Crown Width–Tree Height Models for Magnolia grandiflora, Prunus cerasifera, and Acer negundo Growing in Cities in Northeastern Greece

Abstract

The objective of this study is the development of crown width–tree height (CW-H) models in cities in northeastern Greece, for better urban vegetation management. In the cities of Kavala, Xanthi, Komotini, Alexadroupolis, and Orestiada, in total, 700 trees of Magnolia grandiflora L., Prunus cerasifera Ehrh., and Acer negundo L. were selected. For each selected tree, the total height as well as the minimum and maximum crown diameter were measured, and the average of the minimum and maximum diameter was considered the crown width. The selected CW-H models exhibit satisfactory R² values of 0.60 and above. There is not a common pattern in the value order (or rank) of R² among the M. grandiflora, P. cerasifera, and A. negundo CW-H models in the studied cities. A medium-sized tree such as M. grandiflora, a small-medium sized tree such as A. negundo, and a shrub or small tree such as P. cerasifera did not exhibit substantial differences in estimated and observed crown widths. The results of this study will increase our understanding of CW-H allometries. The main use of these models will be in the selection of the proper above-ground spacing of tree lines and in the spatial planning of a tree’s establishment so that no problems arise from its proximity to infrastructure.

1. Introduction

Trees in cities have the ability to improve the urban environment and provide economic and social advantages [1]. Street trees reduce the temperature of the air and, as a result, mitigate urban heat islands [2], offer shade (especially during the warm months) [3], reduce wind, decelerate the flow of water into the soil, and filter solar radiation [4]. Moreover, street trees provide social benefits, such as a sense of safety and community and a reduction in crime rates, while their advantages are appreciated by city residents whose view of street trees is positive [1]. Spatial arrangement and the dimension of trees determine their effects in city environments regarding cooling and shade provision [2,3]. According to [5], in the co-creation of both annual thermal comfort and annual ecological benefits, the benefit from thermal comfort is higher than the ecological benefit. Accurate measurements of urban tree dimensions, such as crown diameter, height, and biomass, are crucial for quantifying their benefits in urban environments [6]. Moreover, the same authors, based on the importance of urban tree dimension measurements, refer to the fact that their extraction from remotely sensed data can potentially supplement traditional surveys if key limitations have been addressed.

The ability to estimate the space required by street trees as they grow will greatly contribute to species selection during the design of tree establishments in city pavements, as well as in the management of already established trees in street lines [7,8,9,10]. When a tree species of a large size at maturity is planted in a small, above-ground growth space or very close to buildings, there is a need for the repeated reduction of the crown’s dimensions through pruning, leading to a degraded tree form and injured trees [8]. Ref. [11] mentioned that conflicts with infrastructure, such as overhead wires, buildings, and streets, led to the very intense pruning of Ulmus pumila L. in San Francisco. The mature size of the trees selected for establishment in urban areas must match with the dimensions of the available above-ground growth space [10].

The allometry of trees can potentially influence the performance of individual trees [12]. Allometric relationships between dendrometric characteristics help urban green managers predict the above-ground growth of trees in urban areas [7] and to design, plan, and develop urban forests [13]. Moreover, urban tree allometry is useful for the selection of the appropriate species for planting in urban areas [8]. The required space occupied by a tree in an urban environment is determined by its height and crown width [9], and these dimensions can be measured easily. Even though the crown width vs. breast height diameter relationship can be stronger than crown width vs. tree height [14], through this allometry, the space required by tree crowns at different heights (different volumes of space) cannot be predicted with a crown width vs. breast height diameter model [9]. The breast height diameter–crown width allometries can be useful in cases where the measurement of crown width is not easy to make [14]. Additionally, the prediction of crown width from the breast height diameter is a very useful tool in the measurement of stand structures in forests [15]. On the other hand, through the crown width–tree height (CW-H) allometry, the future space requirements of tree crowns can be estimated, and, thus, the dynamics of tree space requirements can be predicted [9]. So, a very significant advantage of tree CW-H models is their use to select the right species of tree in relation to the space available on pavements and other areas in cities where there are area shortages for urban trees. Even though knowledge of the mature size of a tree species can be used in the selection of the most proper tree species in different urban above-ground growth spaces and in the design of tree establishments in urban areas, the crown width–tree height allometry offers a wider field of potentialities. The crown width–tree height allometry, through the dynamic estimation of tree crown width dimensions as the tree becomes taller, can help in the determination of a regular pruning scheme in roadside trees [8] and in trees growing in other above-ground growth spaces. Moreover, crown width simulation at different heights of a tree is useful in the aesthetic assessment of it in the existing above-ground growth space as the tree grows in height. Finally, since the above-ground growth space of a tree can be reduced through the redevelopment of buildings or the widening of roads [8], the awareness of the rate of increase of the crown diameter as the height of a tree species rises can be used in the assessment of the stress imposed on the trees of the species by the above-ground growth space reduction, and, thus, the pruning timing and intensity can be decided.

Magnolia grandiflora L., Prunus cerasifera Ehrh., and Acer negundo L. are ornamental species that are usually used in tree lines on pavements in the cities of northern Greece. M. grandiflora is a medium-sized tree with a thin bark, a green leaf color, and a pyramidal or oval crown shape [16,17]. Its geographical distribution is the coast of Southern Carolina and the southern region of North Carolina, southern Georgia, Alabama, and Mississippi. It also includes parts of Louisiana, southern Arkansas, eastern Texas, and the northern half of Florida [18]. M. grandiflora is an ornamental plant that has been used in urban areas around the world [16]. P. cerasifera Ehrh. is a shrub or small tree with a height up to 8 m [19], native to the Balkans, the Black Sea, Asia Minor [20], and Greece [21]. It grows in orchards, on city pavements, as well as in gardens and parks [22,23]; Furthermore, [24], while analyzing urban forests in China, mentioned that P. cerasifera appeared in a wide variety of land uses. A. negundo is an invasive tree in Europe [25,26]. Its extensive range is from the United States to Canada and Guatemala [16]. It is found in industrial environments [27], in rural areas [25], in urban areas [28], and in forests [29]. A. negundo is a small- to medium-sized tree with a 15 to 23 m height that appears on different soils [16].

The objective of this study is the development of crown width–tree height models for M. grandiflora, P. cerasifera, and A. negundo growing in cities in northeastern Greece, in the context of developing models that are both simple and practical for urban planners. To achieve this, we will select a limited number of explanatory variables, balancing complexity with usability. Through these models, the required space for the tree crowns of the three species as the trees grow will be estimated, and this information will be used for better urban vegetation management. Moreover, significant differences in crown widths among the three different tree species will be checked.

2. Materials and Methods

2.1. Study Area

This research was conducted in Kavala, Xanthi, Komotini, Alexandroupoli, and Orestiada, 5 cities located in northeastern Greece (Figure 1) [30]. According to the 2021 census, the population in Kavala reached 54.065 residents, in Xanthi 58.760 residents, in Komotini 54.165 residents, in Alexandroupoli 59.723 residents, and in Orestiada 19.666 residents [31]. The climate of all 5 cities is classified as temperate, with dry and hot summers (Köppen climate classification: Csa) [32,33,34].

2.2. Sampling and Regression Models Tested

In the cities of Kavala and Xanthi, data from M. grandiflora, P. cerasifera, and A. negundo were collected. In Komotini, only data from the first two species were collected, since there were not many trees that were suitable for sampling of A. negundo. In Alexadroupoli and Orestiada, data from M. grandiflora and P. cerasifera were collected, since the A. negundo street tree allometry had already been analyzed in previous research [9]. Data were collected during the vegetative period in the summer of 2022. In total, 307 M. grandiflora, 284 P. cerasifera, and 109 A. negundo trees were sampled and measured in the context of the present study, distributed as shown in Figure 2.

The trees were randomly selected from tree lines along roads (on pavements). Each selected tree had to satisfy certain conditions to be incorporated into the sample [9]. The tree had to be healthy and robust, without a deformed crown. Its crown had to grow freely, without any restrictions (buildings or other infrastructure, the crown of another tree, etc.). If the crown of the tree was in the vicinity of an obstacle, it would not be deformed, and its branches would not alter their direction because of the obstacle. Additionally, the tree had to have not experienced recent pruning, any injuries (human made or not), or any insect infestations. In each selected tree, the minimum and maximum crown diameter were measured by projecting the shortest and longest measurements along one axis, from the crown’s center to its edges, and their average was considered the tree crown diameter (crown width) [35]. Moreover, the total height of the tree was measured using the Blume-Leiss instrument (Haglöf Sweden AB, Långsele, Sweden). The measurements of individual trees are visualized in Figure 3.

To find the appropriate regression models for crown width–height (CW-H) data, the template of [36] was used. Additionally, the data from 117 A. negundo trees that were collected from Alexandroupoli and Orestiada in the context of [9]’s study were used for the development of the total CW-H model for the A. negundo street trees that grow in the 4 cities (Kavala, Xanthi, Alexandroupoli, and Orestiada). Eleven models were tested for fit with the collected data (

Table 1. Regression models tested for CW-H fitting.

Νο	Model Name	Model
1	Linear	$\widehat{CW}=b_0+b_{1}H$
2	Logarithmic	$\widehat{CW}=b_0+b_1\mathit{ln}H$
3	Inverse	$\widehat{CW}=b_0+{\displaystyle \frac{b_1}{H}}$
4	Quadratic	$\widehat{CW}=b_0+b_{1}H+b_2{H}^2$
5	Cubic	$\widehat{CW}=b_0+b_{1}H+b_2{H}^2+b_3{H}^3$
6	Power	$\widehat{CW}=b_0{H}^{b_1}$
7	Compound	$\widehat{CW}=b_0{b_1}^H$
8	S-curve	$\widehat{CW}=e^{b_0+{\displaystyle \frac{b_1}{H}}}$
9	Logistic	$\widehat{CW}={\displaystyle \frac{1}{\frac{1}{u}+b_0{b_1}^H}}$
10	Growth	$\widehat{CW}=e^{b_0+b_{1}H}$
11	Exponential	$\widehat{CW}=b_0{e}^{b_{1}H}$

$\widehat{CW}$: estimated crown width (m); H: observed total height (m); b_i: regression coefficients; u: upper boundary value = max observed CW, rounded up.

) [37]. In each species, the best models were selected from the ones that satisfied the regression assumptions: linearity, independence, homoscedasticity, residuals’ zero mean, and residuals’ normality [36]. In the event that none of the models satisfied all the assumptions, the selection was made from the models that fulfilled the linearity and the residuals’ normality assumptions. If no model satisfied at least linearity and the residuals’ normality assumptions, the selection was made from the models that satisfied at least the residuals’ normality assumption. If no model satisfied the residuals’ normality assumption, the selection was made from the models that satisfied at least the linearity assumption. After determining which models met the regression assumptions in the manner outlined earlier, three comparison criteria were computed to determine the best model [36,38] (

Table 2. Comparison criteria for the regression models tested for CW-H fitting.

Criterion	Formula	Optimum Value
Coefficient of determination	$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{\left({\widehat{CW}}_i-\overline{CW}\right)}^2}{{\sum }_{i=1}^n{\left(C{W}_i-\overline{CW}\right)}^2}}$	1
Standard Error of the Estimate	$SEE=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{\left({\widehat{CW}}_i-C{W}_i\right)}^2}{n-p}}}$	min
Root of the Mean Squared Error	$RMSE=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{\left({\widehat{CW}}_i-C{W}_i\right)}^2}{n}}}$	min

p: number of regression coefficients; n: number of sampled trees; CW: observed crown width (m); $\widehat{CW}$: estimated crown width (m); $\overline{CW}$: mean observed crown width (m); H: observed total height (m).

), using Microsoft® Excel® 2021 MSO Version 2408 Build 16.0.17928.20114), and IBM ® SPSS® Statistics Version 2021.

3. Results

The statistics of the acquired data are given in

Table 3. (a) Summary statistics for M.grandiflora, (b) summary statistics for P. cerasifera, (c) summary statistics for A. negundo.

(a)
City	Variable	N	Mean	Standard Deviation	Min	Max
Kavala	Total height H (m)	70	5.78	1.89	2.07	11.00
	Crown width CW (m)	70	4.35	1.52	0.61	8.14
Xanthi	Total height H (m)	56	6.78	2.05	2.80	13.40
	Crown width CW (m)	56	4.56	1.25	1.15	7.18
Komotini	Total height H (m)	41	5.88	2.14	2.17	9.40
	Crown width CW (m)	41	4.39	1.77	0.35	7.70
Alexandroupoli	Total height, H (m)	70	5.53	2.01	1.80	9.30
	Crown width, CW (m)	70	3.97	1.44	0.74	6.50
Orestiada	Total height, H (m)	70	5.43	1.95	2.10	13.00
	Crown width, CW (m)	70	4.05	1.47	0.77	7.13
Total	Total height, H (m)	307	5.84	2.04	1.80	13.40
	Crown width, CW (m)	307	4.24	1.49	0.35	8.14
(b)
City	Variable	N	Mean	Standard Deviation	Min	Max
Kavala	Total height H (m)	39	4.78	1.36	2.20	8.40
	Crown width CW (m)	39	4.33	1.15	1.18	7.13
Xanthi	Total height H (m)	69	5.03	1.69	2.50	9.00
	Crown width CW (m)	69	3.92	1.78	1.20	7.00
Komotini	Total height H (m)	38	4.64	1.91	2.10	8.80
	Crown width CW (m)	38	3.48	2.17	0.35	8.25
Alexandroupoli	Total height, H (m)	68	4.22	1.67	1.82	8.00
	Crown width, CW (m)	68	2.81	1.12	0.62	5.65
Orestiada	Total height, H (m)	70	5.29	1.52	1.94	8.90
	Crown width, CW (m)	70	4.53	1.99	0.60	8.46
Total	Total height, H (m)	284	4.81	1.67	1.82	9.00
	Crown width, CW (m)	284	3.80	1.80	0.35	8.46
(c)
City	Variable	N	Mean	Standard Deviation	Min	Max
Kavala	Total height H (m)	47	5.59	1.73	1.60	9.80
	Crown width CW (m)	47	4.35	2.09	0.79	11.20
Xanthi	Total height H (m)	62	6.41	1.82	3.50	13.20
	Crown width CW (m)	62	5.73	1.60	3.05	10.10
Total *	Total height, H (m)	226	6.48	2.29	1.60	15.60
	Crown width, CW (m)	226	5.67	2.44	0.79	17.30

* In the total dataset for A. negundo (226 trees), we included data from 57 trees from Alexandroupoli and 60 trees from Orestiada from previous research [9].

(a)–(c). In the city of Kavala, for M. grandiflora, model 2 (Figure 4) with a coefficient of determination R² = 0.74 meets all the assumptions of regression and exhibits the best values in the statistical comparison criteria compared to the rest of the models, which satisfy all the assumptions of regression (

Table 4. Selected models and model criteria for the M. grandiflora, P. cerasifera, and A. negundo CW-H regressions in Kavala city.

Species	Selected Model	Comparison Criteria
		R2	SEE	RMSE
M. grandiflora	2. CW b0 + b1lnH CW = −1.906 + 3.691lnH	0.74	0.7780	0.7668
P. cerasifera	5. CW = b0 + b1H + b2H2 +b3H3 CW = −7.871 + 6.661H − 1.225H2 + 0.077H3	0.61	0.7291	0.7102
A. negundo	7. CW = b0b1H CW = $0.368\times$ 1.401H	0.77	1.0228	1.0115

).

For P. cerasifera, in all the tested models, the residuals’ normality is not satisfied. From the models that satisfy the linearity assumption, model 5 (Figure 4), with a coefficient of determination of R² = 0.61 (Table 4), has the best values in the statistical comparison criteria. Model 5 fulfills all the assumptions of regression except the residuals’ normality assumption. In A. negundo, none of the tested models satisfy all the regression assumptions. From the models that fulfill the linearity and residuals’ normality assumptions, model 7 (Figure 4) exhibits the best values in statistical comparison criteria and has a coefficient of determination (R²) value of 0.77 (Table 4).

Model 7 satisfies all the regression assumptions except homoscedasticity.

In the city of Xanthi, in M. grandiflora, of the models that satisfy all the assumptions of regression, model 3 (Figure 5), with a coefficient of determination of R² = 0.60 (

Table 5. Selected models and model criteria for the M. grandiflora, P. cerasifera, and A. negundo CW-H regressions in Xanthi city.

Species	Selected Model	Comparison Criteria
		R2	SEE	RMSE
M. grandiflora	$3.CW=b_0+{\displaystyle \frac{b_1}{H}}$ CW = $7.280-{\displaystyle \frac{16.672}{H}}$	0.60	0.7982	0.7839
P. cerasifera	$3.CW=b_0+{\displaystyle \frac{b_1}{H}}$ CW = $8.278-{\displaystyle \frac{19.506}{H}}$	0.73	0.9320	0.9184
A. negundo	11. CW = b0eb1H CW = 0.469e0.774H	0.69	0.9069	0.8927

), exhibits the best values in the statistical comparison criteria. In P. cerasifera, model 4, with a coefficient of determination of R² = 0.76, satisfies all the assumptions of regression and exhibits the best values in the statistical comparison criteria compared to model 3, which also satisfies all the assumptions of regression. However, model 4 does not provide reliable crown width estimations since, in the dataset range, the estimated crown width is reduced as the tree height is increased. Based on that fact, model 3 (Figure 5), with a coefficient of determination of R² = 0.73 (Table 5), is selected. In A. negundo, of the models that satisfy all the assumptions of regression, model 11 (Figure 5), with an R² of 0.69, exhibits the best values in the statistical comparison criteria.

When looking at M. grandiflora in the city of Komotini, from the models that meet all the conditions of regression, model 3 (Figure 6), with an R² value of 0.66 (

Table 6. Selected models and model criteria for the M. grandiflora and P. cerasifera CW-H regressions in Komotini city.

Species	Selected Model	Comparison Criteria
		R2	SEE	RMSE
M. grandiflora	3. CW = b0$+{\displaystyle \frac{b_1}{H}}$ CW = $7.394-{\displaystyle \frac{14.882}{H}}$	0.66	1.0388	1.0131
P. cerasifera	7. CW = b0b1H CW = $0.224\times$ 1.712H	0.71	1.1755	1.2453

), has the best statistical comparison scores. As for P. cerasifera, only model 7 (Figure 6), with an R² value of 0.71 (Table 6), meets the requirements for linearity and the residuals’ normality. Model 7 satisfies all the regression assumptions except homoscedasticity.

For the city of Alexandroupoli, in M. grandiflora, of the models that satisfy all the assumptions of regression, model 4 (Figure 7), with a coefficient of determination of R² = 0.81 (

Table 7. Selected models and model criteria for the M. grandiflora and P. cerasifera CW-H regressions in Alexandroupoli city.

Species	Selected Model	Comparison Criteria
		R2	SEE	RMSE
M. grandiflora	4. CW = b0 + b1H + b2H2 CW = −1.685 + 1.538H − 0.082H2	0.81	0.6327	0.6236
P. cerasifera	7. CW = b0b1H CW = $0.707\times$ 0.951H	0.79	0.5201	0.5165

), exhibits the best values in the statistical comparison criteria. In P. cerasifera, only model 7 (Figure 7), with a coefficient of determination of R² = 0.79, satisfies all the assumptions of regression (Table 7).

In the city of Orestiada, in M. grandiflora, from the models that fulfill the linearity and residuals’ normality assumptions, model 2 (Figure 8) exhibits the best values in statistical comparison criteria and has a coefficient of determination of R² = 0.77 (

Table 8. Selected models and model criteria for the M. grandiflora and P. cerasifera CW-H regressions in Orestiada city.

Species	Selected Model	Comparison Criteria
		R2	SEE	RMSE
M. grandiflora	2. CW = b0 + b1lnH CW = −1.440 + 3.375lnH	0.77	0.7164	0.7061
P. cerasifera	4. CW = b0 + b1H + b2H2 CW = −4.127 + 2.258H − 0.109H2	0.78	0.9467	0.9331

). Model 2 satisfies all the regression assumptions except homoscedasticity.

Among the models in P. cerasifera that meet all regression assumptions, model 4 (Figure 8) shows the best results in terms of the statistical comparison criteria, with a coefficient of determination of R² = 0.78 (Table 8).

Overall, for all 5 cities, for M. grandiflora, only model 5 (Figure 9), with an R² = 0.72 (

Table 9. Selected models and model criteria for the M. grandiflora, P. cerasifera, and A. negundo CW-H regressions, using the total dataset for the 5 cities (Komotini was not included in the dataset for A. negundo).

Species	Selected Model	Comparison Criteria
		R2	SEE	RMSE
M. grandiflora	5. CW = b0 + b1H + b2H2 + b3H3 CW = −2.872 + 2.218H − 0.199H2 + 0.006H3	0.72	0.7890	0.7864
P. cerasifera	4. CW = b0 + b1H + b2H2 CW = −2.551 + 1.813H−0.091H2	0.71	0.9703	0.9669
A. negundo	7. CW = b0b1H CW = $0.676\times$ 1.123H	0.75	1.2221	1.2238

), satisfies all the assumptions of regression. In P. cerasifera, from the models that fulfill the linearity and the residuals’ normality assumptions, model 4 exhibits the best values in the statistical comparison criteria and has a coefficient of determination of R² = 0.71 (Table 9). Model 4 satisfies all the regression assumptions except homoscedasticity.

For A. negundo, in all the models, the residuals’ normality is not satisfied. From the models that fulfill the linearity assumption, model 7 (Figure 9) exhibits the best values in the statistical comparison criteria and has a coefficient of determination of R² = 0.75 (Table 9). Model 7 satisfies all the regression assumptions except homoscedasticity and the residuals’ normality.

4. Discussion

4.1. Developed Models

The previously described results contribute to the existing body of work on models involving tree dimensions. While numerous studies have focused on developing models that relate crown width to breast height diameter [7,8,14,15,39,40,41,42], this research addresses a gap in the literature by examining crown width–tree height (CW-H) relationships, an area less frequently explored [9,14]. This approach allows us to predict future space requirements more effectively, considering the vertical dimension of tree growth.

In all the studied cities and for the total dataset for each species, the selected CW-H models exhibit satisfactory R² values of 0.60 and above. In Kavala, M. grandiflora and A. negundo exhibited close values (0.74 and 0.77, respectively), and P. cerasifera had a lower R² value of 0.61 (Table 4) but was still satisfactory for crown width estimation (Table 4). In Xanthi’s CW-H models, M. grandiflora exhibited a value of R² equal to 0.60, which is the lowest value compared to the other species, while P. cerasifera had the highest R² value of 0.73, and A. negundo exhibited a value of R² equal to 0.69 (Table 5). In the CW-H models of Komotini, also, P. cerasifera exhibited a higher R² value (0.71) compared to the M. grandiflora value (0.66) (Table 6). In Alexandroupoli and Orestiada, the CW-H models of M. grandiflora and P. cerasifera exhibited almost the same R² values (0.81 and 0.79 for Alexandroupoli and 0.77 and 0.78 for Orestiada, respectively) (Table 7 and Table 8). Overall, for the five cities, M. grandiflora and P. cerasifera had almost the same R² values (0.72 for M. grandiflora and 0.71 for P. cerasifera), while A. negundo, for the four cities (Kavala, Xanthi, Alexandroupoli, and Orestiada), exhibited a value of R² equal to 0.75 (Table 9).

Ref. [14] developed allometries for seven species. The biometrical data were collected in urban areas of Great Britain. The R² of the developed CW-H models was lower in most cases than the R² values of the present study. In very few cases, the R² values were over 0.60. The highest observed R² value, when the total dataset for a species was used, was 0.67 for Fagus sylvatica, and for a species in an urban area, it was 0.65 for Quercus robur in Bridgend City [14].

Ref. [9] for the A. negundo CW-H models in Orestiada and Alexandroupoli reported R² values of 0.66 and 0.81, respectively, while the R² for the total data set was 0.77.

Based on the results of the present study, there is no common pattern in the value order (or rank) of R² among the M. grandiflora, P. cerasifera, and A. negundo CW-H models in the studied cities (A. negundo in Kavala and Xanthi only).

An interesting point is that, based on the results (observed values and developed models) of the present study, a medium-sized tree such as M. grandiflora, a small-medium sized A. negundo [16], and a shrub or small tree such as P. cerasifera [19] did not exhibit substantial differences in estimated and observed crown widths (Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9).

According to [43], the allometry of trees is plastic, while [12] mention that differences in above-ground growth environments are related to ponderosa pine allometry variation. The authors of [14] mention that allometries of trees in urban environments are influenced by both the regional climate and the complex effects of management and environmental factors and that these allometry variations are greater in mature trees. Moreover, the differences in the CW-H models for A. negundo in Orestiada and Alexandroupoli are probably related to a greater variability of above-ground growth conditions in Orestiada [9].

4.2. Practical Implications

The cover from the crown is related to the provision of shade, so if the crown is wider and higher, the trees offer more shade [3]. However, if there are obstacles that hinder crown expansion, then the crowns are deformed [44].

In urban environments in Greece, in many cases, there are space shortages for the street trees [44,45]. In Nikosia, Cyprus, 57.7% of street trees (trees on pavements) grew in very close proximity to infrastructure [46]. The close proximity of urban trees to buildings is a disadvantage of urban trees, since they can shade flats and their branches may facilitate thefts [47]. Moreover, if a tree is growing too close to a building or infrastructure, the resultant deformation of its crown is an aesthetic defect, and there arises a need for intense crown pruning. Additionally, reasons for removing urban trees can include their large dimensions and their proximity to houses [48].

According to the developed models (Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9), mature M. grandiflora and P. cerasifera trees require a 7–8 m diameter of above-ground growth space, centered on the tree’s bole, with no obstacles throughout the trunk height, in order to freely expand their crowns without the need for crown pruning (in the majority of cases). This means that the distance between adjacent trees in tree lines (above-ground spacing) must be approximately 7–8 m. This distance (above-ground spacing) is within the recommended range of distances between the trees in tree lines, which is 6–12 m [4]. However, pavements must have a width of at least 7–8 m, in which case, the projection of the crown limits must not extend into the carriageway and the crowns must not touch any infrastructure (building). In the case of a smaller above-ground growth space, the trees will expand their crown freely up to a tree height that can be estimated based on the results of this study, and then a need for pruning will arise. The smaller the above-ground growth space, the greater the need for frequent and intense pruning. Intense and frequent pruning can harm trees [4,8]. In A. negundo, the diameter of the above-ground growth space centered on the tree’s bole (or above-ground spacing in tree lines) can increase to 8.5–9.5 m, since, based on our data, in some cases (model from the total data set), A. negundo can reach greater heights and slightly wider crowns compared to the other two species.

Our findings on the CW-H allometries provide valuable insights into the relationships between crown width and tree height. These insights are crucial for urban vegetation management. Specifically, the developed CW-H models show a substantial potential for assisting urban vegetation managers in optimizing the design and establishment of tree lines on pavements and in other constrained urban spaces. This study highlights the practical applications of the CW-H models in urban environments where space is often limited, thus enabling more informed decision making in urban forestry practices. The main use of these models will be in the selection of the proper above-ground spacing for tree lines and in the spatial planning of a tree’s establishment so that no problems arise from its proximity to infrastructure. The models developed from the total dataset for each species can be used in urban areas of the wider geographical area with analogous climatic conditions. It is true that external factors like microclimate and urban management practices impact above-ground tree growth. However, our findings indicate that the use of fewer explanatory variables does not significantly compromise the models’ effectiveness. The results align with our objectives, providing an initial confirmation that these simplified models can still offer valuable insights for urban forestry management. This simplicity ensures that urban planners can easily implement the models and make data-driven decisions without requiring extensive expertise in complex modeling.

Our study provides foundational models that can be refined further with additional local data, offering a starting point for developing more localized models. There can be no universal model that fits all regions. The selection of different models for various cities in our study demonstrates the adaptability of our approach. Tailoring model selection to fit local conditions ensures that the models are both relevant and accurate for specific urban settings.

4.3. Contributions to the Field

This study has yielded several significant findings that contribute to the field of urban forestry. Firstly, the tailored CW-H models prove to be directly relevant to urban forestry in Greece and, by extension, to Mediterranean environments. This focus addresses a previously identified gap in the literature by providing models that are well suited to Mediterranean climates. The successful application of these models underscores the importance of regional adaptation in urban tree management.

The species-specific insights gained from our detailed analysis of M. grandiflora, P. cerasifera, and A. negundo offer valuable guidance for urban vegetation managers. The models support tailored urban tree management strategies for these commonly planted species, demonstrating their practical utility in planning and maintaining urban greenery. The data indicate that the observed and estimated crown widths are closely aligned, highlighting the models’ effectiveness in urban contexts.

Moreover, our findings contribute to an enhanced understanding of urban tree allometry, particularly in how urban growth conditions influence this relationship. This knowledge can inform adaptive management practices, helping urban planners anticipate and mitigate potential issues related to tree growth in constrained environments. Understanding such dynamics is critical for the successful integration of green spaces in urban planning.

The CW-H models developed in this study also lay a foundation for future research. Their adaptability, with the inclusion of additional local data, allows for the continuous refinement and improvement of urban forestry practices. Future studies can build on our models, expanding their applicability and accuracy in diverse urban settings.

5. Conclusions

In all the studied cities and for the total dataset for each species, the selected CW-H models exhibit satisfactory R² values of 0.60 and above. There is not a common pattern in the value order (or rank) of the R² among M. grandiflora, P. cerasifera, and A. negundo CW-H models in the studied cities (A. negundo in the cities of Kavala and Xanthi only). A medium-sized tree such as M. grandiflora, a small-medium sized tree such as A. negundo, and a shrub or small tree such as P. cerasifera did not exhibit substantial differences in estimated and observed crown widths. The main use of these models will be in the selection of the proper above-ground spacing in tree lines and in the spatial planning of a tree’s establishment so that no problems arise from its proximity to infrastructure. The models developed from the total dataset for each species can be used in urban areas of the wider geographical area with analogous climatic conditions. The results of this study will increase our understanding of CW-H allometries. The developed CW-H models will be a useful tool for urban vegetation managers in the region, aiding in the design and establishment of tree lines on pavements and other urban areas, especially where space is limited.

Regarding the research objectives, we have successfully developed and validated CW-H models that can be applied in urban planning and management. These models provide a foundational understanding of the relationship between crown width and tree height in urban settings. However, the study has some limitations. One limitation is the use of a limited number of explanatory variables, which, while making the models easier to use, may limit their accuracy in different contexts. Another limitation is the geographic focus on Mediterranean urban environments. While the models are applicable in similar climatic conditions, their applicability in other bioclimates remains to be tested. Consequently, future research could focus on validating and refining these models with additional data from various geographic regions to enhance their robustness and accuracy.

In conclusion, this study advances our understanding of urban tree allometries and offers practical tools for urban vegetation management, while also highlighting areas for further research and improvement in model applicability.