# Measuring the Contribution of Leaves to the Structural Complexity of Urban Tree Crowns with Terrestrial Laser Scanning

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## Abstract

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_{b}) metric from point clouds generated for the trees using terrestrial laser scanning, during the leaf-on and -off conditions. Furthermore, we artificially defoliated the leaf-on point clouds by applying an algorithm that separates the foliage from the woody material of the trees, and then recalculated the D

_{b}metric. The D

_{b}of the leaf-on tree point clouds was significantly greater than the D

_{b}of the leaf-off point clouds across all species. Additionally, the leaf removal algorithm introduced bias to the estimation of the leaf-removed D

_{b}of the G. triacanthos and M. glyptostroboides trees. The index capturing the contribution of leaves to the structural complexity of the study trees (the ratio of the D

_{b}of the leaf-on point clouds divided by the D

_{b}of the leaf-off point clouds minus one), was negatively correlated with branch surface area and different metrics of the length of paths through the branch network of the trees, indicating that the contribution of leaves decreases as branch network complexity increases. Underestimation of the D

_{b}of the G. triacanthos trees, after the artificial leaf removal, was related to maximum branch order. These results enhance our understanding of tree structural complexity by disentangling the contribution of leaves from that of the woody structures. The study also highlighted important methodological considerations for studying tree structure, with and without leaves, from laser-derived point clouds.

## 1. Introduction

- How do changes in leaf condition of deciduous tree species with different leaf types affect their structural complexity?
- How do differences in the contribution of leaves to the structural complexity of the study trees relate to their above-ground architecture?
- What is the effect of artificial leaf removal from leaf-on tree point clouds on estimated structural complexity? Is there an error in estimating the structural complexity of the tree point clouds after artificial leaf-removal, compared to leaf-off point clouds of the same trees?
- How does potential error in estimating the structural complexity of the tree point clouds due to the artificial leaf removal relate to the branch architecture of trees?

## 2. Materials and Methods

#### 2.1. Urban Tree Data

#### 2.2. Terrestrial Laser Scanning and Point Cloud Processing

^{3D}× 330 terrestrial laser scanner was used to scan the trees. This laser scanner operates with laser light of 1550 nm wavelength, typical beam divergence 0.19 mrad, and a range of 0.6–330 m. In order to minimize occlusion effects in the point clouds, each individual tree was scanned at high resolution from a minimum of four different directions at different distances, and five reference target-spheres were placed around a laser-scanned tree to spatially reference all scans and create a single point cloud for each tree, following the field scanning protocols suggested by Wilkes et al. [69]. The first two scans were conducted in opposite directions, from distances that allowed the top of the focal tree to be clearly visible. The other two scans were also conducted in opposite directions (perpendicularly to the first two scans) but from a closer distance to the tree, to better capture its branching architecture and get closer views of the main stem. Two or three additional scans were conducted underneath the crown of large trees with wide crowns in order to capture more dense point clouds of the branches. All laser scans were conducted when there was little or no wind.

#### 2.3. Leaf and Wood Classification of the Point Clouds

#### 2.4. Quantification of the Structural Complexity of Trees

_{b}), which is derived from fractal geometry principles [4], was used to quantify the above-ground structural complexity (fractal dimension) of the trees [90] in three conditions: (1) leaf-on, (2) leaf-off, and (3) after the leaves were artificially removed from the leaf-on point clouds. The box-dimension equals the slope of the least-squares line when the logarithm of the number of boxes required to capture all points of a laser-scanned tree is regressed against the logarithm of the inverse of the size of a box relative to the size of the initial box, which is the smallest box encapsulating the whole tree, i.e., “upper cut-off” (Figure 2, [13,90]). The intercept of the regression line describes the size of the crown of a tree (i.e., crown radius, [19]). The size of the smallest box (“lower cut-off”) was 10 cm in this study. This was selected based on a very liberal estimate of the maximum distance between two neighboring laser points at any given location in the tree because the “lower cut-off” must ensure that no box is empty due to missing data, i.e., it fits in the “unsampled” space of a scanned tree. The algorithm written in Mathematica 12.2 [94] for the computation of the D

_{b}metric is available online as Supplementary Materials.

#### 2.5. The LCC Difference Index and Error Metric Computation

_{b}of the leaf-on and leaf-off point clouds of a tree are equal and there is no contribution of the leaves to the structural complexity of the tree. If LCC > 0, it means that the leaf-on D

_{b}of a tree is greater than the leaf-off D

_{b}of the tree, indicating that leaves increase tree structural complexity. Similarly, if LCC < 0, it means that the leaf-off D

_{b}of a tree is greater than the leaf-on D

_{b}of the tree, indicating that leaves reduce structural complexity, most likely because they occlude the woody components that are not adequately laser-scanned.

_{b}of the point cloud of each study tree after the artificial leaf removal.

#### 2.6. Computation of Other Structural Metrics of Trees

#### 2.7. Statistical Analyses

_{b}of the trees for leaves-on versus -off, and leaves-artificially removed versus -off, were evaluated with t-tests, for each species separately (G. triacanthos, Q. macrocarpa, and M. glyptostroboides), and for all species combined. T-tests were also used to evaluate differences in the mean value of the LCC index, %RE, and D

_{b}of leaf-on, leaf-off, and leaf-removed tree point clouds between the study species. The “sma” function of the standardized major axis regression and testing routines (“smatr”) R package [103] was used to conduct hypothesis tests regarding the intercepts and the slopes of the species sub-population regression lines. In all statistical tests, significant differences were assessed at α = 5%.

_{b}values, and the relationships of the LCC index and the %RE with the tree structural metrics (see Section 2.6) were analyzed using linear regression analysis and relationship strength was quantified with the Pearson correlation coefficient (r); statistical significance was assessed at α = 5%.

## 3. Results

#### 3.1. Structural Complexity of Leaf-On versus Leaf-Off Tree Point Clouds

_{b}of the leaf-on tree point clouds of the G. triacanthos (GLTR) and Q. macrocarpa (QUMA) species (p = 0.0194). However, no significant difference was found between the mean D

_{b}of the leaf-on tree point clouds of the G. triacanthos (GLTR) and M. glyptostroboides (MEGL) trees (p > 5%), or for the MEGL and QUMA trees (p > 5%). Significant differences were found between the mean D

_{b}values of the leaf-off tree point clouds of QUMA and MEGL trees (p = 0.0335), GLTR and QUMA trees (p < 0.001), and MEGL and GLTR trees (p = 0.041).

_{b}of the leaf-on tree point clouds was significantly greater than the mean D

_{b}of the leaf-off tree point clouds (Figure 3) across all study tree species combined (p < 0.001), and for each species separately (GLTR: p = 0.0145; QUMA: p < 0.001; MEGL: p = 0.003). Positive relationships were found between the leaf-on and the leaf-off D

_{b}values of the trees across all species combined (Pearson’s r = 0.72, p < 0.001) and for the GLTR (Pearson’s r = 0.91, p < 0.001) and QUMA species (Pearson’s r = 0.6, p = 0.019) (Figure 4). The relationship between the leaf-on and the leaf-off D

_{b}values for the MEGL trees was not significant (Pearson’s r = 0.52, p = 0.055); however, all data points were above the 1:1 line indicating that the D

_{b}of the MEGL leaf-on point clouds was clearly greater than the D

_{b}of the MEGL leaf-off point clouds, except one tree with an LCC index close to zero (LCC = 0.00064) (Figure 4D).

_{GLTR}= 0.03273) and QUMA (mean LCC

_{QUMA}= 0.05867) trees (p = 0.0261). However, the mean LCC index value was not significantly different between QUMA and MEGL (mean LCC

_{MEGL}= 0.04864) trees (p = 0.4559), or between GLTR and MEGL trees (p = 0.181).

^{th}percentile of path lengths (Pearson’s r = −0.41, p = 0.0051) (Figure 6). The “outlier” MEGL data point in Figure 6 (point with LCC > 0.15 in each graph) did not drive the observed relationships because the patterns did not change after the removal of this data point.

#### 3.2. Box-Dimension of Leaf-Off versus Leaf-Removed Tree Point Clouds

_{b}values of the tree point clouds after the artificial leaf removal for QUMA and GLTR trees (p = 0.001), and GLTR and MEGL trees (p = 0.0105), but no significant difference was found between the mean D

_{b}of the MEGL and QUMA trees after the artificial leaf removal (p = 0.9662).

_{b}of the leaf-off tree point clouds was significantly greater than the mean D

_{b}of the leaf-removed tree point clouds across all study tree species combined (p < 0.001), and for the GLTR trees (p < 0.001). No significant difference was found between the mean D

_{b}of the leaf-off and leaf-removed point clouds for the QUMA trees (p = 0.6382), or the MEGL trees (p = 0.1622). Furthermore, the leaf-removed and the leaf-off D

_{b}values of the QUMA trees were positively correlated (Pearson’s r = 0.65, p = 0.0082), but no significant relationship was found between the leaf-removed and the leaf-off D

_{b}values across all study tree species combined (p > 5%), or for the GLTR and MEGL trees (p > 5%) (Figure 7). The standardized major axis tests showed that the intercept and the slope of the regression line of the QUMA trees was not statistically different from the 0 and 1 values, respectively.

_{b}of the leaf-on tree point clouds was significantly greater than the mean D

_{b}of the leaf-removed tree point clouds (Figure 3) across all study tree species combined (p < 0.001), and for each species separately (GLTR, QUMA, MEGL: p < 0.001).

_{GLTR}= 8.91%) and MEGL (mean %RE

_{MEGL}= 5.06%) trees (p = 0.0057), and between GLTR and QUMA (mean %RE

_{QUMA}= 2.43%) trees (p < 0.001), and also between MEGL and QUMA trees (p = 0.0064).

## 4. Discussion

#### 4.1. Structural Complexity of Urban Trees

_{b}of the above-ground components of tree architecture (i.e., main stem, branching network, and leaves) from TLS point clouds, to determine the above-ground structural complexity of trees growing in urban areas. D

_{b}can help to understand how trees maximize resources uptake for their growth while maintaining their mechanical stability [13,90,93]. From an evolutionary perspective, trees have had to develop an “adaptive” geometry [104] to optimize light capture and minimize self-shading [18,91,92], while balancing with other competing functions, such as maintaining mechanical stability [77] and resisting drought [36]. Open-grown trees are relatively free from light competition due to having fewer tree neighbors [77], so they are more likely to be able to maximize their structural complexity and express their inherent fractal-like architecture than trees growing in forests or plantations [17]. The urban open-grown trees in this study were not directly influenced by shading from neighboring trees or from the relatively short buildings that were near to some of the trees. D

_{b}is sensitive to the external shape and the internal structure of trees [90,93], so differences in D

_{b}can capture meaningful differences in tree architecture and physiological function. Therefore, it is important to consider what the maximum structural complexity could be.

_{b}values significantly lower than 2.72, which is the D

_{b}of the Menger sponge (a mathematical object with the greatest surface to volume ratio, [105]), assuming a tree would maximize its surface area for light capture and gas exchange, while minimizing building costs, in the absence of competition with other plants. In previous studies that quantified the above-ground complexity of trees growing in dense rural forest stands, leaf-on D

_{b}values were consistently lower than 2 [13,19,89,90,93,106]. In this study, the mean D

_{b}of the leaf-on tree point clouds was greater than 2 across all study tree species (see Table 1), indicating a possible structural difference between trees in rural versus urban areas. However, rural forest trees growing in more open conditions and facing less competition for light (e.g., in forest gaps and in thinned forest stands), also had larger D

_{b}values [13,19,106], in some cases exceeding 2 [107]. This suggests a benefit to having an increased D

_{b}with more light and fewer neighbors, but at some level the energy benefits from increased photosynthesis would be minimized due to a high level of self-shading [90]. This supports MacFarlane et al.’s [17] assumption that trees growing in the open, without competition, can more closely approach the theoretical maximum D

_{b}(as characterized in Seidel et al. [90]). In this study, the maximum D

_{b}value observed was 2.23, for a large specimen of M. glyptostroboides in the leaf-on condition (Table 1). So, even the largest, open-grown, urban trees in this study were well below the theoretical maximum of 2.72.

#### 4.2. The Role of Leaves in the Structural Complexity of Deciduous Trees

_{b}metric and greater structural complexity [13,89,90]. In a previous study, the difference between the D

_{b}of the leaf-on and leaf-off point clouds of forest-grown trees was not significant [89]. However, that study followed a mixed approach to generate leaf-off point clouds. More specifically, from the 76 leaf-off point clouds, only 15 point clouds were captured during the leaf-off period and the remaining leaf-off point clouds were created after manual segmentation of leaves from the leaf-on point clouds [89].

_{b}observed in this study was relatively small; the LCC index ranged from 0.00064 to 0.16394 across all species combined, indicating that the largest portion of the total above-ground structural complexity of a tree comes from woody components, e.g., branches. However, D

_{b}is constrained to have values between one and three, so a small change in its value can have significant physiological implications. Seidel et al. [90] found that the crown surface area divided by the woody volume of trees increased as a power function of leaf-on D

_{b}, so that, for example, an increase of 0.2 units in leaf-on D

_{b}resulted in approximately 40 units of increase in crown surface area relative to the woody volume of trees. Similarly, the results here in this study show that a small change in the structural complexity has important implications for urban trees. An increase of approximately 0.05 units in the LCC index was associated with approximately 400 m

^{2}reduction in the branch woody surface area of the study trees (Figure 5). Such a change could have important implications for the mechanical stability of trees, i.e., the branch woody surface area affects the bending moments due to wind drag [30,79,117], for the maintenance respiration of trees that relates to their woody surface area [118,119,120,121,122], and for solar radiation and rainfall interception [123].

_{b}value, with and without leaves, for different types of trees. The negative relationships between the LCC index and the branch surface area and the path length metrics indicate that larger trees, with larger and more “branchy” crowns, have a relatively smaller contribution of leaves to structural complexity (Figure 5 and Figure 6). These results can be interpreted within the framework of the pipe model theory [7] and the West–Brown–Enquist or WBE model [11,124], which explain the fractal-like architecture of trees by assuming a vascular tree structure consisting of pipes [11]. According to these theories, as the size (i.e., woody surface area or length) of the pipes of the vascular system of a tree increases, the structural complexity of the woody skeleton of the tree also increases.

_{b}values because the fractal architecture of urban tree crowns is influenced by both crown and leaf shape [36]. G. triacanthos trees had the smallest contribution of the leaves to the structural complexity (smallest LCC). According to Niinemets and Valladares [125], G. triacanthos is the least shade tolerant of the three species studied (shade tolerance index for G. triacanthos = 1.61, Q. macrocarpa = 2.71, and M. glyptostroboides = 3). Species which are very shade tolerant distribute their leaves more evenly within their crown volume [36], whereas species that are less shade tolerant, e.g., G. triacanthos, have their leaves widely spaced mainly in the crown periphery, in order to increase crown porosity and reduce local self-shading [91]. Furthermore, it has been suggested that inter-canopy variation of leaf traits is predominantly affected by the exposure of leaves to light, which makes the sun leaves that are distributed in the crown periphery smaller, with greater leaf mass per unit area compared to the crown-interior leaves, in order to reduce water loss through transpiration [91,92]. Therefore, the uneven distribution of leaves in the crown volume of the G. triacanthos trees, most of which are small sun leaves in the crown top, could explain why the contribution of leaves in the overall structural complexity was the smallest when compared to Q. macrocarpa and M. glyptostroboides trees.

#### 4.3. The Effect of the Leaf Separation Algorithm on the Structural Complexity of the Trees

_{b}of the leaf-off and leaf-removed point clouds and this species has simple leaves with a single flat and lobbed blade (or lamina) [127], which is associated with important leaf physiological functions, e.g., convection heat dissipation, efficient light interception, and reduced leaf hydraulic resistance [91,111]. The TLSeparation algorithm [85] appears to have miss-classified many points of the woody structure as leaves for the G. triacanthos trees, which have compound leaves with a modular architecture, because the leaf blade consists of several leaflets stemming from the leaf rachis [128,129]. The TLSeparation algorithm added significant noise into characterizations of D

_{b}in M. glyptostroboides trees, which are deciduous gymnosperms and have oblong-shaped needles and branches that are either horizontal or curved upward [130]. We might expect the accuracy of the TLSeparation algorithm for needle-leaved trees to be lower compared with the classification accuracy of broad-leaved trees because needles are linear and it is difficult to resolve an individual needle due to its small size and the dense foliage of conifers [81,83]. In a previous study, it was found that artificial leaf removal using a different leaf separation algorithm (i.e., LeWoS algorithm) resulted in the underestimation of the total woody volume of trees in the generated QSMs, while only the stems and some large branches were detected in coniferous trees [83].

_{b}of the Q. macrocarpa and M. glyptostroboides trees on average according to the t-tests, although the D

_{b}of the M. glyptostroboides trees after the artificial leaf removal was imprecise.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Mäkelä, A.; Valentine, H.T. Crown ratio influences allometric scaling in trees. Ecology
**2006**, 87, 2967–2972. [Google Scholar] [CrossRef] - Mäkelä, A. Implications of the pipe model theory on dry matter partitioning and height growth in trees. J. Theor. Biol.
**1986**, 123, 103–120. [Google Scholar] [CrossRef] - Noordwijk, V.M.; Mulia, R. Functional branch analysis as tool for fractal scaling above- and belowground trees for their additive and non-additive properties. Ecol. Model.
**2002**, 149, 41–51. [Google Scholar] [CrossRef] - Mandelbrot, B.B. The Fractal Geometry of Nature; W. H. Freeman: New York, NY, USA, 1977. [Google Scholar]
- Halley, J.M.; Hartley, S.; Kallimanis, A.S.; Kunin, W.E.; Lennon, J.J.; Sgardelis, S.P. Uses and abuses of fractal methodology in ecology. Ecol. Lett.
**2004**, 7, 254–271. [Google Scholar] [CrossRef] - Malhi, Y.; Jackson, T.; Bentley, L.P.; Lau, A.; Shenkin, A.; Herold, M.; Calders, K.; Bartholomeus, H.; Disney, M.I. New perspectives on the ecology of tree structure and tree communities through terrestrial laser scanning. Interface Focus
**2018**, 8, 20170052. [Google Scholar] [CrossRef] [Green Version] - Shinozaki, K.; Yoda, K.; Hozumi, K.; Kira, T. A quantitative analysis of plant form-the pipe model theory. I & II. Jpn. J. Ecol.
**1964**, 14, 133–139. [Google Scholar] - Chiba, Y. Architectural analysis of relationship between biomass and basal area based on pipe model theory. Ecol. Model.
**1998**, 108, 219–225. [Google Scholar] [CrossRef] - Lehnebach, R.; Beyer, R.; Letort, V.; Heuret, P. The pipe model theory half a century on: A review. Ann. Bot.
**2018**, 121, 773–795. [Google Scholar] [CrossRef] [PubMed] - Valentine, H.T. Tree-growth models: Derivations employing the pipe-model theory. J. Theor. Biol.
**1985**, 117, 579–585. [Google Scholar] [CrossRef] - West, G.B.; Brown, J.H.; Enquist, B. A General Model for the Origin of Allometric Scaling Laws in Biology. Science
**1997**, 276, 122–126. [Google Scholar] [CrossRef] - Eloy, C. Leonardo’s Rule, Self-Similarity, and Wind-Induced Stresses in Trees. Phys. Rev. Lett.
**2011**, 107, 258101. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Seidel, D. A holistic approach to determine tree structural complexity based on laser scanning data and fractal analysis. Ecol. Evol.
**2018**, 8, 128–134. [Google Scholar] [CrossRef] [PubMed] - Jonckheere, I.; Nackaerts, K.; Muys, B.; van Aardt, J.; Coppin, P. A fractal dimension-based modelling approach for studying the effect of leaf distribution on LAI retrieval in forest canopies. Ecol. Model.
**2006**, 197, 179–195. [Google Scholar] [CrossRef] - Da Silva, D.; Boudon, F.; Godin, C.; Puech, O.; Smith, C.; Sinoquet, H. A Critical Appraisal of the Box Counting Method to Assess the Fractal Dimension of Tree Crowns. In Advances in Visual Computing. ISVC 2006; Lecture Notes in Computer Sciences; Springer Science and Business Media LLC: Berlin, Germany, 2006; Volume 4291, pp. 751–760. [Google Scholar]
- Metz, J.; Seidel, D.; Schall, P.; Scheffer, D.; Schulze, E.-D.; Ammer, C. Crown modeling by terrestrial laser scanning as an approach to assess the effect of aboveground intra- and interspecific competition on tree growth. For. Ecol. Manag.
**2013**, 310, 275–288. [Google Scholar] [CrossRef] - MacFarlane, D.W.; Kuyah, S.; Mulia, R.; Dietz, J.; Muthuri, C.; Noordwijk, M.V. Evaluating a non-destructive method for calibrating tree biomass equations derived from tree branching architecture. Trees
**2014**, 28, 807–817. [Google Scholar] [CrossRef] - Eloy, C.; Fournier, M.; Lacointe, A.; Moulia, B. Wind loads and competition for light sculpt trees into self-similar structures. Nat. Commun.
**2017**, 8, 1–12. [Google Scholar] [CrossRef] - Dorji, Y.; Annighöfer, P.; Ammer, C.; Seidel, D. Response of beech (Fagus sylvatica L.) trees to competition—New insights from using fractal analysis. Remote Sens.
**2019**, 11, 2656. [Google Scholar] [CrossRef] [Green Version] - Ferrini, F.; Bussotti, F.; Tattini, M.; Fini, A. Trees in the urban environment: Response mechanisms and benefits for the ecosystem should guide plant selection for future plantings. Agrochimica
**2014**, 58, 234–246. [Google Scholar] [CrossRef] - Iakovoglou, V.; Thompson, J.R.; Burras, L. Characteristics of Trees According to Community Population Level and by Land use in the U.S. Midwest. J. Arboric.
**2002**, 28, 59. [Google Scholar] - Kjelgren, R.K.; Clark, J.R. Microclimates and Tree Growth in Three Urban Spaces. J. Environ. Hortic.
**1992**, 10, 139–145. [Google Scholar] [CrossRef] - Jensen, R.R.; Hardln, J.P. Hardln, A.J. Estimating Urban Leaf Area Index (LAI) of Individual Trees with Hyperspectral Data. Photogramm. Eng. Remote Sens.
**2012**, 78, 495–504. [Google Scholar] [CrossRef] - Kostić, S.; Čukanović, J.; Orlović, S.; Ljubojević, M.; MladenoviĆ, E. Allometric Relations of Sycamore Maple (Acer pseudoplatanus) and its Red Leaf Cultivar (A. pseudoplatanus“Atropurpureum”) in Street and Park Habitats of Novi Sad (Serbia, Europe). J. For.
**2019**, 117, 114–127. [Google Scholar] [CrossRef] - Lu, J.W.; Svenden, E.S.; Campbell, L.K.; Greenfeld, J.; Braden, J.; King, K.L.; Flaxa-Raymound, N. Biological, Social, and Urban Design Factors Affecting Young Street Tree Mortality in New York City. Cities Environ.
**2010**, 3, 1–16. [Google Scholar] [CrossRef] - Moran, M.A. Influence of Adjacent Land Use on Understory Vegetation of New York Forests. Urban Ecol.
**1984**, 8, 329–340. [Google Scholar] [CrossRef] - Krizek, D.T.; Dubik, S.P. Influence of Water Stress and Restricted Root Volume on Growth and Development of Urban Trees. J. Arboric.
**1987**, 13, 47–55. [Google Scholar] - Rhoades, R.W.; Stipes, R.J. Growth of trees on the Virginia Tech campus in response to various factors. J. Arboric.
**1999**, 25, 211–215. [Google Scholar] - Vogt, J.M.; Watkins, S.L.; Mincey, S.K.; Patterson, M.S.; Fischer, B.C. Explaining planted-tree survival and growth in urban neighborhoods: A social–ecological approach to studying recently-planted trees in Indianapolis. Landsc. Urban Plan.
**2015**, 136, 130–143. [Google Scholar] [CrossRef] [Green Version] - Pavlis, M.; Kane, B.; Harris, J.R.; Seiler, J.R. The Effects of Pruning on Drag and Bending Moment of Shade Trees. Arboric. Urban For.
**2008**, 34, 207–215. [Google Scholar] - Bourbia, F.; Boucheriba, F. Impact of street design on urban microclimate for semi arid climate (Constantine). Renew. Energy
**2010**, 35, 343–347. [Google Scholar] [CrossRef] - Nowak, D.J.; Greenfield, E.J. The increase of impervious cover and decrease of tree cover within urban areas globally (2012–2017). Urban For. Urban Green.
**2020**, 49, 126638. [Google Scholar] [CrossRef] - Gregg, J.W.; Jones, C.; Dawson, T.E. Urbanization effects on tree growth in the vicinity of New York City. Nat. Cell Biol.
**2003**, 424, 183–187. [Google Scholar] [CrossRef] - Iakovoglou, V.; Thompson, J.; Burras, L.; Kipper, R. Factors related to tree growth across urban-rural gradients in the Midwest, USA. Urban Ecosyst.
**2001**, 5, 71–85. [Google Scholar] [CrossRef] - McHale, M.R.; Burke, I.C.; Lefsky, M.A.; Peper, P.J.; McPherson, E.G. Urban Forest biomass estimates: Is it important to use allometric relationships developed specifically for urban trees? Urban Ecosyst.
**2009**, 12, 95–113. [Google Scholar] [CrossRef] - Arseniou, G.; MacFarlane, D.W. Fractal dimension of tree crowns explains species functional-trait responses to urban environments at different scales. Ecol. Appl.
**2021**, 31, e2297. [Google Scholar] [CrossRef] [PubMed] - Tigges, J.; Tobia Lakes, T. High resolution remote sensing for reducing uncertainties in urban forest carbon offset life cycle assessments. Carbon Balance Manag.
**2017**, 12, 1–18. [Google Scholar] [CrossRef] [Green Version] - MacFarlane, D.W. Potential availability of urban wood biomass in Michigan: Implications for energy production, carbon sequestration and sustainable forest management in the USA. Biomass Bioenergy
**2009**, 33, 628–634. [Google Scholar] [CrossRef] - McPherson, E.G. Atmospheric carbon dioxide reduction by Sacramento’s urban forest. J. Arboric.
**1998**, 24, 215–223. [Google Scholar] - Nowak, D.J.; Crane, D.E. Carbon storage and sequestration by urban trees in the USA. Environ. Pollut.
**2002**, 116, 381–389. [Google Scholar] [CrossRef] - Casalegno, S.; Anderson, K.; Hancock, S.; Gaston, K.J. Improving models of urban greenspace: From vegetation surface cover to volumetric survey, using waveform laser scanning. Methods Ecol. Evol.
**2017**, 8, 1443–1452. [Google Scholar] [CrossRef] [Green Version] - McPherson, E.G.; Nowak, J.D.; Rowan, A.R. (Eds.) Chicago’s Urban Forest Ecosystem: Results of the Chicago Urban Forest Climate Project; Gen. Tech. Rep. NE-186; U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station: Radnor, PA, USA, 1994; p. 201. [Google Scholar]
- Nowak, D.J. Estimating leaf area and leaf biomass of open-grown deciduous urban trees. For. Sci.
**1996**, 42, 504–507. [Google Scholar] - Heisler, G.M. Energy Savings with Trees. J. Arboric.
**1986**, 12, 113–125. [Google Scholar] - Zeide, B.; Gresham, C.A. Fractal dimensions of tree crowns in three loblolly pine plantations of coastal South Carolina. Can. J. For. Res.
**1991**, 21, 1208–1212. [Google Scholar] [CrossRef] - Zeide, B.; Pfeifer, P. A Method for Estimation of Fractal Dimension of Tree Crowns. For. Sci.
**1991**, 37, 1253–1265. [Google Scholar] - Calders, K.; Adams, J.; Armston, J.; Bartholomeus, H.; Bauwens, S.; Bentley, L.P.; Chave, J.; Danson, F.M.; Demol, M.; Disney, M.; et al. Terrestrial Laser Scanning in forest ecology: Expanding the horizon. Remote Sens. Environ.
**2020**, 251, 112102. [Google Scholar] [CrossRef] - Hopkinson, C.; Chasmer, L.; Young-Pow, C.; Treitz, P. Assessing Forest metrics with a ground-based scanning lidar. Can. J. For. Res.
**2004**, 34, 573–583. [Google Scholar] [CrossRef] [Green Version] - Maas, H.; Bienert, A.; Scheller, S.; Keane, E. Automatic forest inventory parameter determination from terrestrial laser scanner data. Int. J. Remote Sens.
**2008**, 29, 1579–1593. [Google Scholar] [CrossRef] - Moskal, L.M.; Zheng, G. Retrieving Forest Inventory Variables with Terrestrial Laser Scanning (TLS) in Urban Heterogeneous Forest. Remote Sens.
**2012**, 4, 1–20. [Google Scholar] [CrossRef] [Green Version] - Olschofsky, K.; Mues, V.; Köhl, M. Operational assessment of aboveground tree volume and biomass by terrestrial laser scanning. Comput. Electron. Agric.
**2016**, 127, 699–707. [Google Scholar] [CrossRef] [Green Version] - Vonderach, C.; Vogtle, T.; Adler, P.; Norra, S. Terrestrial laser scanning for estimating urban tree volume and carbon content. Int. J. Remote Sens.
**2012**, 33, 6652–6667. [Google Scholar] [CrossRef] - Béland, M.; Widlowski, J.L.; Fournier, R.A. A model for deriving voxel-level tree leaf area density estimates from ground-based LiDAR. Environ. Model. Softw.
**2014**, 51, 184–189. [Google Scholar] [CrossRef] - Jung, S.-E.; Kwak, D.-A.; Park, T.; Lee, W.-K.; Yoo, S. Estimating Crown Variables of Individual Trees Using Airborne and Terrestrial Laser Scanners. Remote Sens.
**2011**, 3, 2346–2363. [Google Scholar] [CrossRef] [Green Version] - Moorthy, I.; Millera, J.R.; Antonio Jimenez Bernic, J.; Zarco-Tejadac, P.; Hub, B.; Chend, J. Field characterization of olive (Olea europaea L.) tree crown architecture using terrestrial laser scanning data. Agric. For. Meteorol.
**2011**, 151, 204–214. [Google Scholar] [CrossRef] - Calders, K.; Newnham, G.; Burt, A.; Murphy, S.; Raumonen, P.; Herold, M.; Culvenor, D.S.; Avitabile, V.; Disney, M.; Armston, J.D.; et al. Nondestructive estimates of above-ground biomass using terrestrial laser scanning. Methods Ecol. Evol.
**2015**, 6, 198–208. [Google Scholar] [CrossRef] - Kankare, V.; Holocaine, M.; Vastaranta, M.; Puttonen, E.; Yu, X.; Hyyppä, J.; Vaaja, M.; Hyyppä, H.; Alho, P. Individual tree biomass estimation using terrestrial laser scanning. ISPRS J. Photogramm. Remote Sens.
**2013**, 75, 64–75. [Google Scholar] [CrossRef] - Olagoke, A.; Proisy, C.; Féret, J.B.; Blanchard, E.; Fromard, F.; Mehling, U.; Menezes, M.M.D.; Santos, V.F.D.; Berger, U. Extended biomass allometric equations for large mangrove trees from terrestrial LiDAR data. Trees
**2016**, 30, 935–947. [Google Scholar] [CrossRef] [Green Version] - Stovall, A.E.; Vorster, A.G.; Anderson, R.S.; Evangelista, P.H.; Shugart, H.H. Non-destructive aboveground biomass estimation of coniferous trees using terrestrial LiDAR. Remote Sens. Environ.
**2017**, 200, 31–42. [Google Scholar] [CrossRef] - Tanhuanpää, T.; Kankare, V.; Setälä, H.; Yli-Pelkonen, V.; Vastaranta, M.; Niemi, M.T.; Raisio, J.; Holopainen, M. Assessing above-ground biomass of open-grown urban trees: A comparison between existing models and a volume-based approach. Urban For. Urban Green.
**2017**, 21, 239–246. [Google Scholar] [CrossRef] [Green Version] - Zheng, Y.; Jia, W.; Wang, Q.; Huang, X. Deriving Individual -Tree Biomass from Effective Crown Data Generated by Terrestrial Laser Scanning. Remote Sens.
**2019**, 11, 2793. [Google Scholar] [CrossRef] [Green Version] - Liang, X.; Kankare, V.; Hyyppä, J.; Wang, Y.; Kukko, A.; Haggrén, H.; Yu, X.; Kaartinen, H.; Jaakkola, A.; Guan, F.; et al. Terrestrial laser scanning in forest inventories. ISPRS J. Photogramm. Remote Sens.
**2016**, 115, 63–77. [Google Scholar] [CrossRef] - Bournez, E.; Landes, T.; Saudreau, M.; Kastendeuch, P.; Najjar, G.; Bournez, E.; Landes, T.; Saudreau, M.; Kastendeuch, P.; Najjar, G. From TLS Point Clouds to 3D Models of Trees: A Comparison of Existing Algorithms for 3D Tree Reconstruction. ISPRS Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2017**, XLII-2/W3, 113–120. [Google Scholar] [CrossRef] [Green Version] - Disney, M.I.; Vicari, M.B.; Burt, A.; Calders, K.; Lewis, S.L.; Raumonen, P.; Wilkes, P. Weighing trees with lasers: Advances, challenges and opportunities. Interface Focus
**2018**, 8, 20170048. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hackenberg, J.; Spiecker, H.; Calders, K.; Disney, M.; Raumonen, P. SimpleTree—An Efficient Open Source Tool to Build Tree Models from TLS Clouds. Forests
**2015**, 6, 4245–4294. [Google Scholar] [CrossRef] - Kaasalainen, S.; Krooks, A.; Liski, J.; Raumonen, P.; Kaartinen, H.; Kaasalainen, M.; Puttonen, E.; Anttila, K.; Mäkipää, R. Change Detection of Tree Biomass with Terrestrial Laser Scanning and Quantitative Structure Modelling. Remote Sens.
**2014**, 6, 3906–3922. [Google Scholar] [CrossRef] [Green Version] - Raumonen, P.; Kaasalainen, M.; Åkerblom, M.; Kaasalainen, S.; Kaartinen, H.; Vastaranta, M.; Holopainen, M.; Disney, M.; Lewis, P. Fast automatic precision tree models from terrestrial laser scanner data. Remote Sens.
**2013**, 5, 491–520. [Google Scholar] [CrossRef] [Green Version] - Lau, A.; Martius, C.; Bartholumeus, H.; Shenkin, A.; Jackson, T.; Malhi, Y.; Herold, M.; Bentley, L.P. Estimating architecture-based metabolic scaling exponents of tropical trees using terrestrial LiDAR and 3D modelling. For. Ecol. Manag.
**2019**, 439, 132–145. [Google Scholar] [CrossRef] - Wilkes, P.; Lau, A.; Disney, M.; Calders, K.; Burt, A.; Tanago, J.G.; Bartholomeus, H.; Brede, B.; Herold, M. Data acquisition considerations for Terrestrial Laser Scanning of forest plots. Remote Sens. Environ.
**2017**, 196, 140–153. [Google Scholar] [CrossRef] - Davison, S.; Donoghue, D.N.; Galiatsatos, N. The effect of leaf-on and leaf-off forest canopy conditions on LiDAR derived estimations of forest structural diversity. Int. J. Appl. Earth Obs. Geoinf.
**2020**, 92, 102160. [Google Scholar] [CrossRef] - Anderson, R.S.; Bolstad, P.V. Estimating aboveground biomass and average annual wood biomass increment with airborne leaf-on and leaf-off LiDAR in Great Lakes forest types. North. J. Appl. For.
**2013**, 30, 16–22. [Google Scholar] [CrossRef] - Bouvier, M.; Durrieu, S.; Fournier, R.A.; Renaud, J.-P. Generalizing predictive models of forest inventory attributes using an area-based approach with airborne LiDAR data. Remote Sens. Environ.
**2015**, 156, 322–334. [Google Scholar] [CrossRef] - Hawbaker, T.J.; Gobakken, T.; Lesak, A.; Trømborg, E.; Contrucci, K.; Radeloff, V. Light detection and ranging-based measures of mixed hardwood forest structure. For. Sci.
**2010**, 56, 313–326. [Google Scholar] - Villikka, M.; Packalén, P.; Maltamo, M. The suitability of leaf-off airborne laser scanning data in an area-based forest inventory of coniferous and deciduous trees. Silva Fenn.
**2012**, 46, 99–110. [Google Scholar] [CrossRef] [Green Version] - Zeide, B. Fractal analysis of foliage distribution in loblolly pine crowns. Can. J. For. Res.
**1998**, 28, 114. [Google Scholar] [CrossRef] - Jackson, T.; Shenkin, A.; Wellpott, A.; Calders, K.; Origo, N.; Disney, M.; Burt, A.; Raumonen, P.; Gardiner, B.; Herold, M.; et al. Finite element analysis of trees in the wind based on terrestrial laser scanning data. Agric. For. Meteorol.
**2019**, 265, 137–144. [Google Scholar] [CrossRef] - MacFarlane, D.W.; Kane, B. Neighbour effects on tree architecture: Functional trade-offs balancing crown competitiveness with wind resistance. Funct. Ecol.
**2017**, 31, 1624–1636. [Google Scholar] [CrossRef] [Green Version] - Antonarakis, A.; Richards, K.S.; Brasington, J.; Müller, E. Determining leaf area index and leafy tree roughness using terrestrial laser scanning. Water Resour. Res.
**2010**, 46. [Google Scholar] [CrossRef] [Green Version] - Vollsinger, S.; Mitchell, S.J.; Byrne, K.E.; Novak, M.D.; Rudnicki, M. Wind tunnel measurements of crown streamlining and drag relationships for several hardwood species. Can. J. For. Res.
**2005**, 35, 1238–1249. [Google Scholar] [CrossRef] - Moorthy, S.M.K.; Calders, K.; Vicari, M.B.; Verbeeck, H. Improved Supervised Learning-Based Approach for Leaf and Wood Classification from LiDAR Point Clouds of Forests. IEEE Trans. Geosci. Remote Sens.
**2020**, 58, 3057–3070. [Google Scholar] [CrossRef] [Green Version] - Vicari, M.B.; Disney, M.; Wilkes, P.; Burt, A.; Calders, K.; Woodgate, W. Leaf and wood classification framework for terrestrial LiDAR point clouds. Methods Ecol. Evol.
**2019**, 10, 680–694. [Google Scholar] [CrossRef] [Green Version] - Wang, D.; Brunner, J.; Ma, Z.; Lu, H.; Hollaus, M.; Pang, Y.; Pfeifer, N. Separating Tree Photosynthetic and Non-Photosynthetic Components from Point Cloud Data Using Dynamic Segment Merging. Forests
**2018**, 9, 252. [Google Scholar] [CrossRef] [Green Version] - Wang, D.; Takoudjou, S.M.; Casella, E. LeWoS: A universal leaf-wood classification method to facilitate the 3D modelling of large tropical trees using terrestrial LiDAR. Methods Ecol. Evol.
**2019**, 11, 376–389. [Google Scholar] [CrossRef] - Wang, D.; Hollaus, M.; Pfeifer, N. Feasibility of machine learning methods for separating wood and leaf points from terrestrial laser scanning data. ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci.
**2017**, IV-2/W4, 157–164. [Google Scholar] [CrossRef] [Green Version] - Vicari, M.B. TLSeparation—A Python Library for Material Separation from Tree/Forest 3D Point Clouds. Available online: https://zenodo.org/record/1147706#.YOYIEJhKjIU (accessed on 7 July 2021). [CrossRef]
- Backes, A.R.; Bruno, O. Plant Leaf Identification Using Multi-scale Fractal Dimension. In Image Analysis and Processing. ICIAP 2009; Lecture Notes in Computer Science; Springer: Berlin/Heidelberg, Germany, 2009; Volume 5716, pp. 143–150. [Google Scholar]
- Borkowski, W. Fractal dimension based features are useful descriptors of leaf complexity and shape. Can. J. For. Res.
**1999**, 29, 1301–1310. [Google Scholar] [CrossRef] - Hartvigsen, G. The analysis of leaf shape using fractal geometry. Am. Biol. Teach.
**2000**, 62, 664–669. [Google Scholar] [CrossRef] - Guzmán, J.A.Q.; Sharp, I.; Alecanstro, F.; Sánchez-Azofeifa, G.A. On the relationship of fractal geometry and tree–stand metrics on point clouds derived from terrestrial laser scanning. Methods Ecol. Evol.
**2020**, 11, 1309–1318. [Google Scholar] [CrossRef] - Seidel, D.; Annighöfer, P.; Stiers, M.; Zemp, C.D.; Burkardt, K.; Ehbrecht, M.; Willim, K.; Kreft, H.; Hölscher, D.; Ammer, C. How a measure of tree structural complexity relates to architectural benefit-to-cost ratio, light availability, and growth of trees. Ecol. Evol.
**2019**, 9, 7134–7142. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sack, L.; Melcher, P.; Liu, W.H.; Middleton, E.; Pardee, T. How strong is intracanopy leaf plasticity in temperate deciduous trees? Am. J. Bot.
**2006**, 93, 829–839. [Google Scholar] [CrossRef] [Green Version] - Abrams, M.D.; Kubiske, M.E. Leaf structural characteristics of 31 hardwood and conifer tree species in central Wisconsin: Influence of light regime and shade-tolerance rank. For. Ecol. Manag.
**1990**, 31, 245–253. [Google Scholar] [CrossRef] - Seidel, D.; Ehbrecht, M.; Dorji, Y.; Jambay, J.; Ammer, C.; Annighöfer, P. Identifying architectural characteristics that determine tree structural complexity. Trees
**2019**, 33, 911–919. [Google Scholar] [CrossRef] - Wolfram Research, Inc. Mathematica; Version 12.2; Wolfram Research, Inc.: Champaign, IL, USA, 2020. [Google Scholar]
- Burt, A.; Vicari, M.B.; da Costa, A.C.L.; Coughlin, I.; Meir, P.; Rowland, L.; Disney, M. New insights into large tropical tree mass and structure from direct harvest and terrestrial lidar. R. Soc. Open Sci.
**2021**, 8, 201458. [Google Scholar] [CrossRef] - Sileshi, G.W. A critical review of forest biomass estimation models, common mistakes and corrective measures. For. Ecol. Manag.
**2014**, 329, 237–254. [Google Scholar] [CrossRef] - Enquist, B.J. Universal scaling in tree and vascular plant allometry: Toward a general quantitative theory linking plant form and function from cells to ecosystems. Tree Physiol.
**2002**, 22, 1045–1064. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Price, C.A.; Enquist, B.J. Scaling of mass and morphology in plants with minimal branching: An extension of the WBE model. Funct. Ecol.
**2006**, 20, 11–20. [Google Scholar] [CrossRef] - Smith, D.D.; Sperry, J.S.; Enquist, B.; Savage, V.M.; McCulloh, K.A.; Bentley, L.P. Deviation from symmetrically self-similar branching in trees predicts altered hydraulics, mechanics, light interception and metabolic scaling. New Phytol.
**2014**, 201, 217–229. [Google Scholar] [CrossRef] [PubMed] - TreeQSM. Quantitative Structure Models of Single Trees from Laser Scanner Data. Version 2.3.0. Copyright (C) 2013-2017 Pasi Raumonen. Available online: https://zenodo.org/record/844626#.Xvz_nW1KjIU (accessed on 7 July 2021).
- Raumonen, P.; Casella, E.; Calders, K.; Murphy, S.; Åkerblom, M.; Kaasalainen, M. Massive-scale tree modelling from TLS data. ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci.
**2015**, II-3/W4, 189–196. [Google Scholar] [CrossRef] [Green Version] - R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2015; Available online: https://www.R-project.org/ (accessed on 7 July 2021).
- Warton, D.I.; Duursma, R.; Falster, D.S.; Taskinen, S. smatr 3—An R package for estimation and inference about allometric lines. Methods Ecol. Evol.
**2012**, 3, 257–259. [Google Scholar] [CrossRef] - Borchert, R.; Slade, N.A. Bifurcation Ratios and the Adaptive Geometry of Trees. Int. J. Plant Sci.
**1981**, 142, 394–401. [Google Scholar] [CrossRef] - Menger, K. Über die Dimensionalität von Punktmengen (Zweiter Teil). Mon. Math. Und Phys.
**1926**, 34, 137–161. [Google Scholar] [CrossRef] - Saarinen, N.; Calders, K.; Kankare, V.; Yrttimaa, T.; Junttila, S.; Luoma, V.; Huuskonen, S.; Hynynen, J.; Verbeeck, H. Understanding 3D structural complexity of individual Scots pine trees with different management history. Ecol. Evol.
**2021**, 11, 2561–2572. [Google Scholar] [CrossRef] - Dorji, Y.; Schuldt, B.; Neudam, L.; Dorji, R.; Middleby, K.; Isasa, E.; Körber, K.; Ammer, C.; Annighöfer, P.; Seidel, D. Three-dimensional quantification of tree architecture from mobile laser scanning and geometry analysis. Trees
**2021**, 1–14. [Google Scholar] [CrossRef] - Fridley, J.D. Extended leaf phenology and the autumn niche in deciduous forest invasions. Nat. Cell Biol.
**2012**, 485, 359–362. [Google Scholar] [CrossRef] - Lechowicz, M.J. Why do temperate deciduous trees leaf out at different times? Adaptation and ecology of forest communities. Am. Nat.
**1984**, 124, 821–842. [Google Scholar] [CrossRef] - Bayirli, M.; Selvi, S. Cakilcioglu, U. Determining different plant leaves’ fractal dimensions: A new approach to taxonomical study of plants. Bangladesh J. Bot.
**2014**, 43, 267–275. [Google Scholar] [CrossRef] - Camarero, J.J.; Sisó, S.; Gil-Pelegrin, E. Fractal dimension does not adequately describe the complexity of leaf margin in seedlings of Quercus species. An. Jardín Botánico Madr.
**2002**, 60, 63–71. [Google Scholar] [CrossRef] - Gazda, A. Fractal analysis of leaves: Are all leaves self-similar along the cane? Ekológia
**2013**, 32, 104–110. [Google Scholar] [CrossRef] [Green Version] - Ianovici, N.; Veres, M.; Catrina, R.G.; Pirvulescu, A.M.; Tanase, R.M.; Datcu, D.A. Methods of biomonitoring in urban environment: Leaf area and fractal dimension. Ann. West Univ. Timişoara Ser. Biol.
**2015**, 18, 169–178. [Google Scholar] - Jobin, A.; Nair, M.S.; Tatavarti, R. Plant Identification based on Fractal Refinement Technique (FRT). Procedia Technol.
**2012**, 6, 171–179. [Google Scholar] [CrossRef] [Green Version] - Moraczewski, I.R.; Borkowski, W. Analyzing leaf shapes with the use of fractal measures and a shape feature description language. In Proceedings of the 3th National Conference on Applications of Mathematics in Biology and Medicine, Madralin, Poland, 16–19 September 1997. [Google Scholar]
- Vlcek, J.; Cheung, E. Fractal analysis of leaf shapes. Can. J. For. Res.
**1986**, 16, 124–127. [Google Scholar] [CrossRef] - Gardiner, B.; Berry, P.; Moulia, B. Review: Wind impacts on plant growth, mechanics and damage. Plant Sci.
**2016**, 245, 94–118. [Google Scholar] [CrossRef] [PubMed] - Bosc, A.; De Grandcourt, A.; Loustau, D. Variability of stem and branch maintenance respiration in a Pinus pinaster tree. Tree Physiol.
**2003**, 23, 227–236. [Google Scholar] [CrossRef] [Green Version] - Kim, M.H.; Nakane, K.; Lee, J.T.; Bang, H.S.; Na, Y.E. Stem/branch maintenance respiration of Japanese red pine stand. For. Ecol. Manag.
**2007**, 243, 283–290. [Google Scholar] [CrossRef] [Green Version] - Kinerson, R.S. Relationships between Plant Surface Area and Respiration in Loblolly Pine. J. Appl. Ecol.
**1975**, 12, 965. [Google Scholar] [CrossRef] - Kramer, P.J.; Kozlowski, T.T. Physiology of Woody Plants; Academic Press: New York, NY, USA, 1979. [Google Scholar]
- Yoneda, T. Surface area of woody organs of an evergreen broadleaf forest tree in Japan and Southeast Asia. J. Plant Res.
**1993**, 106, 229–237. [Google Scholar] [CrossRef] - Weiskittel, A.R.; Maguire, D.A. Branch surface area and its vertical distribution in coastal Douglas-fir. Trees
**2006**, 20, 657–667. [Google Scholar] [CrossRef] - West, G.B.; Brown, J.H.; Enquist, B.J. The fourth dimension of life: Fractal geometry and allometric scaling of organisms. Science
**1999**, 284, 1677–1679. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Niinemets, Ü.; Valladares, F. Tolerance to Shade, Drought, and Waterlogging of Temperate Northern Hemisphere Trees and Shrubs. Ecol. Monogr.
**2006**, 76, 521–547. [Google Scholar] [CrossRef] - Zhu, X.; Skidmore, A.K.; Wang, T.; Liu, J.; Darvishzadeh, R.; Shi, Y.; Premier, J.; Heurich, M. Improving leaf area index (LAI) estimation by correcting for clumping and woody effects using terrestrial laser scanning. Agric. For. Meteorol.
**2018**, 263, 276–286. [Google Scholar] [CrossRef] - Efroni, I.; Eshed, Y.; Lifschitz, E. Morphogenesis of Simple and Compound Leaves: A Critical Review. Plant Cell
**2010**, 22, 1019–1032. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Champagne, C.; Sinha, N. Compound leaves: Equal to the sum of their parts? Development
**2004**, 131, 4401–4412. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Klingenberg, C.; Duttke, S.; Whelan, S.; Kim, M.; Klingenberg, C.; Duttke, S.; Whelan, S.; Kim, M. Developmental plasticity, morphological variation and evolvability: A multilevel analysis of morphometric integration in the shape of compound leaves. J. Evol. Biol.
**2011**, 25, 115–129. [Google Scholar] [CrossRef] - Ng, M.; Smith, S.Y. Evaluating stasis in Metasequoia (Cupressaceae): Testing the relationship between leaf traits and climate. Int. J. Plant Sci.
**2020**, 181, 157–174. [Google Scholar] [CrossRef] - Verbeeck, H.; Bauters, M.; Jackson, T.; Shenkin, A.; Disney, M.; Calders, K. Time for a Plant Structural Economics Spectrum. Front. For. Glob. Chang.
**2019**, 2. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Sample of leaves of the species (

**A**) G. triacanthos (

**B**) Q. macrocarpa (

**C**) M. glyptostroboides.

**Figure 2.**(

**A**) Illustration of the virtual boxes of different sizes that capture the leaf-on point cloud of a M. glyptostroboides tree. (

**B**) Exemplary log–log plot for the computation of the box-dimension metric for the same tree. The slope of the regression line equals the box-dimension of the tree, i.e., D

_{b}= 2.05. The 95% confidence interval has been plotted around the regression line. The number of boxes required to capture all points of the tree point cloud is denoted as N, the size of the length of each box is denoted as s, and the size of the length of the initial box that encapsulates the whole tree is denoted as s_initial.

**Figure 3.**Structural complexity quantified with the box-dimension (D

_{b}) metric of the (

**A**) leaf-on, (

**B**) leaf-off, and (

**C**) leaf-removed point clouds of a G. triacanthos tree (first row), a Q. macrocarpa tree (second row), and a M. glyptostroboides tree (third row). The leaf-off and leaf-removed tree point clouds have been artificially colored with brown color.

**Figure 4.**Relationship between the leaf-on and leaf-off box-dimension values across all study tree species combined, and for each species separately with 95% confidence interval around the regression lines. The black dashed line is the 1:1 line.

**Figure 5.**Relationship between the LCC index and the branch woody surface area of the trees with 95% confidence interval around the regression line. The three species M. glyptostroboides (MEGL), G. triacanthos (GLTR), and Q. macrocarpa (QUMA) have been plotted with different colors and symbols.

**Figure 6.**Relationships between the LCC index and different path length variables with 95% confidence interval around the regression lines. The three species M. glyptostroboides (MEGL), G. triacanthos (GLTR), and Q. macrocarpa (QUMA) have been plotted with different colors and symbols.

**Figure 7.**Relationship between the leaf-removed and leaf-off box-dimension values across all study tree species combined, and for each species separately with 95% confidence interval around the regression lines. The black dashed line is the 1:1 line.

**Figure 8.**Relationship between the % Relative Error (RE) and the maximum branch order of the trees with 95% confidence interval around the regression lines. The species M. glyptostroboides (MEGL), G. triacanthos (GLTR), and Q. macrocarpa (QUMA) have been plotted with different colors and symbols.

**Table 1.**Summary statistics resulting from different measurements of tree size and structural complexity.

Summary Statistics | All Trees | Gleditsia triacanthos | Quercus macrocarpa | Metasequoia glyptostroboides |
---|---|---|---|---|

no. trees | 45 | 16 | 15 | 14 |

DBH (cm) * (mean [min, max]) | 54.1 [15, 122.2] | 52.9 [18.4, 72.8] | 58.8 [29, 83.8] | 50.5 [15, 122.2] |

Height (m) (mean [min, max]) | 13.8 [4.4, 24.1] | 12.5 [10.4, 18.4] | 15.8 [9.1, 21.3] | 13.1 [4.4, 24.1] |

WSA (m^{2}) **(mean [min, max]) | 204.2 [29.9, 467.0] | 265.4 [65.2, 408.6] | 225.4 [60.4, 467.0] | 111.5 [29.9, 250.2] |

Stem WSA (m^{2})(mean [min, max]) | 13 [2.1, 44.6] | 11.4 [4.1, 20.1] | 16.2 [4.7, 30.3] | 11.4 [2.1, 44.6] |

Branch WSA (m^{2})(mean [min, max]) | 191.2 [27.7, 436.7] | 253.9 [61.2, 395.5] | 209.2 [55.7, 436.7] | 100.1 [27.7, 231.8] |

D_{b}-leaf.on(mean [min, max]) | 2.06 [1.89, 2.23] | 2.09 [1.89, 2.20] | 2.03 [1.91, 2.11] | 2.07 [1.94, 2.23] |

D_{b}-leaf.off(mean [min, max]) | 1.97 [1.82, 2.11] | 2.02 [1.84, 2.11] | 1.92 [1.82, 2.04] | 1.97 [1.84, 2.1] |

D_{b}-leaf.rm(mean [min, max]) | 1.9 [1.76, 2.14] | 1.84 [1.76, 2.0] | 1.93 [1.83, 2.03] | 1.93 [1.8, 2.14] |

LCC index (mean [min, max]) | 0.04633 [0.00064, 0.16394] | 0.03273 [0.01371, 0.0762] | 0.05867 [0.00667, 0.10883] | 0.04864 [0.00064, 0.16394] |

%RE (mean [min, max]) | 5.55 [0.17, 14.64] | 8.91 [1.07, 14.64] | 2.43 [0.17, 5.46] | 5.06 [0.92, 11.53] |

Mean Path length (m) (mean [min, max]) | 12.9 [3.7, 23.9] | 14.8 [9.5, 22.0] | 14 [6.9, 23.9] | 9.5 [3.7, 18.6] |

Max. Path length (m) (mean [min, max]) | 22.8 [6.5, 42.7] | 24.8 [17.3, 37.5] | 24.9 [12.3, 42.7] | 18.3 [6.5, 35.8] |

25th % Path length (mean [min, max]) | 10.9 [3, 20.6] | 13.2 [7.7, 18.1] | 11.7 [5.4, 20.6] | 7.4 [3, 14.9] |

# of branch orders (median [min, max]) | 5 [1, 11] | 5 [1, 11] | 5 [1, 10] | 4 [1, 9] |

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Arseniou, G.; MacFarlane, D.W.; Seidel, D.
Measuring the Contribution of Leaves to the Structural Complexity of Urban Tree Crowns with Terrestrial Laser Scanning. *Remote Sens.* **2021**, *13*, 2773.
https://doi.org/10.3390/rs13142773

**AMA Style**

Arseniou G, MacFarlane DW, Seidel D.
Measuring the Contribution of Leaves to the Structural Complexity of Urban Tree Crowns with Terrestrial Laser Scanning. *Remote Sensing*. 2021; 13(14):2773.
https://doi.org/10.3390/rs13142773

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Arseniou, Georgios, David W. MacFarlane, and Dominik Seidel.
2021. "Measuring the Contribution of Leaves to the Structural Complexity of Urban Tree Crowns with Terrestrial Laser Scanning" *Remote Sensing* 13, no. 14: 2773.
https://doi.org/10.3390/rs13142773