# Framework of Virtual Plantation Forest Modeling and Data Analysis for Digital Twin

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## Abstract

**:**

^{2}of the tree growth equation with more than 100 data items could reach more than 87%, which greatly improves the performance and accuracy of the system. Thus, utilizing forestry information networking and digitization to support plantation forest experimentation and management contributes to advancing the digital transformation of forestry and the realization of a smart management model for forests.

## 1. Introduction

_{2}levels [2]. Several countries have developed plantation forests for many different functional purposes, such as ecological public interest forests and industrial timber forests, which have made important contributions to ecological restoration [3], environmental improvement [4], and timber security [5]. Due to the special characteristics of experimental space, plantation forests are often located in remote areas, occupying a large area with numerous trees. Therefore, it is challenging to allocate personnel for plantation forest cultivation and management, which requires a considerable amount of manpower, material, and effort. Moreover, the data obtained through traditional measurement methods may have certain abstraction, and the completeness and accuracy may also be affected. In the current rapidly developing information technology environment, it is essential to integrate plantation forests with emerging technologies, and the development of intelligent forest management [6,7,8] becomes an important issue worth considering and discussing.

## 2. Methods

#### 2.1. Framework Overview

#### 2.2. Virtual Forest Modeling

#### 2.2.1. Point Cloud Data Pre-Processing

#### 2.2.2. Tree Modeling

_{n}, y

_{n}).

_{a}, y

_{a}) at the partition, upward along the normal direction, at a distance h′ to obtain the point a′, h′ can be expressed as:

_{a}takes a value equal to h. We performed the calculation of the downward point a″ similarly. The area with a height of 2h′ is the particle flow transition zone, and the part above the transition zone is the random particle flow zone, and the part below is the empty zone. Generally, the value of h′ is set between the main trunk and multiple branches, thus simulating the characteristics of real trees with few leaves at branches.

_{leaf}is the actual number of particles in the region, F is the initial number of emitted particles, RGB

_{black}is the region blackness value, N

_{tree}is the number of tree model vertices in the region, and k is the percentage of particles emitted under RGB

_{black}. When k = 80% and RGB

_{black}= 50% in the transition particle flow region, a more ideal state of the tree leaves emitting particles can be achieved. The particle emitting operation is performed on the overall trunk model to detect the vertex color marker, and the vertices marked as white will not show the emitting particles. The transition area has a higher value of whiteness, but still shows some particles. We set the emitted particles as leaf-shaped facets and the material as a poplar tree leaf map. We randomized the particle size and rotation angle, and emitted according to the markers to obtain the leaf particle stream. The higher the number of particles initially emitted, the higher the overall number of leaves generated. By controlling the amount of foliage to select the season and time of year of the aspen trees, the virtual scene is more selective.

#### 2.2.3. Virtual Plantation Simulation

#### 2.2.4. Scene Optimization

#### 2.3. Data Analysis

^{2}can represent its prediction quality. Thus, by combining existing breast diameter data with data visualization methods, the trends in tree growth can be intuitively represented in the system, and the future trends and range of the data can also be clearly indicated.

#### 2.3.1. Database Construction

#### 2.3.2. Data Visualization

#### 2.3.3. Specific Data Analysis and Simulation

_{1}takes the value of 8.586 and β

_{1}takes the value of 9.1749. The relationship between DBH and total biomass B

_{S}for a given range is shown in Equation (6):

_{S1}includes trunk, branch, root stump, thick root and thin root parts, α

_{2}takes the value of 1.3121 and β

_{2}takes the value of 0.2907; B

_{S2}increased both leaves and deciduous leaves compared to B

_{S1}, with

**α**

_{3}taking the value of 1.7956 and β

_{3}taking the value of 0.2708. The relationship between DBH and aboveground biomass B

_{A}for a given range is shown in Equation (7):

_{A1}represents the above-ground biomass including only the trunk and branch parts, with values of 0.0319 for α

_{4}and 2.8303 for β

_{4}; B

_{A2}represents the above-ground biomass with four parts: trunk, branch, leaf and deciduous leaf, and the value of α

_{5}is 0.0673 and β

_{5}is 2.5651. The relationship between DBH and belowground biomass B

_{U}for a given range is shown in Equation (8):

_{U}mainly includes two parts, root stump and thick root, and the value of α

_{6}is taken as 3.3678 and the value of β

_{6}is taken as 4.0467.

^{2}is a statistic used to evaluate the degree of fit of the regression line to the sample observations. In the process of regression fitting, the value of the fitted object y is mainly influenced by two factors: one is the different values of the explanatory variable x, and the other is the variation of random factors. Taking linear regression as an example, R

^{2}can be expressed as:

^{2}represents the percentage of the regression sum of squares in the total sum of squares of variance for object y, y

_{i}is the sample observation, and $\overline{y}$ is the point on the regression line as shown in Equation (10). From Equation (9), we know that the range of R

^{2}is (0, 1), and the better fit is when R

^{2}is closer to 1. For Equations (5)–(8), the R

^{2}ranges from 74% to 95% as can be seen from Table 2. When the amount of data n ≥ 100, R

^{2}≥ 87%. The physiological data obtained from real-time calculations based on DBH and tree growth equations are continuous. However, the tree model presents the same visual changes in tree height following the update cycle of Table 1, in which the measurement period of DBH still has an impact on it. In addition, other monitoring data, such as transpiration rate, stomatal conductance, and leaf water potential, which are related to stem sap flow, can also be simulated by this method.

## 3. Results

#### 3.1. Virtual Forest Results

#### 3.2. Plantation Forest System

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Forest site point cloud data. (

**a**) Local point cloud data of poplar plantation. (

**b**) Point cloud data of tree branches and trunks.

**Figure 4.**Delaynay triangulation with the empty circle property. (

**a**) The outer circle of a triangle formed by p1, p2 and p4 contains only the points of the triangle. (

**b**) The outer circle of the triangle formed by p1′, p2′ and p3′ contains p4′ and other vertices.

**Figure 5.**The similarity between vertices is checked according to different weights. (

**a**) Points b1 and b2 have high similarity. (

**b**) Point b′ is merged from b1 to b2, thus simplifying the tree skeleton.

**Figure 6.**Particle flow emission region delineation. O is the coordinate origin. A dividing line is made through point a, which is parallel to the x-axis at a distance h.

**Figure 8.**Under adequate drip irrigation treatment, scatter plots with fitted curves were constructed for some tree diameter at breast height (DBH) data as follows: (

**a**) the fitted curve of DBH and tree height data; (

**b**) the fitted curve of DBH and total biomass (excluding leaves and defoliation); (

**c**) the fitted curve of DBH and above-ground biomass (including only trunk and branches); (

**d**) the fitted curve of DBH and below-ground biomass.

**Figure 9.**Models of Triploid Populus Tomentosa. (

**a**) Tree stem model built using the AdTree method. (

**b**) Tree model obtained by emitting leaf particles from the model in (

**a**). (

**b′**) Optimized model based on the model in (

**b**). (

**c**,

**d**) Other models. (

**c′**) Model optimized based on the model in (

**c**). (

**d′**) Model optimized based on the model in (

**d**).

**Figure 11.**Virtual poplar plantation system’s main interface display. The left and right sides are the task bars for the corresponding functions.

**Figure 12.**DBH-related trend plots of predicted stand status results. The five color icons represent the five different treatments (not discussed in this paper). (

**a**) Trend chart of tree DBH. (

**b**) Trend chart of tree height. (

**c**) Trend chart of total biomass (excluding leaves and defoliation). (

**d**) Trend chart of above-ground biomass (excluding leaves and defoliation). (

**e**) Trend chart of total biomass. (

**f**) Trend chart of above-ground biomass. (

**g**) Trend chart of below-ground biomass.

Plantation Forest Object | Update Status | Update Cycle |
---|---|---|

Poplar tree model | Need to be updated | 4 Months |

Plantation forest terrain | No need to update | 0 |

Models of monitoring equipment already in existence | No need to update | 0 |

Newly added monitoring equipment models ^{1} | Need to be updated | 4 Months |

Other models (weeds, etc.) | Need to be updated | 4 Months |

^{1}These devices may be added to real plantation forests in the future.

Physiological Indicators y | Data Volume n (#) | R^{2} (%) |
---|---|---|

Tree height H (m) | 1088 | 87.11% |

Total biomass B_{S1} (kg) | 100 | 92.70% |

Total biomass B_{S2} (kg) | 100 | 92.28% |

Above-ground biomass B_{A1} (kg) | 100 | 94.94% |

Above-ground biomass B_{A2} (kg) | 100 | 94.12% |

Below-ground biomass B_{U} (kg) | 85 | 74.32% |

Initial Number of Particles Emitted (#) | Actual Number of Particles Emitted (#) | Particle Emission Ratio (%) | Storage Size (KB) |
---|---|---|---|

15,000 | 6677 | 44.5 | 972 |

10,000 | 4443 | 44.43 | 689 |

8000 | 3546 | 44.3 | 553 |

4000 | 1773 | 44.3 | 285 |

**Table 4.**Before and after optimization of the number of points, lines and surfaces of the tree model.

Tree Models | Number of Vertices (#) | Number of Lines (#) | Number of Surfaces (#) | Storage Size (KB) | Frame Rate (FPS) |
---|---|---|---|---|---|

Figure 9b | 141,244 | 669,723 | 235,484 | 13,716 | 97.640 |

Figure 9b′ | 23,777 | 67,116 | 22,372 | 4624 | 74.144 |

Figure 9c | 140,844 | 667,826 | 226,672 | 13,029 | 83.96 |

Figure 9c′ | 15,435 | 43,569 | 9521 | 385 | 75.76 |

Figure 9d | 148,854 | 705,807 | 235,484 | 14,113 | 141.09 |

Figure 9d′ | 10,777 | 30,420 | 6360 | 4206 | 46.02 |

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**MDPI and ACS Style**

Li, W.; Yang, M.; Xi, B.; Huang, Q.
Framework of Virtual Plantation Forest Modeling and Data Analysis for Digital Twin. *Forests* **2023**, *14*, 683.
https://doi.org/10.3390/f14040683

**AMA Style**

Li W, Yang M, Xi B, Huang Q.
Framework of Virtual Plantation Forest Modeling and Data Analysis for Digital Twin. *Forests*. 2023; 14(4):683.
https://doi.org/10.3390/f14040683

**Chicago/Turabian Style**

Li, Wanlu, Meng Yang, Benye Xi, and Qingqing Huang.
2023. "Framework of Virtual Plantation Forest Modeling and Data Analysis for Digital Twin" *Forests* 14, no. 4: 683.
https://doi.org/10.3390/f14040683