Point sampling

POINT SAMPLINGA method of sampling based on a tree’s size, ratherthan its frequency of occurrence.Tools: Relaskop, prismsThe probability of tallying a tree depends on itscross-sectional area and the sighting angle used.The smaller the sighting angle, the more treesincluded in the sample.

POINT SAMPLING – AERIAL VIEW

POINT SAMPLINGEach tree has agiven plot size inrelation to it’ssize.How many ofthese plots doesour point fallinto?

POINT SAMPLING – SIDE VIEWUsing a prismOffset tree bole in prismDOES overlap actual treeboleOffset tree bole in prismDOES NOT overlap withactual tree bole

POINT SAMPLING VS.FIXED-AREA PLOT SAMPLINGFixed plotsamplingPoint samplingSamplingbased onFrequency of occurrenceTree sizeExpansionfactorSame for all treesVaries by treePPFPPS

POINT SAMPLING - MAIN IDEAS1. Basal Area Factor (BAF)How much BA does each sampled tree represent?2. Plot Radius FactorHow far away can a tree be and still be sampled?3. Determining the BAF of an unknown prism.4. Calculations from samples:Basal area per acreTrees per acreVolume per acre

POINT SAMPLING - BAFBasal area factor (BAF)Related to the sighting angle size of the prism used inpoint sampling.Chosen to provide a tally of 5 - 12 trees per pointEastern U.S.: 5, 10, 20Western U.S.: 20, 40, 60

POINT SAMPLING - PRFPlot radius factor (PRF)The value to use in determining the maximumdistance a tree of a given diameter can be from thepoint to still be tallied.Example: BAF 10 - the plot radius factor is 2.75.Which means:For each inch of dbh, a tree can be 2.75 feet from the pointto still be included in the point’s tally.

POINT SAMPLING - PRFPlot Radius Factor (BAF 10) = 2.75 ft.For each inch of dbh, a tree can be 2.75 feet from the point tostill be included in the point’s tally. Thus a 12 inch tree can beup to 33 feet (12 x 2.75) from the point and still be included inthe point’s tally.Plot Radius Factor (BAF 20 prism) = 1.944.For each inch of dbh, a tree can be 1.944 feet from the point tostill be included in the point’s tally. Thus a 12 inch tree can beup to 23.3 feet from the point and still be included in thepoint’s tally.

POINT SAMPLING - EXAMPLEProof for BAF 20 (continued)Each 12" tree tallied represents 0.039248 acres.Trees per acre: each tree representsTPA⎛=⎜⎝1plot size⎞⎟⎠(12-inch tree)Basal area per tree⎛ 1 ⎞TPA = ⎜ ⎟ = 25.479⎝ 0.039248 ⎠BA =0.005454per treedbh2(12-inch tree)2BAper tree= 0.005454 ( 12 ) =0.785376 sq.ft.

Therefore each tree tallied represents aBASAL AREA IN SQUARE FEET PER ACRE =BAF OF THE PRISM YOU ARE USING.POINT SAMPLING - EXAMPLEProof for BAF 20 (continued)The basal area per acre represented by each tallied treeBasal area per acreBA = TPA×per acreBAper tree12-inch tree BA per acre= 25.479 × 0.785376 = 20.0

POINT SAMPLING-COMPUTE BASAL AREABA=⎛⎜⎝Total treesnumber oftalliedpoints⎟ ⎞⎠BAFExample:• BAF 20 prism• 402 trees tallied• 25 points⎛ 402 ⎞BA = ⎜ ⎟20= 321.6 sq.ft. / acre⎝ 25 ⎠

POINT SAMPLING-COMPUTE TREES PER ACRE• Requires diameter measurements of prism-selected trees• Requires calculation of “Tree Factors” conversionfactors•Tree factor is the expansion factor of i th sample tree• Hand calculation requires constructing a tableTPA =⎛ (no.trees tallied) × (per − acre conversion factor) ⎞⎜⎟⎝total number of points⎠

POINT SAMPLING-COMPUTE TREES PER ACRERequires tallies of trees in each diameter class (diametersof tallied trees were measured during point cruise)TF i=unit areasample area=⎛⎜⎝BAF ⎞⎟BA per tree ⎠TPA⎛ ∑ ni× TF= ⎜⎝ nsampleipoints⎞⎟⎠Per - acre conversion factor:"TREE FACTOR" for each diameter class iTFi⎛ 43,560⎜⎝π (dbh×plot radius factor)= 2⎞⎟⎠TPA =⎛ (no.trees tallied)(per − acre conversion factor) ⎞⎜⎟⎝total number of points⎠

POINT SAMPLING-COMPUTE TREES PER ACREExample:• BAF 10 prism• Only in the 10-inch diameter class27 trees were measured• 12 pointsTF i=⎛⎜⎝BAFBA per⎞⎟tree ⎠⎛ 10 ⎞TF i= ⎜ ⎟ = 18.349⎝ 0.545 ⎠TPA⎛⎜ ∑ ni× TF= ⎝ npi⎞⎟⎠⎛ 27×18.349⎞TPA = ⎜⎟=41.3treesper acre⎝ 12 ⎠41.3 TPA for the 10-inch diameter class

POINT SAMPLING - VOLUMETwo methods:1. Volume Factor (VF) method• Natural extension from plot sampling2. Volume/Basal Area Ratios (VBAR) method• Can be used in double sampling• Both methods require calculation of Tree Factor• Both methods require diameter and height measurementsfrom some or all prism selected trees• Hand calculation using either method is labor intensive

VOLUME – VF METHODPoint cruise:Measure tree DBHand heightsCalculateVolume Factor foreach dia-height classConstruct a Table:Bin measured treesinto diameter-heightclassesCalculateTree Factor foreach DBH-height classCalculateVolume per acre

VF METHOD - EXAMPLEPoint-sample cruise on a 40 ac tract• BAF 10• 12 pointsVOLUME /AC = TREES/AC x VOLUME/TREETree factorTFiFor=BAFBA per treeBAF= 10=( π ×BAFDBH2/4)Why144?TF10"=π ×BAFDBH2/4=103.141×100 /(4×144)= 18.349TF12"=π ×BAFDBH2/4=103.141×144 /(4×144)= 12.73

VF METHOD - EXAMPLEFirst, compute volume factor foreach diameter-height class using avolume table and Tree Factorcalculated in previous slide:Example: for a BAF 10 prism• TF 10 = 18.349VF = TF × viii• Volume of a 10" /2-log tree is 63 bf.- it is v iv i is determinedfrom a publishedvolume table

VF METHOD - EXAMPLE• n i the total number of trees in diameter class i• n p is the total number of points•VF i is the volume factor for diameter class in∑ i×Volume per acre=npVFiCalculate volume for each diameter-height class.

VF METHOD - EXAMPLEMake a table with the collected data & information•BAF=10• Compute NUMBER of trees per acreTally & #logsDBH 1 2 3 Total BA / tree TF in ix TF i10 20 7 0 27 0.545 18.35 49512 8 25 7 4014 0 10 5 1516 0 4 7 11Total

VF METHOD - EXAMPLETrees per acreRecall:⎛⎜ ∑ (ni)(TFiTPA= ⎝ np) ⎞⎟⎠We know:Σ n i x TF i =n p = 12So, from previous slide:TPA=TPA=⎛ 495+....... ⎞⎜ ⎟= ..........⎝ 12 ⎠⎛ 27×18.35+40×12.74+15×9.35+11×7.16⎞⎜⎟=⎝12⎠102

TotalMake a table with the collected data & information•BAF=10•Board-foot conversion using International ¼ in•Form class 80DBHVF METHOD - EXAMPLETally& # log V i BAVF i1 2 3 1 2 3 /tree TF i1 2 3 n ix VF i10 20 7 0 39 63 0.545 18.35 716 1156 2241212 8 25 7 59 98 12714 0 10 5 141 18616 0 4 7 190 256

VolumeRecall:VF METHOD - EXAMPLE⎛⎜ ∑ (ni)(VFiVolume= ⎝ npΣ n i x VF i = 111100We know:n p = 12So, from previous slide:) ⎞⎟⎠Volume=⎛111100 ⎞⎜ ⎟ = 9258⎝ 12 ⎠10,648 bf/ac.

POINT SAMPLING – VOLUME EXAMPLEMake a table!Example using a 20 BAF prismNumber of point sampled = 8DBH/HT Tally V iBA/tree TF in ix TF iVF i n ix VF i10"/80' 10 40 0.55 36.4 364 1456 1456010"/100' 12 6012"/100' 13 8514"/120' 8 1101279.3 85187Note: You can calculate TPA and volume by hand. However,we usually use a software package to do these tediouscalculations for us.

POINT SAMPLING – VOLUME EXAMPLETrees per acreRecall:⎛⎜ ∑ (ni)(TFiTPA= ⎝ np) ⎞⎟⎠We know:Σ n i x TF i =1279.3n p = 8So, from previous slide:TPA=⎛1279.3⎞⎜ ⎟=⎝ 8 ⎠159.9160 TPA

POINT SAMPLING – VOLUME EXAMPLEVolumeRecall:⎛⎜ ∑ (ni)(VFiVolume= ⎝ npΣ n i x VF i = 85187We know:n p = 8So, from previous slide:) ⎞⎟⎠Volume=⎛ 85187 ⎞⎜ ⎟ =10648.4⎝ 8 ⎠10,648 bf/ac.

• 4 plots were used to cruise a 30 acre stand using aprism with BAF 10• the following tally sheets were obtainedDBH Plot 1 Plot 2 Plot 3 Plot 4Logs Logs Logs Logs1 2 3 1 2 3 1 2 3 1 2 312 * * * *14 * * * * **16 * * * **

• International ¼ in rule• Form class 80DBH Plot 1 Plot 2 Plot 3 Plot 4Logs Logs Logs Logs1 2 3 1 2 3 1 2 3 1 2 312 *98 *98 *127 *9814 *141 *186 *141 *186 **141*18616 *256 *190 *256 *256

DBH Plot 1Logs BA/ TREE TF Per acre …1 2 3 TREES BA VOL12 *98 0.785 12.73 12.73 10 1247.5414 *141 1.07 9.3516 *256 1.396DBH Plot 4Logs BA/ TREE TF Per acre …1 2 3 TREES BA VOL12 0.785 12.7314 **14116 *256 1.396*186 1.07 9.35 28.05 30 4375.80

DBH Plot 2LogsBA/ TF Per acre …1 2 3 TREETREES BA VOL12 *98 *127 0.79 12.7314 *186 1.0716 *190 1.396DBH Plot 3Logs BA/ TREE TF Per acre …1 2 3 TREES BA VOL12 * 98 0.79 12.7314 * 141 *186 1.0716 *256 1.396

DBH Trees/ac BA/ac Volume/acP1 P2 P3 P4 P1 P2 P3 P4 P1 P2 P3 P41212.73 25.46 17.73 0 10 20 10 0 1247 2864 1247 0149.35 9.35 18.70 28.05 10 10 1318167.16 7.16 7.16 7.16 10 10 1832DBH Trees/ac BA/acre Volume/ac12 12.73 10 133914 16.3516 7.16Total 36.3

DBH Trees/ac BA/ac Volume/acP1 P2 P3 P4 P1 P2 P3 P4 P1 P2 P3 P412 12.73 25.46 17.73 0 10 20 10 0 1247 2864 1247 014 9.35 9.35 18.70 28.05 10 10 1318s16 7.16 7.16 7.16 7.16 10 x10 1832Total 29.24 41.97 38.59 35.21 30 40 4397Mean # tree/acre=Variance=( x4−1Std.errormean . = s4∑i=1i− x)x29.24+41.97+38.59+35.21= 36.254=2(29.24−36.25)=variance=n229.474+ .. + (35.21−36.25)3= 2.712= 29.47CI=36.25±t 4-1,0.05 x2.71CI=36.25±8.62t 4-1,0.05 =3.182

Stand and stock table with the confidence intervalsDBH Trees/acBA/ac[ft 2 ]Volume/ac[ft 3 ]Trees/tractVolume/tract12 12.7 10 1339.8 381.0 4019414 16.416 7.2Total 36.3CI 8.64

POINT SAMPLING METHODOLOGYTwo common approaches areBASIC APPROACH• Use ONE prism for entire cruise.• Select BAF that tallies 7-13 trees per point.• Measure DBH and height of all trees tallied.• Use all trees tallied to calculate stand basal area,density, and volume.

POINT SAMPLING METHODOLOGYDOUBLE SAMPLING = NESTED APPROACHBIG BAF METHOD• Use FIRST prism with a BAF that tallies 7-13 trees per pointas primary.• At each sample point, use a SECOND prism with a largerBAF that tallies 1-7 trees per point to select trees for diameterand height measurements. These trees are often called“volume trees” or “VBAR trees”.• Use primary tallies to calculate stand basal area.• Use VBAR tree measurements to calculate stand density andvolume.• Materials are in the textbook (pg250) and online