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Abstract Empirical equations were used to fit tree growth through the analysis of parse wood data， functions with tree growth amount as the dependent variable and annual sunshine duration as the independent variable. According to arithmetical operations like derivation of the functions， the relative contribution rate of light to tree growth was 64.8%， which was almost equal to the relative contribution rate of precipitation to tree growth. Therefore， the light and precipitation were of equal importance to tree growth.
Key words Empirical equation； Parse wood； Annual sunshine duration
It is wellknown that main natural factors affecting the growth of trees and other plants are the interaction of light， temperature， and water. People are also adjusting the 3 factors in production practice to achieve more ideal production purposes， such as watering， tending， soil preparation， protected cultivation， light control， temperature control and humidity adjustment. Based on the analysis of historical data of tree rings， the relationship of parametric equation has been established between tree growth and precipitation， thereby reconstructing the historical data of sunshine duration. Through more than ten years of research， we have also achieved a more satisfactory research results. However， light can play a more active role in plant growth. The reason is that water can be adjusted by human easily， but it will cost a lot to achieve the human adjustment of light. Moreover， it also requires complex light control technologies to achieve the adjustment， which also has quite strict technical requirements for people. So far， there are few reports on the effects of light on tree growth， and most of them only make tests of light effects to some species （mainly flowers and grass）. There are also studies on the direct effects of solar radiation intensity on the growth of trees， but there is still no similar report on the historical influence of tree growth[1-3]. Therefore， in this paper， inspired by the study on the historical influence of precipitation on tree growth， empirical equations were used to study the effects of light on tree growth.
Materials and Methods
Materials
The information of sunshine duration over the years was provided by the Muping District Meteorological Bureau of Yantai City. Due to the lack of annual average solar radiation intensity data， the sunshine duration data over the years was used to study the effect of light on trees. The parse wood was collected from 4 Pinus densiflora trees， 2 of 65year old and 45year old from Kunyushan Forest Farm of Muping District， Yantai City， and the other 2 of 77year old and 61year old from Fengyun Forest Farm. All of the 4 trees were of normal growth with tree heights over 10 m. The diameter of breast height （DBH） was measured at the section distance of 2.6 m， while the others at 2 m. Discs were taken at tree heights of 5 cm （disc 0）， 1.3， 3.6， 5.6， 7.6 and 9.6 m， respectively. If the tree height was less than 10 m， the section distance of 1 m was adopted， and discs were taken at 5 cm （disk 0）， 0.5， 1.5，... 9.5 m. After dried （airdried） and polished， the discs were performed with chromoscan using a high resolution scanner. And the scanned images were put into the CAD operating platform for measurement， and the measured data were used for correction. The southnorth diameter and eastwest diameter were measured separately， and the 5year stage was used for crossing age dating. With data accuracy of 0.01 cm， the diameters of the discs from all collected trees were measured， and related forest measuring technology was used to calculate tree heights and wood volumes. Methods
After more than a decade of research， the growth amount， biomass， and carbon stock of trees were found to have a clear correlation with tree age and annual sunshine hours. Moreover， all that with significant linear correlation had more significant correlation in log values. Based on our careful study， the exponential empirical equation y=exp（a+bx） was used to determine the variation degree （variation rate） of the dependent variable y with the independent variable x， where y represents the indicators of growth amount， biomass and carbon stock of a tree， x the natural factor indicators of tree age and annual sunshine hours， and a and b are the coefficient to be solved （the same below）. The mixed empirical equation y=exp（a-b/x） was to maximize the efficiency index， that is， to use the least input （including time） to obtain the maximum benefit. The indicators of each year were used to make fitting test to the equations， and the results showed that except for some indicators showed significant correlations， most of the indicators had no significant correlations. However， through the cumulative effect （i.e.， establishing regression correlation equation by accumulating the growth amount with tree ages and sunshine hours）， the indicators showed very significant correlations. Many scholars used 5year sliding method to greatly increase the regression correlation coefficient， but in fact， they only used the 5year data accumulation， which was merely the average over the 5 years. As a matter of fact， it was only a method to improve the regression accuracy， but its scientific meaning was not accurate. On the other hand， the cumulative effect used in this paper had a very clear scientific meaning. Taking the growth amount and age of a tree for example， the age of a tree was the accumulation of time， and the accumulation of growth amount of a tree was total tree growth amount. As for the 5year sling method， the average of the 5year data was used as the data of the middle year， which was somewhat farfetched. It was difficult to process the data of the years at both ends when using 5eyear sling method because of the lack of data support. However， it was still possible to study the data variation over hundreds of or thousands of years， in which situation the data of both ends could be discarded. In this paper， the cumulative effect was made full use of， which not only made up for the lack of data in sliding processing， but also showed its scientific meaning. Moreover， it also had relatively small calculation amount. At the beginning， the empirical equations y=exp（a+bx） and y=exp（a-b/x） were used to establish the regression relationship between the amount of tree growth and the tree growth age， obtaining the values of coefficients a， b. Then， the empirical equations y=exp（a+bx） and y=exp（a-b/x） were used to establish the regression coefficients between the amount of tree growth and annual sunshine hours， and then the calculation results of the regression equation of tree age was used to make technical correction to the regression equation of sunshine hours. All processes must be checked and verified. And then the verified regression equation of sunshine hours was used to reconstruct the annual sunshine hours of the years with no records， thereby obtaining the annual sunshine hours during the whole growth process of the tree， so as to carry out the research and analysis on the drywet cycle of climate.
Results and Analysis
Empirical equation fitting results
As for the calculation of the empirical equation y=exp（a+bx）， adding or subtracting the same number to all the data of x at the same time only had the value of a changes， while the value of b and the tvalue， Fvalue Rvalue and test accuracy showed no change. Therefore， the equation made it possible to reconstruct the data without record and keep the test accuracy unchanged.
In this paper， the 77yearold sample tree was taken as the example for the analysis of the research method. The data of the parse wood was used to establish the empirical equation of tree growth amount and tree age. D20 was used to represent the ground diameter， D20.5 was used to represent the tree diameter at the height of 0.5 m， and so were the others. H2 was used to represent tree heights， and V2 the tree volumes. Y（t） was the function with time （tree age） as the independent variable and growth amounts of various tree indicators as the dependent variables. The empirical equations y=exp（a+bx） and y=exp（a-b/x） were used to establish the digital regression equation. Calculated using a spreadsheet， the test results were shown in Table 1， 2， 3 and 4. All items passed the Rtest， Ftest， and ttest， and the fitting accuracy all reached 99.99%. DBH （tree diameter at the tree height of 1.3 m） in Table 2 and most items in Table 4 all had the test accuracy being infinitely closed to 100%. The double time in Table 1 and 3 was the time needed to double the tree growth amount， which was used to express the tree growth rate in a more clear way. As shown in Table 1， the increase of wood volume was the fastest， while in Table 3 the increase of tree diameter at 5.0 m was the fastest. In Table 2 and 4， tm and tz were the first and second derivatives of the function y（t）=exp（a-b/t）. The former was the maximum average growth rate of the tree growth index at the moment， while the latter was the maximum immediate growth rate， and the former was twice of the latter. The high accuracy of the test suggested that the selected method and test data had scientific rationality and accuracy. Hundreds of scientific experiments had been made， and all showed the suitability of the equations， so no similar tests were made to the suitability of the equations. The same method was used to fit empirical equation of the growth amount and sunshine hours of P. densiflora， and the test results were shown in Table 5 and 6. The test results showed no abnormalities and all had consistency， indicating that the test results were stable and reliable， and the test accuracy was over 99.99%. Moreover， some items in Table 5 and 6 even had the test accuracy infinitely close to 100%.
In order to further improve the research accuracy， the empirical equation to fit sunshine hours was corrected to obtain the contribution rate of the effect of sunshine duration on tree growth relative to tree age. In other words， the logarithm of tree growth and the logarithmic difference of tree growth amount obtained from the fitting results of tree age empirical equation were used directly as the dependent variable， and the precipitation data was used as the dependent variable to reconstruct the empirical equation for fitting test， and the results were shown in Table 7 and 8. In Table 7， the logarithm of the fitting results of tree age exponential empirical equation and the logarithmic difference of tree growth amounts were used as the dependent variables Y（p）， and in Table 8， the fitting results of the mixed empirical equation were used for the same test. Because the accuracy was too low from the mixed equation， the results were not listed in the tables. However， the accuracy of D22.5 and H2 was close to 100%， and the results were listed in Table 6， and replaced with D22.5jzh and H2jzh， respectively. In the correction test， only items with high test accuracy were listed. As shown in the tables， in addition to a few items， the accuracy of the test results was infinitely close to 100%. Therefore， the equation could be put into practice. In terms of the development trend of the function curve， all the research indicators were nonnegativity. The exponential function y=exp（a+bx） was used to study the increase of y with x， and the mixed function equation y=exp（a-b/x） was to study the decrease of y with x. In this study， the sunshine hours data in recent 42 years were used directly to fit the growth amount of P. densiflora and sunshine hours. Because of the lack of precipitation information in the previous 35 years， and the growth amount was the accumulation of the whole growth process， the values of b were all negative in Table 7， and the doubling sunshine hours were also negative， referring to the sunshine hours for the double decrease （decreasing 50%）， which were the doubling sunshine hours after converted into positive values. The item of D20 in Table 7 was used to illustrate the calculation of relative contribution rate. The converted doubling time in Table 7 was 34.9 years， which could be the value after deducting the influence of the tree growth curve （Sshape）， and it had a difference value of 9.1 years from the same item of 25.8 years in Table 3. In other words， the growth traits of the tree increased the doubling time by 3.6 years from the single effect of sunshine hours. Therefore， the contribution rate of the time was 1÷[1+（9.1÷34.9）]=79.3%. The relative contribution rates of other items were calculated in the same way. The calculated results showed that in Table 7， the relative contribution rate of precipitation to tree growth amount was 63%-79.3%， while in Table 8 was 51%-58.2%. The values of the index showed no big change， and the difference between Table 7 and 8 was about 12%， which might be caused by the differences in research accuracy. It was believed that the accuracy of Table 7 was much higher and more reliable. Therefore， the weight of the effects of sunshine hours on tree growth amount reached up to 85% or so， and it could show the importance of sunshine hours to tree growth amount. Relative contribution rate could also be called the gain rate of the factor. As shown in Table 7 and 8， the gain rate of light was basically the same as the gain rate of precipitation. Compatibility test of empirical equations
The other 3 sample trees were performed with the same methods， and all got good test results. Therefore， the test results of the 3 sample trees were used to perform the compatibility test to the above results， and the verified results were shown in Table 9. In Table 9， FZ1 and FZj1 were the F values compared with sample tree no.1 before and after the correction of the exponential equation of tree age， FH1 and Fhj1 were the F values compared with sample tree no.1 before and after the correction of the mixed equation of tree age， D0 was the ground diameter， and so were the others （see the discussion of "Results and Analysis."）.
After checking the table， F0.0530 （the F value with reliability of 95%， degree of freedom of 30） was 1.84. In Table 5， any value higher than this value could pass the compatibility test. Only some of the corrected data passed the test， so the sample trees with similar ages could easily pass the compatibility test. Therefore， the empirical equation coefficients could not be borrowed， and data should be fitted by the equations with essential conditions until passed the compatibility test.
Discussion
In this paper， simulation equations are used to study the relationship between tree growth amounts and precipitation， opening up a new approach . Due to the inaccurate or unprofessional measurement， lack of collected data， the previous studies showed that there was no significant correlation between tree growth and precipitation. However， only through a lot of painstaking and meticulous work can we come to a correct conclusion. Most of the previous scholars used isolated tree trunk discs to measure the annual ring width using annual measuring instruments. In this study， multiple tree discs are scanned， and performed with interpretation in the CAD state. Corrections are made using measured data. Therefore， the tests in this study are more scientific and reasonable， which save the research costs， achieving the effects of getting twofold results with half effort. It is believed that the experimental data has more decimal places may not good， because the annual sunshine hours have 4 valid digits， and the measurement of the tree diameter retains 4 valid digits （i.e. accurate to 0.01 mm）. Some scholars are accurate to 0.001 mm， which is essential for mahogany which has particularly slow growth， but it is not necessary for other tree species. Thus， it can save a lot of work. Interpretation is made in the CAD state， which can be accurate to a few decimal places. In order to save working time， only 4 effective digits are retained. This study answers the scientific meaning of empirical equation in a scientific way， and the exponential equation is exponential increase， that is， increasing. It is an expression of the trees growth potential， which reflects the speed of the trees growth. On the other hand， the other mixed equation is the expression of downward pressure on the growth of trees， which reveals the problem of maximizing the benefits. Through the elimination of the trees own growth potential effect， the relative contribution of light to the growth of trees is obtained. From the perspective of growth potential， the relative contribution rate is 74.1%. From the perspective of the downward pressure on growth， the average relative tributary rate is 55.4%. The median value of the two is 64.8%， which means that compared with the growth traits of trees， the effect of light on tree growth is about 65%， the the growth traits of the trees account for only 35%. Therefore， the study on the effect of light on tree growth is very important， which is of farreaching practical significance for our rational organization of forestry production. The contribution of light and precipitation to the growth of trees is roughly equal， indicating that light and water have an equally important effect on the growth of trees. It may be related to the mechanism of photosynthetic photolysis of water， but this effect has to be carried out at a certain temperature， and further research is needed for the effect of temperature on the growth of trees.
References
[1]LIAN LZ， LI WH， ZHU PS. Analysis of climate change in Shandong Province since 1961[J]. Meteorological Science and Technology， 2006， 34 （1）， 57-61.
[2]GAO WD， YUAN YJ， ZHANG RB， et al. The recent 338year precipitation series reconstructed from treering in northern slope of Tianshan Mountains[J]. Journal of Desert Research， 2011， 31 （6）： 1535-1540.
[3]ZHAO GJ. Registered consulting engineer （investment） qualification exam textbook review guide[M]. Tianjin， Tianjin University Press， 2003.
Editor： Na LI Proofreader： Xinxiu ZHU
Key words Empirical equation； Parse wood； Annual sunshine duration
It is wellknown that main natural factors affecting the growth of trees and other plants are the interaction of light， temperature， and water. People are also adjusting the 3 factors in production practice to achieve more ideal production purposes， such as watering， tending， soil preparation， protected cultivation， light control， temperature control and humidity adjustment. Based on the analysis of historical data of tree rings， the relationship of parametric equation has been established between tree growth and precipitation， thereby reconstructing the historical data of sunshine duration. Through more than ten years of research， we have also achieved a more satisfactory research results. However， light can play a more active role in plant growth. The reason is that water can be adjusted by human easily， but it will cost a lot to achieve the human adjustment of light. Moreover， it also requires complex light control technologies to achieve the adjustment， which also has quite strict technical requirements for people. So far， there are few reports on the effects of light on tree growth， and most of them only make tests of light effects to some species （mainly flowers and grass）. There are also studies on the direct effects of solar radiation intensity on the growth of trees， but there is still no similar report on the historical influence of tree growth[1-3]. Therefore， in this paper， inspired by the study on the historical influence of precipitation on tree growth， empirical equations were used to study the effects of light on tree growth.
Materials and Methods
Materials
The information of sunshine duration over the years was provided by the Muping District Meteorological Bureau of Yantai City. Due to the lack of annual average solar radiation intensity data， the sunshine duration data over the years was used to study the effect of light on trees. The parse wood was collected from 4 Pinus densiflora trees， 2 of 65year old and 45year old from Kunyushan Forest Farm of Muping District， Yantai City， and the other 2 of 77year old and 61year old from Fengyun Forest Farm. All of the 4 trees were of normal growth with tree heights over 10 m. The diameter of breast height （DBH） was measured at the section distance of 2.6 m， while the others at 2 m. Discs were taken at tree heights of 5 cm （disc 0）， 1.3， 3.6， 5.6， 7.6 and 9.6 m， respectively. If the tree height was less than 10 m， the section distance of 1 m was adopted， and discs were taken at 5 cm （disk 0）， 0.5， 1.5，... 9.5 m. After dried （airdried） and polished， the discs were performed with chromoscan using a high resolution scanner. And the scanned images were put into the CAD operating platform for measurement， and the measured data were used for correction. The southnorth diameter and eastwest diameter were measured separately， and the 5year stage was used for crossing age dating. With data accuracy of 0.01 cm， the diameters of the discs from all collected trees were measured， and related forest measuring technology was used to calculate tree heights and wood volumes. Methods
After more than a decade of research， the growth amount， biomass， and carbon stock of trees were found to have a clear correlation with tree age and annual sunshine hours. Moreover， all that with significant linear correlation had more significant correlation in log values. Based on our careful study， the exponential empirical equation y=exp（a+bx） was used to determine the variation degree （variation rate） of the dependent variable y with the independent variable x， where y represents the indicators of growth amount， biomass and carbon stock of a tree， x the natural factor indicators of tree age and annual sunshine hours， and a and b are the coefficient to be solved （the same below）. The mixed empirical equation y=exp（a-b/x） was to maximize the efficiency index， that is， to use the least input （including time） to obtain the maximum benefit. The indicators of each year were used to make fitting test to the equations， and the results showed that except for some indicators showed significant correlations， most of the indicators had no significant correlations. However， through the cumulative effect （i.e.， establishing regression correlation equation by accumulating the growth amount with tree ages and sunshine hours）， the indicators showed very significant correlations. Many scholars used 5year sliding method to greatly increase the regression correlation coefficient， but in fact， they only used the 5year data accumulation， which was merely the average over the 5 years. As a matter of fact， it was only a method to improve the regression accuracy， but its scientific meaning was not accurate. On the other hand， the cumulative effect used in this paper had a very clear scientific meaning. Taking the growth amount and age of a tree for example， the age of a tree was the accumulation of time， and the accumulation of growth amount of a tree was total tree growth amount. As for the 5year sling method， the average of the 5year data was used as the data of the middle year， which was somewhat farfetched. It was difficult to process the data of the years at both ends when using 5eyear sling method because of the lack of data support. However， it was still possible to study the data variation over hundreds of or thousands of years， in which situation the data of both ends could be discarded. In this paper， the cumulative effect was made full use of， which not only made up for the lack of data in sliding processing， but also showed its scientific meaning. Moreover， it also had relatively small calculation amount. At the beginning， the empirical equations y=exp（a+bx） and y=exp（a-b/x） were used to establish the regression relationship between the amount of tree growth and the tree growth age， obtaining the values of coefficients a， b. Then， the empirical equations y=exp（a+bx） and y=exp（a-b/x） were used to establish the regression coefficients between the amount of tree growth and annual sunshine hours， and then the calculation results of the regression equation of tree age was used to make technical correction to the regression equation of sunshine hours. All processes must be checked and verified. And then the verified regression equation of sunshine hours was used to reconstruct the annual sunshine hours of the years with no records， thereby obtaining the annual sunshine hours during the whole growth process of the tree， so as to carry out the research and analysis on the drywet cycle of climate.
Results and Analysis
Empirical equation fitting results
As for the calculation of the empirical equation y=exp（a+bx）， adding or subtracting the same number to all the data of x at the same time only had the value of a changes， while the value of b and the tvalue， Fvalue Rvalue and test accuracy showed no change. Therefore， the equation made it possible to reconstruct the data without record and keep the test accuracy unchanged.
In this paper， the 77yearold sample tree was taken as the example for the analysis of the research method. The data of the parse wood was used to establish the empirical equation of tree growth amount and tree age. D20 was used to represent the ground diameter， D20.5 was used to represent the tree diameter at the height of 0.5 m， and so were the others. H2 was used to represent tree heights， and V2 the tree volumes. Y（t） was the function with time （tree age） as the independent variable and growth amounts of various tree indicators as the dependent variables. The empirical equations y=exp（a+bx） and y=exp（a-b/x） were used to establish the digital regression equation. Calculated using a spreadsheet， the test results were shown in Table 1， 2， 3 and 4. All items passed the Rtest， Ftest， and ttest， and the fitting accuracy all reached 99.99%. DBH （tree diameter at the tree height of 1.3 m） in Table 2 and most items in Table 4 all had the test accuracy being infinitely closed to 100%. The double time in Table 1 and 3 was the time needed to double the tree growth amount， which was used to express the tree growth rate in a more clear way. As shown in Table 1， the increase of wood volume was the fastest， while in Table 3 the increase of tree diameter at 5.0 m was the fastest. In Table 2 and 4， tm and tz were the first and second derivatives of the function y（t）=exp（a-b/t）. The former was the maximum average growth rate of the tree growth index at the moment， while the latter was the maximum immediate growth rate， and the former was twice of the latter. The high accuracy of the test suggested that the selected method and test data had scientific rationality and accuracy. Hundreds of scientific experiments had been made， and all showed the suitability of the equations， so no similar tests were made to the suitability of the equations. The same method was used to fit empirical equation of the growth amount and sunshine hours of P. densiflora， and the test results were shown in Table 5 and 6. The test results showed no abnormalities and all had consistency， indicating that the test results were stable and reliable， and the test accuracy was over 99.99%. Moreover， some items in Table 5 and 6 even had the test accuracy infinitely close to 100%.
In order to further improve the research accuracy， the empirical equation to fit sunshine hours was corrected to obtain the contribution rate of the effect of sunshine duration on tree growth relative to tree age. In other words， the logarithm of tree growth and the logarithmic difference of tree growth amount obtained from the fitting results of tree age empirical equation were used directly as the dependent variable， and the precipitation data was used as the dependent variable to reconstruct the empirical equation for fitting test， and the results were shown in Table 7 and 8. In Table 7， the logarithm of the fitting results of tree age exponential empirical equation and the logarithmic difference of tree growth amounts were used as the dependent variables Y（p）， and in Table 8， the fitting results of the mixed empirical equation were used for the same test. Because the accuracy was too low from the mixed equation， the results were not listed in the tables. However， the accuracy of D22.5 and H2 was close to 100%， and the results were listed in Table 6， and replaced with D22.5jzh and H2jzh， respectively. In the correction test， only items with high test accuracy were listed. As shown in the tables， in addition to a few items， the accuracy of the test results was infinitely close to 100%. Therefore， the equation could be put into practice. In terms of the development trend of the function curve， all the research indicators were nonnegativity. The exponential function y=exp（a+bx） was used to study the increase of y with x， and the mixed function equation y=exp（a-b/x） was to study the decrease of y with x. In this study， the sunshine hours data in recent 42 years were used directly to fit the growth amount of P. densiflora and sunshine hours. Because of the lack of precipitation information in the previous 35 years， and the growth amount was the accumulation of the whole growth process， the values of b were all negative in Table 7， and the doubling sunshine hours were also negative， referring to the sunshine hours for the double decrease （decreasing 50%）， which were the doubling sunshine hours after converted into positive values. The item of D20 in Table 7 was used to illustrate the calculation of relative contribution rate. The converted doubling time in Table 7 was 34.9 years， which could be the value after deducting the influence of the tree growth curve （Sshape）， and it had a difference value of 9.1 years from the same item of 25.8 years in Table 3. In other words， the growth traits of the tree increased the doubling time by 3.6 years from the single effect of sunshine hours. Therefore， the contribution rate of the time was 1÷[1+（9.1÷34.9）]=79.3%. The relative contribution rates of other items were calculated in the same way. The calculated results showed that in Table 7， the relative contribution rate of precipitation to tree growth amount was 63%-79.3%， while in Table 8 was 51%-58.2%. The values of the index showed no big change， and the difference between Table 7 and 8 was about 12%， which might be caused by the differences in research accuracy. It was believed that the accuracy of Table 7 was much higher and more reliable. Therefore， the weight of the effects of sunshine hours on tree growth amount reached up to 85% or so， and it could show the importance of sunshine hours to tree growth amount. Relative contribution rate could also be called the gain rate of the factor. As shown in Table 7 and 8， the gain rate of light was basically the same as the gain rate of precipitation. Compatibility test of empirical equations
The other 3 sample trees were performed with the same methods， and all got good test results. Therefore， the test results of the 3 sample trees were used to perform the compatibility test to the above results， and the verified results were shown in Table 9. In Table 9， FZ1 and FZj1 were the F values compared with sample tree no.1 before and after the correction of the exponential equation of tree age， FH1 and Fhj1 were the F values compared with sample tree no.1 before and after the correction of the mixed equation of tree age， D0 was the ground diameter， and so were the others （see the discussion of "Results and Analysis."）.
After checking the table， F0.0530 （the F value with reliability of 95%， degree of freedom of 30） was 1.84. In Table 5， any value higher than this value could pass the compatibility test. Only some of the corrected data passed the test， so the sample trees with similar ages could easily pass the compatibility test. Therefore， the empirical equation coefficients could not be borrowed， and data should be fitted by the equations with essential conditions until passed the compatibility test.
Discussion
In this paper， simulation equations are used to study the relationship between tree growth amounts and precipitation， opening up a new approach . Due to the inaccurate or unprofessional measurement， lack of collected data， the previous studies showed that there was no significant correlation between tree growth and precipitation. However， only through a lot of painstaking and meticulous work can we come to a correct conclusion. Most of the previous scholars used isolated tree trunk discs to measure the annual ring width using annual measuring instruments. In this study， multiple tree discs are scanned， and performed with interpretation in the CAD state. Corrections are made using measured data. Therefore， the tests in this study are more scientific and reasonable， which save the research costs， achieving the effects of getting twofold results with half effort. It is believed that the experimental data has more decimal places may not good， because the annual sunshine hours have 4 valid digits， and the measurement of the tree diameter retains 4 valid digits （i.e. accurate to 0.01 mm）. Some scholars are accurate to 0.001 mm， which is essential for mahogany which has particularly slow growth， but it is not necessary for other tree species. Thus， it can save a lot of work. Interpretation is made in the CAD state， which can be accurate to a few decimal places. In order to save working time， only 4 effective digits are retained. This study answers the scientific meaning of empirical equation in a scientific way， and the exponential equation is exponential increase， that is， increasing. It is an expression of the trees growth potential， which reflects the speed of the trees growth. On the other hand， the other mixed equation is the expression of downward pressure on the growth of trees， which reveals the problem of maximizing the benefits. Through the elimination of the trees own growth potential effect， the relative contribution of light to the growth of trees is obtained. From the perspective of growth potential， the relative contribution rate is 74.1%. From the perspective of the downward pressure on growth， the average relative tributary rate is 55.4%. The median value of the two is 64.8%， which means that compared with the growth traits of trees， the effect of light on tree growth is about 65%， the the growth traits of the trees account for only 35%. Therefore， the study on the effect of light on tree growth is very important， which is of farreaching practical significance for our rational organization of forestry production. The contribution of light and precipitation to the growth of trees is roughly equal， indicating that light and water have an equally important effect on the growth of trees. It may be related to the mechanism of photosynthetic photolysis of water， but this effect has to be carried out at a certain temperature， and further research is needed for the effect of temperature on the growth of trees.
References
[1]LIAN LZ， LI WH， ZHU PS. Analysis of climate change in Shandong Province since 1961[J]. Meteorological Science and Technology， 2006， 34 （1）， 57-61.
[2]GAO WD， YUAN YJ， ZHANG RB， et al. The recent 338year precipitation series reconstructed from treering in northern slope of Tianshan Mountains[J]. Journal of Desert Research， 2011， 31 （6）： 1535-1540.
[3]ZHAO GJ. Registered consulting engineer （investment） qualification exam textbook review guide[M]. Tianjin， Tianjin University Press， 2003.
Editor： Na LI Proofreader： Xinxiu ZHU