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Tree and Forest Measurement / Standing tree volume
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Standing tree volume

Pruned Silver Quandong.

Using measures of Diameter at Breast Height (DBH) and Total Tree Height (Ht), an estimation of total tree volume can be made by assuming the tree has a particular form. For example, if we assume the tree is conical in shape, with the DBH equivalent to the diameter at the base of the cone, then the following formula is appropriate:

Tree volume (m3) = Tree Basal Area (m2) x Tree Height (m) / 3
= (DBH/200)2 x 3.142 x Ht / 3

So, if a tree was 22.7m tall and 42.6cm in DBH, the total tree volume would be:

Tree volume (m3) = (42.6/200)2 x 3.142 x 22.7 / 3 = 1.08 m3

As the diameter is actually measured at 1.3 metres above the ground, not at the base, most trees carry a bit more volume than the cone-form would suggest. This formula is a conservative estimate of total underbark tree volume.

Measurements of a 10 year old eucalypt pruned to 6.5m. Assuming the tree has a conical shape this can be a useful estimate of underbark volume. Source Reid and Stephen (2001) Farmers Forest.

More detailed formulae are available for particular species grown in some areas, although rarely for farm grown trees other than pine.

It is important to be consistent in choice of method of measuring volume, particularly when comparing growth on different sites or over time.

If a tree is clearly not conical or if a farmer is only interested in the volume of the butt log it may be more appropriate to measure the volume of the lower log only.

Estimating the volume of the parts of a standing tree

Assuming a tree is perfectly conical makes it easy to estimate the volume of different sections of the trunk. All that is required is an estimate of the tree taper or rate at which the diameter decreases with height

Taper (T) of a conical tree = Diameter (DBH)/[Height(Ht) – 1.3] cm/m

For example: For a conical tree of 42.6cm DBH and 22.7m tall, the taper (T) is 1.9cm/m.

Using the taper equation, it is possible to estimate the diameter at different points up the tree. For example if the same tree was pruned to 6.7 metres and the stump height was 30cm then it may be assumed to have the following dimensions:

- Total Tree Height (Ht) = 22.7m
- Diameter Breast Height (DBH) = 42.6cm
- Pruned Height (PHt) = 6.7m
- Stump Height (SHt) = 0.3m
- Estimated total tree Volume (Vol)
Vol = (DBH/200)2 x ( x Ht / 3 = 1.08m3
- Estimated Taper (T)
T = DBH/Ht = 1.9cm/m
- Underbark diameter at stump height (LED)
LED = DBH – SHt x T = 42.03cm
- Underbark diameter at pruned height (SED)
SED = DBH – PHt x T = 29.9cm
- Crown Log Vol (Cvol)
Cvol = (SED/200)2 x ( x (Ht-PHt) / 3 = 0.37m3
- Stump Vol (Svol)
Svol = Vol - (LED/200)2 x ( x (Ht-SHt) / 3 = 0.04m3
- Pruned Vol (Pvol)
Pvol = Vol – Cvol – Svol = 1.08-0.37-0.04 = 0.67m3

It is interesting to note that in well-spaced, pruned trees the taper of the pruned butt log tends to decline over time resulting in a more cylindrical log at the base and a more highly tapered upper crown. The graph above shows some evidence of greater diameter growth in the section just above the pruned log, even in a ten-year-old pruned tree.

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