point sampling or variable plot cruising. establishing plots – point sampling a cruise method...
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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
Play video
Which trees to tally?
Notice ‘hidden’ tree
Procedure• The basal area factor (BAF) selected needs to yield an average of 5 to 12 trees per point.
• Do not use a smaller BAF resulting in more sample trees per point. The coefficient of variation (CV) may not be reduced but may result in missed trees. A larger BAF will result in fewer sample trees per point but cause the coefficient of variation to increase.
• Use only one BAF for a particular stratum.
• Larger BAF for larger trees. Western softwoods might use 20 to 60.
• In Kentucky, a BAF of 10 usually fits.
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 • 41-80: 20 + 0.5 * (area in acres) • 81-200: 40 + 0.25 * (area in acres)
Basal Area Factor• indicates the number of square feet of basal area/acre each "in" (measure) tree represents.
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.
Basal Area Factor (BAF)
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 AND METHODS
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
Prisms – easily lost, 1 BAF, $20 to $70
ProcedureLooking through the prism In or Out?
Ways to hold a prism
Procedure
Correct Positioning
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
“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.
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