United States

# Department of

Agriculture

Forest Service

Southern Forest

Experiment Station

New Orleans,

Louisiana

Research Paper

so-205

June, 1984

Sugarberry Volume

and Weight Tables

Bryce E. Schlaegel
SUMMARY

Volume and weight tables were constructed from a 121-tree sample of

sugarberry (Celtis Zaeuigata Willd.) taken in the Mississippi Delta. The tables

present cubic-foot volume, green weight, and dry weight of bole wood, bole

wood plus bark, and total tree excluding leaves above a l-foot stump as predicted from the allometric model Ln Y = b, + b,Ln(D*H). Merchantable bole

volume and weight estimates can be made to any outside bark diameter limit.

More precise bole estimates can be obtained from equations using upper bole

diameters taken at relative heights of 25, 33, and 50 percent of total tree

height.
Sugarberry Volume and Weight Tables

Bryce E. Schlaegel

INTRODUCTION

Sugarberry (Celtis laevigata Willd.) grows on bottomlands of the Piedmont and Coastal Plain of the

southern United States from southeastern Virginia,

south to southern Florida, then west along the Gulf

Coast into Texas, north to western Oklahoma, Missouri, southern Illinois and Indiana, and western

Kentucky (Little 1979) (fig. 1). It is most commonly

found on clay soils of broad flats or shallow sloughs

within the flood plains of major southern rivers but

thrives on various types of soils. This is a slow growing species, with trees reaching 80 feet in height and

20 inches in dbh.

In recent years there has been considerable

demand for volume and weight tables for bottomland

hardwood species. This paper is the fourth 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 (Quercus phelZos L.) (Schlaegel 1981), Nuttall oak (Q. nuttallii Palmer) (Schlaegel and Willson 1983), overcup oak (Q.

lyrata Walt.) (Schlaegel 1984a), sweetgum (Liquidambar styraciflua L.) (Schlaegel 1984b), and green ash

(Fraxinus pennsylvanica Marsh.) (SchIaegel1984c).

METHODS

The data were collected from 15 natural bottomland hardwood stands in west-central Mississippi.

Stands were either even- or uneven-aged with a mixed

species composition. Each stand was measured for

species composition and diameter distribution; 121

trees, ranging in dbh from 1 through 22 inches, were

chosen for destructive sampling. 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 l-inch diameter class. Cutting was done

throughout the year.

Stump height 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 5-foot

intervals measured from ground level for trees 5

inches dbh and larger and at 3-foot intervals for trees

smaller than 5 inches dbh. All limbs, including leaves,

were weighed on 115 of the trees.

In the laboratory, both wood and bark moisture

content and specific gravity were determined as follows:

1 .

2 .

3 .

4 .

5 .

6 .

7 .

Wood and bark were separated with a hammer

and chisel.

Each component was weighed green.

Both wood and bark were soaked in water for at

least an hour to ensure complete swelling.

Volumes were obtained by immersion (Heinrichs and Lassen 1970).

Wood and bark were dried in a forced-air oven

at 105°C for at least 48 hours.

Wood or bark moisture content =

green weight - ovendry weight.

ovendry weight

Specific gravity =

ovendrv wood or bark weight (g)

green wood or bark volume (~2)

Average tree moisture content and specific gravity

were calculated from weighted averages of the disk

moisture contents and specific gravities; each disk

specific gravity or moisture content was weighted by

its squared average diameter.

Taper functions (Schlaegel 19 , Schlaegel and

Willson 1983) of the form

Y = b,(X’ - 1) + bz(XZ- 1) + . . . + b&X’- 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,

H = total height,

bi = coefficients estimated for each tree by linear

regression;i=l,2,...p;4sps7,

Bryce E. Schlaegel is Principal Mensuration&t at the Southern 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.

1
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 to obtain both total and merchantable bole volumes. Bole green and dry weights were

calculated from estimated tree volume and weighted

average tree density and moisture content.

Allometric regression equations were used to estimate volume, green weight, and dry weight of bole

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

plus limbs.

RESULTS

Characteristics of the trees used in this study are:

Average Range

Age (years) 38 8-156

Dbh (in) 8.1 0.8 - 21.9

Total height (ft) 54 11-92

Wood moisture content

(percent) 80 56-9’7

Bark moisture content

(percent) 74 44 - 201

Wood specific gravity 0.481 0.330 - 0.572

Bark specific gravity 0.579 0.283 - 0.782

Wood+barkgreen

density (lb/ft) 54.63 34.88 - 64.53

Wood i-bark dry

density (lb/ft)) 30.54 20.62 - 34.72

Wood + bark moisture

content (percent) 79 57 - 101

Wood + bark specific

gravity 0.489 0.330 - 0.556

Individual tree volumes and weights were fitted to

the allometric model:

Ln(Y) = b, + b, Ln(D*H) (1)

where

Y = the volume or weight variable of interest,

Ln is a natural logarithm;

b, and b, are coefficients estimated from the

data.

Estimates of the coefficients b, and b, are presented in table 1 for predicting cubic foot volume and

green and dry weight of bole wood, bole bark, total

bole, and total tree excluding leaves. Additional statistics presented are the component aver_age, fit

index, regression standard error of estimate (S,) based

on residuals after converting to actual units, and coefficient of variation (C.V.) of predictions in arithmetic

units. Fit index, which is similar to R*, is used to

judge equation efficiency when the dependent variaFigure l.-The range of sugarberry (Fowells 1.965). (F-506584)

2
ble has been transformed (Farrar 1978) and is calculated in untransformed units from the total and residual sums of squares.’ The fit index and R* are equal

when a simple linear regression analysis is performed

on an untransformed dependent variable.

Fit indices range from 0.792 for dry bark weight to

0.988 for bole wood volume. 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 is

desirable. Coefficients of variation, which are indices

of relative precision of prediction, range from 66.1

percent for dry bark weight to 13.8 percent for bole

wood volume.

Using measures of individual tree dbh and total

height, estimates can be made using table 1 for tree

volume (given in table 2), green weight (given in table

3), and dry weight (given in table 4) for bole wood,

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

limbs excluding leaves.

The equations were developed using trees from a

limited geographic range compared to the total range.

Therefore, predictions may be less precise when the

equations are applied in other parts of the range.

Using an upper bole diameter measurement in addition to dbh as described later should alleviate this

problem.

MERCHANTABLE BOLE ESTIMATES

The merchantable bole is defined as the tree bole

from a l-foot stump to a specified top diameter, ignoring limbs. Merchantable bole volume or weight can be

expressed as a proportion of the total bole by a generalized form of the logistic model

R, =(l.O +efcx))-’ (2)

where

R, =ratio of merchantable bole volume or

weight to total bole volume or weight,

where I = top outside bark diameter of merchantable bole,

X = (D - d,)/D,

D = tree dbh outside bark, and

d, = outside bark top diameter.

For a specific top diameter, the ratio of merchantable bole to total bole is the same for volume, green

weight, dry weight, and inside and outside bark

(Schlaegel and Willson 1983).

Model 2 was fitted to the overcup oak data for

trees ~4.6 inches dbh, with f(X) = b, + b,X + b2X2 +

b,X’ + b,X”. Inverting (2) and taking the natural logarithm results in

=bo + b,X + b,X2 + b,X” + b,X”;

‘FI = {l-[C(Y,- +,)2]/[c(Y,- i+])

this was solved using multiple linear regression techniques giving:

R,= [l.O+EXP(1.58529+ 1.83111 X

- 51.10565 X*+91.90861 X’

- 54.30496 X4)] -1, (3)

with fit index = 0.951 and S, = O.O52;,EXP is the base

of the natural logarithm and equals 2.71828.

Volume or weight to any top diameter (Vi) is found

by multiplying the ratio estimate obtained from (3)

by a total bole volume or weight estimate from either

table 2,3, or 4:

V,= R,.VT,

where VT is the total bole volume or weight of interest.

IMPROVED TOTAL BOLE

ESTIMATES

The precision of the merchantable bole estimate

depends upon accuracy in measuring total bole. Total

bole estimates can be significantly improved by measuring one or two additional diameters. Tables 5 and

6 give regression statistics for total bole volume and

weight under two different model forms:

Ln(Y)= b, + b, Ln(D * D, * H) (4)

and

Ln(Y) = b,, + b, Ln[(D*D, + D*,J.H] (5)

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

D,, and D, are diameters measured outside the bark

at one-third, one-half, and one-fourth the total height.

Statistics from tables 5 and 6 show the significant

(a =0.05) improvement over the previous D*H equations of table 1. Measuring one additional diameter at

one-third the tree height reduces S, for bole wood volume, total bole volume, green wood and total bole

weight, and total dry bole weight by 31, 45, 18, 32,

and 30 percent, respectively. Other standard errors

are reduced but not significantly.

Measuring two upper bole diameters at one-fourth

and one-half total height will result in further significant increases in precision. Improvements over the

D2H model range from 17 to 53 percent for bole wood

and total bole and from 6 to 9 percent for bark.

Taking additional bole measures means a higher

inventory cost, since more time will be spent at each

tree, but most of the inventory cost is in traveling to

the candidate tree. Data presented in this paper allow

total and merchantable bole estimates to be made

with high reliability. Each user has to decide when

increased precision is needed and whether the need

offsets the higher cost.

LOCAL VOLUME TABLES

‘Ihere 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 7 gives the sta3
tistics 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

Ln(Y) = b, + b, Ln(D’). 6)

Precision is significantly (a = 0.05) reduced when

only dbh is used to predict bole wood, total bole, and

total tree. But bark estimates are more precise using

the local equations.

CALCULATING CONFIDENCE LIMITS

Confidence limits ((1 - a ) percent confidence limits) of individual predictions can be calculated using

statistics presented in table 8. Clark et al. (1980) used

the technique of Land (1972) to estimate approximate .

confidence limits for lognormal means of scarlet oak:

Y,, = EXP

-

:+=I1

where:

2b+111 /

Y,, = upper and lower limits for Y,

EXP= base of natural logarithm; EXP = e

= 2.71828,

Y = predicted volume or weight of component,

Z,,, = value for the upper a 12 percentage

point from the standard normal table,

Sx= standard error of estimate for prediction equation,

n= number of observations used to

develop the equation,

-TT = sample mean of Ln(X),

E(X - X)* = corrected sum of squares for Ln(X),

X = Ln(D’H); D = dbh and H = total height

of tree for which Y is predicted.

LITERATURE CITED

Clark, Alexander, III; Phillips, Douglas R.; Hitchcock, Harry C., III. Predicted weights and volumes

of scarlet oak trees on the Tennessee Cumberland

Plateau. Res. Pap. SE-214, Asheville, NC: U.S.

Department of Agriculture, Forest Service, Southeastern Forest Experiment Station; 1980.23 p.

Farrar, R. M., Jr. Silvicultural implications of the

growth response of naturally regenerated evenaged stands of longleaf pine (Pinus palustris Mill.)

to varying stand age, site quality, and density and

certain stand structure measures. Athens, GA:

University of Georgia; 1978. 132 p. Ph.D. Dissertation.

Fowells, H. A., camp. Silvics of forest trees of the

United States. Agric. Handb. 271. Washington,

DC: US. Department of Agriculture; 1965.762 p.

Heinrichs, J. Frank; Lassen, L. E. Improved technique for determining the volume of irregularly

shaped wood blocks. For. Prod. J. 20(4): 24; 1970.

Land, Charles E. An evaluation of approximate confidence interval estimation methods for lognormal

means. Technometrics 14(l): 145 - 158; 1972.

Little, Elbert L., Jr. Checklist of United States Trees.

Agric. Handb. 541. Washington, DC: U.S. Department of Agriculture; 1979.375 p.

Schlaegel, Bryce E. Willow oak volume and weight

tables for the Mississippi Delta. Res. Pap. SO-173,

New Orleans, LA: U.S. Department of Agriculture,

Forest Service, Southern Forest Experiment Station; 1981. 14 p.

Schlaegel, Bryce E. Overcup oak volume and weight

tables. Res. Pap. SO-207, New Orleans, LA: U.S.

Department of Agriculture, Forest Service, Southern Forest Experiment Station; 1984a. 14 p.

Schlaegel, Bryce E. Sweetgum volume and weight

tables. Res. Pap. SO-204, New Orleans, LA: U.S.

Department of Agriculture, Forest Service, Southern Forest Experiment Station; 1984b. 14 p.

Schlaegel, Bryce E. Green ash volume and weight

tables. Res. Pap. SO-206, New Orleans, LA: U.S.

Department of Agriculture, Forest Service, Southern Forest Experiment Station; 1984c. 14 p.

Schlaegel, Bryce E.; Willson, Regan B. Nuttall oak

volume and weight tables. Res. Pap. SO-186, New

Orleans, LA: U.S. Department of Agriculture,

Forest Service, Southern Forest Experiment Station; 1983. 14 p.
Table I.-Regression statistics forpredicting sugarberry tree volumes and weights using dbh anu

total height 1

Component

Average

Y b, b,

Fit

index2

C.V.

percent’

Bole wood

Bole bark

Total bole

Total tree,

excluding

leaves

13.1

1.2

14.3

21.1

Volume (cubic feet)

- 5.862 0.95323 0.988 1.81 13.8

- 1.223 0.83390 0.825 0.67 56.9

- 5.649 0.93856 0.986 2.07 14.5

-5.484 0.95437 0.962 5.28 25.0

Green weight (pounds)

Bole wood

Bole bark

Total bole

Total tree,

excluding

leaves

708 - 1.892 0.95566 0.984 111 15.6

78 - 3.332 0.86691 0.806 48 62.2

786 - 1.683 0.94340 0.983 126 16.1

1158 - 1.515 0.95778 0.963 283 24.4

Bole wood

Bole bark

Total bole

Total tree,

excluding

leaves

393 - 2.474

48 - 4.067

441 - 2.287

652 - 2.118

Dry weight (pounds)

0.95535 0.982

0.89204 0.792

0.94643 0.984

0.96116 0.963

6 4 16.4

32 66.1

70 15.8

160 24.5

‘Volumes and weights of trees from a l-foot stump to the tree tip, using Ln(Y) = b, + b, Ln(D’H);

D = dbh, H = total tree height.

*Fit index = 1.0 - [C(Y - Y)’ I C(Y -Y)2], using untransformedvalues.

“S, = [C(Y -Y)’ I (n - 2)]“, using un@msformed values.

‘Coefficient of variation = 100 S, I Y.
inches

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

Table 2.-Cubic-foot volume for sugarberry bole wood, bole wood plus bark, and total tree’

Total height in feet

Dbh 10 20 30 40 50 60 70 80 90 100

0.03’ 0.05

0.03’ 0.06

0.04 0.07

0.10 0.19

0.11 0.22

0.14 0.27

0.40

0.46

0.59

0.27

0.31

0.40

0.59

0.67

0.87

0.70 1.02

0.79 1.16

1.02 1.50

1.57

1.76

2.30

0.78

0.88

1.14

1.35

1.52

1.98

2.06

2.30

3.03

2.92

3.24

4.29

3.91

4.33

5.76

5.05

5.57

7.43

1.67

1.87

2.45

2.55

2.84

3.75

3.61

4.00

5.31

4.84

5.34

7.13

6.24

6.86

9.19

7.81

8.56

11.50

9.55

10.40

14.10

11.5

12.5

16.9

13.5

14.7

19.9

15.7

17.1

23.2

1.98

2.22

2.91

3.03

3.37

4.46

4.29

4.75

6.32

5.76

6.34

8.48

7.43

8.14

10.90

9.30

10.20

13.70

11.4

12.4

16.7

13.6

14.8

20.1

16.1

17.4

23.7

18.7

20.3

27.6

21.6

23.3

31.8

4.97

5.48

7.32

6.67

7.32

9.82

8.60

9.41

12.70

10.8

11.7 *

15.9

13.2

14.3

19.4

15.8

17.1

23.3

18.6

20.1

27.5

21.7

23.4

32.0

25.0

26.9

36.9

24.6 28.5

26.5 30.6

36.3 42.1

27.8

29.9

41.1

31.3

33.5

46.1

34.9

37.3

51.4

32.2

34.6

47.6

36.2

38.7

53.4

40.4

43.1

59.6

7.58

8.30

11.20

9.77

10.70

14.40

12.2

13.3

18.0

14.9

16.2

22.0

17.9

19.4

26.4

21.2

22.8

31.2

24.7

26.5

36.4

28.4

30.5

41.9

32.4

34.7

47.8

36.6

39.2

54.1

41.1

43.9

60.7

45.8

48.9

67.7

16.7

18.1

24.7

20.1

21.7

29.6

23.7

25.5

34.9

27.6

29.6

40.7

31.8

34.1

46.9

36.2

38.8

53.5

41.0

43.8

60.5

46.0

49.0

67.9

45.3

48.3

66.9

50.9

54.1

75.1

51.3 56.7

54.6 60.3

75.7 83.8
Table 2.-Cubic-foot volume for sugarbeny bole wood bole wood plus bark, and total tree-(Continued)

Total height in feet

Dbh 10 20 30 40 50 60 70 80 9 0 100

inches ---_----_ --__ cubic feet

19 38.6 44.8 50.8 56.9 62.9

41.3 47.7 54.1 66.4 66.7

57.0 66.1 75.1 84.0 92.8

20 42.6 49.4 56.0 62.7 69.3

45.5 52.5 59.6 66.5 73.4

62.9 72.9 82.8 92.6 102.0

21 46.8 54.2 61.5 68.8 76.1

49.8 57.6 65.3 72.9 80.5

69.0 80.0 90.9 102.0 112.0

22 51.1 59.2 67.2 75.2 83.2

54.4 62.8 71.2 79.6 87.8

75.4 87.4 99.3 111.0 123.0

23 55.6 64.4 73.2 81.9 90.5

59.1 68.3 77.4 86.5 95.5

82.1 95.2 108.0 121.0 134.0

24 60.3 69.9 79.3 88.8 98.2

64.0 74.0 83.9 93.7 103.0

89.1 103.0 117.0 131.0 145.0

25 65.2 75.5 85.8 96.0 106

69.1 79.9 90.6 101.0 112

96.3 112.0 127.0 142.0 157

26 70.3 81.4 92.4 103 114

74.4 86.0 97.5 109 120

104.0 120.0 137.0 153 169

‘Tree volume from a l-foot stump to the tree tip.

‘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

limbs excluding leaves) last.

;Boldface numbers span the range of the data.

Table 3.-Green weight in pounds for sugarbeny bole wood, bole woodplus bark, and total tree’

Total height in feet

Dbh 10 20 30 40 50 60 70 80 90 100

inches

1

2

3

4

5

6

7

8

--___---_-_-__------

1.4’ 2.6

1.6’ 3.1

2.0 3.9

5.1 9.9 15

6.0 11.6 17

7.5 14.6 22

22 32

25 37

32 47

37 55

43 63

55 81

84

96

125

42

48

62

72

82

107

111

126

164

157

177

233

211

237

313

273

305

404

pounds

90 107

102 121

133 158

137 164

155 184

203 242

195 232

219 260

288 343

261 311

293 348

387 461

337 402

377 447

500 596

268

301

398

360 410

402 456

535 608

465 529

517 587

691 785

7
Table S.-Green weight inpoundsfor sugarberry bole wood bole woodplus bark, and total tree-(Continued)

Total height in feat

Dbh 10 2 0 30 4 0 50 60 70 80 9 0 100

inches pounds

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

422 503

470 559

627 747

517 615

574 681

761 913

620 738

687 816

921 10%

732 872

809 961

1088 12S5

853 1016

941 1118

1268 1510

1170

1286

1740

1335

1464

1986

1510

1654

2247

583

646

865

713

788

1059

8.55

943

1271

1010

1112

1501

1177

1293

1750

1356

1487

2017

1696

1854

2524

1892

2066

2816

2098

2287

3124

662

733

983

810

894

1203

972

1070

1444

1147

1261

1706

1337

1466

1989

1540

1686

2292

1758

1921

2616

1988

2170

2960

2233

2433

3325

2490

2710

3710

2761

3001

4114

2461

2678

3666

2763

3003

4117

3082

3344

4594

3418

3704

5095

2314

2520

3446

2546

2763

3784

2776

3016

4136

3022

3280

4504

1547

1694

2302

1750

1913

2605

1965

2145

2926

2192

2389

3264

2431

2645

3621

2681

2914

3994

2943

3195

4386

3217

3488

4794

3502

3794

5221

3799

4111

5664

4107

4440

6125

3046

3306

4539

3344

3624

4984

3654

3957

5448

3979

4303

5933

906

999

1347

1087

1196

1617

1284

1409

1910

1496

1639

2226

1724

1885

2566

1967

2147

2929

2225

2425

3314

2499

2718

3722

2787

3028

4153

30S0

3353

4606

3409

3694

5081

3742

4050

5579

4996

4422

6099

4452

4809

6641

3770

4080

5621

4138

4473

6172

4523

4884

6747

4924

5311

7346

3278

3554

4887

4316 4830 5341

4663 5211 5755

6437 7205 7970

3544

3839

5284

4666 5222 5775

5036 5628 6216

6960 7791 8619

3820 4427 5029 5628 6224

4134 4781 5423 6060 6694

5696 6602 7503 8399 9291

‘Tree weight from a l-foot stump to the tree tip.

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

limbs excluding leaves) last.

‘Boldface numbers span the range of the data.

8
Table I.-Dry weight in pounds for sugarberry bole wood bole wood plus bark, and total tree’

Total height in feet

Dbh 10 2 0 3 0 4 0 5 0 6 0 7 0 8 0 90 100

inches pounds _--

1 0.8' 1.5

0.9’ 1.7

1.1 2.1

2 2.9 5.5 8.2

3.3 6.4 9.4

4.2 8.1 12.0

3 1 2 1 8 2 3

1 4 2 0 2 7

1 8 2 6 34

4 2 1 3 1 4 0

2 4 3 5 4 6

3 1 4 5 60

5 4 7 6 2

5 3 7 0

7 0 9 2

6 8 8

99

131

7 118

133

176

8 152

171

227

9

50

5 7

7 4

7 7

8 7

114

109

122

162

146

164

218

188

211

281

6 0

6 7

8 8

91

103

136

228

256

342

295

329

442

235

264

353

369

411

554

10 288

322

432

451 505

502 561

679 760

11

12

346

385

519

408

454

613

13 475

529

715

129

145

193

173

195

259

224

251

335

280

313

420

343

382

515

411

458

618

486

540

731

576

628

852

606

672

913

715

793

1079

834

922

1259

14 652

723

983

150

168

224

201

225

301

259

290

389

325

362

487

397

442

597

476

530

717

563

625

847

656

727

988

755

837

1140

541

601

815

639

709

964

745

825

1124

858

949

1296

979

1082

1480

1108

1222

1675

960

1061

1451

1096

1209

1657

1240

1366

1876

1392

1532

2108

15

16

17

18

744 862

824 953

1122 1301

841

931

1270

945

1044

1427

975

1077

1473

1095

1208

1655

1054

1163

1221 1387 1552 1717

1346 1527 1708 1887

1593 1848 2101 2353 2603

1244

1371

1882

1371

1510

2076

1539

1693

2332

9
Table 4.-Dry weight inpoundsfor sugarberry bole wood, bole woodplus bark, and total tree-(Co&inued)

Dbh 10 20 30 40

Total height in feet

50 60 70 80 9 0 100

inches’

19

20

21

22

23

24

25

26

pounds

1168

1289

1768

1289

1420

1951

1354 1538 1721 1964

1491 1692 1892 2090

2050 2331 2610 2888

1493 1696 1899 2100

1643 1865 2084 2303

2263 2572 2881 3188

1415 1639 1862

1558 1802 2045

2143 2485 2825

1546 1792 2035

1701 1968 2233

2343 2717 3090

2084

2286

3164

2278

2497

3466

2305

2526

3501

2519

2758

3829

1683 1950 2216 2480 2742

1850 2141 2429 2716 3000

2552 2960 3365 3769 4170

1826 2116 2403 2690 2975

2005 2320 2633 2944 3252

2770 3212 3652 4090 4526

1974 2287 2598 2908 3216

2167 2507 2845 3180 3513

2996 3474 3950 4424 4895

2128 2465 2801 3134 3466

2334 2700 3064 3425 3784

3231 3747 4260 4770 5279

‘Tree weight from a l-foot stump to the tree tip.

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

limbs excluding leaves) last.

‘Boldface numbers span the range of the data.

Table 5.-Regression statistics forpredicting sugarberry bole volumes and weights using two bole

diameter measurements and total height’

Component

Bole wood

Bole bark

Total bole

Bole wood

Bole bark

Total bole

Average

Y

13.1

1.2

14.3

708

78

786

b,

-5.802

- 7.185

-5.591

- 1.834

- 3.295

- 1.627

Fit

b, index’

Volume (cubic feet)

0.98071 0.994

0.85923 0.847

0.96572 0.996

Green weight (pounds)

0.98331 0.989

0.89339 0.829

0.97083 0.992

Dry weight (pounds)

S,J

1.24*

0.62

1.12*

91*

45

86*

C.V.

percent’

9.5

53.2

7.9

12.9

58.3

11.0

Bole wood 393 - 2.415 0.98301 0.986 58 14.7

Bole bark 48 - 4.030 0.91937 0.816 30 62.2

Total bole 441 - 2.231 0.97398 0.992 49* 11.2

‘Volumes and weights of trees from a l-foot stump to the tree tip, using Ln(Y) = b,+ b,

Ln(D .Dbh. H); D = dbh, H_ = total tree height, D t i = bole diameter outside bark at %H.

*Fit index = t.0 - [C(Y - Y)’ / Z(Y -Y)‘], using untransformed values.

‘S, = [E(Y - Y)’ / (n -2)] ‘, using un&ansformed values.

‘Coefficient of variation = 100 S, / Y.

*Significantly more precise by the F test than D’H model; a = 0.05.

1 0
Table C-Regression statistics for predicting sugarbeny bole volumes and weights using three

bole diameter measurements and total height’

Average Fit C.V.

Component Y bo b, index’ se, percent”

Volume (cubic feet)

Bole wood 13.1 - 6.513 1.00617 0.996 1.00* 7.7

Bole bark 1.2 - 7.812 0.88195 0.852 0.61 52.3

Total bole 14.3 - 6.292 0.99084 0.999 0.64* 4.5

Green weight (pounds)

Bole wood 708 - 2.547 1.00883 0.991 83’ 11.8

Bole bark 78 - 3.946 0.91693 0.835 45 57.3

Total bole 786 - 2.331 0.99606 0.995 71* 9.0

Dry weight (pounds)

Bole wood 393 -3.128 1.00857 0.988 53+ 13.6

Bole bark 4 8 - 4.701 0.94369 0.821 30 61.3

Total bole 441 - 2.938 0.99936 0.995 40* 9.1

‘Volumes and weights of trees from a l-foot stump to the tree tip, using Ln(Y)=b,+ b,

Ln[(D.Ds + DUH]; D = dbh, H = total tree height, DH and Du = bole diameters outside bark at

‘AH and l%H, respectively.

‘Fit index = 1.0 -[C(Y - Y)’ I C(Y - &‘I, using untransformed values.

IS, = [C(Y - Y)’ I (n - 2)]“, using un&ansformed values.

‘Coefficient of variation = 100 S, I Y.

+Significantly more precise by the F test than D .Djh.H model; o = 0.05.

*Significantly more precise by the F test than D*H model; a = 0.05.

Table I.-Local volume and weight equations for sugarberry’

Average Fit C.V.

Component Y b, b, index’ ii3 percent’

Bole wood

Bole bark

Total bole

Total tree,

excluding

leaves

Bole wood

Bole bark

Total bole

Total tree,

excluding

leaves

Volume (cubic feet)

13.1 - 3.179 1.23777 0.934 4.18* 31.9

1.2 - 4.904 1.08668 0.880 0.56+ 47.1

14.3 - 3.011 1.21917 0.950 3.95* 27.7

21.1 - 2.819 1.24272 0.949 6.08 28.8

708 0.796

78 - 0.916

786 0.967

1158 1.159

Green weight (pounds)

1.24113 0.919

1.12891 0.861

1.22559 0.939

1.24723 0.946

249* 35.2

41+ 52.6

241* 30.7

344* 29.7

Dry weight (pounds)

Bole wood

Bole bark

Total bole

Total tree,

excluding

leaves

393 0.217 1.24031 0.909 146* 37.1

48 - 1.591 1.16320 0.849 21’ 56.2

441 0.373 1.22941 0.934 140* 31.7

652 0.566 1.25157 0.941 202* 30.9

lVolumes and weights of trees from a l-foot stump to the tree tip, using Ln(Y) = b, + b, Ln(D*);

D = dbh.

*Fit index = 1.0 -[C(Y -Y)’ I C(Y - rif)‘], using untransformed values.

‘S, = [C(Y - Y)’ I (n - 2)]“, using untransformed values.

“Coefficient of variation = 100 S, I Y.

+ Significantly more precise by the F test than D*H model; u = 0.005.

*Significantly less precise by the F test than D’H model; a = 0.05.

1 1
Table K-Statistics for estimating confidence bounds for sugarberry predictions for the bole and

total tree

Independent

variable - X

Mean of of squares

n X for X’

Bole predictions

Corrected sum SW

-

Ln(D2) 121 3.556 354.483

Ln(D’H) 121 7.422 600.271

Ln(D.Da/,.H) 121 7.148 568.328

Ln[(D.D),,+ D%)H] 121 7.672 540.282

Standard error of estimate

for tree components

Wood Bark Total

Volume 0.1915 0.3029 0.1775

Green weight 0.2053 0.3616 0.1983

Dry weight 0.2178 0.3408 0.2017

Volume 0.1306 0.3188 0.1255

Green weight 0.1548 0.3690 0.1560

Dry weight 0.1617 0.3644 0.1574

Volume 0.0847 0.2889 0.0716

Green weight 0.1143 0.3396 0.1119

Dry weight 0.1227 0.3315 0.1116

Volume 0.0643 0.2791 0.0423

Green weight 0.1004 0.3315 0.0964

Dry weight 0.1079 0.3215 0.0929

Ln(D’)

Total tree predictions

115 3.491 344.521

Ln(D*H) 115 7.339 584.102

Total tree

Volume 0.1540

Green weight 0.1774

Dry weight 0.1786

Volume 0.1555

Green weight 0.1800

Dry weight 0.1799

‘C(X -X)? in base e logarithmic units.

12
APPENDIX

Examples Using the Equations

In this section examples are presented to illustrate

use of the equations. The following tabulation gives

data used to illustrate equation use:

D= 21.7 in.

H = 75.0 ft.

D, = 15.5 in.

DbA = 14.8 in.

DiA = 11.5 in.

Bole wood volume (V) is calculated using X = D*H

and the parameter estimates from table 1 as follows:

Ln(V) = b, + b, Ln(D2H)

= - 5.862 + 0.95323 Ln (21.7 x 21.7 x

75.0)

= - 5.862 + 0.95323 Ln (35316.75)

= - 5.862 + 0.95323 (10.472)

- 5.862 + 9.982

Ln(V) 1 4.120

V = e4.1zo; bole wood volume = 61.6 ft’.

To calculate total green bole weight (W) using

X = De D,A * H and the parameter estimates from table

5:

Ln(W) = b, + b, Ln (D*D,*H)

= - 1.627 + 0.97083 Ln (21.7 x 14.8 x

75.0)

= - 1.627 + 0.97083 Ln (24087.00)

= - 1.627 + 0.97083 (10.089)

- 1.627 + 9.795

Ln(W) 1 8.168

W = es.168; total bole green weight = 3526 lb.

To calculate bole dry weight (W) using X =

[(D * D,,z + D’,, )H] and the parameter estimates from

table 6:

Ln(W) = b, + b, Ln [(D-D, + D*,)H]

=: - 2.938 + 0.99936 Ln [(21.7 x 11.5 +

15.5 x 15.5) x 75.01

= - 2.938 + 0.99936 Ln [(249.55 + 240.25)

x 75.01

= - 2.938 + 0.99936 Ln [489.80 x 75.01

= - 2.938 + 0.99936 Ln [36735.00]

= - 2.938 + 0.99936 (10.511)

= - 2.938 + 10.504

Ln(W) = 7.566

W = e7.s66; total bole dry weight = 1931 lb.

Merchantable bole estimates to, say, an 8-inch top

are calculated using equation 3 to estimate the merchantable portion of the bole and then multiplying

that proportion (R8) by the predicted bole estimate of

interest. Letting DI = 8.0, X = [(21.7 - 8.0)/21.7], or

X = 0.631, and from (3):

R8= [1.0+EXP(1.58529+1.83111(0.631)-

51.10565 (0.631)2+ 91.90861 (0.631)‘-

54.30496 (0.631)4)] -’

= [l.O+EXP (1.58529+ 1.83111 (0.631)-

51.10565 (0.39816) +91.90861 (0.25124) -

54.30496 (0.15853))]-’

= [l.O + EXP (1.58529 + 1.15543 - 20.34823

+ 23.09112 -8.60897)1-l

= [l.O+EXP( -3.12536)1-l

= [l.O + 0.04392]- ’

= [1.04392] - ’ R8= 0.958.

Then bole wood volume to an 8-inch top (V8) can be

calculated:

V8 = (R8)(predicted total bole wood volume)

= (0.958)(61.6)

= 59.0 ft’.

Of course, total bole volumes or weights can be caIculated using any one of the three sets of parameter

estimates given in tables 1, 5, or 6. 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.

13
Schlaegel, Bryce E. Sugarberry volume and weight tables.

Res. Pap. SO-205 New Orleans, LA: U.S. Department of

Agriculture, Forest Service, Southern Forest Experiment

Station; 1984. 13 p.

A sample of 121 trees from the Mississippi Delta is used to

construct volume and weight tables for sugarberry.

Additional keywords: Celtis laevigata, merchantable bole

estimates, biomass.