60 Martin et al.: Open-grown Crown Width Equations for Three Oak Species Table 2. Summary of the Auburn University 100% tree inventory (2009–2010) data for the three selected tree species. Species # of trees Quercus lyrata Quercus nuttallii Quercus phellos 324 243 588 Min. DBH (cm) 4.8 6.4 5.1 Max. DBH Mean DBH Median DBH Min. crown (cm) 51.1 42.9 37.6 (cm) 16.0 15.8 11.9 Nuttall oak which had a P-value of 0.0009. The open grown crown width equations developed for the three southern oak species resulted in R2 for overcup, Nuttall, and willow oak, respectively values of 0.96, 0.94, and 0.91 (Fig- ure 1). The residual plot for each species showed no obvi- ous pattern after including the higher order term indicat- ing that the models are appropriate for the data (Figure 2). A model validation for each species was then conducted by plotting the predicted average crown widths for the 20% sub- sample (obtained by using the 80% equation) against DBH. This yielded an R2 (cm) 9.9 11.9 9.4 width (m) 1.8 2.4 1.5 16.8 14.0 11.9 width (m) 5.1 5.8 4.2 Max. crown Mean crown Median crown width (m) width (m) 3.7 4.9 3.0 value of 0.98, 0.99, and 0.98 for overcup, Nuttall, and willow oak, respectively (data not shown). Again, residual plots for the 20% subsamples showed no patterns, in- dicating that the models are appropriate for the data (Figure 3). DISCUSSION The development of these crown width equations is important to not only provide a tool for designers, developers, and managers, but to also provide a first step in the validation of i-Tree Eco for the southern United States. At the time o this study, these are the first open-grown crown equations developed specifically for oaks common to southern U.S. urban forests. i-Tree Eco uses re- gression equations to derive measurements of leaf area and leaf biomass (i-Tree 2010b), and to derive accurate measurements in a certain region, equations produced from data collected from trees growing in that region are vital. To date, regression equa- tions used in the model are based on work conducted in Chicago (Nowak 1996). These data have been used extensively (Nowak and Crane 1998; Nowak et al. 2008) and provide good, basic in- formation on relative ecosystem services; however, to regional- ize the model, differences in climate, length of growing season, growth patterns, and common tree species need to be considered. The results demonstrated that DBH is a reliable predictor for the three species in the study population. Similar growth patterns were observed for all the species tested where with in- creasing diameters, there were comparable increases in crown width. The strong correlations also indicated that there was minimal management (pruning) performed to control crown spread for these species once they were planted on campus, indi- cated by large R2 values and continual increase in crown width. These results indicate that the predictive open-grown crown width equations developed for the three tree species are valid and applicable for use in the Auburn, Alabama region; however, they need to be tested on other sites throughout the southern U.S. Care should be taken when extrapolating these relationships beyond the range of the data or in situations where management prac- tices are used to control crown spread (e.g., pruning). It should also be noted that a large number of trees in these species have been planted within the last ten years, balled-and-burlapped stock sourced from several nurseries. The cultural practices within these nurseries may have affected the crown width/DBH relationship; however, all small diameter trees were used in the ©2012 International Society of Arboriculture equation development because they are now open-grown trees and are typical of what is commonly purchased from nurseries. Crown width equations developed from urban, open-grown trees are only useful when predicting open-grown crown widths. Using open-grown equations for trees under compe- tition from other trees or adjacent buildings will lead to the DBH/crown width relationship being over predicted. Species- specific equations should also be used when possible to reduce any error. Much research has been conducted on open-grown crown width equations (Ek 1974; Frelich 1992; Nowak 1996; Hasenauer 1997; Peper et al. 2001a; Peper et al. 2001b; Peper and McPherson 2003), but more is needed on species in ur- ban settings, such as the three species described in this study. Predictive open-grown crown width equations can be very ben- eficial to urban planners, managers, and arborists, as well as utility planners. Research has been conducted on urban (deVries, 1987; Fleming 1988; Frelich 1992) and forest tree growth estimates (Smith and Shifley 1984), which has led to the ability to estimate diameter growth rates. Using these estimates, it is then possible to estimate crown width and spread at various points in the future based on DBH measurements and the use of predictive open-grown crown width equations. These approximations allow prediction of events prior to planting, such as: time until adequate shade is pro- vided, when a tree crown will reach buildings and other infrastruc- ture, when a tree may become a hazard to the public, and/or when the crown of a tree will reach power lines or other utilities. Such estimates can help urban and utility planners decide if a tree will be planted or if it should be moved, and can also assist in the deter- mination and prediction of future maintenance, like pruning. Man- agers and arborists can benefit from predictive crown equations by not having to measure crown width while conducting field work. Eliminating the need to measure crown width, which is often times the most difficult and time consuming, will save valuable time. Using existing predictive open-grown crown width equa- tions, and conducting more research to develop more equations for other tree species, can provide tools that can be used by planners in the developmental stages to provide critical information that can be used to enhance the project and prevent future problems. CONCLUSIONS The regression equations developed to predict open-grown crown widths for overcup, Nuttall, and willow oak have potential for use in urban planning throughout the southern U.S. and may be used to validate i-Tree Eco for these species. Using data collected from a region to validate any modeling for that region is crucial and continued research should be carried out in other regions and with other tree species. Equations and models that use accurate field data to validate will help to improve urban forest modeling and provide more accurate results. The use of predictive equations can aid urban developers and utility planners in making the best suitable decisions when it comes to urban tree placement and can provide a valuable time saving tool for managers and arborists.
March 2012
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