New insights into tree architecture from mobile laser scanning and geometry analysis

A ground-based mobile laser scanning (MLS) system was used to obtain 3D point cloud data for accurate measurement and mapping of the environment. The scanning was carried out in February 2020 when the trees were leafless, to ensure free sight on the tree crowns. All 473 trees were scanned carrying the scanner in the hand at around breast height with the arm outstretched while moving at a slow walking pace. We walked in a zig-zag route around the trees and covered two planting rows at a time in each scan by following the direction of the row and finally ending at the exact point where the scan started (up and down the row). We made sure to close the loop every time. By zig-zagging every other tree on the way back, we covered all trees from both sites. All MLS data was processed using GeoSLAM Hub 6 software and subsampled (0.01 m) in Cloud Compare. We obtained records of the periodical circumference measurements for 391 of the individual trees since the time of plantation from the Bavarian State Institute for Viticulture and Horticulture (LWG). Tree circumference was measured using calipers. We calculated the difference between the initial plantation radial measurement and the present radius of the tree individuals as a measure of tree growth and expressed it as annual radial increment. We used an algorithm written in Mathematica (Wolfram Research, Champaign, USA) to determine the structural complexity of each tree individual as shown in Seidel (2018). We used the relative height of maximum horizontal crown area (Rel.Hmaxarea) to describe the top-heaviness of a tree’s geometry. It was calculated based on the height of the maximum horizontal crown area in relation to the total tree height. Therefore, it is a relative measure corrected for tree height and given in percent. The underlying parameter “height of maximum crown area” was calculated as described in Seidel et al. (2011). In short, the tree point clouds were split into horizontal layers of 10 cm in thickness and the area of the convex-hull polygon enclosing all points in each horizontal layer was calculated. The height of the layer with the largest area is considered Hmaxarea (or ‘HCPA’ (height of maximum crown projection area) in earlier studies). The relative Hmaxarea was then given in percent of the total tree height. Tree height was derived from the point cloud as the difference between highest point and lowest point in the point cloud of a tree (zmax – zmin). The secondary data for the places of species origin and latitudinal range were obtained from the database of the European Forest Genetic Resources Program (EUFORGEN 1994) and Van Den Berk Nurseries (Vdberk 2020). Information regarding seed dispersal strategy was obtained from the Royal Botanic Gardens Kew Seed Information Database (SID 2020) as well as from additional literature (Howe and Smallwood 1982; Clark et al. 1999; Loewer 2005; Oyama et al. 2018).

本研究采用地面移动式激光扫描（Mobile Laser Scanning, MLS）系统获取三维点云数据，用于开展环境的精准测量与制图。扫描作业于2020年2月开展，此时树木尚未长叶，可确保树冠视野无遮挡。研究共对473棵树木进行扫描：扫描时手持扫描仪置于约胸高位置，手臂伸展，以缓慢步行速度移动。扫描路线呈之字形沿种植行布设，每次扫描可同时覆盖两行树木，沿行方向行进并最终回到扫描起始点（沿行往返），每次扫描均确保形成闭合环路。返程时对间隔的树木采用之字形扫描，以此覆盖两个样地的全部树木。

所有MLS数据均使用"GeoSLAM Hub 6"软件进行处理，并在"CloudCompare"中以0.01米的步长进行下采样。从巴伐利亚州葡萄栽培与园艺研究所（Bavarian State Institute for Viticulture and Horticulture, LWG）获取了391棵个体树自种植以来的定期周长测量记录。树木周长采用卡尺进行测量。本研究以初始种植时的径向测量值与当前个体树半径的差值作为树木生长量指标，并将其表示为年径向增量。

本研究使用Wolfram Research（美国尚佩恩）基于Mathematica编写的算法，计算每棵个体树的结构复杂度，具体方法详见Seidel（2018）。采用最大水平冠幅面积相对高度（Relative Height of Maximum Horizontal Crown Area, Rel.Hmaxarea）描述树木几何形态的顶重特性：该指标基于最大水平冠幅面积所在高度与树木总高度的比值计算得出，为经树高校正的相对指标，以百分比形式表示。其中"最大冠幅面积高度"这一基础参数的计算方法详见Seidel等（2011）：简言之，将树木点云按10厘米厚度划分为水平层，计算每层所有点集的凸包多边形面积，面积最大的层所在高度即为Hmaxarea（早期研究中亦称"最大冠幅投影面积高度"，即height of maximum crown projection area, HCPA）。随后将相对Hmaxarea以总树高的百分比形式给出。树木高度由点云数据导出，即单棵树点云中最高点与最低点的高程差（z_max - z_min）。

物种起源地与分布纬度范围的二级数据源自欧洲森林遗传资源计划（European Forest Genetic Resources Program, EUFORGEN 1994）数据库与"Van Den Berk"苗圃（Vdberk 2020）。种子传播策略相关信息源自英国皇家植物园邱园种子信息数据库（Royal Botanic Gardens Kew Seed Information Database, SID 2020）及补充文献（Howe and Smallwood 1982; Clark et al. 1999; Loewer 2005; Oyama et al. 2018）。