what do you see?

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

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: A Note on Probability

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 FactorUnit 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 ConceptTherefore, 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)

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.

The Basal Area Factor (BAF) is the number of units of basal area per unit area represented by each tailed tree

Variable Area Plots: Calculating the BAF

In variable probability (or variable area) plots: probability of selecting a tree depends on the size of the tree

Source: Husch Beers and Kershaw

In variable radius plots calculating the BAF is more tricky as the sample area is not constant.

Variable Area Plots: Calculating the BAF

At the edge of the plot the constant, k = 2 sin (θ/2)

By working through the calculations (p275) we find:

BAF = 10890*k2

Plot radius is proportional to tree diameter: For trees right at edge the Ratio of Diameter (D) to Radius (r) = a Constant, k

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) = 0.3333/24θ = 0.79°

k = 2 sin (θ/2) = 0.014BAF = 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 SamplingThe 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

66 Feet (1 chain)

Basal Area: What is it ???

16 sq feet per plot

BA = 160 sq feet

• 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

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 trees1/10th acre plot intermediate DBH trees1/100th 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