3P sampling was developed by Lew
Grosenbaugh in the early 60’s. It has proven to be a very efficient method, and the
central idea of first making an estimate (this greatly helps in improving the statistics)
then measuring some of the trees carefully (which eliminates any bias in the estimation
phase) follows right down the centerline of modern efficient sampling methods. "The problem" with 3P sampling has always been the myth that you had to go to every tree, and therefore it was too much trouble after the inventory reached a certain size. Going to every tree on a marked sale is not a problem, of course, but what about using 3P sampling for large unmarked areas? One way to do this is "Point-3P sampling", suggested by Grosenbaugh in the
early 70’s. Lew saw immediately that a method to expand the system to large areas was
desirable and, as usual, saw how to do it well. To extend the 3P method to large areas the
first step is to do a number of point samples with your usual methods, but for each tree
"in" with the prism you estimate You compare this estimated height to a random number to select
Let’s assume that you want to select about 20 trees during the cruise for careful
measurement. You ask the 3P software to give you random numbers between 0 and . You compare the height of each tree to the random number. If
the random number is less than (or equal to) the tree height, then So much for the mechanics of what you The basal area of the stand (or any species or grouping within the data) is calculated as it would always be: As always, make sure you have at least one measurement on each species so you can do the computations by species. The different process is in calculating the VBAR (Volume/ Basal Area Ratio). [Basal Area of the stand * average VBAR] = Volume per acre (or per hectare in Canada using a metric angle guage). The measured trees are usually the source for computing the VBAR. As we all know,
the VBAR is very proportional to tree height. Just for a moment,
is about ½ what it should be).BF,
The statistics of the cruise would be based on the Volume per acre at each sample
point, just as they normally are when all the trees are "measured". Let’s
say that this comes out to a sampling error of On the other hand, we do not have the For each of the sample trees, compute the ratio between the actual VBAR and the
tree height (which we were using as a rough VBAR). Take the average of these. Let’s
say that comes to . |
Our final answer uses the formula:
so our example yields:
How good it this final answer? Well, we are as sure of the final answer as we are of the two parts that make it up (the rough estimate & the correction ratio). We combine them in the usual way, with "Bruce’s formula".
As always, we want to balance the sampling errors in these two portions of the process. The payoff is being able to put in a large number of plots quickly, since you only need to estimate tree height on each tree. Since the tree height is a consistent estimate of tree VBAR you only have to measure a few trees to calculate the correction ratio. This process allows the power of 3P sampling to be applied to large areas.
There has been some controversy about how to best calculate the sampling error for the
SE% These are covered in: ("Approximate Sampling Variance of Adjusted 3P estimates" by L.R. Grosenbaugh, Forest Science, June, 1976, pp. 173-176, volume 22, number 2). The corrections are very minor, except for very small sample sizes which would not occur in practical work.
The USFS is currently implementing a type of 3P sampling where the volume per hectare is directly estimated, then entire sample plots are chosen for careful measurement (rather than individual trees). This process is essentially the same, with much the same mathematics. This and other applications of 3P sampling are a continuing benefit to the profession from the genius of Lew Grosenbaugh.
John Bell and Associates markets a small program for producing the 3P random number list. John Bell & Associates, Inc. Holmboe Enterprises produces an excellent 3P program using the Hewlett Packard palmtop computer in a waterproof case, which is probably the best field 3P program available anywhere in North America. It can be used to gather all of the information necessary for Point-3P sampling as well, then it can be processed on a PC. Rich Holmboe, Holmboe Enterprises Phone: (250) 756-6199
For those who are interested in an expanded version of this discussion I have one available, and you can contact me at: Kim Iles & Associates If possible, I would prefer to send it to you via e-mail, so include your e-mail address if you have one. [Editor’s note: You can get the basic ideas of this method from this discussion, and this is probably enough to wade through for this issue, but we have asked Kim to produce a numerical example of all of the calculations for the next newsletter. This may make the specific process more clear to many readers.] |