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 con- cept 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 sys- tem. 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 lodge- pole 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 plan- ning 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 northeast- em tree species. U.S. Forest Sen , 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 the frequency 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 character- istics 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

21 2 CHAPTER 10: INVENTORIES WITH SAMPLE STRIPS OA PLOTS

STRIP WIDTH

BETWEEN STRIPS

0 500 1000 FEET

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.

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 %chain in dense stands of young tim- ber 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 to- tal 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.

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

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

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

100 EF =

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 percent- age 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 break- downs. If the 132 lineal chains of strip were made up of 90 chains intersecting ;!

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 rea- sonably good indication of the relative proportions by types.

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 be- ing dragged along as a moving centerline. Trailer tapes may be used where slope cor- rections 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 deter- mining 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 re- cent 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 rectan- gular 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.

LHHPItH IU: lrvvtl4lunlts 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 bor- derline 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:

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 cen- terline 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 spac- ings, 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 tim- ber sizes will be encountered, it is often efficient to use concentric circular plots with each centered at the same point. As an example, %-acre plots might be used to tally sawtimber trees, XO-acre plots 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, %-acre plots are spaced at in- tervals 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 0.2 acres x 100 = ---- x 100 = 10 percent Acres represented 2 acres

By the same token. 10 percent estimates may also be accomplished by spacing the same %-acre plots 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

TABLE 10-2 RADII FOR SEVERAL SIZES OF CIRCULAR SAMPLE PLOTS

Plot size Plot radius Plot size Plot radius (acre) (fi) (ha3 (m)

1 % !A !4

'Xo

'A 'A xo K Xa

IAm 'Xm 'Xm

FIGURE 10-2 Diagrammatic plan for a 10 percent systematic line-plot cruise utilizing X-acre circular sampling units.

W ~ H T I t n IU. 11qv t 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 for- mula form; in order to express the desired relationships algebraically, the follow- ing 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 = number of plots, L = distance between lines, B = distance between plots on a line,

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

21 8 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 read- ily. For square spacing (that is, B = L), we have

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

If the distance between lines (L) is specified to be 5 chains, then the distance be- tween plots on lines will be

a ( l0 ) 0.2(10) B = - - - - - - 4 chains L P 5(0.1)

Figure 10-2 shows a line-plot cruise utilizing %-acre plots spaced 5 by 4 chains.

10-7 -Plot Cruise 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:

Volume Volume Volume Plot (ffl0.2 acre) Plot (ft3/0.2 acre) Plot (ft3/0.2 acre)

The estimated mean volume per plot is

Cyi 7,740 - 15

- 5 16 ft3/0.2 acre y = n - - -

CHAP I t H 10: INVENIOHltS WI I H SAMPLt SI HIPS OH PLOIS i! IU

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 approxi- mated, the standard error of the mean is generally estimated using the formula for simple random sampling (Sec. 3-4), namely

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)

For this example, the variance. s2, is computed as

SL = - - n - l 14

= 26,997

and the standard error of the mean is

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 estab- lished as

10-8 Sampling Intensity and Design The intensity of plot sampling is gov- erned by the variability of the stand, allowable inventory costs, and desired stan- dards 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 pre- liminary field sample of, perhaps. 10 to 30 plots. Then the proper sampling inten- sity 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 es- timate 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 de- fined 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 se- lected randomly from such a listing.

In spite of the statistical difficulties associated with systematic sampling de- signs, such cruises are still employed frequently. Where estimates of sampling pre- cision 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 rect- angular 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 cor- ners 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 chain- ing 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 us- ing 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 re- sult in a final estimate that is 12,000 bd ft too low.

Separate tally sheets are recommended for each plot location and species; de- scriptive 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~dary o\,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, es- pecially long, narrow tracts with a high proportion of edge trees, appropriate pre- cautions should be taken to guard against bias caused by boundary overlap.

One method of dealing with the boundary-overlap problem is to move plot ten-

ters (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 (1 977) 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 com- pletely 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 OUTSIDE CRUISE AREA t

CORRECTION PLOT CENTER

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 ef- fects, 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 line- plot 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 perma- nent 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 dif- ferences 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 preci- sion of "change estimates" is improved. In addition, trees initially sampled but ab- sent 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 represen- tative 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 ques- tionable utility.

One attempt to ensure that sampling units are representative of equal forest ar- eas 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 ~ N I 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 100,000 acres, sampling er- rors of + I0 to 20 percent might be desired for current volume, with 220 to 30 per- cent 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 en- tire forest holding of 1 to 3 million acres should be approximately f 2 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 topo- graphic maps are invaluable aids for the initial location, establishment, and relo- cation 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 bear- ings 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 non- sampled 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 as- sumed 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 i t becomes feasible to use more massive iron

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 measure- ment techniques is as important as precision for evaluating changes over time.

To avoid problems arising from periodic variations in tree merchantability stan- dards, 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 op- erations. 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 measure- ments required will differ for each inventory system; thus the following listings merely include examples of the data that may be required:

Plot 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

Individual tree data

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 inven- tories are preferably made immediately after a growing season and prior to heavy snowfall. For tracts smaller than 100,000 acres, 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 rein- ventories about one-fifth of the forest each year.

- a . ". 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 re- measured 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 cor- rect 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 volume- prediction 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 mortal- ity, represents the growth of the plot.

One of the problems facing field crews who must remeasure permanent sam- pling 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 in- conspicuously marked, relocation time can make up a sizable proportion of the to- tal 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 sam- ple plots could not be found again. Where plots could be relocated, the time re- quired for transportation, relocation (which was done without the aid of GPS), and measurement was distributed as follows:

Activity Percent of total time

Transport by a vehicle 20.6 Walking to, between, and from the plots 22.6 Searching for the plots 12.9 Sample plot measurement 35.7 Pauses 8.2 Total 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 sys- tematic 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 50 acre 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 %-acre circular 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 %-acre circular 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 %"-acre circular 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 520 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 ran-

domly over the tract of interest. The tree count per plot follows:

_ , , , . . . _ . . , " . , . ._,., . . . . , . _ . . . , . LL.,l I , , , -.,,. I L V , d &&"

Plot Count Plot Count

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~.forestsfor a

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.