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# Parameters for Measurement of Tree Bole

## Parameters for Measurement of Tree Bole

Measurement of a tree bole at a nominated height would be easy if the bole corresponded to a simple geometric shape. For example, if we could assume that the bole cross section was like a circle, then we could measure the radius (r), diameter (d), circumference (c) or the area (a). We can calculate all the other variables once we measure any one of them.
However, the tree bole is rarely circular (or any other simple geometric shape) and the use of the above equations will only provide approximate estimates. The selection of which parameter to measure will depend on: the use of the measurement; the resources and tools available; tradition; and the acceptable error.

Radius (r): length from the centre to the outside of the bole. It is rarely measured in forestry. Radius cannot be measured on standing trees because the centre of the tree needs to be accurately located. Because a bole is not circular, different measurements of radius are possible.
Diameter
Diameter (d): length from the outside of the bole, through the centre, to the opposite side. Diameter is commonly measured in forestry. Again, because tree boles are not circular, different measurements of diameter are possible.

Diameter at breast height (dbh) is probably the most common measurement made on a standing tree.

Direct measurement of diameter commonly measures two different axes:

• The diameter of the maximum and minimum axis of the bole on trees that are clearly elliptical;
• The diameter of the maximum axis and the axis at 90 degrees;
• The diameter of any two axes at 90 degrees to each other.

The two diameter measurements are averaged using an arithmetic mean (most common) or a geometric mean (for highly elliptical boles).

The measurement of diameter on one axis is often acceptable when the data is only being used to group trees into a stand table.

Circumference

Circumference (c) – also known as girth: the length around the outside of the bole. Circumference is commonly measured in forestry, but usually it is then used to estimate bole diameter. If the bole were circular, diameter can be estimated as circumference divided by PI. However, if the bole deviates from this ideal shape, then this calculation will overestimate the diameter. This bias is not constant and will vary with the degree and type of deviation. However, this bias is rarely considered significant.

An advantage of measuring the bole girth is that there is no sampling error involved. Unlike diameter measurements, the result does not depend on which axis was selected to measure. This leads to an increase in measurement precision. In addition, if a tree bole changes by 1 cm in diameter, the girth measurement changes by 3.1415… cm (PI). Thus, finer readings of the change can be read.

Cross Section Area

Sectional area (a): the area of the cross-section of the bole. This parameter is very important in forestry. The sectional area at breast height is used in many relationships and is called basal area (g).

Sectional area could be directly measured using a planimeter, but this is rarely done. Instead, sectional area is calculated from diameter after assuming that the bole has a circular shape. If the diameter is estimated from a measurement of circumference, then the basal area estimate will be an overestimate (positively biased). If the diameter is estimated from the mean of measurements on one or two axes, then an over- or under- estimate of the sectional area is possible. The geometric mean of the maximum and minimum axes is less biased than other approaches (Matern 1956, Chacko 1961).

Biging and Wensel (1988) studied ways of measuring basal area increment. They concluded that increment estimates were unbiased if measurements along the minor axis were used.

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