RU2495417C2 - Method of analysis of fir tree branches of crown - Google Patents

Abstract

FIELD: agriculture.

SUBSTANCE: properties of the selected accounting tree and place of its growth are described. The marks on the south side of the fir tree are applied to the trunk. The location of the root collar is determined. The measurement is carried out from the root collar to the top of the terminal leader on whorls of the crown branches. At that the distance between the whorls is measured from up to down, taking as the start the top point of the terminal leader of the fir tree. According to the measured distances the height growth of the accounting fir tree is determined on the biological age, as well as an increment in the height of the accounting fir tree. In addition to the measured parameters of a fir tree trunk the terminal leader at the end of the first year of retrospective age is measured. For environmental analysis one branch from each whorl on the south side of the tree is chosen. At that, the heights of location of bases of the southern branches on all whorls are counted from up to down from the terminal leader to the root collar and from the bottom up from the root collar to the top of the terminal leader. The increment of the fir tree trunk is measured by the base middles of the accounting southern branches. For analysis of lateral development and growth of the accounting southern branches the radius of the branch is measured perpendicular from the vertical axis of the trunk to the extreme branch, parallel to the vertical axis of the fir tree trunk, the height of the branch from the middle of the base of the branch stem to the extreme branch at the end of the branch is measured, and between the longitudinal axes of the trunk and the branch the angle of adjoining the branch to the fir tree trunk is measured.

EFFECT: increased complexity of the analysis of tree trunks with the crowns.

2 cl, 10 dwg, 1 tbl, 1 ex

Description

The invention relates to applied ecology and ecological taxation of growing trees. It can be used in environmental management and industrial ecology, environmental monitoring of the area with spruce trees growing on it, protection and environmental protection in the development of environmental measures, by analyzing the results of measurements of spruce tree branches in an ecological assessment of forest, rural and urban landscapes. The invention may also find application in forestry in assessing and monitoring the quality of undergrowth according to the structure of the crown in spruce and mixed forests with spruce.

Mostly, the proposed method is recommended to be used in the analysis of crown branches in relatively young spruce trees of natural origin or in cultural plantings, for which the height does not exceed two meters for measurement purposes, and the lower whorl of branches near the root neck of the spruce trunk is not subject to drying of needles and transformation of the lower branches in the boughs.

A known method of analyzing a tree trunk according to patent 2201593, including measuring the values of the parameters of the selected tree and the place of its growth, drawing marks on the north and south sides on the trunk, establishing the location of the root neck, measuring the distance on the trunk from the root neck to the first dead knot and the first living branch before the start of the crown, the marking of the trunk is performed on sections of multiple lengths, depending on the location of the bases of the branches.

The disadvantage is the inability to analyze the branches of the crown according to the measurement results from the root neck to the top of the crown by whorls of spruce. This drawback does not allow complex measurement, and then analysis in office conditions of the measured data on individual branches of the crown of the spruce tree. In addition, the registration of branches in the form of dead branches in adults and old trees does not make it possible to accurately determine the age of the registration tree. Moreover, model trees are not considered in the proposed technical solution.

There is also a method for analyzing the crown of a spruce tree according to patent No. 2376749, including a description of the properties of the selected tree and its place of growth, drawing marks on the southern and northern sides of the spruce on the trunk, establishing the location of the root neck, measuring from the root neck to the top of the terminal shoot by whorls branches of the crown, and for the analysis of the crown of the accounting tree of spruce, the distances between the whorls are measured from top to bottom, taking as the origin the top point of the terminal shoot of spruce, according to the measured distances, the statistical model Growth reveals the growth in height of the spruce tree by biological age, and from top-down distances between whorls from the terminal shoot of spruce to the beginning of the crown with branches, statistical modeling reveals a growth in height of the spruce tree.

The disadvantage is the absence in the prototype of the measurement parameters and the subsequent analysis of the branches themselves. But in each whorl there are many branches, therefore, for analysis by the proposed method, only branches on the south side are measured without physical destruction of the tree. In addition, they are most variable in terms of geometric parameters.

Measurements from the south are known. In tests, for example, according to patent No. 2194385, samples are taken from the south side of the spruce tree for environmental monitoring, and from the north side for technological monitoring for the purpose of growing high-quality technical trunk wood.

Thus, the measurement object is known as branches from various whorls of the spruce tree on the southern side of the plant, but the prototype does not allow measuring the parameters of the spruce branches themselves.

The technical result is an increase in the complexity of the analysis of tree trunks with crowns and a functional extension of the application of the method for analyzing the crown of spruce on the branches of all whorls on the south side of a growing reference tree, and based on the results of the analysis of the branches of the crown of accounting trees of spruce on the south side, assess the ecological quality of the surrounding forest or other Wednesday.

This technical result is achieved in that a method for analyzing the branches of the crown of a spruce tree, including a description of the properties of the selected reference tree and the place of its growth, marking the southern side of the spruce on the trunk, determining the location of the root neck, measuring from the root neck to the top of the terminal shoot by whorls branches of the crown, and the distance between the whorls is measured from top to bottom, taking as the origin the top point of the terminal shoot of spruce, according to the measured distances, statistical modeling reveals p the height of the counting spruce tree by biological age, and by the top-down distances between whorls from the terminal shoot of spruce to the beginning of the crown with branches, statistical modeling reveals a growth in height of the counting spruce tree, characterized in that, in addition to the measured parameters of the spruce tree trunk, the terminal shoot they assign a zero rank and the first year of a retrospective age, for the ecological analysis choose the southern side of the spruce tree, from each whorl take one branch, located closer to southern geodesic direction, while the heights of the bases of the southern branches from all whorls are taken into account from top to bottom from the terminal shoot to the root neck and from bottom to top from the root neck to the crown of the terminal shoot, the spruce trunk growth is measured in the middle of the bases of the counting southern branches, and for analysis of lateral development and the growth of the counting southern branches, the radius of the branch is measured perpendicularly from the vertical axis of the trunk to the extreme branch of each southern branch, parallel to the vertical axis of the trunk, the height of the branch from sulfur is measured dines of the base of the stem of the branch to the extreme branch at the end of the branch, and between the longitudinal axes of the trunk and branch, the angle of contact of the branch to the trunk of the spruce tree is measured.

Measurements are carried out after the growing season in late autumn or early winter at the terminal shoot and the extreme branches of the accounting branches on the south side of the accounting spruce tree, and the terminal shoot is taken as one branch common to the spruce tree with zero contact angle and zero branch radius, and the height will be equal to growth of the terminal shoot, and the biological age of the recorded southern branch is taken equal to the retrospective age of the whorl of the spruce.

According to the measured values of the radius of each southern branch, depending on the retrospective age, statistical modeling reveals a biotechnical regularity according to the formula:

, $$R=a_{\mathrm{one}}{A}_p{}^{a_2}+a_3{A}_p{}^{a_{\mathrm{four}}}exp\left(-a_5{A}_p{}^{a_6}\right)$$

,

where R is the radius of the southern branch perpendicular from the vertical axis of the trunk to the extreme branches of each southern branch, m;

And _p is the retrospective age of the whorl of spruce (by the number of whorls, starting from the terminal shoot), years;

α ₁ ... α ₆ are the parameters of the above two-term equation of law as the sum of the law of exponential growth and the law of biotechnical disturbance in changes in the radius of the branch, which receive specific values after identification according to the measurement data of the accounting spruce.

According to the measured values of the height of each southern branch, depending on the retrospective age, statistical modeling reveals a biotechnical regularity according to the formula:

, $$h=a_{\mathrm{one}}exp\left(-a_2{A}_p{}^{a_3}\right)+a_{\mathrm{four}}{A}_p{}^{a_5}exp\left(-a_6{A}_p{}^{a_7}\right)$$

,

where h is the height of the southern branch on each whorl of spruce, from its beginning at the junction of the trunk to its top, m;

And _p is the retrospective age of the whorl of spruce (by the number of whorls, starting from the terminal shoot), years;

α ₁ ... α ₆ are the parameters of the above two-term equation of law, in the form of the sum of the law of exponential death and the law of biotechnical disturbance, changes in the height of the branch, which receive specific values after identifying the formula according to the measurement data of the accounting spruce.

According to the measured values of the angle of contact of each southern branch to the trunk of the spruce tree, depending on the retrospective age, statistical modeling reveals a biotechnical regularity according to the formula:

, $$\lambda =a_{\mathrm{one}}{\left(A_p-\mathrm{one}\right)}^{a_2}=a_{\mathrm{one}}{r}^{a_2}$$

,

where λ is the angle of contact of the southern branch at the base of each whorl to the trunk of the spruce, hail;

And _p is the retrospective age of the whorl of spruce (by the number of whorls, starting from the terminal shoot), years;

r is the rank of the whorl, r = 0 for the terminal shoot;

α ₁ , α ₆ - parameters of the above patterns of change in the contact angle according to the exponential law.

The essence of the technical solution is that the distances between the whorls, showing the growth of the spruce trunk in height, are measured from top to bottom, and thus the abscissa begins the distance along the trunk from the crown of the terminal shoot, and the geometric parameters of the branch become the ordinate axis.

The essence also lies in the fact that in a young spruce with a biological age of less than 30 years, the number of the whorls coincides with its age, therefore, the rank of the whorls starts from zero, marked on the crown of the terminal shoot of the spruce. At the same time, the age of the whorl allows you to look deep into the history of growth and development of the spruce itself up to the time that corresponds to the lowest whorl on the tree trunk. And such a whorl is the last group of living branches on the trunk of a young spruce.

The essence also lies in the fact that a retrospective on simple and clear measurements of growth and growth of spruce on the bases of the southern branch in each whorl allows us to identify using the revealed statistical patterns the wave processes of the past behavior of the organism of a separate southern branch in each whorl in the life of the spruce tree under study. This type of tree is easily adaptable in urban environments, being a stable plant in landscaping various cultural and landscapes, parks, alleys and decorative plantings. Therefore, wave disturbances in the growth along the whorls from the southern side of the spruce and the geometric parameters of the branches show the adaptation of this spruce and its individual southern branches to the environment. A large number of spruce trees measured in this way will highlight the patterns of sustainable growth and development of spruce forest trees as well.

The essence also lies in the fact that the run-out radius of the last branch of the southern branch in a single whorl shows the peculiarities of the growth conditions of this branch on the trunk of the mother spruce tree. At the same time, the abutment angle characterizes the formation of buds on the southern side of the spruce in certain years of growth and development of the spruce accounting tree, and the height of the branch from its base to the trunk to the distant branch shows the flexibility and strength of the branch. In general, the radius R of the branch, the angle λ of its abutment to the trunk, and the height h of the branch along the axis of the vertically standing trunk show the ecological and physiological quality of the measured branch on the south side of this whorl of the spruce tree.

The positive effect is that the identification of statistical patterns of growth of spruce trees will allow you to manage the surrounding ecological environment, for example, in a city or rural area, as well as forest plantations of spruce, growing healthy and tall spruce forests, as well as determine the ecological endurance limits of these subspecies of spruce plants. In addition, the positive effect lies in the fact that measurements can be carried out on accounting trees without cutting model trees, generally abandoning the latter in forest taxation of spruce forests and individual spruce trees. The proposed method does not involve physical damaging effects on the studied accounting trees of spruce.

A significant novelty in addition to the prototype is the measurement of three parameters of a spruce tree branch:

- radius of the southern branch perpendicular from the vertical axis of the trunk to the extreme branches of each southern branch, m;

- the height of the southern branch on each whorl of spruce, from its beginning at the junction of the trunk to its top, m;

- the angle of contact of the southern branch at the base of each whorl to the trunk of the spruce, hail.

In addition, four scales for measuring the parameters of whorls along the southern branches of the spruce tree have novelty:

1) r is the rank of the whorl, r = 0 for the terminal shoot;

2) A _p - retrospective age of the whorls of spruce (by the number of whorls, starting from the terminal shoot, therefore A _p = r + 1), years;

- высота мутовки и ее южной ветви по стволу ели от корневой шейки, м;3) $$H_{\uparrow }$$

- the height of the whorl and its southern branch along the trunk ate from the root neck, m;

- высота мутовки и ее южной ветви по стволу ели от макушки терминального побега дерева ели, м.four) $$H_{\downarrow }$$

- the height of the whorl and its southern branch along the spruce trunk from the crown of the terminal shoot of the spruce tree, m

In this regard, the proposed technical solution has significant features of novelty, ease of implementation in a production environment, a positive effect in environmental engineering and environmental monitoring of the properties of spruce trees.

From the scientific, technical and patent literature, materials discrediting the novelty of the proposed method were not found.

Figure 1 shows the location scheme of the accounting spruce in an urban environment (the spruce is depicted as a circle in a rectangle); figure 2 shows the accounting spruce, in which the right is the south side; figure 3 shows the calculated layout of the accounting branch on the tree trunk of spruce with the designation of the measured parameters; figure 4 shows a graph (correlation coefficient 0.9995) of the effect of retrospective age on the height of the whorls from the root neck; in Fig.5 is the same in Fig.4 graph (correlation coefficient 0.9979) on the height of the whorls and its southern branches along the trunk of the spruce from the top of the spruce; in Fig.6 - the same in Fig.4 is a graph (correlation coefficient 0.7211) for the growth of the trunk of spruce by whorls, and the gain does not depend on the direction of measurement of the height of the whorls; 7 shows a graph (correlation coefficient 0.7943) of the effect of the height of the whorls above the root neck of the trunk on the change in the growth of the trunk in height; in Fig.8 is the same in Fig.4 graph (correlation coefficient 0.9608) on the radius of the southern branch of the whorls from the longitudinal axis of the trunk of the spruce; in Fig.9 - the same in Fig.4 graph (correlation coefficient 0.8461) on the height of the southern branch on each whorl of spruce, from its beginning at the point of contact with the trunk to the top with the last branch; figure 10 shows a graph (correlation coefficient 0.9460) of the effect of the rank of the whorls of spruce on the contact angle at the base of the southern branch of the whorls to the trunk of the spruce.

The method of analysis of the branches of the crown of a spruce tree, for example, spruce up to 30 years of age and two-meter height, includes such actions.

In some territory, the spruce tree is selected.

Next, a description of the property values of the selected registration tree and its place of growth, a mark on the trunk of the southern side of the spruce tree, and location of the root neck are compiled. Measurements along the trunk are performed from the root neck to the top of the terminal shoot along the whorls of the crown branches. The distances between the whorls are measured from top to bottom, taking the top point of the terminal shoot of spruce as the origin, then, using the measured distances, statistical modeling reveals the growth in height of the spruce tree by the biological age, and the top-down distances between the whorls from the terminal shoot of the spruce to the start of the crown with branches of statistical modeling reveal the growth in height of the spruce tree

In addition to the parameters of the spruce tree trunk measured by the prototype, the terminal shoot is assigned a zero rank and the first year of retrospective age, for the environmental analysis, the southern sides of the spruce tree are selected, from each whorl one branch is located closer to the southern geodesic direction, while the heights of the bases of the southern branches from all whorls are taken into account from top to bottom from the terminal shoot to the root neck and from bottom to top from the root neck to the crown of the terminal shoot, trunk growth was measured They are located in the middle of the bases of the recorded southern branches, and to analyze the lateral development and growth of the recorded southern branches, the radius of the branch is measured perpendicularly from the vertical axis of the trunk to the extreme branch of each southern branch, parallel to the vertical axis of the spruce trunk, the height of the branch is measured from the middle of the base of the stem of the branch to the extreme branch at the end of the branch, and between the longitudinal axes of the trunk and branch, measure the angle of the branch connecting to the trunk of the spruce tree.

Measurements are carried out after the growing season in late autumn or early winter at the terminal shoot and the extreme branches of the accounting branches on the south side of the accounting spruce tree, and the terminal shoot is taken as one branch common to the spruce tree with zero contact angle and zero branch radius, and the height will be equal to growth of the terminal shoot, and the biological age of the recorded southern branch is taken equal to the retrospective age of the whorl of the spruce.

According to the measured values of the radius of each southern branch, depending on the retrospective age, statistical modeling reveals a biotechnical regularity according to the formula:

, $$R=a_{\mathrm{one}}{A}_p{}^{a_2}+a_3{A}_p{}^{a_{\mathrm{four}}}exp\left(-a_5{A}_p{}^{a_6}\right)$$

,

where R is the radius of the southern branch perpendicular from the vertical axis of the trunk to the extreme branches of each southern branch, m;

A _p is the retrospective age of the whorl of spruce (according to the number of whorls, starting from the terminal shoot), years;

α ₁ ... α ₆ are the parameters of the above two-term equation of law as the sum of the law of exponential growth and the law of biotechnical disturbance in changes in the radius of the branch, which receive specific values after identification according to the measurement data of the accounting spruce.

According to the measured values of the height of each southern branch, depending on the retrospective age, statistical modeling reveals a biotechnical regularity according to the formula:

, $$h=a_{\mathrm{one}}exp\left(-a_2{A}_p{}^{a_3}\right)+a_{\mathrm{four}}{A}_p{}^{a_5}exp\left(-a_6{A}_p{}^{a_7}\right)$$

,

where h is the height of the southern branch on each whorl of spruce, from its beginning at the junction of the trunk to its top, m;

And _p is the retrospective age of the whorl of spruce (by the number of whorls, starting from the terminal shoot), years;

α ₁ ... α ₇ are the parameters of the above two-term equation of law, in the form of the sum of the law of exponential death and the law of biotechnical disturbance, changes in the height of the branches, which receive specific values after identifying the formula according to the measurement data of the accounting spruce.

According to the measured values of the angle of contact of each southern branch to the trunk of the spruce tree, depending on the retrospective age, statistical modeling reveals a biotechnical regularity according to the formula:

, $$\lambda =a_{\mathrm{one}}{\left(A_p-\mathrm{one}\right)}^{a_2}=a_{\mathrm{one}}{r}^{a_2}$$

,

where λ is the angle of contact of the southern branch at the base of the whorl to the trunk of the spruce, hail;

A _p is the retrospective age of the whorl of spruce (according to the number of whorls, starting from the terminal shoot), years;

r is the rank of the whorl, r = 0 for the terminal shoot;

α ₁ ... α ₆ - parameters of the above patterns of change in the contact angle according to the exponential law.

A method for analyzing the branches of a spruce tree is implemented, for example, according to the results of measurements of a young spruce 1.21 m high, growing in an urban environment, as follows.

On the site of the urban environment for its environmental assessment, a spruce tree is selected.

Visually, a description of the properties of the selected accounting tree and the place of its growth is made up further, marks on the southern side of the spruce are applied with a compass to the trunk, and the locations of the root neck are established. Measurements along the trunk are performed from the root neck to the top of the terminal shoot along the whorls of the crown branches, and the distances between the whorls are measured from top to bottom. In this case, the top point of the terminal shoot of spruce is taken as the origin. Then, in office conditions, the statistical growth reveals the growth in height of the spruce tree by the biological age according to the measured distances, and the height increase in the height of the spruce tree of the spruce tree is revealed by statistical measurements from the top to bottom distances between whorls from the terminal shoot of spruce to the beginning of the crown with branches of statistical modeling

In addition to the parameters of the spruce tree trunk measured by the prototype, the terminal shoot is assigned a zero rank and the first year of retrospective age, for the environmental analysis, the southern sides of the spruce tree are selected, from each whorl one branch is located closer to the southern geodesic direction, while the heights of the bases of the southern branches from all whorls are taken into account from top to bottom from the terminal shoot to the root neck and from bottom to top from the root neck to the crown of the terminal shoot, trunk growth was measured They are located in the middle of the bases of the recorded southern branches, and to analyze the lateral development and growth of the recorded southern branches, the radius of the branch is measured perpendicularly from the vertical axis of the trunk to the extreme branch of each southern branch, parallel to the vertical axis of the spruce trunk, the height of the branch is measured from the middle of the base of the stem of the branch to the extreme branch at the end of the branch, and between the longitudinal axes of the trunk and branch, measure the angle of the branch connecting to the trunk of the spruce tree.

Measurements are carried out after the growing season in late autumn or early winter at the terminal shoot and the extreme branches of the accounting branches on the south side of the accounting spruce tree, and the terminal shoot is taken as one branch common to the spruce tree with zero contact angle and zero branch radius, and the height will be equal to growth of the terminal shoot, and the biological age of the recorded southern branch is taken equal to the retrospective age of the whorl of the spruce.

According to the measured values of the radius of each southern branch, depending on the retrospective age, statistical modeling reveals a biotechnical regularity according to the formula:

, $$R=a_{\mathrm{one}}{A}_p{}^{a_2}+a_3{A}_p{}^{a_{\mathrm{four}}}exp\left(-a_5{A}_p{}^{a_6}\right)$$

,

where R is the radius of the southern branch perpendicular from the vertical axis of the trunk to the extreme branches of each southern branch, m;

A _p is the retrospective age of the whorl of spruce (according to the number of whorls, starting from the terminal shoot), years;

α ₁ ... α ₆ are the parameters of the above two-term equation of law as the sum of the law of exponential growth and the law of biotechnical disturbance in changes in the radius of the branch, which receive specific values after identification according to the measurement data of the accounting spruce.

According to the measured values of the height of each southern branch, depending on the retrospective age, statistical modeling reveals a biotechnical regularity according to the formula:

, $$h=a_{\mathrm{one}}exp\left(-a_2{A}_p{}^{a_3}\right)+a_{\mathrm{four}}{A}_p{}^{a_5}exp\left(-a_6{A}_p{}^{a_7}\right)$$

,

where h is the height of the southern branch on each whorl of spruce, from its beginning at the junction of the trunk to its top, m;

And _p is the retrospective age of the whorl of spruce (by the number of whorls, starting from the terminal shoot), years;

α ₁ ... α ₇ are the parameters of the above two-term equation of law, in the form of the sum of the law of exponential death and the law of biotechnical disturbance, changes in the height of the branches, which receive specific values after identifying the formula according to the measurement data of the accounting spruce.

According to the measured values of the angle of contact of each southern branch to the trunk of the spruce tree, depending on the retrospective age, statistical modeling reveals a biotechnical regularity according to the formula:

, $$\lambda =a_{\mathrm{one}}{\left(A_p-\mathrm{one}\right)}^{a_2}=a_{\mathrm{one}}{r}^{a_2}$$

,

where λ is the angle of contact of the southern branch at the base of the whorl to the trunk of the spruce, hail;

A _p is the retrospective age of the whorl of spruce (according to the number of whorls, starting from the terminal shoot), years;

r is the rank of the whorl, r = 0 for the terminal shoot;

α ₁ , α ₁ - parameters of the above patterns of change in the contact angle according to the exponential law.

Example. The object of study is located in the city of Yoshkar-Ola, next to the building of the Tourist Hotel on one side and the highway along Karl Marx Street on the other, and a parking lot is located on the west side of the site (Fig. 1).

The measurement condition is accepted in the fall, at the end of the growing season of spruce branches.

For the experiment, one accounting tree of European spruce was selected (Fig. 2), growing in urban areas. The tree is located near the buildings. The distance from the highway is more than 50 m. Moreover, the movement of road transport on this road is characterized as intense. In addition, the spruce tree was selected so that the height of the tree was no more than 2.0 m.

The state of spruce for the period of measurements (October 2010) is normal, it has an abundant cover of needles with whorled branching, needles of dark green color, needle-shaped and prickly. From all visual observation, we can conclude that the accounting spruce is in good physiological condition, despite being located in an urban environment.

The accounting spruce has a biological age of 18 years and 17 whorls from the terminal shoot (zero rank and one year old). Table 1 shows the results of measurements of the southern branches from each whorl.

The data in table 1 shows the following conventions for the parameters of the trunk and southern branches of the accounting spruce:

r is the rank of the whorl, r = 0 for the terminal shoot;

A _p is the retrospective age of the whorl of spruce (according to the number of whorls, starting from the terminal shoot), years;

- высота мутовки и ее южной ветви по стволу ели от корневой шейки (фиг.3), м; $$H_{\uparrow }$$

- the height of the whorls and its southern branches along the trunk ate from the root neck (Fig.3), m;

- высота мутовки и ее южной ветви по стволу ели от макушки терминального побега дерева ели (фиг.3), м; $$H_{\downarrow }$$

- the height of the whorls and its southern branches along the spruce trunk from the crown of the terminal shoot of the spruce tree (Fig. 3), m;

Z _H - the growth of the trunk of spruce by whorls (figure 3), m;

R is the radius of the southern branch of the whorl from the longitudinal axis of the trunk of the spruce (figure 3), m;

h - the height of the southern branch on each whorl of spruce, from its beginning at the junction of the trunk to its top (figure 3), m;

λ is the contact angle at the base of the southern branch of the whorl to the trunk of the spruce (figure 3), deg;

Table 1 Distribution dynamics of branches on the south side of spruce Rank r Age of whorl A _r , years The height of the whorl, m The growth of the barrel by whorls Z _H , m Lateral development of the southern branch

from the root neck of the trunk $$H_{\uparrow }$$

from the top of the tree ate $$H_{\downarrow }$$

branch radius R, m branch height h, m contact angle λ, deg 0 one 1.21 0.05 0.05 0 0.050 0 one 2 1.16 0.12 0.07 0.18 0.093 45 2 3 1.09 0.15 0.03 0.63 0.025 63 3 four 1.06 0.23 0.08 0.09 0.047 54 four 5 0.98 0.31 0.08 0.05 0.044 60 5 6 0.90 0.36 0.05 0.04 0.019 70 6 7 0.85 0.41 0.05 0.22 0.090 75 7 8 0.80 0.46 0.05 0.19 0.092 95 8 9 0.75 0.53 0.07 0.26 0.235 60 9 10 0.68 0.59 0.06 0.25 0.080 74 10 eleven 0.62 0.65 0.06 0.24 0.082 80 eleven 12 0.56 0.71 0.06 0.21 0.064 87 12 13 0.50 0.77 0.06 0.29 0.050 85 13 fourteen 0.44 0.85 0.08 0.28 0.020 97 fourteen fifteen 0.36 0.92 0.07 0.31 0.018 105 fifteen 16 0.29 1.00 0.08 0.37 0.010 107 16 17 0.21 1.09 0.09 0.42 0.014 109 17 eighteen 0.12 1.21 0.12 0.52 0.013 110

A retrospective age is taken as an explanatory variable, relative to which biotechnical patterns of other parameters are revealed as dependent indicators of the structure and structure of the southern side of the spruce tree. The effect of retrospective age is clearly manifested.

On the height of the whorls from the root neck (figure 4) H _↑ time A _p affects the two-term formula of the form

$$\begin{array}{l}{H}_{\uparrow }=\mathrm{one},28\mathrm{one}\mathrm{four}\mathrm{four}exp\left(-\mathrm{four},\mathrm{one}3828\cdot \mathrm{one}{0}^{-5}{A}_p{}^{3,06769}\right)-\\ -0,066726A_p{}^{0,9856\mathrm{four}}exp\left(-0,0\mathrm{one}836\mathrm{four}{A}_p{}^{\mathrm{one},00766}\right).\begin{array}{ccc}& & \end{array}\left(\mathrm{one}\right)\end{array}$$

The first component of the mathematical model (1) is the law of exponential death and characterizes the decline over the years of tree height. Before the second component, which is a biotechnical law, prof. P.M. Mazurkina, there is a negative sign. Therefore, the second component of formula (1) shows a crisis in the behavior of the plant organism as it deepens into the past. This crisis was overcome further, if there is no strong anthropogenic impact, the accounting spruce should grow quietly. With high-precision measurements of linear parameters (instead of a measurement error of ± 0.5 cm, ± 0.1 cm is achieved), in addition to model (1), wave changes in the parameters of the spruce tree are obtained in the form of its adaptation by vibrational disturbance of the branches.

On the height of the whorls from the top of the terminal shoot of spruce (Fig. 5) in the form of an indicator H, a retrospective age is influenced by the formula of a simple law of exponential growth

$$H_{\downarrow }=0,0\mathrm{four}562\mathrm{one}{A}_p{}^{\mathrm{one},\mathrm{one}\mathrm{one}70\mathrm{one}}.\begin{array}{ccc}& & \end{array}\left(2\right)$$

The growth rate of 1.11701 shows an accelerating increase in the height of the spruce along the whorls as it approaches the root neck of the trunk.

и $$Z_{Н}=f\left(H_{\downarrow }\right).$$

Причем прирост стола не зависит от направления измерения высоты мутовки.Next, the growth at the trunk of the spruce by whorls is considered three times as a function of Z _H = f (A _p ), $$Z_N=f\left(H_{\uparrow }\right)$$

and $$Z_N=f\left(H_{\downarrow }\right).$$

Moreover, the growth of the table does not depend on the direction of measurement of the height of the whorl.

The growth of the trunk from retrospective age (Fig.6) has the form:

$$Z_H=0,052972exp\left(0,0007\mathrm{four}382A_p{}^{2,3\mathrm{one}359}\right).\begin{array}{ccc}& & \end{array}\left(3\right)$$

The scatter of points shows that the greatest increase was in the last whorl, located near the surface of the soil, then a strong fluctuation in the growth of the trunk occurred 2-6 years ago. Comparing it with events of anthropogenic impact (there was a repair of buildings and the construction of a parking lot), one can quite confidently evaluate the ecological regime of the urban environment surrounding the spruce tree through the variability of wave disturbance in the trunk increment. Although the builders took care of the spruce without destroying it, the plant had to worry a lot about development and growth.

The growth of the trunk from a height above the neck of the root received (Fig.7) a remarkable two-term regularity:

$$Z_H=0,2\mathrm{one}680exp\left(-5,396\mathrm{four}2H_{\uparrow }{}^{0,68980}\right)+0,057\mathrm{four}20.\begin{array}{ccc}& & \end{array}\left(\mathrm{four}\right)$$

As the total height of the spruce tree grows over the years, the trunk growth stabilizes, and the height scale from the root neck of the trunk better shows the growth dynamics of the whole organism of the woody plant.

A remarkable property of formula (4) is that, according to a similar regularity (4), processes of natural drying of needles, wood, and also other types of plants, for example grass, occur.

Model (4) shows that if there are no changes in the ecological situation around the spruce, then, on average, the annual increase in height will be 0.05742 m.You can predict that the spruce will reach a height of 10 m approximately (10-1 , 21) / 0,05742≈153 years, i.e. by 2010 + 153 = 2163. Thus, the urban environment and the lack of support for the family (bio-group) of spruce trees growing together strongly delay the development and growth of the spruce tree.

The correlation coefficient of 0.7943 belongs to the group of strong factor relations, therefore, the behavior of this spruce is predicted adequately.

But from the distribution at the end of the graph (Fig. 7), a strong oscillatory disturbance of the growth at the top of the spruce tree is visible. Therefore, forecasts of the development and growth of the plant are always conditional, since vibrational disturbance can occur at any time in the future due to any undesirable effect on the plant, including due to diseases.

The growth of the trunk, depending on the height from the top of the spruce tree, gave a compound formula with a correlation of 0.8015 of the form:

$$Z_H=0,062735H_{\downarrow }{}^{0,05\mathrm{one}2\mathrm{one}6}+0,0\mathrm{one}6877H_{\uparrow }{}^{6,29805}.\begin{array}{ccc}& & \end{array}\left(5\right)$$

The adequacy of this formula (5) is even higher in comparison with the model (4) in the usual representation of the height to the whorl of the spruce tree. Therefore, the analysis of such a pattern (5) can lead to new scientific and technical solutions, including patentable ones.

Next, we continue the analysis of the effect of retrospective age on the parameters of the branches on the south side of the spruce tree.

The radius of the southern branch of the whorl from the longitudinal axis of the spruce trunk (Fig. 8) gives an extremely strong factorial relation with a correlation coefficient of 0.9608 (which is higher than the requirements of 0.95 even in technical experiments) according to the formula:

$$R=0,0\mathrm{one}\mathrm{one}\mathrm{four}85A_p{}^{\mathrm{one},269\mathrm{four}0}+\mathrm{one},0\mathrm{one}09\mathrm{one}{A}_p{}^{38,88305}exp\left(-\mathrm{one}\mathrm{four},\mathrm{four}22\mathrm{one}9A_p\right).\begin{array}{ccc}& & \end{array}\left(6\right)$$

The first component, in the form of an exponential growth law, gives an idea that the branches nucleate in the form of buds already on the terminal shoot, and with increasing retrospective age, the run-out of branches increases.

But the limit of exponential growth is the surface of the soil.

Therefore, under favorable environmental conditions, some branches rapidly grow to the side of the tree trunk. As you know, the branches are isolated organisms, n without roots and feed on the juices of the mother. This physical phenomenon is shown to her by the second component of formula (6). On the graph (Fig. 8) this stress arousal is clearly visible.

The height of the southern branch on each whorl of spruce (Fig. 9), from its beginning at the point of abutment to the trunk to its top, gives the formula:

$$\begin{array}{l}h=0,08590\mathrm{four}exp\left(-0,30539A_p{}^{0,58595}\right)+\\ +2,\mathrm{four}29\mathrm{four}8\cdot \mathrm{one}{0}^{-22}{A}_p{}^{35,20\mathrm{one}98}exp\left(-2,\mathrm{one}\mathrm{four}60\mathrm{one}{A}_p{}^{\mathrm{one},\mathrm{one}9359}\right).\begin{array}{ccc}& & \end{array}\left(7\right)\end{array}$$

In this biotechnical regularity (7), the influence of the branch’s own weight on the bend of its stem is manifested mainly, that is, the greater the height of the branch, the more “confident” it grows to the side of the tree and, apparently, it is stronger and more flexible.

The first component, according to the law of exponential death, shows the decline in the height of the branch from its base to the top in the form of a year branch of the last vegetation period before measurements in October.

In the period of 6-13 years in the past, stress excitation of branch height occurred. And since 14 years of past time, there has again been (Fig. 9) a calm decrease in the height of the branches of the spruce tree.

The contact angle at the base of the southern branch of the whorl (figure 10) to the trunk of the spruce is determined by a simple exponential law of the form:

$$\lambda =\mathrm{four}0,28690\left(A_p-\mathrm{one}\right)0,33757=\mathrm{four}0b28690r^{0,33757}.\begin{array}{ccc}& & \end{array}\left(8\right)$$

The influence not of a retrospective age, but of a whorl rank r = A _p -1, turned out to be much more accurate (correlation coefficient 0.9460 and close to the adequacy of technical experiments). The whorl rank according to the data in Table 1 shows that a strong and healthy terminal shoot gives a zero contact angle - strictly along the gravity vector to the center of the Earth (the vertical axis at this point of spruce growth).

This fact has long been known: if the terminal shoot is neither vertical nor straight, then the spruce tree got sick.

и λ.The comparison shows that the simplest in design of all eight models are formulas (2) and (8) according to the exponential law. Therefore, students in environmental camps and school forestries can be recommended to measure r, A _p , $$H_{\downarrow }$$

and λ.

The proposed technical solution has the prospect of further expanding the areas of application of landscape ecology with growing spruce trees on the territory of forest, agroecological, rural and urban areas without their destruction, in a growing state. At the same time, repeated measurements of registration trees of spruce will allow for long-term monitoring of the environment surrounding these registration trees to eat the surrounding urban or other environment.

The effectiveness of the new method is manifested in the fact that it allows you to analyze only the southern branches of the accounting tree of spruce and this significantly reduces the complexity of the measurements. The greatest effect will be achieved by repeated measurements of the branches of whorls of spruce on accounting trees located under various pollution conditions in the areas where spruce trees grow. Annual measurements will make it possible to study the behavior of the accounting spruce and conduct environmental monitoring.

Claims (2)

1. A method of measuring the branches of the crown of a spruce tree, including a description of the properties of the selected reference tree and the place of its growth, drawing marks on the southern side of the spruce on the trunk, determining the location of the root neck, measuring from the root neck to the top of the terminal shoot from the whorls of the crown branches, and the distance between whorls they measure from top to bottom, taking the origin of the top point of the terminal shoot of spruce, according to the measured distances, statistical modeling reveals the growth in height of the spruce tree age, and from top-down distances between whorls from the terminal shoot of spruce to the beginning of the crown with branches, statistical modeling reveals a growth in height of the spruce tree of reference, characterized in that in addition to the measured parameters of the spruce tree trunk, a terminal shoot is measured at the end of the first year of retrospective age , for environmental analysis, choose the southern side of the spruce tree, from each whorl take one branch closer to the southern geodesic direction, while the positions of the bases of the southern branches from all whorls are taken into account from top to bottom from the terminal shoot to the root neck and from bottom to top from the root neck to the crown of the terminal shoot, the spruce trunk growth is measured in the middle of the bases of the counting southern branches, and the radius is measured to analyze the lateral development and growth of the counting southern branches branches perpendicular from the vertical axis of the trunk to the extreme branches of each southern branch, parallel to the vertical axis of the trunk of the spruce tree, measure the height of the branches from the middle of the base of the stem of the branch to the extreme branches at the end branches, and between the longitudinal axes of the trunk and branches measure the angle of abutment of the branch to the trunk of the spruce tree. 2. The method of measuring the branches of the crown of a spruce tree according to claim 1, characterized in that the parameters are measured after the growing season in late autumn or early winter at the terminal shoot and the extreme branches of the accounting branches on the south side of the accounting tree of spruce, and the terminal shoot is taken as one a branch common to a spruce tree with a zero contact angle and a zero branch radius, and the height will be equal to the growth of the terminal shoot, and the biological age of the recorded southern branch is taken to be the retrospective age of the spruce whorl.

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