Stand height curve

Stand height curve
Forest Measurement and Modelling.

A stand height curve is a representation of the correlation between tree height (total or bole) and tree diameter (dbh) or basal area (g). The curve can be presented as a plot of height against diameter, or in equation form.

A stand height curve can be used to predict the height or a tree when only the dbh is measured. It is used in this way to determine some types of stand height. The predicted heights are also commonly used as input into 2-way volume tables and taper equations.

The shape of the curve can also provide an indication of the development and growth stage of the stand:

  • Steep slope indicates a young stand which is still sorting out dominance.
  • Shallow or flat slope may indicate a mature or over-mature stand.
  • A right-hand-side of the curve that is relatively high indicates a good site.

Repeated measurement of a stand height curve for one stand over time will generally show the curve moving upwards and to the right. The curve will also tend to flatten and approach a maximum height (determined by the site) as the stand matures.

The slope of the curve is determined by the relative growth of dbh and height. However, the curve is often not well defined because competition affects the growth of dbh significantly more than it does affect height growth. Thus, dbh will vary for trees of a given age and genetic make-up as competition varies within the stand, but height will not.

Sampling to determine the curve The height curve for a stand is normally fitted to data that is collected during a systematic or stratified sample. A stratified sample ensures that the full range of dbh is covered and this allows a more robust relationship to be found.

The number of trees sampled varies. The MicroMARVL inventory (NZFRI, 1990) states that at least two trees are needed, but that it is normal to sample at least 20 or 30 trees across the dbh range. Fewer than 10 trees in the sample is only practical when the form of the equation (see below) is already known and the density is reasonably consistent across the stand. In the UK, for example, the height curve is assumed to be a quadratic polynomial which is fitted to the height and dbh data collected from 10 trees selected systematically across the plot.

Height curve equations
Model forms
A height curve equation is a mathematical or statistical statement of the expected height of a tree with a nominated dbh in a particular stand. As the shape of the curve changes with age, site and density, the form of the equation will also change. Common equation forms include (where h denotes height, b denotes breast height, and a1-3 denote constants):

  • Log : log
  • Log : inverse linear
  • Log linear
  • Inverse
  • Power function
  • Exponential function
  • Quadratic polynomial
  • Petterson's Curve

[hgtcurve.htm] Revision: 6/1999