Arboriculture & Urban Forestry 38(4): July 2012 123 Table 1. Input parameters for a model that assists homeowners in deciding whether to treat or remove an ash tree threatened by EAB. Currency is expressed in 2010 Canadian dollars. Type of information Existing ash tree Replacement tree Model parameters Input value description Diameter at breast height (cm) Cardinal direction from housey Distance from house (m) x Will a new tree be planted? Cardinal direction from housey Distance from house (m) x Type of treew Discount rate (%) Removal cost ($) Replacement cost ($) Treatment cost ($) Treatment frequency (yrs) Removal lag (yrs) Home value ($ × 1000) Estimated contribution of tree to home value (%) Optional features Home value benefits Home energy benefits Hydrology and pollution benefits Ongoing maintenance costs Accepted inputs Real number n = north; s = south; e = east; w = west real number y = yes; n = no n = north; s = south; e = east; w = west numeric c = conifer; d = deciduous Real number Real number Real number Real number Real number Real number Real number Real number 0 = off; 1 = on 0 = off; 1 = on 0 = off; 1 = on 0 = off; 1 = on z These input values were used to generate the output shown in Table 2 and Table 3. y Used to determine home energy benefits; no benefits are accrued for trees to the north of the house. x If >10 m, then home energy benefits are not calculated. w Home energy benefits are not calculated for conifers because they also shade in the winter. v Default removal rates vary with tree size: $16/cm for trees <20 cm DBH; $18/cm for trees >20 and <40 cm DBH; $20/cm for trees >40 cm DBH. time steps, the values were converted to 2010 Canadian dollars and then fitted using Chapman sigmoidal curves of the form: [2] y = a(1 - e-bx)c where y is the benefit in dollars, x is the age of the tree, and a, b, and c are fitted parameters. These curves, which were fit with R2 values >0.9, allowed the values provided by McPherson et al. (2007) to be both interpolated between the five-year intervals provided and extrapolated beyond 40 years of age (Figure 1). Although extrapo- lation is always a risk, the sigmoidal curves used here followed the trajectory of the data closely and ensured that extrapolated values were not vastly different than values within the range of the data. There are several other caveats related to the use of this data. First, the values provided by McPherson et al. (2007) are for red maple (Acer rubrum L.), which they consider a typical, “medium- sized” tree. While these values provide a reasonable estimate for replacement trees in most Canadian cities, they may not accurate- ly represent the benefits and costs associated with some replace- ment trees. Second, their values are based on energy-use patterns and tree growth rates in the northeastern United States. Though the climate in this region is generally similar to that in much of south- eastern Canada (where the majority of Canada’s urban population resides), it differs substantially from the climate in other Canadi- an regions (e.g., the west and north); thus, the extended costs and benefits may not be accurate for all parts of the country. Also note that these categories are a mix of what economists would call public and private benefits. A homeowner could directly accrue financial returns for private benefits, such as energy conservation, but not for categories like hydrology and pollution, where the ben- efits are shared by other members of society. Thus, by including these categories when running the model, users should recognize they will not be the only recipients of these benefits, and these are not likely to result in direct financial gains to the homeowner. Many studies have examined the relationship between trees and property values (see review in Theriault et al. 2002). Most have concluded that trees do indeed add value to properties; the mean for nine studies cited in Theriault et al. (2002) is a 5.5% increase in home value, with a range of -9 % to 19%. However, nearly all of those studies report the changes in home value based on the presence of an unspecified number of ma- ture trees, making it impossible to report those values on a per tree basis. Anderson and Cordell (1985; 1988) report a per tree increase in home value of 0.5 to 1%; their minimum value of 0.5% was used as the default value for this model (Table 1). In order to incorporate this value into the model, it was assumed that the presence of a mature yard tree adds 0.5% to the value of a property; if that tree is treated, then the property value is maintained; if it is cut down and replaced, property value is initially diminished, but slowly returns as the new tree grows. A default property value of $340,000 is employed (based on average reported home sale values in Canada: Canadian Real Estate Association 2010; Table 1). Specifically, it is assumed that a percentage of home value is regained each year until the tree attains a DBH of 20 cm (about 30 years) – at which point the full home value is assumed to have been returned. Growth of the replacement tree is simulated using a DBH-age equa- tion for a plantation-grown maple (McKenney et al. 2008): [3] DBH = 273.9 1× − e [ (−0.0022×Age)1.009 ] ©2012 International Society of Arboriculture Default value User supplied User supplied User supplied User supplied User supplied User supplied User supplied 4 size dependentv $400 $6.50/cm DBH 2 2 340 0.5 User controlled User controlled User controlled User controlled Example valuesz 30 w 10 y w 10 d 4 540 400 6.50 2 2 340 0.5 1 1 1 1
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