《Table 2 Empirical equations of the growth process of main tree-measuring factors within 24 years》

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《Study on Correlation between Increment of Larix gmelinii and Annual Precipitation》

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Through the check analysis of tree growth equation fitting within two years，three tree-measuring factors（tree height，DBH and volume of timber）all had fitting relation with precipitation.Unary linear equations（direction application of unary linear equations）were formed by various arithmetical operations on various fitting equations.Then，parameters a and b were obtained by unary linear regression，and F test and correlation coefficient（R）test were carried out.If the tests are passed，a tree growth fitting equation is established，and the calculation results are shown in Table 1.Table lookup showed that the tests were passed with a reliability over 90%，indicating that these mathematical models（i.e.，empirical fitting equations）are applicative overall.The problem of solving the maximum current annual increment time and quantitative maturity of trees using fitting equations was illustrated taking the DBH item as an example.The precipitation fitting mixed equation of tree DBH growth y（p）=ea-b/p（the increment changing with precipitation，obtained by derivation of Y （t）function，the process of which was omitted，only the extreme point was given，the same below） showed the extreme value pz=272.6mm，i.e.，when the accumulated precipitation reaches 272.6 mm in two years，the current water resource-contributed increment reaches its peak（i.e.，the instant use efficiency of water is the highest），which is the only peak；and the average water use efficiency equation of average tree growth Y（p）/p（precipitation converted from water resource consumed by annual average unit increment，the calculation process of which was omitted，only the extreme value was given，the same as below）had the extreme value pm=545.1 mm，i.e.，when the accumulated precipitation reached 545.1 mm in two years，the current average water resource use efficiency was the highest.Only the calculation of DBH fitting equation was described above，other fitting equations were the same as it，and detailed description was omitted.In the discussion below，growth fitting equations，and symbols such as pz and pm，also had the same meaning，and the calculation results were given without repeated description and explanation.The various calculated parameters and various threshold values are shown in Table 1.It could be seen from Table 1 that in the equation y（p）=ea-b/p，compared with DBH，various parameters of the square of DBH were improved by one time，their precision，F values and R values were equal，which was caused by the exponent mathematic relation，and in order to compared with accumulation，a fitting equation was also established with the square of DBH as a tree-measuring factor.Various equations all could pass F test and R test，and the precision is shown in Table with a lowest value of90%，and the highest value of 99.9%.