论文部分内容阅读
Abstract This study was conducted on the analytic tree and got the fitting empirical equation of tree growth， in which the tree growth rate was used as the variable and time as the independent variable. The arithmetical operation to the function got the mature age of tree growth， and the mature ages of the timer forest， the protection forest and the specialpurpose forest of Platycladus orientalis were 71， 111 and 141 a， respectively. In addition， the application as well as the research direction and matters needing attention were proposed.
Key words Platycladus orientalis; Practical mature age; Empirical equation; Analytic tree
In forestry production， the mature age of trees is the first problem to meet for the formulation of logging quota and the design of cutting areas， but there is little basic work on the forestry tables in Shandong， most of which is borrowed from other places or relevant national standards， and has not changed for decades. It will inevitably lead to large deviations. In this study， the mature age of Platycladus orientalis was studied by analyzing analytic wood data. P. orientalis is the main tree species for afforestation in the limestone mountainous areas of Shandong Province， which has a long history of cultivation in Shandong. The importance of its ecological location has an irreplaceable role， and it is of great significance to explore its growth and development laws.
Source of Information
Due to limited fund， we carried out the study on the basis of previous survey materials. The analytic tree material was obtained from the average tree analytic tree of P. orientalis that had normally grown for 44 years in Niushan Forest Farm， Feicheng City and was collected on August 1， 1983. The DBH was studied using the section of 2.6 m， and others using the 2 m section. Round disks were cut at the tree height of 5 cm （0 disk）， 1.3， 3.6， 5.6 and 6.6 m， respectively. Interpretation was made strictly according to the technology for analytic tree， and relevant data were collected with 5 years as the age class （process omitted）.
Research Methods
In order to save research costs， we carried out fitting test to various regression equations according to the research method introduced in references[1-3]， the research results of reference[6] and the research method and process of references[4-5] based on the analytic tree information， and finally used following mixed empirical equation to study the growth process of trees： Y（t）=ea-b/t
Wherein a， b are the index parameters of the function to be solved， and e is the base of natural logarithm （2.718 28……）.
Tree growth is affected by a variety of factors， but those with the largest influence are the precipitation amount and the spatial and temporal distribution. In this study， we tried to use the empirical equation to fit the growth process of trees. The fitting equation of the maximum age of DBH （including the equation from the derivation， which was stated in the research process） could get the mature age of DBH. The fitting equation of the maximum age of tree height could get the mature age of tree height. The same method was used to get the ages of quantitative maturity of DBH， DBH square and wood volume growth.
Research Process
A linear equation was formed by taking the logarithm of the equation for tree growth process， and then， the unary linear regression was used to get the values of parameters a， b， which were tested by F test and correlation coefficient R test. Passing the test means that the equation of tree growth is established. The calculation results were shown in Table 1. By looking up the table， the fitting results of ground diameter 1 and wood volume passed the F test with the reliability of about 90%， and ground diameter passed the F test with the reliability of over 95%， while others passed the F test and R test with the reliability of over 99% （100% for wood volume 4）. Passing the F test showed that the mathematical model （the empirical fitting equation） was applicable overall， and all itemspassed the correlation coefficient R test with the reliability of 99.9%， indicating that the relationship with the fitting equation was set up. Therefore， the item of ground diameter 1 was an example to illustrate the problems of using the fitting equation to solve the time for maximum current annual increment and quantitative maturity of trees. The extreme point of the equation for the ground diameter growth speed of the tree （current annual increment， which was completed through the derivation of the Y（t） function in the table， and the process was omitted with only the extreme point given， the same below） was tz=2.66 a， which meant that the growth amount of the tree reached the peak at the second or third year， and there was only a single peak. The extreme point of the equation for the average growth speed of the tree （mean annual increment， which was completed through the derivation of the Y （t）/t function， and the process was omitted with only the extreme point given， the same below） was tm=5.73 a， indicating that the age of quantitative maturity of the tree was 5.73 a （only the ground diameter fitting equation was given， and the fitting equation for other items were the same， thus omitted）. In following discussion， the equations for growth fitting， tree growth speed and average growth speed of the tree were the same， and the meanings of tz and tm were also the same， so the calculation results were given directly. The mature ages of all the items are shown in Table 1. As shown in Table 1， comparing the item square with the item， the values of the parameters increased by 1 time， and the accuracy and the tested F values and R values were the same， which was caused by the mathematical relations of the indexes. In order to compare with the cumulative fitting equation， we established the fitting equation of DBH 3 square， the fitting results of which were closer to wood volume 2 and wood volume 4 （the differences were about 10 a， which might be caused by the deviation of the growth trend curve， the same below）， while the fitting results of DBH 1 square were closer to wood volume 1 and wood volume 3. The fitting value of wood volume 1 was closer to wood volume 3， and fitting value of wood volume 2 was closer to wood volume 4， indicating that the test was highly reliable. In Table 1， the value of tn was the age at intersection point between the current annual increment and mean annual increment curves of the sample tree （those over 46 a was obtained from the trend graph of the growth curve）， which could serve as the practical mature age of the tree. the tm value were all very close to the tn values. Due to the lack of data of 46 a and higher age， the results were more reliable when fitting with empirical equations， and it would be more reliable to set the mature age of the stock as the mature age of the tree according to the research results and the needs in production practice. Conclusions and Application
Through the analysis and judgment of the research results， with the quantitative maturity of the stock as the standard， the practical mature ages of P. orientalis were determined to be 71， 111 and 141 a according to the national standards of the age class of 10 years. And the age group of P. orientalis was divided， as shown in Table 2.
The results of this study indicate that the mature age of the timber forest of the original standard and the conclusion of this study is 10 years earlier than the conclusion of another tree， and the mature age of the protection forest is 20 years earlier than that of the another tree， which might be due to that the sample tree grew faster than the another tree， or caused by the systematic deviation of the study. The mature age of the forest for special purpose is in complete agreement with the another tree.
Discussion
The original mature age standard is 81 a， which may be based on the situations at multiple sites at the time or the need to speed up wood production， without taking the second or even multiple peaks of tree growth into account. Therefore， over time， it is necessary to make appropriate adjustments with the times， because at this stage， the main task of Shandong forestry production of P. orientalis is to ensure that the ecological benefits are brought into play， and timber production is in a secondary position. Although this study has high reliability， it can only be a scientific foresight for future development due to the lack of highage materials. To get more accurate and realistic research conclusions， we must have highage materials， while most older trees are classified as ancient and famous trees for protection， which become an obstacle for the further development of this work. The successful application of modern medical imaging technology in tree measurement has provided powerful technical support for the further development of this project， but there must be strong human， material， financial and technological investment to complete it， and interested colleagues can give it a try. Due to the difficulties in collecting tree samples and limited funds， the empirical equations of tree growth were applied to analyze the analytical tree data in this study. By such， the lack of the insufficient age of the tree was compensated while avoiding the noise impact of time and space differences under various natural conditions and tree differentiation phenomenon on the test results. The practical mature age of P. orientalis was obtained， and through repeated verification， analysis and judgment， it was found that the empirical equations for tree growth are indeed applicable， which is difficult to make a scientific explanation. Limited by various conditions， all kinds of deviations can hardly be avoided， which can only be improved and developed in the research and production practice. However， the suggestions for forest production in this paper were only personal opinions， which required the approval and tests from the experts to put into application.
Zhaohua DENG. Study on the Practical Mature Age of Individual Platycladus orientalis
References
[1] LANG KJ. Forest measurement[M]. Beijing： China Forestry Publishing House， 1985. （in Chinese）
[2] CHEN HH. Mathematical statistics[M]. Beijing： China Forestry Publishing House， 1985. （in Chinese）
[3] LIU GJ. Review guide for vocational qualification test of registered consulting engineer （investment）[M]. Tianjin： Tianjin University Press， 2003. （in Chinese）
[4] GAO JH. Approach into desirable period of forest management in Shandong Province[J]. Journal of Forestry Engineering， 2003（3）： 6-8. （in Chinese）
[5] HU HY. Study on the actual maturity age of individual Pinus densiflora[J]. Journal of Shandong Forestry Science and Technology， 2010（6）： 36-37.（in Chinese）
[6] LI LP. Study on expected maturity age of Shandong Pinus densiflora[J]. Journal of Anhui Agricultural Sciences， 2017， 3： 184-186. （in Chinese）
Key words Platycladus orientalis; Practical mature age; Empirical equation; Analytic tree
In forestry production， the mature age of trees is the first problem to meet for the formulation of logging quota and the design of cutting areas， but there is little basic work on the forestry tables in Shandong， most of which is borrowed from other places or relevant national standards， and has not changed for decades. It will inevitably lead to large deviations. In this study， the mature age of Platycladus orientalis was studied by analyzing analytic wood data. P. orientalis is the main tree species for afforestation in the limestone mountainous areas of Shandong Province， which has a long history of cultivation in Shandong. The importance of its ecological location has an irreplaceable role， and it is of great significance to explore its growth and development laws.
Source of Information
Due to limited fund， we carried out the study on the basis of previous survey materials. The analytic tree material was obtained from the average tree analytic tree of P. orientalis that had normally grown for 44 years in Niushan Forest Farm， Feicheng City and was collected on August 1， 1983. The DBH was studied using the section of 2.6 m， and others using the 2 m section. Round disks were cut at the tree height of 5 cm （0 disk）， 1.3， 3.6， 5.6 and 6.6 m， respectively. Interpretation was made strictly according to the technology for analytic tree， and relevant data were collected with 5 years as the age class （process omitted）.
Research Methods
In order to save research costs， we carried out fitting test to various regression equations according to the research method introduced in references[1-3]， the research results of reference[6] and the research method and process of references[4-5] based on the analytic tree information， and finally used following mixed empirical equation to study the growth process of trees： Y（t）=ea-b/t
Wherein a， b are the index parameters of the function to be solved， and e is the base of natural logarithm （2.718 28……）.
Tree growth is affected by a variety of factors， but those with the largest influence are the precipitation amount and the spatial and temporal distribution. In this study， we tried to use the empirical equation to fit the growth process of trees. The fitting equation of the maximum age of DBH （including the equation from the derivation， which was stated in the research process） could get the mature age of DBH. The fitting equation of the maximum age of tree height could get the mature age of tree height. The same method was used to get the ages of quantitative maturity of DBH， DBH square and wood volume growth.
Research Process
A linear equation was formed by taking the logarithm of the equation for tree growth process， and then， the unary linear regression was used to get the values of parameters a， b， which were tested by F test and correlation coefficient R test. Passing the test means that the equation of tree growth is established. The calculation results were shown in Table 1. By looking up the table， the fitting results of ground diameter 1 and wood volume passed the F test with the reliability of about 90%， and ground diameter passed the F test with the reliability of over 95%， while others passed the F test and R test with the reliability of over 99% （100% for wood volume 4）. Passing the F test showed that the mathematical model （the empirical fitting equation） was applicable overall， and all itemspassed the correlation coefficient R test with the reliability of 99.9%， indicating that the relationship with the fitting equation was set up. Therefore， the item of ground diameter 1 was an example to illustrate the problems of using the fitting equation to solve the time for maximum current annual increment and quantitative maturity of trees. The extreme point of the equation for the ground diameter growth speed of the tree （current annual increment， which was completed through the derivation of the Y（t） function in the table， and the process was omitted with only the extreme point given， the same below） was tz=2.66 a， which meant that the growth amount of the tree reached the peak at the second or third year， and there was only a single peak. The extreme point of the equation for the average growth speed of the tree （mean annual increment， which was completed through the derivation of the Y （t）/t function， and the process was omitted with only the extreme point given， the same below） was tm=5.73 a， indicating that the age of quantitative maturity of the tree was 5.73 a （only the ground diameter fitting equation was given， and the fitting equation for other items were the same， thus omitted）. In following discussion， the equations for growth fitting， tree growth speed and average growth speed of the tree were the same， and the meanings of tz and tm were also the same， so the calculation results were given directly. The mature ages of all the items are shown in Table 1. As shown in Table 1， comparing the item square with the item， the values of the parameters increased by 1 time， and the accuracy and the tested F values and R values were the same， which was caused by the mathematical relations of the indexes. In order to compare with the cumulative fitting equation， we established the fitting equation of DBH 3 square， the fitting results of which were closer to wood volume 2 and wood volume 4 （the differences were about 10 a， which might be caused by the deviation of the growth trend curve， the same below）， while the fitting results of DBH 1 square were closer to wood volume 1 and wood volume 3. The fitting value of wood volume 1 was closer to wood volume 3， and fitting value of wood volume 2 was closer to wood volume 4， indicating that the test was highly reliable. In Table 1， the value of tn was the age at intersection point between the current annual increment and mean annual increment curves of the sample tree （those over 46 a was obtained from the trend graph of the growth curve）， which could serve as the practical mature age of the tree. the tm value were all very close to the tn values. Due to the lack of data of 46 a and higher age， the results were more reliable when fitting with empirical equations， and it would be more reliable to set the mature age of the stock as the mature age of the tree according to the research results and the needs in production practice. Conclusions and Application
Through the analysis and judgment of the research results， with the quantitative maturity of the stock as the standard， the practical mature ages of P. orientalis were determined to be 71， 111 and 141 a according to the national standards of the age class of 10 years. And the age group of P. orientalis was divided， as shown in Table 2.
The results of this study indicate that the mature age of the timber forest of the original standard and the conclusion of this study is 10 years earlier than the conclusion of another tree， and the mature age of the protection forest is 20 years earlier than that of the another tree， which might be due to that the sample tree grew faster than the another tree， or caused by the systematic deviation of the study. The mature age of the forest for special purpose is in complete agreement with the another tree.
Discussion
The original mature age standard is 81 a， which may be based on the situations at multiple sites at the time or the need to speed up wood production， without taking the second or even multiple peaks of tree growth into account. Therefore， over time， it is necessary to make appropriate adjustments with the times， because at this stage， the main task of Shandong forestry production of P. orientalis is to ensure that the ecological benefits are brought into play， and timber production is in a secondary position. Although this study has high reliability， it can only be a scientific foresight for future development due to the lack of highage materials. To get more accurate and realistic research conclusions， we must have highage materials， while most older trees are classified as ancient and famous trees for protection， which become an obstacle for the further development of this work. The successful application of modern medical imaging technology in tree measurement has provided powerful technical support for the further development of this project， but there must be strong human， material， financial and technological investment to complete it， and interested colleagues can give it a try. Due to the difficulties in collecting tree samples and limited funds， the empirical equations of tree growth were applied to analyze the analytical tree data in this study. By such， the lack of the insufficient age of the tree was compensated while avoiding the noise impact of time and space differences under various natural conditions and tree differentiation phenomenon on the test results. The practical mature age of P. orientalis was obtained， and through repeated verification， analysis and judgment， it was found that the empirical equations for tree growth are indeed applicable， which is difficult to make a scientific explanation. Limited by various conditions， all kinds of deviations can hardly be avoided， which can only be improved and developed in the research and production practice. However， the suggestions for forest production in this paper were only personal opinions， which required the approval and tests from the experts to put into application.
Zhaohua DENG. Study on the Practical Mature Age of Individual Platycladus orientalis
References
[1] LANG KJ. Forest measurement[M]. Beijing： China Forestry Publishing House， 1985. （in Chinese）
[2] CHEN HH. Mathematical statistics[M]. Beijing： China Forestry Publishing House， 1985. （in Chinese）
[3] LIU GJ. Review guide for vocational qualification test of registered consulting engineer （investment）[M]. Tianjin： Tianjin University Press， 2003. （in Chinese）
[4] GAO JH. Approach into desirable period of forest management in Shandong Province[J]. Journal of Forestry Engineering， 2003（3）： 6-8. （in Chinese）
[5] HU HY. Study on the actual maturity age of individual Pinus densiflora[J]. Journal of Shandong Forestry Science and Technology， 2010（6）： 36-37.（in Chinese）
[6] LI LP. Study on expected maturity age of Shandong Pinus densiflora[J]. Journal of Anhui Agricultural Sciences， 2017， 3： 184-186. （in Chinese）