
Stand height Forest Measurement and Modelling. 

Some measure of stand height is a useful index of the quality or site of a forest stand. It is also related to the volume and biomass of the stand. The parameters used for quantification of stand height include:


Mean height (unweighted) 
The arithmetic mean of the height of all trees in the stand is a useful measure of stand height in evenaged stands. In small stands, the height of every tree could be measured, added together and divided by the total number of trees to derive the mean height (unweighted). However, a samplebased estimate of the mean is the more usual approach. A samplebased mean could be determined via a systematic sample of trees in the stand (e.g. measuring every 100th tree and taking the mean), or a random sample (e.g. selecting the tree nearest to 10 randomly selected points). Alternatively, the height of the average tree may be measured. If the stand has been measured for diameter breast height (dbh), then the quadraticmean diameter can be determined. The three (or n) trees with dbh closest to the quadraticmean diameter are measured and the mean of their heights averaged. The quadraticmean diameter rather than the arithmeticmean is used because this mean is better correlated with volume and other stand parameters of interest. 
Weightedmean height Lorey's mean height 
Lorey's mean height weights the contribution of trees to the stand height by their basal area. Thus Lorey's mean height is calculated by multiplying the tree height (h) by its basal area (g), and then dividing the sum of this calculation by the total stand basal area: This method of calculating stand height is not used in Australia, but is regularly used in the US and Europe. Lorey's mean height is more stable than an unweighted mean height because it is less affected by mortality and harvesting of the smaller trees. A reasonable estimate of Lorey's mean height can be determined by averaging the height of all IN trees selected during an angle count sample. The estimate may be slightly biased (positive) because too few small diameter trees are selected. 
Height of a component of a stand 
Several stand height methodologies select only the biggest trees to avoid the effects of thinning and tree mortality on stand height estimates. The estimates are strongly correlated with site and stand volume, and do not change when (normal) thinning operations remove the smaller trees. Methodologies differ in the way big trees are defined, and the number selected for measurement:
The number of trees selected to derive the mean value varies. NSW, ACT and Victoria traditionally use 40 trees/ha (pro rata to plot size), while Queensland uses 50 trees/ha and South Australia uses 75 trees/ha. New Zealand uses only the tallest tree (free from malformation) in each 0.01 ha plot. Dominant height is usually measured in unevenaged forests. The choice between predominant and top height usually depends on the ease of identifying the tallest trees. Predominant height is the preferred stand height parameter in many evenaged forests. Top height will supplant predominant height when it is difficult to choose reliably the tallest trees (e.g. in a densely stocked stand). The way the trees are selected differs  see the Code of Forest Mensuration Practice, section 3.4.2 here. Relationships between predominant height and top height have been established for many forests. These relationships are useful for comparing inventory and growth data across regional boundaries. Similarly, relationships between stand heights estimated from 40, 50, or 75 trees/ha have been established. Studies in New Zealand found that the average difference between top height and predominant height was 0.35 m for short stands, but that this difference reduced for older and taller forests. 
Using predicted heights in stand height determination 
A measure of stand height may be derived from the predicted height of the largest diameter trees. This approach avoids subjective selection of the tallest trees. In New Zealand, the quadraticmean diameter of the largest 100 trees is determined. The corresponding height for this diameter tree is estimated from a Petterson height:diameter curve  this is termed the top height. A similar approach is adopted in the UK, except instead of the Petterson curve, a quadratic regression to predict height from diameter and diameter squared is fitted to data from 100 trees systematically selected from the stand. 
[s_height.htm] Revision: 6/1999 