Centroid sampling Forest Measurement and Modelling.

Tree volume

Technical Note: A simple procedure for measuring single tree volume using the centroid sampling technique.

C.L. Brack
Department of Forestry
Australian National University
Canberra A.C.T. 0200
E-mail: Cris.Brack@anu.edu.au

Introduction

Recent correspondence amongst practising foresters in Australia suggested that there were problems in communicating forest research findings to potential users (Stewart, 1996; Brack, 1996; Wood 1996). Specifically, it was felt that the advances made in efficient techniques for measuring trees for volume were not available to practising foresters because too much time was needed to learn and understand the advanced theories involved.

Earlier papers by forest mensuration researchers (e.g. Wood and Wiant 1990, 1992; Wiant et al. 1996) provide theoretical evidence that the centroid sampling method is precise and essentially unbiased in estimating a single tree's volume. This note presents a very simple set of instructions to help practising forest workers to use centroid sampling to efficiently determine merchantable volume for single trees. By following this procedure and using good measurement techniques, forest workers will be able to accurately measure merchantable tree volumes easily and efficiently.

Select a sample point

Centroid sampling requires one measurement of diameter at a selected sample height. The selected height is related to the total tree height, and the merchantable height (if crown break or defects in the bole limit the merchantable bole). Measure the total height and the percentage of that height that is merchantable. Select the corresponding sample height from Table 1.

For example, the tree in Figure 1 may be measured as 20 m in total height with the large branch at 8 m reducing the merchantable height to 40% of total height. The corresponding sample height from Table 1 is therefore 3.5 m.

Figure 1: Example eucalypt tree of 20m total height and 8m merchantable height.

Measure at sample height

The diameter (over bark) at the sample height is then measured. If the sample height is low enough, this measurement can be completed using a diameter tape and small ladder or pole callipers. Where the sample height is not within reach from a ladder, the tree will need to be climbed or some type of optical dendrometer used.

The measurement of diameter at the sample height is squared and multiplied by the value in Table 2 that corresponds with the total height and percent merchantable height. For example, the tree in Figure 1 may have a diameter reading of 28 cm at 3 1/2 m height. The multiplier from Table 2 is 0.000610, and the merchantable volume for this tree is therefore 28^2 * 0.000610 = 0.478m^3.

Underbark volumes

If underbark volumes are required, the volume over bark (VOB) estimated above is reduced by a ratio of underbark:overbark sectional area. Measure diameter at breast height (1.3m) overbark (DBHOB) and average bark thickness. The average bark thickness is easiest measured by hammering a nail into the bark at four equally spaced points around the tree at beast height - tapping the nail relatively lightly until you hear or feel the nail reach the wood layer. Measure how much of the nail remains outside the bark and subtract that from the original length of the nail to calculate bark thickness at that point.

Diameter underbark at breast height is calculated as:

DBHUB = DBHOB - 2 * (average bark thickness).

Volume underbark (VUB) then is:

VUB = VOB * DBHUB^2 / DBHOB^2.

For example, the tree in Figure 1 may have a DBHOB of 30cm and 4 bark thickness measurements of 1.8, 1.2, 1.7, 1.3. Average bark thickness is (1.8+1.2+1.7+1.3)/4 = 1.5 and therefore DBHUB = 30 - 2*1.5 = 27. Thus, the volume underbark for the Figure 1 tree is:

VUB = 0.478 * 27^2/30^2
= 0.478 * 0.81
= 0.387 m^3

Conclusions

The above procedure indicates that centroid sampling can be easily carried out by anybody who can use a diameter tape and look up values in 2 simple tables. The most difficult calculation needed is to square a number!

Other authors have shown that centroid sampling is precise and is likely to be much more accurate than applying volume tables or functions from measurements carried out in other forests. This note demonstrates that it is easily carried out as well.

References

Brack, C.L. (1996) Letter to the Editor, IFA Newsletter 37(2):35-36.

Stewart, M. (1996) Letter to the Editor, IFA Newsletter 37(1):27-29.

Wood, G.B. (1996) Letter to the Editor, IFA Newsletter 37(1):26-27.

Wood, G.B. and Wiant, H.V.Jr. (1990) Estimating the volume of Australian hardwoods using centroid sampling. Aus. For. 53(4):271-274.

Wood, G.B. and Wiant, H.V.Jr. (1992) Test of application of centroid and importance sampling in a point-3P forest inventory. For. Ecol. Manage. 53:107-115.

Wiant, H.V. Jr, Wood, G.B. and Williams, M. (1996) Comparison of 3 modern methods for estimating volume of sample trees using one or two diameter measurements. For. Ecol. Manage. 83: 13-16.

Table 1: Sample heights (m) related to total height and percent merchantable height.

Table 2: Multiplier values related to total height and percent merchantable height.