Tilia’s Physical Dimensions Over Time

MATERIALS AND METHODS

The data were recorded in Copenhagen, Denmark, 55° 42’ N, 12° 35’ E. Copenhagen is characterized by a coastal climate. All measurements were carried out on trees that seemed undamaged and unrestricted by wind.

The data were recorded during the period February through April 1997. It covers 331 Tilia (T. cordata, T. europaea, T. euclora, and T. platyphyllos), which were distributed as 251 trees at 25 locations in rows along streets, supplemented by measurements taken from 80 trees in nurseries (Table 1). All were chosen in light of age, with a view toward describing growth throughout the chosen period of 0 to 100 years.

The ages of the plantations were calculated from park administrations’ plant records. If tree size at the time of establishment was not known, then 10 years, which corresponds to a trunk circumference of 18 to 20 cm (7 to 8 in.), was added to the age.

A number of trees representative of each plantation were chosen and measured (Table 1). The choices were made on the basis of the visual impression of the trees’ dimensions. Extremes were excluded (e.g., extremely small trees, damaged trees). The distances between rows and plants were measured with a tape measure and were specified as the average of at least three measurements, rounded off to the nearest 5 cm (2 in.). Tree height, trunk height (from the ground to the bottom of the first influential branch), and crown base height (from the ground to underneath of the crown) were measured by clinometric triangulation and rounded off to the nearest 5 cm. Trunk diameters were calculated from the external trunk circumference, as measured with a tape measure at a height of 1 m (3.3 ft) (relating them to Danish commercial sizes) and rounded off to the nearest whole centimeter. Crown radii were measured along the ground surface with a tape measure from the center of the trunk to the tip of the most remote downward-projecting shoot, rounded off to the nearest 5 cm.

The variability for each plantation was examined and considered homogeneous. The statistical analyses were carried out using SAS.

Analyses of variance for all four species (T. cordata, T. euchlora, T. europaea, and T. platyphyllos) and for a group that included T. cordata, T. europaea, and T. platyphyllos revealed a significant species-related effect on dimensions. As representatives of the Tilia family in the environment in question, T. cordata, T. europaea, and T. platyphyllos can be treated in common. T. euchlora, which is differentiated by its lower growth rate (Table 1), is ignored in the data set and then in further analysis.

Regression analyses were conducted for T. cordata, T. europaea, and T. platyphyllo, collectively, to determine whether the relationships between age and 1) tree height, 2) trunk height, 3) trunk diameter, 4) crown base, and 5) crown radius of both unshaded trees and shaded trees (in avenues and rows) were linear (Y = b₁d) or quadratic (Y = b₁x + b₂d²). [Y is the examined parameter (tree height, trunk diameter, etc.), d is age, and b₁ and b₂ are constants.] Growth rate guides (Table 2) were obtained by differentiating the relationships found through regression analysis.

RESULTS AND DISCUSSION

The regression analyses revealed quadratic correlations for all relationships both for trees affected by shade and for unshaded trees (Table 3 and Figure 1).

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Figure 1.

Tree age versus size parameters of Tilia cordata, T. europaea, and T. platyphyllos.

The correlation between age and tree height (r² = 0.97, P = 0.0001) showed that height increases with age, to 19.5 m (64 ft) at an age of 101 years. Thus, in an urban growing environment, the height curve gives a reasonably certain picture of Tilia’s height as a function of age in the interval 0 to 100 years.

The tree heights given by the relationships of this study were lower than those in the literature. For instance, Johnson (1975) states that Tilia europaea attains a height of about i0 m (33 ft) at the age of 20 years and that the tree can attain a height of up to 40 m (132 ft). This study shows that, in the urban environment, Tilia attains a height of only about 7 m (23 ft) after 20 years and a maximum height of about 20 m (66 ft) after 100 years.

Growth in height decreased steadily as age increased. According to the calculations, Tilia grows to about 5 m (16 ft) during the first 15 years, whereas the height increase from 85 to 100 years is only about 0.5 m (20 in.).

The correlation between age and trunk diameter (r² = 0.97, P = 0.0001) shows that the expected trunk diameter after 100 years is about 55 cm (22 in.).

The correlation between age and trunk height (r² = 0.97, P = 0.0001) shows that trunk height increases with age. The correlation between age and crown base shows that the crown base increases marginally with age (r² = 0.92, P = 0.0001). These values are expected in both cases, because the branching height and crown base are regulated by pruning of the lowest branches. In urban locations, these lowest branches frequently interfere with traffic; thus, they are often removed. Further crown lifting often occurs for aesthetic reasons.

The correlations between age and crown radius for both unshaded trees and shaded trees show that crown diameter increases with age. The r² assumed values of 0.95 and 0.94, respectively. The coefficients of correlation largely coincide up to the age of about 45 years, at which time the growth rate of the crown radii of trees affected by shade flattens out. From that point on, shade (the effects of which depend on the distances between rows and plants) exerts a strong influence on crown radius, which, thereafter, only increases very slowly.

CONCLUSION

In this study, we have described Tilia’s growth from 0 to 100 years, with primary emphasis on the younger years because that is when planners traditionally attempt to forecast its growth.

The duration of the period for which it is actually possible to plan in urban environments presents us with a new problem. Many studies have shown that the average life span of urban trees is very short and can be as low as 10 to 15 years (Foster and Blaine 1978; Gilbertson and Bradshaw 1990; Nowak et al. 1990; Miller and Miller 1991). This study shows that within the actual life span of urban trees, it will be difficult to obtain the expected architectural and aesthetic function.

The new tools presented here make it possible to obtain a dynamic picture of the varying dimensions and visual impression of the trees over time.

With these functions, applications for dynamic illustrations can be made more realistically in urban environments using tools such as AutoCAD.

We described the Tilia species commonly used (except for T. euchlora) to prepare a simple planning tool for the most popular genus of urban tree in Denmark. The species-related differences encountered in the plantations were only minor and lacked significance in this context.