Tree volume estimation: importance and centroid sampling ©

Importance sampling

In 1986, Gregoire et al. introduced importance sampling which provides unbiased estimates of the volume of a tree bole based on one diameter measurement. The height of the point of measurement on the bole is selected randomly proportional to the estimated distribution of volume along the bole as determined by a proxy taper function. The volume estimated by the proxy function is then adjusted by the ratio of the cross-sectional area measured at the sample point to that predicted by the proxy function (see Wiant et al. 1989 for a more detailed explanation of importance sampling).

(Annimated example of Importance Sampling)

Wiant et al. (1989) tested importance sampling on a stand of radiata pine (Pinus radiata D. Don) in the Australian Capital Territory, estimating the total volume of the stand from 3P-selected sample trees measured for volume by intensive dendrometry and by importance sampling. The results were comparable despite the fact that importance sampling reduced the dendrometry required by 96%.

Centroid sampling

In the process of a related study, Wood et al. (1990) found that when comparing importance sample determined volumes with those derived from intensive dendrometry, minimum sampling error occurred in the estimate of bole volume when half the estimated volume occurred on either side of the point of importance measurement, i.e. at the centroid or 0.5 volume position. They established that this position occurs at about 0.3 of total tree height. Based on their findings, Wood et al. (1990) developed a variant of importance sampling which they called centroid sampling.

(Annimated example of Centroid Sampling) NOTE: Error in this animation! The Volume of a second degree parabola is: PI*0.5*Length*Diameter^2/4, where Diameter is the diameter at the base of the shape.

Simulation studies conducted on sample tree data of American and Australian hardwoods have shown promising results for the centroid method in deriving bole volume (Wood and Wiant 1990, Wiant et al. 1991), and in a recent field study at Eden, New South Wales, these findings were confirmed using sample trees drawn from a mature forest of Australian hardwoods (Wood and Wiant 1992).

Centroid sampling is applied at a fixed position on the stem, the centroid, the height of which is the expected mean height at which diameter measurements would be made in importance sampling if the sample were repeated many times. Note that the height of the importance sample is determined using random numbers between 0 and 1, 0.5 being the mean. Centroid sampling has two advantages over importance sampling:

The centroid method is not unbiased for estimating the volume of forest trees, but trials on a wide variety of tree species in both Australia and the U.S.A. indicate that it is negligible.

Constrast between importance and centroid sampling

Centroid sampling differs from importance sampling in that the point (h) on the bole at which diameter is measured coincides with the centre of volume (the centroid) of the bole whereas in importance sampling, h is located at random. In both methods, a proxy taper function is used to derive a first estimate of bole volume and this estimate is then adjusted by the ratio of measured cross-sectional area (A) at h to that estimated from the proxy function. Both types of sampling have been shown to be efficient for estimating the volume of sample plots of radiata pine (Wood et al. 1990; Wiant, Wood and Miles 1989).

The importance and centroid sampling methods enable the volume of the bole of a standing tree or any portion of it (log) to be estimated based on a single diameter measurement (dbhob only needed if volume inside bark is required). The methods eliminate the need for volume tables or equations and the bias which these might incur. They can be used anywhere for any species of tree of excurrent or deliquescent habit which has a well defined main bole, and would seem to be particularly appropriate for inventory of tropical mixed-moist forests. Programs written in BASIC are available to facilitate application of the methods in the field. A simple procedure for centroid sampling is also possible using only 2 tables and a calculator.

Data requirements

The information required to apply either method is:

  1. diameter at breast height outside bark
  2. total height
  3. merchantable height
  4. stump height
  5. diameter outside bark and height at the importance or centroid position
  6. bark thickness at breast height.

Note: the measurements of diameter and bark thickness at breast height are recorded only because volumes inside bark are usually desired. If the volume of a section of the bole (log) is required, the height above ground of each end of the section must also be recorded.

Practical aspects

Should the importance or centroid height fall on an unrepresentative point, e.g. on a whorl, the point of measurement should be moved to the nearest point which appears to be representative of the normal bole taper.

Some difficulty may be experienced when estimating the total height of a tree of deliquescent habit, i.e. the central bole is not continuous from ground to tip (most mature hardwoods). In this case, the assessor should sight to the position in the crown judged by eye to be at the crown surface and vertically above the top of the bole where crown break occurs. Wood and Wiant's experience to date suggests that errors of +/- 10 % in this measurement have a minimal effect on the volume estimate.

A range of instruments is available for measuring upper-stem diameters.

Use in inventory systems

The importance and centroid methods described above can be used in any sampling scheme (3P, 100 % tally, points, plots, etc.) to derive the volume of sample trees. The formulae needed to derive the sampling error are those normally used for the particular sampling scheme being applied. Mixing the two methods on the same inventory is also possible. However this practice might cause theoretical concern, as importance sampling is unbiased while centroid sampling is inherently biased (though this bias is negligible).

Importance and centroid sampling should prove especially useful in tropical mixed-moist forests where reliable volume tables or equations are not available. In many cases, these methods preclude the necessity of large investments in time and money to develop species-specific volume and taper functions.

Other measurement methods

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http://online.anu.edu.au/Forestry/mensuration/IMPORTAN.HTM
Cris.Brack@anu.edu.au
Mon, 29 Apr. 1997