A quantitative analysis of stem form and crown structure: the S-curve and its application

The statical model of Oohata and Shinozaki (1979) was applied to derive a whole stem form function for Cryptomeria japonica D. Don, Chamaecyparis obtusa Endl., and Larix leptolepis Gordon. Defining stem density (weight per unit length) at a depth z from the tree top as S(z), the relationships between the total stem weight T(s)(z) from the apex to the z-horizon and S(z) were examined. A formula with two exponential functions, corresponding to the stem form above and below the crown base, was obtained. This formula was termed the "S-curve." Applying the same analysis to the total weight of a branch and the weight of a unit length (10 cm) at the branch base yielded a similar curve. This result suggests that the formula for branch form can be determined from a single branch in a forest stand. It also provides quantitative evidence of the fractal structure of trees.