HYPERBOLIC MODEL FOR ADJUSTMENT OF SETS O F HEIGHT DIAMETER CURVES

A hyperbolic model is proposed for the construction of sets of height- diameter curves in even-aged stands. On the basis of 86 samples from p ure stands of beech (Fagus silvatica L.) and oak (Quercus petraea (Mat t.) Liebl.), this model fitted adequately the geometry of data sets. T he qualitative behaviour is correct over the whole range of the indepe ndent variable. Each parameter characterizes a significant geometric f eature of the curve. The three parameters correspond to the asymptote, the slope at the origin, and the curve shape (curvature). The latter two are fairly stable over a large range of age (30-150 years) and sta nd density. A fitting procedure is proposed, through step-by-step redu ctions of the model, to overcome the limitations of poorly conditioned samples; only the asymptote, which is very close to top height, is to be estimated from each data set. The time series of estimates exhibit satisfactory evolutions for a large age interval. We interpret the sh ape of curve sets as the consequence of dominance on height and diamet er growth in hierarchized stands.