Measurement of single tree volume ©

Despite the fact that each year, more and more wood is being sold by weight, the forest manager still uses volume data extensively whether they are derived from inventories or yield tables/functions. Even though sale, processing and marketing procedures are changing, volume and the measures used to derive it (diameter, height, form, stand basal area, top height, etc.), are still most important tree and stand parameters.

When foresters speak of volume, they mean the amount of wood in a tree, stand or other specified area, according to some unit of measurement and some standard of use.

• The unit of measurement may be cubic metres or cubic metres per hectare.
• The standard of use may be firewood, pulpwood or sawtimber.

Usually volume is expressed inside bark and according to different specifications.

• Gross total volume: Volume of the main stem(s) of trees or stands including stump and top as well as defective and decayed wood.
• Gross merchantable volume: Volume of the main stem(s) of trees or stands excluding stump and top but including defective and decayed wood.
• Net merchantable volume: Volume of the main stem(s) of trees or stands excluding stump and top as well as defective and decayed wood.

Foresters speak of biological volume and utilisable volume:

• Biological volume - volume of stem with branches trimmed at the junction with the stem. Biological volume excludes irregularities not part of the natural growth habit, e.g. malformation due to insects, fungi, fire, mechanical damage. It is objective but unreal from the utilisation viewpoint.
• Utilisable volume (merchantable volume) - excludes as well the normal irregularities of episodic growth, e.g. branch nodes. This involves some subjective judgement. Potential utilisable volume may closely approximate biological volume, e.g. smooth stemmed species in a pulp operation. In sawlog operations, utilizable volume invariably is less than biological volume.

Tree volume may also be calculated as true cubic volume or product oriented volume:

• True cubic volume: The volume with branches trimmed flush with the stem.
• Product oriented volume: The volume of a theoretical product that could be cut from the log, e.g. the board-foot as the number of 12" by 12" by 1" boards that could be cut from a log. Product volumes are determined from rules that relate diameter, taper, log length, felling technique, saw waste, lumber grade and other factors. Product oriented volumes are not used in Australia. They are still used in the USA, although Avery (1967) states that there is "little to defend board-foot rules other than past use and resistance to change, for they result in nebulous units that bear no resemblance to consistent measures of volume".

Although it would be desirable to be able to make a few simple measurements on a tree, and so deduce its volume, no simple direct procedure or suitable instrumentation yet exists to do this. The volume of a stem has to be determined by more tedious methods. The method adopted should:

• Suit the purpose for which the volume estimate is desired, e.g. if a merchantable volume estimate is required, the method must allow merchantable volume to be derived from the measurements;
• Be simple to perform and check. It should allow errors to be readily detected;
• Be practicable, especially for standing trees;
• Be objective, giving an unbiased estimate of volume which is precise for the same operator and between operators;
• Be economical, particularly if large numbers of trees are involved.

No one method meets all these requirements so a compromise is necessary. Factors to consider before making a decision include type and position of tree.

• Type of tree: A method applicable to an excurrent species (e.g. taper line method) need not be suitable for a deliquescent species; crown break imposes an upper merchantable limit with deliquescent species. With excurrent species, the volume of the complete stem or any part of it can be estimated.
• Position of tree - felled or standing: Practicability sets limits to measurement of the standing tree. Large trees (80+ cm dbhob) can be very difficult to climb.

Methods of estimating tree volume

The methods available fall into two broad categories, direct methods and indirect methods.

Direct methods

• Fluid displacement
• Stem volume derived from summation of sections - The tree is sectioned into a number of lengths, the dimensions of these are measured, section volumes are derived, and then stem volume is obtained by summation:
• Standard Sectional method
• Taper Step method
• Graphical method
• Taper Line method

With the exception of the tip section, section volumes are calculated assuming the solid shape is a frustum of a second degree paraboloid, i.e. plotting cross sectional area against height gives a straight line.

The reliability of the volume estimate therefore depends on:

• the validity of this assumption
• how accurately the appropriate dimensions are measured.

Indirect methods

• volume tables, tariffs,
• volume equations
• variance reduction methods, e.g. importance sampling and the centroid method of sampling.