Derivation of stem taper from the pipe theory in a carbon balance framework

A dynamic tree growth model is described. The model derives the development of stem taper and vertical distribution of branch basal area from the pipe model, assuming that reuse of active pipes is regulated by foliage dynamics in a vertically explicit crown with a foliage distribution of constant shape. Based on empirical findings, the pipe model was modified slightly to allow the foliage/sapwood ratio to vary as a function of distance from the treetop. Growth was derived from carbon balance in a stand of different size trees that may shade each other. The model was applied to old and middle-aged trees growing in dense and sparse stands of Scots pine for which stand-level measurements are available as a chronosequence, but individual trees have been measured only once. Measured trees were compared with corresponding simulated trees for stem taper and vertical distribution of branch basal area. The results indicated that the pipe model assumptions, combined with a model of tree growth, are capable of producing realistic predictions of the vertical distribution of stem and branch diameter in trees of different sizes in the stand. A comparison of the results with a simple form of the uniform stress theory showed good agreement between the two models. However, a significant difference was found between the measured relative contribution of heartwood to total stem diameter and the predicted share of disused pipes in the stem. A possible explanation for this discrepancy is that the transition from sapwood to heartwood is gradual rather than abrupt as assumed in the model. A modification of the pipe model to incorporate a gradual transition is outlined.