* Forest Service

Southern Forest

Experiment Station

Nuttall Oak Volume

and Weight Tables

2’ New Orleans,

Louisiana

Research Paper

SO-l 86 Bryce E. Schlaegel and Regan B. Willson

January, 1983
SUMMARY

Volume and weight tables were constructed from a 62-tree sample of

Nuttall oak (Quercusnutkdlii Palmer) taken in the Mississippi Delta. The

tables present volume, green weight, and dry weight ofbole wood, bole wood

plus bark, and total tree above a one-foot stump as predicted from the

nonlinear model Y = b,Dtl~I+. Merchantable bole volumes and weight

estimates can be made to outside bark diameter limits of 2 to 12 inches in

2-inch increments. More precise bole estimates can be obtained from

equations using upper bole diameters at relative heights of 25, 33, and 50

percent of total tree height.
Nut9tall Oak Volume and Weight Tables

Bryce E. Schlaegel and Regan B. Willson

INTRODUCTION

Nuttall oak (Quercus nuttallii Palmer) grows on

the bottomlands of the Coastal Plain of the

southern United States from Alabama to southeastern Texas, north in the Mississippi Valley to

Arkansas, southeastern Missouri and western

Tennessee (fig. 1). It reaches its best development on

the alluvial bottomlands of the Mississippi River

and its tributaries. On good sites, it is a moderately

rapid grower reaching heights of 120 feet and a dbh

in excess of 36 inches.

In recent years there has been considerable

demand for volume and weight tables for

bottomland hardwood species. This paper is the

second in a series of six giving both volume and

weight tables for some of the major bottomland

hardwood species. The other five species in the

series are willow oak (Q. phellos L.) (Schlaegel

1981), overcup oak (Q. lyrata Walt.), sugarberry

(Celtis laevigata Willd.), sweetgum (Liquidambar

styraciflua L.), and green ash (Fraxinus pennsylvanica Marsh.).

METHODS

The data were collected from 13 natural

bottomland hardwood stands in Mississippi. All

stands were uneven-aged of mixed species composition. Each stand was measured for species composition and diameter distribution. A total of 62 trees

was chosen for destructive sampling and ranged in

dbh from 2 through 38 inches. Growing stock trees

with healthy crowns and no visible signs of disease

or decay were selected from both the overstory and

understory. When available, three trees were

selected from each diameter class.

Stump height, height to base of live crown, and

total height were measured on each felled sample

tree. Disks about l-inch thick were cut from the bole

at regular intervals from the stump to the top of the

tree. These were then sealed in separate polyethylene bags for laboratory determination of moisture

content and specific gravity. The first disk was at

stump height and the remainder at &foot intervals

from the ground for trees 5 inches dbh and larger,

and at 3-foot intervals for trees smaller than 5

inches dbh. All limbs were weighed on 60 of the

trees.

In the laboratory, both wood and bark moisture

content and specific gravity were determined as

follows:

1. Wood and bark were separated with a

hammer and chisel.

2. Each component was weighed green.

3 . Both wood and bark were soaked in water for

at least an hour to ensure complete swelling.

4. Volumes were obtained by immersion

(Heinrichs and Lassen 1970).

5 . Wood and bark were dried in a forced-air oven

at 105°C for at least 48 hours.

6. Wood or bark moisture content =

green weight - ovendry weight

ovendry weight

7. Specific gravity =

ovendry wood or bark weight (g)

green wood or bark volume (cm”) ’ Average tree moisture content and specific

gravity were calculated from weighted averages of

the disk values; each disk specific grav$y or

moisture content was weighted by its squared

average diameter.

Taper functions of the form

Y = bl(X’ -1) + bf(X’ - 1) + . . . + b,(Xp - 1)

where

Y = d/D,

d = diameter at height h on the bole,

D = dbh,

X = h/H,

h = height from ground to a specific measurement point,

Bryce E. Schlaegel is Principal MensurationistSouthern Hardwoods Laboratory, maintained at Stoneville, Mississippi, by the Southern

Forest Experiment Station, Forest Service-USDA, in cooperation with the Mississippi Agricultural and Forestry Experiment Station

and the Southern Hardwood Forest Research Group. Regan B. Willson is Instructor in Computer Information Systems at Delta State

Univ., Cleveland, Mississippi.
Figure I.-The range of Nuttall oak. (F-506656)

H = total height,

b, = coefficients estimated for each tree by

linear regression; i = 1, 2, . . . p; 4 (p 17,

were calculated for each tree, both inside and

outside bark. Cubic-foot volumes were obtained for

each tree by integrating the taper function to

heights of specific top diameters. Bole green and dry

weights were calculated from estimated tree volume

and weighted average tree density and moisture

content.

Nonlinear regression equations were used to

predict volume, green weight, and dry weight ofbole

wood, bole wood plus bark, and bole wood plus bark

plus branches.

RESULTS

Average characteristics for the trees in this study

were:

Average Range

Age (wars) 71 28-123

Dbh (in) 17.6 2.6-37.9

Total height (ft) a2 25-118

Wood moisture content

jpercent) 9 0 57-i12

Bark moisture content

(percent) 64 53-93

Wood specific gravity 0.558 0;505-0.660

Bark specific gravity

Wood + bark green

density (lbs/ft3)

Wood + bark dry density

(lbs/ft3)

Wood + bark moisture

content (percent)

Wood + bark specific

gravity

0.619 0.389-0.702

65.62 61.26-69.19

35.20 32.08-39.90

87 60-107

0.564 0.514-0.639

The nonlinear model used to fit individual tree

volume and weights is

Y = boDbrHbz + e (1)

where

Y = the volume or weight variable of interest,

D = tree dbh in inches,

H = total height in feet,

e = random error for Y, and

bo, bl, and bp are coefficients esti,maled from the

data. An iterative least squares technique proposed

by Hartley (1961) was used to estimate equation

coefficients.

Estimates of the coefficients are presented in

table 1 for predicting cubic-foot volume, green and

dry weight of bole wood, bole wood plus bark, and

bole wood plus bark plus branches. Additional

statistics presented are the component means, fit

index (FI), the regression standard error of estimate

(S&J, and the coefficient of variation (C.V.) of

predictions. Fit index, which is similar to the coeffi2
.

cient of determination (R2) is used to judge equation

efficiency when the dependent variable has been

transformed (Farrar 1978) or has been estimated by

other than linear least squares techniques. It is

calculated from the total and residual sums of

squares of untransformed units.’ The fit index and

R’ are equal when a simple linear regression

analysis is performed on an untransformed

dependent variable.

Fit indices range from 0.982 to 0.988 for all

components. A fit index of 1.0 indicates that

predictions can be made without error with the data

used to fit the model; a value close to 1 .O is desirable.

Coefficients of variation, which are indices of

relative precision of prediction, range from 10.9

percent to 13.3 percent.

Using measures of individual tree dbh and total

height, estimates can be made for tree volume (table

2), green weight (table 3), or dry weight (table 4) for

bole wood, bole wood plus bark, and for bole wood

plus bark plus branches.

MERCHANTABLE BOLE

ESTIMATES

The merchantable bole is defined as that portion

of the tree bole from a one-foot stump to a specific

top diameter outside bark, excluding limbs.>

Merchantable bole volume or weight can be

expressed as a proportion of the total bole by. a

simple asympt.otic model proposed by Stevens

(1951):

RI=a •t PrD (2)

where

D = tree dbh outside bark,

RI = ratio of merchantable bole volume (weight)

to total bole volume (weight), where I = top

d.o.b. of merchantable bole, e.g. R4=

V4/VT, where

R4 = ratio to a 4-inch top

V4 = bole volume to a 4-inch top

VT = bole volume to top of tree

(Y&Y = parameters to be estimated from the data,

where

( Y q the upper asymptote of the ratio, (Y < 1,

p = the change in the ratio estimate as D

extends from 0 toward infinity, and

y = the factor by which the deviation of the

ratio is reduced from its asymptotic value

by each unit step of D.

For each top diameter, separate ratio equations .

were fitted for inside and outside bark volume,

green weight, and dry weight. Placing confidence

‘FI= [l - [z:(Y - $)“I / [,X(Y - y)c]j

bounds on the parameter estimates as

recommended by Gallant (1975) showed no

significant difference between the inside and

outside bark equations for either the volume or

weight ratio estimates. Thus, for a given outside

bark top diameter, both the inside and outside bark

merchantale bole ratio can be estimated using the

same equation.

The data inside and outside bark were then

combined to test the applicability of using a single

ratio equation to predict, for a given top diameter,

either merchantable volume, green weight, or dry

weight. As above, separate equations were derived

for volume, green weight, and dry weight. The three

sets of parameters were compared by using

confidence interval estimation as above. No

significant differences were found between

parameter estimates for volume, green weight, and

dry weight. Thus, for a specific top diameter, the

ratio of merchantable bole to total bole is the same

for either volume, green weight, or dry weight,

inside and outside bark. Thus, only one ratio

equation per top diameter is needed.

Table 5 gives the parameter estimates for this

second model by 2-inch top diameters outside bark

using nonlinear least squares techniques proposed

by Stevens (3951). The volume or weight to any top

diamet,er is found by multiplying the ratio estimate

from one of the equations in table 5 times the total

bole volume or weight estimates from tables 2, 3,

or 4.

IMPROVED TOTAL BOLE

.ESTIMATES

The precision of the merchantable bole estimate

depends upon the precision of the total bole

estimate. The more precisely the total bole is

predicted, the more precise will be the merchantable

bole prediction. But how can total bole estimates be

improved?

Total bole estimates can be significantly

improved by measuring one or two additional

diameters on the bole. Tables 6 and 7 give

regression statistics for total bole volume and

weight under two different model forms:

Y = bo(Dbr + D1,3b2) Hb3 + e

and

Y = bo[(Dbr . D1,2b2) + D1,4b3] Hb4 + e

where D, H, and Y are as defined previously, and

D1,3, D1,2, and Dr14 are diameters outside bark at l/3,

l/2, and l/4 the total height, respectively.

Statistics from tables 6 and 7 show the significant

improvement, based on variance reduction, over the

previous dbh and height equations of table 1.

Measuring one additional diameter at l/3 the tree
I

height, D,,:,, reduces the standard error of estimate

33 to 47 percent for both bole wood and the total

bole. i

Measuring two upper bole diameters at points l/4

and l/2 of the total height result in further significant increases in precision. Improvements in the

standard error of estimate over the dbh and height

model range from 60 to 80 percent for bole wood and

total bole.

Taking additional bole measurements means a

higher inventory cost, since more time will need to

be spent at each tree. However, a large proportion of

inventory cost is travel to the candidate tree. The

data presented in this section allow total and

merchantable bole estimates to bemade with a high

degree of reliability. Each user has to decide when

increased precision is needed and whether the need

will offset the increased cost.

( 1

LOCAL VOLUME TABLES

There are many occasions when the only tree

variable available is dbh, or perhaps only a rough

estimate of tree volume or weight is needed. In these

cases a local volume table will suffice. Table 8 gives

the statistics needed for estimating by the local

volume table technique. However, it must be

realized that estimation precision may be

considerably lessened. The local volume or weight

model is Y = boDbr + e.

LITERATURE CITED

Farrar, R. M., Jr.

1978. Silvicultural implications of the growth

response of naturally regenerated even-aged

stands of longleaf pine (Pinuspalustris Mill,) to

varying stand age, sitequality, and density and

certain stand structure measures. Unpublished

Ph.D. dissertat,ion, University of Georgia,

Athens, Ga. 132 p,

Gallant, A. R.

1975. Nonlinear regression. Am. Stat. 29(2):73-81.

Hartley, H. 0.

1961. The modified Gauss-Newton method for fitting of non-linear regression functions by least

squares. Technometrics 3(2):269-280.

Heinrichs, J. Frank, and L. E. Lassen.

1970. Improved technique for determining the

volume of irregularly shaped wood blocks. For.

Prod. J. 20(4):24.

Schlaegel, Bryce E.

1981. Willow oak volume and weight tables for the

Mississippi Delta. U.S. Dep. Agric. For. Serv.

Res. Pap. SO-173, 14 p. South. For. Exp. Stn.,

New Orleans, La.

Stevens, W. L.

1951. Asymptotic regression. Biometrics 7:247-

267.

Table I.-Regression statistics for predicting Nuttall oak tree volumes and weights’

Component

Bole wood

Total bole

Total tree

Bole wooa

Total bole

Total tree

Bole wooa

Total bole

Total tree

Average Fit C.V.

Y b,, b, bz index8 $,I’:’ percent’

Volume (cubic feet)

68.8 0.00160 1.7760 1.1794 0.987 7.87 11.4

76.6 0.00211 1.7490 1.1609 0.987 8.68 11.3

113.9 0.00844 2.2210 0.6112 0.988 13.23 11.6

Green weight (pounds)

4576 0.05261 1.7910 1.3211 ’ 0.988 40 11.1

5076 0.07352 1.7646 1.2893 0.988 651 10.9,

7540 0.30356 2.2438 0.7269 0.987 934 12.4

Dry weight (pounds)

2324 0.05839 1.7362 1.1899 0.982 308 13.3

2631 0.08238 1.7130 1.1582 0.982 342 13.0

3909 0.31596 2.1854 0.6169 0.984 616 13.2

IVolumes and weights of trees from a I-foot stump to the tree tip, using Y = boDblHb; D = a&

I-l = total height.

PFit index = 1 - [Z(Y - ?)O/I(Y -?)“I.

$&J = [X(Y - Pp/(n - 3)]“‘.

Coefficient of variation = 100 &LX/S,

4
Table Z.-Cubic-loot volume joor Nuttoll oak bole wood, bole wood plus bark, and total tree’

Total height in feet

Dbh 2 0 30 40 50 6 0 70 80 9 0 100 110 120 130

inches

2

3

4

5

6

7

8

9

10

1 1

12

13

1 4

15

16

1 7

18

19

.._._............ _ ..-....._..__._.._..__ _ . . . . ..__._._..... __..__- cubic feet _.....__. __ ._.___. __.__.__ .__.__.__ _ ..__.__..______ ____ ____ ______

0.192

0.23

0.25

0.393 0.62

0.47 0.75

0.60 0.77

1.04 1.45

1.24 1.73

1.47 1.75

1.54 2.16

1.83 2.55

2.41 2.87

2.13 2.99

2.51 3.51

3.61 4.30

3.93

4.59

6.06

4.98

5.80

8.15

6.14

7.13

10.6

3.89

4.55

4.93

5.11

5.95

6.94

6.48

7.52

9.34

7.99

9.24

12.1

9.63

11.1

15.3

11.4

13.1

19.0

13.3

15.3

23.0

6.34

7.36

7.76

8.04

9.29

10.4

9.91

11.4

13.6

11.9

13.7

17.1

14.1

16.2

21.2

16.5

18.9

25.7

19.0

21.7

30.7

21.7

24.7

36.2

24.5

27.9

42.2

9.64

11.1

11.5

11.9

13.7

14.9

14.3

16.4

18.8

17.0

19.4

23.3.

19.8

22.6

28.2

22.8

26.0

33.7

26.0

29.6

39.8

29.4

33.4

46.4

33.0

37.4

53.5

36.8

41.5

61.2

40.7

45.9

69.5

44.8

50.4

78.4

13.9

15.9

16.2

16.8

19.2

20.4

19.9 22.8

22.6 26.0

25.3 27.1

23.2 26.6 30.2

26.4 30.2 34.2

30.6 32.9 35.1

26.7 30.7 34.8

30.3 34.8 39.3

36.6 39.3 42.0

30.5 35.0 39.7

34.5 39.6 44.7

43.2 46.4 49.5

34.5 39.6 44.8

39.0 44.7 50.5

50.3 54.1 57.6

38.6 44.4 50.3 56.3

43.6 50.0 56.5 63.1

58.1 62.4 66.5 70.5

43.0 49.5 56.0 62.7

48.5 55.6 62.8 70.2

66.4 71.4 76.1 80.7

47.6 54.7 62.0 69.4

53.9 61.4 69.4 77.6

75.4 81.0 86.4 91.6

52.4 60.3 68.2 76.3 84.6

58.9 67.5 76.3 85.3 94.3

85.0 91.4 97.5 103.0 109.0

5
Table Z.-Cubic-foot llolume for h’uttall oak bole wood, boir ulood plus bark, and total tree’-Continued

Total heighain feet

Dbh 20 30 40 50 60 70 80 90 100 110 120 130

inches

so

2 1

. . . . . ..___._......_. .____............._.____ _.__ . . . .._._ _ . .._.___ cubic /eel .._____ ___ _____- ____ _.___ _.--.-. ___.___.__.___________ ___________

49.1 57.4 66.0 74.7 83.6 92.7

55.2 64.4 73.9 83.5 93.3 103

87.8 95.3 102 109 116 122

53.5 62.6 72.0 81.5 91.2 101

60.1 70.2 80.5 90.9 102 112

97.9 106 114 122

22 68.0 78.2 88.5

76.1 87.3 98.6

118 127 135

23 7’3.6 84.6 95.8

82.3 94.3 107

130 140 149

24 79.4 91.2 103

25

26

27

28

29

3 0

3 1

3 2

33

34

3 5

36

88.6 102 115

143 154 164

85.4 98.1 111

95.2 109 123

156 168 179

91.5 105 119

102 117 132

171 183 196

97.9 112 127

109 125 141

186 199 213

104 120 136

116 133 150

201 216 231

113 128 145

123 141 160

217 234 249

118 136 154

131 150 170

235 252 269

125 144 163

139 159 180

252 271 289

152 172

168 190

291 310

161 182

177 200

311 332

169 192

187 211

333 355

178 202

197 222

355 378

187 212

207 233

378 403

129 136

99.0 110

110 122

143 151

107 119

119 132

158 167

116 128

128 142

174 183

124 138

138 152

190 200

133 148

148 163

207 219

142 158

158 174

226 238

152 168

168 186

244 258

162 179

179 198

264 279

172 190

190 210

285 300

182 202

201 222

306 323

193 213

212 235

329 347

203 225

224 248

352 371

215 238

236 261

376 397

226 250

248 275

401 423

238 263

261 288

427 450

151

167

210

162

179

230

174

191

250

185

204

271

197

217.

293

209

230

316

222

244

339

235

258

364

248

272

390

261

286

417

275

301

444

289

316

473
Table Z.-Cubic-foot volume for h’uttall oak bole wood, bole wood plus bark, and total tree’-Coniinued

Total height in feet

Dbh 20 30 40 50 60 70 80 90 100 110 120 130

inches _...___......._.....~.....~.~.~.~.~~..~. _..__._ . .._.____ ___ . ..__ _ cubic feet ._.._._ ____--.___.._ ...~~~~~~~~ _._____.___-_._-_ -.._____._.. :....

37 197 223 249 216 304

217 245 274 303 332

402 428 454 479 503

3 8 206 234 261 290 318

221 257 287 317 348

426 454 482 508 533

3 9 216 245 214 303 333

238 268 300 332 364

451 481 510 538 565

4 0 226 256 286 317 349

248 281 313 347 381

477 509 540 569 598

‘Tree volume above a l-foot stump.

‘The three vertical figures for each dbh give volumes of bole wood first, bole wood plus bark second, and total

tree (bole wood plus bark plus branches) last.

sltalicized numbers span the range of the data.

Table S.-Green weight in pounds for Nutsall oak bole wood, bole wood plus bark, and total tree’

Total height in feet

Dbh 20 30 40 50 60 70 80 90 100 110 120 130

inches

2

3

4

5

6

7

8

9

10

__________________________________________________________________________poun&_____ _________________.___________._. ____________________-------------.

102

12

13

203 34

24 41

32 42

5 6

6 8

81

84

101

133

116

139

200

8 2

9 9

100

123

146

164

170

202

247

224

265

349

285

335

471

352

413

614

229

269

291

301

353

411

383

447

554

473

551

722

571

663

914

383

447

469

487

566

633

601

696

824

726

839

1044

597

690

708

~737 879

850 1009

922 1016

890 1062

1023 1215

1167 1286

7
Table 3. -Gwen weight in pounds for Nuttall oak bolr wood, bole wood plus bark, and total tree-Continued

Dbh

inches

1 1

1 2

13

14

1 5

16

1 7

18

19

20

2 1

2 2

2 3

24

25

26

27

28

Total height in feet.

20 30 40 50 60 70 80 90 100 110 120 130

___ ______ _______ ____. ________ _________ _ ____ _________________ ____ __._ ______ poun,js---s ..____._ _.---.... __._-----.-- ___ ---._.--_-. -- -----.__.--._____________

677 861 1056 1260 1472

785 992 1211 1438 1674

1132 1293 1446 1593 1736

791 1007 1234 1472 1720 1977

915 1157 i412 1677 1952 2236

1376 1571 1758 1937 2110 2278

1162 1424 1699 1985 2281

1333 1626 1931 2248 2575

1880 2103 2318 2525 2726

1327 1626 1940 2267 2605

1519 1853 2201 2562 2935

2221 2484 2737 2982 3219

1501 1840 2195 2565 2948

1715 2093 2486 2894 3315

2592 2900 3195 3481 3758

2066 2464 2879 3309 3753

2345 2786 3243 3714 4200

3351 3693 4023 4343 4655

2303 2747 3209 3689 4183

2610 3100 3609 4134 4674

3840 4231 4609 4976 5333

2551 3043 3555 4086 4634

2887 3429 3992 4572 5170

4365 4810 5240 5657 6063

2810 3352 3917 4502 5106 5728

3176 3773 4391 5030 5680 6363

4928 5431 5916 6387 6845 7292

3081 3675 4294 4935 5597 6279

3477 4130 4807 5507 6227 6966

5530 6093 6638 7166 7680 8182

3362 4010 4686 5385 6108 6852

3739 4501 5240 6002 6787 7592

6169 6798 7406 7995 8569 9128

4359 5093 5853 6639 7447

4886 5687 6515 7367 8242

7546 8221 8875 9511 10132

4720 5515 6338 7189 a064

5235 6152 7047 7968 8914

8337 9083 9806 iO509 11395

5094 5951 6840 7758 8703

5697 6632 7597 8590 9610

9173 9993 10788 11562 12317

5480 6403 7359 8347 9363 10408

6123 7127 8164 9232 10328 11450

10053 10951 11823 12671 13499 14307

5879 6869 7895 8954 10045 11166

6562 7638 8749 9893 11068 12271

10978 11959 12911 13837 14740 15623

6290 7349 8447 9580 10747 11946

7013 8164 9352 10574 11830 13116

11948 13016 14052 15060 16043 17004

6713 7844 9015 10225 11470 12750

7478 8705 9971 11275 12614 13986

12964 14122 15246 16340 17407 18450
Table 3.-Green weight in pounds for Nuttell ask bole hood, bole wood plus bark, end total tree’-Confinuecj

Total height in feet

Dbh 20 30 40 50 60 70 80 90 100 110 120 130

inches ______.__ ______________ _ ___ _ __________ __ __._____________________________ poun&~.~..~ ____ _________._.__-.______________ ._.__. ______________..__.___

29 7149

7956

14026

3 0 7596

8447

15134

31 8056

8950

16290

3 2

8353

9261

15279

8875

9832

16487

9412

10417

17746

9963

11018

19056

9600

16495

10201

11262

17799

10818

11933

19158

11451

12621

20573

33 10527 12099

I 1633 13325

20418 22043

34 11105 12764

12262 14046

21833 23570

35 11697 13444

12905 14783

23300 25154

36 12303

13563

24820

37 12921

14235

26394

38 13553

14921

28022

14140 16037 17991 19997

15536 17568 19654 21790

26796 28718 30593 32426

14851 16844 18895 21003

16306 18438 20627 22870

28495 30539 32533 34482

15577 17668 19820 22039

17092 19327 21621 23972

30252 32422 34539 36698

10888 12214

11995 13420

17679 18833

11570 12979

12735 14247

19076 20321

12269 13764

13494 15096

20532 21873

12987 14569

14271 15965

22048 23488

13723 15395 17112

15067 16856 18689

23625 25167 26675

14477 16240 18051

15882 17768 19700

25261 26911 28523

15248 17105 19013

16716 18701 20734

26959 26719 30440

13577

14879

19961

14426

15796

21539

15299

16737

16194

17701

24895

39 14199 16319 18509 20764 23079

15621 17893 20233 22635 25096

29703 32068 34368 36612 38805

40 14857 17076 19368 21727 24150

16334 18711 21158 23669 26243

31440 33942 36377 38752 41074

‘Tree weight above a l-foot stump.

2The three vertical figures for each dbh give green weights of bole wood first, bole wood plus bark second, and

total tree (bole wood plus bark plus branches) last.

3ltaljcized numbers span the range of the data.

9
Ta%mIP-4.-&en-dry weighi in pourrds for Nuttall oak bole wood, bole wood plus bark, and total tree’

Total height in feet

Dbh 20 30 40 50 60 70 80 90 300 110 120 130

inches

2

3

4

5

6

7

8

9

10

11

1 2

1 3

1 4

1 5

16

1 7

1 8

19

12

8

9

143 23

1 7 2 7

22 28

37

4 5

5 3

5 5

6 7

81

75

91

129

52

63

6 4

77

93

104

106 138

127 165

154 177

138 180

166 214

216 248

174 227

208 270

289 332

213 278

255 330

374 430

334

395

541

394

465

666

459

540

806

224

265

278

282

333

372

346

407

481

415

488

605

490

574

745

570

667

901

655

765

1074

745

868

1262

840

977

1468

339

398

409

415

487

529

499

583

666

589

687

820

685

797

991

787

914

1181

895

1038

1388

1009

1168

1614

1128

1305

1859

1253

1447

2122

1384

1596

2405

1520

1751

487

568

574

585

681

723

690

802

890

802

930

1076

922

1067

1282

1049

1212,

1508

1182

1363

1753

1322

1523

2018

1469

1690

2304

1622

1863

2611

1782

2044

794

919

957

923

1066

1158

1061

1223

1379

1207

1389

1621

1360

1563

1885

1521

1745

2171

1690

1936

2478

1866

2136

2808

2050

2343

1047

1205

1235

3 203

1382

1471

1368

1569

1730

1542

1766

2012

1724

1972

2316

1916

2188

2644

2116

2413

2996

2324

2647

.

1932

2202

2457

2146

2443

2805

2310

2694

3178

2603 2887

2956 3269

2706 2939 3160 3372 3576 3774

1 0
Table 4.-Oven-dry weight inpounde for hTuttall oak bole wood, bole woodplus bark, and total tree’-Continwd

Total height in feet

Dbh 20 30 40 50 60 70 80 90 100 110 120 130

-

inches

2 0

..____....._........._. _ . . . . _ . . . . . __ . . . . . . . . . .._._.__..._ __.._.__ _._...

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

,..~~poun&-~__________._ ____________._--_ ______________._ _________.._ ______________ _

1662 1948

1912 2232

3027 3287

1809 2120

2079 2426

3368 3657

2299

2628

4048

2483

2836

4461

2673

3050

4896

2870

3271

5353

3072

3498

5832

3280

3732

6333

3494

3972

6857

3713

4218

7404

3939

4470

7973

4169

4728

2241 2540 2846 3156

2558 2890 3227 3570

3535 3772 4001 4221

2439 2765 3097 3435

2781 3142 3509 3881 .

3933 4197 4451 4696

2644 2998 3358 3724

3012 3403 3800 4203

4353 4646 4927 5199

2857 3238 3627 4023

3250 3672 4100 4535

4797 5120 5430 5729

3076 3486 3905 4331

3496 3950 4411 4878

5265 5619 5959 6287

3302 3743 4192 4649 5114

3749 4236 4730 5232 5740

5756 6143 6515 6874 7222

3534 4006 4487 4977 5474

4010 4530 5059 5595 6139

6272 6693 7098 7489 7868

3774 4278 4791 5314 5845

4277 4832 5397 5969 6549

6811 7268 7708 8133 8545

4020 4556 5104 5660 6226

4552 5143 5743 6352 6969

7374 7869 8346 8806 9252

4272 4843 5424 6016 6617

4834 5462 6099 6746 7401

7962 8497 9011 9508 9989

4531 5136 5753 6381 7018

5123 5788 6464 7149 7844

8574 9150 9704 10239 10757

4796 5437 6090 6754 7429

5419 6123 6837 7562 8297

9211 9830 10425 11000 11556

5068 5745 6435 7137 7850

5722 6465 7219 7985 8761

9873 10536 11174 11790 12387

5346 6060 6788 7529 8281

6032 6815 7610 8417 9235

10560 11269 11951 12610 13248

5631 6383 7149 7929 8722

6348 7172 8010 8859 9719

11272 12028 12757 13460 14142

5921 6712 7518 8339 9172

6672 7538 8417 9310 10214

12009 12815 13591 14341 15066

6218 7049 7895 8757 9631

7001 7910 8833 9770 10719

12771 13629 14454 15251 16023

6521 7392 8280 9183 10101

7338 8290 9258 10240 11234

13559 14470 15346 16192 17012

11
Table I.-Oven-dry weight in pounds /orN~t~all oak bole wood, bole woodplus bark, and total tree’-Continued

Total height in feet

Dbh 20 30 40 50 60 70 80 90 100 110 120 .130

inches ___ _______ ____ ______ _ ________ _ __________ _ _________ _ .______________ _ ________ poun& .___________ __ __________.______._________________ _____ ________

38 6830

7681

14373

39 7145

8030

15213

4 0 7466

8386

16078

7743 8672 9618 10579

8678 9691 10718 11759

15338 16267 17164 18033

8100 9072 10062 11067

9073 10132 11206 12294

16234 17217 18167 19086

8464 9480 10514 11565

9474 10581 11702 12839

17158 18197 19200 20172

‘Tree weight above a l-foot stump.

*The three vertical figures for each dbh give dry weights of bole wood first, bole wood plue bark second, and

total tree (bole wood plus bark plus branches) last.

3ltalicized numbers span the range of the data.

Table 5.-Nuttall oak ratio parameter estimates for estimating

the proporiion of merchantable bole to total bole*

Ratio n a B Y iY.x

R2 5 6 0.999 - 0.270 0.691 0.00175

R4 56 0.989 - 9.461 0.566 0.01172

R 6 54 0.979 -18.577 0.627 0.02203

R8 49 0.972 -24.961 0.690 0.03558

RlO 43 0.964 -30.795 0.729 0.04854

R12 36 0.953 -57.489 0.740 0.04851

‘RI = (I + ByD; D = dbh; R1 = ratio of merchantable bole at top

diameter I to total bole.

Table 6.-Regression statistics for predicting Nuttall oak bole volumes and weights’

Volume (ft3) Green weight (Ibs) Dry weight (lbs)

Bole Total Bole Total Bole Total

wood bole wood bole wood bole

Average Y 68.8 76.6 4575 5076 2324 2631

bo 0.00095 0.00126 0.02923 0.04096 0.03585 0.05108

b, 1.58765 1.55802 1.69554 1.66217 1.49837 1.45780

br 2.01417 1.98440 2.00641 1.97965 1.97468 1.94976

ba 1.17072 1.15284 1.31468 1.28352 1.18306 1.15232

Fit index’ 0.996 0.995 0.995 0.995 0.992 0.992

&.x3 4.19* 5.30’ 335* 351* 206’ 222

C.V. percent 4 6.1 6.9 7.3 6.9 8.9 8.4

‘All predictions from a l-foot stump to the tree tip using Y = bo(Dbr t DI,J~‘J)Hbe; D = dbh,

H = total tree height, l&s = diameter outside bark at l/3 H.

‘FJt index = 1; [P(Y - Y)‘/I(Y- Y)*].

Y$.., = [Z(Y - Y)2/(n - 4)]1’2.

4.Coefficient of variation = 100 &.,/P.

*Significantly more precise than the two variable model Y = boDbrHb2; (I = 0.01.

I 12
Table ‘T.--Regression statistics for predicting h’uttall oak bole volumes and weights’

Volume (ft:‘) Green weight (Ibs) Dry weight (Ibs)

Bole

wood

Total

bole

Bole

wood

Total

bole

Bole

wood

Total

bole

Average Y 68.8 76.6 4575 5076 2324 2631

b,i 0.00127 0.00174 0.04421 0.06615 0.04617 0.06875

b, 0.87745 0.89690 1.12244 1.13885 0.52735 0.60499

bz 1.10015 1.06095 0.88478 0.85108 1.41691 1.32736

b:, I .92812 1.88605 1.87860 1.82274 1.91916 1.87988

b4 I .07231 1.04448 1.20056 1.15453 1.08714 1.04030

Fit index’ 0.999 0.999 0.998 0.998 0.997 0.998

s.2 1.65* 1.74* 204* 201’ 121* 127*

C.V. percent4 2.4 2.3 4.5 4.0 5.2 4.8

‘All predictions from a l-foot stump to the tree tipusing Y = b,,[(Dbt . Dr,yb~)+ Dr,&] H4;D= dbh,

H = total tree height, I& and DL,I = diameters outside bark at SH and %H, respectively.

z:Fit index = 1; [z(Y - Y)2/I(Y - Y)y].

“s& = [UY - Y)2/(n - 5)]"'.

4Coefficient of variation = 100 ^s,.,/~.

*Significantly more precise than either the two variable model Y = b,,DbrHbZ

or the three variable model Y = bo(Dbr + D&r) Hbs; Q = 0.01.

Table 8.-Local volume and weight equations for Nuttall oak’

Component

Average Fit C.V.

Y bo b, index’ $2, percent4

Volume (cubic feet)

Bole wood 68.8

Total bole 76.6

Total tree 113.9

Bole wood 4575

Total bole 5076

Total tree 7540

Bole wood 2324

Total bole 2631

Total tree 3909

0.13184 2.09394 0.972 11.28 16.4

0.16154 2.06406 0.972 12.36 16.1

0.07353 2.41890 0.977 17.71 15.5

Green weight (pounds)

7.51917 2.14149 0.970 787 17.2

9.26000 2.10884 0.971 851 16.8

4.09080 2.47130 0.974 1261 16.7

Dry weight (pounds)

4.99446 2.05787 0.967 411 17.7

6.21402 2.02829 0.967 455 17.3

2.83658 2.38225 0.974 646 16.5

*From a I-foot stump t_o the tree $p, using Y = boDbr; D =dbh.

*Fit index = 1~- [Z(Y - Y)r/Z(Y - Y)*].

3&.x = [I:(Y - Y)*/(n - 2)]1'2.

%oefficient of variation = 100 S&J?.

13
APPENDIX

Examples Using the Equations

In this section examples are presented to

illustrate use of the equations. The following

tabulation gives data needed for equation use:

D = 23.2 in

H= 108 ft

D1,4 = 18.0 in

D,,:, = 16.8 in

D,,n = 10.9 in.

Bole wood volume is calculated using D, H, and

the parameter estimates from table 1 as follows:

V = boDhl Hh2

= 0.0()160 (23.2)1.77”“(108)‘.““4

= 0.00160(266.14)(250.16)

V = 107; bole wood volume = 107 ft:l.

To calculate total green bole weight using D, H,

and D1,:r and the parameter estimates from table 6:

W = b,,[Dhl + Dl,:jh2] H”:J

= 0.04096[(23.2)1.“““17 + (16.8)1.979fi”](108)l.~~:~S~

= 0.04096[186.07 - t 266.49](407.32)

W = 7550; total green bole weight is 7550 lbs.

To calculate total bole dry weight using D, H, Dli4,

and D1,2 and the parameter estimates from table 7:

W = bo[(D)hl(D,/2)bz + (D~4)~33 W4

= 0.06875[(23.2)“~6”4y9(10.9)‘~~~~73”

+ (~~~0)‘.“79SR](~0~)1.“4030

= 0.06875[(6.70)(23.83) •t (228.96)](130.43)

= 3485; total dry bole weight is 3485 pounds.

For purposes of comparison, the measured values

for this tree are: bole wood volume, 88 cu. ft.; total

green bole weight, 6671 lbs.; and total bole dry

weight, 3314 lbs.

Merchantable bole estimates to, say, a lo-inch top

are calculated using table 5 to estimate the

merchantable proportion of the total bole and then

multiplying that proportion by the predicted bole

estimate of interest:

RI=a+j3yD

RlO = 0.964 + (-30.795)(0.729)29~2

= 0.964 •t (-30.795)(0.000654)

= 0.964 - 0.020

RlO = 0.944.

Then bole wood volume to a IO-inch top can be

calculated:

.

VlO q (RlO)(predicted total bole wood volume)

= (0.944)(107)

VlO= 101 cubic feet

Of course, total bole volumes or weights can be

calculated using any one of the three sets of

parameter estimates given in tables 1,6, or 7. Then

any of these total bole calculations can be used with

the estimate of merchantable proportion to

calculate merchantable bole values. The choice of

which set of equations to use is left to the user, who

must balance inventory precision against

inventory cost.

The relative precision of the four different model

forms in estimating the three components in this

example are compared in the following tabulation:

Bole Total Total

Model wood green bole dry bole

volume weight weight

cubic feet pounds pounds

boDbl 95 7018 3656

b,,Dbl Hb2 107 7900 4074

bo(Dbl + Dr,~~2) Hb:j 101 7550 3859

bo[(Dbl - Ihbz)

+ D1,4h3] I-P4 93 6897 3485

Measured 88 6671 3314

This tabulat.ion compares estimates for a single

tree. The estimates based on diameter alone are

close to the estimate from the four-variable model.

This is a chance occurrence in this case which

always must be considered in single estimates. But

on the average, taking more tree measurements will

increase the precision of the estimate.

Q U.S. GOVERNMENT PRINTING OFFICt: 19F3~~~-~~~,i2

14
.

SCHLAEGEL, BRYCE E., AND REGAN B. WJLLSON.

1983. Nuttall oak volume and weight tables. U.S. Dep.

Agric. For. Serv. Res. Pap. SO-186,14 p. South. For. Exp.

Stn., New Orleans, La.

A sample of 62 trees from the Mississippi Delta is used to

construct volume and weight tables for Nuttall oak.

Additional keywords: Quercus nuttallii, merchantable

bole estimates, biomass, nonlinear regression.