RU2376749C1 - Method for analysis of fir tree trunk and crown - Google Patents

Abstract

FIELD: agriculture.

SUBSTANCE: method for analysis of fir tree trunk and crown includes description of selected tree properties values and area of its growth, application of marks on trunk indicating northern and southern sides, identification of root neck location, measurement of distances on trunk from root neck to the first dead knot and the first live branch to the beginning of crown. Trunk marking is arranged on section of aliquant length depending on location of branches and knots bases. Sections of aliquant length are marked at least twice - at first in points of lowest diametres between bases of knots and branches of tree, then on tops of these burrs with measurement of according distances from root neck with estimation of several generatrices on uneven surface of trunk. Measurements and analysis of trunk bottom-up from root neck to the beginning of crown are added with measurements and analysis of fir tree trunk to the top of terminal sprout by nodes of crown branches. For analysis of crown of model registered fir tree, distances between nodes are measured top down. Point of origin is accepted as upper point of terminal sprout of fir tree. Measurements of burrs along bases of branches and knots in crown are carried out bottom-up from terminal sprout to the beginning of crown or knot-free zone of trunk. Along nodes of for tree, burrs are accepted as points from top of terminal sprout to the middle of bases of branches of single node in fir tree crown. Measured distances of alternate height from root neck to each node of crown are used to detect height growth of model or registered fir tree by biological time, using statistical modeling. Distances measured top down between nodes from terminal sprout of fir tree to the beginning of crown with branches and nodes with the help of statistical modeling are used to detect height growth in process of retrospective time from the moment of measurements taking to biological age of branches in single node of model or registered fir tree.

EFFECT: such arrangement of method will make it possible to improve complexity of analysis of wood trunks with crowns and assessment of ecological quality of environment.

9 cl, 12 dwg

Description

The invention relates to environmental taxation of growing trees and technical taxation of fallen model trees and can be used in environmental management and environmental engineering, environmental monitoring and environmental protection by analyzing the measurement results and testing of accounting and model spruce trees (taking into account the quality of the structure of their trunk and crown together or separately) in the environmental assessment of forest, rural and urban landscapes. The invention may also find application in forestry in assessing and monitoring the quality of the trunk shape and crown structure in accounting and model spruce trees in spruce and mixed forests with spruce.

There is a method of analysis of a tree trunk (see, for example, the textbook: N.P. Anuchin. Forest taxation. Publishing house 5th, add. - M .: Forestry industry, 1982. - S.424-426), including the choice test area, selection of a model tree on the test area, description of the properties of the selected model tree and its place of growth, drawing marks on the north and south sides on the trunk, establishing the location of the root neck, cutting the tree near the root neck of the trunk, measuring the distance to the first dead tree and the first living knots, before the start of the crown other taxation indicators, marking the trunk into separate sections of multiple lengths (0.5, 1 or 2 m) or multiple lengths, depending on the purpose of the analysis of the trunk and the required accuracy of the study after the first section, 2.6 m long, marking the middle of the sections, sawing circles starting from the base of the trunk to its top in the middle of the sections, the first cut being made at the place of the mark near the root neck, and the second - stepping from it to the top by the thickness of the circle, each sawn circle is marked with numbers on the trial area of the model tree and sawed circle, and the designations are made on a slightly smoothed upper part of the circles, and the lower parts of the circles in office conditions are used to calculate annual rings and measure diameters.

The disadvantage of this method is the complete destruction of the tree, which is unacceptable in cultural landscapes, where it is possible to isolate from many growing trees only accounting for ecological monitoring of trees. And in relation to spruce trees grown to cut trees into wood in the form of a round timber, model trees themselves are cut off outside the test site. Moreover, forests have long been so upset in structure that it is almost already difficult to find high-quality model trees for trunk analysis in Russian forests. In addition, model trees do not allow the analysis of the crown due to breakage of branches when they fall to the ground, and also do not allow multiple tests and measurements.

There is also a method of analyzing a tree trunk (US Pat. RU 2201593, IPC ⁷ G01N 33/46, A01G 23/00, A01G 23/02. Method for analyzing a tree trunk. / Verkhunov P.M., Mazurkin P.M. (RF); applicant and patent holder, Mariysk State Technical University - No. 2001116223/13; application form 13.06.01; published March 27, 2003, Bulletin No. 5), including a description of the properties of the selected tree and its place of growth, applied to trunk marks on the north and south sides, 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 to the start of the crown, size the trunk is made on sections of non-multiple lengths depending on the location of the bases of branches and branches, and sections of multiple lengths are marked at least twice - first at the places of smallest diameters between the bases of tree branches, and then along the tops of these irregularities with the measurement of the corresponding distances from the root neck with evaluation of several generators on an uneven trunk surface.

The advantage of this method is the ability to measure irregularities in the trunk of accounting trees using geodetic instruments, but the main disadvantage is the inability to analyze the crown according to the measurement results from the root neck to the crown top by whorls of spruce. Thus, the prototype does not allow complex measurement, and then analysis in office conditions of the measured data, the trunk and crown of a growing spruce tree. Moreover, each type of tree has a unique crown structure, and the spruce crown is the most geometrically and mathematically correct. Moreover, spruce is often used in landscaping the main areas of cities, towns and other settlements in the area of distribution of this tree species.

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 analysis method not only to model spruce trees, but also to growing spruce accounting trees, and based on the results of the analysis of crown of model and registration spruce trees, the ecological quality of the surrounding forest and other environment is assessed , including single growing trees ate an assessment of the ecological quality of the rural or urban environment.

This technical result is achieved in that a method for analyzing the trunk and crown of a spruce tree, including a description of the properties 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 from the root neck to the first dead knot and the first living branch to the beginning of the crown, moreover, the marking of the trunk is performed on sections of multiple lengths, depending on the location of the bases of branches and branches, and sections of multiple lengths are marked at least m Here, twice - first at the places of smallest diameters between the bases of branches and tree branches, then at the tops of these irregularities with the measurement of the corresponding distances from the root neck with the assessment of several generators on the uneven surface of the trunk, characterized in that the measurements and analysis of the trunk from bottom to top from the root neck to the beginning of the crown is supplemented by measuring and analyzing the spruce trunk to the top of the terminal shoot along the whorls of the crown branches, and to analyze the crown of the model or registration spruce tree, the distances between the whorls are measured xy down, taking as the origin the top point of the terminal shoot of spruce, measurements of irregularities on the bases of branches and twigs in the crown are carried out from top to bottom from the terminal shoot to the beginning of the crown or knotless zone of the trunk, and on the whorls of the spruce tree, points from the top of the terminal shoot to the midpoints of the bases of the branches of one whorl of the crown of spruce, according to the measured distances of variable height from the root neck to each whorl of the crown, statistical modeling reveals the growth in height of the model or accounting The trees ate according to biological time, and from top-down distances between whorls from the terminal shoot of spruce to the beginning of the crown with branches and branches, statistical modeling reveals a growth in height during the retrospective time from the moment of measurements to the biological age of the branches of one whorl at the model or accounting tree ate.

To identify the annual growth of the terminal shoot, measurements and analysis of the crown of the accounting tree are performed in late autumn or early winter, and to identify the growth of the terminal shoot for the current year, measurements are performed at least five times during the growing season when the first measurement is made before the juice moves in the early spruce tree in the spring.

The data on the cross section at a height of 1.3 m and other characteristic sections of the trunk for comparison with existing methods of taxation of tree trunks and plantings are calculated according to the equation of the lateral generatrix of the trunk or the equations of its individual parts of different curvature obtained after analysis of the trunk of the accounting tree, with the assessment of several generators on uneven trunk surface from the root neck to the crown of the terminal shoot.

The butt part of the trunk to a height of 1.3 m and higher to the waist of the trunk of the counting tree is divided into several small sections of non-multiple lengths by geodetic instruments, for example, on average, about 0.5 m or less, to accurately describe the shape of the stiffness of the trunk of the counting tree.

The knotless zone of the log tree trunk, as well as the trunk zone with dead branches before the live branches of the crown of the spruce tree are marked, are divided into multiple or multiple lengths of sections of the log tree trunk using geodetic instruments, for example, using a theodolite or an electronic total station.

The trunk of a curved reference tree is marked into multiple sections by sighting with geodetic instruments, for example, a theodolite or an electronic total station, at a distance from the reference tree at the places of transitions from one curvature to another with measurements of diameters in these places.

Using the variable distances measured at the end of autumn or the beginning of winter, from the butt of the neck to the crown of the terminal shoot, statistical modeling reveals the annual growth of the spruce tree in height in a retrospective time scale, and the biological time scale is calculated as the difference between the total age of the tree from the root neck to the crown of the terminal shoot and retrospective time from one year of age at the terminal shoot along the whorls of branches and twigs, and the full age of the spruce tree is determined by the model Foot tree on the butt SPIL-circle, and at the accounting year layers of wood on wood core according to the formula:

where t is the retrospective age of the spruce tree starting from the age of the terminal shoot, provided t = 1, years;

N _m - the height of the whorl from the root neck to the middle of the whorl according to measurements from the bottom up, m;

H is the full height of the spruce tree, taking into account the crown with living branches, the zone with knots (dead branches) and the knotless zone from the root neck of the trunk to the tip of the terminal shoot, measured by a geodetic instrument, for example, an eclimeter, a theodolite, or an electronic total station, m;

a ₁ ... a ₆ - parameters of the statistical model, depending on the shape of the trunk and crown structure according to the location of the whorls at a particular spruce tree and calculated from the measured data of the height of the whorl and its serial number starting from the terminal shoot.

By measuring from top to bottom the variable distances between the whorls of the spruce tree, statistical modeling reveals the annual retrospective growth of the spruce accounting tree in height in the middle of the whorls of the branches and twigs of the model or registration spruce tree starting from the terminal shoot, according to the formula:

,

,

,

,

where Z _H is the annual growth in height of the spruce tree starting from the year of measurements deep into the retrospection of the biological time of the tree, m,

Z ₀ - growth for the current year of the terminal shoot of a spruce tree, m,

r is the rank (number) of the whorl of the spruce tree when counting from top to bottom, and for the crown of the terminal shoot when measuring in late autumn or early winter, r = 0, and the first whorl from the terminal shoot from top to bottom gets the rank r = 1,

A is the amplitude (half) of the vibrational disturbance of the growth of the tops of the measured model or accounting spruce tree over the past few years, m,

p - half the period of the oscillatory growth of the top of the model or accounting tree of spruce in recent time, years,

a ₁ ... a ₁₄ are the parameters of the statistical regularity, calculated from the results of measurements of the process of adaptation to the growing conditions of the annual growth of the studied tree of the model or registration spruce tree over the past few years before cutting the model tree or before taking measurements from the registration spruce tree.

By measuring from top to bottom the variable distances between the whorls of the spruce tree by statistical modeling, a retrospective growth of the spruce accounting tree in height along the middle of the whorls of the branches and knots of the model or registration spruce tree is revealed starting from the terminal shoot when vibrational waves of adaptation to the environment and industrial impacts of vital activity in the past were detected throughout the height of the crown of the tree ate according to the formula:

where Z _H is the annual growth in height of the spruce tree starting from the year of measurements deep into the retrospection of the biological time of the tree, m,

Z _H1 ... Z _H7 - components of the growth of the tree trunk by whorls in the coordinate system with a beginning from the crown of the terminal shoot to the root neck of the spruce tree trunk, m,

Z ₀ - growth for the current year of the terminal shoot of a spruce tree, m,

r is the rank (number) of the whorl of the spruce tree when counting from top to bottom, and for the crown of the terminal shoot when measuring in late autumn or early winter, r = 0, and the first whorl from the terminal shoot from top to bottom gets the rank r = 1,

And ₁ is the amplitude (half) of the vibrational disturbance of the growth of the tops of the measured model or accounting spruce tree over the past few years, m,

p ₂ - half the period of the oscillatory growth of the top of the model or accounting tree spruce for the last time, years,

And ₂ ... And ₄ are the amplitudes (half) of the oscillatory disturbance of the growth between the whorls in different parts of the crown of the measured model or accounting tree of spruce over the years of existence of all whorls of the crown, m,

p ₂ ... p ₄ - half the period of the oscillatory growth of the spruce tree trunk between the whorls in the crown of a model or accounting spruce tree, years,

A ₇ - the amplitude (half) of the oscillatory disturbance of the growth of the entire trunk from the terminal shoot to the root neck, taking into account dead branches, fallen branches and overgrown whorls for the entire age of the spruce tree, m,

p ₇ - half the period of the oscillatory growth of the entire model or accounting tree of spruce for its entire age, years,

a ₁ ... a ₄₆ are the parameters of the statistical regularity calculated by the results of measurements on the spruce tree whorls, showing partial processes of the spruce tree adapting to the growing conditions of the annual growth in biological life time of the spruce tree or accounting tree for all years of life from the seedling to the felling of the model tree or until taking measurements at the spruce tree.

The essence of the technical solution lies in the fact that the distances between the whorls, showing the growth of the spruce trunk in height, are measured from top to bottom and thereby the abscissa axis begins at the crown of the terminal shoot, and the ordinate axis at the zero point becomes the total height of the tree, counted from the root neck of the spruce trunk to the crown of the terminal shoot, and the growth of the terminal shoot for the year, if the measurements were taken in late autumn or early winter (in winter measurements are difficult due to the layer of snow on the ground and snow lying on the branches).

The essence also lies in the fact that the number of the whorl in the spruce coincides with its age, therefore, the rank of the whorl 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. Such a whorl is the last group of dried branches (branches) on the knot part of the trunk at the border with the knotless zone. Thus, a retrospective is achieved not only by the lower whorl of the living branches of the crown of the spruce tree, but also by the lower whorl of twigs at the border with the knotless zone of the spruce trunk.

The essence also lies in the fact that a retrospective on simple and clear measurements of growth and growth of spruce from whorls located on the trunk along multiple sections of the trunk allows us to identify wave processes of the past in the life of the studied spruce tree using the identified statistical patterns. This type of tree is also easily adaptable in the urban environment, being a stable plant in the landscaping of various cultural landscapes, parks, alleys and decorative plantings. Therefore, wave disturbances in the gain along the whorls show the adaptation of this spruce to its environment. A large number of spruce trees measured in this way will highlight the patterns of sustainable growth and development of spruce forest trees.

The positive effect is that the identification of statistical patterns of spruce tree growth will allow you to manage spruce forest plantations, grow healthy and tall spruce forests, and also determine the environmental endurance limits of these plant species. In addition, the positive effect lies in the fact that measurements can also be carried out on reference trees without cutting model trees, and then completely abandoning them in the forest taxation of spruce forests. The proposed method does not involve physical damaging effects on the studied accounting trees of spruce.

A significant novelty is the measurement of the surface of the trunk at least three times:

firstly, by reducing the diameters of the cross sections of the trunk for a technical assessment of the trunks of model trees and spruce trees in terms of volume and increase in volumes of wood, that is, in technical forest taxation;

secondly, by elevations in the diameters of the sections of the trunks for engineering and environmental assessment of the spruce and the entire territory on which the studied single or group trees spruce grow in parks and cultural landscapes;

thirdly, by elevations on the whorls of spruce with the determination in the middle of their distances between adjacent whorls, including the length of the terminal shoot of the measured spruce.

In this regard, the proposed technical solution has significant signs of novelty, ease of implementation in production conditions, a positive effect both in the forestry sector and in engineering ecology, as well as the prospect of expanding the areas of practical application of the landscape ecology methodology with growing on the territory of these forest, agroecological, rural and urban areas of trees ate without their destruction in a growing state. At the same time, repeated measurements of spruce accounting trees will allow for long-term monitoring of the surrounding environment of these spruce accounting trees. Although when measuring model trees, only data that is once-in-time is generated, they supplement the existing methodology of forest taxation on model trees with a new method of measuring crown from whorls.

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

Figure 1 shows the parameters of the spruce tree, measured in forest taxation and taxation of individual growing trees: ksh - root neck; D _cr - the diameter of the crown; N _cr - the length or height of the crown of spruce; H - the height of the tree from the root neck to the crown of the terminal shoot of spruce; 1 - crown of the accounting or model spruce tree; 2 - terminal shoot of spruce; figure 2 shows the location of the crown in the new coordinate system, when zero is placed on the crown of the terminal shoot, and the axis of the retrospective time is located from top to bottom until the last whorl of branches on the border with the knotless zone of the trunk; N _m - a variable height from the root neck of the trunk along the whorls to the top of the terminal shoot, that is, to the height of the whole spruce tree; Z _N - annual growth of the spruce trunk along the whorls starting from the terminal shoot along the distances between the whorls to the beginning of the knotless zone of the spruce trunk; figure 3 shows a photo of a young spruce with an additional indication of the rank of the whorls, and the terminal shoot gets a zero rank; figure 4 shows graphs of the rank distribution of the height of the whorls of a model tree of spruce of the first class of age; figure 5 is the same of the third class of age; figure 6 is the same fourth age class; Fig.7 shows a swarm of measuring points of distances between the whorls, that is, the growth of the trunk of this tree, depending on the rank of the whorls starting from the terminal shoot; on Fig - a swarm of points and a graph of the dependence of the growth of the barrel in height from the rank of the whorls with the exception of a sharply deviating one point in Fig.7; figure 9 shows a graph of the fourth component of the statistical regularity, showing the wave adaptation of the studied spruce tree to the conditions of the place of growth, taking into account the crisis year of 16 years ago; figure 10 shows a graph of the fifth component of the wave adaptation of the model spruce tree to the conditions of growth and development over the last 17 years of life before felling; figure 11 shows a graph of the sixth component of the statistical regularity, showing the wave adaptation of the model tree of spruce by the growth of the trunk in retrospect in the period 5 ... 14 years; on Fig shows a graph of a wave adaptation decreasing towards the terminal shoot along the seventh component of the desired pattern for the entire age of the spruce tree, including the fallen whorls on the knotless zone of the tree trunk.

A method for analyzing the trunk and crown of a spruce tree, such as a model spruce tree, includes such actions.

The easiest to implement the proposed method is the measurement of a model tree of spruce, felled and lying on the ground. In this case, well-known methods and tools for taxation of a model tree with a measuring tape are used. Measurement of the accounting tree requires the use of new methods using geodetic instruments.

Using a measuring tape on a dumped model tree, the height H is measured from bottom to top from the root neck to the top of the terminal shoot. Then in crown 1 of the lying trunk, before measuring or after cutting off the branches and branches, a measuring tape is applied to the trunk starting from the crown of the terminal shoot 2. Therefore, the distances between the whorls are measured from top to bottom, taking the top point of the terminal shoot of spruce as the origin. In this case, measurements of irregularities on the bases of branches and branches in the crown are carried out from top to bottom from the terminal shoot to the beginning of the crown or knotless zone of the trunk.

Moreover, according to the whorls of the spruce tree, the points from the top of the terminal shoot to the middle of the bases of the branches of one whorl of the spruce crown are taken for irregularities, according to the measured distances of variable height from the root neck to each whorl of the crown, statistical modeling reveals the growth in height of the model spruce tree by biological time, and by the measured from top to bottom, the distance between the whorls from the terminal shoot of spruce to the beginning of the crown with branches and twigs by statistical modeling reveals a gain in height during retrospective time Meni from the moment of measurement to the biological age of a whorl of branches in the model tree spruce.

Then, measurements are taken over the cross section at a height of 1.3 m and other characteristic sections of the trunk, after which, according to the measurements, the equation of the trunk generatrix is determined. The butt part of the trunk to a height of 1.3 m and higher to the waist of the tree trunk is divided into several small sections of non-multiple lengths, for example, on average about 0.5 m or less, to accurately describe the shape of the stiffness of the tree trunk.

The knotless zone of the tree trunk, as well as the zone of the trunk with dead branches before the start of the living branches of the crown of the spruce tree, is marked on multiple or non-multiple lengths of sections of the tree trunk using a measuring tape.

The trunk of a curved accounting tree is marked on multiple sections with a measuring tape at the places of transitions from one curvature to another with diameter measurements at these places with a measuring fork.

Using the variable distances measured at the end of autumn or the beginning of winter, from the butt of the neck to the crown of the terminal shoot, statistical modeling reveals the annual growth of the spruce tree in height in a retrospective time scale, and the biological time scale is calculated as the difference between the total age of the tree from the root neck to the crown of the terminal shoot and retrospective time from one year of age at the terminal shoot along the whorls of branches and twigs, and the full age of the spruce tree is determined by the model Foot tree on the butt SPIL-circle, and at the accounting year layers of wood on wood core according to the formula:

,

,

where t is the retrospective age of the spruce tree starting from the age of the terminal shoot, provided t = 1, years;

N _m - the height of the whorl from the root neck to the middle of the whorl according to measurements from the bottom up, m;

H is the full height of the spruce tree, taking into account the crown with living branches, the zone with branches (dead branches) and the knotless zone from the root neck of the trunk to the top of the terminal shoot, m;

a ₁ ... a ₆ - parameters of the statistical model, depending on the shape of the trunk and crown structure according to the location of the whorls at a particular spruce tree and calculated from the measured data of the height of the whorl and its serial number starting from the terminal shoot.

By measuring from top to bottom the variable distances between the whorls of the spruce tree, statistical modeling reveals the annual retrospective growth of the spruce tree in height in the middle of the whorls of the branches and branches of the spruce model tree starting from the terminal shoot according to the formula:

,

,

,

,

where Z _H is the annual growth in height of the spruce tree starting from the year of measurements deep into the retrospection of the biological time of the tree, m,

Z ₀ - growth for the current year of the terminal shoot of a spruce tree, m,

r is the rank (number) of the whorl of the spruce tree when counting from top to bottom, and for the crown of the terminal shoot when measuring in late autumn or early winter, r = 0, and the first whorl from the terminal shoot from top to bottom gets the rank r = 1,

A is the amplitude (half) of the vibrational disturbance of the growth of the top of the measured model tree over the past few years, m,

p - half the period of vibrational growth of the top of the model tree spruce in recent time, years,

and ₁ ... a ₁₄ are the parameters of the statistical regularity, calculated by the results of measurements of the process of adaptation to the growing conditions of the annual growth of the studied model tree of spruce over the past few years before cutting the model tree of spruce.

By measuring from top to bottom the variable distances between the whorls of the spruce tree by statistical modeling, a retrospective growth of the spruce tree in height along the middle of the whorls of the branches and branches of the spruce model tree is revealed starting from the terminal shoot when vibrational waves of adaptation to the environment and man-made effects of vital activity in the past were detected over the entire crown height ate according to the formula:

where Z _H is the annual growth in height of the spruce tree starting from the year of measurements deep into the retrospection of the biological time of the tree, m,

Z _H1 ... Z _H7 - components of the growth of the tree trunk by whorls in the coordinate system with the beginning from the top of the terminal shoot to the root neck of the spruce tree trunk, m,

Z ₀ - growth for the current year of the terminal shoot of a spruce tree, m,

r is the rank (number) of the whorl of the spruce tree when counting from top to bottom, and for the crown of the terminal shoot when measuring in late autumn or early winter, r = 0, and the first whorl from the terminal shoot from top to bottom gets the rank r = 1,

And ₁ is the amplitude (half) of the vibrational disturbance of the growth of the top of the measured model tree over the past few years, m,

p ₂ - half the period of vibrational growth of the top of the model tree of spruce in recent time, years,

And ₂ ... And ₄ are the amplitudes (half) of the oscillatory disturbance of the growth between the whorls in different parts of the crown of the measured model tree of spruce over the years of existence of all whorls of the crown, m,

p ₂ ... p ₄ , - half the period of the oscillatory growth of the spruce tree trunk between the whorls in the crown of the spruce model tree, years,

A ₇ - the amplitude (half) of the oscillatory disturbance of the growth of the entire trunk from the terminal shoot to the root neck, taking into account dead branches, fallen branches and overgrown whorls for the entire age of the spruce tree, m,

p ₇ - half the period of vibrational growth of the entire model tree of spruce for its entire age, years,

a ₁ ... a ₄₆ are the parameters of the statistical regularity calculated by the results of measurements on the whorls of the spruce tree, showing partial processes of the annual growth of the trunk adapted to the growing conditions in the biological life of the spruce tree for all years of life from the seedling to the felling of the spruce tree.

A method for analyzing the trunk and crown of a spruce tree is implemented, for example, when processing a forest model tree in a spruce tree as follows.

First, a test plot of the spruce tree is selected, and then model trees of spruce are selected according to their external characteristics. The choice of a model tree and a description of its taxation features on the trial plot are performed according to the intended sequence of rolls, marks on the north and south sides are applied to the trunk, and the location of the root neck is established. The taxation indicators of crown 1 are also measured and the nature of the location of the terminal shoot 2 is indicated.

Tree cutting is performed near the root neck of the trunk. On a felled trunk, the distances to the first dead and first living knots, to the start of the crown, and other taxation indicators are measured. After measuring the fallen spruce tree, the trunk is chopped or cleaned of branches, maintaining its whorls, tops and terminal shoots, and then the trunk is marked into separate sections of multiple (0.5, 1 or 2 m), multiple-multiple lengths (depending on the quality of the trunk shape in individual zones along the length from the butt to the top) or all sections of non-multiple lengths (usually trunks of low-quality forest trees and lonely growing trees), including crown whorls.

All measurements are recorded in a log, and for whorls they show the rank of their location from top to bottom along the trunk from the terminal shoot (assigned a zero rank) to the boundary between the knotless and knot zones of the model tree trunk.

Then the trunk of the model tree is processed according to known methods of cutting the trunk, including the crown zone.

Circles are cut out at the points of section markings and at the places of sharp transitions of the curvature of the generatrix of the trunk (starting from the base of the trunk to its top), the first cut being made at the place of marking near the root collar, and the second - stepping from it to the top by the thickness of the circle, to each sawn off circle they give marks on the numbers of the trial area of the model tree and the sawn circle, moreover, the designations are made on the slightly smoothed upper part of the circles, and the lower parts of the circles in office conditions are used to calculate annual rings and measure diameters.

According to field measurements in office conditions, the analysis of the trunk from the bottom up from the root neck to the beginning of the crown is supplemented by the analysis of the spruce trunk to the top of the terminal shoot along the whorls of the crown branches, and the measured height of the variable tree from the measured height from the root neck to each crown whorl reveals statistical growth ate according to biological time, and according to the measured from top to bottom distances between whorls from the terminal shoot of spruce to the beginning of the crown with branches and branches, statistical modeling reveal a growth in height during the retrospective time from the moment of measurement to the biological age of the branches of one whorl in the model tree of spruce.

According to the variable distances measured at the end of autumn or the beginning of winter, from the butt tree neck to the crown of the terminal shoot, statistical modeling reveals the annual growth of the spruce tree in height in a retrospective time scale, and the biological time scale is calculated as the difference between the total age of the tree from the root neck to the crown of the terminal shoot and retrospective time from one year of age at the terminal shoot along the whorls of branches and twigs, and the full age of the spruce tree is determined by the model tree Islands on the butt SPIL-circle by the formula:

,

,

where t is the retrospective age of the spruce tree starting from the age of the terminal shoot, provided t = 1, years;

N _m - the height of the whorl from the root neck to the middle of the whorl according to measurements from the bottom up, m;

H is the full height of the spruce tree, taking into account the crown with living branches, the zone with branches (dead branches) and the knotless zone from the root neck of the trunk to the top of the terminal shoot, m;

a ₁ ... a ₆ - parameters of the statistical model, depending on the shape of the trunk and crown structure according to the location of the whorls at a particular spruce tree and calculated from the measured data of the height of the whorl and its serial number starting from the terminal shoot.

By measuring from top to bottom the variable distances between the whorls of the spruce tree, statistical modeling reveals the annual retrospective growth of the spruce accounting tree in height along the middle of the whorls of the branches and branches of the spruce model tree starting from the terminal shoot according to the formula:

,

,

,

,

,

,

where Z _H is the annual growth in height of the spruce tree starting from the year of measurements deep into the retrospection of the biological time of the tree, m,

Z ₀ - growth for the current year of the terminal shoot of a spruce tree, m,

r is the rank (number) of the whorl of the spruce tree when counting from top to bottom, and for the crown of the terminal shoot when measuring in late autumn or early winter, r = 0, and the first whorl from the terminal shoot from top to bottom gets the rank r = 1,

A is the amplitude (half) of the vibrational disturbance of the growth of the top of the measured model tree over the past few years, m,

p - half the period of the oscillatory growth of the top of the model or accounting tree of spruce in recent time, years,

and ₁ ... a ₁₄ are the parameters of the statistical regularity, calculated from the results of measurements of the process of adaptation to the growing conditions of the annual growth of the studied model tree of spruce over the past few years before cutting the model tree of spruce.

By measuring from top to bottom the variable distances between the whorls of the spruce tree by statistical modeling, a retrospective growth of the counting tree of spruce in height along the middle of the whorls of the branches and branches of the spruce model tree is revealed starting from the terminal shoot when vibrational waves of adaptation to the environment and industrial impacts in the past were detected over the entire crown height spruce tree according to the formula:

where Z _H is the annual growth in height of the spruce tree starting from the year of measurements deep into the retrospection of the biological time of the tree, m,

Z _H1 ... Z _H7 - components of the growth of the tree trunk by whorls in the coordinate system with a beginning from the crown of the terminal shoot to the root neck of the spruce tree trunk, m,

Z ₀ - growth for the current year of the terminal shoot of a spruce tree, m,

r is the rank (number) of the whorl of the spruce tree when counting from top to bottom, and for the crown of the terminal shoot when measuring in late autumn or early winter, r = 0, and the first whorl from the terminal shoot from top to bottom gets the rank r = 1,

And ₁ is the amplitude (half) of the vibrational disturbance of the growth of the top of the measured model tree over the past few years, m,

p ₂ - half the period of vibrational growth of the top of the model tree ate over the past time, years,

And ₂ ... And ₄ are the amplitudes (half) of the oscillatory disturbance of the growth between the whorls in different parts of the crown of the measured model tree of spruce over the years of existence of all whorls of the crown, m,

p ₂ ... p ₄ - half the period of the oscillatory growth of the spruce tree trunk between the whorls in the crown of the spruce model tree, years,

A ₇ - the amplitude (half) of the oscillatory disturbance of the growth of the entire trunk from the terminal shoot to the root neck, taking into account dead branches, fallen branches and overgrown whorls for the entire age of the spruce tree, m,

p ₇ - half the period of vibrational growth of the entire model tree of spruce for its entire age, years,

a ₁ ... a ₄₆ are the parameters of the statistical regularity calculated by the results of measurements on the whorls of the spruce tree, showing partial processes of the annual growth of the trunk adapted to the growing conditions in the biological life of the spruce tree for all years of life from the seedling to the felling of the spruce tree.

Examples. In the article (Starostin V.A. On the distribution of branches by thickness in the crown of spruce in forest crops. // Interuniversity collection of scientific tr. "Forestry, forest crops and soil science." - L .: LTA, 1991. - S. 105-109) shows statistical tabular data on the average values of the parameters of the living crown in spruce trees of different growth classes.

Tables 1-3 and Figs. 4-6 show graphs of changes in the height N _{m of the} whorl arrangement depending on the rank r (this code scale differs from the serial number by introducing a zero value) whorls starting from the top of the tree (terminal shoot) for I, III and IV classes of spruce tree growth.

In this case, the origin of the coordinate system under the condition r = 0 is located on the top of the terminal shoot of the spruce tree. Then it coincides with the movement of the flows of nutrients (assimilates) coming through the sapwood of the woody body from the crown to the roots of the tree.

For the first class of age of the spruce tree, a model was obtained (Fig. 4)

The adaptability coefficient is taken into account with its negative sign, which characterizes the crisis process of the influence of the external environment on the first natural component of formula (1). The first class of tree growth differs in that genetically, according to the law of death, the flow of nutrients from top to bottom in the tree spreads almost evenly. However, this process is hindered by the allometric growth of the nutrient supply crisis. If the age at which each whorl appeared was taken into account, the explanation would be clearer than that given here. But the functional relationship between the variable age and the distribution of whorls along the trunk of a spruce tree will be mutually inverse.

For the third growth class, the formula is obtained (Table 2, Fig. 5)

.

.

In the fir tree of the third growth class, the first component rapidly decreases, which also means a decrease in the flow of nutrients with increasing whorl rank. In this case, the maximum of the second component falls on the fifth whorl from the top of the tree. Moreover, the crisis influence of the external environment is insignificant and was manifested already in the oppression of this tree ate by other individuals in the spruce (and maybe by other natural and artificial reasons).

The spruce tree of the fourth growth class has a regularity (Table 3 and Fig. 6) of a change in the height of the whorl of branches in the form of a formula

in which the influence of the second crisis component is even less significant.

From these examples it can be seen that the general pattern of change in the height of the whorls depending on the rank of the whorls (groups of shoots) by design has the form

and is identical to the equation of the generatrix of the trunk.

In this case, the age of the spruce tree starting from the terminal shoot will be equal to the equation t = r + 1.

Then the growth of the spruce tree in height is determined by an equation of the form

,

,

where t is the retrospective age of the spruce tree starting from the age of the terminal shoot, provided t = 0, years.

The annual growth of Z _{H of the} trunk of a spruce tree of the first growth class according to formula (1) and FIG. 4, starting from a terminal shoot at the age of one year to the end of the whorls taken into account by rank, is determined by complex equations containing seven components. Moreover, in the past, as shown in Fig. 7, from the moment of cutting down the model tree 16 years ago by rank or 17 years ago from the crown of the terminal shoot, there was a sharp decrease in growth between the whorls.

At first, this sharply defined point is excluded. Then a trend pattern was obtained (the first two components) with additional wave adaptation according to the third component of the growth equation of the form

A = 124.3819r ^3.13020 exp (-8.08701r ^0.23853 ).

p = 6.82675-0.28175r ^0.99606 .

Comparison with formula (4) shows that the difference lies in the positive retrospective growth dynamics. In other words, with a decrease in the height of the whorl N _m there is an increase in the growth of the trunk Z _H to the early age of the spruce tree. But the earliest branches died out, even the branches fell off and were overgrown with bark and wood. Therefore, the trend in the first two components of formula (6) will continue only of the 2nd rank according to the data in Table 1. For an earlier age, spruce trees in the past without distance measurements by whorls or by their noticeable traces in the form of a knot zone of a spruce trunk according to formula (6) cannot be said a posteriori.

The third component of formula (6), as can be seen from the graph in Fig. 8, when considering the graph from right to left, it shows not only a decrease in growth in height between the whorls, but also shows a calming vibrational adaptation of the tree to its environment (conditions of the place of growth). The frequency of vibrational disturbance gradually decreases, the plant organism receives smooth vibrational changes in growth in height, and this indicates the relatively comfortable living conditions of this fir-tree of the first growth class.

Thus, there is the possibility of biometric substantiation of growth classes and then it will be possible to abandon such a grouping.

Residues from formula (7) with the inclusion of a previously excluded point are shown as a swarm of points in Fig.9. At the same time, we note here that in heuristic-statistical modeling using the methodology for identifying stable distribution laws it is impossible without any justification, as is done in classical statistics according to mass statistical data, to throw out certain points.

Sharply deviating years in the life of a spruce tree should find a physiological explanation, but in an article by V.A. Starostin said nothing about this. Therefore, the recommendation applies to future experiments.

Figure 9 shows a graph of the fourth component (the second component of the wave vibrational disturbance of the body to external influences) according to the equation of the wavelet function prof. P.M. Mazurkina species

The amplitude of the oscillation changes according to the biotechnical law, as it was in the previous formulas, that is, it shows the stress excitation of the organism of the model spruce tree (of course, only for the duration of the life span before cutting - after death the model tree will not show anything and will dry in the wood for the loggers ) to external stimuli.

The pulse change in height growth occurred over six years, from the time 20 years ago (r = 19) to 14 years (r = 13). During these six years, three positive changes in growth (above the abscissa axis) gave way to two negative growths (below the abscissa axis), and one impulsive crisis turned out to be the largest in amplitude. By definition, this graph will be a graph of the wavelet function when the area on the upper side of the coordinate plane is equal to the area in the negative half-plane. Due to the biotechnological change in the amplitude and period of the oscillatory disturbance of the studied spruce tree, the wavelet function will be asymmetric, and this feature is not inherent in ordinary signals (symmetrical impulses), but inherent in signals from living matter.

The further 14 years of growth and development of the studied spruce occurred along a calm wave, as can be seen from right to left at the points in Fig. 9. This fact means that this tree has overcome the crisis period in its growth and development.

However, as can be seen from figure 10, there is a new wave of indignation with increasing frequency and increasing amplitude (you need to look from right to left in the chronological time scale). Although the amplitude of the increasing vibration reached only ± 6 cm, it is not yet known what would happen in the future if the model tree became a counting tree and it could be measured in the distant future by modern geodetic instruments with an accuracy of ± 1 ... 3 mm. But the life of this spruce was interrupted and the wave palpitations in the terminal shoot were brutally destroyed.

The equation of this incomplete oscillation has the form

Another ten times smaller amplitude compared to FIG. 9 from 16 to 6 years ago, another signal change in height growth occurred at the whorls No. 5 ... No. 15 according to the formula (FIG. 11)

If it were possible to compare with climatic measurements, as well as with the registration of phenomena and processes in the territory of the place of growth of the spruce tree, then it would be possible to indicate the reasons for the appearance of certain asymmetric wavelet signals.

The graph in Fig. 11 shows that four years ago, before his forced death from a person, the spruce tree successfully overcame this small excitement in the physiological processes of his body.

All partial unrest was left behind in a retrospective time of 23 years (from rank 22), which is the age of the crown, and the spruce tree itself was much older than 23 years, but we do not know about this from the literary source. Thus, the spruce crown has its own age, changing during the life of the tree depending on the conditions of the place of growth.

For the entire age of the crown according to the graph in Fig. 12, there was a decreasing oscillation (again, we recall that we must look from right to left in the biological time of the crown) of trunk growth in height.

This is almost mystical for us 23-year-old action of spruce due to the similarity of the extreme points of the wave with the shape of the crown of the spruce itself is characterized by the equation of the statistical regularity of the form

It may well turn out that such an oscillatory disturbance in retrospective time will continue until the beginning of the tree’s life, that is, until the first year of the seedling. The fact is that almost up to the age of 30, the spruce forest boils with the values of taxation indicators for the damping waves of the oscillatory adaptation of the population to the conditions of the place of growth, and only after 30 years the arborist will confidently point out the leading trees in growth and development. A person changes the conditions of his living so quickly and so fundamentally that the trees ate for almost 350 million years of their evolution are simply not used to the frenzied revolutionary pace of change in the external environment and thus the spruce trees are degrading.

Thus, all seven components of the same general formula for the behavior of spruce were identified by measuring the location of the whorls on the trunk. This gives a hypothesis that on registration trees it will be possible to monitor the environment for the age of the crown of even one single spruce growing on a given territory in rural or urban areas. The high accuracy of modern geodetic measurements allows us to hope that by repeated measurements during the growing season it will be possible to determine the patterns and physiological processes of the spruce tree.

The effectiveness of the new method is manifested in the fact that it allows us to analyze not only model trees with trunks of irregular stereometric shape along the crown with whorls of spruce. The greatest effect will be achieved by multiple measurements of whorls of spruce on the accounting trees located in different growing conditions.

Claims (9)

1. A method for analyzing the trunk and crown of a spruce tree, including a description of the properties of the selected tree and the place of its growth, drawing marks on the north and south sides on the trunk, determining 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 branches to the beginning of the crown, moreover, the marking of the trunk is performed on sections of non-multiple lengths, depending on the location of the bases of the branches and branches, and sections of short lengths are marked at least twice - first in the places of the smallest diameter between the bases of the branches and branches of the tree, then along the tops of these irregularities with the measurement of the corresponding distances from the root neck with the assessment of several generators on the uneven surface of the trunk, characterized in that the measurements and analysis of the trunk from the bottom up from the root neck to the beginning of the crown complement measurements and analysis of the trunk they ate to the top of the terminal shoot along the whorls of the crown branches, and for the analysis of the crown of a model or accounting tree, the spruce distances between the whorls were measured from top to bottom, taking the top coordinate as the origin point of the terminal shoot of spruce, measurements of irregularities on the bases of branches and twigs in the crown are carried out from top to bottom from the terminal shoot to the beginning of the crown or knotless zone of the trunk, and on the whorls of the spruce tree, points from the top of the terminal shoot to the middle of the bases of the branches of one whorl of the spruce tree are taken , by measured distances of variable height from the root neck to each crown whorl, statistical modeling reveals the growth in height of the model or reference spruce tree by biological time, and by The top-down distances between whorls from the terminal shoot of spruce to the beginning of the crown with branches and twigs by statistical modeling reveal a growth in height during the retrospective time from the moment of measurements to the biological age of the branches of one whorl from a model or registration spruce tree. 2. The method for analyzing the trunk and crown of a spruce tree according to claim 1, characterized in that to determine the annual growth of the terminal shoot, measurements and analysis of the crown of the accounting tree are performed in late autumn or early winter, and to detect the growth of the terminal shoot for the current year, the measurements are not less than five times during the growing season during the first measurement before the movement of juices in the spruce tree in early spring. 3. The method of analysis of the trunk and crown of a spruce tree according to claim 1, characterized in that the data on the cross section at a height of 1.3 m and other characteristic sections of the trunk for comparison with existing methods of taxation of tree trunks and stands are calculated according to the equation of the lateral trunk or equations its individual parts of different curvature obtained after analysis of the trunk of the accounting tree, with the assessment of several generators on the uneven surface of the trunk from the root neck to the crown of the terminal shoot. 4. The method of analysis of the trunk and crown of a spruce tree according to claim 1, characterized in that the butt of the trunk to a height of 1.3 m and higher to the waist of the stem of the accounting tree is divided into several small sections of non-multiple lengths with geodetic instruments, for example, on average about 0 , 5 m or less, for an accurate description of the shape of the bumpiness of the trunk of the accounting tree. 5. The method for analyzing the trunk and crown of a spruce tree according to claim 1, characterized in that the knotless zone of the trunk of the counting tree, as well as the zone of the trunk with dead branches before the live branches of the crown of the spruce tree are marked, is divided into multiple or non-multiple lengths of the sections of the trunk of the counting tree with using geodetic instruments, for example, using a theodolite or an electronic total station. 6. The method for analyzing the trunk and crown of a spruce tree according to claim 1, characterized in that the trunk of the curved reference tree is marked in multiple sections by sighting with geodetic instruments, for example, a theodolite or an electronic total station, at a distance from the reference tree, at the points of transition from one curvature to another with measurements of diameters in these places. 7. The method for analyzing the trunk and crown of a spruce tree according to claim 2, characterized in that, according to the variable distances measured from the butt tree neck to the crown of the terminal shoot at the end of autumn or the beginning of winter, the annual growth of the spruce tree in height in a retrospective time scale is revealed by statistical modeling, moreover, the biological time scale is calculated as the difference between the total age of the tree from the root neck to the crown of the terminal shoot and the retrospective time from one year of age at the terminal shoot, according to whorls branches and twigs, and the full age of the spruce tree is determined from the model tree according to the butt cut-circle, and from the reference tree from the annual layers of the core of the wood, according to the formula:
N _m = N exp (-a ₁ (t-1) ^a2 ) -a ₃ (t-1) ^a4 exp (-a ₅ (t-1) ^a6 ,
where t is the retrospective age of the spruce tree, starting from the age of the terminal shoot, provided t = 1, years;
N _m - the height of the whorl from the root neck to the middle of the whorl according to measurements from the bottom up, m;
H is the full height of the spruce tree, taking into account the crown with living branches, the zone with knots (dead branches) and the knotless zone from the root neck of the trunk to the tip of the terminal shoot, measured by a geodetic instrument, for example, an eclimeter, a theodolite, or an electronic total station, m;
a ₁ ... a ₆ - parameters of the statistical model, depending on the shape of the trunk and crown structure by the location of the whorls at a particular spruce tree and calculated from the measured data of the height of the whorl and its serial number, starting from the terminal shoot. 8. The method for analyzing the trunk and crown of a spruce tree according to claim 1, characterized in that, according to the variable top-down distances between the spruce whorls, statistical modeling reveals the annual retrospective growth of the spruce tree in height along the middle of the whorls of the branches and knots of the spruce tree starting from the terminal shoot, according to the formula:
Z _H = Z ₀ exp (a ₁ r ^a2 ) -a ₃ r ^a4 exp (-a ₅ r ^a6 ) + Acos (πr / pa ₁₄ ),
A = a ₇ r ^a8 exp (-a ₉ r ¹⁰ ), p = a ₁₁ ± a ₁₂ r ^a13 ,
where Z _H is the annual growth in height of the spruce tree, starting from the year of measurements deep into the retrospection of the biological time of the tree, m;
Z ₀ - growth for the current year of the terminal shoot of a spruce tree, m;
r is the rank (number) of the whorl of the spruce tree when counting from top to bottom, and for the crown of the terminal shoot when measuring in late autumn or early winter, r = 0, and the first whorl from the terminal shoot from top to bottom gets the rank r = 1;
A is the amplitude (half) of the vibrational disturbance of the growth of the tops of the measured model or reference spruce tree over the past few years, m;
p - half of the period of oscillatory growth of the top of the model or accounting tree of spruce in recent time, years;
a ₁ ... a ₁₄ are the parameters of the statistical regularity calculated by the results of measurements of the process of adaptation to the growing conditions of the annual growth of the studied tree of the model or registration tree of spruce over the past few years before cutting the model tree or before taking measurements at the registration tree of spruce. 9. The method for analyzing the trunk and crown of a spruce tree according to claim 9, characterized in that, according to the measured from top to bottom, the variable distances between the whorls of the spruce, statistical modeling reveals a retrospective growth of the spruce accounting tree in height along the middle of the whorls of the branches and branches of the spruce model or registration tree, starting from the terminal shoot, in the detection of vibrational waves adaptive to the environment and the anthropogenic effects of life in the past, over the entire height of the spruce tree crown, according to the formula:
Z _H = Z _H1 + Z _H2 + Z _H3 + Z _H4 + Z _H5 + Z _H6 + Z _H7 ,
Z _H1 = Z ₀ exp (a ₁ r ^a2 ),
Z _H2 = -a ₃ r ^a4 exp (-a ₅ r ^a6 ),
Z _H3 = A ₁ cos (πr / p ₁ -a ₁₄ ), A ₁ = a ₇ r ^a8 exp (-a ₉ r ^a10 ), p ₁ = a ₁₁ ± a ₁₂ r ^a13 ,
Z _H4 = A ₂ cos (πr / p ₂ ± a ₂₂ ), A ₂ = a ₁₅ r ^al6 exp (-a ₁₇ r ^a18 ), p ₂ = a ₁₉ ± a ₂₀ r ^a21 ,
Z _H5 = A ₃ cos (πr / p ₃ ± a ₃₀ ), A ₃ = a ₂₃ r ^a24 exp (-a ₂₅ r ^a26 ), p ₃ = a ₂₇ ± a ₂₈ r ^a29 ,
Z _H6 = A ₄ cos (πr / p ₄ ± a ₃₈ ), A ₄ = a ₃₁ r ³² exp (-a ₃₃ r ^a34 ), p ₄ = a ₃₅ ± a ₃₆ r ^a37 ,
Z _H7 = A ₅ cos (πr / p ₅ ± a ₄₆ ), A ₅ = a ₃₉ r ^a40 , p ₅ = a ₄₁ ± a ₄₂ r ^a43 exp (-a ₄₄ r ^a45 ),
where, Z _H is the annual growth in height of the spruce tree, starting from the year of measurements deep into the retrospection of the biological time of the tree, m;
Z _H1 ... Z _H7 - components of the growth of the tree trunk by whorls, in the coordinate system from the top of the terminal shoot to the root neck of the spruce tree trunk, m;
Z ₀ - growth for the current year of the terminal shoot of a spruce tree, m;
r is the rank (number) of the whorl of the spruce tree when counting from top to bottom, and for the crown of the terminal shoot when measuring in late autumn or early winter, r = 0, and the first whorl from the terminal shoot from top to bottom gets the rank r = 1;
A ₁ - the amplitude (half) of the vibrational disturbance of the growth of the tops of the measured model or accounting spruce tree over the past few years, m;
p ₂ - half the period of the oscillatory growth of the top of the model or accounting tree of spruce in recent time, years;
A ₂ ... A ₄ - amplitudes (half) of the oscillatory disturbance of the growth between the whorls in different parts of the crown of the measured model or accounting tree of spruce over the years of existence of all whorls of the crown, m;
p ₂ ... p ₄ - half the period of the oscillatory growth of the spruce tree trunk between the whorls in the crown of a model or reference spruce tree, years;
And ₇ is the amplitude (half) of the oscillatory disturbance of the growth of the entire trunk from the terminal shoot to the root neck, taking into account dead branches, dropped branches and overgrown whorls for the entire age of the spruce tree, m;
p ₇ - half the period of oscillatory growth of the entire model or accounting tree of spruce for its entire age, years;
a ₁ ... a ₄₆ - statistical regularity parameters calculated by the results of measurements on the spruce tree whorls, showing partial processes of the spruce tree adaptive to the growing conditions of the annual growth in biological life span of the model or accounting spruce tree for all years of life from the seedling to the felling of the model tree or until taking measurements at the spruce tree.

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