A flexible radial increment taper equation derived from a process-based carbon partitioning model

Abstract

Carbon allocation to the cambium along the stem is represented by a reaction-diffusion model along a continuous sink. Verti- cal variations of stem area increment along the stem are then theoretically connected to partitioning coefficients between tree compart- ments, at different spatial scales. This model is very sensitive to environmental growth conditions, and demonstrates the importance of topology and geometry in models of secondary tree growth. An analytical resolution is proposed to describe the vertical profile of stem area increment between crown basis and soil level. An empirical parametric equation is derived from this theoretical model. The 3 para- meters of this equation are related to the internal and environmental conditions of the tree. These parameters can be used as indicators in order to study the variability of stem taper. This equation is separately fitted on data from two experiments, with different silviculture and site quality, for Picea abies of different ages. Variation in the parameters is discussed according to growth conditions. This equation is further integrated in order to predict stem volume increment. Finally, some simple characteristic heights are derived from this function as indicators of functional crown basis. These heights are systematically calculated to predict crown recession. They are finally compared to heights measured during field work.