What Do You See?
Message of the Day: Use variable area plots
to measure tree volume
FOR 274: Forest Measurements and Inventory
Variable Radius Plots and Plot Boundaries
• Measuring BAF
• Measuring Basal Area
• Slope and Stand Boundaries
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.
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)
Fixed and Variable Area Plots: The Factor Concept
Therefore, each tree selected for measurement represents
*TF* trees per units area: hence “Tree Factor”
For this 1/10th acre square plot
each measured tree “represents”
10 trees per acre.
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 = 0.005454*(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.
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
Source: Husch Beers and Kershaw
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
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) = 0.3333/24
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”
BAF: Calculating Whether Trees are In
For a known BAF, say 10, we can work out k
10 = 10,890 k2
k = 0.0303
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 = 10/0.0303 = 330” = 27.5 feet
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.
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
Measuring Basal Area: Using Your Angle Gauge
FOR 274: Forest Measurements and Inventory
Variable Radius Plots and Plot Boundaries
• Measuring BAF
• Measuring Basal Area
• Slope and Stand Boundaries
Thinking About Measurements: Basal Area
Basal Area: What is it ???
66 Feet (1 chain)
16 sq feet per plot
BA = 160 sq feet
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
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
Thinking About Measurements: Basal Area
Prisms and Slope:
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
Angle Gauge Example: BAF = 10
Angle Gauge Example: BAF = 10
BAF: Using Reloskops
FOR 274: Forest Measurements and Inventory
Variable Radius Plots and Plot Boundaries
• Measuring BAF
• Measuring Basal Area
• Slope and Stand Boundaries
Fixed Area Plots: Common Sizes
Source: Husch Beers and Kershaw
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?
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
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)
= 38.41 ft (not 37.2!)
Fixed Area Plots: Stand Boundaries
How do we deal with plots located at a boundary?
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
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
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
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
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
In the next lab we will use these instruments