Methods for modeling whole stem diameter growth and taper

Stem profile models which allow for both taper and form changes (Gray 1956) were constructed and evaluated. Gray defined form to be the basic shape of the tree, e.g. cone or parabolid, and taper to be the rate of narrowing in diameter given a tree form. Ormerod's stem profile model was selected as the basic model since its parameters were readily interpretable in terms of Gray's taper and form definitions. Two stage modeling procedures were used to relate individual tree taper and form parameters to tree and stand characteristics. Two second-stage parameter estimation alternatives were evaluated. Parameter estimates for both techniques, ordinary least squares and random function analysis, were similar. Characteristics used to predict stem form were total tree height, crown ratio, height to the live crown, site index, and tree age. The taper parameter was related to diameter at breast height, crown ratio and site index. Error evaluations suggest that substantial gains in predicting stem diameters were not made using the variable taper and form stem profile models.

Two methods were proposed for modeling whole stem inside-bark diameter or cross-sectional area increment. Whole stem increment models were derived from several stem profile models and Presseler's hypothesis on the vertical distribution of cross-sectional area growth. Stem profile models evaluated for constructing compatible increment models were Kozak and others (1969), Ormerod (1973), Goulding and Murray (1976), Max and Burkhart (1976), Cao and others (1980), and Amidon (1984). The increment model based on Presseler's hypothesis was derived as a generalization of the work of Mitchell (1975). Evaluations, with limited increment data, consistently showed that the models based on Presseler's hypothesis predict inside-bark diameter increment with less error than do the profile model compatible increment models. This may be due to the lack of crown information currently used in stem profile models.