1. What Do You See?
Message of the Day: Use variable area plots to measure tree volume

2. FOR 274: Forest Measurements and Inventory
Variable Radius Plots and Plot Boundaries
Measuring BAF
Measuring Basal Area
Slope and Stand Boundaries

3. Fixed and Variable Area Plots: A Note on Probability
To obtain information about a stand it is very common to sample the area with plots
In fixed area plots the probability of selecting a tree about the plot center is constant for all trees
Sampling methods exist where the decision to include a tree in a plot depends on the size of that tree
These are called probability proportional to size (PPS) methods. PPS methods are used to measure stand volume as the selection probability of the tree will be proportional to its basal area.

4. Fixed and Variable Area Plots: The Factor Concept
In forestry we often summarize data in terms of measures per plot but often we really want a per acre measure
To convert from per plot to per unit acre we scale the measures by a factor
TF = Unit Area (Acre) / Sample Area (Plot)
TF = Tree Factor
Unit Area = 43,560 ft2 or for metric: 10,000 m2
Sample Area = size of plot (ft2 or m2)
Therefore if constant factor used – trees sampled * Factor = number of trees per unit area 4

5. Fixed and Variable Area Plots: The Factor Concept
Therefore, each tree selected for measurement represents *TF* trees per units area: hence “Tree Factor”
Therefore if constant factor used – trees sampled * Factor = number of trees per unit area
For this 1/10th acre square plot each measured tree “represents” 10 trees per acre. 5

6. Expansion Factors: The Basal Area Factor (BAF)
The Basal Area Factor (BAF) is the number of units of basal area per unit area represented by each tailed tree
BAF = Basal Area * Tree Factor (TF)
BAF = *(DBH)2*(unit area/plot area)
BA per unit area = SUM (BAF)
= TF * SUM (BA of all trees)
In fixed area plots, the Tree Factor is constant making the calculation of basal area easy. 6

7. Variable Area Plots: Calculating the BAF
In variable radius plots calculating the BAF is more tricky as the sample area is not constant.
In variable probability (or variable area) plots: probability of selecting a tree depends on the size of the tree
First developed for use in forestry in the 1950s by Bitterlich
Source: Husch Beers and Kershaw 7

8. Variable Area Plots: Calculating the BAF
Plot radius is proportional to tree diameter: For trees right at edge the Ratio of Diameter (D) to Radius (r) = a Constant, k
At the edge of the plot the constant, k = 2 sin (θ/2)
By working through the calculations (p275) we find:
BAF = 10890*k2
At 2nd last step – divide both sides by ½ to get the pi * D2/4 formulation 8

9. BAF: Calculating BAF from an angle
For an object of fixed width, held a fixed distance away from your eye you can work out the angle θ:
Thumb: 2/3 “ held at 24” away
θ = tan -1 (half width / distance) = /24
θ = 0.79°
k = 2 sin (θ/2) = 0.014
BAF = 10,890 k2 = 2.13
Therefore your thumb “represents 2.13 units of basal area for each tree measured” 9

10. BAF: Calculating Whether Trees are In
For a known BAF, say 10, we can work out k
10 = 10,890 k2
k =
For known tree diameters: We can work out the maximum (or limiting) distance a tree can be at to be “Included” within the plot
Remember: k = D/r therefore, r = D/k
For example a 10” tree will be “in” if within:
r = 10/ = 330” = 27.5 feet 10

11. BAF: Calculating Whether Trees are In
To make things easier, we often use limiting distance tables to calculate whether the trees are IN or OUT of the plot. 11

12. Variable Probability Plots: Horizontal Point Sampling
The Method:
Observed stands at plot center
Uses a device to projects an angle horizontally to each tree – aiming at DBH height
All trees with diameters > apparent object width are counted
Then scale all measures to per unit area using the BAF 12

13. Measuring Basal Area: Using Your Angle Gauge

14. FOR 274: Forest Measurements and Inventory
Variable Radius Plots and Plot Boundaries
Measuring BAF
Measuring Basal Area
Slope and Stand Boundaries

15. Thinking About Measurements: Basal Area

16. Basal Area: What is it ??? 16 sq feet per plot BA = 160 sq feet
66 Feet (1 chain)
16 sq feet per plot
BA = 160 sq feet

17. Thinking About Measurements: Basal Area
Prisms
Most commonly used sighting angle gauge
Relatively inexpensive
“Built-in” method for correcting for slope
Infinite number of BAFs available.
Offsets the viewed image slightly

18. Thinking About Measurements: Basal Area
Trees is counted if its image overlaps the image seen above and below the prism
Borderline trees
Trees not counted if image does not overlap

19. Thinking About Measurements: Basal Area
Prisms and Slope:

20. Basal Area: The Angle Gauge
Select BA Factor (5, 10, 20, 40) to ensure tally of 5-12 trees
Center eye over Plot Center
Hold chain ‘like an archer’ and aim the gauge at the target trees’ breast height
Circle around plot center and aim gauge at tree’s DBH
If tree DBH > Angle Gauge Width ADD to tally
BA/unit area = BAF * Tally

21. Angle Gauge Example: BAF = 10

22. Angle Gauge Example: BAF = 10

23. BAF: Using Reloskops 23

24. FOR 274: Forest Measurements and Inventory
Variable Radius Plots and Plot Boundaries
Measuring BAF
Measuring Basal Area
Slope and Stand Boundaries

25. Fixed Area Plots: Common Sizes
Source: Husch Beers and Kershaw 25

26. Fixed Area Plots: Sub Plots
In natural forests there are more small DBH trees than large DBH trees.
Therefore, in fixed area plots you will always measure more small trees than large ones
How would we change our design to measure more large trees? 26

27. Fixed Area Plots: Sub Plots
Solution: Use nested plot design
Nested Plot Design: Increasing size classes are measured in plots of increasing area
Example:
1 acre plot for very large DBH trees
1/10th acre plot intermediate DBH trees
1/100th acre plot for small DBH trees 27

28. Circular Plots: Slope Correction
To adjust the radius (on the slope) to always measure a fixed area on the horizontally projected slope we use the equation:
Area = πr2 * cos ά
Therefore:
Radius = √ (Area / π * cos ά)
Example:
1/10 ac plots, slope of 20°
Radius = √ (4356 / π * cos 20)
= ft (not 37.2!)
15° yields 37.8 feet 28

29. Fixed Area Plots: Stand Boundaries
How do we deal with plots located at a boundary? 29

30. Fixed Area Plots: Stand Boundaries
Solution 1: Move plot so it falls within boundary
Worst Method!
Edge trees will be under sampled
Can lead to significant bias if stand has lots of edges!
Source: Husch Beers and Kershaw 30

31. Fixed Area Plots: Stand Boundaries
Solution 2: Add additional radius to account for lost area
Intermediate Method
Edge trees will be under sampled
Source: Husch Beers and Kershaw 31

32. Fixed Area Plots: Stand Boundaries
Solution 3: Re-calculate area and only measure within stand
Intermediate Method
Very time consuming as need to infer samples under correct areas
Source: Husch Beers and Kershaw 32

33. Fixed Area Plots: Stand Boundaries
Solution 4: Establish exactly half a plot at the stand edge  Then double counts
Intermediate Method!
Edge trees will be over sampled leading to bias
Source: Husch Beers and Kershaw 33

34. Fixed Area Plots: Stand Boundaries
Solution 5: Don’t Place a Plot at the edge in the first place!
Use Buffers around edges, roads, and rivers 34

35. In the next lab we will use these instruments