A simple theory to link bole surface area, stem density and average tree dimensions in a forest stand

Abstract

A geometrical model of a forest stand has been analyzed. A forest stand has been modeled as a population of cones which was described by the change of total bole surface area with density $$\hat{S}(N)$$ , relation between density and a horizontal dimension (radius r) r(N), and the relation between vertical dimension (generatrix l) and radius l(r). It has been shown that there are close relationships between $$\hat{S}(N)$$ , l(r) and r(N). In case of $$\hat{S}(N) = const$$ , power exponent of l(r) can be predicted from the power exponent of r(N) and vice versa. A comparison of the model analysis with the data available on Scots pine (Pinus sylvestris L.) stands has been performed. In spite of the model simplicity, its inferences proved to be workable in many cases where the data can be interpreted as a dynamics of an even-aged forest stand. In particular, if the estimation of total bole surface area is constant, the power exponent in the relation of diameter and stand density DBH(SD) can be calculated on the basis of the power exponent in the relation of height and diameter H(DBH) and vice versa. Possible limitations and the meaning of the analysis are discussed.