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Bridging process-based and empirical approaches to modeling tree growth

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Valentine, Harry T.; Makela, Annikki; Makela, Annikki

Year Published



Tree Physiology. 25: 769-779.


The gulf between process-based and empirical approaches to modeling tree growth may be bridged, in part, by the use of a common model. To this end, we have formulated a process-based model of tree growth that can be fitted and applied in an empirical mode. The growth model is grounded in pipe model theory and an optimal control model of crown development. Together, the pipe model and the optimal control model provide a framework for expressing the components of tree biomass in terms of three standard inventory variables: tree height, crown height and stem cross-sectional area. Growth rates of the inventory variables and the components of biomass are formulated from a carbon balance. Fundamentally, the parameters of the model comprise physiological rates and morphological ratios. In principle, the values of these parameters may be estimated by lower-level process models. Alternatively, the physiological and morphological parameters combine, under reasonable assumptions, into a set of aggregate parameters, whose values can be estimated from inventory data with a statistical fitting procedure


carbon balance; crown length; crown rise; diameter; height; optimal control model; pipe model; self-thinning


Valentine, Harry T.; Makela, Annikki. 2005. Bridging process-based and empirical approaches to modeling tree growth. Tree Physiology. 25: 769-779.

Last updated on: April 8, 2021