POINT SAMPLING OR 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 Play video 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 fifthacre plot is associated with a plot radius of 52.7 feet. Common BAF and PRF used in the United States BAF k PRF 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 still be 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 Distance SCF 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” k Diameter Plot _ Radius 0 . 85 0 . 034 gauge _ constant 25 . 0 BAF 10890 k 2 10890 ( 0 . 034 ) 12 . 59 2 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 “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 Null Plots • Must be tallied as having no trees for correct expansion factor to apply to whole site. Boundary Points – Half points The 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 points If 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 Points 1. 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 points Least 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 Summary 1. 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. POINT SAMPLING Calculations 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 acre Frequency of stems tallied by DBH and Height classes from 12 point samples BAF = 10 Height (no. of logs) DBH(in.) 1 2 10 20 7 12 8 25 7 40 14 10 5 15 16 4 7 11 46 19 93 Total 28 3 Total 27 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 Frequency of stems tallied by DBH and Height classes Height (no. of logs) DBH(in.) 1 2 10 20 7 12 8 25 7 40 14 10 5 15 16 4 7 11 46 19 93 Total • • • • • 28 3 Total 27 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 Volume-Factor Approach (Part 1) • Create a table of the calculations from previous slide 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 acre Height (no. of logs) • 18.35 X 39 = 716 • And so on DBH(in.) 1 2 3 10 716 1156 12 752 1248 1618 14 1318 1739 16 1360 1833 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 10 39 63 12 59 98 14 16 Basal Area by 16-ft logs 3 DBH(in.) 1 2 3 10 .545 .545 127 12 .785 .785 .785 141 186 14 1.069 1.069 190 256 16 1.396 1.396 For 10 inch, 1 log tree the ratio = 39/.545 = 72 Populating the table with the remaining calculations… 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/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 acre Differs from 9258 found earlier due to rounding errors. Catch all that?