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Tree and Forest Measurement / Stand basal area
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Stand basal area

Farmers measuring stand basal area using the Australian Master TreeGrower Tape.

Stand Basal Area (SBA) is simply the cross-sectional area of all the trees at breast height per hectare of forest or plantation (m2/ha). Stand Basal Area can be used to estimate stand volume and is a useful measure of the degree of competition in the stand.

Measuring Stand Basal Area

The basal area of a stand or plot can be determined in different ways:

  1. The sum of individual tree basal areas.
  2. The optical method of assessing basal area.
  3. The spacing factor method.

1. Sum of individual tree basal areas

The most accurate method of assessing the basal area of a stand of trees is to measure all tree diameters in a plot, calculate the individual tree basal areas and then add them up. Computer spreadsheets are ideal for this.

Basal Area of a tree (m2) = (DBH/200)2 x 3.142

Stand Basal Area (m2/ha) = (Sum of the basal area of each tree in the plot)
(Area of the plot (ha))

A quicker method is to calculate the basal area using the average tree diameter. Because larger trees contribute more to the basal area than small trees, this technique may underestimate the true basal area of a stand by about 10%, depending upon how varied the tree size is on the plot:

Stand Basal Area (m2/ha) = (Basal area of the average tree diameter) x (Stocking (tree/ha))

2. Optical methods of assessing Basal Area

Basal Area per hectare can be estimated using an optical method. A gauge of known width is held at a set distance from the eye. The observer then turns around on a set point observing each tree (at breast height) counting the number of trees that appear wider than the width of the gauge. If a tree appears wider than the gauge, it is considered as 'in' and counted as 1. If a tree appears to be exactly the same width as the gauge it is counted as 1/2. Trees that appear smaller than the width of the gauge are ignored. The total count is multiplied by the "factor" of the gauge to give the basal area per hectare.

Example:
Using a 2 factor gauge, the operator counts 11 trees that appear wider than the gauge and 3 that appear to be the same width:.

The Basal Area (m2/ha) = Factor x Count
= 2 x (11 + (3 x 0.5))
= 25 m2/ha

 

Measuring Stand BA using an optical gauge. If the tree appears wider than the tree stem at breast height, the tree is counted as "in" or "1". If the tree is the same width as the gauge, it is counted as "1/2". Any tree smaller than the width of the gauge is ignored. Count x Gauge Factor = Stand Basal Area (m2/ha).

This method was developed by foresters in Europe in the 1930s and was introduced to Australia in 1952. In some cases foresters use a glass prism that subtends the angle, although the gauge method is just as legitimate and much cheaper. The mathematics behind the technique is not complicated but it is not important to understand it in order to use the technique anyway. See Additional Information.

All that is needed to make up an optical basal area gauge is something of known width that can be held at a set distance from the eye. The table below gives the specifications for gauges of different factors and shows the distance a gauge of a particular width should be held from the eye. Distances of less than 40cm are impractical due to the difficulty of simultaneously focusing the eye on both the gauge and the tree in the distance. Distances of more than 60cm are difficult to reach.

  Factor 1 Factor 2 Factor 3 Factor 4
Gauge Width (cm) Calculation:
50xWidth
50xWidth/SQRT(2) 50xWidth/SQRT(3) 50xWidth/SQRT(4)
1.0 50 35.4 28.9 25.0
1.4 70 49.5 40.4 35.0
1.6 80 56.6 46.2 40.0
1.8 90 63.6 52.0 45.0
2.0 100 70.7 57.7 50.0

Testing doubtful trees.
If a high degree of accuracy is required it is necessary to test doubtful trees:

A tree is "in" if its DBH is greater than:

- the distance from the operator/50.0 for a 1-factor gauge,
- the distance from the operator/35.4 for a 2-factor gauge,
- the distance from the operator/25.0 for a 4-factor gauge.

Precautions

  • Each tree must be viewed at breast height (1.3m).
  • It is important to turn on a single point keeping an eye over the same point on the ground.
  • Leaning trees should be viewed at right angles to the stem.
  • The distance from the eye to the gauge is important, although if the user holds the tape 1cm away from the correct position then the error will be less than about 5%.
  • The greater the number of "1/2" trees the less reliable the result. For accurate measurements the diameter and distance to these trees must be measured to confirm their status.
  • Care must be taken to view trees hidden behind other stems or undergrowth. If necessary the user can move sideways provided the distance to the tree is not altered. The user should then return to the original point before turning to view the next tree.
  • A total count of about 10 trees is recommended. If the count is lower than 5 or greater than 15, a different factor gauge should be used.

Basal areas in plantations and native forests normally vary from about 10 to more than 60 m2/ha and therefore gauges with factors of 2 and 4 should be sufficient in most cases. The more sample points used and care by the operator to ensure that the correct method is implemented, will increase the accuracy of the results.

3. Spacing Factor Method of Estimating Basal Area

In planning silvicultural regimes, it is useful to have a feel for how basal area varies with the average spacing between trees. The spacing factor is simply the average distance between the trees (in cms not metres) divided by the average stem diameter (cms), and is a useful way of estimating basal area in uniform plantations. For example, if the trees are spaced at an average of 5m (500cm) and the mean diameter is 20cm, the spacing factor is 500/20 = 25. The figure below shows the relationship between the spacing factor and basal area.

This technique assumes all trees are of equal size and is helpful to predict the basal area at maturity for a given final stocking and tree size. To thin a plantation to a certain basal area, simply thin to an average spacing equal to the diameter of the retained trees, multiplied by the appropriate spacing
factor. The higher the spacing factor the lower the competition or basal area.

Some useful numbers to remember are:

If the spacing factor = 12.5, basal area is approximately 50m2/ha
If the spacing factor = 15, basal area is approximately 35m2/ha
If the spacing factor = 20, basal area is approximately 20m2/ha
If the spacing factor = 30, basal area is approximately 10m2/ha

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