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A Mathematically Tractable Stem Profile Model for Jack Pine in Ontario

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A new model was derived to describe the inside bark cross-sectional area of tree stems. It is a rational function. The inputs required by the model are outside bark tree diameter at breast height (DBH) and total tree height (H). Knowledge of a species-specific bark thickness at 1.3 m expressed in terms of input variables is also needed. Defining the model involves estimating two regression coefficients using either nonlinear or linear regression (after linearization of the model). The formula is analytically integrable and thus provides analytical inside bark volume estimates for any stem section defined by height limits. The model is analytically solvable for a stem height location at any given inside bark diameter, so that stem sections can be defined by the required inside bark diameter limits. The new model can be calibrated using either section diameter or section volume data. It is suggested that involving the ratio H/DBH in the model accounts for the influence of stand density on stem profile. The formula was calibrated for jack pine (Pinus banksiana Lamb.) in Ontario. Wider applicability of the model is supported by results obtained for sugar maple (Acer saccharum Marsh.) in Ontario and Scots pine (Pinus silvestris L.) in Finland. Comparing volume estimates from the new model with those generated by Honer's formula confirms the advantages of the new model. North. J. Appl. For. 16(3):138-143.
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Document Type: Journal Article

Affiliations: Ontario Forest Research Institute, Sault Ste. Marie, Ontario P6A 2E5, (705) 946-2981;, Fax: (705) 946-2030

Publication date: 1999-09-01

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