Mitscherlich式による森林の生長予測

概要

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Various formulas for the expression of the growth of the volume, height and diameter of the tree, have been designed empirically. In 1962, Dr. Suzuki succeeded in expressing the growth of trees very accurately by Mitscherlich's curve empirically. From this fact, the authors show a Model of tree growth as follows: 〓where a, b, c: constant x(t): the growth of trees at a time (t) f(t): productivity at a time (t) when f(t)=constant, the solution are (i) x(t)=α0+c1eαt+c2eβt b2-4ac>0 (ii) x(t)=α0+c1eαt+c2teαt b2-4ac=0 (iii) x(t)=eαt(c1cosβt+c2sinβt) b2-4ac<0 Here"x(t)" is the expression of tree growth, therefore solution (iii) is not our Model and solution (ii) is in very rare case, thus our model can be written as follows: x(t)=α0+c1eαt+c2eβt From this solution, we can conclude that the tree grows exponentially. Now the condition of "f(t)=const" is realistic in a closed forest, at α0=M, c1=-Meαt0 α=-k c2=0 x(t)=M(1-e-k(t-t0)) this is the Mitscherlich's formula, and it is Dr. Suzuki's model. On the prediction of the future tree growth by this formula, it gives us very good estimation in case of short period such as 5 years or so, but not so good in case of long period, because even in closed forest, productivity changes gradually.
東京大学大学院農学生命科学研究科附属演習林,The Tokyo University Forestsの論文