A model for the relationship between form-factors for stem volume and those for stem surface area in coniferous species

A model that describes the relationship between the form-factors for stem volume and those for stem surface area in coniferous species is proposed. The model is derived assuming that the stem form of a tree can be expressed by Kunze's equation. The model indicated that the form-factor for stem surface area was directly proportional to the square root of the form-factor for stem surface volume, independent of the stem position. The proposed model expressed the relationship of the form-factors for Japanese cedar (Cryptomeria japonica D. Don) and Japanese cypress (Chamaecyparis obtusa Endl.) trees well. Therefore, the form-factors for stem surface area could be estimated from those for stem volume. No significant difference in the coefficient was found between Japanese cedar and Japanese cypress trees, indicating that the proportional coefficient would be common between the two species. Many studies have shown that the form-factors for stem volume at 0.7 and 0.5 in relative height were, respectively, almost steady at 0.7 and 1.0, independent of species, district, density control, and growth stage. Substituting these universal values into the proposed model, the form-factors for stem surface area at 0.7 and 0.5 in relative height were estimated to be 0.730 and 0.873, respectively. The estimated values of the form-factors for stem surface area would be universal for coniferous species. The proposed model also showed that the breast height form-factor for stem surface area decreased sharply with the increase in total tree height, when the height was less than 10m. However, after the tree attained the total height of 10m, the breast height form-factor gradually decreased with the total tree height approaching its asymptotic value of 0.605. In conclusion, the model proposed here can be used to describe the relationship between form-factors for stem volume and those for stem surface area successfully.