International board-foot volume tables for trees in the Susitna River Basin, Alaska

Historic, archived document

Do not assume content reflects current
scientific knowledge, policies, or practices.

a /
6250

gam United States

2 Department of
3), Agriculture

ae Forest Service

Pacific Northwest
Research Station

Research Note
PNW-RN-495

June 1990

Abstract

Introduction

International Board-Foot
Volume Tables for Trees in
the Susitna River Basin,
Alaska

Frederic R. Larson

International 1/4-inch board-foot volume equations and tables were derived from fall,
buck, and scale data for 374 trees at 78 ‘ocations in the Susitna River Basin, Alaska.
Tree species included white and black siruce, paper birch, black cottonwood, and
quaking aspen.

Keywords: Volume tables, volume equations, white spruce, black spruce, paper birch,
black cottonwood, quaking aspen, Susitna River Basin, Alaska.

Several volume tables have been used to describe stand volume in the Susitna River
basin, but none has been totally satisfactory. The most popular volume tables have
been Haack’s (1963), developed with data from throughout the interior of Alaska, and
Kerr and Eleazer’s (1980), which are Tyonek site specific. Our experience has been
that Haack’s tables tend to overestimate and Kerr and Eleazer’s tend to underestim-
ate tree volumes in the Sustina Valley.

A fall, buck, and scale study provided both an opportunity and the data to develop
accurate tables specifically for the Susitna Valley.

International 1/4-inch board-foot volume .:quations were derived from an analysis of
this fall, buck, and scale data obtained during a multiresource inventory of the
Susitna River basin, Alaska (USDA, Soil Conservation Service 1986). Volumes are
presented for combinations of diameter at breast height (dbh) and total tree height,
and for dbh and height to a 6-inch top.

A total of 374 trees were used in the analysis: 208 white spruce (Picea glauca
(Moench) Voss), 27 black spruce (P. mariana (Mill.) B.S.P.), 84 paper birch (Betula
papyifera Marsh.), 13 quaking aspen (Populus tremuloides Michx.), and 42 black
cottonwood (P. trichocarpa Torr. & Gray). Tables 1 through 6 list the distribution of
sample trees by species and diameter classes. Data were collected at 78 randomly
located plots in the Susitna River basin, an area roughly bounded by the Alaska
Range to the north and west, the Talkeetna Mountains to the east, and Cook Inlet
and Knik Arm to the south (fig. 1). Larson and Winterberger (1988) used the same
trees to develop cubic-foot and Scribner noard-foot volume tables.

FREDERIC R. LARSON is a research forester, Fo ?stry
Sciences Laboratory, 201 East Ninth Avenue, Ancl.orage,
Alaska 99501.

Methodology

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Susitna River basin

Inventory unit boundary:
Talkeetna, Beluga, and
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@ Fall, buck, and scale plot locations 0
Hs Major Rivers = SS ==
vies Major roads 05 OMEN 100
@ = Cities and towns Kilometers

Figure 1—The Susitna River basin, Alaska, where fall, buck, and scale data were collected.

Fall, buck, and scale sample trees were selected by using a 40-basal area factor
prism rotated about points located 200 feet north of point 3; east of points 4, 5, and
6; south of point 7; and west of points 8, 9, and 10 of the forest survey 10-point
inventory plots (USDA, Forest Service 1967). All tally trees greater than 5 inches dbh
were destructively sampled. Each sample tree was measured and marked at the
1-foot stump and at breast height. After felling and limbing, total height and height to
a 6-inch top diameter inside bark (dib) were recorded. The tree was bucked into
16.3-foot logs above the 1-foot stump and at the 6-inch top. If severe stem deformi-
ties occurred, such as forks, broken tops, or evidence of rot, additional cuts were
made to isolate that portion of the stem. Two cross-sectional diameters were meas-
ured inside bark at each cut point along the stem with the second measurement
taken at right angles to the first.

Tree data were used to build a data file consisting of species, dbh, total height,
height to a 6-inch top, and International 1/4-inch board-foot volume. Deformed, cull
trees, and trees with missing data or data obviously in error were eliminated. All
merchantable portions of forked trees were included. Tree data were then examined
to assure that the bucking was consistent with USDA, Forest Service, log scaling
rules.’ If a log segment was too short or too long because of attempts by field crews
to isolate rot, then a portion of the next log was “added” or the log was “cut” to a
standard length. A new diameter was cak:ulated by assuming that logs were circular
in cross section with linear taper betweer the existing end measurements.

Board-foot volumes were not computed fur trees having less than 8 feet of height to
a 6-inch top inside bark or for pieces wit! less than a 6-inch diameter inside bark at
the small end. All top sections at least 2 ieet long to a 6-inch top were included in
volume calculations. Board-foot volumes, International rule, were computed from
Clark’s formula modified for 1/4-inch kerf and 4-foot sections (Chapman 1942):

volume = 0.905 x (0.22 x diameter® — 0.71 x diameter) .

Plottings of volume over dbh? x height (ht) indicated that volumes were curvilinearly
related. The independent variables tested therefore included dbh, dbh?, ht, dbh? x ht,
1/dbh, 1/dbh?, and (dbh? x ht)°, where c is an unknown coefficient.

FSCREEN? (Frayer and others 1971) was used to screen for the best independent
variable or combination of independent variables of dbh and ht to predict volume.
The term (dbh? x ht) was fitted after transformation with logarithms; for example,
In(volume) = bo + bi x In(dbh? x ht). Both weighted (using the inverse of expected
variance in volume) and unweighted linear regressions were tested as described by
Furnival (1961) with various results. Weighted results were superior to unweighted as
was expected. The logarithm transformaiion to obtain an equation with (dbh? x ht)°
avoids the need of weights because it tends to equalize variance in volume and
linearize the relation.

Analysis of covariance was used to test the selected regressions for significant differ-
ences among all species. Equations for white and black spruce were not significantly
different, nor were those for paper birch and quaking aspen. Equations for these two
species groups therefore were pooled.

U.S. Department of Agriculture, Forest Service. Forest
Service Manual, title 2400, Timber Management. Alaska
Region Supplement 228. On file with: Alaska Regi n, Federal
Office Building, Box 21628, Juneau, Alaska 99802 1628.

? The use of trade, firm, or corporation names in tt 's
publication is for the information and convenience f the
reader. Such use does not constitute an official en.iorsement
or approval by the U.S. Department of Agriculture of any
product or service to the exclusion of others that may be
suitable.

Discussion

The regression equation with the best fitting combination of variables for each spe-
cies or species group was selected. These equations are presented at the bottom of
the appropriate table followed by the increased pete of the equation used over
the unweighted linear model, where volume = a + b(dbh*ht). The standard error of
the estimate is also presented. The shading in the tables ale the limits of the
data. The number of trees in each diameter class by species is also given.

Predicted board-foot volumes for white and black spruce (table 1) were generally
lower than predicted volumes in other published tables (Dippold and Farr 1971,
Farr 1967, Haack 1963) for total tree height in the range of tree data for all tables.
Dippold and Farr’s (1971) table for the Kushokwim River Valley gives slightly lower
volumes at the table extremes; that is, in small-diameter short trees and large-
diameter tall trees. Farr’s (1967) table for th> Alaska interior presents slightly lower
volumes at the high end of the table for large-diameter tall trees but much higher
volumes at the low end of the table for smaii-diameter short trees. Haack’s (1963)
table presents slightly lower volumes at the low end of the table for small-diameter
short trees.

The board-foot volumes for paper birch and quaking aspen (table 2) are slightly
higher than those reported by Haack (1963) over the range of data. The differences
are minimal in the center of the table and increase at both ends for small-diameter
short trees and large-diameter tall trees.

The black cottonwood board-foot volumes (table 3) are consistently higher throughout
the range of the table than those reported by Haack (1963) for balsam poplar (Popu-
lus balsamifera L.) in interior Alaska. Cottonwood and poplar are nearly identical in
form and appearance and are difficult to distinguish without chemical analysis.

There are no published International board-foot tables for Alaska trees where height
was measured to a 6-inch top diameter, so no comparisons could be made to pre-
vious work for tables 4, 5, and 6.

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10

Literature Cited

Chapman, H.H. 1942. The International log rule for 1/4-inch kerf. Can it replace the
Doyle rule? Journal of Forestry. 40: 224-234.

Dippold, Ronald M; Farr, Wilbur A. 1971. Volume tables and equations for white
spruce, balsam poplar, and paper birch of the Kuskokwim River Valley, Alaska.
Res. Note PNW-147. Portland, OR: U.S. Department of Agriculture, Forest Serv-
ice, Pacific Northwest Forest and Range Experiment Station. 8 p.

Farr, Wilbur A. 1967. Board-foot tree vo.ume tables and equations for white spruce
in interior Alaska. Res. Note PNW-59. Portland, OR: U.S. Department of Agri-
culture, Forest Service, Pacific Northwest Forest and Range Experiment Station.
4p.

Frayer, Warren E.; Wilson, Robert W.; Furnival, George M. 1971. FSCREEN (fast
SCREEN), a computer program for sc eening all combinations of independent
variables in univariate multiple linear regressions. Fort Collins, CO: Department of
Forest and Wood Sciences, College o* Forestry and Natural Resources, Colorado
State University. 23 p.

Furnival, George M. 1961. An index for comparing equations used in constructing
volume tables. Forest Science. 7: 337-341.

Haack, Paul M. 1963. Volume tables for trees of interior Alaska. Res. Note NOR-5.
Juneau, AK: U.S. Department of Agriculture, Forest Service, Northern Forest
Experiment Station. 11 p.

Kerr, Calvin L.; Eleazer, James A. 1980. Interim volume tables and equations for
white spruce and paper birch in Tyonek, Alaska. Anchorage, AK: Department of
Natural Resources, Division of Forest, Land and Water Management, State of
Alaska. 8 p.

Larson, Frederic R.; Winterberger, Kenneth C. 1988. Tables and equations for
estimating volumes of trees in the Susitna River basin, Alaska. Res. Note PNW-
RN-478. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific
Northwest Research Station. 20 p.

U.S. Department of Agriculture, Forest Service. 1967. Forest survey handbook,
FSH 4813.1. Washington, DC. 128 p.

U.S. Department of Agriculture, Soil Conservation Service. 1986. Timber and
vegetation resources of the Susitna River basin—Alaska. Fort Richardson, AK:
U.S. Army, Publications Center. 224 p In cooperation with: State of Alaska,
Department of Natural Resources.

The Forest Service of the U.S. Department of
Agriculture is dedicated to the principle of multiple
use management of the Nation’s forest resources
for sustained yields of wood, water, forage, wildlife,
and recreation. Through forestry research,
cooperation with the States and private forest
[NATIONAL] owners, and management of the National Forests
[FORESTS] and National Grasslands, it strives — as directed by
1891-1991 Congress — to provide increasingly greater service
to a growing Nation.

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Opportunity Employer. Applicants for all Department
programs will be given equal consideration without
regard to age, race, color, sex, religion, or national
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