Representation of Tree Stem Taper Curves and Their Dynamic, Using a Linear Model and the Centroaffine Transformation

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Abstract
One main task of forestry is a reliable estimation of the stem form and its development applied in calculating total and log volume. As long as process-oriented models are not available for this practical use, empirical models must serve instead. Taper curve data of trees within stands normally show a rank maintenance,i.e., a tree which has a greater diameter than another one at a certain height, is most probably bigger at any other height, too. This property also applies to the analysed tree species, sugi (Cryptomeria japonica) and hinoki (Chamaecyparis obtusa), and will be well-represented by a linear model formulation. As model parameter sets of single stands have a very limited time validity, two approaches for future stem form prediction are discussed. The one, the centroaffine transformation of a linear taper curve function, is not suitable for representing the time-depending change of the stem form. However, this can be done by a linear unit taper curve model, the parameters of which are based on sample trees of stands of several age classes. Temporary unit parameter sets are derived for sugi and hinoki and the estimated stand volumes are compared to the real ones to evaluate the model performance, which turned out to be very good.