pq United.States

&b& ;ge;;p;t Of

Forest Service

Green Ash Volume

. Southern Forest

Experiment Station and Weight Tables

New Orleans,

Louisiana

Research Paper

SO-206

June, 1984 Bryce E. Schlaegel

c+I

I@I.
SUMMARY

Volume and weight tables were constructed from a ?O-tree sample of grean

ash (Frajcinus pennsyluanica Marsh.) 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, + bLn(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.
Green Ash Volume and Weight Tables

, Bryce E. Schlaegel

INTRODUCTION

.

Green ash (Fraxinus pennsylvanica Marsh.) is distributed over most of the United States and southern

Canada east of the Rocky Mountains (Little 1979)

(fig. 1). It is most commonly found on alluvial soils

along rivers and streams. On good sites it can develope a large, clear bole, reach a height of 110 feet, and

have a dbh in excess of 30 inches. Commonly the trees

reach heights of 60 to 80 feet with dbh ranging from

22 to 26 inches.

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 65 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.

In recent years there has been considerable

demand for volume and weight tables for bottomland

hardwood species. This paper is the sixth 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 phel10s L.) (Schlaegel 1981), Nuttall oak (Q. nuttallii Palmer) (Schlaegel and Willson 1983), overcup oak (Q.

Lyruta Walt.) (Schlaegel 1984a), sugarberry (Celtis

Zaeuigata Willd.) (Schlaegel 1984b), and sweetgum

(Liquidambar styruciflua L.) (Schlaegd 1984c).

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 =

METHODS

The data were collected from 12 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; 70

trees, ranging in dbh from 1 through 31 inches, were

chosen for destructive sampling. The sample consisted of growing stock trees from both the overstory

and understory with healthy crowns and no visible

signs of disease or decay. 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 &foot

intervals measured from ground level for trees 5

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

moisture contents and specific gravities; each disk

specific gravity or moisture content was weighted by

its squared average diameter.

Taper functions (Schlaegel 1981, Schlaegel and

Willson 1983) of the form

Y =b,(X’-1) + bt(X’-1) + . . . + b,(XP--1)

where

Y =dlD,

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=1,2,...p;4=pr7,

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 merchant-

.__ . _ . __ _

Boyce E. Scblaegel is Principal Mensurationist at the Southern Hardwoods Laboratory, maintained at Stoneville, Mississippi, by the Soutbem Forest Experiment Station, Forest Service-USDA, in cooperation with the Mississippi Agricultural and Forestry Experiment Station

and the Southern Hardwood Forest Research Group.

1
able 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:

Age (years)

Dbh (in)

Total height Cft)

Wood moisture content

Bz%~~~ure content

(percent)

Wood specific gravity

Bark specific gravity

Wood-tbarkgreen

density (lb/ft)

Wood -+ bark dry

density (lb/ftA

Wood + bark moisture

content (percent)

Wood + bark specific

gravity

Average Range

50 14-168

8.0 0.9 - 30.6

51 14-110

57 40 - 141

115 45 - 236

0.563 0.416 - 0.694

0.456 0.259 - 0.610

55.95 43.46 - 72.00

33.84 26.23 - 40.55

66 46 - 177

0.542 0.420 - 0.649

.

Individual tree volumes and weights were fitted to

the allometric model:

Ln(Y) = b0 + b, Ln(D’H)

where

-

(1)

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 average, 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 variable 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 0.887 for dry total tree

weight to 0.975 for bole wood volume. A fit index of

1.0 indicates that predictions can be made without

‘FI = {l-[C(Yi- Yi)‘]I[E(Yi- %I}

Figure l.-The mnge ofgreen ash (FoweUs 1965) (F&m94
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

62.6 percent for dry total tree weight to 29.3 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 +er(‘))-’ (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 r 4.6 inches dbh, with f(X) = b, + b,X + b,X’ +

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

I-R,

Ln (7

)

= b, + b,X + b,X’ + b,X” + b,X”;

I

this was’solved using multiple linear regression techniques giving:

R, = [l.O + EXP (0.77188 + 11.26543 X

-73.62613 X2 + 111.38621 X3

- 59.39594 X’)] -1. (3)

with fit index = 0.921 and S, = 0.065; EXP is the base

of the natural logarithm and equals 2.71828.

Volume or weight to any top diameter (V,) 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:

VI= R,.Vr,

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, + D2,)*H] (5)

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

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 DzH equations of table 1. Measuring one additional diameter at

one-third the tree height reduces S, for all bole components from 31 percent for dry bole bark to 63 percent

for bole wood volume.

Measuring two upper bole diameters at one-fourth

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

D*H model range from 46 to 81 percent for bole wood

and total bole and from 38 to 49 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

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 7 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

Ln(Y) = b, + b, Ln(D2). 6)

Precision is significantly (a =0.05) reduced when

only dbh is used for prediction, except for total tree

and dry bole wood.

CALCULATING CONFIDENCE LIMITS

Confidence limits ((I- 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 log-normal means of scarlet oak:

3
-

Y .,,=EXP i+ (‘-?!)*

n x(X-X)* 1

where:

2h-tU.J /

YuL, = upper and lower limits for Y,

EXP= base of natural logarithm; EXP = e =

2.71828,

Y = predicted volume or weight of component,

Zo,*= value for the upper Q /2 percentage

point from the standard normal table,

Sy.== standard error of estimate for prediction equation,

n= number of observations used to

develop the equation,

-Z = sample mean of Ln(X),

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

X = Ln(DZH); 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.

Fo,wells, H. A., camp. Silvics of forest trees of the

United States. Agric. Handb. 271. Washington, x

DC: U.S. 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, Southem Forest Experiment Station; 1984a. 14 p.

Schlaegel, Bryce E. Sugar-berry volume and weight

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

Department of Agriculture, Forest Service, Southem Forest Experiment Station; 1984b. 13 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; 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 for predicting green ash tree volumes and weights using d&h and

tot&height’

Component

Average

Y b, b,

Fit

index’ 6,s

C.V.

percent’

Bole wood

Bole bark

Total bole

Total tree,

excluding

leaves

Bole wood

Bole bark

Total bole

Total tree,

excluding

Volume (cubic feet)

14.4 - 5.817 0.93265 0.975 4.22 29.3

2.5 -6.743 0.85307 0.939 0.99 40.4

16.9 -5.502 0.91740 0.973 4.99 29.6

22.7 -5.371 0.92436 0.947 9.60 42.3

Green weight (pounds)

717 -1.616 0.90470 0.939 322 44.9

127 . -2.335 0.80534 0.953 4 5 35.3

844 -1.246 0.88369 0.945 355 42.0

1138 -1.104 0.88814 0.908 632 55.5

Dry weight (pounds)

Bole wood

Bole bark

Total bole

Total tree,

excluding

leaves

469 -2.123 0.91416 0.907 263 56.1

77 -3.536 0.87524 0.?41 3 2 41.1

546 - 1.905 0.90737 0.917 285 52.3

133 - 1.759 0.91023 0.887 459 62.6

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 = !.O - [UY- Y)’ / C(Y -ii)>], using untransformed values.

3, = [C(Y -Y)’ / (n - 2)]%, usingun@nsformed values.

‘Coefficient of variation = 100 S, I Y.

5
Table 2.-Cubic-foot volume for green ash bole wood, bole woodplus bark, and total tree’

Total heieht in feet

Dbh 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 100 110 120 130

inches

1

2

3

4

5

6

7

8

9

1 0

1 1

1 2

1 3

1 4

1 5

1 6

1 7

1 8

cubic feet

0.03’ 0.05

0.03 0.06

0.04 0.07

0.09 0.18

0.12 0.23

0.14 0.27

0.38

0.48

0.57

0.07

0.09

0.11

0.26

0.33

0.39

0.55

0.69

0.82

0.65 0.94

0.81 1.18

0.96 1.40

1.43

1.77

2.11

0.09

0.12

0.14

0.34

0.43

0.51

0.72

0.90

1.07

1.23

1.53

1.83

1.87

2.31

2.76

2.01 2.63

2.47 3.22

2.96 3.86

3.50

4.27

5.14

4.49

5.46

6.57

5.60

6.78

8.17

0.42

0.53

0.62

0.89

1.11

1.32

1.52 1.80

1.88 2.22

2.24 2.66

2.30 2.73

2.63 3.34

3.39 4.01

3.23 3.83

3.95 4.67

4.75 5.62

4.31 5.11

5.24 6.29

6.31 7.47

5.53 6.56

6.70 7.92

8.08 9.56

3.15

3.85

4.63

4.43

5.38

6.48

5.90

7.14

8.62

7.57

9.12

11.0

6.68

8.07

9.75

8.57

10.30

12.50

6.89 8.17 9.43 10.7

8.32 9.83 11.39 12.8

10.00 11.99 13.71 15.5

8.39 9.94 11.5 13.0

10.10 11.90 13.7 15.6

12.20 14.40 16.7 18.8

10.0 11.9 13.7 15.5

12.0 14.2 16.4 18.5

14.6 17.2 19.9 22.5

11.8

14.1

17.1

13.7

16.3

19.8

14.0

16.7

20.2

16.2

19.3

23.5

16.1

19.2

23.3

18.7

22.2

27.1

21.5

25.5

31.0

24.4

28.9

35.2

iii

39.7

30.9

36.4

44.4

34.4

40.4

49.4

18.3

21.7

26.4

21.2

25.1

36.6

24.3

28.8

36.1

27.7

32.7

39.9

31.2

36.8

44.9

35.0

41.1

50.3

18.6

22.1

26.9

21.2

25.1

30.6

23.9

28.3

34.4

26.7

31.6

38.5

29.8

35.1

42.8

14.5

17.3

21.0

17.3

20.6

25.1

20.4

24.2

29.4

23.7

28.0

34.1

27.2

32.1

39.1

22.5

26.6

32.4

26.1

30.8

37.6

30.0

35.3

43.1

30.9

36.4

44.5

34.9

41.0

50.1

39.0

45.8

56.0

34.1

40.1

49.0

38.6

45.1

55.2

43.1

50.5

61.8

38.9 43.4 47.9

45.7 50.9 56.0

55.9 62.3 68.7
.

Table 2.-Cubic-foot volume for green ash bole wood, bole woodplus bark, and total tree-(Continued)

Total height in feet

Dbh 10 2 0 30 40 50 60 70 8 0 9 0 100 110 120 130

inches

* 19

2 0

21

22

2 3

24

25

26

27

28

29

30

31

32

33

34

35

cubic feet

38.0’

44.6

54.6

36.2

42.5

52.0

39.7

46.5

56.9

43.3

50.7

62.1

47.0

55.0

67.4

50.9

59.5

72.9

54.9

64.1

78.6

59.1

68.9

84.5

63.4

73.8

90.6

41.8

49.0

60.0

45.8

53.6

65.7

49.9

58.4

71.6

54.3

63.3

77.7

58.8

68;5

84.0

63.4

73.8

90.6

68.2

79.3

97.5

73.2

85.0

104.0

78.3

90.9

112.0

83.6

96.9

119.0

89.1

103.0

127.0

94.7

110.0

135.0

100

116

143

106

123

151

43.0 48.0

50.4 56.2

61.7 68.8

47.4 52.9

55.4 61.7

67.9 75.7

51.9 57.9

60.6 67.5

74.3 82.8

56.6 63.1

66.0 73.5

81.0 90.3

61.5 68.6

71.6 79.8

87.9 98.0

66.5 74.3

77.4 86.3

95.1 106.0

71.8 80.1

83.4 93.0

103.0 114.0

77.3 86.2

89.7 99.9

110.0 123.0

82.9 92.5

96.1 107.0

118.0 132.0

88.7 9 9

103.0 114

126.0 141

94.7 106

110.0 122

135.0 150

101 113

117 130

144 160

107 120

124 138

153 170

114 127

131 146

162 180

121 135

139 155

171 191

113 127 142

130 147 163

160 181 202

119

137

135 150

155 172

169 191 213

53.0

61.9

75.9

58.3

68.0

83.4

63.9

74.4

91.3

69.7

81.0

99.5

75.7

87.9

108.0

81.9

95.0

117.0

88.4

102.0

126.0

95.1

110.0

136.0

102

118

145

109

126

155

117

134

166

124

143

177

132

152

188

140

161

199

148

170

211

157

180

223

166

190

235

63.7

74.2

91.1

69.8

81.1

99.7

76.1

88.4

109.0

82.7

95.9

118.0

89.6

104.0

128.0

96.6

112.0

138.0

104

120

148

112

129

159

119

138

170

127

147

181

136

156

193

144

166

205

153

176

217

162

186

230

172

196

243

181

207

256

82.6

95.7

118.0

as.7

104.0

128.0

97.1

112.0

138.0

105

121

149

113

130

160

121

139

172

129

149

184

138

159

196

147

169

209

157

180

222

166

190

235

176

201

249

186

213

263

196

224

278

105

121

149

113

130

161

121

140

173

130

150

185

139

160

198

149

171

211

159

182

225

169

193

239

179

205

253

190

217

268

200

229

284

212

241

299

‘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 exchrding leaves) last.

‘Boldface numbers span the range of the data.

7
Table 3.-Green weight in pounds forgreen ash bole wood, bole woodplus bark, and total tree’

Total height in feet

Dbh 10 20 3 0 40 50 6 0 IO 80 9 0 100 110 120 130

inches

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

1 7

18

1.6’ 3.0

2.2’ 4.1

2.6 4.7

5.6 10.5

7.5 13.8

8.8 16.0

2 2

2 8

33

3 7

4 7

5 6

4.3

5.8

6.8

15

20

23

31

40

48

53

6’7

8 0

7 9

100

119

110

138

164

5.6

7.5

8.8

20

26

30

41

52

62

69

87

103

103

129

153

143

178

212

189

233

278

241

296

353

298

364

435

24

31

37

5 0

64

75

84

106

126

126

157

187

175

217

258

231

284

339

295

360

430

365

443

530

441

534

639

524

632

757

614

737

884

709

849

1019

9 9

124

148

148

184

219

206

254

303

273

334

399

347

423

506

430

521

623

520

627

762

618

743

890

171

211

252

237

292

348

314

383

457

399

485

580

354

431

515

451

545

653

724

866

1039

836

998

1198

494

597

715

598

719

862

711

851

1021

832

992

1192

962

1143

1374

751

898

1078

892

1063

1276

1044

1239

1499

1207

1427

1717

956

1137

1367

1084

1285

1545

1218

1440

1732

1359

1603

1929

1100

1303

1567

1246

1472

1771

1400

1650

1987

558

672

805

675

809

971

802

958

1150

939

1117

1342

1085

1286

1547

1241

1466

1764

1496

1657

1994

1580

1857

2237

1763

2067

2491

1380

1627

1959

1149

1360

1636

1328

1567

1886

1518

1786

2151

1564 1720

1838 2018

2214 2432

1758

2060

2483

1961

2293

2766

1933

2261

2727

1562

1837

2212

2158

2517

3037

1507 1733 1955 2175 2393

1773 2032 2286 2537 2785

2136 2449 2757 3061 3362
:able 3.-Green weight in pounds for green ash bole wood, bole woodplus bark, and total tree-(Continued)

)bh

riches

10 2 0 3 0 4 0 50

Total height in feet

6 0 70 8 0 9 0 100 110 120 130

pounds

.9

20

21

22

23

2 4

2 6

2 6

2 7

2 8

2 9

3 0

31

3 2

3 3

3 4

35

1662 1911 2156

1951 2236 2516

2351 2696 3035

1824

2136

2575

1992

2328

2808

2167

2528

3050

2348

2735

3301

2536

2948

3560

2097

2448

2953

2290

2668

3220

2491

2897

3498

2700

3134

3785

2916

3378

4082

3140

3631

4389

3370

3892

4706

3609

4160

5032

3854

4437

5368

4107

4720

5713

4367

5012

6068

2366

2754

3325

2584

3002

3626

2811

3260

3938

3047

3526

4261

3290

3802

4596

2731

3169

3828

2932

3396

4104

3139

3631

4388

3543

4086

4942

3803

4379

5298

4w2

4681

5666

4634

5311

6432

4907

5617

6805

5188

5931

7187

5476

6253

7578

5771

658’l

4349

4992

6044

4634

6312

6432

4927

5640

6832

5228

5976

7241

5538

6321

7662

5855

6674

8092

6180

7036

8533

6512

7406

8984

2399

2792

3370

2632

3057

3691

2875

3332

4025

3127

3617

4372

3389

3913

4731

3660

4219

5103

3941

4534

5487

4231

4860

5883

4530

5195

6290

4838

5640

6710

5155

5894

7142

6481

6258

7585

6816

6632

8040

6160

7014

8506

6513

7406

8984

6875

7808

9474

7245

8218

2638

3064

3700

2895

3355

4053

3162

3657

4420

3440

3970

4801

3728

5196

4027

4630

5604

4335

4977

6025

4654

5334

6460

4983

5702

6908

5322

6080

7368

!5671

6469

7842

6030

6869

8329

6398

7279

8829

6776

7699

9341

7164

8129

9866

7562

8569

10403

7969

9020

9974 10953

3156

3650

4411

3447

3978

4811

3760

4319

5225

4064

4672

5654

4389

6037

6098

4726

5414

6557

5073

6803

7030

5432

6203

7518

5801

6615

8019

6181

7Q38

8535

6573

7472

9065

6974

7918

9609

7387

8375

10166

7810

8843

10737

8243

9323

11322

8687

9813

11920

4057

4664

5645

4397

5046

6109

4749

5440

6588

5113

5847

7084

5489

6266

7595

5877

6699

8122

6276

7143

8664

6688

7600

9221

7111

8070

9793

7545

8551

10381

7992

9045

10983

8449

9560

11600

8918

10068

12231

9398

10697

12878

5105

5838

7074

5497

6275

7606

6901

6726

8155

6318

7190

8720

6748

7667

9302

7190

8157

9900

7645

8661

10615

8112

9178

11145

8592

9708

11792

9084

10260

12454

9588

10806

13133

10104

11374

13827

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

*The three vertical figures for each dbh give weights of bole wood firat. 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 4.-Dry weight inpounds forgreen ash bole wood, bole woodplus bark, and total tree’

Total height in feet

Dbh 1 0 2 0 3 0 4 0 5 0 6 0 IO 8 0 9 0 100 110 120 130

inches

1

2

3

4

5

6

7

8

9

1 0

1 1

12.

1 3

1 4

1 5

1 6

1 7

1 8

1.0’ 1.8 2.7

1.2’ 2.3 3.3

1.4 2.6 3.8

3.5 6.6 9.5

4.2 7.9 11.5

4.9 9.3 13.4

1 4 2 0

1 7 2 4

1 9 2 8

2 3 3 4

2 8 4 0

3 3 4 7

5 1

6 0

7 1

7 1

8 4

9 9

3.5

4.2

5.0

12.4

14.9

17.0

2 6

3 1

3 7

4 4

5 2

6 2

6 6

7 8

9 3

9 2

109

129

122

145

171

156

184

218

194

228

270

1 5

1 8

2 1

3 2

3 8

4 5

5 4

6 4

7 6

8 1

9 6

113

113

134

158

150

177

209

192

225

267

238

279

331

ZSS,

338

401

343

402

477

402

471

559

465

544

646

6 4

7 6

8 9

9 6

113

134

134

158

187

177

209

247

226

266

315

281

329’

391

340

399

473

405

474

563

475

555

659

550

642

763

630

735

873

714

833

990

804

936

1113

898

1045

1243

997

1159

1380

110

130

154

154

182

215

204

240

284

261

306

363

323

379

449

392

459

545

466

545

648

647

639

759

633

739

878

725

845

1005

822

958

1139

925

1077

1281

1034

1202

1431

1147

1333

1587

231

271

321

294

345

410

365

428

508

443

518

615

527

616

731

618

721

857

715

834

991

819

954

1135

929

1061

1286

1045

1215

1447

1168

1357

1616

129s:

1505

1793

493

576

684

587

685

814

688

802

954

796

928

1104

912

1061

1263

758

883

1050

877

1021

1215

1004

1168

1390

1035

1203

1432

1164

1352

1610

1139

1323

1576

1282

1488

1773

1301 1432

1510 1661

1798 1979

1444 1590

1674 1842

1996 2196

10
‘able 4.-Dy weight in pounds forgreen ash bole wood, bole woodplus bark, and total tree-(Continued)

4 Total height in feet

>bh 10 20 3 0 4 0 50 60 70 8 0 9 0 100 110 120 130

riches pounds

19

20

1100

1279

1522

1208

1403

1671

21

22

23

24

25

2 6

27

1321

1533

1827

1438

1668

1988

1560

‘1808

2156

1686

1954

2329

1817

2104

2509

1952

2259

2695

2092

2419

2886

2 8

2 9

3 0

31

1267

1470

1752

1391

1614

1923

1521

1763

2102

1656

1919

2288

1796

2080

2480

1942

2247

2680

2092

2420

2887

2248

2598

3101

2408

2782

3321

2574

2972

3548

2744

3168

3782

2920

3369

4023

3100

3 2

3 3

3 4

35

1431

1660

1978

1572

1822

2172

1719

1990

2373

1871

2166

2583

2030

2348

2801

2194

2536

3027

2364

2731

3260

2539

2933

3501

2721

3141

3756

2908

3355

4007

3101

3576

4271

3299

3802

4543

3503

4036

4823

3712

4275

5110

3927

4520

5404

4147

4772

5706

4373

5030

6015

1594

1847

2702

1751

2027

2417

1914

2215

2642

2084

2410

2875

2260

2613

3118

2443

2822

3369

2632

3039

3629

2828

3264

3898

3030

3495

4175

3239

3733

4460

3453

3979

4755

1755

2032

2424

1928

2231

2661

2107

2437

2908

2295

2652

3165

2489

2875

3432

2690

3106

3708

.

2711

3129

3736

2940

3392

4051

3178

3664

4378

3419

3940

4708

3674

4231

5057

2899

3344

3994

3114

3591

4290

3337

3846

4595

3566

4108

4909

3802

4378

5233

4045

4656

5566

3684

4243

5072

3958

4556

5447

4241

4879

5834

4533

5212

6234

4833

5555

6645

3575

4271

3286

3787

4525

3901 4295

4491 4941

5368 5909

3424

3946

4715

3619

4237

5064

3942

4537

5424

4213

4847

5796

4492

5166

6178

4779

5493

6571

5074

5830

6975

4134

4757

5688

5142

5907

7068

5460

6269

7503

5786

6641

7949

3476

4005

4786

4373

5030

6016

4619

5310

6352

4552

5234

6260

48i6

5535

6621

8038

2103

2432

2902

2299

2657

3171

2503

2891

3452

2715

3134

3743

2935

3386

4044

3163

3646

4356

3398

3915

4679

3640

4193

5011

3891

4479

5354

4148

4774

5708

4414

5076

6071

4686

5388

6444

4966

5707

6828

75254

6035

7221

5549

6371

7624

5851

6715

5378

6176

7391

5689

6531

7816

6008

6894

8253

6121

7023

8407

, 3671

4228

5053

5086

5843

6991

6464

7414

8877

3870

4456

5327

4870 5362

5597 6159

6696 7370

6335 6816

7267 7814

8700 9358

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.

1 1
Table L-Regression statistics forpredicting green ash bole volumes and weights using two bole

diameter measurements and total height’

Average Fit C.V.

Component Y b. b, index’ se, percent’

Volume (cubic feet)

Bole wood 14.4 -5.868 0.97694 0.997 1.57+ 10.9

Bole bark 2.5 - 6.804 0.89660 0.975 0.63’ 25.8

Total bole 16.9 - 5.556 0.96315 0.996 1.86+ 11.0

Green weight (pounds)

Bole wood 717 - 1.671 0.94999 0.978 193* 26.9

Bole bark 127 - 2.394 0.84651 I 0.982 28, 21.7

Total bole 844 - 1.301 0.92811 0.981 208” 24.6

Dry weight (pounds)

Bole wood 469 - 2.183 0.96029 0.960 171* 36.6

Bole bark 77 - 3.606 0.92033 0.971 22. 29.0

’ Totalbole 546 - 1.967 0.95330 0.967 MO* 33.0

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

Ln(D*DH.H); D = dbh, H = total tree height, DX = bole diameter outside bark at %H.

‘Fit index = !.O -[E:(Y - Y)z I C(Y - &I, using untransformed values.

‘S, = [C(Y - Y)l I (II- Z)]“, using unlansformed vahrF?s.

‘Coefficient of variation = 100 S, I Y.

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

Table 6.-Regression statistics firpmdicting green ash bole volumes and weights using three bole

diameter measurements and totalheight’

Average Fit C.V.

Component Y b, b, index* k3 percent’

Volume (cubic feet,

Bole wood 14.4 - 6.609 1.00941 0.999 0.90+ 6.2

Bole bark 2.5 - 7.490 0.92503 0.981 0.56* 22.8

Total bole 16.9 - 6.286 0.99323 0.999 0.97+ 5.7

Green weight (pounds)

Bole wood 717 - 2.392 0.97969 0.987 151+ 21.0

Bole bark 127 - 3.042 0.87346 0.988 23+ 17.9

Total bole 844 - 2.607 0.95724 0.989 159+ 18.8

Dry weight fpounc2.s~

Bole wood 469 - 2.914 0.99049 0.973 141* 30.1

Bole bark 7 7 - 4.312 0.94977 0.976 20* 26.0

Total bole 546 - 2.693 0.98336 0.979 144’ 26.4

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

Ln[(D.D++ + D’%)H]; D = dbh, H = total tree height, Ds and Db = bole diameters outside bark at

%H and %H,respectiv_ely.

‘Fit index = l:O -[C(Y - Y)’ I C(Y - y)l], using untransformed values.

‘Se = [C (Y-Y)’ I (II- 2)]M, using untrausformedvahles.

‘Coefficient of variation = 160 S, I P.

+Significantly more precise by the F test than b*Dw-H model; a E 0.05.

*Significantly more precise by the F test than D’H modal; a = 0.65.

.

12
Table 7.-Local volume and weight equations for green ash’

Average Fit

Component Y bo b, index’

Volume (cubic feet)

Bole wood 14.4 - 3.060 1.17920 0.940

Bole bark 2.5 - 4.222 1.07848 0.885

Total bole 16.9 - 2.791 1.15993 0.938

Total tree, 22.7 - 2.644 1.17048, 0.928

excluding

leaves

Green weight (pounds)

Bole wood 717 1.062 1.14335 0.904

Bole bark 127 0.036 1.01914 0.923

Total bole 844 1.367 1.11714 0.915

Total tree, 1138 1.518 1.12431 0.900

excluding

leaves

S,l

6.48”

1.36”

7.57*

11.14

405*

57*

441*

660

C.V.

percent’

45.0

55.6

44.9

49.2

56.5

44.9

52.2

58.0

Dry weight (poarafs)

Bole wood

Bole bark

Total bole

Total tree,

excluding

leaves

469 0.589 1.15466 0.861 321 68.5

77 - 0.953 1.10694 0.901 41* 53.3

546 0.784 1.14630 0.873 352* 64.6

733 0.935 1.15150 0.871 489 66.8

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

D = dbh.

lFit index = 1.0 -[c(Y - ?)I I C(Y - %zJ, using untransformed values.

& = (C(Y -?)I I (n -2)]K,‘using untransformed values.

‘Coefficient of variation = 100 S, I Y.

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

Table 8.-Statistics for estimating confidence bounds for green ash predictions for the bole and

total tree

corrected sum S,..

Independent Mean of of squares Standard error of estimate

variable - X n X for X’ for tree components’

Bole predictions Wood

Ln(D*) 70 3.155 312.623 Volume 0.2213

Green weight 0.2610

Dry weight 0.2977

Ln(D*H) 70 6.930 501.821 Volume 0.1502

Green weight 0.1949

Dry weight 0.2257

Ln(D*D%*H) 70 6.647 456.642 Volume 0.0789

Green weight 0.1329

Dry weight 0.1594

Ln[(D.D% + DUH] 70 7.179 429.668 Volume 0.0593

Green weight 0.1162

Dry weight 0.1378

Bark Total

0.3014 0.2227

0.3127 0.2509

0.3569 0.2892

0.2603 0.1553

0.2942 0.1941

0.3279 0.2209

0.1994 0.0743

0.2464 0.1267

0.2696 0.1477

0.1773 0.0405

0.2283 0.1033

0.2466 0.1202

Total tree predictions Total tree

I.m(D’l 65 3.001 290.532 Vohune 0.2374

Green weight 0.2596

Dry weight 0.2963

Ln(D’H) 65 6.738 467.493 Volume 0.1841

Green weight 0.2088 . Dry weight 0.2335

T(X -k)l in base e logarithmic units.

13
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.

D,= 14.8i.n.

D, = 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(D*H)

= - 5.817 +0.93265 Ln (21.7 x 21.7 x

75.0)

F - 5.817 + 0.93265 Ln (35316.75)

= - 5.817 + 0.93265 (10.472)

= - 5.817 + 9.767

Ln(V) = 3.950

V = e3.950; bole wood volume = 51.9 ft’.

To calculate total green bole weight (W) using

X = D nD,b. II and the parameter estimates from table

5:

In(W)= bo+b, Ln(D*DtA*H)

= - 1.301+0.92811 Ln (21.7 x 14.8 x

75.0)

= - 1.301+0.92811 Ln (24087.00)

= - 1.301+0.92811 (10.089)

= - 1.301+ 9.364

Ln(W) = 8.063

W = e8.063; total bole green weight = 3175 lb.

To calculate bole dry weight (W) using X =

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

table 6:

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

= - 2.693 + 0.98336 Ln [(21.7 x 11.5 +

15.5 x 15.5) x 75.01

= - 2.693 + 0.98336 Ln ((249.55 -t 240.25)

x 75.0)

= - 2.693 + 0.98336 Ln [489.80 x 75.01

= - 2.693 + 0.98336 Ln [36735.00]

= - 2.693 + 0.98336 (10.511)

= -2.693 + 10.336

Ln(W) = 7.643

W = e7.643; total bole dry weight = 2086 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.OY21.71, .or

X = 0.631, and from (3):

R8 = [l.O + EXP (0.77188 + 11.26543.(0.631) -

73.62613 (0.631)*+ 111.38621(0.631)‘-

59.39594 (0.631)‘)] -’

= [l.O + EXP (0.77188 + 11.26543 (0.631) -

73.62613 (0.39816) + 111.38621 (0.25124) -

59.39594 (0.15853))]-’

= [l.O+EXP (0.77188-t-7.10849-29.31498

+ 27.98467 - 9.41604)]-

= [l.O+EXP(-2.86598)1-l

= [LO + 0.05693]-’

= [1.05693]-’

R8= 0.946.

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

calculated:

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

= (0.946)(51.9)

= 49.1 ft’.

Of course, total bole volumes or weights can be calculated 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.

14
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; 1984.14 p.

A sample of 70 trees from the Mississippi Delta is used to

construct volume and weight tables for green ash.

Additional keywords: Fmxinus pennsylvanica, merchantable bole estimates, biomass.

* U.S. COVE-NT PRINTING OFFICE: 1964-769-089:37