# Woody Surface Area Measurements with Terrestrial Laser Scanning Relate to the Anatomical and Structural Complexity of Urban Trees

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{b}) metric, also known as Minkowski-Bouligand dimension [27]. The box-dimension metric is derived from fractal geometry principles [47], and it is a measure of plant material density and distribution [48]. The estimation of the total woody surface area of trees from TLS data does not rely on biological assumptions and it is relatively new [35], for example, Ma et al. [49] used terrestrial laser scanning data to compute the woody to total surface area ratio of trees, to estimate their leaf area index. In general, TLS data have been previously used to mainly study other important aspects of tree allometry and ecology, e.g., stem density, stem profiles, and timber volume [50,51,52,53,54], leaf and canopy properties [55,56,57,58,59,60,61,62,63,64,65,66], above-ground tree biomass and carbon stocks [45,53,67,68,69].

## 2. Materials and Methods

#### 2.1. Urban Tree Data

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

^{3D}X 330 terrestrial laser scanner (FARO Technologies Inc., Lake Mary, FL, USA), which operates with a laser light of 1550 nm wavelength, typical beam divergence 0.19 mrad, and range of 0.6–330 m. Each individual tree was scanned with high resolution from a minimum of four different directions and distances in order to minimize occlusion effects, and five reference target-spheres were placed around each focal 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. [70]. The first two scans of each tree were conducted in opposite directions from distances that allowed the top of the tree to be clearly visible. The other two scans were conducted in opposite directions (perpendicularly to the first two scans) from a closer distance to the focal tree to better capture its branching architecture and get closer views of the main stem. For large trees with complex crowns two or three additional scans were conducted below the tree crown to capture more dense point clouds of the branches. All laser scans were conducted when there was little or no wind.

#### 2.3. Tree Reconstruction from Quantitative Structure Models

#### 2.4. Tree Woody Surface Area Computation

^{2}) was computed as the total surface area of the cylinders that were fitted to the point cloud of each tree (Figure 2). Note: total “woody” surface area in this study is technically the surface area outside of the bark tissues. Next, the total WSA of each tree was separated between the main stem woody component and the branches woody component. The branch WSA was further analyzed by branch order (there was a maximum of eleven branching orders across all species combined), by branch-base diameter classes of 1 cm size from the diameter of the cylinder at the base of a branch (there were 48 classes across all species combined), and by branch-base height classes of 1 m size, based on the height from the base of a tree to the base cylinder of a branch (there were 25 classes across all species combined; described in detail in the Results Section).

#### 2.5. Computation of Other Tree Structural Metrics

_{b}) metric [27], as a direct measure of above-ground structural complexity, calculated directly from the leaf-off point cloud of each tree. D

_{b}has the advantage of not having to apply a QSM to the data, it uses only the original tree point cloud. The D

_{b}metric takes into account the number of boxes that are needed to encapsulate all points of a laser-scanned tree, and how the number of boxes varies with the ratio of the box size to the original box size, which is defined as the smallest box that encapsulates the whole tree [15]. The smallest box encapsulating the entire tree point cloud is the so-called “upper cut-off”, as it represents the largest box applied to the tree for counting the number of consecutive boxes needed. Consecutive boxes always have half the edge length of the previous box so that eight of them fit exactly in the initial box. The smallest box-size among all boxes is the so-called “lower cut-off”, and it was defined to be 10 cm in this study (Figure 3A). It is a very liberal estimate of the maximum distance between two neighboring laser points at any given location in the tree. The “lower cut-off” must ensure that no virtual box is considered empty only because it fits in the “unsampled” space that was not reached by any laser beam of the laser scans. This “unsampled” space may be the result of the diverging beams emitted from the scanner leaving unscanned areas at greater distances to the scanner or simply due to occlusion effects in the tree.

_{b}is equal to the slope of the least-squares line when the logarithm of the number of boxes is regressed against the logarithm of the inverse of the size of a box relative to the size of the initial box [15,27] (Figure 3B). D

_{b}, which is unitless, takes values between one and three. Values smaller than one are only possible if the “lower cut-off” has not been properly chosen (i.e., mean distance between neighboring points is greater than the edge-length of the smallest box). Values of three (or greater) are not possible in reality, since it would imply that a tree is a solid cube. D

_{b}values close to but smaller than three imply trees with greater crown complexity and “space-filling character”, whereas, a perfectly cylindrical stem without branches would have D

_{b}equal to one [27]. Both the path fraction [78] and the D

_{b}[27] metrics are meant to capture the fractal-like nature of trees [42,43,44], which should explain a portion of the variation in their WSA.

#### 2.6. Statistical Analyses

^{2}) of the trees, b is the normalization constant, D

_{b}is the box-dimension (unitless), L is one of the path length metrics in meters that were described previously, c is the scaling exponent parameter of the box-dimension (fixed effect), d is the scaling exponent parameter of the path length metrics (fixed effect), and S

_{c}and S

_{d}are the species random effects added to the candidate models to modify the c and d parameters, respectively, and they have three levels (i.e., G. triacanthos, Q. macrocarpa, and M. glyptostroboides). The error term ($\mathsf{\epsilon}$) has a multiplicative structure, which is additive on a log-log scale. Assumptions of variance homoscedasticity and error normality were checked by plotting the model residuals against the fitted values, and the Q-Q plots and the histograms of the model residuals. The “nlme” function of the linear and nonlinear mixed effects models (“nlme”) R package [81] was used to fit the models. The best models were selected considering both the coefficient of determination (adjusted R

^{2}) and the Akaike information criterion (AIC).

## 3. Results

#### 3.1. Estimated Total and Component Woody Surface Areas

_{GLTR}= 24.1, mean BMS

_{QUMA}= 13.4, and mean BMS

_{MEGL}= 12.1. Furthermore, a strong positive relationship was found between the BMS ratio and the D

_{b}metric of the trees (Pearson’s r = 0.6, p < 0.001).

#### 3.2. Uncertainty Analysis of the Estimated Woody Surface Areas

#### 3.3. Relationships between Woody Surface Area and Metrics of Tree Architecture and Structural Complexity

_{b}metric, and the different metrics that account for the length of all paths from the tree base to each branch tip (Table 2, Figure 8A–H). The strongest positive relationship was found between the WSA of the trees and the 25th percentile of path lengths (Pearson’s r = 0.87, p < 0.001, Figure 8F). However, the relationships between the WSA and the 25th percentile of path lengths, the mean path length, and the 50th percentile of path lengths, were not very different (Figure 8). The best and most parsimonious predictors of WSA (Equation (1)) were the combination of the D

_{b}metric and the 25th percentile of path lengths with species effects (Table 2). The correlation between the D

_{b}metric and the other predictor variables in each model of WSA (Table 2) was not statistically significant (i.e., p > 5%).

## 4. Discussion

#### 4.1. Advances in Urban Tree Surface Area Measurement

_{b}metric.

#### 4.2. Relationships of the Woody Surface Area of Trees Explained by Major Theories of Tree Structure (WBE Model and Pipe Model Theory)

_{b}metric), and “hydraulic” size (quantified by the Euclidean metric of the 25th percentile of the path lengths; see Smith et al. [78]), which are constrained by the genetics of tree species.

_{b}metric [15]. According to the WBE model [42], this pattern could imply efficient respiration rates and sufficient supply for energy demanding units, e.g., leaves, chloroplasts [86], since the inherent fractal character of trees allows them to maximize the scaling of their external surface areas for gas exchange with the atmosphere, while minimizing the internal vascular distances for transferring and allocating the available resources to different organs and tissues [85,86,87].

_{b}metric is reported to be scale and tree-size independent [15,48], and therefore, we can use it to compare trees of different sizes [15]. Further analysis showed that the relationship between the total woody volume of the study urban trees computed from QSMs and the D

_{b}metric was not statistically significant (p > 5%), suggesting that both smaller- and larger-volume trees can be structurally complex. This could mean that architectural changes that occur through the ontogeny of trees, e.g., development of higher order branches and altered stem to branch relationships [48], might explain more complex structures in larger trees, more than their size, per se.

#### 4.3. Anatomical and Physiological Implications of Surface Area Allocation Patterns

_{b}metric), underscoring the contribution of branching to crown complexity [15]. This ratio was found to significantly differ among the studied species, so, in this sense, it describes the resource allocation “decision” of different species to invest in increasing branch versus stem surface areas, as a functional response to urban environments. The squat form of urban trees (i.e., a wide tree crown with a short trunk) gives them mechanical stability against wind loads in cities [88], and reflects the tendency of trees to allocate less resources to growing a taller main stem as the crowding conditions decrease [88,89]. Mäkelä [90] found that “branchiness” of Scots pine (Pinus sylvestris) trees (described as the ratio of total branch cross-sectional area to stem surface area), increased as stand density decreased. Therefore, this pattern appears to hold for trees growing in both rural and urban areas. As such, the branch to stem surface area ratio could be an important component of the plant “structural economics spectrum”, which explains species-structural diversity in terms of tree architectural traits along a spectrum balancing light interception, carbon allocation, and mechanical stability [91].

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Heisler, G.M. Energy Savings with Trees. J. Arboric.
**1986**, 12, 113–125. [Google Scholar] - 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.
- 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] - 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] - Pretzsch, H.; Biber, P.; Uhl, E.; Dahlhausen, J.; Rötzer, T.; Caldentey, J.; Koike, T.; van Con, T.; Chavanne, A.; Seifert, T.; et al. Crown size and growing space requirement of common tree species in urban centres, parks, and forests. Urban. For. Urban. Green.
**2015**, 14, 466–479. [Google Scholar] [CrossRef] [Green Version] - 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] - 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] - Calfapietra, C.; Peñuelas, J.; Niinemets, Ü. Urban plant physiology: Adaptation-mitigation strategies under permanent stress. Trends Plant. Sci.
**2015**, 20, 72–75. [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] - Lambers, H.; Chapin, F.S.; Pons, T.L. Plant Physiological Ecology, 2nd ed.; Springer: New York, NY, USA, 2008. [Google Scholar]
- Pallardy, S.G. Physiology of Woody Plants, 3rd ed.; Academic Press: Cambridge, MA, USA, 2008. [Google Scholar]
- Whittaker, R.H.; Woodwell, G.M. Surface area relations of woody plants and forest communities. Am. J. Bot.
**1967**, 54, 931–939. [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] - 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] [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] - 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] - 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] - MacFarlane, D.W.; Luo, A. Quantifying tree and forest bark structure with a bark-fissure index. Can. J. For. Res.
**2009**, 39, 1859–1870. [Google Scholar] [CrossRef] - 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] - 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, 1014. [Google Scholar] [CrossRef] - 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] - 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] - 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] - Kucharik, C.J.; Norman, J.M.; Gower, S.T. Measurements of branch area and adjusting leaf area index indirect measurements. Agric. For. Meteorol.
**1998**, 91, 69–88. [Google Scholar] [CrossRef] - Halldin, S. Leaf and Bark Area Distribution in a Pine Forest. In The Forest-Atmosphere Interaction; Hutchison, B.A., Hicks, B.B., Eds.; Springer: Dordrecht, The Netherlands, 1985. [Google Scholar] [CrossRef]
- Baldwin, B.C.; Peterson, K.D.; Burkhart, H.E.; Amateis, R.L.; Doughterty, P.M. Equations for estimating loblolly pine branch and foliage weight and surface area distributions. Can. J. For. Res.
**1997**, 27, 918–927. [Google Scholar] [CrossRef] - Damesin, C.; Ceschia, E.; Le Goff, N.; Ottorini, J.M.; Dufrêne, E. Stem and branch respiration of beech: From tree measurements to estimations at the stand level. New Phytol.
**2002**, 153, 159–172. [Google Scholar] [CrossRef] - Meir, P.; Shenkin, A.; Disney, M.; Rowland, L.; Malhi, Y.; Herold, M.; da Costa, A.C.L. Plant Structure-Function Relationships and Woody Tissue Respiration: Upscaling to Forests from Laser-Derived Measurements. In Plant Respiration: Metabolic Fluxes and Carbon Balance, Advances in Photosynthesis and Respiration 43; Tcherkez, G., Ghashghaie, J., Eds.; Springer International Publishing AG: New York, NY, USA, 2017; pp. 92–105. [Google Scholar]
- 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] - Yoneda, T.; Tamin, R.; Ogino, K. Dynamics of Aboveground Big Woody Organs in a Foothill Dipterocarp Forest, West Sumatra, Indonesia. Ecol. Res.
**1990**, 5, 111–130. [Google Scholar] [CrossRef] - Jennings, D.T.; Diamond, J.B.; Watt, B.A. Population densities of spiders (Araneae) and spruce budworms (Lepidptera tortricidae) on foliage of balsam fir and red spruce in east-central Maine. J. Arachnol.
**1990**, 18, 181–193. [Google Scholar] - Zou, J.; Yan, G.; Zhu, L.; Zhang, W. Woody-to-total area ratio determination with a multispectral canopy imager. Tree Physiol.
**2009**, 29, 1069–1080. [Google Scholar] [CrossRef] [Green Version] - Inoue, A.; Nishizono, T. Conservation rule of stem surface area: A hypothesis. Eur. J. For. Res.
**2015**, 134, 599–608. [Google Scholar] [CrossRef] - 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] - 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] - 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] - Van Noordwijk, 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] - Mäkelä, A.; Valentine, H.T. Crown ratio influences allometric scaling in trees. Ecology
**2006**, 87, 2967–2972. [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] - 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] - Mandelbrot, B.B. The Fractal Geometry of Nature; W. H. Freeman: New York, NY, USA, 1977. [Google Scholar]
- 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] - Ma, L.; Zheng, G.; Eitel, J.U.H.; Magney, T.S.; Moskal, L.M. Determining woody-to-total area ratio using terrestrial laser scanning (TLS). Agric. For. Meteorol.
**2016**, 228–229, 217–228. [Google Scholar] [CrossRef] [Green Version] - 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] - 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] - 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] - Danson, F.M.; Hetherington, D.; Morsdorf, F.; Koetz, B.; Allgower, B. Forest canopy gap fraction from terrestrial laser scanning. IEEE Geosci. Remote Sens. Lett.
**2007**, 4, 157–160. [Google Scholar] [CrossRef] [Green Version] - Strahler, A.H.; Jupp, D.L.; Woodcock, C.E.; Schaaf, C.B.; Yao, T.; Zhao, F.; Yang, X.; Lovell, J.; Culvenor, D.; Newnham, G.; et al. Retrieval of forest structural parameters using a ground-based lidar instrument (Echidna (R)). Can. J. Remote Sens.
**2008**, 34, 426–440. [Google Scholar] [CrossRef] [Green Version] - Hosoi, F.; Omasa, K. Estimating Vertical Leaf Area Density Profiles of Tree Canopies Using Three-Dimensional Portable LIDAR Imaging. In Proceedings of the ISPRS Workshop Laser-Scanning, Paris, France, 1–2 September 2009; Volume 9. Part 3/W8. [Google Scholar]
- Polo, J.R.R.; Sanz, R.; Llorens, J.; Arnó, J.; Escolà, A.; Ribes-Dasi, M.; Masip, J.; Camp, F.; Gràcia, F.; Solanelles, F.; et al. A tractor-mounted scanning LIDAR for the non-destructive measurement of vegetative volume and surface area of tree-row plantations: A comparison with conventional destructive measurements. Biosyst. Eng.
**2009**, 102, 128–134. [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] - 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] - Béland, M.; Widlowski, J.L.; Fournier, R.A.; Côté, J.F.; Verstraete, M.M. Estimating leaf area distribution in savanna trees from terrestrial LiDAR measurements. Agric. For. Meteorol.
**2011**, 151, 1252–1266. [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] - 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] - Li, Y.; Guo, Q.; Su, Y.; Tao, S.; Zhao, K.; Xu, G. Retrieving the gap fraction, element clumping index, and leaf area index of individual trees using single-scan data from a terrestrial laser scanner. ISPRS J. Photogramm. Remote Sens.
**2017**, 130, 308–316. [Google Scholar] [CrossRef] - Hu, R.; Bournez, E.; Cheng, S.; Jiang, H.; Nerry, F.; Landes, T.; Saudreau, M.; Kastendeuch, P.; Najjar, G.; Colin, J.; et al. Estimating the leaf area of an individual tree in urban areas using terrestrial laser scanner and path length distribution model. ISPRS J. Photogramm. Remote Sens.
**2018**, 144, 357–368. [Google Scholar] [CrossRef] [Green Version] - Vicari, M.B.; Pisek, J.; Disney, M. New estimates of leaf angle distribution from terrestrial LiDAR: Comparison with measured and modeled estimates from nine broadleaf tree species. Agric. For. Meteorol.
**2019**, 264, 322–333. [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] - 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] - 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] - 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] - 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] - 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] - 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**, 42, 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] [Green Version] - 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] - 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] - 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 9 August 2021).
- 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] - Pinheiro, J.; Bates, D.; DebRoy, S.; Sarkar, D.; R Core Team. Linear and Nonlinear Mixed Effects Models, R package version 3.1-152; 2021. Available online: https://CRAN.R-project.org/package=nlme (accessed on 9 August 2021).
- 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] - Lau, A.; Bentley, L.P.; Martius, C.; Shenkin, A.; Bartholomeus, H.; Raumonen, P.; Malhi, Y.; Jackson, T.; Herold, M. Quantifying branch architecture of tropical trees using terrestrial LiDAR and 3D modelling. Trees
**2018**, 32, 1219–1231. [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] - 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] [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] - 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] [Green Version] - 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] - Weiner, J. Allocation, plasticity and allometry in plants. Perspect. Plant. Ecol. Evol. Syst.
**2004**, 6, 207–215. [Google Scholar] [CrossRef] - Mäkelä, A. A carbon balance model of growth and self-pruning in trees based on structural relationships. For. Sci.
**1997**, 43, 7–24. [Google Scholar] - 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] - Xu, M.; Harrington, T.B. Foliage biomass distribution of loblolly pine as affected by tree dominance, crown size, and stand characteristics. Can. J. For. Res.
**1998**, 28, 887–892. [Google Scholar] [CrossRef] - 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] - Duursma, R.A.; Mäkelä, A.; Reid, D.E.; Jokela, E.J.; Porté, A.J.; Roberts, S.D. Self-shading affects allometric scaling in trees. Funct. Ecol.
**2010**, 24, 723–730. [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] - 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] [PubMed] - Bowler, D.E.; Buyung-Ali, L.; Knight, T.M.; Pullin, A.S. Urban greening to cool towns and cities: A systematic review of the empirical evidence. Landsc. Urban. Plan.
**2010**, 97, 147–155. [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] - Ryan, M.G.; Yoder, B.J. Hydraulic limits to tree height and tree growth. Bioscience
**1997**, 47, 235–242. [Google Scholar] [CrossRef] [Green Version] - Ryan, M.G.; Phillips, N.; Bond, B.J. The hydraulic limitation hypothesis revisited. Plant. Cell Environ.
**2006**, 29, 67–381. [Google Scholar] [CrossRef] - Lindsey, P.A.; Bassuk, N.L. A nondestructive image analysis technique for estimating whole-tree leaf area. Hort. Technol.
**1992**, 2, 66–72. [Google Scholar] [CrossRef] [Green Version] - Nowak, D.J. Estimating leaf area and leaf biomass of open-grown deciduous urban trees. For. Sci.
**1996**, 42, 504–507. [Google Scholar] - Cutini, A.; Matteucci, G.; Mugnozza, G.S. Estimation of leaf area index with the Li-Cor LAI 2000 in deciduous forests. For. Ecol. Manag.
**1998**, 105, 55–65. [Google Scholar] [CrossRef] - Reich, P.B. Body size, geometry, longevity and metabolism: Do plant leaves behave like animal bodies? Trends Ecol. Evol.
**2001**, 16, 674–680. [Google Scholar] [CrossRef] - Peper, P.J.; McPherson, E.G. Evaluation of four methods for estimating leaf area of isolated trees. Urban. For. Urban. Green.
**2003**, 2, 019–029. [Google Scholar] [CrossRef] - McPherson, E.G.; Van Doorn, N.S.; Peper, P.J. Urban Tree Database; Forest Service Research Data Archive: Fort Collins, CO, USA, 2016. [CrossRef]
- Dettman, G.T.; MacFarlane, D.W. Trans-species predictors of tree leaf mass. Ecol. Appl.
**2018**, 29, e01817. [Google Scholar] [CrossRef] [Green Version] - Chianucci, F.; Ferrara, C.; Pollastrini, M.; Corona, P. Development of digital photographic approaches to assess leaf traits in broadleaf tree species. Ecol. Indic.
**2019**, 106, 105547. [Google Scholar] [CrossRef] - Sprugel, D.G. Components of woody-tissue respiration in young Abies amabilis (Dougl.) Forbes trees. Trees
**1990**, 4, 88–98. [Google Scholar] [CrossRef] - Valentine, H.; Amateis, R.L.; Burkhart, H.E.; Gregoire, T.G.; Hollinger, D.Y.; MacFarlane, D.W. Projecting the growth of Loblolly pine in a changing atmosphere. South. J. Appl. For.
**1999**, 23, 212–216. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Leaf-off images of (

**A**) a G. triacanthos tree, (

**B**) a Q. macrocarpa tree, (

**C**) a M. Glyptostroboides tree. All trees have been flagged with a pink-color tape.

**Figure 2.**(

**A**) The leaf-off point cloud of the G. triacanthos tree from Figure 1 (artificially colored with brown color). (

**B**) The QSM of the same tree. (

**C**) A close-up picture of the generated QSM, composed of many cylinders fitted to the point cloud data. The colors denote the different branching orders, i.e., the main stem is colored blue, the first-order branches are colored green, the second-order branches are colored red, etc. Four facets have been used to visualize the QSM cylinders.

**Figure 3.**(

**A**) Illustration of the virtual boxes of different sizes that capture the leaf-off point cloud of a G. tiacanthos tree. (

**B**) The log-log plot for the quantification of the box-dimension metric for the same tree. The regression line slope is the box-dimension of the tree, i.e., D

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

**Figure 4.**Box-plots of branch woody surface area per branch order across (

**A**) all species combined, (

**B**) for G. triacanthos trees, (

**C**) Q. macrocarpa trees, and (

**D**) M. glyptostroboides trees.

**Figure 5.**Box-plots of branch woody surface area per branch-base diameter class across (

**A**) all species combined, (

**B**) for G. triacanthos trees, (

**C**) Q. macrocarpa trees, and (

**D**) M. glyptostroboides trees. The size of each class is 1 cm.

**Figure 6.**Relative vertical distribution (branch base height divided by total tree height) of branch woody surface area (proportion of total branch area) for (

**A**) all study trees, (

**B**) G. triacanthos trees, (

**C**) Q. macrocarpa trees, and (

**D**) M. glyptostroboides trees. The horizontal dashed line is halfway up the tree.

**Figure 7.**Density plots of the coefficient of variation of the woody surface area (CV WSA) for (

**A**) all study trees, (

**B**) G. triacanthos trees, (

**C**) Q. macrocarpa trees, and (

**D**) M. glyptostroboides trees.

**Figure 8.**Relationships between the woody surface area of the study trees (WSA in m

^{2}) and (

**A**) the box-dimension metric, (

**B**–

**H**) different path length metrics with 95% confidence interval around the regression lines. The SpCode refers to the three species codes, i.e., M. glyptostroboides (MEGL), G. triacanthos (GLTR), and Q. macrocarpa (QUMA). The three species are represented with different symbols and colors.

**Figure 9.**Relationships of the woody surface area (WSA in m

^{2}) with the crown surface area (CSA in m

^{2}) of (

**A**) all study trees, (

**B**) G. triacanthos trees, (

**C**) Q. macrocarpa trees, and (

**D**) M. glyptostroboides trees. The data points of the three species are represented with different colors. The 95% confidence interval has been plotted around the regression lines.

**Table 1.**Summary statistics resulting from different measurements of tree size and structural complexity. DBH: Diameter at Breast Height (cm); WSA: Woody Surface Area (m

^{2}); CSA: Crown Surface Area (m

^{2}); CV: Coefficient of Variation; D

_{b}: Box-Dimension; SD: Standard Deviation (m); Min: Minimum (m); Max: Maximum (m).

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

No. of trees | 56 | 18 | 15 | 23 |

DBH (cm) (mean [min, max]) | 53.4 [10.9, 122.2] | 53.4 [18.4, 72.8] | 58.8 [29.0, 83.8] | 49.8 [10.9, 122.2] |

Height (m) (mean [min, max]) | 13.8 [3.8, 24.1] | 12.5 [10.4, 18.4] | 15.8 [9.1, 21.3] | 13.6 [3.8, 24.1] |

CSA.leaf.on (m^{2}) (mean [min, max]) | 611.9 [78.3, 1238.9] | 663.9 [203.6, 1017.4] | 747.8 [172.9, 1238.9] | 407 [78.3, 1217.1] |

Total WSA (m^{2}) (mean [min, max]) | 199.3 [13.9, 467.0] | 267.6 [65.2, 408.6] | 225.4 [60.4, 467.0] | 128.9 [13.9, 372] |

CV WSA (mean [min, max]) | 0.024 [0.005, 0.07] | 0.027 [0.007, 0.054] | 0.024 [0.005, 0.047] | 0.021 [0.007, 0.07] |

Stem WSA (m^{2}) (mean [min, max]) | 12.5 [1.5, 44.6] | 11.3 [4.1, 20.1] | 16.2 [4.7, 30.3] | 11.0 [1.5, 44.6] |

Branch WSA (m^{2}) (mean [min, max]) | 186.8 [12.4, 436.7] | 256.3 [61.2, 395.5] | 209.2 [55.7, 436.7] | 117.9 [12.4, 352.9] |

No. of branch orders (median [min, max]) | 5 [1, 11] | 5 [1, 11] | 5 [1, 10] | 4 [1, 9] |

D_{b} leaf.off (mean [min, max]) | 1.98 [1.82, 2.15] | 2.03 [1.84, 2.11] | 1.92 [1.82, 2.04] | 1.99 [1.84, 2.15] |

Mean Path length (m) (mean [min, max]) | 12.4 [3.7, 23.9] | 14.6 [9.5, 22] | 14.0 [6.9, 23.9] | 9.8 [3.7, 23.8] |

Min Path length (m) (mean [min, max]) | 3.4 [0.8, 7.9] | 4.5 [2.4, 7.0] | 3.7 [2.1, 7.0] | 2.3 [0.8, 7.9] |

Max Path length (m) (mean [min, max]) | 22.1 [6.5, 44.0] | 24.5 [17.3, 37.5] | 24.9 [12.3, 42.7] | 18.5 [6.5, 44.0] |

SD Path length (m) (mean [min, max]) | 3.1 [1, 6.9] | 2.8 [2, 5.1] | 3.6 [1.5, 6.1] | 2.9 [1, 6.9] |

25th % Path length (mean [min, max]) | 10.4 [2.9, 20.6] | 13 [7.7, 18.1] | 11.7 [5.4, 20.6] | 7.7 [2.9, 19.5] |

50th % Path length (mean [min, max]) | 12.5 [3.6, 24.5] | 14.6 [9.8, 23] | 14.1 [6.6, 24.1] | 9.7 [3.6, 24.5] |

75th % Path length (mean [min, max]) | 14.4 [4.4, 28.7] | 16.1 [11.4, 25.1] | 16.5 [8.3, 28.7] | 11.7 [4.4, 28] |

**Table 2.**Woody surface area models with the highest adjusted R

^{2}and lowest AIC values among all candidate models fitted to the data. Tree woody surface area (WSA) was modeled as a power function of different predictor-combinations (Equation (1)), including box-dimension (D

_{b}) and various statistics of path length (L), i.e., mean and the 25th, 50th, and 75th percentiles of path lengths. The character “|spp” denotes that species was added as a random effect, modifying the exponent of each predictor variable in the model. The best model by each statistic is highlighted in bold.

Model | Adjusted R^{2} | AIC Values |
---|---|---|

WSA ~ D_{b} + Mean L|spp. + ε | 0.856 | 599.02 |

WSA ~ D_{b} + 25th % L|spp. + ε | 0.863 | 595.49 |

WSA ~ D_{b} + 50th % L|spp. + ε | 0.855 | 599.78 |

WSA ~ D_{b} + 75th % L|spp. + ε | 0.852 | 601.38 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Arseniou, G.; MacFarlane, D.W.; Seidel, D.
Woody Surface Area Measurements with Terrestrial Laser Scanning Relate to the Anatomical and Structural Complexity of Urban Trees. *Remote Sens.* **2021**, *13*, 3153.
https://doi.org/10.3390/rs13163153

**AMA Style**

Arseniou G, MacFarlane DW, Seidel D.
Woody Surface Area Measurements with Terrestrial Laser Scanning Relate to the Anatomical and Structural Complexity of Urban Trees. *Remote Sensing*. 2021; 13(16):3153.
https://doi.org/10.3390/rs13163153

**Chicago/Turabian Style**

Arseniou, Georgios, David W. MacFarlane, and Dominik Seidel.
2021. "Woody Surface Area Measurements with Terrestrial Laser Scanning Relate to the Anatomical and Structural Complexity of Urban Trees" *Remote Sensing* 13, no. 16: 3153.
https://doi.org/10.3390/rs13163153