© 2005 Heron Publishing—Victoria, Canada
Bridging process-based and empirical approaches to modeling tree growth
Harry T. Valentine (1, 2) and Annikki Mäkelä (3)
1. USDA Forest Service, Northeastern Research Station, P.O. Box 640, Durham, NH 03824-0640, USA / 2. Corresponding author (hvalentine@fs.fed.us) / 3. Department of Forest Ecology, P.O. Box 27, FIN-00014 University of Helsinki, Finland / Received May 25, 2004; accepted December 4, 2004; published online May 2, 2005
Summary
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.
Keywords:
carbon balance, crown length, crown rise, diameter, height, optimal control model, pipe model, self-thinning.
