.010 0.014 0.009 0.020 0.010 0.011 0.011 0.013 0.013 0.011 0.012 0.010 0.011 0.010
0.234 0.072 0.075 0.034 0.044 0.016 0.024 0.037 0.027 0.014 0.015 0.017 0.011 0.011 0.015 0.018 0.019 0.013 0.018 0.007 0.018 0.017 0.015 0.012 0.011 0.012 0.010 0.012 0.010 0.011
0.193 0.084 0.050 0.043 0.038 0.031 0.031 0.025 0.025 0.023 0.019 0.017 0.017 0.017 0.016 0.015 0.015 0.014 0.014 0.014 0.014 0.014 0.013 0.013 0.012 0.012 0.011 0.011 0.011 0.011
Table 2 Number of trees, age after planting and diameter range used in the development of the growth equations. Species
n
Min. age
Max. age
Min. DBH
Max. DBH
Acer platanoides Fraxinus angustifolia Lagerstroemia indica Prunus cerasifera Tilia x vulgaris Total
186 240 167 190 739 1522
1 3 3 2 2
25 26 34 25 84
2 2 1 2 1
50 61 42 25 146
Table 3 Summary of the best predictive growth models for DBH, height, crown diameter and leaf area: estimated parameters (a and b), adjusted coefficients of determinations (R2 ) and root mean squared error (RMSE). Species DBH vs. age Acer platanoides Fraxinus angustifolia Lagerstroemia indica Prunus cerasifera Tilia x vulgaris Height vs. DBH Acer platanoides Fraxinus angustifolia Lagerstroemia indica Prunus cerasifera Tilia x vulgaris Crown diameter vs. DBH Acer platanoides Fraxinus angustifolia Lagerstroemia indica Prunus cerasifera Tilia x vulgaris Leaf area vs. DBH Acer platanoides Fraxinus angustifolia Lagerstroemia indica Prunus cerasifera Tilia x vulgaris
b2
b3
R2
RMSE
0.205 1.159 2.596 1.395 2.601
−0.049 −0.480 −1.316 −0.155 −0.690
0.056 0.121 0.262 – 0.083
0.760 0.907 0.746 0.532 0.910
0.3392 0.2039 0.3988 0.4085 0.2472
2.454 1.063 0.643 −0.873 1.512
−2.227 0.303 1.290 3.569 −0.469
1.160 – −0.782 −1.885 0.303
−0.152 – 0.146 0.320 −0.031
0.548 0.575 0.156 0.093 0.638
0.3688 0.1735 0.3645 0.3176 0.2970
y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2
0.602 −3.579 −1.248 −3.771 −0.801
−0.843 4.862 1.604 6.425 0.901
0.718 −1.630 −0.504 −3.149 −0.039
−0.098 0.193 0.086 0.523 –
0.791 0.579 0.616 0.434 0.800
0.2884 0.2529 0.4683 0.3716 0.2669
y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 y = a + b1 x + b2 x2 + b3 x3 y = a (ebx − 1) y = a + b1 x + b2 x2
2.865 1.906 −3.195 3.036 −4.801
−1.445 0.064 7.726 0.090 5.321
1.215 0.247 −2.973 – −0.629
−0.163 – 0.400 –
0.982 0.883 0.909 0.802 0.965
0.1255 0.3124 0.3021 0.2703 0.1344
Model
a
y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 y = a + b1 x + b2 x2 + b3 x3
1.636 0.847 −0.965 −0.300 −0.738
y = a + b1 x + b2 x2 + b3 x3 y = a + bx y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3
b1
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Fig. 1. Tree diameter (DBH) regressed on tree age (years). Actual measurements (points), predicted responses (solid line), and confidence intervals at a level of 95% (dotted lines).
Fig. 2. Tree leaf area regressed on tree diameter (DBH). Actual measurements (points), predicted responses (solid line), and confidence intervals at a level of 95% (dotted lines).
P. Semenzato et al. / Urban Forestry & Urban Greening 10 (2011) 169–176
29 individuals for each species). Two digital photos of each tree crown taken at perpendicular angles (to provide the most unobstructed view of the crown) were collected. A carboard square of known size was placed near the tree trunks to obtain the scale of the images. Relationship between biometric parameters and tree growth prediction To predict the changes of biometric parameters in time, age should be used as the independent variable. However, stem diameter is usually available from existing tree inventories and in any case easier to measure. For this reason, after finding a good fit for age against DBH, the latter has been used as the independent variable. The selection of an appropriate growth model was done by applying several equations. We first tested the logarithmic and nonlinear exponential equations proposed by Peper et al. (2001a,b), that also showed a good prediction in other environments (Stoffberg et al., 2008, 2009, 2010). The logarithmic regression model was therefore applied to predict DBH from age after transplant and to predict total height and crown diameter from DBH using the following equation (Peper et al., 2001a,b): yi = a[log(xi + 1)]b
(1)
where yi is the observed response for the ith tree, i = 1, 2, . . ., n; the number of observations; xi the age or the DBH of the ith tree; a and b the parameters to be estimated. Because of heteroscedasticity of the data, Eq. (1) was logarithmically transformed into linear form, as: log(yi ) = log(a) + b log(log(xi + 1))
(2)
The nonlinear exponential model was used for the prediction of leaf area from DBH as follows (Peper et al., 2001a,b): leafareai = a(ebDBHi − 1)
(3)
Again, Eq. (3) was logarithmically transformed into linear form to account the heteroscedasticity of the data, as: log(leafareai ) = log(a) + log(ebDBHi − 1)
(4)
In logarithmic and exponential models we applied the Baskerville (1972) bias correction as proposed by Peper et al. (2001a,b). Ordinary least squares (OLS) regressions with simple, quadratic and cubic terms were also tested (Peper, personal communication). Because variance increased with tree size, data were transformed using the log function as follows: log(yi ) = a + b1 log(xi )
(5)
log(yi ) =
a + b1 log(xi ) + b2 log(xi2 )
log(yi ) =
a + b1 log(xi ) + b2 log(xi2 ) + b3
(6) log(xi3 )
(7)
where yi is the observed response for the ith tree, i = 1, 2, . . ., n; the number of observations; xi the age or the DBH of the ith tree;
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a, b the parameters to be estimated. These transformations (Eqs. (2) and (4)–(7)) increase the statistical validity of the analysis by homogenizing the variance over the entire range of the sample data. Commonly, the spread of the points around the best-fit line is much greater for large values of y than it is for small values; the log transformation tends to equalize the variance over the entire range of y-values, which satisfies one of the prerequisites for proper use of parametric regression. In a preliminary analyses we also tested as series of weighted least squares regression, but we found a lower prediction than Peper’s models and OLS models. Models that produce high R2 and low RMSE were selected as the superior models. Statistical analyses were performed using R software (R Development Core Team, 2008). Results and discussion The summary of the best predictive growth models is presented in Table 3. Generally, we found that OLS regressions with cubic terms giving the best models with high R2 and low RMSE (the comparison between the models are reported in Appendix). The relationship between DBH and age was better predicted by OLS regression with cubic terms for A. platanoides, F. angustifolia, L. indica and T. x vulgaris (R2 ranged between 0.75 and 0.91) and with quadratic terms for P. cerasifera (R2 = 0.53) (Fig. 1). The OLS model with showed the best coefficients in height-DBH relationships. The R2 ranged between 0.55 and 0.64 in A. platanoides, F. angustifolia and T. x vulgaris respectively, while between 0.09 and 0.16 in L. indica and P. cerasifera. The relationship between crown diameter and DBH was better predicted by OLS regression with cubic terms for A. platanoides, F. angustifolia, L. indica and P. cerasifera (R2 ranged between 0.43 and 0.79) and with quadratic terms for T. x vulgaris (R2 = 0.80). Finally, the models used for the prediction of leaf area from DBH are: OLS regression with cubic terms for A. platanoides and L. indica (R2 0.91–0.98), OLS regression with quadratic terms for F. angustifolia and T. x vulgaris (R2 0.88–0.96) and nonlinear exponential model for P. cerasifera (R2 = 0.88) (Fig. 2). We estimated tree diameter, total height, crown diameter, and leaf area, at 15 and 25 years after planting (Table 4). Twentyfive years was used as the upper age limit for prediction since it was the maximum age of two of the five species analysed. The mean rate of annual DBH growth is very similar between 0 and 15 years and 15 and 25 years varying between 0.93 cm years−1 in the first period to 1.02 cm years−1 in the second. Considering species individually, P. cerasifera (from 0.69 to 0.53 cm years−1 ) and T. x vulgaris (from 1.21 to 1.04 cm years−1 ) showed a faster stem growth in the first 15 years than in the second period, while A. platanoides (from 1.25 to 1.52 cm years−1 ), F. angustifolia (from 1.16 to 1.49 cm years−1 ) and L. indica (from 0.34 to 0.48 cm years−1 ) increased its annual DBH growth in the second period. A. platanoides attained the largest DBH dimension overall (38.12 cm), 25 years after planting. Mean tree height and crown diameter growth rates are highest in the first 15 years than in the second period. The mean annual rates of height and crown diameter dropped from 0.40 to
Table 4 Predicted value of DBH, height, crown diameter and leaf area at 15 and 25 years after planting. Species
Acer platanoides Fraxinus angustifolia Lagerstroemia indica Prunus cerasifera Tilia x vulgaris
DBH (cm)
Height (m)
Crown diameter (m)
Leaf area (m2 )
15
25
15
25
15
25
15
25
18.82 17.37 5.04 10.41 18.17
38.12 37.26 12.12 13.29 26.10
7.94 6.87 4.71 3.53 7.02
10.99 8.65 6.20 3.63 8.47
6.26 4.48 1.48 2.07 4.40
10.16 6.06 2.60 2.31 5.59
143.95 60.61 24.95 52.95 220.60
345.44 215.90 44.24 68.54 352.91
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0.30 m years−1 and from 0.25 to 0.21 m years−1 , respectively. The same pattern is found in all the species examined. A. platanoides is the tallest (tree height 10.99 m) and the widest (crown diameter 10.16 m) after 25 years. The mean yearly leaf area growth is faster in the second period than in the first (8.23 and 6.61 m2 year−1 , respectively). P. cerasifera (from 3.53 to 2.74 m2 years−1 ) and T. x vulgaris (from 14.71 to 14.12 m2 years−1 ) showed a faster leaf area growth rate in the first 15 years than in the second period while A. platanoides (from 9.60 to 13.82 m2 years−1 ) and F. angustifolia (from 4.04 to 8.64 m2 years−1 ) increased its annual leaf area growth in the second period.). L. indica (from 1.66 to 1.77 m2 years−1 ) showed the same leaf area growth in the two periods. T. x vulgaris attained the largest leaf area (352.91 m2 ), 25 years after planting.
Conclusions All the predictive models tested in our study give a better fit with the larger growing species. For smaller trees, the relationship between age and stem diameter, and between stem diameter and other dimensions of growth, could not always be reliably predicted. The difficulty in estimating tree growth in the smaller species could be due to many causes. A possible explanation could be the more frequent and heavier pruning that, in some cases, characterizes the maintenance of these species, often planted where space is a limiting factor. The lack of data on the pruning cycle used in management, made it impossible for us to stratify the sample according to the different regimes, in order to verify this hypothesis. Only one of the species in the study, the crapemyrtle, has been studied by other authors (Peper et al., 2001b). From a comparison between the two studies, it appears that in the warmer climate of the San Joaquin Valley (Peper et al., 2001b) this species shows a faster growth and reaches larger crown width than in our study, although leaf area shows similar values 25 years after planting. These differences emphasize the need for specific growth analysis for different regional settings. Considering the similarity in climate and urban tree management practices, the equations tested in this study to predict tree dimensions and growth can likely be used in other areas of northern Italy (within the Po river valley). Having considered species that show high importance values in urban tree populations in the area, this study can offer a good basis for the development of environmental benefit models for the urban forest of northeastern Italy. The equations can also be used for a more accurate estimate of tree spacing requirements in public and private landscape design projects. However, there is clearly a need to extend the knowledge to the behavior of more species and more specific site conditions. As noted by other authors (Stoffberg et al., 2008), the predictive equations that were derived from a large datatset, including trees growing in a range of soil types and microclimatic conditions, can be considered robust enough to be applied to other similar urban situations. In our study, however, differences in site conditions and particularly in management practices, could be responsible for poor growth predictions for some of the species investigated. Standardized major axis slopes (SMAs), also known as reduced major axis slopes (Sokal and Rohlf, 1995), could be employed to compare the growth curves for different populations of the same species, isolated according to such cultural differences. The continued collection of data and development of predictive equations for additional species can provide a basis for comparing the effects of climate and alternative management scenarios on like species of trees throughout different regions of the world (Peper et al., 2001a,b).
Appendix A. Summary of equation models for Acer platanoides predicting DBH, height, crown diameter and leaf area: estimated parameters (a and b), adjusted coefficients of determinations (R2 ) and root mean squared error (RMSE). In bold reported the best models with low RMSE. Model 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 Leaf area vs. DBH y = a (ebx − 1) y = a + bx y = a + b1 x + b2 x2 y = a + b1 x + b2 x2 + b3 x3
a
b1 0.942 1.347 1.727 1.636
0.598 0.592 −0.127 0.205
0.125 0.325 0.714 2.454
0.525 0.579 0.244 −2.227
−0.864 −0.591 −0.522 0.602
0.765 0.812 0.753 −0.843
3.263 0.712 −0.719 2.865
0.073 1.428 2.514 −1.445
b2
0.214 −0.049
0.067 1.160
0.012 0.718
−0.195 1.215
b3
R2
RMSE
0.056
0.737 0.721 0.759 0.760
0.3554 0.3661 0.3400 0.3392
−0.152
0.538 0.535 0.536 0.548
0.3729 0.3743 0.3739 0.3688
−0.098
0.789 0.789 0.787 0.791
0.2897 0.2901 0.2909 0.2884
−0.163
0.881 0.980 0.983 0.982
0.3238 0.1335 0.1229 0.1255
Appendix B. Summary of equation models for Fraxinus angustifolia predicting DBH, height, crown diameter and leaf area: estimated parameters (a and b), adjusted coefficients of determinations (R2 ) and root mean squared error (RMSE). In bold reported the best models with low RMSE. Model
a
b1
DBH vs. age 0.172 0.900 y = a [log (x + 1)]b y = a + bx 0.526 0.904 2 y = a + b1 x + b2 x 1.991 −0.530 2 3 0.847 1.159 y = a + b1 x + b2 x + b3 x Height vs. DBH 0.972 0.300 y = a [log (x + 1)]b y = a + bx 1.063 0.303 0.979 0.371 y = a + b1 x + b2 x2 1.185 0.115 y = a + b1 x + b2 x2 + b3 x3 Crown diameter vs. DBH b 0.142 0.405 y = a [log (x + 1)] y = a + bx 0.266 0.429 −0.563 1.107 y = a + b1 x + b2 x2 4.862 y = a + b1 x + b2 x2 + b3 x3 −3.579 Leaf area vs. DBH 2.675 0.074 y = a (ebx − 1) y = a + bx 0.147 1.427 2 1.906 0.064 y = a + b1 x + b2 x y = a + b1 x + b2 x2 + b3 x3 11.411 −10.892
R2
RMSE
0.121
0.900 0.897 0.906 0.907
0.2114 0.2141 0.2040 0.2039
−0.013 0.089 −0.013
0.574 0.575 0.573 0.571
0.1736 0.1735 0.1738 0.1741
−0.129 −1.630
0.193
0.532 0.537 0.548 0.579
0.2665 0.2651 0.2618 0.2529
0.247 4.253 −0.471
0.847 0.881 0.883 0.880
0.3570 0.3152 0.3124 0.3158
b2
0.317 −0.480
b3
Appendix C. Summary of equation models for Lagerstroemia indica predicting DBH, height, crown diameter and leaf area: estimated parameters (a and b), adjusted coefficients of determinations (R2 ) and root mean squared error (RMSE). In bold reported the best models with low RMSE. Model
a
b1
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
−1.714 −1.291 1.996 −0.965
1.005 1.165 −1.646 2.596
b2
0.562 −1.316
b3
R2
0.262
0.680 0.668 0.740 0.746
RMSE 0.4481 0.4566 0.4038 0.3988
P. Semenzato et al. / Urban Forestry & Urban Greening 10 (2011) 169–176 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 Leaf area vs. DBH y = a (ebx − 1) y = a + bx y = a + b1 x + b2 x2 y = a + b1 x + b2 x2 + b3 x3
References 0.994 1.067 1.451 0.643
0.125 0.127 −0.322 1.290
−1.226 −0.856 −0.773 −1.248
0.681 0.750 0.652 1.604
2.636 1.362 0.826 −3.195
0.062 0.957 1.493 7.726
0.111 −0.782
0.024 −0.504
−0.113 −2.973
0.146
0.063 0.059 0.095 0.156
0.3841 0.3850 0.3774 0.3645
0.086
0.612 0.614 0.612 0.616
0.4705 0.4696 0.4707 0.4683
0.400
0.756 0.891 0.889 0.909
0.4940 0.3307 0.3337 0.3021
Appendix D. Summary of equation models for Prunus cerasifera predicting DBH, height, crown diameter and leaf area: estimated parameters (a and b), adjusted coefficients of determinations (R2 ) and root mean squared error (RMSE). In bold reported the best models with low RMSE. Model 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 + bx + bx2 y = a + bx + bx2 + bx3 Leaf area vs. DBH y = a (ebx − 1) y = a + bx y = a + b1 x + b2 x2 y = a + b1 x + b2 x2 + b3 x3
a
b1
0.149 0.417 −0.300 0.567
R2
RMSE
0.523 0.527 0.532 0.531
0.4123 0.4107 0.4085 0.4090
0.320
0.042 0.042 0.041 0.093
0.3263 0.3264 0.3265 0.3176
0.523
0.370 0.371 0.369 0.434
0.3920 0.3915 0.3925 0.3716
0.413 13.009 −1.613
0.802 0.801 0.782 0.766
0.2703 0.2713 0.2840 0.2940
b2
b3
0.632 0.697 1.395 −0.155 0.073 0.474 −0.095
0.997 1.052 1.283 −0.873
0.118 0.121 −0.124 0.060 3.569 −1.885
−0.577 −0.355 −0.250 −3.771
0.473 0.506 0.394 0.027 6.425 −3.149
3.036 0.090 0.947 1.307 3.736 −0.866 31.152 −33.253
Appendix E. Summary of equation models for Tilia x vulgaris predicting DBH, height, crown diameter and leaf area: estimated parameters (a and b), adjusted coefficients of determinations (R2 ) and root mean squared error (RMSE). In bold reported the best models with low RMSE. Model 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 Leaf area vs. DBH y = a (ebx − 1) y = a + bx y = a + b1 x + b2 x2 y = a + b1 x + b2 x2 + b3 x3
175
a
b1
0.394 0.605 0.919 −0.738
0.781 0.849 0.623 2.601
0.483 0.588 0.804 1.512
0.429 0.476 0.334 −0.469
−0.549 −0.414 −0.801 −0.680
0.591 0.646 0.901 0.764
4.129 0.922 −4.801 1.689
0.057 1.480 5.321 −1.313
b2
0.037 −0.690
0.022 0.303
−0.039 0.009
−0.629 1.585
R2
RMSE
0.083
0.903 0.903 0.904 0.910
0.2572 0.2572 0.2558 0.2472
−0.031
0.635 0.633 0.633 0.638
0.2985 0.2992 0.2990 0.2970
−0.005
0.795 0.798 0.800 0.800
0.2700 0.2685 0.2669 0.2670
−0.242
0.753 0.918 0.965 0.965
0.3577 0.2066 0.1344 0.1348
b3
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Growth prediction for five tree species in an Italian urban forest Paolo Semenzato ∗ , Dina Cattaneo, Matteo Dainese Department TeSAF, University of Padova, Viale dell’Università 16, 35020 Legnaro, PD, Italy
a r t i c l e Keywords: Predictive equations Tree growth Urban forest Allometry
i n f o
a b s t r a c t Modeling the environmental benefits of urban trees requires data which relate crown height, crown diameter, and leaf area to tree age or stem diameter (DBH). Growth prediction curves, that can be derived from the same data, can also be very useful for a better planning, design and development of the urban forest. However, very little information is available on the growth behavior of urban trees, and limited to few species and regional contexts. The aim of this study was to determine the relationships between tree age and various parameters of tree size in order to develop models to predict the growth of the most important species of an urban forest in northeastern Italy. The logarithmic regression model, proposed by Peper et al. (2001a,b) and applied by Stoffberg et al. (2008, 2009), and other equations were tested in order to obtain the best fit for each species and parameter. All the models provided a better fit for the larger species (Tilia x vulgaris Hayne, Fraxinus angustifolia Vahl., Acer platanoides L.) than for the smaller ones (Prunus cerasifera “pissardi” (Carriere) L.H. Bailey and Lagerstroemia indica L.). The equations for predicting tree sizes and leaf area are presented and applied to compare size and growth 15 and 25 years after planting. According to the models A. platanoides attained the largest average annual DBH growth with values ranging from an average of 1.25 cm years−1 between 0 and 15 years after planting and 1.52 cm years−1 between 15 and 25 years after planting. L. indica showed the smaller DBH growth, ranging from 0.34 cm years−1 in the first period to 0.48 cm years−1 in the second period. 25 years after planting. A. platanoides L. is the tallest species and reaches the largest crown diameter, whith the largest average annual growth, followed by F. angustifolia and Tilia x vulgaris that show similar growth patterns. A comparison with predicted sizes in other studies confirms the need to extend the knowledge to the behavior of more species and more site specific conditions. © 2011 Elsevier GmbH. All rights reserved.
Introduction Most of the environmental benefits associated with urban trees, such as CO2 sequestration (McPherson, 1998; McPherson and Simpson, 2000; Nowak and Crane, 2000), air pollution removal (Beckett et al., 1998; Nowak, 1994, 2006; Nowak et al., 2002; Donovan et al., 2005; Yang et al., 2005; Escobedo and Nowak, 2009), reduction of stormwater runoff (Sanders, 1986; Xiao et al., 1998, 2000a,b), microclimate modification and reduction of the urban heat island through shading and evaporative cooling (Rosenfeld et al., 1998; Simpson, 1998; Akbari et al., 1998; Akbari, 2002; Donovan and Butry, 2009), are related to their size, and particularly to the size of their crowns. Many of the benefits are directly related to leaf-atmosphere processes and thus they are a function of tree canopy cover and leaf area (Scott et al., 1998; Dwyer and Miller, 1999; Xiao et al., 2000a,b; Stoffberg et al., 2010). Estimating the environmental benefits of urban trees is particularly important in strengthening the position of the green
∗ Corresponding author. E-mail address: [email protected] (P. Semenzato). 1618-8667/$ – see front matter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.ufug.2011.05.001
infrastructure in the political agenda of public administrations and gaining more substantial financial and technical support for the planning, development and management of the urban forest, through evidence of economic return for the resources allocated, and of forgone benefits when green spaces are not adequately supported (Wolf, 2004; Schwab, 2009). Models have been developed to assess costs and benefits of the existing urban forest, compare alternative management scenarios, and determine the best management practices to maximize the environmental benefits of urban trees (Nowak and Crane, 2000; Nowak and Dwyer, 2000; Nowak et al., 2008; McPherson et al., 1999, 2000; McPherson and Simpson, 2000; Peper et al., 2001a,b; Maco and McPherson, 2003). Such models have been applied to many case studies, mainly in North America but also in other countries (McPherson et al., 2008; Nowak et al., 2002, 2007a,b; Peper et al., 2009; Soares, 2006; Siena and Buffoni, 2007). Many of the existing models are based on tree inventories and rely on algorithms and allometry that estimate canopy cover and leaf area from easily measured parameters such as DBH (Maco and McPherson, 2003) and, in some cases, crown shape and density descriptors (Nowak, 2006). Since these parameters are already often collected in inventories conducted for tree management
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purposes, they do not require additional data collection and associated cost for the municipalities. The relationships between such parameters are likely to be not only species-specific but also site specific, since growth behavior is influenced by climate and management practices (irrigation, pruning, soil management). Therefore, in applying, the models knowledge of the relationship between age, DBH, tree height, crown width and leaf area, must be available for different species in different geographic areas. The size of trees at maturity and their growth rate have also a considerable importance in guiding planning and design decisions and management practices (Larsen and Kristoffersen, 2002; Stoffberg et al., 2008). Decisions regarding tree spacing and setbacks from buildings, distances from overhead utilities, parking lot shading ordinances, landscape requirement regulations, should be based on reasonable assumptions on tree canopy growth rate. More reliable information on the growth of urban trees makes it possible to develop more feasible requirements (McPherson, 2001). Scientific evidence of urban tree growth is however available only for a limited number of species and for specific geographic areas. Data are available for North America (Frelich, 1992; Peper et al., 2001a,b), while few studies have been carried out in other countries (Stoffberg et al., 2008, 2009). The lack of regional specific data on urban tree growth is a major obstacle to the application of models that quantify tree benefits (McPherson, 2010). In southern Europe and specifically in Italy, scant information on urban tree population, composition and urban street species behavior makes it therefore difficult to estimate their potential environmental role. Growth prediction equations exist for only few of the species found in the urban forest that was studied (Frelich, 1992; Peper et al., 2001a), but not for the specific climatic zone. The purpose of this paper is to study the relationship between age and allometric parameters for the most important species identified in a typical urban forest population of northeastern Italy and provide growth prediction equations for these species. Methods Data collection The age and allometric data for the urban trees derived mostly from a series of inventories that were carried out in previous years (between 2003 and 2006) to develop urban forest plans for the cities of Piazzola sul Brenta (45◦ 32 31.21 N, 11◦ 47 .70 E), Pontelongo (45◦ 15 0.28 N, 12◦ 1 11.28 E), Vigonovo (45◦ 23 21.80 N, 12◦ 0 22.51 E) and Piove di Sacco (45◦ 17 46.20 N and 12◦ 2 5.38 E). The towns selected for the study represented fairly typical examples of urban development for north-eastern Italy. The public urban forest in the area is mainly characterized by linear planting along urban and suburban streets, and by relatively sparse tree patches in urban parks, historical gardens and city squares. The towns are in the same geographical area, in the adjacent provinces of Padua and Venice. They are all characterized by a similar climate, typical of the eastern Po Valley: growing season from March to October with mean annual temperature of 13 ◦ C; mean winter lows at −1 ◦ C, and mean summer highs at 30 ◦ C, mean annual precipitation at 900 mm with two peaks, the higher in the spring and the lower in the fall. The trees selected for the study are not subject to irrigation. The following variables were obtained from the tree inventory database that contained 7278 records: tree species and variety, stem diameter at breast height to the nearest 1 cm (DBH), tree height to the nearest 10 cm, height to base of live crown to the nearest 10 cm, the average of two crown diameters (N–S; E–W) to the nearest 10 cm, and crown height to the nearest 10 cm.
Tree age was also available for a large sample of the population as obtained through tree planting records provided by the city administrators. It must be pointed out that the age obtained through planting records refers to the age since planting date and not to the true age. It was assumed, based on the type of nursery stock used in recent public urban planting in the area, the majority of trees were between 3 and 5 years old when planted. The difference in age of planting is believed to have a minor effect on the mean growth rates calculated over a 15 year period from actual planting. The records were also used to identify the most important species in the urban tree population. In urban forestry, species importance values (IV) have been calculated in different ways (Miller and Winer, 1984; Rowntree, 1984; Welch, 1994; Maco and McPherson, 2003) to quantify the relative degree to which a species dominates a population also in terms of the potential environmental services it can provide. Because tree services are mainly linked to crown dimensions, IV has been calculated in recent studies as the average of relative abundance, relative crown projection area and/or relative leaf area (Nowak and Crane, 2000; McPherson et al., 2005; Nowak et al., 2007a,b, 2008). In our case, leaf area measurements or estimates were unavailable prior to the study, thus IV was calculated as the average of relative abundance (RA) and relative crown projection area (RC). The species were selected for the study based on the following criteria: (1) high importance value, considering also trends in species selection for the new plantings (species with a larger number of individuals in the lower DBH classes); (2) availability of reliable information on tree age/planting dates; (3) relatively wide range in age and diameter in the population; and (4) the inclusion of species pertaining to different size groups (large, medium, small). Five species met the criteria described in the methods and were used in the growth prediction study (Tables 1 and 2). Common lime (Tilia x vulgaris Hayne) was selected because it is the most important species in the study area with a RA of 15% and a RC of 23%, it also presents a good distribution of individuals in age classes (Table 2). The second and third species in the list ordered by species importance, European hornbeam and southern magnolia (Carpinus betulus L. and Magnolia grandiflora L.), were not considered, because their populations in the study area are characterized by very few age classes. Narrowleaf ash (Fraxinus angustifolia Vahl.), Norway maple (Acer platanoides L.) and Purple leaf plum (Prunus cerasifera “pissardi” (Carriere) L.H. Bailey) were selected because they were 4th, 5th and 6th, respectively, within the species importance list, characterized by a wide range of age classes in the population and extensively used in new plantings. Crapemyrtle (Lagerstroemia indica L.) was selected to include a small size species in the study having the highest IV among that category. All the inventoried trees of the five species were used in the growth study. Only trees with significant crown defects (mainly deriving from topping), trees whose age could not be determined, and those with evident space constraints physically limiting the crown growth were excluded. The tree sampled were all single stemmed, with the exception of the crapemyrtles that included a few multistemmed trees. Leaf area had to be estimated, since this parameter was not measured nor estimated in the original inventory. The image processing method proposed by Peper and McPherson (2003) was used. The protocol was slightly changed by using newer technology. A SONY alpha 700 DSRL camera with a 50 mm focal length equivalent was used to capture the images, and the public domain software ImageJ was employed to measure the crown silouette in the digital photos on an apple MacBook pro. Due to limited resources for the analysis and limited availability of images where the crown could be clearly identified, leaf area estimation was performed on a subsample of trees (between 10 and
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Table 1 Most important tree species in the inventoried urban forest (the species selected for the study are bolded). SPECIES
RA
RC
IV
Tilia x vulgaris Hayne Carpinus betulus L. Magnolia grandiflora L. Fraxinus angustifolia Vahl. Acer platanoides L. Prunus cerasifera “pissardi” (Carriere)L.H. Bailey Aesculus hippocastanum L. Cedrus deodara G. Don Robinia pseudoacacia L. Acer campestre L. Lagerstroemia indica L. Liquidambar styraciflua L. Populus nigra L. var. italica Prunus avium L. Quercus rubra L. Acer saccarinum L. Picea abies (L.) Karst Salix alba L. Pinus pinea L. Crataegus monogyna Jacq. Platanus hybrida Brot. Tilia cordata Miller Ulmus minor Miller Populus nigra L. Populus alba L. Albizzia julibrissin (Willd.) Durazzo Prunus laurocerasus L. Taxus baccata L. Acer pseudoplatanus L. Ginkgo biloba L.
0.152 0.095 0.024 0.051 0.031 0.045 0.037 0.012 0.023 0.032 0.023 0.016 0.022 0.022 0.017 0.011 0.010 0.014 0.009 0.020 0.010 0.011 0.011 0.013 0.013 0.011 0.012 0.010 0.011 0.010
0.234 0.072 0.075 0.034 0.044 0.016 0.024 0.037 0.027 0.014 0.015 0.017 0.011 0.011 0.015 0.018 0.019 0.013 0.018 0.007 0.018 0.017 0.015 0.012 0.011 0.012 0.010 0.012 0.010 0.011
0.193 0.084 0.050 0.043 0.038 0.031 0.031 0.025 0.025 0.023 0.019 0.017 0.017 0.017 0.016 0.015 0.015 0.014 0.014 0.014 0.014 0.014 0.013 0.013 0.012 0.012 0.011 0.011 0.011 0.011
Table 2 Number of trees, age after planting and diameter range used in the development of the growth equations. Species
n
Min. age
Max. age
Min. DBH
Max. DBH
Acer platanoides Fraxinus angustifolia Lagerstroemia indica Prunus cerasifera Tilia x vulgaris Total
186 240 167 190 739 1522
1 3 3 2 2
25 26 34 25 84
2 2 1 2 1
50 61 42 25 146
Table 3 Summary of the best predictive growth models for DBH, height, crown diameter and leaf area: estimated parameters (a and b), adjusted coefficients of determinations (R2 ) and root mean squared error (RMSE). Species DBH vs. age Acer platanoides Fraxinus angustifolia Lagerstroemia indica Prunus cerasifera Tilia x vulgaris Height vs. DBH Acer platanoides Fraxinus angustifolia Lagerstroemia indica Prunus cerasifera Tilia x vulgaris Crown diameter vs. DBH Acer platanoides Fraxinus angustifolia Lagerstroemia indica Prunus cerasifera Tilia x vulgaris Leaf area vs. DBH Acer platanoides Fraxinus angustifolia Lagerstroemia indica Prunus cerasifera Tilia x vulgaris
b2
b3
R2
RMSE
0.205 1.159 2.596 1.395 2.601
−0.049 −0.480 −1.316 −0.155 −0.690
0.056 0.121 0.262 – 0.083
0.760 0.907 0.746 0.532 0.910
0.3392 0.2039 0.3988 0.4085 0.2472
2.454 1.063 0.643 −0.873 1.512
−2.227 0.303 1.290 3.569 −0.469
1.160 – −0.782 −1.885 0.303
−0.152 – 0.146 0.320 −0.031
0.548 0.575 0.156 0.093 0.638
0.3688 0.1735 0.3645 0.3176 0.2970
y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2
0.602 −3.579 −1.248 −3.771 −0.801
−0.843 4.862 1.604 6.425 0.901
0.718 −1.630 −0.504 −3.149 −0.039
−0.098 0.193 0.086 0.523 –
0.791 0.579 0.616 0.434 0.800
0.2884 0.2529 0.4683 0.3716 0.2669
y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 y = a + b1 x + b2 x2 + b3 x3 y = a (ebx − 1) y = a + b1 x + b2 x2
2.865 1.906 −3.195 3.036 −4.801
−1.445 0.064 7.726 0.090 5.321
1.215 0.247 −2.973 – −0.629
−0.163 – 0.400 –
0.982 0.883 0.909 0.802 0.965
0.1255 0.3124 0.3021 0.2703 0.1344
Model
a
y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 y = a + b1 x + b2 x2 + b3 x3
1.636 0.847 −0.965 −0.300 −0.738
y = a + b1 x + b2 x2 + b3 x3 y = a + bx y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3 y = a + b1 x + b2 x2 + b3 x3
b1
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P. Semenzato et al. / Urban Forestry & Urban Greening 10 (2011) 169–176
Fig. 1. Tree diameter (DBH) regressed on tree age (years). Actual measurements (points), predicted responses (solid line), and confidence intervals at a level of 95% (dotted lines).
Fig. 2. Tree leaf area regressed on tree diameter (DBH). Actual measurements (points), predicted responses (solid line), and confidence intervals at a level of 95% (dotted lines).
P. Semenzato et al. / Urban Forestry & Urban Greening 10 (2011) 169–176
29 individuals for each species). Two digital photos of each tree crown taken at perpendicular angles (to provide the most unobstructed view of the crown) were collected. A carboard square of known size was placed near the tree trunks to obtain the scale of the images. Relationship between biometric parameters and tree growth prediction To predict the changes of biometric parameters in time, age should be used as the independent variable. However, stem diameter is usually available from existing tree inventories and in any case easier to measure. For this reason, after finding a good fit for age against DBH, the latter has been used as the independent variable. The selection of an appropriate growth model was done by applying several equations. We first tested the logarithmic and nonlinear exponential equations proposed by Peper et al. (2001a,b), that also showed a good prediction in other environments (Stoffberg et al., 2008, 2009, 2010). The logarithmic regression model was therefore applied to predict DBH from age after transplant and to predict total height and crown diameter from DBH using the following equation (Peper et al., 2001a,b): yi = a[log(xi + 1)]b
(1)
where yi is the observed response for the ith tree, i = 1, 2, . . ., n; the number of observations; xi the age or the DBH of the ith tree; a and b the parameters to be estimated. Because of heteroscedasticity of the data, Eq. (1) was logarithmically transformed into linear form, as: log(yi ) = log(a) + b log(log(xi + 1))
(2)
The nonlinear exponential model was used for the prediction of leaf area from DBH as follows (Peper et al., 2001a,b): leafareai = a(ebDBHi − 1)
(3)
Again, Eq. (3) was logarithmically transformed into linear form to account the heteroscedasticity of the data, as: log(leafareai ) = log(a) + log(ebDBHi − 1)
(4)
In logarithmic and exponential models we applied the Baskerville (1972) bias correction as proposed by Peper et al. (2001a,b). Ordinary least squares (OLS) regressions with simple, quadratic and cubic terms were also tested (Peper, personal communication). Because variance increased with tree size, data were transformed using the log function as follows: log(yi ) = a + b1 log(xi )
(5)
log(yi ) =
a + b1 log(xi ) + b2 log(xi2 )
log(yi ) =
a + b1 log(xi ) + b2 log(xi2 ) + b3
(6) log(xi3 )
(7)
where yi is the observed response for the ith tree, i = 1, 2, . . ., n; the number of observations; xi the age or the DBH of the ith tree;
173
a, b the parameters to be estimated. These transformations (Eqs. (2) and (4)–(7)) increase the statistical validity of the analysis by homogenizing the variance over the entire range of the sample data. Commonly, the spread of the points around the best-fit line is much greater for large values of y than it is for small values; the log transformation tends to equalize the variance over the entire range of y-values, which satisfies one of the prerequisites for proper use of parametric regression. In a preliminary analyses we also tested as series of weighted least squares regression, but we found a lower prediction than Peper’s models and OLS models. Models that produce high R2 and low RMSE were selected as the superior models. Statistical analyses were performed using R software (R Development Core Team, 2008). Results and discussion The summary of the best predictive growth models is presented in Table 3. Generally, we found that OLS regressions with cubic terms giving the best models with high R2 and low RMSE (the comparison between the models are reported in Appendix). The relationship between DBH and age was better predicted by OLS regression with cubic terms for A. platanoides, F. angustifolia, L. indica and T. x vulgaris (R2 ranged between 0.75 and 0.91) and with quadratic terms for P. cerasifera (R2 = 0.53) (Fig. 1). The OLS model with showed the best coefficients in height-DBH relationships. The R2 ranged between 0.55 and 0.64 in A. platanoides, F. angustifolia and T. x vulgaris respectively, while between 0.09 and 0.16 in L. indica and P. cerasifera. The relationship between crown diameter and DBH was better predicted by OLS regression with cubic terms for A. platanoides, F. angustifolia, L. indica and P. cerasifera (R2 ranged between 0.43 and 0.79) and with quadratic terms for T. x vulgaris (R2 = 0.80). Finally, the models used for the prediction of leaf area from DBH are: OLS regression with cubic terms for A. platanoides and L. indica (R2 0.91–0.98), OLS regression with quadratic terms for F. angustifolia and T. x vulgaris (R2 0.88–0.96) and nonlinear exponential model for P. cerasifera (R2 = 0.88) (Fig. 2). We estimated tree diameter, total height, crown diameter, and leaf area, at 15 and 25 years after planting (Table 4). Twentyfive years was used as the upper age limit for prediction since it was the maximum age of two of the five species analysed. The mean rate of annual DBH growth is very similar between 0 and 15 years and 15 and 25 years varying between 0.93 cm years−1 in the first period to 1.02 cm years−1 in the second. Considering species individually, P. cerasifera (from 0.69 to 0.53 cm years−1 ) and T. x vulgaris (from 1.21 to 1.04 cm years−1 ) showed a faster stem growth in the first 15 years than in the second period, while A. platanoides (from 1.25 to 1.52 cm years−1 ), F. angustifolia (from 1.16 to 1.49 cm years−1 ) and L. indica (from 0.34 to 0.48 cm years−1 ) increased its annual DBH growth in the second period. A. platanoides attained the largest DBH dimension overall (38.12 cm), 25 years after planting. Mean tree height and crown diameter growth rates are highest in the first 15 years than in the second period. The mean annual rates of height and crown diameter dropped from 0.40 to
Table 4 Predicted value of DBH, height, crown diameter and leaf area at 15 and 25 years after planting. Species
Acer platanoides Fraxinus angustifolia Lagerstroemia indica Prunus cerasifera Tilia x vulgaris
DBH (cm)
Height (m)
Crown diameter (m)
Leaf area (m2 )
15
25
15
25
15
25
15
25
18.82 17.37 5.04 10.41 18.17
38.12 37.26 12.12 13.29 26.10
7.94 6.87 4.71 3.53 7.02
10.99 8.65 6.20 3.63 8.47
6.26 4.48 1.48 2.07 4.40
10.16 6.06 2.60 2.31 5.59
143.95 60.61 24.95 52.95 220.60
345.44 215.90 44.24 68.54 352.91
174
P. Semenzato et al. / Urban Forestry & Urban Greening 10 (2011) 169–176
0.30 m years−1 and from 0.25 to 0.21 m years−1 , respectively. The same pattern is found in all the species examined. A. platanoides is the tallest (tree height 10.99 m) and the widest (crown diameter 10.16 m) after 25 years. The mean yearly leaf area growth is faster in the second period than in the first (8.23 and 6.61 m2 year−1 , respectively). P. cerasifera (from 3.53 to 2.74 m2 years−1 ) and T. x vulgaris (from 14.71 to 14.12 m2 years−1 ) showed a faster leaf area growth rate in the first 15 years than in the second period while A. platanoides (from 9.60 to 13.82 m2 years−1 ) and F. angustifolia (from 4.04 to 8.64 m2 years−1 ) increased its annual leaf area growth in the second period.). L. indica (from 1.66 to 1.77 m2 years−1 ) showed the same leaf area growth in the two periods. T. x vulgaris attained the largest leaf area (352.91 m2 ), 25 years after planting.
Conclusions All the predictive models tested in our study give a better fit with the larger growing species. For smaller trees, the relationship between age and stem diameter, and between stem diameter and other dimensions of growth, could not always be reliably predicted. The difficulty in estimating tree growth in the smaller species could be due to many causes. A possible explanation could be the more frequent and heavier pruning that, in some cases, characterizes the maintenance of these species, often planted where space is a limiting factor. The lack of data on the pruning cycle used in management, made it impossible for us to stratify the sample according to the different regimes, in order to verify this hypothesis. Only one of the species in the study, the crapemyrtle, has been studied by other authors (Peper et al., 2001b). From a comparison between the two studies, it appears that in the warmer climate of the San Joaquin Valley (Peper et al., 2001b) this species shows a faster growth and reaches larger crown width than in our study, although leaf area shows similar values 25 years after planting. These differences emphasize the need for specific growth analysis for different regional settings. Considering the similarity in climate and urban tree management practices, the equations tested in this study to predict tree dimensions and growth can likely be used in other areas of northern Italy (within the Po river valley). Having considered species that show high importance values in urban tree populations in the area, this study can offer a good basis for the development of environmental benefit models for the urban forest of northeastern Italy. The equations can also be used for a more accurate estimate of tree spacing requirements in public and private landscape design projects. However, there is clearly a need to extend the knowledge to the behavior of more species and more specific site conditions. As noted by other authors (Stoffberg et al., 2008), the predictive equations that were derived from a large datatset, including trees growing in a range of soil types and microclimatic conditions, can be considered robust enough to be applied to other similar urban situations. In our study, however, differences in site conditions and particularly in management practices, could be responsible for poor growth predictions for some of the species investigated. Standardized major axis slopes (SMAs), also known as reduced major axis slopes (Sokal and Rohlf, 1995), could be employed to compare the growth curves for different populations of the same species, isolated according to such cultural differences. The continued collection of data and development of predictive equations for additional species can provide a basis for comparing the effects of climate and alternative management scenarios on like species of trees throughout different regions of the world (Peper et al., 2001a,b).
Appendix A. Summary of equation models for Acer platanoides predicting DBH, height, crown diameter and leaf area: estimated parameters (a and b), adjusted coefficients of determinations (R2 ) and root mean squared error (RMSE). In bold reported the best models with low RMSE. Model 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 Leaf area vs. DBH y = a (ebx − 1) y = a + bx y = a + b1 x + b2 x2 y = a + b1 x + b2 x2 + b3 x3
a
b1 0.942 1.347 1.727 1.636
0.598 0.592 −0.127 0.205
0.125 0.325 0.714 2.454
0.525 0.579 0.244 −2.227
−0.864 −0.591 −0.522 0.602
0.765 0.812 0.753 −0.843
3.263 0.712 −0.719 2.865
0.073 1.428 2.514 −1.445
b2
0.214 −0.049
0.067 1.160
0.012 0.718
−0.195 1.215
b3
R2
RMSE
0.056
0.737 0.721 0.759 0.760
0.3554 0.3661 0.3400 0.3392
−0.152
0.538 0.535 0.536 0.548
0.3729 0.3743 0.3739 0.3688
−0.098
0.789 0.789 0.787 0.791
0.2897 0.2901 0.2909 0.2884
−0.163
0.881 0.980 0.983 0.982
0.3238 0.1335 0.1229 0.1255
Appendix B. Summary of equation models for Fraxinus angustifolia predicting DBH, height, crown diameter and leaf area: estimated parameters (a and b), adjusted coefficients of determinations (R2 ) and root mean squared error (RMSE). In bold reported the best models with low RMSE. Model
a
b1
DBH vs. age 0.172 0.900 y = a [log (x + 1)]b y = a + bx 0.526 0.904 2 y = a + b1 x + b2 x 1.991 −0.530 2 3 0.847 1.159 y = a + b1 x + b2 x + b3 x Height vs. DBH 0.972 0.300 y = a [log (x + 1)]b y = a + bx 1.063 0.303 0.979 0.371 y = a + b1 x + b2 x2 1.185 0.115 y = a + b1 x + b2 x2 + b3 x3 Crown diameter vs. DBH b 0.142 0.405 y = a [log (x + 1)] y = a + bx 0.266 0.429 −0.563 1.107 y = a + b1 x + b2 x2 4.862 y = a + b1 x + b2 x2 + b3 x3 −3.579 Leaf area vs. DBH 2.675 0.074 y = a (ebx − 1) y = a + bx 0.147 1.427 2 1.906 0.064 y = a + b1 x + b2 x y = a + b1 x + b2 x2 + b3 x3 11.411 −10.892
R2
RMSE
0.121
0.900 0.897 0.906 0.907
0.2114 0.2141 0.2040 0.2039
−0.013 0.089 −0.013
0.574 0.575 0.573 0.571
0.1736 0.1735 0.1738 0.1741
−0.129 −1.630
0.193
0.532 0.537 0.548 0.579
0.2665 0.2651 0.2618 0.2529
0.247 4.253 −0.471
0.847 0.881 0.883 0.880
0.3570 0.3152 0.3124 0.3158
b2
0.317 −0.480
b3
Appendix C. Summary of equation models for Lagerstroemia indica predicting DBH, height, crown diameter and leaf area: estimated parameters (a and b), adjusted coefficients of determinations (R2 ) and root mean squared error (RMSE). In bold reported the best models with low RMSE. Model
a
b1
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
−1.714 −1.291 1.996 −0.965
1.005 1.165 −1.646 2.596
b2
0.562 −1.316
b3
R2
0.262
0.680 0.668 0.740 0.746
RMSE 0.4481 0.4566 0.4038 0.3988
P. Semenzato et al. / Urban Forestry & Urban Greening 10 (2011) 169–176 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 Leaf area vs. DBH y = a (ebx − 1) y = a + bx y = a + b1 x + b2 x2 y = a + b1 x + b2 x2 + b3 x3
References 0.994 1.067 1.451 0.643
0.125 0.127 −0.322 1.290
−1.226 −0.856 −0.773 −1.248
0.681 0.750 0.652 1.604
2.636 1.362 0.826 −3.195
0.062 0.957 1.493 7.726
0.111 −0.782
0.024 −0.504
−0.113 −2.973
0.146
0.063 0.059 0.095 0.156
0.3841 0.3850 0.3774 0.3645
0.086
0.612 0.614 0.612 0.616
0.4705 0.4696 0.4707 0.4683
0.400
0.756 0.891 0.889 0.909
0.4940 0.3307 0.3337 0.3021
Appendix D. Summary of equation models for Prunus cerasifera predicting DBH, height, crown diameter and leaf area: estimated parameters (a and b), adjusted coefficients of determinations (R2 ) and root mean squared error (RMSE). In bold reported the best models with low RMSE. Model 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 + bx + bx2 y = a + bx + bx2 + bx3 Leaf area vs. DBH y = a (ebx − 1) y = a + bx y = a + b1 x + b2 x2 y = a + b1 x + b2 x2 + b3 x3
a
b1
0.149 0.417 −0.300 0.567
R2
RMSE
0.523 0.527 0.532 0.531
0.4123 0.4107 0.4085 0.4090
0.320
0.042 0.042 0.041 0.093
0.3263 0.3264 0.3265 0.3176
0.523
0.370 0.371 0.369 0.434
0.3920 0.3915 0.3925 0.3716
0.413 13.009 −1.613
0.802 0.801 0.782 0.766
0.2703 0.2713 0.2840 0.2940
b2
b3
0.632 0.697 1.395 −0.155 0.073 0.474 −0.095
0.997 1.052 1.283 −0.873
0.118 0.121 −0.124 0.060 3.569 −1.885
−0.577 −0.355 −0.250 −3.771
0.473 0.506 0.394 0.027 6.425 −3.149
3.036 0.090 0.947 1.307 3.736 −0.866 31.152 −33.253
Appendix E. Summary of equation models for Tilia x vulgaris predicting DBH, height, crown diameter and leaf area: estimated parameters (a and b), adjusted coefficients of determinations (R2 ) and root mean squared error (RMSE). In bold reported the best models with low RMSE. Model 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 Leaf area vs. DBH y = a (ebx − 1) y = a + bx y = a + b1 x + b2 x2 y = a + b1 x + b2 x2 + b3 x3
175
a
b1
0.394 0.605 0.919 −0.738
0.781 0.849 0.623 2.601
0.483 0.588 0.804 1.512
0.429 0.476 0.334 −0.469
−0.549 −0.414 −0.801 −0.680
0.591 0.646 0.901 0.764
4.129 0.922 −4.801 1.689
0.057 1.480 5.321 −1.313
b2
0.037 −0.690
0.022 0.303
−0.039 0.009
−0.629 1.585
R2
RMSE
0.083
0.903 0.903 0.904 0.910
0.2572 0.2572 0.2558 0.2472
−0.031
0.635 0.633 0.633 0.638
0.2985 0.2992 0.2990 0.2970
−0.005
0.795 0.798 0.800 0.800
0.2700 0.2685 0.2669 0.2670
−0.242
0.753 0.918 0.965 0.965
0.3577 0.2066 0.1344 0.1348
b3
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