3P- Centroid volume sampling

The 3P - Centroid volume sampling described here is an efficient technique that enables one or two people to accurately determine the volume of small woodlots or plantations. It will be most suited to inventories where every tree can be visited, and to areas where no volume tables or functions are readily available.

No sophisticated instruments or tools are essential, although a calculator is very useful.

General technique

Example of use

Modifying the general technique

Data recording sheet

General technique

• Survey
• Calculations
• Main Survey
• Final Calculations

It is possible for this inventory to be carried out by one person alone, although for safety reasons it is recommended that at least one other person is nearby and able to render assistance in case of accidents or injury. Where more than one person is involved, all guesses of tree volume should be completed by the same person at every stage.

Survey

1. Find 4 or 5 average trees in the woodlot. (These do not need to be very carefully chosen).
2. Guess the volume for each tree, and record in column 2 of the recording sheet. (Make these guesses relatively quickly, do not spend too much time at this stage).
3. Measure or estimate the total height and stump height for each of the trees and record the values in columns 3-4 of the recording sheet. If some bole defect, eg a fork or broken top, would cause the top of the tree to be unusable, measure and record percentage merchantable height in column 5.
4. Calculate centroid height:
• If defects mean that the stump will be relatively high, subtract the stump height from the total height and use this value in Tables 1 and 2 following.
• Use Table 1 in the simple centroid measurement technique for find the centroid sample height.
• Find the height in the table for the tree total height (or total-stump height) and percentage height that is merchantable.
5. Measure or estimate the diameter (centroid diameter) at the centroid height and record the value in column 7 for each tree. If the stump height was high, measure the centroid sample height from the top of the proposed stump.
6. Make an estimate the total number of trees in the stand. (This guess does not need to be very accurate, for example multiply the number of planted rows by your guess of the average number of trees per row.)

Calculations

1. Calculate the centroid volume of the selected trees, and record in Column 8 of the recording sheet.:
• Use Table 2 in the simple centroid measurement technique.
• Find the multiplier in the table for the tree total height and percentage height that is merchantable
• Multiply the above value by the square of centroid diameter (column 7).
2. Calculate and record in Column 9 the ratio of centroid volume : guess volume, ie Column 8 divided by Column 2.
3. Calculate the average of tree volume guessed by adding all the guessed volumes and dividing by the number of trees.
4. Determine the reliability (called the coefficient of variance or CV%) of your guesses by calculating:
• Ratio sum = add all the values in Column 9
• Ratio square = square all the values in Column 9 and then add them together
• Average ratio = Ratio sum / Number of trees selected
• SD ratio = square root ( (Ratio square - ((Ratio sum)^2 / Number of average trees selected)) / (Number of average trees selected - 1))
• CV% = 100 x SD ratio / Average ratio
5. Once you have determined CV%, you can calculate the approximate number of trees (n) required for centroid measurement in the main survey. This number will also depend on the precision you want in your result. For example, a desired precision of 10% means you want to be pretty sure that your final volume estimate will be within 10% of the true volume of the woodlot:
• n = (CV% x 2 / E%)^2
6. Determine the value, known in the technical literature as KZ, as:
• KZ = average of tree volume guessed x estimate the total number of trees / n
7. Select a random number table with a KZ close to your above calculation.

Main survey

The main survey uses a recording sheet with enough rows to record each tree in the woodlot. Use the following procedure (also shown as a flow diagram):

1. Plan to move through the woodlot in a systematic manner so that every tree will be visited. If the trees are not in well planted rows, it may be useful to mark each tree with a chalk or crayon as it is visited to help ensure none are missed or double counted.
2. Estimate and record the guessed volume in Column 2 of each tree as you visit it.
3. Compare your guessed volume with the next number on the random number table selected in step 7 of calculations. If your estimated volume is less than the random number, move on to the next tree and return to step 2 above.
4. If your estimated volume is equal or greater than the random number, the tree is classified as a 3P sample tree and you need to make the measurements outlined in steps 3, 4 and 5 of survey.
5. Continue steps 2 to 4 above until all trees have been visited and all have a guessed volume. Some trees, about the number estimated in step 5 of calculations, will be 3P samples and have additional information recorded in Columns 3 - 7. Complete steps 1 and 2 of calculations (Columns 8 and 9) for the 3P sample trees.

Final calculations

1. Complete step 4 of calculations for only the 3P trees to derive 3P sample based calculations of Average ratio, SD ratio and CV%.
2. Calculate the total guessed volume by adding Column 2 for all trees (not just the 3P sample trees).
3. Calculate the total volume as total guessed volume x Average ratio
4. Calculate the precision of this total volume as:
   Precision = CV% x 2 / square root (number of 3P samples)

If the reliability of your guesses for volume has been constant, and the estimates made in steps 1 and 6 of survey were reasonable, then the precision of your volume estimate should be within the acceptable range set in step 5 of calculations.

Example of use

The example data is based on a small woodlot of about 0.4 ha on the Australian National University grounds. The woodlot contains Eucalyptus globulus spp globulus planted in semi-regular rows around buildings and other structures. The form of the trees varied from poor with numerous double leaders to good with straight boles.

The inventory was designed to determine the volume of pulp (overbark) potentially available from the woodlot. Field measurements were collected in one morning by an undergraduate forestry student team of three equipped with a spiegal relaskop and 30 m tape.

The students had had relatively little experience with estimating tree volume, and this is demonstrated by the range of ratios of centroid:guess volume (1.2 to 2.1). Their use of the relaskop may also contribute to this imprecision as it apparently was only read to the nearest 5 cm. With experience, volume estimates and improved Relaskop practice would improve the CV%. This would result in fewer 3P sample trees being needed for the inventory to reach the desired reliability of 10%.

Recording Sheet for initial survey

Note that malformed trees were not selected during this initial survey.

Example calculations from main survey

• 3P trees- ratio of centroid volume : estimated volume
  Average ratio = 0.78
  SD = 0.21
  CV% = 27%
• Sum of all estimated volumes = 188
• Total volume = 188 x 0.78 = 146
• Precision = 2 x 27 / square root (17) = 13%

Modifying the general approach

• Underbark or Overbark volume
• Regular woodlots too large to visit every tree
• Irregular woodlots too large to visit every tree

Underbark or Overbark volume

This method can estimate underbark or overbark volumes by entering the centroid diameter estimate (Column 7) of the recording sheet as an underbark or overbark diameter estimate respectively. All calculations remain the same.

If the tree is being climbed in order to get the centroid diameter, underbark diameter can be estimated by measuring the bark thickness at centroid height.

However, if the centroid diameter is remotely estimated (eg using pole callipers or dendrometer), and underbark volume is required, then an estimate of the underbark : overbark ratio is needed. In conifers, this ratio is reasonably constant over the length of the bole so it is possible to make appropriate measurements at a location easily managed from the ground. Measure the diameter at about 1.3 m (DBHOB) from the ground and then determine bark thickness at this point. Take four measurement of the bark thickness around the tree at 1.3 m from the ground and determine the ratio as:

Under:Overbark = (DBHOB - (0.25 x sum of four bark thicknesses)) / DBHOB

Multiply the overbark centroid diameter measured with the callipers or dendrometer by the Under:Overbark ratio and record the answer in Column 7.

The recording sheet could be easily modified to include these extra diameter and bark thickness measurements.

Regular woodlots too large to visit every tree

The general 3P centroid technique can be easily adapted to apply to larger woodlots that have easily detectable rows. Visiting only those trees in every 4th or 5th (or n'th) row, complete the entire general 3P centroid technique. The total volume estimate can be reliably determined by multiplying the figure obtained in step 3 of the final calculations by 4 or 5 (or n) respectively.

The precision of the total volume estimate may be reduced by this approach. Determine the total guessed volume for each row, then calculate the average, SD and CV% of these total row guesses. The overall precision for the total volume is calculated as:

square root ( (CV% from step 4 of the final calculations)^2 + (CV% row guesses)^2 )

Irregular woodlots too large to visit every tree

If the woodlot is not planted in regular rows, but the area of the woodlot is known, then the general technique can still be modified for use. Instead of using rows in the modification suggested in the section Regular woodlots too large to visit every tree, you can use small plots.

Select about 20 random points in the woodlot and mark out a circular plot at each point. Each plot should be the same size and have a diameter big enough to include about 10 trees. Each plot then is like a row in the modification described in Regular woodlots too large to visit every tree, except that where you multiplied your estimated volume by the number of rows you skipped, in this technique you multiply the volume by the woodlot area divided by the area in all your plots.

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