ca. j’-i) United States

%d i-3

Department of

Agriculture

Forest Service

w Southsrn Forest W-34?

Experiment Station June 1988

Volume Equations for Plantation Cottonwood Trees

(Populus deltoides)

Roger M. Krinard

SUMMARY

Equations and tables for cubic-foot volume of outside

bark to the top of the tree and inside bark to a 3-inch top

are given for plantation-grown cottonwoods (Populus

delfoides Bartr. ex Marsh.) from 5 to 22 inches in d.b.h.

INTRODUCTIOM

A previous publication of volume tables for plantation-grown cottonwood (Populus deltoides Bartr. ex

Marsh.) trees was based on 650 3- or 5year-old trees

sampled from 3 plantations near Greenville, Mississippi

(Mohn and Krinard 1971). Diameters ranged from 2.3 to

9.9 inches, and heights ranged from about 25 to 65 feet.

Volume equations have now been developed from

planted cottonwoods near Fitler, Mississippi, that are up

to 20 years old and more than 20 inches in d.b.h. This

expands the range of tree sizes used in cottonwood

volume determinations.

SAMPLE TREES

The sample trees came from a spacing study in the

Mississippi River batture on Crown Zellerbach land (Krinard and Johnson 1984). Soil series were mainly Commerce and Convent silt loams, which have estimated site

indices at age 30 of 105 to 125 feet for natural cottonwood

stands (Broadfoot 1976). Cuttings used in the plantings

were run-of-the-bar stock (nonselect material). Spacings

were 4 by 9,8 by 9, 12 by 12, and 16 by 18 feet. Several

thinning treatments were applied, starting after the 4th

year and ending after the 15th year.

Volumes were obtained both from trees cut in thinnings, with diameters measured at 4-foot intervals starting with a 1 -f.oot stump, and from standing trees, using a

dendrometer and also starting with a l-foot stump,

Whether trees were cut or standing, volumes were determined by summing It-foot frustrums (Grosenbaugh

1954), with the top calculated as a cone. Two bark

thicknesses were measured at d.b.h. Inside bark diameters (d.i.b.) were calculated from outside bark diameters

(d.o.b.) by d.i.b. = d.o.b. (l-(l-d.b.h.i.b./d.b.h.o.b.)(1/(2-

d.o.b.1d.b.h.o.b.))) (Mesavage 1969).

Distribution of sample trees by age, spacing, and

whether cut or standing are given in table 1. Tree distribution by 1 -inch diameter class and 1 O-foot height class is

given in table 2 with the average measured total outside

bark volume.

Tables for total stem cubic-foot volume outside bark

from a l-foot stump to the top of the tree (table 3) and

inside bark stem volume to a 3-inch top (table 4) were constructed from the following regression equations:

Volume outside bark = 0.06 + 0.00222LD2H

r2 = 0.987, S, = 2.4 fP, CV = 10.5%, V = 23.1 ft3

Volume inside bark = -0.86 + 0.001 90$D2H

r2 = 0.987, S, = 2.1 fP, CV = 10.9%, V = 18.9 ft3

where D = d.b.h. and H = total height.

Intercept and slope coefficients based on smaller,

younger trees (Mohn and Hrinard 1971) were 0.21 and

0.00221 for outside bark volumes and -0.62 and 0.00204

for inside bark volumes.

A weighted regression may be used to correct for

nonhomogeneity of variance and may give a more precise

estimate. Use of weights, whether 1/(D2H) or 1/(D2H)2,

provided the same or very slightly larger values of S,, CV,

and fit index (1-X(Y-Y)2/C(Y-Y)2) with this data. The

index of fit (Furnival1961) was slightly better for weighted

regiessions, with values of 1.6 and 1.3 compared to 2.4

for outside barkvolumes and 1.4 and 1.2 compared to 2.1

for inside bark volumes. Weighted regressions, with

Southern Forest Experiment StationA- U.S. Postal Services Bldg., 7M Loyola Avenue, New Orleans, La. 70113

Forest Service, U.S. Department of Agriculture.

Serving Alabama, Arkansas, Louisiana, Mlssisslppi, E. Oklahoma, Tennsssss, E. Texas, Puerto Rico, U.S. Virgin Islands

1

weight 1/(D2H)2, changed the coefficients slightly, as

follows:

Volume outside bark = 0.09 + 0.002216 D2H

Volume inside bark = -0.41 + 0.001852 D2H

The volumes generated by these equations should

be applicable to most commercial cottonwood plantation

spacings. The equations represent trees froni a mixture of

four planting spacings, with 20,26, 31, and 23 percent of

sample trees coming from 4- by 9-, 8-by g-,12- by 12-, and

16- by 18-foot spacings, respectively. There were differences between spacings in volume equations, partly due

to the number of trees measured and to differences in tree

sizes between spacings, where mean measured outside

bark volumes were 19.0, 19.4, 23.6, and 30.2 cubic feet

from closest to widest spacing. Spacing variables incorporated in the volume equations improved the fit statistics

so very little that there was no useful benefit in doing so.

Whether these equations would apply to cottonwood

trees of genetically improved material-which would include most current and future plantations-is not known,

but with slash (Tankersley and others 1983) and loblolly

(Buford and Burkhart 1987) pine, improved and

unimproved trees did not need separate equations.

Table 1 - Number of sample trees by age, spacing, and whether cut or standing

Age of cut trees Age of standing trees Standing and

Spacing 6 7 6 12 15 7 9 10 15 20 cuttreetotal

Feet __-____--__-_--- -------- ~~_______~.~__-~~ Number ________________________________________--

4 by 9 2 0 11 19 7 26 12 7 102

6 by 9 30 7 5 10 15 14 23 16 3 8 131

12 by12 32 10 20 6 10 11 23 35 3 10 160

16by18 10 10 1 10 4 37 38 2 7 119

Total 82 27 35 28 54 36 109 101 8 32 512

Table 2. -Number of trees and average measured cubic-foot volume outside bark from a l-foot s&mp to the top of the

tree by lo-foot total height class and l-inch diameter class

-

Height classes

D.6.h. 40-49 50-59 60-69 70-79 80-89 90-99 100-109 110-119 Total

lnchest ----------------------.-- -___________-_____-_-------------------- Cubic feefi ---_--___--____-________________________--------------------------

4 1.8(l) 2.W 3.9(l) 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(O) (8)

5 0.0(O) 3.6(16) 4.8(6) 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(O) (22)

6 0.0(O) 5.0(9) 6.2(43) 7.4(11) 9.1(l) 0.0(O) 0.0(O) 0.0(O) 64

7 0.0(O) 0.0(O) 7.7(21) 9.4(24) 11.6(3) 0.0(O) 0.0(O) 0.0(O) w

8 0.0(O) 0.0(O) 9.5(8) 12.0(37) 15.0(12) 16.8(5) 0.0(O) 0.0(O) (62)

9 0.0(O) 0.0(O) 14.4(l) 15.0(26) 16.1(15) 21.7(2) 0.0(O) 0.0(O) (44

1 0 0.0(O) 0.0(O) 0.0(O) 18.4(20) 20.9(36) 24.7(12) 24.6(l) 0.0(O) (69)

11 0.0(O) 0.0(O) 0.0(O) 21.6(12) 24.9(40) 27.4(11) 30.3(3) 0.0(O) (66)

1 2 0.0(O) 0.0(O) 0.0(O) 23.5(6) 27.9(27) 32.4(14) 36.7(2) 0.0(O) (49)

1 3 0.0(O) 0.0(O) 0.0(O) 27.8(3) 31.4(11) 38.5(6) 43.2(3) 0.0(O) (23)

1 4 0.0(O) 0.0(O) 0.0(O) 0.0(O) 38.4(3) 40.0(2) 0.0(O) 0.0(O) (5)

1 5 0.0(O) 0.0(O) 0.0(O) 0.0(O) 38.5(2) 45.2(2) 58.0(5) 65.4(2) (11)

1 6 0.0(O) 0.0(O) 0.0(O) 0.0(O) 452(l) 48.9(2) 67.4(4) 74.7(l) (8)

1 7 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(O) 60.8(l) 73.0(11) 78.8(l) (13)

1 8 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(O) 79.4(2) 91.8(4) (6)

1 9 0.0(O) 0.w 0.0(O) 0.0(O) 0.0(O) 0.0(O) 90.0(l) 97.4(3) (4)

2 0 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(O) 90.8(4) 100.9(3) (7)

2 1 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(o) 118.W (1)

2 2 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(O) 0.0(o) 121.W (2)

Total (1) (31) (8’3) (139) (151) (57) (36) (17) (512)

t Example: the 4-inch d.b.h. class represents trees whose d.b.h’s range from 4.0 to 4.9 inches.

$ Numeral in parentheses represents the number of trees in this height and d.b.h. class.

Roger M. Krinard is mensurationist at the Southern Hardwoods Laboratory, maintained at Stoneville, Mississippi, by the Southern Forest Experiment

Station, Forest Se&+USDA, in cooperation with the Mississippi Agricultural and Forestry Experiment Station and the Southern Hardwood Forest

Research Group.

The use of trade or firm names in this publication is for reader information and does not imply endorsement by the U.S. Department of Agriculture

of any product or service.

2

Table 3 - Cubic-foot volumes outside bark from a l-foot stump to the top of the free ‘

Total tree height (ft)

D.b.h. 5 0 6 0 7 0 8 0 9 0 100 110 120

inches

5

21.6 24.2

25.6 28.8

30.1 33.8

30.5 34.9 39.2

35.0 40.0 45.0

39.9 45.5 51.2

51.4 157.8

64.8

72.2

80.0

--- -

t Area outlined represents range of measured trees.

6

7

8

9

1 0

11

1 2

1 3

1 4

1 5

1 6

1 7

1 8

1 9

2 0

2 1

2 2

_____--__-___-___ _ ___----___---_____ --- ----- _ ---- Feet3t ---- ---- --- -_--_--_____________------------------

2.8 3.9 4.5

6.5 7.3

8.8 9.9

11.4 12.9 114.3

14.5 16.3

17.8 20.0

-l 18.0

22.3 24.5

26.9 29.6

32.0 35.2

37.6 41.3

(43.6 47.9

50.0 55.0 60.0

56.9 62.6 68.3

64.2 70.7 77.1

72.0 79.2 86.4

80.2 88.3 96.3

.88.9 97.8 106.7

98.0 107.8 117.6

107.6 118.3 129.1

Table 4 -- Cubic-foot volumes inside bark from a 1 -foot stump :o a d-inch top

Total tree height (ft)

D.b.h. 5 0 6 0 7 0 8 0 90 100 110 120

Inches ______________-_________________________--------- &&3t_-_--_-__._-_____-. _____________-______-.--------

5 i 1.5 2.0 1 2.5 2.9

6 2.6 * 3.3 3.9 4.6 1 5.3

7 3.8 4.7

8 5.2 1 6.5

5.7 6.6

7.7 8.9 11.3

9

1 0 6.g %-

11 13.0

1 2 15.6

1 3 18.4

1 4

1 5

1 6

1 7

1 8

1 9

2 0

2 1

1

9.9 11.5 13.0

12.5 14.4 16.3 20.1

15.3 17.6 19.9 22.2 24.5

18.3 21.1 23.8 26.6 29.3

21.7

25.3 129.1

33.3 52.8 57.6

59.7 65.2

67.0 73.2

74.7 81.6

82.9 90.5

91.5 99.9

2 2

t Area outlined represents range of measured trees.

LITERATURE CITED Fumival, George M. 1961. An index for comparing

equations used in constructing volume tables. Forest

Broadfoot, Walter M. 1976. Hardwood suitability for and

properties of important Midsouth soils. Res. Pap. SO127. New Orleans, LA: U.S. Department of Agriculture,

Forest Service, Southern Forest Experiment Station.

84 p.

Buford, Marilyn A.; Burkhart, Harold E. 1987. Genetic

improvement effects on growth and yield of loblolly pine

plantations. Forest Science. 33(3): 707-724.

Sdience. 7(4): 337-341. -

Grosenbaugh, L. Ft. 1954. New tree measurement concepts: height accumulation, giant tree, taper and

shape. Occas. Pap. 134. New Orleans, LA: U.S. Depattment of Agriculture, Forest Service, Southern Forest Experiment Station. 32 p.

Krinard, Roger M.; Johnson, Robert L. 1984. Cottonwood

plantation growth through 20 years. Res. Pap. SO-21 2.

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

Forest Service, Southern Forest Experiment Station.

11 p.

Mesavage, Clement. 1969. Converting dendrometer

estimates of outside-bark stem diameters to wood diameters on major southern pines. Res. Note SO-93.

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

Forest Service, Southern Forest Experiment Station.

4 P*

Mohn, C.A.; Krinard, R. M. 1971. Volume tables for small

cottonwoods in plantations. Res. Note SO-l 13. New

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

Service, Southern Forest Experiment Station. 4 p.

Tankersley, Larry; Bongatten, Bruce; Brister, Graham;

Zoerb, Marvin. 1983. Operational p!antations of improved slash pine: Age 15 results. In: Proceedings,

17th Southern Forest Tree Improvement Conference;

1983 June 7-9; Athens, GA. Springfield, VA: National

Technical Information Service: 271-280.