Equations Expressing the Relationship Dt/d1,3 In the Form: Dt = A + B.d1,3 At Different Ages

n 2

n

2  W

 W bi . b i 

. b 2 i  1 

n

(4.3)

b

i  1

ball​

n

W ball

i  1

With W bi being the weight of the regression coefficient b i and W bi = 1/Sb i 2 ; where Sb i 2 is the variance of the regression coefficient b i . If  2 is calculated   05 2 and the table with k = n-1 degrees of freedom is consulted, then the regression coefficients b i are homogeneous, meaning that the hypothesis H 0 is accepted, then the simple linear regression equations will be combined into a common equation.

After establishing the correlation equations at different ages, check the homogeneity of the regression coefficients b i . The results show that  2 = 56.05 >  2 05

= 15.5 (with k = 8). Thus, it is not possible to determine a general equation expressing the relationship D t /D 1.3 for all Acacia mangium stands of different ages. In other words, it is only possible to use the equation expressing the relationship D t /D 1.3 for each age in Acacia mangium stands.

4.1.7. Correlation rule between volume of barkless tree trunk and diameter

and tree height (V kv /D 1.3 /H vn )

Volume is an important factor and the target of forest resource investigation. Like other factors, there is always a close relationship between the volume of the barkless tree trunk and the diameter and height of the tree trunk, expressed in many different mathematical equations. The topic will test some popular equations, used by many domestic and foreign experts. The tested equations are in the form: (3.7), (3.8), (3.9), (3.10).

To establish the relationship between the volume of the barkless tree trunk and the diameter and height of the tree trunk, the study used data from 16 analytical trees (including 144 trees from 2 to 10 years old). The processing results are summarized in table (4.7) as follows:

Table 4.7 : Summary of parameters when analyzing regression and correlation

of function forms

PT form

Note: R 2 has been linearized.

Table 4.7 shows that all four equations give very high coefficients of determination and small regression variances. This shows that there is a very close relationship between the volume of the barkless tree trunk and the height and diameter of the tree trunk.

y

Of the four equations above, form (3.9) has the highest coefficient of determination (R 2 = 0.9932) and the smallest regression variance (S 2 = 6.68E-5). Therefore, the topic decided to choose function (3.9) to describe the relationship between the volume of the barkless tree trunk and the diameter and height of the tree trunk. The specific equation is:

V = 3.19E-5.D 1.839214 .H 1.21037 (4.4)

4.1.7.1. Checking systematic errors of the V/D/H relation equation

To select a suitable regression equation to represent the V/D/H relationship, in addition to relying on statistical indicators such as coefficient of determination, regression variance, ... the topic uses the currently popular standard and has also been included in SPSS software, the Durbin - Watson d standard to check the systematic error of equation (4.4). This standard has the formula:

2

  e i e i  1 

i

d  e 2

(4.5)

In which: the sum sign in the numerator runs from 2 to n because an observation point is lost when taking the difference of successive observations. And the sum in the denominator is QE in the table.

^  2

analysis of variance with

QE    y  y 

. Range for accepting the null hypothesis H 0



There is no negative or positive autocorrelation or no systematic error as follows:

Assume

In which: G t and G d are looked up in table [29] corresponding to n being the sample size, k being the number of independent variables with significance level  = 0.05.

The advantage of this method of calculating systematic errors is that it does not require additional survey capacity beyond the sample capacity of the equation to check. In addition, the calculation is simple and accurate. But the disadvantage is that there are some regions that cannot be concluded.

The result of checking equation (4.4) is d = 1.843. With n = 144, k = 2, looking up the table, we get G d = 1.076 and G t = 1.760. Thus, d is in the range G t < d < 4-G t, which means that the equation does not have negative or positive autocorrelation, or in other words, the equation does not have systematic errors.

4.1.7.2. Check the suitability of the V/D/H relationship equation

To test the accuracy of formula (4.4), the topic used the calculated data of 28 felled trees (from age 4 to age 10) that did not participate in the equation establishment process. The data of these felled trees were inherited from Ham Yen Forestry and analyzed in 2006. By the method of determining the error

V expression V observe​

V observe

The relative (∆%) between the actual volume of the tree trunk and the volume obtained from the value of D 1.3 , H vn of the tree is calculated using formula (4.4):

 v % 

*100

(4.6)

The test results show that: the relative error ranges from 0.1% to 18.62%, the average relative error is 8.75%, less than 10% (which is the allowable relative error in forest survey), the number of positive errors is 17, the number of negative errors is 11. This proves that formula (4.4) has the necessary accuracy. This equation can be used to determine the volume of each individual Acacia mangium tree or forest stand in the research area.

4.1.7.3. Correlation between volume of barked tree trunk and volume of barkless tree trunk

From formula (4.4) the volume of the tree trunk can be determined, however, it is only the volume of the tree trunk without bark. To determine the volume of the tree trunk with bark, the topic conducts a study on the relationship between the volume of the tree trunk with bark and without bark for Acacia mangium in the research area.

From the data of V cv and V kv of 44 felled trees of different ages, site conditions and densities. Of which: 16 felled trees at the age of 10, combined with the inherited data of Ham Yen Forestry, there are 28 trees at the ages from 4 to 10. Through the chart to detect the rule shown in figure (4.9):

etc

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

0

0.1

0.2

0.3

VK

0.4

Figure 4.9 : Diagram showing the relationship between V cv and V kv

Based on the above point cloud diagram, the topic has established the relationship between the volume of the barked tree trunk and the volume of the barkless tree trunk through the form of a straight line relationship. The calculation results on Excel are specifically expressed in the following equation:

V cv = 0.008867 + 1.077386.V kv (4.7)

The correlation coefficient of the equation is very high (R = 0.996), the regression standard error is small (S y = 0.00894). The regression coefficients a and b both exist (because there is probability P(a)

= 2.47E-03 and P(b) = 6.16E-46 are both less than 0.05). Thus, the relationship between

The correlation between the volume of a tree trunk without bark and the volume with bark is very close. In other words, determining the volume of a tree trunk with bark from the volume of a tree trunk without bark (or vice versa) is appropriate and gives high accuracy.

4.1.8. Relationship between regular geometry (f 1.3 ) and tree trunk diameter and height

Shape is an important factor in the volume of a tree trunk but cannot be measured directly on the tree like its diameter or height. Therefore, understanding shape has special significance in the theory and practice of tree measurement.

The purpose of determining the shape is to calculate the volume of a standing tree trunk, so it is not possible to use known conceptual formulas and calculation formulas for this purpose. The shape on a standing tree trunk can only be determined through its relationship with easily measurable factors on the trunk.

When determining the forest reserve, it is possible to study to find an average numerical value for use in calculations that will be simpler while still ensuring accuracy. However, this value will deviate from the actual value of each individual tree. Based on the above reasons, to solve the problem of determining f 1.3 for each individual tree, the topic conducts research on its relationship with easily measured factors on the tree trunk, which are d 1.3 and h vn .

The research material is the 10-year-old trees (planted forest in 2005).

1997), with a sample size of 16 trees, it is sufficient to calculate the characteristics.

necessary sample. Because according to Dong Sy Hien (1974) [10], when studying the shape of natural forest tree trunks, he used units with 10 or more standard trees.

However, when studying for ages before 10, the factors f 1.3 and d 1.3 including bark could not be calculated (because when analyzing the diameter measured at the tree rings, they are diameters without bark). In practice, investigating Acacia mangium forests, usually the values ​​f 1.3 including bark and d 1.3 including bark are meaningful. To solve this problem, the topic establishes the relationship between f 1,3 bark trees and f 13 barkless trees, and the relationship between d 1,3 bark trees and d 1,3 barkless trees, from which f 1,3 and d 1,3 bark trees are deduced for ages before 10. The data to establish these relationships are 16 trees at age 10. In addition, to increase the accuracy of the research results, the topic has inherited the data of 28 analytical trees at Ham Yen Forestry - Tuyen Quang (from age 4 to age 10 - each age has 4 analytical trees). Thus, the total number of trees to establish the relationships of f 1,3 and d 1,3 is 44 trees at ages 4 to 10.

4.1.8.1. Correlation between f 1.3 of barked trees (f 1.3 Cv) and f 1.3 of barkless trees (f 1.3 Kv)

Based on the data of 44 pairs of barked and barkless trees, the study established a correlation between f 1.3 Cv and f 1.3 Kv for Acacia mangium species in the study area. The results calculated on Excel software showed a very high correlation coefficient (R

= 0.922), the regression standard error is small (S y = 0.023), the equation and the regression coefficient b exist (because the probability P(Fr) = 6.31E-19 and P(b) = 6.31E-19 are both less than 0.05), but the coefficient a is very small (a = 0.008417) and does not exist (probability P(a) = 0.79 > 0.05). The equation is adjusted and gives the following correlation results:

f 1.3 Cv = 0.999254.f 1.3 Kv (4.8)