forestry bulletin no 14 practical point sampling

BULLETIN NO. 14 APRIL, 1967

PRACTICAL POINT-SAMPLING

ELLIS V. HUNT, JR.

and

ROBERT D. BAKER

School of Forestry

STEPHEN F. AUSTIN STATE COLLEGE

Nacogdoches, Texas


SCHOOL OF FORESTRY FACULTY

LAURENCE C. WALKER, Ph.D Dean and Professor

ARTHUR VERRALL, Ph.D Professor

NELSON T. SAMSON, Ph.D. Professor

M. VICTOR BILAN, D.F Professor

ROBERT D. BAKER, Ph.D Associate Professor

HARRY V. WIANT, JR., Ph.D Associate Professor

LEONARD BURKART, Ph.D. Associate Professor

ELLIS V. HUNT, JR., M.S Assistant Professor

EUGENE HASTINGS, Ph.D Assistant Professor

KENNETH G. WATTERSTON, Ph.D.. . Assistant Professor

J. ROBERT SINGER, Sc.D Assistant Professor

BILL H. WILPORD Visiting Professor

ROBERT S. MAXWELL, Ph.D Professor of ForestHistory

LOWELL K. HALLS, M.S. Part-Time Instructor,Forest Game Management

HENRY L. SHORT, Ph.D Part-Time Instructor,Forest Game Management

MARY Jo LINTHICUM, B.S Forestry Librarian


118354



ELLIS V. HUNT, JR.

and

ROBERT D. BAKER

School of Forestry


Nacogdoches, Texas

$1.00


FOREWORD

Point-sampling is a valuable tool in the kit of the practicing forester.It is employed for permanent and temporary sampling and for growthstudies. Since the concept of point-sampling is new in American forestry,different approaches have been employed to explain its application. Thisbulletin consists of a synthesis of point-sampling lectures and lessonplans developed at Stephen F. Austin State College and presented as aforestry short course in 1963. It explains these sampling techniques andsuggests choices in methodology and computational procedures. As a seriesof lectures, it was written in outline form, and this form was retainedbecause the organization and use of the ideas seemed to be facilitated inthis way. It is a revision of the first part of a two-part bulletin on point-sampling published by the School in 1964.

TABLE OF CONTENTS

Point-sampling theory 5

Calibrating an angle-gauge or prism 9

Constructing a stand-table 9

Computing board-foot and cubic-foot volumes 11

Sampling techniques 13

Constructing point-sample volume factors 19

Miscellaneous volume factors 28

The stand-table blow-up factor 29

Constructing a table of limiting distances 31

Slope corrections in point-sampling 34

Growth-projection with point samples 37

Number of points to achieve stated precision 37

Comparing methods of per acre point-sample volume estimates 39

Literature cited 42

Abbreviations 43

LIBRARYP. AUSTIN STATE COLLEGE

NACOGDOCHES., TEXAS


Ellis V. Hunt, Jr., and Robert D. Baker

POINT SAMPLING—THEORY

Mr. L. R. Grosenbaugh (1952) introduced point-sampling to Americanforesters, citing Mr. W. Bitterlich's earlier work in Europe. Primarily it is,he said, "A rapid method of sampling tree basal area per acre . . ." Itis rapid and in 1952 it was revolutionary! Since then, it has been explained,re-explained, embellished, tested and discussed. Here is how it is done andwhy it works.

I. Tally the selected trees at the point.A. With the angle-gauge, tally all trees appearing larger than the

angle.B. With the prism, tally all trees that are not wholly offset.C. Be sure to look at trees at dbh (diameter breast height, 4.5 feet

above ground line).D. Tally every borderline tree (those exactly coinciding with the

angle or those just exactly offset by the prism) as Vz tree.

OUT BORDERLINE

II. Multiply the number of trees tallied per point by the BAP (basalarea factor) that fits the instrument used, to obtain basal area peracre in square feet.A. For an angle-gauge describing 104.18 minutes, the BAP = 10.

1. A gauge 33 inches long with a cross arm 1 inch wide describesan angle of 104.18 minutes.

2. A 3.03 diopter prism does the same job.B. This is why it works—using a BAF of 10 as an example:

1. The area of a circle is 0.7854 D2.7rD2 3.1416 D2

a. Area of a circle = = = 0.785 D=.4 4

i Stephen F. Austin State College

2. The area of the "tree circle" is 662 X BA (basal area) of thetree.

a. The "tree circle," with the tree at its center, has a diameter66 X the diameter of the tree; it describes the boundarieswithin which one mu"t stand if he is to tally the tree withan angle gauge of 104.18 minutes or a 3.03 diopter prism.

b. These are examples of "tree circles" showing maximumdistance one may stand from a tree and still tally it (ra-dius of "tree circle").(1) For a tree of 1 foot dbh, one must stand not more

than 33 feet away.(2) For a tree of 2 feet dbh, stand not over 66 feet away.(3) For a tree of 3 feet dbh, stand not over 99 feet away.

III. Now consider a tree which is 0.5 foot dbh:

A. BA (basal area) of the tree is 0.7854 D° = 0.196 square feet.

B. One could count such a tree if he stood not farther than 16.5 feetaway from it.

C. The diameter of the "tree circle" for this tree is therefore 2 Xthe radius, or 33 feet.

D. The area of this "tree circle" is 0.7854 D2 or 0.7854 X 332 or0.7854 X 1089 or 855.3 square feet.

E. Statement II.B.2. said the area of the "tree circle" was exactlythe BA of the tree X 662. If this is true for this 6-inch dbh tree,then:1. BA of the tree = 0.196 square feet,

area of the "tree circle" = 855.3 square feet,66 squared = 4356.

2. 855.3/4356 = 0.19630.

IV. Then, for a tree that has a BA of 1 square foot (approximately13.55 inches dbh):

A. The "tree circle" has 1 X 662 square feet of area (as stated inII.B.2. and proved in IIT.E.) or 4356 X 1 square foot or 4356square feet.

B. Visualize this tree in the center of its "tree circle," the latterbeing in the center of an acre of land (Figure 1).1. Tree BA is 1 square foot.2. "Tree circle" area is 4356 square feet.3. Acre area is 43,560 square feet.

V. If a cruiser stands at random inside this acre, what chance wouldhe have of being inside the "tree circle" (i.e., close enough to thetree to count it with an angle gauge or prism defining an angle of104.18 minutes)?

Practical Point-Sampling

Figure 1. A one-square foot BA tree in its 4356-square-foot "tree circle"inside a circular acre of 43560 square feet.

A. The chances are equal to the proportion of the areas of the "treecircle" and the acre, or 4356 to 43560, or 1 to 10.

VI. If there were a single tree on each of 100 such acres and each treecontained 1 square foot of BA, and if the cruiser were on each acreat random, he would tally 10 trees in 100 chances.

VII. Change tally to total BA of trees by multiplying the tally by 10,because 10 X 10 = 100, and on 100 acres there would be 100 squarefeet of BA.

VIII. Compute BA per acre from such a tally by multiplying the tallyby 10 and dividing by the number of "points" the cruiser visited, or10 X 10 -f- 100 = 1 BA per acre.

IX. Conclusion: The BAF of an angle gauge or prism denning an angleof 104.18 minutes is 10, and the formula for computing BA in squarefeet per acre is:

Stephen F. Austin State College

BA per acre =SX

N(BAF)

where X = number of trees tallied,N = number of points, and

BAF = basal area factor of the instrument.

Figure 2. 10-BAF—Illustration of 3.03 diopter count. A 9.55-inch treeof BA = 0.5 square feet has "tree circle of (0.5) (662) = 2178 square feet

2178 1and a random tally chance in 1 acre of = or 1 in 20. A 13.55-

43560 20inch dbh tree has a BA = 1.0 square foot, a "tree circle" of (1) (662) =4356 square feet and a random chance of 1 in 10. The "tree circle" overlaparea, because of the position of trees, is 871.5 square feet with a randomchance of 1 in 50. In 100 random counts, one would get:

2 overlaps of count 2 each total 48 other big tree counts of 1 total 83 other little tree counts of 1 total 3

total 15 in 100 random-chances.SX 15

BA per acre is (BAF) or X 10 or 1.5 square feet per acre.N 100

Practical Point-Sampling 9

CALIBRATING AN ANGLE-GAUGE OR PRISM

I. As explained earlier, the BAP is the reciprocal of the random chanceone has of being in the "tree circle" of a single tree containing 1 squarefoot BA, if this tree is in a circular acre, and one is taking a point-sample in this acre.

II. One can find the radius of the "tree circle" by sighting at the treewith the instrument from such a distance that the angle just coincideswith the tree's diameter at breast height (with a prism, just soopposite sides of the tree coincide). High accuracy prisms, which aremore expensive, are calibrated at the factory. Uncalibrated prisms,available at about $1.00 each, must be calibrated by the user.

III. Procedure

A. Set up a rectangular target of a convenient width, such as 1 foot.

B. Lay a steel tape along the center line, perpendicular to the target.

C. Move back along this line until one side of the target image seenthrough the prism is precisely aligned with the other side seen overthe prism. Make sure the axis of the prism is perpendicular to theline of sight.

D. Measure accurately the distance from prism to target.

E. Compute the BAF using the following formula:43,560

BAF =l+4(d/w)2

where w = target width in feet,d = distance from prism to target in feet.

IV. As an alternate procedure, Dixon (1958) suggests using the sameformula but measuring "the amount of deflection at a fixed distance:

A. Fix prism in position at one end of a long table.

B. At the other end, at a right angle to face of the prism, set up atarget of two vertical pins that can be moved.

C. Measure accurately (d) the distance between the target and prism.D. Move pins until the displaced image of one pin coincides exactly

with the image of the other. Measure the distance between thepins (w) precisely."

E. BAF "calculated using formula above. It is essential that d r.nd wbe measured in the same units."

CONSTRUCTING A STAND TABLE

I. The probability of a tree dbh class being sampled is in direct ratio toits BA.

A. Consider a tree with BA of 0.5 square foot in the center of a cir-cular acre.

10 Stephen F. Austin State College

1. Its "tree circle" contains 662 times as much area, or 2172 squarefeet, or 1/20 acre if an angle of 104.18 minutes is used.

2. Its chance of being tallied in any one sample is therefore 1 in 20.

B. It was stated earlier that under the same circumstances a tree of1 square foot BA had 1 in 10 chances of being tallied. Thus thechance of a tree being in a sample is exactly proportional toits BA.

II. To construct a stand table, it is necessary to measure the dbh oftallied trees.

A. Formulating a conventional stand table most simply requires twosteps.1. Convert the tree count to BA in each dbh class per acre.2. Then divide each of these BA's by the BA of the tree at nominal

class center.

B. As an example, if an angle-gauge having 104.18 minutes is used,the following trees are tallied at 5 points:

1. Point Tally by DBH-—Inches1 6, 12, 16, 202 10, 18, 14, 6, 16, 10, 8, 8, 12, 143 10, 2, 20, 18, 12, 184 16, 10, 10, 12, 12, 10, 14, 14, 14, 85 14, 16, 18, 16, 8, 10, 12, 12, 10, 4

2. The total tally is 40 trees at 5 points.

C. In our example, from Grosenbaugh (1952), we have two 6-inch,one 4-inch and one 2-inch trees.1. To convert these to BA per acre, multiply by BAF and divide by

the number of sample points.2. To convert to trees per acre, divide this (Item 2) by BA of the

the tree of nominal class midpoint (Item 3).

Item 2-Inch Class 4-Inch Class 6-Inch Class1 . Count 1 1 22 . S q . f t . B A p e r acre 2 2 43. Sq. ft. BA per tree .022 .087 .1964. Trees per acre 90.90 22.98 20.40

D. The entire stand table could be constructed in this manner fromtree dbh's recorded for the trees counted as samples at the points.

III. In summary, to get frequency per acre (f), multiply the tree count bythe BAF, divide the product by N (number of points), and divide this

quotient by BA of a tree at nominal midpoint diameter (0.00545415D2). Putting this in equation form, we get:

BAFCount X

Nf = , or

0.00545415 D2


BAP

NX Count,

0.00545415 D2

BAF

Nso factor is

0.00545415 D2

COMPUTING BOARD FOOT AND CUBIC FOOT VOLUMES

Note: The first step (as for any volume estimating) is to secure an appro-priate volume table.

I. A suitable standard volume table in cubic feet or board feet may bemodified (for instance, a Girard Form Class Volume Table).

A. To modify the table, divide each tree volume in the table by its treeBA. Enter these quotients, called bff [board foot factor] or cff[cubic foot factor], in a new table by tree dbh and height class.1. This table may be used as follows:

a. Tally trees in each point sample by dbh and height.b. Secure the sum of the bff or cff for the trees in the sample.c. Divide this sum by the number of trees.d. Multiply this quotient by BA per acre when:

no. treesBA per acre = - - X BAF.

no. points

B. To further modify the tables of factors (described in I.A.) divideeach value by 10 to reduce the size of the numbers for easy mentalarithmetic, and round off all values to whole numbers.1. This will not introduce any serious errors where samples of

reasonable size are to be collected to compute volume per acre.2. This table may be used exactly as outlined before except that

the quotient (I.A.l.d.) will need to be multiplied by 10 beforemultiplying by BA per acre.

II. A different kind of table may be similarly produced giving a bff orcff for height classes only, instead of dbh and height classes.

A. This is true because the height-tree-volume relationship is prac-tically a. straight line.1. Thus for Mesavage & Girard Form Class 80, Grosenbaugh (1952)

showed these bff's divided by 10 (International %-inch log rule):

DBH ILog 2 Log 3 Log 4 Log10 7 12 — —12 8 12 16 —14 8 13 17 2016 8 14 18 2218 8 14 19 2320 8 14 20 23


B. From the table, it can be seen, for instance, that if 2-log treesaverage 14 inches dbh, the Bff is 13.

C. Using the table, the procedure for determining volume per acre is:

1. Tally point sample trees by height classes.

2. Total the trees in each height class.3. Multiply each sum by the appropriate Bff.

4. Total these products.5. Divide this total by the number of points in the sample.6. Multiply by BAF to get board feet per acre.

(Note that since Bff was obtained by dividing tree volume byBA X 10, it will be necessary as a final step to multiply finalanswer by 10.)(Note, too, that the procedure above is simplified, but likeI.A.I., where:

2 bff no. treesVolume = X X BAF,

no. trees no. pointshere:

2 BffVolume = - - X BAF X 10.

no. points

III. If no suitable volume table is available the bff or cff may be determinedby felling timber in each height class or, if preferred, each dbh-heightclass, and measuring it for volume.

A. The following procedure is used:

1. Fell the sample trees.

2. Secure suitable tree measures (usually d.i.b. at some regularlength interval, and dbh).

3. Apply a suitable log rule to obtain log volume.

4. Total to obtain tree volume.5. Calculate the average tree volume and basal area for each dbh-

height class, or each height class.

6. Divide tree volume by tree BA, or usually in case of Bff divideby 10 times BA.

IV. Appropriate factors for southern pine were suggested by Grosenbaugh(1962ft).

A. Bff's based on Mesavage and Girard Form Class 80 (about averagefor reasonably well-stocked second-growth southern pine) :

BffInternational

Merch. Lengthzero log

12345

B. The cff s for reasonably stocked southern pine:

International% Inch0713182328

Scribner0611162025

Doyle048121521


Merch. Length, cff Merch. Length, cfffeet feet

0 0 40 2610 7 50 3120 14 60 3630 20 70 39

V. A formula suggested by Grosenbaugh (1955) for International boardfoot volume per acre in southern pine is:

(SL) (60) (BAF)Board foot volume per acre = ,

Nwhere L is merch. height of trees in 16-foot logs,

N is number of sample points.A. The factor 60 is based on average southern pine and allows for an

increase in tree dbh and form class with tree heights.

SAMPLING TECHNIQUES

I. Point-sampling is tree sampling proportional to tree BA. This wasshown in the section concerning construction of a stand table, wherethe equation for computing the stand table blow-up factor was:

BAF

NFactor =

0.00545415 D2

A. The factors for three common values of BAF are:1

DBH ClassInches

468

1012141618202224

Stand5-BAF

57.3025.4714.329.166.374.683.582.832.291.891.59

Table Blow-up10-BAF

114.5950.9328.6618.3312.739.357.165.664.583.793.18

Factors20-BAF229.20101.86

57.3036.6725.4718.7114.3211.329.167.586.37

1Some values in the tabulation are slightly different from those whichwould be computed from values in Table 6, due to rounding off.

B. These are easily computed using the equation shown as, for in-stance, the 10-BAF and dbh class of 4 inches:

Factor =

10

1

(0.00545415) (42)

14 Stephen F, Austin State College

10

(0.00545415) (16)

10

0.0872664

= 114.5916.

C. Hence, the smaller the dbh class, the smaller the percent of sample,and therefore the larger the multiplier must be to convert toper-acre values. This is an advantage over some other samplingmethods since the bulk of counting or measuring labor is usedon the more valuable, larger dbh classes.

II. Several other kinds of sampling are proportional to area, as for in-stance plot-sampling.

A. In plot-sampling, if one wanted to change count of sample trees ona 1/5-acre plot to trees per acre, the same multiplier (5) would beused for all dbh classes.

B. Generally, the same principle applies to line sampling and tran-sect-sampling. Counts along a line or transect are related to thecount for an area, and all dbh class counts are multiplied by aconstant to obtain per acre counts.

C. Actually, as the typical uneven-aged stand table clearly shows,there are far more small trees than large trees in the forest, soa cruiser spends more time than warranted, by volume or value,in measuring or counting them. (For instance, on 110 circular1/5-acre CFI plots established in Sabine County by the Schoolof Forestry, over half of the stems came from the 5- and 6-inchdiameter classes.)

D. The same considerations would be valid for a mixture of smalleven-aged stands. One would expect to stratify and sample dif-ferently in even-aged stands large enough to be treated separately.

III. Some problems perhaps best solved by a sampling method otherthan point-sampling are:

A. To determine survival of seedlings in plantings, sample-row count-ing is practicable.

B. In natural reproduction inventories, random quadrat counts ortransect or line counts may be more reasonable.

C. For forage volume inventories, quadrat clippings may be desired.

D. When a count is not directly related to area, transect or line countsmay suffice.

IV. There are many considerations involved when trying to devise a point-sampling scheme. Some of the most obvious are discussed, but manyothers are encountered in the field. One must be alert to note themand to make field time as productive as possible.


A. Random sampling- principles should be used whenever reasonablebecause any measure which is averaged will be of limited valueif not accompanied by a measure of variability or accuracy.

B. Systematic samples may be subjected to analyses suitable for ran-dom samples but the results must be accepted with reservation.Nevertheless, the systematic forest sample will generally be moreprecise than other kinds of samples of the same size, so systematicsampling does have some advantage.

C. Two-prism sampling may be advantageous when two arbitrarilydefined populations occupy the same area.1. A sawtimber population and a pulpwood population are present.

To count the sawtimber trees with a 5-BAF prism would be tootime consuming, but to count pulpwood size trees with a 10-BAFprism might admit too few trees for an adequate sample.

2. The obvious solution is to sample each arbitrarily defined popu-lation with the instrument best suited to measure it.

D. Combined plot and point-sampling may be suitable for some situa-tions similar to that discussed above, or perhaps combined pointand transect or line-sampling would be better.1. For timber volume and reproduction counts, one might use

point-samples for volume, and stocked quadrats for reproduc-tion.

2. For timber volume and thinning prescription, one could userow tree counts for prescribing, and point-sampling for timbervolume estimating.

E. Subsampling (to save time) may be desirable in situations whensome attribute with small variance is needed in combination withsome other of larger variance, or where economics may dictatefewer measurements of a difficult nature.1. For estimating volume in pulpwood size plantations, use point-

sampling to count trees, and randomly select trees out of thepoint-sample count for height measures (height is a time-con-suming measure, and all the merchantable trees may be nearlythe same height).

2. The same kind of solution might apply if one were sampling toconstruct a stand table or to obtain volume when volume fac-tors are based on dbh.

3. Particularly, in IV.E.2., the random, selection of individualsample trees for the measured subsample would be important(avoid the idea of measuring trees you select on the premisethat a set number should be measured in each class).

4. Because some size class may be limited by the nature of thestand (40-inch dbh trees for example), perhaps all individualsof some classes should be measured in the subsample. Whenthis is done, computational procedures must take this into ac-count.

F. Proportional sampling might be used in areas where stands can bestratified.


1. Separate hardwood from pine stands or young timber from oldtimber, etc.; then sample each stand.

2. This may involve not only variance of the populations, but alsototal stand area, value per unit, etc.

G. Cluster sampling may be better than the selection of a single sam-pling unit at each location.

1. In 1957-58, an area was sampled using the average of two 10-BAF samples as a measure of BA per acre with the followingresults, compared to 1/5-acre plots also measured in 1957-58and a subsequent single 10-BAF sample in 1962 at the samelocation:

Sampling Unit

Avg. of 2 prism samples1957-58

1/5-acre plot 1957-58One prism sample 19621/5-acre plot 1962

BA per A(Sq.Ft.)

70.1870.7262.8770.99

am.(Sq.Ft.)

2.172.202.802.44

C(Per Cent)

30.9231.1144.5336.00

2. The sampling scheme referred to above contained 110 samplingunits, so a am. of about ±10% could have been obtained in the1957-58 inventory with only about 10.52 or 11 points, but usingonly one prism count, as the sampling unit in 1962, would haverequired about 21 points for similar precision. (Note: Theprobability is 68 in 100 chances.)

3. Also, the 1957-58 point-sampling was as precise as 1/5-acreplot-sampling, showing that on this area it is just as efficientfor BA data as the larger plot-sample.

4. Point-sampling is now employed in the Southern Forest Surveywhere 10 points, each a chain apart on varying azimuths, areused with limiting distances for a 37.5-BAF prism.

H. Prescription sampling with the prism may be done advantageously.

1. Grosenbaugh (1955) described a method of prescribing andmarking thinnings in southern forests. With a 50-BAF prism,the count should never be 3 (over 2) when the "leave" BAtarget is about 83 square feet.

2. Similarly, where one-fourth or more points contain zero poten-tial crop trees with 50-BAF prism, the area needs special atten-tion for restocking or increasing stocking.

3. On the Texas National Forests, a 37.5-BAF prism is similarlyused in sampling during pre-sale planning.

4. Seed tree marking, or checking of marked stands, may wellbe accomplished after marking standards have been formulated.For instance, if the goal is 7 large (average 19-20-inch dbh)trees per acre to be left as seed trees, then BA per acre of seedtrees would be about 15 square feet; so with a 5-BAF prism,seed tree counts should average 3.


V. The choice of a point-sampling instrument (choice of a BAF) mightmake point-sampling somewhat comparable to plot-sampling in theconcept of percent of sample.

A. This concept is disclaimed by authorities contacted by the authorsand by published material on point-sampling or forest samplingbecause sampling varies with BA.

B. Nevertheless, a case example from a Texas industrial forest ispresented here because it may have value for some situations:

1. Trees on company land average slightly over 12 inches dbh, andwith a 10-BAF prism, this size tree has a tree circle (or plot)of about 0.08 acre; thus plot size averages 0.08 acre.

2. 500 points will be located on 200,000 acres.3. Equivalent acres tallied: (500) (0.08) = 40.00 acres.4. Percentage cruise: 100 X 40.00/200,000 = 0.2 percent.

VI. Bias in point-sampling is as important a consideration as in anysampling. It is to be avoided.

A. Systematic instead of random samples may cause bias.

1. As a result of the coincidence of the natural population dis-tribution and sample point locations, all points could fall inhigh site-class areas, thus omitting ridge tops and dry sites.

2. Bias could happen as a result of man's activities. By randomselection of a starting point for a systematic cruise, one mightselect a spot 2 chains southeast of the northwest corner ofeach 160-acre square block of forest land, not knowing that 50years ago a steam skidder yard was located in each of thesespots, making each such spot non-representative of the wholeforest.

B. Improper use of tools causes bias.1. If the prism is hand-held and by some quirk always 4-5 degrees

out of horizontal (which would not be compensating), the countwill be in error.

2. If the cruiser swings the prism around him instead of viceversa, the count will be wrong.

3. If one measures distance from the point to the nearest edgeof a borderline tree instead of to center of tree, the count willbe incorrect. (Note if one-half dbh is subtracted, then nearestedge of tree would be correct.)

C. Ignoring slope correction may be acceptable for some southern for-ests; for many in East Texas it would not.

D. Borderline trees, if not properly handled, may be a source of bias.1. As a result of erroneous reading or writing of a rule, bias

may be introduced.a. The rule should be: "Include border trees on the west side,

exclude those on the east side" or, rephrased, "Count everyborderline tree as % tree."


b. The rule should not be: "At each point, count the first bor-derline tree, omit the second, count the third, etc." (Becauseborderline trees will be about 1 in 20, and because ordinarilyonly one would be found on 2 or 3 plots, all would getcounted.)

2. If borderline trees are not measured to accurately determinewhether in or out, an unconscious bias may develop whereinmany "out" trees are counted, or vice versa. This may not becompensating.

3. Looking at trees always at eye level or some place other than4.5 feet above average ground line would not be compensating.

E. "Brush bias" (trees behind brush or other trees) may cause countto be low, but never high.1. Proper use of the prism and proper selection of BAP can

usually overcome this in southern forests (a problem in "BigThicket" country).

2. In the Pacific Northwest this bias is controlled by looking ateach tree at top of first 16-foot log instead of breast height(Bruce 1961).

VII. Point-sampling statistical analysis is similar to that for any sam-pling, particularly where one is working with relatively large samplesand a continuous variable. Actually, tree counts, as in BA estimationwith point-samples, are discrete; but this should not be a barrier tothe use of normal statistical analyses for continuous variables, sincebasal area per acre is a continuous variable.

Statistical analysis uses variance as measured in a sample. If X isthe measured variable, then its value must be ascertained for eachsample point. The variance is computed with the equation:

NV =

N — 1where V = variance of X,

X = measurement at a point,N = number of points.

Other statistical values normally needed from point sample cruisesare:

A. Standard deviation = a = V V.

B. Standard error of the meanir(100)

C. Coefficient of variation = C =

Jl= am = \.

M2 am (100)

D. Proportional limit of error = Pie. —M


E. Number of observations for 68 percent confidence in <rm = N =V a2

Number of observations for 95 percent confidence in am = N =4V

cF. Sampling error of mean in percent = S = —

NG. Combined sampling error in percent = Se%, where

Se% = VlSTof bff (or'cff))2 + (S of tree count)2'.

CONSTRUCTING POINT-SAMPLE VOLUME FACTORS

I. There are many ways of computing timber volumes from point-sam-ples. Five are illustrated:

A. The first is similar to the standard volume table approach in plotcruising, sample trees being classified by height and diameter.

B. The second is based on local volume tables as used in conventionalplot cruising, sample trees being classified by diameter only.

C. The next is like the local volume table approach except that sampletrees are classified by height rather than dbh, with a volume factorfor each height class.

D. The fourth method is like I.C. except that a single average factoris used for all height classes.

E. The last method involves converting trees tallied in the field intovolumes per acre in a cumulative tally.

II. The system wherein sample trees are classified by height and dbh issimple and direct.

A. A good standard volume table is needed. To illustrate the proce-dure, a volume table for an area on the Sabine National Forestfor loblolly pine is shown in Table 1.

B. Each tree volume in the table is divided by the BA of the dbh classto which it belongs.1. For 10-inch dbh, 1 log, the volume is 23 bd. ft., and

23bff =

(3.1416) (10)V144(4)— 23/0.545,= 42.

2. As a further refinement, each of the basal area factors thusderived is commonly divided by 10 to reduce the size of thenumbers involved; thus

bff

10= 42/10,= 4.2 which is frequently rounded off to 4.


C. Table 2 was made in that manner from Table 1.

TABLE 1. LOBLOLLY PINE GROSS BOARD FOOT VOLUMES(SCRIBNER LOG RULE), SABINE NATIONAL FOREST.

Form Class

DBH Class10111213141516171819202122232425

74

12330384756667688101114128142157174191208

76Height in

1.5314152657793110127144163182203225250274302

77Logs

239526583101119138162186212238266293327362396

79

2.5506888112136163190222254291327368409456503550

80

3537493119144174205239273312351394437488537592

82

3.5

106137166201236279322365410461511570630693

TABLE 2. LOBLOLLY PINE BOARD FOOT FACTORS BY DBH ANDHEIGHT CLASSES, SABINE NATIONAL FOREST.

DBH Class10111213141516171819202122232425

14.24.54.85.15.25.45.45.65.75.85.95.95.96.06.16.1

1.55.76.26.67.07.27.67.98.18.18.38.38.48.58.78.78.9

Height in2

7.27.98.39.09.49.79.9

10.310.510.810.911.111.111.311.511.6

Logs2.59.2

10.311.212.112.713.313.614.114.414.815.015.315.515.816.016.1

39.7

11.211.812.913.514.214.715.215.415.816.116.416.616.917.117.4

3.5

13.514.915.516.416.917.718.218.518.819.219.819.820.120.3

D. A three-step procedure then determines volume per acre frompoint-samples.

1. Tally sample trees by dbh and height at the sample points.

2. For each tree tallied, extract the appropriate Bff from thetable.

3. Sum the Bff's, divide by the number of points, and multiplyby 10 X BAF to obtain board foot volume per acre.

Practical Point-Sampling

E. A suitable tally sheet is shown in Figure 3.


Point-Sample Tally Sheet

21

School of Forestry

DBH

Class

10

II

12

13

14

15

16

17

18

19

20

21

22

23

24

25

Lmft

No. of

1

Points

T

1.5

TYF

ree Height

2

10

in 16 Foot L

2.5

Estimator _

ogs

3

Date

3.5

Figure 3. A tally sheet for use when all point-samples in a line or unit aretallied together as a single unit.

III. The system wherein the sample trees are tallied by dbh class onlysimplifies field work.

A. A local volume table is used without modification.

B. Stand blowup factors, one for each dbh class, are computed asfollows:

BAFStand blowup factor = • ,

BA per treewhere: BA per tree is in square feet,

and BAF is determined by the prism.C. For the 5-inch class and for a 3.03 diopter prism, for instance:

Stand blowup factor = 10/0.1364,= 73.3


D. With the local volume table and the stand blowup factor, to getvolume per acre in each dbh class, multiply sample tree count bystand blowup factor, then multiply that product by volume pertree (Figure 4).

S. F. Austin State Col lege

TALLY SHEET

School of Forestry

FOR POINT SAMPLES ONLY

Llr.e

Poi nt

Type

Est ima tor

DiameterClass

F ie ldTa 1 1 y

5&7S91C1?516182022•2i42628JO

Treesper

Point

StandTab le

BlowupFactor

Treesper

Acre

CubicFoot

Vo 1 LrneB ! owu p

Short leaf Pir.e.

73.370.9

37.1*S3. 622,6

Hi2t ^ o V

9. It7.15.71*.6•;.e3.2?./gi3?.G

l.irfl&^7u.286,09s,te

BeardFoot

Vo ! umeB lowup

S38li.5

11*0.7?0%l281.5353.6Ii8.7

5UB.O66ii.8790.8922.0

CubicFoot

Volumeper

BoardFoot

Vo lumeper

Loblo l ly Pins

5o789

1012m161820222u26

£S^0

Total

73.350.937. i*?8.622.6

17.312.79.1*7.15.71*.63.83.22.72.32.0

l.t*32.6?1*.366.208.69

1*9.382.0

I30jt720^ Ji280.138£*.91*57.7559.0678.1808.691*0.1*

Sawtimber Volume by Scribner Log Rule

Figure 4. A tally sheet for use when point-sample tree dbh only will bemeasured and local volume table employed.

IV. When sample trees are classified by height only, field time is saved.


A. To develop the factors needed for this point-sampling, start witha curve of dbh over height and a standard volume table as, forinstance, Table 1 from which Table 2 could be developed.

B. Then, for each height class from the curve, determine averagedbh, and from Table 2 extract the proper Bff for that height class.

C. If a suitable volume table is not available, derive the factors frombasic data.

D. The necessary tree measurements by height classes will be:

1. Tree volume, and2. Tree dbh.

Note: To show the procedure, Table 3 presents some data fromthe Sabine National Forest.

E. Compute a bff for each height class by dividing average volumeby average BA in each height class (Table 3).

TABLE 3. LOBLOLLY PINE SAWTIMBER TREE MEASUREMENTSFROM SABINE NATIONAL FOREST, 1958 (300 trees)

Ht. Class(feet)12161820222426283032343638404244

Trees( number)

1

3654

1299

192320132313

710

AVK. dbh(inches)

10.39.8

10.710.911.111.411.011.511.911.513.213.512.814.614.215.1

AVK. Vol.(bd. ft. Scrib.)

36.437.946.651.355.861.060.369,478.174.9

107.2115.8110.0149.1143.0176.8

Ht. Class(feet)

464850525456586062646668707276

Total

Trees( number )

211612138

12984455231

300

Avg. dbh Avg. Vol.(inches) (bd. ft. Scrib.)

16.316.816.417.316.716.717.517.720.417.618.117.618.120.119.2

220.0240.1231.3273.0258.9270.6308.4323.8456.5335.9377.7354.6384.6506.8477.9

F. Make a curve of bff over height. This may be done graphically ormathematically. From Table 3 the equation for this line wasy = 15.2 + 2.9x (When y was bff and x was height class).

G. For each height class, take from the curve (or compute by theequation of the curve) the bff.1. The equation from Table 3 gave these:

Ht. Logs~0

0.511.522.5

bff

386285

108131

Ht. Logs33.544.555.5

bff154178201224247270


H. To use these in point-sampling, tally sample trees by height classesand determine the sum of bff by multiplying the number of treesin each class by the appropriate bff.

I. Then compute volume per acre with the equation:

2 bffVol., bd.ft. per acre = (BAF).

no. points

J. Table 4 shows similar basic data and Table 5 the cff's from cubicfoot volumes from the Sabine National Forest.

V. The system where one average factor is used to compute volume inboard feet when sample trees are classified by height only is explainedby Grosenbaugh (1955). Hunt (1961) said that the bff (a numbernormally near 60 for average southern pine timber volumes based onInternational J/4-inch log rule) could be derived from tree height andstock and stand tables usually available.

A. When the bff has been obtained, board foot volume may be computedby the equation:

(ZL)(BAF)(a number near 60)Vol., bd. ft. per acre =

Nwhere N is the number of points, and

2L is the sum of sample tree heights in 16-foot logs atthose points.

B. A suitable field form when using a factor like this is shown inFigure 5, where the bff is 55 for hardwood and 60 for pine, andthe local cord volume factors are given.

Note: Throughout this discussion, bff and board foot volumes generallyhave been used, but cff's are similarly computed.

VI. A cumulative tally sheet using adapted values obtained from a standardvolume table may be preferred in converting point-sample measure-ments into per acre volumes rather than to compute special volumefactors as in II-V, above.

A. The procedure to convert volume per tree into volume per acre:

1. Determine the volume of each tree from a standard volume table.For instance, a 12-inch, 3-log loblolly pine tree in the SabineNational Forest has a gross volume of 93 board feet, ScribnerLog Rule (Table 1).

2. Multiply volume per tree by stand table blowup factor for thediameter class. A 12-inch tree has a factor of 12.7 (Figure 4):93 board feet X 12.7 = 1181.1 board feet per acre.

3. Round this value to the nearest hundred board feet per acre andenter in the cumulative tally sheet (Figure 6). The entries are12, 24, and 35, respectively under 12 inches, 3 logs.

4. In like manner, cubic-foot volume per acre can be employed inthe cumulative tally (Figure 6).


TABLE 4. LOBLOLLY PINE PULPWOOD TREE MEASUREMENTSFROM SABINE NATIONAL FOREST (437 trees).

Ht. Class(feet)

8101214161820222426

Trees( number )

15275453544630342328

Avg. dbh(inches)

4.95.15.45.95.96.56.87.17.57.3

Avg. Vol(cu. ft.)

.951.181.552.062.393.163.794.405.385.55

Ht. Clai(feet)

28303234363840424448

is Trees(number)

721208733211

Avg. dbh(inches)

8.27.98.28.28.59.29.38.49.19.3

Avg. Vol.(cu. ft.)

7.337.318.368.799.95

11.9812.8411.4913.6215.32

TABLE 5. LOBLOLLY PINE CUBIC FOOT VOLUME FACTORS FORPOINT-SAMPLING, FROM THE EQUATION—CFF = 1.98 + 0.65 H.

Merch. Ht.(feet)

08

12162024

Cu. Ft. Factor

7.189.78

12.3814.9817.58

Merch. Ht.(feet)

283236404448

Cu. Ft. Factor

20.1822.7825.3827.9830.5833.18


3, Fo Aus t i n S ta te Co l lege SchooI of Forestry

POINT SAMPLE TALLY SHEET

SIO ID

Figure 5. A tally sheet for use when point-sample tree heights are talliedand a single factor for each product is applied in computingvolume per acre.


CUMULATIVE TAL

Line Point

R u n n i n q o n

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MISCELLANEOUS VOLUME FACTORS

I. Using shortleaf pine tree measurement averages from the Sabine Na-tional Forest, and the procedure illustrated for board feet by Hunt(1961), a cff of 0.7 was computed for use as follows:

(sum tree merch. ht. in feet) (0.7) (BAF)Cubic feet per acre =

number of sample pointsII. Grosenbaugh (1955) offers the following equation for computing south-

ern pine cord volume per acre, using an instrument with BAF = 10:

Volume per acrein roughstacked sum of total tree height in feet of all sample treescords =

(20) (number of sample points)A. If a local factor other than 20 is desired, it can be calculated and

is usually between 18 and 21.

B. The procedure:1. Select several small representative areas.2. On each, measure to determine individual tree BA and total

height in feet.3. Determine sum of (BA X height) for each area.4. Cut the trees into pulpwood; stack and measure cords for each

area.5. Compute the factor for each area with the equation:

sum of [(BA) (height)]Factor =

sum of volume (cords)

III. Grosenbaugh (1955) rewrites his equation so that it may be used forany instrument with a known BAF in sampling southern pines:

Volume per acrein rough (sum total tree hts.) (0.005) (BAF)stacked cords —

number of sample pointsA. This is the same equation as in II, with the BAF inserted and the

values rearranged.

B. If a locally more accurate factor than 0.005 is desired, it may becomputed in the same manner as described for the 20-factor above,except that the right side of the equation is inverted to read:

sum of volume (cords)Factor =

sum of [(BA)(hts.)]IV. Using the procedure in III., and values from yield tables, classes at

Stephen F. Austin State College devised factors for three southernpine species in various localities:

Virginia pine in east Tennessee 0.0047,Longleaf pine in Georgia 0.00524,Shortleaf pine plantation of low form

class in east Tennessee 0.0045.


A. Note that some of these are appreciably different from 0.005, andtherefore a locally derived factor may be of some importance.

V. If we rewrite Grosenbaugh's equation in II., to include the BAF, itbecomes:

Volume per acrein rough (no. trees) (BAF) (avg. total tree ht.)stacked cords = -

(10) (20) (no. sample points)

A. Rearranged, this equation could be shown thus:

Volume per acrein rough (no. trees) (BAF) avg. total tree ht.stacked cords = X .

100(no. sample points) 2i

no. treesB. But (BAF) = BA per acre,

no. pointsso, BA per acre in 100 square feet units X half the average totaltree height = volume per acre in rough stacked cords.

THE STAND TABLE BLOW-UP FACTOR

I. The stand table blow-up factor (S.T.F.) gives the stand table valueswhen multiplied by point-sample tree counts tallied by dbh class at onepoint.

A. Therefore, for each dbh class:Trees per acre = (S.T.F.) (point-sample tree count).

B. A stand table may be made in this manner.

C. In addition, if the count came from N points, the product is dividedby N.

II. The S.T.F. for each dbh class and BAF can be computed by the equa-tion:

BAFS.T.F. =

BA per tree

A. It would be easier to compute for any particular BAF if multiplica-tion by the constant BAF could be performed.

B. This can be accomplished if the equation is changed to:S.T.F. = (BAF) (reciprocal of BA per tree)

C. Table 6 is a list of these reciprocals; the values may be used in theabove equation to produce the appropriate S.T.F.'s for any BAF.


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rH CXI CO Tj< 10CX|


CONSTRUCTING A TABLE OF "LIMITING DISTANCES"

I. A diopter is 1 centimeter of displacement of a light ray at a distanceof 100 centimeters from the optical lens—in our case a prism.

II. A wedge or triangular prism is a piece of optical glass which refractsa light beam the refraction (or deflection) being a factor of the rateof convergence of its non-parallel sides.

A. Therefore, with a 10-BAF prism, which is 3.03 diopters, a 12-inchdbh tree would be on the borderline at 33 feet:

12 X 100= 12 X 33 inches = 33 feet.

3.03

B. By like reasoning, a 12-inch dbh tree viewed through a 20-BAFprism, having- 4.29 diopters, would be borderline at 23.3 feet:

12 X 100= 12 X 23.3 inches = 23.3 feet.

4.29

C. For ease in computation, derive a multiplying factor for inches ofdbh to get the borderline, or limiting distance. For a 10-BAF prism,12 inches of dbh had 33 feet to its borderline and, therefore, the"tree circle" factor is 2.75:

33— = 2.75 the "tree circle" factor.12

D. The "tree circle" factor for a 20-BAF prism is 1.944:

23.3= 1.94

12

E. In like manner, by knowing the BAF of the prism and its diop-ter power, we can calculate the multiplying factor for dbh toconvert to feet for the borderline distance (Hovind and Rieck,1961).

III. Tables 7 through 10 give the borderline distances by tenth-inch dbhclasses for 5-, 10-, 20-, and 37.5-BAF prisms. Actually, by chainingto the center of each tree and measuring its diameter, point-samplingis performed without a prism.


TABLE 7. LIMITING DISTANCES FOR 5-PACTOR PRISMS-HORIZONTAL.

DBH .0 1 .2 .3 .4 .5 .6 .7 .8 .9FEET

567

89

10

1112131415

1617181920

2122232425

2627282930

19.4423.3327.2231.1135.0038.89

42.7846.6750.5654.4558.34

62.2266.1170.0073.8977.78

81.6785.5689.4593.3497.22

101.11105.00108.89112.78116.67

19.8323.27,3135,39,

43,47,5054.58,

62,66.70.7478.

82.85,

,72,61.50.39,28

.17

.06

.95

.83

.72

,61.50.39.28.17

.06,95

89.8493,97,

101,105,

,72.61

50,39

109.28113.117,

17.06

20.2224.1128.0031.8935.7839.67

43.5647.4551.3355.2259.11

63.0066.8970.7874.6778.56

82.4586.3490.2294.1198.00

101.89105.78109.67113.56117.45

20.6124.5028.3932.2836.1740.06

43.9547.8351.7255.6159.50

63.3967.2871.1775.0678.95

82.8486.7290.6194.5098.39

102.28106.17110.06113.95117.84

21.0024.8928.7832.6736.5640.45

44.3348.2252.1156.0059.89

63.7867.6771.5675.4579.34

83.2287.1191.0094.8998.78

102.67106.56110.45114.34118.23

21.3925.2829.1733.0636.9540.83

44.7248.6152.5056.3960.28

64.1768.0671.9575.8479.72

83.6187.5091.3995.2899.17

103.06106.95110.84114.73118.61

21.7825.6729.5633.4537.3341.22

45.1149.0052.8956.7860.67

64.5668.4572.3476.2280.11

84.0087.8991.7895.6799.56

103.45107.34111.23115.11119.00

22.1726.0629.9533.8337.7241.61

45.5049.3953.2857.1761.06

64.9568.8472.7276.6180.50

84.3988.2892.1796.0699.95

103.84107.73111.61115.50119.39

22.5626.4530.3334.2238.1142.00

45.8949.7853.6757.5661.45

65.3569.2273.1177.0080.89

84.7888.6792.5696.45

100.34

104.23108.11112.00115.89119.78

22.9526.8330.7234.6138.5042.39

46.2850.1754.0657.9561.84

65.7269.6173.5077.3981.28

85.1789.0692.9496.84

100.73

104.61108.50112.39116.28120.17

TABLE 8. LIMITING DISTANCES FOR 10-FACTOR PRISMS-HORIZONTAL.

DBH .0 .1 .2 .3 .4 .5 .6 .7 .8 .9FEET

56789

10

1112131415

1617181920

13.7516.5019.2522.0024.7527.50

30.2533.0035.7538.5041.25

44.0046.7549.5052.2555.00

14.0216.7719.5222.2725.0227.77

30.5233.2736.0238.7741.52

44.2747.0249.7752.5255.27

14.3017.0519.8022.5525.3028.05

30.8033.5536.3039.0541.80

44.5547.3050.0552.8055.55

14.5717.3220.0722.8225.5728.32

31.0733.8236.5739.3242.07

44.8247.5750.3253.0755.82

14.8517.6020.3523.1025.8528.60

31.3534.1036.8539.6042.35

45.1047.8550.6053.3556.10

15.1217.8720.6223.3726.1228.87

31.6234.3737.1239.8742.62

45.3748.1250.8753.6256.37

15.4018.1520.9023.6526.4029.15

31.9034.6537.4040.1542.90

45.6548.4051.1553.9056.65

15.6718.4221.1723.9226.6729.42

32.1734.9237.6740.4243.17

45.9248.6751.4254.1756.92

15.9518.7021.4524.2026.9529.70

32.4535.2037.9540.7043.65

46.2048.9551.7054.4557.20

16.2218.9721.7224.4727.2229.97

32.7235.4738.2240.9743.72

46.4749.2251.9754.7257.47


2122232425

2627282930

57.7560.5063.2566.0068.75

71.5074.2577.0079.7582.50

58.0260.7763.5266.2769.02

71.7774.5277.2780.0282.77

58.3061.0563.8066.5569.30

72.0574.8077.5580.3083.05

58.5761.3264.0766.8269.57

72.3275.0777.8280.5783.32

58.8561.6064.3567.1069.85

72.6075.3578.1080.8583.60

59.1261.8764.6267.3770.12

72.8775.6278.3781.1283.87

59.4062.1564.9067.6570.40

73.1575.9078.6581.4084.15

59.6762.4265.1767.9270.67

73.4276.1778.9281.6784.42

59.9562.7065.4568.2070.95

73.7076.4579.2081.9584.70

60.2262.9765.7268.4771.22

73.9776.7279.4782.2284.97

TABLE 9. LIMITING DISTANCES FOR 20-FACTOR PRISMS-HORIZONTAL.

DBH .0 .1 .2 .3 .4 .5 .6 .7 .8 .9FEET

56789

10

1112131415

1617181920

2122232425

2627282930

9.7211.6613.6115.5617.5019.44

21.3923.3425.2827.2229.17

31.1133.0635.0036.9538.89

40.8342.7844.7246.6748.61

50.5652.5054.4556.3958.34

9.9211.8613.8115.7517.6919.64

21.5823.5325.4727.4229.36

31.3133.2535.2037.1439.08

41.0342.9744.9246.8648.81

50.7552.7054.6456.5858.53

10.1112.0614.0015.9417.8919.83

21.7823.7225.6727.6129.56

31.5033.4535.3937.3339.28

41.2243.1745.1147.0649.00

50.9552.8954.8356.7858.72

10.3012.2514.1916.1418.0820.03

21.9723.9225.8627.8129.75

31.7033.6435.5837.5239.47

41.4243.3645.3147.2849.20

51.1453.0855.0356.9758.92

10.5012.4414.3916.3318.2820.22

22.1724.1126.0628.0029.95

31.8933.8335.7837.7239.67

41.6143.5645.5047.4549.39

51.3353.2855.2257.1759.11

10.6912.6414.5816.5318.4720.42

22.3624.3126.2528.2030.14

32.0834.0335.9737.9239.86

41.8043.7545.7047.6449.58

51.5353.4755.4257.3659.31

10.8812.8314.7816.7218.6720.61

22.5624.5026.4528.3930.33

32.2834.2236.1738.1140.06

42.0043.9545.8947.8349.78

51.7253.6755.6157.5659.50

11.0813.0314.9716.9118.8620.81

22.7524.7026.6428.5830.53

32.4734.4236.3638.3140.25

42.2044.1446.0848.0349.97

51.9253.8655.8157.7559.70

11.2813.2215.1717.1119.0621.00

22.9524.8926.8328.7830.72

32.6734.6136.5638.5040.45

42.3944.3346.2848.2250.17

52.1154.0656.0057.9559.89

11.4713.4215.3617.3119.2521.19

23.1425.0827.0328.9730.92

32.8634.8136.7538.7040.64

42.5844.5346.4748.4250.36

52.3154.2556.2058.1460.09


TABLE 10. LIMITING DISTANCES FOR 37.5-FACTOR PRISMS-HORIZONTAL.

DBH .0 .1 .2 .3 .4 .5 .6 .7 .8 .9FEET

56789

10

1112131415

1617181920

2122232425

2627282930

7.138.519.97

11.3512.8014.19

15.6417.0318.4819.8721.32

22.7024.1625.5426.9928.38

29.8331.2232.6734.0635.51

36.8938.3539.7341.1842.57

7.268.65

10.1011.4812.9414.32

15.7717.1618.6120.0021.45

22.8424.2925.6727.1328.51

29.9631.4232.8034.2535.64

37.0938.4839.9341.3242.77

7.398.78

10.2311.6213.0714.45

15.9117.3618.7420.2021.58

23.0324.4225.8727.2628.71

30.1031.5532.9334.3935.77

37.2238.6140.0641.4542.90

7.528.98

10.3611.8113.2014.65

16.0417.4918.8820.3321.71

23.1724.5526.0027.3928.84

30.2331.6833.0734.5235.90

37.3638.7440.1941.5843.03

7.669.11

10.4911.9513.3314.78

16.1717.6219.0120.4621.85

23.3024.6826.1327.5228.94

30.3631.8133.2034.6536.10

37.4938.9440.3341.7843.16

7.799.24

10.6312.0813.4614.92

16.3017.7519.1420.5922.04

23.4324.8826.2727.7229.11

30.5631.9433.4034.7836.23

37.6239.0740.4641.9143.30

7.929.37

10.8212.2113.6615.05

16.5017.8919.3420.7222.18

23.5625.0126.4027.8529.24

30.6932.0833.5334.9136.37

37.7539.2040.5942.0443.43

8.129.50

10.9612.3413.7915.18

16.6318.0219.4720.8622.31

23.6925.1526.5327.9829.37

30.8232.2133.6635.0536.50

37.8839.3440.7942.1743.63

8.259.64

11.0912.4813.9315.31

16.7618.1519.6020.9922.44

23.8325.2826.7328.1229.57

30.9532.4133.7935.2436.63

38.0839.4740.9242.3143.76

8.389.77

11.2212.6114.0615.51

16.9018.3519.7321.1922.57

24.0225.4126.8628.2529.70

31.0932.5433.9235.3836.76

38.2139.6041.0542.4443.89

SLOPE CORRECTIONS IN POINT-SAMPLING

I. Sloping land complicates point-sampling just as it complicates plot-sampling. If slope correction is neglected, the errors will be of sig-nificant magnitude when slope is more than about 10 percent.

A. A slope factor (s.f.) may be easily determined using the averageslope at each point, because:

s.f. = secant of angle of slope.

B. With this factor, point-sample tree counts may be corrected bymerely multiplying:

Corrected count = (tree count) (s.f.)

C. Using this method, the correction can be made for any slope situa-tion although, in some western states, cruisers have encountered agreat deal of difficulty and noted some significant inaccuracies inactual application.

D. Grosenbaugh (1955) gives correction factors for most slopes (Table11). Note the equation at the foot of the table.


II. Slope may be corrected also by rotating the prism through a verticalangle equal to the angle of the slope.

A. Certain prisms are manufactured with a rounded top to facilitateuse in the rotated position.

B. This is perhaps the best solution of the slope problem.

C. It has been used throughout the United States and, in some westernpoint-sampling—wherein the tree is always viewed at the top ofthe first 16-foot log as a hedge against brush-bias—almost everytree is on a slope (Bruce 1961).

TABLE 11. APPROPRIATE CORRECTION FACTORS FOR BA ORVOLUME PER ACRE CALCULATED FROM UNADJUSTED ANGLE-GAUGE TALLIES TAKEN ON A SLOPE, WHERE SLOPE PERCENTIS MEASURED AT RIGHT ANGLES TO CONTOUR.

Limitsof

PercentSlope10.0

17.4

22.5

26.7

30.4

33.6

36.6

39.5

42.1

44.6

47.0

49.3

51.5

53.7

55.8

SlopeCorrection

Factor

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.10

1.11

1.12

1.13

1.14

Limits Slopeof Correction

Percent FactorSlope55.8

57.8

59.8

61.7

63.6

65.4

67.2

69.0

70.8

72.5

74.2

75.8

77.5

79.1

80.7Correction factor for

1 /Slope

\5

1.16

1.17

1.18

1.19

1.20

1.21

1.22

1.23

1.24

1.25

1.26

1.27

1.28

Limitsof

PercentSlope80.7

82.3

83.9

85.4

86.9

88.4

89.9

91.4

92.9

94.3

95.8

97.2

98.7

100.1

101.5

SlopeCorrection

Factor

1.29

1.30

1.31

1.32

1.33

1.34

1.35

1.36

1.37

1.38

1.39

1.40

1.41

1.42

steeper slopes is:

percent >

100 /1

2

Source: Grosenbaugh, L. R. "Better diagnosis and prescription in southernforest management." U. S. Forest Service, Southern Forest Ex-periment Station, Occasional Paper 145, 1955.


CONTINUOUS FOREST INVENTORY WITH POINT-SAMPLING

I. Point-sampling techniques are just as suitable for continuous forestinventory (CFI) as are plot sampling techniques.

A. Point-sampling has the special advantage of taking a smaller per-cent sample of the many small stems in uneven-aged forests, whilesampling the fewer large stems in much the same proportion as infifth-acre plot-sampling.

B. This is illustrated from experience with CFI in the Sabine NationalForest:

DBH Class Number of Trees Tallied—110 Locations1/5-Acre Plots 10-BAF Point Samples

(1957-58) (1962)5 - 9 1782 23910 -14 601 21115 -19 248 18420 - 24 55 5025+ 2 5

II. The techniques of point-sampling, and the resulting calculations, areas convenient for electronic data processing as are the mechanics ofplot-sampling.

A. U. S. Steel in Alabama (University of Georgia, 1959) used point-sampling in its CFI plan and measured six to eight stems at eachpoint. They measured all trees due to the small number at each loca-tion, and thus have a permanent record of trees from seedling-sizeup.

B. The Southern Forest Survey, a large-scale CFI system, now em-ploys point-sampling as its inventory technique. Samples are ona 3 x 3-mile grid. Clusters of ten 37.5-BAF samples are collectedat each survey location.

III. Several problems not attributed to plot-sampling are present whenpoint-samples are used in continuous forest inventory.A. Trees grow into the sample according to their size and distance

from the point, not just according to their size. In other words, a20.0-inch tree 79.34 feet from the point will come into the samplewhen it grows to 20.4 inches dbh, if the sample is being taken witha 5-BAF prism. Since its total volume is not really ingrowth, thevolume per acre and the number of stems per acre it representswill be used for future growth determination, but will not neces-sarily figure in past growth calculations.

B. Unless dbh and distance are both remeasured, omitted or extratrees will severely affect stand and stock table values. In brushyareas, obscured trees may be omitted accidentally in the point-sample.

C. Since a CFI sample is exceedingly small and blowups are large,extreme care must be exercised in taking the CFI point-sample.


GROWTH PROJECTION WITH POINT-SAMPLES

I. Point-sampling can be applied to growth projection studies (Fenderand Brock, 1963) for future volume or basal area as well as to deter-mine actual current volume or basal area.

II. To show the principle involved, in an exceedingly simplified method,trees in a southern pine plantation were bored to determine averageprojected 5-year diameter growth. Using a table of limiting distancesfor the "new" diameters, the projected stand 5 years hence was "tal-lied," giving the following results:

Present FutureCount BA/Acre Count BA/Acre

8 160 9 1809 180 10 2009 180 13 2609 180 10 2006 120 8 160

Average 164 Average 200

NUMBER OF POINTS TO ACHIEVE STATED PRECISION

I. The forester, contemplating a point-sample cruise, must know howits accuracy compares with that of the conventional plot cruise he haspreviously employed. He needs to know the total number of points toobserve on a property of given acreage to yield the required precision.

A. Bruce (1961) says that in western timber, point-sampling requiresabout the same number of points as 1/4- or 1/5-acre plots to achievea stated precision of volume estimate, if the prism is properlymatched to tree size in the stands sampled. This means that countsper point must average about 5 trees.

B. For southern forests, Grosenbaugh (1955) wrote, "The reconnais-sance would require a minimum of about 20 unbiased sample pointswell distributed throughout the record unit for a standard error ofabout ± 25 percent in volume per record unit. A volume total of25 such record-units would have a standard sampling error of onlyabout ± 5 percent for the ownership or working circle as a whole."

C. Bell and Alexander (1957) said, "present experience shows that thesame intensity as that used for one-quarter-acre plots will resultin a stastically better sample than given by the one-quarter acreplot method."

D. Putnam et al. (1960) wrote, "The reconnaissance preceding thefirst managed cut should ordinarily be an inexpensive affair. Aninspection and sight estimate may suffice for experienced men,though a more formal approach will be necessary for most foresters.The point-sampling technique makes it possible to get approximateestimates of volume with very little effort. If a prism or anglegauge with a basal area factor of 10 is employed to select sampletrees, 25 sample points distributed systematically over manage-ment unit will usually give a sampling error for board-foot volume

118854


of less than 23 percent. The aggregate volume on four managementunits will ordinarily be estimated within twelve percent. The goalis not extreme accuracy but rather rough estimates obtained asquickly and cheaply as possible.

"If a more intensive survey is needed, the following tabulation maybe used to obtain approximate and usually conservative samplingerrors as a percent of the total volume.

Points Error(number) (percent)

25 2350 17

100 12200 8400 6

1600 3"For cruises of the specified intensity, differences between samplevolume and volume by 100-percent tally will be exceeded, on theaverage, in only one cruise in three. Five percent of the time, thedifference might be twice the chosen limit, but 50 percent of thetime the difference will be less than 68 percent of the tabulatederror.

"This means, for example, that a cruiser choosing 12 percent as hislimit of sampling error may be wrong by more than this amount onone cruise out of three. In fact, one time in twenty his actual errormay be more than 24 percent, but half the time his error will beless than 8 percent. In the rare cases where a sample of low in-tensity might deviate from the true mean considerably, an ex-perienced cruiser will suspect the lack of representativeness andintensify the sampling accordingly.

"Whether sample points are located systematically or at random,the area of the tract has little effect on the number of points re-quired for a given sampling error. The important thing is thevariability among the aggregate volumes sampled at various points.The tabulation is based on average variation over a large portion ofan entire southern state. Errors may be larger in extremely ir-regular stands and smaller where stands are relatively uniform."

E. Kendall and Sayn-Wittgenstein (1959) said, ". . . The number ofpoint samples required to give a precision equal to that from con-ventional 1/5-acre-plots varied with the type of stand and averaged2 0.o.

NUMBER OF POINT SAMPLES (N) EQUIVALENT TO 1/5-ACREPLOT

(basal area factor = 10)Location Stocking Diameter Modal N

Type of (trees Range Diameter (by randomStand per acre) (inches) (inches) selection)

Eagle Depot even-aged pine 340 1-25 5 3.1Forbes Depot pine-spruce 760 1-14 4 2.3


"Although no detailed time study was undertaken, it is estimatedthat with the relascope, BA was sampled to a given precision inone-half or one-third the time required when 1/5-acre plots wereused. In the tests carried out in the Forbes Depot and Eagle Depotareas in 1957, the number of trees tallied for volume calculationsin the point samples numbered, 1,290, whereas 12,301 were talliedin the corresponding 1/5-acre plots. This is partly due to the factthat with the relascope each tree size is sampled on a land areawhich is proportional to its BA. A greater proportion of largetrees is therefore sampled, and the time consuming measurementof small trees is largely eliminated."

F. For 110 double sample points, the error of BA would be onlyabout ± 3.1 percent and for 110 single points the error would beabout ± 4.5 percent on a pine-hardwood area in the Sabine NationalForest (see page 16).

COMPARING METHODS OF PER ACRE POINT-SAMPLEVOLUME ESTIMATES

I. The School of Forestry, Stephen F. Austin State College, maintains110 permanent continuous forest inventory plots on the Sabine NationalForest, Texas. These were measured in 1957-58 and remeasured in1962. At the time of remeasurement, a point-sample using a 10-BAFprism was made in addition to the fifth-acre plot-sample. As an indi-cation of the various per acre volumes, using various methods andfactors in computation, the following data are presented from ten ofthe 110 point samples. The range of per acre volumes may be less ifdata from the entire array of 110 points were presented (Table 12).

TABLE 12. SUMMARY OF THE FACTORS BY POINTS USED TOCOMPUTE VOLUMES IN VARIOUS WAYS

Point X Bff

212223242526372829210

Saw-timber

(1)27.942.510.820.019.184.030.460.217.338.8

351.0

SbflSaw-

timber(2)

193.0416.8131.2239.2239.2980.2308.8594.4216.0393.6

3712.4

2 LogsSaw-

timber(3)3.58.02.54.54.5

18.56.0

11.54.07.5

70.5

2 Bd. Ft.Saw-

timber(4)

2677.704326.711442.012395.732515.169972.113209.106299.681927.774100.79

38866.32

2 Cu. Ft.PulpTrees

(5)105.552366.048701.001893.298120.813494.318705.422

0541.352450.957

4388.761

2 cffPulpTrees

(6)12.3842.9672.9295.0814.9855.3477.50

049.5247.54

468.02

2 FeetPulpTrees

(7)15.957.1

102.2128.0

18.973.4

100.20

71.162.9

629.7

(1). Using the standard volume table type of approach:

2 bff 351.0Vol. bd. ft. per acre = (BAF) (10) = (10) (10) = 3510.0

N I D


(2). Using the board foot factor per height class method:

2 bff 3712.4Vol. bd. ft. per acre — (BAP) = (10) = 3712.4

N 10

(3). Using the 60 factor and sum of logs method:

(2 L) (60) (BAF) (70.5) (60) (10)Vol. bd. ft. per acre = = = 4320.0

N 10

(4). Using the stand table approach with volume for each d.b.h. class:

2[(T) (S.T.F.) (Vol)] 38,866.32Vol. bd. ft. per acre = = = 3886.6

N 10

(5). Using the stand table method for cubic foot volume of pulpwood:

2[(T) (S.T.F.) (Vol)] 4388.761Vol. cu. ft. per acre = = = 438.9

N 10

(6). Using the c.f.f. for each height class in pulpwood trees:

2 cff 468.02Vol. cu. ft. per acre = (BAF) = (10) = 468.02

N 10

(7). Using the cubic foot factor 0.7052 and merchantable pulp tree height(in feet) method:Vol. cu. ft. per acre =

( 2 H ) (.7052) (BAF) (629.7) (.7052) (10)= = 444.06

10 10

For comparison: 1958 volumes of 10 fifth-acre plots at same location:

410.02 cu. ft. per acre and 4806.8 bd. ft. per acre.

A TEST OF POINT-SAMPLING IN A PLANTATION

I. Whether point-sampling gives adequate results in a plantation is notreadily resolved. The Nacogdoches City Plantation was inventoried in1966 by several methods. The results indicate that point-sampling doesadequately inventory plantations, although the 1/20-acre circular plotsyield basal area and cubic foot volumes which were closer to the 100%tallv than were the Doint-saniDles (Table 13).

TABLE 13. METHODS OF SAMPLING, NACOGDOCHES CITY PLANTATION, 1966.

Inventory Method

100% Stand TableSystematic Point-Sample2

Number of Basal AreaSamples

_20

Systematic 1/20-acre Circular Plot 20Random Point-SampleRandom 1/20-acre CircularRandom 1/20 Row PlotSwinford's Progressive

Point-Sampling1

Systematic 1/20-acre RowSwinford's Progressive

Point-Sampling1

20Plot 20

20

12Plot 20

8

per Acre(sq.ft.)

91.643103.00088.488

108.00091.08299.698

106.66094.356

100.000

ProportionalLimit ofError

(Percent)

none13.37.8

16.06.7

14.9

15.612.4

21.4

crMofBasalArea

none6.8603.4568.6323.0626.807

8.3105.831

10.690

Cubic FeetPer Acre

1960.982229.471835.342359.821899.212073.74

2343.222094.89

2251.18

ProportionalLimit ofError

(Percent)

none13.99.9

16.77.8

14.4

15.713.8

22.8

aMofCubic

Volume

none156.280

90.620196.62074.320

149.54

183.74141.660

256.160

TreesPer

Aero

236254241238243267

264226

236

-sa

£.h_J

0

ftCos

"8.H

Adapted from Swinford (1966).

2A11 systematic samples taken at same locations.


LITERATURE CITED

Bell, J. F. and L. B. Alexander. Application of the variable plot method ofsampling forest stands. Oregon. State Board of Forestry. ResearchNote. No. 30. 1957.

Bruce, Donald. Prism cruising in the western United States and volumetables for use therewith. Mason, Bruce and Girard, Consulting For-esters, Portland, Oregon. 1961.

Dixon, R. M. Point sampling, wedge prisms and their application in forestinventories. Ontario Department of Lands and Forests. 1958.

Fender, Darwin E. and Gerald A. Brock. Point center extension: a tech-nique for measuring current economic growth and yield of merchantableforest stands. Journal of Forestry 61: 109-114. 1963.

Grosenbaugh, L. R. Plotless timber estimates . . . new, fast, easy. Journalof Forestry 50: 32-37. 1952.

Grosenbaugh, L. R. Shortcuts for cruisers and sealers. U. S. Forest Serv-ice. Southern Forest Experiment Station. Occasional Paper 126. 1952a.

Grosenbaugh, L. R. Better diagnosis and prescription in southern forestmanagement. U. S. Forest Service. Southern Forest Experiment Sta-tion. Occasional Paper 145. 1955.

Hovind, H. J. and C. E. Rieck. Basal area and point sampling WisconsinConservation Department. Technical Bulletin 23. 1961.

Hunt, Ellis V., Jr. Need a reliable point sampling board foot factor?—Lookin your files. Journal of Forestry 59: 512-513. 1961.

Kendall, R. H. and L. Sayn-Wittgenstein. An evaluation of the relascope.Canada Dept. of Northern Affairs and Natural Resources. Forest Re-search Division. Technical Note 77. 1959.

Putnam, J. A., et al. Management and inventory of southern hardwoods.U. S. Department of Agriculture. Agriculture Handbook No. 181: p. 83.1960.

Swinford, Kenneth R. Plantation measurements. Proceedings of 15th annualForestry Symposium, Louisiana State University, p. 136-162. 1966.

University of Georgia. Continuous inventory control in forest manage-ment, short course proceedings. Athens, Georgia. May 4-8, 1959.


ABBREVIATIONS

BA basal areaBAP basal area factorbff board foot factorBff modified board foot factorC coefficient of variationCFI continuous forest inventorycff cubic foot factord distance between target and prismD tree diameter in inchesdbh or DBH diameter at breast heightf frequencyP tree total height in 10 foot unitsH total height of tree in feetht. heightL merchantable height of trees in 16-foot logsM meanN number of points or observationsPie. proportional limit of errorS sampling error of a mean in percentSe. combined sampling error in percents.f. slope factorS.T.F. stand table blowup factorT tree count in a diameter classV variancew target width, or distance between pinsS sum ofa standard deviationo-m standard error of the mean

FORESTRY BULLETINS, Stephen F. Austin State College

1. References of Value in Studies of Insects Affecting the Southern Pines,an Annotated List, by R. C. Thatcher. 1957.

2. Directory of Wood-using and Related Industries in East Texas, by N. T.Samson. 1957. (Out of print.)

3. Bibliography of Forestry Films and Filmstrips, by N. T. Samson. 1958.(Out of print.)

4. Root Development of Loblolly Pine Seedlings in Modified Environments,by M. V. Bilan. 1960.

5. Continuous Forest Inventory with Punched Card Machines for a SmallProperty, by R. D. Baker and E. V. Hunt, Jr. 1960.

6. Point-sampling from Two Angles, by E. V. Hunt, Jr., R. D. Baker andL. A. Biskamp. 1964. (Out of print.)

7. Films and Filmstrips on Forestry, by N. T. Samson. 1965.8. Soil Moisture and Soil Temperature under a Post Oak-Shortleaf Pine

Stand, by G. Schneider and J. J. Stransky. 1966.9. Silviculture of Shortleaf Pine, by L. C. Walker and H. V. Wiant, Jr.

1966. Price $1.10. Texas Pulpwood Production, by N. T. Samson. 1966.11. Silviculture of Longleaf Pine, by L. C. Walker and H. V. Wiant, Jr.

1966. Price $1.12. Pine Seedling Survival and Growth Response to Soils of the Texas

Post-oak Belt, by M. V. Bilan and J. J. Stransky. 1966.13. Directory of Wood-using and Related Industries in East Texas, by

N. T. Samson. 1966. Price $2.14. Practical Point Sampling, by E. V. Hunt, Jr. and R. D. Baker. 1967.

Price $1.

forestry bulletin no 14 practical point sampling

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