Pipe Model Theory for Prediction Tree Sapwood and Heartwood Profiles

• The classical pipe model theory introduced by Shinozaki, Yoda, Hozumi,and Kira (1964a,b) is used to estimate tree sapwood area. It rests on theconceptual idea that leaves are supported by pipes, serving as vascularpassages. The simple pipe model of plant form does not predict the heartwood area and is thus not suitable for stem diameter estimates below thetree crown. For this reason, Shinozaki, Yoda, Hozumi, and Kira (1964a)verbally described an extended pipe model theory of tree form that inprinciple accounts for the accumulation of disused pipes from discardedbranches and leaves. However, this pipe model theory of tree form is difficultto apply in practice as lost branches and leaves are rarely known. Here, we synthesize the pipe model theory of plant form with a recentlydeveloped theory of branch thinning that quantify discarded branches andleaves. This allows us to develop a new stem model of tree profiles frombreast height up to the top of the tree. We test the stem model performance on empirical data from four tree species across three continents.We find that the stem model accurately describes heartwood and sapwoodprofiles of all tested tree species (calibration; R2: 84-99 %). Furthermore,once calibrated to a tree species, the stem model predicts heartwood andsapwood profiles of conspecific trees in similar growing environments basedonly on the age and height of a tree (cross-validation / prediction; R2:62-98 %).

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