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United States

Department of

Agriculture

Forest Service

Southern

Research Station

Research Note

SRS–12 April 2003

Comparison of Past, Present,

and Future Volume Estimation

Methods for Tennessee

Stanley J. Zarnoch, Alexander Clark III, and

Ray A. Souter

Abstract

Forest Inventory and Analysis 1999 survey data for Tennessee

were used to compare stem-volume estimates obtained using a

previous method, the current method, and newly developed taper

models that will be used in the future. Compared to the current

method, individual tree volumes were consistently underestimated

with the previous method, especially for the hardwoods. The taper

models produced estimates very similar to the current method for

both hardwoods and softwoods. When expanded to a statewide

basis, the previous method differed from the current by -2.128 by

109

 cubic feet, which represents an 8.16-percent underestimate.

Hardwoods again were more severely underestimated than

softwoods. Conversely, results from the taper method deviated only

0.230 by 109 cubic feet from the current method, or 0.88 percent,

which is of little concern.

Keywords: FIA, taper equations, volume

Introduction

The Forest Inventory and Analysis (FIA) Program in the

Southern Research Station (SRS) has conducted volume

surveys across the Southern States for the past several

decades. During this time, there have been many changes

in technology and survey methodologies that have

resulted in alterations of the survey protocol. In addition,

the original Southeastern and Southern Forest Experiment Stations, which were responsible for the eastern

and western halves, respectively, of the surveys of the

Southern States, have been merged into the current

Southern Research Station. This also has resulted in

various changes to ensure uniformity of methods

throughout the South. Hence, comparing surveys over

time for any one State is difficult because any changes

observed might be due to changes in the forest resource

or merely changes in the methodology used in the survey

or a combination of both. The objectives of this paper are

to (1) summarize the evolution of individual tree volume

methodologies used by the Southern Research Station,

and (2) compare the volume estimates on an individual

tree and total State basis derived from past, present, and

future methods for the 1999 Tennessee survey.

Volume Estimation

The 1999 Tennessee survey (Schweitzer 2000) was

analyzed using the SRS volume methodology, which is

based on the typical D2H volume equations (Spurr 1952)

produced on a species or species group basis using a

simple linear regression model. Gross cubic foot volume

inside bark from a 1-foot stump to a 4-inch upper

diameter outside bark (d.o.b.) was predicted for each

sample tree based on diameter at breast height (d.b.h.)

and total height (H) and did not include forks or limbs

outside of the main bole. This method is identical to the

original volume methodology used by the Southeastern

Forest Experiment Station (SE), except that the SE

method included forks and limbs in the volume estimates. Because the SE method was never used in

Tennessee, it will not be discussed further in this paper.

The previous Tennessee survey in 1989 was the responsibility of the Southern Forest Experiment Station (SO)

and was based on obtaining numerous d.o.b. measurements on each sample tree and computing volume by

accumulating Smalian bolt-volume estimates. Hence, the

Stanley J. Zarnoch is Mathematical Statistician, USDA Forest

Service, Southern Research Station, Asheville, NC 28802-2680;

Alexander Clark is Wood Scientist in the Disturbance and

Management of Southern Forest Ecosystems, USDA Forest

Service, Southern Research Station, Forest Sciences Laboratory,

Athens, GA 30602-2044; and Ray A. Souter is Forest Biometrician, Forestech International, LLC, Athens, GA 30604-6412.
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typical regression volume equations that were used with

the SRS methodology in 1999 never were developed for

the 1989 survey. The SO method computed volume

inside bark based on a 1-foot stump height to an arbitrary

cruiser-selected upper stem d.o.b., which usually was

around 4 inches but often was quite larger, depending on

the size and condition of the tree and merchantable top

limit as estimated at the time of the inventory. Merchantable top limits have changed since then and are now to a

fixed 4-inch d.o.b. top. Thus, compared to the 1999

survey, the 1989 volume should be considerably less.

Recently, advances in analytical techniques have led to

the development of a new system of volume equations

based on tree taper models (Souter and others, in press).

A system of nonlinear equations was fitted to stem

diameter inside bark (d.i.b.) measurements to produce a

taper curve that is integrated between any two heights to

obtain the volume of wood between those two points.

The advantage is the potential to have a somewhat better

fit than the typical regression volume equations. More

importantly, however, volume can be obtained for any set

of merchantability standards simply by changing the

points of integration on the tree bole model; no new

models need to be refitted. The default is volume inside

bark from a 1-foot stump height to a height where upper

stem d.o.b. is 4 inches. The taper model is similar to the

SRS method in that it is based on the main tree bole and

does not include volume in forks or limbs. Table 1 gives

a summary of the four volume methods used throughout

the South.

Methods

The 1999 Tennessee survey was used to compare three

volume estimation methods: the Southern Forest Experiment Station (SO) method, the Southern Research

Station (SRS) method, and the taper (TAPER) model.

Limitations of funds and time prohibited resurveying

Tennessee to produce the SO estimate based on Smalian

tree bolts; however, an approximation was used to mimic

the methodology. In essence, the 1989 Tennessee data

were used as a basis for the SO method to which D2

H

regression equations were fitted for seven species groups

(table 2). These equations were used on the 1999 Tennessee survey to calculate volume on an individual-tree basis

and then expanded to a total State basis by applying the

appropriate plot and county expansion factors. The SRS

and TAPER method results were computed simply by

applying their equations to the 1999 Tennessee survey

data.

Evaluation of the three methods was on an individualtree and total State volume basis. Volume differences and

percentage differences were calculated for hardwoods

and softwoods for each of the poletimber and sawtimber

categories.

Results and Discussion

The 1999 Tennessee survey (Schweitzer 2000) was based

on the SRS method, which was used as the standard for

Table 1—Summary of volume methods used in the past, present, and future

Main Limbs and Analytical

Method Stump height Upper d.o.b. bole forks method

feet inches

Southern Forest 1 Field cruiserExperiment Station selected Yes No Cumulative Smalian bolts

Southeastern Forest 1 4 Yes Yes Linear regression

Experiment Station

Southern Research 1 4 Yes No Linear regression

Station

Taper Model Variable Variable Yes No System of nonlinear

(1-foot (4-inch equations

default) default)

d.o.b. = diameter outside bark.
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Table 2—Gross cubic volume equationsa developed from the 1989 data for the Southern Forest

Experiment Station method

Volume Timber Mean 1989 Mean square

equationb c type stopper d.o.b. Trees 0

ˆ

β 1 βˆ R2 error

inches no.

2 Pole 4.1 895 -0.71267 0.00206 0.87 1.07

Saw 4.6 1,057 1.69682 0.00180 0.87 17.92

3 Pole 4.6 9 -0.75168 0.00218 0.90 4.13

Saw 7.3 55 3.16103 0.00158 0.80 574.82

4 Pole 4.3 1,272 -0.32465 0.00210 0.87 0.96

Saw 4.9 1,700 2.69948 0.00168 0.94 32.27

5 Pole 4.6 4,725 -0.25893 0.00174 0.87 2.28

Saw 6.8 8,295 8.09304 0.00122 0.81 114.14

6 Pole 4.4 1,589 -0.47320 0.00176 0.88 2.45

Saw 5.8 2,606 7.78129 0.00133 0.86 124.15

7 Pole 4.7 5,503 -0.31562 0.00173 0.87 2.21

Saw 6.9 5,312 6.62802 0.00132 0.87 190.83

8 Pole 4.7 695 -0.33101 0.00173 0.83 1.09

Saw 7.0 91 5.01258 0.00111 0.62 25.04

a Gross cubic volume (cubic feet) = 2

0 1 β β

ˆ ˆ + D H , where D is d.b.h. (inches) and H is total tree height (feet).

b Volume equation 1 is for longleaf pine and because there was no longleaf pine in Tennessee, a volume equation was not developed

for this species.

c Species composition for the volume equations that were developed from the 1989 data. Boldfaced species were not present in the

1989 data that were used to fit the volume equations but were in the 1999 data for which a volume equation was required for the

subsequent analysis. Volume equation 2 = Pinus (echinata, taeda); volume equation 3 = Taxodium (distichum), Nyssa (aquatica);

volume equation 4 = Juniperus (virginiana), Pinus (pungens, rigida, stobus, virginiana), Tsuga (canadensis, caroliniana); volume

equation 5 = Quercus (alba, bicolor, coccinea, falcata, imbricaria, laevis, lyrata, macrocarpa, michauxii, muehlenbergii, nigra,

nuttallii, palustris, phellos, prinus, rubra, shumardii, stellata, velutina); volume equation 6 = Liquidambar (styraciflua),

Liriodendron (tulipifera), Nyssa (sylvatica); volume equation 7 = Acer (barbatum, negundo, nigrum, pennsylvanicum, rubrum,

saccharinum, saccharum), Aesculus (glabra, octandra), Betula (alleghaniensis, lenta, nigra), Carya (sp., aquatica, cordiformis,

glabra, illinoensis, laciniosa, ovata, texana, tomentosa, pallida), Castanea (dentata), Catalpa (sp.), Celtis (laevigata,

occidentalis), Cornus (florida), Diospyros (virginiana), Fagus (grandifolia), Fraxinus (americana, pennsylvanica, quadrangulata),

Gleditsia (aquatica, triacanthos), Gymnocladus (dioicus), Ilex (opaca), Halesia (carolina), Juglans (cinerea, nigra), Maclura

(pomifera), Magnolia (acuminata, grandiflora, virginiana, fraseri), Morus (rubra), Persea (borbonia), Planera (aquatica),

Platanus (occidentalis), Populus (sp., deltoides), Prunus (serotina), Robinia (pseudoacacia), Salix (sp.), Sassafras (albidum), Tilia

(americana, heterophylla, caroliniana), Ulmus (alata, americana, crassifolia, rubra, serotina, thomasii); volume equation 8 =

Ailanthus (altissima), Amelanchier (sp., arborea), Alnus (glutinosa), Bumelia (sp.), Carpinus (caroliniana), Cercis (canadensis),

Crataegus (sp.), Halesia (sp.), Magnolia (macrophylla), Malus/Pyrus (sp.), Morus (alba), Ostrya (virginiana), Oxydendrum

(arboreum), Paulownia (tomentosa), Prunus (sp. except serotina), Quercus (marilandica), Citrus (sp.), miscellaneous species.

comparison purposes in this study. Generally, the SO

method consistently underestimated individual tree

volume, as expected, because it usually does not go to

the upper 4-inch d.o.b. Hardwoods are more affected

than softwoods (table 3); absolute cubic foot differences

for hardwoods were nearly three times that of softwoods,

and percentage differences were a little less than twice.

For both hardwoods and softwoods, absolute differences

for sawtimber were seven times that of poletimber, but

on a percentage basis poletimber was about three times

that of sawtimber.

Little difference was observed between the TAPER and

SRS methods; hardwoods and softwoods responded

somewhat similarly (table 3). Poletimber exhibited a very

small absolute underestimate, and sawtimber had a larger

overestimate; however, both were within three-fourths of

a cubic foot of the SRS method. The trends were the
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Table 3—Average individual tree volumes based on the SRS, SO, and Taper volume equation methods for the 1999 data

SO versus SRS Taper versus SRS

Mean 1989 SRS SO Diff. Diff. Taper Diff. Diff.

Wood Timber stopper Sample volume volume from from volume from from

species type d.o.b. trees per tree per tree SRS SRSa per tree SRS SRSa

inches number - - - - - - - cubic feet - - - - - - - % - - - cubic feet - - - %

Hard Pole 4.6 32,322 5.75 5.33 -0.42 -7.00 5.74 -0.01 -1.68

Hard Saw 6.7 12,247 35.61 32.32 -3.29 -2.15 35.97 0.36 1.94

Soft Pole 4.2 6,720 4.18 3.99 -0.20 -4.21 4.17 -0.01 -0.17

Soft Saw 4.9 3,647 22.57 21.34 -1.23 -1.69 23.23 0.66 2.18

SRS = Southern Research Station; SO = Southern Forest Experiment Station; d.o.b. = diameter outside bark.

a The average Diff. from SRS (percent) is calculated as the average of the percentage difference from the SRS method on an individual tree basis. This is not

equivalent to the ratio of Diff. from SRS divided by SRS volume per tree converted to a percentage, which can be calculated simply from the entries in the

table and is approximately equivalent to the Diff. from SRS (percent) calculated on the total State basis using the appropriate plot and county expansion

factors (refer to table 4).

Figure 1—Individual tree volume for the 1999 Tennessee survey.

Hardwoods

d.b.h. (in.)

5 10 15 20 25 30

Individual tree volume (ft3

)

0

20

40

60

80

100

120

140

SO

TAPER

SRS

Softwoods

d.b.h. (in.)

5 10 15 20 25 30

Individual tree volume (ft3

)

0

20

40

60

80

100

120

140

SO

TAPER

SRS

same on a percentage basis and were within about 2

percent of the SRS method, which had substantially less

variation than with the SO method.

Further comparisons of the three methods on an individual tree basis are shown in figure 1, where volume

versus d.b.h. is illustrated. The SRS and TAPER methods

produce virtually identical results for hardwoods; the SO

results deviate substantially at larger d.b.h. This underestimation by the SO method is most probably due to the

tendency of selecting upper d.o.b.’s at a lower height on

large d.b.h. trees, resulting in less volume. All three

methods are similar for softwoods; the SRS and TAPER

results are nearly the same for d.b.h.’s less than 20

inches.

An evaluation expanded over the whole State is important because it takes into account the distribution of trees

among the various tree species and size classes, giving a

representative picture of the differences in estimates by

the three methods. Overall, the SO method results

differed from the SRS by -2.128 by 109

 cubic feet, which

represents an 8.16-percent underestimate (table 4).

Hardwoods again were more severely underestimated on

an absolute and percentage basis than softwoods.

Conversely, the TAPER method results deviated only

0.230 by 109 cubic feet, from the SRS, or 0.88 percent,

which is of little concern.

Figure 2 illustrates the distribution of total volume versus

d.b.h. class for the three methods. Again, the TAPER and
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SRS method estimates are very similar for hardwoods,

but the SO estimate deviates substantially, especially at

larger d.b.h. The results of all three methods are similar

for softwoods; SRS and TAPER are nearly the same.

The SRS estimates are very close to those of the original

1999 Tennessee survey because the identical methodology was used. The total State gross cubic foot volume

estimate for the SRS method was 26.081 by 109

 cubic

feet; in table 19, Schweitzer (2000) listed 26.287 by 109.

This minor discrepancy of less than 1 percent is probably

due to a slightly different grouping of species.

Table 4—Total State volume based on the SRS, SO, and Taper volume equation methods for the 1999 data

SO versus SRS Taper versus SRS

Mean 1989 SRS SO Diff. Diff. Taper Diff. Diff.

Wood Timber stopper total total from from total from from

species type d.o.b. Trees volume volume SRS SRSa volume SRS SRSa

inches no. - - - - - - 109 cubic feet - - - - - - - % - - 109 cubic feet - - %

Hard Pole 4.6 32,322 6.643 6.154 -0.489 -7.36 6.630 -0.013 -0.20

Hard Saw 6.7 12,247 15.611 14.176 -1.435 -9.19 15.768 0.156 1.00

Soft Pole 4.2 6,720 0.983 0.936 -0.047 -4.81 0.981 -0.002 -0.20

Soft Saw 4.9 3,647 2.844 2.687 -0.157 -5.50 2.933 0.090 3.16

Total 5.6 54,936 26.081 23.953 -2.128 -8.16 26.312 0.230 0.88

SRS = Southern Research Station; SO = Southern Forest Experiment Station; d.o.b. = diameter outside bark.

a The average Diff. from SRS (percent) is calculated as the average of the percentage difference from the SRS method on an individual tree basis. This is not

equivalent to the ratio of Diff. from SRS divided by SRS volume per tree converted to a percentage, which can be calculated simply from the entries in the

table and is approximately equivalent to the Diff. from SRS (percent) calculated on the total State basis using the appropriate plot and county expansion

factors.

Figure 2—Total State volume for the 1999 Tennessee survey.

Hardwoods

d.b.h. (in.)

5 10 15 20 25 30

Total state volume (109 ft3

)

0

1

2

3

4

SO

TAPER

SRS

Softwoods

d.b.h. (in.)

5 10 15 20 25 30

Total state volume (109 ft3

)

0.0

0.2

0.4

0.6

0.8

1.0

SO

TAPER

SRS

Because the true volume is an unknown, it is impossible

to determine which of the three methods provides the

best approximation. Although comparisons were made

with respect to the SRS as the standard, this was only

done for convenience and does not imply any more

confidence in this method. Generally, the SO method

underestimates volume by about 8 percent as compared

to the other two methods, which produce virtually

identical results. The SRS method is composed of a

much simpler set of volume equations than the TAPER

method, but it is restrictive in that it is useful only for a

fixed stump and upper d.o.b. limit. Although the TAPER

method is initially more complex, once it is developed
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and programmed into a computer, it has the flexibility to

give estimates to any merchantability limit. Hence, it is

believed that comparison of future estimates based on

either the SRS or TAPER methods to the 1999 Tennessee

survey should reflect changes in the forest resource and

not changes in methodology.

Literature Cited

Schweitzer, C. J. 2000. Forest statistics for Tennessee, 1999. Resour. Bull.

SRS-52. Asheville, NC: U.S. Department of Agriculture, Forest

Service, Southern Research Station. 78 p.

Souter, R.A.; Clark, A.; Zarnoch, S.J. [In press]. Southern tree species stem

taper and volume prediction equations. Res. Pap. Asheville, NC: U.S.

Department of Agriculture, Forest Service, Southern Research Station.

Spurr, S.H. 1952. Forest inventory. New York: The Ronald Press Co. 476 p.
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