POINT SAMPLINGOR VARIABLE PLOT CRUISING

Establishing Plots – Point Sampling

A cruise method where the sample trees are selected proportional to their basal area. Thus larger trees sampled in greater proportions.

Fixed angle projected from plot center to determine ‘IN’ trees

As we learned before, Basal Area in square feet in expressed as below with DBH in inches

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Procedure• The basal area factor (BAF) selected needs to yield an average of 4 to 8 trees per point.

• Smaller BAF will tally more trees per point, larger BAF will tally fewer. In other words, use larger BAF for larger trees. Western softwoods might use 20 to 60.

• In Kentucky, a BAF of 10 usually fits.

• Use only one BAF for a particular stratum. Just like the way we don’t vary the plot size in fixed plot cruising.

Basal Area Factor (BAF)

Larger trees counted “IN” at longer distances

Basal Area Factor• indicates the number of square feet of basal area/acre each "in" (measure) tree represents.

Smaller BAF causes smaller trees to be “IN” further from the sample point.

Which trees to tally?

Notice ‘hidden’ tree

How many points? Rule of Thumb• If area in acres is: Number of points should be: • Less than 10: 10 • 11-40: 1 per acre (this fits our lab area)• 41-80: 20 + 0.5 * (area in acres) • 81-200: 40 + 0.25 * (area in acres)

Basal Area Factor (BAF)• Each sample tree, regardless of DBH, represents the same basal area per acre for a given critical angle. This constant is the basal area factor (BAF) of the angle gauge.

• In fixed area sampling, when using circular plots, the plot radius is fixed for a plot of a given size. For example, the plot radius for a fifth-acre plot is 52.7 feet. Each tree, regardless of size, on a fifth-acre plot is associated with a plot radius of 52.7 feet.

Common BAF and PRF used in the United States

BAF PRFk

Plot Radius Factor

Can use to calculate limiting distance to determine ‘IN’ trees

Plot Radius Factor = 8.696/SQRT(BAF)

Which means:For each inch of DBH, a tree can be 2.75 feet from the point to stillbe included in the point’s tally.

Limiting Distance• Since a basal area factor of 10 has a plot radius factor of we know that any tree farther away than 2.75ft * DBH from our point center will be considered out.

•We measure the distance from point center to the middle of the tree (not the point facing side)

Limiting Distance

Variable Plot

Another way of looking at it is as a multiplot.

Each tree has its own plot, whose size is dependent on the diameter of the tree

Those trees whose plots overlap the center point get measured.

How many trees at this point will be tallied?

Slope Limiting Distance• 1. Measure the diameter to the tenth of an inch• 2. Determine the horizontal limiting distance from the face of the

tree (HLD = PRF X DBH)• 3. Determine the percent of slope from the face of the tree at DBH

to where the wire pin or wooden stake penetrates the ground.• 4. If the slope is 10% or greater, correct the horizontal limiting

distance to slope limiting distance (SLD). To obtain the slope limiting distance, multiply the horizontal limiting distance by the appropriate slope correction factor (SCF). (SLD = HLD X SCF)• 5. Use a tape graduated in tenths of feet to measure the distance

from the face of the tree at DBH to plot center. The plot center is where the wire pin or wooden stake enters the ground. These are two exact points that can be measured "to" and "from". If the measured distance is equal to or less than the slope limiting distance, the tree is "IN" and is sampled. If no slope correction is needed, the horizontal limiting distance is compared to the measured distance.

Slope Limiting Distance

Slope Correction Factor X Horizontal Limiting Distance = Slope Limiting DistanceSCF X HLD = SLD

Slope Correction

POINT SAMPLING TOOLS

Cruise Angle – 4 BAFs, $10

Cruiser’s Crutch• 4 BAFs• Compensates for slope• ~$30

Cruise Gauge App – >1 BAF, $10

iBitterlich

Laser – corrects for slope, > 1 BAF, $1500

Panama Basal Area Angle Gauge – 1 BAF, $40

Relaskop – corrects for slope, > 1 BAF, $1800

Thumb as an angle gauge

Let thumb width = 0.85”Eye to thumb distance = 25”

constantgaugeRadiusPlot

Diameterk _034.0

0.25

85.0

_

59.12)034.0(1089010890 22 kBAF

BAF = 12.59 ft2/acre

Try this at home

Prisms – easily lost, 1 BAF, $20 to $70

Ways to hold a prism

Procedure• Looking through the prism

Procedure

Correct Positioning - Point Sampling

X

“IN” Trees(determined then measured)

Fixed Plot Variable Plot

Problem Trees• Forked Trees - Use measurement rules to determine if measuring one or two trees and to determine diameter. Then calculate limiting distance.• Leaning Trees - Angle gauges are always used by looking at the diameter of a tree at breast height. When a tree is leaning to the left or to the right, as viewed from point center, the angle gauge is tilted so it is oriented along the axis of the tree rather than vertically. If the tree is leaning toward or away from point center, the angle gauge is held as it would be for a vertical tree. If a limiting distance calculation is required for a leaning tree, the distance from point center to the tree is measured to the center of the tree at breast height, just like it is for vertical trees.

Problem Trees• Down trees -- Trees of this nature are determined to be "in" or "out" depending upon the location of DBH in relation to the plot center and the appropriate limiting distance. That is, all measurements are made between the plot center and DBH and the tree is "in" or "out" regardless of root location, etc.• Hidden trees -- It is possible that a tree or some other object obscures the view of a tree behind it. A cruiser must be careful to recognize this possibility and check to see if there are any hidden trees which could be "in" trees. If there is an obscured tree which might be "in", the cruiser moves away from point center in a direction perpendicular to the direction to the tree just far enough to be able to clearly see the tree at breast height. The same rules then apply as for any other tree.• Distant Large Trees

• Must be tallied as having no trees for correct expansion factor to apply to whole site.

Null Plots

Boundary Points – Half pointsThe simplest method for dealing with boundary points is also the most prone to bias. Basically, an imaginary dividing line is drawn through the point center in such a way it does not cross the boundary. Only those trees whose center point is on the side of the line away from the boundary are considered. Since this represents only half a regular point, every tree that is "in" is recorded twice.

Boundary Points – Quarter pointsIf a point center falls near a corner or other area where even a half point is not possible, the quarter point method can be used. This method is basically the same as the half point method except two imaginary lines extend at a right angle from the point center in such a way that they do not cross the boundary. The only trees considered are in the area between the two imaginary lines. Since this represents only a quarter of a point, every tree that is "in" is recorded four times.

Boundary Points - Mirage Points1. Establish plot

2. Measure all trees within the plot that are in the unit

3. Measure distance from plot center to boundary

4. Set mirage plot center on the same line at an equal distance outside of unit boundary

5. Establish a second plot of equal size from mirage plot center

6. Rerecord all trees in the mirage plot which are also in the original plot

Mirage points should not be used where the boundary is curved or irregularly shaped. In addition, someone must be able to actually stand at the mirage point center. What situations would exclude the use of this type of point?

Boundary Points - Walkthrough pointsLeast Biased and Easy to use

Works for curvy boundaries

For any tree that is "in", measure the distance from the point center to the tree then measure that same distance beyond the tree. In other words, walk through the tree the same distance the tree is from point center. If the ending point is outside the boundary the tree is recorded a second time. It also works even if a person can't go beyond the boundary.

Point Sampling Summary1. It is not necessary to establish a fixed plot boundary;

thus greater cruising speed is possible.

2. Large high-value trees are sampled in greater proportions than smaller stems.

3. BA and volume per acre may be derived without direct measurement of stem diameters.

4. When volume-per-acre conversions are developed in advance of fieldwork, efficient volume determinations can be made in a minimum of time. Thus the method is particularly suited to quick cruises.

5. Does not work well in heavy underbrush.

Calculations

POINT SAMPLING

Basal Area per Acre• BA per acre = (total trees tallied/no. of points) X BAF

• Sum total for cruise and also sum by species

• (93/12) X 10 = 77.5 sq ft per acreFrequency of stems tallied by DBH and Height classes from 12

point samples

BAF = 10 Height (no. of logs)

DBH(in.) 1 2 3 Total

10 20 7 27

12 8 25 7 40

14 10 5 15

16 4 7 11

Total 28 46 19 93

Trees per acre – single tree example•.oo5454 X DBH2 = ft2 Area of tree•If DBH = 12 then•.005454 X 144 = .785 ft2 area for that tree

•BAF / ft2 Area of tree = trees per acre•Using a BAF of 10•10 / .785 = 12.7 trees per acre represented by each 12 inch DBH tree

Trees per Acre• Trees per acre = no. trees tallied X per-acre conversion factor

---------------------------------------------------------total no. of points

• Must be calculated for each

Tree size then summed for entire

tract

Trees per acre - Example

• 10-in. class = 27(18.35)/12 = 41 trees per acre• 12-in. class = 40(12.74)/12 = 42 trees per acre• 14-in. class = 15(9.35)/12 = 12 trees per acre• 16-in. class = 11(7.16)/12 = 7 trees per acre• Total = 102 trees per acre

Frequency of stems tallied by DBH and Height classes

Height (no. of logs)

DBH(in.)

1 2 3 Total

10 20 7 27

12 8 25 7 40

14 10 5 15

16 4 7 11

Total 28 46 19 93

Volume-Factor Approach (Part 1)• Create a table of the calculations from previous slide

• 18.35 X 39 = 716• And so on

Board-foot volume per acre

Height (no. of logs)

DBH(in.) 1 2 3

10 716 1156

12 752 1248 1618

14 1318 1739

16 1360 1833

Board-foot volume by 16-ft logs

DBH(in.) 1 2 3

10 39 63

12 59 98 127

14 141 186

16 190 256

Volume-Factor Approach (Part 2)Board-foot volume per acre

Height (no. of logs)

DBH(in.) 1 2 3

10 716 1156

12 752 1248 1618

14 1318 1739

16 1360 1833

Volume per acre = (20 X 716 + 7 X 1156 + 8 X 752 + 25 X 1248 +7 X 1618

+10 X 1318 + 5 X 1318+ 4 X 1360 + 7 X 1833)/12 points = 9258 board feet

per acre

Volume/Basal-Area Ratios Approach (Part 1)Basal Area = .005454 (DBH)2

Board-foot volume by 16-ft logs

DBH(in.) 1 2 3

10 39 63

12 59 98 127

14 141 186

16 190 256

Board-foot volume per sq ft of basal area by 16-ft logs

DBH (in.) 1 2 3

10 72 116

12 75 125 162

14 132 174

16 136 183

Basal Area by 16-ft logs

DBH(in.) 1 2 3

10 .545 .545

12 .785 .785 .785

14 1.069 1.069

16 1.396 1.396

For 10 inch, 1 log tree the ratio = 39/.545 = 72Populating the table with the remaining calculations…

Volume/Basal-Area Ratios Approach (Part 2)

Board-foot volume per sq ft of basal area by 16-ft logs

DBH (in.) 1 2 3

10 72 116

12 75 125 162

14 132 174

16 136 183

Volume per acre = (sum of ratios/no. of trees) X BA per acre

Sum of ratios =20 X 72 + 7 X 116 + 8 X 75 + 25 X 125 + 7 X 162 + 10 X 132 + 5 X 174 + 4 X 136 + 7 X 183 = 11126

Recall BA per acre was the easy calculation at the beginning of all this – BA per acre = total trees tallied/no. of points X BAF = 93/12 X 10 = 77.5 sq ft per acre

Volume per acre = 11126/93 X 77.5 = 9272 bd ft per acreDiffers from 9258 found earlier due to rounding errors.

Catch all that?