Developed of Taper Equation and Volume for Eucalyptus camaldulensis Dem. in the Nineveh Region

This study aimed to estimate a taper equation for eucalyptus trees growing in Nineveh Governorate, it is used in forest inventory or management planning systems, giving information about the diameter at any point along the main stem of the tree. Data were collected from three naturally growing trees for diameter at breast height, total height, and diameter at different levels, starting from 0.5 m above ground level, with distances of half a meter along the main stem, using computer and regression methods. different. Linear and non-linear. In the preparation of the taper equation, as well as the use of statistical measures, namely, the coefficient of determination R2, the standard error attributed to the S.E rate, in the test of the best taper equation, and through the comparison between equations through statistical measures, we were able to obtain the following taper equation: d = 14.2299 * hi -0.1873 And by taking the integration of the taper equation, we got an equation for estimating the size of eucalyptus trees, which is:V1 = 0.02542(hi)0.6254.


Introduction
Forests are renewable natural resources that have many benefits for humanity that cannot be underestimated.Trees improve the environment, soften the atmosphere and lower the water temperature.Forests also have economic, preventive, environmental, and tourism benefits [1].Measuring the volume of the main stem of the tree is one of the variables.It is difficult to measure in forest measurements, due to the irregular shape of the main stem of the tree, as most of the trunks contain visible bends and clumps, or their shape is affected by the surrounding environmental conditions [2].The volume of trees is estimated by the basic characteristics of forests in general, such as diameter and height, but this estimate is often associated with errors resulting from the difference in the shape of tree trunks, as a result of changes in the growth rate of diameter at different heights of the stem and changes in the longitudinal growth of trees [3].Study of the shape of the stem of different types of trees for years several researchers who tried to explain their shape therefore, there is a lot of literature related to the shape of the tree and the shape of the stem, and one of the important reasons for continuing to study this subject is the lack of a theory developed that can explain all the various shapes that can be The other reason is that the taper equations are indispensable tools for predicting the commercial volume of standing trees, and for giving information about marketable heights and 1259 (2023) 012052 IOP Publishing doi:10.1088/1755-1315/1259/1/012052 2 diameters, and the first attempt to represent the shape of trees was made by [4], and since then several Forms and types of trunk profile models.At first, the models were relatively simple but with the advent of computers in the 1970s more complex models were used to derive the taper functions in search of better results until the mid-1970s researchers tried to express the entire profile of the leg using a single equation several good models were developed from this type, but they often do not describe well the area near the base or top of the stem, therefore, alternative procedures were investigated [5], were the first to apply a segmented model regression to model the taper of the stem, using this model, where the stem is divided into Three sections are represented by three separate submodels, which are then sliced together at two "joining points" to produce a comprehensive polynomial taper function.The size of the trunks can be estimated after preparation by the integration method, so we thought that the subject of our study would be the preparation of a taper equation for eucalyptus trees, and then Calculating the volume, by taking the integration of the taper equation, and thus we can measure the volume of the trees.

Materials and Methods
This study was conducted in Nineveh Governorate, which is located at the intersection of longitude 15.43 east with latitude 35.36 north, at an altitude of 223 m above sea level.mm.Three Eucalyptus camaldulensis Dem.trees were selected, then these trees were cut at a height of (30) cm (the height of the stem), after which the branches were separated from the main stem, and measurements of the diameter were taken from the height of the stem, then every (50) cm a measurement was taken of the diameter to the end of the main stem as was done Measure the total height of the tree and the diameter from the level of the breast height, then the tree was cut in the form of trunks, the length of each trunk is (1) m for the three trees, then prepare table (1) which shows the data of each tree.
Table 1.Eucalyptus tree data from the Nineveh region.Measurement of volume by integration method is one of the methods that depend on the estimation of the (stereoscopic) geometry.The two-dimensional surfaces, when they rotate a full circle around a fixed axis, form a geometric body in space Fig.In the triangle geometric figure, when it rotates a complete revolution on a fixed axis in space, the result of the rotation process is the volume of a geometric body known as the cone, while the rotation of the rectangle results in the volume of a geometric body known as the cylinder, and accordingly, the rotation of the longitudinal section of a tree will result in the volume of this tree Fig. (1 a,b,c ), When applying the specific integration to calculate the sizes of trees, a taper equation must be available for the tree whose size is to be estimated.The taper equation is an equation that estimates the diameter depending on the height of the measurement point, so its function appears as follows:

whereas : d i = the diameter at any point H-h = height of the measurement point
The integration method is one of the methods with acceptable accuracy in the estimate, and the accuracy of this method depends on the accuracy of the pre-prepared tapering equation.

Statistical Measures
Coefficient of determination ( R 2 ): The coefficient of determination is a measure of the quality of the prepared model and can be obtained from the analysis of the variance table as follows: R 2 = (Explained variations / Total variations ) =( SSR / SST ) whereas : SSR = sum of squared errors SST = sum of squares of the grand It explains the specific percentage of the variances in the dependent variable (Y) with a linear or nonlinear relationship for the model used, while the remaining percentage of unexplained variances in the model is due to random factors, such as if there are important variables that were not included in the prepared model and in general the closer the value of R 2 out of (1) indicates the quality of the model.Standard Error ( S.E): It is a measure of the dispersion of the observed values from the regression line of the prepared model.The small value of this indicator and its closeness to zero indicates the quality of the regression line's representation of the model spread points.Therefore, whenever the values are close to zero, the prepared model is good, and its value can be found through the relationship: √ whereas : S 2 = variance.n= several observations.

Residual Analysis
To illustrate the random errors of the data representing the model we can represent it graphically; This is by fixing the deviation between the estimated values and the real values from the relationship for the various observations on the vertical axis and the values estimated from the equation on the horizontal axis and drawing a relationship between them.A problem as a result of the heterogeneity of the random error variance, and at the same time the model expresses the data accurately, in addition to that, the lack of data appearing in different forms of distribution represents the lack of a partial correlation between the independent variables themselves and the dependent variable, so the data appears randomly distributed in the form of (scatter plots ( gives an image that the model is good to use.

Results and Discussion
Calculating the size of forest trees is one of the most important variables that foresters care about because of its impact on the various developmental processes that take place in forest trees.Evaluating the wood product of trees comes in the priorities of administrative work in forests, so the process of accurately measuring it comes at the forefront of priorities.Eucalyptus is one of the trees introduced to Iraq and is widely cultivated in various artificial trees and has proven successful [6].This study came to evaluate the different methods of measuring the volume of this type of tree, by taking three naturally growing trees and the main stem part of each of them into parts.With a length of one meter, one and a half meters again, and dimensions were taken for these parts, as shown in Tables (2).It is noted from Table (2) that the quotient of the shape of the three sample trees is (0.59, 0.64, 0.5) respectively [7], and through these numbers, we find that the quotient of the shape of these trees was close to some extent, that is, the degree of taper of the trunks of these trees They grew close together, but there are differences, and this is what we notice in the heights of these trees, which were (15.5, 17, and 21) m, respectively [8].From that, we note that height has a relationship with the degree of taper.The first and second trees are close in height.And outside the division of the shape, it differed as a result of the height of the third tree, and this proves the diameters of these trees at chest level (16, 22.4, 29.6) cm, respectively.To some extent, and because of the existence of this discrepancy in the degrees of taper, and to increase the accuracy of calculating the size of the pieces at equal distances, which is one and a half meters, and to overcome this discrepancy and increase the accuracy of the measurements of the pieces, however, we determined the average for the diameters of the pieces at the largest part (upper) d 1 and the diameter at the average d 2 and the diameter at the upper (lower) d 3 part of the wooden piece.At the same time, the average diameters were taken for cutting trees, so the averages of the largest, average and minimum diameters were (11.5, 11.1, 10.9) cm and (17.2, 16.6, 15.7) cm and also (19.3, 18.6, 18.0).) cm for the three trees in a row and pieces with a length of 1 meter, we notice that the taper in one piece was minimal and this is what we notice when we note the standard deviation of the average diameters of trees at the largest, average and minimum diameters (2.6372, 2.2506, 2.6645) and (4.7420, 5.3046, 5.3183 ) and (7.6774, 7.3956, 7.1912) for the three trees respectively, from the foregoing, we note that the standard deviation of the first tree and the diameters at various measurements were low, which indicates a decrease in the degree of tapering in it to a large extent, while we find that these values increase in the second tree Likewise, the degree of taper increases in the third tree, and this is confirmed by the increase in the degree of the standard deviation of this tree [9].Indicated the use of statistical measures to determine the amount of variation in the wooden sections along the stem, and that these measures explain the degree of tapering in the tree.From that, we see that there is a correlation between the degree of taper, diameter, and height of the trees.Whenever the trees have high heights and have a clear increase in their diameters, we find that the degree of their taper is high, and this is what we noticed in the third tree.

Prepare Taper Equations
The degree of taper of the main stem of trees varies according to the types of trees, the type of trees, their density, and the age stage in which they were calculated, so the process of estimating the degree of taper is of great importance because of its impact on the amount and quality of the wood product in those characteristics, and this degree of taper can be analyzed graphically or by Through mathematical models linking the height of the measurement point to that point and the diameter at the different heights of those trees, so I took the data that was then collected from the three trees of eucalyptus trees with the use of linear and non-linear regression methods and then preparing the equations Table (3).
Table 3. Equations of taper for eucalyptus trees and some statistical measures.
1.1515 0.8 1 2.7557 0.62 2 3.8011 0.75 3 From the observation of Table (3), we find that there are three non-linear mathematical equations represented by the relationship between the diameter at different levels along the stem and the total height of the tree.The first equation gave the best measurements for each of them.Its coefficient of determination, R 2 , is (0.80), while the values of the standard error attributed to the S.E rate are IOP Publishing doi:10.1088/1755-1315/1259/1/0120526 (1.1515), while they are respectively test values, and we find through the values of the statistical measures that they refer to reliable values by referring to the validity of these equations for guessing, that is, we can Using them, but after making sure that there is no self-correlation between the observations of the independent variable in the model, and this is done by performing the residual analysis, as in  Through Figure (2) we notice that there is a random distribution of errors and that they do not give an autocorrelation between the observations of the independent variable, so it is possible to use these first equations to estimate the degree of tapering of these trees [10].Since the aim of extracting the taper equation for the three trees is to find the size of these trees using the taper equations method, and for this, we can find the size of the whole tree and any piece of wood for these trees by performing the integration process for them, and thus we reached the volume equations that estimate the volumes of wooden trunks by the method of integration as follows.
di=14.2299×h (-0.1873)V 1 = 0.02542(hi) 0.6254 By using the above equations, table (3) was prepared: The above results in Table (4) proved that the technique of estimating the volume of the log pieces of the overall main stem is effective, and the degree of its accuracy [11], and calculating the volume of the wooden pieces for it along the main stem was of high accuracy using the integration method.

Figure 1 .
Volumes of rotating bodies.

Figure 2 .
Figure 2. The distribution of random deviations between the real and estimated values for the degrees of taper of eucalyptus trees of the first equation grown in the Nineveh region.

Table 2 .
Structural characteristics of cross-sections of eucalyptus trees with a length of one meter for commercial purposes.

Table 4 .
Diameter at different levels and volume for different logs.