3P Sampling

Why Use the DBH in 3P Sampling?

Published January 1995

The number of people doing 3P sampling is increasing. All of the partial cutting–small area–fuzzy boundary–high value kinds of trends in timber harvest are pointing us toward more 3P sales.

 In addition, 3P sampling is a much more general sampling method, just as applicable to sampling ducks or lichen as it is to trees. Those of us in the measurement business must start thinking of measuring "things," not just trees, and we need to develop these skills. Variable plot sampling, charming as it is, is really just a trick which we can use because trees have circular cross sections. A really great trick, mind you – but pretty much confined to trees.

 For each tree in 3P sampling we need an estimate which is proportional to what we eventually want to measure. Some people prefer to directly estimate the volume or the value of each standing tree. In addition, they feel that developing such a skill is useful in its own right. We agree.

 On the other hand, we usually recommend that people use the DBH of the tree to calculate a value for the tree. Why go through the extra step? Good question – let’s see if we can answer it.

 First of all, using DBH will not generally result in a much better answer than direct estimation of volume. We think that there are other advantages which are very useful. As is often the case in forest measurement, the indirect effects are often as important as the answer we directly attack. The reasoning goes like this:


  1. You automatically end up with a terrific stand and stock table. Because you are going to every tree, you get an excellent view of the number and volume of the trees by diameter class – even if these are only estimated diameters.

There are ways to adjust the numbers and class limits if you are interested, but even in their raw form these stand tables are far superior to what we are used to seeing. You could always calculate a stand table from only the measured trees, but it will not be nearly as good, particularly for infrequent sizes or species.

  1. DBH is a pretty good predictor. It is a simple matter to do a quick regression with some sample trees and figure out the equation:

Volume = DBHP*Constant

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You should probably take DBH to somewhere between the 2.5 and 3.5 power, depending on how variable height is with the diameter. The constant is used to adjust the ratio to about 1, because it is useful for planning when the anticipated sum of all the estimates will come up to about the volume of the tract. On the other hand, maybe you want the ratio of be about 10 – in that case just adjust the constant. You could also use a local volume table giving volume for a particular DBH.

For cases where you run into temporarily tall or short trees (like valleys or ridges inside the stand) it is desirable to be able to bump this estimate up or down.

  1. It is easy for temporary crews to do. In addition, you can probably combine the efforts of all the estimators into one group, since it is unlikely that one of the group will be consistently very different from the others.

It is no big deal to work up the results of different groups separately, but this ability to do so might be an advantage in some instances.

The Down-Side

The problem is to keep people concentrating on the right thing. In 3P sampling you are interested in getting the RATIO of measured to estimated volume to be consistent. Getting the right DBH is not the objective, so you have to find a way to get that through to the crew. If they are not correcting the estimate for defect or broken tops they can be getting inefficient cruises even when the DBHs are right on. It is easy to forget that the ratio is important when you are guessing DBHs all day – don’t let them do it.

Find a way to get this idea through to the crews – perhaps by offering a reward for the most consistent ratios (and make the point that DBHs are not of interest and you will not even talk about them, let alone reward them).

Make sure that the crews promptly get a look at their ratios after a cruise. Have them try to figure out what went wrong and made some ratios inconsistent with the other ones. Make sure they look for other reasons than DBH. One technique would be to fill in exactly the right DBH and then show them that the ratios are still not consistent – it also puts an upper limit on their consistency if DBH is the only thing they are considering.

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