United States

Department of

Agriculture

Forest Service

Southern Forest

Experiment Station

Volume Prediction from Stump

Diameter and Stump Height of

Selected Species in Louisiana’

New Orleans,

Louisiana

Reseat&h Paper

SO-182

August, 1982

- ,

?

Carl V. Bylin
SUMMARY

Equations for predicting cubic foot volumes from stump diameter and stump

height are presented for 15 southern species. Of the two separate sets of equations developed, one predicts volumes from stump diameter and the other

predicts volume from stump diameter and stump height. In each set, six equations for each species predict total, merchantable, and sawtimber volumes. Two

equations for each of the above are presented using stump diameter inside bark

and stump diameter outside bark.

Equations were verified on independent test subsets using the F distribution

statistic with a significance level of .05. Equations will predict volume within

+ 2 standard errors 95 percent of the time.
Volume Prediction from Stump Diameter and Stump Height of

Selected Species in Louisiana

Carl V. Bylin

INTRODUCTION

Sometimes foresters must estimate the volume of

timber harvested from the stumps which remain after

logging. This study provides reasonably accurate

equations for prediction of the tree volume using

stump diameter and stump height as the independent

variables.

The Southern Forest Experiment Station’s Renewable Resources Evaluation Unit currently remeasures

sample plots on a 10 year cycle. Frequently, previously

measured trees have been harvested. Volume must be

estimated to report removals for the state. Presently,

these volumes are calculated from past diameter at

breast height, adding the average increment for 5

years and the resultant diameter is used to estimate

volume using B&E coefficients1 and diameter classes.

Equations which predict cubic foot merchantable and

sawtimber volumes from stumps will also be useful for

reporting removals statistics.

Since the energy crisis, interest has increased in

wood as a source of heat. Some people who invade the

National Forests and forest industries’ lands in search

of firewood cut any tree they desire. In American

Forests, Rolleston (1980) and Schwarz (1980) investigated the problem of timber rustling in the East and

West, respectively.

The value of a stolen tree is determined by many

factors. The tree’s size-class (sapling, poletimber, or

sawtimber) and volume are two major factors. If a

forester knows the volume of a tree and its size-class,

he could easily calculate the financial value of that

tree using the current market price. Predicting

volume from stump diameters should be useful to public and private owners of timber.

LITERATURE REVIEW

Available literature on prediction of tree volume

from stump diameter is relatively sparse. Most articles predict diameter at breast height (dbh), rather

‘B&E coefficients give average volume as a second degree function

of diameter from volumes in 2 inch diameter classes.

than volume, from stump diameter. Generally, two

phases of estimation are suggested. After dbh is predicted from stump diameter, estimated volume is

obtained by the use of local volume tables. Study results appear as charts, curves, graphs, tables, regression equations, “rule of thumb” equations, or combinations of the above. The earlier studies use charts

whereas the later studies use tables and regression

equations.

Studies which utilize graphs, charts, or curves include Hough (1930), Ostrom and Taylor (1938), Rapraeger (1941), and Endicott (1959). Studies which utilize tables or “rule of thumb” for predicting dbh include

Cunningham et al. (1947), McCormack (1953), Eie

(1959), Almedag and Honer (1973, 1977), and Horn

and Keller (1957). Tables for predicting tree volume

are presented by Decourt (1973) and Quigley (1954).

Studies which utilize regression techniques for predicting dbh include Schaeffer (1953), Bones (1960,

1961), Myers (1963), Lange (1973), McClure (1968),

Raile (1977), and others. Regression equations for predicting volume from stump measurements are presented by Nyland (1975).

Review of the literature indicated that prediction of

dbh from stump measurement is common, but predictions of volume, also possible, are not. Therefore, a

need for methods to predict volume directly from

stump measurements exists. Such methods for predicting volume of removed trees are useful both to

foresters and owners of private timber lands.

METHODS

Data Collection

In 1973, data used in this study were gathered in

Louisiana as part of a wood utilization study. Twenty

trees were measured at each of 77 logging sites. Each

tree was assigned a site number and a tree number.

Measurements were made on the main bole and limbs.

The main bole was divided into sections in order to

separate stump, sawlog portion, jump butt or cull section, upper stem, pole section, stem section of cull tree,

or portions used for a variety of products.

The following items were measured on each tree:

stump height, stump diameter, double bark thickness

Carl V. Bylin is Research Forester, Renewable Resources Evaluation, Southern Forest Experiment Station, Forest Service-USDA, New

Orleans, Louisiana.

1
at stump height, dbh, double bark thickness at dbh,

diameters at upper and lower ends of each section,

double bark thickness at upper and lower ends of each

section, length of each section, and length from the

base of the crown to the terminal bud. Each section

was assigned a product code. The product codes are

stump, sawlog, poletimber, limbs, non-inventory section, or crown left in the woods.

The utilization study used National Forest Survey

Handbook standards to assign tree size class. A tree

was classified as poletimber if its dbh was between 5.0

inches and 9.0 inches for softwoods and between 5.0

inches and 11.0 inches for hardwoods.’ A tree was

classified as sawtimber if its dbh was greater than 9.0

inches for softwoods or greater than 11.0 inches for

hardwoods. 3

Total cubic foot volume4 is the volume in the main

bole from a one-foot stump to the top of the tree. Merchantable cubic foot volume is the volume in the main

bole from a one-foot stump to a height where the diameter outside bark is 4.0 inches or to the place where

the length was terminated due to the presence of rot,

forks, or other limiting defects. Sawtimber cubic foot

volume is the volume from a one-foot stump to the

height where the diameter outside bark is 7.0 inches

for softwoods and 9.0 inches for hardwoods or to the

place were the length was terminated due to the presence of rot, forks, or other limiting defects.5

Due to these limiting defects, some trees’ merchantable length terminated before reaching the standard

4-inch diameter outside bark for growing stock trees.

Similarly, saw log length sometimes terminated before the standard 7-inch diameter outside bark on softwoods or g-inch diameter outside bark on hardwoods.

On these trees, diameter observations were recorded

at the place on the main bole where the length was

terminated.

Each tree volume (cubic feet) was calculated using a

neiloid frustrum and Smalian’s formula. The volume

between stump height and dbh was calculated using a

neiloid frustrum:

V = (4.5-SHT) l [BASDIB + {BADBH l

(BASDIBj2j’ + {BASDIB l (BADBH)2)‘/” +

BADBHI / 4

where

V = Volume (cubic feet)

SHT = Stump height (feet)

BASDIB =Basal area of stump diameter inside

bark (feet’)

BADBH = Basal area of dbh inside bark (feet2)

‘Forest Survey Handbook, 1967.

31bid.

4This volume is the gross volume. It includes any cull or defect that

occurs between the stump and top termination point.

5Forest Survey Handbook.

The volume above dbh was calculated using Smalian’s

formula:

n

Li l 7r DIB’ii + DIB 2ui

2l l ( 1

i=l 288 4

where

DIBii =Diameter inside bark at the lower or

larger end (inches)

DIB,i =Diameter inside bark at the upper or

smaller end (inches)

Li = Length of tree section (feet)

7-r = 3.14159

n = number of sections measured

i = the ith section

Section lengths ranged from less than one foot to a

maximum of 17 feet with the majority of the lengths

being approximately 8 feet. Stump diameters outside

bark ranged from 4.2 to 45.3 inches. For softwoods,

stump heights ranged from 0.1 to 1.5 feet with a mean

of 0.8 foot. For hardwoods, stump heights ranged from

0.1 to 2.9 feet with a mean of 1.0 foot.

Table 1 lists the scientific and common name of each

species used. Table 2 lists mean, range, and number of

samples for each species or combination of species for

which equations were developed. Several trees in the

data set had a merchantable top diameter outside bark

of less than 4.0 inches. Merchantable top diameter

outside bark ranged from 2.0 to 23.5 inches. Sawtimber top diameters outside bark ranged from 7.0 to 26.0

inches. Table 3 presents the name of each species and

the number of samples included in the otherhardwoods classification.

Table l.-Scientific and common name of species

Scientific name Common name

Softwoods

Pinus elliottii

Pinus echinata

Pinus palustris

Pinus taeo!a

Hardwoods

Slash pine

Shortleaf pine

Longleaf pine

Loblolly pine

Quercus alba White oak

Quercus falcata var pagodifolia Cherrybark oak

Quercus stellata Post oak

Quercus nigra Water oak

Quercus falcata Southern red oak

Carya sps. Hickory

Liquidxzmbar styraciflua Sweetgum

Fagus grandifolia American beech

Nyssa sylvatica Black tupelo

Liriodendron tuplipifera Yellow-poplar

Celtis laevigata Sugarberry

2
Table Z.-Mean, range’, and number of samples for selected parameters in the data sets

No. samples Dbh Stump height

Species

Total or

Sawtimber merchantable Mean

Slash Pine 71 137 9.6 3.4-17.2

Shortleaf Pine 151 196 12.8 4.5-23.5

Longleaf Pine 35 4 2 13.3 7.5-19.4

Loblolly Pine 337 436 13.5 3.0-27.0

All Pines 671 914 12.7 3.0-27.0

Hickory 3 0 3 6 15.0 6.7-24.2

White Oak 5 7 72 13.9 6.3-23.3

Water Oak 52 62 16.8 6.6-36.9

Post oak 3 2 68 11.6 4.1-22.6

Cherrybark Oak 2 2 28 15.0 7.3-28.5

S. Red Oak 50 89 11.8 4.4-22.0

Sweetgum 6 6 119 12.7 4.0-41.4

Black Tupelo 13 23 13.2 6.6-20.2

Yellow-poplar 14 14 17.3 15.3-22.5

Sugarberry 17 21 15.8 8.4-26.2

Beech 13 15 16.4 8.9-21.9

Other Hardwoods

All Hardwoods

7 4

408

113 14.4 4.4-29.8

619 13.8 4.0-41.4

Range Mean Range

Stump diameters Merchantable top diameters Sawtimber top diameters

Inside bark Outside bark Inside bark Outside bark Inside bark Outside bark

range range Mean Max. Mean Max. Mean Max. Mean Max.

.7 0.4-1.2

.7 0.2-1.2

.7 0.5-1.3

.8 0.1-1.5

.8 0.1-1.5

1.1 0.5-1.5

1.1 0.1-2.1

1.1 0.5-1.8

.9 0.5-1.5

1.1 0.5-1.5

1.0 0.4-2.9

1.0 0.3-1.5

1.1 0.3-1.5

1.0 0.5-1.5

1.4 1.0-2.5

1.2 0.7-1.5

1.0 0.3-1.5

1.0 0.1-2.9

3.6-27.2 4.8-29.1

4.4-24.0 5.3-26.1

7.1-20.3 8.5-23.4

3.3-28.8 4.2-31.3

3.3-32.5 4.2-35.4

7.9-26.7 9.0-28.2

7.4-26.1 7.9-27.5

8.3-41.6 9.0-43.2

4.9-27.4 6.0-29.0

8.7-32.1 9.4-34.3

4.7-25.9 5.2-27.4

4.9-27.4 5.3-28.5

8.7-26.4 9.6-27.3

16.2-23.4 17.6-25.2

12.9-32.1 13.7-33.7

10.5-25.9 10.9-27.0

5.2-34.9

4.7-43.4

5.8-36.5

5.2-45.3

3.3 5.9 3.7 6.9

4.8 10.9 5.2 12.4

4.6 9.0 5.0 9.7

4.5 12.0 4.9 12.7

4.4 12.0 4.8 12.7

8.5 17.1 9.3 18.2

8.3 22.3 9.0 23.5

8.3 19.6 8.8 20.5

7.0 19.8 7.8 21.9

7.1 16.4 7.6 17.2

6.4 16.6 7.0 17.4

6.1 16.9 6.6 17.5

6.7 11.3 7.3 12.1

7.6 10.2 8.4 11.0

8.5 15.3 8.9 16.0

9.5 16.2 9.7 16.8

7.8 17.7 8.3 18.4

7.4 22.3 8.0 23.5

6.6 9.9 7.4 11 1

8.3 15.5 9.0 ii:2

7.8 11.7 8.4 12.3

8.5 20.3 9.1 21.8

8.2 20.3 8.9 21.8

12.1 18.6 13.2 19.5

11.1 22.1 12.0 23.5

12.7 23.8 13.4 24.8

10.6 18.1 11.7 20.1

11.2 16.7 12.0 17.3

10.1 16.6 11.1 17.4

9.9 16.9 10.7 17.5

10.4 12.6 11.2 13.3

12.0 15.5 13.0 17.0

11.8 15.3 12.4 16.0

14.3 18.0 14.6 18.5

12.4 20.0 13.2 20.9

11.2 24.7 12.1 26.0

‘Due to the selection of test subsets, ranges for all-pines and all-hard woods data sets may differ from species ranges.
Table J.-Species and number of trees included in other-hardwoods

data set and test subset

Species Number of trees

Boxelder 6

Red Maple 4

Water hickory 3

Pecan 1 2

Persimmon 1

American beech 15

Water locust 3

Honey locust 2

Black walnut 2

Cucumbertree 1

Sweetbay 1

Sassafras 1

Basswood 2

Winged elm 6

American elm 8

Cedar elm 1

Mulberry 1

Black cherry 3

Laurel oak 1

Overcup oak 1

Bur oak 3

Chinkapin oak 2

Swamp chestnut oak 1 2

Nuttall oak 8

Willow oak 8

Chestnut oak 1

Black oak 1 1

White ash 7

Green ash 6

Selection of ‘I&t Subsets

A species test subset was extracted from every species data set which contained more than 30 sample

trees. Each species data set was sorted in ascending

order by dbh. The test subset was extracted from the

data set by systematic sampling with a random start.

The all-pines test subset consisted of 10 percent of

the samples in the all-pines data set. All other test

subsets consisted of 20 percent of their respective data

set. Black tupelo, yellow-poplar, sugarberry, and

beech data sets had less than 30 sample trees; consequently, no test subsets were selected from these species.

The test subset and the remaining data set are

mutually exclusive. From here on, reference to the

data set excludes all trees in the test subset.

Anomalies in Data Sets

Some anomalies were present within the data sets.

The majority of trees were sawtimber size. From table

2, the ,mean dbh was approximately 14 inches. The

distribution of sample trees by dbh class was skewed

because the sample came from logging sites. Therefore, prediction equations are most appropriately applied to sawtimber trees.

4

Some data sets were consistent in having the top

diameters larger than the minimum. Hickory merchantable top diameters were generally greater than

4.0 inches. Hickory and post oak sawtimber top diameters were generally greater than 9.0 inches. White

oaks greater than 13.0 inches dbh had sawtimber top

diameters generally greater than 9.0 inches. The

equations developed from these data sets will therefore predict a lower volume than expected for trees

which meet the National Forest Survey Handbook

standards.6

Yellow-poplar dbh’s ranged from 15.3 to 22.5 inches.

Beech dbh’s ranged from 8.9 to 21.9 inches. Volume

prediction of poletimber trees for yellow-poplar and

beech is not recommended.

Selection of Regression Equation

Trends of linearly increasing absolute residuals

with increasing stump diameters indicate that

weighted regression techniques may yield better predictive equations. After preliminary analysis using

both weighted and unweighted regression techniques,

the weighted regression equations were better (Bylin,

1979). The weights used were:

1 / (stump diameter inside bark)

or

1 / (stump diameter outside bark)

The general equation used is:

V = bo + bl*D2 + ba*SHT

where

V =Volume in cubic feet (total, merchantable, or sawtimber)

D =Stump diameter in inches (inside or

outside bark)

SHT =Stump height in feet

bi =Coefficients (i = 0,1,2)

RESULTS AND DISCUSSION

I tested the hypothesis:

H, : b2 = 0

using unweighted step-wise regression techniques

with the partial F-test at .05 level. The hypothesis was

not rejected. The results of a previous study (Bylin,

1979) conflict with this finding. Greater variation in

stump height in the former study may explain the

significance of stump height in that study and the lack

of significance in the present one.

‘Ibid.
Stump height was eliminated from the equations

before weighted regression equations were developed.

Table 4 presents coefficients of the weighted regression equations, the standard error, the coefficient of

determination (R2), and the number of samples. Mean

stump height was 0.8 foot for softwoods and 1.0 foot for

hardwoods.

The standard errors ranged from 3.70 cubic feet for

post oak to 14.54 cubic feet for beech. The coefficient of

determination ranged from 52 for other-hardwoods to

.94 for post oak. The majority of R2’s were greater than

.78.

The equations for predicting sawtimber volumes (C

and F) normally had a lower R2 and a larger standard

error. The equations using stump diameter inside

bark (A, B, and C) generally had better R2 and standard errors than the other equations (D, E, and F).

The equations for elm, ash, and beech sawtimber

trees were rejected due to low R2, large standard

errors, and small sample size (13-15). Other equations

were developed using various combinations of variables. In addition to stump diameter squared, the following were included in a step-wise regression: stump

diameter cubed; square root of stump diameter cubed;

stump diameter times stump height; stump diameter

squared times stump height; stump height; and a third

degree polynomial of stump diameter. None of these

variables significantly improved the equations.

The inclusion of stump height improved slightly,

but not significantly, the equations’ volume prediction. Some users of the equations might prefer this

slight improvement. Regression equations were developed including stump diameter squared and stump

height as independent variables. Table 5 presents the

coefficients, standard errors, coefficients of determination (R2), and number of samples.

Equations in table 5 differ from those in table 4

because stump height is included and unweighted regression was used. The inclusion of stump height in

the equations posed a weighting problem since it is

often difficult to obtain specific information regarding

the nature of the weighting vector (Draper and Smith,

1966). Thus, no weighting was attempted in this case.

Equations in table 5 were formulated before those in

table 4. Differences in the number of observations

between table 4 and 5 result from the identification

and rejection of a number of observations due to duplication or coding errors.

Testing the Equations

The equations in table 4 were verified by the comparison of variances or F-test between the equations

and the test subsets.

The following hypotheses were tested:

Hi: sf >s;

where

2

St

2 2

St = Sr

= Variance of test subset

= Variance of regression equation (mean

square error)

and

2

St = (Z residuals2) / (Number of test trees)

F-test =s; 1s;

Those trees in the test subset whose residuals were

greater than * 4 standard errors were reexamined.

Examples of the abnormalities of these atypical trees

were: the merchantable top diameter was 17.0 inches

instead of 4.0 inches; the height ofthe tree was 20 to 30

feet greater than other trees in the same dbh class; and

the difference between stump diameter and dbh was

10.0 inches. Elimination of these trees from the test

subset a posteriori lead to the adoption of a modified

F-test.

Using the F-test or, when required, the modified

F-test, all equations failed to be rejected at the .05

significance level.

Results of Test Subsets

Based on the F-tests, all equations presented in

table 4 are sufficiently accurate for the prediction of

volumes. These equations will predict volume within

+ 2 standard errors 95 percent of the time.

Water oak sawtimber equations were the worst predictors of volume. Clues to this poor performance are

offered by several unusual characteristics in the data

set. Sawtimber top diameter was generally greater

than 9.0 inches. This caused the actual volume to be

less than the predicted volume. Many trees had large

butt swell (large stump diameter) which caused the

predicted volume to be larger than the actual volume.

Southern red oak prediction equations slightly overestimate the volume of their test subset. Stump

heights, ranging from 0.4 to 2.9 feet (table 2), contributed to the small overestimation. Overestimations

were too small to cause rejection of the equations.

In spite of the variety of species within the otherhardwoods data set (table 3), these equations had excellent volume prediction, Both the other-hardwoods

5
Table 4.-Equations using stump diameter to predict total, merchantable, and sawtimber volumes.

Equation* bo bl SE? R2$

Slash Pine

A

B

C

D

E

F

Shortleaf Pine

A

B

C

D

E

F

Longleaf Pine

A

B

C

D

E

F

Loblolly Pine

A

B

C

D

E

F

All Pines

A

B

C

D

E

F

Hickory

A

B

C

D

E

F

Sweetgum

A

B

C

D

E

F

Beech

A

B

D

E

-3.188 .164 5.31 .83 137

- 3.430 .164 5.31 .83 137

- 6.073 .171 8.04 .59 71

- 3.981 .123 5.68 .81 137

- 4.225 .123 5.67 .81 137

- 7.493 .130 8.57 .55 71

White Oak

A - 4.004

B - 1.111

C - 1.793

D - 4.979

E - 1.943

F -2.827

Cherrybark Oak

A - 1.833

B - 1.113

C - 5.736

D - 2.236

E - 1.504

F - 6.233

Post Oak

A - 2.054

B - 1.037

C 1.800

D - 2.962

E - 1.738

F 1.125

Water Oak

A 1.208

B .222

C 2.654

D .380

E -.592

F 1.901

Southern Red Oak

.i28 7.91 .80 72

,100 6.16 .80 72

,087 6.17 .69 57

,113 8.20 .79 72

.088 6.28 .80 72

,078 6.41 .67 57

- 2.522 .186 6.26 .92 196

- 2.566 .182 6.39 .91 196

- 3.526 .174 7.66 .81 151

- 3.453 .152 6.93 .90 196

- 3.466 .149 7.06 .89 196

-4.710 ,144 8.38 .77 151

.126 9.66 .89 2 8

.113 9.93 .86 28

,108 9.68 .81 22

.112 9.77 .89 28

.lOO 9.95 .86 2 8

,096 9.74 .81 22

.603 .137 4.33 .87 42

.508 .134 4.63 .85 42

- 1.514 .133 4.45 .83 35

-.043 .107 4.48 .87 42

-.134 ,105 4.76 .85 42

-2.156 .104 4.50 .82 35

.106 3.70 .94 68

.085 3.75 .90 6 8

.064 5.36 .57 32

,090 3.93 .93 68

.071 3.91 .90 68

.054 5.41 .57 32

- 5.256 ,189 9.71 .89 436

- 5.452 ,186 9.66 .89 436

- 9.012 .183 11.21 .79 337

-7.198 .158 10.32 .87 436

- 7.376 ,156 10.26 .87 436

- 11.627 .155 11.74 .77 337

.112 11.06 .90 62

.103 11.07 .89 62

.078 11.21 .75 52

.103 11.00 .91 62

.095 10.93 .89 62

,072 11.19 .76 52

-4.319 .184 8.05 .89 914 A - 1.552 .112 4.63 .89 89

- 4.458 .181 8.01 .89 914 B ,042 ,090 3.82 .88 89

- 6.659 ,176 9.61 .79 671 C - 2.429 .087 4.84 .73 50

- 6.073 .153 8.80 .88 914 D - 2.176 ,095 4.92 .87 89

-6.192 ,150 8.74 .87 914 E -,410 ,076 4.08 .87 89

- 9.073 ,148 10.32 .76 671 F - 2.827 ,073 5.18 .70 50

-3.681 .144 7.60 .88 36

- 1.708 .118 7.43 .84 36

-.929 .093 6.96 .74 30

- 6.099 .126 7.37 .89 36

- 3.613 .103 7.35 .85 36

- 3.366 .083 6.55 .77 30

Sugarberry

A

B

C

D

E

F

2.290 .073 6.79 .83 21

3.707 .059 7.06 .75 21

- 1.267 .056 6.34 .72 17

1.843 ,068 6.93 .83 21

3.248 ,055 7.09 .75 21

- 2.084 .052 6.24 .74 17

- 2.575 .132 7.01 .86

- 1.996 ,120 6.54 .85

- 6.901 .120 8.97 .63

- 3.360 .121 7.06 .85

- 2.706 ,110 6.56 .85

- 8.916 .113 9.02 .62

- 2.388 .142 14.46 .67

- 3.713 .126 11.51 .71

- 1.725 .131 14.54 .66

- 3.354 ,117 11.44 .72

119

119

66

119

119

66

15

15

1 5

1 5

Black Tupelo

A

B

C

D

E

F

Yellow-poplar

A

B

C

D

E

,523 ,101 9.16 .75 23

.653 .092 8.88 .73 23

6.715 ,059 7.47 .54 1 3

-.649 .092 8.90 .77 23

-.549 .084 8.52 .75 23

5.727 ,054 7.60 .53 13

- 5.930

-8.151

- 15.190

- 2.401

- 5.086

,198 13.00 .66 14

.193 13.66 .63 14

,183 12.70 .63 14

.165 13.65 .63 14

.162 14.13 .60 14

.154 13.15 .60 14

No.

samples Equation* bn h SEt

F - 12.518

No.

R2$ samples

6
Table 4.-Equations using stump diameter to predict total, merchantable, and sawtimber volumes.--Continued

Equation* bo bl SE? R2$ sa!i;es 1 Equation* b, bl SEI- R23: s,f;Iiies

Other Hardwoods

A 1.249 ,108

B .643 .097

C 5.708 ,068

D 556 .097

E -,047 .087

F 4.498 ,063

All Hardwoods

A -.924 .117 9.33 .83 619

B -.841 .103 8.96 .80 619

C .290 .084 9.46 .62 408

D - 2.108 .105 9.51 .82 619

E - 1.863 ,093 9.16 .80 619

F - 1.000 .077 9.64 .61 408

TV = Total volume (cubic feet)

MV = Merchantable volume (cubic feet)

s v = Sawtimber volume (cubic feet)

SDIB = Stump diameter inside bark (inches)

SDOB = Stump diameter outside bark (inches)

b’i = Coefficients

*A. TV = b,, + bl l SDIB’

B. MV = b,, + bl l SDIB2

C. SV = b0 + b1 l SDIB2

D. TV = b, + b, l SDOB2

E. MV = b0 + b1 l SDOB2

F. SV = b. + bl l SDOB2

TSE = Standard error (cubic feet).

tR2 = Coefficient of determination.

Table B.-Equations using stump diameter and stump height to predict total, merchantable, and sawtimber volumes.

r

b SEt R2$

No.

Samples

8.654 8.75 .81 73

6.814 6.31 .82 73

12.868 6.27 .78 5 8

8.833 9.00 .80 73

6.850 6.36 .82 73

13.534 6.44 .77 58

1.763 12.29 .88 28

4.299 12.41 .85 2 8

-.408 13.61 .82 22

.429 12.43 .88 28

3.108 12.46 .85 2 8

- 1.524 13.76 .82 22

4.747 4.26 .94 68

6.477 4.31 .90 6 8

4.794 5.63 .59 32

4.464 4.59 .93 6 8

6.285 4.51 .89 68

5.497 5.54 .60 32

4.619 12.58 .92 62

2.970 12.85 .90 62

1.338 13.86 .80 52

4.377 12.49 .92 62

2.766 12.63 .90 62

1.241 13.83 .80 52

- ,486 5.48 .88 89

.752 4.41 .87 89

-.183 5.38 .78 5 0

-.887 5.78 .86 8 9

.489 4.71 .85 89

-.708 5.72 .76 50

bo bl b, SE? R2$

No.

Samples

-9.361 .153 10.093 6.33 .82 137

-9.593 .153 10.051 6.34 .82 137

-15.064 ,156 13.876 8.52 .61 71

-10.385 .115 10.375 6.65 .80 137

-10.616 ,115 10.332 6.65 .80 137

- 16.790 .120 14.056 8.95 .57 71

-4.602 .180 4.426 7.38 .90 196

-4.732 .176 4.559 7.53 .89 196

-5.475 ,166 5.170 8.75 .80 151

-6.289 ,147 5.478 8.07 .88 196

-6.381 .144 5.623 8.22 .87 196

-7.018 .135 6.237 9.50 .77 151

3.749 ,140 -4.964 4.92 .86 43

3.699 .137 -4.892 5.29 .84 43

1.486 ,134 -3.932 5.33 .81 36

3.898 .lll -6.248 5.21 .85 43

3.845 .108 -6.145 5.55 .82 43

1.537 .105 -4.758 5.57 .79 36

-13.587 ,185 11.177 11.88 .87 436

-13.843 .183 11.255 11.82 .87 436

-23.889 .174 20.326 13.29 .79 337

-15.558 ,155 10.904 12.36 .86 436

-15.787 .153 10.971 12.28 .86 436

-26.456 .148 20.121 13.65 .78 337

- 10.776 .181 9.029 9.95 .88 914

- 10.956 .178 9.079 9.90 .88 914

-16.384 .169 13.888 11.54 .80 671

- 12.963 .151 9.223 10.60 .86 914

- 13.109 ,149 9.259 10.52 .86 914

-19.244 .143 14.143 12.07 .78 671

Equation*

Slash Pine

A

B

C

D

E

F

Shortleaf Pine

A

B

C

D

E

F

Longleaf Pine

A

-B

C

D

E

F

Loblolly Pine

A

B

C

D

E

F

All Pines

A

B

C

D

E

F

Equation* bo bl

White Oak

A - 12.130 .124

B - 6.392 .092

C - 15.498 .083

D - 13.545 .llO

E - 7.510 .082

F - 17.416 ,075

Cherrybark Oak

A - 3.346 ,125

B -4.857 ,110

C - 5.716 .109

D -2.377 .lll

E - 4.020 ,098

F - 4.991 .097

Post Oak

A - 5.903 ,103

B - 5.438 .077

C - 1.101 .056

D - 6.785 .088

E - 6.095 ,066

F - 3.275 ,050

Water Oak

A -3.441 .112

B - 2.925 ,104

C 2.540 ,075

D -4.173 .103

E - 3.685 .096

F 1.865 .070

Southern Red Oak

A - 1.644 ,115

B -.136 .087

C - 1.476 ,084

D - 2.133 ,098

E -.480 .074

F - 1.518 ,072

,

7
Table 5.-Equations using stump diameter and stump height to predict total, merchantable, and sawtimber volumes.-Continued

No.

Samples SEt R2t

No.

Samples

.069 -2.638 6.88 236 21

.055 -2.107 7.28 .77 21

.056 -1.829 6.17 .83 1 7

.063 -2.393 7.18 34 21

,050 -1.884 7.41 .76 21

.051 -1.522 6.24 32 1 7

.080 13.810 10.23 .73 23

.076 9.092 10.28 .68 23

.034 24.299 6.22 .71 13

,075 14.012 9.65 .76 23

,071 9.161 9.68 .72 23

,033 24.360 6.21 .71 13

Eauation* b, b, b, SE-F R2+ Equation* bo

- 7.247 ,135 5.392 8.58 38 36

- 5.236 .106 5.835 8.34 33 36

- 5.156 ,089 4.406 8.64 .73 30

- 10.750 ,121 5.793 8.04 239 36

- 8.017 .096 6.176 8.02 234 36

- 10.536 ,082 6.241 7.87 .77 30

- 4.396 .129 2.750 8.50 32

- 2.592 ,116 1.609 7.80 22

- 13.361 ,122 5.388 9.68 .65

- 5.073 .119 2.363 8.49 32

- 3.208 .107 1.215 7.75 22

- 15.405 .114 5.610 9.67 .65

- 33.518 ,075 46.426 12.90 .95

- 27.434 .066 38.208 11.02 .95

- 32.765 .062 48.550 13.16 .94

- 26.762 ,054 40.055 11.27 .95

Yellow-poplar

A -40.982 .240 16.916

B -44.836 .238 19.644

C -46.355 .220 16.694

D -36.493 .201 16.656

E -41.361 ,200 19.717

F -42.710 .185 16.617

13.45 .69

14.18 .66

14.06 .63

14.21 .65

14.74 .63

14.61 .61

119

119

66

119

119

66

15

1 5

1 5

1 5

1 4

1 4

1 4

1 4

1 4

1 4

Hickory

A

B

C

D

E

F

Sweetgum

A

B

C

D

E

F

Beech

A

B’

D

E

Sugarberry

A 7.898

B 8.377

C 1.349

D 7.382

E 7.854

F .678

Black Tupelo

A - 7.758

B -4.191

C - 13.135

D - 9.585

E - 5.925

F - 14.189

Other Hardwoods

A - 12.412

B - 8.891

C 6.345

D - 13.697

E - 10.283

F 4.117

All Hardwoods

A - 4.239

B - 2.599

C 2.936

D - 5.584

E - 3.792

F .925

.103 15.340 11.43 .83 85

.093 10.774 10.91 .81 85

.059 1.951 10.66 .57 56

,093 16.108 11.49 23 85

,085 11.403 10.82 .81 85

,055 3.162 10.62 .58 5 6

.llO 5.222 11.34 .81 620

,099 2.973 10.99 .79 620

.076 .267 11.44 .65 409

,100 5.029 11.39 .81 620

,090 2.824 11.08 .79 620

,070 ,665 11.45 .65 409

*A. TV = b,, + bl l SDIB’ + b2 l SHT

B. MV = b, + bl l SDIB’ + bz l SHT

C. SV = b, + b1 l SDIBZ + bz l SHT

D. TV = b, + b1*SDOB2 + bz*SHT

E. MV = b. + b1*SDOB2 + ba*SHT

F. SV = b. + b,*SDOB’ + ba*SHT

PSE = Standard error (cubic feet).

$R2 = Coefficient of determination.

TV = Total volume (cubic feet)

MV = Merchantable volume (cubic feet)

s v = Sawtimber volume (cubic feet)

SDIB = Stump diameter inside bark (inches)

SDOB = Stump diameter outside bark (inches)

SHT = Stump height (feet)

b’i = Coefficients

and the all-hardwoods equations generally overestimated volume of small trees (< 10 inches dbh). The

other-hardwoods and all-hardwoods equations were

tested on yellow-poplar, sugarberry, beech, and black

tupelo. These equations overestimated the volume for

sugarberry and underestimated the volume for yellow-poplar and beech. The all-hardwoods equations

predicted black tupelo volume very well, and can be

used to predict volumes of beech and black tupelo.

Volume for yellow-poplar and sugarberry, however,

should not be predicted using the all-hardwoods or

other-hardwoods equations.

Since the beech sawtimber equations were rejected,

all-hardwoods sawtimber equations on the beech data

set were tested. Using the F-test, the equations failed

to be rejected. For beech sawtimber volume prediction,

the all-hardwoods sawtimber equations can be used.

Longleaf pine equations in table 5 were verified

using the F-test. The F-test failed to reject any of the

equations. Without further testing of the other species

equations, all equations presented in table 5 were

judged accurate enough to predict volume. These

equations have the same confidence level for prediction of volumes as those in table 4.

Using the Equations

The equations presented in table 4 and table 5 are

most applicable in Louisiana. Prediction of tree

volume for other species, other locations, or outside the

range of stump diameters should be verified with an

independent sample data set. The equations should

not be used to predict volume of trees with stump

8
diameters less than 5.0 inches. For example, hickory

equations are valid only for trees with stump diameters between 9.0 and 28.2 inches. Ranges of stump

diameters are presented in table 2. In using equations

from table 4, the stump height should be close to the

mean of 1.0 foot for hardwoods and 0.8 foot for softwoods.

The all-pines equations can be used on loblolly,

slash, longleaf, and shortleaf pine, although they

would be less accurate than each individual species

equations. The other-hardwoods and all-hardwoods

equations can be used to predict volume of most hardwoods species. As illustrated with yellow-poplar and

sugarberry, these equations may overestimate or

underestimate the volume of particular species.

These equations are invalid when applied to irregular stumps, i.e. those with rot, large cracks, etc.

CONCLUSION

Predicting volume directly from stump dimensions

is useful in many situations. The Renewable Resources Evaluation Unit can now use these equations

to calculate directly volume of cut trees which were not

in the previous survey. These equations can be used to

obtain the volume of stolen trees. Researchers who

have lost permanent trees in their experiment can

obtain estimates of volume from these equations.

These equations predict gross volumes. Estimation

of gross volume ignore any cull or defect that might

have been present in the tree.

Similar studies are planned for Alabama and other

southern states. These studies will include measurement of diameter at one-half foot intervals from

ground level to dbh to improve volume calculations. To

insure accurate results, the maximum length of any

section shall be 8 feet.

Using these equations, total, merchantable, and

sawtimber volumes are predicted accurately. Equations presented in tables 4 and 5 will predict the

volume within * 2 standard errors 95 percent of the

time.

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9
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10
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11

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Equations for predicting cubic foot volumes from stump diameter and stump height.

Additional keywords: Volume, sawtimber volume, total

volume, merchantable volume, stump diameter, Ttump height.