1. The development of Variable Plot Sampling by Kim Iles

2. There are only 3 major methods for timber cruising.
Fixed Plots (ancient, but easy)
Variable Plots (1946) WWII
3P Sampling (1960’s, the beetles)

3. What is the trend?
Each newer method further separates the field work into parts that are :
Quick vs. slow
unskilled vs. skilled work
An estimate, then a correction
Efficiency issues
Accuracy issues

4. Walter Bitterlich had an idea, based on circular tree cross-sections.

5. Bitterlich – 1946, said …
Just “count” trees – that gives you basal area.
Counting is in percent (no units involved).
You then assign units (10,000 m2/ha)
( 43,560 ft2/acre)
The angle and units give the “Basal Area Factor” or “BAF” for the process.

6. Are you “in” or “out” of an invisible circle around each tree?
Just use an angle to decide that.
Imagine using your thumb for that.

7. Lew Grosenbaugh immediately read about this idea.

8. In 1947 he says …
If you have the basal area, just find out how much is “sitting on each square foot” to calculate all the other stuff.
For this, measure a few trees for any value you want (BF, grade, $, etc).
This Volume / Basal Area factor is called the “VBAR”.

9. Don Bruce & his son Dave

10. Mason Bruce and Girard (1950) introduced “Count and Measure” plots.
Since Basal Area is more variable than the VBAR, just measure the trees on some of the plots, only counting trees on the others.
This concentrated the effort toward more counts, which mattered more in getting better answers.
If plots were too far apart, people lost their nerve … at about a 4 or 5 to one ratio.

11. This is called “Double Sampling”
1) Do all plots with some easy and quick variable (basal area, in this case).
Measure some plots for the ratio of BF to basal area, then you use that to convert all the plots.
Only the measure plots are matched for both Volume and Basal Area.

12. This gives the same answer as …
Average Basal Area/acre from all plots
times
(Total volume / Total basal area) on just the “measure plots”.
The trees are measured in “clusters” at the measured points.

13. There is sampling error in the average Basal Area and the Vol/BA correction.
Line is the Ratio of volume to Basal Area
Right Ratio ?
Individual plot volume vs estimate using BA.
Average BA ?

14. The statistical formula is messy for Double Sampling
In essence it is :
Error in Average Basal Area
plus
Error in [Total plot Volume / Total Basal Area]
known as “Johnson’s Formula” in forestry

15. A “Product Estimator” is different Dave Bruce (1950s) (Dave also invented the wedge prism)
(1) Find BA somehow.
(2) Find the VBAR correction somehow
(3) Multiply them together.
This clearly separates (1) and (2), although we often do both on the same sample points. We no longer need to measure all the trees on a plot.

16. The Statistics (Bruce’s Formula)
(SE% basal area plots) 2 SE% combined = + (SE% VBAR trees) 2
Combined SE%
VBAR SE%
Basal area SE%

17. BIG BAF sampling (1980)
If you can “spread out” the trees through the stand (several ways to do that), you get about double the affect of taking trees in clumps at “measured plots”.
This is becoming a standard approach in many places, and available in newer computer programs.
The advantage is the Systematic affect

18. How many of each item? (TC vs VBAR)
Effort in each phase is pretty much given by :
CV of Tree Count vs. CV of VBAR
40% and 30% indicate [40 counts & 30 trees], in multiples sufficient for the SE% you want (better yet, “The SE% you can live with”).
There is a simple EXCEL spreadsheet for exact sample size computation.

19. Do you need more measurements?
You might measure more VBAR trees, if it turns out that it matters.
It’s easy to tell – just change the data and compile the results to see if anything changes.
Beliefs do not matter here …
This is Algebra, not Theology
It is usually the case that you need more counts.

20. What will more measured trees do for you?
They might give better product percentages.
Products will never be known better than the basal area they are multiplied by.
All totals will change proportionally with BA for virtually all variables (BF, Grade, $, etc).
If necessary, you can go back and put more counts into the stand.

21. VBAR calculation
Usually done by measuring a tree on a plot for its total volume, then dividing by that tree’s basal area at DBH.
VBAR = Volume / tree basal area = m3/m2.
There are other ways as well.
VBAR

22. Other ways to get VBAR
1) Estimate the logs in the tree (MB&G, 1950’s) for logs/m2, then get m3/log to correct that.
The extra units cancel out …
m2/ha * logs/m2 * m3/log = m3/ha
This amounts to using logs as an uncorrected estimate of VBAR (you could use height).

23. Other ways to get VBAR
2) Use a percentage of tree height roughly (1/3 of total tree height) = m3/m2
3) Use the vertical distance to where the tree is “borderline” (critical height).
Use historical data
5) % of stand height

24. What should you look at?
Any computer program needs to report how variable the Basal Area is, and how variable the VBAR is (The “CV” for each).
VBAR can be any tree measurement divided by the tree basal area (giving statistics).
The program should give you the measured tree data, so you can research it on your own.

25. What is next? Perhaps …
A different estimate of basal area or equivalent “base” {tree crowns?}. OR
3P sampling, which :
Makes quick estimates for everything. 2) Corrects those estimates.
3P is good for anything, not just trees.

26. Some instruments I brought, along for you to check out.

27. The first Relascope target

28. Bitterlich wanted this target featured on his tombstone

29. Bitterlich’s metal Relascope

30. Bitterlich’s Wooden Relascope

31. The 8-power Relascope

32. The Bitterlich teaching tool for 2, 3, and 4 dimensional VP sampling

33. The first wedge prism

34. The first published prism (6X)

35. Also, some publications and handouts on …
VP sampling (and the story of its development, according to Bitterlich)
The Relascope
Prism Cruising
Story of the development of it (by Bruce)

36. Thanks for your patience

39. Take to conference prism publications.
Relascope publications & reviews.