Stand Height Curve ©

A stand height curve (SHC) is:

the curve of best fit to a series of points representing the plot of height against diameter (or basal area) for some or all trees in the stand.

The trend of the stand height curve in even-aged stands is usually apparent but not well defined because, within any diameter class, the height of individual trees may vary considerably due to genetic differences and differences in point density (affects d but has little effect on h). The trend is better defined by plotting class means of d and h against each other. The relationship invariably is curvilinear and concave to the abscissa.

The curve is steep for young crops on good sites and near flat and linear for old crops and those on poor sites (height growth arrested but diameter growth still active). With time, the relationship moves upwards and to the right, the movement being governed by the relative growth rates of d and h with time. The stand height curve cannot be used to determine site or height growth over a period because the particular relationship is dominated entirely by the density environment under which the trees are growing.

Stand Height Curves for Even-aged stands

The SHC partly describes stand structure so it is important to the silviculturist.
The SHC is used in one method of estimating stand volume, viz.:
- Enumerate the stand and draw up a stand table based on d.
- Compile the SHC.
- Derive from the SHC the heights of the mid-values of the diameter classes of the stand table.
- Read from an appropriate volume table the volumes of trees of class mid- diameter and corresponding height.
- Class volume = class average volume x frequency.
- Stand volume = Sum of all class volumes.

The method is best suited to species or stands in which variation of h within a d-class is small.

Stand Height Curves for Uneven-aged stands

The stand height curve in uneven-aged stands depends on the species composition of the stand and the treatment the stand has been given. In intensively managed selection forests of a single species in Europe and elsewhere, reasonable relationships can be established, i.e. certain heights are found to correspond with certain diameters. Contrast this with Australian native hardwood forests managed under the group selection system, for which a satisfactory relationship between h and d is difficult to establish.

However, the relationship between merchantable height and d is often satisfactory. If this relationship can be accepted as being constant over time, h need not be measured repeatedly in PMI. This has one main advantage, i.e. errors in the estimate of volume increment are reduced because errors in h measurement are held constant and differences of opinion on the merchantable limit are eliminated. (These differences of opinion can be minimised if the crown length branch is used to define the merchantable limit).

Sampling for the Stand Height Curve

A stratified random sample usually constitutes the most efficient design in sampling for the stand height curve (use d classes as strata and sample within strata weighting the sample according to the relative frequency). Nevertheless, systematic sampling with the start located at random is commonly applied. Subjective sampling is not uncommon particularly in small plantations.

If the stand height curve is compiled periodically, e.g. in periodic management inventory (PMI), a permanent sample may be advisable for several reasons:

to retain uniformity in the position of curves and in their change of slope.
to maintain selection bias constant.
to check on the meas

urement of tree height. In intensively managed forests, thinning may make it impossible to maintain a permanent sample. In this case, selection of the sample on each occasion should be done objectively to avoid bias.

Stand height curves are often fitted by eye but there are advantages in fitting them mathematically. This avoids bias and maintains uniformity in periodic measurement.

An excellent fit is often achieved with equations of the form:

  
   ln (h) = a + bd^-1, 
or in exponential from: 
   h = EXP (a + bd - 1).
   ln (h) = a + b ln (d)                                                   
   h = a + b ln (d)
   h = a + bd + cd^2

Petterson's Curve (Schmidt, A. von, 1967. Forstwiss. ZentBl. 86: 370-382) is used by New Zealanders to establish the stand-height model from sample tree data. They estimate mean height from the model by calculating the height corresponding to dg, the quadratic mean diameter of trees in the stand. The form of Petterson's Curve is:

  
  Y	= bo + b1 X
where	
  Y	= (1/(h - 1.4))0.4  and  X = 1/d
  h	= total tree height (m)
  1.4	= height of the breast high point above ground (m)
  d	= dbhob (cm)
  and bo, b1	= regression constants.

Other height/diameter relationships worth testing will be found in standard mensurational texts, e.g. Carron 1968, p.90.

Experience suggests no single model is likely to be satisfactory in all cases because the stand height curve changes with time in a given stand and changes from stand to stand at a particular time.

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Document URL	http://online.anu.edu.au/Forestry/mensuration/HGTCRV.HTM
Editor	Cris Brack ©
Last Modified Date	Fri, 9 Feb 1996