## How do I make a stand table with the trees that “Big BAF” and other systems choose?

Jason Teraoka asked us to explain exactly how you make a stand table when you are using one of the other ways to choose VBARs in Variable Plot sampling – such as rolling dice or choosing every 5th tree.  He had read the recent article called “How Else Can I Choose VBAR Trees?”

In general, we call these “distributed VBARs” because they are spread out through the stand, and our recent article described several ways to choose them.  It’s a good question.  We will explain it, and offer a spreadsheet that shows all the details.  This method is very general, and will work for any of the systems (including the more traditional ones like count-measure plots or completely measured plots).

The answer is that you make these stand tables the same way you make any stand table with variable plot sampling, but you must adjust the result of that stand table to match the basal area that the tree counting process gives you.

Let’s review the main concepts

·         The counts give you a good basal area (meaning it is better than you might get with a larger BAF, for instance).

·         The measured trees give you a volume to basal area ratio (VBAR) to convert that basal area, and they also give you relative numbers of trees by diameter class.  Actual numbers of trees come from the basal area.

When you measured all the trees or you used simple count‑measure plots, the balancing (for basal area) was automatic.  Otherwise, when you make up a stand table you need to make sure the stand table adds up to your best estimate of the basal area per acre wherever you get that.

As a short example, suppose you have the following number of DBH measurements on the cruise and you want to make a stand table from them.

 DBH number Number per acre? 12 1 ? 13 0 ? 14 3 ? 15 1 ? 16 2 ? 17 1 ?

They were chosen with equal probability after they had originally been selected with a Relaskop.  At the same time, you counted trees with a different BAF from the Relaskop, and estimated the basal area per acre to be 156 ft2/acre.

Trees were actually chosen by rolling a die, and measuring if a “1” came up.  This means that each of these trees represents roughly 6 other trees and you just assume that the other trees were exactly the same (as you do with any sampling procedure).

You do not need to know exactly how they were chosen, what proportion they were, or how many plots were taken to select those trees.  You know that they represent the relative numbers of tree sizes in the stand, and when you add up their basal areas they should equal 156 ft2/acre.  Assume any BAF to start the process, say 50 as an example.  For each DBH, compute the Stand Table Factor (STF = [BAF/ basal area of that tree]) and estimate a number of trees per acre for each tree class.  Also compute the basal area of each tree class, and the sum, based on the number of trees/acre in that class.

 DBH number STF Trees/ac * ba/tree =  ft2/acre 12 inch 1 63.66 63.7 .785 50.0 13 0 54.24 0.0 .922 0.0 14 3 46.77 140.3 1.069 150.0 15 1 40.74 40.7 1.227 50.0 16 2 35.81 71.6 1.396 100.0 17 1 31.72 31.7 1.576 50.0 348.1 trees/ac 400.0  ft2/ac

Here you can see that each of the DBH trees represents 50 ft2/acre.  At that rate, they do not add up to the 156 ft2/ac that you got from counting trees with the Relaskop.  You must adjust the number of trees per acre so that happens.  You can do these adjustments with the “Goal Seek” option on EXCEL, or do the math as follows.  The basal area you have is 400 ft2/acre, and you want 156 ft2/acre.  If you multiply all the numbers of trees/acre by (156/400 = 0.390) you will get what you want.

 You can also change the BAF and rework the problem, which will also give the correct answers.  New BAF = ( 50 * 156/400) = 19.5 

The number of trees is now adjusted, and the basal areas along with them.  You now have the stand table that you need.

 DBH number STF Trees/ac * BA/tree =  ft2/acre 12 inch 1 63.66 24.8 .785 19.5 13 0 54.24 0.0 .922 0.0 14 3 46.77 54.7 1.069 58.5 15 1 40.74 15.9 1.227 19.5 16 2 35.81 27.9 1.396 39.0 17 1 31.72 12.4 1.576 19.5 135.7 trees/ac 156.0

The attached EXCEL worksheet shows all the math involved, and in this case is also set up to adjust the results using the “Goal Seek” option.  We actually prefer that each tree be individually used to compute a number of trees per acre, then we would accumulate these into DBH classes later (rather than rounding to 1 inch classes), but the affect is not huge, and rounding them into classes right away is easier to explain for this example.  Rounding to something like 4 inch classes might be too much.

Suppose you think this number of trees per acre is not “smooth enough” for you.  How can you fix that?  Well, one option is to measure many more trees (at least for DBH, nothing else is required).  As always, suffering is one option.  A second option is simply to “smooth out” the numbers based on the graph of accumulated basal areas.  This will “fill in the blanks” too.  The only time this will not work reasonably well is when a certain DBH class has been harvested from the stand.  In the second page of the EXCEL spreadsheet is an example of this.  As you fill in a better cumulative basal area in column “I”, the resulting number of trees is computed, and plotted on the graph as a “+” sign.  This method is almost sure to give you better results – just as using a “regression formula” smoothes out the relationship of data points.  This method of adjusting the cumulative basal areas is taught at the OSU short course each year.

We appreciate Jason asking this question, and hope that this explanation is clear enough.  There are also other approaches that you could use and other assumptions that those methods could be based upon.  The advantage of this method is that it works for any process that produces DBHs from subsampled trees.  If you choose different proportions of trees by species (1:5 in one species and 1:10 in others) an additional weighting process is needed, but that is not yet commonly done, and has been ignored here.

As you might expect, this process can also be extended to fixed plots.  This might be desirable if you care a great deal about small trees.  Again, you adjust an initial stand table so that it adds up to your best estimate of the stand basal area (probably obtained with an angle gauge like the Relaskop).  In the case of fixed plots, the Stand Table Factor is just the area of one acre divided by the plot size.

 Actually you could have gone directly to this step by the following procedure.

1. Determine the basal area per acre.

2. Add up the number of trees you have DBH measurements for.

3. Divide that BA/acre by that number of trees to give a BAF to use in creating the stand table.

This would have led you to a BAF that worked immediately, without balancing, but it would have skipped all the logic of what you were doing.  Now that you know the logic, you can go directly to this method.

Originally published May, 2005 Back to Contents