Kozak, A., and Omule, S. A. Y. 1902. Estimating stump volume, stump inside bark diameter
and diameter at breast height from stump measurements. Forestry Chmn. 68:623-627.
Ojasvi, P. R., Ramm, C. W., Lantagne, D. 0..and Bruggink, J. 1991. Stump diameter and
DBH relationships for white oak and black oak in the Lower Peninsula of Michigan.
Can. J. For. Res. 21: 1596-1600.
McClure, J. P.,Cost, N. D., and Knight, H. A. 1979. Multiresource inventories-A new concept for forest survey. US. Forest Sent, Southeast. Forest Expt. Sta., Res. PaperSE-191.
68 PP.
Reams. G. A., and Van Deusen, P. C. 1999. The southern annual forest inventory system.
J. Agric., Biol., and Env. Stat. 4:346-360.
Reams, G. A., Roesch. F. A., and Cost, N. D. 1999. Annual forest inventory: Cornerstone
of sustainability in the South. J. Forestry 97(12):21-26.
Roesch, F. A., and Reams, G. A. 1999. Analytical alternatives for an annual inventory system. J. Forestry 97(12):33-37.
Scott, C. T., Kohl, M., and Schnellbkher, H. J. 1999. A comparison of periodic and annual
forest surveys. Forest Sci. 45:43345 1.
Schlieter, J. A. 1986. Estimation of diameter at breast height from stump diameter for lodgepole pine. US. Forest Serv., Intermountain Research Sta., Res. Note INT-359.4 pp.
Stage. A. R., and Alley, J. R. 1972. An inventory design using stand examinations for planning and programming timber management. U.S. Forest Serv., Intermountain Forest
Expt. Sta., Res. Paper INT- 126. 17 pp.
U.S. Department of Agriculture. 1958. Measuring and marketing farm timber. Farmers'
Bull. 1210, U.S. Forest Service, Washington, D.C. 33 pp.
. 1982. Forest Service resource inventory: An overview. U.S. Forest Sent, Forest
Resources Economics Research Stafi Washington. D.C. 22 pp.
Van Deusen, J. L. 1975. Estimating breast height diameters from stump diameters for Black
Hills ponderosa pine. U.S. Forest Serv.. Rocky MI. Forest and Range Expt. Sta., Res.
Note RM-283.3 pp.
Warton, E. H. 1984. Predicting diameter at breast height from stump diameters for northeastem tree species. U.S. Forest S e n , Northeast. Forest Expt. Sta., Res. Note NE-322.4 pp.
Wildman, W. D., Oderwald, R. G., Boucher, B. A.. and Helm, A. C. 1997. Hand-held field
computers and inventory software-Weighing costs and benefits. Tlre Compiler
15(1):28-30.
CHAPTER
10
INVENTORIES WITH SAMPLE
STRIPS OR PLOTS
10-1 Fixed-Area Sampling Units Many forest inventories are carried out
using fixed-area sampling units. These fixed-area sampling units are called strips
or plots, depending on their dimensions. Sample plots can be any shape (e.g.,
square, rectangular, circular, or triangular); however, square- and circular-plot
shapes are most commonly employed. A strip can be thought of as a rectangular
plot whose length is many times its width.
When employing sample plots or strips, the likelihood of selecting trees of a
given size for measurement is dependent on thefrequency with which that tree size
occurs in the stand. That is, strip and plot inventories are methods of selecting
sample trees with probability proportional to frequency. Within the sample area
defined by the strips or plots, individual trees are tallied in terms of the characteristics to be assessed, such as species, dbh, and height. Then the sample-area tallies
are expanded to a per-unit-area basis by applying an appropriate expansion factor.
STRIP SYSTEM OF CRUISING
10-2 Strip-Cruise Layout With this system, sample areas take the form of
continuous strips of uniform width that are established through the forest at equally
spaced intervals, such as 5, 10, or 20 chains. The sample strip itself is usually
212
CHAPTER 10: INVENTORIES WITH SAMPLE STRIPS OA PLOTS
STRIP WIDTH
The computation of cruise intensity and expansion factor can be expressed in
formula form. If W = strip width, D = distance between strip centerlines, and W
and D are in the same units, then nominal cruise intensity (I)in percent equals
BETWEEN STRIPS
It is important to remember that nominal cruise percent and actual cruise percent
are seldom equal because timbered tracts generally are not perfectly rectangular
in shape. The actual cruise percentage can be calculated as
0
500
FEET
1000
FIGURE 10-1
Diagrammatic plan for a 20 percent systematic strip cruise. Sample strips 1 chain wide are
spaced at regular intervals of 5 chains.
Area in sample
Total tract area
In this calculation, area in sample and total tract area must be in the same units.
To convert sample volume to total tract volume, one computes the expansion,
or blow-up, factor (EF) as
TABLE 10-1
EXAMPLE OF CRUISING INTENSITIES FOR
1-CHAIN SAMPLE STRIP WIDTHS
Distance between
strip centedines
Nominal
No. of strips
cruise
ft
chains
per "forty"
percent
1 chain wide, although it may be narrowed to %chainin dense stands of young timber or increased to 2 chains and wider in scattered, old-growth sawtimber. Strips
are commonly run straight through the tract in a north-south or east-west direction,
preferably oriented to cross topography and drainage at right angles (Fig. 10- 1). By
this technique, all soil types and timber conditions from ridge top to valley floor are
theoretically intersected to provide a representative sample tally.
Strip cruises are usually organized to sample a predetermined percentage of the
forest area. One-chain sample strips spaced 10 chains apart provide a nominal 10
percent estimate, and %-chain strips at 20-chain intervals produce a nominal 2%
percent cruise (Table 10- 1). The conversion factor to expand sample volume to total volume may be derived by ( I ) dividing the cruising percentage into 100 or
(2) dividing the total tract acreage by the number of acres sampled.
EF
=
100
cruise percent
In the computation of the expansion factor, the cruise percent should be the actual,
not the nominal, percent. Alternatively, the expansion factor can be computed as
total tract arealarea in sample. The estimate of total volume for the entire tract is
obtained by multiplying volume tallied in all the sample strips times the expansion
factor.
10-3 Computing Tract Acreage from Sample Strips If the boundaries of a
tract are well-established, but the total area is unknown, a fixed cruising percentage may be decided upon. and the tract area can be estimated from the total
chainage of strips composing the sample. A 5 percent cruise utilizing strips I chain
wide spaced at 20-chain intervals provides a good example. The centerline of the
first sample strip is offset 10 chains from one corner of the tract (i.e., one-half the
planned interval between lines), and parallel strips are alternately run 20 chains
apart until the entire area has been traversed by a pattern similar to that shown in
Figure 10-I. If 132 lineal chains of sample strips are required, the area sampled is
(1 32 X 1)/10 = 13.2 acres. Because the strips were spaced for a 5 percent estimate.
the total tract area is approximately 20 X 13.2, or 264 acres. The expansion fact01
of 20 is also used to convert the sampled timber volume to total tract volume.
When trees are tallied according to forest types and acreages are desired for each
type encountered, the preceding technique may also be used to develop these breakdowns. If the 132 lineal chains of strip were made up of 90 chains intersecting ;!
LHHPItH IU: lrvvtl4lunlts
coniferous type and 42 chains intersecting a hardwood type, sampled areas would
be 9 and 4.2 acres, respectively. Applying the expansion factor of 20 would result
in estimated areas of 180 acres for conifers and 84 acres for hardwoods. Although
this procedure does not necessarily provide exact values, it generally gives a reasonably good indication of the relative proportions by types.
vrl~ri
at+lvlrLca~rllra
u r t I L U I ~
LI-J
2 In comparison with a plot cruise of the same intensity, strips have fewer borderline trees, because the total perimeter of the sample is usually sma1li.i.
3 With two persons working together, there is less risk to personnel in remote
or hazardous regions.
Disadvantages of strip cruising are as follows:
10-4 Field Pmcedure for Strip Cruising Accurate determination of strip
lengths and centerlines on the ground requires that distances be chained rather than
paced; thus a two-person crew is needed for reliable fieldwork. One person locates the
centerline with a hand or staff compass and also serves as head chainman; the other
cruises the timber on the sample strip and acts as rear chainman. Either person may
handle the tree tally, depending on underbrush and density of the timber. The width of
the sample strip is ordinarily checked by occasional pacing from the 2-chain tape being dragged along as a moving centerline. Trailer tapes may be used where slope corrections are necessary. When offsetting between strip centerlines, it is important that
the distance be carefully measured perpendicularly to the orientation of the strips.
Because many timbered tracts have irregular borders, it is also important to "square
off" the ends of strips so that the strip area can be computed easily as a rectangle.
In an efficient cruising party, the compassman is always 1 to I X chains ahead
of the cruiser, and the sampling progresses in a smooth. continuous fashion.
Experienced cruisers learn to "size up" tree heights well ahead, because there is a
tendency toward underestimation when standing directly under a tree. At the end
of each cruise line, the strip chainage should be recorded to the nearest link. Strip
cruising can be speeded up appreciably by tallying tree diameters only and determining timber volumes from single-entry volume equations.
When timber type maps are prepared as cruising progresses, strips are preferably
spaced no more than 10 chains apart. There are few forest stands where the cruiser
can map more than 5 chains to either side of the centerline without having to make
frequent side checks to verify the trends of type boundaries, streams, trails, or fence
lines. The preferred technique for mapping is to sketch cruise lines directly on a recent aerial photograph; approximate type lines and drainage can also be interpreted
in advance of fieldwork. Then, during the conduct of fieldwork, type lines can be
verified and cover types correctly identified with the photographs in hand.
10-5 Pros and Cons of Strip Cruising The strip system of cruising is not as
popular as in previous years. Its loss of favor is probably because two-person
crews are needed and volume estimates are difficult to analyze statistically unless
the tally is separated every few chains (resulting in a series of contiguous rectangular plots). In addition to items cited previously, the principal advantages claimed
for strip cruising are
1 Sampling is continuous, and less time is wasted in traveling between strips
than would be the case for a plot cruise of equal intensity.
1 Errors are easily incurred through inaccurate estimation of strip width. Since
the cruiser is constantly walking while tallying, there is little incentive to leave the
centerline of the strip to check borderline trees.
2 Unless tree heights are checked at a considerable distance from the bases of
trees, they may be easily underestimated.
3 Brush and windfalls are more of a hindrance to the strip cruiser than to the
plot cruiser.
4 It is difficult to make spot checks of the cruise results because the strip centerline is rarely marked on the ground.
LINE-PLOT SYSTEM OF CRUISING
10-6 The Traditional Approach As the name implies, line-plot cruising
consists of a systematic tally of timber on a series of plots that are arranged in a
rectangular or square grid pattern. Compass lines are established at uniform spacings, and plots of equal area are located at predetermined intervals along these
lines. Plots are usually circular in shape, but they may also take the form of
squares, rectangles, or triangles. In the United States, %- and Kacre circular plots
are most commonly employed for sawtimber tallies; smaller plots are preferred for
cruising poletimber or sapling stands. For inventories where a wide variety of timber sizes will be encountered, it is often efficient to use concentric circular plots
with each centered at the same point. As an example, %-acreplots might be used
to tally sawtimber trees, XO-acreplots for pulpwood trees, and Xm-acre plots for
regeneration counts. Radii for circular plots frequently used in timber inventory
are given in Table 10-2.
As with the strip method, systematic line-plot inventories are often planned on
a percent cruise bdsis. In Figure 10-2, for example, %-acreplots are spaced at intervals of 4 chains on cruise lines that are 5 chains apart. As each plot "represents"
an area of 20 square chains, the nominal cruising percentage is computed as
Plot size in acres
Acres represented
0.2 acres
2 acres
x 100 = ---- x 100 = 10 percent
By the same token. 10 percent estimates may also be accomplished by spacing the
same %-acreplots at intervals of 2% x 8 chains, 2 X 10 chains, and so on. If a
1:I square grid arrangement is desired, the intervals between both plot centers and
W ~ H TI
TABLE 10-2
RADII FOR SEVERAL SIZES OF CIRCULAR SAMPLE PLOTS
Plot size
(acre)
Plot radius
(fi)
Plot size
(ha3
Plot radius
(m)
1
%
!A
!4
'Xo
'A
'A
xo
K
Xa
IAm
'Xm
tn
IU.
11qvt 1 4 I units vvl I H SAMPLt
S 1 HIPS OR PLOTS
21 7
compass lines would be calculated as d% square chains. or 4.47 X 4.47 chains.
Similar computations can be made for other plot sizes and cruising intensities. Cruise
expansion factors are calculated by the same methods described for strip cruises.
The number and spacing of plots for line-plot cruises can be expressed in formula form; in order to express the desired relationships algebraically, the following symbols (after Burkhart, Barrett, and Lund, 1984) are defined:
A = total tract area,
A, = area of all plots,
P = APIA = intensity of cruise as a decimal,
a = area of one plot,
n
L
B
=
=
=
number of plots,
distance between lines,
distance between plots on a line,
'Xm
FIGURE 10-2
Diagrammaticplan for a 10 percent systematic line-plot cruise utilizing X-acre circular
sampling units.
where A, A,, and a are all in square units of L and B. When line plot cruises are
designed on a percentage basis, P is specified. Assuming that the total area of the
tract being inventoried is known, the area of the sample is
The plot size (a) is specified in advance, thus the number of plots (n) needed is
Next. one must determine how to space the plots. If B and L are in chains and A,
A,, and a are in acres, then
That is, each sample plot of "a" acres represents an area BL 1 10 acres (there are
10 square chains per acre). The expression for P can be algebraically rearranged
as
218
CHAP I t H 10: INVENIOHltS W I I H SAMPLt S I HIPS OH PLOIS
CHAPTER 10: INVENTORIES WITH SAMPLE STRIPS OR PLOTS
Thus, if either B or L (as well as P) is specified, the other can be computed readily. For square spacing (that is, B = L), we have
i! I U
and the estimated volume per acre is
The reliability of the estimated mean is indicated by the magnitude of the standard
error of the mean and the width of the computed confidence interval. Although
line-plot cruises are systematic samples, and thus precision can only be approximated, the standard error of the mean is generally estimated using the formula for
simple random sampling (Sec. 3-4), namely
and
To design a 10 percent line-plot cruise for an 86-acre tract using X-acre sample
plots, the sample area is computed as
A, = AP = 86(0.1) = 8.6 acres
Next, the number of plots needed is computed as
where s2 = variance among individual sampling units
n = sample size (15 in this case)
N = population size (expressed in number of sampling units or
(34)(5) = 170 in this illustration)
If the distance between lines (L) is specified to be 5 chains, then the distance between plots on lines will be
For this example, the variance. s2,is computed as
B = -a-( l-0-)
LP
-
0.2(10) - 4 chains
5(0.1)
SL
=
-
n - l
= 26,997
14
Figure 10-2 shows a line-plot cruise utilizing %-acreplots spaced 5 by 4 chains.
and the standard error of the mean is
10-7 -PlotCruise Example For purposes of illustration, it may be assumed that
a line-plot cruise was performed using X-acre plots on a 34-acre tract. Fifteen plots were
established, and the volume per plot was computed for each with the following result:
Plot
Volume
(ffl0.2 acre)
Plot
Volume
(ft3/0.2 acre)
Plot
Volume
(ft3/0.2 acre)
SF =
=
40.5 ft3/0.2 acre or 202.5 ft3/acre
The 95 percent confidence interval for the mean on a per acre basis is established as
The estimated mean volume per plot is
y=
C y i - 7,740
n - - - 15 - 5 16 ft3/0.2 acre
10-8 Sampling Intensity and Design The intensity of plot sampling is governed by the variability of the stand, allowable inventory costs, and desired standards of precition. The coefficient of variation in volume per unit area should first
be estimated, either on the basis of existing stand records or by measuring a preliminary field sample of, perhaps. 10 to 30 plots. Then the proper sampling intensity can be. calculated by the procedures outlined in Chapter 3.
The trend is away from the concept of fixed cruising percentages, for it is not the
sampling fraction that is important; it is the number of sampling units (of a specified
kind) needed to produce estimates with a specified precision. In the final analysis,
the best endorsement for a given plot size and sampling intensity is an unbiased estimate of stand volume that is bracketed by acceptable confidence limits.
In addition to determining the sampling intensity, it is necessary to decide on
the sampling design, that is, the method of selecting the nonoverlapping plots for
field measurement. When sample plots are employed, the sampling frame is defined as a listing of all possible plots that may be. drawn from the specified (finite)
population or tract of land. The sample plots to be. visited on the ground can be selected randomly from such a listing.
In spite of the statistical difficulties associated with systematic sampling designs, such cruises are still employed frequently. Where estimates of sampling precision are regarded as unnecessary, systematic sampling may provide a useful
alternative to random sampling methods.
10-9 Cruising Techniques Circular-plot inventories are often handled by
one person, but two or three persons can be used efficiently when square or rectangular plots are employed. Field directions are established with a hand or staff
compass, and intervals between sample plots may be either taped or paced. The
exact location of plot centers is unimportant, provided the centers are established
in an unbiased manner. When "check cruises" are to be made, plot centers or corners should be marked with stakes, with cairns, or by reference to scribed trees.
With square or rectangular plots, the four comer stakes make it a simple matter
todetermine which trees are inside the plot boundaries. However, with circular plots,
inaccurate estimation of the plot radii is a common source of error. As a minimum.
four radii should be. measured to establish the sample perimeter. If an ordinary chaining pin is canied to denote plot centers, a tape can be. tied to the pin for one-person
checks of plot radii. When trees appear to be borderline, the center of the stem (pith)
determines whether they are "in" or "out." For plots on sloping ground, one must be.
careful to measure horizontal (not slope) distances when checking plot boundaries.
Inaccurate estimation of plot radii is one of the greatest sources of error in using circular samples. The gravity of such errors is exemplified by a 2% percent
cruise; every stem erroneously tallied or ignored has its volume expanded
40 times. Thus the failure to include one tree having a volume of 300 bd ft will result in a final estimate that is 12,000 bd ft too low.
Separate tally sheets are recommended for each plot location and species; descriptive plot data can be handwritten or designated by special numerical codes. It
is usually most efficient to begin the tally at a natural stand opening (or due north)
and record trees in a clockwise sweep around the plot. When the tally is com-
pleted, a quick stem count made from the opposite direction provides a valuable
check on the number of trees sampled.
10-10 Boundary Overlap A probleni arises when a plot does not lie wholly
within the area being sampled. This problem, commonly referred to as edge-effect
bias or boro~daryo\,erlap, can introduce a bias in the plot cruise statistics if it is
not treated properly. When large areas are cruised with small circular plots, the
bias due to boundary overlap is usually negligible. However, for small areas, especially long, narrow tracts with a high proportion of edge trees, appropriate precautions should be taken to guard against bias caused by boundary overlap.
One method of dealing with the boundary-overlap problem is to move plot tenters (back on the line of travel in the case of line-plot cruises) until the entire plot
lies in the area being sampled. This method is generally satisfactory if the timber
along the edge is similar to that in the remainder of the tract, but it is not likely to
be suitable for small woodlots that have edges strikingly different from the tract
interior. Adjustment of the plot-center location may introduce bias because the
trees in the edge z.one may he undersampled.
In a cruise of small tracts with a high proportion of "edge," a procedure for
dealing with boundary overlap should be adopted. The mirage method developed
by Schmid in 1969 and described by Beers (1977) and others in the American
forestry literature is a simple and, for most situations, easily applied technique.
When the plot center falls near the stand boundary so that the plot is not completely within the tract being sampled, the cruiser measures the distance D from
plot center to the boundary. A correction-plot center is then established by going
this distance D beyond the boundary. All trees in the overlap of the original plot
and the correction plot are tallied twice (Fig. 10-3).
Similar boundary-overlap prohlems arise when volume estirnntes are being
summarized hy different types and a sample plot happens to fall at a transition line
that divides two types. If the cruise estimate is to be summarized by types and
FIGURE 10-3
The mirage method for correction of boundary-overlap bias when circular plots are used.
Trees in the shaded area are tallied twice.
FORESTED AREA OF CONCERN
TRACT BOUNDARY
D
t
CORRECTION PLOT CENTER
OUTSIDE CRUISE AREA
222
CHAPTER 10: INVENTORIES WITH SAMPLE STRIPS OR PLOTS
expansion factors for each type (including nonforest areas) are determined, the
plot should be moved until it falls entirely within the type indicated by its original
center location, or a boundary-overlap correction, such as the mirage method,
should be applied.
In contrast to the foregoing, plots should not be shifted if a single area expansion
factor is to be used for deriving total tract volumes. Under these conditions, edge effects, type transition zones, and stand openings are typically part of the population;
therefore, a representative sample would be expected to result in occasional plots
that are part sawtimber and part seedlings-or half-timbered and half-cutover land.
To arbitrarily move these plot locations would result in a biased sample.
10-11 Merits of the Plot System The principal advantages claimed for lineplot cruising over the strip system are as follows:
1 The system is suitable for one-person cruising.
2 Cruisers are not hindered by brush and windfalls as in strip cruising, for they
do not have to tally trees while following a compass line.
3 A pause at each plot center allows the cruiser more time for checking stem
dimensions, borderline trees, and defective timber.
4 The tree tally is separated for each plot, thus permitting quick summaries of
data by timber types, stand sizes, or area condition classes.
USE OF PERMANENT SAMPLE PLOTS
10-12 Criteria for Inventory Plots The periodic remeasurement of permanent sample plots is statistically superior to successive independent inventories for
evaluating changes in forest conditions. When independent surveys are repeated,
the sampling errors of both inventories must be considered in assessing stand differences or changes over time. But when identical sample plots are remeasured,
sampling errors relating to such differences are apt to be lower; that is, the precision of "change estimates" is improved. In addition, trees initially sampled but absent at a later remeasurement can be classified as to the cause of removal (e.g..
harvested yield, natural mortality, and so on).
Regardless of whether temporary or permanent sampling units are employed
for an inventory, two basic criteria must be met: the field plots must be representative of the forest area for which inferences are made, and they must be subjected
to the same treatments as the nonsampled portion of the forest. If these conditions
are not fully achieved, inferences drawn from such sampling units will be of questionable utility.
One attempt to ensure that sampling units are representative of equal forest areas is illustrated by some rigid continuous forest inventory (CFI) procedures
whereby field plots are systematically arranged on a square grid basis; thus each
plot represents a fixed and equal proportion of the total forest area. However, such
r
CHAP I t~ 10: I N V ~ IN
U H I VVI
~ I~H bHMPLk b~Htrb OH r L v I b
ZLJ
sampling designs tend to be inflexible in meeting the changing requirements of
management and therefore are not recommended for most forest inventories. Even
though systematic samples are sometimes quite efficient, especially from the
viewpoint of reducing field travel time, it is generally better to use other methods
of sampling that will permit calculation of the reliability of sample estimates.
10-13 Sampling Units: Size, Shape, and Number Circular sample plots of
!4 acre have been widely used for CFI systems in the past. Nevertheless, square or
rectangular plots may be more efficient because the establishment of four comer
stakes, however inconspicuously, improves the chances for plot relocation at a
later date. Depending on the size and variability of timber stands, an ideal plot size
for second-growth forests will generally fall in the range of X to % acre.
As outlined previously, the number of permanent sample plots to be established
and measured is dependent on the variability of the quantity being assessed and
the desired sampling precision. For tracts of 50,000 to 100,000acres, sampling errors of I0 to 20 percent might be desired for current volume, with 2 2 0 to 30 percent being accepted for growth (probability level of 0.95). If this precision is
maintained on parcels of 50,000 to 100,000 acres, the overall precision for an entire forest holding of 1 to 3 million acres should be approximately f2 to 3 percent
for current volume and 2 5 percent for growth.
+
10-14 Field-Plot Establishment Increasingly, global positioning systems
(Chap. 4) are being used to establish the locations of permanent field plots. If
global positioning systems are not available, recent aerial photographs and topographic maps are invaluable aids for the initial location, establishment, and relocation of permanent sample plots. All pertinent data relative to bearings of
approach lines, distances, and reference points or monuments should be recorded
on a plot-location sheet and on the back of the appropriate aerial photograph. It is
essential that such information be complete and coherent because subsequent plot
relocations are often made by entirely different field crews.
Plot centers or comer stakes are preferably inconspicuous and are referenced
by using a permanent landmark at least 100 to 300 ft distant and by recording bearings and distances to two or more scribed or tagged "witness trees" that are nearer
(but not within) the plot. There is some disagreement as to whether permanent
plots should be marked ( I ) conspicuously, so that they can be easily relocated, or
(2) inconspicuously, to ensure that they are accorded the same treatment as nonsampled portions of the forest. The trend is toward essentially "hidden plots." for
it is mandatory that :hey be subjected to e.ract1~the same conditions or treatments
as the surrounding forest, whether this be stand improvement, harvesting, fires,
floods. or insect and disease infestations. Only under these conditions can i t be assumed that the sample plots are representative.
Small sections of welding rods, projecting perhaps 6 to 12 in. above ground level,
are useful for plot comer stakes. Where it becomes feasible to use more massive iron
- a .
stakes, it may be possible to find them again with a "dip needle" or other magnetic
detection devices. If individual trees on the plot are marked at all, the preferable
method is to nail numbered metal tags into the stumps near ground level so that they
will not be noticeable to timber markers and other forest workers. As an alternative
to tagging the sample trees, individual stem locations may be numbered and mapped
by coordinate positions on a plotdiagram sheet.
10-15 Field-Plot Measurements The inventory forester in charge of the
permanent plot system should assume the responsibility for training field crews
and for deciding how measurements should be taken on each sample plot.
Standardized field procedures are emphasized because consistency in measurement techniques is as important as precision for evaluating changes over time.
To avoid problems arising from periodic variations in tree merchantability standards, field measurements should be planned so that tree volumes are expressed
in terms of cubic measure (inside bark) for the entire stem, including stump and
top. It may also be necessary to estimate the volume of branch wood on some operations. Techniques for predicting merchantable volumes for various portions of
trees are given in Chapter 8.
The field information collected for each sampling unit is recorded under one of
two categories: plot description data and individual tree data. The exact measurements required will differ for each inventory system; thus the following listings
merely include examples of the data that may be required:
Plot data
Individual tree data
Plot number and location
Date of measurement
Forest cover type
Stand size and condition
Stand age
Stocking or density class
Site index
Slope or topography
Soil classification
Understory vegetation
Treatments needed
Tree number
Species
dbh
Total height
Merchantable stem lengths
Form or upper-stem diameters
Crown class
Treequality class
Vigor
Diameter growth
Mortality (and cause)
All field measurement data are numerically coded and recorded on tally forms
or directly onto a machine-readable medium for computer processing. Plot inventories are preferably made immediately after a growing season and prior to heavy
snowfall. For tracts smaller than 100,000acres, it may be possible to establish all
plots in a single season and remeasure them within similar time limitations. On
larger areas, fieldwork may be conducted each fall on a rotation system that reinventories about one-fifth of the forest each year.
".
i.....
..--
. . 1 1 .
-.,,.I,
L L U I , , , , U
" 1 I I
L U I V
LLJ
10-16 Periodic Reinventories Permanent sample plots are commonly remeasured at intervals of 3 to 10 years, depending on timber growth rates, expected
changes in stand conditions, and the intensity of management. The interval must be
long enough to permit a measurable degree of change, but short enough so that a
fair proportion of the trees originally measured will be present for remeasurement.
At each reinventory, trees that have attained the minimum diameter during the
measurement interval are tallied as ingrowth. Also, felling records are kept to correct yields for those plots cut during the measurement interval. This information,
along with mortality estimates, is essential for the prediction of future stand yields.
The data needed to calculate volume growth include stand tables prepared from
two consecutive inventories, felling records, mortality estimates, and a volumeprediction equation that is applicable to the previous and present stands. First, the
stand tables for the two inventories are converted to corresponding stock tables;
then, the difference in volume, after accounting for harvested yields and mortality, represents the growth of the plot.
One of the problems facing field crews who must remeasure permanent sampling units is that of finding the plots. Difficulties with relocating plots can be
greatly reduced with global positioning systems technology, but there are still
many permanent plot installations without GPS coordinates. When plots are inconspicuously marked, relocation time can make up a sizable proportion of the total time allotted for reinventories. A study conducted by Nyssonen (1967) in
Norway revealed that, after a 7-year interval, 4 to 8 percent of the permanent sample plots could not be found again. Where plots could be relocated, the time required for transportation, relocation (which was done without the aid of GPS), and
measurement was distributed as follows:
Activity
Transport by a vehicle
Walking to, between, and from the plots
Searching for the plots
Sample plot measurement
Pauses
Total
Percent of
total time
20.6
22.6
12.9
35.7
8.2
100.0
Even though time factors will obviously differ for every inventory system, the
foregoing tabulation serves to illustrate some of the nonproductive aspects that
should be recognized in the application of permanent plot-inventory systems.
REGENERATION SURVEYS WITH SAMPLE PLOTS
10-17 Need for Regeneration Surveys Evaluations of forest regeneration
efforts are of critical importance in on-the-ground forest management.
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PROBLEMS
10-1 Compute the nominal cruising percents and expansion factors for the following systematic samples:
a Strips H chain wide spaced 10 chains apart
b Four I -chain strips run through a quarter section of land
c Plots of 50acre spaced at 2%X 5 chains
d Plots of % acre spaced at 5 X 15 chains
10-2 For the same plot sizes shown in Table 10-2, compile a similar tabulation for square
sample plots. In lieu of plot radii, show the length of one side of the squares in feet
and in meters.
10-3 a If you space I-chain strips at 10-chain intervals through a square section of land
and tally 350 MBF on the sample, what would be the total-volume estimate for the
entire tract?
b If you space %-acrecircular plots at 5 X 10 chains through a 240-acre tract, and
the volume tallied on the sample is 68.4 MBF, what would be the total-volume
estimate for the entire tract?
c How many lineal chains of sample strips I chain wide would be run through a
township to obtain a 2 percent cruising intensity?
d If you made a 0.05 percent inventory of the total land area in a state consisting of
30 million acres, how many %-acrecircular plots would be required'?For a square
grid arrangement of samples, what would be the distance (in chains) between
plots?
10-4 Design and conduct a field study to compare the relative efficiencies of circular,
square, and rectangular sample plots in your locality.
10-5 The coefficient of variation for %"-acrecircular plots was estimated to be 90 percent
for a timbered tract of 50 acres. If one wishes to estimate the mean volume per acre
of this tract within 5 2 0 percent unless a I-in-20 chance occurs.
a Compute the number of plots to be measured assuming simple random sampling
without replacement.
b Calculate the distance between plot centers in chains assuming the plots will be
systematically established on a square grid.
10-6 Assume that desirable stocking for mature timber of species of interest is 150 trees
per acre.
a When conducting a stocked-quadrat survey of regeneration for this species, what
plot size should be used?
b Suppose that 50 plots were established. Acceptable trees were found on 42 plots.
What is the stocking percent?
10-7 Using the data in the line-plot cruise example in Section 10-7:
a Compute the coefficient of variation on a per plot and a per acre basis.
b Estimate the total volume on the tract and establish the 95 percent confidence
interval for the estimated total.
10-8 A plot-count regeneration surrey was conducted using Km-acre plots located randomly over the tract of interest. The tree count per plot follows:
. _ . . ,".
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,
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a Estimate the mean number of trees per acre.
b Compute the coefficient of variation for numbers of trees per acre.
c Compute the 90 percent confidence interval for the mean.
REFERENCES
Avery, T. E., and Newton, R. 1965. Plot sizes for timber cruising in Georgia. J. Forestry
63:93&932.
Beers, T. W. 1977. Practical correction of boundary overlap. So. J. Appl. Fo,: 1: 16-18.
Brand, D. G. 1988. A systematic approach to assess forest regeneration. Forestry Chmn.
64:4 14420.
Burkhart, H. E., Barrett, J. P., and Lund, H. G. 1984. Timber inventory. Pp. 361-41 1 in
Forestry handbook. K. F. Wenger (ed.), John Wiley & Sons, New York.
Fowler, G. W., and Arvanitis, L. G. 1979. Aspects of statistical bias due to the forest edge:
Fixed-area circular plots. Can. J. Fo,: Res. 9:383-389.
Johnson, F. A,. and Hixon, H. J. 1952. The most efficient size and shape of plot to use for
cruising in old-growth Douglas-fir timber. J. Forestry 50:17-20.
Kendall, R. H., and Sayn-Wittgenstein,L. 1960.Arapid method of laying out circularplots.
Forest? Chmn. 36:23&233.
Nyssonen, A. 1967. Remeasured sarnple plots in forest inventory. Norwegian Forest
Research Inst., Vollebekk, Norway, 25 pp.
Schmid, P, 1969. Sichproben am Waldrand. Mitt. Schwei:. Anst. Forstl. Versuchswes
49234-303.
Stein, W. 1. 1984a. Regeneration surveys: An overview. Pp. I 11-1 16 in Neb~.forestsfora
changing ivorld, Proceedings of the 1983 Society of American Foresters National
Convention, Portland, Oreg.
. 1984b. Fixed-plot methods for evaluating forest regeneration. Pp. 129- 135 in New
forestsfor a changing world, Proceedings of the 1983 Society of American Foresters
National Convention, Portland, Oreg.
Wiant, H. V., and Yandle, D. 0 . 1980. Optimum plot size for cruising sawtimber in Eastern
forests. J. Forestry 78:642-643.
Zeide, B. 1980. Plot size optimization. Forest Sci. 26:25 1-257.