Questions from the Field:

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

Jason Teraoka asked us to explain

exactlyhow 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

anyof 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

anystand table with variable plot sampling,butyou 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

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

measured treesgive you a volume to basal area ratio (VBAR) to convert that basal area,and they. Actual numbers of trees come from the basal area.alsogive yourelativenumbers of trees by diameter classWhen 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

yourof the basal area per acrebestestimatewhereveryou 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

numberNumber 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 ft

^{2}/acre.Trees were actually chosen by rolling a die, and measuring if a “1” came up. This means that each of these trees represents

roughly6 other trees and you just assume that the other trees were exactly the same (as you do withanysampling procedure).You do not

needto 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,relativenumbers of tree sizes in the standand when you add up their basal areas they should equal 156 ft^{2}/acre. AssumeanyBAF 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

STFTrees/ac

* ba/tree

= ft^{2}/acre12 inch

1

63.66

63.7

.785

50.013

0

54.24

0.0

.922

0.014

3

46.77

140.3

1.069

150.015

1

40.74

40.7

1.227

50.016

2

35.81

71.6

1.396

100.017

1

31.72

31.71.576

50.0

348.1 trees/ac

400.0ft

^{2}/ac

Here you can see that each of the DBH trees represents 50 ft

^{2}/acre. At that rate, they do not add up to the 156 ft^{2}/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 is400ft^{2}/acre, and you want156ft^{2}/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[1]

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

= ft^{2}/acre12 inch

1

63.66

24.8

.785

19.513

0

54.24

0.0

.922

0.014

3

46.77

54.7

1.069

58.515

1

40.74

15.9

1.227

19.516

2

35.81

27.9

1.396

39.017

1

31.72

12.41.576

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 useand other assumptions that those methods could be based upon. The advantage of this method is that it works foranyprocess 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.

[1] Actually you could have gone

directlyto this step by the following procedure.

Determine the basal area per acre.

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

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