# Retrieval of Aerodynamic Parameters in Rubber Tree Forests Based on the Computer Simulation Technique and Terrestrial Laser Scanning Data

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site and Data Collection

^{−2}and 88,249 pts m

^{−2}for Rubber Tree 1 (PR107) and Rubber Tree 2 (CATAS7-20-59), respectively. The individual tree height, branch diameter, crown width, single-leaf area and angle between the branches were measured in situ. The tree height was measured using a Vertex IV hypsometer. The branch diameter was measured using a diameter tape. Crown widths were obtained as two values measured along two perpendicular directions from the treetop location. The single-leaf area and the angles between the trunk and branches were measured using an LI-3000C portable area metre and an angle measurement device, respectively.

#### 2.2. Data Preprocessing

#### 2.3. Branch Skeleton Reconstruction

#### 2.3.1. Stratifying Branch Points and Obtaining the Central Points of Each Layer

#### 2.3.2. Adopting the Cylinder Model to Form the Tree Skeleton

- Root node: root node ${c}_{1}^{1}$ is the lowermost central point.
- Bifurcation node: bifurcation node ${n}_{j}^{l}$ (${n}_{j}^{l}\in {c}_{j}^{l}$) has two or more connected child nodes.
- Edge node: edge node ${e}_{i}^{l}({e}_{i}^{l}\in {c}_{j}^{l})$ has no connected child nodes (the nearest central point to ${c}_{j}^{l}$ is in the upper layer).

#### 2.3.3. Recognizing the Trunk and First-Order Branches

#### 2.3.4. Determining Foliage Clumps based on the Trunk and First-Order Branches

#### 2.3.5. Retrieving the Foliage Clump Properties

- LAI is the ratio of the total leaf area to ground area. First, after the single-leaf extraction and the number of leaves in each foliage clump were obtained using the method described in [29], Delaunay triangulation was adopted to deduce the area of each leaf. We acquired the LAI by computing the ratio of the sum of all leaf areas in each foliage clump to the projected area of each foliage clump.
- Crown volume and foliage clump volume: A 3D convex hull algorithm [6] was used to deduce the tree crown volume and volume of each foliage clump.
- Leaf area density: For each foliage clump, the leaf area density was expressed as the ratio of total leaf area to the volume of each foliage clump.
- Gap fraction: The detailed derivation of the gap fraction of each foliage clump is available in Appendix B.

#### 2.3.6. Retrieval of the Wind-Related Parameters in the Rubber Tree Plot

## 3. Results

#### 3.1. Properties of the Two Rubber Trees

#### 3.2. Reconstruction of the Forest Plot Model

#### 3.3. Analysing the Wind-Related Parameters in Forest Plots of Different Clones

## 4. Discussion

## 5. Conclusions

- Trees with large or dense crowns are more vulnerable to windthrow than are trees with smaller open crowns. Crown modification techniques, such as pruning and topping to reduce the effective crown size and density, can considerably reduce the risk of windthrow. Where possible, creating gaps that are too large and exposing individual branches or foliage clumps through these types of cuts should be avoided.
- A wide variety of rubber tree clones is planted in the coastal areas of China. The choice of rubber tree clones should take into account the probability of wind damage. Before extensively promoting a new clone of rubber trees, our method can be used to analyse the forest parameters, determine their aerodynamic parameters under windy conditions and measure the resistance capability of tree clones.
- Quantification of wind damage under different forest cultivation practices (e.g., adjusting the spatial distance between trees or changing the arrangement of trees) in the forest can be explored using our method to analyse to identify suitable silvicultural management strategies for different rubber tree clones.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Rule of Minimal Change in the Growth Angle

**Figure A1.**Our algorithm for performing trunk chain extraction using the rule of minimal change in the growth angle. If bifurcation nodes ${n}_{j}^{layer}$ occur in the trunk chain, we compare the included angle between $\overrightarrow{\left({c}_{k}^{layer-1},{n}_{j}^{layer}\right)}$ and $\overrightarrow{\left({n}_{j}^{layer},{c}_{i}^{layer+1}\right)}$ or $\overrightarrow{\left({n}_{j}^{layer},{c}_{i+1}^{layer+1}\right)}$ and take the trunk chain composed of the central points $\left({c}_{k}^{layer-1},{n}_{j}^{layer},{c}_{i}^{layer+1}\right)$, depending on the rule of minimal angle change, as the trunk.

## Appendix B. Derivation of the Gap Fraction

**Figure A2.**Schematic diagrams illustrating the extinction coefficient calculation. (

**a**) Three-dimensional convex hull construction based on the point cloud data of each foliage clump in Rubber Tree 1 (PR107). (

**b**) Tree rotated counter-clockwise into the required relative position, and (

**c**) nine horizontal slicing planes for Rubber Tree 1 (PR107) with a bounding box for the convenient extinction coefficient inversion computation.

## Appendix C. Standard k-ϵ Two Equation Model

#### Appendix C.1. Momentum Model

#### Appendix C.2. $k-\u03f5$ Model

${\mathit{C}}_{\mathit{\mu}}$ | ${\mathit{C}}_{\mathit{\epsilon}1}$ | C_{ε}_{2} | ${\mathit{\sigma}}_{\mathit{k}}$ | ${\mathit{\sigma}}_{\mathit{\epsilon}}$ |
---|---|---|---|---|

0.09 | 1.42 | 1.92 | 1.0 | 1.3 |

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**Figure 1.**Location of the study area and the two forest plots of rubber trees within the Chinese Academy of Tropical Agricultural Sciences (CATAS) experimental farm in Danzhou, Hainan Island, China. (

**a**) and (

**b**) show the remote sensing images acquired from Google Earth, in which the green rectangles mark the edges of Forest Plot 1 (PR107) and the blue rectangles mark the edges of Forest Plot 2 (CATAS7-20-59). The photos on the right side show the environments of Forest Plot 1 (

**c**) and Forest Plot 2 (

**d**).

**Figure 2.**Scanned point clouds of two typical tree types in two different forest plots were collected by terrestrial laser scanning (TLS) and coloured based on height. (

**a**) Typical rubber tree of Forest Plot 1 (PR107); and (

**b**) typical rubber tree of Forest Plot 2 (CATAS7-20-59).

**Figure 3.**Separating the scanned points of the rubber trees into two parts (i.e., branch and leaf), where red represents branch point clouds (${p}_{i}^{b}$) and green represents leaf point clouds (${p}_{i}^{l}$). The segmentation results include a typical rubber tree of (

**a**) clone PR107 and (

**b**) clone CATAS 7-20-59.

**Figure 4.**Our programming results show the stratification of the branch point cloud and the extracted central points of each branch using a cluster algorithm. For Rubber Tree 1 (PR107), yellow, red and green points represent the calculated central points of the branches in the 29th, 30th and 31st layers, respectively. Blue points represent the original scanned points of the branches, and black lines represent the depicted local 3D tree skeleton between the adjacent layers based on the corresponding central points and the minimum Dijkstra distance.

**Figure 5.**Our programming results show the classification of the central points in each layer into three categories, i.e., root nodes, bifurcation nodes and edge nodes. Extraction results for (

**a**) Rubber Tree 1 (PR107) and (

**b**) Rubber Tree 2 (CATAS7-20-59).

**Figure 6.**Our programming results show the reconstructions of the two rubber trees. (

**a**) Different colours represent the central points of the branches in each layer of Rubber Tree 1 (PR107). (

**b**) Cylinders in different colours with different radii assembled into the tree skeleton according to the directions and the properties of the branches of Rubber Tree 1 (PR107). (

**c**,

**d**) Equivalent figures for Rubber Tree 2 (CATAS7-20-59).

**Figure 7.**Diagrams of the trunk and first-order branch classifications using our algorithm. The trunk chain, which indicated in yellow, connected by the central points of each layer was started from the root node with a nearly straight extension depending on the minimal change in the growth angle. Other first-order branches stemming from the bifurcation nodes on the trunk and the corresponding connection chains are represented in different colours. Classification results for (

**a**) Rubber Tree 1 (PR107) and (

**b**) Rubber Tree 2 (CATAS 7-20-59), where A, B, D and E represent first-order branches and C represents the trunk.

**Figure 8.**Foliage clump segmentation results using a 3D watershed algorithm based on the location of the extracted trunk and different first-order branches, where different colours indicate different foliage clumps. The segmentation results show that the two typical rubber trees have five foliage clumps. Results for (

**a**) Rubber Tree 1 (PR107) and (

**b**) Rubber Tree 2 (CATAS7-20-59).

**Figure 9.**Three-dimensional meshing step for calculating the flow field, in which the rubber tree models are constructed according to the derived forest properties of the foliage clumps and branch attributes. Different colours indicated different foliage clump, where A, B, D and E represent foliage clump belonging to first-order branches and C represents foliage clump belonging to the trunk. Tree model reconstruction results for (

**a**) Rubber Tree 1 (PR107) and (

**b**) Rubber Tree 2 (CATAS 7-20-59). Three-dimensional meshing for the scenarios of (

**c**) Forest Plot 1 and (

**d**) Forest Plot 2 composed with trees of clones PR107 and CATAS 7-20-59 for the discrete solution of the aerodynamic formulas.

**Figure 10.**Horizontal profiles at Z = 7 m showing the velocity, dynamic pressure and turbulent intensity of the wind flow field in the two forest plots using a computer simulation technique. (

**a**,

**b**) Velocity distributions in Forest Plot 1 (PR107) and Forest Plot 2 (CATAS 7-20-59), respectively. (

**c**,

**d**) Dynamic pressure distributions in Forest Plot 1 and Forest Plot 2, respectively. (

**e**,

**f**) Turbulent intensity distributions in Forest Plot 1 and Forest Plot 2, respectively.

**Figure 11.**Vertical profiles at Y = 15 m of the velocity distribution (

**a**,

**b**), dynamic pressure distribution (

**c**,

**d**) and turbulent intensity (

**e**,

**f**) in Forest Plot 1 (PR107) and Forest Plot 2 (CATAS 7-20-59), respectively.

**Figure 12.**Cuboids in red were extracted in the forest plot scenario that pass through the tree crowns and record the dynamic pressure, velocity and turbulent intensity values in (

**a**) Forest Plot 1 (PR107) and (

**b**) Forest Plot 2 (CATAS 7-20-59). (

**c**–

**e**) Area range graphs of the wind-related parameters in the two cuboids, where the red area represents the retrieved wind-related parameters in Forest Plot 1, the blue area represents the retrieved wind-related parameters in Forest Plot 2, the red bidirectional arrows represent the location of typical trees in Forest Plot 1 and the blue bidirectional arrows represent the location of typical trees in Forest Plot 2. Distributions of (

**c**) velocity, (

**d**) dynamic pressure and (

**e**) turbulent intensity in the cuboids.

Tree | Total Number of Leaf Points | Tree Crown Volume (m ^{3}) | Average Single-Leaf Area (cm ^{2}) | Tree Crown Projection Area (m ^{2}) | LAI (m ^{2}/m^{2}) |
---|---|---|---|---|---|

Tree 1 | 117,615 | 168.73 | 75.53 | 16.08 | 3.08 |

Tree 2 | 88,249 | 142.51 | 79.54 | 12.65 | 2.62 |

Tree | Height (m)/ Crown Diameter (m) (E-W) × (N-S) | Branch Diameter (cm) (Our Method/ Field Measurement) | Angle between the Trunk and the First-Order Branch (°) (Our Method/Field Measurement) | |||
---|---|---|---|---|---|---|

$\angle (\mathbf{A},\mathbf{C})$ | $\angle (\mathbf{B},\mathbf{C})$ | $\angle (\mathbf{D},\mathbf{C})$ | $\angle (\mathbf{E},\mathbf{C})$ | |||

Tree 1 | 15.36/ 3.85 × 5.71 | A:21.6/22.1 B:22.3/20.8 C:28.7/30.5 D:25.3/23.9 E:18.7/20.8 | 45.19/ 47.23 | 53.14/ 49.36 | 47.37/ 45.64 | 60.72/ 57.56 |

Tree 2 | 17.13/ 3.07 × 5.59 | A:20.7/22.8 B:16.4/15.7 C:35.1/36.8 D:25.6/27.3 E:18.6/19.5 | 42.36/ 41.78 | 37.89/ 40.25 | 34.47/ 32.92 | 43.91/ 42.24 |

Tree | Foliage Clump Belonging to T/Fb | Number of Leaf Cloud Points | Foliage Clump Volume (m^{3})/Projection Area (m ^{2}) | Number of Leaves [29] | Leaf Area (m^{2})/LAI | Estimated Leaf Area Density (m^{2}/m^{3}) | Gap Fraction |
---|---|---|---|---|---|---|---|

(Our Method/ Field Measurement) | |||||||

Tree 1 | A(Fb) | 20832 | 29.28/3.26 | 1157/1274 | 8.74/2.68 | 0.30 | 0.42 |

B(Fb) | 17411 | 27.65/2.87 | 967/1027 | 7.30/2.54 | 0.26 | 0.53 | |

C(T) | 21548 | 28.86/3.38 | 1197/1007 | 9.04/2.67 | 0.31 | 0.48 | |

D(Fb) | 38216 | 49.12/4.23 | 2123/2242 | 16.03/3.78 | 0.33 | 0.43 | |

E(Fb) | 19608 | 26.78/3.21 | 1089/1026 | 8.23/2.56 | 0.31 | 0.39 | |

Tree 2 | A(Fb) | 11410 | 22.75/2.13 | 543/609 | 4.32/2.02 | 0.19 | 0.63 |

B(Fb) | 14821 | 20.34/2.30 | 706/789 | 5.62/2.44 | 0.28 | 0.61 | |

C(T) | 8852 | 24.70/1.81 | 421/494 | 3.35/1.85 | 0.14 | 0.73 | |

D(Fb) | 11884 | 25.05/2.23 | 565/487 | 4.49/2.01 | 0.18 | 0.75 | |

E(Fb) | 41282 | 55.14/5.11 | 1966/2118 | 15.64/3.06 | 0.28 | 0.57 |

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## Share and Cite

**MDPI and ACS Style**

Huang, Z.; Huang, X.; Fan, J.; Eichhorn, M.P.; An, F.; Chen, B.; Cao, L.; Zhu, Z.; Yun, T. Retrieval of Aerodynamic Parameters in Rubber Tree Forests Based on the Computer Simulation Technique and Terrestrial Laser Scanning Data. *Remote Sens.* **2020**, *12*, 1318.
https://doi.org/10.3390/rs12081318

**AMA Style**

Huang Z, Huang X, Fan J, Eichhorn MP, An F, Chen B, Cao L, Zhu Z, Yun T. Retrieval of Aerodynamic Parameters in Rubber Tree Forests Based on the Computer Simulation Technique and Terrestrial Laser Scanning Data. *Remote Sensing*. 2020; 12(8):1318.
https://doi.org/10.3390/rs12081318

**Chicago/Turabian Style**

Huang, Zhixian, Xiao Huang, Jiangchuan Fan, Markus P. Eichhorn, Feng An, Bangqian Chen, Lin Cao, Zhengli Zhu, and Ting Yun. 2020. "Retrieval of Aerodynamic Parameters in Rubber Tree Forests Based on the Computer Simulation Technique and Terrestrial Laser Scanning Data" *Remote Sensing* 12, no. 8: 1318.
https://doi.org/10.3390/rs12081318