In the research area, Acacia mangium stands are usually planted with the same age, concentrated from 1 to 11 years old, planted with seedlings in pots, according to the technical process of planting and caring for forests issued by Vietnam Paper Corporation, the initial planting density is from 1111 - 1666 trees/ha and during the nurturing process, thinning is usually not done.
2.2. Research objectives
- In theory: Contribute to clarifying the structural, growth and shape models for Acacia mangium plantations in the region to serve as a predictive tool for investigation and assessment of reserves and output.
- In practice: Applying structural, growth and shape models to develop a method to predict the reserve and yield of Acacia mangium forests in Ham Yen - Tuyen Quang area.
2.3. Scope and limitations of the topic
- Research subjects: The research subjects are pure-planted Acacia mangium stands of all ages from 1 to 11 years old. The topic only focuses on studying stands from 3 to 11 years old and not yet impacted by thinning measures.
- About the research area: The areas of concentrated distribution and characteristics for
Research subjects in Ham Yen area - Tuyen Quang
- Research content: Establishing structural laws, growth models and shapes of Acacia mangium forests and providing some application cases as a basis for in-depth research into determining the yield reserves of planted forests in the region.
Chapter 3
RESEARCH CONTENT AND METHODS
3.1. Research content
3.1.1. Study of structural laws and construction of structural models
Acacia mangium
3.1.1.1. The rule for distributing the number of trees according to diameter at breast height (ND)
3.1.1.2. Law of tree number distribution according to height (NH)
3.1.1.3. Correlation rule between height and trunk diameter (H/D)
3.1.1.4. Correlation rule between crown diameter and diameter at breast height (Dt/D 1.3 )
3.1.1.5. Correlation rule between volume of barkless tree trunk with diameter and height of tree trunk (V kv /D 1.3 /H vn )
3.1.1.6. Relationship between regular geometry (f 1.3 ) and tree trunk diameter and height.
3.1.2. Research on the construction of the tree trunk generatrix equation
3.1.3. Research on growth laws and construction of some growth models of Acacia mangium forests
3.1.3.1. Research on the growth laws of individual plants
a. Study on the growth pattern of diameter according to age
b. Research on the law of height growth according to age
c. Study the growth law of tree trunk volume according to age
3.1.3.2. Research on forest growth laws
a. Growth process of forest stand diameter
b. Growth process of forest stand height
c. Volumetric growth process
3.1.4. Applying the laws of structure, growth and shape to predict the yield of Acacia mangium forests
3.1.4.1. Determine f 1.3 of standing tree trunk of Acacia auriculiformis species
3.1.4.2. Formula for determining the volume of standing Acacia mangium trees
3.1.4.3. Prediction of percentage of trees and volume according to size D 1.3 and H vn
3.1.4.4. Determining forest reserves by age
3.1.4.5. Create a volume table
3.1.4.6. Estimated age of maturity for Acacia mangium species in Ham Yen
through the volumetric growth equations of individual trees and forest stands
3.2. Research method
3.2.1. Methodological perspective
Research methodology: research must ensure synthesis and comprehensiveness, thoroughly applying precise mathematical quantitative methods on the basis of faithfully reflecting the biological laws of trees and forest stands.
From the perspective of applied research in forest production and business, when conducting research, it is necessary to inherit the achievements of previous authors as a basis for choosing appropriate mathematical forms, ensuring allowable accuracy and simplicity when applied.
3.2.2. Data collection and processing methods
- Data collection method:
+ Use typical survey methods in Acacia mangium forests after conducting general surveys of different forest stands regarding growth status and ecological conditions.
+ Data collected on typical standard plots (STP) with an area of 1500 m 2. Each age group surveyed 2 STPs (from age 3 to age 11), so the total number of STPs to be surveyed is 18. On each of these STPs, the following indicators are measured: Measure D 1.3 comprehensively, measure H vn and D t ≥ 50 trees respectively.
+ On the forest subject at age 10, randomly select 16 trees to conduct analysis. Divide the tree trunk into 10 equal segments and clamp the glass at the position of diameter with bark and without bark in each segment. The analyzed tree is cut into 1 meter segments, sawed and counted and measured the diameter of annual rings to determine the growth quantities (D, H, V) for each age. In addition, sawed and measured annual rings at the position of diameter 1.3 meters.
+ Inherit data related to the topic such as: Natural conditions, economy, society, land, pests and diseases...
- Data processing method:
+ Using mathematical biology as a tool to apply to processing, analyzing, testing, selecting, and modeling growth processes, structural laws, and shapes of trees and forest stands.
+ Before being analyzed, the raw data of measurement documents was screened using SPSS software. In addition, to check the possibility of combining data of OTCs in different locations but of the same age, the topic used the Mann & Whitney standard for the case of two samples.
+ Measurement data on the OTCs are adjusted and calculated to synthesize the basic investigation factors of each OTC and synthesized by age for all research subjects.
3.2.3. Research method of some forest structure laws
3.2.3.1. Distribution rules of some forest survey factors
Applying Weibull distribution function to describe the structure law of ND, NH of Acacia mangium forest. The reason for using Weibull distribution for research is because this is a probability distribution that allows simulating experimental distributions with decreasing, left-skewed, right-skewed and symmetrical forms. This is also the form of function chosen by the authors to simulate the distribution of ND, NH, ND t for fast-growing planted forest species in our country.
The Weibull distribution is the probability distribution of a continuous random variable with
value range (0 to + ). The density function has the form:
F ( X ) . . X 1 e . X (3.1)
In which: and are two parameters of the Weibull distribution. When the parameters of Weibull change, the shape of the distribution curve also changes. The parameter represents the kurtosis, the parameter represents the skewness of the distribution.
If = 1 the distribution has a decreasing shape;
=3 distribution has symmetric shape;
>3 distribution is right skewed;
<3 distribution is left skewed.
After the data is edited and grouped, a spreadsheet is created to adjust the distribution according to the Weibull function (see Appendix 01).
3.2.3.2. Correlation rules of some investigated factors
The law of correlation between height and diameter:
The mathematical equations representing the relationship between height and diameter are very diverse. With the data collected between D 1.3 and H vn, we need to compare and choose the best form of relationship. Within the framework of the topic with the help of SPSS 11.5 for Windows software, the topic only simulates in the following forms:
Y = a + b.lnX | (3.2) | |
Quadratic Parabolic Function (QUA): | Y = a 0 + a 1 .X + a 2 .X 2 | (3.3) |
Power (POW) function: | Y = aX b | (3.4) |
Compound Function (COM): | Y = ab X | (3.5) |
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From the best relationship form selected for each standard cell, it is used as a basis to determine the average height types.
Relationship between canopy diameter and diameter at breast height: This relationship is modeled by the equation of a straight line:
D t = a + bD 1.3 (3.6)
Based on this relationship, determine the forest canopy through ND distribution.
Correlation rule between volume of barkless tree trunk with diameter and height of tree trunk:
Similar to other investigated factors, there is a relationship between the volume of the barkless tree trunk and the diameter and height of the tree trunk. The topic will test some of the following equations:
(3.7) | |
V = a + bH + cD 2 .H | (3.8) |
V = aD b .H c | (3.9) |
V = a + bD 2 .H | (3.10) |
From the selected equation, the volume of each individual Acacia mangium tree or forest stand in the study area can be determined.
Relationship between regular geometry (f 1.3 ) and tree trunk diameter and height:
From the research of previous authors, the topic will test some of the following types of relational equations:
- Relationship between f 1.3 and d:
f 1,3 = a+ b/d 2 1,3 (3.11)
- Relationship between f 1.3 with d and h:
f 1,3 = a + b/d 2 1,3 .h vn (3.12)
- Relationship between height (hf 1,3 ) and height (h):
h vn .f 1.3 = a + bh vn (3.13)
- Based on the experience of previous authors, it is assumed that: between the height and the height of the forest trees there is a relationship according to the form (3.13), between the height and the diameter of the forest trees there is a relationship according to the form (3.2). From that, it can be inferred that:
h vn f 1,3 = a + b.[a' + b'.ln(d 1,3 )]
h vn f 1,3 = a + b.a' + b.b'.ln(d 1,3 )
h vn f 1,3 = a 0 + a 1 .ln(d 1,3 ). With: a 0 = a + b.a' and a 1 = b.b'
From the above analysis, the topic tests the relationship between height (hf 1.3 ) and diameter (d 1.3 ) in the following form:
h vn .f 1,3 = a + b.ln(d 1,3 ) (3.14)
3.2.3.3. Research method of the relationship between investigated factors
Based on the experimental chart, select the theoretical equation form. Nonlinear equations are converted to linear form. Use the least squares method to estimate parameters. Calculate statistical indicators such as: correlation coefficient (R) or coefficient of determination (R 2 ), regression standard error (H y/x ) ... Check the existence of parameters, correlation coefficients and relationship forms using Fisher's F criteria, Student's t criteria at the significance level
= 0.05 on SPSS [28] or Excel [17] software.
The chosen equation must be highly accurate, simple and accurately reflect the biological laws of the studied plant species. The canonical equation has the highest coefficient of determination, the smallest regression standard error and the probability of the criterion for testing the existence of regression coefficients is less than 0.05.
3.2.4. Method of constructing the generatrix equation of a tree trunk
From the measurement data on the standard trees cut at the right angle, calculate the Koi tapering coefficient with and without bark at the i-th 10th position of the tree trunk.
y = Koi Couple
D 01
(3.15)
with: Koi(shell) = D oi(shell) /D 01(shell) and Koi(no shell) = D oi(no shell) /D 01(shell) .
To establish the generatrix equation, it is necessary to calculate the Koi :
Koi =
n
1
nj 1
Koi ( j )
(3.16)
After calculating the Koi with and without shell, proceed to determine the appropriate equation for the tree trunk generatum. The tree trunk generatum equation has the general form:
y = a 0 + a 1 x + a 2 x 2 + ... + a n x n (3.17)
In which: y: is K oi
x: is the corresponding tenth value of the height (from the top)
with diameter D oi
a i : are the parameters of the equation n: is the degree of the equation
Proceed to establish the generatrix equations for barked and barkless tree trunks at different levels.