3P Sampling

Changing the Area of a 3P Cruise After the Field Work

Published January 1996

Suppose that you have a 30 acre area which has already been cruised with the 3P method, then someone decides to remove 12 acres for some reason.

Not easy – but possible.

There are 3 techniques that come quickly to mind:

  1. Recruise, and take out that sum of KPIs out of the original cruise, then recalculate (an approximate solution)
  2. Take out just the strips of estimates in the affected area, then recalculate.
  3. Do a separate cruise of the area, then subtract it from the overall cruise.

If you are using some function of DBH to calculate the KPI value you can go through the area to be removed, estimate and add up all of the KPI values of the trees involved, and reduce the original sum of the estimates by this amount. This, of course, is only an approximation – but it is probably a pretty good one for practical purposes.

How do you know that you are estimating the trees the same way as you did the first time so that you are removing an identical amount? You don’t, but how far wrong could you go? For gross volume it will be very close, and for net volume it is probably not far off either.

If you have the possibility of going to court, however, an exact solution is probably worth the extra effort, and it is not much more trouble. The following two solutions are unbiased, and provide valid statistics.

2) If you have done the estimates in separate strips, then you can remove the sum of the estimates on those strips, along with any sample trees that occur there, then recalculate the reduced cruise. Next Column


If you can anticipate the possible removal of some of the timber sale along nice boundaries such as streams or ridge lines then make this the boundary of some of your strips as you do the original cruise.

The statistics are computed on the remaining information. Sample trees on the strips removed are also dropped, of course.

Even if you cannot do this for the entire removal area, if a few entire strips can be removed then it at least reduces the problem of validly removing the remaining volume. This process can be combined with solution #3 to improve the efficiency of solution #3.

3) In solution #1 you went through the area and removed the trees which were "added into the cruise incorrectly." Of course that would not be an exact solution, since you are not sure that you are estimating in exactly the same way. This is a potential bias, and you don’t need that sort of grief in your life.

Since you already have an answer for the complete area, it is not much more effort to do a second 3P cruise on the area to be removed. You now have two separate cruises, each with a volume and standard error.

You may recall how to add two strata into a combined total volume and combined sampling error. Well, the same process can be used when you are subtracting two areas. The statistics and the logic are exactly the same.

Strata sums and differences are covered in all standard texts (the statistics use "Bruce’s formula", and the Newsletter explained it in issue #19, July 1992.

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