Point Sampling Introduction BAF sq.ft./acre regardless of D. Plot Radius

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Victoria Carroll
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1 Point Sampling Introduction - pps: sampling with probability proportional to size. - variable-plot or plotless cruising. - sampling points (similar to plot centers) can be systematic or random. - count trees whose dbh's appear larger than some fixed angle. - each "in" tree represents BAF sq.ft./acre (10 sq.ft./acre). BAF 10 Plot radius: R.75 D, where R in feet and D in inches. Plot size πr Expansion Factor BA/acre Tree BA plot size π(.75d) sq.ft. or π(.75 )D /43560 acres. 1 plot size 43, π (.75 )D D Tree BA (EF) D (43,560) (43,560) π (.75 )D π (.75 ) 10 sq.ft./acre regardless of D. Plot Radius R c D 1 tree tallied (of dbh D) is equivalent to EF trees per acre. Tree basal area ( D ) represents BAF sq.ft./acre. > BAF ( D ) (EF) where Expansion Factor: BAF D πc D c (75.65 / BAF) 0.5 (43,560) 1 plot size 43,560 πc D (43,560) πc

2 BAF c Expansion Factor for BAF 10 EF / D DBH BAF 5 BAF 10 BAF 0 (in) EF (number of trees / acre) Instruments - Stick-type angle gauge. - Wedge prism. - Spiegel relaskop. To check borderline trees, measure D and R. For BAF 10: R.75 D. Example Point Suppose a forester used a BAF-10 prism to establish 4 sampling points on an 8-acre tract. The tally sheet is as follows. 10" 1" 14" 1 log 1.5 logs logs 1 log 1.5 logs logs 1 log 1.5 logs logs Total trees tallied

3 Combine data into 1 tally sheet for all plots: a. Average BA/acre BA/acre b. Number of trees/acre DBH 1 log 1.5 logs logs Total Total 7 BAF(No. trees tallied) 10 (7) 67.5 sq.ft./acre No. points 4 EF /D for BAF 10. (Trees tallied)(ef) Trees/acre No. points points trees/acre c. Volume/acre from the stand table method We will use Doyle form class 78 volume table. Volume/acre for each dbh class [ (Trees tallied)(tree volume)] (EF) / No. points 10": [4(14) + 5(17)] ( /10 ) / 4 points bd.ft./acre 1": [5(9) + 6(43)] ( /1 ) / 4 points 18.8 bd.ft./acre 14": [1(48) + 5(6)] ( /14 ) / 4 points 837. bd.ft./acre Volume per acre 766 bd.ft./acre d Volume per acre from the VBAR method Establish the Volume factor table. VBAR V / BA volume-basal area ratio, or volume for each sq.ft. of basal area. Volume Factor VBAR (BAF) volume per acre each tree tallied represents. V 14 For 10 and 1 log, Volume Factor (BAF) (10) BA x

4 DBH 1 log 1.5 logs logs (inches) Board feet / acre Volume per acre (Trees tallied)(volume Factor) No. points 4 (56.69) + 5(311.70) (579.99) 4 points 766 bd.ft./acre e. 95% Confidence Interval y i Volume/acre of plot i. Point y i y i 1,38.6 5,4,38,10.9 4,4,357 3, ,409, , ,943,353 Total 11,066 3,197,779 s y i ( yi ) n n 1 11,066 3,197, Var (V/acre) s /n 57,897 / 4 131,974 95% C.I. for V/acre y ± Var(V/acre) 57, ± 131,974 (766 ± 77) bd.ft./acre f. Average sampling intensity: (using the quadratic mean dbh). Average BA/tree BA/acre 67.5 sq.ft./acre sq.ft./tree Trees/acre 9.6 trees/acre Mean dbh: Dq inches Imaginary plot size for Dq π (.75 x 11.6) 43, ac

5 4 x acres Average sampling intensity % cruise. 8 acres If he had used four 1/10-acre plots (instead of points), the sampling intensity is: 4 x 0.1acres 100 5% cruise. 8 acres g. Sample size needed 1. Suppose we want to attain a bound of ± 600 bd.ft./acre. The sample size needed is n 4 s B 4 x 57, points. We need more points To determine a sample size to attain a 10% cruise: Cruise % x 8 > n n ( acres) 8 acres points. We need 7 more points. Unusual situations a. Borderline trees: check limiting distance (plot radius) R.75 D for BAF 10. b. Slope - less than 15%, ignore. - angle gauge: sighting base longer. - prism: right angles to line of sight, and rotate prism an angle equal to slope angle. - Relaskop: automatic slope correction. c. Edge bias A tree on the edge of a tract cannot generate its full imaginary plot zone, and edge bias may result. We do not know how to handle this situation satisfactorily. Simply put points in side the tract. If edge is a problem with the tract, don't use point sampling. Advantages - No plot boundaries, thus faster in the field. - Large, high-valued trees are sampled more intensively. - BA/acre is obtained without diameter measurements.

6 Disadvantages - Heavy underbrush hinders sighting visibility. - Usually low sampling intensity > more error when expand. - Slope is a problem with prism and angle gauge. - Edge bias when small tracts or long, narrow tracts. - Too many borderline trees, thus still have to measure dbh and distance. Comparison between plots and points - Low sampling intensity: Plot size Dq for BAF 10 1/10-acre 13" 1/5-acre 19" - More points needed for same precision as plot sampling. But point sampling is faster, thus overall faster. - Uniform stands (plantations): use plots. - Natural stands: use points.

Extension Bulletin E-1757, May "1984 " Cooperative Extension Service Michigan State University $1.00 AIDS TO PROFESSIONAL FORESTRY PRACTICE

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