Taper Function Project - 130-702

Description: Development of taper equations is a basic prerequisite to estimating individual tree volumes and product yields. These equations are used to estimate diameters along the bole at any given height. Individual tree volume can then be calculated based on these diameters and corresponding heights. Moreover, the product recovery of different trees with the same total volume could be different. Two trees with different shape, conic and cylindrical, for example, will have different product recoveries and hence significantly different economic values.

Historically the growth and yield program of the OMNR has relied on taper equations that were developed from data derived from natural stands. Although sufficient for natural stands, these equations have been used to calculate individual stem volumes for plantation grown trees. This has the potential to introduce bias into the individual tree volume estimates, and this bias will be magnified when used in association with Ontario's new benchmark yield curves.

In plantation grown tree stems, the shape of the tree is influenced by stand density:a variable not included in the current taper functions. Stnad density can be regulated either by planting trees at different initial spacings or by thinning stands to different densities. However, the trees of a particular species grown in a plantation and in a natural stand thinned to the same density may not have the same form, especially if the thinning is carried out at a later age.

Consequently, the objectives of this study are to:

1) Evaluate the potential bias in the existing taper functions when applied to plantation grown jack pine and black spruce trees.

2) Initiate the development of new and more appropriate taper functions for these species; specifically, incorporating stand density and individual tree crown height.

3) Evaluate the long term density effects on tree form which arise from different planting density and by thinning.

4) Determine the most appropriate sampling design in terms of the sample size and selection procedures which minimize prediction error when building taper equations.The results obtained from this last objective will be useful in the development of taper models for other Ontario species.


The Project Team: Mahadev Sharma, OFRI, John Parton, OMNR



Sharma, M. and J. Parton. 2007. Height–diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach. Forest Ecology and Management 249: 187–198.

Sharma, M. and J. Parton. 2009. Modeling Stand Density Effects on Taper for Jack Pine and Black Spruce Plantations Using Dimensional Analysis. Forest Science 55: 268-282.


Status Reports:

Status Report (2007-2008)

Project Work Report (2007-2008)

Status Report (2008-2009)

Financial Summary (2008-2009)


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