Arboriculture & Urban Forestry 34(3): May 2008 regression model under examination was described by two val- ues of the age parameter: • actual value (known from the source documents and field research); and • value calculated with the model under verification (Table 3). The subsequent stage of verification determined the accuracy of the developed regression model. In presented research, accu- racy determines the degree of concordance of calculated tree age with actual tree age value. It was described as bias in percentage value calculated with the application of Equation 2. Formula 2. The accuracy of the method interpreted as bias (%). BIAS = Agecalculated − Ageactual Ageactual 100 % For all populations of sample trees, the calculated age is very close to the actual age; however, accuracy for horsechestnut is less than for other two species. Table 3 presents mean results of age readouts. The verification of independent control groups demonstrated that the model shows accuracy in determining the average age of streetside trees. For each species, the concordance between the average age estimate and actual age described by mean bias did not exceed 15%. At this stage of research, it seems that achieved accuracy (mean bias values) indicate good appli- cation potential. DISCUSSION According to the literature (e.g., Brack and Wood 1998; Banks et al. 1999; Peper et al. 2001a, 2001b; Larsen and Kristoffersen 2002; Grabosky and Gilman 2004; Linsen et al. 2005), dbh, basal area, and tree height parameters can be used to predict growth or size of tree dimensions, including height, crown height and radius, leaf area, and so on. Researchers (e.g., Pigott 1989; Peper et al. 2001a, 2001b; Gutsell and Johnson 2002; Larsen and Kristoffersen 2002) focus primarily on examining the growth of dendrometric parameters over time, but they hardly ever exam- ine the issue in reverse order, that is, as time flow (tree aging), 141 as described by changing dendrometric parameters. Undoubt- edly, planting dates are one of the key sources of information on tree age. However, the field methods of determining tree age in situ seems to be particularly important in the case of incomplete, fragmented, or lack of inventory data on the actual calendar year of planting trees. This article presents a model of multifactorial regression, which is rarely found in other research work on the growth of urban trees (e.g., Neely 1988; Banks et al. 1999; Peper et al. 2001b; Larsen and Kristoffersen 2002, Linsen et al. 2005). The presented model allows to effectively determine the age of tree populations based on two dendrometric parameters: mean dbh and H. The use of two parameters simultaneously on nomograms makes for a more reliable outcome of tree age assessment. If the compliance of investigated trees to those ones used by authors is good, the crossing point of mean dbh values and mean H values should be located between hashed lines (95% calculated age values of all unrelated trees of known age taken from a test group) as shown in Figure 1. If this is not the case (age readout outside an area bordered with hashed lines), it means that inves- tigated trees are different (e.g., different density of tree stand, pruning effect ,or incomparable site conditions) and their age readout could be biased with significant error. Potential expansion of research shall take into account differ- ent planting locations and site conditions, including downtown areas (very unfavorable for trees) and park areas (optimal con- ditions for tree growth). In this way, the age assessment of each investigated tree species shall be described by at least three sets of coefficients for the presented regression model. The next step should make it possible to elaborate computer software allowing us to determine tree age based on dendrometric parameters. It is possible in the future to increase the number of tree species included in the regression model as presented. In the first place, species planted most commonly along streets in Warsaw shall be mentioned [e.g., Norway maple (Acer platanoides L.), Sycamore (Acer pseudoplatanus L.), Silver lime (Tilia tomen- tosa Moench.), Crimean lime (Tilia × euchlora Koch.), Red oak (Quercus rubra L.), Rowan (Sorbus aucuparia L.), False acacia (Robinia pseudoacacia L.)]. Besides dbh and height parameters, further research shall take into account the possibility of the Table 3. Comparison of street trees common lime, common ash, and horsechestnut age classes known and calculated age with multifactorial nonlinear regression model. Common lime Age class number 1 2 3 4 5 6 7 10 Actual agez (years) 7 18 25 34 34 36 53 858 975 85 Mean bias (%) Calcult. agey (years) 7.2 21.9 27.9 35.2 35.2 42.2 49.8 59.4 66.7 79.5 3.9 Age class number 1 2 3 4 5 6 7 Common ash Actual age (years) 10 16 20 26 43 45 80 Calcult. age (years) 8.0 18.0 21.0 29.1 43.5 45.3 81.2 Age class number 1 2 3 4 5 6 7 Horsechestnut Actual age (years) 16 22 25 30 38 58 60 Calcult. age (years) 17.8 27.6 26.9 36.0 33.5 59.4 67.3 Mean bias (%) zThe actual age of trees taken from historical records or/and tree rings number (Pressler borer). y 1.8 Mean bias (%) Age calculated with developed multifactorial regression model applied on trees’ dbh and height of each species taken from the control group. dbh diameter at breast height. ©2008 International Society of Arboriculture 9.5
May 2008
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