Arboriculture & Urban Forestry 38(2): March 2012 open-grown crown width equations. The predictive equations, although created from data obtained from one specific location in the southern U.S., will help in development of future regional equations including other tree species modeled after this approach. MATERIALS AND METHODS Field Data Collection Field data were collected on the Auburn University campus (32°36’N, 85°30’W) located in Auburn, Alabama, U.S. Auburn is in USDA plant hardiness zone 7b, with minimum temperatures averaging -15°C to -12°C (USDA 2003). Standard i-Tree Eco data were collected following i-Tree Eco protocol (i-Tree 2010a; i-Tree 2010b) during the 2009–2010 tree inventory (100%) of the managed portions of campus encompassing approximately 243 ha (Martin et al. 2011). Data collected from each tree included DBH, tree height, average crown width, percent dieback, and a relative tree condition rating, among other attributes. i-Tree Eco, originally called the Urban Forest Effects (UFORE) model (i-Tree 2010c), was then used to estimate leaf area and leaf biomass by species equations, among other ecosystem services (i-Tree 2010b). Overcup, Nuttall, and willow oak were selected for the study because they are common southern urban tree species (Dirr 1975), account for large percentages of the campus tree popu- lation, and had a broad distribution of diameters (DBH) within the dataset. The species selected were among the ten most nu- merous tree species on campus, but none of the other common species had sufficient numbers across a wide range of diam- eters to facilitate model building (Martin et al. 2011). Over- cup, Nuttall, and willow oaks have been planted on campus for decades, providing a wide range of diameters. The combi- nation of the size and distribution of the test population pro- vided a good dataset for developing open-grown crown width equations for these common southern U.S. urban tree species. For this study, the definition of an open-grown tree was modi- fied after Frelich (1992), Nowak (1996), and Hasenauer (1997); a tree was considered open-grown if it was planted in the managed landscape and the canopy was not in direct competition for grow- ing space with other trees or buildings. The overwhelming major- ity of the trees selected were classified as open-grown, with possi- bly 1%–2% of the trees having been in slight canopy competition (one side of the tree crown touching the side of a building or an- other crown) at the time of inventory; however, all trees had leaves present from the top down to the base of the crown on all sides. DBH and mean crown width data from the inventory were used to create the predictive equations. DBH measurements, recorded to the nearest 0.25 cm, were taken at 1.37 m above the ground. Mean crown width was determined by measuring along the two cardinal directions (North-South and East-West) from the crown edges (i-Tree 2010a) and averaging the two widths; mean crown widths were rounded to the nearest 0.31 m. Development of Predictive Equations A subset of the total population of each species was created. Each was then divided into 5 cm classes based on DBH. Data were truncated at the point where there were fewer than ten trees in a class. The maximum DBH measurements used to create the crown width equations for overcup, Nuttall, and willow oak were 59 51.1 cm, 42.9 cm, and 37.6 cm, respectively. Any outliers (<5) re- sulting from measurement or recording errors or possible circum- stances present at the nursery were removed from the truncated data. Outliers were determined by visually examining data and residual plots were created using DBH and mean crown width and identifying those observations that were ≥2 units larger than the general spread of observations in the same range on the residual plots. Four outliers were removed from the Nuttall oak data, four outliers were removed from the overcup oak data, and none from the willow oak data; resulting in 323 overcup, 243 Nuttall, and 588 willow oak trees remaining for the development of equations. DBH (independent variable), DBH2 (independent variable), and mean crown width (dependent variable) data were used to derive a regression equation (SAS® [1] crown width = β0 + β1 (DBH)2 9.2). The equations were of the form: DBH + β2 The DBH was squared for each tree and was included in the predictive equations to provide the best fit based on residual plot examinations, all of which showed patterns indicating that a higher order term should be added to the model. None of the three species exhibited a pattern in the residual plots after add- ing the DBH2 there was a parabolic pattern in the residuals for all three spe- cies (data not shown). The inclusion of the DBH2 Previously published open-grown crown width equations also use a DBH2 term to the model. Without the term in the model, term in the models was further justified by the fact that much of the exist- ing literature dealing with crown width and DBH includes a DBH2 term (Hasenauer 1997; Lhotka and Loewenstein 2008). term (Paine and Hann 1982; Smith et al. 1992). To further evaluate the appropriateness of using this informa- tion to develop accurate open-grown crown width equations, ad- ditional analyses were performed. The data used to develop the initial equations for each species were divided into four groups according to DBH (Table 1). A 20% subsample of each group was then randomly selected (equaling 20% of the total popu- lation). The subsample was then removed from the population and the remaining 80% were used to create a new crown width equation. This equation was then used to predict the crown widths of the 20% subsample. Residual (observed-fitted) values were then plotted against the predicted average crown widths. Table 1. Summary of Auburn University 100% tree inventory (2009–2010), showing the number of trees in each DBH cat- egory used to further evaluate the predictive open-grown crown width equations for the three selected tree species. Species Quercus lyrata Quercus nuttallii Quercus phellos 2.5–12.6 (cm) 209 126 399 12.7–17.7 (cm) 38 59 93 RESULTS Results regarding DBH and crown width from the 100% inven- tory are presented in Table 2. The field data indicated strong linear relationships for all species (Figure 1), and linear mod- els that were created were significant with all coefficients hav- ing a P-value < 0.0001 except for the intercept coefficient for ©2012 International Society of Arboriculture 17.8–27.8 (cm) 15 22 66 27.9+ (cm) 61 36 30
March 2012
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