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Abstract According to the data of analytic trees， an empirical equation of tree growth was constructed， with annual growth as variable and time and annual precipitation as independent variables. Through arithmetical operation including derivation of function and so on， the effect of precipitation on tree growth was studied through the rejection of effect of time factor.
Key words Empirical equation； Analytic tree； Time Factor
Illumination， rainfall and air temperature are the three main factors affecting growth of trees. The writers studied the effects of them on growth of trees and their interaction with time as measure through more than 20 years of experiments， and constructed an empirical equation. However， some scholars deem that the effect of time factor should be eliminated， while there have been no reports about the elimination of various factors （including time） so far. The experiments done by the writers were all performed under the premise of supposing other factors were basically stable without the need for elimination of effects from factors. In this study， the effect of elimination of time factor on the effect of precipitation on trees were investigated.
Sources of Information
The precipitation information over the years was provided by Muping Weather Bureau of Yantai City. The information of analytic trees was collected from two plants in Kunyu Mountain Forestry Farm in Muping District， Yantai City， which were Pinus densiflora trees growing normally of 65 and 45 years old， respectively， and two plants in Fengyun Forestry Farm， which were P. densiflora trees growing normally of 77 and 61 years old， respectively， in mid March of 2013. The trees higher than 10 m were segmented according to 2.6 m， other parts were segmented according to 2 m， and round plates were obtained at the tree heights of 5 cm （0 plate）， 1.3， 3.6， 5.6， 7.6 and 9.6 m； and trees not longer than 10 m was segmented according to 1 m， and round plates were cut at the tree height of 5 cm （0 plate）， 1.3， 0.5， 1.5 ……9.5 m. The materials were air-dried， polished and subjected to chromoscan with a high-resolution scanner， and the obtained images were put into a CAD operating platform for measurement， and correlation was performed with measured information. North-south diameter and east-west diameter values were measured， respectively， and cross-dating was performed according to five-year age group， with data accuracy of 0.01 cm. The tree diameter of each tree plate in each year was measured， and according to related technical principles of forest measurement， tree height and volume of timber were calculated. Research Method
After nearly 10 years of experiments， tree increment， biomass and carbon storage were in very remarkable correlation with tree age and annual precipitation. Furthermore， when the linear correlation was very significant， the logarithmic values were in more significant correlation. According to the research results of Gong and Zhang et al.[1-6]， empirical equation y=exp（a+bx） was used for judging the degree of change （rate of change） of dependent variable following independent variable， wherein y is indexes including increment of tree， biomass and carbon storage， x is natural factors such as tree age and annual precipitation， and a and b are undetermined coefficients （the same below）. Empirical equation y=exp（a-b/x） was used for seeking maximum benefit index， i.e.， obtaining maximum benefit with the lowest input （including time）. The writers performed a fitting test to the equation with each year as the object of study， and the results showed that except that few indexes exhibited significant correlation， most indexes exhibited non-significant correlation， but through additive effect （i.e.， constructing correlation regression equation using accumulative growth quantity and accumulative quantities of tree age and precipitation）， very significant correlation was obtained. Many scholars greatly improved correlation coefficient by five-year sliding method， during which the data in five years are accumulated and averaged， which is only a method for improving regression precision， while the scientific meaning is thus not accurate. On the contrary， the additive effect has very specific scientific meaning， such as tree growth increment and tree age. Annual tree age is the accumulative quantity of time， and the accumulation of tree increment is the total increment of tree. However， when processing data by the five-year sliding method， the average values of the five years are used as the data index of the middle year， which is considered to be far-fetched， and it is difficult to deal with the data at the two ends due to the lack of data support， though the method could be used for studying change of data of hundreds or thousands of years as the data at the two ends could be given up. The writers took full advantage of additive effect， not only the shortage of sliding data processing was made up， but also the scientific meaning of data index could be shown better， and the calculation was relatively less.
The regression relation between tree increment and tree age was constructed using empirical equations y=exp（a+bt） and y=exp（a-b/t） at first， obtaining undetermined coefficients. Then， the regression coefficient between tree increment and annual precipitation was solved using empirical equations y=exp（a+bp）and y=exp（a-b/p）， and the calculation results of the regression equation of tree age were used for performing technical correction on the regression equation of precipitation. All the equations should be checked and validated. Because the effect of each factor on tree growth is a kind of multiplier effect， i.e.， a kind of index effect， and according to deflation of index of empirical equation， factor rejection was performed. Empirical equation yc=exp（a+bx） （yc is the fitted value of the equation， and a and b are undetermined coefficients） was called growth equation （also known as evolution equation）， and compound function， yz=exp（a-b/x） （yz is the fitted value of the equation， and a and b are undetermined coefficients） was called as resistance equation. If y is original value of tree growth （measured value， calculated value）， the rejection of factor growth force is performed using the test results of equation yjc=y^（nc+1）/yc^nc （wherein nc is a real number larger than 1 with multiple as unit， and called as multiple value for effect elimination， multiple for short， which is solved through spreadsheet trial， the same below） in various time scales. Similarly， the rejection of factor growth resistance is performed using the test results of equation yjz=y^（nz+1）/yz^nz （wherein nz is a real number larger than 1 with multiple as unit） in various time scales. For determination of nc and nz， when the test precision is just below 95%， the effect of the factor is regarded as to be eliminated， and larger multiple value indicates that the effect of the factor on tree growth is profounder and stronger， otherwise the effect is more superficial， and weaker. Weighting was performed according to respective effects using equation ycz=y^（ncz+1）/[p*yc^ncz]/（q*yz^ncz） （ycz is the fitted value realizing the elimination of growth force and resistance， and p and q are the weights of effects of growth force and resistance）， and fitting was performed using equations of yjc and yjz， obtaining weighted value when the precision is just lower than 95%. In the equation， p and q are calculated according to p=nc/（nc+nz） and q=nz/（nc+nz）， respectively， and it is obviously that the sum of p and q is equal to 1. ncz refers to the multiple value obtained by performing fitting with the growth equation constructed with ycz as variable and other impact factor as independent variable， when the test precision is just lower than 95%. The specific method was expounded in detail hereinafter.
Research Process
It was found that for the calculation of the empirical equation y=exp（a+bx）， when all the data of x are added with or subtract the same value， only the value of a changes， b and other test values including t， F and R remain unchanged. Therefore， according to this equation， the rebuilding of data without recording becomes possible when keeping the precision of the test constant. Function relationships were constructed using growth equation and resistance equation with tree increment as dependent variable y（t） and t as independent variable， and through regression analysis， the test results are shown in Table 1 and Table 2. The unit of length was cm， the unit of volume of timber was cm3， D1-0 and D1-0.5 represented the tree diameters at the heights of 0 and 0.5 m， respectively， and so on， H1 represented tree height， and v1 represented volume of timber （the same below）. It could be seen from Table 1 that the higher the tree， the fast the tree diameter grows， and the growth rates of tree height and tree diameter are basically equivalent. The volume of timber and tree D1-4.0 increase at basically the same rate， which is about 30% of the rate of other tree diameters and tree height.
According to above methods， the test results are given as below （the calculation process was omitted）. It was found that during the rejection of time effect of the growth equation， the undetermined coefficients of the growth equation maintain unchanged， while the test precision decreases； and on the contrary， the undetermined coefficients of the resistance equation change， and the test precision is improved or far higher than the test precision of the growth equation. However， during the rejection of time effect of the resistance equation， the undermined coefficients of the resistance equation maintain unchanged， while the test precision decreases； and on the contrary， the undetermined coefficients of the growth equation change， and the test precision is improved or far higher than the test precision of the resistance equation.
It could be seen from Table 1 that all the tests were regarded as being passed when the precision exceeded 99.85%， and tree height item exhibited the precision of 99.99%. Except that the tree diameter items of 1.3 and 2.5 m had the precision slightly lower than original test precision， other items showed precision higher than original test precision， indicating the experimental design was rational. The doubling time in Table 1 refers to the time for doubling of the index （the same below）.
As shown in Table 2， except the tree diameter items of 0.5， 1.3， 1.5 and 3.5 m， other items were all higher than original test levels， and the lower ones also showed no big differences. All the items passed the validation with precision higher than 99.82%， and the precision of many items was close to 100%， indicated that the selected test path was right. In the table， tm refers to the theoretical age of quantitative maturity when the average growth rate of the time is the highest， and tz means the time when the item has the highest instant growth rate （the same below）. It could be seen from Table 3 that various items all passed the validation with precision higher than 99.79%. Under the premise of sample number larger than 28， the precision was higher than original test precision （without the rejection of the effect of time factor， the same below）， indicating that the design of the experimental technical path is very scientific and rational， and in order to ensure test precision， the improvement of sample number is very important. Compared with Table 4， except the item of volume of timber， the test precision was all reduced， which was caused by uneven distribution of annual precipitation， indicating that the effect of time on tree is more intense. Except the tree height item， the rate of change （tree growth rate） was all improved， indicating that precipitation is a very active factor influencing tree growth.
The results in Table 4 showed when sample number was as high as 42， the test precision was reduced compared with original test， other values were all improved. It indicated that with the increase of tree height， the b value of its diameter equation had a trend of gradually increasing， which showed that the growth of tree might have multiple growth peaks， which would be investigated in another study. All the items passed the validation with precision higher than 99.61%， indicating that the test has higher reliability.
Table 1-Table 4 show that the effect of time factor could be reduced by such method， and the reduction of time effect would enhance the effect of precipitation on tree growth.
Compatibility Test of Empirical Equation
Another sample tree was tested with the same method， and better test results were obtained. The test results of this sample tree were used for compatibility test of above test results. The test results are shown in Table 5. In the table， FZ-2 and FZj-2 represented the F values obtained from the comparison with sample tree No. 2 before and after the rejection of tree age factor of the development equation， respectively； FH-2 and Fhj-2 represented the F values obtained from the comparison with sample tree No. 2 before and after the correction of tree age factor of the resistance equation， respectively； FpZ-2 and FpZj-2 represented the F values obtained from the comparison of the effect of precipitation with sample tree No. 2 before and after the rejection of tree age factor of the development equation， respectively； and FpH-2 and Fphj-2 represented the F values obtained from the comparison of the effect of precipitation with sample tree No. 2 before and after the correction of tree age factor of the resistance equation， respectively. D0 represented the ground diameter item， and so on. According to the table， under the premise of not rejecting the effect of any factor， the fitted values of most items exhibited no significant differences between the two sample trees， only few items showed significant but not very significant differences， indicating that the application of time empirical equation was very scientific and rational. After the effects of time and resistance were rejected partially， the development and resistance equations of time and the development and resistance equations of precipitation （including before and after the rejection of partial effect of time factor） exhibited very strong differences， only very few items （diameter item of 4.0 m） showed no remarkable differences， indicating that in relation to time factor， precipitation was a more active influencing factor.
Discussion
The application of empirical equation actually is to regard time as a variable， which exits in the form of substance. Dialectical materialism reckons that time and space are both the existence forms of substance. During block design， only space （section） is divided to multiple plots， which are then applied with the effects of different equivalents， and various data are analyzed according to the differences shown over time， so as to find corresponding laws. However， with the help of the characteristics of growth ring of trees， block division was performed based on time， and due to the analysis on the same tree， noise caused by difference in site condition was avoided objectively. Conventional test of factor effect adopts space block design， objective error caused by site factor is difficult to be avoided， and single factor test could be performed （by comparison with control）， while the results of multi-factor and interaction test would not be ideal. In this study， tests were carried out using empirical equation. Time was used as the basis of block design， the deviation caused by site factor was completely avoided， the effect of time on tree growth was mainly decided by physiological properties of tree species， and whether it should be eliminated was further studied. Research shows that the interaction of various factors is a kind of superimposed effect， i.e.， multiplier effect （index effect）， rather than additive effect. On the basis of the thought and practice of additive effect， it is found that test precision is reduced， and the operability is poor. Therefore， the old mode and frame should be broken. Changing space with time and changing space with time have been widely applied in military and social practice. Based on this， changing space with time is worthy of trying in scientific experiment. It is concluded from research that the effect of time factor could be rejected partially by this method， but could not be rejected completely， because the effect of time factor is the expression of the result of the co-action of various factors including illumination， air temperature and water in time scale though it is decided by the characteristics of tree itself. When rejecting the effect of time factor using empirical equation， the effects of other factors are also rejected partially， and how to completely reject the effect of time factor is a more complicated research subject， which will be solved gradually with the improvement of scientific means. Research shows that precipitation is a more active factor than time in the effect on tree growth. Due to the application of this method， the test precision is improved， and the research precision of resistance equation is made close to that of development equation， which proves the rationality of the resistance and development equations defined by the writers. Through this study and other long-term research， the writers deem that tree growth might experience two or more growth peaks， which is not accordant with conventional thought that trees only have one growth peak. The writers deem that through this method， test precision could be improved， but the effect of time factor only could be rejected partially rather than completely. Though rejection could be further performed by this method， the test precision would be further improved， but the writers reckon that this makes little sense. Under the premise of ensuring test precision， the effect of time factor is not necessary to be rejected， unless the tree species is very precious with very high economic value， because this research requires massive input of manpower， material resources and financial resource， as well as longer research time， and the research and computation process is also much complicated.
References
[1] GONG YP. Relationship between growth and annual precipitation of Pinus thunbergii×P. densiflora[J]. Protection Forest Science and Technology， 2017（6）： 41-44.
[2] ZHANG J. Study on climate cycle[J]. Protection Forest Science and Technology， 2017（11）： 38-42.
[3] LIAN LS， LI WH， ZHU PS. Analysis of climate change in Shandong Province since 1961[J]. Meteorological Science and Technology， 2006： 34（1）： 57-61.
[4] GAO WD， YUAN YJ， ZHANG RB， et al. The recent 338-year precipitation series reconstructed from tree-ring in northern slope of Tianshan mountains[J]. Journal of Desert Research， 2011， 31（6）： 1535-1540.
[5] LIU GJ. Review of registered consulting engineer （investment） certified qualification examination textbook[M]. Tianjin： Tianjin University Press， 2003.
[6] ZHAO XP， GUO MH， ZHU XL. Advance in research on the effects of temperature on trees growth and wood formation[J]. Forest Engineering， 2005， 21（6）： 6.
Key words Empirical equation； Analytic tree； Time Factor
Illumination， rainfall and air temperature are the three main factors affecting growth of trees. The writers studied the effects of them on growth of trees and their interaction with time as measure through more than 20 years of experiments， and constructed an empirical equation. However， some scholars deem that the effect of time factor should be eliminated， while there have been no reports about the elimination of various factors （including time） so far. The experiments done by the writers were all performed under the premise of supposing other factors were basically stable without the need for elimination of effects from factors. In this study， the effect of elimination of time factor on the effect of precipitation on trees were investigated.
Sources of Information
The precipitation information over the years was provided by Muping Weather Bureau of Yantai City. The information of analytic trees was collected from two plants in Kunyu Mountain Forestry Farm in Muping District， Yantai City， which were Pinus densiflora trees growing normally of 65 and 45 years old， respectively， and two plants in Fengyun Forestry Farm， which were P. densiflora trees growing normally of 77 and 61 years old， respectively， in mid March of 2013. The trees higher than 10 m were segmented according to 2.6 m， other parts were segmented according to 2 m， and round plates were obtained at the tree heights of 5 cm （0 plate）， 1.3， 3.6， 5.6， 7.6 and 9.6 m； and trees not longer than 10 m was segmented according to 1 m， and round plates were cut at the tree height of 5 cm （0 plate）， 1.3， 0.5， 1.5 ……9.5 m. The materials were air-dried， polished and subjected to chromoscan with a high-resolution scanner， and the obtained images were put into a CAD operating platform for measurement， and correlation was performed with measured information. North-south diameter and east-west diameter values were measured， respectively， and cross-dating was performed according to five-year age group， with data accuracy of 0.01 cm. The tree diameter of each tree plate in each year was measured， and according to related technical principles of forest measurement， tree height and volume of timber were calculated. Research Method
After nearly 10 years of experiments， tree increment， biomass and carbon storage were in very remarkable correlation with tree age and annual precipitation. Furthermore， when the linear correlation was very significant， the logarithmic values were in more significant correlation. According to the research results of Gong and Zhang et al.[1-6]， empirical equation y=exp（a+bx） was used for judging the degree of change （rate of change） of dependent variable following independent variable， wherein y is indexes including increment of tree， biomass and carbon storage， x is natural factors such as tree age and annual precipitation， and a and b are undetermined coefficients （the same below）. Empirical equation y=exp（a-b/x） was used for seeking maximum benefit index， i.e.， obtaining maximum benefit with the lowest input （including time）. The writers performed a fitting test to the equation with each year as the object of study， and the results showed that except that few indexes exhibited significant correlation， most indexes exhibited non-significant correlation， but through additive effect （i.e.， constructing correlation regression equation using accumulative growth quantity and accumulative quantities of tree age and precipitation）， very significant correlation was obtained. Many scholars greatly improved correlation coefficient by five-year sliding method， during which the data in five years are accumulated and averaged， which is only a method for improving regression precision， while the scientific meaning is thus not accurate. On the contrary， the additive effect has very specific scientific meaning， such as tree growth increment and tree age. Annual tree age is the accumulative quantity of time， and the accumulation of tree increment is the total increment of tree. However， when processing data by the five-year sliding method， the average values of the five years are used as the data index of the middle year， which is considered to be far-fetched， and it is difficult to deal with the data at the two ends due to the lack of data support， though the method could be used for studying change of data of hundreds or thousands of years as the data at the two ends could be given up. The writers took full advantage of additive effect， not only the shortage of sliding data processing was made up， but also the scientific meaning of data index could be shown better， and the calculation was relatively less.
The regression relation between tree increment and tree age was constructed using empirical equations y=exp（a+bt） and y=exp（a-b/t） at first， obtaining undetermined coefficients. Then， the regression coefficient between tree increment and annual precipitation was solved using empirical equations y=exp（a+bp）and y=exp（a-b/p）， and the calculation results of the regression equation of tree age were used for performing technical correction on the regression equation of precipitation. All the equations should be checked and validated. Because the effect of each factor on tree growth is a kind of multiplier effect， i.e.， a kind of index effect， and according to deflation of index of empirical equation， factor rejection was performed. Empirical equation yc=exp（a+bx） （yc is the fitted value of the equation， and a and b are undetermined coefficients） was called growth equation （also known as evolution equation）， and compound function， yz=exp（a-b/x） （yz is the fitted value of the equation， and a and b are undetermined coefficients） was called as resistance equation. If y is original value of tree growth （measured value， calculated value）， the rejection of factor growth force is performed using the test results of equation yjc=y^（nc+1）/yc^nc （wherein nc is a real number larger than 1 with multiple as unit， and called as multiple value for effect elimination， multiple for short， which is solved through spreadsheet trial， the same below） in various time scales. Similarly， the rejection of factor growth resistance is performed using the test results of equation yjz=y^（nz+1）/yz^nz （wherein nz is a real number larger than 1 with multiple as unit） in various time scales. For determination of nc and nz， when the test precision is just below 95%， the effect of the factor is regarded as to be eliminated， and larger multiple value indicates that the effect of the factor on tree growth is profounder and stronger， otherwise the effect is more superficial， and weaker. Weighting was performed according to respective effects using equation ycz=y^（ncz+1）/[p*yc^ncz]/（q*yz^ncz） （ycz is the fitted value realizing the elimination of growth force and resistance， and p and q are the weights of effects of growth force and resistance）， and fitting was performed using equations of yjc and yjz， obtaining weighted value when the precision is just lower than 95%. In the equation， p and q are calculated according to p=nc/（nc+nz） and q=nz/（nc+nz）， respectively， and it is obviously that the sum of p and q is equal to 1. ncz refers to the multiple value obtained by performing fitting with the growth equation constructed with ycz as variable and other impact factor as independent variable， when the test precision is just lower than 95%. The specific method was expounded in detail hereinafter.
Research Process
It was found that for the calculation of the empirical equation y=exp（a+bx）， when all the data of x are added with or subtract the same value， only the value of a changes， b and other test values including t， F and R remain unchanged. Therefore， according to this equation， the rebuilding of data without recording becomes possible when keeping the precision of the test constant. Function relationships were constructed using growth equation and resistance equation with tree increment as dependent variable y（t） and t as independent variable， and through regression analysis， the test results are shown in Table 1 and Table 2. The unit of length was cm， the unit of volume of timber was cm3， D1-0 and D1-0.5 represented the tree diameters at the heights of 0 and 0.5 m， respectively， and so on， H1 represented tree height， and v1 represented volume of timber （the same below）. It could be seen from Table 1 that the higher the tree， the fast the tree diameter grows， and the growth rates of tree height and tree diameter are basically equivalent. The volume of timber and tree D1-4.0 increase at basically the same rate， which is about 30% of the rate of other tree diameters and tree height.
According to above methods， the test results are given as below （the calculation process was omitted）. It was found that during the rejection of time effect of the growth equation， the undetermined coefficients of the growth equation maintain unchanged， while the test precision decreases； and on the contrary， the undetermined coefficients of the resistance equation change， and the test precision is improved or far higher than the test precision of the growth equation. However， during the rejection of time effect of the resistance equation， the undermined coefficients of the resistance equation maintain unchanged， while the test precision decreases； and on the contrary， the undetermined coefficients of the growth equation change， and the test precision is improved or far higher than the test precision of the resistance equation.
It could be seen from Table 1 that all the tests were regarded as being passed when the precision exceeded 99.85%， and tree height item exhibited the precision of 99.99%. Except that the tree diameter items of 1.3 and 2.5 m had the precision slightly lower than original test precision， other items showed precision higher than original test precision， indicating the experimental design was rational. The doubling time in Table 1 refers to the time for doubling of the index （the same below）.
As shown in Table 2， except the tree diameter items of 0.5， 1.3， 1.5 and 3.5 m， other items were all higher than original test levels， and the lower ones also showed no big differences. All the items passed the validation with precision higher than 99.82%， and the precision of many items was close to 100%， indicated that the selected test path was right. In the table， tm refers to the theoretical age of quantitative maturity when the average growth rate of the time is the highest， and tz means the time when the item has the highest instant growth rate （the same below）. It could be seen from Table 3 that various items all passed the validation with precision higher than 99.79%. Under the premise of sample number larger than 28， the precision was higher than original test precision （without the rejection of the effect of time factor， the same below）， indicating that the design of the experimental technical path is very scientific and rational， and in order to ensure test precision， the improvement of sample number is very important. Compared with Table 4， except the item of volume of timber， the test precision was all reduced， which was caused by uneven distribution of annual precipitation， indicating that the effect of time on tree is more intense. Except the tree height item， the rate of change （tree growth rate） was all improved， indicating that precipitation is a very active factor influencing tree growth.
The results in Table 4 showed when sample number was as high as 42， the test precision was reduced compared with original test， other values were all improved. It indicated that with the increase of tree height， the b value of its diameter equation had a trend of gradually increasing， which showed that the growth of tree might have multiple growth peaks， which would be investigated in another study. All the items passed the validation with precision higher than 99.61%， indicating that the test has higher reliability.
Table 1-Table 4 show that the effect of time factor could be reduced by such method， and the reduction of time effect would enhance the effect of precipitation on tree growth.
Compatibility Test of Empirical Equation
Another sample tree was tested with the same method， and better test results were obtained. The test results of this sample tree were used for compatibility test of above test results. The test results are shown in Table 5. In the table， FZ-2 and FZj-2 represented the F values obtained from the comparison with sample tree No. 2 before and after the rejection of tree age factor of the development equation， respectively； FH-2 and Fhj-2 represented the F values obtained from the comparison with sample tree No. 2 before and after the correction of tree age factor of the resistance equation， respectively； FpZ-2 and FpZj-2 represented the F values obtained from the comparison of the effect of precipitation with sample tree No. 2 before and after the rejection of tree age factor of the development equation， respectively； and FpH-2 and Fphj-2 represented the F values obtained from the comparison of the effect of precipitation with sample tree No. 2 before and after the correction of tree age factor of the resistance equation， respectively. D0 represented the ground diameter item， and so on. According to the table， under the premise of not rejecting the effect of any factor， the fitted values of most items exhibited no significant differences between the two sample trees， only few items showed significant but not very significant differences， indicating that the application of time empirical equation was very scientific and rational. After the effects of time and resistance were rejected partially， the development and resistance equations of time and the development and resistance equations of precipitation （including before and after the rejection of partial effect of time factor） exhibited very strong differences， only very few items （diameter item of 4.0 m） showed no remarkable differences， indicating that in relation to time factor， precipitation was a more active influencing factor.
Discussion
The application of empirical equation actually is to regard time as a variable， which exits in the form of substance. Dialectical materialism reckons that time and space are both the existence forms of substance. During block design， only space （section） is divided to multiple plots， which are then applied with the effects of different equivalents， and various data are analyzed according to the differences shown over time， so as to find corresponding laws. However， with the help of the characteristics of growth ring of trees， block division was performed based on time， and due to the analysis on the same tree， noise caused by difference in site condition was avoided objectively. Conventional test of factor effect adopts space block design， objective error caused by site factor is difficult to be avoided， and single factor test could be performed （by comparison with control）， while the results of multi-factor and interaction test would not be ideal. In this study， tests were carried out using empirical equation. Time was used as the basis of block design， the deviation caused by site factor was completely avoided， the effect of time on tree growth was mainly decided by physiological properties of tree species， and whether it should be eliminated was further studied. Research shows that the interaction of various factors is a kind of superimposed effect， i.e.， multiplier effect （index effect）， rather than additive effect. On the basis of the thought and practice of additive effect， it is found that test precision is reduced， and the operability is poor. Therefore， the old mode and frame should be broken. Changing space with time and changing space with time have been widely applied in military and social practice. Based on this， changing space with time is worthy of trying in scientific experiment. It is concluded from research that the effect of time factor could be rejected partially by this method， but could not be rejected completely， because the effect of time factor is the expression of the result of the co-action of various factors including illumination， air temperature and water in time scale though it is decided by the characteristics of tree itself. When rejecting the effect of time factor using empirical equation， the effects of other factors are also rejected partially， and how to completely reject the effect of time factor is a more complicated research subject， which will be solved gradually with the improvement of scientific means. Research shows that precipitation is a more active factor than time in the effect on tree growth. Due to the application of this method， the test precision is improved， and the research precision of resistance equation is made close to that of development equation， which proves the rationality of the resistance and development equations defined by the writers. Through this study and other long-term research， the writers deem that tree growth might experience two or more growth peaks， which is not accordant with conventional thought that trees only have one growth peak. The writers deem that through this method， test precision could be improved， but the effect of time factor only could be rejected partially rather than completely. Though rejection could be further performed by this method， the test precision would be further improved， but the writers reckon that this makes little sense. Under the premise of ensuring test precision， the effect of time factor is not necessary to be rejected， unless the tree species is very precious with very high economic value， because this research requires massive input of manpower， material resources and financial resource， as well as longer research time， and the research and computation process is also much complicated.
References
[1] GONG YP. Relationship between growth and annual precipitation of Pinus thunbergii×P. densiflora[J]. Protection Forest Science and Technology， 2017（6）： 41-44.
[2] ZHANG J. Study on climate cycle[J]. Protection Forest Science and Technology， 2017（11）： 38-42.
[3] LIAN LS， LI WH， ZHU PS. Analysis of climate change in Shandong Province since 1961[J]. Meteorological Science and Technology， 2006： 34（1）： 57-61.
[4] GAO WD， YUAN YJ， ZHANG RB， et al. The recent 338-year precipitation series reconstructed from tree-ring in northern slope of Tianshan mountains[J]. Journal of Desert Research， 2011， 31（6）： 1535-1540.
[5] LIU GJ. Review of registered consulting engineer （investment） certified qualification examination textbook[M]. Tianjin： Tianjin University Press， 2003.
[6] ZHAO XP， GUO MH， ZHU XL. Advance in research on the effects of temperature on trees growth and wood formation[J]. Forest Engineering， 2005， 21（6）： 6.